Finite Group Databasebeta

← #11883964

Subgroups — #11883964

Order 1152.

1159 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5598C211yesmaximal, characteristic, complemented
2C2×#63925C211yesmaximal, characteristic, complemented
3D12×#67C211yesmaximal, characteristic, complemented
4C22×#3715C211yesmaximal, characteristic, complemented
5#10592737C211yesmaximal, characteristic, complemented
6C3×#5036C211yesmaximal, characteristic, complemented
7#10591483C211yesmaximal, characteristic, complemented
8#10591450C211yesmaximal, characteristic, complemented
9#10591431C211yesmaximal, characteristic, complemented
10#10591174C211yesmaximal, characteristic, complemented
11#10591158C211yesmaximal, characteristic, complemented
12#10590596C211yesmaximal, characteristic, complemented
13#10590549C211yesmaximal, characteristic, complemented
14#10590503C211yesmaximal, characteristic, complemented
15#10590454C211yesmaximal, characteristic, complemented
16#83542—31nomaximal
17#80025—31nomaximal
18C2×C3×#237C2211yescharacteristic, complemented
19C22×C3×D12C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic, complemented
21C2×D3×#67—21no—
22C2×D3×D12C2211yescharacteristic
23C32×#121C2211yescharacteristic, complemented
24C2×#3753C2211yescharacteristic, complemented
25#64139C2211yescharacteristic
26C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
27C3×#939—21no—
28C3×#936C2211yescharacteristic, complemented
29C3×D4×Dic3—21no—
30C2×C3×#213C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic, complemented
32C3×C4×#67C2211yescharacteristic
33C3×#897C2211yescharacteristic, complemented
34C3×#887C2211yescharacteristic, complemented
35C3×#885—21no—
36C3×#878—21no—
37#63977—21no—
38#63925—24no—
39#63922—21no—
40#63911C2211yescharacteristic
41#63908C2211yescharacteristic
42Dic3×D12C2211yescharacteristic
43#63886—21no—
44C2×#3717C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic, complemented
46C2×#3715—24no—
47C2×#3715C2211yescharacteristic
48C2×#3715C2211yescharacteristic
49C2×#3715C2211yescharacteristic, complemented
50C2×#3715C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52#63659C2211yescharacteristic, complemented
53#63636C2211yescharacteristic, complemented
54#63634C2211yescharacteristic, complemented
55C3×#830C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C3×#548—31no—
64C2×#949—31no—
65C22×#215—31no—
66D4×#67—31no—
67C22×#214—31no—
68C2×#911—31no—
69#5598D311yescharacteristic, complemented
70D4×D12—31no—
71C3×#447—31no—
72#5238—31no—
73#5227—31no—
74#5158—31no—
75#5154—31no—
76#5153—31no—
77#5058—31no—
78#5057—31no—
79#5049—31no—
80#5046—31no—
81#5038—31no—
82#5038—31no—
83#5038—61no—
84#5036D311yescharacteristic, complemented
85#5027—31no—
86#5026—31no—
87#5011—31no—
88#4780—31no—
89#4776—31no—
90#4762—31no—
91#4757—31no—
92#4738—31no—
93#4730—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C2×#638—21no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67D411yescharacteristic
103C22×C3×Dic3—21no—
104C22×C3×Dic3—21no—
105C3×#237—22no—
106C3×#237—41no—
107C2×C3×D12—22no—
108C2×C3×D12—21no—
109C2×C3×D12—41no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×Dic6—22no—
114C2×C3×Dic6—21no—
115C2×C3×Dic6—41no—
116C2×C3×Dic6C2311yescharacteristic
117C2×C3×Dic6C2311yescharacteristic
