Finite Group Databasebeta

← #11903768

Subgroups — #11903768

Order 1152.

2242 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596193C211yesmaximal, characteristic, complemented
2C3×#5730C211yesmaximal, characteristic, complemented
3C3×#5728C211yesmaximal, characteristic, complemented
4#10595370C214yesmaximal, complemented
5#10595367C214yesmaximal, complemented
6#10594532C212yesmaximal, complemented
7#10594526C212yesmaximal, complemented
8#10594485C212yesmaximal, complemented
9#10594477C212yesmaximal, complemented
10#10594385C212yesmaximal, complemented
11#10594358C212yesmaximal
12D3×#887C212yesmaximal, complemented
13#10594324C212yesmaximal, complemented
14#10593904C211yesmaximal, characteristic, complemented
15C4×#3795C211yesmaximal, characteristic
16C4×D3×Dic6C211yesmaximal, characteristic, complemented
17#10593864C211yesmaximal, characteristic, complemented
18#86923—31nomaximal
19#86277—31nomaximal
20C2×#3795C2211yescharacteristic
21C2×D3×Dic6C2212yes—
22C2×D3×Dic6C2211yescharacteristic
23C32×C4⋊Q8C2211yescharacteristic
24#64153C2214yes—
25#64097C2212yes—
26#64097C2212yes—
27#64096C2212yes—
28#64096C2212yes—
29C4×#634C2211yescharacteristic
30C4×#634C2211yescharacteristic
31C3×#946C2214yes—
32C3×#946C2212yes—
33C3×Q8×Dic3C2212yes—
34C3×#897C2212yes—
35C3×#897C2212yes—
36C3×#893C2212yes—
37C3×#892C2212yes—
38C3×D3×C4⋊C4C2212yes—
39C3×#890C2212yes—
40C3×#890C2212yes—
41C3×#887C2212yes—
42C3×C4×D12C2211yescharacteristic
43C3×C42×D3C2211yescharacteristic
44C3×#869C2211yescharacteristic
45C3×C4×Dic6C2211yescharacteristic
46#63919C2214yes—
47#63919C2212yes—
48C4×#627C2212yes—
49#63902C2214yes—
50C4×#625C2212yes—
51#63899C2214yes—
52#63899C2214yes—
53#63899C2214yes—
54#63898C2212yes—
55#63896C2214yes—
56#63896C2214yes—
57Dic3×D12C2211yescharacteristic
58D3×C4⋊Dic3C2211yescharacteristic
59#63879C2212yes—
60#63879C2214yes—
61#63877C2212yes—
62#63877C2214yes—
63D3×Dic3⋊C4C2212yes—
64D3×Dic3⋊C4C2214yes—
65C4×D3×Dic3C2214yes—
66C4×D3×Dic3C2212yes—
67C4×D3×Dic3C2212yes—
68#63873C2212yes—
69#63869C2212yes—
70#63857C2214yes—
71#63856C2212yes—
72#63847C2214yes—
73#63847C2214yes—
74#63847C2214yes—
75#63844C2211yescharacteristic
76#63844C2212yes—
77#63844C2214yes—
78#63844C2211yescharacteristic
79#63843C2212yes—
80Dic3×Dic6C2211yescharacteristic
81#63841C2211yescharacteristic
82#63838C2214yes—
