Finite Group Databasebeta

← #11901839

Subgroups — #11901839

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#10595989C211yesmaximal, characteristic, complemented
2C3×#5535C211yesmaximal, characteristic, complemented
3C3×D3×#117C211yesmaximal, characteristic, complemented
4#10594983C212yesmaximal, complemented
5#10594892C212yesmaximal, complemented
6#10594539C214yesmaximal, complemented
7#10594404C214yesmaximal, complemented
8#10594195C214yesmaximal, complemented
9#10594086C214yesmaximal, complemented
10#10593983C212yesmaximal, complemented
11#10593949C211yesmaximal, characteristic, complemented
12#10593897C211yesmaximal, characteristic, complemented
13C4×#3795C212yesmaximal, complemented
14#10593881C211yesmaximal, characteristic, complemented
15#10593874C211yesmaximal, characteristic, complemented
16#86467—31nomaximal
17#85738—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C2×#3795C2212yes—
20C32×#117C2211yescharacteristic
21#64133C2212yes—
22#64098C2214yescomplemented
23#64088C2214yes—
24#64079C2211yescharacteristic, complemented
25#64078C2211yescharacteristic, complemented
26C4×#634C2212yescomplemented
27C3×#930C2212yes—
28C3×#926C2211yescharacteristic
29C3×#894C2214yescomplemented
30C3×#892C2212yes—
31C3×D3×C4⋊C4C2212yes—
32C3×#884C2214yes—
33C3×D3×C22⋊C4C2212yes—
34C3×#877C2212yes—
35C3×#874C2211yescharacteristic, complemented
36C3×C4×D12C2212yescomplemented
37C3×#872C2211yescharacteristic
38C3×#872C2211yescharacteristic
39C3×C42×D3C2211yescharacteristic
40C3×C42×D3C2211yescharacteristic
41C3×#870C2211yescharacteristic, complemented
42#63976C2214yes—
43Dic3×#67C2214yes—
44#63969C2214yes—
45#63959C2214yes—
46#63918C2212yescomplemented
47#63915C2214yes—
48#63908C2212yes—
49#63908C2214yes—
50#63905C2214yes—
51#63905C2214yes—
52C4×#625C2214yes—
53#63899C2214yescomplemented
54Dic3×D12C2214yescomplemented
55Dic3×D12C2212yescomplemented
56#63885C2214yes—
57#63884C2214yescomplemented
58#63879C2214yes—
59#63879C2214yes—
60#63877C2214yescomplemented
61C4×D3×Dic3C2214yescomplemented
62#63862C2214yescomplemented
63#63861C2214yes—
64#63860C2212yescomplemented
65#63858C2214yescomplemented
66#63857C2212yes—
67#63851C2214yes—
68#63851C2214yescomplemented
69#63845C2214yescomplemented
70#63844C2212yescomplemented
71#63841C2212yes—
72#63837C2214yescomplemented
73C3×#540—31no—
74C2×C3×#117—31no—
75#5791—32no—
76#5719—31no—
77#5716—31no—
78#5698—31no—
79#5688—31no—
80#5660—34no—
81#5649—34no—
82#5613—34no—
83#5606—32no—
84#5603—32no—
85#5600—34no—
86#5561—32no—
87C4×#237—32no—
88#5535—31no—
89#5535D311yescharacteristic, complemented
90#5534—32no—
91#5534—32no—
92#5528—34no—
93#5528—34no—
94D3×#117D311yescharacteristic, complemented
95#5518—31no—
96#5518—31no—
97#5518—31no—
98#5518—61no—
99#5515—34no—
100#5494—34no—
101#5477—31no—
102C4×#235—32no—
103#5470—31no—
104C23×C3×D3C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C2×#634C2312yes—
