Finite Group Databasebeta

← #11887035

Subgroups — #11887035

Order 1152.

1202 conjugacy classes of subgroups.

The subgroup lattice has 929 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596080C211yesmaximal, characteristic, complemented
2#10594928C211yesmaximal, characteristic, complemented
3C3×#5038C211yesmaximal, characteristic, complemented
4C3×#5033C211yesmaximal, characteristic, complemented
5#10591456C211yesmaximal, characteristic, complemented
6#10591433C211yesmaximal, characteristic, complemented
7#10591416C211yesmaximal, characteristic, complemented
8#10591402C211yesmaximal, characteristic, complemented
9#10591168C211yesmaximal, characteristic, complemented
10#10591148C211yesmaximal, characteristic, complemented
11C2×#63564C211yesmaximal, characteristic, complemented
12#10590509C211yesmaximal, characteristic, complemented
13#10590459C211yesmaximal, characteristic, complemented
14#10590442C211yesmaximal, characteristic, complemented
15#10590430C211yesmaximal, characteristic, complemented
16#81302—31nomaximal
17#80731—31nomaximal
18C2×D4×C3⋊D3—21no—
19C2×D4×C3⋊D3C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×#3804—21no—
22C32×#121C2211yescharacteristic
23#64149C2211yescharacteristic
24#64146—21no—
25C4×#638C2211yescharacteristic
26#64104C2211yescharacteristic
27#64102C2211yescharacteristic
28#64093—21no—
29#64091—21no—
30C2×C3×#213C2211yescharacteristic, complemented
31C3×#930C2211yescharacteristic, complemented
32C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
33C22×C3×C3⋊C8C2211yescharacteristic, complemented
34#63961—21no—
35#63919C2211yescharacteristic, complemented
36#63916C2211yescharacteristic, complemented
37#63900C2211yescharacteristic, complemented
38#63899—21no—
39#63898C2211yescharacteristic, complemented
40#63854—21no—
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic, complemented
43C2×#3710C2211yescharacteristic, complemented
44C3×#832C2211yescharacteristic, complemented
45C3×#832C2211yescharacteristic, complemented
46C3×#832C2211yescharacteristic, complemented
47C3×#830C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic, complemented
49C3×#807C2211yescharacteristic, complemented
50C3×#807C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52#63572C2211yescharacteristic, complemented
53#63564C2211yescharacteristic
54#63564C2211yescharacteristic
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63564C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61#5611—31no—
62#5609—31no—
63#5609—31no—
64#5609—61no—
65#5507—31no—
66C3×#480—31no—
67C3×#466—31no—
68#5156—31no—
69#5150—31no—
70C2×#821—31no—
71C8×#67—31no—
72#5038D311yescharacteristic, complemented
73#5036—31no—
74#5033D311yescharacteristic, complemented
75C2×#809—31no—
76#4890—31no—
77#4890—31no—
78#4883—31no—
79#4882—31no—
80#4882—31no—
81#4872—31no—
82#4786—31no—
83#4775—31no—
84#4773—31no—
85D3×#102—31no—
86D3×#102—31no—
87#4760—31no—
88#4760—31no—
89#4756—31no—
90#4732—31no—
91#67⋊C8—31no—
92C23×C3⋊D3—21no—
93C23×C3⋊D3—21no—
94C2×C32×D4—21no—
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×#638—21no—
98C2×#638—21no—
99C2×#638—21no—
100C2×#638D411yescharacteristic
101D4×C3⋊D3—22no—
102D4×C3⋊D3—41no—
103D4×C3⋊D3—44no—