118D3×#67—44no—
119C2×#626—21no—
120C2×#626—21no—
121C2×#626—21no—
122C2×#625—21no—
123C2×D3×Dic3—21no—
124D3×D12—22no—
125D3×D12—41no—
126C32×C4⋊C4C2311yescharacteristic
127C32×C22⋊C4—21no—
128#3753—22no—
129#3752—21no—
130C4⋊(C3⋊Dic3)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)—22no—
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134C3×#217—21no—
135C3×#217—21no—
136C3×#217D411yescharacteristic
137C3×#213—22no—
138C3×#213—41no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4D411yescharacteristic
141C3×C4⋊Dic3—21no—
142C3×Dic3⋊C4—21no—
143C3×Dic3⋊C4D411yescharacteristic
144C3×C4×Dic3—21no—
145C3×C4×Dic3C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150#3717—22no—
151#3717—41no—
152#3715—22no—
153#3715—22no—
154#3715—22no—
155#3715D414yescomplemented
156#3711—22no—
157#3265—91noSylow
158C2×C3×#41—31no—
159C22×C3×Q8—31no—
160C22×C3×D4—31no—
161C22×#67—61no—
162C2×#237C2×D311yescharacteristic, complemented
163C2×D3×D4—31no—
164C2×D3×D4—61no—
165C22×D12—31no—
166C22×D12C2×D311yescharacteristic
167C22×Dic6C2×D311yescharacteristic, complemented
168C2×C3×D8—31no—
169C2×C3×D8—31no—
170C3×#124—31no—
171C3×#124—61no—
172C3×C22⋊Q8—31no—
173C3×C22⋊Q8—61no—
174C3×#121—21no—
175C3×#121—61no—
176C3×#121C2×D311yescharacteristic, complemented
177C3×#121C2×D311yescharacteristic, complemented
178C3×C4×Q8—31no—
179C3×C4×D4—31no—
180C3×C4×D4—61no—
181#953—61no—
182#949—64no—
183C2×#215—31no—
184C2×#215—31no—
185C2×#215—31no—
186C2×#215—31no—
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—64no—
190#940—31no—
191#939—21no—
192#939—61no—
193#938—31no—
194#937—61no—
195#936C2×D311yescharacteristic, complemented
196D4×Dic3—21no—
197D4×Dic3—31no—
198C2×#214—31no—
199C2×#214—31no—
200C2×#214—31no—
201C2×#214—31no—
202C2×#214—64no—
203C2×#213—31no—
204C2×#213—31no—
205C2×#213—61no—
206C2×#213C2×D311yescharacteristic
207C2×#213C2×D311yescharacteristic, complemented
208#930—31no—
209#930—31no—
210#930—31no—
211#930—61no—
212C4×#67C2×D311yescharacteristic
213C2×#208—31no—
214C22×C3⋊C8—31no—
215C22×C3⋊C8—31no—
216C22×C3⋊C8—61no—
217#911—64no—
218C2×#204—31no—
219C2×#204—31no—
220C2×ΓL(1,𝔽25)—31no—
221#897C2×D311yescharacteristic, complemented
222#895—61no—
223#887C2×D311yescharacteristic, complemented
224#885—21no—
225#882—61no—
226#882—61no—
227#878—21no—
228#874—31no—
229C4×D12—31no—
230C3×#102—31no—
231C3×#102—31no—
232C3×C22⋊C8—31no—
233#835—31no—
234#835—31no—
235#832—31no—
236#832—31no—
237#832—61no—
238#830—31no—
239#830C2×D311yescharacteristic, complemented
240(C2×D3)⋊C8—31no—
241#816—31no—
242#816—31no—
243#815—31no—
244Dic3⋊C8—31no—
245#809—31no—
246#809—31no—
247#809—61no—
248#809C2×D311yescharacteristic
249#809C2×D311yescharacteristic, complemented
250#807—31no—
251#807—31no—
252#807—61no—
253C4⋊(C3⋊C8)—31no—
254#803—31no—
255C23×C32—21no—
256C23×C32C2×D411yescharacteristic
257C22×C3⋊D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—81no—
263C22×C3×D3C2×D411yescharacteristic
264C2×D32—42no—
265C2×D32—42no—
266C2×D32—81no—
267C32×D4—21no—
268C32×D4—21no—
269C32×D4—42no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4C2×D411yescharacteristic
274C2×C32×C4C2411yescharacteristic
275#638—42no—
276C2×C3⋊Dic3—21no—
277C4⋊(C3⋊D3)—21no—
278C4⋊(C3⋊D3)—21no—
279C3×#67—22no—
