Finite Group Databasebeta

← #11884018

Subgroups — #11884018

Order 1152.

1152 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595293C211yesmaximal, characteristic, complemented
2C2×D3×#214C211yesmaximal, characteristic, complemented
3C2×#63798C211yesmaximal, characteristic, complemented
4#10594382C211yesmaximal, characteristic, complemented
5#10592479C211yesmaximal, characteristic, complemented
6C3×#4773C211yesmaximal, characteristic, complemented
7C3×#4762C211yesmaximal, characteristic, complemented
8#10591520C211yesmaximal, characteristic, complemented
9#10591469C211yesmaximal, characteristic, complemented
10#10590907C211yesmaximal, characteristic, complemented
11#10590822C211yesmaximal, characteristic, complemented
12#10590755C211yesmaximal, characteristic, complemented
13#10590597C211yesmaximal, characteristic, complemented
14#10590499C211yesmaximal, characteristic, complemented
15#10590454C211yesmaximal, characteristic, complemented
16#80404—31nomaximal
17#80025—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×#3802C2211yescharacteristic
21C2×#3796C2211yescharacteristic, complemented
22C2×D3×Dic6C2211yescharacteristic, complemented
23#64147C2211yescharacteristic
24C2×#3754C2211yescharacteristic, complemented
25C2×#3743C2211yescharacteristic, complemented
26#64106C2211yescharacteristic, complemented
27C3×#940C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic, complemented
29C2×C3×#213C2211yescharacteristic, complemented
30C2×C3×D24C2211yescharacteristic
31C2×C3×#204C2211yescharacteristic, complemented
32C3×#895C2211yescharacteristic, complemented
33C3×#887C2211yescharacteristic, complemented
34#63983—21no—
35#63976—21no—
36#63970—21no—
37D3×#214—24no—
38#63908C2211yescharacteristic
39C4×#626C2211yescharacteristic
40#63893—21no—
41Dic3×D12—21no—
42Dic3×D12C2211yescharacteristic
43#63886—21no—
44#63860C2211yescharacteristic, complemented
45#63852—21no—
46C2×#3716C2211yescharacteristic
47C2×#3716C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic
49C2×#3713C2211yescharacteristic, complemented
50C2×D3×C3⋊C8C2211yescharacteristic, complemented
51#63798—24no—
52C32×#102C2211yescharacteristic, complemented
53#63643C2211yescharacteristic, complemented
54#63634C2211yescharacteristic, complemented
55C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63557C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63D4×#67—31no—
64C22×#214—31no—
65C2×#914—31no—
66C2×D3×SD16—31no—
67C2×#911—31no—
68#5717—31no—
69#5598—31no—
70#5576—31no—
71C3×#460—31no—
72C3×#447—31no—
73#5172—31no—
74#5170—31no—
75#5158—31no—
76#5154—31no—
77#5153—31no—
78#5074—31no—
79#5038—31no—
80#5026—31no—
81#4844—31no—
82#4836—31no—
83#4780—31no—
84#4780—31no—
85#4780—61no—
86#4776—31no—
87#4776—31no—
88#4775—31no—
89#4773D311yescharacteristic, complemented
90#4762D311yescharacteristic, complemented
91#4757—31no—
92#4738—31no—
93#4730—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C3×D3×D4—22no—
104C3×D3×D4—41no—
105C2×C3×D12—21no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111D3×#67—44no—
112C2×#627—21no—
113C2×#626—21no—
