Finite Group Databasebeta

← #11889104

Subgroups — #11889104

Order 1152.

962 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D12×#67C211yesmaximal, characteristic
2#10594849C211yesmaximal, characteristic, complemented
3#10592813C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic, complemented
5C3×#5111C211yesmaximal, characteristic, complemented
6#10591172C211yesmaximal, characteristic, complemented
7#10591133C211yesmaximal, characteristic, complemented
8#10590946C211yesmaximal, characteristic, complemented
9#10590939C211yesmaximal, characteristic, complemented
10#10590882C211yesmaximal, characteristic, complemented
11#10590879C211yesmaximal, characteristic, complemented
12#10590837C211yesmaximal, characteristic, complemented
13#10590828C211yesmaximal, characteristic, complemented
14#10590772C211yesmaximal, characteristic, complemented
15#10590747C211yesmaximal, characteristic, complemented
16#79501—31nomaximal
17#78762—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×D12C2211yescharacteristic
21C22×C32×C8C2211yescharacteristic, complemented
22#64139C2211yescharacteristic
23#64133C2211yescharacteristic, complemented
24C2×#3744C2211yescharacteristic, complemented
25C3×C4×#67C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
27C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
28#63977—21no—
29#63961—21no—
30#63955—21no—
31#63922—21no—
32#63911C2211yescharacteristic
33#63908C2211yescharacteristic
34Dic3×D12C2211yescharacteristic
35#63886—21no—
36#63869C2211yescharacteristic, complemented
37#63858—21no—
38#63857C2211yescharacteristic, complemented
39#63847—21no—
40#63844C2211yescharacteristic, complemented
41#63841C2211yescharacteristic, complemented
42C2×#3716C2211yescharacteristic
43C2×#3716C2211yescharacteristic, complemented
44#63648C2211yescharacteristic, complemented
45#63644C2211yescharacteristic, complemented
46#63643C2211yescharacteristic, complemented
47C3×#830C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic, complemented
51C3×#821C2211yescharacteristic, complemented
52C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
53C3×#815C2211yescharacteristic, complemented
54C3×Dic3⋊C8C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63575C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63564C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic, complemented
61D4×#67—31no—
62D4×D12—31no—
63#5541—31no—
64#5513—31no—
65C3×#435—31no—
66C2×C3×#102—31no—
67#5218—31no—
68#5134—31no—
69#5131—31no—
70#5114—31no—
71#5114—31no—
72#5114—61no—
73C2×#821D311yescharacteristic, complemented
74#5111D311yescharacteristic, complemented
75#4967—31no—
76#4848—31no—
77#4847—31no—
78#4780—31no—
79#4779—31no—
80#4776—31no—
81#4770—31no—
82#4764—31no—
83#4763—31no—
84#4762—31no—
85#4757—31no—
86#4737—31no—
87#4736—31no—
88#4731—31no—
89#4731—31no—
90#4713—31no—
91#4710—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C22×C32×C4C2311yescharacteristic
95C2×#638—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×#67D411yescharacteristic
99C22×C3×Dic3—21no—
100C2×C3×D12—22no—
101C2×C3×D12—21no—
102C2×C3×D12—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106D3×#67—44no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#626—21no—
110C2×#625—21no—
111C2×D3×Dic3—21no—
112D3×D12—22no—
113D3×D12—41no—
114C2×C32×C8—41no—
115C2×C32×C8C2311yescharacteristic
116C2×C32×C8C2311yescharacteristic
117#3757—21no—
118#3752—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121#3750—21no—
