Finite Group Databasebeta

← C2×#82909 #11430271

Subgroups — C2×#82909 #11430271

Order 768.

3542 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#123C211yesmaximal, characteristic, complemented
2C22×#884C211yesmaximal, characteristic, complemented
3C2×#5223C211yesmaximal, characteristic, complemented
4C2×#5223C211yesmaximal, characteristic, complemented
5C2×#5213C211yesmaximal, characteristic, complemented
6C2×#5213C211yesmaximal, characteristic, complemented
7#82909C2116yesmaximal, direct product factor
8C2×#4992C211yesmaximal, characteristic, complemented
9C2×#4987C211yesmaximal, characteristic, complemented
10C2×#4985C211yesmaximal, characteristic, complemented
11C2×#4988C211yesmaximal, characteristic, complemented
12C2×#4960C211yesmaximal, characteristic, complemented
13C2×#4956C211yesmaximal, characteristic, complemented
14C2×#4961C211yesmaximal, characteristic, complemented
15C2×#4945C211yesmaximal, characteristic, complemented
16C2×#4951C211yesmaximal, characteristic, complemented
17C2×#2703—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C24×C3×C4C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×#67C2211yescharacteristic
22C23×#67C2211yescharacteristic
23C23×#67C2211yescharacteristic
24C23×D12C2211yescharacteristic
25C23×C4×D3C2211yescharacteristic
26C2×C3×#123—28no—
27C2×C3×#123C2218yescomplemented
28C22×C3×C4⋊C4C2211yescharacteristic
29C22×C3×C4⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×C3×C22⋊C4C2211yescharacteristic
32C22×C3×C22⋊C4C2211yescharacteristic
33C22×#217C2211yescharacteristic
34C22×#217C2211yescharacteristic
35C22×#217C2211yescharacteristic
36C22×#217C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
45C22×Dic3⋊C4C2211yescharacteristic
46C22×C4×Dic3C2211yescharacteristic
47C2×#884—28no—
48C2×#884C2218yescomplemented
49#5223C2218yescomplemented
50#5223C2218yescomplemented
51#5213C2218yescomplemented
52#5213C2218yescomplemented
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61#4992C2218yescomplemented
62#4988C2218yescomplemented
63#4987C2218yescomplemented
64#4985C2218yescomplemented
65#4961C2218yescomplemented
66#4960C2218yescomplemented
67#4956C2218yescomplemented
68#4951C2218yescomplemented
69#4945C2218yescomplemented
70C22×#123D311yescharacteristic, complemented
71C22×#121—31no—
72#2703—316no—
73C2×#400—31no—
74C2×#397—31no—
75C2×#394—31no—
76C2×#392—31no—
77C2×#392—31no—
78C2×#392—31no—
79C2×#390—31no—
80C2×#388—31no—
81C2×#388—31no—
82C2×#386—31no—
83C2×#386—31no—
84C2×#386—31no—
85C2×#380—31no—
86C25×C3C2311yescharacteristic
87C25×C3C2311yescharacteristic
88C24×D3C2311yescharacteristic
89C24×D3C2311yescharacteristic
90C22×C3×D4—24no—
91C22×C3×D4—42no—
92C22×C3×D4—42no—
93C22×C3×D4C2314yes—
94C23×C3×C4—24no—
95C23×C3×C4—42no—
96C23×C3×C4—42no—