104C2×C4⋊(C3⋊D3)—22no—
105C2×C4⋊(C3⋊D3)—21no—
106C2×C4⋊(C3⋊D3)—21no—
107C2×C4⋊(C3⋊D3)—41no—
108C2×C4⋊(C3⋊D3)C2311yescharacteristic
109C2×C4⋊(C3⋊D3)C2311yescharacteristic
110C2×C4×C3⋊D3—21no—
111C2×C4×C3⋊D3C2311yescharacteristic
112C2×C3×#67—21no—
113C22×C3×Dic3—21no—
114C2×C3×D12C2311yescharacteristic
115C2×#627—21no—
116C2×#626—21no—
117C2×#624—21no—
118#3804—44no—
119C2×D3×Dic3—21no—
120C32×C4⋊C4C2311yescharacteristic
121C32×C22⋊C4—21no—
122#3757D411yescharacteristic
123#3752—21no—
124#3752—21no—
125#3752D411yescharacteristic
126#3750D411yescharacteristic
127C4×C3⋊Dic3C2311yescharacteristic
128C3×#213—41no—
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C2×C3×C3⋊C8—41no—
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139#3724—21no—
140#3724—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143#3714—22no—
144#3714—41no—
145#3710—41no—
146#3294—91noSylow
147C2×#237—61no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C2×D3×D4—61no—
152C2×D3×D4—61no—
153C2×D3×D4—62no—
154C2×#235—61no—
155C22×D12—31no—
156C22×D12—31no—
157C22×D12—61no—
158C2×C3×D8—31no—
159C22×C3×C8—31no—
160C3×#121—21no—
161C3×#121—31no—
162C3×#121C2×D311yescharacteristic
163C3×#121C2×D311yescharacteristic
164C2×C3×C4⋊C4—31no—
165#940—31no—
166#940—31no—
167#940—61no—
168#938—31no—
169#937—61no—
170#937—61no—
171#937—62no—
172#935—61no—
173D4×Dic3—31no—
174C2×#213—31no—
175C2×#213—31no—
176C2×#213C2×D311yescharacteristic, complemented
177#930C2×D311yescharacteristic, complemented
178#929—61no—
179C4×#67—31no—
180C4×#67—31no—
181C4×#67—61no—
182C2×C4⋊Dic3C2×D311yescharacteristic, complemented
183C22×C3⋊C8C2×D311yescharacteristic, complemented
184C2×D24—31no—
185C2×D24—31no—
186C2×D3×C8—31no—
187C2×D3×C8—31no—
188#896—61no—
189#895—31no—
190#895—31no—
191#895—31no—
192#895—61no—
193#894—61no—
194#893—31no—
195#893—31no—
196#893—31no—
197#893—61no—
198D3×C4⋊C4—31no—
199D3×C4⋊C4—31no—
200#888—31no—
201#888—31no—
202#884—61no—
203#884—61no—
204#884—62no—
205#883—61no—
206#882—61no—
207#882—61no—
208#882—62no—
209#878—61no—
210C3×#107—31no—
211C3×#107—31no—
212C3×#107—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×#102—31no—
217C3×C22⋊C8—31no—
218#832C2×D311yescharacteristic, complemented
219#832C2×D311yescharacteristic, complemented
220#832C2×D311yescharacteristic, complemented
221#830C2×D311yescharacteristic, complemented
222#821—31no—
223#821—31no—
224#821—31no—
225#821—31no—
226#821—31no—
227#821—31no—
228(C2×D3)⋊C8—31no—
229(C2×D3)⋊C8—31no—
230Dic3⋊C8—31no—
231Dic3⋊C8—31no—
232C8×Dic3—31no—
233C8×Dic3—31no—
234#809—31no—
235#809—31no—
236#809—31no—
237#809—31no—
238#809—31no—
239#809—31no—
240#809C2×D311yescharacteristic, complemented
241#807C2×D311yescharacteristic, complemented
242#807C2×D311yescharacteristic, complemented
243#807C2×D311yescharacteristic, complemented
244C23×C32—21no—
245C23×C32C2×D411yescharacteristic
246C22×C3⋊D3—21no—
247C22×C3⋊D3—21no—
248C22×C3⋊D3—42no—
249C22×C3⋊D3—42no—
250C22×C3⋊D3—42no—
251C22×C3⋊D3—42no—
252C22×C3⋊D3—81no—
253C22×C3⋊D3—81no—
254C22×C3⋊D3C2×D411yescharacteristic
255C22×C3×D3—21no—
256C32×D4—21no—
257C32×D4—21no—
258C32×D4—42no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4C2×D411yescharacteristic
