Finite Group Databasebeta

← #11884295

Subgroups — #11884295

Order 1152.

1094 conjugacy classes of subgroups.

The subgroup lattice has 903 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595254C211yesmaximal, characteristic, complemented
2C2×#63937C211yesmaximal, characteristic, complemented
3C2×#63933C211yesmaximal, characteristic, complemented
4#10594381C211yesmaximal, characteristic, complemented
5#10592475C211yesmaximal, characteristic, complemented
6C3×#4785C211yesmaximal, characteristic, complemented
7C3×#4783C211yesmaximal, characteristic, complemented
8#10591489C211yesmaximal, characteristic, complemented
9#10590968C211yesmaximal, characteristic, complemented
10#10590965C211yesmaximal, characteristic, complemented
11#10590899C211yesmaximal, characteristic, complemented
12#10590728C211yesmaximal, characteristic, complemented
13#10590577C211yesmaximal, characteristic, complemented
14#10590534C211yesmaximal, characteristic, complemented
15#10590524C211yesmaximal, characteristic, complemented
16#80264—31nomaximal
17#79879—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×#3796C2211yescharacteristic
21C2×#3795C2211yescharacteristic, complemented
22C2×#3754C2211yescharacteristic
23C2×#3744C2211yescharacteristic
24#64106C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27C2×C3×#213C2211yescharacteristic
28C2×C3×Dic12C2211yescharacteristic, complemented
29C3×#897C2211yescharacteristic, complemented
30C3×#893C2211yescharacteristic, complemented
31#63981—21no—
32#63978—21no—
33#63966—21no—
34C2×#3722—21no—
35#63937—24no—
36#63933—24no—
37#63909C2211yescharacteristic
38#63906—21no—
39C4×#626C2211yescharacteristic
40#63891—21no—
41#63890—21no—
42D3×C4⋊Dic3—21no—
43#63871C2211yescharacteristic
44#63866C2211yescharacteristic, complemented
45#63864C2211yescharacteristic
46C2×#3719C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic
48C2×#3715C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic
50C2×#3712C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52C32×#102C2211yescharacteristic
53#63647C2211yescharacteristic
54#63636C2211yescharacteristic
55C3×#821C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×#815C2211yescharacteristic, complemented
58C3×#810C2211yescharacteristic, complemented
59C3×#808C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63565C2211yescharacteristic, complemented
63#5829—31no—
64C2×#950—31no—
65C2×#914—31no—
66C2×#912—31no—
67C2×#911—31no—
68#5631—31no—
69#5555—31no—
70#5554—31no—
71C3×#452—31no—
72C3×#442—31no—
73#5190—31no—
74#5187—31no—
75#5162—31no—
76#5048—31no—
77#5019—31no—
78#5016—31no—
79#4867—31no—
80#4864—31no—
81#4819—31no—
82#4816—31no—
83#4785D311yescharacteristic, complemented
84#4783—31no—
85#4783D311yescharacteristic, complemented
86#4781—31no—
87#4776—31no—
88#4776—31no—
89#4776—61no—
90#4734—31no—
91#4730—31no—
92#4715—31no—
93#4706—31no—
94C23×C3⋊D3—21no—
95C2×C32×D4C2311yescharacteristic
96C2×#638—21no—
97D4×C3⋊D3—22no—
98D4×C3⋊D3—41no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×#634C2311yescharacteristic
102C2×C3×#67—21no—
103C22×C3×Dic3—21no—
104C22×C3×Dic3—21no—
105C3×#237—22no—
