Finite Group Databasebeta

← D3×#14757 #72271256

Subgroups — D3×#14757 #72271256

Order 1536.

26916 conjugacy classes of subgroups.

The subgroup lattice has 1682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×#121C213yesmaximal, complemented
2C2×D3×#392C211yesmaximal, characteristic, complemented
3C2×D3×#386C213yesmaximal, complemented
4C22×D3×#95C211yesmaximal, characteristic, complemented
5#10727097C211yesmaximal, characteristic, complemented
6#10727096C211yesmaximal, characteristic, complemented
7#10727095C213yesmaximal, complemented
8#10727094C213yesmaximal, complemented
9#10727093C213yesmaximal, complemented
10#10727092C213yesmaximal, complemented
11#10727091C211yesmaximal, characteristic, complemented
12D3×#1444C211yesmaximal, characteristic, complemented
13D3×#1439C213yesmaximal, complemented
14D3×#1438C213yesmaximal, complemented
15C3×#14757C211yesmaximal, characteristic, complemented
16C2×#14757—31nomaximal, Sylow
17C23×D3×D4C2213yes—
18C23×D3×D4C2213yes—
19C24×C4×D3C2213yes—
20C22×C3×#121C2213yescomplemented
21C22×#938C2213yescomplemented
22C22×#939C2216yescomplemented
23C22×#930C2213yescomplemented
24C2×D3×#121—248no—
25C2×D3×#121—224no—
26C22×#895C2213yescomplemented
27C22×D3×C4⋊C4C2213yes—
28C22×#884C2216yescomplemented
29C22×D3×C22⋊C4C2211yescharacteristic
30C22×D3×C22⋊C4C2213yes—
31C22×D3×C22⋊C4C2216yes—
32C22×D3×C22⋊C4C2213yes—
33C2×C3×#392C2211yescharacteristic, complemented
34C2×C3×#386C2213yescomplemented
35C22×C3×#95C2211yescharacteristic, complemented
36C2×#5223C2213yescomplemented
37C2×#5220C2213yescomplemented
38C2×#5213C2213yescomplemented
39C22×C3⋊#95C2213yescomplemented
40C2×#4960C2213yescomplemented
41C2×#4956C2213yescomplemented
42C2×#4956C2213yescomplemented
43C2×#4958C2213yescomplemented
44D3×#392—28no—
45D3×#386—224no—
46C2×#4671C2211yescharacteristic, complemented
47C2×#4665C2213yescomplemented
48C2×#4665C2213yescomplemented
49C2×D3×#95—28no—
50C2×D3×#95C2213yes—
51C2×D3×#95C2213yes—
52C2×D3×#95C2213yes—
53C2×D3×#95C2211yescharacteristic
54C2×D3×#95C2211yescharacteristic, complemented
55C2×D3×#95C2213yescomplemented
56C3×#1444C2211yescharacteristic, complemented
57C3×#1439C2213yescomplemented
58C3×#1438C2213yescomplemented
59#72131C2213yescomplemented
60#71570C2213yescomplemented
61#71568C2213yescomplemented
62#71550C2216yescomplemented
63#71550C2216yescomplemented
64#71547C2216yescomplemented
65#71546C2213yescomplemented
66#69428C2216yescomplemented
67#69427C2213yescomplemented
68#69426C2213yescomplemented
69#69426C2213yescomplemented
70#69420C2213yescomplemented
71#69419C2211yescharacteristic, complemented
72C23×#121—33no—
73C22×#392—31no—
74C22×#386—33no—
75C23×#95—31no—
76#14757—33no—
77#14757—31no—
78#14757—31no—
79#14757—33no—
80#14757—33no—
81#14757—33no—
82#14757—31no—
83#14757D311yescharacteristic, direct product factor
84C2×#1444—31no—
85C2×#1439—33no—
86C2×#1438—33no—
87C25×D3C2313yes—
88C25×D3C2311yescharacteristic
89C23×C3×D4C2313yes—
90C23×C3×D4C2313yes—
91C24×C3×C4C2313yes—
92C23×#67C2313yes—
93C23×#67C2313yes—
94C23×#67C2316yes—
95C24×Dic3C2313yes—
96C22×D3×D4—212no—
97C22×D3×D4—224no—
98C22×D3×D4—224no—
99C22×D3×D4—224no—
100C22×D3×D4—212no—
101C22×D3×D4—212no—
102C22×D3×D4—212no—
103C22×D3×D4—212no—
104C22×D3×D4—412no—
105C22×D3×D4D4124yescomplemented
106C23×D12C2313yes—
107C23×D12C2313yes—
108C23×C4×D3—224no—
109C23×C4×D3—212no—
110C23×C4×D3—212no—
111C23×C4×D3—412no—
112C23×C4×D3D4124yescomplemented
113C23×C4×D3C2311yescharacteristic
114C23×C4×D3C2311yescharacteristic
115C23×C4×D3C2313yes—
116C23×C4×D3C2313yes—
117C23×C4×D3C2313yes—
118C23×C4×D3C2313yes—
119C23×C4×D3C2313yes—
120C2×C3×#121—224no—
121C2×C3×#121—212no—
122C22×C3×C4⋊C4C2313yes—
123C22×C3×C22⋊C4C2316yes—
124C22×C3×C22⋊C4C2313yes—
125C22×C3×C22⋊C4C2311yescharacteristic
126C22×C3×C22⋊C4C2313yes—
127C22×#217C2311yescharacteristic
128C22×#217C2313yes—
129C22×#217C2316yes—
130C22×#217C2313yes—
131C2×#939—224no—
132C2×#939—224no—
133C2×#939—224no—
134C2×#938—224no—
135C2×#938—212no—
136C2×#930—212no—
137C2×#930—224no—
138C22×(C2×D3)⋊C4C2316yes—
139C22×(C2×D3)⋊C4C2316yes—
140C22×(C2×D3)⋊C4C2313yes—
141C22×(C2×D3)⋊C4C2313yes—
142C22×(C2×D3)⋊C4C2311yescharacteristic
143C22×(C2×D3)⋊C4C2311yescharacteristic
144C22×(C2×D3)⋊C4C2313yes—
145C22×(C2×D3)⋊C4C2313yes—
146C22×C4⋊Dic3C2313yes—
147C22×Dic3⋊C4C2316yes—
148D3×#121—2384no—
149C2×#895—224no—
150C2×#895—212no—
151C2×D3×C4⋊C4—224no—
152C2×D3×C4⋊C4—212no—