263C2×C32×C4C2411yescharacteristic
264#638—42no—
265#638—42no—
266#638—81no—
267#638D814yescomplemented
268C2×C3⋊Dic3C2×D411yescharacteristic
269C2×C3⋊Dic3C2×D411yescharacteristic
270C2×C3⋊Dic3C2×D411yescharacteristic
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—42no—
275C4⋊(C3⋊D3)—42no—
276C4⋊(C3⋊D3)#4112yescomplemented
277C4×C3⋊D3—21no—
278C4×C3⋊D3—21no—
279C4×C3⋊D3—42no—
280C3×#67—42no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—42no—
285C3×D12—21no—
286C3×D12—21no—
287#627—42no—
288#626—42no—
289#624—42no—
290D3×Dic3—42no—
291C3×C3⋊C8—21no—
292C3×C3⋊C8—21no—
293C3×C3⋊C8—21no—
294C3×C3⋊C8—21no—
295#547—91no—
296D42—91no—
297#486—91no—
298#480—31no—
299#480—91no—
300#474—91no—
301#466—31no—
302#466—91no—
303#459—91no—
304#447—91no—
305#447—91no—
306C4×D8—91no—
307C8×D4—91no—
308C2×#102—91no—
309C2×#102—91no—
310C23×D3—61no—
311C23×D3—61no—
312C23×D3—62no—
313C23×D3—62no—
314C23×D3—61no—
315C23×D3—61no—
316C2×C3×D4—22no—
317C2×C3×D4—21no—
318C2×C3×D4—21no—
319C2×C3×D4—21no—
320C2×C3×D4—31no—
321C2×C3×D4—61no—
322C2×C3×D4C22×D311yescharacteristic
323C2×C3×D4C22×D311yescharacteristic
324C22×C3×C4—21no—
325C22×C3×C4—61no—
326C22×C3×C4C22×D311yescharacteristic
327C22×C3×C4C22×D311yescharacteristic
328C2×#67—21no—
329C2×#67—31no—
330C2×#67—31no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—62no—
340C2×#67—62no—
341C2×#67—62no—
342C22×Dic3—21no—
343C22×Dic3—61no—
344#237—124no—
345D3×D4—62no—
346D3×D4—62no—
347D3×D4—122no—
348D3×D4—121no—
349D3×D4—121no—
350D3×D4—122no—
351D3×D4—124no—
352D3×D4—124no—
353D3×D4—128no—
354#235—124no—
355C2×D12—31no—
356C2×D12—31no—
357C2×D12—31no—
358C2×D12—31no—
359C2×D12—61no—
360C2×D12—61no—
361C2×D12—62no—
362C2×D12—62no—
363C2×D12—61no—
364C2×D12—61no—
365C2×D12—62no—
366C2×D12—62no—
367C2×D12—61no—
368C2×D12—61no—
369C2×D12—61no—
370C2×D12—122no—
371C2×D12—121no—
372C2×D12—121no—
373C2×D12—122no—
374C2×D12C22×D311yescharacteristic
375C2×C4×D3—31no—
376C2×C4×D3—31no—
377C2×C4×D3—61no—
378C2×C4×D3—61no—
379C2×C4×D3—61no—
380C2×C4×D3—61no—
381C2×C4×D3—61no—
382C2×C4×D3—61no—
383C2×C4×D3—62no—
384C2×Dic6—61no—
385C2×Dic6—61no—
386C3×D8—121no—
387C2×C3×C8—31no—
388C2×C3×C8—31no—
389C2×C3×C8—31no—
390C2×C3×C8—31no—
391C2×C3×C8—121no—
392C3×C4⋊C4—21no—
393C3×C4⋊C4—31no—
394C3×C4⋊C4—31no—
395C3×C4⋊C4—31no—
396C3×C4⋊C4—61no—
397C3×C4⋊C4C22×D311yescharacteristic
398C3×C4⋊C4C22×D311yescharacteristic
399C3×C22⋊C4—22no—
400C3×C22⋊C4—21no—
401C3×C22⋊C4—21no—
402C3×C22⋊C4—61no—
403#217—31no—
404#217—31no—
405#217—61no—
406#217—61no—
407#217—61no—
408#213—41no—
409#213—62no—
410#213—121no—
411(C2×D3)⋊C4—21no—
412(C2×D3)⋊C4—31no—
413(C2×D3)⋊C4—31no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
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—62no—
422(C2×D3)⋊C4—62no—
423C4⋊Dic3—21no—
424C4⋊Dic3C22×D311yescharacteristic
425C4⋊Dic3C22×D311yescharacteristic
426C4⋊Dic3C22×D311yescharacteristic
427Dic3⋊C4—31no—
428Dic3⋊C4—31no—
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434C4×Dic3—31no—
435C4×Dic3—31no—
436C4×Dic3—61no—
437C2×C3⋊C8—41no—
438C2×C3⋊C8C22×D311yescharacteristic
439C2×C3⋊C8C22×D311yescharacteristic
440C2×C3⋊C8C22×D311yescharacteristic
441C2×C3⋊C8C22×D311yescharacteristic
442D24—62no—
443D24—121no—
