Finite Group Databasebeta

← #11906389

Subgroups — #11906389

Order 1152.

2226 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
1Q8×#634C211yesmaximal, characteristic, complemented
2C3×#5579C211yesmaximal, characteristic, complemented
3C3×#5578C211yesmaximal, characteristic, complemented
4#10595407C212yesmaximal, complemented
5#10595368C212yesmaximal, complemented
6#10594532C212yesmaximal, complemented
7#10594390C214yesmaximal, complemented
8#10594377C214yesmaximal, complemented
9D3×#888C212yesmaximal, complemented
10#10593960C211yesmaximal, characteristic, complemented
11#10593959C212yesmaximal, complemented
12Dic6×D12C212yesmaximal, complemented
13D3×#869C211yesmaximal, characteristic, complemented
14#10593887C212yesmaximal
15C4×#3795C211yesmaximal, characteristic
16#10593856C211yesmaximal, characteristic, complemented
17#10593852C212yesmaximal, complemented
18#86926—31nomaximal
19#86281—31nomaximal
20C2×#3795C2211yescharacteristic
21C2×D3×Dic6C2214yes—
22C2×D3×Dic6C2212yes—
23C32×C4×Q8C2211yescharacteristic
24Q8×C3⋊Dic3C2212yes—
25#64097C2212yes—
26#64097C2214yes—
27#64078C2211yescharacteristic
28#64078C2212yes—
29C4×#634C2212yes—
30C4×#634C2211yescharacteristic
31C3×#946C2212yes—
32C3×#946C2211yescharacteristic
33C3×#944C2211yescharacteristic
34C3×#897C2211yescharacteristic
35C3×#896C2212yes—
36C3×#896C2214yes—
37C3×D3×C4⋊C4C2212yes—
38C3×#889C2212yes—
39C3×#888C2211yescharacteristic
40C3×C4×D12C2211yescharacteristic
41C3×C4×D12C2212yes—
42C3×#872C2212yes—
43C3×C42×D3C2211yescharacteristic
44C3×#870C2212yes—
45C3×#869C2211yescharacteristic
46C3×C4×Dic6C2212yes—
47C3×C4×Dic6C2211yescharacteristic
48#63919C2212yes—
49#63918C2212yes—
50#63918C2212yes—
51#63918C2212yes—
52#63902C2214yes—
53C4×#625C2212yes—
54#63896C2214yes—
55#63896C2214yes—
56#63893C2214yes—
57#63893C2214yes—
58#63893C2214yes—
59Dic3×D12C2211yescharacteristic
60Dic3×D12C2212yes—
61D3×C4⋊Dic3C2212yes—
62D3×C4⋊Dic3C2212yes—
63D3×C4⋊Dic3C2212yes—
64#63879C2212yes—
65#63879C2214yes—
66#63878C2214yes—
67#63877C2212yes—
68D3×Dic3⋊C4C2214yes—
69C4×D3×Dic3C2212yes—
70#63870C2214yes—
71#63869C2212yes—
72#63866C2212yes—
73#63857C2214yes—
74#63856C2212yes—
75#63847C2214yes—
76#63845C2214yes—
77#63844C2211yescharacteristic
78#63844C2212yes—
79#63843C2212yes—
80#63841C2211yescharacteristic
81#63840C2214yes—