107C2×C3×#67C2314yes—
108C22×C3×Dic3C2311yescharacteristic
109C2×C3×D12C2312yes—
110C2×C3×D12C2314yes—
111C2×C3×C4×D3—24no—
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×C4×D3C2312yes—
116C2×C3×C4×D3C2312yes—
117C2×C3×C4×D3C2314yes—
118C2×C3×C4×D3C2311yescharacteristic
119C2×#627C2314yes—
120C2×#625C2314yes—
121C2×#625C2314yes—
122C2×D3×Dic3C2314yes—
123C2×D3×Dic3C2314yes—
124#3795—28no—
125C32×C4⋊C4C2312yes—
126C32×C22⋊C4C2312yes—
127C32×C42C2311yescharacteristic
128C32×C42C2311yescharacteristic
129#3757C2314yes—
130C4⋊(C3⋊Dic3)C2312yes—
131C4⋊(C3⋊Dic3)C2314yes—
132#3750C2314yes—
133#3750C2314yes—
134#3750C2314yes—
135C4×C3⋊Dic3C2314yes—
136C3×#217C2312yes—
137C3×(C2×D3)⋊C4C2312yes—
138C3×(C2×D3)⋊C4C2312yes—
139C3×(C2×D3)⋊C4C2314yes—
140C3×(C2×D3)⋊C4C2314yes—
141C3×C4⋊Dic3C2312yes—
142C3×C4⋊Dic3C2312yes—
143C3×Dic3⋊C4C2312yes—
144C3×Dic3⋊C4C2312yes—
145C3×Dic3⋊C4C2314yes—
146C3×C4×Dic3C2312yes—
147C3×C4×Dic3C2312yes—
148C3×C4×Dic3C2311yescharacteristic
149C3×C4×Dic3C2311yescharacteristic
150#3724C2314yes—
151Dic3⋊Dic3C2314yes—
152Dic3⋊Dic3C2314yes—
153(C2×D3)⋊Dic3C2314yes—
154(C2×D3)⋊Dic3C2314yes—
155(C2×D3)⋊Dic3C2314yes—
156(C2×D3)⋊Dic3C2314yes—
157(C2×D3)⋊Dic3C2314yes—
158(C2×D3)⋊Dic3C2314yes—
159Dic32C2314yes—
160Dic32C2314yes—
161#3455—91noSylow
162C23×C3×C4—31no—
163C2×#237—32no—
164C2×#235—32no—
165C22×C4×D3C2×D311yescharacteristic
166C3×#127—31no—
167C3×#125—31no—
168C3×#123—34no—
169C3×#121—32no—
170C3×#121—34no—
171C3×C4×D4—32no—
172C3×#117—21no—
173C3×#117—31no—
174C3×#117—32no—
175C3×#117—32no—
176C3×#117—31no—
177C3×#117—31no—
178C3×#117C2×D311yescharacteristic
179C3×#117C2×D311yescharacteristic
180C2×C3×C4⋊C4—32no—
181C2×C3×C22⋊C4—32no—
182C2×C3×C42—31no—
183C2×C3×C42—31no—
184#953—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—34no—
194D4×Dic3—34no—
195D4×Dic3—32no—
196#930—34no—
197#930—32no—
198#930C2×D312yes—
199#929—34no—
200#929—34no—
201C4×#67—34no—
202C4×#67—34no—
203C4×#67—34no—
204C4×#67—34no—
205C4×#67—34no—
206#926—32no—
207#926C2×D311yescharacteristic
208#924—32no—
209#924—32no—
210#924—32no—
211#924—34no—
212#924—34no—
213#924—62no—
214C2×C4×Dic3—34no—
215#898—34no—
216#898—34no—
217#898—34no—
218#897—32no—
219#896—34no—
220#896—34no—
221#896—34no—
222#894—34no—
223#894C2×D314yescomplemented
224#892—32no—
225#892C2×D312yes—
226D3×C4⋊C4C2×D312yes—
227#890—34no—
228#889—34no—
229#889—34no—
230#889—34no—
231#889—64no—
232#888—32no—
233#887—34no—
234#887—32no—
235#885—34no—
236#885—34no—
237#885—34no—
238#884—34no—
239#884C2×D314yes—
240#883—34no—
241#883—34no—
242#883—34no—
243#67⋊C4—34no—
244#67⋊C4—34no—
245D3×C22⋊C4C2×D312yes—
246#879—34no—
247#879—34no—
248#879—34no—
249#879—34no—
250#879—34no—
251#879—64no—
252#878—34no—
253#877—34no—
254#877C2×D312yes—
255#875—32no—
256#874C2×D311yescharacteristic, complemented
257C4×D12—32no—