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C2314yes—
103C22×#67—24no—
104C22×#67—24no—
105C22×#67—24no—
106C22×#67—24no—
107C22×#67—24no—
108C22×#67—42no—
109C22×#67—42no—
110C22×#67—42no—
111C22×#67—42no—
112C22×#67—42no—
113C22×#67—42no—
114C22×#67—42no—
115C22×#67C2314yes—
116C22×#67C2314yes—
117C22×#67C2314yes—
118C22×#67C2314yes—
119C23×Dic3C2311yescharacteristic
120C23×Dic3C2311yescharacteristic
121C23×Dic3C2311yescharacteristic
122C23×Dic3C2311yescharacteristic
123C23×Dic3C2311yescharacteristic
124C23×Dic3C2311yescharacteristic
125C22×D12—24no—
126C22×D12—24no—
127C22×D12—42no—
128C22×D12C2314yes—
129C22×C4×D3—24no—
130C22×C4×D3—24no—
131C22×C4×D3—42no—
132C22×C4×D3C2314yes—
133C3×#123—232no—
134C2×C3×C4⋊C4—24no—
135C2×C3×C4⋊C4—24no—
136C2×C3×C4⋊C4C2314yes—
137C2×C3×C4⋊C4C2314yes—
138C2×C3×C22⋊C4—24no—
139C2×C3×C22⋊C4—24no—
140C2×C3×C22⋊C4D418yescomplemented
141C2×C3×C22⋊C4C2314yes—
142C2×C3×C22⋊C4C2314yes—
143C2×C3×C22⋊C4C2314yes—
144C2×#217—24no—
145C2×#217—42no—
146C2×#217—42no—
147C2×#217—42no—
148C2×#217C2314yes—
149C2×#217C2314yes—
150C2×#217C2314yes—
151C2×#217C2314yes—
152C2×(C2×D3)⋊C4—24no—
153C2×(C2×D3)⋊C4—42no—
154C2×(C2×D3)⋊C4—42no—
155C2×(C2×D3)⋊C4—42no—
156C2×(C2×D3)⋊C4—42no—
157C2×(C2×D3)⋊C4—42no—
158C2×(C2×D3)⋊C4—42no—
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×C4⋊Dic3—42no—
167C2×C4⋊Dic3C2314yes—
168C2×Dic3⋊C4—24no—
169C2×Dic3⋊C4C2314yes—
170C2×C4×Dic3—42no—
171C2×C4×Dic3C2314yes—
172#884—232no—
173C3⋊#95C2314yes—
174C3⋊#95C2314yes—
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×D4C2×D311yescharacteristic
187C24×C4—31no—
188C24×C4C2×D311yescharacteristic
189C2×#123—28no—
190C2×#123C2×D318yescomplemented
191C2×#121—38no—
192C2×#121—68no—
193C22×C4⋊C4—31no—
194C22×C4⋊C4—31no—
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⋊C4C2×D311yescharacteristic
209C22×C22⋊C4C2×D311yescharacteristic
210C22×C22⋊C4C2×D311yescharacteristic
211C22×C42—31no—
212#400—38no—
213#397—38no—
214#394—38no—
215#392—38no—
216#392—38no—
217#392—38no—
218#390—38no—
219#388—38no—
220#388—38no—
221#386—38no—
222#386—38no—
223#386—38no—
224#380—38no—
225C2×#95—31no—
226C2×#95—31no—
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×C3—22no—
241C24×C3—22no—
242C24×C3—22no—
243C24×C3—22no—
244C24×C3—22no—
245C24×C3—22no—
246C24×C3C2×D414yes—
247C24×C3C2412yes—
248C24×C3C2412yes—
249C24×C3C2411yescharacteristic
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—22no—
263C23×D3#4114yes—
264C23×D3C2412yes—
265C23×D3C2412yes—
266C2×C3×D4—28no—
267C2×C3×D4—44no—
268C2×C3×D4—44no—
269C2×C3×D4—416no—
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—28no—
278C22×C3×C4—22no—
279C22×C3×C4—22no—
280C22×C3×C4—22no—
281C22×C3×C4—22no—
282C22×C3×C4—22no—
283C22×C3×C4—22no—
284C22×C3×C4—44no—
285C22×C3×C4—44no—
