Finite Group Databasebeta

← #11884029

Subgroups — #11884029

Order 1152.

1186 conjugacy classes of subgroups.

The subgroup lattice has 943 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595297C211yesmaximal, characteristic, complemented
2C2×#63937C211yesmaximal, characteristic, complemented
3C2×D3×#204C211yesmaximal, characteristic, complemented
4#10594382C211yesmaximal, characteristic, complemented
5#10592475C211yesmaximal, characteristic, complemented
6C3×#4775C211yesmaximal, characteristic, complemented
7C3×#4762C211yesmaximal, characteristic, complemented
8#10591517C211yesmaximal, characteristic, complemented
9#10591469C211yesmaximal, characteristic, complemented
10#10590964C211yesmaximal, characteristic, complemented
11#10590860C211yesmaximal, characteristic, complemented
12#10590727C211yesmaximal, characteristic, complemented
13#10590595C211yesmaximal, characteristic, complemented
14#10590506C211yesmaximal, characteristic, complemented
15#10590457C211yesmaximal, characteristic, complemented
16#80727—31nomaximal
17#80404—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3811—21no—
20C2×D3×D12C2211yescharacteristic
21C2×#3796C2211yescharacteristic, complemented
22C2×D3×Dic6C2211yescharacteristic, complemented
23C2×#3754C2211yescharacteristic, complemented
24C2×#3744C2211yescharacteristic
25#64106C2211yescharacteristic, complemented
26C3×#940C2211yescharacteristic
27C3×#938C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic, complemented
29C2×C3×#213C2211yescharacteristic, complemented
30C2×C3×#204C2211yescharacteristic, complemented
31C2×C3×D3×C8C2211yescharacteristic, complemented
32C3×#895C2211yescharacteristic, complemented
33C3×#887C2211yescharacteristic, complemented
34#63983—21no—
35#63981—21no—
36#63958—21no—
37#63937—24no—
38#63916C2211yescharacteristic
39C4×#626C2211yescharacteristic
40#63894C2211yescharacteristic
41#63893—21no—
42Dic3×D12—21no—
43#63886—21no—
44#63860C2211yescharacteristic, complemented
45#63852—21no—
46C2×#3717C2211yescharacteristic
47C2×#3716C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic
49C2×#3713C2211yescharacteristic, complemented
50C2×#3712C2211yescharacteristic, complemented
51D3×#204—24no—
52C32×#102C2211yescharacteristic, complemented
53#63647C2211yescharacteristic, complemented
54#63636C2211yescharacteristic
55C3×#821C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58C3×#807C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C2×#914—31no—
64C2×D3×SD16—31no—
65C2×#911—31no—
66C22×#204—31no—
67#5717—31no—
68#5609—31no—
69#5598—31no—
70#5576—31no—
71C3×#466—31no—
72C3×#460—31no—
73#5172—31no—
74#5170—31no—
75#5154—31no—
76#5111—31no—
77#5074—31no—
78#5040—31no—
79#5036—31no—
80#5026—31no—
81#4889—31no—
82#4886—31no—
83#4844—31no—
84#4836—31no—
85#4787—31no—
86#4781—31no—
87#4780—31no—
88#4776—31no—
89#4776—31no—
90#4776—61no—
91#4775D311yescharacteristic, complemented
92#4773—31no—
93#4762D311yescharacteristic, complemented
94C23×C3⋊D3—21no—
95C22×D32—21no—
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98D4×C3⋊D3—22no—
