Finite Group Databasebeta

← #11885821

Subgroups — #11885821

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 929 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595246C211yesmaximal, characteristic, complemented
2C2×#63936C211yesmaximal, characteristic, complemented
3C2×D3×#213C211yesmaximal, characteristic, complemented
4#10594629C211yesmaximal, characteristic, complemented
5#10592480C211yesmaximal, characteristic, complemented
6C3×#4776C211yesmaximal, characteristic, complemented
7C3×#4756C211yesmaximal, characteristic, complemented
8#10591471C211yesmaximal, characteristic, complemented
9#10590964C211yesmaximal, characteristic, complemented
10#10590946C211yesmaximal, characteristic, complemented
11#10590862C211yesmaximal, characteristic, complemented
12#10590721C211yesmaximal, characteristic, complemented
13#10590579C211yesmaximal, characteristic, complemented
14#10590530C211yesmaximal, characteristic, complemented
15#10590509C211yesmaximal, characteristic, complemented
16#80168—31nomaximal
17#79606—31nomaximal
18C2×#3830C2211yescharacteristic, complemented
19C2×C3×D3×D4C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C2×#3796C2211yescharacteristic, complemented
22C2×#3753C2211yescharacteristic
23C2×#3744C2211yescharacteristic, complemented
24#64104C2211yescharacteristic, complemented
25C3×D4×Dic3C2211yescharacteristic, complemented
26C2×C3×#214C2211yescharacteristic, complemented
27C2×C3×#213C2211yescharacteristic
28C2×C3×#204C2211yescharacteristic, complemented
29C3×#897C2211yescharacteristic
30C3×#893C2211yescharacteristic, complemented
31#63978—21no—
32#63977—21no—
33#63962—21no—
34C2×(C2×D3)⋊Dic3—21no—
35#63936—24no—
36D3×#213—24no—
37#63923—21no—
38D3×(C2×D3)⋊C4—21no—
39#63916C2211yescharacteristic, complemented
40#63909—21no—
41C4×#626C2211yescharacteristic
42#63890—21no—
43#63864C2211yescharacteristic, complemented
44#63860C2211yescharacteristic, complemented
45#63857C2211yescharacteristic
46C2×#3719C2211yescharacteristic, complemented
47C2×#3716C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50C2×#3710C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic
52C32×#102C2211yescharacteristic, complemented
53#63647C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic
57C3×C8×Dic3C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59C3×#807C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63#5806—31no—
64C22×#213—31no—
65C2×#916—31no—
66C2×#912—31no—
67C2×D3×D8—31no—
68#5630—31no—
69#5554—31no—
70#5554—31no—
71C3×#450—31no—
72C3×C4×D8—31no—
73#5172—31no—
74#5168—31no—
75#5165—31no—
76#5051—31no—
77#5016—31no—
78#5016—31no—
79#4887—31no—
80#4883—31no—
81#4787—31no—
82#4781—31no—
83#4781—31no—
84#4781—31no—
85#4781—61no—
86#4776—31no—
87#4776D311yescharacteristic, complemented
88#4775—31no—
89#4756D311yescharacteristic, complemented
90#4731—31no—
91#67⋊C8—31no—
92#4696—31no—
93C8×D12—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98C22×C3⋊Dic3—21no—