280C3×#67—42no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—42no—
284C2×C3×Dic3—42no—
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—21no—
291C3×D12—42no—
292C3×D12C2×D412yes—
293C3×C4×D3—21no—
294C3×C4×D3—21no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297C3×Dic6—21no—
298C3×Dic6—42no—
299C3×Dic6C2×D412yescomplemented
300#626—42no—
301#626—42no—
302#626—81no—
303#625—42no—
304D3×Dic3—42no—
305C3⋊(C3⋊C8)—21no—
306C3⋊(C3⋊C8)C2×D412yescomplemented
307C3×C3⋊C8—21no—
308C3×C3⋊C8—21no—
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—91no—
311#548—31no—
312D42—91no—
313#496—91no—
314#468—91no—
315#466—91no—
316#463—91no—
317#460—91no—
318#450—91no—
319#449—91no—
320#448—91no—
321#447—31no—
322#440—91no—
323#435—91no—
324C24×C3—61no—
325C23×D3—21no—
326C23×D3—61no—
327C23×D3—61no—
328C3×#41—62no—
329C3×#41—121no—
330C2×C3×Q8—31no—
331C2×C3×Q8—31no—
332C2×C3×Q8—62no—
333C2×C3×Q8—61no—
334C2×C3×Q8—121no—
335C2×C3×D4—21no—
336C2×C3×D4—21no—
337C2×C3×D4—21no—
338C2×C3×D4—31no—
339C2×C3×D4—31no—
340C2×C3×D4—31no—
341C2×C3×D4—41no—
342C2×C3×D4—62no—
343C2×C3×D4—61no—
344C2×C3×D4—61no—
345C2×C3×D4—121no—
346C2×C3×D4C22×D311yescharacteristic
347C2×C3×D4C22×D311yescharacteristic
348C22×C3×C4—21no—
349C22×C3×C4—31no—
350C22×C3×C4—61no—
351C22×C3×C4—61no—
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C2×#67—21no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—61no—
359C2×#67—61no—
360C2×#67—61no—
361C2×#67—61no—
362C2×#67—121no—
363C2×#67—124no—
364C2×#67#6711yescharacteristic
365C22×Dic3—21no—
366C22×Dic3—21no—
367C22×Dic3—61no—
368#237—22no—
369#237—41no—
370D3×D4—62no—
371D3×D4—121no—
372D3×D4—124no—
373C2×D12—22no—
374C2×D12—21no—
375C2×D12—31no—
376C2×D12—31no—
377C2×D12—41no—
378C2×D12—61no—
379C2×D12—62no—
380C2×D12—61no—
381C2×D12—61no—
382C2×D12—61no—
383C2×D12—121no—
384C2×D12C22×D311yescharacteristic
385C2×D12C22×D311yescharacteristic
386C2×C4×D3—61no—
387C2×C4×D3C22×D311yescharacteristic
388C2×Dic6—22no—
389C2×Dic6—21no—
390C2×Dic6—41no—
391C2×Dic6C22×D311yescharacteristic
392C2×Dic6C22×D311yescharacteristic
393C3×D8—62no—
394C3×D8—121no—
395C2×C3×C8—31no—
396C2×C3×C8—31no—
397C3×C4⋊C4—21no—
398C3×C4⋊C4—31no—
399C3×C4⋊C4—61no—
400C3×C4⋊C4—61no—
401C3×C4⋊C4C22×D311yescharacteristic
402C3×C4⋊C4C22×D311yescharacteristic
403C3×C22⋊C4—21no—
404C3×C22⋊C4—21no—
405C3×C22⋊C4—31no—
406C3×C22⋊C4—31no—
407C3×C22⋊C4—41no—
408C3×C22⋊C4—61no—
409C3×C22⋊C4—61no—
410C3×C22⋊C4—61no—
411C3×C42—31no—
412C3×C42—61no—
413#217—21no—
414#217—21no—
415#217—61no—
416#217—61no—
417#217#6711yescharacteristic
418#215—34no—
419#215—62no—
420#215—62no—
421#215—62no—
422#215—62no—
423#215—121no—
424#214—34no—
425#214—62no—
426#214—62no—
427#214—62no—
428#213—22no—
429#213—41no—
430#213—62no—
431#213—62no—
432#213—122no—
433(C2×D3)⋊C4—21no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4—121no—
439(C2×D3)⋊C4#6711yescharacteristic
440C4⋊Dic3—21no—
441C4⋊Dic3—31no—
442C4⋊Dic3—31no—
443C4⋊Dic3—61no—
444Dic3⋊C4—21no—
445Dic3⋊C4#6711yescharacteristic
446C4×Dic3—21no—
447C4×Dic3C22×D311yescharacteristic
448#208—62no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—31no—
453C2×C3⋊C8—61no—
454C2×C3⋊C8—61no—
455C2×C3⋊C8—62no—
456C2×C3⋊C8—62no—
457C2×C3⋊C8—122no—
458C2×C3⋊C8C22×D311yescharacteristic