106C3×#237—41no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×#626—21no—
113C2×#626—21no—
114C2×#626D411yescharacteristic
115C2×#625—21no—
116C2×D3×Dic3—21no—
117C2×D3×Dic3—21no—
118#3796—22no—
119#3796—41no—
120#3795—22no—
121#3795—41no—
122C2×C32×C8C2311yescharacteristic
123C32×C4⋊C4C2311yescharacteristic
124#3754—22no—
125#3752—21no—
126C4⋊(C3⋊Dic3)—21no—
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128#3744—41no—
129C3×#217—21no—
130C3×#214—22no—
131C3×#213D414yescomplemented
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×C4⋊Dic3—21no—
135C3×C4⋊Dic3C2311yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×Dic12—41no—
140Dic3⋊Dic3—21no—
141Dic3⋊Dic3—21no—
142Dic3⋊Dic3—21no—
143Dic3⋊Dic3D411yescharacteristic
144#3722—21no—
145#3722—21no—
146#3722—21no—
147#3722—21no—
148#3722D411yescharacteristic
149(C2×D3)⋊Dic3D411yescharacteristic
150#3719—22no—
151#3717—22no—
152#3715—22no—
153#3714—22no—
154#3712—22no—
155D3×C3⋊C8—22no—
156#3267—91noSylow
157C2×C3×#41—31no—
158C2×#239—31no—
159C2×#237—31no—
160C2×#237—31no—
161C2×#237C2×D311yescharacteristic
162C2×D3×D4—31no—
163C2×D3×D4—31no—
164C2×D3×D4—61no—
165C2×#235—31no—
166C2×C3×Q16—31no—
167C2×C3×SD16—31no—
168C2×C3×D8—31no—
169C3×C22⋊Q8—31no—
170C3×C4×D4—31no—
171C3×C4×D4—31no—
172#950—64no—
173#947—31no—
174#946—31no—
175#944—31no—
176C2×#216—31no—
177C2×#215—31no—
178C2×#215—31no—
179#939—61no—
180#937—61no—
181D4×Dic3C2×D311yescharacteristic
182C2×#214—31no—
183C2×#214—31no—
184C2×#214—31no—
185C2×#214—61no—
186C2×#214C2×D311yescharacteristic
187C2×#213—31no—
188C2×#213C2×D311yescharacteristic
189#930—31no—
190#930—61no—
191#930—61no—
192#929—61no—
193C4×#67—31no—
194C2×(C2×D3)⋊C4—61no—
195C2×(C2×D3)⋊C4—61no—
196C2×C4⋊Dic3—61no—
197C22×C3⋊C8—31no—
198#914—64no—
199#912—64no—
200#911—64no—
201C2×Dic12—31no—
202C2×Dic12C2×D311yescharacteristic, complemented
203C2×D24—31no—
204C2×#204—31no—
205C2×#204—31no—
206C2×#204—31no—
207C2×#204—61no—
208C2×ΓL(1,𝔽25)—31no—
209C2×ΓL(1,𝔽25)—31no—
210C2×D3×C8—31no—
211#897—31no—
212#897—31no—
213#897—31no—
214#897—61no—
215#897C2×D311yescharacteristic, complemented
216#895—31no—
217#894—61no—
218#893C2×D311yescharacteristic, complemented
219D3×C4⋊C4—61no—
220#886—61no—
221#886—61no—
222#886—61no—
223#884—61no—
224#883—61no—
225#882—61no—
226#875—31no—
227C4×D12—31no—
228#869—31no—
229C3×#106—31no—
230C3×#103—31no—
231C3×#102—21no—
232C3×#102—31no—
233C3×#102C2×D311yescharacteristic
234C3×#102C2×D311yescharacteristic
235C3×C22⋊C8—31no—
236C3×#97—31no—
237#835—31no—
238#821C2×D311yescharacteristic, complemented
239(C2×D3)⋊C8—31no—
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—61no—
242(C2×D3)⋊C8C2×D311yescharacteristic, complemented
243#816—31no—
244#815C2×D311yescharacteristic, complemented
245Dic3⋊C8—31no—
246#810—31no—
247#810—31no—
248#810C2×D311yescharacteristic, complemented
249#809—31no—
250#809—31no—
251#809—61no—
252#808C2×D311yescharacteristic, complemented
253C4⋊(C3⋊C8)—31no—
254C23×C32—21no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3—42no—
257C22×C3⋊D3—42no—
258C22×C3⋊D3—81no—
259C22×C3⋊D3C2×D411yescharacteristic
260C22×C3×D3—21no—
