Finite Group Databasebeta

← #11906360

Subgroups — #11906360

Order 1152.

2231 conjugacy classes of subgroups.

The subgroup lattice has 819 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596093C211yesmaximal, characteristic, complemented
2C3×#5635C212yesmaximal, complemented
3Q8×#627C211yesmaximal, characteristic, complemented
4#10595407C211yesmaximal, characteristic, complemented
5#10595367C212yesmaximal, complemented
6C2×#63919C211yesmaximal, characteristic, complemented
7#10594988C212yesmaximal, complemented
8C4×#3805C211yesmaximal, characteristic
9#10594597C212yesmaximal, complemented
10#10594531C211yesmaximal, characteristic, complemented
11#10594526C212yesmaximal, complemented
12#10594389C214yesmaximal, complemented
13D3×#888C212yesmaximal, complemented
14#10594313C211yesmaximal, characteristic, complemented
15#10594071C214yesmaximal, complemented
16#10594051C212yesmaximal
17#10594033C212yesmaximal, complemented
18#86926—32nomaximal
19C22×#627C2212yes—
20C2×#3805C2211yescharacteristic
21C2×D3×Dic6C2214yes—
22C32×C22⋊Q8C2211yescharacteristic
23Q8×C3⋊Dic3C2211yescharacteristic
24#64153C2211yescharacteristic
25#64133C2211yescharacteristic
26C2×C4×C3⋊Dic3C2211yescharacteristic
27#64098C2212yes—
28#64097C2211yescharacteristic
29#64096C2211yescharacteristic
30#64096C2212yes—
31#64087C2212yes—
32#64086C2212yes—
33C3×#946C2212yes—
34C3×Q8×Dic3C2212yes—
35C3×C4×#67C2212yes—
36C2×C3×C4⋊Dic3C2212yes—
37C3×#897C2214yes—
38C3×D3×C4⋊C4C2212yes—
39C3×#889C2214yes—
40C3×#888C2212yes—
41C3×#67⋊C4C2214yes—
42C3×#878C2214yes—
43#67⋊Dic3C2212yes—
44Dic3×#67C2214yes—
45C2×#3724C2212yes—
46#63964C2214yes—
47#63957C2211yescharacteristic
48#63919C2211yescharacteristic
49#63919C2212yes—
50#63919C2212yes—
51#63919C2212yes—
52#63919C2212yes—
53#63919C2211yescharacteristic
54#63918C2214yes—
55#63918C2212yes—
56C4×#627C2212yes—
57C4×#627C2211yescharacteristic
58#63902C2212yes—
59#63902C2211yescharacteristic
60C4×#625C2212yes—
61C4×#625C2211yescharacteristic
62#63899C2214yes—
63#63899C2214yes—
64#63893C2214yes—
65D3×C4⋊Dic3C2212yes—
66#63878C2212yes—
67#63877C2214yes—
68D3×Dic3⋊C4C2214yes—
69C4×D3×Dic3C2212yes—
70#63873C2212yes—
71#63870C2212yes—
72#63870C2212yes—
73#63857C2212yes—
74#63851C2214yes—
75#63847C2214yes—
76#63846C2214yes—
77#63844C2212yes—
78#63840C2214yes—
79#63839C2214yes—
80#63839C2214yes—
81#63838C2212yes—