258C4×D12—34no—
259C4×D12C2×D312yescomplemented
260#872—34no—
261#872C2×D311yescharacteristic
262#872C2×D311yescharacteristic
263C42×D3—34no—
264C42×D3C2×D311yescharacteristic
265C42×D3C2×D311yescharacteristic
266#870—31no—
267#870—31no—
268#870—61no—
269#870C2×D311yescharacteristic, complemented
270#869—31no—
271#869—31no—
272#869—32no—
273#869—61no—
274C4×Dic6—32no—
275C4×Dic6—32no—
276C4×Dic6—32no—
277C4×Dic6—34no—
278C4×Dic6—62no—
279C23×C32C2411yescharacteristic
280C22×C3×D3—22no—
281C22×C3×D3—42no—
282C22×C3×D3C2411yescharacteristic
283C22×C3×D3C2414yes—
284C22×C3×D3C2411yescharacteristic
285C2×C32×C4—22no—
286C2×C32×C4C2412yes—
287C2×C32×C4C2412yes—
288C2×C32×C4C2411yescharacteristic
289C2×C32×C4C2411yescharacteristic
290C2×C3⋊Dic3C2414yes—
291C2×C3⋊Dic3C2414yes—
292#634—24no—
293C3×#67—44no—
294C2×C3×Dic3—22no—
295C2×C3×Dic3C2414yes—
296C2×C3×Dic3C2412yes—
297C2×C3×Dic3C2411yescharacteristic
298C2×C3×Dic3C2412yes—
299C2×C3×Dic3C2411yescharacteristic
300C3×D12—24no—
301C3×D12—44no—
302C3×C4×D3—22no—
303C3×C4×D3—22no—
304C3×C4×D3—22no—
305C3×C4×D3—42no—
306C3×C4×D3—42no—
307C3×C4×D3—44no—
308C3×C4×D3#4114yes—
309#627—44no—
310#625—28no—
311#625—44no—
312D3×Dic3—28no—
313D3×Dic3—44no—
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—91no—
323#532—91no—
324#529—94no—
325#529—94no—
326#525—92no—
327C4×#41—92no—
328C2×#117—31no—
329C24×C3—31no—
330C23×D3C22×D311yescharacteristic
331C2×C3×D4—34no—
332C2×C3×D4—32no—
333C2×C3×D4—34no—
334C22×C3×C4—21no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—34no—
341C22×C3×C4—32no—
342C22×C3×C4—32no—
343C22×C3×C4—64no—
344C22×C3×C4C22×D311yescharacteristic
345C22×C3×C4C22×D311yescharacteristic
346C2×#67—34no—
347C2×#67—34no—
348C2×#67—34no—
349C2×#67—34no—
350C2×#67C22×D314yes—
351C22×Dic3—34no—
352C22×Dic3—34no—
353C22×Dic3C22×D311yescharacteristic
354#237—68no—
355#235—68no—
356C2×D12C22×D312yes—
357C2×D12C22×D314yes—
358C2×C4×D3—24no—
359C2×C4×D3—34no—
360C2×C4×D3—34no—
361C2×C4×D3C22×D311yescharacteristic
362C2×C4×D3C22×D311yescharacteristic
363C2×C4×D3C22×D311yescharacteristic
364C2×C4×D3C22×D314yes—
365C2×C4×D3C22×D312yes—
366C2×C4×D3C22×D312yes—
367C2×C4×D3C22×D311yescharacteristic
368C2×Dic6—32no—
369C2×Dic6—32no—
370C2×Dic6—34no—
371C2×Dic6—34no—
372C2×Dic6—62no—
373C3×C4⋊C4—22no—
374C3×C4⋊C4—32no—
375C3×C4⋊C4—34no—
376C3×C4⋊C4—32no—
377C3×C4⋊C4—32no—
378C3×C4⋊C4—32no—
379C3×C4⋊C4C22×D312yes—
380C3×C4⋊C4C22×D312yes—
381C3×C22⋊C4—22no—
382C3×C22⋊C4—32no—
383C3×C22⋊C4—34no—
384C3×C22⋊C4—34no—
385C3×C22⋊C4—32no—
386C3×C22⋊C4—32no—
387C3×C22⋊C4C22×D312yes—
388C3×C22⋊C4C22×D312yes—
389C3×C42—21no—
390C3×C42—21no—
391C3×C42—32no—
392C3×C42—31no—
393C3×C42—31no—
394C3×C42—32no—
395C3×C42C22×D311yescharacteristic
396C3×C42C22×D311yescharacteristic
397C3×C42C22×D311yescharacteristic
398C3×C42C22×D311yescharacteristic
399#217—34no—
400#217—34no—
