Finite Group Databasebeta

← #11903771

Subgroups — #11903771

Order 1152.

2236 conjugacy classes of subgroups.

The subgroup lattice has 913 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596038C211yesmaximal, characteristic, complemented
2C3×#5579C211yesmaximal, characteristic, complemented
3C3×C4×D3×Q8C211yesmaximal, characteristic, complemented
4#10595400C212yesmaximal, complemented
5#10595367C212yesmaximal, complemented
6#10594533C214yesmaximal, complemented
7#10594531C212yesmaximal, complemented
8#10594386C214yesmaximal, complemented
9D3×#887C212yesmaximal, complemented
10#10593929C212yesmaximal, complemented
11Dic6×D12C211yesmaximal, characteristic, complemented
12C4×#3795C212yesmaximal
13C4×#3795C211yesmaximal, characteristic
14#10593874C212yesmaximal, complemented
15#10593859C211yesmaximal, characteristic, complemented
16#10593856C211yesmaximal, characteristic, complemented
17#10593852C212yesmaximal, complemented
18#86923—31nomaximal
19Q8×#235—31nomaximal
20C2×C3×D3×Q8C2211yescharacteristic
21C2×#3795C2211yescharacteristic
22C2×D3×Dic6C2212yes—
23C32×C4×Q8C2211yescharacteristic
24#64153C2212yes—
25#64098C2214yes—
26#64096C2212yes—
27#64079C2212yes—
28#64078C2211yescharacteristic
29C4×#634C2212yes—
30C4×#634C2211yescharacteristic
31C3×#946C2212yes—
32C3×Q8×Dic3C2211yescharacteristic
33C3×#896C2214yes—
34C3×D3×C4⋊C4C2212yes—
35C3×D3×C4⋊C4C2211yescharacteristic
36C3×D3×C4⋊C4C2212yes—
37C3×#887C2211yescharacteristic
38C3×#887C2212yes—
39C3×C4×D12C2211yescharacteristic
40C3×C4×D12C2212yes—
41C3×C42×D3C2211yescharacteristic
42C3×C42×D3C2212yes—
43C3×#870C2212yes—
44C3×#869C2211yescharacteristic
45C3×C4×Dic6C2212yes—
46C3×C4×Dic6C2211yescharacteristic
47#63919C2212yes—
48#63918C2212yes—
49#63918C2212yes—
50C4×#625C2212yes—
51C4×#625C2214yes—
52#63899C2214yes—
53#63893C2214yes—
54Dic3×D12C2212yes—
55Dic3×D12C2211yescharacteristic
56#63887C2214yes—
57#63879C2214yes—
58#63879C2212yes—
59#63877C2214yes—
60#63877C2212yes—
61D3×Dic3⋊C4C2214yes—
62C4×D3×Dic3C2212yes—
63C4×D3×Dic3C2214yes—
64#63870C2214yes—
65#63869C2212yes—
66#63857C2212yes—
67#63857C2212yes—
68#63856C2212yes—
69#63851C2214yes—
70#63851C2214yes—
71#63851C2214yes—
72#63847C2214yes—
73#63844C2212yes—
74#63844C2211yescharacteristic
75#63844C2212yes—
76#63843C2212yes—
77Dic3×Dic6C2212yes—
78#63841C2212yes—
79#63841C2211yescharacteristic
80#63839C2214yes—
81#63839C2214yes—
82#63838C2214yes—
