Finite Group Databasebeta

← #11901849

Subgroups — #11901849

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#10596169C211yesmaximal, characteristic, complemented
2C3×#5697C211yesmaximal, characteristic, complemented
3C3×#5688C211yesmaximal, characteristic, complemented
4#10594651C214yesmaximal, complemented
5#10594626C212yesmaximal, complemented
6#10594494C212yesmaximal, complemented
7#10594455C214yesmaximal, complemented
8#10594426C214yesmaximal, complemented
9#10594416C214yesmaximal, complemented
10#10594358C212yesmaximal, complemented
11#10594341C212yesmaximal, complemented
12D3×#872C211yesmaximal, characteristic, complemented
13#10593950C211yesmaximal, characteristic, complemented
14#10593897C211yesmaximal, characteristic, complemented
15#10593881C211yesmaximal, characteristic, complemented
16#86467—31nomaximal
17#86273—31nomaximal
18C2×C4×D32C2211yescharacteristic
19C2×#3795C2212yes—
20C32×#125C2211yescharacteristic, complemented
21#64107C2214yes—
22#64106C2212yes—
23#64099C2214yescomplemented
24#64096C2212yescomplemented
25#64081C2211yescharacteristic
26#64078C2211yescharacteristic, complemented
27C3×#896C2214yes—
28C3×#895C2212yes—
29C3×#895C2214yes—
30C3×#894C2214yescomplemented
31C3×#893C2212yescomplemented
32C3×#892C2212yes—
33C3×#888C2212yescomplemented
34C3×#887C2214yescomplemented
35C3×#874C2211yescharacteristic, complemented
36C3×#872C2211yescharacteristic
37C3×C42×D3C2211yescharacteristic
38C3×#870C2211yescharacteristic, complemented
39#63922C2214yes—
40D3×(C2×D3)⋊C4C2212yes—
41#63916C2212yes—
42#63908C2214yes—
43#63907C2214yes—
44#63902C2214yes—
45#63898C2212yescomplemented
46Dic3×D12C2214yes—
47Dic3×D12C2214yescomplemented
48#63891C2214yes—
49#63887C2214yescomplemented
50#63886C2214yes—
51#63884C2214yes—
52#63884C2214yescomplemented
53#63880C2214yes—
54#63879C2214yes—
55#63877C2212yes—
56#63877C2214yescomplemented
57D3×Dic3⋊C4C2212yes—
58C4×D3×Dic3C2211yescharacteristic
59C4×D3×Dic3C2214yescomplemented
60#63874C2211yescharacteristic
61#63863C2214yes—
62#63862C2214yescomplemented
63#63861C2214yes—
64#63861C2214yescomplemented
65#63860C2212yescomplemented
66#63857C2212yes—
67#63856C2214yescomplemented
68#63855C2211yescharacteristic
69#63850C2214yes—
70#63845C2214yescomplemented
71#63844C2212yescomplemented
72#63836C2212yes—
73C3×#540—31no—
74C3×#533—31no—
75#5733—32no—
76#5733—32no—
77#5719—31no—
78#5716—31no—
79#5698—31no—
80#5698—31no—
81#5698—31no—
82#5698—61no—
83#5697—31no—
84#5697D311yescharacteristic, complemented
85#5688D311yescharacteristic, complemented
86#5660—34no—
87#5649—34no—
88#5645—34no—
89#5644—34no—
90#5613—34no—
91#5606—32no—
92#5603—32no—
93#5600—34no—
