Finite Group Databasebeta

← #11884033

Subgroups — #11884033

Order 1152.

1173 conjugacy classes of subgroups.

The subgroup lattice has 941 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595161C211yesmaximal, characteristic, complemented
2C2×#63927C211yesmaximal, characteristic, complemented
3C2×D3×#204C211yesmaximal, characteristic, complemented
4#10594621C211yesmaximal, characteristic, complemented
5#10592480C211yesmaximal, characteristic, complemented
6C3×#4787C211yesmaximal, characteristic, complemented
7C3×#4775C211yesmaximal, characteristic, complemented
8#10591515C211yesmaximal, characteristic, complemented
9#10591483C211yesmaximal, characteristic, complemented
10#10590943C211yesmaximal, characteristic, complemented
11#10590879C211yesmaximal, characteristic, complemented
12#10590727C211yesmaximal, characteristic, complemented
13#10590603C211yesmaximal, characteristic, complemented
14#10590590C211yesmaximal, characteristic, complemented
15#10590522C211yesmaximal, characteristic, complemented
16#80727—31nomaximal
17#80553—31nomaximal
18C2×#3830C2211yescharacteristic, complemented
19C2×#3802C2211yescharacteristic
20C2×D3×D12—21no—
21C2×D3×D12C2211yescharacteristic
22C2×D3×Dic6C2211yescharacteristic, complemented
23C2×#3753C2211yescharacteristic, complemented
24C2×#3744C2211yescharacteristic, complemented
25#64104C2211yescharacteristic
26C3×#938C2211yescharacteristic, complemented
27C3×#936C2211yescharacteristic, complemented
28C2×C3×#213C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic, complemented
30C2×C3×#204C2211yescharacteristic
31C2×C3×D3×C8C2211yescharacteristic, complemented
32C3×#895C2211yescharacteristic
33C3×#893C2211yescharacteristic
34#63982—21no—
35#67⋊Dic3—21no—
36#63971—21no—
37#63953—21no—
38#63927—24no—
39#63923—21no—
40#63922—21no—
41#63911C2211yescharacteristic
42#63906—21no—
43C4×#626C2211yescharacteristic
44#63871C2211yescharacteristic, complemented
45#63844C2211yescharacteristic, complemented
46C2×#3717C2211yescharacteristic, complemented
47C2×#3716C2211yescharacteristic
48C2×#3716C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50C2×#3712C2211yescharacteristic, complemented
51D3×#204—24no—
52C32×#102C2211yescharacteristic, complemented
53#63647C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#807C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C2×D3×SD16—31no—
64C2×#911—31no—
65C2×#911—31no—
66C22×#204—31no—
67#5677—31no—
68#5609—31no—
69#5598—31no—
70D4×D12—31no—
71C3×#466—31no—
72C3×#463—31no—
73#5169—31no—
74#5156—31no—
75#5154—31no—
76#5111—31no—
77#5058—31no—
78#5040—31no—
79#5036—31no—
80#5018—31no—
81#4889—31no—
82#4886—31no—
83#4848—31no—
84#4836—31no—
85#4812—31no—
86#4806—31no—
87#4787D311yescharacteristic, complemented
88#4781—31no—
89#4781—31no—
90#4781—61no—
91#4776—31no—
92#4775D311yescharacteristic, complemented
93#4762—31no—
94C22×D32—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—
106C2×C3×D12—21no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×#627—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#626—21no—
116C2×#626D411yescharacteristic
117C2×#625—21no—
118C2×D3×Dic3—21no—
119#3802—22no—
120#3802—41no—