444D3×C8—121no—
445D3×C8—121no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—41no—
449C22×C32—41no—
450C22×C32—41no—
451C22×C32C2×D812yes—
452C22×C32C22×D411yescharacteristic
453C2×C3⋊D3—22no—
454C2×C3⋊D3—21no—
455C2×C3⋊D3—21no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
458C2×C3⋊D3—41no—
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3⋊D3—84no—
462C2×C3⋊D3—84no—
463C2×C3⋊D3C2×D812yes—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C32×C4—21no—
468C32×C4—41no—
469C32×C4C2×#4111yescharacteristic
470C32×C4H(5,𝔽2)11yescharacteristic
471C3⋊Dic3—21no—
472C3⋊Dic3—21no—
473C3⋊Dic3C2×D812yes—
474C3×Dic3—41no—
475C3×Dic3—41no—
476C3×Dic3—41no—
477C2×#41—181no—
478C22×D4—91no—
479C22×D4—91no—
480C22×D4—181no—
481C2×D8—31no—
482C2×D8—91no—
483C2×D8—91no—
484C22×C8—31no—
485C22×C8—91no—
486C4⋊Q8—91no—
487#127—91no—
488#123—181no—
489#123—181no—
490C22⋊Q8—181no—
491#121—31no—
492#121—91no—
493#121—91no—
494#121—181no—
495#121D3211yescharacteristic
496#120—181no—
497#120—181no—
498C4×D4—91no—
499C4×D4—91no—
500C4×D4—91no—
501C2×C4⋊C4—31no—
502C2×C4⋊C4—91no—
503#107—31no—
504#107—31no—
505#107—31no—
506C4⋊C8—91no—
507#102—31no—
508#102—31no—
509#102—31no—
510#102—31no—
511#102—91no—
512#102—91no—
513#102—91no—
514#102—91no—
515#102—91no—
516#102—91no—
517C22⋊C8—31no—
518C22⋊C8—91no—
519C4×C8—91no—
520C23×C3—22no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—61no—
525C23×C3D3×D411yescharacteristic
526C23×C3D3×D411yescharacteristic
527C22×D3—21no—
528C22×D3—31no—
529C22×D3—31no—
530C22×D3—61no—
531C22×D3—62no—
532C22×D3—61no—
533C22×D3—61no—
534C22×D3—62no—
535C22×D3—61no—
536C22×D3—61no—
537C22×D3—122no—
538C22×D3—122no—
539C22×D3—122no—
540C22×D3—122no—
541C22×D3—122no—
542C22×D3—122no—
543C22×D3—124no—
544C22×D3—124no—
545C22×D3—124no—
546C22×D3—124no—
547C22×D3—122no—
548C22×D3—122no—
549C22×D3—241no—
550C22×D3—241no—
551C22×D3—241no—
552C22×D3—241no—
553C22×D3—242no—
554C22×D3—242no—
555C3×D4—21no—
556C3×D4—21no—
557C3×D4—21no—
558C3×D4—21no—
559C3×D4—41no—
560C3×D4—41no—
561C3×D4—44no—
562C3×D4—42no—
563C3×D4—42no—
564C3×D4—61no—
565C3×D4—61no—
566C3×D4—122no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—22no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—122no—
582C2×C3×C4D3×D411yescharacteristic
583C2×C3×C4D3×D411yescharacteristic
584C2×C3×C4C23×D311yescharacteristic
585C2×C3×C4C23×D311yescharacteristic
586#67—34no—
587#67—34no—
588#67—42no—
589#67—64no—
590#67—122no—
591#67—122no—
592#67—122no—
593#67—122no—
594#67—122no—
595#67—124no—
596#67—124no—
597#67—241no—
598#67—241no—
599#67—242no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—31no—
604C2×Dic3—31no—
605C2×Dic3—31no—
606C2×Dic3—31no—
607C2×Dic3—31no—
608C2×Dic3—31no—
609C2×Dic3—42no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—122no—
614D12—21no—
615D12—21no—
616D12—32no—
617D12—32no—
618D12—62no—
619D12—62no—
620D12—61no—
621D12—61no—
622D12—61no—
623D12—61no—
624D12—61no—
625D12—61no—
626D12—121no—
627D12—121no—
628D12—122no—
629D12—122no—
630D12—122no—
631D12—122no—
632D12—124no—
633D12—124no—
634D12—122no—
635C4×D3—61no—
636C4×D3—61no—
637C4×D3—61no—
638C4×D3—61no—
639C4×D3—121no—
640C4×D3—121no—
641C4×D3—122no—
642C4×D3—122no—
