Finite Group Databasebeta

← #11903760

Subgroups — #11903760

Order 1152.

2276 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596198C211yesmaximal, characteristic, complemented
2C3×#5728C211yesmaximal, characteristic, complemented
3C3×#5721C211yesmaximal, characteristic, complemented
4#10595374C212yesmaximal, complemented
5Q8×#624C212yesmaximal, complemented
6#10595371C212yesmaximal, complemented
7#10595361C212yesmaximal, complemented
8#10594484C212yesmaximal, complemented
9#10594477C212yesmaximal, complemented
10#10594398C214yesmaximal, complemented
11#10594395C214yesmaximal, complemented
12#10594362C212yesmaximal
13#10594322C212yesmaximal, complemented
14C4×#3799C211yesmaximal, characteristic
15#10593958C211yesmaximal, characteristic, complemented
16C4×D3×Dic6C211yesmaximal, characteristic, complemented
17#10593856C211yesmaximal, characteristic, complemented
18#87015—31nomaximal
19#86277—31nomaximal
20C2×Q8×C3⋊D3C2212yes—
21C2×#3799C2211yescharacteristic
22C2×D3×Dic6C2211yescharacteristic
23C32×C4⋊Q8C2211yescharacteristic
24#64155C2212yes—
25#64105C2214yes—
26#64102C2212yes—
27#64097C2212yes—
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C3×#946C2212yes—
31C3×Q8×Dic3C2212yes—
32C3×Q8×Dic3C2212yes—
33C3×#944C2212yes—
34C3×#897C2212yes—
35C3×#892C2212yes—
36C3×#890C2212yes—
37C3×#890C2212yes—
38C3×#889C2214yes—
39C3×#887C2212yes—
40C3×#887C2212yes—
41C3×C42×D3C2211yescharacteristic
42C3×#869C2211yescharacteristic
43C3×C4×Dic6C2211yescharacteristic
44C3×C4×Dic6C2211yescharacteristic
45#63919C2212yes—
46#63918C2212yes—
47C4×#627C2212yes—
48#63904C2212yes—
49C4×#626C2212yes—
50#63900C2212yes—
51#63900C2214yes—
52#63899C2214yes—
53#63896C2214yes—
54#63895C2214yes—
55#63895C2214yes—
56#63894C2212yes—
57#63894C2211yescharacteristic
58D3×C4⋊Dic3C2211yescharacteristic
59#63888C2214yes—
60C4×#624C2212yes—
61C4×#624C2214yes—
62#63881C2214yes—
63#63880C2214yes—
64D3×Dic3⋊C4C2212yes—
65C4×D3×Dic3C2212yes—
66#63871C2212yes—
67#63869C2212yes—
68#63867C2214yes—
69#63865C2214yes—
70#63846C2214yes—
71#63844C2214yes—
72#63844C2212yes—
73#63844C2211yescharacteristic
74#63844C2214yes—
75#63843C2212yes—
76Dic3×Dic6C2211yescharacteristic
77Dic3×Dic6C2211yescharacteristic
78#63841C2211yescharacteristic
79#63840C2214yes—
80#63839C2214yes—
81#63837C2214yes—
82#63837C2212yes—
83#63836C2214yes—
84#63836C2212yes—
85C3×#557—31no—
86C3×#533—31no—