121D3×D12—22no—
122D3×D12—44no—
123D3×D12—41no—
124D3×Dic6—22no—
125D3×Dic6—41no—
126C2×C32×C8C2311yescharacteristic
127C32×C4⋊C4C2311yescharacteristic
128#3753—41no—
129#3752—21no—
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131#3744—22no—
132C3×#217—21no—
133C3×#217—21no—
134C3×#217—21no—
135C3×#213—22no—
136C3×#213—22no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×C4⋊Dic3C2311yescharacteristic
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×#204—22no—
144C3×D3×C8—22no—
145#3724—21no—
146Dic3⋊Dic3—21no—
147Dic3⋊Dic3D411yescharacteristic
148#3722—21no—
149#3722D411yescharacteristic
150(C2×D3)⋊Dic3D411yescharacteristic
151Dic32—21no—
152#3717—22no—
153#3716—22no—
154#3716D414yescomplemented
155#3715—41no—
156#3712—22no—
157#3265—91noSylow
158C2×D3×Q8—31no—
159C2×#237—31no—
160C2×#237—31no—
161C2×#237—61no—
162C2×D3×D4—31no—
163C2×D3×D4—31no—
164C2×D3×D4—31no—
165C2×D3×D4—61no—
166C22×D12—31no—
167C22×D12—61no—
168C22×Dic6—31no—
169C2×C3×SD16—31no—
170C2×C3×D8—31no—
171C2×C3×D8—31no—
172C22×C3×C8—31no—
173C3×#124—31no—
174C3×#121—31no—
175C3×#121—31no—
176C3×C4×D4—31no—
177#946—31no—
178C2×#215—31no—
179C2×#215—31no—
180#940—31no—
181#939—61no—
182#938C2×D311yescharacteristic, complemented
183#937—61no—
184#936C2×D311yescharacteristic, complemented
185D4×Dic3—61no—
186C2×#214—31no—
187C2×#214—31no—
188C2×#214—31no—
189C2×#213—31no—
190C2×#213—31no—
191C2×#213—61no—
192C2×#213C2×D311yescharacteristic
193C2×#213C2×D311yescharacteristic, complemented
194#930—61no—
195C4×#67—31no—
196D3×SD16—64no—
197#911—64no—
198#911—64no—
199C2×#204—31no—
200C2×#204—31no—
201C2×#204—31no—
202C2×#204—31no—
203C2×#204—31no—
204C2×#204—61no—
205C2×#204—64no—
206C2×#204C2×D311yescharacteristic
207C2×ΓL(1,𝔽25)—31no—
208C2×ΓL(1,𝔽25)—31no—
209C2×D3×C8C2×D311yescharacteristic, complemented
210#897—31no—
211#895—31no—
212#895—31no—
213#895—61no—
214#895C2×D311yescharacteristic
215#893C2×D311yescharacteristic
216#887—31no—
217#885—61no—
218#885—61no—
219#884—61no—
220#884—61no—
221#882—61no—
222#882—61no—
223#882—61no—
224#67⋊C4—61no—
225#878—61no—
226#878—61no—
227#874—31no—
228C4×D12—31no—
229C4×Dic6—31no—
230C3×#107—31no—
231C3×C4⋊C8—31no—
232C3×#103—31no—
233C3×#102—21no—
234C3×#102—31no—
235C3×#102C2×D311yescharacteristic, complemented
236C3×#102C2×D311yescharacteristic, complemented
237#832—31no—
238#830—31no—
239#821—31no—
240#821C2×D311yescharacteristic, complemented
241(C2×D3)⋊C8—31no—
242(C2×D3)⋊C8—31no—
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8—61no—
245#815—31no—
246Dic3⋊C8C2×D311yescharacteristic, complemented
247#810—31no—
248#810—31no—
249#810—61no—
250#810C2×D311yescharacteristic, complemented
251#809—31no—
252#809—31no—
253#807C2×D311yescharacteristic, complemented
254#803—31no—
255C23×C32—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3C2×D411yescharacteristic
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3C2×D411yescharacteristic
261C2×D32—42no—
262C2×D32—42no—
263C2×D32—42no—
264C2×D32—42no—
265C2×D32—81no—
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—42no—
274C2×C3⋊Dic3C2×D411yescharacteristic
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)—42no—