99D4×C3⋊D3—41no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×D12—21no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111#3811—44no—
112C2×#627—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#626—21no—
116C2×#626D411yescharacteristic
117C2×#624—21no—
118C2×D3×Dic3—21no—
119C2×D3×Dic3—21no—
120D3×D12—22no—
121D3×D12—41no—
122#3796—22no—
123#3796—41no—
124D3×Dic6—22no—
125D3×Dic6—41no—
126C2×C32×C8C2311yescharacteristic
127C32×C4⋊C4C2311yescharacteristic
128#3754—41no—
129#3752—21no—
130C4⋊(C3⋊Dic3)—21no—
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132#3744—22no—
133C3×#217—21no—
134C3×#214—22no—
135C3×#213—22no—
136C3×(C2×D3)⋊C4—21no—
137C3×C4⋊Dic3C2311yescharacteristic
138C3×Dic3⋊C4—21no—
139C3×C4×Dic3—21no—
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×#204—22no—
144C3×D3×C8—22no—
145Dic3⋊Dic3D411yescharacteristic
146#3722—21no—
147#3722D411yescharacteristic
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3D411yescharacteristic
152#3717D414yescomplemented
153#3716—22no—
154#3714—22no—
155#3713—41no—
156#3712—22no—
157#3265—91noSylow
158C2×#239—31no—
159C2×D3×Q8—31no—
160C2×#237—31no—
161C2×D3×D4—31no—
162C2×D3×D4—31no—
163C2×D3×D4—31no—
164C2×D3×D4—61no—
165C2×D3×D4—61no—
166C2×D3×D4—61no—
167C22×D12—31no—
168C22×Dic6—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×D8—31no—
172C22×C3×C8—31no—
173C3×#127—31no—
174C3×#121—31no—
175C3×#121—31no—
176C3×C4×Q8—31no—
177C2×#215—31no—
178#940C2×D311yescharacteristic
179#939—61no—
180#938—31no—
181#938—61no—
182#938C2×D311yescharacteristic
183#937—61no—
184#937—61no—
185#937—61no—
186#936—31no—
187D4×Dic3—61no—
188C2×#214—31no—
189C2×#214—31no—
190C2×#214—31no—
191C2×#214—61no—
192C2×#214C2×D311yescharacteristic, complemented
193C2×#213—31no—
194C2×#213—31no—
195C2×#213—31no—
196C2×#213C2×D311yescharacteristic, complemented
197C4×#67—31no—
198#914—64no—
199D3×SD16—64no—
200#911—64no—
201C2×D24—31no—
202C2×#204—31no—
203C2×#204—31no—
204C2×#204—31no—
205C2×#204—31no—
206C2×#204—61no—
207C2×#204—64no—
208C2×#204C2×D311yescharacteristic, complemented
209C2×ΓL(1,𝔽25)—31no—
210C2×ΓL(1,𝔽25)—31no—
211C2×D3×C8C2×D311yescharacteristic, complemented
212#897—31no—
213#897—31no—
214#897—61no—
215#897—61no—
216#895—31no—
217#895—61no—
218#895C2×D311yescharacteristic, complemented
219#893—31no—
220#887C2×D311yescharacteristic, complemented
221#885—61no—
222#884—61no—
223#882—61no—
224#878—61no—
225#875—31no—
226#875—61no—
227C4×D12—31no—
228C4×D12—31no—
229C4×D12—61no—
230C3×#107—31no—
231C3×C4⋊C8—31no—
232C3×#102—21no—
233C3×#102—31no—
234C3×#102—31no—
235C3×#102C2×D311yescharacteristic, complemented
236C3×#102C2×D311yescharacteristic, complemented
237#835—31no—
238#830—31no—
239#821C2×D311yescharacteristic, complemented
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—31no—
242(C2×D3)⋊C8—31no—
243(C2×D3)⋊C8—61no—
244#816—31no—
245#815—31no—
246Dic3⋊C8C2×D311yescharacteristic, complemented
247#810—31no—
248#810—31no—
249#809—31no—
250#809—31no—
251#809—61no—
252#809C2×D311yescharacteristic, complemented
253#807C2×D311yescharacteristic, complemented
254#803—31no—