83#63837C2212yes—
84#63837C2214yes—
85C3×#554—31no—
86C3×#533—31no—
87#5730D311yescharacteristic, complemented
88#5728D311yescharacteristic, complemented
89#5727—31no—
90#5722—31no—
91#5722—31no—
92#5722—61no—
93#5721—31no—
94#5690—32no—
95#5688—32no—
96#5685—32no—
97#5685—32no—
98#5636—34no—
99#5636—34no—
100#5635—32no—
101#5632—32no—
102#5632—32no—
103#5622—34no—
104#5622—32no—
105#5578—34no—
106#5578—32no—
107C4×D3×Q8—32no—
108C4×D3×Q8—31no—
109#5567—31no—
110#5539—32no—
111D4×Dic6—31no—
112C4×#237—32no—
113C4×#237—31no—
114#5522—32no—
115#5517—32no—
116#5511—32no—
117C2×#887—32no—
118C4×#235—31no—
119C2×C4×Dic6—31no—
120C2×C32×Q8C2312yes—
121C2×#634C2314yes—
122C2×#634C2311yescharacteristic
123C2×#634C2311yescharacteristic
124C2×C3×D12C2311yescharacteristic
125C2×C3×C4×D3C2312yes—
126C2×C3×C4×D3C2311yescharacteristic
127C2×C3×C4×D3C2314yes—
128C2×C3×C4×D3C2311yescharacteristic
129C2×C3×C4×D3C2311yescharacteristic
130C2×C3×Dic6C2312yes—
131C2×C3×Dic6C2311yescharacteristic
132C2×#627C2314yes—
133C2×#627C2312yes—
134C2×#625C2312yes—
135C2×D3×Dic3C2314yes—
136C2×D3×Dic3C2312yes—
137C2×D3×Dic3C2312yes—
138C2×D3×Dic3C2312yes—
139C2×D3×Dic3C2312yes—
140#3795Q818yescomplemented
141D3×Dic6—28no—
142D3×Dic6—24no—
143C32×C4⋊C4C2312yes—
144C32×C4⋊C4C2312yes—
145C32×C42C2311yescharacteristic
146C4⋊(C3⋊Dic3)C2311yescharacteristic
147C4⋊(C3⋊Dic3)C2311yescharacteristic
148#3750C2312yes—
149#3750C2312yes—
150#3750C2314yes—
151#3750C2314yes—
152C4×C3⋊Dic3C2312yes—
153C4×C3⋊Dic3C2312yes—
154C4×C3⋊Dic3C2314yes—
155C3×(C2×D3)⋊C4C2314yes—
156C3×(C2×D3)⋊C4C2314yes—
157C3×(C2×D3)⋊C4C2312yes—
158C3×C4⋊Dic3C2311yescharacteristic
159C3×C4⋊Dic3C2312yes—
160C3×C4⋊Dic3C2314yes—
161C3×C4⋊Dic3C2314yes—
162C3×C4⋊Dic3C2311yescharacteristic
163C3×C4⋊Dic3C2312yes—
164C3×Dic3⋊C4C2314yes—
165C3×Dic3⋊C4C2314yes—
166C3×Dic3⋊C4C2312yes—
167C3×C4×Dic3C2311yescharacteristic
168C3×C4×Dic3C2314yes—
169C3×C4×Dic3C2311yescharacteristic
170C3×C4×Dic3C2312yes—
171C3×C4×Dic3C2311yescharacteristic
172#3724C2312yes—
173#3724C2314yes—
174#3724C2314yes—
175#3724C2312yes—
176#3724C2314yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2312yes—
179Dic3⋊Dic3C2312yes—
180(C2×D3)⋊Dic3C2312yes—
181(C2×D3)⋊Dic3C2314yes—
182(C2×D3)⋊Dic3C2312yes—
183Dic32C2312yes—
184Dic32C2312yes—
185Dic32C2312yes—
186Dic32C2312yes—
187Dic32C2314yes—
188Q8×#41—91noSylow
