Finite Group Databasebeta

← #11887015

Subgroups — #11887015

Order 1152.

1089 conjugacy classes of subgroups.

The subgroup lattice has 885 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595074C211yesmaximal, characteristic, complemented
2#10594907C211yesmaximal, characteristic, complemented
3C2×#63648C211yesmaximal, characteristic, complemented
4C3×#5115C211yesmaximal, characteristic, complemented
5C3×C8×#67C211yesmaximal, characteristic, complemented
6#10591168C211yesmaximal, characteristic, complemented
7#10591094C211yesmaximal, characteristic, complemented
8#10590944C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590878C211yesmaximal, characteristic, complemented
11#10590826C211yesmaximal, characteristic, complemented
12#10590764C211yesmaximal, characteristic, complemented
13#10590753C211yesmaximal, characteristic, complemented
14#10590745C211yesmaximal, characteristic, complemented
15#10590679C211yesmaximal, characteristic, complemented
16#80731—31nomaximal
17#79438—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×#3811—21no—
20C2×#3805—21no—
21C2×D3×D12C2211yescharacteristic
22C22×C32×C8C2211yescharacteristic, complemented
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
24C3×#930C2211yescharacteristic
25C3×#930C2211yescharacteristic, complemented
26C3×C4×#67C2211yescharacteristic
27C2×C3×D24C2211yescharacteristic, complemented
28C2×C3×D3×C8C2211yescharacteristic, complemented
29#63981—21no—
30#63962—21no—
31#63923—21no—
32#63918C2211yescharacteristic, complemented
33#63911C2211yescharacteristic
34#63910—21no—
35#63909C2211yescharacteristic
36#63908C2211yescharacteristic, complemented
37#63894C2211yescharacteristic
38#63893—21no—
39Dic3×D12C2211yescharacteristic, complemented
40#63891—21no—
41D3×C4⋊Dic3C2211yescharacteristic, complemented
42C2×#3714C2211yescharacteristic
43C2×#3714C2211yescharacteristic, complemented
44#63648C2211yescharacteristic
45#63648C2211yescharacteristic
46#63648C2211yescharacteristic, complemented
47#63648C2211yescharacteristic, complemented
48C3×#830C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic, complemented
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×#818C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×C8×Dic3C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63575C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#5611—31no—
62#5609—31no—
63#5555—31no—
64D4×D12—31no—
65C3×#466—31no—
66C3×C8×D4—31no—
67#5156—31no—
68#5150—31no—
69#5115—31no—
70#5115D311yescharacteristic, complemented
71C2×#821—31no—
72C2×#821—31no—
73C2×#821—31no—
74C2×#821—61no—
75C8×#67D311yescharacteristic, complemented
76#5036—31no—
77#5033—31no—
78#4890—31no—
79#4882—31no—
80#4846—31no—
81#4843—31no—
82#4775—31no—
83D3×#102—31no—
84#4760—31no—
85#4756—31no—
86#4736—31no—
87#4736—31no—
88#4732—31no—
89#4732—31no—
90#4694—31no—
91C4×D24—31no—
92C23×C3⋊D3—21no—
93C22×D32—21no—
94C22×C32×C4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C2×C4⋊(C3⋊D3)—22no—
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)—41no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67D411yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107#3811—44no—