82#63839C2214yes—
83#63839C2214yes—
84#63838C2214yes—
85C3×#554—31no—
86C3×#533—31no—
87#5728—32no—
88D3×C4⋊Q8—32no—
89D3×C4⋊Q8—31no—
90#5722—31no—
91#5689—34no—
92#5689—32no—
93#5685—32no—
94#5635—32no—
95#5635—32no—
96#5635—32no—
97#5632—34no—
98#5632—34no—
99#5623—34no—
100#5622—32no—
101#5579—31no—
102#5579D311yescharacteristic, complemented
103#5578D311yescharacteristic, complemented
104Q8×D12—32no—
105#5567—32no—
106Q8×Dic6—31no—
107Q8×Dic6—31no—
108Q8×Dic6—31no—
109Q8×Dic6—61no—
110#5546—32no—
111#5543—31no—
112D4×Dic6—32no—
113C4×#237—31no—
114#5523—32no—
115#5519—32no—
116#5511—32no—
117C2×#888—32no—
118C4×#235—31no—
119C2×#869—31no—
120C2×C32×Q8C2311yescharacteristic
121C2×#634C2314yes—
122C2×#634C2312yes—
123C2×#634C2311yescharacteristic
124C2×C3×D12C2311yescharacteristic
125C2×C3×C4×D3C2312yes—
126C2×C3×C4×D3C2311yescharacteristic
127C2×C3×C4×D3C2311yescharacteristic
128C2×C3×C4×D3C2314yes—
129C2×C3×C4×D3C2311yescharacteristic
130C2×C3×Dic6C2312yes—
131C2×C3×Dic6C2311yescharacteristic
132C2×C3×Dic6C2312yes—
133C2×#627C2314yes—
134C2×#627C2314yes—
135C2×#625C2312yes—
136C2×D3×Dic3C2312yes—
137C2×D3×Dic3C2314yes—
138C2×D3×Dic3C2314yes—
139C2×D3×Dic3C2312yes—
140#3795Q818yescomplemented
141D3×Dic6—48no—
142D3×Dic6—44no—
143C32×C4⋊C4C2311yescharacteristic
144C32×C4⋊C4C2312yes—
145C32×C42C2311yescharacteristic
146C32×C42C2312yes—
147C4⋊(C3⋊Dic3)C2311yescharacteristic
148C4⋊(C3⋊Dic3)C2312yes—
149C4⋊(C3⋊Dic3)C2314yes—
150C4⋊(C3⋊Dic3)C2312yes—
151#3750C2312yes—
152#3750C2314yes—
153C4×C3⋊Dic3C2314yes—
154C4×C3⋊Dic3C2312yes—
155C3×(C2×D3)⋊C4C2312yes—
156C3×(C2×D3)⋊C4C2312yes—
157C3×(C2×D3)⋊C4C2314yes—
158C3×(C2×D3)⋊C4C2312yes—
159C3×C4⋊Dic3C2311yescharacteristic
160C3×C4⋊Dic3C2312yes—
161C3×C4⋊Dic3C2312yes—
162C3×C4⋊Dic3C2311yescharacteristic
163C3×C4⋊Dic3C2312yes—
164C3×Dic3⋊C4C2312yes—
165C3×Dic3⋊C4C2312yes—
166C3×Dic3⋊C4C2312yes—
167C3×Dic3⋊C4C2312yes—
168C3×Dic3⋊C4C2314yes—
169C3×Dic3⋊C4C2312yes—
170C3×Dic3⋊C4C2314yes—
171C3×C4×Dic3C2311yescharacteristic
172C3×C4×Dic3C2311yescharacteristic
173C3×C4×Dic3C2312yes—
174C3×C4×Dic3C2311yescharacteristic
175#3724C2314yes—
176#3724C2314yes—
177#3724C2312yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2314yes—
182(C2×D3)⋊Dic3C2312yes—
183(C2×D3)⋊Dic3C2314yes—
184(C2×D3)⋊Dic3C2312yes—
185Dic32C2312yes—
186Dic32C2314yes—
