Finite Group Databasebeta

← #11889128

Subgroups — #11889128

Order 1152.

964 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D122C211yesmaximal, characteristic
2#10593920C211yesmaximal, characteristic, complemented
3#10592547C211yesmaximal, characteristic, complemented
4C3×#4847C211yesmaximal, characteristic, complemented
5C3×#4836C211yesmaximal, characteristic, complemented
6#10590946C211yesmaximal, characteristic, complemented
7#10590946C211yesmaximal, characteristic, complemented
8#10590939C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590838C211yesmaximal, characteristic, complemented
11#10590830C211yesmaximal, characteristic, complemented
12#10590704C211yesmaximal, characteristic, complemented
13#10590679C211yesmaximal, characteristic, complemented
14#10590360C211yesmaximal, characteristic, complemented
15#10590282C211yesmaximal, characteristic, complemented
16#81189—31nomaximal
17#79501—31nomaximal
18C2×D3×D12—21no—
19C2×D3×D12C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C2×#3744C2211yescharacteristic, complemented
22C2×#3744C2211yescharacteristic, complemented
23#64083C2211yescharacteristic
24C4×#634C2211yescharacteristic, complemented
25C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
26C2×C3×D3×C8C2211yescharacteristic, complemented
27C3×C4×D12C2211yescharacteristic
28C3×C4×D12C2211yescharacteristic
29C3×#870C2211yescharacteristic, complemented
30#63923—21no—
31#63923—21no—
32#63909—21no—
33#63909C2211yescharacteristic
34#63909C2211yescharacteristic
35D3×C4⋊Dic3C2211yescharacteristic, complemented
36#63884—21no—
37#63878—21no—
38#63862—21no—
39#63857C2211yescharacteristic, complemented
40#63857C2211yescharacteristic, complemented
41#63846—21no—
42#63841C2211yescharacteristic, complemented
43C2×#3716C2211yescharacteristic
44C32×C4⋊C8C2211yescharacteristic, complemented
45#63648C2211yescharacteristic, complemented
46#63648C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
50C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C3×#818C2211yescharacteristic, complemented
52C3×#817C2211yescharacteristic, complemented
53C3×#803C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63564C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63563C2211yescharacteristic
61#5694—31no—
62D4×D12—31no—
63D4×D12—31no—
64#5541—31no—
65C3×#478—31no—
66C3×#435—31no—
67#5134—31no—
68#5131—31no—
69#5114—31no—
70C2×#821—31no—
71#5067—31no—
72#5018—31no—
73#4886—31no—
74#4882—31no—
75#4866—31no—
76#4864—31no—
77#4848—31no—
78#4848—31no—
79#4848—61no—
80#4847D311yescharacteristic, complemented
81#4836D311yescharacteristic, complemented
82#4776—31no—
83#4776—31no—
84#4770—31no—
85D3×#102—31no—
86#4737—31no—
87#4736—31no—
88#4731—31no—
89#4731—31no—
90#4713—31no—
91#4710—31no—
92C22×D32—21no—
93C22×D32—21no—
94C2×C4⋊(C3⋊D3)—21no—
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C2×C3×D12D411yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×#626—21no—
105C2×#626—21no—
106C2×#626—21no—
107C2×#626—21no—
108C2×D3×Dic3—21no—
109D3×D12—22no—
110D3×D12—22no—
111D3×D12—41no—
112D3×D12—41no—
113D3×D12—44no—
114C2×C32×C8C2311yescharacteristic
115C2×C32×C8C2311yescharacteristic
116C32×C42C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119C4×C3⋊Dic3—21no—
120#3744—41no—
