Finite Group Databasebeta

← #11885819

Subgroups — #11885819

Order 1152.

1146 conjugacy classes of subgroups.

The subgroup lattice has 931 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595254C211yesmaximal, characteristic, complemented
2C2×#63933C211yesmaximal, characteristic, complemented
3C2×#63926C211yesmaximal, characteristic, complemented
4#10594630C211yesmaximal, characteristic, complemented
5#10592475C211yesmaximal, characteristic, complemented
6C3×#4781C211yesmaximal, characteristic, complemented
7C3×#4756C211yesmaximal, characteristic, complemented
8#10591468C211yesmaximal, characteristic, complemented
9#10590968C211yesmaximal, characteristic, complemented
10#10590943C211yesmaximal, characteristic, complemented
11#10590862C211yesmaximal, characteristic, complemented
12#10590721C211yesmaximal, characteristic, complemented
13#10590576C211yesmaximal, characteristic, complemented
14#10590534C211yesmaximal, characteristic, complemented
15#10590525C211yesmaximal, characteristic, complemented
16#80101—31nomaximal
17#79606—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic, complemented
20C2×#3802C2211yescharacteristic
21C2×#3795C2211yescharacteristic, complemented
22C2×#3754C2211yescharacteristic, complemented
23C2×#3744C2211yescharacteristic, complemented
24#64106C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic, complemented
26C2×C3×#213C2211yescharacteristic
27C2×C3×#213C2211yescharacteristic
28C2×C3×#204C2211yescharacteristic, complemented
29C3×#895C2211yescharacteristic, complemented
30C3×#893C2211yescharacteristic, complemented
31#63981—21no—
32#63978—21no—
33#63966—21no—
34C2×#3722—21no—
35#63933—24no—
36#63926—24no—
37#63922—21no—
38D3×(C2×D3)⋊C4—21no—
39#63909C2211yescharacteristic, complemented
40#63908—21no—
41C4×#626C2211yescharacteristic
42#63891—21no—
43#63871C2211yescharacteristic
44#63864C2211yescharacteristic, complemented
45#63860C2211yescharacteristic, complemented
46C2×#3719C2211yescharacteristic, complemented
47C2×#3715C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50C2×#3710C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52C32×#102C2211yescharacteristic, complemented
53#63647C2211yescharacteristic
54#63636C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×C8×Dic3C2211yescharacteristic, complemented
58C3×#810C2211yescharacteristic, complemented
59C3×#807C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#5829—31no—
64C2×#950—31no—
65C2×#912—31no—
66C2×D3×D8—31no—
67C2×D3×D8—31no—
68#5612—31no—
69#5554—31no—
70#5554—31no—
71C3×#449—31no—
72C3×C4×D8—31no—
73#5169—31no—
74#5168—31no—
75#5153—31no—
76#5038—31no—
77#5016—31no—
78#5016—31no—
79#4887—31no—
80#4883—31no—
81#4819—31no—
82#4813—31no—
83#4781—31no—
84#4781D311yescharacteristic, complemented
85#4776—31no—
86#4776—31no—
87#4776—31no—
88#4776—61no—
89#4756D311yescharacteristic, complemented
90#4734—31no—
91#67⋊C8—31no—
92#4696—31no—
93C8×D12—31no—
94C23×C3⋊D3—21no—
95C22×D32—21no—
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98D4×C3⋊D3—22no—
99D4×C3⋊D3—41no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C2×C3×#67—21no—
104C22×C3×Dic3—21no—
105C22×C3×Dic3—21no—
106C3×#237—22no—
107C3×#237—41no—
108C2×C3×D12—21no—
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×Dic6C2311yescharacteristic