286C22×C3×C4—416no—
287C22×C3×C4C2×D414yes—
288C22×C3×C4C2×D414yes—
289C22×C3×C4C2412yes—
290C22×C3×C4C2412yes—
291C22×C3×C4C2412yes—
292C22×C3×C4C2412yes—
293C22×C3×C4C2412yes—
294C2×#67—28no—
295C2×#67—28no—
296C2×#67—28no—
297C2×#67—28no—
298C2×#67—28no—
299C2×#67—44no—
300C2×#67—44no—
301C2×#67—44no—
302C2×#67—44no—
303C2×#67—44no—
304C2×#67—44no—
305C2×#67—44no—
306C2×#67—416no—
307C2×#67—416no—
308C2×#67—416no—
309C2×#67—416no—
310C22×Dic3—22no—
311C22×Dic3—22no—
312C22×Dic3—22no—
313C22×Dic3—22no—
314C22×Dic3—22no—
315C22×Dic3—22no—
316C22×Dic3—22no—
317C22×Dic3—22no—
318C22×Dic3—22no—
319C22×Dic3—22no—
320C22×Dic3—22no—
321C22×Dic3—22no—
322C22×Dic3—22no—
323C22×Dic3—22no—
324C22×Dic3—22no—
325C22×Dic3—22no—
326C22×Dic3—22no—
327C22×Dic3#4114yes—
328C22×Dic3C2412yes—
329C22×Dic3C2412yes—
330C22×Dic3C2412yes—
331C22×Dic3C2412yes—
332C22×Dic3C2412yes—
333C22×Dic3C2412yes—
334C2×D12—28no—
335C2×D12—28no—
336C2×D12—44no—
337C2×D12—416no—
338C2×C4×D3—28no—
339C2×C4×D3—28no—
340C2×C4×D3—44no—
341C2×C4×D3—416no—
342C3×C4⋊C4—28no—
343C3×C4⋊C4—28no—
344C3×C22⋊C4—28no—
345C3×C22⋊C4—28no—
346C3×C22⋊C4C2×D4116yescomplemented
347#217—28no—
348#217—44no—
349#217—44no—
350#217—44no—
351(C2×D3)⋊C4—28no—
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—
357(C2×D3)⋊C4—44no—
358C4⋊Dic3—44no—
359Dic3⋊C4—28no—
360C4×Dic3—44no—
361C25—31no—
362C25—31no—
363C25C22×D311yescharacteristic
364C25C22×D311yescharacteristic
365C22×D4—24no—
366C22×D4—34no—
367C22×D4—34no—
368C22×D4—34no—
369C22×D4—34no—
370C22×D4—34no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—64no—
374C22×D4—64no—
375C22×D4—64no—
376C22×D4—64no—
377C22×D4—64no—
378C22×D4—64no—
379C22×D4—64no—
380C22×D4—122no—
381C22×D4—122no—
382C22×D4—122no—
383C22×D4—122no—
384C22×D4—122no—
385C22×D4—122no—
386C22×D4—122no—
387C22×D4—122no—
388C22×D4C22×D314yes—
389C23×C4—24no—
390C23×C4—31no—
391C23×C4—31no—
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—31no—
395C23×C4—31no—
396C23×C4—34no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—64no—
400C23×C4—64no—
401C23×C4—122no—
402C23×C4C22×D311yescharacteristic
403C23×C4C22×D311yescharacteristic
404C23×C4C22×D311yescharacteristic
405C23×C4C22×D311yescharacteristic
406C23×C4C22×D311yescharacteristic
407C23×C4C22×D314yes—
408#123—232no—
409#121—632no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—34no—
413C2×C4⋊C4—34no—
414C2×C4⋊C4—64no—
415C2×C4⋊C4—122no—
416C2×C4⋊C4C22×D314yes—
417C2×C4⋊C4C22×D314yes—
418C2×C22⋊C4—24no—
419C2×C22⋊C4—24no—
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—34no—
431C2×C22⋊C4—64no—
432C2×C22⋊C4—64no—
433C2×C22⋊C4—122no—
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⋊C4#6718yescomplemented
443C2×C22⋊C4C22×D314yes—
444C2×C22⋊C4C22×D314yes—
445C2×C22⋊C4C22×D314yes—
