Finite Group Databasebeta

← #11906346

Subgroups — #11906346

Order 1152.

2220 conjugacy classes of subgroups.

The subgroup lattice has 917 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596038C211yesmaximal, characteristic, complemented
2C3×#5578C211yesmaximal, characteristic, complemented
3C3×Q8×D12C211yesmaximal, characteristic, complemented
4#10595400C212yesmaximal, complemented
5D3×#944C212yesmaximal, complemented
6#10594535C214yesmaximal, complemented
7#10594526C212yesmaximal, complemented
8#10594389C214yesmaximal, complemented
9#10594387C212yesmaximal, complemented
10#10593954C212yesmaximal, complemented
11#10593929C212yesmaximal, complemented
12Dic6×D12C211yesmaximal, characteristic, complemented
13D3×#869C211yesmaximal, characteristic, complemented
14#10593887C212yesmaximal
15C4×#3795C211yesmaximal, characteristic
16#10593864C211yesmaximal, characteristic, complemented
17#10593856C212yesmaximal, complemented
18#86747—31nomaximal
19#86281—31nomaximal
20C2×C3×D3×Q8C2212yes—
21C2×#3795C2211yescharacteristic
22C2×D3×Dic6C2212yes—
23C2×D3×Dic6C2212yes—
24C32×C4×Q8C2211yescharacteristic
25#64153C2212yes—
26#64098C2214yes—
27#64096C2212yes—
28#64079C2212yes—
29#64078C2211yescharacteristic
30C4×#634C2212yes—
31C4×#634C2211yescharacteristic
32C3×#946C2211yescharacteristic
33C3×#944C2211yescharacteristic
34C3×#897C2212yes—
35C3×#897C2214yes—
36C3×#897C2211yescharacteristic
37C3×#896C2212yes—
38C3×#889C2212yes—
39C3×#888C2211yescharacteristic
40C3×C4×D12C2211yescharacteristic
41C3×C4×D12C2212yes—
42C3×#872C2212yes—
43C3×C42×D3C2211yescharacteristic
44C3×#869C2212yes—
45C3×#869C2211yescharacteristic
46C3×C4×Dic6C2212yes—
47C3×C4×Dic6C2211yescharacteristic
48#63919C2214yes—
49#63918C2212yes—
50#63918C2212yes—
51#63918C2212yes—
52#63902C2214yes—
53C4×#625C2212yes—
54#63899C2214yes—
55#63899C2214yes—
56#63893C2214yes—
57Dic3×D12C2211yescharacteristic
58Dic3×D12C2212yes—
59D3×C4⋊Dic3C2212yes—
60D3×C4⋊Dic3C2212yes—
61#63887C2214yes—
62#63887C2214yes—
63#63879C2214yes—
64#63879C2212yes—
65#63878C2214yes—
66#63877C2212yes—
67D3×Dic3⋊C4C2214yes—
68D3×Dic3⋊C4C2214yes—
69C4×D3×Dic3C2212yes—
70#63873C2212yes—
71#63869C2212yes—
72#63866C2212yes—
73#63857C2212yes—
74#63851C2214yes—
75#63847C2214yes—
76#63846C2214yes—
77#63844C2211yescharacteristic
78#63844C2212yes—
79#63843C2214yes—
80#63843C2212yes—
81#63841C2211yescharacteristic
82#63839C2214yes—
83#63839C2214yes—
