Finite Group Databasebeta

← #11903759

Subgroups — #11903759

Order 1152.

2285 conjugacy classes of subgroups.

The subgroup lattice has 821 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64096C211yesmaximal, characteristic, complemented
2C3×#5511C212yesmaximal, complemented
3#10594959C214yesmaximal, complemented
4#10594915C212yesmaximal, complemented
5C4×#3805C211yesmaximal, characteristic
6C4×#3805C212yesmaximal
7#10594810C211yesmaximal, characteristic, complemented
8#10594810C212yesmaximal, complemented
9#10594597C212yesmaximal, complemented
10#10594595C211yesmaximal, characteristic, complemented
11#10594534C212yesmaximal, complemented
12#10594531C211yesmaximal, characteristic, complemented
13#10594526C211yesmaximal, characteristic, complemented
14#10594388C214yesmaximal, complemented
15#10594387C212yesmaximal, complemented
16D3×#887C212yesmaximal, complemented
17#10594313C211yesmaximal, characteristic, complemented
18#86923—32nomaximal
19C22×#634C2211yescharacteristic
20C2×#3805C2211yescharacteristic
21C2×D3×Dic6C2212yes—
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×#3750C2212yes—
24C2×C4×C3⋊Dic3C2212yes—
25C2×C4×C3⋊Dic3C2211yescharacteristic
26#64096C2211yescharacteristic
27#64096C2211yescharacteristic
28#64096C2212yes—
29#64096C2211yescharacteristic
30#64096C2211yescharacteristic
31#64096C2212yes—
32C3×C4×#67C2212yes—
33C3×C4×#67C2214yes—
34C3×#924C2212yes—
35C3×#924C2214yes—
36C3×#897C2212yes—
37C3×#896C2214yes—
38C3×D3×C4⋊C4C2212yes—
39C3×#889C2214yes—
40C3×#888C2212yes—
41C3×#887C2212yes—
42#63982C2214yes—
43#63982C2212yes—
44#67⋊Dic3C2214yes—
45#67⋊Dic3C2212yes—
46#63957C2212yes—
47#63957C2211yescharacteristic
48#63919C2211yescharacteristic
49#63919C2212yes—
50C4×#627C2211yescharacteristic
51C4×#627C2212yes—
52#63902C2212yes—
53#63902C2211yescharacteristic
54C4×#625C2211yescharacteristic
55C4×#625C2212yes—
56#63899C2214yes—
57#63896C2214yes—
58#63887C2214yes—
59#63878C2214yes—
60#63878C2212yes—
61D3×Dic3⋊C4C2214yes—
62C4×D3×Dic3C2212yes—
63C4×D3×Dic3C2214yes—
64#63873C2212yes—
65#63873C2211yescharacteristic
66#63870C2212yes—
67#63870C2212yes—
68#63870C2212yes—
69#63867C2214yes—
70#63866C2212yes—
71#63857C2212yes—
72#63851C2214yes—
73#63846C2214yes—
74#63844C2212yes—
75#63843C2212yes—
76#63843C2214yes—
77#63840C2214yes—
78#63839C2214yes—
79#63838C2212yes—
80#63838C2211yescharacteristic
81#63838C2214yes—
