Finite Group Databasebeta

← C2×#83117 #11430468

Subgroups — C2×#83117 #11430468

Order 768.

3434 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#126C211yesmaximal, characteristic, complemented
2C22×#895C211yesmaximal, characteristic, complemented
3#83117C2116yesmaximal, direct product factor
4C2×#4992C211yesmaximal, characteristic, complemented
5C2×#4991C211yesmaximal, characteristic, complemented
6C2×#4989C211yesmaximal, characteristic, complemented
7C2×#4988C211yesmaximal, characteristic, complemented
8C2×#4980C211yesmaximal, characteristic, complemented
9C2×#4960C211yesmaximal, characteristic, complemented
10C2×#4960C211yesmaximal, characteristic, complemented
11C2×#4960C211yesmaximal, characteristic, complemented
12C2×#4956C211yesmaximal, characteristic, complemented
13C2×#4961C211yesmaximal, characteristic, complemented
14C2×#4957C211yesmaximal, characteristic, complemented
15C2×#4939C211yesmaximal, characteristic, complemented
16C2×#4940C211yesmaximal, characteristic, complemented
17C2×#2714—31nomaximal, Sylow
18C23×#67C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×D12C2211yescharacteristic
22C23×D12C2211yescharacteristic
23C23×D12C2211yescharacteristic
24C23×C4×D3C2211yescharacteristic
25C2×C3×#126—28no—
26C2×C3×#126C2218yescomplemented
27C22×C3×C4⋊C4C2211yescharacteristic
28C22×C3×C4⋊C4C2211yescharacteristic
29C22×C3×C4⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×C3×C22⋊C4C2211yescharacteristic
32C22×C3×C22⋊C4C2211yescharacteristic
33C22×C3×C42C2211yescharacteristic
34C22×#217C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×(C2×D3)⋊C4C2211yescharacteristic
38C22×(C2×D3)⋊C4C2211yescharacteristic
39C22×(C2×D3)⋊C4C2211yescharacteristic
40C22×(C2×D3)⋊C4C2211yescharacteristic
41C22×(C2×D3)⋊C4C2211yescharacteristic
42C22×(C2×D3)⋊C4C2211yescharacteristic
43C22×(C2×D3)⋊C4C2211yescharacteristic
44C22×(C2×D3)⋊C4C2211yescharacteristic
45C22×(C2×D3)⋊C4C2211yescharacteristic
46C22×C4⋊Dic3C2211yescharacteristic
47C22×Dic3⋊C4C2211yescharacteristic
48C22×C4×Dic3C2211yescharacteristic
49C2×#895—28no—
50C2×#895C2218yescomplemented
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57#4992C2218yescomplemented
58#4991C2218yescomplemented
59#4989C2218yescomplemented
60#4988C2218yescomplemented
61#4980C2218yescomplemented
62#4961C2218yescomplemented
63#4960C2218yescomplemented
64#4960C2218yescomplemented
65#4960C2218yescomplemented
66#4957C2218yescomplemented
67#4956C2218yescomplemented
68#4940C2218yescomplemented
69#4939C2218yescomplemented
70C22×#126D311yescharacteristic, complemented
71C22×#121—31no—
72#2714—316no—
73C2×#397—31no—
74C2×#394—31no—
75C2×#394—31no—
76C2×#392—31no—
77C2×#392—31no—
78C2×#392—31no—