189C2×D3×Q8—31no—
190C2×D3×Q8—32no—
191C2×#237—31no—
192C2×#235—31no—
193C22×Dic6—31no—
194C22×Dic6—32no—
195C3×C4⋊Q8—21no—
196C3×C4⋊Q8—31no—
197C3×C4⋊Q8C2×D311yescharacteristic
198C3×C4⋊Q8C2×D311yescharacteristic
199C3×#125—32no—
200C3×#125—32no—
201C3×C22⋊Q8—32no—
202C3×C22⋊Q8—34no—
203C3×C22⋊Q8—32no—
204C3×C22⋊Q8—32no—
205C3×C4×Q8—32no—
206C3×C4×Q8—32no—
207C3×C4×Q8—31no—
208C3×C4×D4—32no—
209C3×C4×D4—31no—
210C3×#117—32no—
211C2×C3×C4⋊C4—32no—
212C2×C3×C42—31no—
213#946—32no—
214#946C2×D312yes—
215#946C2×D314yes—
216Q8×Dic3—32no—
217Q8×Dic3—31no—
218Q8×Dic3C2×D312yes—
219#944—34no—
220#944—34no—
221#944—32no—
222#944—32no—
223#944—64no—
224D4×Dic3—32no—
225D4×Dic3—31no—
226C4×#67—32no—
227C4×#67—32no—
228C4×#67—32no—
229C4×#67—34no—
230#926—31no—
231C2×C4⋊Dic3—31no—
232#924—32no—
233#924—34no—
234C2×Dic3⋊C4—32no—
235C2×Dic3⋊C4—34no—
236C2×C4×Dic3—32no—
237C2×C4×Dic3—32no—
238C2×C4×Dic3—34no—
239#897—34no—
240#897C2×D312yes—
241#897C2×D312yes—
242#896—34no—
243#896—34no—
244#896—34no—
245#896—34no—
246#896—34no—
247#893—32no—
248#893C2×D312yes—
249#892—31no—
250#892C2×D312yes—
251D3×C4⋊C4—32no—
252D3×C4⋊C4—34no—
253D3×C4⋊C4—31no—
254D3×C4⋊C4C2×D312yes—
255#890—32no—
256#890C2×D312yes—
257#890C2×D312yes—
258#889—34no—
259#889—34no—
260#889—34no—
261#889—34no—
262#889—34no—
263#889—34no—
264#888—32no—
265#888—32no—
266#888—32no—
267#888—32no—
268#888—34no—
269#888—34no—
270#888—32no—
271#888—32no—
272#888—62no—
273#888—62no—
274#887—32no—
275#887—32no—
276#887—32no—
277#887—32no—
278#887—32no—
279#887—34no—
280#887—34no—
281#887—31no—
282#887—32no—
283#887—34no—
284#887—34no—
285#887—32no—
286#887—31no—
287#887—62no—
288#887—62no—
289#887C2×D312yes—
290#67⋊C4—34no—
291#67⋊C4—32no—
292#67⋊C4—34no—
293#67⋊C4—34no—
294#878—34no—
295#878—34no—
296#878—34no—
297#878—34no—
298#878—34no—
299#877—34no—
300#877—32no—
301C4×D12—31no—
302C4×D12C2×D311yescharacteristic
303#872—32no—
304#872—34no—
305C42×D3—32no—
306C42×D3—32no—
307C42×D3—34no—
308C42×D3C2×D311yescharacteristic
309#870—32no—
310#869C2×D311yescharacteristic
311C4×Dic6—31no—
312C4×Dic6—31no—
313C4×Dic6—31no—
314C4×Dic6—31no—
315C4×Dic6—31no—
316C4×Dic6—31no—
317C4×Dic6—32no—
318C4×Dic6—31no—
319C4×Dic6—34no—
320C4×Dic6—32no—
321C4×Dic6—34no—
322C4×Dic6—32no—
323C4×Dic6—32no—
324C4×Dic6—61no—
325C4×Dic6—61no—
326C4×Dic6C2×D311yescharacteristic