99#3830—22no—
100#3830—41no—
101C2×C4⋊(C3⋊D3)—21no—
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4×C3⋊D3C2311yescharacteristic
104C2×#634C2311yescharacteristic
105C2×C3×#67—21no—
106C22×C3×Dic3—21no—
107C3×D3×D4—22no—
108C3×D3×D4—41no—
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×Dic6C2311yescharacteristic
114C2×#626—21no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#626D411yescharacteristic
118C2×D3×Dic3—21no—
119D3×D12—22no—
120D3×D12—41no—
121#3796—22no—
122#3796—41no—
123C2×C32×C8C2311yescharacteristic
124C32×C4⋊C4C2311yescharacteristic
125#3753—22no—
126#3752—21no—
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128#3744—41no—
129C3×#217—21no—
130C3×#214—22no—
131C3×#213D414yescomplemented
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×C4⋊Dic3—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#3722D411yescharacteristic
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3D411yescharacteristic
150#3719—22no—
151#3716—22no—
152#3714—22no—
153#3713—22no—
154#3710—22no—
155D3×C3⋊C8—22no—
156#3280—91noSylow
157C22×C3×D4—31no—
158C2×#239—31no—
159C2×#237—31no—
160C2×#237—31no—
161C2×#237—31no—
162C2×#237—61no—
163C2×D3×D4—31no—
164C2×D3×D4C2×D311yescharacteristic
165C22×D12—31no—
166C2×C3×SD16—31no—
167C2×C3×SD16—31no—
168C2×C3×D8—31no—
169C3×C22⋊Q8—31no—
170C3×C4×D4—31no—
171C3×C4×D4—31no—
172#953—61no—
173C2×#217—61no—
174#947—31no—
175C2×#216—31no—
176#939—61no—
177#938—31no—
178#936—31no—
179#935—61no—
180D4×Dic3C2×D311yescharacteristic, complemented
181C2×#214—31no—
182C2×#214C2×D311yescharacteristic, complemented
183C2×#213—31no—
184C2×#213—31no—
185C2×#213—31no—
186C2×#213—31no—
187C2×#213—31no—
188C2×#213—61no—
189C2×#213—64no—
190C2×#213C2×D311yescharacteristic
191#930—61no—
192#930—61no—
193C4×#67—31no—
194C2×(C2×D3)⋊C4—61no—
195C2×(C2×D3)⋊C4—61no—
196#924—31no—
197C22×C3⋊C8—31no—
198#916—64no—
199#912—64no—
200D3×D8—64no—
201C2×Dic12—31no—
202C2×D24—31no—
203C2×#204—31no—
204C2×#204—31no—
205C2×#204—31no—
206C2×#204—61no—
207C2×#204C2×D311yescharacteristic, complemented
208C2×D3×C8—31no—
209C2×D3×C8—31no—
210C2×D3×C8—31no—
211#897—31no—
212#897C2×D311yescharacteristic
213#895—31no—
214#895—31no—
215#895—31no—
216#895—61no—
217#895—61no—
218#894—61no—
219#893C2×D311yescharacteristic, complemented
220#886—61no—
221#886—61no—
222#882—61no—
223#882—61no—
224#882—61no—
225D3×C22⋊C4—61no—
226#875—31no—
227#875—31no—
228C4×D12—31no—
229C3×#107—31no—
230C3×#102—21no—
231C3×#102—31no—
232C3×#102—31no—
233C3×#102C2×D311yescharacteristic, complemented
234C3×#102C2×D311yescharacteristic, complemented
235C3×C22⋊C8—31no—
236C3×C4×C8—31no—
237#835—31no—
238#821—31no—
239#821C2×D311yescharacteristic, complemented
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—31no—
242(C2×D3)⋊C8—61no—
243(C2×D3)⋊C8C2×D311yescharacteristic
244Dic3⋊C8—31no—
245C8×Dic3C2×D311yescharacteristic, complemented
246#810—31no—
247#810—31no—
248#810—31no—
249#810—61no—
250#809—31no—