83#63837C2214yes—
84#63837C2214yes—
85C3×#554—31no—
86C2×C3×C4×Q8—31no—
87Q8×#67—32no—
88#5728—31no—
89#5722—31no—
90#5688—32no—
91#5685—32no—
92#5636—34no—
93#5632—32no—
94#5622—32no—
95#5622—34no—
96#5579—32no—
97#5579D311yescharacteristic, complemented
98#5578—32no—
99#5578—34no—
100Q8×D12—31no—
101C4×D3×Q8—32no—
102C4×D3×Q8D311yescharacteristic, complemented
103#5567—31no—
104#5567—31no—
105#5567—32no—
106#5567—61no—
107Q8×Dic6—31no—
108#5539—32no—
109D4×Dic6—31no—
110C4×#237—32no—
111C4×#237—31no—
112#5511—34no—
113#5511—32no—
114#5511—32no—
115C2×#887—32no—
116C4×#235—31no—
117C4×#235—32no—
118#5470—32no—
119#5470—31no—
120C2×C32×Q8C2311yescharacteristic
121C2×#634C2312yes—
122C2×#634C2311yescharacteristic
123C3×D3×Q8—24no—
124C2×C3×D12C2311yescharacteristic
125C2×C3×C4×D3C2312yes—
126C2×C3×C4×D3C2312yes—
127C2×C3×C4×D3C2311yescharacteristic
128C2×C3×C4×D3C2312yes—
129C2×C3×C4×D3C2311yescharacteristic
130C2×C3×C4×D3C2314yes—
131C2×C3×C4×D3C2311yescharacteristic
132C2×C3×Dic6C2312yes—
133C2×C3×Dic6C2312yes—
134C2×C3×Dic6C2311yescharacteristic
135C2×#627C2314yes—
136C2×#627C2314yes—
137C2×#625C2312yes—
138C2×D3×Dic3C2314yes—
139C2×D3×Dic3C2312yes—
140C2×D3×Dic3C2312yes—
141#3795Q818yescomplemented
142D3×Dic6—28no—
143C32×C4⋊C4C2311yescharacteristic
144C32×C4⋊C4C2312yes—
145C32×C42C2311yescharacteristic
146C32×C42C2312yes—
147C4⋊(C3⋊Dic3)C2312yes—
148C4⋊(C3⋊Dic3)C2311yescharacteristic
149C4⋊(C3⋊Dic3)C2312yes—
150#3750C2312yes—
151#3750C2314yes—
152#3750C2314yes—
153#3750C2314yes—
154C4×C3⋊Dic3C2314yes—
155C4×C3⋊Dic3C2312yes—
156C3×(C2×D3)⋊C4C2312yes—
157C3×(C2×D3)⋊C4C2314yes—
158C3×C4⋊Dic3C2312yes—
159C3×C4⋊Dic3C2311yescharacteristic
160C3×C4⋊Dic3C2312yes—
161C3×C4⋊Dic3C2312yes—
162C3×C4⋊Dic3C2311yescharacteristic
163C3×Dic3⋊C4C2312yes—
164C3×Dic3⋊C4C2312yes—
165C3×Dic3⋊C4C2312yes—
166C3×Dic3⋊C4C2314yes—
167C3×Dic3⋊C4C2314yes—
168C3×C4×Dic3C2312yes—
169C3×C4×Dic3C2311yescharacteristic
170C3×C4×Dic3C2312yes—
171C3×C4×Dic3C2311yescharacteristic
172C3×C4×Dic3C2311yescharacteristic
173C3×C4×Dic3C2312yes—
174#3724C2314yes—
175#3724C2312yes—
176#3724C2314yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180(C2×D3)⋊Dic3C2312yes—
181(C2×D3)⋊Dic3C2314yes—
182(C2×D3)⋊Dic3C2312yes—
183(C2×D3)⋊Dic3C2314yes—
184Dic32C2312yes—
185Dic32C2314yes—
186Dic32C2312yes—
187Dic32C2314yes—
188Q8×#41—91noSylow
189C22×C3×Q8—31no—
190C2×D3×Q8—32no—
191C2×D3×Q8C2×D311yescharacteristic
