Finite Group Databasebeta

← #11901850

Subgroups — #11901850

Order 1152.

2176 conjugacy classes of subgroups.

The subgroup lattice has 811 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596202C211yesmaximal, characteristic, complemented
2C3×#5731C211yesmaximal, characteristic, complemented
3C3×#5725C211yesmaximal, characteristic, complemented
4#10595424C212yesmaximal, complemented
5#10595396C212yesmaximal, complemented
6#10595395C212yesmaximal, complemented
7Dic3×#239C212yesmaximal, complemented
8#10594646C214yesmaximal, complemented
9#10594428C214yesmaximal, complemented
10#10594405C214yesmaximal, complemented
11#10594403C214yesmaximal, complemented
12D3×#872C211yesmaximal, characteristic, complemented
13#10593950C211yesmaximal, characteristic, complemented
14#10593949C211yesmaximal, characteristic, complemented
15#10593874C211yesmaximal, characteristic, complemented
16#86495—31nomaximal
17#86236—31nomaximal
18C2×C3×#239C2212yes—
19C2×C4×D32C2211yescharacteristic
20C32×C4⋊Q8C2211yescharacteristic, complemented
21#64155C2212yes—
22Q8×C3⋊Dic3C2212yescomplemented
23#64107C2214yes—
24#64098C2214yescomplemented
25#64081C2211yescharacteristic
26#64079C2211yescharacteristic, complemented
27C3×#947C2212yescomplemented
28C3×#946C2212yes—
29C3×Q8×Dic3C2212yescomplemented
30C3×#898C2214yes—
31C3×#895C2214yes—
32C3×#893C2214yescomplemented
33C3×#889C2214yescomplemented
34C3×#874C2211yescharacteristic, complemented
35C3×#872C2211yescharacteristic
36C3×C42×D3C2211yescharacteristic
37C3×#870C2211yescharacteristic, complemented
38#63922C2214yes—
39D3×(C2×D3)⋊C4C2212yes—
40#63918C2212yescomplemented
41#63916C2212yes—
42#63915C2214yes—
43#63908C2212yes—
44#63904C2214yes—
45#63899C2214yescomplemented
46#63898C2214yes—
47#63898C2212yescomplemented
48#63893C2214yescomplemented
49Dic3×D12C2214yes—
50Dic3×D12C2212yescomplemented
51#63891C2214yes—
52#63890C2214yes—
53#63886C2214yes—
54#63885C2214yes—
55#63884C2214yes—
56#63884C2214yescomplemented
57#63884C2214yescomplemented
58#63879C2214yes—
59#63877C2212yes—
60D3×Dic3⋊C4C2212yes—
61C4×D3×Dic3C2211yescharacteristic
62C4×D3×Dic3C2214yescomplemented
63#63874C2211yescharacteristic
64#63862C2214yescomplemented
65#63859C2214yescomplemented
66#63855C2211yescharacteristic
67#63852C2214yes—
68#63851C2214yes—
69#63841C2212yes—
70#63841C2214yescomplemented
71#63837C2214yescomplemented
72#63836C2212yes—
73C3×#541—31no—
74C3×#532—31no—
75#5828—32no—
76Dic3×#41—32no—
77#5731—31no—
78#5731—31no—
79#5731—61no—