79C2×#390—31no—
80C2×#390—31no—
81C2×#390—31no—
82C2×#388—31no—
83C2×#387—31no—
84C2×#386—31no—
85C2×#385—31no—
86C25×C3C2311yescharacteristic
87C24×D3C2311yescharacteristic
88C24×D3C2311yescharacteristic
89C24×D3C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C22×#67—24no—
97C22×#67—24no—
98C22×#67—42no—
99C22×#67—42no—
100C22×#67—42no—
101C22×#67—42no—
102C22×#67—42no—
103C22×#67—42no—
104C22×#67—42no—
105C22×#67C2314yes—
106C22×#67C2314yes—
107C22×#67C2314yes—
108C23×Dic3C2311yescharacteristic
109C23×Dic3C2311yescharacteristic
110C23×Dic3C2311yescharacteristic
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C22×D12—24no—
114C22×D12—24no—
115C22×D12—24no—
116C22×D12—24no—
117C22×D12—24no—
118C22×D12—42no—
119C22×D12—42no—
120C22×D12—42no—
121C22×D12—42no—
122C22×D12C2314yes—
123C22×D12C2314yes—
124C22×D12C2314yes—
125C22×C4×D3—24no—
126C22×C4×D3—42no—
127C22×C4×D3—42no—
128C22×C4×D3C2314yes—
129C3×#126—232no—
130C2×C3×C4⋊C4—24no—
131C2×C3×C4⋊C4—24no—
132C2×C3×C4⋊C4D418yescomplemented
133C2×C3×C4⋊C4C2314yes—
134C2×C3×C4⋊C4C2314yes—
135C2×C3×C4⋊C4C2314yes—
136C2×C3×C22⋊C4—24no—
137C2×C3×C22⋊C4—24no—
138C2×C3×C22⋊C4—24no—
139C2×C3×C22⋊C4C2314yes—
140C2×C3×C22⋊C4C2314yes—
141C2×C3×C22⋊C4C2314yes—
142C2×C3×C42—24no—
143C2×C3×C42C2314yes—
144C2×#217—42no—
145C2×#217C2314yes—
146C2×(C2×D3)⋊C4—24no—
147C2×(C2×D3)⋊C4—24no—
148C2×(C2×D3)⋊C4—24no—
149C2×(C2×D3)⋊C4—24no—
150C2×(C2×D3)⋊C4—42no—
151C2×(C2×D3)⋊C4—42no—
152C2×(C2×D3)⋊C4—42no—
153C2×(C2×D3)⋊C4—42no—
154C2×(C2×D3)⋊C4—42no—
155C2×(C2×D3)⋊C4—42no—
156C2×(C2×D3)⋊C4—42no—
157C2×(C2×D3)⋊C4C2314yes—
158C2×(C2×D3)⋊C4C2314yes—
159C2×(C2×D3)⋊C4C2314yes—
160C2×(C2×D3)⋊C4C2314yes—
161C2×(C2×D3)⋊C4C2314yes—
162C2×(C2×D3)⋊C4C2314yes—
163C2×(C2×D3)⋊C4C2314yes—
164C2×(C2×D3)⋊C4C2314yes—
165C2×(C2×D3)⋊C4C2314yes—
166C2×(C2×D3)⋊C4C2314yes—
167C2×(C2×D3)⋊C4C2314yes—
168C2×C4⋊Dic3—42no—
169C2×C4⋊Dic3C2314yes—
170C2×Dic3⋊C4—42no—
171C2×Dic3⋊C4C2314yes—
172C2×C4×Dic3—42no—
173C2×C4×Dic3C2314yes—
174#895—232no—
175C3⋊#95C2314yes—
176C3⋊#95C2314yes—
177C3⋊#95C2314yes—
178C3⋊#95C2314yes—
179C3⋊#95C2314yes—
180C3⋊#95C2314yes—
181C23×D4—31no—
182C23×D4—31no—
183C23×D4—31no—
184C23×D4—31no—
185C23×D4—31no—
186C23×D4—31no—
187C24×C4—31no—
188C2×#126—28no—
189C2×#126C2×D318yescomplemented
190C2×#121—38no—
191C2×#121—68no—
192C22×C4⋊C4—31no—
193C22×C4⋊C4—31no—
194C22×C4⋊C4C2×D311yescharacteristic
195C22×C4⋊C4C2×D311yescharacteristic
196C22×C4⋊C4C2×D311yescharacteristic
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4—31no—
200C22×C22⋊C4—31no—
201C22×C22⋊C4—31no—
202C22×C22⋊C4—31no—
203C22×C22⋊C4—31no—
204C22×C22⋊C4—31no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4C2×D311yescharacteristic