261C22×C3×D3C2×D411yescharacteristic
262C32×D4—21no—
263C32×D4C2×D412yes—
264C2×C32×C4—21no—
265C2×C32×C4C2411yescharacteristic
266#638—42no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3C2×D411yescharacteristic
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—21no—
271C4×C3⋊D3—21no—
272C4×C3⋊D3—21no—
273#634—21no—
274#634—21no—
275C3×#67—42no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—42no—
280C2×C3×Dic3—81no—
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C3×D12—21no—
285C3×D12C2×D412yes—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288C3×C4×D3—42no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293#626—41no—
294#626—42no—
295#626—81no—
296#625—42no—
297D3×Dic3—42no—
298D3×Dic3—42no—
299C32×C8—21no—
300C3⋊(C3⋊C8)—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yes—
303C2×AGL(1,ℤ/8)—91no—
304C2×#135—91no—
305#547—91no—
306#546—91no—
307#497—91no—
308#470—91no—
309#465—91no—
310#463—91no—
311#461—91no—
312#452—31no—
313#452—91no—
314#450—91no—
315#449—91no—
316#442—31no—
317#435—91no—
318C23×D3—61no—
319C23×D3—61no—
320C23×D3—121no—
321C3×#41—62no—
322C3×#41—121no—
323C2×C3×Q8—31no—
324C2×C3×Q8—31no—
325C2×C3×D4—21no—
326C2×C3×D4—31no—
327C2×C3×D4—61no—
328C2×C3×D4C22×D311yescharacteristic
329C2×C3×D4C22×D311yescharacteristic
330C22×C3×C4—31no—
331C22×C3×C4—61no—
332C22×C3×C4—61no—
333C22×C3×C4—61no—
334C2×#67—21no—
335C2×#67—31no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—121no—
343C22×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—61no—
346C22×Dic3—61no—
347#239—62no—
348#239—121no—
349#237—22no—
350#237—41no—
351#237—62no—
352#237—62no—
353#237—121no—
354#237—121no—
355D3×D4—62no—
356D3×D4—62no—
357D3×D4—122no—
358D3×D4—121no—
359D3×D4—121no—
360D3×D4—122no—
361#235—62no—
362#235—121no—
363C2×D12—31no—
364C2×D12—31no—
365C2×D12—31no—
366C2×D12—61no—
367C2×D12—61no—
368C2×D12—61no—
369C2×D12C22×D311yescharacteristic
370C2×C4×D3—21no—
371C2×C4×D3—31no—
372C2×C4×D3—31no—
373C2×C4×D3—61no—
374C2×C4×D3—61no—
375C2×C4×D3—61no—
376C2×C4×D3C22×D311yescharacteristic
377C2×Dic6—31no—
378C2×Dic6—31no—
379C2×Dic6—61no—
380C2×Dic6C22×D311yescharacteristic
381C2×Dic6C22×D311yescharacteristic
382C3×Q16—121no—
383C3×SD16—62no—
384C3×D8—34no—
385C2×C3×C8—21no—
386C2×C3×C8—31no—
387C2×C3×C8—31no—
388C2×C3×C8C22×D311yescharacteristic
389C2×C3×C8C22×D311yescharacteristic
390C3×C4⋊C4—21no—
391C3×C4⋊C4—31no—
392C3×C4⋊C4—61no—
393C3×C4⋊C4C22×D311yescharacteristic
394C3×C4⋊C4C22×D311yescharacteristic
395C3×C22⋊C4—61no—
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398C3×C42—31no—
399#217—21no—
400#217—31no—
401#216—62no—
402#215—62no—
403#215—62no—
404#214—22no—
405#214—62no—
406#214—62no—
407#214—62no—
408#214—122no—
409#213—62no—
410#213D1214yescomplemented
411(C2×D3)⋊C4—21no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—31no—
414(C2×D3)⋊C4—31no—
415(C2×D3)⋊C4—31no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—121no—
427C4⋊Dic3—21no—
428C4⋊Dic3—31no—
429C4⋊Dic3—61no—
430C4⋊Dic3—61no—
431C4⋊Dic3—61no—
432C4⋊Dic3—61no—
433C4⋊Dic3—61no—
434C4⋊Dic3—121no—
435C4⋊Dic3C22×D311yescharacteristic
436Dic3⋊C4—31no—