187Dic32C2312yes—
188#3503—91noSylow
189C2×D3×Q8—32no—
190C2×D3×Q8—34no—
191C2×#237—31no—
192C2×#235—31no—
193C22×Dic6—32no—
194C22×Dic6—34no—
195C3×C4⋊Q8—31no—
196C3×C4⋊Q8—31no—
197C3×C4⋊Q8—31no—
198C3×#125—32no—
199C3×#125—32no—
200C3×C22⋊Q8—31no—
201C3×C22⋊Q8—32no—
202C3×C22⋊Q8—32no—
203C3×C22⋊Q8—34no—
204C3×C22⋊Q8—31no—
205C3×C4×Q8—21no—
206C3×C4×Q8—31no—
207C3×C4×Q8—32no—
208C3×C4×Q8C2×D311yescharacteristic
209C3×C4×Q8C2×D311yescharacteristic
210C3×C4×D4—31no—
211C3×C4×D4—32no—
212C3×#117—32no—
213C2×C3×C4⋊C4—32no—
214C2×C3×C42—31no—
215#946—32no—
216#946C2×D311yescharacteristic
217#946C2×D312yes—
218Q8×Dic3—32no—
219Q8×Dic3—32no—
220Q8×Dic3—32no—
221Q8×Dic3—62no—
222#944—34no—
223#944—34no—
224#944—32no—
225#944C2×D311yescharacteristic
226D4×Dic3—31no—
227D4×Dic3—32no—
228C4×#67—32no—
229C4×#67—32no—
230C4×#67—32no—
231C4×#67—34no—
232#926—31no—
233C2×C4⋊Dic3—32no—
234C2×C4⋊Dic3—32no—
235C2×C4⋊Dic3—32no—
236#924—32no—
237#924—34no—
238C2×Dic3⋊C4—34no—
239C2×C4×Dic3—32no—
240#897—34no—
241#897—34no—
242#897—34no—
243#897—34no—
244#897C2×D311yescharacteristic
245#896—34no—
246#896—34no—
247#896C2×D312yes—
248#896C2×D314yes—
249#892—31no—
250#892—34no—
251D3×C4⋊C4—32no—
252D3×C4⋊C4—32no—
253D3×C4⋊C4—34no—
254D3×C4⋊C4—32no—
255D3×C4⋊C4C2×D312yes—
256#890—34no—
257#890—32no—
258#889—34no—
259#889—34no—
260#889—34no—
261#889—34no—
262#889—34no—
263#889C2×D312yes—
264#888—34no—
265#888—34no—
266#888—34no—
267#888—34no—
268#888—32no—
269#888—32no—
270#888—32no—
271#888—32no—
272#888—34no—
273#888—34no—
274#888—32no—
275#888—32no—
276#888—32no—
277#888—62no—
278#888—64no—
279#888C2×D311yescharacteristic
280#887—32no—
281#887—34no—
282#887—34no—
283#887—31no—
284#887—32no—
285#67⋊C4—32no—
286#67⋊C4—34no—
287#67⋊C4—34no—
288#67⋊C4—34no—
289#878—34no—
290#878—34no—
291#878—34no—
292#878—34no—
293#878—34no—
294#877—34no—
295#877—32no—
296C4×D12—31no—
297C4×D12—32no—
298C4×D12C2×D311yescharacteristic
299C4×D12C2×D312yes—
300#872—32no—
301#872C2×D312yes—
302C42×D3—32no—
303C42×D3C2×D311yescharacteristic
304#870—32no—
305#870C2×D312yes—
306#869—32no—
307#869—32no—
308#869—31no—
309#869—31no—
310#869—32no—
311#869—32no—
312#869—32no—
313#869—32no—
314#869—61no—
315#869—62no—
316#869C2×D311yescharacteristic
317C4×Dic6—32no—
318C4×Dic6—31no—
319C4×Dic6—31no—
320C4×Dic6—32no—