87#5730—31no—
88#5728—32no—
89#5728D311yescharacteristic, complemented
90#5727—31no—
91#5727—31no—
92#5727—32no—
93#5727—61no—
94#5722—31no—
95#5721D311yescharacteristic, complemented
96#5690—34no—
97#5690—32no—
98#5690—32no—
99#5688—32no—
100#5688—34no—
101#5685—32no—
102#5636—34no—
103#5635—32no—
104#5632—32no—
105#5579—32no—
106#5579—31no—
107#5578—32no—
108#5578—34no—
109C4×#239—32no—
110C4×#239—31no—
111C4×D3×Q8—32no—
112C4×D3×Q8—32no—
113C4×D3×Q8—31no—
114#5569—32no—
115Q8×Dic6—31no—
116#5522—32no—
117#5517—32no—
118C4×#235—31no—
119C2×C4×Dic6—31no—
120C2×C32×Q8C2312yes—
121Q8×C3⋊D3—28no—
122C2×C4⋊(C3⋊D3)C2311yescharacteristic
123C2×C4×C3⋊D3C2312yes—
124C2×C4×C3⋊D3C2314yes—
125C2×#634C2314yes—
126C2×#634C2311yescharacteristic
127C2×C3×C4×D3C2311yescharacteristic
128C2×C3×C4×D3C2311yescharacteristic
129C2×C3×C4×D3C2311yescharacteristic
130C2×C3×Dic6C2311yescharacteristic
131C2×C3×Dic6C2312yes—
132C2×C3×Dic6C2311yescharacteristic
133C2×#627C2312yes—
134C2×#627C2314yes—
135C2×#626C2312yes—
136C2×#624C2314yes—
137C2×#624C2312yes—
138C2×#624C2312yes—
139C2×D3×Dic3C2312yes—
140C2×D3×Dic3C2312yes—
141#3799Q818yescomplemented
142D3×Dic6—24no—
143C32×C4⋊C4C2312yes—
144C32×C4⋊C4C2312yes—
145C32×C42C2311yescharacteristic
146#3752C2312yes—
147#3752C2314yes—
148C4⋊(C3⋊Dic3)C2311yescharacteristic
149C4⋊(C3⋊Dic3)C2311yescharacteristic
150#3750C2312yes—
151#3750C2314yes—
152C4×C3⋊Dic3C2312yes—
153C3×(C2×D3)⋊C4C2314yes—
154C3×C4⋊Dic3C2314yes—
155C3×C4⋊Dic3C2311yescharacteristic
156C3×C4⋊Dic3C2312yes—
157C3×C4⋊Dic3C2314yes—
158C3×C4⋊Dic3C2311yescharacteristic
159C3×C4⋊Dic3C2312yes—
160C3×Dic3⋊C4C2314yes—
161C3×Dic3⋊C4C2314yes—
162C3×Dic3⋊C4C2312yes—
163C3×Dic3⋊C4C2312yes—
164C3×Dic3⋊C4C2314yes—
165C3×C4×Dic3C2311yescharacteristic
166C3×C4×Dic3C2314yes—
167C3×C4×Dic3C2312yes—
168C3×C4×Dic3C2314yes—
169C3×C4×Dic3C2311yescharacteristic
170C3×C4×Dic3C2312yes—
171C3×C4×Dic3C2311yescharacteristic
172#3724C2314yes—
173#3724C2312yes—
174#3724C2314yes—
175Dic3⋊Dic3C2314yes—
176Dic3⋊Dic3C2312yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2312yes—
179Dic3⋊Dic3C2312yes—
180#3722C2312yes—
181#3722C2314yes—
182(C2×D3)⋊Dic3C2312yes—
183Dic32C2312yes—
184Dic32C2312yes—
185Dic32C2312yes—
186Dic32C2314yes—
187Dic32C2312yes—
188Q8×#41—91noSylow
189C2×#239—31no—
190C2×D3×Q8—32no—
191C2×D3×Q8—32no—
192C2×D3×Q8—31no—
193C2×D3×Q8—62no—
194C2×#235—31no—