94#5580—34no—
95#5580—34no—
96#5561—32no—
97C4×#237—32no—
98#5524—32no—
99#5522—32no—
100D3×#117—31no—
101#5518—31no—
102#5477—31no—
103C2×#872—31no—
104C22×D32C2311yescharacteristic
105C2×C4×C3⋊D3C2311yescharacteristic
106C2×#634C2312yes—
107C2×C3×D12C2312yes—
108C2×C3×D12C2314yes—
109C2×C3×D12C2314yes—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×C4×D3C2314yes—
112C2×C3×C4×D3C2312yes—
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×Dic6C2314yes—
115C2×#626C2314yes—
116C2×#625C2314yes—
117C2×#624C2311yescharacteristic
118C2×D3×Dic3C2314yes—
119C2×D3×Dic3C2311yescharacteristic
120C2×D3×Dic3C2311yescharacteristic
121C2×D3×Dic3C2312yes—
122C2×D3×Dic3C2314yes—
123C4×D32—24no—
124#3795—28no—
125C32×C4⋊C4C2314yes—
126C32×C4⋊C4C2312yes—
127C32×C42C2311yescharacteristic
128#3752C2312yes—
129#3752C2314yes—
130C4⋊(C3⋊Dic3)C2314yes—
131C4⋊(C3⋊Dic3)C2314yes—
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⋊Dic3C2312yes—
141C3×Dic3⋊C4C2314yes—
142C3×Dic3⋊C4C2314yes—
143C3×Dic3⋊C4C2312yes—
144C3×C4×Dic3C2314yes—
145C3×C4×Dic3C2312yes—
146C3×C4×Dic3C2311yescharacteristic
147C3×C4×Dic3C2311yescharacteristic
148#3724C2314yes—
149#3724C2312yes—
150Dic3⋊Dic3C2312yes—
151Dic3⋊Dic3C2314yes—
152#3722C2312yes—
153(C2×D3)⋊Dic3C2314yes—
154(C2×D3)⋊Dic3C2312yes—
155(C2×D3)⋊Dic3C2314yes—
156(C2×D3)⋊Dic3C2314yes—
157(C2×D3)⋊Dic3C2314yes—
158(C2×D3)⋊Dic3C2314yes—
159Dic32C2312yes—
160Dic32C2314yes—
161#3455—91noSylow
162C2×#237—32no—
163C2×#235—32no—
164C22×C4×D3—31no—
165C22×C4×D3—31no—
166C3×C4⋊Q8—32no—
167C3×#127—31no—
168C3×#125—21no—
169C3×#125—31no—
170C3×#125C2×D311yescharacteristic, complemented
171C3×#125C2×D311yescharacteristic, complemented
172C3×#123—34no—
173C3×C22⋊Q8—34no—
174C3×#121—34no—
175C3×#121—32no—
176C3×C4×Q8—34no—
177C3×C4×D4—32no—
178C3×#117—32no—
179C3×#117—31no—
180C2×C3×C42—31no—
181#947—34no—
182#947—34no—
183#946—34no—
184#946—34no—
185#939—34no—
186#938—34no—
187#938—32no—
188#937—34no—
189#936—34no—
190#936—32no—
191#935—34no—
192#935—34no—
193D4×Dic3—32no—
194D4×Dic3—34no—
195D4×Dic3—34no—
196#930—34no—
197#929—34no—
198C4×#67—34no—
199C2×(C2×D3)⋊C4—32no—
200#926—31no—
201#924—34no—
202#924—32no—
203C2×Dic3⋊C4—32no—
204C2×C4×Dic3—34no—
205C2×C4×Dic3—31no—
206#898—34no—
207#898—34no—
208#898—34no—
209#898—34no—
210#898—34no—
211#898—64no—
212#897—32no—
213#897—32no—
214#897—32no—
215#897—62no—
216#896C2×D314yes—
217#895—34no—
218#895—32no—
219#895C2×D314yes—
220#895C2×D312yes—
221#894—34no—
222#894—34no—
223#894—34no—
224#894C2×D314yescomplemented
225#893—32no—
226#893C2×D312yescomplemented
227#892—32no—
228#892C2×D312yes—
229D3×C4⋊C4—32no—
230#890—34no—
231#890—34no—