114C2×#626D411yescharacteristic
115C2×#625—21no—
116C2×#625—21no—
117C2×D3×Dic3—21no—
118C2×D3×Dic3—21no—
119C2×D3×Dic3—21no—
120#3802—22no—
121#3802—41no—
122#3796—22no—
123#3796—41no—
124D3×Dic6—22no—
125D3×Dic6—41no—
126C2×C32×C8C2311yescharacteristic
127C32×C4⋊C4C2311yescharacteristic
128#3757—21no—
129#3754—22no—
130#3752—21no—
131C4⋊(C3⋊Dic3)—21no—
132C4⋊(C3⋊Dic3)C2311yescharacteristic
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134#3743—22no—
135C3×#214—22no—
136C3×#213—41no—
137C3×(C2×D3)⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×C4×Dic3—21no—
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×D24—22no—
144C3×#204—22no—
145Dic3⋊Dic3D411yescharacteristic
146#3722D411yescharacteristic
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3D411yescharacteristic
152#3716—22no—
153#3716—41no—
154#3715D414yescomplemented
155#3713—22no—
156D3×C3⋊C8—22no—
157#3265—91noSylow
158C22×C3×D4—31no—
159C22×#67—61no—
160C2×#239—31no—
161C2×D3×Q8—31no—
162C2×#237—31no—
163C2×D3×D4—31no—
164C2×D3×D4—31no—
165C2×D3×D4—61no—
166C2×D3×D4C2×D311yescharacteristic
167C22×Dic6—31no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×D8—31no—
171C2×C3×D8—31no—
172C3×#127—31no—
173C3×#121—31no—
174C3×C4×Q8—31no—
175#953—61no—
176C2×#215—31no—
177#940C2×D311yescharacteristic
178#939—61no—
179#939—61no—
180#938—31no—
181#938—31no—
182#938—31no—
183#938—61no—
184#938—61no—
185#937—61no—
186#937—61no—
187#937—61no—
188#936—31no—
189D4×Dic3—31no—
190D4×Dic3—61no—
191C2×#214—31no—
192C2×#214—31no—
193C2×#214—31no—
194C2×#214—31no—
195C2×#214—31no—
196C2×#214—61no—
197C2×#214—64no—
198C2×#214C2×D311yescharacteristic, complemented
199C2×#213—31no—
200C2×#213—31no—
201C2×#213C2×D311yescharacteristic, complemented
202#930—31no—
203C4×#67—31no—
204C22×C3⋊C8—31no—
205#914—64no—
206D3×SD16—64no—
207#911—64no—
208C2×D24C2×D311yescharacteristic
209C2×#204—31no—
210C2×#204—31no—
211C2×#204C2×D311yescharacteristic, complemented
212C2×ΓL(1,𝔽25)—31no—
213C2×ΓL(1,𝔽25)—31no—
214C2×ΓL(1,𝔽25)—61no—
215C2×D3×C8—31no—
216#897—31no—
217#897—31no—
218#897—61no—
219#897—61no—
220#895—61no—
221#895C2×D311yescharacteristic, complemented
222#887C2×D311yescharacteristic, complemented
223#885—61no—
224#878—61no—
225#875—31no—
226#875—61no—
227C4×D12—31no—
228C4×D12—31no—
229C4×D12—61no—
230C3×C4⋊C8—31no—
231C3×#102—21no—
232C3×#102—31no—
233C3×#102—31no—
234C3×#102C2×D311yescharacteristic, complemented
235C3×#102C2×D311yescharacteristic, complemented
236C3×C22⋊C8—31no—
237#835—31no—
238#832—31no—
239#821—31no—
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—31no—
242(C2×D3)⋊C8C2×D311yescharacteristic, complemented
243#816—31no—
244#816—31no—
245#816—31no—
246#816—61no—
247#815—31no—
248Dic3⋊C8C2×D311yescharacteristic, complemented
249#809C2×D311yescharacteristic
250#809C2×D311yescharacteristic, complemented
251#807—31no—
252#807—31no—
253#807—61no—
254#803—31no—
255C23×C32—21no—
256C22×C3⋊D3C2×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—
269C2×C32×C4—21no—
270C2×C32×C4C2411yescharacteristic
