Finite Group Databasebeta

← #11884032

Subgroups — #11884032

Order 1152.

1154 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#10595157C211yesmaximal, characteristic, complemented
2C2×#63925C211yesmaximal, characteristic, complemented
3C2×D3×#204C211yesmaximal, characteristic, complemented
4#10594618C211yesmaximal, characteristic, complemented
5#10592486C211yesmaximal, characteristic, complemented
6C3×#4781C211yesmaximal, characteristic, complemented
7C3×#4775C211yesmaximal, characteristic, complemented
8#10591515C211yesmaximal, characteristic, complemented
9#10591485C211yesmaximal, characteristic, complemented
10#10590946C211yesmaximal, characteristic, complemented
11#10590876C211yesmaximal, characteristic, complemented
12#10590723C211yesmaximal, characteristic, complemented
13#10590603C211yesmaximal, characteristic, complemented
14#10590588C211yesmaximal, characteristic, complemented
15#10590484C211yesmaximal, characteristic, complemented
16#80727—31nomaximal
17#80121—31nomaximal
18C2×C3×#237C2211yescharacteristic, complemented
19C2×#3802—21no—
20C2×D3×D12C2211yescharacteristic
21C2×D3×D12C2211yescharacteristic
22C2×D3×Dic6C2211yescharacteristic, complemented
23#64145C2211yescharacteristic, complemented
24C2×#3753C2211yescharacteristic
25C2×#3744C2211yescharacteristic
26#64102C2211yescharacteristic
27C3×#938C2211yescharacteristic, complemented
28C2×C3×#213C2211yescharacteristic, complemented
29C2×C3×#213C2211yescharacteristic, complemented
30C2×C3×#204C2211yescharacteristic, complemented
31C2×C3×D3×C8C2211yescharacteristic, complemented
32C3×#895C2211yescharacteristic
33C3×#895C2211yescharacteristic
34Dic3×#67—21no—
35#63970—21no—
36#63964—21no—
37#63959—21no—
38#63925—24no—
39#63922—21no—
40#63922—21no—
41#63914C2211yescharacteristic
42#63912—21no—
43C4×#625C2211yescharacteristic
44#63857C2211yescharacteristic, complemented
45#63843C2211yescharacteristic, complemented
46C2×#3717C2211yescharacteristic
47C2×#3716C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50C2×#3711C2211yescharacteristic, complemented
51D3×#204—24no—
52C32×#102C2211yescharacteristic, complemented
53#63641C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#807C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63555C2211yescharacteristic, complemented
63#5831—31no—
64C2×#949—31no—
65C2×D3×SD16—31no—
66C2×#911—31no—
67C22×#204—31no—
68#5609—31no—
69#5609—31no—
70#5598—31no—
71C3×#466—31no—
72C3×#449—31no—
73#5163—31no—
74#5156—31no—
75#5154—31no—
76#5154—31no—
77#5111—31no—
78#5042—31no—
79#5040—31no—
80#5036—31no—
81#4889—31no—
82#4886—31no—
83#4817—31no—
84#4806—31no—
85#4787—31no—
86#4787—31no—
87#4787—61no—
88#4781D311yescharacteristic, complemented
89#4776—31no—
90#4775D311yescharacteristic, complemented
91#4762—31no—
92#4731—31no—
93#4728—31no—
94C22×D32—21no—
95C22×D32—21no—
96C2×C32×D4C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C22×C3×Dic3—21no—
103C3×#237—22no—
104C3×#237—41no—
105C2×C3×D12—21no—