192C2×#237—31no—
193C2×#235—31no—
194C22×Dic6—32no—
195C3×C4⋊Q8—31no—
196C3×#125—32no—
197C3×C22⋊Q8—32no—
198C3×C22⋊Q8—34no—
199C3×C4×Q8—21no—
200C3×C4×Q8—31no—
201C3×C4×Q8—31no—
202C3×C4×Q8—32no—
203C3×C4×Q8—31no—
204C3×C4×Q8—32no—
205C3×C4×Q8C2×D311yescharacteristic
206C3×C4×Q8C2×D311yescharacteristic
207C3×C4×D4—31no—
208C3×C4×D4—32no—
209C2×C3×C4⋊C4—32no—
210C2×C3×C4⋊C4—32no—
211C2×C3×C4⋊C4—31no—
212C2×C3×C42—32no—
213C2×C3×C42—31no—
214#946—32no—
215#946—34no—
216#946C2×D312yes—
217Q8×Dic3—32no—
218Q8×Dic3—32no—
219Q8×Dic3C2×D311yescharacteristic
220#944—32no—
221#944—32no—
222#944—34no—
223#944—34no—
224#944—62no—
225D4×Dic3—32no—
226D4×Dic3—31no—
227C4×#67—32no—
228C4×#67—34no—
229C4×#67—34no—
230C4×#67—32no—
231C4×#67—32no—
232C4×#67—34no—
233#926—31no—
234#926—32no—
235#924—32no—
236#924—32no—
237#924—32no—
238#924—34no—
239#924—34no—
240#924—34no—
241C2×Dic3⋊C4—34no—
242C2×C4×Dic3—32no—
243C2×C4×Dic3—34no—
244#897—32no—
245#897—32no—
246#897—34no—
247#896—34no—
248#896—34no—
249#896—34no—
250#896—34no—
251#896C2×D314yes—
252#892—31no—
253#892—32no—
254D3×C4⋊C4—34no—
255D3×C4⋊C4C2×D312yes—
256D3×C4⋊C4C2×D311yescharacteristic
257D3×C4⋊C4C2×D312yes—
258#890—32no—
259#889—34no—
260#889—34no—
261#889—34no—
262#889—34no—
263#889—34no—
264#889—34no—
265#889—64no—
266#888—34no—
267#888—34no—
268#888—32no—
269#888—32no—
270#888—32no—
271#888—32no—
272#887—32no—
273#887—32no—
274#887—32no—
275#887—34no—
276#887—34no—
277#887—31no—
278#887—32no—
279#887—34no—
280#887—34no—
281#887—32no—
282#887—62no—
283#887C2×D311yescharacteristic
284#887C2×D312yes—
285#67⋊C4—34no—
286#67⋊C4—32no—
287#878—34no—
288#878—34no—
289#878—34no—
290#877—32no—
291#877—34no—
292C4×D12—32no—
293C4×D12—31no—
294C4×D12C2×D311yescharacteristic
295C4×D12C2×D312yes—
296#872—32no—
297#872—34no—
298C42×D3—34no—
299C42×D3—32no—
300C42×D3C2×D312yes—
301C42×D3C2×D311yescharacteristic
302#870—32no—
303#870—32no—
304#870—32no—
305#870—62no—
306#870C2×D312yes—
307#869—31no—
308#869—31no—
309#869—32no—
310#869—32no—
311#869—61no—
312#869C2×D311yescharacteristic
313C4×Dic6—32no—
314C4×Dic6—32no—
315C4×Dic6—31no—
316C4×Dic6—31no—
317C4×Dic6—32no—
318C4×Dic6—32no—
319C4×Dic6—32no—
320C4×Dic6—31no—
321C4×Dic6—34no—
322C4×Dic6—34no—
323C4×Dic6—62no—
324C4×Dic6—61no—
325C4×Dic6C2×D312yes—
326C4×Dic6C2×D311yescharacteristic
327C22×C3×D3C2411yescharacteristic
328C22×C3×D3C2412yes—
329C32×Q8—22no—
330C2×C32×C4C2412yes—