195C22×Dic6—31no—
196C3×C4⋊Q8—21no—
197C3×C4⋊Q8—32no—
198C3×C4⋊Q8—31no—
199C3×C4⋊Q8C2×D311yescharacteristic
200C3×C4⋊Q8C2×D311yescharacteristic
201C3×#125—34no—
202C3×#125—32no—
203C3×#125—32no—
204C3×C22⋊Q8—32no—
205C3×C22⋊Q8—32no—
206C3×C4×Q8—32no—
207C3×C4×Q8—32no—
208C3×C4×Q8—32no—
209C3×C4×Q8—32no—
210C3×C4×Q8—31no—
211C3×C4×Q8—31no—
212C3×#117—32no—
213C2×C3×C42—31no—
214#946—32no—
215#946—32no—
216#946—32no—
217#946—34no—
218#946—62no—
219#946C2×D312yes—
220Q8×Dic3—32no—
221Q8×Dic3—31no—
222Q8×Dic3—31no—
223Q8×Dic3C2×D312yes—
224Q8×Dic3C2×D312yes—
225#944—34no—
226#944C2×D312yes—
227C4×#67—32no—
228C4×#67—32no—
229#926—31no—
230C2×C4⋊Dic3—31no—
231C2×Dic3⋊C4—32no—
232C2×C4×Dic3—32no—
233#897—32no—
234#897—34no—
235#897—34no—
236#897C2×D312yes—
237#896—34no—
238#896—34no—
239#896—34no—
240#896—34no—
241#896—34no—
242#896—34no—
243#896—34no—
244#896—34no—
245#896—34no—
246#896—64no—
247#893—32no—
248#893—32no—
249#893—32no—
250#893—34no—
251#893—31no—
252#893—32no—
253#893—62no—
254#892—31no—
255#892—32no—
256#892—34no—
257#892C2×D312yes—
258D3×C4⋊C4—32no—
259D3×C4⋊C4—31no—
260D3×C4⋊C4—32no—
261D3×C4⋊C4—34no—
262D3×C4⋊C4—34no—
263D3×C4⋊C4—32no—
264#890—34no—
265#890—32no—
266#890C2×D312yes—
267#890C2×D312yes—
268#889—34no—
269#889—34no—
270#889C2×D314yes—
271#888—34no—
272#888—32no—
273#888—32no—
274#888—32no—
275#888—32no—
276#888—34no—
277#888—34no—
278#888—32no—
279#888—62no—
280#887—32no—
281#887—32no—
282#887—34no—
283#887—34no—
284#887—32no—
285#887—34no—
286#887—31no—
287#887C2×D312yes—
288#887C2×D312yes—
289#67⋊C4—34no—
290#67⋊C4—34no—
291#878—34no—
292#878—34no—
293C4×D12—32no—
294C4×D12—31no—
295C4×D12—31no—
296C4×D12—34no—
297C4×D12—31no—
298C4×D12—32no—
299C4×D12—61no—
300#872—32no—
301#872—34no—
302C42×D3—32no—
303C42×D3—34no—
304C42×D3—32no—
305C42×D3—32no—
306C42×D3—34no—
307C42×D3C2×D311yescharacteristic
308#870—32no—
309#870—34no—
310#869—32no—
311#869C2×D311yescharacteristic
312C4×Dic6—31no—
313C4×Dic6—31no—
314C4×Dic6—31no—
315C4×Dic6—31no—
316C4×Dic6—34no—
317C4×Dic6—31no—
318C4×Dic6—32no—
319C4×Dic6—34no—
320C4×Dic6—32no—
321C4×Dic6—34no—
322C4×Dic6—32no—
323C4×Dic6—32no—
324C4×Dic6—61no—
325C4×Dic6C2×D311yescharacteristic
326C4×Dic6C2×D311yescharacteristic
327C22×C3⋊D3C2412yes—
328C22×C3×D3C2411yescharacteristic
329C32×Q8—24no—
330C2×C32×C4C2414yes—
331C2×C32×C4C2411yescharacteristic
332C2×C32×C4C2411yescharacteristic