82#63838C2211yescharacteristic
83#63837C2214yes—
84C3×#554—32no—
85D3×C4⋊Q8—32no—
86#5722—32no—
87#5689—34no—
88#5685—34no—
89#5635—32no—
90#5635D312yescomplemented
91#5632—34no—
92#5632—34no—
93#5623—34no—
94#5623—34no—
95#5622—32no—
96#5622—32no—
97#5622—61no—
98#5578—32no—
99Q8×Dic6—32no—
100#5546—34no—
101#5543—32no—
102D4×Dic6—34no—
103C4×#237—32no—
104#5511—32no—
105#5511—32no—
106C2×#888—32no—
107C2×#888—32no—
108C2×C32×Q8C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C2×#634C2312yes—
113C2×#634C2311yescharacteristic
114C2×C3×#67C2312yes—
115C22×C3×Dic3C2314yes—
116C2×C3×C4×D3C2312yes—
117C2×C3×C4×D3C2314yes—
118C2×C3×Dic6C2314yes—
119C2×#627—44no—
120C2×#627C2314yes—
121C2×#627C2314yes—
122C2×#627C2312yes—
123C2×#627C2312yes—
124C2×#627C2311yescharacteristic
125C2×#625C2311yescharacteristic
126#3805Q818yescomplemented
127C2×D3×Dic3C2312yes—
128C2×D3×Dic3C2314yes—
129C2×D3×Dic3C2312yes—
130D3×Dic6—48no—
131C32×C4⋊C4C2311yescharacteristic
132C32×C4⋊C4C2312yes—
133C32×C22⋊C4C2312yes—
134#3757C2312yes—
135C4⋊(C3⋊Dic3)C2312yes—
136C4⋊(C3⋊Dic3)C2311yescharacteristic
137#3750C2312yes—
138#3750C2312yes—
139#3750C2312yes—
140#3750C2312yes—
141#3750C2312yes—
142C4×C3⋊Dic3C2312yes—
143C4×C3⋊Dic3C2312yes—
144C4×C3⋊Dic3C2311yescharacteristic
145C4×C3⋊Dic3C2311yescharacteristic
146C4×C3⋊Dic3C2311yescharacteristic
147C4×C3⋊Dic3C2311yescharacteristic
148C3×#217C2312yes—
149C3×(C2×D3)⋊C4C2314yes—
150C3×(C2×D3)⋊C4C2312yes—
151C3×C4⋊Dic3C2314yes—
152C3×C4⋊Dic3C2312yes—
153C3×C4⋊Dic3C2314yes—
154C3×C4⋊Dic3C2312yes—
155C3×Dic3⋊C4C2314yes—
156C3×Dic3⋊C4C2314yes—
157C3×Dic3⋊C4C2314yes—
158C3×Dic3⋊C4C2312yes—
159C3×C4×Dic3C2314yes—
160C3×C4×Dic3C2312yes—
161#3724C2311yescharacteristic
162#3724C2312yes—
163#3724C2314yes—
164#3724C2314yes—
165#3724C2312yes—
166#3724C2311yescharacteristic
167Dic3⋊Dic3C2314yes—
168Dic3⋊Dic3C2312yes—
169Dic3⋊Dic3C2314yes—
170Dic3⋊Dic3C2314yes—
171(C2×D3)⋊Dic3C2312yes—
172(C2×D3)⋊Dic3C2314yes—
173Dic32C2312yes—
174Dic32C2314yes—
175Dic32C2312yes—
176#3503—91noSylow
177C2×D3×Q8—34no—
178C2×#237—32no—
179C22×Dic6—34no—
180C22×Dic6—34no—
181C3×C4⋊Q8—32no—
182C3×#125—34no—
183C3×C22⋊Q8—21no—
184C3×C22⋊Q8—32no—
185C3×C22⋊Q8—34no—
186C3×C22⋊Q8—34no—
187C3×C22⋊Q8C2×D312yes—
188C3×C4×Q8—32no—
189C3×C4×D4—32no—
190C3×C4×D4—34no—
191C2×C3×C4⋊C4—32no—
192C2×C3×C4⋊C4—32no—
193#946C2×D312yes—
194Q8×Dic3—32no—