331C2×C32×C4C2412yes—
332C2×C32×C4C2411yescharacteristic
333C2×C32×C4C2411yescharacteristic
334C2×C32×C4C2411yescharacteristic
335C2×C3⋊Dic3C2414yes—
336C2×C3⋊Dic3C2412yes—
337C2×C3⋊Dic3C2412yes—
338#634—24no—
339#634C2×Q814yescomplemented
340C2×C3×Dic3C2414yes—
341C2×C3×Dic3C2412yes—
342C2×C3×Dic3C2411yescharacteristic
343C2×C3×Dic3C2411yescharacteristic
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2411yescharacteristic
346C2×C3×Dic3C2412yes—
347C3×D12C2×Q814yescomplemented
348C3×C4×D3—24no—
349C3×C4×D3—22no—
350C3×C4×D3—24no—
351C3×C4×D3—41no—
352C3×C4×D3—42no—
353C3×C4×D3—44no—
354C3×C4×D3C2×Q814yescomplemented
355C3×Dic6—24no—
356C3×Dic6—42no—
357C3×Dic6#4114yescomplemented
358#627—28no—
359#627—44no—
360#625C2×Q818yescomplemented
361D3×Dic3—28no—
362D3×Dic3—42no—
363D3×Dic3C2×Q818yescomplemented
364Q82—91no—
365#557—92no—
366#557—91no—
367#554—31no—
368#554—92no—
369#554—94no—
370#554—92no—
371D4×Q8—91no—
372D4×Q8—92no—
373#533—92no—
374#533—91no—
375#533—92no—
376#533—94no—
377C4×#41—91no—
378C4×#41—92no—
379C2×C4×Q8—31no—
380C2×C4×Q8—92no—
381C2×C3×Q8—21no—
382C2×C3×Q8—31no—
383C2×C3×Q8—32no—
384C2×C3×Q8—32no—
385C2×C3×Q8—64no—
386C2×C3×Q8C22×D311yescharacteristic
387C2×C3×Q8C22×D311yescharacteristic
388C2×C3×D4—31no—
389C22×C3×C4—31no—
390C22×C3×C4—32no—
391C22×C3×C4—32no—
392C22×C3×C4—31no—
393C22×C3×C4—34no—
394C22×C3×C4—31no—
395C22×C3×C4—32no—
396C2×#67—32no—
397C2×#67—32no—
398C22×Dic3—32no—
399C22×Dic3—34no—
400C22×Dic3—32no—
401D3×Q8—24no—
402D3×Q8—68no—
403#237—38no—
404#235—38no—
405C2×D12C22×D311yescharacteristic
406C2×C4×D3—32no—
407C2×C4×D3—34no—
408C2×C4×D3—32no—
409C2×C4×D3C22×D312yes—
410C2×C4×D3C22×D312yes—
411C2×C4×D3C22×D311yescharacteristic
412C2×C4×D3C22×D314yes—
413C2×C4×D3C22×D311yescharacteristic
414C2×C4×D3C22×D312yes—
415C2×C4×D3C22×D311yescharacteristic
416C2×Dic6—31no—
417C2×Dic6—31no—
418C2×Dic6—32no—
419C2×Dic6—32no—
420C2×Dic6—34no—
421C2×Dic6—34no—
422C2×Dic6—34no—
423C2×Dic6—34no—
424C2×Dic6—61no—
425C2×Dic6—62no—
426C2×Dic6—68no—
427C2×Dic6C22×D312yes—
428C2×Dic6C22×D312yes—
429C2×Dic6C22×D311yescharacteristic
430C3×C4⋊C4—21no—
431C3×C4⋊C4—22no—
432C3×C4⋊C4—32no—
433C3×C4⋊C4—34no—
434C3×C4⋊C4—32no—
435C3×C4⋊C4—31no—
436C3×C4⋊C4—34no—
437C3×C4⋊C4—32no—
438C3×C4⋊C4—32no—
439C3×C4⋊C4—31no—
440C3×C4⋊C4—32no—
441C3×C4⋊C4—32no—
442C3×C4⋊C4C22×D311yescharacteristic
443C3×C4⋊C4C22×D311yescharacteristic
444C3×C4⋊C4C22×D312yes—