121#3744—41no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×C4⋊Dic3D411yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C3×ΓL(1,𝔽25)—41no—
134C3×D3×C8—41no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138#3722—21no—
139#3722—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143Dic32—21no—
144#3716—22no—
145#3310—91noSylow
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×D3×D4—61no—
149C22×D12—31no—
150C22×D12—31no—
151C22×D12—61no—
152C2×C3×M16—31no—
153C22×C3×C8—31no—
154C3×#125—31no—
155C3×C4×D4—31no—
156C3×C4×D4—31no—
157#935—61no—
158C2×#214—31no—
159#930—31no—
160#930—31no—
161#930—61no—
162#926—31no—
163C2×C4⋊Dic3—31no—
164#924—31no—
165#924—31no—
166C2×#204—31no—
167C2×#204—31no—
168C2×#204—31no—
169C2×#204—31no—
170C2×#204—31no—
171C2×#204—61no—
172C2×#204—61no—
173C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
174C2×D3×C8C2×D311yescharacteristic, complemented
175#898—61no—
176#897—31no—
177#897—31no—
178#895—31no—
179#895—31no—
180#895—61no—
181#894—61no—
182#892—31no—
183#892—61no—
184D3×C4⋊C4—31no—
185#890—61no—
186#889—61no—
187#882—61no—
188#882—61no—
189#882—61no—
190#882—61no—
191#879—61no—
192#877—61no—
193#874—31no—
194#874—31no—
195#874—61no—
196C4×D12C2×D311yescharacteristic
197C4×D12C2×D311yescharacteristic
198#870C2×D311yescharacteristic, complemented
199C4×Dic6—31no—
200C4×Dic6—31no—
201C4×Dic6—61no—
202C3×#107—31no—
203C3×#106—31no—
204C3×C4⋊C8—21no—
205C3×C4⋊C8C2×D311yescharacteristic, complemented
206C3×C4⋊C8C2×D311yescharacteristic, complemented
207C3×#102—31no—
208C3×#102—31no—
209C3×C22⋊C8—31no—
210C3×C22⋊C8—31no—
211C3×#97—31no—
212#832—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—61no—
223#821—61no—
224#821C2×D311yescharacteristic
225#821C2×D311yescharacteristic
226(C2×D3)⋊C8C2×D311yescharacteristic, complemented
227(C2×D3)⋊C8C2×D311yescharacteristic, complemented
228#818—31no—
229#818C2×D311yescharacteristic, complemented
230#817C2×D311yescharacteristic, complemented
231#816—31no—
232#810—31no—
233#809—31no—
234#809—31no—
235#809—31no—
236#809—31no—
237#807—31no—
238#803C2×D311yescharacteristic, complemented
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3C2×D411yescharacteristic
243C22×C3×D3C2×D411yescharacteristic
244C2×D32—42no—
245C2×D32—42no—
246C2×D32—42no—
247C2×D32—42no—
248C2×D32—81no—
249C2×D32—81no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)—21no—
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)—42no—
260C4⋊(C3⋊D3)—81no—
261#634—21no—
262#634—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×D12—22no—
269C3×D12—21no—
270C3×D12#4112yes—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×C4×D3—21no—
275C3×C4×D3—42no—
276#626—42no—
277#626—42no—
278#626—42no—
279#626—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—31no—
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—91no—
300C23×D3—61no—
301C23×D3—61no—
302C23×D3—61no—
303C23×D3—61no—
304C2×C3×D4—31no—
305C2×C3×D4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C22×Dic3—61no—
314D3×D4—62no—
315D3×D4—62no—
316D3×D4—121no—
317D3×D4—121no—
318D3×D4—124no—
319C2×D12—31no—
320C2×D12—31no—
321C2×D12—31no—
322C2×D12—31no—
323C2×D12—61no—
324C2×D12—61no—
325C2×D12—62no—
326C2×D12—62no—
327C2×D12—61no—
328C2×D12—61no—
329C2×D12—61no—
330C2×D12—61no—