278C4×C3⋊D3—21no—
279C4×C3⋊D3—21no—
280#634—21no—
281#634C2×D412yescomplemented
282C3×#67—42no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
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×C4×D3—42no—
296C3×Dic6—21no—
297C3×Dic6—21no—
298#627—42no—
299#626—22no—
300#626—42no—
301#626—42no—
302#626—81no—
303#625—42no—
304D3×Dic3—42no—
305C32×C8—21no—
306C3⋊(C3⋊C8)—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8C2×D412yescomplemented
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—91no—
311#548—91no—
312D42—91no—
313#496—91no—
314#468—91no—
315#466—31no—
316#463—31no—
317#460—91no—
318#450—91no—
319#449—91no—
320#448—91no—
321#447—91no—
322#440—91no—
323#435—91no—
324C23×D3—61no—
325C23×D3—61no—
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—61no—
333C2×C3×D4—61no—
334C2×C3×D4C22×D311yescharacteristic
335C2×C3×D4C22×D311yescharacteristic
336C22×C3×C4—31no—
337C22×C3×C4—61no—
338C2×#67—21no—
339C2×#67—31no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—121no—
348C22×Dic3—61no—
349C22×Dic3—61no—
350C22×Dic3—61no—
351C22×Dic3—121no—
352D3×Q8—62no—
353D3×Q8—121no—
354#237—62no—
355#237—62no—
356#237—122no—
357#237—121no—
358#237—121no—
359#237—122no—
360D3×D4—62no—
361D3×D4—62no—
362D3×D4—62no—
363D3×D4—121no—
364D3×D4—124no—
365D3×D4—121no—
366D3×D4—121no—
367C2×D12—21no—
368C2×D12—31no—
369C2×D12—31no—
370C2×D12—31no—
371C2×D12—61no—
372C2×D12—62no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—61no—
378C2×D12—121no—
379C2×D12—121no—
380C2×D12—124no—
381C2×D12C22×D311yescharacteristic
382C2×D12C22×D311yescharacteristic
383C2×C4×D3—21no—
384C2×C4×D3—31no—
385C2×C4×D3—31no—
386C2×C4×D3—61no—
387C2×C4×D3—61no—
388C2×C4×D3C22×D311yescharacteristic
389C2×Dic6—31no—
390C2×Dic6—31no—
391C2×Dic6—61no—
392C2×Dic6—62no—
393C2×Dic6—61no—
394C2×Dic6—61no—
395C2×Dic6—121no—
396C2×Dic6C22×D311yescharacteristic
397C3×SD16—62no—
398C3×D8—62no—
399C3×D8—62no—
400C2×C3×C8—21no—
401C2×C3×C8—31no—
402C2×C3×C8—31no—
403C2×C3×C8—62no—
404C2×C3×C8C22×D311yescharacteristic
405C2×C3×C8C22×D311yescharacteristic
406C3×C4⋊C4—21no—
407C3×C4⋊C4—31no—
408C3×C4⋊C4C22×D311yescharacteristic
409C3×C4⋊C4C22×D311yescharacteristic
410C3×C22⋊C4—61no—
411C3×C22⋊C4—61no—
412C3×C22⋊C4—61no—
413C3×C22⋊C4—61no—
414C3×C22⋊C4—61no—
415C3×C42—31no—
416#217—21no—
417#217—21no—
418#217—21no—
419#217—31no—
420#215—62no—
421#215—121no—
422#214—34no—
423#214—62no—
424#214—121no—
425#213—22no—
426#213—22no—
427#213—121no—
428#213—121no—
429#213—122no—
430(C2×D3)⋊C4—21no—
431(C2×D3)⋊C4—21no—
432(C2×D3)⋊C4—31no—
433(C2×D3)⋊C4—31no—
434(C2×D3)⋊C4—31no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4—61no—
439(C2×D3)⋊C4—121no—
440C4⋊Dic3—31no—
441C4⋊Dic3—61no—
442C4⋊Dic3C22×D311yescharacteristic
443Dic3⋊C4—31no—
444Dic3⋊C4—61no—
445Dic3⋊C4—61no—
446Dic3⋊C4—61no—
447C4×Dic3—61no—
448C4×Dic3—61no—
449C4×Dic3C22×D311yescharacteristic
450C2×C3⋊C8—31no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—61no—
453C2×C3⋊C8C22×D311yescharacteristic
454C2×C3⋊C8C22×D311yescharacteristic
455#204—22no—
456#204—34no—
457#204—62no—
458#204—62no—
459#204—62no—
460#204—62no—
461#204—122no—
462ΓL(1,𝔽25)—62no—