321C4×Dic6—31no—
322C4×Dic6—32no—
323C4×Dic6—61no—
324C4×Dic6—62no—
325C4×Dic6C2×D312yes—
326C4×Dic6C2×D311yescharacteristic
327C22×C3×D3C2412yes—
328C22×C3×D3C2411yescharacteristic
329C32×Q8—22no—
330C2×C32×C4C2411yescharacteristic
331C2×C32×C4C2412yes—
332C2×C32×C4C2412yes—
333C2×C32×C4C2411yescharacteristic
334C2×C32×C4C2411yescharacteristic
335C2×C3⋊Dic3C2412yes—
336C2×C3⋊Dic3C2414yes—
337C2×C3⋊Dic3C2412yes—
338#634—44no—
339#634—42no—
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—24no—
350C3×C4×D3—22no—
351C3×C4×D3—22no—
352C3×C4×D3—44no—
353C3×C4×D3C2×Q814yescomplemented
354C3×Dic6—22no—
355C3×Dic6—24no—
356C3×Dic6—42no—
357#627—28no—
358#627—44no—
359#625C2×Q818yescomplemented
360D3×Dic3—24no—
361D3×Dic3—44no—
362D3×Dic3—44no—
363D3×Dic3C2×Q818yescomplemented
364Q82—91no—
365Q82—91no—
366#557—92no—
367#554—31no—
368#554—92no—
369#554—91no—
370#554—92no—
371D4×Q8—92no—
372D4×Q8—94no—
373#544—92no—
374#544—94no—
375#533—31no—
376#533—92no—
377C2×C4⋊Q8—91no—
378C2×C4⋊Q8—92no—
379#520—92no—
380C4×#41—91no—
381C2×C3×Q8—21no—
382C2×C3×Q8—32no—
383C2×C3×Q8—31no—
384C2×C3×Q8—32no—
385C2×C3×Q8C22×D311yescharacteristic
386C2×C3×Q8C22×D311yescharacteristic
387C2×C3×D4—31no—
388C22×C3×C4—31no—
389C22×C3×C4—32no—
390C22×C3×C4—31no—
391C22×C3×C4—31no—
392C22×C3×C4—34no—
393C2×#67—32no—
394C2×#67—32no—
395C22×Dic3—32no—
396C22×Dic3—32no—
397C22×Dic3—34no—
398C22×Dic3—34no—
399D3×Q8—124no—
400D3×Q8—128no—
401#237—38no—
402#235—38no—
403C2×D12C22×D311yescharacteristic
404C2×C4×D3—32no—
405C2×C4×D3—32no—
406C2×C4×D3—34no—
407C2×C4×D3—34no—
408C2×C4×D3C22×D312yes—
409C2×C4×D3C22×D311yescharacteristic
410C2×C4×D3C22×D311yescharacteristic
411C2×C4×D3C22×D314yes—
412C2×C4×D3C22×D311yescharacteristic
413C2×Dic6—31no—
414C2×Dic6—31no—
415C2×Dic6—34no—
416C2×Dic6—34no—
417C2×Dic6—32no—
418C2×Dic6—32no—
419C2×Dic6—34no—
420C2×Dic6—34no—
421C2×Dic6—34no—
422C2×Dic6—34no—
423C2×Dic6—61no—
424C2×Dic6—64no—
425C2×Dic6—62no—
426C2×Dic6—128no—
427C2×Dic6—124no—
428C2×Dic6C22×D311yescharacteristic
429C2×Dic6C22×D312yes—
430C2×Dic6C22×D312yes—
431C3×C4⋊C4—21no—
432C3×C4⋊C4—22no—
433C3×C4⋊C4—32no—
434C3×C4⋊C4—32no—
435C3×C4⋊C4—32no—
436C3×C4⋊C4—34no—
437C3×C4⋊C4—31no—
438C3×C4⋊C4—34no—
439C3×C4⋊C4—32no—
440C3×C4⋊C4—31no—
441C3×C4⋊C4—32no—
442C3×C4⋊C4—32no—
443C3×C4⋊C4—32no—
444C3×C4⋊C4—32no—