108C2×#627—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#625—21no—
114C2×#624—21no—
115#3805—44no—
116C2×D3×Dic3—21no—
117C2×D3×Dic3—21no—
118D3×D12—22no—
119D3×D12—41no—
120C2×C32×C8—41no—
121C2×C32×C8C2311yescharacteristic
122C2×C32×C8C2311yescharacteristic
123C4⋊(C3⋊Dic3)—21no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126C3×#217D411yescharacteristic
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4D411yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×D24—41no—
137C3×D3×C8—41no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140#3722—21no—
141#3722—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144#3714—22no—
145#3714—41no—
146#3294—91noSylow
147C2×#237—61no—
148C2×#237—61no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C2×D3×D4—61no—
152C22×D12—31no—
153C22×D12—31no—
154C22×D12—31no—
155C22×D12—61no—
156C2×C3×D8—31no—
157C22×C3×C8—21no—
158C22×C3×C8—31no—
159C22×C3×C8C2×D311yescharacteristic, complemented
160C22×C3×C8C2×D311yescharacteristic, complemented
161C3×#121—31no—
162C3×#121—31no—
163C3×C4×D4—31no—
164#940—31no—
165#938—31no—
166#937—61no—
167#935—61no—
168D4×Dic3—31no—
169C2×#213—31no—
170C2×#213—31no—
171#930—31no—
172#930—31no—
173#930C2×D311yescharacteristic
174#930C2×D311yescharacteristic, complemented
175C4×#67C2×D311yescharacteristic
176C2×C4⋊Dic3—31no—
177C2×C4⋊Dic3—31no—
178C2×C4⋊Dic3—31no—
179C2×C4⋊Dic3—61no—
180C2×D24—31no—
181C2×D24—31no—
182C2×D24C2×D311yescharacteristic, complemented
183C2×D3×C8C2×D311yescharacteristic, complemented
184#897—61no—
185#895—31no—
186#895—61no—
187#893—31no—
188D3×C4⋊C4—31no—
189#888—31no—
190#886—61no—
191#886—61no—
192#884—61no—
193#883—61no—
194#882—61no—
195#882—61no—
196#882—61no—
197#878—61no—
198#874—31no—
199C4×D12—31no—
200C4×D12—31no—
201#869—31no—
202C3×#107—31no—
203C3×C4⋊C8—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×C22⋊C8—31no—
207C3×C22⋊C8—31no—
208C3×C4×C8—31no—
209#832—31no—
210#832—31no—
211#830C2×D311yescharacteristic, complemented
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#821—31no—
222#821—31no—
223#821—31no—
224#821—61no—
225#821—61no—
226#821—61no—
227#821—61no—
228#821C2×D311yescharacteristic, complemented
229#821C2×D311yescharacteristic, complemented
230(C2×D3)⋊C8C2×D311yescharacteristic, complemented
231#818—31no—
232#818—31no—
233#818C2×D311yescharacteristic, complemented
234Dic3⋊C8C2×D311yescharacteristic, complemented
235C8×Dic3C2×D311yescharacteristic, complemented
236#809—31no—
237#809—31no—
238#807—31no—
239#807—31no—
240C23×C32C2×D411yescharacteristic
241C22×C3⋊D3—21no—
242C22×C3⋊D3—21no—
243C22×C3⋊D3—42no—
244C22×C3⋊D3—42no—
245C22×C3⋊D3—81no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3C2×D411yescharacteristic
249C2×D32—42no—
250C2×D32—42no—
251C2×D32—81no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—42no—
259C4⋊(C3⋊D3)—21no—
260C4⋊(C3⋊D3)—21no—
261C4⋊(C3⋊D3)—21no—
262C4⋊(C3⋊D3)—42no—
263C4⋊(C3⋊D3)#4112yescomplemented
264C3×#67—42no—
265C3×#67—42no—
266C3×#67D814yescomplemented
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C2×C3×Dic3C2×D411yescharacteristic