106C2×C3×D12—21no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×#627—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#625—21no—
116C2×#625—21no—
117C2×#625D411yescharacteristic
118C2×D3×Dic3—21no—
119#3802—44no—
120D3×D12—22no—
121D3×D12—22no—
122D3×D12—41no—
123D3×D12—41no—
124D3×Dic6—22no—
125D3×Dic6—41no—
126C2×C32×C8C2311yescharacteristic
127C32×C4⋊C4C2311yescharacteristic
128#3757—21no—
129#3757—21no—
130#3753—22no—
131#3752—21no—
132C4×C3⋊Dic3C2311yescharacteristic
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134#3744—22no—
135C3×#217—21no—
136C3×#213—22no—
137C3×#213—41no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×C4⋊Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×#204—22no—
144C3×D3×C8—22no—
145#3724D411yescharacteristic
146Dic3⋊Dic3—21no—
147Dic3⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3D411yescharacteristic
150(C2×D3)⋊Dic3D411yescharacteristic
151Dic32—21no—
152#3717D414yescomplemented
153#3716—22no—
154#3716—41no—
155#3715—22no—
156#3711—22no—
157#3265—91noSylow
158C2×C3×#41—31no—
159C2×D3×Q8—31no—
160C2×#237C2×D311yescharacteristic, complemented
161C2×D3×D4—31no—
162C2×D3×D4—31no—
163C2×D3×D4—61no—
164C2×D3×D4—61no—
165C22×D12—31no—
166C22×D12—31no—
167C22×Dic6—31no—
168C2×C3×SD16—31no—
169C2×C3×D8—31no—
170C2×C3×D8—31no—
171C22×C3×C8—31no—
172C3×#121—31no—
173C3×#121—31no—
174C3×#121—31no—
175#949—64no—
176Q8×Dic3—31no—
177C2×#215—31no—
178C2×#215—31no—
179#940—31no—
180#940—31no—
181#939—61no—
182#938—61no—
183#938C2×D311yescharacteristic, complemented
184#937—61no—
185#937—61no—
186#936—31no—
187#936—31no—
188#936—61no—
189#936—61no—
190D4×Dic3—61no—
191C2×#214—31no—
192C2×#214—31no—
193C2×#214—31no—
194C2×#213—31no—
195C2×#213—31no—
196C2×#213—61no—
197C2×#213C2×D311yescharacteristic, complemented
198C2×#213C2×D311yescharacteristic, complemented
199C4×#67—31no—
200C4×#67—31no—
201C4×#67—61no—
202#924—31no—
203#924—61no—
204C2×#208—31no—
205D3×SD16—64no—
206#911—64no—
207C2×#204—31no—
208C2×#204—31no—
209C2×#204—31no—
210C2×#204—31no—
211C2×#204—31no—
212C2×#204—61no—
213C2×#204—64no—
214C2×#204C2×D311yescharacteristic, complemented
215C2×ΓL(1,𝔽25)—31no—
216C2×D3×C8C2×D311yescharacteristic, complemented
217#897—31no—
218#895C2×D311yescharacteristic
219#895C2×D311yescharacteristic
220#893—31no—
221#893—31no—
222#893—61no—
223#887—31no—
224#885—61no—
225#884—61no—
226#884—61no—
227#882—61no—
228#882—61no—
229#878—61no—
230C3×#107—31no—
231C3×#103—31no—
232C3×#102—21no—
233C3×#102—31no—
234C3×#102C2×D311yescharacteristic, complemented
235C3×#102C2×D311yescharacteristic, complemented
236C3×C22⋊C8—31no—
237#832—31no—
238#830—31no—
239#821—31no—
240#821C2×D311yescharacteristic, complemented
241(C2×D3)⋊C8—31no—
242(C2×D3)⋊C8C2×D311yescharacteristic, complemented
243#815—31no—
244#815—31no—
245Dic3⋊C8—31no—
246Dic3⋊C8—31no—
247Dic3⋊C8—61no—
248#810—31no—
249#810—31no—
250#810—61no—
251#810C2×D311yescharacteristic, complemented
252#809—31no—
253#809—31no—
254#807C2×D311yescharacteristic, complemented
255C23×C32—21no—
256C22×C3⋊D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3C2×D411yescharacteristic