122#3744—41no—
123C3×#217D411yescharacteristic
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4D411yescharacteristic
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×ΓL(1,𝔽25)—41no—
133#3724—21no—
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142Dic32—21no—
143#3716—22no—
144#3716—41no—
145#3310—91noSylow
146C22×C3×D4—31no—
147C22×#67—61no—
148C2×D3×D4—31no—
149C2×D3×D4—61no—
150C22×D12—31no—
151C22×D12C2×D311yescharacteristic
152C2×C3×M16—31no—
153C22×C3×C8—21no—
154C22×C3×C8C2×D311yescharacteristic, complemented
155C22×C3×C8C2×D311yescharacteristic, complemented
156C3×C4×D4—31no—
157C2×C3×C4⋊C4—31no—
158#953—61no—
159#940—31no—
160#939—61no—
161#938—31no—
162#937—61no—
163#935—61no—
164D4×Dic3—31no—
165C2×#214—31no—
166C2×#214—31no—
167#930—31no—
168#930—31no—
169#930—31no—
170#930—61no—
171#929—61no—
172C4×#67C2×D311yescharacteristic
173#926—31no—
174#926—61no—
175C2×C4⋊Dic3C2×D311yescharacteristic, complemented
176#924—31no—
177#924—31no—
178#924—31no—
179#924—61no—
180C2×#204—31no—
181C2×#204—31no—
182C2×#204—31no—
183C2×#204—31no—
184C2×#204—61no—
185C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
186#898—61no—
187#897—31no—
188#895—61no—
189#892—31no—
190#890—31no—
191#889—61no—
192#889—61no—
193#887—31no—
194#882—61no—
195#882—61no—
196#879—61no—
197#877—61no—
198#874—31no—
199C4×D12—31no—
200#870—31no—
201C4×Dic6—31no—
202C3×C4⋊C8—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×C22⋊C8—31no—
208C3×C22⋊C8—31no—
209C3×#97—31no—
210#832—31no—
211#832—31no—
212#830C2×D311yescharacteristic, complemented
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—61no—
220#821C2×D311yescharacteristic
221#821C2×D311yescharacteristic
222#821C2×D311yescharacteristic, complemented
223#821C2×D311yescharacteristic, complemented
224(C2×D3)⋊C8C2×D311yescharacteristic, complemented
225#818—31no—
226#818—31no—
227#817—31no—
228#817—31no—
229#817—61no—
230#816—31no—
231#816—31no—
232#816—61no—
233#815C2×D311yescharacteristic, complemented
234Dic3⋊C8C2×D311yescharacteristic, complemented
235#809—31no—
236#809—31no—
237#807—31no—
238#807—31no—
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—42no—
244C22×C3×D3—42no—
245C22×C3×D3—81no—
246C22×C3×D3C2×D411yescharacteristic
247C2×D32—42no—
248C2×D32—42no—
249C2×D32—81no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254#638—42no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3—21no—
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)—21no—
260#634—21no—
261#634—21no—
262C3×#67—22no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—42no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C3×D12—21no—
270C3×D12—21no—
271C3×D12—21no—
272C3×D12—42no—
273C3×D12#4112yes—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276#626—42no—
277#626—42no—
278#626—81no—
279#625—42no—
280D3×Dic3—42no—
281C32×C8—21no—
282C32×C8—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#552—91no—
286D42—91no—
287#490—91no—
288#482—91no—
289#480—91no—
290#478—91no—
291#468—91no—
292#465—91no—
293#460—91no—
294#450—91no—
295#450—91no—
296#440—91no—
297#435—31no—
298#418—91no—
299C2×#102—31no—
300C24×C3—61no—
301C23×D3—21no—
302C23×D3—61no—
303C23×D3—61no—
304C2×C3×D4—31no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—62no—
308C2×C3×D4—61no—
309C2×C3×D4—121no—
310C22×C3×C4—21no—
311C22×C3×C4—31no—
312C22×C3×C4—61no—
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—121no—