272C3×D12—21no—
273C3×D12—21no—
274C3×D12—21no—
275C3×D12—21no—
276C3×C4×D3—21no—
277C3×C4×D3—21no—
278#627—42no—
279#626—42no—
280#626—42no—
281#626—42no—
282#626—81no—
283#625—42no—
284#624—42no—
285D3×Dic3—42no—
286D3×Dic3—42no—
287C32×C8—21no—
288C32×C8—21no—
289C3×C3⋊C8—21no—
290C3×C3⋊C8—21no—
291#547—91no—
292D42—91no—
293#486—91no—
294#480—91no—
295#480—91no—
296#474—91no—
297#466—31no—
298#466—91no—
299#459—91no—
300#447—91no—
301#447—91no—
302C4×D8—91no—
303C8×D4—31no—
304C2×#102—91no—
305C2×#102—91no—
306C23×D3—61no—
307C23×D3—61no—
308C23×D3—61no—
309C23×D3—61no—
310C23×D3—121no—
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—61no—
315C2×C3×D4—61no—
316C22×C3×C4—21no—
317C22×C3×C4—31no—
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C2×#67—21no—
321C2×#67—21no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67D1211yescharacteristic
329C22×Dic3—61no—
330C22×Dic3—61no—
331C22×Dic3—61no—
332C22×Dic3—61no—
333C22×Dic3—121no—
334#237—124no—
335#237—124no—
336D3×D4—62no—
337D3×D4—121no—
338D3×D4—124no—
339D3×D4—124no—
340C2×D12—31no—
341C2×D12—31no—
342C2×D12—31no—
343C2×D12—31no—
344C2×D12—61no—
345C2×D12—61no—
346C2×D12—62no—
347C2×D12—62no—
348C2×D12—62no—
349C2×D12—64no—
350C2×D12—61no—
351C2×D12—61no—
352C2×D12—61no—
353C2×D12—61no—
354C2×D12—61no—
355C2×D12—61no—
356C2×D12—121no—
357C2×D12—121no—
358C2×D12—121no—
359C2×D12—121no—
360C2×D12—122no—
361C2×D12C22×D311yescharacteristic
362C2×D12C22×D311yescharacteristic
363C2×C4×D3—61no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×C4×D3—61no—
367C2×C4×D3C22×D311yescharacteristic
368C2×Dic6—61no—
369C2×Dic6—61no—
370C3×D8—121no—
371C2×C3×C8—21no—
372C2×C3×C8—21no—
373C2×C3×C8—31no—
374C2×C3×C8—31no—
375C2×C3×C8—41no—
376C2×C3×C8—41no—
377C2×C3×C8—42no—
378C2×C3×C8—121no—
379C2×C3×C8C22×D311yescharacteristic
380C2×C3×C8C22×D311yescharacteristic
381C2×C3×C8C22×D311yescharacteristic
382C2×C3×C8C22×D311yescharacteristic
383C3×C4⋊C4—31no—
384C3×C4⋊C4—31no—
385C3×C4⋊C4—31no—
386C3×C22⋊C4—31no—
387C3×C22⋊C4—31no—
388C3×C22⋊C4—61no—
389C3×C22⋊C4—61no—
390C3×C42—31no—
391#217—61no—
392#217—61no—
393#217D1211yescharacteristic
394#213—62no—
395#213—121no—
396(C2×D3)⋊C4—21no—
397(C2×D3)⋊C4—21no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402(C2×D3)⋊C4—61no—
403(C2×D3)⋊C4—61no—
404(C2×D3)⋊C4D1211yescharacteristic
405C4⋊Dic3—31no—
406C4⋊Dic3—31no—
407C4⋊Dic3—31no—
408C4⋊Dic3—31no—
409C4⋊Dic3—61no—
410C4⋊Dic3—61no—
411C4⋊Dic3—61no—
412C4⋊Dic3—61no—
413C4⋊Dic3—61no—
414C4⋊Dic3—61no—
415C4⋊Dic3—121no—
416C4⋊Dic3C22×D311yescharacteristic
417C4⋊Dic3C22×D311yescharacteristic
418Dic3⋊C4—61no—
419Dic3⋊C4—61no—
420Dic3⋊C4D1211yescharacteristic
421C4×Dic3C22×D311yescharacteristic
422C2×C3⋊C8C22×D311yescharacteristic
423C2×C3⋊C8C22×D311yescharacteristic
424D24—41no—
425D24—62no—
426D24—121no—
427D3×C8—41no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32C2×D812yes—
431C22×C32C22×D411yescharacteristic
432C2×C3⋊D3—22no—
433C2×C3⋊D3—41no—
434C2×C3⋊D3—41no—
435C2×C3⋊D3—41no—
436C2×C3⋊D3—41no—
437C2×C3⋊D3—41no—
438C2×C3⋊D3—84no—
439C2×C3×D3—21no—