195Q8×Dic3—61no—
196Q8×Dic3C2×D312yes—
197#944—32no—
198#944—34no—
199#944—34no—
200#944—34no—
201#944—61no—
202D4×Dic3—34no—
203D4×Dic3—32no—
204C4×#67—34no—
205C4×#67—34no—
206C4×#67—32no—
207C4×#67C2×D312yes—
208C2×C4⋊Dic3—32no—
209C2×C4⋊Dic3C2×D312yes—
210#924—32no—
211#924—34no—
212#924—32no—
213#924—34no—
214#924—61no—
215C2×Dic3⋊C4—34no—
216C2×Dic3⋊C4—34no—
217C2×C4×Dic3—32no—
218C2×C4×Dic3—32no—
219C2×C4×Dic3—61no—
220#897—32no—
221#897—34no—
222#897C2×D314yes—
223#896—34no—
224#896—34no—
225#896—34no—
226#892—32no—
227D3×C4⋊C4—32no—
228D3×C4⋊C4—34no—
229D3×C4⋊C4C2×D312yes—
230#890—34no—
231#889—34no—
232#889—34no—
233#889—34no—
234#889—34no—
235#889—34no—
236#889—34no—
237#889—62no—
238#889C2×D314yes—
239#888—34no—
240#888—34no—
241#888—32no—
242#888—34no—
243#888—34no—
244#888—32no—
245#888—34no—
246#888—32no—
247#888—32no—
248#888—32no—
249#888—34no—
250#888—34no—
251#888—34no—
252#888—32no—
253#888—61no—
254#888C2×D312yes—
255#887—34no—
256#887—32no—
257#887—32no—
258#887—34no—
259#887—34no—
260#887—32no—
261#887—62no—
262#887—61no—
263#67⋊C4—32no—
264#67⋊C4—32no—
265#67⋊C4—34no—
266#67⋊C4C2×D314yes—
267#878—34no—
268#878—34no—
269#878—34no—
270#878—34no—
271#878—34no—
272#878—62no—
273#878C2×D314yes—
274#877—34no—
275#877—32no—
276#877—32no—
277#877—34no—
278#877—62no—
279#872—34no—
280C42×D3—32no—
281#869—34no—
282#869—32no—
283C4×Dic6—32no—
284C4×Dic6—34no—
285C4×Dic6—34no—
286C4×Dic6—32no—
287C23×C32C2411yescharacteristic
288C22×C3×D3C2412yes—
289C32×Q8—22no—
290C2×C32×C4—22no—
291C2×C32×C4C2412yes—
292C2×C32×C4C2412yes—
293C2×C32×C4C2411yescharacteristic
294C2×C32×C4C2411yescharacteristic
295C2×C3⋊Dic3—22no—
296C2×C3⋊Dic3C2×Q814yescomplemented
297C2×C3⋊Dic3C2412yes—
298C2×C3⋊Dic3C2411yescharacteristic
299C2×C3⋊Dic3C2412yes—
300C2×C3⋊Dic3C2411yescharacteristic
301C2×C3⋊Dic3C2411yescharacteristic
302C2×C3⋊Dic3C2411yescharacteristic
303#634—22no—
304#634—24no—
305C3×#67C2×Q818yescomplemented
306C2×C3×Dic3—44no—
307C2×C3×Dic3C2412yes—
308C2×C3×Dic3C2412yes—
309C2×C3×Dic3C2414yes—
310C2×C3×Dic3C2414yes—
311C2×C3×Dic3C2412yes—
312C3×C4×D3—24no—
313C3×C4×D3—44no—
314C3×Dic6—44no—
315#627—28no—
316#627—44no—
317#627—42no—
318#627—42no—
319#627C2×Q814yescomplemented
320#625C2×Q814yescomplemented
321D3×Dic3—24no—
322D3×Dic3—44no—
323D3×Dic3C2×Q818yescomplemented
324Q82—91no—
325Q82—91no—
326#557—92no—
327#554—32no—