445C3×C4⋊C4C22×D311yescharacteristic
446C3×C4⋊C4C22×D312yes—
447C3×C4⋊C4C22×D311yescharacteristic
448C3×C4⋊C4C22×D312yes—
449C3×C22⋊C4—32no—
450C3×C22⋊C4—34no—
451C3×C22⋊C4—32no—
452C3×C22⋊C4—32no—
453C3×C42—21no—
454C3×C42—22no—
455C3×C42—31no—
456C3×C42—32no—
457C3×C42—31no—
458C3×C42—31no—
459C3×C42C22×D311yescharacteristic
460C3×C42C22×D312yes—
461C3×C42C22×D311yescharacteristic
462C3×C42C22×D312yes—
463#217—32no—
464#217—34no—
465#217—32no—
466(C2×D3)⋊C4—32no—
467(C2×D3)⋊C4—34no—
468(C2×D3)⋊C4—32no—
469(C2×D3)⋊C4C22×D312yes—
470(C2×D3)⋊C4C22×D312yes—
471(C2×D3)⋊C4C22×D312yes—
472(C2×D3)⋊C4C22×D314yes—
473C4⋊Dic3—31no—
474C4⋊Dic3—32no—
475C4⋊Dic3—31no—
476C4⋊Dic3—32no—
477C4⋊Dic3—32no—
478C4⋊Dic3—34no—
479C4⋊Dic3—34no—
480C4⋊Dic3—32no—
481C4⋊Dic3—34no—
482C4⋊Dic3—34no—
483C4⋊Dic3—34no—
484C4⋊Dic3—34no—
485C4⋊Dic3—62no—
486C4⋊Dic3—61no—
487C4⋊Dic3—62no—
488C4⋊Dic3—64no—
489C4⋊Dic3C22×D312yes—
490C4⋊Dic3C22×D311yescharacteristic
491C4⋊Dic3C22×D311yescharacteristic
492C4⋊Dic3C22×D312yes—
493C4⋊Dic3C22×D312yes—
494Dic3⋊C4—32no—
495Dic3⋊C4—32no—
496Dic3⋊C4—34no—
497Dic3⋊C4—34no—
498Dic3⋊C4—32no—
499Dic3⋊C4—34no—
500Dic3⋊C4—34no—
501Dic3⋊C4—34no—
502Dic3⋊C4—32no—
503Dic3⋊C4—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—34no—
507Dic3⋊C4—34no—
508Dic3⋊C4—64no—
509Dic3⋊C4—62no—
510Dic3⋊C4C22×D312yes—
511Dic3⋊C4C22×D312yes—
512Dic3⋊C4C22×D312yes—
513Dic3⋊C4C22×D314yes—
514Dic3⋊C4C22×D314yes—
515Dic3⋊C4C22×D312yes—
516Dic3⋊C4C22×D312yes—
517C4×Dic3—32no—
518C4×Dic3—34no—
519C4×Dic3—34no—
520C4×Dic3—32no—
521C4×Dic3—32no—
522C4×Dic3—34no—
523C4×Dic3—32no—
524C4×Dic3—34no—
525C4×Dic3—32no—
526C4×Dic3—32no—
527C4×Dic3—62no—
528C4×Dic3—64no—
529C4×Dic3C22×D311yescharacteristic
530C4×Dic3C22×D312yes—
531C4×Dic3C22×D311yescharacteristic
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—22no—
542C32×C4—21no—
543C32×C4C22×Q812yes—
544C32×C42−1+412yes—
545C3⋊Dic3—22no—
546C3⋊Dic3—24no—
547C3⋊Dic3C22×Q814yes—
548C3×Dic3—22no—
549C3×Dic3—24no—
550C3×Dic3—22no—
551C3×Dic3—22no—
552C3×Dic3—21no—
553C3×Dic3C22×Q812yes—
554C3×Dic3H(5,𝔽2)12yes—
555C2×#41—91no—
556C22×Q8—92no—
557C22×Q8—94no—
558C4⋊Q8—31no—
559C4⋊Q8—31no—
560C4⋊Q8—31no—
561C4⋊Q8—92no—
562C4⋊Q8—92no—
563C4⋊Q8—92no—
564C4⋊Q8—92no—
565C4⋊Q8—94no—
566C4⋊Q8—92no—
567C4⋊Q8—94no—
568C4⋊Q8—94no—
569C4⋊Q8—92no—