153C2×#884—224no—
154C2×#884—224no—
155C2×#884—224no—
156C2×D3×C22⋊C4—224no—
157C2×D3×C22⋊C4—224no—
158C2×D3×C22⋊C4—224no—
159C2×D3×C22⋊C4—212no—
160C2×D3×C22⋊C4—212no—
161C2×D3×C22⋊C4—212no—
162C2×D3×C22⋊C4—212no—
163C2×D3×C22⋊C4—212no—
164C2×D3×C22⋊C4—412no—
165C3×#392—24no—
166C3×#386—212no—
167C2×C3×#95—24no—
168C2×C3×#95C2313yes—
169C2×C3×#95C2313yes—
170C2×C3×#95C2313yes—
171C2×C3×#95C2311yescharacteristic
172#5223—212no—
173#5220—212no—
174#5213—212no—
175C2×C3⋊#95—212no—
176C2×C3⋊#95C2313yes—
177C2×C3⋊#95C2313yes—
178C2×C3⋊#95C2313yes—
179C2×C3⋊#95C2313yes—
180C2×C3⋊#95C2313yes—
181C2×C3⋊#95C2316yes—
182C2×C3⋊#95C2313yes—
183C2×C3⋊#95C2313yes—
184C2×C3⋊#95C2313yes—
185#4960—212no—
186#4958—212no—
187#4956—212no—
188#4956—212no—
189#4671—24no—
190#4665—212no—
191#4665—212no—
192D3×#95—212no—
193D3×#95—212no—
194D3×#95—212no—
195D3×#95—24no—
196D3×#95—212no—
197D3×#95D418yescomplemented
198C24×D4—33no—
199C24×D4—33no—
200C25×C4—33no—
201C22×#121—36no—
202C22×#121—33no—
203C22×#121—33no—
204C22×#121—33no—
205C22×#121—36no—
206C22×#121—624no—
207C22×#121—648no—
208C22×#121C2×D313yescomplemented
209C23×C4⋊C4—33no—
210C23×C22⋊C4—36no—
211C23×C22⋊C4—33no—
212C23×C22⋊C4—31no—
213C23×C22⋊C4—33no—
214C2×#392—31no—
215C2×#392—33no—
216C2×#392—33no—
217C2×#392—68no—
218C2×#392C2×D311yescharacteristic, complemented
219C2×#386—33no—
220C2×#386—33no—
221C2×#386—33no—
222C2×#386—33no—
223C2×#386—33no—
224C2×#386—33no—
225C2×#386—33no—
226C2×#386—624no—
227C2×#386C2×D313yescomplemented
228C22×#95—31no—
229C22×#95—33no—
230C22×#95—33no—
231C22×#95—33no—
232C22×#95—33no—
233C22×#95—31no—
234C22×#95—33no—
235C22×#95—68no—
236C22×#95C2×D311yescharacteristic, complemented
237#1444—31no—
238#1444—33no—
239#1444—33no—
240#1444C2×D311yescharacteristic, complemented
241#1439—33no—
242#1439—36no—
243#1439—33no—
244#1439—33no—
245#1439—36no—
246#1439C2×D313yescomplemented
247#1438—33no—
248#1438—33no—
249#1438—33no—
250#1438—36no—
251#1438—36no—
252#1438C2×D313yescomplemented
253C25×C3C2413yes—
254C25×C3C2411yescharacteristic
255C24×D3—22no—
256C24×D3—26no—
257C24×D3—26no—
258C24×D3—22no—
259C24×D3—212no—
260C24×D3—212no—
261C24×D3—26no—
262C24×D3—26no—
263C24×D3—26no—
264C24×D3—212no—
265C24×D3—26no—
266C24×D3—26no—
267C24×D3—212no—
268C24×D3—26no—
269C24×D3C2×D4112yes—
270C24×D3C2×D4112yes—
271C24×D3C2×D4112yes—
272C24×D3#4114yes—
273C24×D3C2413yes—
274C24×D3C2411yescharacteristic
275C24×D3C2411yescharacteristic
276C22×C3×D4—26no—
277C22×C3×D4—212no—
278C22×C3×D4—212no—
279C22×C3×D4—212no—
280C22×C3×D4—26no—
281C22×C3×D4—26no—
282C22×C3×D4—26no—
283C22×C3×D4—26no—
284C22×C3×D4—46no—
285C22×C3×D4C2×D4112yescomplemented
286C23×C3×C4—212no—
287C23×C3×C4—26no—
288C23×C3×C4—26no—
289C23×C3×C4—46no—
290C23×C3×C4C2×D4112yescomplemented
291C23×C3×C4C2411yescharacteristic
292C23×C3×C4C2411yescharacteristic
293C23×C3×C4C2413yes—
294C23×C3×C4C2413yes—
295C23×C3×C4C2413yes—
296C22×#67—26no—
297C22×#67—212no—
298C22×#67—212no—
299C22×#67—212no—
300C22×#67—26no—
301C22×#67—26no—
302C22×#67—212no—
303C22×#67—212no—
304C22×#67—212no—
305C22×#67—26no—
306C22×#67—212no—
307C22×#67—212no—
308C22×#67—212no—
309C22×#67—46no—
310C22×#67—46no—
311C22×#67C2×D4112yescomplemented
312C22×#67C2×D4112yescomplemented
313C23×Dic3—212no—
314C23×Dic3—26no—
315C23×Dic3—26no—
316C23×Dic3—46no—
317C23×Dic3C2×D4112yescomplemented
318C23×Dic3C2411yescharacteristic
319C23×Dic3C2411yescharacteristic
320C23×Dic3C2413yes—
321C23×Dic3C2413yes—
322C23×Dic3C2413yes—
323C2×D3×D4—296no—
324C2×D3×D4—2192no—
325C2×D3×D4—296no—
326C2×D3×D4—496no—
327C2×D3×D4—496no—
328C2×D3×D4—448no—
329C2×D3×D4—448no—
330C2×D3×D4—496no—
331C2×D3×D4—448no—
332C2×D3×D4—448no—
333C22×D12—26no—
334C22×D12—212no—
335C22×D12—212no—
336C22×D12—212no—
337C22×D12—26no—
338C22×D12—26no—
339C22×D12—26no—
340C22×D12—26no—
341C22×D12—46no—
342C22×D12C2×D4112yescomplemented
343C22×C4×D3—212no—
344C22×C4×D3—212no—
345C22×C4×D3—296no—
346C22×C4×D3—26no—
347C22×C4×D3—26no—
348C22×C4×D3—212no—
349C22×C4×D3—212no—
350C22×C4×D3—212no—
351C22×C4×D3—212no—
352C22×C4×D3—212no—
353C22×C4×D3—26no—
354C22×C4×D3—26no—
355C22×C4×D3—212no—
356C22×C4×D3—26no—
357C22×C4×D3—26no—
358C22×C4×D3—26no—
359C22×C4×D3—26no—
360C22×C4×D3—296no—
361C22×C4×D3—26no—
362C22×C4×D3—26no—
363C22×C4×D3—22no—
364C22×C4×D3—26no—
365C22×C4×D3—26no—
366C22×C4×D3—22no—
367C22×C4×D3—448no—
368C22×C4×D3—496no—
369C22×C4×D3—496no—
370C22×C4×D3—46no—