84#63839C2214yes—
85C3×D4×Q8—31no—
86C3×#533—31no—
87Q8×#67—32no—
88C2×#944—32no—
89#5729—32no—
90#5728—32no—
91D3×C4⋊Q8—32no—
92D3×C4⋊Q8—31no—
93#5722—32no—
94#5721—31no—
95#5689—34no—
96#5636—34no—
97#5635—34no—
98#5632—32no—
99#5632—32no—
100#5632—32no—
101#5623—34no—
102#5622—32no—
103#5579—32no—
104#5578D311yescharacteristic, complemented
105Q8×D12—31no—
106Q8×D12D311yescharacteristic, complemented
107#5567—31no—
108#5567—31no—
109#5567—31no—
110#5567—61no—
111Q8×Dic6—32no—
112#5546—32no—
113#5539—32no—
114D4×Dic6—31no—
115C4×#237—31no—
116#5523—32no—
117#5519—32no—
118C4×#235—31no—
119C2×#869—31no—
120C2×C32×Q8C2311yescharacteristic
121C2×#634C2312yes—
122C2×#634C2311yescharacteristic
123C3×D3×Q8—44no—
124C2×C3×D12C2311yescharacteristic
125C2×C3×C4×D3C2311yescharacteristic
126C2×C3×C4×D3C2311yescharacteristic
127C2×C3×C4×D3C2312yes—
128C2×C3×C4×D3C2314yes—
129C2×C3×C4×D3C2311yescharacteristic
130C2×C3×Dic6C2312yes—
131C2×C3×Dic6C2311yescharacteristic
132C2×C3×Dic6C2312yes—
133C2×C3×Dic6C2314yes—
134C2×#627C2314yes—
135C2×#627C2314yes—
136C2×#625C2312yes—
137C2×D3×Dic3C2312yes—
138C2×D3×Dic3C2314yes—
139C2×D3×Dic3C2314yes—
140C2×D3×Dic3C2312yes—
141#3795Q818yescomplemented
142D3×Dic6—44no—
143D3×Dic6—44no—
144C32×C4⋊C4C2311yescharacteristic
145C32×C4⋊C4C2312yes—
146C32×C42C2311yescharacteristic
147C32×C42C2312yes—
148C4⋊(C3⋊Dic3)C2312yes—
149C4⋊(C3⋊Dic3)C2311yescharacteristic
150C4⋊(C3⋊Dic3)C2312yes—
151#3750C2314yes—
152#3750C2312yes—
153#3750C2314yes—
154#3750C2314yes—
155C4×C3⋊Dic3C2314yes—
156C4×C3⋊Dic3C2312yes—
157C3×(C2×D3)⋊C4C2312yes—
158C3×(C2×D3)⋊C4C2312yes—
159C3×(C2×D3)⋊C4C2312yes—
160C3×(C2×D3)⋊C4C2314yes—
161C3×C4⋊Dic3C2311yescharacteristic
162C3×C4⋊Dic3C2312yes—
163C3×C4⋊Dic3C2314yes—
164C3×C4⋊Dic3C2312yes—
165C3×C4⋊Dic3C2311yescharacteristic
166C3×C4⋊Dic3C2312yes—
167C3×Dic3⋊C4C2312yes—
168C3×Dic3⋊C4C2312yes—
169C3×Dic3⋊C4C2312yes—
170C3×Dic3⋊C4C2312yes—
171C3×Dic3⋊C4C2312yes—
172C3×C4×Dic3C2311yescharacteristic
173C3×C4×Dic3C2311yescharacteristic
174C3×C4×Dic3C2312yes—
175C3×C4×Dic3C2311yescharacteristic
176#3724C2312yes—
177#3724C2314yes—
178#3724C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2314yes—
182Dic3⋊Dic3C2314yes—
183(C2×D3)⋊Dic3C2312yes—
184(C2×D3)⋊Dic3C2312yes—
185(C2×D3)⋊Dic3C2314yes—
186Dic32C2312yes—
187Dic32C2312yes—
188Dic32C2314yes—
189#3503—91noSylow
190C22×C3×Q8—32no—
191C2×D3×Q8—32no—
192C2×D3×Q8—32no—
193C2×D3×Q8C2×D312yes—