210C22×C22⋊C4C2×D311yescharacteristic
211C22×C22⋊C4C2×D311yescharacteristic
212C22×C42—31no—
213C22×C42C2×D311yescharacteristic
214#397—38no—
215#394—38no—
216#394—38no—
217#392—38no—
218#392—38no—
219#392—38no—
220#390—38no—
221#390—38no—
222#390—38no—
223#388—38no—
224#387—38no—
225#386—38no—
226#385—38no—
227C2×#95—31no—
228C2×#95—31no—
229C2×#95—31no—
230C2×#95—31no—
231C2×#95—31no—
232C2×#95—31no—
233C24×C3—22no—
234C24×C3—22no—
235C24×C3—22no—
236C24×C3—22no—
237C24×C3—22no—
238C24×C3—22no—
239C24×C3—22no—
240C24×C3C2412yes—
241C24×C3C2411yescharacteristic
242C23×D3—22no—
243C23×D3—22no—
244C23×D3—22no—
245C23×D3—22no—
246C23×D3—22no—
247C23×D3—22no—
248C23×D3—22no—
249C23×D3—22no—
250C23×D3—22no—
251C23×D3—22no—
252C23×D3—22no—
253C23×D3—22no—
254C23×D3—22no—
255C23×D3—22no—
256C23×D3—22no—
257C23×D3—22no—
258C23×D3—22no—
259C23×D3—22no—
260C23×D3—22no—
261C23×D3—22no—
262C23×D3#4114yes—
263C23×D3C2412yes—
264C23×D3C2412yes—
265C23×D3C2412yes—
266C22×C3×C4—22no—
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—22no—
274C22×C3×C4—22no—
275C22×C3×C4—22no—
276C22×C3×C4—22no—
277C22×C3×C4—22no—
278C22×C3×C4—22no—
279C22×C3×C4—22no—
280C22×C3×C4—22no—
281C22×C3×C4C2×D414yes—
282C22×C3×C4C2×D414yes—
283C22×C3×C4C2×D414yes—
284C22×C3×C4C2412yes—
285C22×C3×C4C2412yes—
286C22×C3×C4C2412yes—
287C22×C3×C4C2412yes—
288C22×C3×C4C2412yes—
289C22×C3×C4C2412yes—
290C2×#67—28no—
291C2×#67—28no—
292C2×#67—44no—
293C2×#67—44no—
294C2×#67—44no—
295C2×#67—44no—
296C2×#67—44no—
297C2×#67—44no—
298C2×#67—44no—
299C2×#67—416no—
300C2×#67—416no—
301C2×#67—416no—
302C22×Dic3—22no—
303C22×Dic3—22no—
304C22×Dic3—22no—
305C22×Dic3—22no—
306C22×Dic3—22no—
307C22×Dic3—22no—
308C22×Dic3—22no—
309C22×Dic3—22no—
310C22×Dic3—22no—
311C22×Dic3—22no—
312C22×Dic3—22no—
313C22×Dic3—22no—
314C22×Dic3—22no—
315C22×Dic3—22no—
316C22×Dic3#4114yes—
317C22×Dic3C2412yes—
318C22×Dic3C2412yes—
319C22×Dic3C2412yes—
320C22×Dic3C2412yes—
321C22×Dic3C2412yes—
322C2×D12—28no—
323C2×D12—28no—
324C2×D12—28no—
325C2×D12—28no—
326C2×D12—28no—
327C2×D12—44no—
328C2×D12—44no—
329C2×D12—44no—
330C2×D12—44no—
331C2×D12—416no—
332C2×D12—416no—
333C2×D12—416no—
334C2×C4×D3—28no—
335C2×C4×D3—44no—
336C2×C4×D3—44no—
337C2×C4×D3—416no—
338C3×C4⋊C4—28no—
339C3×C4⋊C4—28no—
340C3×C4⋊C4C2×D4116yescomplemented
341C3×C22⋊C4—28no—
342C3×C22⋊C4—28no—
343C3×C22⋊C4—28no—
344C3×C42—28no—
345#217—44no—
346(C2×D3)⋊C4—28no—
347(C2×D3)⋊C4—28no—
348(C2×D3)⋊C4—28no—
349(C2×D3)⋊C4—28no—
350(C2×D3)⋊C4—44no—
351(C2×D3)⋊C4—44no—
352(C2×D3)⋊C4—44no—
353(C2×D3)⋊C4—44no—
354(C2×D3)⋊C4—44no—
355(C2×D3)⋊C4—44no—
356(C2×D3)⋊C4—44no—
357C4⋊Dic3—44no—
358Dic3⋊C4—44no—
359C4×Dic3—44no—
360C25—31no—
361C25—31no—