114C2×#626—21no—
115C2×#626D411yescharacteristic
116C2×#625—21no—
117C2×#625—21no—
118C2×D3×Dic3—21no—
119#3802—22no—
120#3802—41no—
121#3795—22no—
122#3795—41no—
123C2×C32×C8C2311yescharacteristic
124C32×C4⋊C4C2311yescharacteristic
125#3754—22no—
126#3752—21no—
127C4⋊(C3⋊Dic3)—21no—
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129#3744—41no—
130C3×#217—21no—
131C3×#213—22no—
132C3×#213D414yescomplemented
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×C4⋊Dic3C2311yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×#204—41no—
140Dic3⋊Dic3—21no—
141Dic3⋊Dic3D411yescharacteristic
142#3722—21no—
143#3722—21no—
144#3722—21no—
145#3722—21no—
146#3722D411yescharacteristic
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3D411yescharacteristic
150#3719—22no—
151#3715—22no—
152#3714—22no—
153#3714—22no—
154#3710—22no—
155D3×C3⋊C8—22no—
156#3280—91noSylow
157C2×C3×#41—31no—
158C2×#237—31no—
159C2×#237C2×D311yescharacteristic, complemented
160C2×D3×D4—31no—
161C2×D3×D4—31no—
162C2×D3×D4—31no—
163C2×D3×D4—31no—
164C2×D3×D4—61no—
165C2×#235—31no—
166C2×C3×SD16—31no—
167C2×C3×D8—31no—
168C2×C3×D8—31no—
169C3×#121—31no—
170C3×C4×D4—31no—
171C3×C4×D4—31no—
172#950—64no—
173#947—31no—
174#946—31no—
175C2×#216—31no—
176C2×#215—31no—
177#939—61no—
178#938—61no—
179#937—61no—
180#937—61no—
181#936—31no—
182D4×Dic3C2×D311yescharacteristic, complemented
183C2×#214—31no—
184C2×#214—31no—
185C2×#214—31no—
186C2×#214—61no—
187C2×#213—31no—
188C2×#213—31no—
189C2×#213C2×D311yescharacteristic
190C2×#213C2×D311yescharacteristic
191#930—31no—
192#930—61no—
193#930—61no—
194#929—61no—
195C4×#67—31no—
196C2×(C2×D3)⋊C4—61no—
197C2×(C2×D3)⋊C4—61no—
198C2×(C2×D3)⋊C4—61no—
199C22×C3⋊C8—31no—
200#912—64no—
201D3×D8—64no—
202D3×D8—64no—
203C2×Dic12—31no—
204C2×D24—31no—
205C2×D24—31no—
206C2×#204—31no—
207C2×#204—31no—
208C2×#204—61no—
209C2×#204C2×D311yescharacteristic, complemented
210C2×D3×C8—31no—
211C2×D3×C8—31no—
212C2×D3×C8—31no—
213#897—31no—
214#897—31no—
215#897—31no—
216#897—61no—
217#895—31no—
218#895C2×D311yescharacteristic, complemented
219#893C2×D311yescharacteristic, complemented
220#886—61no—
221#886—61no—
222#883—61no—
223#882—61no—
224#882—61no—
225D3×C22⋊C4—61no—
226#875—31no—
227#875—31no—
228C4×D12—31no—
229C3×#107—31no—
230C3×#103—31no—
231C3×#102—21no—
232C3×#102—31no—
233C3×#102C2×D311yescharacteristic, complemented
234C3×#102C2×D311yescharacteristic, complemented
235C3×C22⋊C8—31no—
236C3×C4×C8—31no—
237#832—31no—
238#821C2×D311yescharacteristic, complemented
239(C2×D3)⋊C8—31no—
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—61no—
242(C2×D3)⋊C8C2×D311yescharacteristic, complemented
243#816—31no—
244Dic3⋊C8—31no—
245C8×Dic3C2×D311yescharacteristic, complemented
246#810—31no—
247#810C2×D311yescharacteristic, complemented
248#809—31no—
249#809—31no—
250#809—31no—
251#809—61no—
252#807C2×D311yescharacteristic, complemented
253C4⋊(C3⋊C8)—31no—
254C23×C32—21no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3—42no—
257C22×C3⋊D3—42no—
258C22×C3⋊D3—81no—
259C22×C3⋊D3C2×D411yescharacteristic
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3C2×D411yescharacteristic
263C2×D32—42no—
264C2×D32—42no—
265C2×D32—81no—
266C32×D4—21no—