82#63838C2212yes—
83#63837C2214yes—
84C3×#554—32no—
85#5728—32no—
86#5722—32no—
87#5688—34no—
88#5685—34no—
89#5636—34no—
90#5636—34no—
91#5632—32no—
92#5632—32no—
93#5622—34no—
94#5622—32no—
95#5622—34no—
96#5622—32no—
97C4×D3×Q8—32no—
98#5567—32no—
99#5539—34no—
100D4×Dic6—32no—
101C4×#237—34no—
102C4×#237—32no—
103#5511—32no—
104#5511D312yescomplemented
105C2×#887—32no—
106C2×#887—32no—
107C2×#887—61no—
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2312yes—
110C22×C3⋊Dic3C2312yes—
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C2×#634—24no—
114C2×#634C2312yes—
115C2×#634C2311yescharacteristic
116C2×#634C2311yescharacteristic
117C2×C3×#67C2312yes—
118C2×C3×C4×D3C2312yes—
119C2×C3×C4×D3C2314yes—
120C2×C3×Dic6C2312yes—
121C2×C3×Dic6C2314yes—
122C2×#627C2314yes—
123C2×#627C2312yes—
124C2×#627C2311yescharacteristic
125C2×#625C2311yescharacteristic
126#3805Q818yescomplemented
127C2×D3×Dic3C2314yes—
128C2×D3×Dic3C2312yes—
129C2×D3×Dic3C2312yes—
130D3×Dic6—28no—
131C32×C4⋊C4C2311yescharacteristic
132C32×C4⋊C4C2311yescharacteristic
133C32×C4⋊C4C2312yes—
134#3750C2312yes—
135#3750C2312yes—
136#3750C2312yes—
137#3750C2312yes—
138C4×C3⋊Dic3C2312yes—
139C4×C3⋊Dic3C2311yescharacteristic
140C4×C3⋊Dic3C2311yescharacteristic
141C4×C3⋊Dic3C2312yes—
142C4×C3⋊Dic3C2311yescharacteristic
143C4×C3⋊Dic3C2312yes—
144C4×C3⋊Dic3C2312yes—
145C4×C3⋊Dic3C2311yescharacteristic
146C3×#217C2314yes—
147C3×#217C2312yes—
148C3×(C2×D3)⋊C4C2312yes—
149C3×(C2×D3)⋊C4C2314yes—
150C3×C4⋊Dic3C2312yes—
151C3×C4⋊Dic3C2314yes—
152C3×Dic3⋊C4C2314yes—
153C3×Dic3⋊C4C2314yes—
154C3×Dic3⋊C4C2312yes—
155C3×Dic3⋊C4C2314yes—
156C3×Dic3⋊C4C2314yes—
157C3×C4×Dic3C2312yes—
158C3×C4×Dic3C2314yes—
159#3724C2314yes—
160#3724C2312yes—
161#3724C2312yes—
162#3724C2311yescharacteristic
163#3724C2311yescharacteristic
164#3724C2312yes—
165Dic3⋊Dic3C2314yes—
166Dic3⋊Dic3C2312yes—
167Dic3⋊Dic3C2314yes—
168Dic3⋊Dic3C2314yes—
169Dic3⋊Dic3C2314yes—
170(C2×D3)⋊Dic3C2312yes—
171(C2×D3)⋊Dic3C2314yes—
172Dic32C2312yes—
173Dic32C2314yes—
174Dic32C2314yes—
175Dic32C2312yes—
176Q8×#41—91noSylow
177C2×D3×Q8—32no—
178C2×#237—32no—
179C22×Dic6—32no—
180C22×Dic6—32no—
181C22×Dic6—61no—
182C3×C4⋊Q8—32no—
183C3×#125—34no—
184C3×C22⋊Q8—32no—
185C3×C22⋊Q8—34no—
186C3×C22⋊Q8—32no—
187C3×C22⋊Q8—34no—
188C3×C4×Q8—32no—
189C3×C4×D4—32no—
190C3×C4×D4—34no—
191C2×C3×C4⋊C4—21no—
192C2×C3×C4⋊C4—32no—