463ΓL(1,𝔽25)—62no—
464D3×C8—22no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32C22×D411yescharacteristic
469C2×C3⋊D3—21no—
470C2×C3⋊D3—21no—
471C2×C3⋊D3—21no—
472C2×C3⋊D3—41no—
473C2×C3⋊D3—41no—
474C2×C3⋊D3—41no—
475C2×C3×D3—21no—
476C2×C3×D3—21no—
477C2×C3×D3—22no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3AGL(1,ℤ/8)12yescomplemented
484D32—84no—
485D32—84no—
486C32×C4—41no—
487C32×C4C22×D411yescharacteristic
488C32×C4H(5,𝔽2)11yescharacteristic
489C3⋊Dic3—22no—
490C3⋊Dic3—21no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—41no—
495C3×Dic3—41no—
496C2×#41—91no—
497C22×Q8—91no—
498C22×D4—91no—
499C22×D4—91no—
500C22×D4—181no—
501AGL(1,ℤ/8)—184no—
502C2×SD16—31no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—91no—
507C2×SD16—91no—
508C2×SD16—184no—
509C2×D8—31no—
510C2×D8—31no—
511C2×D8—91no—
512C2×M16—91no—
513C22×C8—31no—
514#127—91no—
515#124—31no—
516#124—181no—
517C22⋊Q8—91no—
518C22⋊Q8—181no—
519#121—31no—
520#121—31no—
521#121—91no—
522#121—181no—
523#121—181no—
524#120—181no—
525#120—181no—
526C4×Q8—91no—
527C4×D4—31no—
528C4×D4—91no—
529C4×D4—181no—
530#107—31no—
531C4⋊C8—31no—
532#103—31no—
533#103—91no—
534#102—31no—
535#102—91no—
536#102—91no—
537#102D3211yescharacteristic, complemented
538C22⋊C8—91no—
539C22⋊C8—91no—
540#97—91no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—31no—
544C23×C3—41no—
545C23×C3—61no—
546C23×C3—61no—
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—31no—
550C22×D3—31no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—61no—
554C22×D3—121no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—122no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—122no—
562C22×D3—122no—
563C22×D3—241no—
564C22×D3—241no—
565C22×D3—241no—
566C22×D3—241no—
567C22×D3D3×D411yescharacteristic
568C3×Q8—61no—
569C3×Q8—61no—
570C3×D4—22no—
571C3×D4—21no—
572C3×D4—21no—
573C3×D4—21no—
574C3×D4—21no—
575C3×D4—32no—
576C3×D4—41no—
577C3×D4—61no—
578C3×D4—61no—
579C3×D4—61no—
580C3×D4—122no—
581C3×D4—122no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—31no—
586C2×C3×C4—31no—
587C2×C3×C4—31no—
588C2×C3×C4—41no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—122no—
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—61no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—121no—
614C2×Dic3—122no—
615C2×Dic3—122no—
616C2×Dic3—122no—
617C2×Dic3—124no—
618C2×Dic3D3×D411yescharacteristic
619C2×Dic3D3×D411yescharacteristic
620C2×Dic3D3×D411yescharacteristic
621D12—21no—
622D12—21no—
623D12—21no—
624D12—42no—
625D12—62no—
626D12—61no—
627D12—61no—
628D12—61no—
629D12—61no—
630D12—121no—
631D12—121no—
632D12—122no—
633D12—122no—
634D12—122no—
635D12—122no—
636D12—242no—
637D12—241no—
638D12D3×D412yes—
639C4×D3—21no—
640C4×D3—21no—
641C4×D3—42no—
642C4×D3—61no—
643C4×D3—61no—
644C4×D3—61no—
645C4×D3—61no—
646C4×D3—121no—
647C4×D3—121no—
648C4×D3—122no—
649Dic6—21no—
650Dic6—21no—
651Dic6—32no—
652Dic6—32no—
653Dic6—62no—
654Dic6—61no—
655Dic6—61no—
656Dic6—121no—
657Dic6—122no—
658Dic6—122no—
659C3×C8—21no—
660C3×C8—21no—
661C3×C8—32no—
662C3×C8—41no—
663C3×C8—61no—
664C3⋊C8—21no—
665C3⋊C8—61no—
666C3⋊C8—61no—
667C3⋊C8—121no—
668C3⋊C8D3×D412yescomplemented