80#5731D311yescharacteristic, complemented
81#5725D311yescharacteristic, complemented
82#5719—31no—
83#5719—31no—
84#5706—34no—
85#5704—34no—
86#5697—31no—
87#5692—34no—
88#5691—34no—
89#5688—31no—
90#5682—32no—
91#5682—32no—
92#5643—32no—
93#5627—32no—
94#5617—34no—
95#5602—34no—
96#5582—32no—
97C4×#239—32no—
98#5538—34no—
99#5538—34no—
100#5535—31no—
101D3×#117—31no—
102C2×#872—31no—
103#5470—31no—
104C22×D32C2311yescharacteristic
105C2×C32×Q8C2312yes—
106C2×C4×C3⋊D3C2311yescharacteristic
107C3×#239—28no—
108C2×C3×D12C2314yes—
109C2×C3×D12C2312yes—
110C2×C3×D12C2314yes—
111C2×C3×C4×D3C2314yes—
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×C4×D3C2312yes—
114C2×C3×C4×D3C2311yescharacteristic
115C2×#627C2314yes—
116C2×#626C2314yes—
117C2×#625C2314yes—
118C2×#624C2311yescharacteristic
119C2×D3×Dic3C2311yescharacteristic
120C2×D3×Dic3C2311yescharacteristic
121C2×D3×Dic3C2312yes—
122C2×D3×Dic3C2314yes—
123C2×D3×Dic3C2314yes—
124C4×D32—24no—
125C32×C4⋊C4C2314yes—
126C32×C42C2311yescharacteristic
127#3752C2312yes—
128#3752C2314yes—
129C4⋊(C3⋊Dic3)C2312yes—
130C4⋊(C3⋊Dic3)C2314yes—
131#3750C2314yes—
132#3750C2312yes—
133#3750C2314yes—
134C4×C3⋊Dic3C2311yescharacteristic
135C4×C3⋊Dic3C2314yes—
136C3×(C2×D3)⋊C4C2314yes—
137C3×(C2×D3)⋊C4C2314yes—
138C3×(C2×D3)⋊C4C2314yes—
139C3×(C2×D3)⋊C4C2312yes—
140C3×C4⋊Dic3C2314yes—
141C3×C4⋊Dic3C2312yes—
142C3×Dic3⋊C4C2314yes—
143C3×Dic3⋊C4C2312yes—
144C3×Dic3⋊C4C2314yes—
145C3×C4×Dic3C2314yes—
146C3×C4×Dic3C2312yes—
147C3×C4×Dic3C2311yescharacteristic
148C3×C4×Dic3C2311yescharacteristic
149#3724C2312yes—
150Dic3⋊Dic3C2312yes—
151Dic3⋊Dic3C2314yes—
152#3722C2312yes—
153(C2×D3)⋊Dic3C2314yes—
154(C2×D3)⋊Dic3C2314yes—
155(C2×D3)⋊Dic3C2314yes—
156(C2×D3)⋊Dic3C2312yes—
157(C2×D3)⋊Dic3C2314yes—
158(C2×D3)⋊Dic3C2314yes—
159Dic32C2312yes—
160Dic32C2314yes—
161#3455—91noSylow
162C2×C3×#41—32no—
163C2×#239C2×D312yes—
164C22×C4×D3—31no—
165C22×C4×D3—31no—
166C3×C4⋊Q8—21no—
167C3×C4⋊Q8C2×D311yescharacteristic, complemented
168C3×C4⋊Q8C2×D311yescharacteristic, complemented
169C3×#127—31no—
170C3×#126—34no—
171C3×#125—34no—
172C3×#125—31no—
173C3×#124—32no—
174C3×C22⋊Q8—32no—
175C3×#121—34no—
176C3×C4×Q8—32no—
177C3×C4×D4—34no—
178C3×#117—31no—
179C2×C3×C42—31no—
180#947C2×D312yescomplemented
181#946—32no—
182#946—32no—
183#946—62no—
184#946C2×D312yes—
185Q8×Dic3—32no—
186Q8×Dic3—32no—
187Q8×Dic3—62no—
188Q8×Dic3C2×D312yescomplemented
189#939—34no—
190#939—34no—
191#938—32no—
192#938—32no—
193#937—34no—
194#935—34no—
195#935—34no—