371C22×C4×D3—46no—
372C22×C4×D3C2×D4112yes—
373C22×C4×D3C2×D4112yes—
374C22×C4×D3C2×D4112yes—
375C22×C4×D3C2×D4112yes—
376C22×C4×D3C2×D4112yescomplemented
377C22×C4×D3C2×D4112yescomplemented
378C22×C4×D3#41112yes—
379C3×#121—296no—
380C2×C3×C4⋊C4—212no—
381C2×C3×C4⋊C4—26no—
382C2×C3×C22⋊C4—212no—
383C2×C3×C22⋊C4—212no—
384C2×C3×C22⋊C4—212no—
385C2×C3×C22⋊C4—26no—
386C2×C3×C22⋊C4—26no—
387C2×C3×C22⋊C4—26no—
388C2×C3×C22⋊C4—26no—
389C2×C3×C22⋊C4—26no—
390C2×C3×C22⋊C4—46no—
391C2×#217—212no—
392C2×#217—212no—
393C2×#217—212no—
394C2×#217—26no—
395C2×#217—26no—
396C2×#217—26no—
397C2×#217—26no—
398C2×#217—26no—
399C2×#217—46no—
400#939—2192no—
401#938—296no—
402#930—296no—
403C2×(C2×D3)⋊C4—212no—
404C2×(C2×D3)⋊C4—212no—
405C2×(C2×D3)⋊C4—212no—
406C2×(C2×D3)⋊C4—212no—
407C2×(C2×D3)⋊C4—212no—
408C2×(C2×D3)⋊C4—212no—
409C2×(C2×D3)⋊C4—26no—
410C2×(C2×D3)⋊C4—26no—
411C2×(C2×D3)⋊C4—26no—
412C2×(C2×D3)⋊C4—26no—
413C2×(C2×D3)⋊C4—26no—
414C2×(C2×D3)⋊C4—26no—
415C2×(C2×D3)⋊C4—26no—
416C2×(C2×D3)⋊C4—26no—
417C2×(C2×D3)⋊C4—26no—
418C2×(C2×D3)⋊C4—26no—
419C2×(C2×D3)⋊C4—46no—
420C2×(C2×D3)⋊C4—46no—
421C2×C4⋊Dic3—26no—
422C2×C4⋊Dic3—212no—
423C2×Dic3⋊C4—212no—
424C2×Dic3⋊C4—212no—
425C2×Dic3⋊C4—212no—
426#895—296no—
427D3×C4⋊C4—296no—
428#884—2192no—
429D3×C22⋊C4—2192no—
430D3×C22⋊C4—448no—
431D3×C22⋊C4—416no—
432D3×C22⋊C4—448no—
433C3×#95—26no—
434C3×#95—26no—
435C3×#95—26no—
436C3×#95C2×D414yescomplemented
437C3⋊#95—26no—
438C3⋊#95—26no—
439C3⋊#95—26no—
440C3⋊#95—212no—
441C3⋊#95—26no—
442C3⋊#95—26no—
443C3⋊#95—26no—
444C3⋊#95—26no—
445C3⋊#95C2×D4112yescomplemented
446C26—31no—
447C26—33no—
448C23×D4—33no—
449C23×D4—33no—
450C23×D4—324no—
451C23×D4—36no—
452C23×D4—33no—
453C23×D4—33no—
454C23×D4—612no—
455C23×D4—612no—
456C23×D4—612no—
457C23×D4—612no—
458C23×D4—624no—
459C23×D4—624no—
460C23×D4—624no—
461C23×D4—612no—
462C23×D4—1212no—
463C23×D4C22×D313yes—
464C23×D4C22×D313yes—
465C24×C4—33no—
466C24×C4—33no—
467C24×C4—33no—
468C24×C4—33no—
469C24×C4—324no—
470C24×C4—33no—
471C24×C4—33no—
472C24×C4—31no—
473C24×C4—31no—
474C24×C4—612no—
475C24×C4—612no—
476C24×C4—624no—
477C24×C4—1212no—
478C24×C4C22×D313yes—
479C2×#121—224no—
480C2×#121—212no—
481C2×#121—624no—
482C2×#121—624no—
483C2×#121—624no—
484C2×#121—612no—
485C2×#121—624no—
486C2×#121—6384no—
487C2×#121—624no—
488C2×#121—612no—
489C2×#121—624no—
490C2×#121—624no—
491C2×#121—624no—
492C2×#121—624no—
493C2×#121—612no—
494C22×C4⋊C4—36no—
495C22×C4⋊C4—33no—
496C22×C4⋊C4—612no—
497C22×C4⋊C4—624no—
498C22×C4⋊C4C22×D313yes—
499C22×C22⋊C4—33no—
500C22×C22⋊C4—36no—
501C22×C22⋊C4—31no—
502C22×C22⋊C4—33no—
503C22×C22⋊C4—33no—
504C22×C22⋊C4—36no—
505C22×C22⋊C4—36no—
506C22×C22⋊C4—31no—
507C22×C22⋊C4—31no—
508C22×C22⋊C4—33no—
509C22×C22⋊C4—33no—
510C22×C22⋊C4—33no—
511C22×C22⋊C4—624no—
512C22×C22⋊C4—624no—
513C22×C22⋊C4—624no—
514C22×C22⋊C4—612no—
515C22×C22⋊C4—612no—
516C22×C22⋊C4—612no—
517C22×C22⋊C4—612no—
518C22×C22⋊C4—612no—
519C22×C22⋊C4—1212no—
520C22×C22⋊C4C22×D313yes—
521C22×C22⋊C4C22×D316yes—
522C22×C22⋊C4C22×D311yescharacteristic
523C22×C22⋊C4C22×D313yes—
524#392—24no—
525#392—612no—
526#392—612no—
527#392—64no—
528#386—212no—
529#386—612no—
530#386—612no—
531#386—612no—
532#386—612no—
533#386—612no—
534#386—612no—
535#386—612no—
536C2×#95—24no—
537C2×#95—33no—
538C2×#95—38no—
539C2×#95—36no—
540C2×#95—33no—
541C2×#95—33no—
542C2×#95—33no—
543C2×#95—33no—
544C2×#95—33no—
545C2×#95—33no—
546C2×#95—33no—
547C2×#95—612no—
548C2×#95—612no—
549C2×#95—612no—
550C2×#95—612no—
551C2×#95—612no—
552C2×#95—64no—
553C2×#95C22×D313yes—
554C2×#95C22×D313yes—
555C2×#95C22×D313yes—
556C2×#95C22×D311yescharacteristic
557C24×C3—21no—
558C24×C3—23no—
559C24×C3—23no—
560C24×C3—21no—
561C24×C3—23no—
562C24×C3—26no—
563C24×C3—26no—
564C24×C3—23no—
565C24×C3—23no—
566C24×C3—23no—
567C24×C3—26no—
568C24×C3—26no—
569C24×C3—23no—
570C24×C3—23no—
571C24×C3C22×D416yes—
572C24×C3C22×D416yes—
573C24×C3C22×D416yes—
574C24×C3C2×#4112yes—
575C24×C3C2511yescharacteristic
576C23×D3—21no—
577C23×D3—23no—
578C23×D3—23no—
579C23×D3—21no—
580C23×D3—224no—
581C23×D3—224no—
582C23×D3—224no—
583C23×D3—224no—
584C23×D3—224no—
585C23×D3—248no—
586C23×D3—224no—
587C23×D3—28no—
588C23×D3—224no—
589C23×D3—23no—
590C23×D3—26no—
591C23×D3—26no—
592C23×D3—23no—
593C23×D3—23no—
594C23×D3—23no—
595C23×D3—26no—
596C23×D3—26no—
597C23×D3—23no—
598C23×D3—23no—
599C23×D3—248no—
600C23×D3—224no—
601C23×D3—224no—
602C23×D3—248no—
603C23×D3—224no—