232#890—34no—
233#890—64no—
234#889—34no—
235#888C2×D312yescomplemented
236#887—32no—
237#887—32no—
238#887—32no—
239#887—62no—
240#887C2×D314yescomplemented
241#886—34no—
242#885—34no—
243#883—34no—
244#882—34no—
245#67⋊C4—34no—
246#67⋊C4—34no—
247#67⋊C4—34no—
248#67⋊C4—34no—
249D3×C22⋊C4—32no—
250#879—34no—
251#879—34no—
252#879—34no—
253#878—34no—
254#877—34no—
255#877—32no—
256#875—32no—
257#874C2×D311yescharacteristic, complemented
258C4×D12—34no—
259C4×D12—34no—
260C4×D12—34no—
261#872—31no—
262#872—31no—
263#872—31no—
264#872—32no—
265#872—34no—
266#872—32no—
267#872—31no—
268#872—31no—
269#872—61no—
270#872C2×D311yescharacteristic
271C42×D3—31no—
272C42×D3—34no—
273C42×D3C2×D311yescharacteristic
274#870C2×D311yescharacteristic, complemented
275#869—31no—
276#869—31no—
277#869—61no—
278C4×Dic6—32no—
279C22×C3⋊D3C2411yescharacteristic
280C22×C3×D3C2411yescharacteristic
281C22×C3×D3C2414yes—
282C22×C3×D3C2411yescharacteristic
283C2×D32—22no—
284C2×D32—42no—
285C2×C32×C4C2412yes—
286C2×C32×C4C2414yes—
287C2×C32×C4C2411yescharacteristic
288C2×C3⋊Dic3C2414yes—
289C2×C3⋊Dic3C2412yes—
290C2×C3⋊Dic3C2411yescharacteristic
291C4×C3⋊D3—22no—
292#634—24no—
293C2×C3×Dic3C2412yes—
294C2×C3×Dic3C2414yes—
295C2×C3×Dic3C2412yes—
296C2×C3×Dic3C2411yescharacteristic
297C2×C3×Dic3C2411yescharacteristic
298C3×D12—24no—
299C3×D12—44no—
300C3×D12—44no—
301C3×C4×D3—22no—
302C3×C4×D3—44no—
303C3×C4×D3—42no—
304C3×C4×D3#4114yes—
305C3×Dic6—44no—
306#626—44no—
307#625—28no—
308#624—22no—
309D3×Dic3—22no—
310D3×Dic3—28no—
311D3×Dic3—22no—
312D3×Dic3—44no—
313D3×Dic3—42no—
314#542—92no—
315#542—92no—
316#541—91no—
317#541—91no—
318#540—31no—
319#540—91no—
320#539—94no—
321#538—94no—
322#533—31no—
323#532—91no—
324#529—94no—
325#529—94no—
326#525—92no—
327C4×#41—92no—
328C2×#117—91no—
329C23×D3—31no—
330C23×D3—31no—
331C2×C3×Q8—34no—
332C2×C3×D4—32no—
333C2×C3×D4—34no—
334C2×C3×D4—34no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—34no—
338C22×C3×C4—32no—
339C2×#67—34no—
340C2×#67—34no—
341C2×#67—34no—
342C22×Dic3—31no—
343C22×Dic3—34no—
344C22×Dic3—31no—
345C22×Dic3—34no—
346C22×Dic3—32no—
347#237—68no—
348#235—68no—
349C2×D12—34no—
350C2×D12C22×D312yes—
351C2×D12C22×D314yes—
352C2×D12C22×D314yes—
353C2×C4×D3—34no—
354C2×C4×D3—31no—
355C2×C4×D3—31no—
356C2×C4×D3—31no—
357C2×C4×D3—31no—
358C2×C4×D3—31no—
359C2×C4×D3—31no—
360C2×C4×D3—32no—
361C2×C4×D3—34no—
362C2×C4×D3—61no—
363C2×C4×D3—64no—
364C2×C4×D3—64no—
365C2×C4×D3C22×D311yescharacteristic
366C2×C4×D3C22×D314yes—
367C2×C4×D3C22×D312yes—
368C2×C4×D3C22×D311yescharacteristic
369C2×Dic6—32no—
370C2×Dic6—32no—
371C2×Dic6—62no—
372C2×Dic6C22×D314yes—