271#638—42no—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3C2×D411yescharacteristic
275C4×C3⋊D3—21no—
276C4×C3⋊D3—21no—
277#634—21no—
278#634—21no—
279C3×#67—42no—
280C3×#67—42no—
281C3×#67—81no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C3×D12—21no—
287C3×D12—21no—
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×Dic6C2×D412yescomplemented
297#627—42no—
298#626—22no—
299#626—42no—
300#625—42no—
301#625—42no—
302D3×Dic3—42no—
303D3×Dic3—42no—
304D3×Dic3—42no—
305C32×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—91no—
312D42—91no—
313#496—91no—
314#468—91no—
315#466—91no—
316#463—91no—
317#460—31no—
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—
328C2×C3×Q8—31no—
329C2×C3×D4—21no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4—61no—
337C2×C3×D4—62no—
338C2×C3×D4—121no—
339C2×C3×D4C22×D311yescharacteristic
340C2×C3×D4C22×D311yescharacteristic
341C22×C3×C4—31no—
342C2×#67—21no—
343C2×#67—21no—
344C2×#67—21no—
345C2×#67—31no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—121no—
354C2×#67—124no—
355C22×Dic3—61no—
356C22×Dic3—61no—
357C22×Dic3—61no—
358#239—62no—
359#239—121no—
360D3×Q8—62no—
361D3×Q8—121no—
362#237—62no—
363#237—121no—
364D3×D4—22no—
365D3×D4—41no—
366D3×D4—62no—
367D3×D4—62no—
368D3×D4—121no—
369D3×D4—121no—
370D3×D4—124no—
371C2×D12—21no—
372C2×D12—31no—
373C2×D12—61no—
374C2×D12C22×D311yescharacteristic
375C2×D12C22×D311yescharacteristic
376C2×D12C22×D311yescharacteristic
377C2×C4×D3—31no—
378C2×C4×D3—31no—
379C2×C4×D3—61no—
380C2×C4×D3—61no—
381C2×C4×D3—61no—
382C2×C4×D3—61no—
383C2×C4×D3C22×D311yescharacteristic
384C2×Dic6—31no—
385C2×Dic6—31no—
386C2×Dic6—61no—
387C2×Dic6—62no—
388C2×Dic6—61no—
389C2×Dic6—61no—
390C2×Dic6—121no—
391C2×Dic6C22×D311yescharacteristic
392C3×SD16—62no—
393C3×SD16—62no—
394C3×D8—62no—
395C3×D8—121no—
396C2×C3×C8—21no—
397C2×C3×C8—31no—
398C2×C3×C8—31no—
399C2×C3×C8C22×D311yescharacteristic
400C2×C3×C8C22×D311yescharacteristic
401C3×C4⋊C4—21no—
402C3×C4⋊C4—61no—
403C3×C4⋊C4C22×D311yescharacteristic
404C3×C4⋊C4C22×D311yescharacteristic
405C3×C22⋊C4—61no—
406C3×C42—31no—
407C3×C42—61no—
408#217—31no—
409#217—61no—
410#217—61no—
411#217—61no—
412#217—61no—
413#217—61no—
414#217—61no—
415#217—121no—
416#215—34no—
417#214—22no—
418#214—34no—
419#214—62no—
420#214—62no—
421#214—62no—
422#214—122no—
423#214—121no—
424#213—41no—
425#213—62no—
426#213—62no—
427(C2×D3)⋊C4—21no—
428(C2×D3)⋊C4—31no—
429(C2×D3)⋊C4—31no—
430(C2×D3)⋊C4—31no—
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—61no—
437(C2×D3)⋊C4—121no—
438C4⋊Dic3—31no—
439C4⋊Dic3—31no—
440C4⋊Dic3—31no—
441C4⋊Dic3—61no—
442C4⋊Dic3—61no—
443C4⋊Dic3—61no—
444C4⋊Dic3—121no—
445Dic3⋊C4—21no—
446Dic3⋊C4—31no—
447C4×Dic3—21no—
448C4×Dic3C22×D311yescharacteristic
449C2×C3⋊C8—31no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—61no—
452C2×C3⋊C8—62no—
453C2×C3⋊C8C22×D311yescharacteristic
454C2×C3⋊C8C22×D311yescharacteristic
455D24—22no—
456#204—22no—
457#204—62no—
458#204—121no—
459ΓL(1,𝔽25)—62no—
460ΓL(1,𝔽25)—62no—
461ΓL(1,𝔽25)—122no—
462D3×C8—62no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32C22×D411yescharacteristic