604C23×D3—412no—
605C23×D3—412no—
606C23×D3—424no—
607C23×D3—424no—
608C23×D3—412no—
609C23×D3—424no—
610C23×D3—412no—
611C23×D3—412no—
612C23×D3—424no—
613C23×D3—412no—
614C23×D3—424no—
615C23×D3—424no—
616C23×D3—424no—
617C23×D3—424no—
618C23×D3—424no—
619C23×D3—412no—
620C23×D3—412no—
621C23×D3—424no—
622C23×D3#120148yes—
623C23×D3#121148yes—
624C23×D3#127116yes—
625C23×D3C22×D416yes—
626C23×D3C22×D416yes—
627C23×D3C22×D416yes—
628C23×D3C22×D416yes—
629C23×D3C22×D416yes—
630C23×D3C22×D412yes—
631C23×D3C2×#4112yes—
632C23×D3C2×#4112yes—
633C23×D3C2×#4116yes—
634C23×D3H(5,𝔽2)16yes—
635C23×D32−1+412yes—
636C2×C3×D4—224no—
637C2×C3×D4—248no—
638C2×C3×D4—224no—
639C2×C3×D4—424no—
640C2×C3×D4—424no—
641C2×C3×D4—412no—
642C2×C3×D4—412no—
643C2×C3×D4—424no—
644C2×C3×D4—412no—
645C2×C3×D4—412no—
646C22×C3×C4—26no—
647C22×C3×C4—26no—
648C22×C3×C4—224no—
649C22×C3×C4—23no—
650C22×C3×C4—23no—
651C22×C3×C4—26no—
652C22×C3×C4—26no—
653C22×C3×C4—26no—
654C22×C3×C4—23no—
655C22×C3×C4—23no—
656C22×C3×C4—26no—
657C22×C3×C4—224no—
658C22×C3×C4—23no—
659C22×C3×C4—23no—
660C22×C3×C4—21no—
661C22×C3×C4—23no—
662C22×C3×C4—23no—
663C22×C3×C4—21no—
664C22×C3×C4—412no—
665C22×C3×C4—424no—
666C22×C3×C4—424no—
667C22×C3×C4C22×D416yes—
668C22×C3×C4C22×D416yes—
669C22×C3×C4C22×D416yes—
670C22×C3×C4C22×D416yes—
671C22×C3×C4C2×#4116yes—
672C2×#67—248no—
673C2×#67—248no—
674C2×#67—224no—
675C2×#67—248no—
676C2×#67—224no—
677C2×#67—424no—
678C2×#67—424no—
679C2×#67—424no—
680C2×#67—424no—
681C2×#67—424no—
682C2×#67—412no—
683C2×#67—424no—
684C2×#67—412no—
685C2×#67—412no—
686C2×#67—424no—
687C2×#67—412no—
688C2×#67—424no—
689C22×Dic3—26no—
690C22×Dic3—26no—
691C22×Dic3—224no—
692C22×Dic3—23no—
693C22×Dic3—23no—
694C22×Dic3—26no—
695C22×Dic3—26no—
696C22×Dic3—26no—
697C22×Dic3—23no—
698C22×Dic3—23no—
699C22×Dic3—26no—
700C22×Dic3—224no—
701C22×Dic3—23no—
702C22×Dic3—23no—
703C22×Dic3—21no—
704C22×Dic3—23no—
705C22×Dic3—23no—
706C22×Dic3—21no—
707C22×Dic3—412no—
708C22×Dic3—424no—
709C22×Dic3—424no—
710C22×Dic3C22×D416yes—
711C22×Dic3C22×D416yes—
712C22×Dic3C22×D416yes—
713C22×Dic3C22×D416yes—
714C22×Dic3C2×#4116yes—
715D3×D4—4384no—
716D3×D4—4384no—
717C2×D12—224no—
718C2×D12—248no—
719C2×D12—224no—
720C2×D12—424no—
721C2×D12—424no—
722C2×D12—412no—
723C2×D12—412no—
724C2×D12—424no—
725C2×D12—412no—
726C2×D12—412no—
727C2×C4×D3—224no—
728C2×C4×D3—224no—
729C2×C4×D3—248no—
730C2×C4×D3—248no—
731C2×C4×D3—224no—
732C2×C4×D3—248no—
733C2×C4×D3—224no—
734C2×C4×D3—224no—
735C2×C4×D3—224no—
736C2×C4×D3—224no—
737C2×C4×D3—224no—
738C2×C4×D3—224no—
739C2×C4×D3—224no—
740C2×C4×D3—4384no—
741C2×C4×D3—412no—
742C2×C4×D3—412no—
743C2×C4×D3—424no—
744C2×C4×D3—424no—
745C2×C4×D3—424no—
746C2×C4×D3—424no—
747C2×C4×D3—412no—
748C2×C4×D3—424no—
749C2×C4×D3—412no—
750C2×C4×D3—424no—
751C2×C4×D3—424no—
752C2×C4×D3—412no—
753C2×C4×D3—44no—
754C2×C4×D3—44no—
755C2×C4×D3—412no—
756C2×C4×D3—412no—
757C2×C4×D3—412no—
758C2×C4×D3#121148yescomplemented
759C3×C4⋊C4—224no—
760C3×C22⋊C4—248no—
761C3×C22⋊C4—412no—
762C3×C22⋊C4—44no—
763C3×C22⋊C4—412no—
764#217—248no—
765#217—412no—
766#217—44no—
767#217—412no—
768(C2×D3)⋊C4—248no—
769(C2×D3)⋊C4—248no—
770(C2×D3)⋊C4—412no—
771(C2×D3)⋊C4—412no—
772(C2×D3)⋊C4—44no—
773(C2×D3)⋊C4—44no—
774(C2×D3)⋊C4—412no—
775(C2×D3)⋊C4—412no—
776C4⋊Dic3—224no—
777Dic3⋊C4—248no—
778C25—31no—
779C25—312no—
780C25—312no—
781C25—34no—
782C25—31no—
783C25—312no—
784C25—33no—
785C25—62no—
786C25—66no—
787C25—66no—
788C25—62no—
789C25—66no—
790C25—66no—
791C25—612no—
792C25—612no—
793C25—66no—
794C25—612no—
795C25—612no—
796C25—66no—
797C25—66no—
798C25—66no—
799C25C23×D313yes—
800C25C23×D311yescharacteristic
801C22×D4—212no—
802C22×D4—212no—
803C22×D4—212no—
804C22×D4—26no—
805C22×D4—26no—
806C22×D4—26no—
807C22×D4—26no—
808C22×D4—26no—
809C22×D4—312no—
810C22×D4—312no—
811C22×D4—312no—
812C22×D4—46no—
813C22×D4—612no—
814C22×D4—612no—
815C22×D4—612no—
816C22×D4—66no—
817C22×D4—66no—
818C22×D4—612no—
819C22×D4—612no—
820C22×D4—612no—
821C22×D4—6192no—
822C22×D4—696no—
823C22×D4—696no—
824C22×D4—612no—
825C22×D4—612no—
826C22×D4—612no—
827C22×D4—66no—
828C22×D4—66no—
829C22×D4—612no—
830C22×D4—612no—
831C22×D4—612no—
832C22×D4—66no—
833C22×D4—66no—
834C22×D4—66no—
835C22×D4—66no—
836C22×D4—66no—
837C22×D4—126no—
838C22×D4—1248no—
839C22×D4—1296no—
840C22×D4—1296no—
841C22×D4—1248no—
842C22×D4—126no—
843C22×D4—126no—
844C22×D4—1248no—
845C22×D4—1248no—