459C2×C3⋊C8C22×D311yescharacteristic
460#204—62no—
461#204—121no—
462ΓL(1,𝔽25)—62no—
463C22×C32—21no—
464C22×C32—21no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32AGL(1,ℤ/8)12yescomplemented
469C22×C32C22×D411yescharacteristic
470C2×C3⋊D3—41no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3—41no—
473C2×C3×D3—22no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—21no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—84no—
483D32—84no—
484C32×C4—21no—
485C32×C4—41no—
486C32×C4C22×D411yescharacteristic
487C32×C4H(5,𝔽2)11yescharacteristic
488C3⋊Dic3—41no—
489C3×Dic3—21no—
490C3×Dic3—22no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—41no—
494C2×#41—31no—
495C22×Q8—31no—
496C22×D4—31no—
497C22×D4—91no—
498C22×D4—181no—
499AGL(1,ℤ/8)—184no—
500C2×SD16—91no—
501C2×SD16—91no—
502C2×SD16—91no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—184no—
507C2×D8—31no—
508C2×D8—31no—
509C2×D8—91no—
510C2×M16—91no—
511C22×C8—91no—
512#127—91no—
513#124—31no—
514#124—61no—
515C22⋊Q8—31no—
516C22⋊Q8—61no—
517#121—61no—
518#121—91no—
519#121—91no—
520#121—181no—
521#121D3211yescharacteristic, complemented
522#120—181no—
523#120—181no—
524C4×Q8—31no—
525C4×D4—31no—
526C4×D4—61no—
527C4×D4—91no—
528#107—91no—
529C4⋊C8—91no—
530#103—91no—
531#103—91no—
532#102—31no—
533#102—31no—
534#102—91no—
535#102—91no—
536C22⋊C8—31no—
537C22⋊C8—91no—
538#97—91no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—21no—
542C23×C3—31no—
543C23×C3—41no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—122no—
547C23×C3—122no—
548C23×C3—241no—
549C23×C3D3×D411yescharacteristic
550C23×C3C2×#6711yescharacteristic
551C22×D3—21no—
552C22×D3—21no—
553C22×D3—42no—
554C22×D3—42no—
555C22×D3—61no—
556C22×D3—61no—
557C22×D3—81no—
558C22×D3—121no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—122no—
562C22×D3—122no—
563C22×D3—241no—
564C22×D3—241no—
565C22×D3C2×#6711yescharacteristic
566C3×Q8—32no—
567C3×Q8—61no—
568C3×Q8—61no—
569C3×Q8—61no—
570C3×Q8—122no—
571C3×D4—21no—
572C3×D4—21no—
573C3×D4—21no—
574C3×D4—21no—
575C3×D4—32no—
576C3×D4—41no—
577C3×D4—41no—
578C3×D4—42no—
579C3×D4—42no—
580C3×D4—62no—
581C3×D4—61no—
582C3×D4—61no—
583C3×D4—61no—
584C3×D4—82no—
585C3×D4—122no—
586C3×D4—122no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—31no—
596C2×C3×C4—31no—
597C2×C3×C4—31no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—122no—
606C2×C3×C4—122no—
607C2×C3×C4D3×D411yescharacteristic
608C2×C3×C4C2×#6711yescharacteristic
609C2×C3×C4C23×D311yescharacteristic
610C2×C3×C4C23×D311yescharacteristic
611#67—22no—
612#67—42no—
613#67—122no—
614#67—122no—
615#67—122no—
616#67—122no—
617#67—122no—
618#67—122no—
619#67—242no—
620#67—241no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—42no—
624C2×Dic3—42no—
625C2×Dic3—61no—
626C2×Dic3—61no—
627C2×Dic3—121no—
628C2×Dic3—122no—
629C2×Dic3C2×#6711yescharacteristic
630C2×Dic3C2×#6711yescharacteristic
631C2×Dic3C2×#6711yescharacteristic
632D12—21no—
633D12—21no—
634D12—21no—
635D12—42no—
636D12—61no—
637D12—61no—
638D12—61no—
639D12—61no—
640D12—121no—
641D12—121no—
642D12—122no—
643D12—122no—
644D12—241no—
645D12D3×D412yes—
646C4×D3—21no—
647C4×D3—21no—
648C4×D3—122no—
649Dic6—21no—
650Dic6—21no—
651Dic6—21no—
652Dic6—42no—
653Dic6D3×D412yescomplemented