194C2×#237—31no—
195C2×#235—31no—
196C22×Dic6—32no—
197C22×Dic6—32no—
198C3×C4⋊Q8—31no—
199C3×C4⋊Q8—31no—
200C3×C4⋊Q8—31no—
201C3×C4⋊Q8—32no—
202C3×#125—32no—
203C3×C22⋊Q8—31no—
204C3×C22⋊Q8—31no—
205C3×C22⋊Q8—32no—
206C3×C22⋊Q8—32no—
207C3×C22⋊Q8—34no—
208C3×C4×Q8—21no—
209C3×C4×Q8—32no—
210C3×C4×Q8—31no—
211C3×C4×Q8C2×D311yescharacteristic
212C3×C4×Q8C2×D311yescharacteristic
213C3×C4×D4—31no—
214C3×C4×D4—32no—
215C3×#117—32no—
216C2×C3×C42—31no—
217#946—34no—
218#946—34no—
219#946C2×D311yescharacteristic
220Q8×Dic3—34no—
221Q8×Dic3—32no—
222#944—32no—
223#944—32no—
224#944—32no—
225#944—32no—
226#944—34no—
227#944—34no—
228#944—34no—
229#944—32no—
230#944—62no—
231#944C2×D311yescharacteristic
232D4×Dic3—31no—
233D4×Dic3—32no—
234C4×#67—32no—
235C4×#67—32no—
236C4×#67—32no—
237C4×#67—34no—
238#926—31no—
239C2×C4⋊Dic3—32no—
240C2×C4⋊Dic3—32no—
241#924—32no—
242#924—34no—
243C2×Dic3⋊C4—34no—
244C2×Dic3⋊C4—34no—
245C2×C4×Dic3—32no—
246#897—32no—
247#897—34no—
248#897C2×D311yescharacteristic
249#897C2×D312yes—
250#897C2×D314yes—
251#896—34no—
252#896—34no—
253#896—34no—
254#896C2×D312yes—
255#892—31no—
256#892—34no—
257D3×C4⋊C4—34no—
258D3×C4⋊C4—32no—
259D3×C4⋊C4—34no—
260D3×C4⋊C4—32no—
261#890—34no—
262#890—32no—
263#889—34no—
264#889—34no—
265#889—34no—
266#889—34no—
267#889—34no—
268#889—64no—
269#889C2×D312yes—
270#888—34no—
271#888—34no—
272#888—34no—
273#888—34no—
274#888—34no—
275#888—32no—
276#888—32no—
277#888—32no—
278#888C2×D311yescharacteristic
279#887—32no—
280#887—34no—
281#887—32no—
282#887—32no—
283#887—32no—
284#887—31no—
285#887—62no—
286#67⋊C4—34no—
287#67⋊C4—32no—
288#67⋊C4—34no—
289#67⋊C4—34no—
290#878—34no—
291#878—34no—
292#878—34no—
293#878—34no—
294#878—34no—
295#877—34no—
296#877—32no—
297C4×D12—31no—
298C4×D12—32no—
299C4×D12C2×D311yescharacteristic
300C4×D12C2×D312yes—
301#872—32no—
302#872C2×D312yes—
303C42×D3—32no—
304C42×D3C2×D311yescharacteristic
305#870—32no—
306#870—32no—
307#870—32no—
308#870—62no—
309#869—32no—
310#869—31no—
311#869—31no—
312#869—32no—
313#869—32no—
314#869—32no—
315#869—61no—
316#869C2×D311yescharacteristic
317#869C2×D312yes—
318C4×Dic6—31no—
319C4×Dic6—32no—
320C4×Dic6—31no—
321C4×Dic6—32no—
322C4×Dic6—31no—
323C4×Dic6—32no—
324C4×Dic6—61no—
325C4×Dic6—62no—
326C4×Dic6C2×D311yescharacteristic
327C4×Dic6C2×D312yes—
328C22×C3×D3C2412yes—
329C22×C3×D3C2411yescharacteristic
330C32×Q8—22no—
331C2×C32×C4C2411yescharacteristic