193C2×C3×C4⋊C4C2×D312yes—
194#946—34no—
195Q8×Dic3—34no—
196Q8×Dic3—32no—
197#944—32no—
198#944—34no—
199#944—34no—
200#944—32no—
201D4×Dic3—34no—
202D4×Dic3—32no—
203C4×#67—32no—
204C4×#67—34no—
205C4×#67C2×D312yes—
206C4×#67C2×D314yes—
207#924—32no—
208#924—34no—
209#924C2×D312yes—
210#924C2×D314yes—
211C2×Dic3⋊C4—34no—
212C2×Dic3⋊C4—34no—
213C2×Dic3⋊C4—62no—
214C2×C4×Dic3—32no—
215C2×C4×Dic3—34no—
216C2×C4×Dic3—34no—
217C2×C4×Dic3—32no—
218C2×C4×Dic3—62no—
219C2×C4×Dic3—61no—
220#897—32no—
221#897C2×D312yes—
222#896—34no—
223#896—34no—
224#896—34no—
225#896C2×D314yes—
226#892—32no—
227#892—34no—
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#889C2×D314yes—
237#888—34no—
238#888—34no—
239#888—32no—
240#888—34no—
241#888—34no—
242#888C2×D312yes—
243#887—34no—
244#887—32no—
245#887—32no—
246#887—34no—
247#887—34no—
248#887—32no—
249#887—32no—
250#887—32no—
251#887—32no—
252#887—34no—
253#887—34no—
254#887—34no—
255#887—34no—
256#887—32no—
257#887—34no—
258#887—61no—
259#887—61no—
260#887—62no—
261#887—61no—
262#887—61no—
263#887—62no—
264#887C2×D312yes—
265#67⋊C4—34no—
266#67⋊C4—32no—
267#67⋊C4—34no—
268#67⋊C4—32no—
269#878—34no—
270#878—34no—
271#878—34no—
272#878—34no—
273#878—34no—
274#878—34no—
275#877—34no—
276#877—32no—
277#877—32no—
278#877—34no—
279C42×D3—34no—
280C42×D3—32no—
281#870—34no—
282#869—32no—
283C4×Dic6—32no—
284C4×Dic6—34no—
285C4×Dic6—34no—
286C4×Dic6—32no—
287C23×C32C2411yescharacteristic
288C22×C3×D3C2412yes—
289C2×C32×C4—22no—
290C2×C32×C4—42no—
291C2×C32×C4C2412yes—
292C2×C32×C4C2411yescharacteristic
293C2×C32×C4C2412yes—
294C2×C32×C4C2411yescharacteristic
295C2×C3⋊Dic3—24no—
296C2×C3⋊Dic3—41no—
297C2×C3⋊Dic3C2×Q814yescomplemented
298C2×C3⋊Dic3C2411yescharacteristic
299C2×C3⋊Dic3C2412yes—
300C2×C3⋊Dic3C2411yescharacteristic
301C2×C3⋊Dic3C2411yescharacteristic
302C2×C3⋊Dic3C2411yescharacteristic
303C2×C3⋊Dic3C2412yes—
304#634—22no—
305#634—24no—
306#634#4114yescomplemented
307C3×#67C2×Q818yescomplemented
308C2×C3×Dic3C2414yes—
309C2×C3×Dic3C2412yes—
310C2×C3×Dic3C2412yes—
311C2×C3×Dic3C2414yes—
312C2×C3×Dic3C2412yes—
313C3×C4×D3—24no—
314C3×C4×D3—44no—
315C3×Dic6—24no—
316C3×Dic6—44no—
317#627—28no—
318#627—42no—
319#627C2×Q814yescomplemented
320#625C2×Q814yescomplemented
321D3×Dic3—28no—
322D3×Dic3—42no—
323D3×Dic3C2×Q818yescomplemented
324Q82—91no—
325#557—91no—
326#557—92no—
327#554—32no—
328#554—91no—