373C3×C4⋊C4—22no—
374C3×C4⋊C4—24no—
375C3×C4⋊C4—32no—
376C3×C4⋊C4—32no—
377C3×C4⋊C4—34no—
378C3×C4⋊C4—34no—
379C3×C4⋊C4C22×D312yes—
380C3×C4⋊C4C22×D312yes—
381C3×C4⋊C4C22×D314yes—
382C3×C4⋊C4C22×D314yes—
383C3×C22⋊C4—32no—
384C3×C22⋊C4—34no—
385C3×C22⋊C4—34no—
386C3×C22⋊C4—34no—
387C3×C42—21no—
388C3×C42—31no—
389C3×C42—34no—
390C3×C42—32no—
391C3×C42—31no—
392C3×C42C22×D311yescharacteristic
393C3×C42C22×D311yescharacteristic
394#217—34no—
395#217—32no—
396#217—34no—
397#217—34no—
398#217—34no—
399#217—34no—
400(C2×D3)⋊C4—32no—
401(C2×D3)⋊C4—34no—
402(C2×D3)⋊C4—34no—
403(C2×D3)⋊C4—34no—
404(C2×D3)⋊C4—34no—
405(C2×D3)⋊C4—34no—
406(C2×D3)⋊C4—32no—
407(C2×D3)⋊C4—32no—
408(C2×D3)⋊C4—34no—
409(C2×D3)⋊C4—34no—
410(C2×D3)⋊C4—32no—
411(C2×D3)⋊C4—32no—
412(C2×D3)⋊C4—62no—
413(C2×D3)⋊C4—64no—
414(C2×D3)⋊C4C22×D312yes—
415(C2×D3)⋊C4C22×D314yes—
416(C2×D3)⋊C4C22×D314yes—
417(C2×D3)⋊C4C22×D314yes—
418C4⋊Dic3—34no—
419C4⋊Dic3—34no—
420C4⋊Dic3—34no—
421C4⋊Dic3—34no—
422C4⋊Dic3—34no—
423C4⋊Dic3—32no—
424C4⋊Dic3—64no—
425C4⋊Dic3—64no—
426C4⋊Dic3C22×D312yes—
427Dic3⋊C4—32no—
428Dic3⋊C4—32no—
429Dic3⋊C4—34no—
430Dic3⋊C4—34no—
431Dic3⋊C4—34no—
432Dic3⋊C4—32no—
433Dic3⋊C4—32no—
434Dic3⋊C4—32no—
435Dic3⋊C4—34no—
436Dic3⋊C4—34no—
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—32no—
449C4×Dic3—34no—
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—24no—
461C2×C3×D3—21no—
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—24no—
472C3⋊Dic3—22no—
473C3×Dic3—21no—
474C3×Dic3—24no—
475C3×Dic3—22no—
476C3×Dic3—22no—
477C3×Dic3C2×#4112yes—
478C2×#41—92no—
479C23×C4—91no—
480C4⋊Q8—32no—
481C4⋊Q8—91no—
482#127—31no—
483#126—94no—
484#126—94no—
485#126—94no—
486#126—94no—
487#125—31no—
488#125—94no—
489#125—94no—
490#125D3211yescharacteristic, complemented
491#124—92no—
492#124—94no—
493#124—94no—
494#123—34no—
495#123—94no—
496#123—94no—
497#123—94no—
498#123—94no—
499C22⋊Q8—34no—
500C22⋊Q8—94no—
501C22⋊Q8—92no—
502C22⋊Q8—94no—
503C22⋊Q8—92no—
504#121—32no—
505#121—34no—
506#121—92no—
507#121—94no—
508#121—94no—
509#120—94no—
510C4×Q8—34no—
511C4×Q8—92no—
512C4×Q8—92no—
513C4×D4—32no—
514C4×D4—94no—
515C4×D4—94no—
516C4×D4—94no—
517C4×D4—94no—
518C4×D4—94no—
519C4×D4—92no—
520#117—32no—
521#117—31no—
522#117—91no—
523#117—92no—
524#117—94no—
525#117—92no—
526#117—91no—
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—31no—
535C23×C3—34no—
536C22×D3—31no—
537C22×D3—31no—
538C22×D3—61no—
539C22×D3—62no—
540C22×D3—62no—
541C22×D3—122no—
542C22×D3—122no—
543C22×D3C23×D311yescharacteristic
544C22×D3C23×D314yes—
545C22×D3C23×D311yescharacteristic
546C3×Q8—124no—
547C3×D4—64no—
548C3×D4—124no—
549C3×D4—124no—