440C2×C3×D3—21no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C2×C3×D3—41no—
445C2×C3×D3—41no—
446C2×C3×D3—41no—
447C2×C3×D3C2×D812yes—
448D32—84no—
449C32×C4—21no—
450C32×C4C2×#4111yescharacteristic
451C32×C4H(5,𝔽2)11yescharacteristic
452C3⋊Dic3—41no—
453C3⋊Dic3—41no—
454C3×Dic3—21no—
455C3×Dic3—21no—
456C3×Dic3—41no—
457C3×Dic3—41no—
458C3×Dic3C2×D812yes—
459C2×#41—181no—
460C22×D4—91no—
461C22×D4—91no—
462C22×D4—181no—
463C2×D8—31no—
464C2×D8—91no—
465C2×D8—91no—
466C22×C8—31no—
467C22×C8D3211yescharacteristic, complemented
468C4⋊Q8—91no—
469#127—91no—
470#123—181no—
471#123—181no—
472C22⋊Q8—181no—
473#121—31no—
474#121—31no—
475#121—91no—
476#121—91no—
477#121—181no—
478#120—181no—
479#120—181no—
480C4×D4—31no—
481C4×D4—91no—
482C4×D4—91no—
483C2×C4⋊C4—91no—
484C2×C4⋊C4—91no—
485#107—31no—
486#107—91no—
487#107—91no—
488C4⋊C8—31no—
489#102—31no—
490#102—31no—
491#102—91no—
492#102—91no—
493#102—91no—
494#102—91no—
495#102—91no—
496#102—91no—
497#102—91no—
498#102—91no—
499C22⋊C8—31no—
500C22⋊C8—31no—
501C4×C8—31no—
502C23×C3—21no—
503C23×C3—31no—
504C23×C3—61no—
505C23×C3—61no—
506C23×C3C2×D1211yescharacteristic
507C23×C3D3×D411yescharacteristic
508C22×D3—21no—
509C22×D3—21no—
510C22×D3—61no—
511C22×D3—61no—
512C22×D3—61no—
513C22×D3—61no—
514C22×D3—121no—
515C22×D3—121no—
516C22×D3—122no—
517C22×D3—122no—
518C22×D3—122no—
519C22×D3—122no—
520C22×D3—122no—
521C22×D3—124no—
522C22×D3—122no—
523C22×D3—122no—
524C22×D3—122no—
525C22×D3—242no—
526C22×D3—241no—
527C22×D3—241no—
528C22×D3—241no—
529C22×D3—241no—
530C22×D3—242no—
531C22×D3C2×D1211yescharacteristic
532C3×D4—34no—
533C3×D4—61no—
534C3×D4—61no—
535C3×D4—61no—
536C3×D4—61no—
537C3×D4—122no—
538C3×D4—122no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—31no—
548C2×C3×C4—31no—
549C2×C3×C4—31no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4C2×D1211yescharacteristic
555C2×C3×C4D3×D411yescharacteristic
556C2×C3×C4C23×D311yescharacteristic
557C2×C3×C4C23×D311yescharacteristic
558#67—42no—
559#67—42no—
560#67—122no—
561#67—122no—
562#67—122no—
563#67—122no—
564#67—122no—
565#67—241no—
566#67D2414yescomplemented
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—121no—
574C2×Dic3—121no—
575C2×Dic3—122no—
576C2×Dic3—122no—
577C2×Dic3—122no—
578C2×Dic3—122no—
579C2×Dic3—242no—
580C2×Dic3C2×D1211yescharacteristic
581C2×Dic3C2×D1211yescharacteristic
582C2×Dic3C2×D1211yescharacteristic
583D12—21no—
584D12—21no—
585D12—21no—
586D12—21no—
587D12—32no—
588D12—32no—
589D12—62no—
590D12—62no—
591D12—61no—
592D12—61no—
593D12—61no—
594D12—61no—
595D12—61no—
596D12—61no—
597D12—121no—
598D12—121no—
599D12—122no—
600D12—122no—
601D12—124no—
602D12—122no—
603D12—122no—
604D12—122no—
605D12—241no—
606C4×D3—21no—
607C4×D3—21no—
608C4×D3—122no—
609C4×D3—122no—
610C4×D3—122no—
611C4×D3—122no—
612Dic6—122no—
613Dic6—122no—
614C3×C8—21no—
615C3×C8—21no—
616C3×C8—21no—
617C3×C8—21no—
618C3×C8—41no—
619C3×C8—41no—
620C3×C8—61no—
621C3×C8—61no—
622C3⋊C8—21no—
623C3⋊C8—21no—
624C2×C32—22no—
625C2×C32#54611yescharacteristic
626C2×C32C22×D811yescharacteristic
627C2×C32#57711yescharacteristic
628C3⋊D3—42no—