570C4⋊Q8—94no—
571C4⋊Q8—91no—
572C4⋊Q8—92no—
573#125—32no—
574#125—32no—
575#125—92no—
576#125—94no—
577#125—94no—
578#125—94no—
579C22⋊Q8—31no—
580C22⋊Q8—32no—
581C22⋊Q8—32no—
582C22⋊Q8—31no—
583C22⋊Q8—34no—
584C22⋊Q8—94no—
585C22⋊Q8—94no—
586C22⋊Q8—94no—
587C22⋊Q8—94no—
588C22⋊Q8—94no—
589C22⋊Q8—94no—
590C22⋊Q8—92no—
591C4×Q8—32no—
592C4×Q8—31no—
593C4×Q8—91no—
594C4×Q8—92no—
595C4×Q8—94no—
596C4×Q8—92no—
597C4×Q8—92no—
598C4×Q8—91no—
599C4×Q8—92no—
600C4×Q8D3211yescharacteristic
601C4×D4—31no—
602C4×D4—32no—
603C4×D4—91no—
604C4×D4—92no—
605C4×D4—94no—
606C4×D4—92no—
607C4×D4—94no—
608C4×D4—92no—
609#117—32no—
610#117—92no—
611#117—94no—
612#117—91no—
613C2×C4⋊C4—32no—
614C2×C4⋊C4—94no—
615C2×C4⋊C4—92no—
616C2×C4⋊C4—92no—
617C2×C4⋊C4—92no—
618C2×C42—31no—
619C2×C42—92no—
620C23×C3—32no—
621C23×C3—31no—
622C22×D3C23×D312yes—
623C22×D3C23×D311yescharacteristic
624C3×Q8—24no—
625C3×Q8—22no—
626C3×Q8—22no—
627C3×Q8—64no—
628C3×Q8—62no—
629C3×Q8—122no—
630C3×D4—34no—
631C2×C3×C4—22no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—22no—
636C2×C3×C4—31no—
637C2×C3×C4—31no—
638C2×C3×C4—34no—
639C2×C3×C4—32no—
640C2×C3×C4—32no—
641C2×C3×C4—34no—
642C2×C3×C4—32no—
643C2×C3×C4—31no—
644C2×C3×C4—62no—
645C2×C3×C4—64no—
646C2×C3×C4—62no—
647C2×C3×C4—124no—
648C2×C3×C4C23×D312yes—
649C2×C3×C4C23×D312yes—
650C2×C3×C4C23×D311yescharacteristic
651C2×C3×C4C23×D312yes—
652C2×C3×C4C23×D312yes—
653C2×C3×C4C23×D311yescharacteristic
654C2×C3×C4C23×D311yescharacteristic
655C2×C3×C4C23×D311yescharacteristic
656C2×C3×C4C23×D311yescharacteristic
657C2×C3×C4C23×D311yescharacteristic
658#67—38no—
659#67—38no—
660C2×Dic3—32no—
661C2×Dic3—32no—
662C2×Dic3—38no—
663C2×Dic3—32no—
664C2×Dic3—32no—
665C2×Dic3—34no—
666C2×Dic3—34no—
667C2×Dic3—62no—
668C2×Dic3—62no—
669C2×Dic3—64no—
670C2×Dic3—64no—
671C2×Dic3—124no—
672C2×Dic3—124no—
673C2×Dic3C23×D312yes—
674C2×Dic3C23×D312yes—
675C2×Dic3C23×D314yes—
676C2×Dic3C23×D311yescharacteristic
677C2×Dic3C23×D312yes—
678C2×Dic3C23×D311yescharacteristic
679C2×Dic3C23×D311yescharacteristic
680D12D3×Q814yescomplemented
681C4×D3—22no—
682C4×D3—24no—
683C4×D3—22no—
684C4×D3—38no—
685C4×D3—44no—
686C4×D3—64no—
687C4×D3—124no—
688C4×D3—124no—
689C4×D3D3×Q814yescomplemented
690Dic6—22no—
691Dic6—24no—
692Dic6—34no—
693Dic6—34no—
694Dic6—42no—
695Dic6—64no—
696Dic6—68no—