327C22×C3×D3C2412yes—
328C22×C3×D3C2411yescharacteristic
329C32×Q8—42no—
330C2×C32×C4C2414yes—
331C2×C32×C4C2411yescharacteristic
332C2×C32×C4C2411yescharacteristic
333C2×C32×C4C2411yescharacteristic
334C2×C3⋊Dic3C2412yes—
335C2×C3⋊Dic3C2412yes—
336C2×C3⋊Dic3C2412yes—
337C2×C3⋊Dic3C2412yes—
338#634—44no—
339#634C2×Q814yescomplemented
340#634#4114yescomplemented
341C2×C3×Dic3C2412yes—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2411yescharacteristic
344C2×C3×Dic3C2414yes—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2411yescharacteristic
347C2×C3×Dic3C2411yescharacteristic
348C3×D12C2×Q814yescomplemented
349C3×C4×D3—24no—
350C3×C4×D3—22no—
351C3×C4×D3—41no—
352C3×C4×D3—44no—
353C3×C4×D3C2×Q814yescomplemented
354C3×Dic6—24no—
355C3×Dic6—22no—
356#627—28no—
357#627—24no—
358#625C2×Q818yescomplemented
359D3×Dic3—28no—
360D3×Dic3—24no—
361D3×Dic3—42no—
362D3×Dic3—42no—
363D3×Dic3C2×Q818yescomplemented
364Q82—91no—
365#557—91no—
366#557—92no—
367#554—31no—
368#554—92no—
369#554—92no—
370#554—94no—
371D4×Q8—91no—
372D4×Q8—92no—
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—32no—
384C2×C3×Q8C22×D312yes—
385C2×C3×Q8C22×D312yes—
386C2×C3×D4—31no—
387C22×C3×C4—31no—
388C22×C3×C4—32no—
389C22×C3×C4—31no—
390C22×C3×C4—34no—
391C22×C3×C4—31no—
392C2×#67—32no—
393C2×#67—32no—
394C22×Dic3—32no—
395C22×Dic3—32no—
396C22×Dic3—34no—
397C22×Dic3—32no—
398C22×Dic3—32no—
399D3×Q8—64no—
400D3×Q8—68no—
401#237—38no—
402#235—38no—
403C2×D12C22×D311yescharacteristic
404C2×C4×D3—32no—
405C2×C4×D3—32no—
406C2×C4×D3—34no—
407C2×C4×D3—32no—
408C2×C4×D3—32no—
409C2×C4×D3C22×D312yes—
410C2×C4×D3C22×D311yescharacteristic
411C2×C4×D3C22×D314yes—
412C2×C4×D3C22×D311yescharacteristic
413C2×C4×D3C22×D311yescharacteristic
414C2×Dic6—31no—
415C2×Dic6—31no—
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—61no—
426C2×Dic6—64no—
427C2×Dic6—68no—
428C2×Dic6—64no—
429C2×Dic6C22×D311yescharacteristic
430C2×Dic6C22×D312yes—
431C3×C4⋊C4—22no—
432C3×C4⋊C4—22no—
433C3×C4⋊C4—31no—
434C3×C4⋊C4—34no—
435C3×C4⋊C4—31no—
436C3×C4⋊C4—34no—
437C3×C4⋊C4—32no—
438C3×C4⋊C4—32no—
439C3×C4⋊C4—34no—
440C3×C4⋊C4—34no—
441C3×C4⋊C4—32no—
442C3×C4⋊C4C22×D312yes—
443C3×C4⋊C4C22×D312yes—
444C3×C4⋊C4C22×D312yes—
445C3×C4⋊C4C22×D312yes—
446C3×C22⋊C4—32no—
447C3×C22⋊C4—34no—
448C3×C22⋊C4—34no—
449C3×C42—21no—
450C3×C42—31no—