323C2×#67—124no—
324C2×#67D1211yescharacteristic
325C22×Dic3—21no—
326C22×Dic3—61no—
327D3×D4—62no—
328D3×D4—121no—
329D3×D4—124no—
330C2×D12—22no—
331C2×D12—21no—
332C2×D12—31no—
333C2×D12—31no—
334C2×D12—41no—
335C2×D12—61no—
336C2×D12—62no—
337C2×D12—61no—
338C2×D12—61no—
339C2×D12—61no—
340C2×D12—121no—
341C2×D12C22×D311yescharacteristic
342C2×D12C22×D311yescharacteristic
343C2×C4×D3—61no—
344C2×C4×D3C22×D311yescharacteristic
345C2×Dic6—31no—
346C2×Dic6—31no—
347C2×Dic6—61no—
348C3×M16—121no—
349C2×C3×C8—21no—
350C2×C3×C8—21no—
351C2×C3×C8—31no—
352C2×C3×C8—31no—
353C2×C3×C8—41no—
354C2×C3×C8—41no—
355C2×C3×C8—42no—
356C2×C3×C8C22×D311yescharacteristic
357C2×C3×C8C22×D311yescharacteristic
358C2×C3×C8C22×D311yescharacteristic
359C2×C3×C8C22×D311yescharacteristic
360C3×C4⋊C4—31no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—61no—
364C3×C22⋊C4—31no—
365C3×C22⋊C4—31no—
366C3×C42—31no—
367#217—61no—
368#217—61no—
369#217—61no—
370#217—61no—
371#217—61no—
372#217—61no—
373#217—121no—
374#217D1211yescharacteristic
375#214—62no—
376#214—121no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—121no—
384(C2×D3)⋊C4D1211yescharacteristic
385C4⋊Dic3—21no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3C22×D311yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—121no—
405Dic3⋊C4D1211yescharacteristic
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C4×Dic3—61no—
410C4×Dic3C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412C2×C3⋊C8C22×D311yescharacteristic
413#204—62no—
414#204—121no—
415#204—121no—
416#204—122no—
417#204—121no—
418ΓL(1,𝔽25)—41no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32AGL(1,ℤ/8)12yes—
422C22×C32C22×D411yescharacteristic
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C2×C3×D3—22no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—84no—
436D32—84no—
437C32×C4—21no—
438C32×C4C2×#4111yescharacteristic
439C32×C4H(5,𝔽2)11yescharacteristic
440C3⋊Dic3—41no—
441C3⋊Dic3—41no—
442C3⋊Dic3—41no—
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C22×D4—31no—
449C22×D4—91no—
450C22×D4—181no—
451C2×SD16—91no—
452C2×SD16—91no—
453C2×SD16—91no—
454C2×M16—31no—
455C22×C8D3211yescharacteristic, complemented
456#127—91no—
457#126—181no—
458#125—91no—
459#125—181no—
460#123—181no—
461C22⋊Q8—91no—
462C22⋊Q8—91no—
463#121—91no—
464#121—91no—
465#121—181no—
466#120—181no—
467#120—181no—
468C4×Q8—91no—
469C4×D4—31no—
470C4×D4—91no—
471#117—91no—
472#117—181no—
473C2×C4⋊C4—31no—
474#107—91no—
475#107—91no—
476#106—91no—
477C4⋊C8—31no—
478#103—91no—
479#102—31no—
480#102—31no—
481#102—31no—
482#102—31no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102—91no—
488C22⋊C8—31no—
489C22⋊C8—31no—
490#97—31no—
491C23×C3—21no—
492C23×C3—31no—
493C23×C3—61no—
494C23×C3—61no—
495C23×C3—122no—
496C23×C3—122no—
497C23×C3—241no—
498C23×C3C2×D1211yescharacteristic
499C23×C3D3×D411yescharacteristic
500C22×D3—21no—
501C22×D3—21no—
502C22×D3—42no—
503C22×D3—42no—
504C22×D3—61no—
505C22×D3—61no—
506C22×D3—81no—
507C22×D3—121no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—122no—
511C22×D3—122no—
512C22×D3—241no—
513C22×D3—241no—
514C22×D3C2×D1211yescharacteristic
515C3×D4—32no—
516C3×D4—62no—
517C3×D4—61no—
518C3×D4—61no—
519C3×D4—61no—
520C3×D4—122no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—31no—
528C2×C3×C4—31no—
529C2×C3×C4—31no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—122no—
537C2×C3×C4C2×D1211yescharacteristic