331C2×D12—61no—
332C2×D12—61no—
333C2×D12—61no—
334C2×D12—61no—
335C2×D12—121no—
336C2×D12—121no—
337C2×D12—121no—
338C2×D12—121no—
339C2×D12—124no—
340C2×D12D1211yescharacteristic
341C2×D12C22×D311yescharacteristic
342C2×C4×D3—21no—
343C2×C4×D3—61no—
344C2×C4×D3C22×D311yescharacteristic
345C2×C4×D3C22×D311yescharacteristic
346C2×Dic6—31no—
347C2×Dic6—31no—
348C2×Dic6—61no—
349C3×M16—121no—
350C2×C3×C8—21no—
351C2×C3×C8—21no—
352C2×C3×C8—31no—
353C2×C3×C8—31no—
354C2×C3×C8—121no—
355C2×C3×C8C22×D311yescharacteristic
356C2×C3×C8C22×D311yescharacteristic
357C2×C3×C8C22×D311yescharacteristic
358C2×C3×C8C22×D311yescharacteristic
359C3×C4⋊C4—31no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C22⋊C4—31no—
366C3×C22⋊C4—31no—
367C3×C22⋊C4—61no—
368C3×C42—21no—
369C3×C42C22×D311yescharacteristic
370C3×C42C22×D311yescharacteristic
371#217—61no—
372#217—61no—
373#217—61no—
374#214—62no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—61no—
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)⋊C4D1211yescharacteristic
384(C2×D3)⋊C4D1211yescharacteristic
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3D1211yescharacteristic
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—121no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—121no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410#204—62no—
411#204—121no—
412#204—121no—
413#204—121no—
414#204—121no—
415#204—122no—
416#204—122no—
417ΓL(1,𝔽25)—41no—
418D3×C8—41no—
419C22×C32C22×D411yescharacteristic
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—22no—
429C2×C3×D3—21no—
430C2×C3×D3—21no—
431C2×C3×D3—21no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3AGL(1,ℤ/8)12yes—
435D32—84no—
436D32—84no—
437C32×C4—21no—
438C32×C4—21no—
439C32×C4C2×#4111yescharacteristic
440C32×C4H(5,𝔽2)11yescharacteristic
441C3⋊Dic3—41no—
442C3⋊Dic3—41no—
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C22×D4—91no—
449C22×D4—91no—
450C22×D4—181no—
451C2×SD16—91no—
452C2×SD16—91no—
453C2×SD16—91no—
454C2×M16—31no—
455C22×C8—31no—
456#127—91no—
457#126—181no—
458#125—31no—
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—31no—
471#117—91no—
472#117—181no—
473C2×C4⋊C4—91no—
474#107—31no—
475#107—91no—
476#106—31no—
477C4⋊C8D3211yescharacteristic, complemented
478#103—91no—
479#102—31no—
480#102—31no—
481#102—91no—
482#102—91no—
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—31no—
492C23×C3—31no—
493C23×C3—61no—
494C22×D3—21no—
495C22×D3—61no—
496C22×D3—61no—
497C22×D3—61no—
498C22×D3—61no—
499C22×D3—121no—
500C22×D3—121no—
501C22×D3—122no—
502C22×D3—122no—
503C22×D3—122no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3—241no—
510C22×D3—241no—
511C22×D3—241no—
512C22×D3—241no—
513C22×D3C2×D1211yescharacteristic
514C22×D3C2×D1211yescharacteristic
515C3×D4—32no—
516C3×D4—62no—
517C3×D4—61no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—122no—
531C2×C3×C4C2×D1211yescharacteristic
532C2×C3×C4C2×D1211yescharacteristic
533C2×C3×C4D3×D411yescharacteristic
534C2×C3×C4D3×D411yescharacteristic
535C2×C3×C4C23×D311yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537#67—122no—
538#67—122no—
539#67—122no—
540#67—122no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—121no—
549C2×Dic3—121no—
550C2×Dic3—122no—
551C2×Dic3C2×D1211yescharacteristic