251#809C2×D311yescharacteristic, complemented
252#807C2×D311yescharacteristic, complemented
253C4⋊(C3⋊C8)—31no—
254C23×C32—21no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3C2×D411yescharacteristic
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—81no—
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⋊Dic3—42no—
273C2×C3⋊Dic3C2×D411yescharacteristic
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—81no—
277C4×C3⋊D3—21no—
278C4×C3⋊D3—21no—
279#634—21no—
280#634—21no—
281C3×#67—42no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—81no—
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—21no—
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—42no—
299#626—42no—
300#626—81no—
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—31no—
316#450—91no—
317#449—91no—
318#449—91no—
319C4×D8—31no—
320C8×D4—91no—
321C24×C3—61no—
322C23×D3—21no—
323C23×D3—61no—
324C23×D3—61no—
325C2×C3×Q8—31no—
326C2×C3×D4—21no—
327C2×C3×D4—31no—
328C2×C3×D4—31no—
329C2×C3×D4—61no—
330C2×C3×D4—62no—
331C2×C3×D4—121no—
332C2×C3×D4C22×D311yescharacteristic
333C2×C3×D4C22×D311yescharacteristic
334C22×C3×C4—31no—
335C22×C3×C4—61no—
336C22×C3×C4—61no—
337C2×#67—21no—
338C2×#67—31no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—121no—
345C22×Dic3—21no—
346C22×Dic3—61no—
347C22×Dic3—61no—
348C22×Dic3—61no—
349C22×Dic3—121no—
350#239—62no—
351#239—121no—
352#237—62no—
353#237—62no—
354#237—62no—
355#237—122no—
356#237—121no—
357#237—121no—
358#237—121no—
359#237—122no—
360D3×D4—22no—
361D3×D4—41no—
362D3×D4—62no—
363D3×D4—121no—
364C2×D12—31no—
365C2×D12—31no—
366C2×D12—31no—
367C2×D12—61no—
368C2×D12—62no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—61no—
373C2×D12—61no—
374C2×D12—121no—
375C2×D12—121no—
376C2×D12C22×D311yescharacteristic
377C2×D12C22×D311yescharacteristic
378C2×C4×D3—21no—
379C2×C4×D3—31no—
380C2×C4×D3—31no—
381C2×C4×D3—61no—
382C2×C4×D3—61no—
383C2×C4×D3C22×D311yescharacteristic
384C2×Dic6—31no—
385C2×Dic6—31no—
386C2×Dic6—61no—
387C2×Dic6C22×D311yescharacteristic
388C3×SD16—62no—
389C3×SD16—121no—
390C3×D8—34no—
391C2×C3×C8—21no—
392C2×C3×C8—31no—
393C2×C3×C8—31no—
394C2×C3×C8C22×D311yescharacteristic
395C2×C3×C8C22×D311yescharacteristic
396C3×C4⋊C4—21no—
397C3×C4⋊C4—31no—
398C3×C4⋊C4—61no—
399C3×C4⋊C4C22×D311yescharacteristic
400C3×C4⋊C4C22×D311yescharacteristic
401C3×C22⋊C4—61no—
402C3×C22⋊C4—61no—
403C3×C22⋊C4—61no—
404C3×C42—31no—
405#217—21no—
406#217—31no—
407#217—61no—
408#217—61no—
409#217—61no—
410#217—61no—
411#216—62no—
412#214—22no—
413#214—62no—
414#213—62no—
415#213—62no—
416#213—62no—
417#213—62no—
418#213—62no—
419#213—122no—
420#213D1214yescomplemented
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—31no—
424(C2×D3)⋊C4—31no—
425(C2×D3)⋊C4—31no—
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—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—121no—
437C4⋊Dic3—21no—
438C4⋊Dic3—31no—
439C4⋊Dic3—61no—
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—