332C2×C32×C4C2412yes—
333C2×C32×C4C2412yes—
334C2×C32×C4C2411yescharacteristic
335C2×C32×C4C2411yescharacteristic
336C2×C3⋊Dic3C2412yes—
337C2×C3⋊Dic3C2414yes—
338C2×C3⋊Dic3C2412yes—
339#634—24no—
340#634C2×Q814yescomplemented
341C2×C3×Dic3C2412yes—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2414yes—
344C2×C3×Dic3C2411yescharacteristic
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2411yescharacteristic
347C2×C3×Dic3C2411yescharacteristic
348C3×D12C2×Q814yescomplemented
349C3×C4×D3—22no—
350C3×C4×D3—24no—
351C3×C4×D3—22no—
352C3×C4×D3—44no—
353C3×C4×D3C2×Q814yescomplemented
354C3×Dic6—22no—
355C3×Dic6—24no—
356C3×Dic6—24no—
357C3×Dic6—44no—
358#627—44no—
359#627—44no—
360#625C2×Q818yescomplemented
361D3×Dic3—24no—
362D3×Dic3—44no—
363D3×Dic3—44no—
364D3×Dic3C2×Q818yescomplemented
365Q82—92no—
366#557—91no—
367#557—91no—
368#554—92no—
369#554—94no—
370D4×Q8—31no—
371D4×Q8—91no—
372D4×Q8—92no—
373D4×Q8—92no—
374#544—92no—
375#544—94no—
376#533—31no—
377#533—92no—
378C2×C4⋊Q8—91no—
379C2×C4⋊Q8—92no—
380#520—92no—
381C4×#41—91no—
382C2×C3×Q8—21no—
383C2×C3×Q8—32no—
384C2×C3×Q8—31no—
385C2×C3×Q8—32no—
386C2×C3×Q8—34no—
387C2×C3×Q8—124no—
388C2×C3×Q8C22×D311yescharacteristic
389C2×C3×Q8C22×D311yescharacteristic
390C2×C3×D4—31no—
391C22×C3×C4—31no—
392C22×C3×C4—32no—
393C22×C3×C4—31no—
394C22×C3×C4—31no—
395C22×C3×C4—34no—
396C2×#67—32no—
397C2×#67—32no—
398C22×Dic3—32no—
399C22×Dic3—32no—
400C22×Dic3—34no—
401C22×Dic3—34no—
402D3×Q8—44no—
403D3×Q8—124no—
404D3×Q8—124no—
405#237—38no—
406#235—38no—
407C2×D12C22×D311yescharacteristic
408C2×C4×D3—32no—
409C2×C4×D3—32no—
410C2×C4×D3—34no—
411C2×C4×D3—34no—
412C2×C4×D3C22×D312yes—
413C2×C4×D3C22×D311yescharacteristic
414C2×C4×D3C22×D311yescharacteristic
415C2×C4×D3C22×D314yes—
416C2×C4×D3C22×D311yescharacteristic
417C2×Dic6—31no—
418C2×Dic6—31no—
419C2×Dic6—32no—
420C2×Dic6—32no—
421C2×Dic6—34no—
422C2×Dic6—34no—
423C2×Dic6—34no—
424C2×Dic6—34no—
425C2×Dic6—61no—
426C2×Dic6—62no—
427C2×Dic6—124no—
428C2×Dic6—124no—
429C2×Dic6C22×D312yes—
430C2×Dic6C22×D311yescharacteristic
431C2×Dic6C22×D312yes—
432C2×Dic6C22×D314yes—
433C3×C4⋊C4—21no—
434C3×C4⋊C4—22no—
435C3×C4⋊C4—31no—
436C3×C4⋊C4—31no—
437C3×C4⋊C4—34no—
438C3×C4⋊C4—32no—
439C3×C4⋊C4—32no—
440C3×C4⋊C4—32no—
441C3×C4⋊C4—32no—
442C3×C4⋊C4—32no—
443C3×C4⋊C4—32no—
444C3×C4⋊C4—32no—
445C3×C4⋊C4—32no—
446C3×C4⋊C4C22×D311yescharacteristic
447C3×C4⋊C4C22×D311yescharacteristic