401#217—34no—
402#217—34no—
403#217—34no—
404#217—34no—
405#217—34no—
406#217—34no—
407#217—64no—
408#217C22×D312yes—
409(C2×D3)⋊C4—34no—
410(C2×D3)⋊C4—34no—
411(C2×D3)⋊C4—34no—
412(C2×D3)⋊C4—34no—
413(C2×D3)⋊C4—34no—
414(C2×D3)⋊C4—34no—
415(C2×D3)⋊C4C22×D314yes—
416(C2×D3)⋊C4C22×D312yes—
417(C2×D3)⋊C4C22×D312yes—
418(C2×D3)⋊C4C22×D314yes—
419C4⋊Dic3—32no—
420C4⋊Dic3—32no—
421C4⋊Dic3—34no—
422C4⋊Dic3—34no—
423C4⋊Dic3—34no—
424C4⋊Dic3—34no—
425C4⋊Dic3—62no—
426C4⋊Dic3—64no—
427C4⋊Dic3C22×D312yes—
428C4⋊Dic3C22×D312yes—
429Dic3⋊C4—34no—
430Dic3⋊C4—34no—
431Dic3⋊C4—34no—
432Dic3⋊C4—34no—
433Dic3⋊C4—34no—
434Dic3⋊C4—34no—
435Dic3⋊C4—34no—
436Dic3⋊C4—34no—
437Dic3⋊C4—34no—
438Dic3⋊C4—34no—
439Dic3⋊C4—64no—
440Dic3⋊C4—64no—
441Dic3⋊C4—64no—
442Dic3⋊C4C22×D314yes—
443Dic3⋊C4C22×D312yes—
444Dic3⋊C4C22×D312yes—
445C4×Dic3—34no—
446C4×Dic3—34no—
447C4×Dic3—34no—
448C4×Dic3—34no—
449C4×Dic3—34no—
450C4×Dic3—34no—
451C4×Dic3—64no—
452C4×Dic3C22×D311yescharacteristic
453C4×Dic3C22×D311yescharacteristic
454C4×Dic3C22×D312yes—
455C4×Dic3C22×D312yes—
456C22×C32—21no—
457C22×C32—22no—
458C22×C32C2511yescharacteristic
459C2×C3×D3—22no—
460C2×C3×D3—24no—
461C2×C3×D3—21no—
462C2×C3×D3—24no—
463C2×C3×D3—22no—
464C2×C3×D3—24no—
465C2×C3×D3—44no—
466C2×C3×D3C2×#4112yes—
467C32×C4—21no—
468C32×C4—22no—
469C32×C4—22no—
470C32×C4C2×#4112yes—
471C3⋊Dic3—24no—
472C3⋊Dic3—24no—
473C3×Dic3—21no—
474C3×Dic3—22no—
475C3×Dic3—22no—
476C3×Dic3—24no—
477C3×Dic3C2×#4112yes—
478C2×#41—92no—
479C23×C4—31no—
480C4⋊Q8—92no—
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#125—91no—
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—94no—
500C22⋊Q8—92no—
501C22⋊Q8—94no—
502C22⋊Q8—94no—
503C22⋊Q8—92no—
504#121—32no—
505#121—34no—
506#121—94no—
507#121—92no—
508#121—94no—
509#120—94no—
510C4×Q8—92no—
511C4×Q8—94no—
512C4×Q8—92no—
513C4×D4—32no—
514C4×D4—92no—
515C4×D4—94no—
516C4×D4—94no—
517C4×D4—94no—
518C4×D4—94no—
519C4×D4—94no—
520#117—31no—
521#117—32no—
522#117—32no—
523#117—31no—
524#117—31no—
525#117—94no—
526#117—92no—
527#117D3211yescharacteristic
528C2×C4⋊C4—32no—
529C2×C22⋊C4—32no—
530C2×C42—31no—
531C2×C42—31no—
532C2×C42—94no—
533C23×C3—21no—
534C23×C3—31no—
535C23×C3—31no—
536C23×C3—34no—
537C23×C3—62no—
538C23×C3—122no—
539C23×C3C23×D311yescharacteristic
540C23×C3C23×D311yescharacteristic
541C22×D3—22no—
542C22×D3—42no—
543C22×D3C23×D311yescharacteristic
544C22×D3C23×D314yes—
545C22×D3C23×D311yescharacteristic
546C3×D4—64no—
547C3×D4—124no—
548C3×D4—124no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—21no—
552C2×C3×C4—22no—
553C2×C3×C4—21no—
554C2×C3×C4—22no—
555C2×C3×C4—31no—
556C2×C3×C4—34no—
557C2×C3×C4—34no—
558C2×C3×C4—32no—
559C2×C3×C4—31no—
560C2×C3×C4—32no—
561C2×C3×C4—42no—
562C2×C3×C4—62no—
563C2×C3×C4—62no—
564C2×C3×C4—62no—
565C2×C3×C4—62no—
566C2×C3×C4—124no—
567C2×C3×C4—122no—
568C2×C3×C4—122no—