552C2×Dic3C2×D1211yescharacteristic
553D12—22no—
554D12—21no—
555D12—61no—
556D12—61no—
557D12—61no—
558D12—61no—
559D12—61no—
560D12—61no—
561D12—61no—
562D12—61no—
563D12—121no—
564D12—121no—
565D12—121no—
566D12—121no—
567D12—122no—
568D12—122no—
569D12—122no—
570D12—122no—
571D12—122no—
572D12—122no—
573D12—242no—
574D12—241no—
575D12—241no—
576D12—242no—
577D12#23912yes—
578C4×D3—21no—
579C4×D3—21no—
580C4×D3—21no—
581C4×D3—21no—
582C4×D3—42no—
583C4×D3—122no—
584Dic6—62no—
585Dic6—61no—
586Dic6—61no—
587Dic6—61no—
588Dic6—61no—
589Dic6—121no—
590C3×C8—21no—
591C3×C8—21no—
592C3×C8—21no—
593C3×C8—21no—
594C3×C8—41no—
595C3×C8—41no—
596C3×C8—61no—
597C3×C8—61no—
598C3⋊C8—21no—
599C3⋊C8—21no—
600C2×C32#54611yescharacteristic
601C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
602C2×C32#57711yescharacteristic
603C3⋊D3—81no—
604C3⋊D3—81no—
605C3×D3—22no—
606C3×D3—41no—
607C3×D3—42no—
608C24—181no—
609C24—181no—
610C2×Q8—91no—
611C2×D4—31no—
612C2×D4—31no—
613C2×D4—91no—
614C2×D4—91no—
615C2×D4—181no—
616C2×D4—181no—
617C2×D4—182no—
618C2×D4—182no—
619C2×D4—181no—
620C2×D4—181no—
621C2×D4—181no—
622C2×D4—181no—
623C2×D4—361no—
624C2×D4—361no—
625C2×D4—364no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—61no—
629C22×C4—181no—
630SD16—182no—
631SD16—361no—
632SD16—361no—
633M16—121no—
634C2×C8—31no—
635C2×C8—31no—
636C2×C8—121no—
637C2×C8C2×D3211yescharacteristic
638C2×C8C2×D3211yescharacteristic
639C4⋊C4—31no—
640C4⋊C4—31no—
641C4⋊C4—31no—
642C4⋊C4—31no—
643C4⋊C4—61no—
644C4⋊C4—61no—
645C4⋊C4—91no—
646C4⋊C4—181no—
647C4⋊C4—181no—
648C4⋊C4—181no—
649C4⋊C4—181no—
650C22⋊C4—31no—
651C22⋊C4—31no—
652C22⋊C4—61no—
653C22⋊C4—181no—
654C22⋊C4—181no—
655C22⋊C4—181no—
656C22⋊C4—181no—
657C22⋊C4—181no—
658C42—181no—
659C42—181no—
660C42C2×D3211yescharacteristic
661C22×C3—21no—
662C22×C3—32no—
663C22×C3—61no—
664C22×C3—61no—
665C22×C3—61no—
666C22×C3—61no—
667C22×C3—62no—
668C22×C3—61no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3C22×D1211yescharacteristic
672C22×C3C2×D3×D411yescharacteristic
673C2×D3—21no—
674C2×D3—21no—
675C2×D3—21no—
676C2×D3—21no—
677C2×D3—21no—
678C2×D3—22no—
679C2×D3—41no—
680C2×D3—41no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—121no—
689C2×D3—121no—
690C2×D3—121no—
691C2×D3—121no—
692C2×D3—121no—
693C2×D3—241no—
694C2×D3—241no—
695C2×D3—241no—
696C2×D3—241no—
697C2×D3—241no—
698C2×D3—241no—
699C2×D3—244no—
700C2×D3—244no—
701C2×D3—244no—
702C2×D3—244no—
703C2×D3#90812yes—
704C3×C4—22no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—21no—
710C3×C4—21no—
711C3×C4—41no—
712C3×C4—61no—
713C3×C4—61no—
714C3×C4—121no—
715C3×C4—121no—
716C3×C4—121no—
717C3×C4#100411yescharacteristic
718C3×C4C2×#23911yescharacteristic
719C3×C4D3×#4111yescharacteristic
720C3×C4#100911yescharacteristic
721Dic3—21no—
722Dic3—21no—
723Dic3—41no—
724Dic3—41no—
725Dic3—41no—
726Dic3—122no—
727Dic3—121no—
728Dic3—121no—
729Dic3—121no—
730Dic3—121no—
731Dic3—241no—
732C32#331011yescharacteristic, complemented, Sylow
733C23—31no—
734C23—31no—
735C23—61no—
736C23—181no—
737C23—181no—
738C23—362no—
739C23—362no—
740C23—362no—
741C23—362no—
742C23—721no—
743C23—721no—
744Q8—181no—
745Q8—181no—
746D4—32no—
747D4—62no—
748D4—61no—
749D4—181no—
750D4—181no—
751D4—181no—
752D4—181no—