448C3×C4⋊C4C22×D312yes—
449C3×C4⋊C4C22×D312yes—
450C3×C22⋊C4—32no—
451C3×C22⋊C4—34no—
452C3×C22⋊C4—32no—
453C3×C22⋊C4—32no—
454C3×C42—21no—
455C3×C42—22no—
456C3×C42—31no—
457C3×C42—32no—
458C3×C42—31no—
459C3×C42—31no—
460C3×C42C22×D311yescharacteristic
461C3×C42C22×D312yes—
462C3×C42C22×D311yescharacteristic
463C3×C42C22×D312yes—
464#217—32no—
465#217—34no—
466#217—32no—
467(C2×D3)⋊C4—32no—
468(C2×D3)⋊C4—34no—
469(C2×D3)⋊C4—32no—
470(C2×D3)⋊C4C22×D312yes—
471(C2×D3)⋊C4C22×D312yes—
472(C2×D3)⋊C4C22×D312yes—
473(C2×D3)⋊C4C22×D314yes—
474C4⋊Dic3—32no—
475C4⋊Dic3—32no—
476C4⋊Dic3—31no—
477C4⋊Dic3—31no—
478C4⋊Dic3—32no—
479C4⋊Dic3—32no—
480C4⋊Dic3—34no—
481C4⋊Dic3—34no—
482C4⋊Dic3—34no—
483C4⋊Dic3—34no—
484C4⋊Dic3—62no—
485C4⋊Dic3—61no—
486C4⋊Dic3—62no—
487C4⋊Dic3C22×D311yescharacteristic
488C4⋊Dic3C22×D312yes—
489C4⋊Dic3C22×D312yes—
490C4⋊Dic3C22×D311yescharacteristic
491C4⋊Dic3C22×D312yes—
492C4⋊Dic3C22×D314yes—
493Dic3⋊C4—32no—
494Dic3⋊C4—32no—
495Dic3⋊C4—34no—
496Dic3⋊C4—34no—
497Dic3⋊C4—34no—
498Dic3⋊C4—34no—
499Dic3⋊C4—34no—
500Dic3⋊C4—34no—
501Dic3⋊C4—32no—
502Dic3⋊C4—34no—
503Dic3⋊C4—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—32no—
506Dic3⋊C4—34no—
507Dic3⋊C4—34no—
508Dic3⋊C4—34no—
509Dic3⋊C4—34no—
510Dic3⋊C4—34no—
511Dic3⋊C4—62no—
512Dic3⋊C4—64no—
513Dic3⋊C4—64no—
514Dic3⋊C4—64no—
515Dic3⋊C4C22×D312yes—
516Dic3⋊C4C22×D312yes—
517Dic3⋊C4C22×D312yes—
518Dic3⋊C4C22×D312yes—
519Dic3⋊C4C22×D312yes—
520C4×Dic3—32no—
521C4×Dic3—34no—
522C4×Dic3—34no—
523C4×Dic3—32no—
524C4×Dic3—32no—
525C4×Dic3—34no—
526C4×Dic3—32no—
527C4×Dic3—34no—
528C4×Dic3—32no—
529C4×Dic3—32no—
530C4×Dic3—64no—
531C4×Dic3—62no—
532C4×Dic3C22×D311yescharacteristic
533C4×Dic3C22×D312yes—
534C4×Dic3C22×D311yescharacteristic
535C4×Dic3C22×D311yescharacteristic
536C22×C32C2511yescharacteristic
537C2×C3×D3—21no—
538C2×C3×D3—22no—
539C2×C3×D3—22no—
540C2×C3×D3—21no—
541C2×C3×D3C22×Q814yes—
542C2×C3×D3C22×Q812yes—
543C32×C4—22no—
544C32×C4—22no—
545C32×C4—21no—
546C32×C4C22×Q812yes—
547C32×C4H(5,𝔽2)12yes—
548C3⋊Dic3—24no—
549C3⋊Dic3—22no—
550C3⋊Dic3C22×Q814yes—
551C3×Dic3—22no—
552C3×Dic3—24no—
553C3×Dic3—21no—
554C3×Dic3—22no—
555C3×Dic3—22no—
556C3×Dic3C22×Q812yes—
557C3×Dic32−1+412yes—
558C2×#41—91no—
559C22×Q8—32no—
560C22×Q8—92no—
561C22×Q8—92no—
562C4⋊Q8—31no—
563C4⋊Q8—31no—
564C4⋊Q8—31no—
565C4⋊Q8—32no—
566C4⋊Q8—92no—
567C4⋊Q8—92no—
568C4⋊Q8—92no—
569C4⋊Q8—92no—
570C4⋊Q8—94no—