846C22×D4—1296no—
847C22×D4D3×D4112yescomplemented
848C23×C4—212no—
849C23×C4—26no—
850C23×C4—26no—
851C23×C4—33no—
852C23×C4—312no—
853C23×C4—312no—
854C23×C4—312no—
855C23×C4—33no—
856C23×C4—33no—
857C23×C4—312no—
858C23×C4—312no—
859C23×C4—312no—
860C23×C4—312no—
861C23×C4—312no—
862C23×C4—31no—
863C23×C4—31no—
864C23×C4—46no—
865C23×C4—66no—
866C23×C4—66no—
867C23×C4—696no—
868C23×C4—612no—
869C23×C4—612no—
870C23×C4—612no—
871C23×C4—612no—
872C23×C4—612no—
873C23×C4—612no—
874C23×C4—612no—
875C23×C4—612no—
876C23×C4—696no—
877C23×C4—66no—
878C23×C4—66no—
879C23×C4—66no—
880C23×C4—66no—
881C23×C4—62no—
882C23×C4—66no—
883C23×C4—66no—
884C23×C4—66no—
885C23×C4—66no—
886C23×C4—62no—
887C23×C4—66no—
888C23×C4—66no—
889C23×C4—612no—
890C23×C4—66no—
891C23×C4—66no—
892C23×C4—126no—
893C23×C4—126no—
894C23×C4—1248no—
895C23×C4—1296no—
896C23×C4—1296no—
897C23×C4—126no—
898C23×C4D3×D4112yescomplemented
899C23×C4C23×D311yescharacteristic
900C23×C4C23×D311yescharacteristic
901C23×C4C23×D313yes—
902C23×C4C23×D313yes—
903C23×C4C23×D313yes—
904#121—296no—
905#121—6192no—
906#121—696no—
907#121—696no—
908#121—696no—
909#121—6192no—
910C2×C4⋊C4—212no—
911C2×C4⋊C4—26no—
912C2×C4⋊C4—696no—
913C2×C4⋊C4—612no—
914C2×C4⋊C4—612no—
915C2×C4⋊C4—612no—
916C2×C4⋊C4—612no—
917C2×C4⋊C4—66no—
918C2×C22⋊C4—212no—
919C2×C22⋊C4—212no—
920C2×C22⋊C4—212no—
921C2×C22⋊C4—26no—
922C2×C22⋊C4—26no—
923C2×C22⋊C4—26no—
924C2×C22⋊C4—26no—
925C2×C22⋊C4—26no—
926C2×C22⋊C4—46no—
927C2×C22⋊C4—6192no—
928C2×C22⋊C4—612no—
929C2×C22⋊C4—612no—
930C2×C22⋊C4—612no—
931C2×C22⋊C4—612no—
932C2×C22⋊C4—612no—
933C2×C22⋊C4—612no—
934C2×C22⋊C4—612no—
935C2×C22⋊C4—612no—
936C2×C22⋊C4—612no—
937C2×C22⋊C4—66no—
938C2×C22⋊C4—66no—
939C2×C22⋊C4—66no—
940C2×C22⋊C4—66no—
941C2×C22⋊C4—66no—
942C2×C22⋊C4—66no—
943C2×C22⋊C4—66no—
944C2×C22⋊C4—66no—
945C2×C22⋊C4—66no—
946C2×C22⋊C4—66no—
947C2×C22⋊C4—66no—
948C2×C22⋊C4—66no—
949C2×C22⋊C4—66no—
950C2×C22⋊C4—66no—
951C2×C22⋊C4—66no—
952C2×C22⋊C4—1248no—
953C2×C22⋊C4—1248no—
954C2×C22⋊C4—1216no—
955C2×C22⋊C4—126no—
956C2×C22⋊C4—126no—
957C2×C22⋊C4—126no—
958#95—26no—
959#95—26no—
960#95—26no—
961#95—312no—
962#95—612no—
963#95—66no—
964#95—66no—
965#95—66no—
966#95—66no—
967#95—66no—
968#95—66no—
969#95—66no—
970#95D3×D414yescomplemented
971C23×C3—26no—
972C23×C3—26no—
973C23×C3—26no—
974C23×C3—26no—
975C23×C3—26no—
976C23×C3—212no—
977C23×C3—26no—
978C23×C3—22no—
979C23×C3—26no—
980C23×C3—212no—
981C23×C3—26no—
982C23×C3—26no—
983C23×C3—212no—
984C23×C3—26no—
985C23×C3—43no—
986C23×C3—43no—
987C23×C3—46no—
988C23×C3—46no—
989C23×C3—43no—
990C23×C3—43no—
991C23×C3—46no—
992C23×C3—43no—
993C23×C3—46no—
994C23×C3—43no—
995C23×C3—46no—
996C23×C3—46no—
997C23×C3—46no—
998C23×C3—46no—
999C23×C3—46no—
1000C23×C3—43no—
1001C23×C3—46no—
1002C23×C3—43no—
1003C23×C3C2×#120112yes—
1004C23×C3C2×#121112yes—
1005C23×C3C2×#12714yes—
1006C23×C3C23×D413yes—
1007C23×C3C23×D413yes—
1008C23×C3C23×D411yescharacteristic
1009C23×C3C22×#4111yescharacteristic
1010C23×C3C22×#4113yes—
1011C23×C3C2×H(5,𝔽2)13yes—
1012C23×C3C2×2−1+411yescharacteristic
1013C22×D3—26no—
1014C22×D3—26no—
1015C22×D3—26no—
1016C22×D3—26no—
1017C22×D3—26no—
1018C22×D3—212no—
1019C22×D3—26no—
1020C22×D3—22no—
1021C22×D3—26no—
1022C22×D3—232no—
1023C22×D3—232no—
1024C22×D3—296no—
1025C22×D3—296no—
1026C22×D3—296no—
1027C22×D3—296no—
1028C22×D3—212no—
1029C22×D3—26no—
1030C22×D3—26no—
1031C22×D3—212no—
1032C22×D3—26no—
1033C22×D3—43no—
1034C22×D3—43no—
1035C22×D3—46no—
1036C22×D3—46no—
1037C22×D3—43no—
1038C22×D3—43no—
1039C22×D3—46no—
1040C22×D3—43no—
1041C22×D3—46no—
1042C22×D3—43no—
1043C22×D3—46no—
1044C22×D3—46no—
1045C22×D3—46no—
1046C22×D3—46no—
1047C22×D3—46no—
1048C22×D3—43no—
1049C22×D3—46no—
1050C22×D3—43no—
1051C22×D3—448no—
1052C22×D3—496no—
1053C22×D3—448no—
1054C22×D3—496no—
1055C22×D3—448no—
1056C22×D3—824no—
1057C22×D3—824no—
1058C22×D3—824no—
1059C22×D3—848no—
1060C22×D3—824no—
1061C22×D3—848no—
1062C22×D3#392164yescomplemented
1063C22×D3C2×#120112yes—
1064C22×D3C2×#120112yes—
1065C22×D3C2×#121112yes—
1066C22×D3C2×#121112yes—
1067C22×D3C2×#121112yes—
1068C22×D3C2×#12714yes—
1069C22×D3C2×#12714yes—
1070C22×D3#532112yes—
1071C22×D3#534112yes—
1072C22×D3#537112yes—
1073C22×D3D42112yes—
1074C22×D3#546124yes—
1075C22×D3#547112yes—
1076C22×D3#54814yes—
1077C22×D3#553112yes—
1078C3×D4—448no—
1079C3×D4—448no—
1080C2×C3×C4—26no—
1081C2×C3×C4—26no—
1082C2×C3×C4—212no—
1083C2×C3×C4—212no—