550C2×C3×C4—21no—
551C2×C3×C4—24no—
552C2×C3×C4—22no—
553C2×C3×C4—31no—
554C2×C3×C4—34no—
555C2×C3×C4—32no—
556C2×C3×C4—34no—
557C2×C3×C4—31no—
558C2×C3×C4—32no—
559C2×C3×C4—62no—
560C2×C3×C4—124no—
561C2×C3×C4—122no—
562C2×C3×C4C23×D314yes—
563C2×C3×C4C23×D314yes—
564C2×C3×C4C23×D312yes—
565C2×C3×C4C23×D312yes—
566C2×C3×C4C23×D311yescharacteristic
567C2×C3×C4C23×D311yescharacteristic
568#67—68no—
569#67—68no—
570#67—124no—
571C2×Dic3—32no—
572C2×Dic3—32no—
573C2×Dic3—34no—
574C2×Dic3—34no—
575C2×Dic3—31no—
576C2×Dic3—31no—
577C2×Dic3—62no—
578C2×Dic3—64no—
579C2×Dic3—61no—
580C2×Dic3—62no—
581C2×Dic3—62no—
582C2×Dic3—68no—
583C2×Dic3—124no—
584C2×Dic3—122no—
585C2×Dic3C23×D312yes—
586C2×Dic3C23×D314yes—
587C2×Dic3C23×D312yes—
588C2×Dic3C23×D311yescharacteristic
589C2×Dic3C23×D311yescharacteristic
590D12—24no—
591D12—44no—
592D12—44no—
593D12—124no—
594C4×D3—22no—
595C4×D3—42no—
596C4×D3—44no—
597C4×D3—62no—
598C4×D3—62no—
599C4×D3—68no—
600C4×D3—62no—
601C4×D3—62no—
602C4×D3—62no—
603C4×D3—62no—
604C4×D3—122no—
605C4×D3—122no—
606C4×D3—124no—
607C4×D3#23914yes—
608Dic6—44no—
609Dic6—64no—
610Dic6—64no—
611Dic6—124no—
612C2×C32C22×#4111yescharacteristic
613C2×C32#58512yes—
614C3⋊D3—41no—
615C3×D3—22no—
616C3×D3—41no—
617C3×D3—44no—
618C24—91no—
619#41—188no—
620C2×Q8—34no—
621C2×Q8—92no—
622C2×D4—32no—
623C2×D4—34no—
624C2×D4—34no—
625C2×D4—94no—
626C2×D4—94no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—32no—
630C22×C4—34no—
631C22×C4—91no—
632C22×C4—94no—
633C22×C4—91no—
634C22×C4—91no—
635C22×C4—92no—
636C22×C4—94no—
637C22×C4—91no—
638C22×C4—184no—
639C4⋊C4—32no—
640C4⋊C4—32no—
641C4⋊C4—34no—
642C4⋊C4—34no—
643C4⋊C4—92no—
644C4⋊C4—92no—
645C4⋊C4—94no—
646C4⋊C4—94no—
647C4⋊C4—92no—
648C4⋊C4—94no—
649C4⋊C4—94no—
650C4⋊C4—94no—
651C4⋊C4C2×D3212yes—
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—64no—
679C22×C3—61no—
680C22×C3—64no—
681C22×C3—64no—
682C22×C3—62no—
683C22×C3C24×D311yescharacteristic
684C22×C3C24×D311yescharacteristic
685C2×D3—22no—
686C2×D3—21no—
687C2×D3—24no—
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×#23912yes—
700C3×C4—24no—
701C3×C4—22no—
702C3×C4—24no—
703C3×C4—22no—
704C3×C4—22no—
705C3×C4—32no—
706C3×C4—42no—
707C3×C4—44no—
708C3×C4—61no—
709C3×C4—62no—
710C3×C4—64no—
711C3×C4—62no—
712C3×C4C2×#23912yes—
713C3×C4D3×#4112yes—
714Dic3—21no—
715Dic3—22no—
716Dic3—24no—
717Dic3—22no—
718Dic3—64no—
719Dic3—61no—
720Dic3—64no—
721Dic3—61no—
722Dic3—62no—
723Dic3—62no—
724Dic3—124no—
725Dic3—121no—
726Dic3—122no—
727Dic3C2×#23912yes—
728C32#345511yescharacteristic, complemented, Sylow
729C23—31no—
730C23—31no—
731C23—34no—
732C23—91no—
733C23—182no—