267C32×D4C2×D412yes—
268C2×C32×C4—21no—
269C2×C32×C4C2411yescharacteristic
270#638—42no—
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3C2×D411yescharacteristic
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—21no—
275C4×C3⋊D3—21no—
276C4×C3⋊D3—21no—
277#634—21no—
278#634—21no—
279C3×#67—42no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—42no—
283C2×C3×Dic3—81no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—81no—
291C3×D12C2×D412yes—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×C4×D3—81no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297#626—22no—
298#626—81no—
299#625—42no—
300#625—42no—
301D3×Dic3—42no—
302C32×C8—21no—
303C3⋊(C3⋊C8)—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×#135—91no—
307C22×D8—91no—
308#546—91no—
309#546—91no—
310#495—91no—
311#467—91no—
312#466—91no—
313#463—91no—
314#463—91no—
315#450—91no—
316#450—91no—
317#449—31no—
318#449—91no—
319C4×D8—31no—
320C8×D4—91no—
321C23×D3—61no—
322C23×D3—61no—
323C23×D3—61no—
324C23×D3—61no—
325C23×D3—121no—
326C3×#41—62no—
327C3×#41—121no—
328C2×C3×Q8—31no—
329C2×C3×D4—21no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—61no—
333C2×C3×D4—61no—
334C2×C3×D4C22×D311yescharacteristic
335C2×C3×D4C22×D311yescharacteristic
336C22×C3×C4—31no—
337C22×C3×C4—61no—
338C22×C3×C4—61no—
339C22×C3×C4—61no—
340C2×#67—21no—
341C2×#67—31no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—121no—
350C22×Dic3—21no—
351C22×Dic3—21no—
352C22×Dic3—61no—
353#237—22no—
354#237—41no—
355#237—62no—
356#237—121no—
357D3×D4—62no—
358D3×D4—62no—
359D3×D4—62no—
360D3×D4—62no—
361D3×D4—122no—
362D3×D4—121no—
363D3×D4—121no—
364D3×D4—121no—
365D3×D4—121no—
366D3×D4—122no—
367#235—62no—
368#235—121no—
369C2×D12—21no—
370C2×D12—31no—
371C2×D12—31no—
372C2×D12—31no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12C22×D311yescharacteristic
376C2×D12C22×D311yescharacteristic
377C2×C4×D3—21no—
378C2×C4×D3—31no—
379C2×C4×D3—31no—
380C2×C4×D3—61no—
381C2×C4×D3—61no—
382C2×C4×D3C22×D311yescharacteristic
383C2×Dic6—31no—
384C2×Dic6—31no—
385C2×Dic6—61no—
386C2×Dic6C22×D311yescharacteristic
387C3×SD16—121no—
388C3×D8—34no—
389C3×D8—62no—
390C2×C3×C8—21no—
391C2×C3×C8—31no—
392C2×C3×C8—31no—
393C2×C3×C8C22×D311yescharacteristic
394C2×C3×C8C22×D311yescharacteristic
395C3×C4⋊C4—21no—
396C3×C4⋊C4—31no—
397C3×C4⋊C4C22×D311yescharacteristic
398C3×C4⋊C4C22×D311yescharacteristic
399C3×C22⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C42—31no—
403#217—21no—
404#217—31no—
405#217—61no—
406#217—61no—
407#216—62no—
408#215—62no—
409#214—62no—
410#214—62no—
411#214—62no—
412#214—122no—
413#213—22no—
414#213—62no—
415#213—62no—
416#213D1214yescomplemented
417(C2×D3)⋊C4—21no—
418(C2×D3)⋊C4—21no—
419(C2×D3)⋊C4—31no—
420(C2×D3)⋊C4—31no—
421(C2×D3)⋊C4—31no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—121no—
435C4⋊Dic3—31no—
436C4⋊Dic3—61no—
437C4⋊Dic3—61no—
438C4⋊Dic3—61no—
439C4⋊Dic3—121no—
440C4⋊Dic3C22×D311yescharacteristic
441Dic3⋊C4—31no—
442Dic3⋊C4—61no—
443C4×Dic3C22×D311yescharacteristic
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—61no—
447C2×C3⋊C8—62no—
448C2×C3⋊C8C22×D311yescharacteristic
449C2×C3⋊C8C22×D311yescharacteristic
450Dic12—62no—
451D24—62no—
452D24—62no—
453#204—41no—
454#204—121no—