467C2×C3⋊D3—21no—
468C2×C3⋊D3—21no—
469C2×C3⋊D3—21no—
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—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—84no—
482C2×C3×D3AGL(1,ℤ/8)12yescomplemented
483D32—84no—
484C32×C4—41no—
485C32×C4C22×D411yescharacteristic
486C32×C4H(5,𝔽2)11yescharacteristic
487C3⋊Dic3—21no—
488C3⋊Dic3—41no—
489C3⋊Dic3—41no—
490C3×Dic3—22no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C2×#41—91no—
495C22×Q8—91no—
496C22×D4—31no—
497C22×D4—91no—
498C22×D4—181no—
499AGL(1,ℤ/8)—184no—
500C2×SD16—31no—
501C2×SD16—31no—
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—31no—
513#124—91no—
514#124—181no—
515C22⋊Q8—91no—
516C22⋊Q8—181no—
517#121—31no—
518#121—91no—
519#121—91no—
520#121—181no—
521#121—181no—
522#120—181no—
523#120—181no—
524C4×Q8—31no—
525C4×D4—91no—
526C4×D4—91no—
527C4×D4—181no—
528#107—91no—
529C4⋊C8—31no—
530#103—91no—
531#103—91no—
532#102—31no—
533#102—31no—
534#102—91no—
535#102D3211yescharacteristic, complemented
536C22⋊C8—31no—
537C22⋊C8—91no—
538#97—91no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—31no—
542C23×C3—41no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—122no—
547C23×C3—122no—
548C23×C3—241no—
549C22×D3—21no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—31no—
553C22×D3—31no—
554C22×D3—42no—
555C22×D3—42no—
556C22×D3—61no—
557C22×D3—81no—
558C22×D3—122no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—122no—
562C22×D3—241no—
563C22×D3—241no—
564C22×D3D3×D411yescharacteristic
565C3×Q8—32no—
566C3×Q8—61no—
567C3×D4—21no—
568C3×D4—21no—
569C3×D4—21no—
570C3×D4—21no—
571C3×D4—32no—
572C3×D4—41no—
573C3×D4—41no—
574C3×D4—61no—
575C3×D4—61no—
576C3×D4—61no—
577C3×D4—61no—
578C3×D4—61no—
579C3×D4—122no—
580C3×D4—122no—
581C3×D4—122no—
582C3×D4—241no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—31no—
587C2×C3×C4—31no—
588C2×C3×C4—31no—
589C2×C3×C4—41no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4C23×D311yescharacteristic
594C2×C3×C4C23×D311yescharacteristic
595#67—42no—
596#67—42no—
597#67—62no—
598#67—81no—
599#67—122no—
600#67—122no—
601#67—122no—
602#67—122no—
603#67—122no—
604#67—122no—
605#67—122no—
606#67—242no—
607C2×Dic3—21no—
608C2×Dic3—31no—
609C2×Dic3—31no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—121no—
616C2×Dic3—121no—
617C2×Dic3—122no—
618C2×Dic3—122no—
619C2×Dic3—122no—
620C2×Dic3D3×D411yescharacteristic
621C2×Dic3D3×D411yescharacteristic
622C2×Dic3D3×D411yescharacteristic
623D12—21no—
624D12—21no—
625D12—21no—
626D12—21no—
627D12—21no—
628D12—42no—
629D12—62no—
630D12—122no—
631D12D3×D412yes—
632C4×D3—21no—
633C4×D3—21no—
634C4×D3—61no—
635C4×D3—61no—
636C4×D3—61no—
637C4×D3—61no—
638C4×D3—121no—
639C4×D3—121no—
640C4×D3—122no—
641C4×D3—122no—
642C4×D3—122no—
643Dic6—21no—
644Dic6—61no—
645Dic6—61no—
646Dic6—61no—
647Dic6—61no—
648Dic6—121no—
649Dic6—121no—
650Dic6—122no—
651Dic6—122no—
652Dic6D3×D412yescomplemented
653C3×C8—21no—
654C3×C8—21no—
655C3×C8—41no—
656C3×C8—61no—
657C3×C8—61no—
658C3⋊C8—21no—
659C3⋊C8—21no—
660C3⋊C8—32no—
661C3⋊C8—32no—
662C3⋊C8—62no—
663C2×C32—81no—