196#935—34no—
197D4×Dic3—32no—
198D4×Dic3—34no—
199D4×Dic3—32no—
200D4×Dic3—34no—
201#930—32no—
202C4×#67—34no—
203C4×#67—34no—
204C2×(C2×D3)⋊C4—32no—
205#926—32no—
206#926—34no—
207#926—31no—
208#924—34no—
209C2×Dic3⋊C4—32no—
210C2×C4×Dic3—31no—
211C2×C4×Dic3—34no—
212#898—34no—
213#898—34no—
214#898—34no—
215#898—64no—
216#898C2×D314yes—
217#897—34no—
218#896—34no—
219#896—34no—
220#895—34no—
221#895—32no—
222#895C2×D314yes—
223#894—34no—
224#894—34no—
225#894—34no—
226#894—34no—
227#893—32no—
228#893—34no—
229#893—34no—
230#893C2×D314yescomplemented
231#892—32no—
232#892—34no—
233#892—32no—
234D3×C4⋊C4—32no—
235#889—34no—
236#889—34no—
237#889—64no—
238#889C2×D314yescomplemented
239#888—32no—
240#887—34no—
241#886—34no—
242#886—34no—
243#885—34no—
244#885—34no—
245#885—34no—
246#884—34no—
247#883—34no—
248#882—34no—
249#67⋊C4—34no—
250D3×C22⋊C4—32no—
251#879—34no—
252#879—34no—
253#878—34no—
254#878—34no—
255#877—32no—
256#876—34no—
257#875—34no—
258#874C2×D311yescharacteristic, complemented
259C4×D12—34no—
260C4×D12—32no—
261#872—31no—
262#872—31no—
263#872—31no—
264#872—32no—
265#872—32no—
266#872—31no—
267#872—31no—
268#872—61no—
269#872C2×D311yescharacteristic
270C42×D3—34no—
271C42×D3—31no—
272C42×D3C2×D311yescharacteristic
273#870—31no—
274#870—31no—
275#870—61no—
276#870C2×D311yescharacteristic, complemented
277#869—32no—
278C4×Dic6—34no—
279C22×C3⋊D3C2411yescharacteristic
280C22×C3×D3C2411yescharacteristic
281C22×C3×D3C2414yes—
282C22×C3×D3C2411yescharacteristic
283C2×D32—22no—
284C2×D32—42no—
285C32×Q8—24no—
286C2×C32×C4C2412yes—
287C2×C32×C4C2414yes—
288C2×C32×C4C2411yescharacteristic
289C2×C3⋊Dic3C2412yes—
290C2×C3⋊Dic3C2414yes—
291C2×C3⋊Dic3C2411yescharacteristic
292C4×C3⋊D3—22no—
293C2×C3×Dic3C2414yes—
294C2×C3×Dic3C2412yes—
295C2×C3×Dic3C2411yescharacteristic
296C2×C3×Dic3C2412yes—
297C2×C3×Dic3C2411yescharacteristic
298C3×D12—28no—
299C3×D12—24no—
300C3×D12—44no—
301C3×C4×D3—22no—
302C3×C4×D3—28no—
303C3×C4×D3—42no—
304C3×C4×D3#4114yes—
305#627—44no—
306#626—44no—
307#625—44no—
308#624—22no—
309D3×Dic3—22no—
310D3×Dic3—22no—
311D3×Dic3—42no—
312D3×Dic3—44no—
313D3×Dic3—44no—
314#542—92no—
315#542—92no—
316#541—31no—
317#541—91no—
318#540—91no—
319#540—91no—
320#539—94no—
321#538—94no—
322#533—91no—
323#532—31no—
324#529—94no—
325#529—94no—
326#525—92no—
327C4×#41—92no—
328C2×#117—91no—
329C23×D3—31no—
330C23×D3—31no—
331C3×#41—68no—
332C2×C3×Q8—22no—
333C2×C3×Q8C22×D312yes—
334C2×C3×Q8C22×D312yes—
335C2×C3×D4—34no—
336C2×C3×D4—32no—