569C2×C3×C4C23×D312yes—
570C2×C3×C4C23×D312yes—
571C2×C3×C4C23×D312yes—
572C2×C3×C4C23×D311yescharacteristic
573C2×C3×C4C23×D311yescharacteristic
574C2×C3×C4C23×D312yes—
575C2×C3×C4C23×D311yescharacteristic
576C2×C3×C4C23×D311yescharacteristic
577#67—44no—
578#67—68no—
579#67—68no—
580#67—124no—
581#67—124no—
582C2×Dic3—22no—
583C2×Dic3—34no—
584C2×Dic3—34no—
585C2×Dic3—34no—
586C2×Dic3—34no—
587C2×Dic3—64no—
588C2×Dic3—64no—
589C2×Dic3—68no—
590C2×Dic3—124no—
591C2×Dic3C23×D312yes—
592C2×Dic3C23×D314yes—
593C2×Dic3C23×D312yes—
594C2×Dic3C23×D311yescharacteristic
595C2×Dic3C23×D311yescharacteristic
596D12—24no—
597D12—44no—
598C4×D3—22no—
599C4×D3—22no—
600C4×D3—22no—
601C4×D3—42no—
602C4×D3—42no—
603C4×D3—44no—
604C4×D3—68no—
605C4×D3—124no—
606C4×D3#23514yes—
607Dic6—64no—
608Dic6—64no—
609Dic6—124no—
610Dic6—124no—
611Dic6—124no—
612C2×C32—41no—
613C2×C32C22×#4111yescharacteristic
614C2×C32#58512yes—
615C3×D3—22no—
616C3×D3—44no—
617C3×D3—41no—
618C24—31no—
619#41—188no—
620C2×Q8—94no—
621C2×Q8—92no—
622C2×D4—34no—
623C2×D4—32no—
624C2×D4—34no—
625C2×D4—94no—
626C2×D4—94no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—31no—
630C22×C4—31no—
631C22×C4—31no—
632C22×C4—32no—
633C22×C4—32no—
634C22×C4—34no—
635C22×C4—64no—
636C22×C4—94no—
637C22×C4—94no—
638C22×C4C2×D3211yescharacteristic
639C4⋊C4—32no—
640C4⋊C4—32no—
641C4⋊C4—32no—
642C4⋊C4—32no—
643C4⋊C4—34no—
644C4⋊C4—94no—
645C4⋊C4—94no—
646C4⋊C4—94no—
647C4⋊C4—92no—
648C4⋊C4—94no—
649C4⋊C4—94no—
650C4⋊C4—94no—
651C4⋊C4—94no—
652C4⋊C4C2×D3212yes—
653C22⋊C4—32no—
654C22⋊C4—32no—
655C22⋊C4—32no—
656C22⋊C4—34no—
657C22⋊C4—34no—
658C22⋊C4—94no—
659C22⋊C4—94no—
660C22⋊C4—94no—
661C22⋊C4—94no—
662C22⋊C4—94no—
663C22⋊C4—94no—
664C22⋊C4—94no—
665C22⋊C4C2×D3212yes—
666C42—32no—
667C42—32no—
668C42—31no—
669C42—31no—
670C42—94no—
671C42—94no—
672C42—94no—
673C42C2×D3211yescharacteristic
674C42C2×D3211yescharacteristic
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—22no—
678C22×C3—22no—
679C22×C3—21no—
680C22×C3—32no—
681C22×C3—41no—
682C22×C3—42no—
683C22×C3—62no—
684C22×C3—64no—
685C22×C3—61no—
686C22×C3—64no—
687C22×C3—64no—
688C22×C3—62no—
689C22×C3—124no—
690C22×C3C24×D311yescharacteristic
691C22×C3C24×D311yescharacteristic
692C2×D3—22no—
693C2×D3—21no—
694C2×D3—24no—
695C2×D3—22no—
696C2×D3—24no—
697C2×D3—24no—
698C2×D3—44no—
699C2×D3C2×#23512yes—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—22no—
703C3×C4—22no—
704C3×C4—22no—
705C3×C4—22no—
706C3×C4—22no—
707C3×C4—32no—
708C3×C4—41no—
709C3×C4—42no—
710C3×C4—42no—
711C3×C4—61no—
712C3×C4—64no—
713C3×C4—62no—
714C3×C4—62no—
715C3×C4C2×#23512yes—
716C3×C4D3×#4112yes—
717Dic3—21no—
718Dic3—22no—
719Dic3—22no—
720Dic3—24no—
721Dic3—64no—
722Dic3—64no—
723Dic3—64no—
724Dic3—64no—
725Dic3—124no—
726Dic3—124no—
727Dic3C2×#23512yes—
728C32#345511yescharacteristic, complemented, Sylow
729C23—31no—