643C4×D3—122no—
644C4×D3—122no—
645C4×D3—122no—
646C4×D3—124no—
647Dic6—122no—
648Dic6—122no—
649C3×C8—61no—
650C3×C8—61no—
651C3×C8—61no—
652C3×C8—61no—
653C3⋊C8—21no—
654C3⋊C8—21no—
655C3⋊C8—21no—
656C3⋊C8—21no—
657C2×C32—22no—
658C2×C32—81no—
659C2×C32#54611yescharacteristic
660C2×C32C22×D811yescharacteristic
661C2×C32#57711yescharacteristic
662C3⋊D3—22no—
663C3⋊D3—42no—
664C3⋊D3—81no—
665C3×D3—81no—
666C24—181no—
667C24—181no—
668#41—364no—
669C2×Q8—181no—
670C2×D4—21no—
671C2×D4—31no—
672C2×D4—61no—
673C2×D4—91no—
674C2×D4—91no—
675C2×D4—91no—
676C2×D4—182no—
677C2×D4—181no—
678C2×D4—181no—
679C2×D4—181no—
680C2×D4—181no—
681C2×D4—181no—
682C2×D4—182no—
683C2×D4—181no—
684C2×D4—361no—
685C2×D4—361no—
686C2×D4—364no—
687C2×D4C2×D3211yescharacteristic
688C22×C4—61no—
689C22×C4—91no—
690C22×C4—181no—
691C22×C4—181no—
692C22×C4—181no—
693C22×C4C2×D3211yescharacteristic
694D8—121no—
695D8—182no—
696D8—361no—
697C2×C8—31no—
698C2×C8—31no—
699C2×C8—31no—
700C2×C8—31no—
701C2×C8—121no—
702C2×C8—361no—
703C4⋊C4—31no—
704C4⋊C4—31no—
705C4⋊C4—31no—
706C4⋊C4—61no—
707C4⋊C4—91no—
708C4⋊C4—181no—
709C4⋊C4—181no—
710C4⋊C4C2×D3211yescharacteristic
711C22⋊C4—21no—
712C22⋊C4—61no—
713C22⋊C4—91no—
714C22⋊C4—91no—
715C22⋊C4—181no—
716C22⋊C4—181no—
717C22⋊C4—181no—
718C22⋊C4—181no—
719C42—91no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—22no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—42no—
729C22×C3—42no—
730C22×C3—42no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3D3×D812yes—
741C22×C3D3×D812yes—
742C22×C3C2×D3×D411yescharacteristic
743C22×C3C2×D3×D411yescharacteristic
744C2×D3—32no—
745C2×D3—32no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—62no—
750C2×D3—61no—
751C2×D3—61no—
752C2×D3—61no—
753C2×D3—61no—
754C2×D3—64no—
755C2×D3—62no—
756C2×D3—62no—
757C2×D3—121no—
758C2×D3—121no—
759C2×D3—122no—
760C2×D3—122no—
761C2×D3—121no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—122no—
766C2×D3—122no—
767C2×D3—122no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—244no—
775C2×D3—244no—
776C2×D3—248no—
777C2×D3—244no—
778C2×D3—244no—
779C2×D3—248no—
780C3×C4—21no—
781C3×C4—21no—
782C3×C4—21no—
783C3×C4—21no—
784C3×C4—41no—
785C3×C4—42no—
786C3×C4—41no—
787C3×C4—41no—
788C3×C4—121no—
789C3×C4—121no—
790C3×C4—121no—
791C3×C4#100411yescharacteristic
792C3×C4D3×#4111yescharacteristic
793C3×C4D3×#4111yescharacteristic
794C3×C4#100911yescharacteristic
795Dic3—32no—
796Dic3—32no—
797Dic3—41no—
798Dic3—41no—
799Dic3—41no—
800Dic3—62no—
801Dic3—61no—
802Dic3—61no—
803Dic3—61no—
804Dic3—61no—
805Dic3—121no—
806Dic3—121no—
807C32#329411yescharacteristic, complemented, Sylow
808C23—21no—
809C23—61no—
810C23—91no—
811C23—181no—
812C23—181no—
813C23—362no—
814C23—362no—
815C23—362no—
816C23—362no—
817C23—721no—
818C23—721no—
819C23#381111yescharacteristic
820Q8—362no—
821D4—21no—
822D4—21no—
823D4—42no—
824D4—61no—
825D4—61no—
826D4—94no—
827D4—92no—
828D4—122no—
829D4—181no—
830D4—181no—
831D4—181no—
832D4—362no—
833D4—362no—
834D4—362no—
835D4—362no—
836D4—362no—
837D4—721no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—91no—
845C2×C4—91no—
846C2×C4—91no—
847C2×C4—122no—
848C2×C4—181no—
849C2×C4—181no—
850C2×C4—362no—
851C2×C4—362no—