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
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3C2×D411yescharacteristic
273C2×C3⋊Dic3C2×D411yescharacteristic
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)C2×D412yes—
276C4×C3⋊D3—42no—
277#634—21no—
278#634—21no—
279C3×#67—42no—
280C3×#67—42no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—42no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—42no—
291C3×D12—42no—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×C4×D3—21no—
295C3×C4×D3—21no—
296C3×Dic6—21no—
297C3×Dic6C2×D412yescomplemented
298#627—42no—
299#626—42no—
300#626—42no—
301#625—22no—
302#625—42no—
303#625—81no—
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—91no—
317#460—91no—
318#450—91no—
319#449—31no—
320#448—91no—
321#447—91no—
322#440—91no—
323#435—91no—
324C23×D3—61no—
325C23×D3—61no—
326C23×D3—61no—
327C23×D3—61no—
328C3×#41—62no—
329C3×#41—121no—
330C2×C3×Q8—31no—
331C2×C3×D4—21no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4—61no—
337C2×C3×D4—61no—
338C2×C3×D4C22×D311yescharacteristic
339C2×C3×D4C22×D311yescharacteristic
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—61no—
343C2×#67—21no—
344C2×#67—21no—
345C2×#67—31no—
346C2×#67—31no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—61no—
353C22×Dic3—21no—
354C22×Dic3—61no—
355D3×Q8—62no—
356D3×Q8—121no—
357#237—22no—
358#237—41no—
359D3×D4—62no—
360D3×D4—62no—
361D3×D4—121no—
362D3×D4—121no—
363D3×D4—124no—
364D3×D4—124no—
365C2×D12—21no—
366C2×D12—21no—
367C2×D12—31no—
368C2×D12—31no—
369C2×D12—61no—
370C2×D12—62no—
371C2×D12—62no—
372C2×D12—61no—
373C2×D12—61no—
374C2×D12—121no—
375C2×D12—121no—
376C2×D12C22×D311yescharacteristic
377C2×D12C22×D311yescharacteristic
378C2×C4×D3—61no—
379C2×C4×D3—61no—
380C2×C4×D3—61no—
381C2×C4×D3—121no—
382C2×C4×D3C22×D311yescharacteristic
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×D8—62no—
394C3×D8—121no—
395C2×C3×C8—21no—
396C2×C3×C8—31no—
397C2×C3×C8—31no—
398C2×C3×C8—62no—
399C2×C3×C8C22×D311yescharacteristic
400C2×C3×C8C22×D311yescharacteristic
401C3×C4⋊C4—21no—
402C3×C4⋊C4—31no—
403C3×C4⋊C4C22×D311yescharacteristic
404C3×C4⋊C4C22×D311yescharacteristic
405C3×C22⋊C4—61no—
406C3×C22⋊C4—61no—
407C3×C22⋊C4—61no—
408#217—21no—
409#217—31no—
410#217—31no—
411#217—61no—
412#217—61no—
413#217—61no—
414#217—61no—
415#217—61no—
416#217—121no—
417#217—121no—
418#215—34no—
419#215—62no—
420#214—62no—
421#214—62no—
422#214—121no—
423#213—22no—
424#213—41no—
425#213—62no—
426#213—62no—
427#213—122no—
428(C2×D3)⋊C4—21no—
429(C2×D3)⋊C4—21no—
430(C2×D3)⋊C4—31no—
431(C2×D3)⋊C4—31no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—121no—
436C4⋊Dic3—61no—
437C4⋊Dic3—61no—
438C4⋊Dic3C22×D311yescharacteristic
439Dic3⋊C4—31no—
440Dic3⋊C4—31no—
441Dic3⋊C4—61no—
442Dic3⋊C4—61no—
443C4×Dic3—31no—
444C4×Dic3—31no—
445C4×Dic3—61no—
446C4×Dic3—61no—
447C4×Dic3—61no—
448#208—62no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—61no—
452C2×C3⋊C8C22×D311yescharacteristic