538C2×C3×C4D3×D411yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540C2×C3×C4C23×D311yescharacteristic
541#67—22no—
542#67—122no—
543#67—122no—
544#67—122no—
545#67—122no—
546#67—122no—
547#67—122no—
548#67—242no—
549#67—241no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—42no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—121no—
560C2×Dic3—121no—
561C2×Dic3—121no—
562C2×Dic3—122no—
563C2×Dic3C2×D1211yescharacteristic
564C2×Dic3C2×D1211yescharacteristic
565C2×Dic3C2×D1211yescharacteristic
566D12—21no—
567D12—21no—
568D12—21no—
569D12—42no—
570D12—61no—
571D12—61no—
572D12—61no—
573D12—61no—
574D12—121no—
575D12—121no—
576D12—122no—
577D12—122no—
578D12—241no—
579D12#23512yes—
580C4×D3—21no—
581C4×D3—21no—
582C4×D3—122no—
583Dic6—61no—
584Dic6—61no—
585Dic6—61no—
586Dic6—61no—
587Dic6—121no—
588Dic6—121no—
589C3×C8—22no—
590C3×C8—21no—
591C3×C8—21no—
592C3×C8—21no—
593C3×C8—21no—
594C3×C8—41no—
595C3×C8—61no—
596C3×C8—61no—
597C3⋊C8—21no—
598C3⋊C8—21no—
599C2×C32—22no—
600C2×C32#54611yescharacteristic
601C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
602C2×C32#57711yescharacteristic
603C3⋊D3—81no—
604C3×D3—41no—
605C3×D3—42no—
606C3×D3—81no—
607C24—61no—
608C24—181no—
609C2×Q8—91no—
610C2×D4—31no—
611C2×D4—31no—
612C2×D4—31no—
613C2×D4—62no—
614C2×D4—61no—
615C2×D4—91no—
616C2×D4—121no—
617C2×D4—181no—
618C2×D4—181no—
619C2×D4—181no—
620C2×D4—182no—
621C2×D4—181no—
622C2×D4—181no—
623C2×D4—361no—
624C2×D4—364no—
625C22×C4—31no—
626C22×C4—61no—
627C22×C4—181no—
628C22×C4C2×D3211yescharacteristic
629SD16—182no—
630SD16—361no—
631SD16—361no—
632M16—121no—
633C2×C8—31no—
634C2×C8—31no—
635C2×C8—41no—
636C2×C8C2×D3211yescharacteristic
637C2×C8C2×D3211yescharacteristic
638C4⋊C4—31no—
639C4⋊C4—31no—
640C4⋊C4—31no—
641C4⋊C4—61no—
642C4⋊C4—91no—
643C4⋊C4—91no—
644C4⋊C4—181no—
645C4⋊C4—181no—
646C4⋊C4—181no—
647C4⋊C4—181no—
648C4⋊C4—181no—
649C22⋊C4—31no—
650C22⋊C4—31no—
651C22⋊C4—181no—
652C22⋊C4—181no—
653C22⋊C4—181no—
654C22⋊C4—181no—
655C22⋊C4—181no—
656C22⋊C4—181no—
657C42—31no—
658C42—181no—
659C42—181no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—22no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—61no—
669C22×C3—61no—
670C22×C3—61no—
671C22×C3—62no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3—121no—
676C22×C3—121no—
677C22×C3—244no—
678C22×C3#90812yes—
679C22×C3#91112yes—
680C22×C3C22×D1211yescharacteristic
681C22×C3C2×D3×D411yescharacteristic
682C2×D3—22no—
683C2×D3—21no—
684C2×D3—21no—
685C2×D3—21no—
686C2×D3—41no—
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—84no—
692C2×D3—121no—
693C2×D3—121no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—241no—
699C2×D3—241no—
700C2×D3—241no—
701C2×D3—244no—
702C2×D3—244no—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—41no—
708C3×C4—61no—
709C3×C4—61no—
710C3×C4—61no—
711C3×C4—121no—
712C3×C4—121no—
713C3×C4C2×#23511yescharacteristic
714C3×C4#100411yescharacteristic
715C3×C4#100411yescharacteristic
716C3×C4D3×#4111yescharacteristic
717Dic3—21no—
718Dic3—21no—
719Dic3—21no—
720Dic3—41no—
721Dic3—41no—
722Dic3—121no—
723Dic3—121no—
724Dic3—121no—
725Dic3—121no—
726Dic3—121no—
727Dic3—121no—
728Dic3—241no—
729Dic3—241no—
730Dic3—241no—
731C32#331011yescharacteristic, complemented, Sylow
732C23—31no—
733C23—61no—
734C23—61no—
735C23—122no—
736C23—122no—
737C23—181no—
738C23—241no—
739C23—362no—
740C23—362no—
741C23—721no—
742C23D3×D1211yescharacteristic
743Q8—181no—
744Q8—181no—