664C2×C32D4211yescharacteristic
665C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
666C2×C32#57711yescharacteristic
667C3⋊D3—41no—
668C3×D3—22no—
669C3×D3—42no—
670C3×D3—81no—
671C3×D3—81no—
672C24—61no—
673C24—181no—
674#41—182no—
675#41—361no—
676C2×Q8—31no—
677C2×Q8—91no—
678C2×Q8—181no—
679C2×Q8—182no—
680C2×Q8—361no—
681C2×D4—31no—
682C2×D4—31no—
683C2×D4—31no—
684C2×D4—61no—
685C2×D4—61no—
686C2×D4—61no—
687C2×D4—61no—
688C2×D4—62no—
689C2×D4—91no—
690C2×D4—121no—
691C2×D4—181no—
692C2×D4—181no—
693C2×D4—182no—
694C2×D4—181no—
695C2×D4—181no—
696C2×D4—361no—
697C2×D4—364no—
698C2×D4C2×D3211yescharacteristic
699C22×C4—31no—
700C22×C4—91no—
701C22×C4—181no—
702C22×C4—181no—
703C22×C4—181no—
704SD16—62no—
705SD16—62no—
706SD16—94no—
707SD16—182no—
708SD16—182no—
709SD16—361no—
710D8—62no—
711D8—121no—
712D8—182no—
713M16—182no—
714C2×C8—31no—
715C2×C8—31no—
716C2×C8—91no—
717C2×C8—182no—
718C2×C8C2×D3211yescharacteristic
719C4⋊C4—61no—
720C4⋊C4—91no—
721C4⋊C4—91no—
722C4⋊C4—181no—
723C4⋊C4C2×D3211yescharacteristic
724C22⋊C4—61no—
725C22⋊C4—91no—
726C22⋊C4—91no—
727C22⋊C4—181no—
728C22⋊C4—181no—
729C22⋊C4—181no—
730C22⋊C4—181no—
731C22⋊C4—181no—
732C22⋊C4—181no—
733C42—31no—
734C42—61no—
735C22×C3—21no—
736C22×C3—32no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—61no—
744C22×C3—61no—
745C22×C3—62no—
746C22×C3—81no—
747C22×C3—81no—
748C22×C3—81no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—244no—
758C22×C3C2×D3×D411yescharacteristic
759C22×C3C2×D3×D411yescharacteristic
760C2×D3—21no—
761C2×D3—21no—
762C2×D3—22no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—61no—
772C2×D3—61no—
773C2×D3—61no—
774C2×D3—61no—
775C2×D3—61no—
776C2×D3—61no—
777C2×D3—84no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—244no—
782C2×D3—244no—
783C2×D3#91112yescomplemented
784C3×C4—21no—
785C3×C4—21no—
786C3×C4—41no—
787C3×C4—41no—
788C3×C4—61no—
789C3×C4—61no—
790C3×C4—62no—
791C3×C4—61no—
792C3×C4—81no—
793C3×C4C2×D3×D411yescharacteristic
794C3×C4C2×D3×D411yescharacteristic
795C3×C4#100411yescharacteristic
796C3×C4#100911yescharacteristic
797Dic3—21no—
798Dic3—21no—
799Dic3—21no—
800Dic3—22no—
801Dic3—61no—
802Dic3—61no—
803Dic3—121no—
804Dic3—121no—
805Dic3—121no—
806Dic3—121no—
807Dic3—121no—
808Dic3—241no—
809Dic3—241no—
810C32#326511yescharacteristic, complemented, Sylow
811C23—21no—
812C23—31no—
813C23—61no—
814C23—61no—
815C23—61no—
816C23—91no—
817C23—122no—
818C23—122no—
819C23—241no—
820C23—362no—
821C23—362no—
822C23—721no—
823Q8—32no—
824Q8—61no—
825Q8—181no—
826Q8—181no—
827Q8—362no—
828D4—21no—
829D4—21no—
830D4—32no—
831D4—61no—
832D4—61no—
833D4—61no—
834D4—61no—
835D4—61no—
836D4—122no—
837D4—122no—
838D4—122no—
839D4—182no—
840D4—241no—
841D4—362no—
842D4—362no—
843D4—362no—
844D4—362no—
845C2×C4—21no—
846C2×C4—31no—
847C2×C4—31no—
848C2×C4—31no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—91no—
853C2×C4—181no—
854C2×C4—181no—
855C2×C4—181no—
856C2×C4—181no—
857C2×C4—362no—
858C2×C4—362no—
859C2×C4—362no—
860C2×C4C22×D3211yescharacteristic
861C8—21no—
862C8—61no—
863C8—61no—
864C8—92no—