654C3×C8—61no—
655C3×C8—61no—
656C3⋊C8—21no—
657C3⋊C8—21no—
658C3⋊C8—32no—
659C3⋊C8—32no—
660C3⋊C8—62no—
661C3⋊C8—61no—
662C3⋊C8—61no—
663C3⋊C8—121no—
664C2×C32—22no—
665C2×C32—81no—
666C2×C32D4211yescharacteristic
667C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
668C2×C32#57711yescharacteristic
669C3⋊D3—81no—
670C3×D3—41no—
671C3×D3—42no—
672C3×D3—81no—
673C24—61no—
674C24—181no—
675#41—62no—
676#41—121no—
677C2×Q8—31no—
678C2×Q8—31no—
679C2×Q8—62no—
680C2×Q8—61no—
681C2×Q8—121no—
682C2×D4—21no—
683C2×D4—31no—
684C2×D4—31no—
685C2×D4—31no—
686C2×D4—62no—
687C2×D4—61no—
688C2×D4—61no—
689C2×D4—91no—
690C2×D4—121no—
691C2×D4—181no—
692C2×D4—181no—
693C2×D4—181no—
694C2×D4—182no—
695C2×D4—181no—
696C2×D4—181no—
697C2×D4—361no—
698C2×D4—364no—
699C2×D4C2×D3211yescharacteristic
700C22×C4—31no—
701C22×C4—61no—
702C22×C4—61no—
703C22×C4—181no—
704C22×C4C2×D3211yescharacteristic
705SD16—94no—
706SD16—182no—
707SD16—182no—
708SD16—182no—
709SD16—182no—
710SD16—361no—
711D8—62no—
712D8—121no—
713D8—182no—
714M16—182no—
715C2×C8—31no—
716C2×C8—31no—
717C2×C8—91no—
718C2×C8—91no—
719C2×C8—182no—
720C4⋊C4—31no—
721C4⋊C4—61no—
722C4⋊C4—61no—
723C4⋊C4—91no—
724C4⋊C4C2×D3211yescharacteristic
725C22⋊C4—21no—
726C22⋊C4—31no—
727C22⋊C4—31no—
728C22⋊C4—61no—
729C22⋊C4—61no—
730C22⋊C4—61no—
731C22⋊C4—181no—
732C22⋊C4—181no—
733C22⋊C4—181no—
734C42—31no—
735C42—61no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—22no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—61no—
751C22×C3—61no—
752C22×C3—62no—
753C22×C3—61no—
754C22×C3—81no—
755C22×C3—81no—
756C22×C3—81no—
757C22×C3—121no—
758C22×C3—121no—
759C22×C3—121no—
760C22×C3—121no—
761C22×C3—121no—
762C22×C3—244no—
763C22×C3#91112yescomplemented
764C22×C3#94912yescomplemented
765C22×C3C2×D3×D411yescharacteristic
766C22×C3C22×#6711yescharacteristic
767C2×D3—21no—
768C2×D3—21no—
769C2×D3—21no—
770C2×D3—22no—
771C2×D3—41no—
772C2×D3—41no—
773C2×D3—41no—
774C2×D3—41no—
775C2×D3—41no—
776C2×D3—84no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—121no—
783C2×D3—241no—
784C2×D3—241no—
785C2×D3—241no—
786C2×D3—244no—
787C2×D3—244no—
788C3×C4—21no—
789C3×C4—21no—
790C3×C4—21no—
791C3×C4—21no—
792C3×C4—41no—
793C3×C4—41no—
794C3×C4—41no—
795C3×C4—61no—
796C3×C4—61no—
797C3×C4—61no—
798C3×C4—62no—
799C3×C4—81no—
800C3×C4—121no—
801C3×C4C2×D3×D411yescharacteristic
802C3×C4C2×D3×D411yescharacteristic
803C3×C4#100411yescharacteristic
804C3×C4#100411yescharacteristic
805Dic3—22no—
806Dic3—21no—
807Dic3—21no—
808Dic3—21no—
809Dic3—41no—
810Dic3—121no—
811Dic3—121no—
812Dic3—241no—
813C32#326511yescharacteristic, complemented, Sylow
814C23—21no—
815C23—31no—
816C23—61no—
817C23—61no—
818C23—122no—
819C23—122no—
820C23—181no—
821C23—241no—
822C23—362no—
823C23—362no—
824C23—721no—
825C23D3×#6711yescharacteristic
826Q8—32no—
827Q8—61no—
828Q8—61no—
829Q8—61no—
830Q8—122no—
831D4—21no—
832D4—21no—
833D4—32no—
834D4—42no—
835D4—62no—
836D4—61no—
837D4—61no—
838D4—61no—
839D4—122no—
840D4—122no—
841D4—181no—
842D4—181no—
843D4—362no—
844D4—362no—
845D4—362no—
846D4—362no—
847D4—721no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—31no—
852C2×C4—31no—
853C2×C4—31no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—122no—
859C2×C4—122no—
860C2×C4—181no—