452#204—41no—
453#204—62no—
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—21no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—22no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—84no—
479C2×C3×D3#13512yescomplemented
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—91no—
492C2×#41—91no—
493C22×D4—31no—
494C22×D4—91no—
495#135—184no—
496C2×Q16—91no—
497C2×SD16—31no—
498C2×SD16—31no—
499C2×SD16—91no—
500C2×SD16—91no—
501C2×D8—31no—
502C2×D8—91no—
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—31no—
513C22⋊Q8—91no—
514#121—91no—
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—91no—
528#103—91no—
529#102—31no—
530#102—31no—
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—
542C23×C3—122no—
543C23×C3—122no—
544C23×C3—241no—
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—31no—
548C22×D3—31no—
549C22×D3—42no—
550C22×D3—42no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—61no—
554C22×D3—81no—
555C22×D3—121no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—122no—
559C22×D3—122no—
560C22×D3—241no—
561C22×D3—241no—
562C22×D3D3×D411yescharacteristic
563C3×Q8—61no—
564C3×Q8—61no—
565C3×D4—21no—
566C3×D4—21no—
567C3×D4—22no—
568C3×D4—32no—
569C3×D4—41no—
570C3×D4—61no—
571C3×D4—61no—
572C3×D4—61no—
573C3×D4—122no—
574C3×D4C2×D1212yes—
575C3×D4D3×D412yes—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—31no—
580C2×C3×C4—31no—
581C2×C3×C4—31no—
582C2×C3×C4—41no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—241no—
588C2×C3×C4—241no—
589C2×C3×C4C23×D311yescharacteristic
590C2×C3×C4C23×D311yescharacteristic
591#67—42no—
592#67—62no—
593#67—122no—
594#67—122no—
595#67—122no—
596#67—122no—
597#67—124no—
598#67—241no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—31no—
602C2×Dic3—31no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—81no—
607C2×Dic3—121no—
608C2×Dic3—122no—
609C2×Dic3—122no—
610C2×Dic3—122no—
611C2×Dic3—124no—
612C2×Dic3D3×D411yescharacteristic
613C2×Dic3D3×D411yescharacteristic
614C2×Dic3D3×D411yescharacteristic
615D12—21no—
616D12—21no—
617D12—21no—
618D12—62no—
619D12—61no—
620D12—61no—
621D12—61no—
622D12—61no—
623D12—121no—
624D12—121no—
625D12—122no—
626D12—122no—
627D12—241no—
628D12—241no—
629D12—242no—
630D12—241no—
631D12C2×D1212yes—
632C4×D3—21no—
633C4×D3—21no—
634C4×D3—61no—
635C4×D3—61no—
636C4×D3—61no—
637C4×D3—61no—
638C4×D3—81no—
639C4×D3—121no—
640C4×D3—121no—
641C4×D3—122no—
642Dic6—21no—
643Dic6—21no—
644Dic6—62no—
645Dic6—61no—
646Dic6—61no—
647Dic6—61no—
648Dic6—61no—
649Dic6—121no—
650C3×C8—21no—
651C3×C8—21no—
652C3×C8—32no—
653C3×C8—41no—
654C3×C8—61no—
655C3⋊C8—21no—
656C3⋊C8—61no—
657C3⋊C8—61no—
658C3⋊C8—121no—
659C3⋊C8C2×D1212yes—
660C2×C32—42no—
661C2×C32D4211yescharacteristic
662C2×C32C2×#13511yescharacteristic
663C2×C32#57611yescharacteristic
664C3⋊D3—41no—
665C3⋊D3—81no—
666C3×D3—22no—
667C3×D3—42no—
668C3×D3—81no—
669C24—61no—
670C24—181no—
671#41—182no—
672#41—182no—