333C2×C32×C4C2411yescharacteristic
334C2×C3⋊Dic3C2412yes—
335C2×C3⋊Dic3C2412yes—
336C2×C3⋊Dic3C2412yes—
337C4⋊(C3⋊D3)C2×Q814yescomplemented
338C4×C3⋊D3—24no—
339C4×C3⋊D3—28no—
340#634—28no—
341#634#4114yescomplemented
342C2×C3×Dic3C2411yescharacteristic
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2414yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2411yescharacteristic
348C2×C3×Dic3C2411yescharacteristic
349C2×C3×Dic3C2412yes—
350C3×C4×D3—22no—
351C3×C4×D3—41no—
352C3×C4×D3C2×Q814yescomplemented
353C3×Dic6—22no—
354C3×Dic6—42no—
355C3×Dic6C2×Q814yescomplemented
356#627—24no—
357#627—44no—
358#626C2×Q818yescomplemented
359#624—44no—
360#624—42no—
361#624C2×Q818yescomplemented
362D3×Dic3—24no—
363D3×Dic3—42no—
364Q82—91no—
365#557—31no—
366#557—92no—
367#554—92no—
368#554—91no—
369#554—94no—
370#554—92no—
371D4×Q8—92no—
372D4×Q8—91no—
373#533—31no—
374#533—92no—
375#533—94no—
376#533—92no—
377C4×#41—91no—
378C4×#41—92no—
379C2×C4×Q8—91no—
380C2×C4×Q8—92no—
381C2×C3×Q8—22no—
382C2×C3×Q8—31no—
383C2×C3×Q8—31no—
384C2×C3×Q8—32no—
385C2×C3×Q8C22×D312yes—
386C2×C3×Q8C22×D312yes—
387C22×C3×C4—31no—
388C22×C3×C4—31no—
389C22×C3×C4—31no—
390C2×#67—32no—
391C22×Dic3—32no—
392C22×Dic3—32no—
393#239—38no—
394D3×Q8—64no—
395D3×Q8—68no—
396D3×Q8—68no—
397D3×Q8—128no—
398#235—38no—
399C2×D12—32no—
400C2×D12—31no—
401C2×D12—31no—
402C2×D12—61no—
403C2×C4×D3—32no—
404C2×C4×D3—32no—
405C2×C4×D3—32no—
406C2×C4×D3—32no—
407C2×C4×D3—32no—
408C2×C4×D3—34no—
409C2×C4×D3—34no—
410C2×C4×D3—32no—
411C2×C4×D3—34no—
412C2×C4×D3—32no—
413C2×C4×D3—34no—
414C2×C4×D3—32no—
415C2×C4×D3—62no—
416C2×C4×D3—64no—
417C2×C4×D3C22×D311yescharacteristic
418C2×C4×D3C22×D311yescharacteristic
419C2×C4×D3C22×D311yescharacteristic
420C2×Dic6—31no—
421C2×Dic6—31no—
422C2×Dic6—34no—
423C2×Dic6—34no—
424C2×Dic6—32no—
425C2×Dic6—32no—
426C2×Dic6—34no—
427C2×Dic6—34no—
428C2×Dic6—61no—
429C2×Dic6—64no—
430C2×Dic6—64no—
431C2×Dic6C22×D311yescharacteristic
432C2×Dic6C22×D312yes—
433C2×Dic6C22×D311yescharacteristic
434C3×C4⋊C4—22no—
435C3×C4⋊C4—22no—
436C3×C4⋊C4—32no—
437C3×C4⋊C4—32no—
438C3×C4⋊C4—34no—
439C3×C4⋊C4—31no—
440C3×C4⋊C4—32no—
441C3×C4⋊C4—34no—
442C3×C4⋊C4—34no—
443C3×C4⋊C4—32no—
444C3×C4⋊C4—31no—
445C3×C4⋊C4—34no—
446C3×C4⋊C4—34no—
447C3×C4⋊C4C22×D312yes—
448C3×C4⋊C4C22×D312yes—
449C3×C4⋊C4C22×D312yes—
450C3×C4⋊C4C22×D312yes—
451C3×C22⋊C4—34no—
452C3×C42—21no—