328#554—91no—
329#554—92no—
330#554—91no—
331D4×Q8—94no—
332D4×Q8—92no—
333#544—92no—
334#544—94no—
335#533—92no—
336#533—91no—
337C2×C4⋊Q8—91no—
338C2×C4⋊Q8—92no—
339#520—92no—
340C4×#41—91no—
341C2×C3×Q8—21no—
342C2×C3×Q8—34no—
343C2×C3×Q8C22×D312yes—
344C2×C3×D4—32no—
345C22×C3×C4—21no—
346C22×C3×C4—34no—
347C22×C3×C4—32no—
348C22×C3×C4—34no—
349C22×C3×C4C22×D312yes—
350C2×#67—32no—
351C2×#67C22×D312yes—
352C22×Dic3—32no—
353C22×Dic3—32no—
354C22×Dic3—32no—
355C22×Dic3—32no—
356C22×Dic3—34no—
357C22×Dic3—61no—
358C22×Dic3—61no—
359C22×Dic3C22×D314yes—
360D3×Q8—128no—
361#237—316no—
362C2×C4×D3—32no—
363C2×C4×D3—32no—
364C2×C4×D3—34no—
365C2×C4×D3C22×D312yes—
366C2×C4×D3C22×D314yes—
367C2×Dic6—32no—
368C2×Dic6—32no—
369C2×Dic6—34no—
370C2×Dic6—34no—
371C2×Dic6—34no—
372C2×Dic6—34no—
373C2×Dic6—34no—
374C2×Dic6—34no—
375C2×Dic6—34no—
376C2×Dic6—62no—
377C2×Dic6—61no—
378C2×Dic6—128no—
379C2×Dic6—128no—
380C2×Dic6C22×D314yes—
381C3×C4⋊C4—21no—
382C3×C4⋊C4—22no—
383C3×C4⋊C4—34no—
384C3×C4⋊C4—32no—
385C3×C4⋊C4—34no—
386C3×C4⋊C4—32no—
387C3×C4⋊C4—32no—
388C3×C4⋊C4—34no—
389C3×C4⋊C4—34no—
390C3×C4⋊C4—34no—
391C3×C4⋊C4C22×D312yes—
392C3×C4⋊C4C22×D314yes—
393C3×C22⋊C4—22no—
394C3×C22⋊C4—32no—
395C3×C22⋊C4—32no—
396C3×C22⋊C4—34no—
397C3×C22⋊C4C22×D314yes—
398C3×C42—32no—
399C3×C42—34no—
400#217—34no—
401#217—34no—
402#217—32no—
403#217—62no—
404#217C22×D312yes—
405(C2×D3)⋊C4—34no—
406(C2×D3)⋊C4—32no—
407(C2×D3)⋊C4C22×D314yes—
408(C2×D3)⋊C4C22×D312yes—
409C4⋊Dic3—34no—
410C4⋊Dic3—32no—
411C4⋊Dic3—32no—
412C4⋊Dic3—34no—
413C4⋊Dic3—34no—
414C4⋊Dic3—34no—
415C4⋊Dic3—62no—
416C4⋊Dic3—61no—
417C4⋊Dic3C22×D312yes—
418C4⋊Dic3C22×D314yes—
419C4⋊Dic3C22×D312yes—
420C4⋊Dic3C22×D314yes—
421Dic3⋊C4—34no—
422Dic3⋊C4—34no—
423Dic3⋊C4—34no—
424Dic3⋊C4—34no—
425Dic3⋊C4—34no—
426Dic3⋊C4—32no—
427Dic3⋊C4—32no—
428Dic3⋊C4—34no—
429Dic3⋊C4—34no—
430Dic3⋊C4—34no—
431Dic3⋊C4—34no—
432Dic3⋊C4—32no—
433Dic3⋊C4—34no—
434Dic3⋊C4—34no—
435Dic3⋊C4—34no—
436Dic3⋊C4—34no—
437Dic3⋊C4—34no—
438Dic3⋊C4—62no—
439Dic3⋊C4—62no—
440Dic3⋊C4—62no—
441Dic3⋊C4—62no—
442Dic3⋊C4—62no—
443Dic3⋊C4C22×D314yes—
444Dic3⋊C4C22×D312yes—
445Dic3⋊C4C22×D314yes—
446Dic3⋊C4C22×D314yes—
447C4×Dic3—34no—
448C4×Dic3—32no—
449C4×Dic3—32no—
450C4×Dic3—34no—
451C4×Dic3—32no—
452C4×Dic3—32no—
453C4×Dic3—32no—
454C4×Dic3—34no—
455C4×Dic3—32no—
456C4×Dic3—34no—
457C4×Dic3—32no—