337C2×C3×D4—34no—
338C22×C3×C4—31no—
339C22×C3×C4—34no—
340C22×C3×C4—31no—
341C22×C3×C4—32no—
342C2×#67—34no—
343C2×#67—34no—
344C2×#67—34no—
345C22×Dic3—31no—
346C22×Dic3—31no—
347C22×Dic3—34no—
348C22×Dic3—34no—
349C22×Dic3—32no—
350#239—28no—
351C2×D12—34no—
352C2×D12C22×D312yes—
353C2×D12C22×D314yes—
354C2×D12C22×D314yes—
355C2×C4×D3—31no—
356C2×C4×D3—31no—
357C2×C4×D3—31no—
358C2×C4×D3—31no—
359C2×C4×D3—31no—
360C2×C4×D3—31no—
361C2×C4×D3—32no—
362C2×C4×D3—34no—
363C2×C4×D3—34no—
364C2×C4×D3—61no—
365C2×C4×D3—64no—
366C2×C4×D3—64no—
367C2×C4×D3C22×D314yes—
368C2×C4×D3C22×D311yescharacteristic
369C2×C4×D3C22×D312yes—
370C2×C4×D3C22×D311yescharacteristic
371C2×Dic6—34no—
372C2×Dic6—34no—
373C3×C4⋊C4—24no—
374C3×C4⋊C4—34no—
375C3×C4⋊C4—32no—
376C3×C4⋊C4—32no—
377C3×C4⋊C4—34no—
378C3×C4⋊C4—34no—
379C3×C4⋊C4C22×D314yes—
380C3×C4⋊C4C22×D314yes—
381C3×C22⋊C4—32no—
382C3×C22⋊C4—34no—
383C3×C22⋊C4—34no—
384C3×C22⋊C4—34no—
385C3×C42—21no—
386C3×C42—32no—
387C3×C42—31no—
388C3×C42—31no—
389C3×C42—34no—
390C3×C42C22×D311yescharacteristic
391C3×C42C22×D311yescharacteristic
392#217—32no—
393#217—34no—
394#217—34no—
395#217—34no—
396#217—34no—
397#217—34no—
398(C2×D3)⋊C4—32no—
399(C2×D3)⋊C4—34no—
400(C2×D3)⋊C4—34no—
401(C2×D3)⋊C4—34no—
402(C2×D3)⋊C4—34no—
403(C2×D3)⋊C4—34no—
404(C2×D3)⋊C4—32no—
405(C2×D3)⋊C4—32no—
406(C2×D3)⋊C4—34no—
407(C2×D3)⋊C4—34no—
408(C2×D3)⋊C4—32no—
409(C2×D3)⋊C4—32no—
410(C2×D3)⋊C4—62no—
411(C2×D3)⋊C4—64no—
412(C2×D3)⋊C4C22×D312yes—
413(C2×D3)⋊C4C22×D314yes—
414(C2×D3)⋊C4C22×D314yes—
415(C2×D3)⋊C4C22×D314yes—
416C4⋊Dic3—32no—
417C4⋊Dic3—32no—
418C4⋊Dic3—34no—
419C4⋊Dic3—34no—
420C4⋊Dic3—34no—
421C4⋊Dic3—32no—
422C4⋊Dic3—62no—
423C4⋊Dic3—64no—
424C4⋊Dic3C22×D312yes—
425C4⋊Dic3C22×D314yes—
426Dic3⋊C4—34no—
427Dic3⋊C4—34no—
428Dic3⋊C4—32no—
429Dic3⋊C4—32no—
430Dic3⋊C4—34no—
431Dic3⋊C4—34no—
432Dic3⋊C4—32no—
433Dic3⋊C4—32no—
434Dic3⋊C4—32no—
435Dic3⋊C4—34no—
436Dic3⋊C4—64no—
437Dic3⋊C4—62no—
438Dic3⋊C4—64no—
439Dic3⋊C4C22×D314yes—
440Dic3⋊C4C22×D312yes—
441Dic3⋊C4C22×D314yes—
442C4×Dic3—31no—
443C4×Dic3—34no—
444C4×Dic3—31no—
445C4×Dic3—34no—
446C4×Dic3—34no—
447C4×Dic3—32no—
448C4×Dic3—34no—
449C4×Dic3—32no—
450C4×Dic3—61no—
451C4×Dic3—64no—
452C4×Dic3C22×D311yescharacteristic
453C4×Dic3C22×D312yes—
454C4×Dic3C22×D311yescharacteristic
455C4×Dic3C22×D314yes—
456C22×C32C2511yescharacteristic
457C2×C3⋊D3—21no—
458C2×C3⋊D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—21no—
461C2×C3×D3—24no—
462C2×C3×D3—24no—
463C2×C3×D3—24no—