437Dic3⋊C4—61no—
438Dic3⋊C4—61no—
439Dic3⋊C4—61no—
440C4×Dic3C22×D311yescharacteristic
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—61no—
444C2×C3⋊C8—62no—
445C2×C3⋊C8C22×D311yescharacteristic
446C2×C3⋊C8C22×D311yescharacteristic
447Dic12—41no—
448Dic12—62no—
449D24—62no—
450#204—62no—
451#204—121no—
452#204—121no—
453#204—122no—
454ΓL(1,𝔽25)—62no—
455ΓL(1,𝔽25)—62no—
456D3×C8—62no—
457C22×C32—22no—
458C22×C32—41no—
459C22×C32—41no—
460C22×C32C22×D411yescharacteristic
461C2×C3⋊D3—21no—
462C2×C3⋊D3—21no—
463C2×C3⋊D3—21no—
464C2×C3⋊D3—41no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—41no—
467C2×C3⋊D3—84no—
468C2×C3×D3—22no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C32×C4—41no—
475C32×C4C22×D411yescharacteristic
476C32×C4H(5,𝔽2)11yescharacteristic
477C3⋊Dic3—21no—
478C3⋊Dic3—41no—
479C3×Dic3—21no—
480C3×Dic3—21no—
481C3×Dic3—21no—
482C3×Dic3—41no—
483C3×Dic3—41no—
484C3×Dic3—41no—
485C2×#41—31no—
486C2×#41—91no—
487C2×#41—91no—
488C22×D4—91no—
489AGL(1,ℤ/8)—184no—
490#135—184no—
491C2×Q16—31no—
492C2×Q16—91no—
493C2×SD16—31no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×D8—31no—
499C2×D8—91no—
500C2×M16—91no—
501C22×C8—91no—
502C4⋊Q8—91no—
503#124—91no—
504#123—181no—
505#123—181no—
506#123—181no—
507C22⋊Q8—31no—
508C22⋊Q8—91no—
509C22⋊Q8—91no—
510#121—91no—
511#121—181no—
512#121—181no—
513#120—181no—
514C4×D4—31no—
515C4×D4—31no—
516C4×D4—91no—
517C2×C4⋊C4—181no—
518C2×C22⋊C4—181no—
519#106—31no—
520C4⋊C8—91no—
521#103—31no—
522#103—91no—
523#103—91no—
524#102—31no—
525#102—91no—
526#102D3211yescharacteristic
527C22⋊C8—31no—
528C22⋊C8—91no—
529#97—31no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—31no—
533C23×C3—41no—
534C23×C3—61no—
535C22×D3—21no—
536C22×D3—31no—
537C22×D3—31no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—61no—
541C22×D3—121no—
542C22×D3—122no—
543C22×D3—122no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3—124no—
547C22×D3—242no—
548C22×D3—241no—
549C22×D3—241no—
550C22×D3—242no—
551C22×D3D3×D411yescharacteristic
552C3×Q8—61no—
553C3×Q8—61no—
554C3×Q8—61no—
555C3×Q8—61no—
556C3×D4—21no—
557C3×D4—21no—
558C3×D4—22no—
559C3×D4—32no—
560C3×D4—41no—
561C3×D4—61no—
562C3×D4—122no—
563C3×D4C2×D1212yes—
564C3×D4D3×D412yes—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—31no—
569C2×C3×C4—31no—
570C2×C3×C4—31no—
571C2×C3×C4—41no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—122no—
578C2×C3×C4—122no—
579C2×C3×C4—241no—
580C2×C3×C4C23×D311yescharacteristic
581C2×C3×C4C23×D311yescharacteristic
582#67—42no—
583#67—121no—
584#67—122no—
585#67—122no—
586#67—122no—
587#67—122no—
588#67—122no—
589#67—124no—
590#67—241no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—31no—
595C2×Dic3—31no—
596C2×Dic3—42no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—81no—
601C2×Dic3—121no—
602C2×Dic3—122no—
603C2×Dic3—122no—
604C2×Dic3D3×D411yescharacteristic
605C2×Dic3D3×D411yescharacteristic
606C2×Dic3D3×D411yescharacteristic
607D12—21no—
608D12—62no—
609D12—61no—
610D12—61no—
611D12—61no—
612D12—61no—
613D12—121no—
614D12—121no—
615D12—122no—
616D12—241no—
617D12C2×D1212yes—
618C4×D3—21no—
619C4×D3—21no—