453C3×C42—31no—
454C3×C42—31no—
455C3×C42—34no—
456C3×C42—31no—
457C3×C42—32no—
458C3×C42—34no—
459C3×C42—32no—
460C3×C42C22×D311yescharacteristic
461C3×C42C22×D311yescharacteristic
462#217—32no—
463(C2×D3)⋊C4—32no—
464(C2×D3)⋊C4—32no—
465(C2×D3)⋊C4—34no—
466(C2×D3)⋊C4—32no—
467(C2×D3)⋊C4—34no—
468(C2×D3)⋊C4—32no—
469(C2×D3)⋊C4—34no—
470(C2×D3)⋊C4—32no—
471(C2×D3)⋊C4—34no—
472(C2×D3)⋊C4—62no—
473(C2×D3)⋊C4—64no—
474(C2×D3)⋊C4C22×D314yes—
475C4⋊Dic3—31no—
476C4⋊Dic3—31no—
477C4⋊Dic3—31no—
478C4⋊Dic3—31no—
479C4⋊Dic3—32no—
480C4⋊Dic3—34no—
481C4⋊Dic3—32no—
482C4⋊Dic3—34no—
483C4⋊Dic3—32no—
484C4⋊Dic3—61no—
485C4⋊Dic3—61no—
486C4⋊Dic3C22×D311yescharacteristic
487C4⋊Dic3C22×D312yes—
488C4⋊Dic3C22×D314yes—
489C4⋊Dic3C22×D314yes—
490C4⋊Dic3C22×D311yescharacteristic
491C4⋊Dic3C22×D312yes—
492Dic3⋊C4—32no—
493Dic3⋊C4—34no—
494Dic3⋊C4—32no—
495Dic3⋊C4—34no—
496Dic3⋊C4—32no—
497Dic3⋊C4—32no—
498Dic3⋊C4—32no—
499Dic3⋊C4—32no—
500Dic3⋊C4—34no—
501Dic3⋊C4—32no—
502Dic3⋊C4—34no—
503Dic3⋊C4—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—34no—
507Dic3⋊C4—62no—
508Dic3⋊C4—64no—
509Dic3⋊C4C22×D312yes—
510Dic3⋊C4C22×D314yes—
511Dic3⋊C4C22×D312yes—
512Dic3⋊C4C22×D314yes—
513Dic3⋊C4C22×D314yes—
514C4×Dic3—32no—
515C4×Dic3—32no—
516C4×Dic3—32no—
517C4×Dic3—32no—
518C4×Dic3—32no—
519C4×Dic3—34no—
520C4×Dic3—32no—
521C4×Dic3—32no—
522C4×Dic3—32no—
523C4×Dic3—34no—
524C4×Dic3—32no—
525C4×Dic3—32no—
526C4×Dic3—62no—
527C4×Dic3C22×D311yescharacteristic
528C4×Dic3C22×D312yes—
529C4×Dic3C22×D312yes—
530C4×Dic3C22×D311yescharacteristic
531C4×Dic3C22×D314yes—
532C4×Dic3C22×D314yes—
533C4×Dic3C22×D311yescharacteristic
534C22×C32C2511yescharacteristic
535C2×C3⋊D3—22no—
536C2×C3⋊D3—22no—
537C2×C3⋊D3C22×Q814yes—
538C2×C3×D3—21no—
539C2×C3×D3—21no—
540C2×C3×D3C22×Q812yes—
541C32×C4—24no—
542C32×C4—21no—
543C32×C4C22×Q812yes—
544C32×C4C2×#4112yes—
545C3⋊Dic3—22no—
546C3⋊Dic3—22no—
547C3⋊Dic3C2×#4114yes—
548C3×Dic3—22no—
549C3×Dic3—21no—
550C3×Dic3—22no—
551C3×Dic3—21no—
552C3×Dic3—22no—
553C3×Dic3—24no—
554C3×Dic3C22×Q812yes—
555C3×Dic3C22×Q814yes—
556C2×#41—91no—
557C22×Q8—91no—
558C22×Q8—92no—
559C4⋊Q8—32no—
560C4⋊Q8—31no—
561C4⋊Q8—92no—
562C4⋊Q8—94no—
563C4⋊Q8—92no—
564C4⋊Q8—94no—
565C4⋊Q8—92no—
566C4⋊Q8D3211yescharacteristic
567#125—32no—
568#125—34no—
569#125—32no—
570#125—94no—
571#125—92no—
572#125—94no—
573C22⋊Q8—32no—
574C22⋊Q8—32no—
575C22⋊Q8—94no—