1084C2×C3×C4—212no—
1085C2×C3×C4—26no—
1086C2×C3×C4—26no—
1087C2×C3×C4—26no—
1088C2×C3×C4—26no—
1089C2×C3×C4—448no—
1090C2×C3×C4—43no—
1091C2×C3×C4—46no—
1092C2×C3×C4—43no—
1093C2×C3×C4—46no—
1094C2×C3×C4—46no—
1095C2×C3×C4—43no—
1096C2×C3×C4—41no—
1097C2×C3×C4—41no—
1098C2×C3×C4—43no—
1099C2×C3×C4—43no—
1100C2×C3×C4—43no—
1101C2×C3×C4C2×#121112yescomplemented
1102#67—496no—
1103#67—448no—
1104#67—448no—
1105C2×Dic3—26no—
1106C2×Dic3—26no—
1107C2×Dic3—212no—
1108C2×Dic3—212no—
1109C2×Dic3—212no—
1110C2×Dic3—26no—
1111C2×Dic3—26no—
1112C2×Dic3—26no—
1113C2×Dic3—26no—
1114C2×Dic3—448no—
1115C2×Dic3—43no—
1116C2×Dic3—46no—
1117C2×Dic3—43no—
1118C2×Dic3—46no—
1119C2×Dic3—46no—
1120C2×Dic3—43no—
1121C2×Dic3—41no—
1122C2×Dic3—41no—
1123C2×Dic3—43no—
1124C2×Dic3—43no—
1125C2×Dic3—43no—
1126C2×Dic3C2×#121112yescomplemented
1127D12—448no—
1128D12—448no—
1129C4×D3—296no—
1130C4×D3—448no—
1131C4×D3—448no—
1132C4×D3—448no—
1133C4×D3—448no—
1134C4×D3—88no—
1135C4×D3—88no—
1136C24—21no—
1137C24—23no—
1138C24—23no—
1139C24—21no—
1140C24—23no—
1141C24—23no—
1142C24—26no—
1143C24—26no—
1144C24—23no—
1145C24—26no—
1146C24—23no—
1147C24—26no—
1148C24—23no—
1149C24—23no—
1150C24—32no—
1151C24—36no—
1152C24—36no—
1153C24—36no—
1154C24—32no—
1155C24—36no—
1156C24—32no—
1157C24—36no—
1158C24—36no—
1159C24—32no—
1160C24—316no—
1161C24—348no—
1162C24—348no—
1163C24—36no—
1164C24—624no—
1165C24—624no—
1166C24—624no—
1167C24—648no—
1168C24—624no—
1169C24—624no—
1170C24—624no—
1171C24—68no—
1172C24—624no—
1173C24—648no—
1174C24—624no—
1175C24—624no—
1176C24—648no—
1177C24—624no—
1178C24—61no—
1179C24—63no—
1180C24—63no—
1181C24—61no—
1182C24—63no—
1183C24—63no—
1184C24—66no—
1185C24—66no—
1186C24—63no—
1187C24—66no—
1188C24—63no—
1189C24—66no—
1190C24—63no—
1191C24—63no—
1192C24—1212no—
1193C24—1212no—
1194C24—1224no—
1195C24—1224no—
1196C24—1224no—
1197C24—1212no—
1198C24—1212no—
1199C24—1224no—
1200C24—1224no—
1201C24—1212no—
1202C24—1224no—
1203C24—1212no—
1204C24—1224no—
1205C24—1224no—
1206C24—1224no—
1207C24—1212no—
1208C24—1212no—
1209C24—1224no—
1210C24C2×D3×D416yes—
1211C24C2×D3×D416yes—
1212C24C2×D3×D416yes—
1213C24D3×#4112yes—
1214C24C24×D311yescharacteristic
1215C2×D4—224no—
1216C2×D4—248no—
1217C2×D4—224no—
1218C2×D4—424no—
1219C2×D4—424no—
1220C2×D4—412no—
1221C2×D4—412no—
1222C2×D4—412no—
1223C2×D4—424no—
1224C2×D4—412no—
1225C2×D4—648no—
1226C2×D4—624no—
1227C2×D4—624no—
1228C2×D4—648no—
1229C2×D4—624no—
1230C2×D4—648no—
1231C2×D4—648no—
1232C2×D4—624no—
1233C2×D4—1224no—
1234C2×D4—1224no—
1235C2×D4—1212no—
1236C2×D4—1224no—
1237C2×D4—1212no—
1238C2×D4—1212no—
1239C2×D4—1224no—
1240C2×D4—12384no—
1241C2×D4—1224no—
1242C2×D4—1224no—
1243C2×D4—1224no—
1244C2×D4—1224no—
1245C2×D4—1224no—
1246C2×D4—12384no—
1247C2×D4—1212no—
1248C2×D4—1212no—
1249C2×D4—1224no—
1250C2×D4—1212no—
1251C2×D4—1212no—
1252C2×D4—1224no—
1253C2×D4—1212no—
1254C22×C4—26no—
1255C22×C4—26no—
1256C22×C4—23no—
1257C22×C4—23no—
1258C22×C4—26no—
1259C22×C4—26no—
1260C22×C4—26no—
1261C22×C4—23no—
1262C22×C4—23no—
1263C22×C4—26no—
1264C22×C4—224no—
1265C22×C4—224no—
1266C22×C4—23no—
1267C22×C4—23no—
1268C22×C4—21no—
1269C22×C4—23no—
1270C22×C4—23no—
1271C22×C4—21no—
1272C22×C4—36no—
1273C22×C4—36no—
1274C22×C4—36no—
1275C22×C4—348no—
1276C22×C4—36no—
1277C22×C4—36no—
1278C22×C4—412no—
1279C22×C4—424no—
1280C22×C4—424no—
1281C22×C4—624no—
1282C22×C4—624no—
1283C22×C4—624no—
1284C22×C4—648no—
1285C22×C4—648no—
1286C22×C4—624no—
1287C22×C4—648no—
1288C22×C4—624no—
1289C22×C4—624no—
1290C22×C4—624no—
1291C22×C4—624no—
1292C22×C4—624no—
1293C22×C4—624no—
1294C22×C4—66no—
1295C22×C4—66no—
1296C22×C4—63no—
1297C22×C4—63no—
1298C22×C4—66no—
1299C22×C4—66no—
1300C22×C4—66no—
1301C22×C4—63no—
1302C22×C4—63no—
1303C22×C4—66no—
1304C22×C4—624no—
1305C22×C4—624no—
1306C22×C4—63no—
1307C22×C4—63no—
1308C22×C4—61no—
1309C22×C4—63no—
1310C22×C4—63no—
1311C22×C4—61no—
1312C22×C4—1212no—
1313C22×C4—1212no—
1314C22×C4—1224no—
1315C22×C4—1224no—
1316C22×C4—12384no—
1317C22×C4—1224no—
1318C22×C4—1224no—
1319C22×C4—1224no—
1320C22×C4—1224no—
1321C22×C4—1212no—
1322C22×C4—1212no—
1323C22×C4—1224no—
1324C22×C4—1212no—
1325C22×C4—124no—
1326C22×C4—124no—
1327C22×C4—1212no—
1328C22×C4—1212no—
1329C22×C4—1212no—
1330C22×C4—1212no—
1331C22×C4—1224no—
1332C22×C4—1224no—
1333C22×C4C2×D3×D416yes—
1334C22×C4C2×D3×D416yes—
1335C22×C4C2×D3×D416yes—
1336C22×C4C2×D3×D416yes—
1337C22×C4D3×#4116yes—