329#554—94no—
330#554—92no—
331D4×Q8—92no—
332D4×Q8—91no—
333#533—92no—
334#533—91no—
335#533—94no—
336#533—92no—
337C4×#41—91no—
338C4×#41—92no—
339C2×C4×Q8—92no—
340C2×C4×Q8—91no—
341C2×C3×Q8—32no—
342C2×C3×Q8—34no—
343C2×C3×D4—32no—
344C22×C3×C4—21no—
345C22×C3×C4—22no—
346C22×C3×C4—32no—
347C22×C3×C4—34no—
348C22×C3×C4C22×D312yes—
349C22×C3×C4C22×D314yes—
350C2×#67—32no—
351C2×#67C22×D312yes—
352C22×Dic3—32no—
353C22×Dic3—32no—
354C22×Dic3—34no—
355C22×Dic3—32no—
356C22×Dic3—34no—
357C22×Dic3—32no—
358C22×Dic3—61no—
359C22×Dic3—62no—
360C22×Dic3—61no—
361D3×Q8—68no—
362#237—316no—
363C2×C4×D3—32no—
364C2×C4×D3—34no—
365C2×C4×D3—32no—
366C2×C4×D3C22×D312yes—
367C2×C4×D3C22×D314yes—
368C2×Dic6—32no—
369C2×Dic6—32no—
370C2×Dic6—32no—
371C2×Dic6—34no—
372C2×Dic6—34no—
373C2×Dic6—34no—
374C2×Dic6—34no—
375C2×Dic6—61no—
376C2×Dic6—62no—
377C2×Dic6—61no—
378C2×Dic6—68no—
379C2×Dic6—68no—
380C2×Dic6—68no—
381C2×Dic6C22×D312yes—
382C2×Dic6C22×D314yes—
383C3×C4⋊C4—21no—
384C3×C4⋊C4—22no—
385C3×C4⋊C4—21no—
386C3×C4⋊C4—32no—
387C3×C4⋊C4—34no—
388C3×C4⋊C4—32no—
389C3×C4⋊C4—34no—
390C3×C4⋊C4—34no—
391C3×C4⋊C4—34no—
392C3×C4⋊C4—34no—
393C3×C4⋊C4C22×D312yes—
394C3×C4⋊C4C22×D312yes—
395C3×C4⋊C4C22×D314yes—
396C3×C22⋊C4—34no—
397C3×C22⋊C4—32no—
398C3×C22⋊C4—32no—
399C3×C22⋊C4—34no—
400C3×C42—32no—
401C3×C42—34no—
402#217—32no—
403#217—34no—
404#217C22×D314yes—
405#217C22×D312yes—
406(C2×D3)⋊C4—32no—
407(C2×D3)⋊C4—34no—
408(C2×D3)⋊C4C22×D312yes—
409(C2×D3)⋊C4C22×D314yes—
410C4⋊Dic3—34no—
411C4⋊Dic3—32no—
412C4⋊Dic3—34no—
413C4⋊Dic3—34no—
414C4⋊Dic3—34no—
415C4⋊Dic3C22×D312yes—
416C4⋊Dic3C22×D314yes—
417Dic3⋊C4—34no—
418Dic3⋊C4—34no—
419Dic3⋊C4—34no—
420Dic3⋊C4—34no—
421Dic3⋊C4—34no—
422Dic3⋊C4—34no—
423Dic3⋊C4—32no—
424Dic3⋊C4—32no—
425Dic3⋊C4—34no—
426Dic3⋊C4—34no—
427Dic3⋊C4—34no—
428Dic3⋊C4—32no—
429Dic3⋊C4—34no—
430Dic3⋊C4—34no—
431Dic3⋊C4—34no—
432Dic3⋊C4—34no—
433Dic3⋊C4—62no—
434Dic3⋊C4—62no—
435Dic3⋊C4—62no—
436Dic3⋊C4—62no—
437Dic3⋊C4C22×D314yes—
438Dic3⋊C4C22×D314yes—
439Dic3⋊C4C22×D312yes—
440Dic3⋊C4C22×D314yes—
441Dic3⋊C4C22×D314yes—
442C4×Dic3—32no—
443C4×Dic3—34no—
444C4×Dic3—34no—
445C4×Dic3—32no—
446C4×Dic3—32no—
447C4×Dic3—34no—
448C4×Dic3—34no—
449C4×Dic3—32no—
450C4×Dic3—34no—
451C4×Dic3—32no—
452C4×Dic3—34no—
453C4×Dic3—32no—
454C4×Dic3—32no—
455C4×Dic3—34no—
456C4×Dic3—34no—
457C4×Dic3—32no—
458C4×Dic3—62no—