445C3×C4⋊C4C22×D312yes—
446C3×C22⋊C4—34no—
447C3×C22⋊C4—32no—
448C3×C42—21no—
449C3×C42—22no—
450C3×C42—32no—
451C3×C42—31no—
452C3×C42—31no—
453C3×C42—32no—
454C3×C42—32no—
455C3×C42—31no—
456C3×C42C22×D311yescharacteristic
457C3×C42C22×D312yes—
458C3×C42C22×D311yescharacteristic
459C3×C42C22×D312yes—
460#217—32no—
461#217—34no—
462#217—34no—
463#217—32no—
464(C2×D3)⋊C4—34no—
465(C2×D3)⋊C4—32no—
466(C2×D3)⋊C4—32no—
467(C2×D3)⋊C4—34no—
468(C2×D3)⋊C4C22×D314yes—
469(C2×D3)⋊C4C22×D312yes—
470C4⋊Dic3—31no—
471C4⋊Dic3—32no—
472C4⋊Dic3—32no—
473C4⋊Dic3—32no—
474C4⋊Dic3—31no—
475C4⋊Dic3—32no—
476C4⋊Dic3—34no—
477C4⋊Dic3—34no—
478C4⋊Dic3—34no—
479C4⋊Dic3—62no—
480C4⋊Dic3—61no—
481C4⋊Dic3—62no—
482C4⋊Dic3C22×D311yescharacteristic
483C4⋊Dic3C22×D312yes—
484C4⋊Dic3C22×D312yes—
485C4⋊Dic3C22×D312yes—
486C4⋊Dic3C22×D311yescharacteristic
487Dic3⋊C4—34no—
488Dic3⋊C4—34no—
489Dic3⋊C4—32no—
490Dic3⋊C4—34no—
491Dic3⋊C4—34no—
492Dic3⋊C4—32no—
493Dic3⋊C4—34no—
494Dic3⋊C4—34no—
495Dic3⋊C4—34no—
496Dic3⋊C4—34no—
497Dic3⋊C4—34no—
498Dic3⋊C4—32no—
499Dic3⋊C4—32no—
500Dic3⋊C4—34no—
501Dic3⋊C4—34no—
502Dic3⋊C4—34no—
503Dic3⋊C4—34no—
504Dic3⋊C4—62no—
505Dic3⋊C4—64no—
506Dic3⋊C4—64no—
507Dic3⋊C4—64no—
508Dic3⋊C4C22×D314yes—
509Dic3⋊C4C22×D314yes—
510Dic3⋊C4C22×D312yes—
511Dic3⋊C4C22×D312yes—
512Dic3⋊C4C22×D312yes—
513C4×Dic3—34no—
514C4×Dic3—32no—
515C4×Dic3—32no—
516C4×Dic3—34no—
517C4×Dic3—34no—
518C4×Dic3—32no—
519C4×Dic3—32no—
520C4×Dic3—34no—
521C4×Dic3—32no—
522C4×Dic3—34no—
523C4×Dic3—34no—
524C4×Dic3—32no—
525C4×Dic3—64no—
526C4×Dic3—62no—
527C4×Dic3C22×D312yes—
528C4×Dic3C22×D311yescharacteristic
529C4×Dic3C22×D312yes—
530C4×Dic3C22×D311yescharacteristic
531C4×Dic3C22×D312yes—
532C4×Dic3C22×D311yescharacteristic
533C22×C32C2511yescharacteristic
534C2×C3×D3—22no—
535C2×C3×D3—21no—
536C2×C3×D3—22no—
537C2×C3×D3—21no—
538C2×C3×D3C22×Q814yes—
539C2×C3×D3C22×Q812yes—
540C32×C4—22no—
541C32×C4—21no—
542C32×C4—22no—
543C32×C4C22×Q812yes—
544C32×C4C2×#4112yes—
545C3⋊Dic3—24no—
546C3⋊Dic3—22no—
547C3⋊Dic3C22×Q814yes—
548C3×Dic3—22no—
549C3×Dic3—21no—
550C3×Dic3—21no—
551C3×Dic3—22no—
552C3×Dic3—24no—
553C3×Dic3C22×Q812yes—
554C3×Dic3C2×#4114yes—
555C2×#41—91no—
556C22×Q8—31no—
557C22×Q8—92no—
558C4⋊Q8—31no—
559C4⋊Q8—92no—
560C4⋊Q8—92no—
561C4⋊Q8—92no—
562C4⋊Q8—94no—
563C4⋊Q8—94no—
564C4⋊Q8—92no—
565C4⋊Q8—91no—
566#125—32no—
567#125—92no—
568#125—94no—
569#125—94no—
570#125—94no—