458C4×Dic3—32no—
459C4×Dic3—62no—
460C4×Dic3—62no—
461C4×Dic3—61no—
462C4×Dic3—61no—
463C4×Dic3—61no—
464C4×Dic3—61no—
465C4×Dic3C22×D314yes—
466C4×Dic3C22×D312yes—
467C22×C32—21no—
468C22×C32—21no—
469C22×C32C22×Q812yes—
470C22×C32C2511yescharacteristic
471C2×C3×D3—22no—
472C2×C3×D3—22no—
473C2×C3×D3C22×Q814yes—
474C32×C4—22no—
475C32×C4—21no—
476C32×C4—22no—
477C32×C42−1+412yes—
478C3⋊Dic3—22no—
479C3⋊Dic3—21no—
480C3⋊Dic3—22no—
481C3⋊Dic3C22×Q812yes—
482C3⋊Dic3C22×Q812yes—
483C3⋊Dic3H(5,𝔽2)12yes—
484C3×Dic3—22no—
485C3×Dic3—24no—
486C3×Dic3—24no—
487C3×Dic3—22no—
488C3×Dic3C22×Q814yes—
489C2×#41—91no—
490C22×Q8—92no—
491C22×Q8—94no—
492C4⋊Q8—32no—
493C4⋊Q8—92no—
494C4⋊Q8—94no—
495C4⋊Q8—92no—
496C4⋊Q8—92no—
497C4⋊Q8—94no—
498C4⋊Q8—92no—
499C4⋊Q8—91no—
500C4⋊Q8—91no—
501C4⋊Q8—92no—
502C4⋊Q8—94no—
503C4⋊Q8—94no—
504C4⋊Q8—92no—
505C4⋊Q8—91no—
506C4⋊Q8—91no—
507#125—34no—
508#125—94no—
509#125—92no—
510#125—92no—
511#125—94no—
512#125—92no—
513C22⋊Q8—32no—
514C22⋊Q8—34no—
515C22⋊Q8—34no—
516C22⋊Q8—94no—
517C22⋊Q8—94no—
518C22⋊Q8—94no—
519C22⋊Q8—94no—
520C22⋊Q8—92no—
521C22⋊Q8—94no—
522C22⋊Q8—91no—
523C22⋊Q8—92no—
524C22⋊Q8D3211yescharacteristic
525C4×Q8—32no—
526C4×Q8—91no—
527C4×Q8—92no—
528C4×Q8—94no—
529C4×Q8—92no—
530C4×Q8—91no—
531C4×Q8—92no—
532C4×Q8—91no—
533C4×Q8—92no—
534C4×Q8—91no—
535C4×D4—32no—
536C4×D4—34no—
537C4×D4—91no—
538C4×D4—92no—
539C4×D4—92no—
540C4×D4—91no—
541C4×D4—92no—
542C4×D4—94no—
543#117—94no—
544#117—91no—
545#117—92no—
546#117—92no—
547C2×C4⋊C4—32no—
548C2×C4⋊C4—32no—
549C2×C4⋊C4—94no—
550C2×C4⋊C4—92no—
551C2×C4⋊C4—92no—
552C2×C42—92no—
553C2×C42—91no—
554C23×C3—21no—
555C23×C3—32no—
556C23×C3C23×D312yes—
557C22×D3C23×D312yes—
558C3×Q8—24no—
559C3×Q8—42no—
560C3×Q8—124no—
561C3×D4—38no—
562C2×C3×C4—24no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—32no—
568C2×C3×C4—32no—
569C2×C3×C4—32no—
570C2×C3×C4—34no—
571C2×C3×C4—34no—
572C2×C3×C4—42no—
573C2×C3×C4—64no—
574C2×C3×C4—124no—
575C2×C3×C4—124no—
576C2×C3×C4C23×D312yes—
577C2×C3×C4C23×D314yes—
578C2×C3×C4C23×D314yes—
579C2×C3×C4C23×D312yes—
580#67—38no—
581#67D3×Q818yescomplemented
582C2×Dic3—38no—
583C2×Dic3—32no—
584C2×Dic3—32no—
585C2×Dic3—32no—
586C2×Dic3—38no—
587C2×Dic3—34no—
588C2×Dic3—32no—
589C2×Dic3—34no—
590C2×Dic3—44no—
591C2×Dic3—64no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—62no—
597C2×Dic3—62no—
598C2×Dic3—64no—