446C2×C42—34no—
447C2×C42—122no—
448#95—34no—
449#95—34no—
450#95—34no—
451#95—34no—
452#95—34no—
453#95—34no—
454#95—34no—
455#95—34no—
456C23×C3—28no—
457C23×C3—28no—
458C23×C3—28no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—44no—
473C23×C3—44no—
474C23×C3—44no—
475C23×C3—44no—
476C23×C3—44no—
477C23×C3—44no—
478C23×C3—44no—
479C23×C3—44no—
480C23×C3—44no—
481C23×C3—44no—
482C23×C3—44no—
483C23×C3C22×D414yes—
484C23×C3C22×D412yes—
485C23×C3C2×#4112yes—
486C23×C3C2×#4112yes—
487C23×C3H(5,𝔽2)12yes—
488C23×C3H(5,𝔽2)12yes—
489C23×C3H(5,𝔽2)12yes—
490C23×C3H(5,𝔽2)12yes—
491C23×C3C2511yescharacteristic
492C22×D3—28no—
493C22×D3—28no—
494C22×D3—28no—
495C22×D3—22no—
496C22×D3—22no—
497C22×D3—22no—
498C22×D3—22no—
499C22×D3—22no—
500C22×D3—22no—
501C22×D3—22no—
502C22×D3—22no—
503C22×D3—22no—
504C22×D3—22no—
505C22×D3—22no—
506C22×D3—22no—
507C22×D3—22no—
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×D3—44no—
519C22×D3C2×#4114yes—
520C3×D4—416no—
521C2×C3×C4—28no—
522C2×C3×C4—28no—
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—416no—
537C2×C3×C4—44no—
538C2×C3×C4—44no—
539C2×C3×C4—44no—
540C2×C3×C4C22×D414yes—
541C2×C3×C4C22×D414yes—
542#67—416no—
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—22no—
562C2×Dic3—22no—
563C2×Dic3—22no—
564C2×Dic3—44no—
565C2×Dic3—44no—
566C2×Dic3—44no—
567C2×Dic3—44no—
568C2×Dic3—44no—
569C2×Dic3C2×#4114yes—
570D12—416no—
571C4×D3—416no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—34no—
586C24—32no—
587C24—32no—
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—
601C24C2×#6714yes—
602C24C23×D312yes—
603C24C23×D312yes—
604C24C23×D311yescharacteristic
605C2×D4—28no—
606C2×D4—44no—
607C2×D4—44no—
608C2×D4—416no—
609C2×D4—68no—
610C2×D4—68no—
611C2×D4—68no—
612C2×D4—68no—
613C2×D4—68no—
614C2×D4—68no—
615C2×D4—68no—
616C2×D4—124no—
617C2×D4—1216no—
618C2×D4—124no—
619C2×D4—124no—
620C2×D4—124no—
621C2×D4—124no—
622C2×D4—124no—
623C2×D4—124no—
624C2×D4—124no—
625C2×D4—1216no—
626C2×D4—1216no—
627C2×D4—1216no—
628C2×D4—1216no—
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—28no—
643C22×C4—34no—
644C22×C4—32no—
645C22×C4—32no—
646C22×C4—32no—
647C22×C4—32no—
648C22×C4—32no—
649C22×C4—32no—
650C22×C4—44no—
651C22×C4—44no—
652C22×C4—416no—
653C22×C4—68no—
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—62no—
663C22×C4—62no—
664C22×C4—62no—
665C22×C4—62no—
666C22×C4—62no—
667C22×C4—62no—
668C22×C4—62no—
669C22×C4—62no—
670C22×C4—62no—
671C22×C4—68no—
672C22×C4—124no—
673C22×C4—1216no—
674C22×C4C2×#6714yes—
675C22×C4C2×#6714yes—
676C22×C4C23×D312yes—
677C22×C4C23×D312yes—
678C22×C4C23×D312yes—
679C22×C4C23×D312yes—
680C22×C4C23×D312yes—
681C4⋊C4—28no—
682C4⋊C4—28no—
683C4⋊C4—68no—
684C4⋊C4—124no—
685C22⋊C4—28no—
686C22⋊C4—28no—
687C22⋊C4—68no—
688C22⋊C4—68no—