459C4×Dic3—61no—
460C4×Dic3—62no—
461C4×Dic3—61no—
462C4×Dic3—62no—
463C4×Dic3—61no—
464C4×Dic3—62no—
465C4×Dic3—61no—
466C4×Dic3C22×D312yes—
467C4×Dic3C22×D314yes—
468C22×C32—21no—
469C22×C32—21no—
470C22×C32C22×Q812yes—
471C22×C32C2511yescharacteristic
472C2×C3×D3—22no—
473C2×C3×D3—22no—
474C2×C3×D3C22×Q814yes—
475C32×C4—21no—
476C32×C4—22no—
477C32×C4—22no—
478C32×C4C2×#4112yes—
479C3⋊Dic3—22no—
480C3⋊Dic3—21no—
481C3⋊Dic3—21no—
482C3⋊Dic3C22×Q812yes—
483C3⋊Dic3C22×Q812yes—
484C3⋊Dic3C2×#4114yes—
485C3×Dic3—24no—
486C3×Dic3—22no—
487C3×Dic3—22no—
488C3×Dic3—24no—
489C3×Dic3C22×Q814yes—
490C2×#41—91no—
491C22×Q8—92no—
492C22×Q8—91no—
493C4⋊Q8—32no—
494C4⋊Q8—92no—
495C4⋊Q8—94no—
496C4⋊Q8—92no—
497C4⋊Q8—91no—
498C4⋊Q8—94no—
499C4⋊Q8—91no—
500C4⋊Q8—92no—
501#125—34no—
502#125—94no—
503#125—92no—
504#125—92no—
505#125—92no—
506#125—94no—
507C22⋊Q8—32no—
508C22⋊Q8—34no—
509C22⋊Q8—32no—
510C22⋊Q8—34no—
511C22⋊Q8—94no—
512C22⋊Q8—92no—
513C22⋊Q8—94no—
514C22⋊Q8—94no—
515C22⋊Q8—94no—
516C22⋊Q8—92no—
517C22⋊Q8—94no—
518C4×Q8—32no—
519C4×Q8—92no—
520C4×Q8—91no—
521C4×Q8—92no—
522C4×Q8—94no—
523C4×Q8—94no—
524C4×Q8—91no—
525C4×Q8—92no—
526C4×Q8—92no—
527C4×Q8—92no—
528C4×Q8—94no—
529C4×Q8—91no—
530C4×Q8—91no—
531C4×Q8—92no—
532C4×Q8—91no—
533C4×Q8—92no—
534C4×Q8—91no—
535C4×D4—32no—
536C4×D4—34no—
537C4×D4—92no—
538C4×D4—91no—
539C4×D4—94no—
540C4×D4—92no—
541C4×D4—91no—
542C4×D4—92no—
543#117—92no—
544#117—91no—
545#117—92no—
546#117—94no—
547C2×C4⋊C4—32no—
548C2×C4⋊C4—94no—
549C2×C4⋊C4—92no—
550C2×C4⋊C4D3211yescharacteristic
551C2×C42—94no—
552C2×C42—92no—
553C2×C42—92no—
554C2×C42—91no—
555C23×C3—21no—
556C23×C3—32no—
557C23×C3C23×D312yes—
558C22×D3C23×D312yes—
559C3×Q8—64no—
560C3×Q8—124no—
561C3×D4—38no—
562C2×C3×C4—24no—
563C2×C3×C4—24no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—32no—
569C2×C3×C4—34no—
570C2×C3×C4—32no—
571C2×C3×C4—32no—
572C2×C3×C4—34no—
573C2×C3×C4—44no—
574C2×C3×C4—44no—
575C2×C3×C4—64no—
576C2×C3×C4—124no—
577C2×C3×C4C23×D314yes—
578C2×C3×C4C23×D314yes—
579C2×C3×C4C23×D312yes—
580C2×C3×C4C23×D312yes—
581#67—38no—
582#67D3×Q818yescomplemented
583C2×Dic3—38no—
584C2×Dic3—32no—
585C2×Dic3—32no—
586C2×Dic3—34no—
587C2×Dic3—38no—
588C2×Dic3—32no—
589C2×Dic3—32no—
590C2×Dic3—34no—
591C2×Dic3—64no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—62no—
595C2×Dic3—62no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—68no—