571C4⋊Q8—94no—
572C4⋊Q8—94no—
573C4⋊Q8—94no—
574C4⋊Q8—92no—
575C4⋊Q8—92no—
576C4⋊Q8—91no—
577#125—32no—
578#125—92no—
579#125—94no—
580#125—94no—
581#125—94no—
582#125—92no—
583C22⋊Q8—31no—
584C22⋊Q8—31no—
585C22⋊Q8—32no—
586C22⋊Q8—32no—
587C22⋊Q8—34no—
588C22⋊Q8—94no—
589C22⋊Q8—94no—
590C22⋊Q8—94no—
591C22⋊Q8—94no—
592C22⋊Q8—94no—
593C22⋊Q8—92no—
594C22⋊Q8—94no—
595C4×Q8—31no—
596C4×Q8—32no—
597C4×Q8—91no—
598C4×Q8—92no—
599C4×Q8—92no—
600C4×Q8—94no—
601C4×Q8—92no—
602C4×Q8—91no—
603C4×Q8—92no—
604C4×Q8D3211yescharacteristic
605C4×D4—31no—
606C4×D4—32no—
607C4×D4—91no—
608C4×D4—92no—
609C4×D4—94no—
610C4×D4—92no—
611C4×D4—94no—
612C4×D4—92no—
613#117—32no—
614#117—92no—
615#117—94no—
616#117—91no—
617C2×C4⋊C4—94no—
618C2×C4⋊C4—92no—
619C2×C4⋊C4—94no—
620C2×C4⋊C4—92no—
621C2×C42—31no—
622C2×C42—92no—
623C23×C3—32no—
624C23×C3—31no—
625C22×D3C23×D312yes—
626C22×D3C23×D311yescharacteristic
627C3×Q8—22no—
628C3×Q8—22no—
629C3×Q8—42no—
630C3×Q8—64no—
631C3×Q8—62no—
632C3×Q8—64no—
633C3×Q8—124no—
634C3×D4—34no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—22no—
638C2×C3×C4—22no—
639C2×C3×C4—21no—
640C2×C3×C4—31no—
641C2×C3×C4—31no—
642C2×C3×C4—34no—
643C2×C3×C4—32no—
644C2×C3×C4—32no—
645C2×C3×C4—34no—
646C2×C3×C4—32no—
647C2×C3×C4—31no—
648C2×C3×C4—62no—
649C2×C3×C4—62no—
650C2×C3×C4—64no—
651C2×C3×C4—124no—
652C2×C3×C4C23×D312yes—
653C2×C3×C4C23×D312yes—
654C2×C3×C4C23×D311yescharacteristic
655C2×C3×C4C23×D312yes—
656C2×C3×C4C23×D312yes—
657C2×C3×C4C23×D311yescharacteristic
658C2×C3×C4C23×D311yescharacteristic
659C2×C3×C4C23×D311yescharacteristic
660C2×C3×C4C23×D311yescharacteristic
661C2×C3×C4C23×D311yescharacteristic
662#67—38no—
663#67—38no—
664C2×Dic3—32no—
665C2×Dic3—32no—
666C2×Dic3—38no—
667C2×Dic3—32no—
668C2×Dic3—32no—
669C2×Dic3—34no—
670C2×Dic3—34no—
671C2×Dic3—62no—
672C2×Dic3—62no—
673C2×Dic3—64no—
674C2×Dic3—64no—
675C2×Dic3—124no—
676C2×Dic3—124no—
677C2×Dic3C23×D312yes—
678C2×Dic3C23×D312yes—
679C2×Dic3C23×D314yes—
680C2×Dic3C23×D311yescharacteristic
681C2×Dic3C23×D312yes—
682C2×Dic3C23×D311yescharacteristic
683C2×Dic3C23×D311yescharacteristic
684D12D3×Q814yescomplemented
685C4×D3—24no—
686C4×D3—22no—
687C4×D3—22no—
688C4×D3—38no—
689C4×D3—44no—
690C4×D3—64no—
691C4×D3—124no—
692C4×D3—124no—
693C4×D3D3×Q814yescomplemented
694Dic6—24no—
695Dic6—22no—
696Dic6—24no—
697Dic6—34no—
698Dic6—34no—
699Dic6—44no—
700Dic6—64no—
701Dic6—64no—
702Dic6—64no—