689C22⋊C4—124no—
690C22⋊C4—124no—
691C22⋊C4—124no—
692C22⋊C4—124no—
693C22⋊C4—124no—
694C22⋊C4—124no—
695C22⋊C4—124no—
696C22⋊C4—124no—
697C22⋊C4—124no—
698C22⋊C4C2×#67116yescomplemented
699C42—124no—
700C22×C3—24no—
701C22×C3—24no—
702C22×C3—24no—
703C22×C3—42no—
704C22×C3—42no—
705C22×C3—416no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—42no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—42no—
713C22×C3—42no—
714C22×C3—42no—
715C22×C3—88no—
716C22×C3#53514yes—
717C22×C3#53814yes—
718C22×C3#54014yes—
719C22×C3#54614yes—
720C22×C3#54614yes—
721C22×C3#55314yes—
722C22×C3#56014yes—
723C22×C3C23×D411yescharacteristic
724C22×C3C22×#4111yescharacteristic
725C22×C3C22×#4111yescharacteristic
726C22×C3C2×H(5,𝔽2)11yescharacteristic
727C22×C3C2×H(5,𝔽2)11yescharacteristic
728C22×C3C2×H(5,𝔽2)11yescharacteristic
729C22×C3C2×H(5,𝔽2)11yescharacteristic
730C2×D3—24no—
731C2×D3—24no—
732C2×D3—24no—
733C2×D3—42no—
734C2×D3—42no—
735C2×D3—42no—
736C2×D3—416no—
737C2×D3—42no—
738C2×D3—42no—
739C2×D3—42no—
740C2×D3—42no—
741C2×D3—42no—
742C2×D3—42no—
743C2×D3—42no—
744C2×D3—42no—
745C2×D3—88no—
746C3×C4—24no—
747C3×C4—24no—
748C3×C4—42no—
749C3×C4—42no—
750C3×C4—42no—
751Dic3—24no—
752Dic3—42no—
753Dic3—42no—
754Dic3—42no—
755Dic3—42no—
756Dic3—42no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—28no—
764C23—28no—
765C23—28no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—34no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—44no—
778C23—44no—
779C23—44no—
780C23—44no—
781C23—44no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23—68no—
786C23—68no—
787C23—62no—
788C23—62no—
789C23—62no—
790C23—62no—
791C23—62no—
792C23—62no—
793C23—68no—
794C23—62no—
795C23—62no—
796C23—62no—
797C23—62no—
798C23—62no—
799C23—62no—
800C23—62no—
801C23—124no—
802C23—124no—
803C23—124no—
804C23—124no—
805C23—124no—
806C23—124no—
807C23—124no—
808C23—124no—
809C23—124no—
810C23—124no—
811C23—124no—
812C23#100412yes—
813C23#100412yes—
814C23D3×#4112yes—
815C23D3×#4112yes—
816C23#100912yes—
817C23#100912yes—
818C23C22×#6714yes—
819C23C22×#6712yes—
820C23C24×D311yescharacteristic
821D4—416no—
822D4—1216no—
823D4—1216no—
824D4—1216no—
825D4—1216no—
826D4—1216no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
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—416no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—44no—
847C2×C4—62no—
848C2×C4—62no—
849C2×C4—68no—
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—62no—
862C2×C4—62no—
863C2×C4—62no—
864C2×C4—62no—
865C2×C4—1216no—
866C2×C4—124no—
867C2×C4—124no—
868C2×C4—124no—
869C2×C4—124no—
870C2×C4—124no—
871C2×C4C22×#6714yes—
872C2×C4C22×#6714yes—
873C2×C3—44no—
874C2×C3—82no—
875C2×C3#270318yescomplemented
876C2×C3C2×#53511yescharacteristic