730C23—31no—
731C23—34no—
732C23—62no—
733C23—122no—
734C23C22×D3211yescharacteristic
735Q8—184no—
736Q8—364no—
737D4—64no—
738D4—124no—
739D4—124no—
740D4—188no—
741D4—364no—
742C2×C4—22no—
743C2×C4—31no—
744C2×C4—34no—
745C2×C4—32no—
746C2×C4—32no—
747C2×C4—34no—
748C2×C4—31no—
749C2×C4—62no—
750C2×C4—62no—
751C2×C4—62no—
752C2×C4—62no—
753C2×C4—94no—
754C2×C4—94no—
755C2×C4—122no—
756C2×C4—124no—
757C2×C4—122no—
758C2×C4—188no—
759C2×C4—364no—
760C2×C4C22×D3212yes—
761C2×C4C22×D3212yes—
762C2×C4C22×D3211yescharacteristic
763C2×C4C22×D3211yescharacteristic
764C2×C3—21no—
765C2×C3—22no—
766C2×C3—41no—
767C2×C3—41no—
768C2×C3—62no—
769C2×C3—81no—
770C2×C3—121no—
771C2×C3—124no—
772C2×C3C22×#23511yescharacteristic
773C2×C3C2×D3×#4111yescharacteristic
774C2×C3#596412yes—
775C2×C3#596612yes—
776D3—22no—
777D3—44no—
778D3—41no—
779C22—21no—
780C22—22no—
781C22—32no—
782C22—62no—
783C22—61no—
784C22—64no—
785C22—64no—
786C22—64no—
787C22—62no—
788C22—124no—
789C22C23×D3211yescharacteristic
790C4—21no—
791C4—22no—
792C4—22no—
793C4—32no—
794C4—61no—
795C4—62no—
796C4—64no—
797C4—62no—
798C4—184no—
799C4—184no—
800C4D3×#23512yes—
801C3—21no—
802C3#8573811yescharacteristic, complemented
803C3#8646711yescharacteristic, complemented
804C2—41no—
805C2—62no—
806C2—121no—
807C2—124no—
808C2C2×D3×#23511yescharacteristic
809C2#1059669612yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3455
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595989C2semidirect
2. C3×#5535C2semidirect
3. C3×D3×#117C2semidirect
4. #10594983C2semidirect
5. #10594892C2semidirect
6. #10594539C2semidirect
7. #10594404C2semidirect
8. #10594195C2semidirect
9. #10594086C2semidirect
10. #10593983C2semidirect
11. #10593949C2semidirect
12. #10593897C2semidirect
13. C4×#3795C2semidirect
14. #10593881C2semidirect
15. #10593874C2semidirect
22. #64098C22semidirect
24. #64079C22semidirect
25. #64078C22semidirect
26. C4×#634C22semidirect
29. C3×#894C22semidirect
35. C3×#874C22semidirect
36. C3×C4×D12C22semidirect
41. C3×#870C22semidirect
46. #63918C22semidirect
53. #63899C22semidirect
54. Dic3×D12C22semidirect
55. Dic3×D12C22semidirect
57. #63884C22semidirect
60. #63877C22semidirect
61. C4×D3×Dic3C22semidirect
62. #63862C22semidirect
64. #63860C22semidirect
65. #63858C22semidirect
68. #63851C22semidirect
69. #63845C22semidirect
70. #63844C22semidirect
72. #63837C22semidirect
89. #5535D3semidirect
94. D3×#117D3semidirect
223. #894C2×D3semidirect
256. #874C2×D3semidirect
259. C4×D12C2×D3semidirect
269. #870C2×D3semidirect
728. C32#3455semidirect
802. C3#85738semidirect
803. C3#86467semidirect

Maximal subgroups

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

subgroupindex
#105959892
C3×#55352
C3×D3×#1172
#105949832
#105948922
#105945392
#105944042
#105941952
#105940862
#105939832
#105939492
#105938972
C4×#37952
#105938812
#105938742
#864673
#857383