362C25—31no—
363C25C22×D311yescharacteristic
364C22×D4—34no—
365C22×D4—34no—
366C22×D4—34no—
367C22×D4—34no—
368C22×D4—34no—
369C22×D4—34no—
370C22×D4—64no—
371C22×D4—64no—
372C22×D4—64no—
373C22×D4—64no—
374C22×D4—64no—
375C22×D4—64no—
376C22×D4—64no—
377C22×D4—122no—
378C22×D4—122no—
379C22×D4—122no—
380C22×D4—122no—
381C22×D4—122no—
382C22×D4—122no—
383C22×D4—122no—
384C22×D4—122no—
385C22×D4—122no—
386C22×D4—122no—
387C22×D4—122no—
388C23×C4—31no—
389C23×C4—31no—
390C23×C4—31no—
391C23×C4—31no—
392C23×C4—31no—
393C23×C4—34no—
394C23×C4—64no—
395C23×C4—122no—
396C23×C4—122no—
397C23×C4C22×D311yescharacteristic
398C23×C4C22×D311yescharacteristic
399C23×C4C22×D311yescharacteristic
400C23×C4C22×D311yescharacteristic
401C23×C4C22×D311yescharacteristic
402C23×C4C22×D311yescharacteristic
403#126—232no—
404#121—632no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—34no—
408C2×C4⋊C4—34no—
409C2×C4⋊C4—122no—
410C2×C4⋊C4—122no—
411C2×C4⋊C4#6718yescomplemented
412C2×C4⋊C4C22×D314yes—
413C2×C4⋊C4C22×D314yes—
414C2×C4⋊C4C22×D314yes—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—24no—
418C2×C22⋊C4—34no—
419C2×C22⋊C4—34no—
420C2×C22⋊C4—34no—
421C2×C22⋊C4—34no—
422C2×C22⋊C4—34no—
423C2×C22⋊C4—34no—
424C2×C22⋊C4—34no—
425C2×C22⋊C4—34no—
426C2×C22⋊C4—34no—
427C2×C22⋊C4—34no—
428C2×C22⋊C4—34no—
429C2×C22⋊C4—34no—
430C2×C22⋊C4—64no—
431C2×C22⋊C4—64no—
432C2×C22⋊C4—64no—
433C2×C22⋊C4—64no—
434C2×C22⋊C4—122no—
435C2×C22⋊C4—122no—
436C2×C22⋊C4—122no—
437C2×C22⋊C4—122no—
438C2×C22⋊C4—122no—
439C2×C22⋊C4—122no—
440C2×C22⋊C4—122no—
441C2×C22⋊C4—122no—
442C2×C22⋊C4C22×D314yes—
443C2×C22⋊C4C22×D314yes—
444C2×C22⋊C4C22×D314yes—
445C2×C42—24no—
446C2×C42—34no—
447C2×C42—122no—
448C2×C42C22×D314yes—
449#95—34no—
450#95—34no—
451#95—34no—
452#95—34no—
453#95—34no—
454#95—34no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—44no—
463C23×C3—44no—
464C23×C3—44no—
465C23×C3—44no—
466C23×C3—44no—
467C23×C3—44no—
468C23×C3—44no—
469C23×C3C22×D412yes—
470C23×C3C2×#4112yes—
471C23×C3C2×#4112yes—
472C23×C3H(5,𝔽2)12yes—
473C23×C3H(5,𝔽2)12yes—
474C23×C3H(5,𝔽2)12yes—
475C23×C3H(5,𝔽2)12yes—
476C23×C3C2511yescharacteristic
477C22×D3—28no—
478C22×D3—28no—
479C22×D3—28no—
480C22×D3—22no—
481C22×D3—22no—
482C22×D3—22no—
483C22×D3—22no—
484C22×D3—22no—
485C22×D3—22no—
486C22×D3—22no—
487C22×D3—22no—
488C22×D3—22no—
489C22×D3—22no—
490C22×D3—22no—
491C22×D3—22no—
492C22×D3—22no—
493C22×D3—22no—
494C22×D3—22no—
495C22×D3—22no—
496C22×D3—22no—
497C22×D3—22no—
498C22×D3—22no—
499C22×D3—22no—
500C22×D3—44no—
501C22×D3—44no—
502C22×D3—44no—
503C22×D3—44no—
504C22×D3—44no—
505C22×D3—44no—
506C22×D3—44no—
507C22×D3—44no—
508C22×D3—44no—
509C22×D3—44no—
510C22×D3—44no—