255C23×C32—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3—42no—
258C22×C3⋊D3—42no—
259C22×C3⋊D3—81no—
260C22×C3⋊D3C2×D411yescharacteristic
261C22×C3×D3—21no—
262C22×C3×D3—21no—
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⋊Dic3C2×D411yescharacteristic
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)C2×D412yes—
276C4×C3⋊D3—21no—
277C4×C3⋊D3—21no—
278#634—21no—
279#634—21no—
280C3×#67—42no—
281C3×#67—42no—
282C3×#67—81no—
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—21no—
292C3×D12—42no—
293C3×C4×D3—21no—
294C3×C4×D3—21no—
295C3×Dic6—21no—
296C3×Dic6C2×D412yescomplemented
297#627—42no—
298#626—22no—
299#626—42no—
300#626—42no—
301#626—42no—
302#624—42no—
303D3×Dic3—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—91no—
317#460—31no—
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—
328C23×D3—121no—
329C2×C3×Q8—31no—
330C2×C3×D4—21no—
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×D4C22×D311yescharacteristic
338C2×C3×D4C22×D311yescharacteristic
339C22×C3×C4—31no—
340C2×#67—21no—
341C2×#67—21no—
342C2×#67—21no—
343C2×#67—31no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—121no—
350C22×Dic3—61no—
351C22×Dic3—61no—
352#239—62no—
353#239—121no—
354D3×Q8—62no—
355D3×Q8—121no—
356#237—62no—
357#237—121no—
358D3×D4—62no—
359D3×D4—62no—
360D3×D4—62no—
361D3×D4—122no—
362D3×D4—121no—
363D3×D4—121no—
364D3×D4—121no—
365D3×D4—124no—
366D3×D4—124no—
367D3×D4—122no—
368C2×D12—21no—
369C2×D12—31no—
370C2×D12—31no—
371C2×D12—31no—
372C2×D12—61no—
373C2×D12—62no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—121no—
378C2×D12C22×D311yescharacteristic
379C2×D12C22×D311yescharacteristic
380C2×C4×D3—31no—
381C2×C4×D3—31no—
382C2×C4×D3—61no—
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×C4×D3—61no—
387C2×C4×D3C22×D311yescharacteristic
388C2×Dic6—31no—
389C2×Dic6—31no—
390C2×Dic6—61no—
391C2×Dic6—62no—
392C2×Dic6—61no—
393C2×Dic6—61no—
394C2×Dic6—121no—
395C2×Dic6C22×D311yescharacteristic
396C3×SD16—62no—
397C3×SD16—62no—
398C3×D8—62no—
399C2×C3×C8—21no—
400C2×C3×C8—31no—
401C2×C3×C8—31no—
402C2×C3×C8—62no—
403C2×C3×C8C22×D311yescharacteristic
404C2×C3×C8C22×D311yescharacteristic
405C3×C4⋊C4—21no—
406C3×C4⋊C4—31no—
407C3×C4⋊C4—61no—
408C3×C4⋊C4C22×D311yescharacteristic
409C3×C4⋊C4C22×D311yescharacteristic
410C3×C22⋊C4—61no—
411C3×C22⋊C4—61no—
412C3×C42—31no—
413C3×C42—61no—
414#217—21no—
415#217—31no—
416#217—61no—
417#217—61no—
418#217—61no—
419#215—34no—
420#214—22no—
421#214—62no—
422#214—121no—
423#214—121no—
424#214—122no—
425#213—22no—
426#213—62no—
427#213—121no—
428#213—121no—
429(C2×D3)⋊C4—21no—
430(C2×D3)⋊C4—31no—
431(C2×D3)⋊C4—31no—
432(C2×D3)⋊C4—31no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4—61no—
439(C2×D3)⋊C4—61no—
440(C2×D3)⋊C4—121no—
441C4⋊Dic3—31no—
442C4⋊Dic3—61no—
443C4⋊Dic3—61no—
444C4⋊Dic3—121no—
445C4⋊Dic3C22×D311yescharacteristic
446Dic3⋊C4—21no—
447Dic3⋊C4—31no—
448C4×Dic3—21no—
449C4×Dic3C22×D311yescharacteristic
450C2×C3⋊C8—31no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—61no—
453C2×C3⋊C8C22×D311yescharacteristic
454C2×C3⋊C8C22×D311yescharacteristic