571#125—92no—
572C22⋊Q8—32no—
573C22⋊Q8—34no—
574C22⋊Q8—94no—
575C22⋊Q8—94no—
576C22⋊Q8—94no—
577C22⋊Q8—94no—
578C22⋊Q8—92no—
579C22⋊Q8—92no—
580C22⋊Q8—94no—
581C22⋊Q8—94no—
582C22⋊Q8—92no—
583C4×Q8—31no—
584C4×Q8—31no—
585C4×Q8—32no—
586C4×Q8—31no—
587C4×Q8—32no—
588C4×Q8—94no—
589C4×Q8—92no—
590C4×Q8—91no—
591C4×Q8—92no—
592C4×Q8—94no—
593C4×Q8—92no—
594C4×Q8—94no—
595C4×Q8—92no—
596C4×Q8—92no—
597C4×Q8—92no—
598C4×Q8—91no—
599C4×Q8D3211yescharacteristic
600C4×D4—31no—
601C4×D4—32no—
602C4×D4—92no—
603C4×D4—91no—
604C4×D4—94no—
605C4×D4—92no—
606C4×D4—92no—
607C4×D4—94no—
608#117—94no—
609#117—92no—
610#117—91no—
611#117—92no—
612C2×C4⋊C4—32no—
613C2×C4⋊C4—31no—
614C2×C4⋊C4—32no—
615C2×C4⋊C4—94no—
616C2×C42—31no—
617C2×C42—32no—
618C2×C42—92no—
619C2×C42—94no—
620C23×C3—31no—
621C23×C3—32no—
622C22×D3C23×D311yescharacteristic
623C22×D3C23×D312yes—
624C3×Q8—22no—
625C3×Q8—22no—
626C3×Q8—34no—
627C3×Q8—42no—
628C3×Q8—64no—
629C3×Q8—122no—
630C3×D4—34no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—22no—
634C2×C3×C4—22no—
635C2×C3×C4—21no—
636C2×C3×C4—31no—
637C2×C3×C4—32no—
638C2×C3×C4—34no—
639C2×C3×C4—31no—
640C2×C3×C4—34no—
641C2×C3×C4—32no—
642C2×C3×C4—31no—
643C2×C3×C4—32no—
644C2×C3×C4—64no—
645C2×C3×C4—64no—
646C2×C3×C4—62no—
647C2×C3×C4—124no—
648C2×C3×C4—121no—
649C2×C3×C4—122no—
650C2×C3×C4C23×D312yes—
651C2×C3×C4C23×D312yes—
652C2×C3×C4C23×D312yes—
653C2×C3×C4C23×D311yescharacteristic
654C2×C3×C4C23×D312yes—
655C2×C3×C4C23×D311yescharacteristic
656C2×C3×C4C23×D311yescharacteristic
657C2×C3×C4C23×D311yescharacteristic
658C2×C3×C4C23×D311yescharacteristic
659C2×C3×C4C23×D311yescharacteristic
660#67—38no—
661#67—38no—
662C2×Dic3—32no—
663C2×Dic3—32no—
664C2×Dic3—38no—
665C2×Dic3—32no—
666C2×Dic3—34no—
667C2×Dic3—32no—
668C2×Dic3—34no—
669C2×Dic3—62no—
670C2×Dic3—62no—
671C2×Dic3—64no—
672C2×Dic3—68no—
673C2×Dic3—122no—
674C2×Dic3C23×D311yescharacteristic
675C2×Dic3C23×D314yes—
676C2×Dic3C23×D312yes—
677C2×Dic3C23×D312yes—
678C2×Dic3C23×D311yescharacteristic
679C2×Dic3C23×D312yes—
680C2×Dic3C23×D311yescharacteristic
681D12D3×Q814yescomplemented
682C4×D3—22no—
683C4×D3—24no—
684C4×D3—24no—
685C4×D3—38no—
686C4×D3—42no—
687C4×D3—41no—
688C4×D3—44no—
689C4×D3—68no—
690C4×D3—122no—
691C4×D3D3×Q814yescomplemented
692Dic6—24no—
693Dic6—34no—
694Dic6—34no—
695Dic6—42no—
696Dic6—64no—
697Dic6—68no—
698Dic6—64no—
699Dic6—64no—
700Dic6—68no—
701Dic6—124no—