511C22×D3—44no—
512C22×D3—44no—
513C22×D3—44no—
514C22×D3—44no—
515C22×D3—44no—
516C22×D3—44no—
517C22×D3—44no—
518C22×D3C2×#4114yes—
519C2×C3×C4—28no—
520C2×C3×C4—28no—
521C2×C3×C4—28no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—44no—
538C2×C3×C4—44no—
539C2×C3×C4—44no—
540C2×C3×C4C22×D414yes—
541C2×C3×C4C22×D414yes—
542C2×C3×C4C22×D414yes—
543#67—416no—
544#67—416no—
545#67—416no—
546C2×Dic3—28no—
547C2×Dic3—22no—
548C2×Dic3—22no—
549C2×Dic3—22no—
550C2×Dic3—22no—
551C2×Dic3—22no—
552C2×Dic3—22no—
553C2×Dic3—22no—
554C2×Dic3—22no—
555C2×Dic3—22no—
556C2×Dic3—22no—
557C2×Dic3—22no—
558C2×Dic3—22no—
559C2×Dic3—22no—
560C2×Dic3—22no—
561C2×Dic3—44no—
562C2×Dic3—44no—
563C2×Dic3—44no—
564C2×Dic3—44no—
565C2×Dic3C2×#4114yes—
566D12—416no—
567D12—416no—
568D12—416no—
569C4×D3—416no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—34no—
578C24—32no—
579C24—32no—
580C24—32no—
581C24—62no—
582C24—62no—
583C24—62no—
584C24—62no—
585C24—62no—
586C24—62no—
587C24—62no—
588C24—62no—
589C24—62no—
590C24—62no—
591C24—62no—
592C24—62no—
593C24—62no—
594C24—62no—
595C24—62no—
596C24—62no—
597C24—62no—
598C24—62no—
599C24—62no—
600C24—62no—
601C24C23×D312yes—
602C24C23×D311yescharacteristic
603C2×D4—68no—
604C2×D4—68no—
605C2×D4—68no—
606C2×D4—68no—
607C2×D4—68no—
608C2×D4—68no—
609C2×D4—68no—
610C2×D4—124no—
611C2×D4—124no—
612C2×D4—124no—
613C2×D4—124no—
614C2×D4—1216no—
615C2×D4—1216no—
616C2×D4—1216no—
617C2×D4—124no—
618C2×D4—124no—
619C2×D4—124no—
620C2×D4—124no—
621C2×D4—124no—
622C2×D4—124no—
623C2×D4—124no—
624C2×D4—1216no—
625C2×D4—1216no—
626C2×D4—1216no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—34no—
643C22×C4—32no—
644C22×C4—32no—
645C22×C4—32no—
646C22×C4—32no—
647C22×C4—32no—
648C22×C4—62no—
649C22×C4—62no—
650C22×C4—62no—
651C22×C4—62no—
652C22×C4—62no—
653C22×C4—62no—
654C22×C4—62no—
655C22×C4—62no—
656C22×C4—62no—
657C22×C4—62no—
658C22×C4—62no—
659C22×C4—62no—
660C22×C4—62no—
661C22×C4—62no—
662C22×C4—68no—
663C22×C4—124no—
664C22×C4—124no—
665C22×C4—1216no—
666C22×C4C2×#6714yes—
667C22×C4C2×#6714yes—
668C22×C4C2×#6714yes—
669C22×C4C23×D312yes—
670C22×C4C23×D312yes—
671C22×C4C23×D312yes—
672C22×C4C23×D312yes—
673C22×C4C23×D312yes—
674C22×C4C23×D312yes—
675C4⋊C4—28no—
676C4⋊C4—28no—
677C4⋊C4—124no—
678C4⋊C4—124no—
679C4⋊C4C2×#67116yescomplemented
680C22⋊C4—28no—
681C22⋊C4—28no—
682C22⋊C4—28no—
683C22⋊C4—68no—
684C22⋊C4—68no—
685C22⋊C4—68no—
686C22⋊C4—68no—
687C22⋊C4—124no—
688C22⋊C4—124no—
689C22⋊C4—124no—
690C22⋊C4—124no—
691C22⋊C4—124no—
692C22⋊C4—124no—
693C22⋊C4—124no—
694C22⋊C4—124no—
695C42—28no—
696C42—124no—
697C22×C3—42no—
698C22×C3—42no—
699C22×C3—42no—
700C22×C3—42no—
701C22×C3—42no—