455D24—62no—
456#204—22no—
457#204—34no—
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—22no—
472C2×C3⋊D3—21no—
473C2×C3⋊D3—41no—
474C2×C3⋊D3—41no—
475C2×C3⋊D3—84no—
476C2×C3×D3—21no—
477C2×C3×D3—21no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C2×C3×D3AGL(1,ℤ/8)12yescomplemented
485D32—84no—
486C32×C4—41no—
487C32×C4C22×D411yescharacteristic
488C32×C4H(5,𝔽2)11yescharacteristic
489C3⋊Dic3—21no—
490C3⋊Dic3—41no—
491C3×Dic3—22no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—21no—
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—31no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—91no—
507C2×SD16—91no—
508C2×SD16—184no—
509C2×D8—31no—
510C2×D8—91no—
511C2×D8—91no—
512C2×M16—91no—
513C22×C8—31no—
514#127—31no—
515#124—91no—
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—31no—
527C4×D4—91no—
528C4×D4—91no—
529C4×D4—181no—
530#107—31no—
531C4⋊C8—31no—
532#103—91no—
533#103—91no—
534#102—31no—
535#102—31no—
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—124no—
563C22×D3—122no—
564C22×D3—242no—
565C22×D3—241no—
566C22×D3—241no—
567C22×D3—241no—
568C22×D3—241no—
569C22×D3—242no—
570C22×D3D3×D411yescharacteristic
571C3×Q8—32no—
572C3×Q8—61no—
573C3×D4—22no—
574C3×D4—21no—
575C3×D4—21no—
576C3×D4—21no—
577C3×D4—21no—
578C3×D4—41no—
579C3×D4—61no—
580C3×D4—61no—
581C3×D4—61no—
582C3×D4—61no—
583C3×D4—122no—
584C3×D4—122no—
585C3×D4—122no—
586C3×D4—241no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—31no—
591C2×C3×C4—31no—
592C2×C3×C4—31no—
593C2×C3×C4—41no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4C23×D311yescharacteristic
599C2×C3×C4C23×D311yescharacteristic
600#67—42no—
601#67—42no—
602#67—62no—
603#67—81no—
604#67—122no—
605#67—122no—
606#67—122no—
607#67—122no—
608#67—122no—
609#67—124no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—31no—
613C2×Dic3—31no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—121no—
618C2×Dic3—122no—
619C2×Dic3—122no—
620C2×Dic3D3×D411yescharacteristic
621C2×Dic3D3×D411yescharacteristic
622C2×Dic3D3×D411yescharacteristic
623D12—21no—
624D12—21no—
625D12—21no—
626D12—21no—
627D12—32no—
628D12—32no—
629D12—42no—
630D12—62no—
631D12—62no—
632D12—61no—
633D12—61no—
634D12—121no—
635D12—122no—
636D12—122no—
637D12—122no—
638C4×D3—21no—
639C4×D3—21no—
640C4×D3—61no—
641C4×D3—61no—
642C4×D3—61no—
643C4×D3—61no—
644C4×D3—121no—
645C4×D3—121no—
646C4×D3—122no—
647C4×D3—122no—
648C4×D3—122no—
649C4×D3—122no—
650Dic6—21no—
651Dic6—61no—
652Dic6—61no—
653Dic6—61no—
654Dic6—61no—
655Dic6—121no—
656Dic6—121no—
657Dic6—122no—
658Dic6—122no—
659Dic6D3×D412yescomplemented
660C3×C8—21no—
661C3×C8—21no—
662C3×C8—32no—
663C3×C8—41no—
664C3×C8—61no—
665C3⋊C8—21no—
666C3⋊C8—61no—
667C3⋊C8—61no—
668C3⋊C8—121no—
669C3⋊C8D3×D412yescomplemented
670C2×C32—81no—
671C2×C32D4211yescharacteristic
672C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
673C2×C32#57711yescharacteristic
674C3⋊D3—41no—
675C3⋊D3—42no—
676C3×D3—22no—
677C3×D3—81no—
678C3×D3—81no—
679C24—181no—
680C24—181no—
681#41—182no—
682#41—361no—
683C2×Q8—31no—
684C2×Q8—91no—
685C2×Q8—181no—