877C2×C3C2×#53811yescharacteristic
878C2×C3C2×#54011yescharacteristic
879C2×C3C2×#54611yescharacteristic
880C2×C3C2×#54611yescharacteristic
881C2×C3C2×#55311yescharacteristic
882C2×C3C2×#56011yescharacteristic
883D3—44no—
884D3—82no—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—416no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—64no—
901C22—64no—
902C22—64no—
903C22—88no—
904C22—122no—
905C22—1216no—
906C22—122no—
907C22—122no—
908C22—122no—
909C22—122no—
910C22—122no—
911C22—122no—
912C22—122no—
913C22—122no—
914C22—122no—
915C22—122no—
916C22—248no—
917C22#565714yes—
918C22#566114yes—
919C22#566314yes—
920C22#566614yes—
921C22#580514yes—
922C22#582914yes—
923C22#582914yes—
924C22C2×#100411yescharacteristic
925C22C2×#100411yescharacteristic
926C22C2×D3×#4111yescharacteristic
927C22C2×D3×#4111yescharacteristic
928C22C2×#100911yescharacteristic
929C22C2×#100911yescharacteristic
930C22C23×#6711yescharacteristic
931C4—24no—
932C4—24no—
933C4—42no—
934C4—42no—
935C4—42no—
936C4—64no—
937C4—122no—
938C4—122no—
939C4—122no—
940C4—122no—
941C4—122no—
942C3C2×#270311yescharacteristic, complemented, Sylow
943C2—44no—
944C2—82no—
945C2—124no—
946C2—242no—
947C2#8290918yesdirect product factor
948C2C2×#566311yescharacteristic
949C2C2×#566111yescharacteristic
950C2C2×#565711yescharacteristic
951C2C2×#566611yescharacteristic
952C2C2×#580511yescharacteristic
953C2C2×#582911yescharacteristic
954C2C2×#582911yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC22×C3×#123C2
socleC24×C3C24
hypercenterC22×#123D3
hypocenterC3C2×#2703
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×C3×#123C2semidirect
2. C22×#884C2semidirect
3. C2×#5223C2semidirect
4. C2×#5223C2semidirect
5. C2×#5213C2semidirect
6. C2×#5213C2semidirect
7. #82909C2direct (N × H)
8. C2×#4992C2semidirect
9. C2×#4987C2semidirect
10. C2×#4985C2semidirect
11. C2×#4988C2semidirect
12. C2×#4960C2semidirect
13. C2×#4956C2semidirect
14. C2×#4961C2semidirect
15. C2×#4945C2semidirect
16. C2×#4951C2semidirect
27. C2×C3×#123C22semidirect
48. C2×#884C22semidirect
49. #5223C22semidirect
50. #5223C22semidirect
51. #5213C22semidirect
52. #5213C22semidirect
61. #4992C22semidirect
62. #4988C22semidirect
63. #4987C22semidirect
64. #4985C22semidirect
65. #4961C22semidirect
66. #4960C22semidirect
67. #4956C22semidirect
68. #4951C22semidirect
69. #4945C22semidirect
70. C22×#123D3semidirect
140. C2×C3×C22⋊C4D4semidirect
190. C2×#123C2×D3semidirect
346. C3×C22⋊C4C2×D4semidirect
442. C2×C22⋊C4#67semidirect
698. C22⋊C4C2×#67semidirect
875. C2×C3#2703semidirect
942. C3C2×#2703semidirect
947. C2#82909direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1232
C22×#8842
C2×#52232
C2×#52132
#829092
C2×#49922
C2×#49872
C2×#49852
C2×#49882
C2×#49602
C2×#49562
C2×#49612
C2×#49452
C2×#49512
C2×#27033