455#204—121no—
456#204—122no—
457D3×C8—62no—
458D3×C8—62no—
459D3×C8—62no—
460C22×C32—22no—
461C22×C32—41no—
462C22×C32—41no—
463C22×C32C22×D411yescharacteristic
464C2×C3⋊D3—21no—
465C2×C3⋊D3—21no—
466C2×C3⋊D3—41no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—84no—
470C2×C3⋊D3#13512yescomplemented
471C2×C3×D3—22no—
472C2×C3×D3—21no—
473C2×C3×D3—21no—
474C2×C3×D3—21no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480D32—84no—
481C32×C4—41no—
482C32×C4C22×D411yescharacteristic
483C32×C4H(5,𝔽2)11yescharacteristic
484C3⋊Dic3—21no—
485C3⋊Dic3—41no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—21no—
489C3×Dic3—41no—
490C3×Dic3—41no—
491C2×#41—31no—
492C2×#41—91no—
493C22×D4—91no—
494C22×D4—91no—
495#135—184no—
496C2×Q16—91no—
497C2×SD16—31no—
498C2×SD16—91no—
499C2×SD16—91no—
500C2×SD16—91no—
501C2×D8—31no—
502C2×D8—31no—
503C2×D8—91no—
504C2×D8—91no—
505C2×D8—184no—
506C22×C8—91no—
507C22×C8—91no—
508#124—91no—
509#124—91no—
510#123—181no—
511#123—181no—
512C22⋊Q8—91no—
513C22⋊Q8—91no—
514#121—31no—
515#121—91no—
516#121—181no—
517#121—181no—
518#120—181no—
519#120—181no—
520C4×D4—31no—
521C4×D4—31no—
522C4×D4—91no—
523C2×C22⋊C4—181no—
524C2×C22⋊C4—181no—
525#107—31no—
526C4⋊C8—91no—
527#103—31no—
528#103—91no—
529#102—31no—
530#102—91no—
531#102—91no—
532#102D3211yescharacteristic, complemented
533C22⋊C8—31no—
534C22⋊C8—91no—
535C4×C8—31no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—31no—
539C23×C3—41no—
540C23×C3—61no—
541C23×C3—61no—
542C22×D3—21no—
543C22×D3—21no—
544C22×D3—31no—
545C22×D3—31no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—61no—
549C22×D3—121no—
550C22×D3—122no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3—122no—
554C22×D3—122no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—124no—
559C22×D3—242no—
560C22×D3—241no—
561C22×D3—241no—
562C22×D3—241no—
563C22×D3—241no—
564C22×D3—242no—
565C22×D3D3×D411yescharacteristic
566C3×Q8—61no—
567C3×Q8—61no—
568C3×D4—21no—
569C3×D4—21no—
570C3×D4—22no—
571C3×D4—32no—
572C3×D4—41no—
573C3×D4—61no—
574C3×D4—61no—
575C3×D4—61no—
576C3×D4—122no—
577C3×D4—241no—
578C3×D4C2×D1212yes—
579C3×D4D3×D412yes—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—31no—
584C2×C3×C4—31no—
585C2×C3×C4—31no—
586C2×C3×C4—41no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—122no—
592C2×C3×C4—241no—
593C2×C3×C4—241no—
594C2×C3×C4C23×D311yescharacteristic
595C2×C3×C4C23×D311yescharacteristic
596#67—42no—
597#67—62no—
598#67—122no—
599#67—122no—
600#67—122no—
601#67—122no—
602#67—122no—
603#67—122no—
604#67—124no—
605#67—241no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—31no—
609C2×Dic3—31no—
610C2×Dic3—42no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—81no—
615C2×Dic3—121no—
616C2×Dic3—122no—
617C2×Dic3D3×D411yescharacteristic
618C2×Dic3D3×D411yescharacteristic
619C2×Dic3D3×D411yescharacteristic
620D12—21no—
621D12—21no—
622D12—21no—
623D12—62no—
624D12—62no—
625D12—61no—
626D12—61no—
627D12—61no—
628D12—61no—
629D12—81no—
630D12—121no—
631D12—241no—
632D12C2×D1212yes—
633C4×D3—21no—
634C4×D3—21no—
635C4×D3—61no—
636C4×D3—61no—
637C4×D3—61no—
638C4×D3—61no—
639C4×D3—81no—
640C4×D3—121no—
641C4×D3—121no—
642C4×D3—122no—
643Dic6—21no—
644Dic6—21no—
645Dic6—61no—
646Dic6—61no—