852C2×C4—362no—
853C2×C4#381111yescharacteristic
854C2×C4C22×D3211yescharacteristic
855C8—61no—
856C8—61no—
857C8—61no—
858C8—61no—
859C2×C3—22no—
860C2×C3—22no—
861C2×C3—21no—
862C2×C3—21no—
863C2×C3—21no—
864C2×C3—42no—
865C2×C3—82no—
866C2×C3—81no—
867C2×C3—81no—
868C2×C3—241no—
869C2×C3#561011yescharacteristic
870C2×C3#565411yescharacteristic
871C2×C3C2×D3×D811yescharacteristic
872C2×C3C2×D3×D811yescharacteristic
873C2×C3#577011yescharacteristic
874C2×C3#577811yescharacteristic
875D3—62no—
876D3—62no—
877D3—81no—
878D3—122no—
879D3—124no—
880D3—122no—
881D3—122no—
882D3—242no—
883D3—241no—
884D3—241no—
885C22—21no—
886C22—21no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—92no—
891C22—121no—
892C22—121no—
893C22—121no—
894C22—181no—
895C22—181no—
896C22—182no—
897C22—361no—
898C22—361no—
899C22—361no—
900C22—361no—
901C22—361no—
902C22—724no—
903C22—724no—
904C22#6392612yes—
905C22C2×#381111yescharacteristic
906C4—21no—
907C4—41no—
908C4—92no—
909C4—121no—
910C4—121no—
911C4—121no—
912C4—181no—
913C4—181no—
914C4#6431211yescharacteristic
915C4#6431411yescharacteristic
916C3—21no—
917C3#8073111yescharacteristic, complemented
918C3#8130211yescharacteristic, complemented
919C2—22no—
920C2—81no—
921C2—182no—
922C2—241no—
923C2—362no—
924C2—721no—
925C2C2×#6392611yescharacteristic
926C2#1059516311yescharacteristic
927C2#1059547311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3294
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #10596080C2semidirect
2. #10594928C2semidirect
3. C3×#5038C2semidirect
4. C3×#5033C2semidirect
5. #10591456C2semidirect
6. #10591433C2semidirect
7. #10591416C2semidirect
8. #10591402C2semidirect
9. #10591168C2semidirect
10. #10591148C2semidirect
11. C2×#63564C2semidirect
12. #10590509C2semidirect
13. #10590459C2semidirect
14. #10590442C2semidirect
15. #10590430C2semidirect
30. C2×C3×#213C22semidirect
31. C3×#930C22semidirect
32. C2×C3×C4⋊Dic3C22semidirect
33. C22×C3×C3⋊C8C22semidirect
35. #63919C22semidirect
36. #63916C22semidirect
37. #63900C22semidirect
39. #63898C22semidirect
42. C2×#3714C22semidirect
43. C2×#3710C22semidirect
44. C3×#832C22semidirect
45. C3×#832C22semidirect
46. C3×#832C22semidirect
47. C3×#830C22semidirect
48. C3×#809C22semidirect
49. C3×#807C22semidirect
50. C3×#807C22semidirect
51. C3×#807C22semidirect
52. #63572C22semidirect
56. #63564C22semidirect
57. #63564C22semidirect
58. #63564C22semidirect
59. #63557C22semidirect
60. #63553C22semidirect
72. #5038D3semidirect
74. #5033D3semidirect
176. C2×#213C2×D3semidirect
177. #930C2×D3semidirect
182. C2×C4⋊Dic3C2×D3semidirect
183. C22×C3⋊C8C2×D3semidirect
218. #832C2×D3semidirect
219. #832C2×D3semidirect
220. #832C2×D3semidirect
221. #830C2×D3semidirect
240. #809C2×D3semidirect
241. #807C2×D3semidirect
242. #807C2×D3semidirect
243. #807C2×D3semidirect
267. #638D8semidirect
276. C4⋊(C3⋊D3)#41semidirect
807. C32#3294semidirect
917. C3#80731semidirect
918. C3#81302semidirect

Maximal subgroups

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

subgroupindex
#105960802
#105949282
C3×#50382
C3×#50332
#105914562
#105914332
#105914162
#105914022
#105911682
#105911482
C2×#635642
#105905092
#105904592
#105904422
#105904302
#813023
#807313