686C2×Q8—182no—
687C2×Q8—361no—
688C2×D4—31no—
689C2×D4—31no—
690C2×D4—61no—
691C2×D4—61no—
692C2×D4—61no—
693C2×D4—61no—
694C2×D4—91no—
695C2×D4—91no—
696C2×D4—181no—
697C2×D4—182no—
698C2×D4—181no—
699C2×D4—181no—
700C2×D4—181no—
701C2×D4—182no—
702C2×D4—361no—
703C2×D4—361no—
704C2×D4—364no—
705C2×D4C2×D3211yescharacteristic
706C22×C4—31no—
707C22×C4—91no—
708C22×C4—181no—
709C22×C4—181no—
710C22×C4—181no—
711SD16—62no—
712SD16—62no—
713SD16—94no—
714SD16—182no—
715SD16—182no—
716SD16—361no—
717D8—62no—
718D8—182no—
719D8—361no—
720M16—182no—
721C2×C8—31no—
722C2×C8—31no—
723C2×C8—62no—
724C2×C8—91no—
725C2×C8C2×D3211yescharacteristic
726C4⋊C4—31no—
727C4⋊C4—61no—
728C4⋊C4—91no—
729C4⋊C4—181no—
730C4⋊C4C2×D3211yescharacteristic
731C22⋊C4—61no—
732C22⋊C4—61no—
733C22⋊C4—91no—
734C22⋊C4—91no—
735C22⋊C4—181no—
736C22⋊C4—181no—
737C22⋊C4—181no—
738C22⋊C4—181no—
739C22⋊C4—181no—
740C42—31no—
741C42—61no—
742C22×C3—21no—
743C22×C3—32no—
744C22×C3—42no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—61no—
752C22×C3—61no—
753C22×C3—81no—
754C22×C3—81no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—121no—
758C22×C3—121no—
759C22×C3—121no—
760C22×C3—121no—
761C22×C3C2×D3×D411yescharacteristic
762C22×C3C2×D3×D411yescharacteristic
763C2×D3—21no—
764C2×D3—21no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—62no—
772C2×D3—61no—
773C2×D3—61no—
774C2×D3—61no—
775C2×D3—61no—
776C2×D3—61no—
777C2×D3—61no—
778C2×D3—62no—
779C2×D3—62no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—122no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—241no—
788C2×D3—241no—
789C2×D3—244no—
790C2×D3—244no—
791C2×D3—244no—
792C2×D3—244no—
793C2×D3—248no—
794C2×D3#91112yescomplemented
795C3×C4—21no—
796C3×C4—21no—
797C3×C4—41no—
798C3×C4—41no—
799C3×C4—61no—
800C3×C4—61no—
801C3×C4—61no—
802C3×C4—62no—
803C3×C4—81no—
804C3×C4—121no—
805C3×C4C2×D3×D411yescharacteristic
806C3×C4C2×D3×D411yescharacteristic
807C3×C4#100911yescharacteristic
808C3×C4#100911yescharacteristic
809Dic3—21no—
810Dic3—21no—
811Dic3—22no—
812Dic3—21no—
813Dic3—41no—
814Dic3—61no—
815Dic3—61no—
816Dic3—121no—
817Dic3—121no—
818Dic3—121no—
819Dic3—241no—
820C32#326511yescharacteristic, complemented, Sylow
821C23—21no—
822C23—31no—
823C23—61no—
824C23—61no—
825C23—91no—
826C23—181no—
827C23—362no—
828C23—362no—
829C23—362no—
830C23—362no—
831C23—721no—
832C23—721no—
833Q8—32no—
834Q8—61no—
835Q8—181no—
836Q8—181no—
837Q8—362no—
838D4—21no—
839D4—21no—
840D4—61no—
841D4—61no—
842D4—61no—
843D4—61no—
844D4—92no—
845D4—122no—
846D4—122no—
847D4—122no—
848D4—182no—
849D4—181no—
850D4—241no—
851D4—362no—
852D4—362no—
853D4—362no—
854D4—362no—
855C2×C4—21no—
856C2×C4—31no—
857C2×C4—31no—
858C2×C4—31no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—91no—
864C2×C4—181no—
865C2×C4—181no—
866C2×C4—181no—
867C2×C4—362no—
868C2×C4—362no—
869C2×C4—362no—
870C2×C4C22×D3211yescharacteristic
871C8—21no—
872C8—32no—
873C8—61no—
874C8—181no—
875C2×C3—21no—
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—62no—
879C2×C3—82no—
880C2×C3—81no—
881C2×C3—81no—
882C2×C3—241no—