1338C4⋊C4—224no—
1339C4⋊C4—648no—
1340C4⋊C4—624no—
1341C22⋊C4—248no—
1342C22⋊C4—412no—
1343C22⋊C4—44no—
1344C22⋊C4—412no—
1345C22⋊C4—648no—
1346C22⋊C4—648no—
1347C22⋊C4—648no—
1348C22⋊C4—1212no—
1349C22⋊C4—1212no—
1350C22⋊C4—1212no—
1351C22⋊C4—1212no—
1352C22⋊C4—124no—
1353C22⋊C4—124no—
1354C22⋊C4—1212no—
1355C22⋊C4—124no—
1356C22⋊C4—1212no—
1357C22×C3—212no—
1358C22×C3—24no—
1359C22×C3—24no—
1360C22×C3—212no—
1361C22×C3—212no—
1362C22×C3—212no—
1363C22×C3—46no—
1364C22×C3—412no—
1365C22×C3—46no—
1366C22×C3—412no—
1367C22×C3—46no—
1368C22×C3—86no—
1369C22×C3—83no—
1370C22×C3—83no—
1371C22×C3—83no—
1372C22×C3—86no—
1373C22×C3—83no—
1374C22×C3C2×#39218yescomplemented
1375C22×C3C22×#12013yes—
1376C22×C3C22×#12113yes—
1377C22×C3C22×#12113yes—
1378C22×C3C22×#12711yescharacteristic
1379C22×C3C2×#53213yes—
1380C22×C3C2×#53413yes—
1381C22×C3C2×#53713yes—
1382C22×C3C2×D4213yes—
1383C22×C3C2×#54616yes—
1384C22×C3C2×#54713yes—
1385C22×C3C2×#54811yescharacteristic
1386C22×C3C2×#55313yes—
1387C2×D3—212no—
1388C2×D3—24no—
1389C2×D3—24no—
1390C2×D3—212no—
1391C2×D3—212no—
1392C2×D3—212no—
1393C2×D3—2128no—
1394C2×D3—46no—
1395C2×D3—412no—
1396C2×D3—46no—
1397C2×D3—412no—
1398C2×D3—46no—
1399C2×D3—86no—
1400C2×D3—83no—
1401C2×D3—83no—
1402C2×D3—83no—
1403C2×D3—86no—
1404C2×D3—83no—
1405C2×D3—896no—
1406C2×D3C2×#39218yes—
1407C2×D3C2×#39218yescomplemented
1408C2×D3#2410124yes—
1409C2×D3#2416124yes—
1410C2×D3#2430124yes—
1411C2×D3#2543124yes—
1412C2×D3#265618yes—
1413C2×D3#285618yes—
1414C3×C4—212no—
1415C3×C4—46no—
1416C3×C4—46no—
1417C3×C4—81no—
1418C3×C4—81no—
1419Dic3—212no—
1420Dic3—46no—
1421Dic3—46no—
1422Dic3—81no—
1423Dic3—81no—
1424C23—26no—
1425C23—26no—
1426C23—26no—
1427C23—26no—
1428C23—212no—
1429C23—26no—
1430C23—26no—
1431C23—22no—
1432C23—26no—
1433C23—26no—
1434C23—212no—
1435C23—212no—
1436C23—26no—
1437C23—26no—
1438C23—312no—
1439C23—312no—
1440C23—312no—
1441C23—312no—
1442C23—324no—
1443C23—312no—
1444C23—312no—
1445C23—34no—
1446C23—312no—
1447C23—312no—
1448C23—34no—
1449C23—312no—
1450C23—312no—
1451C23—34no—
1452C23—312no—
1453C23—364no—
1454C23—43no—
1455C23—46no—
1456C23—46no—
1457C23—43no—
1458C23—46no—
1459C23—43no—
1460C23—46no—
1461C23—46no—
1462C23—46no—
1463C23—43no—
1464C23—46no—
1465C23—43no—
1466C23—43no—
1467C23—46no—
1468C23—46no—
1469C23—43no—
1470C23—46no—
1471C23—43no—
1472C23—696no—
1473C23—632no—
1474C23—696no—
1475C23—632no—
1476C23—696no—
1477C23—696no—
1478C23—66no—
1479C23—66no—
1480C23—66no—
1481C23—66no—
1482C23—612no—
1483C23—66no—
1484C23—66no—
1485C23—62no—
1486C23—66no—
1487C23—66no—
1488C23—612no—
1489C23—612no—
1490C23—66no—
1491C23—66no—
1492C23—1296no—
1493C23—1248no—
1494C23—1248no—
1495C23—1296no—
1496C23—1248no—
1497C23—123no—
1498C23—126no—
1499C23—126no—
1500C23—123no—
1501C23—126no—
1502C23—123no—
1503C23—126no—
1504C23—126no—
1505C23—126no—
1506C23—123no—
1507C23—126no—
1508C23—123no—
1509C23—123no—
1510C23—126no—
1511C23—126no—
1512C23—123no—
1513C23—126no—
1514C23—123no—
1515C23—2424no—
1516C23—2448no—
1517C23—2424no—
1518C23—2424no—
1519C23—2424no—
1520C23—2448no—
1521C23D3×#120112yes—
1522C23D3×#121112yes—
1523C23D3×#12714yes—
1524C23C22×D3×D413yes—
1525C23C22×D3×D411yescharacteristic
1526C23C22×D3×D413yes—
1527C23C2×D3×#4111yescharacteristic
1528C23C2×D3×#4113yes—
1529C23D3×H(5,𝔽2)13yes—
1530C23D3×2−1+411yescharacteristic
1531D4—448no—
1532D4—448no—
1533D4—1248no—
1534D4—1248no—
1535D4—1296no—
1536D4—1248no—
1537D4—1248no—
1538C2×C4—26no—
1539C2×C4—212no—
1540C2×C4—212no—
1541C2×C4—26no—
1542C2×C4—26no—
1543C2×C4—26no—
1544C2×C4—212no—
1545C2×C4—26no—
1546C2×C4—26no—
1547C2×C4—312no—
1548C2×C4—448no—
1549C2×C4—46no—
1550C2×C4—46no—
1551C2×C4—43no—
1552C2×C4—43no—
1553C2×C4—46no—
1554C2×C4—43no—
1555C2×C4—43no—
1556C2×C4—41no—
1557C2×C4—41no—
1558C2×C4—43no—
1559C2×C4—43no—
1560C2×C4—696no—
1561C2×C4—66no—
1562C2×C4—612no—
1563C2×C4—612no—
1564C2×C4—66no—
1565C2×C4—66no—
1566C2×C4—66no—
1567C2×C4—612no—
1568C2×C4—66no—
1569C2×C4—66no—
1570C2×C4—1248no—
1571C2×C4—1248no—
1572C2×C4—1248no—
1573C2×C4—1248no—
1574C2×C4—1248no—
1575C2×C4—126no—
1576C2×C4—126no—
1577C2×C4—123no—
1578C2×C4—123no—
1579C2×C4—126no—
1580C2×C4—123no—
1581C2×C4—123no—
1582C2×C4—121no—
1583C2×C4—121no—
1584C2×C4—123no—
1585C2×C4—123no—
1586C2×C4—248no—
1587C2×C4—248no—
1588C2×C4D3×#121112yescomplemented
1589C2×C3—28no—
1590C2×C3—86no—
1591C2×C3C22×#39211yescharacteristic
1592C2×C3C2×#265611yescharacteristic