673#41—361no—
674#41—361no—
675C2×Q8—31no—
676C2×Q8—91no—
677C2×D4—31no—
678C2×D4—31no—
679C2×D4—61no—
680C2×D4—62no—
681C2×D4—91no—
682C2×D4—91no—
683C2×D4—121no—
684C2×D4—181no—
685C2×D4—181no—
686C2×D4—182no—
687C2×D4—181no—
688C2×D4—181no—
689C2×D4—181no—
690C2×D4—361no—
691C2×D4C2×D3211yescharacteristic
692C22×C4—31no—
693C22×C4—61no—
694C22×C4—61no—
695C22×C4—91no—
696C22×C4—181no—
697C22×C4—181no—
698Q16—182no—
699SD16—62no—
700SD16—121no—
701SD16—182no—
702SD16—361no—
703D8—34no—
704D8—182no—
705D8—182no—
706D8—182no—
707C2×C8—31no—
708C2×C8—31no—
709C2×C8—91no—
710C2×C8—182no—
711C2×C8—182no—
712C2×C8C2×D3211yescharacteristic
713C4⋊C4—31no—
714C4⋊C4—61no—
715C4⋊C4—91no—
716C4⋊C4—181no—
717C4⋊C4C2×D3211yescharacteristic
718C22⋊C4—61no—
719C22⋊C4—61no—
720C22⋊C4—61no—
721C22⋊C4—91no—
722C22⋊C4—91no—
723C22⋊C4—181no—
724C22⋊C4—181no—
725C22⋊C4—181no—
726C22⋊C4—181no—
727C22⋊C4—181no—
728C22⋊C4—181no—
729C22⋊C4—181no—
730C42—31no—
731C22×C3—22no—
732C22×C3—22no—
733C22×C3—21no—
734C22×C3—32no—
735C22×C3—42no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—61no—
741C22×C3—61no—
742C22×C3—62no—
743C22×C3—81no—
744C22×C3—81no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—244no—
751C22×C3C2×D3×D411yescharacteristic
752C22×C3C2×D3×D411yescharacteristic
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—22no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—61no—
762C2×D3—61no—
763C2×D3—61no—
764C2×D3—61no—
765C2×D3—61no—
766C2×D3—61no—
767C2×D3—84no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—241no—
778C2×D3—241no—
779C2×D3—241no—
780C2×D3—244no—
781C2×D3—244no—
782C2×D3#91612yescomplemented
783C3×C4—21no—
784C3×C4—21no—
785C3×C4—41no—
786C3×C4—41no—
787C3×C4—61no—
788C3×C4—61no—
789C3×C4—61no—
790C3×C4—81no—
791C3×C4—121no—
792C3×C4—121no—
793C3×C4C22×D1211yescharacteristic
794C3×C4C2×D3×D411yescharacteristic
795C3×C4#100411yescharacteristic
796C3×C4#100911yescharacteristic
797Dic3—21no—
798Dic3—21no—
799Dic3—21no—
800Dic3—41no—
801Dic3—41no—
802Dic3—61no—
803Dic3—61no—
804Dic3—121no—
805Dic3—122no—
806Dic3—121no—
807Dic3—121no—
808C32#328011yescharacteristic, complemented, Sylow
809C23—21no—
810C23—31no—
811C23—61no—
812C23—61no—
813C23—91no—
814C23—122no—
815C23—122no—
816C23—181no—
817C23—241no—
818C23—362no—
819C23—362no—
820C23—721no—
821Q8—61no—
822Q8—61no—
823Q8—181no—
824Q8—181no—
825D4—21no—
826D4—32no—
827D4—61no—
828D4—61no—
829D4—61no—
830D4—122no—
831D4—182no—
832D4—181no—
833D4—181no—
834D4—362no—
835D4—362no—
836D4—362no—
837D4—721no—
838D4—721no—
839D4D3×D1212yes—
840C2×C4—21no—
841C2×C4—31no—
842C2×C4—31no—
843C2×C4—31no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—91no—
849C2×C4—181no—
850C2×C4—181no—
851C2×C4—181no—
852C2×C4—241no—
853C2×C4—241no—
854C2×C4—362no—
855C2×C4—362no—
856C2×C4C22×D3211yescharacteristic
857C8—21no—
858C8—32no—
859C8—61no—
860C8—181no—
861C2×C3—21no—
862C2×C3—21no—
863C2×C3—21no—
864C2×C3—42no—
865C2×C3—42no—