669C2×C32—81no—
670C2×C32D4211yescharacteristic
671C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
672C2×C32#57711yescharacteristic
673C3⋊D3—41no—
674C3⋊D3—81no—
675C3×D3—22no—
676C3×D3—42no—
677C3×D3—81no—
678C24—181no—
679C24—181no—
680#41—182no—
681#41—361no—
682C2×Q8—31no—
683C2×Q8—91no—
684C2×Q8—181no—
685C2×Q8—182no—
686C2×Q8—361no—
687C2×D4—31no—
688C2×D4—31no—
689C2×D4—61no—
690C2×D4—61no—
691C2×D4—91no—
692C2×D4—91no—
693C2×D4—181no—
694C2×D4—181no—
695C2×D4—181no—
696C2×D4—181no—
697C2×D4—182no—
698C2×D4—181no—
699C2×D4—182no—
700C2×D4—181no—
701C2×D4—361no—
702C2×D4—364no—
703C2×D4—361no—
704C2×D4C2×D3211yescharacteristic
705C22×C4—31no—
706C22×C4—61no—
707C22×C4—91no—
708C22×C4—181no—
709C22×C4—181no—
710SD16—62no—
711SD16—94no—
712SD16—182no—
713SD16—182no—
714SD16—182no—
715SD16—361no—
716D8—62no—
717D8—62no—
718D8—361no—
719M16—182no—
720C2×C8—31no—
721C2×C8—31no—
722C2×C8—62no—
723C2×C8—91no—
724C2×C8C2×D3211yescharacteristic
725C4⋊C4—31no—
726C4⋊C4—91no—
727C4⋊C4—181no—
728C4⋊C4—181no—
729C4⋊C4C2×D3211yescharacteristic
730C22⋊C4—61no—
731C22⋊C4—61no—
732C22⋊C4—61no—
733C22⋊C4—61no—
734C22⋊C4—61no—
735C22⋊C4—91no—
736C22⋊C4—91no—
737C22⋊C4—181no—
738C22⋊C4—181no—
739C42—31no—
740C42—181no—
741C22×C3—21no—
742C22×C3—32no—
743C22×C3—42no—
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—81no—
754C22×C3—81no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—121no—
758C22×C3—121no—
759C22×C3—121no—
760C22×C3C2×D3×D411yescharacteristic
761C22×C3C2×D3×D411yescharacteristic
762C2×D3—21no—
763C2×D3—21no—
764C2×D3—22no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—61no—
771C2×D3—61no—
772C2×D3—61no—
773C2×D3—61no—
774C2×D3—61no—
775C2×D3—61no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—121no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—241no—
786C2×D3—241no—
787C2×D3—241no—
788C2×D3—244no—
789C2×D3—244no—
790C2×D3—244no—
791C2×D3—244no—
792C2×D3#91112yescomplemented
793C3×C4—21no—
794C3×C4—21no—
795C3×C4—41no—
796C3×C4—41no—
797C3×C4—61no—
798C3×C4—61no—
799C3×C4—61no—
800C3×C4—81no—
801C3×C4—121no—
802C3×C4—121no—
803C3×C4C2×D3×D411yescharacteristic
804C3×C4C2×D3×D411yescharacteristic
805C3×C4#100911yescharacteristic
806C3×C4#100911yescharacteristic
807Dic3—21no—
808Dic3—21no—
809Dic3—21no—
810Dic3—41no—
811Dic3—41no—
812Dic3—62no—
813Dic3—62no—
814Dic3—61no—
815Dic3—61no—
816Dic3—122no—
817Dic3—121no—
818C32#326511yescharacteristic, complemented, Sylow
819C23—21no—
820C23—31no—
821C23—61no—
822C23—61no—
823C23—91no—
824C23—181no—
825C23—362no—
826C23—362no—
827C23—362no—
828C23—362no—
829C23—721no—
830C23—721no—
831Q8—61no—
832Q8—61no—
833Q8—92no—
834Q8—181no—
835Q8—362no—
836D4—21no—
837D4—21no—
838D4—32no—
839D4—61no—
840D4—61no—
841D4—61no—
842D4—122no—
843D4—122no—
844D4—182no—
845D4—181no—
846D4—181no—
847D4—362no—
848D4—362no—
849D4—362no—
850D4—362no—
851D4—362no—
852D4—721no—
853C2×C4—21no—
854C2×C4—31no—
855C2×C4—31no—
856C2×C4—31no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—91no—
862C2×C4—122no—
863C2×C4—181no—
864C2×C4—181no—
865C2×C4—181no—
866C2×C4—362no—
867C2×C4—362no—
868C2×C4C22×D3211yescharacteristic
869C8—21no—