629C3⋊D3—81no—
630C3×D3—22no—
631C3×D3—81no—
632C3×D3—81no—
633C24—181no—
634C24—181no—
635#41—364no—
636C2×Q8—181no—
637C2×D4—31no—
638C2×D4—31no—
639C2×D4—31no—
640C2×D4—61no—
641C2×D4—61no—
642C2×D4—91no—
643C2×D4—91no—
644C2×D4—182no—
645C2×D4—181no—
646C2×D4—181no—
647C2×D4—181no—
648C2×D4—182no—
649C2×D4—181no—
650C2×D4—181no—
651C2×D4—181no—
652C2×D4—361no—
653C2×D4—361no—
654C2×D4—364no—
655C22×C4—31no—
656C22×C4—181no—
657C22×C4—181no—
658C22×C4—181no—
659C22×C4—181no—
660C22×C4C2×D3211yescharacteristic
661D8—121no—
662D8—182no—
663D8—361no—
664C2×C8—31no—
665C2×C8—31no—
666C2×C8—41no—
667C2×C8—121no—
668C2×C8C2×D3211yescharacteristic
669C2×C8C2×D3211yescharacteristic
670C4⋊C4—31no—
671C4⋊C4—31no—
672C4⋊C4—31no—
673C4⋊C4—91no—
674C4⋊C4—91no—
675C4⋊C4—181no—
676C4⋊C4—181no—
677C4⋊C4—181no—
678C22⋊C4—31no—
679C22⋊C4—31no—
680C22⋊C4—61no—
681C22⋊C4—61no—
682C22⋊C4—181no—
683C22⋊C4—181no—
684C22⋊C4—181no—
685C22⋊C4—181no—
686C42—31no—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—22no—
695C22×C3—32no—
696C22×C3—61no—
697C22×C3—61no—
698C22×C3—121no—
699C22×C3—121no—
700C22×C3—121no—
701C22×C3—121no—
702C22×C3—121no—
703C22×C3—121no—
704C22×C3C2×D2412yes—
705C22×C3D3×D812yes—
706C22×C3C22×D1211yescharacteristic
707C22×C3C2×D3×D411yescharacteristic
708C2×D3—21no—
709C2×D3—21no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3—41no—
714C2×D3—41no—
715C2×D3—41no—
716C2×D3—62no—
717C2×D3—62no—
718C2×D3—122no—
719C2×D3—121no—
720C2×D3—121no—
721C2×D3—121no—
722C2×D3—121no—
723C2×D3—122no—
724C2×D3—121no—
725C2×D3—121no—
726C2×D3—121no—
727C2×D3—121no—
728C2×D3—121no—
729C2×D3—121no—
730C2×D3—241no—
731C2×D3—241no—
732C2×D3—241no—
733C2×D3—241no—
734C2×D3—244no—
735C2×D3—244no—
736C2×D3—244no—
737C2×D3—244no—
738C2×D3—248no—
739C2×D3C2×D2412yes—
740C3×C4—22no—
741C3×C4—21no—
742C3×C4—21no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—32no—
746C3×C4—61no—
747C3×C4—61no—
748C3×C4—121no—
749C3×C4—121no—
750C3×C4#100411yescharacteristic
751C3×C4#100411yescharacteristic
752C3×C4D3×#4111yescharacteristic
753C3×C4D3×#4111yescharacteristic
754Dic3—21no—
755Dic3—21no—
756Dic3—41no—
757Dic3—41no—
758Dic3—121no—
759Dic3—121no—
760Dic3—121no—
761Dic3—121no—
762Dic3—241no—
763Dic3—241no—
764Dic3C2×D2412yes—
765C32#329411yescharacteristic, complemented, Sylow
766C23—31no—
767C23—61no—
768C23—61no—
769C23—181no—
770C23—181no—
771C23—362no—
772C23—362no—
773C23—362no—
774C23—362no—
775C23—721no—
776C23—721no—
777C23D3×D1211yescharacteristic
778Q8—362no—
779D4—34no—
780D4—61no—
781D4—61no—
782D4—61no—
783D4—61no—
784D4—92no—
785D4—122no—
786D4—122no—
787D4—181no—
788D4—181no—
789D4—181no—
790D4—362no—
791D4—362no—
792D4—362no—
793D4—362no—
794D4—362no—
795D4—721no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—31no—
799C2×C4—31no—
800C2×C4—31no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—181no—
806C2×C4—181no—
807C2×C4—362no—
808C2×C4—362no—
809C2×C4—362no—
810C2×C4—362no—
811C2×C4D3×D1211yescharacteristic
812C2×C4C22×D3211yescharacteristic
813C8—21no—
814C8—21no—
815C8—61no—
816C8—61no—
817C2×C3—24no—
818C2×C3—22no—