464C2×C3×D3—22no—
465C2×C3×D3C2×#4112yes—
466D32—44no—
467C32×C4—24no—
468C32×C4—22no—
469C32×C4C2×#4112yes—
470C3⋊Dic3—21no—
471C3⋊Dic3—22no—
472C3⋊Dic3—24no—
473C3×Dic3—21no—
474C3×Dic3—22no—
475C3×Dic3—24no—
476C3×Dic3—22no—
477C3×Dic3C2×#4112yes—
478C2×#41—32no—
479C23×C4—91no—
480C4⋊Q8—92no—
481C4⋊Q8D3211yescharacteristic, complemented
482#127—31no—
483#126—34no—
484#126—94no—
485#126—94no—
486#126—94no—
487#125—34no—
488#125—31no—
489#125—94no—
490#125—91no—
491#124—32no—
492#124—94no—
493#124—94no—
494#123—94no—
495#123—94no—
496#123—94no—
497#123—94no—
498#123—94no—
499C22⋊Q8—32no—
500C22⋊Q8—94no—
501C22⋊Q8—94no—
502C22⋊Q8—94no—
503C22⋊Q8—92no—
504#121—34no—
505#121—94no—
506#121—92no—
507#121—94no—
508#121—92no—
509#120—94no—
510C4×Q8—32no—
511C4×Q8—94no—
512C4×Q8—92no—
513C4×D4—34no—
514C4×D4—94no—
515C4×D4—92no—
516C4×D4—94no—
517C4×D4—94no—
518C4×D4—94no—
519C4×D4—92no—
520#117—31no—
521#117—91no—
522#117—92no—
523#117—92no—
524#117—91no—
525#117—92no—
526#117—94no—
527#117—91no—
528C2×C4⋊C4—92no—
529C2×C22⋊C4—92no—
530C2×C42—31no—
531C2×C42—91no—
532C2×C42—94no—
533C23×C3—31no—
534C23×C3—34no—
535C23×C3—31no—
536C22×D3—31no—
537C22×D3—31no—
538C22×D3—61no—
539C22×D3—62no—
540C22×D3—62no—
541C22×D3—122no—
542C22×D3—122no—
543C22×D3C23×D314yes—
544C22×D3C23×D311yescharacteristic
545C22×D3C23×D311yescharacteristic
546C3×Q8—24no—
547C3×Q8—24no—
548C3×Q8—44no—
549C3×D4—68no—
550C3×D4—64no—
551C3×D4—124no—
552C2×C3×C4—21no—
553C2×C3×C4—24no—
554C2×C3×C4—22no—
555C2×C3×C4—31no—
556C2×C3×C4—34no—
557C2×C3×C4—32no—
558C2×C3×C4—34no—
559C2×C3×C4—32no—
560C2×C3×C4—31no—
561C2×C3×C4—68no—
562C2×C3×C4—62no—
563C2×C3×C4—122no—
564C2×C3×C4C23×D314yes—
565C2×C3×C4C23×D314yes—
566C2×C3×C4C23×D312yes—
567C2×C3×C4C23×D312yes—
568C2×C3×C4C23×D311yescharacteristic
569C2×C3×C4C23×D311yescharacteristic
570#67—124no—
571#67—124no—
572#67—124no—
573C2×Dic3—32no—
574C2×Dic3—32no—
575C2×Dic3—34no—
576C2×Dic3—34no—
577C2×Dic3—31no—
578C2×Dic3—31no—
579C2×Dic3—62no—
580C2×Dic3—64no—
581C2×Dic3—61no—
582C2×Dic3—62no—
583C2×Dic3—62no—
584C2×Dic3—124no—
585C2×Dic3—124no—
586C2×Dic3—122no—
587C2×Dic3C23×D312yes—
588C2×Dic3C23×D314yes—
589C2×Dic3C23×D312yes—
590C2×Dic3C23×D311yescharacteristic
591C2×Dic3C23×D311yescharacteristic
592D12—28no—
593D12—24no—
594D12—44no—
595D12—124no—
596C4×D3—22no—
597C4×D3—28no—
598C4×D3—42no—
599C4×D3—62no—
600C4×D3—62no—
601C4×D3—62no—
602C4×D3—62no—
603C4×D3—62no—
604C4×D3—62no—
605C4×D3—122no—
606C4×D3—124no—
607C4×D3—124no—