599C2×Dic3—68no—
600C2×Dic3—68no—
601C2×Dic3—122no—
602C2×Dic3—122no—
603C2×Dic3—122no—
604C2×Dic3C23×D314yes—
605C2×Dic3C23×D312yes—
606C2×Dic3C23×D312yes—
607C2×Dic3C23×D314yes—
608C2×Dic3C23×D312yes—
609C4×D3—24no—
610C4×D3—38no—
611C4×D3—44no—
612C4×D3—68no—
613C4×D3—122no—
614Dic6—24no—
615Dic6—38no—
616Dic6—38no—
617Dic6—44no—
618Dic6—64no—
619Dic6—68no—
620Dic6—68no—
621Dic6—68no—
622Dic6—68no—
623Dic6—64no—
624Dic6—64no—
625Dic6—124no—
626C2×C32—22no—
627C2×C32C23×Q811yescharacteristic
628C2×C32C22×#4111yescharacteristic
629C2×C32#58511yescharacteristic
630C3×D3—24no—
631#41—98no—
632C2×Q8—32no—
633C2×Q8—34no—
634C2×Q8—91no—
635C2×Q8—94no—
636C2×Q8—92no—
637C2×Q8—91no—
638C2×Q8—92no—
639C2×Q8—91no—
640C2×Q8—184no—
641C2×Q8—188no—
642C2×D4—32no—
643C2×D4—91no—
644C22×C4—32no—
645C22×C4—34no—
646C22×C4—92no—
647C22×C4—94no—
648C22×C4—92no—
649C22×C4—91no—
650C22×C4—92no—
651C22×C4—91no—
652C22×C4C2×D3211yescharacteristic
653C22×C4C2×D3212yes—
654C4⋊C4—34no—
655C4⋊C4—32no—
656C4⋊C4—34no—
657C4⋊C4—32no—
658C4⋊C4—34no—
659C4⋊C4—34no—
660C4⋊C4—34no—
661C4⋊C4—94no—
662C4⋊C4—94no—
663C4⋊C4—92no—
664C4⋊C4—91no—
665C4⋊C4—91no—
666C4⋊C4—92no—
667C4⋊C4—94no—
668C4⋊C4—92no—
669C4⋊C4—92no—
670C4⋊C4—94no—
671C4⋊C4—94no—
672C4⋊C4—92no—
673C4⋊C4—92no—
674C4⋊C4—92no—
675C4⋊C4—92no—
676C4⋊C4C2×D3211yescharacteristic
677C4⋊C4C2×D3212yes—
678C4⋊C4C2×D3211yescharacteristic
679C22⋊C4—34no—
680C22⋊C4—32no—
681C22⋊C4—34no—
682C22⋊C4—32no—
683C22⋊C4—92no—
684C22⋊C4—94no—
685C42—34no—
686C42—32no—
687C42—94no—
688C42—92no—
689C42—92no—
690C42—94no—
691C42—92no—
692C42—91no—
693C42—91no—
694C42—92no—
695C42—91no—
696C42—92no—
697C42—92no—
698C42—91no—
699C22×C3—22no—
700C22×C3—22no—
701C22×C3—22no—
702C22×C3—22no—
703C22×C3—22no—
704C22×C3—21no—
705C22×C3—34no—
706C22×C3—62no—
707C22×C3—62no—
708C22×C3C2×D3×Q814yes—
709C22×C3C24×D312yes—
710C2×D3—22no—
711C2×D3—22no—
712C2×D3C2×D3×Q814yes—
713C3×C4—22no—
714C3×C4—22no—
715C3×C4—24no—
716C3×C4—24no—
717C3×C4—22no—
718C3×C4—34no—
719C3×C4—42no—
720C3×C4—42no—
721C3×C4—62no—
722C3×C4—64no—
723C3×C4—64no—
724C3×C4—62no—
725C3×C4D3×#4114yes—
726Dic3—24no—
727Dic3—22no—
728Dic3—22no—
729Dic3—24no—
730Dic3—34no—
731Dic3—34no—
732Dic3—38no—
733Dic3—64no—
734Dic3—62no—
735Dic3—62no—
736Dic3—64no—
737Dic3—64no—
738Dic3—62no—
739Dic3—62no—
740Dic3—121no—
741Dic3—121no—
742Dic3C2×D3×Q814yes—