576C22⋊Q8—94no—
577C22⋊Q8—94no—
578C22⋊Q8—94no—
579C22⋊Q8—94no—
580C22⋊Q8—92no—
581C22⋊Q8—94no—
582C22⋊Q8—92no—
583C22⋊Q8—94no—
584C4×Q8—32no—
585C4×Q8—32no—
586C4×Q8—32no—
587C4×Q8—32no—
588C4×Q8—31no—
589C4×Q8—31no—
590C4×Q8—92no—
591C4×Q8—91no—
592C4×Q8—92no—
593C4×Q8—94no—
594C4×Q8—92no—
595C4×Q8—94no—
596C4×Q8—94no—
597C4×Q8—91no—
598C4×Q8—91no—
599C4×Q8—92no—
600C4×Q8—91no—
601C4×D4—94no—
602C4×D4—91no—
603C4×D4—92no—
604C4×D4—92no—
605C4×D4—94no—
606C4×D4—92no—
607C4×D4—92no—
608C4×D4—91no—
609#117—32no—
610#117—92no—
611#117—94no—
612#117—91no—
613C2×C4⋊C4—92no—
614C2×C4⋊C4—94no—
615C2×C4⋊C4—92no—
616C2×C4⋊C4—91no—
617C2×C42—31no—
618C2×C42—92no—
619C2×C42—94no—
620C2×C42—92no—
621C23×C3—31no—
622C22×D3—32no—
623C22×D3—32no—
624C22×D3—62no—
625C22×D3C23×D311yescharacteristic
626C3×Q8—24no—
627C3×Q8—24no—
628C3×Q8—34no—
629C3×Q8—44no—
630C3×Q8—62no—
631C3×Q8—122no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—24no—
636C2×C3×C4—31no—
637C2×C3×C4—32no—
638C2×C3×C4—34no—
639C2×C3×C4—31no—
640C2×C3×C4—32no—
641C2×C3×C4—34no—
642C2×C3×C4—32no—
643C2×C3×C4—32no—
644C2×C3×C4—31no—
645C2×C3×C4—62no—
646C2×C3×C4—121no—
647C2×C3×C4C23×D311yescharacteristic
648C2×C3×C4C23×D314yes—
649C2×C3×C4C23×D314yes—
650C2×C3×C4C23×D311yescharacteristic
651C2×C3×C4C23×D311yescharacteristic
652C2×C3×C4C23×D311yescharacteristic
653C2×C3×C4C23×D311yescharacteristic
654C2×C3×C4C23×D311yescharacteristic
655#67—38no—
656C2×Dic3—32no—
657C2×Dic3—32no—
658C2×Dic3—32no—
659C2×Dic3—32no—
660C2×Dic3—32no—
661C2×Dic3—32no—
662C2×Dic3—62no—
663C2×Dic3—62no—
664C2×Dic3—62no—
665C2×Dic3—64no—
666C2×Dic3—122no—
667C2×Dic3C23×D311yescharacteristic
668C2×Dic3C23×D312yes—
669C2×Dic3C23×D314yes—
670C2×Dic3C23×D312yes—
671C2×Dic3C23×D312yes—
672C2×Dic3C23×D311yescharacteristic
673C2×Dic3C23×D311yescharacteristic
674C2×Dic3C23×D312yes—
675D12—38no—
676D12—34no—
677D12—34no—
678D12—64no—
679C4×D3—22no—
680C4×D3—38no—
681C4×D3—38no—
682C4×D3—41no—
683C4×D3—68no—
684C4×D3—68no—
685C4×D3—64no—
686C4×D3—64no—
687C4×D3—64no—
688C4×D3—128no—
689C4×D3—124no—
690C4×D3—124no—
691C4×D3—122no—
692C4×D3—122no—
693C4×D3—124no—
694C4×D3—122no—
695C4×D3D3×Q814yescomplemented
696Dic6—22no—
697Dic6—34no—
698Dic6—34no—
699Dic6—42no—
700Dic6—64no—
701Dic6—64no—
702Dic6—64no—
703Dic6—68no—
704Dic6—68no—
705Dic6—128no—
706Dic6—124no—
707Dic6—124no—
708Dic6D3×Q814yescomplemented