599C2×Dic3—64no—
600C2×Dic3—122no—
601C2×Dic3—124no—
602C2×Dic3C23×D312yes—
603C2×Dic3C23×D312yes—
604C2×Dic3C23×D314yes—
605C2×Dic3C23×D314yes—
606C2×Dic3C23×D312yes—
607C4×D3—24no—
608C4×D3—38no—
609C4×D3—44no—
610C4×D3—64no—
611C4×D3—124no—
612Dic6—38no—
613Dic6—44no—
614Dic6—68no—
615Dic6—68no—
616Dic6—68no—
617Dic6—64no—
618Dic6—124no—
619Dic6—122no—
620Dic6—124no—
621Dic6—124no—
622Dic6—124no—
623Dic6—124no—
624C2×C32—22no—
625C2×C32C23×Q811yescharacteristic
626C2×C32C2×H(5,𝔽2)11yescharacteristic
627C2×C32C2×2−1+411yescharacteristic
628C3×D3—24no—
629#41—98no—
630C2×Q8—34no—
631C2×Q8—91no—
632C2×Q8—94no—
633C2×Q8—94no—
634C2×Q8—92no—
635C2×Q8—92no—
636C2×Q8—91no—
637C2×Q8—92no—
638C2×Q8—364no—
639C2×Q8—368no—
640C2×Q8C2×D3211yescharacteristic
641C2×D4—32no—
642C2×D4—91no—
643C22×C4—34no—
644C22×C4—32no—
645C22×C4—34no—
646C22×C4—92no—
647C22×C4—92no—
648C22×C4—94no—
649C22×C4—91no—
650C22×C4—91no—
651C22×C4C2×D3211yescharacteristic
652C4⋊C4—32no—
653C4⋊C4—32no—
654C4⋊C4—34no—
655C4⋊C4—34no—
656C4⋊C4—34no—
657C4⋊C4—32no—
658C4⋊C4—34no—
659C4⋊C4—34no—
660C4⋊C4—94no—
661C4⋊C4—92no—
662C4⋊C4—92no—
663C4⋊C4—94no—
664C4⋊C4—94no—
665C4⋊C4—91no—
666C4⋊C4—91no—
667C4⋊C4—92no—
668C4⋊C4—94no—
669C4⋊C4—94no—
670C4⋊C4—92no—
671C4⋊C4—91no—
672C4⋊C4—92no—
673C4⋊C4—92no—
674C4⋊C4—92no—
675C4⋊C4—92no—
676C4⋊C4—92no—
677C4⋊C4C2×D3211yescharacteristic
678C4⋊C4C2×D3212yes—
679C22⋊C4—32no—
680C22⋊C4—32no—
681C22⋊C4—34no—
682C22⋊C4—94no—
683C22⋊C4—92no—
684C22⋊C4—92no—
685C22⋊C4C2×D3212yes—
686C42—32no—
687C42—34no—
688C42—92no—
689C42—92no—
690C42—94no—
691C42—91no—
692C42—91no—
693C42—91no—
694C42—91no—
695C42—92no—
696C42—92no—
697C22×C3—22no—
698C22×C3—22no—
699C22×C3—22no—
700C22×C3—21no—
701C22×C3—34no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—62no—
705C22×C3—62no—
706C22×C3C2×D3×Q814yes—
707C22×C3C24×D312yes—
708C2×D3—22no—
709C2×D3—22no—
710C2×D3C2×D3×Q814yes—
711C3×C4—22no—
712C3×C4—24no—
713C3×C4—24no—
714C3×C4—22no—
715C3×C4—34no—
716C3×C4—42no—
717C3×C4—41no—
718C3×C4—42no—
719C3×C4—62no—
720C3×C4—64no—
721C3×C4—64no—
722C3×C4—62no—
723C3×C4#101014yes—
724Dic3—22no—
725Dic3—22no—
726Dic3—24no—
727Dic3—24no—
728Dic3—34no—
729Dic3—34no—
730Dic3—34no—
731Dic3—62no—
732Dic3—62no—
733Dic3—62no—
734Dic3—64no—
735Dic3—64no—
736Dic3—62no—
737Dic3—122no—
738Dic3—122no—
739Dic3—121no—
740Dic3C2×D3×Q814yes—