451C3×C42—32no—
452C3×C42—31no—
453C3×C42—34no—
454C3×C42—31no—
455C3×C42C22×D311yescharacteristic
456C3×C42C22×D311yescharacteristic
457#217—32no—
458#217—34no—
459#217—32no—
460(C2×D3)⋊C4—32no—
461(C2×D3)⋊C4—34no—
462(C2×D3)⋊C4—32no—
463(C2×D3)⋊C4C22×D312yes—
464(C2×D3)⋊C4C22×D314yes—
465(C2×D3)⋊C4C22×D314yes—
466C4⋊Dic3—31no—
467C4⋊Dic3—31no—
468C4⋊Dic3—31no—
469C4⋊Dic3—31no—
470C4⋊Dic3—32no—
471C4⋊Dic3—32no—
472C4⋊Dic3—34no—
473C4⋊Dic3—61no—
474C4⋊Dic3—61no—
475C4⋊Dic3C22×D311yescharacteristic
476C4⋊Dic3C22×D312yes—
477C4⋊Dic3C22×D311yescharacteristic
478C4⋊Dic3C22×D314yes—
479C4⋊Dic3C22×D312yes—
480C4⋊Dic3C22×D314yes—
481Dic3⋊C4—32no—
482Dic3⋊C4—32no—
483Dic3⋊C4—32no—
484Dic3⋊C4—32no—
485Dic3⋊C4—34no—
486Dic3⋊C4—34no—
487Dic3⋊C4—34no—
488Dic3⋊C4—34no—
489Dic3⋊C4—32no—
490Dic3⋊C4—32no—
491Dic3⋊C4—32no—
492Dic3⋊C4—34no—
493Dic3⋊C4—34no—
494Dic3⋊C4—34no—
495Dic3⋊C4—32no—
496Dic3⋊C4—32no—
497Dic3⋊C4—34no—
498Dic3⋊C4—34no—
499Dic3⋊C4—34no—
500Dic3⋊C4—32no—
501Dic3⋊C4—34no—
502Dic3⋊C4—62no—
503Dic3⋊C4—62no—
504Dic3⋊C4—64no—
505Dic3⋊C4—64no—
506Dic3⋊C4C22×D312yes—
507Dic3⋊C4C22×D314yes—
508Dic3⋊C4C22×D314yes—
509C4×Dic3—32no—
510C4×Dic3—32no—
511C4×Dic3—32no—
512C4×Dic3—32no—
513C4×Dic3—34no—
514C4×Dic3—34no—
515C4×Dic3—32no—
516C4×Dic3—32no—
517C4×Dic3—32no—
518C4×Dic3—32no—
519C4×Dic3—34no—
520C4×Dic3—32no—
521C4×Dic3—34no—
522C4×Dic3—32no—
523C4×Dic3—32no—
524C4×Dic3—32no—
525C4×Dic3—62no—
526C4×Dic3—62no—
527C4×Dic3—64no—
528C4×Dic3C22×D311yescharacteristic
529C4×Dic3C22×D312yes—
530C4×Dic3C22×D311yescharacteristic
531C4×Dic3C22×D311yescharacteristic
532C4×Dic3C22×D314yes—
533C22×C32C2511yescharacteristic
534C2×C3×D3—22no—
535C2×C3×D3—21no—
536C2×C3×D3—21no—
537C2×C3×D3—22no—
538C2×C3×D3C22×Q814yes—
539C2×C3×D3C22×Q812yes—
540C32×C4—24no—
541C32×C4—21no—
542C32×C4C22×Q812yes—
543C32×C4C2×#4112yes—
544C3⋊Dic3—22no—
545C3⋊Dic3—22no—
546C3⋊Dic3C22×Q814yes—
547C3⋊Dic3C2×#4114yes—
548C3×Dic3—24no—
549C3×Dic3—22no—
550C3×Dic3—22no—
551C3×Dic3—21no—
552C3×Dic3—21no—
553C3×Dic3—22no—
554C3×Dic3C22×Q812yes—
555C2×#41—91no—
556C22×Q8—91no—
557C22×Q8—92no—
558C4⋊Q8—31no—
559C4⋊Q8—92no—
560C4⋊Q8—94no—
561C4⋊Q8—92no—
562C4⋊Q8—94no—
563C4⋊Q8—92no—
564C4⋊Q8—92no—
565C4⋊Q8D3211yescharacteristic
566#125—32no—
567#125—32no—
568#125—92no—
569#125—94no—
570#125—94no—
571#125—94no—
572C22⋊Q8—32no—
573C22⋊Q8—34no—