753D4—362no—
754D4—362no—
755D4—362no—
756D4—362no—
757D4—362no—
758D4—721no—
759C2×C4—31no—
760C2×C4—31no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—122no—
769C2×C4—181no—
770C2×C4—181no—
771C2×C4—362no—
772C2×C4D3×D1211yescharacteristic
773C2×C4D3×D1211yescharacteristic
774C2×C4C22×D3211yescharacteristic
775C8—21no—
776C8—21no—
777C8—61no—
778C8—61no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—62no—
783C2×C3—121no—
784C2×C3—122no—
785C2×C3#555411yescharacteristic
786C2×C3#563011yescharacteristic
787C2×C3C2×#90811yescharacteristic
788C2×C3#575111yescharacteristic
789C2×C3#577011yescharacteristic
790C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
791D3—22no—
792D3—42no—
793D3—41no—
794D3—241no—
795D3—241no—
796D3—241no—
797D3—241no—
798D3—481no—
799D3—481no—
800C22—32no—
801C22—61no—
802C22—61no—
803C22—61no—
804C22—62no—
805C22—61no—
806C22—61no—
807C22—121no—
808C22—121no—
809C22—361no—
810C22—361no—
811C22—361no—
812C22—361no—
813C22—361no—
814C22—361no—
815C22—724no—
816C22—724no—
817C22C2×D3×D1211yescharacteristic
818C4—21no—
819C4—21no—
820C4—61no—
821C4—61no—
822C4—121no—
823C4—121no—
824C4—121no—
825C4—361no—
826C4—361no—
827C4#6431411yescharacteristic
828C4D3×#23911yescharacteristic
829C3—21no—
830C3#7950111yescharacteristic, complemented
831C3#8118911yescharacteristic, complemented
832C2—62no—
833C2—121no—
834C2—122no—
835C2—721no—
836C2—721no—
837C2#1059462911yescharacteristic
838C2#1059467911yescharacteristic
839C2D3×#90811yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalD122C2
hypercenterC4⋊C8D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593920C2semidirect
3. #10592547C2semidirect
4. C3×#4847C2semidirect
5. C3×#4836C2semidirect
6. #10590946C2semidirect
7. #10590946C2semidirect
8. #10590939C2semidirect
9. D3×#821C2semidirect
10. #10590838C2semidirect
11. #10590830C2semidirect
12. #10590704C2semidirect
13. #10590679C2semidirect
14. #10590360C2semidirect
15. #10590282C2semidirect
21. C2×#3744C22semidirect
22. C2×#3744C22semidirect
24. C4×#634C22semidirect
25. C2×C3×ΓL(1,𝔽25)C22semidirect
26. C2×C3×D3×C8C22semidirect
29. C3×#870C22semidirect
35. D3×C4⋊Dic3C22semidirect
39. #63857C22semidirect
40. #63857C22semidirect
42. #63841C22semidirect
44. C32×C4⋊C8C22semidirect
45. #63648C22semidirect
46. #63648C22semidirect
49. C3×(C2×D3)⋊C8C22semidirect
50. C3×(C2×D3)⋊C8C22semidirect
51. C3×#818C22semidirect
52. C3×#817C22semidirect
53. C3×#803C22semidirect
54. #63575C22semidirect
55. #63567C22semidirect
56. #63564C22semidirect
57. #63564C22semidirect
58. #63564C22semidirect
59. #63564C22semidirect
80. #4847D3semidirect
81. #4836D3semidirect
173. C2×ΓL(1,𝔽25)C2×D3semidirect
174. C2×D3×C8C2×D3semidirect
198. #870C2×D3semidirect
205. C3×C4⋊C8C2×D3semidirect
206. C3×C4⋊C8C2×D3semidirect
226. (C2×D3)⋊C8C2×D3semidirect
227. (C2×D3)⋊C8C2×D3semidirect
229. #818C2×D3semidirect
230. #817C2×D3semidirect
238. #803C2×D3semidirect
477. C4⋊C8D32semidirect
732. C32#3310semidirect
830. C3#79501semidirect
831. C3#81189semidirect

Maximal subgroups

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

subgroupindex
D1222
#105939202
#105925472
C3×#48472
C3×#48362
#105909462
#105909392
D3×#8212
#105908382
#105908302
#105907042
#105906792
#105903602
#105902822
#811893
#795013