861C2×C4—362no—
862C2×C4D3×#6711yescharacteristic
863C2×C4C22×D3211yescharacteristic
864C8—61no—
865C8—61no—
866C8—92no—
867C8—181no—
868C2×C3—22no—
869C2×C3—22no—
870C2×C3—21no—
871C2×C3—21no—
872C2×C3—21no—
873C2×C3—42no—
874C2×C3—81no—
875C2×C3—81no—
876C2×C3—122no—
877C2×C3—121no—
878C2×C3—161no—
879C2×C3—241no—
880C2×C3#559011yescharacteristic
881C2×C3C2×#91111yescharacteristic
882C2×C3#577511yescharacteristic
883C2×C3D4×#6711yescharacteristic
884C2×C3C2×#94911yescharacteristic
885C2×C3#583711yescharacteristic
886D3—41no—
887D3—42no—
888D3—81no—
889D3—241no—
890D3—241no—
891D3—481no—
892C22—21no—
893C22—21no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—61no—
898C22—61no—
899C22—61no—
900C22—62no—
901C22—121no—
902C22—121no—
903C22—121no—
904C22—121no—
905C22—121no—
906C22—244no—
907C22—361no—
908C22—361no—
909C22—361no—
910C22—724no—
911C22#6392512yescomplemented
912C22C2×D3×#6711yescharacteristic
913C4—21no—
914C4—41no—
915C4—61no—
916C4—61no—
917C4—61no—
918C4—62no—
919C4—121no—
920C4—361no—
921C4D32×D411yescharacteristic
922C4#6431311yescharacteristic
923C3—21no—
924C3#8002511yescharacteristic, complemented
925C3#8354211yescharacteristic, complemented
926C2—22no—
927C2—81no—
928C2—121no—
929C2—122no—
930C2—241no—
931C2—721no—
932C2C2×#6392511yescharacteristic
933C2#1059528711yescharacteristic
934C2#1059545511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#5598C2semidirect
2. C2×#63925C2semidirect
3. D12×#67C2semidirect
4. C22×#3715C2semidirect
5. #10592737C2semidirect
6. C3×#5036C2semidirect
7. #10591483C2semidirect
8. #10591450C2semidirect
9. #10591431C2semidirect
10. #10591174C2semidirect
11. #10591158C2semidirect
12. #10590596C2semidirect
13. #10590549C2semidirect
14. #10590503C2semidirect
15. #10590454C2semidirect
18. C2×C3×#237C22semidirect
20. C22×C3×Dic6C22semidirect
23. C32×#121C22semidirect
24. C2×#3753C22semidirect
26. C22×C3⋊(C3⋊C8)C22semidirect
28. C3×#936C22semidirect
31. C2×C3×#213C22semidirect
33. C3×#897C22semidirect
34. C3×#887C22semidirect
44. C2×#3717C22semidirect
45. C2×#3717C22semidirect
49. C2×#3715C22semidirect
50. C2×#3715C22semidirect
51. C2×#3711C22semidirect
52. #63659C22semidirect
53. #63636C22semidirect
54. #63634C22semidirect
55. C3×#830C22semidirect
57. C3×#809C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
60. #63566C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
69. #5598D3semidirect
84. #5036D3semidirect
155. #3715D4semidirect
162. C2×#237C2×D3semidirect
167. C22×Dic6C2×D3semidirect
176. C3×#121C2×D3semidirect
177. C3×#121C2×D3semidirect
195. #936C2×D3semidirect
207. C2×#213C2×D3semidirect
221. #897C2×D3semidirect
223. #887C2×D3semidirect
239. #830C2×D3semidirect
249. #809C2×D3semidirect
299. C3×Dic6C2×D4semidirect
306. C3⋊(C3⋊C8)C2×D4semidirect
468. C22×C32AGL(1,ℤ/8)semidirect
521. #121D32semidirect
653. Dic6D3×D4semidirect
763. C22×C3#911semidirect
764. C22×C3#949semidirect
813. C32#3265semidirect
911. C22#63925semidirect
924. C3#80025semidirect
925. C3#83542semidirect

Maximal subgroups

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

subgroupindex
C3×#55982
C2×#639252
D12×#672
C22×#37152
#105927372
C3×#50362
#105914832
#105914502
#105914312
#105911742
#105911582
#105905962
#105905492
#105905032
#105904542
#835423
#800253