574C22⋊Q8—32no—
575C22⋊Q8—32no—
576C22⋊Q8—94no—
577C22⋊Q8—94no—
578C22⋊Q8—94no—
579C22⋊Q8—94no—
580C22⋊Q8—94no—
581C22⋊Q8—94no—
582C22⋊Q8—92no—
583C4×Q8—32no—
584C4×Q8—32no—
585C4×Q8—31no—
586C4×Q8—92no—
587C4×Q8—91no—
588C4×Q8—92no—
589C4×Q8—94no—
590C4×Q8—91no—
591C4×Q8—92no—
592C4×Q8—94no—
593C4×Q8—91no—
594C4×Q8—94no—
595C4×Q8—92no—
596C4×Q8—92no—
597C4×Q8—92no—
598C4×Q8—91no—
599C4×Q8—91no—
600C4×D4—32no—
601C4×D4—31no—
602C4×D4—91no—
603C4×D4—94no—
604C4×D4—94no—
605C4×D4—92no—
606C4×D4—92no—
607C4×D4—92no—
608#117—32no—
609#117—92no—
610#117—94no—
611#117—91no—
612C2×C4⋊C4—32no—
613C2×C4⋊C4—92no—
614C2×C4⋊C4—94no—
615C2×C4⋊C4—91no—
616C2×C42—31no—
617C2×C42—92no—
618C2×C42—94no—
619C2×C42—92no—
620C23×C3—32no—
621C23×C3—31no—
622C22×D3C23×D312yes—
623C22×D3C23×D311yescharacteristic
624C3×Q8—42no—
625C3×Q8—42no—
626C3×Q8—62no—
627C3×Q8—64no—
628C3×Q8—82no—
629C3×D4—34no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—24no—
633C2×C3×C4—21no—
634C2×C3×C4—31no—
635C2×C3×C4—34no—
636C2×C3×C4—32no—
637C2×C3×C4—31no—
638C2×C3×C4—32no—
639C2×C3×C4—32no—
640C2×C3×C4—34no—
641C2×C3×C4—31no—
642C2×C3×C4—64no—
643C2×C3×C4—62no—
644C2×C3×C4—124no—
645C2×C3×C4—121no—
646C2×C3×C4C23×D314yes—
647C2×C3×C4C23×D314yes—
648C2×C3×C4C23×D311yescharacteristic
649C2×C3×C4C23×D311yescharacteristic
650C2×C3×C4C23×D311yescharacteristic
651C2×C3×C4C23×D311yescharacteristic
652C2×C3×C4C23×D311yescharacteristic
653C2×C3×C4C23×D311yescharacteristic
654#67—38no—
655#67—38no—
656C2×Dic3—32no—
657C2×Dic3—32no—
658C2×Dic3—32no—
659C2×Dic3—32no—
660C2×Dic3—38no—
661C2×Dic3—32no—
662C2×Dic3—32no—
663C2×Dic3—32no—
664C2×Dic3—32no—
665C2×Dic3—62no—
666C2×Dic3—62no—
667C2×Dic3—62no—
668C2×Dic3—62no—
669C2×Dic3—64no—
670C2×Dic3—68no—
671C2×Dic3—122no—
672C2×Dic3—122no—
673C2×Dic3C23×D312yes—
674C2×Dic3C23×D311yescharacteristic
675C2×Dic3C23×D312yes—
676C2×Dic3C23×D312yes—
677C2×Dic3C23×D314yes—
678C2×Dic3C23×D311yescharacteristic
679C2×Dic3C23×D311yescharacteristic
680D12D3×Q814yescomplemented
681C4×D3—22no—
682C4×D3—24no—
683C4×D3—38no—
684C4×D3—41no—
685C4×D3—44no—
686C4×D3—68no—
687C4×D3—64no—
688C4×D3—122no—
689C4×D3—122no—
690C4×D3D3×Q814yescomplemented
691Dic6—24no—
692Dic6—22no—
693Dic6—34no—
694Dic6—34no—
695Dic6—34no—
696Dic6—34no—
697Dic6—64no—
698Dic6—64no—
699Dic6—64no—
700Dic6—68no—
701Dic6—68no—
702Dic6—64no—