819C2×C3—22no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—62no—
824C2×C3—241no—
825C2×C3—241no—
826C2×C3#555411yescharacteristic
827C2×C3#561011yescharacteristic
828C2×C3C22×D2411yescharacteristic
829C2×C3#575111yescharacteristic
830C2×C3C2×D3×D811yescharacteristic
831C2×C3#577011yescharacteristic
832D3—22no—
833D3—81no—
834D3—81no—
835D3—122no—
836D3—122no—
837D3—242no—
838D3—242no—
839D3—241no—
840D3—241no—
841C22—21no—
842C22—21no—
843C22—32no—
844C22—61no—
845C22—61no—
846C22—121no—
847C22—121no—
848C22—121no—
849C22—121no—
850C22—121no—
851C22—121no—
852C22—182no—
853C22—361no—
854C22—361no—
855C22—361no—
856C22—361no—
857C22—361no—
858C22—724no—
859C22—724no—
860C22D3×D2412yes—
861C22C2×D3×D1211yescharacteristic
862C4—21no—
863C4—32no—
864C4—61no—
865C4—61no—
866C4—121no—
867C4—121no—
868C4—361no—
869C4—361no—
870C4#6430611yescharacteristic
871C4#6433011yescharacteristic
872C3—21no—
873C3#7943811yescharacteristic, complemented
874C3#8073111yescharacteristic, complemented
875C2—22no—
876C2—62no—
877C2—241no—
878C2—241no—
879C2—362no—
880C2—721no—
881C2C2×D3×D2411yescharacteristic
882C2#1059467911yescharacteristic
883C2#1059507511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
hypercenterC22×C8D32
hypocenterC32#3294
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #10595074C2semidirect
2. #10594907C2semidirect
3. C2×#63648C2semidirect
4. C3×#5115C2semidirect
5. C3×C8×#67C2semidirect
6. #10591168C2semidirect
7. #10591094C2semidirect
8. #10590944C2semidirect
9. D3×#821C2semidirect
10. #10590878C2semidirect
11. #10590826C2semidirect
12. #10590764C2semidirect
13. #10590753C2semidirect
14. #10590745C2semidirect
15. #10590679C2semidirect
22. C22×C32×C8C22semidirect
23. C2×C4⋊(C3⋊Dic3)C22semidirect
25. C3×#930C22semidirect
27. C2×C3×D24C22semidirect
28. C2×C3×D3×C8C22semidirect
32. #63918C22semidirect
36. #63908C22semidirect
39. Dic3×D12C22semidirect
41. D3×C4⋊Dic3C22semidirect
43. C2×#3714C22semidirect
46. #63648C22semidirect
47. #63648C22semidirect
48. C3×#830C22semidirect
49. C3×#821C22semidirect
50. C3×#821C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×#818C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. C3×C8×Dic3C22semidirect
55. #63575C22semidirect
56. #63575C22semidirect
58. #63564C22semidirect
59. #63563C22semidirect
60. #63563C22semidirect
70. #5115D3semidirect
75. C8×#67D3semidirect
159. C22×C3×C8C2×D3semidirect
160. C22×C3×C8C2×D3semidirect
174. #930C2×D3semidirect
182. C2×D24C2×D3semidirect
183. C2×D3×C8C2×D3semidirect
211. #830C2×D3semidirect
228. #821C2×D3semidirect
229. #821C2×D3semidirect
230. (C2×D3)⋊C8C2×D3semidirect
233. #818C2×D3semidirect
234. Dic3⋊C8C2×D3semidirect
235. C8×Dic3C2×D3semidirect
263. C4⋊(C3⋊D3)#41semidirect
266. C3×#67D8semidirect
467. C22×C8D32semidirect
566. #67D24semidirect
765. C32#3294semidirect
873. C3#79438semidirect
874. C3#80731semidirect

Maximal subgroups

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

subgroupindex
#105950742
#105949072
C2×#636482
C3×#51152
C3×C8×#672
#105911682
#105910942
#105909442
D3×#8212
#105908782
#105908262
#105907642
#105907532
#105907452
#105906792
#807313
#794383