702Dic6—124no—
703Dic6—124no—
704Dic6#23514yescomplemented
705C2×C32C23×Q811yescharacteristic
706C2×C32C22×#4111yescharacteristic
707C2×C32#58511yescharacteristic
708C3×D3—22no—
709C3×D3—24no—
710#41—98no—
711C2×Q8—31no—
712C2×Q8—32no—
713C2×Q8—32no—
714C2×Q8—64no—
715C2×Q8—94no—
716C2×Q8—94no—
717C2×Q8—91no—
718C2×Q8—92no—
719C2×Q8—188no—
720C2×Q8C2×D3211yescharacteristic
721C2×D4—31no—
722C2×D4—92no—
723C22×C4—31no—
724C22×C4—32no—
725C22×C4—31no—
726C22×C4—32no—
727C22×C4—31no—
728C22×C4—32no—
729C22×C4—34no—
730C22×C4—92no—
731C22×C4—94no—
732C22×C4—92no—
733C4⋊C4—32no—
734C4⋊C4—32no—
735C4⋊C4—32no—
736C4⋊C4—32no—
737C4⋊C4—31no—
738C4⋊C4—34no—
739C4⋊C4—32no—
740C4⋊C4—31no—
741C4⋊C4—32no—
742C4⋊C4—34no—
743C4⋊C4—94no—
744C4⋊C4—94no—
745C4⋊C4—94no—
746C4⋊C4—92no—
747C4⋊C4—94no—
748C4⋊C4—94no—
749C4⋊C4—94no—
750C4⋊C4—94no—
751C4⋊C4—92no—
752C4⋊C4—92no—
753C4⋊C4—91no—
754C4⋊C4—94no—
755C4⋊C4—92no—
756C4⋊C4C2×D3211yescharacteristic
757C4⋊C4C2×D3212yes—
758C22⋊C4—32no—
759C22⋊C4—34no—
760C22⋊C4—94no—
761C22⋊C4—92no—
762C22⋊C4—92no—
763C22⋊C4—94no—
764C42—32no—
765C42—31no—
766C42—32no—
767C42—31no—
768C42—31no—
769C42—32no—
770C42—92no—
771C42—94no—
772C42—92no—
773C42—94no—
774C42—94no—
775C42—92no—
776C42C2×D3212yes—
777C42C2×D3211yescharacteristic
778C22×C3—21no—
779C22×C3—34no—
780C22×C3—32no—
781C22×C3—62no—
782C22×C3—61no—
783C22×C3—62no—
784C22×C3—61no—
785C22×C3C24×D311yescharacteristic
786C22×C3C24×D311yescharacteristic
787C2×D3—21no—
788C2×D3—22no—
789C2×D3—21no—
790C2×D3—22no—
791C2×D3C2×D3×Q814yes—
792C2×D3C2×D3×Q812yes—
793C3×C4—22no—
794C3×C4—22no—
795C3×C4—22no—
796C3×C4—21no—
797C3×C4—21no—
798C3×C4—22no—
799C3×C4—22no—
800C3×C4—22no—
801C3×C4—32no—
802C3×C4—34no—
803C3×C4—42no—
804C3×C4—42no—
805C3×C4—41no—
806C3×C4—62no—
807C3×C4—61no—
808C3×C4—64no—
809C3×C4—62no—
810C3×C4—61no—
811C3×C4C2×#23512yes—
812C3×C4C2×D3×Q812yes—
813C3×C4C2×D3×Q812yes—
814C3×C4D3×#4112yes—
815Dic3—21no—
816Dic3—22no—
817Dic3—22no—
818Dic3—21no—
819Dic3—24no—
820Dic3—34no—
821Dic3—34no—
822Dic3—64no—
823Dic3—64no—
824Dic3—64no—
825Dic3—62no—
826Dic3—62no—
827Dic3—124no—
828Dic3—122no—
829Dic3C2×#23514yes—
830Dic3C2×D3×Q812yes—
831C32Q8×#4111yescharacteristic, complemented, Sylow
832C23—32no—
833C23—31no—
834Q8—22no—
835Q8—34no—
836Q8—64no—
837Q8—94no—
838Q8—122no—
839Q8—188no—
840Q8—184no—
841Q8—364no—
842D4—34no—
843D4—98no—
844C2×C4—31no—
845C2×C4—32no—
846C2×C4—34no—