647Dic6—61no—
648Dic6—61no—
649Dic6—121no—
650Dic6—121no—
651C3×C8—21no—
652C3×C8—21no—
653C3×C8—32no—
654C3×C8—41no—
655C3×C8—61no—
656C3⋊C8—21no—
657C3⋊C8—61no—
658C3⋊C8—61no—
659C3⋊C8—121no—
660C3⋊C8C2×D1212yes—
661C2×C32—42no—
662C2×C32D4211yescharacteristic
663C2×C32C2×#13511yescharacteristic
664C2×C32#57611yescharacteristic
665C3⋊D3—22no—
666C3⋊D3—81no—
667C3×D3—42no—
668C3×D3—41no—
669C3×D3—81no—
670C24—181no—
671C24—181no—
672#41—62no—
673#41—121no—
674#41—182no—
675#41—361no—
676C2×Q8—31no—
677C2×Q8—91no—
678C2×D4—31no—
679C2×D4—31no—
680C2×D4—61no—
681C2×D4—61no—
682C2×D4—91no—
683C2×D4—91no—
684C2×D4—181no—
685C2×D4—181no—
686C2×D4—181no—
687C2×D4—182no—
688C2×D4—182no—
689C2×D4—181no—
690C2×D4—361no—
691C2×D4—361no—
692C2×D4C2×D3211yescharacteristic
693C22×C4—31no—
694C22×C4—61no—
695C22×C4—61no—
696C22×C4—61no—
697C22×C4—91no—
698C22×C4—181no—
699Q16—182no—
700SD16—121no—
701SD16—182no—
702SD16—182no—
703SD16—361no—
704D8—34no—
705D8—62no—
706D8—182no—
707D8—182no—
708C2×C8—31no—
709C2×C8—31no—
710C2×C8—91no—
711C2×C8—182no—
712C2×C8—182no—
713C2×C8C2×D3211yescharacteristic
714C4⋊C4—31no—
715C4⋊C4—91no—
716C4⋊C4—181no—
717C4⋊C4—181no—
718C4⋊C4C2×D3211yescharacteristic
719C22⋊C4—61no—
720C22⋊C4—61no—
721C22⋊C4—61no—
722C22⋊C4—91no—
723C22⋊C4—91no—
724C22⋊C4—181no—
725C22⋊C4—181no—
726C22⋊C4—181no—
727C22⋊C4—181no—
728C22⋊C4—181no—
729C22⋊C4—181no—
730C22⋊C4—181no—
731C42—31no—
732C22×C3—22no—
733C22×C3—22no—
734C22×C3—21no—
735C22×C3—42no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—61no—
741C22×C3—61no—
742C22×C3—61no—
743C22×C3—62no—
744C22×C3—81no—
745C22×C3—81no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3C2×D3×D411yescharacteristic
752C22×C3C2×D3×D411yescharacteristic
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—22no—
756C2×D3—21no—
757C2×D3—32no—
758C2×D3—32no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—62no—
765C2×D3—61no—
766C2×D3—61no—
767C2×D3—61no—
768C2×D3—61no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—122no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—241no—
779C2×D3—241no—
780C2×D3—244no—
781C2×D3—244no—
782C2×D3—244no—
783C2×D3—244no—
784C2×D3—248no—
785C3×C4—21no—
786C3×C4—21no—
787C3×C4—41no—
788C3×C4—41no—
789C3×C4—61no—
790C3×C4—61no—
791C3×C4—61no—
792C3×C4—81no—
793C3×C4—121no—
794C3×C4—121no—
795C3×C4C22×D1211yescharacteristic
796C3×C4C2×D3×D411yescharacteristic
797C3×C4#100411yescharacteristic
798C3×C4#100911yescharacteristic
799Dic3—21no—
800Dic3—21no—
801Dic3—21no—
802Dic3—41no—
803Dic3—41no—
804Dic3—61no—
805Dic3—61no—
806Dic3—121no—
807Dic3—121no—
808Dic3—121no—
809Dic3—241no—
810C32#328011yescharacteristic, complemented, Sylow
811C23—21no—
812C23—31no—
813C23—61no—
814C23—61no—
815C23—91no—
816C23—181no—
817C23—362no—
818C23—362no—
819C23—362no—
820C23—362no—
821C23—721no—
822C23—721no—
823Q8—61no—
824Q8—61no—
825Q8—181no—
826Q8—181no—
827D4—21no—
828D4—32no—
829D4—61no—
830D4—61no—
831D4—61no—
832D4—122no—
833D4—182no—
834D4—181no—
835D4—181no—
836D4—241no—
837D4—362no—
838D4—362no—
839D4—362no—
840D4—721no—
841D4D3×D1212yes—
842C2×C4—21no—
843C2×C4—31no—
844C2×C4—31no—
845C2×C4—31no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—91no—
851C2×C4—122no—
852C2×C4—181no—
853C2×C4—181no—