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—62no—
869C2×C3—81no—
870C2×C3—81no—
871C2×C3—122no—
872C2×C3—161no—
873C2×C3—241no—
874C2×C3—241no—
875C2×C3#559011yescharacteristic
876C2×C3#560911yescharacteristic
877C2×C3C2×#91111yescharacteristic
878C2×C3#576211yescharacteristic
879C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
880C2×C3#577511yescharacteristic
881D3—22no—
882D3—42no—
883D3—81no—
884D3—81no—
885D3—121no—
886D3—121no—
887D3—241no—
888C22—32no—
889C22—41no—
890C22—41no—
891C22—41no—
892C22—61no—
893C22—61no—
894C22—62no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—181no—
904C22—181no—
905C22—181no—
906C22—244no—
907C22—724no—
908C22D32×D411yescharacteristic
909C4—41no—
910C4—61no—
911C4—61no—
912C4—61no—
913C4—62no—
914C4—181no—
915C4—361no—
916C4—361no—
917C4#6430711yescharacteristic
918C4D32×D411yescharacteristic
919C3—21no—
920C3#8002511yescharacteristic, complemented
921C3#8040411yescharacteristic, complemented
922C2—62no—
923C2—81no—
924C2—122no—
925C2—241no—
926C2—241no—
927C2—361no—
928C2#1059427511yescharacteristic
929C2D3×#91111yescharacteristic
930C2#1059474911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3265
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. #10595293C2semidirect
2. C2×D3×#214C2semidirect
3. C2×#63798C2semidirect
4. #10594382C2semidirect
5. #10592479C2semidirect
6. C3×#4773C2semidirect
7. C3×#4762C2semidirect
8. #10591520C2semidirect
9. #10591469C2semidirect
10. #10590907C2semidirect
11. #10590822C2semidirect
12. #10590755C2semidirect
13. #10590597C2semidirect
14. #10590499C2semidirect
15. #10590454C2semidirect
21. C2×#3796C22semidirect
22. C2×D3×Dic6C22semidirect
24. C2×#3754C22semidirect
25. C2×#3743C22semidirect
26. #64106C22semidirect
28. C2×C3×#214C22semidirect
29. C2×C3×#213C22semidirect
31. C2×C3×#204C22semidirect
32. C3×#895C22semidirect
33. C3×#887C22semidirect
44. #63860C22semidirect
47. C2×#3716C22semidirect
49. C2×#3713C22semidirect
50. C2×D3×C3⋊C8C22semidirect
52. C32×#102C22semidirect
53. #63643C22semidirect
54. #63634C22semidirect
55. C3×(C2×D3)⋊C8C22semidirect
56. C3×Dic3⋊C8C22semidirect
58. C3×#809C22semidirect
59. #63566C22semidirect
60. #63563C22semidirect
61. #63557C22semidirect
62. #63554C22semidirect
89. #4773D3semidirect
90. #4762D3semidirect
154. #3715D4semidirect
198. C2×#214C2×D3semidirect
201. C2×#213C2×D3semidirect
211. C2×#204C2×D3semidirect
221. #895C2×D3semidirect
222. #887C2×D3semidirect
234. C3×#102C2×D3semidirect
235. C3×#102C2×D3semidirect
242. (C2×D3)⋊C8C2×D3semidirect
248. Dic3⋊C8C2×D3semidirect
250. #809C2×D3semidirect
296. C3×Dic6C2×D4semidirect
306. C3⋊(C3⋊C8)C2×D4semidirect
482. C2×C3×D3AGL(1,ℤ/8)semidirect
535. #102D32semidirect
652. Dic6D3×D4semidirect
783. C2×D3#911semidirect
810. C32#3265semidirect
920. C3#80025semidirect
921. C3#80404semidirect

Maximal subgroups

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

subgroupindex
#105952932
C2×D3×#2142
C2×#637982
#105943822
#105924792
C3×#47732
C3×#47622
#105915202
#105914692
#105909072
#105908222
#105907552
#105905972
#105904992
#105904542
#804043
#800253