866C2×C3—62no—
867C2×C3—82no—
868C2×C3—122no—
869C2×C3—241no—
870C2×C3D4×D1211yescharacteristic
871C2×C3#559011yescharacteristic
872C2×C3#575711yescharacteristic
873C2×C3C2×#91611yescharacteristic
874C2×C3D3×#13511yescharacteristic
875C2×C3#577411yescharacteristic
876D3—22no—
877D3—42no—
878D3—81no—
879D3—121no—
880D3—121no—
881D3—241no—
882D3—241no—
883D3—241no—
884D3—481no—
885C22—22no—
886C22—32no—
887C22—41no—
888C22—41no—
889C22—61no—
890C22—61no—
891C22—62no—
892C22—121no—
893C22—121no—
894C22—121no—
895C22—121no—
896C22—121no—
897C22—181no—
898C22—181no—
899C22—181no—
900C22—244no—
901C22—361no—
902C22—361no—
903C22—361no—
904C22—724no—
905C22D32×D411yescharacteristic
906C4—41no—
907C4—61no—
908C4—61no—
909C4—61no—
910C4—121no—
911C4—121no—
912C4—181no—
913C4—361no—
914C4C2×D3×D1211yescharacteristic
915C4#6431411yescharacteristic
916C3—21no—
917C3#7960611yescharacteristic, complemented
918C3#8016811yescharacteristic, complemented
919C2—42no—
920C2—62no—
921C2—122no—
922C2—241no—
923C2—361no—
924C2—721no—
925C2#1059427711yescharacteristic
926C2#1059473211yescharacteristic
927C2D3×#91611yescharacteristic
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. #10595246C2semidirect
2. C2×#63936C2semidirect
3. C2×D3×#213C2semidirect
4. #10594629C2semidirect
5. #10592480C2semidirect
6. C3×#4776C2semidirect
7. C3×#4756C2semidirect
8. #10591471C2semidirect
9. #10590964C2semidirect
10. #10590946C2semidirect
11. #10590862C2semidirect
12. #10590721C2semidirect
13. #10590579C2semidirect
14. #10590530C2semidirect
15. #10590509C2semidirect
18. C2×#3830C22semidirect
21. C2×#3796C22semidirect
23. C2×#3744C22semidirect
24. #64104C22semidirect
25. C3×D4×Dic3C22semidirect
26. C2×C3×#214C22semidirect
28. C2×C3×#204C22semidirect
30. C3×#893C22semidirect
39. #63916C22semidirect
43. #63864C22semidirect
44. #63860C22semidirect
46. C2×#3719C22semidirect
47. C2×#3716C22semidirect
50. C2×#3710C22semidirect
52. C32×#102C22semidirect
53. #63647C22semidirect
54. #63637C22semidirect
55. C3×#821C22semidirect
57. C3×C8×Dic3C22semidirect
58. C3×#809C22semidirect
59. C3×#807C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63565C22semidirect
62. #63564C22semidirect
87. #4776D3semidirect
89. #4756D3semidirect
131. C3×#213D4semidirect
180. D4×Dic3C2×D3semidirect
182. C2×#214C2×D3semidirect
207. C2×#204C2×D3semidirect
219. #893C2×D3semidirect
233. C3×#102C2×D3semidirect
234. C3×#102C2×D3semidirect
239. #821C2×D3semidirect
245. C8×Dic3C2×D3semidirect
251. #809C2×D3semidirect
252. #807C2×D3semidirect
420. #213D12semidirect
479. C2×C3×D3#135semidirect
532. #102D32semidirect
782. C2×D3#916semidirect
808. C32#3280semidirect
917. C3#79606semidirect
918. C3#80168semidirect

Maximal subgroups

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

subgroupindex
#105952462
C2×#639362
C2×D3×#2132
#105946292
#105924802
C3×#47762
C3×#47562
#105914712
#105909642
#105909462
#105908622
#105907212
#105905792
#105905302
#105905092
#801683
#796063