703Dic6—124no—
704Dic6—124no—
705Dic6—244no—
706C2×C32C23×Q811yescharacteristic
707C2×C32C22×#4111yescharacteristic
708C2×C32#58511yescharacteristic
709C3×D3—22no—
710C3×D3—24no—
711#41—98no—
712C2×Q8—31no—
713C2×Q8—32no—
714C2×Q8—92no—
715C2×Q8—94no—
716C2×Q8—91no—
717C2×Q8—91no—
718C2×Q8—94no—
719C2×Q8—184no—
720C2×Q8—188no—
721C2×Q8C2×D3212yes—
722C2×D4—31no—
723C2×D4—92no—
724C22×C4—31no—
725C22×C4—31no—
726C22×C4—32no—
727C22×C4—31no—
728C22×C4—34no—
729C22×C4—92no—
730C22×C4—92no—
731C22×C4—94no—
732C22×C4—92no—
733C22×C4—92no—
734C4⋊C4—31no—
735C4⋊C4—34no—
736C4⋊C4—32no—
737C4⋊C4—34no—
738C4⋊C4—32no—
739C4⋊C4—31no—
740C4⋊C4—34no—
741C4⋊C4—32no—
742C4⋊C4—34no—
743C4⋊C4—92no—
744C4⋊C4—92no—
745C4⋊C4—92no—
746C4⋊C4—94no—
747C4⋊C4—92no—
748C4⋊C4—94no—
749C4⋊C4—94no—
750C4⋊C4—94no—
751C4⋊C4—94no—
752C4⋊C4—92no—
753C4⋊C4—91no—
754C4⋊C4—94no—
755C4⋊C4—92no—
756C4⋊C4—91no—
757C4⋊C4C2×D3212yes—
758C4⋊C4C2×D3212yes—
759C22⋊C4—34no—
760C22⋊C4—34no—
761C22⋊C4—32no—
762C22⋊C4—92no—
763C22⋊C4—94no—
764C22⋊C4—92no—
765C42—31no—
766C42—31no—
767C42—31no—
768C42—34no—
769C42—32no—
770C42—92no—
771C42—92no—
772C42—92no—
773C42—92no—
774C42—94no—
775C42—94no—
776C42—92no—
777C42—92no—
778C42C2×D3211yescharacteristic
779C22×C3—21no—
780C22×C3—34no—
781C22×C3—32no—
782C22×C3—62no—
783C22×C3—61no—
784C22×C3—62no—
785C22×C3—61no—
786C22×C3C24×D311yescharacteristic
787C22×C3C24×D311yescharacteristic
788C2×D3—21no—
789C2×D3—22no—
790C2×D3—21no—
791C2×D3—22no—
792C2×D3C2×D3×Q814yes—
793C2×D3C2×D3×Q812yes—
794C3×C4—24no—
795C3×C4—21no—
796C3×C4—24no—
797C3×C4—21no—
798C3×C4—22no—
799C3×C4—22no—
800C3×C4—32no—
801C3×C4—44no—
802C3×C4—41no—
803C3×C4—62no—
804C3×C4—61no—
805C3×C4—62no—
806C3×C4—64no—
807C3×C4—62no—
808C3×C4—61no—
809C3×C4C2×D3×Q812yes—
810C3×C4C2×D3×Q812yes—
811C3×C4D3×#4112yes—
812C3×C4D3×#4112yes—
813Dic3—24no—
814Dic3—22no—
815Dic3—21no—
816Dic3—22no—
817Dic3—21no—
818Dic3—22no—
819Dic3—34no—
820Dic3—34no—
821Dic3—34no—
822Dic3—34no—
823Dic3—64no—
824Dic3—64no—
825Dic3—62no—
826Dic3—62no—
827Dic3—62no—
828Dic3—62no—
829Dic3—122no—
830Dic3—122no—
831Dic3C2×D3×Q812yes—
832C32Q8×#4111yescharacteristic, complemented, Sylow
833C23—31no—
834C23—32no—
835Q8—42no—
836Q8—62no—
837Q8—64no—
838Q8—94no—
839Q8—94no—
840Q8—184no—
841Q8—188no—
842Q8—364no—
843D4—34no—
844D4—98no—
845C2×C4—31no—
846C2×C4—34no—