745D4—32no—
746D4—62no—
747D4—61no—
748D4—61no—
749D4—61no—
750D4—122no—
751D4—181no—
752D4—181no—
753D4—362no—
754D4—362no—
755D4—362no—
756D4—362no—
757D4—721no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—31no—
761C2×C4—31no—
762C2×C4—31no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—122no—
768C2×C4—181no—
769C2×C4—181no—
770C2×C4—181no—
771C2×C4—362no—
772C2×C4D3×D1211yescharacteristic
773C2×C4C22×D3211yescharacteristic
774C8—21no—
775C8—21no—
776C8—61no—
777C8—61no—
778C2×C3—22no—
779C2×C3—22no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—42no—
784C2×C3—122no—
785C2×C3—121no—
786C2×C3—241no—
787C2×C3#549011yescharacteristic
788C2×C3#555411yescharacteristic
789C2×C3C2×#90811yescharacteristic
790C2×C3#575111yescharacteristic
791C2×C3C2×#91111yescharacteristic
792C2×C3#576211yescharacteristic
793D3—41no—
794D3—42no—
795D3—81no—
796D3—241no—
797D3—241no—
798D3—481no—
799C22—21no—
800C22—21no—
801C22—61no—
802C22—62no—
803C22—61no—
804C22—61no—
805C22—121no—
806C22—121no—
807C22—121no—
808C22—121no—
809C22—121no—
810C22—244no—
811C22—361no—
812C22—361no—
813C22—361no—
814C22—724no—
815C22#6379512yes—
816C22C2×D3×D1211yescharacteristic
817C4—21no—
818C4—61no—
819C4—61no—
820C4—61no—
821C4—121no—
822C4—121no—
823C4—361no—
824C4—361no—
825C4—361no—
826C4D3×#23511yescharacteristic
827C4#6433011yescharacteristic
828C3—21no—
829C3#7876211yescharacteristic, complemented
830C3#7950111yescharacteristic, complemented
831C2—22no—
832C2—121no—
833C2—122no—
834C2—241no—
835C2—721no—
836C2C2×#6379511yescharacteristic
837C2#1059467711yescharacteristic
838C2#1059507311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radicalD12×#67C2
hypercenterC22×C8D32
hypocenterC32#3310
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
2. #10594849C2semidirect
3. #10592813C2semidirect
4. C2×C3×#821C2semidirect
5. C3×#5111C2semidirect
6. #10591172C2semidirect
7. #10591133C2semidirect
8. #10590946C2semidirect
9. #10590939C2semidirect
10. #10590882C2semidirect
11. #10590879C2semidirect
12. #10590837C2semidirect
13. #10590828C2semidirect
14. #10590772C2semidirect
15. #10590747C2semidirect
21. C22×C32×C8C22semidirect
23. #64133C22semidirect
24. C2×#3744C22semidirect
26. C2×C3×C4⋊Dic3C22semidirect
27. C2×C3×ΓL(1,𝔽25)C22semidirect
36. #63869C22semidirect
38. #63857C22semidirect
40. #63844C22semidirect
41. #63841C22semidirect
43. C2×#3716C22semidirect
44. #63648C22semidirect
45. #63644C22semidirect
46. #63643C22semidirect
47. C3×#830C22semidirect
50. C3×#821C22semidirect
51. C3×#821C22semidirect
52. C3×(C2×D3)⋊C8C22semidirect
53. C3×#815C22semidirect
54. C3×Dic3⋊C8C22semidirect
55. #63575C22semidirect
56. #63575C22semidirect
57. #63564C22semidirect
58. #63564C22semidirect
60. #63563C22semidirect
73. C2×#821D3semidirect
74. #5111D3semidirect
154. C22×C3×C8C2×D3semidirect
155. C22×C3×C8C2×D3semidirect
175. C2×C4⋊Dic3C2×D3semidirect
185. C2×ΓL(1,𝔽25)C2×D3semidirect
212. #830C2×D3semidirect
222. #821C2×D3semidirect
223. #821C2×D3semidirect
224. (C2×D3)⋊C8C2×D3semidirect
233. #815C2×D3semidirect
234. Dic3⋊C8C2×D3semidirect
455. C22×C8D32semidirect
731. C32#3310semidirect
829. C3#78762semidirect
830. C3#79501semidirect

Maximal subgroups

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

subgroupindex
D12×#672
#105948492
#105928132
C2×C3×#8212
C3×#51112
#105911722
#105911332
#105909462
#105909392
#105908822
#105908792
#105908372
#105908282
#105907722
#105907472
#795013
#787623