702C22×C3—42no—
703C22×C3—42no—
704C22×C3—88no—
705C22×C3#53514yes—
706C22×C3#53814yes—
707C22×C3#53814yes—
708C22×C3#54614yes—
709C22×C3#55014yes—
710C22×C3#55314yes—
711C22×C3#56014yes—
712C22×C3C23×D411yescharacteristic
713C22×C3C22×#4111yescharacteristic
714C22×C3C22×#4111yescharacteristic
715C22×C3C2×H(5,𝔽2)11yescharacteristic
716C22×C3C2×H(5,𝔽2)11yescharacteristic
717C22×C3C2×H(5,𝔽2)11yescharacteristic
718C22×C3C2×H(5,𝔽2)11yescharacteristic
719C2×D3—24no—
720C2×D3—24no—
721C2×D3—24no—
722C2×D3—42no—
723C2×D3—42no—
724C2×D3—42no—
725C2×D3—416no—
726C2×D3—42no—
727C2×D3—42no—
728C2×D3—42no—
729C2×D3—42no—
730C2×D3—42no—
731C2×D3—42no—
732C2×D3—42no—
733C2×D3—42no—
734C2×D3—42no—
735C2×D3—42no—
736C2×D3—42no—
737C2×D3—42no—
738C2×D3—42no—
739C2×D3—42no—
740C2×D3—42no—
741C2×D3—88no—
742C2×D3—88no—
743C3×C4—24no—
744C3×C4—24no—
745C3×C4—24no—
746C3×C4—42no—
747C3×C4—42no—
748C3×C4—42no—
749Dic3—24no—
750Dic3—42no—
751Dic3—42no—
752Dic3—42no—
753Dic3—42no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—34no—
762C23—44no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23—68no—
770C23—62no—
771C23—62no—
772C23—62no—
773C23—62no—
774C23—62no—
775C23—68no—
776C23—62no—
777C23—68no—
778C23—62no—
779C23—62no—
780C23—62no—
781C23—62no—
782C23—62no—
783C23—62no—
784C23—62no—
785C23—62no—
786C23—62no—
787C23—62no—
788C23—62no—
789C23—62no—
790C23—62no—
791C23—62no—
792C23—124no—
793C23—124no—
794C23—124no—
795C23—124no—
796C23—124no—
797C23—124no—
798C23—124no—
799C23—124no—
800C23—124no—
801C23—124no—
802C23—124no—
803C23—124no—
804C23—124no—
805C23—124no—
806C23—124no—
807C23—124no—
808C23—124no—
809C23—124no—
810C23D3×#4112yes—
811C23D3×#4112yes—
812C23#100912yes—
813C23#100912yes—
814C23#100912yes—
815C23#100912yes—
816C23C22×#6712yes—
817C23C24×D311yescharacteristic
818D4—1216no—
819D4—1216no—
820D4—1216no—
821D4—1216no—
822D4—1216no—
823D4—1216no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—28no—
831C2×C4—28no—
832C2×C4—28no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—34no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—68no—
847C2×C4—62no—
848C2×C4—62no—
849C2×C4—62no—
850C2×C4—62no—
851C2×C4—62no—
852C2×C4—62no—
853C2×C4—62no—
854C2×C4—62no—
855C2×C4—62no—
856C2×C4—62no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—1216no—
862C2×C4—124no—
863C2×C4—124no—
864C2×C4—124no—
865C2×C4—124no—
866C2×C4C22×#6714yes—
867C2×C4C22×#6714yes—
868C2×C4C22×#6714yes—
869C2×C3—82no—
870C2×C3#271418yescomplemented
871C2×C3C2×#53511yescharacteristic
872C2×C3C2×#53811yescharacteristic
873C2×C3C2×#53811yescharacteristic
874C2×C3C2×#54611yescharacteristic
875C2×C3C2×#55011yescharacteristic
876C2×C3C2×#55311yescharacteristic