847C2×C4—31no—
848C2×C4—31no—
849C2×C4—32no—
850C2×C4—32no—
851C2×C4—34no—
852C2×C4—32no—
853C2×C4—62no—
854C2×C4—64no—
855C2×C4—98no—
856C2×C4—92no—
857C2×C4—92no—
858C2×C4—92no—
859C2×C4—92no—
860C2×C4—121no—
861C2×C4—124no—
862C2×C4—184no—
863C2×C4—188no—
864C2×C4—362no—
865C2×C4—362no—
866C2×C4C22×D3214yes—
867C2×C4C22×D3211yescharacteristic
868C2×C4C22×D3211yescharacteristic
869C2×C4C22×D3211yescharacteristic
870C2×C3—21no—
871C2×C3—21no—
872C2×C3—21no—
873C2×C3—64no—
874C2×C3—62no—
875C2×C3C22×D3×Q811yescharacteristic
876C2×C3C22×D3×Q811yescharacteristic
877C2×C3C2×D3×#4111yescharacteristic
878C2×C3C2×D3×#4111yescharacteristic
879C2×C3#596411yescharacteristic
880C2×C3#596611yescharacteristic
881D3—22no—
882D3—24no—
883C22—32no—
884C22—34no—
885C22—62no—
886C22—61no—
887C22—61no—
888C22—62no—
889C22C23×D3211yescharacteristic
890C4—21no—
891C4—24no—
892C4—32no—
893C4—62no—
894C4—61no—
895C4—61no—
896C4—62no—
897C4—62no—
898C4—64no—
899C4—94no—
900C4—94no—
901C4—182no—
902C4—182no—
903C4D32×Q812yes—
904C4#6431912yes—
905C3—21no—
906C3#8627711yescharacteristic, complemented
907C3#8692311yescharacteristic, complemented
908C2—62no—
909C2—64no—
910C2#1059667811yescharacteristic
911C2C2×D32×Q811yescharacteristic
912C2C2×#6431911yescharacteristic
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. #10596193C2semidirect
2. C3×#5730C2semidirect
3. C3×#5728C2semidirect
4. #10595370C2semidirect
5. #10595367C2semidirect
6. #10594532C2semidirect
7. #10594526C2semidirect
8. #10594485C2semidirect
9. #10594477C2semidirect
10. #10594385C2semidirect
12. D3×#887C2semidirect
13. #10594324C2semidirect
14. #10593904C2semidirect
16. C4×D3×Dic6C2semidirect
17. #10593864C2semidirect
87. #5730D3semidirect
88. #5728D3semidirect
140. #3795Q8semidirect
339. #634C2×Q8semidirect
340. #634#41semidirect
348. C3×D12C2×Q8semidirect
353. C3×C4×D3C2×Q8semidirect
358. #625C2×Q8semidirect
363. D3×Dic3C2×Q8semidirect
680. D12D3×Q8semidirect
690. C4×D3D3×Q8semidirect
832. C32Q8×#41semidirect
906. C3#86277semidirect
907. C3#86923semidirect

Maximal subgroups

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

subgroupindex
#105961932
C3×#57302
C3×#57282
#105953702
#105953672
#105945322
#105945262
#105944852
#105944772
#105943852
#105943582
D3×#8872
#105943242
#105939042
C4×#37952
C4×D3×Dic62
#105938642
#869233
#862773