620C4×D3—42no—
621C4×D3—61no—
622C4×D3—61no—
623C4×D3—61no—
624C4×D3—61no—
625C4×D3—121no—
626C4×D3—121no—
627C4×D3—122no—
628C4×D3—122no—
629Dic6—21no—
630Dic6—21no—
631Dic6—21no—
632Dic6—21no—
633Dic6—61no—
634Dic6—61no—
635Dic6—61no—
636Dic6—61no—
637Dic6—121no—
638Dic6—121no—
639C3×C8—21no—
640C3×C8—21no—
641C3×C8—32no—
642C3×C8—41no—
643C3×C8—61no—
644C3⋊C8—21no—
645C3⋊C8—61no—
646C3⋊C8—61no—
647C3⋊C8—121no—
648C3⋊C8C2×D1212yes—
649C2×C32—42no—
650C2×C32D4211yescharacteristic
651C2×C32#57511yescharacteristic
652C2×C32#57711yescharacteristic
653C3⋊D3—41no—
654C3⋊D3—81no—
655C3×D3—41no—
656C3×D3—42no—
657C24—181no—
658#41—62no—
659#41—121no—
660#41—182no—
661#41—182no—
662#41—361no—
663#41—361no—
664C2×Q8—31no—
665C2×Q8—31no—
666C2×Q8—91no—
667C2×D4—31no—
668C2×D4—61no—
669C2×D4—91no—
670C2×D4—91no—
671C2×D4—181no—
672C2×D4—181no—
673C2×D4—181no—
674C2×D4—182no—
675C2×D4—181no—
676C2×D4—361no—
677C2×D4C2×D3211yescharacteristic
678C22×C4—31no—
679C22×C4—61no—
680C22×C4—61no—
681C22×C4—61no—
682C22×C4—91no—
683C22×C4—181no—
684C22×C4—181no—
685Q16—121no—
686Q16—182no—
687SD16—62no—
688SD16—182no—
689SD16—182no—
690SD16—182no—
691SD16—361no—
692D8—34no—
693D8—182no—
694M16—182no—
695C2×C8—31no—
696C2×C8—31no—
697C2×C8—91no—
698C2×C8—182no—
699C2×C8C2×D3211yescharacteristic
700C4⋊C4—31no—
701C4⋊C4—61no—
702C4⋊C4—91no—
703C4⋊C4—181no—
704C4⋊C4—181no—
705C4⋊C4—181no—
706C4⋊C4—181no—
707C4⋊C4C2×D3211yescharacteristic
708C22⋊C4—61no—
709C22⋊C4—61no—
710C22⋊C4—61no—
711C22⋊C4—91no—
712C22⋊C4—91no—
713C22⋊C4—181no—
714C22⋊C4—181no—
715C22⋊C4—181no—
716C22⋊C4—181no—
717C22⋊C4—181no—
718C42—31no—
719C22×C3—22no—
720C22×C3—22no—
721C22×C3—21no—
722C22×C3—42no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—61no—
728C22×C3—61no—
729C22×C3—61no—
730C22×C3—62no—
731C22×C3—81no—
732C22×C3—81no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3C2×D3×D411yescharacteristic
736C22×C3C2×D3×D411yescharacteristic
737C2×D3—21no—
738C2×D3—21no—
739C2×D3—22no—
740C2×D3—21no—
741C2×D3—41no—
742C2×D3—41no—
743C2×D3—62no—
744C2×D3—61no—
745C2×D3—61no—
746C2×D3—61no—
747C2×D3—61no—
748C2×D3—61no—
749C2×D3—61no—
750C2×D3—121no—
751C2×D3—121no—
752C2×D3—122no—
753C2×D3—121no—
754C2×D3—121no—
755C2×D3—121no—
756C2×D3—121no—
757C2×D3—121no—
758C2×D3—121no—
759C2×D3—241no—
760C2×D3—241no—
761C2×D3—244no—
762C2×D3—244no—
763C2×D3—248no—
764C3×C4—21no—
765C3×C4—21no—
766C3×C4—41no—
767C3×C4—41no—
768C3×C4—61no—
769C3×C4—61no—
770C3×C4—61no—
771C3×C4—81no—
772C3×C4—121no—
773C3×C4—121no—
774C3×C4—121no—
775C3×C4C22×D1211yescharacteristic
776C3×C4C2×D3×D411yescharacteristic
777C3×C4#100411yescharacteristic
778C3×C4#100911yescharacteristic
779Dic3—21no—
780Dic3—21no—
781Dic3—21no—
782Dic3—41no—
783Dic3—41no—
784Dic3—41no—
785Dic3—61no—
786Dic3—61no—
787Dic3—121no—
788Dic3—121no—
789Dic3—121no—
790Dic3—241no—
791C32#326711yescharacteristic, complemented, Sylow
792C23—21no—
793C23—31no—
794C23—61no—
795C23—91no—
796C23—181no—
797C23—362no—
798C23—362no—
799C23—721no—
800Q8—61no—
801Q8—61no—
802Q8—61no—
803Q8—61no—
804Q8—181no—
805Q8—181no—
806D4—21no—
807D4—32no—
808D4—61no—
809D4—122no—
810D4—181no—