847C2×C4—31no—
848C2×C4—32no—
849C2×C4—31no—
850C2×C4—32no—
851C2×C4—34no—
852C2×C4—64no—
853C2×C4—62no—
854C2×C4—64no—
855C2×C4—98no—
856C2×C4—92no—
857C2×C4—94no—
858C2×C4—92no—
859C2×C4—124no—
860C2×C4—122no—
861C2×C4—121no—
862C2×C4—188no—
863C2×C4—362no—
864C2×C4C22×D3212yes—
865C2×C4C22×D3212yes—
866C2×C4C22×D3211yescharacteristic
867C2×C4C22×D3211yescharacteristic
868C2×C4C22×D3211yescharacteristic
869C2×C3—21no—
870C2×C3—21no—
871C2×C3—21no—
872C2×C3—64no—
873C2×C3—62no—
874C2×C3C22×#23511yescharacteristic
875C2×C3C22×D3×Q811yescharacteristic
876C2×C3C22×D3×Q811yescharacteristic
877C2×C3C2×D3×#4111yescharacteristic
878C2×C3#596411yescharacteristic
879C2×C3#596611yescharacteristic
880D3—22no—
881D3—24no—
882C22—32no—
883C22—34no—
884C22—61no—
885C22—62no—
886C22—61no—
887C22—62no—
888C22C23×D3211yescharacteristic
889C4—22no—
890C4—22no—
891C4—21no—
892C4—34no—
893C4—32no—
894C4—61no—
895C4—62no—
896C4—61no—
897C4—64no—
898C4—62no—
899C4—94no—
900C4—184no—
901C4—182no—
902C4D3×#23512yes—
903C4D32×Q812yes—
904C3—21no—
905C3Q8×#23511yescharacteristic, complemented
906C3#8692311yescharacteristic, complemented
907C2—62no—
908C2—64no—
909C2C2×D3×#23511yescharacteristic
910C2C2×D32×Q811yescharacteristic
911C2#1059669611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radicalC2×#3795C22
hypercenterC4×Q8D32
hypocenterC32Q8×#41
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×#5579C2semidirect
3. C3×C4×D3×Q8C2semidirect
4. #10595400C2semidirect
5. #10595367C2semidirect
6. #10594533C2semidirect
7. #10594531C2semidirect
8. #10594386C2semidirect
9. D3×#887C2semidirect
10. #10593929C2semidirect
11. Dic6×D12C2semidirect
14. #10593874C2semidirect
15. #10593859C2semidirect
16. #10593856C2semidirect
17. #10593852C2semidirect
97. #5579D3semidirect
102. C4×D3×Q8D3semidirect
141. #3795Q8semidirect
339. #634C2×Q8semidirect
347. C3×D12C2×Q8semidirect
354. C3×C4×D3C2×Q8semidirect
357. C3×Dic6#41semidirect
360. #625C2×Q8semidirect
363. D3×Dic3C2×Q8semidirect
681. D12D3×Q8semidirect
691. C4×D3D3×Q8semidirect
704. Dic6#235semidirect
831. C32Q8×#41semidirect
905. C3Q8×#235semidirect
906. C3#86923semidirect

Maximal subgroups

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

subgroupindex
#105960382
C3×#55792
C3×C4×D3×Q82
#105954002
#105953672
#105945332
#105945312
#105943862
D3×#8872
#105939292
Dic6×D122
C4×#37952
#105938742
#105938592
#105938562
#105938522
#869233
Q8×#2353