1593C2×C3C2×#241013yes—
1594C2×C3C2×#241613yes—
1595C2×C3C2×#243013yes—
1596C2×C3C2×#254313yes—
1597C2×C3C2×#285611yescharacteristic
1598D3—28no—
1599D3—86no—
1600D3#14757116yesdirect product factor
1601C22—24no—
1602C22—212no—
1603C22—24no—
1604C22—212no—
1605C22—212no—
1606C22—212no—
1607C22—38no—
1608C22—324no—
1609C22—38no—
1610C22—324no—
1611C22—324no—
1612C22—38no—
1613C22—324no—
1614C22—38no—
1615C22—46no—
1616C22—412no—
1617C22—412no—
1618C22—46no—
1619C22—46no—
1620C22—6128no—
1621C22—64no—
1622C22—612no—
1623C22—64no—
1624C22—612no—
1625C22—612no—
1626C22—612no—
1627C22—83no—
1628C22—86no—
1629C22—83no—
1630C22—83no—
1631C22—83no—
1632C22—86no—
1633C22—126no—
1634C22—1212no—
1635C22—1212no—
1636C22—126no—
1637C22—126no—
1638C22—2496no—
1639C22—243no—
1640C22—246no—
1641C22—243no—
1642C22—243no—
1643C22—243no—
1644C22—246no—
1645C22D3×#39218yescomplemented
1646C22C2×D3×#12013yes—
1647C22C2×D3×#12113yes—
1648C22C2×D3×#12113yes—
1649C22C2×D3×#12711yescharacteristic
1650C22D3×#53213yes—
1651C22D3×#53413yes—
1652C22D3×#53713yes—
1653C22D3×D4213yes—
1654C22D3×#54616yes—
1655C22D3×#54713yes—
1656C22D3×#54811yescharacteristic
1657C22D3×#55313yes—
1658C4—212no—
1659C4—46no—
1660C4—46no—
1661C4—612no—
1662C4—81no—
1663C4—81no—
1664C4—126no—
1665C4—126no—
1666C4—241no—
1667C4—241no—
1668C3C2×#1475711yescharacteristic, complemented, Sylow
1669C2—28no—
1670C2—316no—
1671C2—68no—
1672C2—86no—
1673C2—246no—
1674C2C2×D3×#39211yescharacteristic
1675C2D3×#265611yescharacteristic
1676C2D3×#241013yes—
1677C2D3×#241613yes—
1678C2D3×#243013yes—
1679C2D3×#254313yes—
1680C2D3×#285611yescharacteristic
subgroupG/H
center, FrattiniC24C24×D3
commutator, socle, cosocleC24×C3C25
FittingC3×#14757C2
hypercenter#14757D3
hypocenterC3C2×#14757
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #14757

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×D3×#121C2semidirect
2. C2×D3×#392C2semidirect
3. C2×D3×#386C2semidirect
4. C22×D3×#95C2semidirect
5. #10727097C2semidirect
6. #10727096C2semidirect
7. #10727095C2semidirect
8. #10727094C2semidirect
9. #10727093C2semidirect
10. #10727092C2semidirect
11. #10727091C2semidirect
12. D3×#1444C2semidirect
13. D3×#1439C2semidirect
14. D3×#1438C2semidirect
15. C3×#14757C2semidirect
20. C22×C3×#121C22semidirect
21. C22×#938C22semidirect
22. C22×#939C22semidirect
23. C22×#930C22semidirect
26. C22×#895C22semidirect
28. C22×#884C22semidirect
33. C2×C3×#392C22semidirect
34. C2×C3×#386C22semidirect
35. C22×C3×#95C22semidirect
36. C2×#5223C22semidirect
37. C2×#5220C22semidirect
38. C2×#5213C22semidirect
39. C22×C3⋊#95C22semidirect
40. C2×#4960C22semidirect
41. C2×#4956C22semidirect
42. C2×#4956C22semidirect
43. C2×#4958C22semidirect
46. C2×#4671C22semidirect
47. C2×#4665C22semidirect
48. C2×#4665C22semidirect
54. C2×D3×#95C22semidirect
55. C2×D3×#95C22semidirect
56. C3×#1444C22semidirect
57. C3×#1439C22semidirect
58. C3×#1438C22semidirect
59. #72131C22semidirect
60. #71570C22semidirect
61. #71568C22semidirect
62. #71550C22semidirect
63. #71550C22semidirect
64. #71547C22semidirect
65. #71546C22semidirect
66. #69428C22semidirect
67. #69427C22semidirect
68. #69426C22semidirect
69. #69426C22semidirect
70. #69420C22semidirect
71. #69419C22semidirect
83. #14757D3direct (N × H)
105. C22×D3×D4D4semidirect
112. C23×C4×D3D4semidirect
197. D3×#95D4semidirect
208. C22×#121C2×D3semidirect
218. C2×#392C2×D3semidirect
227. C2×#386C2×D3semidirect
236. C22×#95C2×D3semidirect
240. #1444C2×D3semidirect
246. #1439C2×D3semidirect
252. #1438C2×D3semidirect
285. C22×C3×D4C2×D4semidirect
290. C23×C3×C4C2×D4semidirect
311. C22×#67C2×D4semidirect
312. C22×#67C2×D4semidirect
317. C23×Dic3C2×D4semidirect
342. C22×D12C2×D4semidirect
376. C22×C4×D3C2×D4semidirect
377. C22×C4×D3C2×D4semidirect
436. C3×#95C2×D4semidirect
445. C3⋊#95C2×D4semidirect
758. C2×C4×D3#121semidirect
847. C22×D4D3×D4semidirect
898. C23×C4D3×D4semidirect
970. #95D3×D4semidirect
1062. C22×D3#392semidirect
1101. C2×C3×C4C2×#121semidirect
1126. C2×Dic3C2×#121semidirect
1374. C22×C3C2×#392semidirect
1407. C2×D3C2×#392semidirect
1588. C2×C4D3×#121semidirect
1600. D3#14757direct (N × H)
1645. C22D3×#392semidirect
1668. C3C2×#14757semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×D3×#1212
C2×D3×#3922
C2×D3×#3862
C22×D3×#952
#107270972
#107270962
#107270952
#107270942
#107270932
#107270922
#107270912
D3×#14442
D3×#14392
D3×#14382
C3×#147572
C2×#147573