608C4×D3—122no—
609C4×D3#23714yes—
610Dic6—124no—
611Dic6—124no—
612C2×C32C22×#4111yescharacteristic
613C2×C32#58512yes—
614C3⋊D3—41no—
615C3×D3—22no—
616C3×D3—41no—
617C3×D3—44no—
618C24—91no—
619#41—68no—
620C2×Q8—94no—
621C2×Q8C2×D3212yes—
622C2×D4—34no—
623C2×D4—32no—
624C2×D4—34no—
625C2×D4—94no—
626C2×D4—94no—
627C22×C4—31no—
628C22×C4—34no—
629C22×C4—31no—
630C22×C4—32no—
631C22×C4—91no—
632C22×C4—91no—
633C22×C4—91no—
634C22×C4—92no—
635C22×C4—94no—
636C22×C4—94no—
637C22×C4—91no—
638C22×C4—184no—
639C4⋊C4—32no—
640C4⋊C4—32no—
641C4⋊C4—34no—
642C4⋊C4—34no—
643C4⋊C4—34no—
644C4⋊C4—92no—
645C4⋊C4—92no—
646C4⋊C4—94no—
647C4⋊C4—92no—
648C4⋊C4—92no—
649C4⋊C4—94no—
650C4⋊C4—94no—
651C4⋊C4—94no—
652C4⋊C4C2×D3214yes—
653C22⋊C4—32no—
654C22⋊C4—34no—
655C22⋊C4—34no—
656C22⋊C4—34no—
657C22⋊C4—92no—
658C22⋊C4—92no—
659C22⋊C4—94no—
660C22⋊C4—94no—
661C22⋊C4—94no—
662C22⋊C4—94no—
663C22⋊C4—94no—
664C22⋊C4—92no—
665C22⋊C4—94no—
666C42—32no—
667C42—31no—
668C42—31no—
669C42—34no—
670C42—92no—
671C42—94no—
672C42—91no—
673C42—94no—
674C42C2×D3211yescharacteristic
675C22×C3—21no—
676C22×C3—32no—
677C22×C3—62no—
678C22×C3—61no—
679C22×C3—64no—
680C22×C3—62no—
681C22×C3—64no—
682C22×C3—64no—
683C22×C3C24×D311yescharacteristic
684C22×C3C24×D311yescharacteristic
685C2×D3—22no—
686C2×D3—24no—
687C2×D3—21no—
688C2×D3—24no—
689C2×D3—24no—
690C2×D3—22no—
691C2×D3—61no—
692C2×D3—61no—
693C2×D3—62no—
694C2×D3—62no—
695C2×D3—121no—
696C2×D3—122no—
697C2×D3—124no—
698C2×D3—124no—
699C2×D3C2×#23712yes—
700C3×C4—24no—
701C3×C4—24no—
702C3×C4—22no—
703C3×C4—22no—
704C3×C4—22no—
705C3×C4—32no—
706C3×C4—44no—
707C3×C4—42no—
708C3×C4—61no—
709C3×C4—64no—
710C3×C4—62no—
711C3×C4—62no—
712C3×C4C2×#23712yes—
713C3×C4D3×#4112yes—
714Dic3—21no—
715Dic3—22no—
716Dic3—24no—
717Dic3—22no—
718Dic3—61no—
719Dic3—61no—
720Dic3—64no—
721Dic3—62no—
722Dic3—64no—
723Dic3—62no—
724Dic3—121no—
725Dic3—122no—
726Dic3—124no—
727Dic3C2×#23712yes—
728C32#345511yescharacteristic, complemented, Sylow
729C23—31no—
730C23—31no—
731C23—34no—
732C23—91no—
733C23—182no—
734C23—362no—
735Q8—24no—
736Q8—364no—
737D4—68no—
738D4—64no—
739D4—124no—
740D4—364no—
741D4—364no—
742C2×C4—31no—
743C2×C4—34no—
744C2×C4—32no—
745C2×C4—32no—
746C2×C4—34no—
747C2×C4—31no—
748C2×C4—68no—
749C2×C4—62no—
750C2×C4—92no—
751C2×C4—94no—
752C2×C4—91no—
753C2×C4—122no—
754C2×C4—182no—
755C2×C4—182no—
756C2×C4—182no—
757C2×C4—182no—
758C2×C4—362no—
759C2×C4—364no—
760C2×C4—364no—
761C2×C4C22×D3214yes—
762C2×C4C22×D3212yes—