743C32Q8×#4111yescharacteristic, complemented, Sylow
744C23—32no—
745C23C22×D3211yescharacteristic
746Q8—64no—
747Q8—94no—
748Q8—94no—
749Q8—124no—
750Q8—184no—
751Q8—188no—
752Q8—182no—
753Q8—362no—
754D4—38no—
755D4—94no—
756C2×C4—22no—
757C2×C4—32no—
758C2×C4—34no—
759C2×C4—32no—
760C2×C4—32no—
761C2×C4—34no—
762C2×C4—42no—
763C2×C4—64no—
764C2×C4—98no—
765C2×C4—94no—
766C2×C4—91no—
767C2×C4—91no—
768C2×C4—92no—
769C2×C4—91no—
770C2×C4—92no—
771C2×C4—91no—
772C2×C4—124no—
773C2×C4—188no—
774C2×C4—184no—
775C2×C4—362no—
776C2×C4—361no—
777C2×C4C22×D3212yes—
778C2×C4C22×D3211yescharacteristic
779C2×C4C22×D3212yes—
780C2×C4C22×D3211yescharacteristic
781C2×C3—24no—
782C2×C3—24no—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—64no—
787C2×C3C22×D3×Q812yes—
788C2×C3C2×D3×#4112yes—
789C2×C3#596612yes—
790D3—24no—
791C22—21no—
792C22—21no—
793C22—34no—
794C22—62no—
795C22—62no—
796C22D32×Q812yes—
797C22C23×D3211yescharacteristic
798C4—21no—
799C4—22no—
800C4—22no—
801C4—34no—
802C4—62no—
803C4—64no—
804C4—64no—
805C4—62no—
806C4—94no—
807C4—92no—
808C4—92no—
809C4—182no—
810C4—181no—
811C4—181no—
812C4#6430612yes—
813C3—21no—
814C3#8692312yescomplemented
815C2—22no—
816C2—64no—
817C2C2×#6430611yescharacteristic
818C2#1059667911yescharacteristic
819C2C2×D32×Q811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C4⋊C4C22
prime radicalC2×#3805C22
hypercenterC2×C4⋊C4D32
hypocenterC32Q8×#41
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64096C2semidirect
2. C3×#5511C2semidirect
3. #10594959C2semidirect
4. #10594915C2semidirect
7. #10594810C2semidirect
8. #10594810C2semidirect
9. #10594597C2semidirect
10. #10594595C2semidirect
11. #10594534C2semidirect
12. #10594531C2semidirect
13. #10594526C2semidirect
14. #10594388C2semidirect
15. #10594387C2semidirect
16. D3×#887C2semidirect
17. #10594313C2semidirect
104. #5511D3semidirect
126. #3805Q8semidirect
297. C2×C3⋊Dic3C2×Q8semidirect
306. #634#41semidirect
307. C3×#67C2×Q8semidirect
319. #627C2×Q8semidirect
320. #625C2×Q8semidirect
323. D3×Dic3C2×Q8semidirect
582. #67D3×Q8semidirect
743. C32Q8×#41semidirect
814. C3#86923semidirect

Maximal subgroups

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

subgroupindex
C2×#640962
C3×#55112
#105949592
#105949152
C4×#38052
#105948102
#105945972
#105945952
#105945342
#105945312
#105945262
#105943882
#105943872
D3×#8872
#105943132
#869233