741C32#350311yescharacteristic, complemented, Sylow
742C23—32no—
743C23C22×D3211yescharacteristic
744Q8—22no—
745Q8—94no—
746Q8—124no—
747Q8—184no—
748Q8—188no—
749Q8—182no—
750Q8—362no—
751Q8—364no—
752Q8—362no—
753D4—38no—
754D4—94no—
755C2×C4—22no—
756C2×C4—32no—
757C2×C4—32no—
758C2×C4—34no—
759C2×C4—32no—
760C2×C4—34no—
761C2×C4—64no—
762C2×C4—98no—
763C2×C4—94no—
764C2×C4—91no—
765C2×C4—91no—
766C2×C4—91no—
767C2×C4—92no—
768C2×C4—91no—
769C2×C4—92no—
770C2×C4—124no—
771C2×C4—124no—
772C2×C4—184no—
773C2×C4—182no—
774C2×C4—364no—
775C2×C4C22×D3212yes—
776C2×C4C22×D3211yescharacteristic
777C2×C4C22×D3212yes—
778C2×C4C22×D3211yescharacteristic
779C2×C3—24no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—42no—
784C2×C3—64no—
785C2×C3C22×D3×Q812yes—
786C2×C3C2×#101012yes—
787C2×C3D3×H(5,𝔽2)12yes—
788D3—24no—
789C22—21no—
790C22—21no—
791C22—34no—
792C22—62no—
793C22—62no—
794C22D32×Q812yes—
795C22C23×D3211yescharacteristic
796C4—21no—
797C4—22no—
798C4—22no—
799C4—34no—
800C4—62no—
801C4—64no—
802C4—64no—
803C4—62no—
804C4—92no—
805C4—92no—
806C4—92no—
807C4—182no—
808C4—181no—
809C4—182no—
810C4#6430912yes—
811C3—21no—
812C3#8692612yescomplemented
813C2—22no—
814C2—64no—
815C2C2×#6430911yescharacteristic
816C2C2×D32×Q811yescharacteristic
817C2#1059669211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C22⋊Q8C22
prime radicalC2×#3805C22
hypercenterC22⋊Q8D32
hypocenterC32#3503
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596093C2semidirect
2. C3×#5635C2semidirect
3. Q8×#627C2semidirect
4. #10595407C2semidirect
5. #10595367C2semidirect
6. C2×#63919C2semidirect
7. #10594988C2semidirect
9. #10594597C2semidirect
10. #10594531C2semidirect
11. #10594526C2semidirect
12. #10594389C2semidirect
13. D3×#888C2semidirect
14. #10594313C2semidirect
15. #10594071C2semidirect
17. #10594033C2semidirect
90. #5635D3semidirect
126. #3805Q8semidirect
296. C2×C3⋊Dic3C2×Q8semidirect
305. C3×#67C2×Q8semidirect
319. #627C2×Q8semidirect
320. #625C2×Q8semidirect
323. D3×Dic3C2×Q8semidirect
581. #67D3×Q8semidirect
741. C32#3503semidirect
812. C3#86926semidirect

Maximal subgroups

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

subgroupindex
#105960932
C3×#56352
Q8×#6272
#105954072
#105953672
C2×#639192
#105949882
C4×#38052
#105945972
#105945312
#105945262
#105943892
D3×#8882
#105943132
#105940712
#105940512
#105940332
#869263