453C2×C3⋊C8C22×D311yescharacteristic
454#204—22no—
455#204—34no—
456#204—62no—
457#204—62no—
458#204—62no—
459#204—122no—
460#204—121no—
461ΓL(1,𝔽25)—62no—
462D3×C8—22no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32C22×D411yescharacteristic
467C2×C3⋊D3—22no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
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—
480C2×C3×D3—41no—
481C2×C3×D3AGL(1,ℤ/8)12yescomplemented
482D32—84no—
483D32—84no—
484C32×C4—41no—
485C32×C4C22×D411yescharacteristic
486C32×C4H(5,𝔽2)11yescharacteristic
487C3⋊Dic3—21no—
488C3⋊Dic3—21no—
489C3⋊Dic3—41no—
490C3×Dic3—22no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—41no—
494C2×#41—31no—
495C22×Q8—91no—
496C22×D4—91no—
497C22×D4—91no—
498C22×D4—181no—
499AGL(1,ℤ/8)—184no—
500C2×SD16—31no—
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—31no—
512#127—91no—
513#124—91no—
514#124—181no—
515C22⋊Q8—91no—
516C22⋊Q8—181no—
517#121—31no—
518#121—31no—
519#121—31no—
520#121—181no—
521#121—181no—
522#120—181no—
523#120—181no—
524C4×Q8—91no—
525C4×D4—91no—
526C4×D4—91no—
527C4×D4—181no—
528#107—31no—
529C4⋊C8—91no—
530#103—31no—
531#103—91no—
532#102—31no—
533#102—91no—
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—31no—
543C23×C3—41no—
544C23×C3—61no—
545C23×C3—61no—
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—61no—
549C22×D3—61no—
550C22×D3—121no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3—122no—
554C22×D3—122no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—122no—
559C22×D3—241no—
560C22×D3—241no—
561C22×D3—241no—
562C22×D3—241no—
563C22×D3D3×D411yescharacteristic
564C22×D3D3×D411yescharacteristic
565C3×Q8—32no—
566C3×Q8—61no—
567C3×D4—21no—
568C3×D4—21no—
569C3×D4—21no—
570C3×D4—21no—
571C3×D4—41no—
572C3×D4—41no—
573C3×D4—61no—
574C3×D4—61no—
575C3×D4—61no—
576C3×D4—61no—
577C3×D4—122no—
578C3×D4—122no—
579C3×D4—122no—
580C3×D4—122no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
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—61no—
592C2×C3×C4—61no—
593C2×C3×C4—122no—
594C2×C3×C4C23×D311yescharacteristic
595C2×C3×C4C23×D311yescharacteristic
596#67—42no—
597#67—42no—
598#67—62no—
599#67—62no—
600#67—122no—
601#67—122no—
602#67—122no—
603#67—122no—
604#67—241no—
605#67—241no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—31no—
609C2×Dic3—31no—
610C2×Dic3—31no—
611C2×Dic3—31no—
612C2×Dic3—42no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—121no—
618C2×Dic3—122no—
619C2×Dic3D3×D411yescharacteristic
620C2×Dic3D3×D411yescharacteristic
621D12—21no—
622D12—21no—
623D12—21no—
624D12—21no—
625D12—32no—
626D12—32no—
627D12—42no—
628D12—42no—
629D12—62no—
630D12—61no—
631D12—61no—
632D12—121no—
633D12—122no—
634D12—122no—
635C4×D3—21no—
636C4×D3—21no—
637C4×D3—21no—
638C4×D3—21no—
639C4×D3—122no—
640C4×D3—122no—
641C4×D3—122no—
642C4×D3—242no—
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—32no—
656C3×C8—41no—
657C3×C8—61no—
658C3⋊C8—21no—
659C3⋊C8—61no—
660C3⋊C8—61no—
661C3⋊C8—121no—
662C3⋊C8D3×D412yescomplemented
663C2×C32—81no—