734C23—362no—
735Q8—124no—
736Q8—184no—
737D4—64no—
738D4—124no—
739D4—124no—
740D4—188no—
741D4—364no—
742C2×C4—31no—
743C2×C4—34no—
744C2×C4—32no—
745C2×C4—32no—
746C2×C4—34no—
747C2×C4—31no—
748C2×C4—62no—
749C2×C4—92no—
750C2×C4—94no—
751C2×C4—91no—
752C2×C4—122no—
753C2×C4—124no—
754C2×C4—182no—
755C2×C4—182no—
756C2×C4—188no—
757C2×C4—182no—
758C2×C4—182no—
759C2×C4—362no—
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×#23911yescharacteristic
770C2×C3C2×D3×#4111yescharacteristic
771C2×C3#596412yes—
772C2×C3#596612yes—
773D3—22no—
774D3—41no—
775D3—44no—
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—22no—
791C4—24no—
792C4—32no—
793C4—61no—
794C4—62no—
795C4—62no—
796C4—64no—
797C4—181no—
798C4—184no—
799C4—182no—
800C4D3×#23912yes—
801C3—21no—
802C3#8627311yescharacteristic, complemented
803C3#8646711yescharacteristic, complemented
804C2—62no—
805C2—121no—
806C2—124no—
807C2—361no—
808C2C2×D3×#23911yescharacteristic
809C2#1059669612yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#125C22
hypercenter#125D32
hypocenterC32#3455
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #10596169C2semidirect
2. C3×#5697C2semidirect
3. C3×#5688C2semidirect
4. #10594651C2semidirect
5. #10594626C2semidirect
6. #10594494C2semidirect
7. #10594455C2semidirect
8. #10594426C2semidirect
9. #10594416C2semidirect
10. #10594358C2semidirect
11. #10594341C2semidirect
12. D3×#872C2semidirect
13. #10593950C2semidirect
14. #10593897C2semidirect
15. #10593881C2semidirect
20. C32×#125C22semidirect
23. #64099C22semidirect
24. #64096C22semidirect
26. #64078C22semidirect
30. C3×#894C22semidirect
31. C3×#893C22semidirect
33. C3×#888C22semidirect
34. C3×#887C22semidirect
35. C3×#874C22semidirect
38. C3×#870C22semidirect
45. #63898C22semidirect
47. Dic3×D12C22semidirect
49. #63887C22semidirect
52. #63884C22semidirect
56. #63877C22semidirect
59. C4×D3×Dic3C22semidirect
62. #63862C22semidirect
64. #63861C22semidirect
65. #63860C22semidirect
67. #63856C22semidirect
70. #63845C22semidirect
71. #63844C22semidirect
84. #5697D3semidirect
85. #5688D3semidirect
170. C3×#125C2×D3semidirect
171. C3×#125C2×D3semidirect
224. #894C2×D3semidirect
226. #893C2×D3semidirect
235. #888C2×D3semidirect
240. #887C2×D3semidirect
257. #874C2×D3semidirect
274. #870C2×D3semidirect
490. #125D32semidirect
728. C32#3455semidirect
802. C3#86273semidirect
803. C3#86467semidirect

Maximal subgroups

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

subgroupindex
#105961692
C3×#56972
C3×#56882
#105946512
#105946262
#105944942
#105944552
#105944262
#105944162
#105943582
#105943412
D3×#8722
#105939502
#105938972
#105938812
#864673
#862733