697Dic6—68no—
698Dic6—124no—
699Dic6—124no—
700Dic6—124no—
701Dic6—122no—
702Dic6—122no—
703Dic6—124no—
704Dic6—242no—
705Dic6—244no—
706C2×C32C23×Q811yescharacteristic
707C2×C32C2×H(5,𝔽2)11yescharacteristic
708C2×C32C2×2−1+411yescharacteristic
709C3×D3—22no—
710C3×D3—24no—
711#41—98no—
712C2×Q8—31no—
713C2×Q8—32no—
714C2×Q8—32no—
715C2×Q8—94no—
716C2×Q8—94no—
717C2×Q8—91no—
718C2×Q8—94no—
719C2×Q8—92no—
720C2×Q8—364no—
721C2×Q8—368no—
722C2×Q8C2×D3211yescharacteristic
723C2×D4—31no—
724C2×D4—92no—
725C22×C4—31no—
726C22×C4—31no—
727C22×C4—31no—
728C22×C4—32no—
729C22×C4—34no—
730C22×C4—92no—
731C22×C4—92no—
732C22×C4—94no—
733C22×C4—94no—
734C4⋊C4—32no—
735C4⋊C4—34no—
736C4⋊C4—32no—
737C4⋊C4—31no—
738C4⋊C4—32no—
739C4⋊C4—32no—
740C4⋊C4—31no—
741C4⋊C4—32no—
742C4⋊C4—32no—
743C4⋊C4—32no—
744C4⋊C4—32no—
745C4⋊C4—34no—
746C4⋊C4—94no—
747C4⋊C4—94no—
748C4⋊C4—94no—
749C4⋊C4—94no—
750C4⋊C4—92no—
751C4⋊C4—94no—
752C4⋊C4—94no—
753C4⋊C4—92no—
754C4⋊C4—94no—
755C4⋊C4—92no—
756C4⋊C4—92no—
757C4⋊C4—91no—
758C4⋊C4—94no—
759C4⋊C4C2×D3211yescharacteristic
760C4⋊C4C2×D3212yes—
761C22⋊C4—32no—
762C22⋊C4—32no—
763C22⋊C4—32no—
764C22⋊C4—34no—
765C22⋊C4—92no—
766C22⋊C4—94no—
767C22⋊C4—92no—
768C42—31no—
769C42—31no—
770C42—31no—
771C42—32no—
772C42—92no—
773C42—92no—
774C42—94no—
775C42—92no—
776C42—94no—
777C42C2×D3211yescharacteristic
778C42C2×D3212yes—
779C22×C3—21no—
780C22×C3—34no—
781C22×C3—32no—
782C22×C3—62no—
783C22×C3—62no—
784C22×C3—61no—
785C22×C3—61no—
786C22×C3C24×D311yescharacteristic
787C22×C3C24×D311yescharacteristic
788C2×D3—21no—
789C2×D3—21no—
790C2×D3—22no—
791C2×D3—22no—
792C2×D3C2×D3×Q814yes—
793C2×D3C2×D3×Q812yes—
794C3×C4—24no—
795C3×C4—22no—
796C3×C4—21no—
797C3×C4—22no—
798C3×C4—22no—
799C3×C4—21no—
800C3×C4—22no—
801C3×C4—22no—
802C3×C4—22no—
803C3×C4—32no—
804C3×C4—32no—
805C3×C4—41no—
806C3×C4—42no—
807C3×C4—64no—
808C3×C4—62no—
809C3×C4—61no—
810C3×C4—62no—
811C3×C4—62no—
812C3×C4C2×D3×Q812yes—
813C3×C4C2×D3×Q812yes—
814C3×C4#101012yes—
815C3×C4#101012yes—
816Dic3—22no—
817Dic3—22no—
818Dic3—21no—
819Dic3—22no—
820Dic3—24no—
821Dic3—34no—
822Dic3—34no—
823Dic3—64no—
824Dic3—64no—
825Dic3—62no—
826Dic3—64no—
827Dic3—62no—
828Dic3—122no—
829Dic3—124no—
830Dic3C2×D3×Q812yes—
831Dic3#100912yes—
832C32#350311yescharacteristic, complemented, Sylow
833C23—31no—