664C2×C32D4211yescharacteristic
665C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
666C2×C32#57711yescharacteristic
667C3⋊D3—42no—
668C3×D3—22no—
669C3×D3—41no—
670C3×D3—81no—
671C3×D3—81no—
672C24—181no—
673C24—181no—
674#41—62no—
675#41—121no—
676C2×Q8—31no—
677C2×Q8—91no—
678C2×Q8—181no—
679C2×Q8—182no—
680C2×Q8—361no—
681C2×D4—31no—
682C2×D4—31no—
683C2×D4—61no—
684C2×D4—61no—
685C2×D4—61no—
686C2×D4—61no—
687C2×D4—91no—
688C2×D4—91no—
689C2×D4—181no—
690C2×D4—181no—
691C2×D4—182no—
692C2×D4—182no—
693C2×D4—181no—
694C2×D4—181no—
695C2×D4—361no—
696C2×D4—361no—
697C2×D4—364no—
698C2×D4C2×D3211yescharacteristic
699C22×C4—31no—
700C22×C4—31no—
701C22×C4—61no—
702C22×C4—181no—
703C22×C4—181no—
704SD16—62no—
705SD16—94no—
706SD16—182no—
707SD16—182no—
708SD16—182no—
709SD16—361no—
710D8—62no—
711D8—121no—
712D8—182no—
713M16—182no—
714C2×C8—31no—
715C2×C8—31no—
716C2×C8—62no—
717C2×C8—91no—
718C2×C8C2×D3211yescharacteristic
719C4⋊C4—31no—
720C4⋊C4—91no—
721C4⋊C4—181no—
722C4⋊C4—181no—
723C4⋊C4C2×D3211yescharacteristic
724C22⋊C4—61no—
725C22⋊C4—61no—
726C22⋊C4—61no—
727C22⋊C4—91no—
728C22⋊C4—91no—
729C22⋊C4—181no—
730C22⋊C4—181no—
731C22⋊C4—181no—
732C22⋊C4—181no—
733C42—91no—
734C42—181no—
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—61no—
746C22×C3—61no—
747C22×C3—61no—
748C22×C3—81no—
749C22×C3—81no—
750C22×C3—81no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3C2×D3×D411yescharacteristic
758C22×C3C2×D3×D411yescharacteristic
759C2×D3—21no—
760C2×D3—21no—
761C2×D3—21no—
762C2×D3—21no—
763C2×D3—21no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—62no—
771C2×D3—62no—
772C2×D3—122no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—241no—
778C2×D3—241no—
779C2×D3—244no—
780C2×D3—244no—
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—62no—
790C3×C4—61no—
791C3×C4—81no—
792C3×C4—121no—
793C3×C4C2×D3×D411yescharacteristic
794C3×C4C2×D3×D411yescharacteristic
795C3×C4#100411yescharacteristic
796C3×C4#100911yescharacteristic
797Dic3—22no—
798Dic3—21no—
799Dic3—21no—
800Dic3—41no—
801Dic3—61no—
802Dic3—61no—
803Dic3—61no—
804Dic3—61no—
805Dic3—121no—
806Dic3—121no—
807Dic3—121no—
808Dic3—121no—
809Dic3—241no—
810C32#326511yescharacteristic, complemented, Sylow
811C23—21no—
812C23—31no—
813C23—31no—
814C23—61no—
815C23—61no—
816C23—181no—
817C23—362no—
818C23—362no—
819C23—362no—
820C23—362no—
821C23—721no—
822C23—721no—
823Q8—32no—
824Q8—61no—
825Q8—181no—
826Q8—181no—
827Q8—362no—
828D4—21no—
829D4—21no—
830D4—61no—
831D4—61no—
832D4—61no—
833D4—61no—
834D4—92no—
835D4—122no—
836D4—122no—
837D4—122no—
838D4—122no—
839D4—182no—
840D4—181no—
841D4—362no—
842D4—362no—
843D4—362no—
844D4—721no—
845C2×C4—21no—
846C2×C4—31no—
847C2×C4—31no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—91no—
855C2×C4—91no—
856C2×C4—122no—
857C2×C4—181no—
858C2×C4—362no—
859C2×C4—362no—
860C2×C4C22×D3211yescharacteristic
861C8—21no—
862C8—32no—
863C8—61no—
864C8—181no—
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—62no—
869C2×C3—81no—
870C2×C3—81no—