763C2×C4C22×D3211yescharacteristic
764C2×C3—21no—
765C2×C3—22no—
766C2×C3—62no—
767C2×C3—121no—
768C2×C3—124no—
769C2×C3C22×#23711yescharacteristic
770C2×C3C2×D3×#4111yescharacteristic
771C2×C3#596412yes—
772C2×C3#596812yes—
773D3—22no—
774D3—44no—
775D3—41no—
776D3—121no—
777D3—121no—
778D3—241no—
779C22—32no—
780C22—62no—
781C22—61no—
782C22—64no—
783C22—64no—
784C22—64no—
785C22—62no—
786C22—181no—
787C22—182no—
788C22—364no—
789C22C23×D3211yescharacteristic
790C4—24no—
791C4—22no—
792C4—32no—
793C4—61no—
794C4—62no—
795C4—62no—
796C4—64no—
797C4—181no—
798C4—182no—
799C4—184no—
800C4D3×#23712yes—
801C3—21no—
802C3#8623611yescharacteristic, complemented
803C3#8649511yescharacteristic, complemented
804C2—62no—
805C2—121no—
806C2—124no—
807C2—361no—
808C2C2×D3×#23711yescharacteristic
809C2#1059668812yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
hypercenterC4⋊Q8D32
hypocenterC32#3455
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596202C2semidirect
2. C3×#5731C2semidirect
3. C3×#5725C2semidirect
4. #10595424C2semidirect
5. #10595396C2semidirect
6. #10595395C2semidirect
7. Dic3×#239C2semidirect
8. #10594646C2semidirect
9. #10594428C2semidirect
10. #10594405C2semidirect
11. #10594403C2semidirect
12. D3×#872C2semidirect
13. #10593950C2semidirect
14. #10593949C2semidirect
15. #10593874C2semidirect
20. C32×C4⋊Q8C22semidirect
22. Q8×C3⋊Dic3C22semidirect
24. #64098C22semidirect
26. #64079C22semidirect
27. C3×#947C22semidirect
29. C3×Q8×Dic3C22semidirect
32. C3×#893C22semidirect
33. C3×#889C22semidirect
34. C3×#874C22semidirect
37. C3×#870C22semidirect
40. #63918C22semidirect
45. #63899C22semidirect
47. #63898C22semidirect
48. #63893C22semidirect
50. Dic3×D12C22semidirect
56. #63884C22semidirect
57. #63884C22semidirect
62. C4×D3×Dic3C22semidirect
64. #63862C22semidirect
65. #63859C22semidirect
70. #63841C22semidirect
71. #63837C22semidirect
80. #5731D3semidirect
81. #5725D3semidirect
167. C3×C4⋊Q8C2×D3semidirect
168. C3×C4⋊Q8C2×D3semidirect
180. #947C2×D3semidirect
188. Q8×Dic3C2×D3semidirect
230. #893C2×D3semidirect
238. #889C2×D3semidirect
258. #874C2×D3semidirect
276. #870C2×D3semidirect
481. C4⋊Q8D32semidirect
728. C32#3455semidirect
802. C3#86236semidirect
803. C3#86495semidirect

Maximal subgroups

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

subgroupindex
#105962022
C3×#57312
C3×#57252
#105954242
#105953962
#105953952
Dic3×#2392
#105946462
#105944282
#105944052
#105944032
D3×#8722
#105939502
#105939492
#105938742
#864953
#862363