834C23—32no—
835Q8—22no—
836Q8—64no—
837Q8—62no—
838Q8—94no—
839Q8—122no—
840Q8—188no—
841Q8—362no—
842Q8—364no—
843Q8—364no—
844D4—34no—
845D4—98no—
846C2×C4—31no—
847C2×C4—31no—
848C2×C4—34no—
849C2×C4—31no—
850C2×C4—32no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—34no—
854C2×C4—62no—
855C2×C4—62no—
856C2×C4—64no—
857C2×C4—98no—
858C2×C4—92no—
859C2×C4—92no—
860C2×C4—94no—
861C2×C4—124no—
862C2×C4—184no—
863C2×C4—364no—
864C2×C4—364no—
865C2×C4C22×D3211yescharacteristic
866C2×C4C22×D3212yes—
867C2×C4C22×D3212yes—
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×#100911yescharacteristic
878C2×C3C2×#101011yescharacteristic
879C2×C3C2×#101011yescharacteristic
880C2×C3D3×H(5,𝔽2)11yescharacteristic
881D3—22no—
882D3—24no—
883C22—32no—
884C22—34no—
885C22—61no—
886C22—62no—
887C22—61no—
888C22—62no—
889C22C23×D3211yescharacteristic
890C4—22no—
891C4—21no—
892C4—22no—
893C4—32no—
894C4—32no—
895C4—61no—
896C4—62no—
897C4—62no—
898C4—64no—
899C4—62no—
900C4—94no—
901C4—182no—
902C4—184no—
903C4#6429812yes—
904C4D32×Q812yes—
905C3—21no—
906C3#8628111yescharacteristic, complemented
907C3#8692611yescharacteristic, complemented
908C2—62no—
909C2—64no—
910C2C2×#6429811yescharacteristic
911C2C2×D32×Q811yescharacteristic
912C2D3×#100911yescharacteristic
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. Q8×#634C2semidirect
2. C3×#5579C2semidirect
3. C3×#5578C2semidirect
4. #10595407C2semidirect
5. #10595368C2semidirect
6. #10594532C2semidirect
7. #10594390C2semidirect
8. #10594377C2semidirect
9. D3×#888C2semidirect
10. #10593960C2semidirect
11. #10593959C2semidirect
12. Dic6×D12C2semidirect
13. D3×#869C2semidirect
16. #10593856C2semidirect
17. #10593852C2semidirect
102. #5579D3semidirect
103. #5578D3semidirect
140. #3795Q8semidirect
340. #634C2×Q8semidirect
348. C3×D12C2×Q8semidirect
353. C3×C4×D3C2×Q8semidirect
359. #625C2×Q8semidirect
363. D3×Dic3C2×Q8semidirect
680. D12D3×Q8semidirect
689. C4×D3D3×Q8semidirect
832. C32#3503semidirect
906. C3#86281semidirect
907. C3#86926semidirect

Maximal subgroups

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

subgroupindex
Q8×#6342
C3×#55792
C3×#55782
#105954072
#105953682
#105945322
#105943902
#105943772
D3×#8882
#105939602
#105939592
Dic6×D122
D3×#8692
#105938872
C4×#37952
#105938562
#105938522
#869263
#862813