703Dic6—124no—
704Dic6—124no—
705Dic6—124no—
706Dic6—124no—
707Dic6—124no—
708C2×C32C23×Q811yescharacteristic
709C2×C32C2×H(5,𝔽2)11yescharacteristic
710C2×C32C2×2−1+411yescharacteristic
711C3×D3—22no—
712C3×D3—24no—
713#41—98no—
714C2×Q8—32no—
715C2×Q8—31no—
716C2×Q8—32no—
717C2×Q8—34no—
718C2×Q8—94no—
719C2×Q8—94no—
720C2×Q8—91no—
721C2×Q8—92no—
722C2×Q8—124no—
723C2×Q8—364no—
724C2×Q8—364no—
725C2×Q8C2×D3211yescharacteristic
726C2×D4—31no—
727C2×D4—92no—
728C22×C4—31no—
729C22×C4—31no—
730C22×C4—31no—
731C22×C4—32no—
732C22×C4—34no—
733C22×C4—92no—
734C22×C4—92no—
735C22×C4—94no—
736C22×C4—94no—
737C4⋊C4—32no—
738C4⋊C4—32no—
739C4⋊C4—32no—
740C4⋊C4—32no—
741C4⋊C4—32no—
742C4⋊C4—31no—
743C4⋊C4—31no—
744C4⋊C4—32no—
745C4⋊C4—32no—
746C4⋊C4—32no—
747C4⋊C4—34no—
748C4⋊C4—94no—
749C4⋊C4—94no—
750C4⋊C4—94no—
751C4⋊C4—94no—
752C4⋊C4—92no—
753C4⋊C4—94no—
754C4⋊C4—94no—
755C4⋊C4—94no—
756C4⋊C4—92no—
757C4⋊C4—94no—
758C4⋊C4—92no—
759C4⋊C4—92no—
760C4⋊C4—91no—
761C4⋊C4—94no—
762C4⋊C4C2×D3211yescharacteristic
763C4⋊C4C2×D3212yes—
764C22⋊C4—32no—
765C22⋊C4—32no—
766C22⋊C4—32no—
767C22⋊C4—34no—
768C22⋊C4—92no—
769C22⋊C4—94no—
770C22⋊C4—92no—
771C42—31no—
772C42—31no—
773C42—31no—
774C42—32no—
775C42—92no—
776C42—92no—
777C42—94no—
778C42—92no—
779C42—94no—
780C42C2×D3211yescharacteristic
781C42C2×D3212yes—
782C22×C3—21no—
783C22×C3—34no—
784C22×C3—32no—
785C22×C3—61no—
786C22×C3—62no—
787C22×C3—62no—
788C22×C3—61no—
789C22×C3C24×D311yescharacteristic
790C22×C3C24×D311yescharacteristic
791C2×D3—22no—
792C2×D3—21no—
793C2×D3—21no—
794C2×D3—22no—
795C2×D3C2×D3×Q814yes—
796C2×D3C2×D3×Q812yes—
797C3×C4—22no—
798C3×C4—22no—
799C3×C4—22no—
800C3×C4—21no—
801C3×C4—21no—
802C3×C4—22no—
803C3×C4—22no—
804C3×C4—22no—
805C3×C4—32no—
806C3×C4—32no—
807C3×C4—42no—
808C3×C4—41no—
809C3×C4—42no—
810C3×C4—61no—
811C3×C4—62no—
812C3×C4—62no—
813C3×C4—64no—
814C3×C4—62no—
815C3×C4#100412yes—
816C3×C4C2×D3×Q812yes—
817C3×C4C2×D3×Q812yes—
818C3×C4#100912yes—
819Dic3—24no—
820Dic3—22no—
821Dic3—22no—
822Dic3—21no—
823Dic3—22no—
824Dic3—34no—
825Dic3—34no—
826Dic3—64no—
827Dic3—64no—
828Dic3—64no—
829Dic3—62no—
830Dic3—62no—
831Dic3—124no—
832Dic3—122no—
833Dic3C2×D3×Q812yes—
834Dic3#101012yes—
835C32#350311yescharacteristic, complemented, Sylow
836C23—31no—
837C23—32no—
838Q8—22no—
839Q8—64no—
840Q8—64no—
841Q8—62no—
842Q8—94no—
843Q8—124no—
844Q8—184no—
845Q8—364no—
846Q8—364no—
847D4—34no—
848D4—98no—