709C2×C32C23×Q811yescharacteristic
710C2×C32C22×#4111yescharacteristic
711C2×C32#58511yescharacteristic
712C3⋊D3—24no—
713C3×D3—22no—
714#41—98no—
715C2×Q8—31no—
716C2×Q8—31no—
717C2×Q8—32no—
718C2×Q8—92no—
719C2×Q8—94no—
720C2×Q8—91no—
721C2×Q8—94no—
722C2×Q8—184no—
723C2×Q8—188no—
724C2×Q8C2×D3212yes—
725C2×D4—92no—
726C2×D4—91no—
727C22×C4—31no—
728C22×C4—31no—
729C22×C4—31no—
730C22×C4—92no—
731C22×C4—94no—
732C22×C4—92no—
733C22×C4—92no—
734C22×C4—92no—
735C22×C4—94no—
736C22×C4—92no—
737C4⋊C4—31no—
738C4⋊C4—34no—
739C4⋊C4—32no—
740C4⋊C4—32no—
741C4⋊C4—34no—
742C4⋊C4—32no—
743C4⋊C4—32no—
744C4⋊C4—31no—
745C4⋊C4—34no—
746C4⋊C4—34no—
747C4⋊C4—34no—
748C4⋊C4—92no—
749C4⋊C4—94no—
750C4⋊C4—92no—
751C4⋊C4—92no—
752C4⋊C4—94no—
753C4⋊C4—92no—
754C4⋊C4—94no—
755C4⋊C4—94no—
756C4⋊C4—92no—
757C4⋊C4—91no—
758C4⋊C4—91no—
759C4⋊C4—94no—
760C4⋊C4C2×D3212yes—
761C4⋊C4C2×D3212yes—
762C22⋊C4—34no—
763C22⋊C4—92no—
764C22⋊C4—94no—
765C22⋊C4—92no—
766C22⋊C4—94no—
767C22⋊C4—92no—
768C42—31no—
769C42—31no—
770C42—31no—
771C42—34no—
772C42—34no—
773C42—32no—
774C42—32no—
775C42—92no—
776C42—92no—
777C42—92no—
778C42—92no—
779C42—94no—
780C42—92no—
781C42C2×D3211yescharacteristic
782C22×C3—21no—
783C22×C3—32no—
784C22×C3—61no—
785C22×C3—61no—
786C22×C3C24×D311yescharacteristic
787C22×C3C24×D311yescharacteristic
788C2×D3—21no—
789C2×D3—21no—
790C2×D3—34no—
791C2×D3—34no—
792C2×D3—64no—
793C2×D3—62no—
794C2×D3—62no—
795C2×D3—62no—
796C2×D3—62no—
797C2×D3—122no—
798C2×D3—122no—
799C2×D3C2×D3×Q812yes—
800C3×C4—24no—
801C3×C4—24no—
802C3×C4—21no—
803C3×C4—21no—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—32no—
807C3×C4—34no—
808C3×C4—44no—
809C3×C4—41no—
810C3×C4—61no—
811C3×C4—62no—
812C3×C4—62no—
813C3×C4—62no—
814C3×C4—64no—
815C3×C4—61no—
816C3×C4C2×D3×Q812yes—
817C3×C4C2×D3×Q812yes—
818C3×C4D3×#4112yes—
819C3×C4D3×#4112yes—
820Dic3—22no—
821Dic3—21no—
822Dic3—24no—
823Dic3—21no—
824Dic3—22no—
825Dic3—22no—
826Dic3—34no—
827Dic3—34no—
828Dic3—64no—
829Dic3—62no—
830Dic3—62no—
831Dic3—62no—
832Dic3—62no—
833Dic3—122no—
834Dic3—122no—
835Dic3C2×D3×Q814yes—
836Dic3C2×D3×Q812yes—
837C32Q8×#4111yescharacteristic, complemented, Sylow
838C23—31no—
839C23—92no—
840Q8—24no—
841Q8—34no—
842Q8—62no—
843Q8—94no—
844Q8—122no—
845Q8—188no—
846Q8—184no—
847Q8—364no—
848D4—98no—
849D4—94no—
850C2×C4—31no—
851C2×C4—32no—
852C2×C4—34no—
853C2×C4—32no—
854C2×C4—31no—