854C2×C4—181no—
855C2×C4—241no—
856C2×C4—241no—
857C2×C4—362no—
858C2×C4C22×D3211yescharacteristic
859C8—21no—
860C8—32no—
861C8—61no—
862C8—181no—
863C2×C3—21no—
864C2×C3—21no—
865C2×C3—21no—
866C2×C3—42no—
867C2×C3—42no—
868C2×C3—82no—
869C2×C3—122no—
870C2×C3—121no—
871C2×C3—241no—
872C2×C3D4×D1211yescharacteristic
873C2×C3#559011yescharacteristic
874C2×C3#575711yescharacteristic
875C2×C3D3×#13511yescharacteristic
876C2×C3D3×#13511yescharacteristic
877C2×C3#577411yescharacteristic
878D3—41no—
879D3—42no—
880D3—62no—
881D3—62no—
882D3—81no—
883D3—122no—
884D3—242no—
885D3—241no—
886D3—241no—
887C22—22no—
888C22—41no—
889C22—41no—
890C22—61no—
891C22—61no—
892C22—61no—
893C22—62no—
894C22—92no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—181no—
901C22—181no—
902C22—361no—
903C22—361no—
904C22—361no—
905C22—724no—
906C22—724no—
907C22D32×D411yescharacteristic
908C4—41no—
909C4—61no—
910C4—61no—
911C4—61no—
912C4—121no—
913C4—121no—
914C4—181no—
915C4—361no—
916C4C2×D3×D1211yescharacteristic
917C4#6431411yescharacteristic
918C3—21no—
919C3#7960611yescharacteristic, complemented
920C3#8010111yescharacteristic, complemented
921C2—42no—
922C2—121no—
923C2—122no—
924C2—182no—
925C2—241no—
926C2—721no—
927C2#1059427711yescharacteristic
928C2#1059473211yescharacteristic
929C2#1059474711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3280
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595254C2semidirect
2. C2×#63933C2semidirect
3. C2×#63926C2semidirect
4. #10594630C2semidirect
5. #10592475C2semidirect
6. C3×#4781C2semidirect
7. C3×#4756C2semidirect
8. #10591468C2semidirect
9. #10590968C2semidirect
10. #10590943C2semidirect
11. #10590862C2semidirect
12. #10590721C2semidirect
13. #10590576C2semidirect
14. #10590534C2semidirect
15. #10590525C2semidirect
19. C2×C3×#237C22semidirect
21. C2×#3795C22semidirect
22. C2×#3754C22semidirect
23. C2×#3744C22semidirect
25. C3×D4×Dic3C22semidirect
28. C2×C3×#204C22semidirect
29. C3×#895C22semidirect
30. C3×#893C22semidirect
39. #63909C22semidirect
44. #63864C22semidirect
45. #63860C22semidirect
46. C2×#3719C22semidirect
47. C2×#3715C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. C32×#102C22semidirect
54. #63636C22semidirect
55. C3×#821C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×C8×Dic3C22semidirect
58. C3×#810C22semidirect
59. C3×#807C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63567C22semidirect
62. #63562C22semidirect
84. #4781D3semidirect
89. #4756D3semidirect
132. C3×#213D4semidirect
159. C2×#237C2×D3semidirect
182. D4×Dic3C2×D3semidirect
209. C2×#204C2×D3semidirect
218. #895C2×D3semidirect
219. #893C2×D3semidirect
233. C3×#102C2×D3semidirect
234. C3×#102C2×D3semidirect
238. #821C2×D3semidirect
242. (C2×D3)⋊C8C2×D3semidirect
245. C8×Dic3C2×D3semidirect
247. #810C2×D3semidirect
252. #807C2×D3semidirect
416. #213D12semidirect
470. C2×C3⋊D3#135semidirect
532. #102D32semidirect
810. C32#3280semidirect
919. C3#79606semidirect
920. C3#80101semidirect

Maximal subgroups

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

subgroupindex
#105952542
C2×#639332
C2×#639262
#105946302
#105924752
C3×#47812
C3×#47562
#105914682
#105909682
#105909432
#105908622
#105907212
#105905762
#105905342
#105905252
#801013
#796063