811D4—181no—
812D4—361no—
813D4—362no—
814D4—362no—
815D4—362no—
816D4—721no—
817D4D3×D1212yes—
818C2×C4—21no—
819C2×C4—31no—
820C2×C4—31no—
821C2×C4—31no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—61no—
825C2×C4—61no—
826C2×C4—61no—
827C2×C4—91no—
828C2×C4—122no—
829C2×C4—122no—
830C2×C4—181no—
831C2×C4—181no—
832C2×C4—181no—
833C2×C4—241no—
834C2×C4—362no—
835C2×C4—362no—
836C2×C4C22×D3211yescharacteristic
837C8—21no—
838C8—32no—
839C8—61no—
840C8—181no—
841C2×C3—21no—
842C2×C3—21no—
843C2×C3—21no—
844C2×C3—42no—
845C2×C3—42no—
846C2×C3—82no—
847C2×C3—121no—
848C2×C3—122no—
849C2×C3D4×D1211yescharacteristic
850C2×C3#559011yescharacteristic
851C2×C3#576811yescharacteristic
852C2×C3#577311yescharacteristic
853C2×C3#577511yescharacteristic
854C2×C3#577811yescharacteristic
855D3—42no—
856D3—41no—
857D3—122no—
858D3—121no—
859D3—121no—
860D3—242no—
861D3—241no—
862D3—241no—
863C22—22no—
864C22—41no—
865C22—41no—
866C22—61no—
867C22—61no—
868C22—61no—
869C22—62no—
870C22—121no—
871C22—121no—
872C22—181no—
873C22—181no—
874C22—181no—
875C22—361no—
876C22—361no—
877C22—361no—
878C22—724no—
879C22D32×D411yescharacteristic
880C4—41no—
881C4—61no—
882C4—61no—
883C4—61no—
884C4—121no—
885C4—121no—
886C4—121no—
887C4—181no—
888C4—361no—
889C4C2×D3×D1211yescharacteristic
890C4#6431411yescharacteristic
891C3—21no—
892C3#7987911yescharacteristic, complemented
893C3#8026411yescharacteristic, complemented
894C2—42no—
895C2—121no—
896C2—122no—
897C2—361no—
898C2—721no—
899C2#1059427711yescharacteristic
900C2#1059472911yescharacteristic
901C2#1059475411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3267
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. #10595254C2semidirect
2. C2×#63937C2semidirect
3. C2×#63933C2semidirect
4. #10594381C2semidirect
5. #10592475C2semidirect
6. C3×#4785C2semidirect
7. C3×#4783C2semidirect
8. #10591489C2semidirect
9. #10590968C2semidirect
10. #10590965C2semidirect
11. #10590899C2semidirect
12. #10590728C2semidirect
13. #10590577C2semidirect
14. #10590534C2semidirect
15. #10590524C2semidirect
21. C2×#3795C22semidirect
28. C2×C3×Dic12C22semidirect
29. C3×#897C22semidirect
30. C3×#893C22semidirect
44. #63866C22semidirect
46. C2×#3719C22semidirect
48. C2×#3715C22semidirect
51. C2×D3×C3⋊C8C22semidirect
55. C3×#821C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×#815C22semidirect
58. C3×#810C22semidirect
59. C3×#808C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63567C22semidirect
62. #63565C22semidirect
83. #4785D3semidirect
85. #4783D3semidirect
131. C3×#213D4semidirect
202. C2×Dic12C2×D3semidirect
215. #897C2×D3semidirect
218. #893C2×D3semidirect
238. #821C2×D3semidirect
242. (C2×D3)⋊C8C2×D3semidirect
244. #815C2×D3semidirect
248. #810C2×D3semidirect
252. #808C2×D3semidirect
410. #213D12semidirect
791. C32#3267semidirect
892. C3#79879semidirect
893. C3#80264semidirect

Maximal subgroups

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

subgroupindex
#105952542
C2×#639372
C2×#639332
#105943812
#105924752
C3×#47852
C3×#47832
#105914892
#105909682
#105909652
#105908992
#105907282
#105905772
#105905342
#105905242
#802643
#798793