849C2×C4—31no—
850C2×C4—31no—
851C2×C4—34no—
852C2×C4—31no—
853C2×C4—32no—
854C2×C4—32no—
855C2×C4—32no—
856C2×C4—34no—
857C2×C4—62no—
858C2×C4—64no—
859C2×C4—62no—
860C2×C4—98no—
861C2×C4—92no—
862C2×C4—92no—
863C2×C4—94no—
864C2×C4—124no—
865C2×C4—184no—
866C2×C4—364no—
867C2×C4—364no—
868C2×C4C22×D3211yescharacteristic
869C2×C4C22×D3212yes—
870C2×C4C22×D3212yes—
871C2×C4C22×D3211yescharacteristic
872C2×C4C22×D3211yescharacteristic
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—64no—
877C2×C3—62no—
878C2×C3C2×#100411yescharacteristic
879C2×C3C22×D3×Q811yescharacteristic
880C2×C3C22×D3×Q811yescharacteristic
881C2×C3C2×#100911yescharacteristic
882C2×C3C2×#101011yescharacteristic
883C2×C3D3×2−1+411yescharacteristic
884D3—22no—
885D3—24no—
886C22—32no—
887C22—34no—
888C22—62no—
889C22—61no—
890C22—61no—
891C22—62no—
892C22C23×D3211yescharacteristic
893C4—22no—
894C4—21no—
895C4—22no—
896C4—32no—
897C4—32no—
898C4—62no—
899C4—61no—
900C4—64no—
901C4—62no—
902C4—62no—
903C4—94no—
904C4—184no—
905C4—182no—
906C4#6430712yes—
907C4D32×Q812yes—
908C3—21no—
909C3#8628111yescharacteristic, complemented
910C3#8674711yescharacteristic, complemented
911C2—62no—
912C2—64no—
913C2C2×#6430711yescharacteristic
914C2C2×D32×Q811yescharacteristic
915C2D3×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radicalC2×#3795C22
hypercenterC4×Q8D32
hypocenterC32#3503
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596038C2semidirect
2. C3×#5578C2semidirect
3. C3×Q8×D12C2semidirect
4. #10595400C2semidirect
5. D3×#944C2semidirect
6. #10594535C2semidirect
7. #10594526C2semidirect
8. #10594389C2semidirect
9. #10594387C2semidirect
10. #10593954C2semidirect
11. #10593929C2semidirect
12. Dic6×D12C2semidirect
13. D3×#869C2semidirect
16. #10593864C2semidirect
17. #10593856C2semidirect
104. #5578D3semidirect
106. Q8×D12D3semidirect
141. #3795Q8semidirect
340. #634C2×Q8semidirect
348. C3×D12C2×Q8semidirect
353. C3×C4×D3C2×Q8semidirect
360. #625C2×Q8semidirect
364. D3×Dic3C2×Q8semidirect
684. D12D3×Q8semidirect
693. C4×D3D3×Q8semidirect
835. C32#3503semidirect
909. C3#86281semidirect
910. C3#86747semidirect

Maximal subgroups

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

subgroupindex
#105960382
C3×#55782
C3×Q8×D122
#105954002
D3×#9442
#105945352
#105945262
#105943892
#105943872
#105939542
#105939292
Dic6×D122
D3×#8692
#105938872
C4×#37952
#105938642
#105938562
#867473
#862813