870C8—32no—
871C8—61no—
872C8—181no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—62no—
877C2×C3—82no—
878C2×C3—81no—
879C2×C3—81no—
880C2×C3—122no—
881C2×C3—241no—
882C2×C3#560911yescharacteristic
883C2×C3#560911yescharacteristic
884C2×C3C2×#91111yescharacteristic
885C2×C3#577011yescharacteristic
886C2×C3#577011yescharacteristic
887C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
888D3—22no—
889D3—42no—
890D3—81no—
891D3—121no—
892D3—121no—
893D3—241no—
894D3—241no—
895D3—241no—
896D3—481no—
897C22—32no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—61no—
902C22—61no—
903C22—62no—
904C22—121no—
905C22—121no—
906C22—121no—
907C22—121no—
908C22—121no—
909C22—181no—
910C22—181no—
911C22—181no—
912C22—361no—
913C22—361no—
914C22—361no—
915C22—724no—
916C22—724no—
917C22D32×D411yescharacteristic
918C4—41no—
919C4—61no—
920C4—61no—
921C4—61no—
922C4—121no—
923C4—121no—
924C4—181no—
925C4—182no—
926C4#6430811yescharacteristic
927C4D32×D411yescharacteristic
928C3—21no—
929C3#8055311yescharacteristic, complemented
930C3#8072711yescharacteristic, complemented
931C2—62no—
932C2—81no—
933C2—122no—
934C2—241no—
935C2—361no—
936C2—721no—
937C2#1059428411yescharacteristic
938C2D3×#91111yescharacteristic
939C2#1059475711yescharacteristic
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. #10595161C2semidirect
2. C2×#63927C2semidirect
3. C2×D3×#204C2semidirect
4. #10594621C2semidirect
5. #10592480C2semidirect
6. C3×#4787C2semidirect
7. C3×#4775C2semidirect
8. #10591515C2semidirect
9. #10591483C2semidirect
10. #10590943C2semidirect
11. #10590879C2semidirect
12. #10590727C2semidirect
13. #10590603C2semidirect
14. #10590590C2semidirect
15. #10590522C2semidirect
18. C2×#3830C22semidirect
22. C2×D3×Dic6C22semidirect
23. C2×#3753C22semidirect
24. C2×#3744C22semidirect
26. C3×#938C22semidirect
27. C3×#936C22semidirect
29. C2×C3×#213C22semidirect
31. C2×C3×D3×C8C22semidirect
44. #63871C22semidirect
45. #63844C22semidirect
46. C2×#3717C22semidirect
48. C2×#3716C22semidirect
49. C2×#3715C22semidirect
50. C2×#3712C22semidirect
52. C32×#102C22semidirect
53. #63647C22semidirect
54. #63637C22semidirect
55. C3×#821C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#810C22semidirect
58. C3×#807C22semidirect
59. #63564C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
87. #4787D3semidirect
92. #4775D3semidirect
154. #3716D4semidirect
182. #938C2×D3semidirect
184. #936C2×D3semidirect
193. C2×#213C2×D3semidirect
209. C2×D3×C8C2×D3semidirect
235. C3×#102C2×D3semidirect
236. C3×#102C2×D3semidirect
240. #821C2×D3semidirect
246. Dic3⋊C8C2×D3semidirect
250. #810C2×D3semidirect
253. #807C2×D3semidirect
281. #634C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
483. C2×C3×D3AGL(1,ℤ/8)semidirect
537. #102D32semidirect
668. C3⋊C8D3×D4semidirect
792. C2×D3#911semidirect
818. C32#3265semidirect
929. C3#80553semidirect
930. C3#80727semidirect

Maximal subgroups

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

subgroupindex
#105951612
C2×#639272
C2×D3×#2042
#105946212
#105924802
C3×#47872
C3×#47752
#105915152
#105914832
#105909432
#105908792
#105907272
#105906032
#105905902
#105905222
#807273
#805533