871C2×C3—121no—
872C2×C3—161no—
873C2×C3—241no—
874C2×C3—241no—
875C2×C3#559011yescharacteristic
876C2×C3#560911yescharacteristic
877C2×C3C2×#91111yescharacteristic
878C2×C3#577011yescharacteristic
879C2×C3#577011yescharacteristic
880C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
881D3—22no—
882D3—41no—
883D3—81no—
884D3—81no—
885D3—122no—
886D3—122no—
887D3—242no—
888C22—32no—
889C22—41no—
890C22—41no—
891C22—41no—
892C22—61no—
893C22—61no—
894C22—61no—
895C22—61no—
896C22—61no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—182no—
904C22—361no—
905C22—361no—
906C22—724no—
907C22—724no—
908C22D32×D411yescharacteristic
909C4—41no—
910C4—61no—
911C4—61no—
912C4—62no—
913C4—121no—
914C4—181no—
915C4—181no—
916C4—361no—
917C4#6430711yescharacteristic
918C4D32×D411yescharacteristic
919C3—21no—
920C3#8012111yescharacteristic, complemented
921C3#8072711yescharacteristic, complemented
922C2—62no—
923C2—81no—
924C2—121no—
925C2—241no—
926C2—241no—
927C2—362no—
928C2#1059427511yescharacteristic
929C2D3×#91111yescharacteristic
930C2#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. #10595157C2semidirect
2. C2×#63925C2semidirect
3. C2×D3×#204C2semidirect
4. #10594618C2semidirect
5. #10592486C2semidirect
6. C3×#4781C2semidirect
7. C3×#4775C2semidirect
8. #10591515C2semidirect
9. #10591485C2semidirect
10. #10590946C2semidirect
11. #10590876C2semidirect
12. #10590723C2semidirect
13. #10590603C2semidirect
14. #10590588C2semidirect
15. #10590484C2semidirect
18. C2×C3×#237C22semidirect
22. C2×D3×Dic6C22semidirect
23. #64145C22semidirect
27. C3×#938C22semidirect
28. C2×C3×#213C22semidirect
29. C2×C3×#213C22semidirect
30. C2×C3×#204C22semidirect
31. C2×C3×D3×C8C22semidirect
44. #63857C22semidirect
45. #63843C22semidirect
47. C2×#3716C22semidirect
48. C2×#3716C22semidirect
49. C2×#3715C22semidirect
50. C2×#3711C22semidirect
52. C32×#102C22semidirect
53. #63641C22semidirect
54. #63637C22semidirect
55. C3×#821C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×#810C22semidirect
58. C3×#807C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63555C22semidirect
88. #4781D3semidirect
90. #4775D3semidirect
152. #3717D4semidirect
160. C2×#237C2×D3semidirect
183. #938C2×D3semidirect
197. C2×#213C2×D3semidirect
198. C2×#213C2×D3semidirect
214. C2×#204C2×D3semidirect
216. C2×D3×C8C2×D3semidirect
234. C3×#102C2×D3semidirect
235. C3×#102C2×D3semidirect
240. #821C2×D3semidirect
242. (C2×D3)⋊C8C2×D3semidirect
251. #810C2×D3semidirect
254. #807C2×D3semidirect
297. C3×Dic6C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
481. C2×C3×D3AGL(1,ℤ/8)semidirect
535. #102D32semidirect
652. Dic6D3×D4semidirect
662. C3⋊C8D3×D4semidirect
783. C2×D3#911semidirect
810. C32#3265semidirect
920. C3#80121semidirect
921. C3#80727semidirect

Maximal subgroups

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

subgroupindex
#105951572
C2×#639252
C2×D3×#2042
#105946182
#105924862
C3×#47812
C3×#47752
#105915152
#105914852
#105909462
#105908762
#105907232
#105906032
#105905882
#105904842
#807273
#801213