877C2×C3C2×#56011yescharacteristic
878D3—44no—
879D3—82no—
880D3—82no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—64no—
889C22—64no—
890C22—64no—
891C22—88no—
892C22—122no—
893C22—122no—
894C22—1216no—
895C22—122no—
896C22—122no—
897C22—122no—
898C22—122no—
899C22—122no—
900C22—122no—
901C22—122no—
902C22—122no—
903C22—122no—
904C22—122no—
905C22—122no—
906C22—122no—
907C22—122no—
908C22—122no—
909C22—122no—
910C22—122no—
911C22—248no—
912C22—248no—
913C22#570414yes—
914C22#570414yes—
915C22#570914yes—
916C22#571114yes—
917C22#582914yes—
918C22#583014yes—
919C22#583414yes—
920C22C2×D3×#4111yescharacteristic
921C22C2×D3×#4111yescharacteristic
922C22C2×#100911yescharacteristic
923C22C2×#100911yescharacteristic
924C22C2×#100911yescharacteristic
925C22C2×#100911yescharacteristic
926C22C23×#6711yescharacteristic
927C4—24no—
928C4—24no—
929C4—24no—
930C4—42no—
931C4—42no—
932C4—42no—
933C4—64no—
934C4—122no—
935C4—122no—
936C4—122no—
937C4—122no—
938C3C2×#271411yescharacteristic, complemented, Sylow
939C2—82no—
940C2—124no—
941C2—242no—
942C2—242no—
943C2#8311718yesdirect product factor
944C2C2×#570911yescharacteristic
945C2C2×#570411yescharacteristic
946C2C2×#570411yescharacteristic
947C2C2×#571111yescharacteristic
948C2C2×#583011yescharacteristic
949C2C2×#582911yescharacteristic
950C2C2×#583411yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC22×C3×#126C2
socleC24×C3C24
hypercenterC22×#126D3
hypocenterC3C2×#2714
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
1. C22×C3×#126C2semidirect
2. C22×#895C2semidirect
3. #83117C2direct (N × H)
4. C2×#4992C2semidirect
5. C2×#4991C2semidirect
6. C2×#4989C2semidirect
7. C2×#4988C2semidirect
8. C2×#4980C2semidirect
9. C2×#4960C2semidirect
10. C2×#4960C2semidirect
11. C2×#4960C2semidirect
12. C2×#4956C2semidirect
13. C2×#4961C2semidirect
14. C2×#4957C2semidirect
15. C2×#4939C2semidirect
16. C2×#4940C2semidirect
26. C2×C3×#126C22semidirect
50. C2×#895C22semidirect
57. #4992C22semidirect
58. #4991C22semidirect
59. #4989C22semidirect
60. #4988C22semidirect
61. #4980C22semidirect
62. #4961C22semidirect
63. #4960C22semidirect
64. #4960C22semidirect
65. #4960C22semidirect
66. #4957C22semidirect
67. #4956C22semidirect
68. #4940C22semidirect
69. #4939C22semidirect
70. C22×#126D3semidirect
132. C2×C3×C4⋊C4D4semidirect
189. C2×#126C2×D3semidirect
340. C3×C4⋊C4C2×D4semidirect
411. C2×C4⋊C4#67semidirect
679. C4⋊C4C2×#67semidirect
870. C2×C3#2714semidirect
938. C3C2×#2714semidirect
943. C2#83117direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1262
C22×#8952
#831172
C2×#49922
C2×#49912
C2×#49892
C2×#49882
C2×#49802
C2×#49602
C2×#49562
C2×#49612
C2×#49572
C2×#49392
C2×#49402
C2×#27143