883C2×C3—241no—
884C2×C3#560911yescharacteristic
885C2×C3#560911yescharacteristic
886C2×C3C2×#91111yescharacteristic
887C2×C3#576211yescharacteristic
888C2×C3#577011yescharacteristic
889C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
890D3—22no—
891D3—81no—
892D3—81no—
893D3—122no—
894D3—121no—
895D3—122no—
896D3—121no—
897D3—122no—
898D3—242no—
899C22—32no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—61no—
904C22—61no—
905C22—121no—
906C22—121no—
907C22—121no—
908C22—121no—
909C22—121no—
910C22—121no—
911C22—181no—
912C22—181no—
913C22—181no—
914C22—182no—
915C22—361no—
916C22—361no—
917C22—724no—
918C22—724no—
919C22D32×D411yescharacteristic
920C4—41no—
921C4—61no—
922C4—61no—
923C4—61no—
924C4—62no—
925C4—121no—
926C4—181no—
927C4—361no—
928C4#6430811yescharacteristic
929C4D32×D411yescharacteristic
930C3—21no—
931C3#8040411yescharacteristic, complemented
932C3#8072711yescharacteristic, complemented
933C2—62no—
934C2—81no—
935C2—241no—
936C2—241no—
937C2—361no—
938C2—362no—
939C2#1059428411yescharacteristic
940C2D3×#91111yescharacteristic
941C2#1059475311yescharacteristic
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. #10595297C2semidirect
2. C2×#63937C2semidirect
3. C2×D3×#204C2semidirect
4. #10594382C2semidirect
5. #10592475C2semidirect
6. C3×#4775C2semidirect
7. C3×#4762C2semidirect
8. #10591517C2semidirect
9. #10591469C2semidirect
10. #10590964C2semidirect
11. #10590860C2semidirect
12. #10590727C2semidirect
13. #10590595C2semidirect
14. #10590506C2semidirect
15. #10590457C2semidirect
21. C2×#3796C22semidirect
22. C2×D3×Dic6C22semidirect
23. C2×#3754C22semidirect
25. #64106C22semidirect
28. C2×C3×#214C22semidirect
29. C2×C3×#213C22semidirect
30. C2×C3×#204C22semidirect
31. C2×C3×D3×C8C22semidirect
32. C3×#895C22semidirect
33. C3×#887C22semidirect
44. #63860C22semidirect
47. C2×#3716C22semidirect
49. C2×#3713C22semidirect
50. C2×#3712C22semidirect
52. C32×#102C22semidirect
53. #63647C22semidirect
55. C3×#821C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#809C22semidirect
58. C3×#807C22semidirect
59. #63567C22semidirect
60. #63565C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
91. #4775D3semidirect
93. #4762D3semidirect
152. #3717D4semidirect
192. C2×#214C2×D3semidirect
196. C2×#213C2×D3semidirect
208. C2×#204C2×D3semidirect
211. C2×D3×C8C2×D3semidirect
218. #895C2×D3semidirect
220. #887C2×D3semidirect
235. C3×#102C2×D3semidirect
236. C3×#102C2×D3semidirect
239. #821C2×D3semidirect
246. Dic3⋊C8C2×D3semidirect
252. #809C2×D3semidirect
253. #807C2×D3semidirect
296. C3×Dic6C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
484. C2×C3×D3AGL(1,ℤ/8)semidirect
537. #102D32semidirect
659. Dic6D3×D4semidirect
669. C3⋊C8D3×D4semidirect
794. C2×D3#911semidirect
820. C32#3265semidirect
931. C3#80404semidirect
932. C3#80727semidirect

Maximal subgroups

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

subgroupindex
#105952972
C2×#639372
C2×D3×#2042
#105943822
#105924752
C3×#47752
C3×#47622
#105915172
#105914692
#105909642
#105908602
#105907272
#105905952
#105905062
#105904572
#807273
#804043