855C2×C4—31no—
856C2×C4—34no—
857C2×C4—32no—
858C2×C4—32no—
859C2×C4—62no—
860C2×C4—98no—
861C2×C4—92no—
862C2×C4—92no—
863C2×C4—92no—
864C2×C4—121no—
865C2×C4—188no—
866C2×C4—184no—
867C2×C4—184no—
868C2×C4—362no—
869C2×C4—364no—
870C2×C4—362no—
871C2×C4C22×D3214yes—
872C2×C4C22×D3211yescharacteristic
873C2×C4C22×D3211yescharacteristic
874C2×C4C22×D3211yescharacteristic
875C2×C3—21no—
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—62no—
879C2×C3C22×D3×Q811yescharacteristic
880C2×C3C22×D3×Q811yescharacteristic
881C2×C3C2×D3×#4111yescharacteristic
882C2×C3C2×D3×#4111yescharacteristic
883C2×C3#596411yescharacteristic
884C2×C3#596811yescharacteristic
885D3—22no—
886D3—64no—
887D3—64no—
888D3—124no—
889C22—32no—
890C22—61no—
891C22—61no—
892C22—94no—
893C22—182no—
894C22—182no—
895C22C23×D3211yescharacteristic
896C4—24no—
897C4—21no—
898C4—32no—
899C4—34no—
900C4—61no—
901C4—62no—
902C4—61no—
903C4—62no—
904C4—64no—
905C4—62no—
906C4—94no—
907C4—182no—
908C4—182no—
909C4#6431212yes—
910C4D32×Q812yes—
911C3—21no—
912C3#8627711yescharacteristic, complemented
913C3#8701511yescharacteristic, complemented
914C2—62no—
915C2—184no—
916C2C2×#6431211yescharacteristic
917C2C2×D32×Q811yescharacteristic
918C2#1059668811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
prime radicalC2×#3799C22
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. #10596198C2semidirect
2. C3×#5728C2semidirect
3. C3×#5721C2semidirect
4. #10595374C2semidirect
5. Q8×#624C2semidirect
6. #10595371C2semidirect
7. #10595361C2semidirect
8. #10594484C2semidirect
9. #10594477C2semidirect
10. #10594398C2semidirect
11. #10594395C2semidirect
13. #10594322C2semidirect
15. #10593958C2semidirect
16. C4×D3×Dic6C2semidirect
17. #10593856C2semidirect
89. #5728D3semidirect
95. #5721D3semidirect
141. #3799Q8semidirect
337. C4⋊(C3⋊D3)C2×Q8semidirect
341. #634#41semidirect
352. C3×C4×D3C2×Q8semidirect
355. C3×Dic6C2×Q8semidirect
358. #626C2×Q8semidirect
361. #624C2×Q8semidirect
695. C4×D3D3×Q8semidirect
708. Dic6D3×Q8semidirect
837. C32Q8×#41semidirect
912. C3#86277semidirect
913. C3#87015semidirect

Maximal subgroups

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

subgroupindex
#105961982
C3×#57282
C3×#57212
#105953742
Q8×#6242
#105953712
#105953612
#105944842
#105944772
#105943982
#105943952
#105943622
#105943222
C4×#37992
#105939582
C4×D3×Dic62
#105938562
#870153
#862773