Finite Group Databasebeta

← #11889124

Subgroups — #11889124

Order 1152.

1007 conjugacy classes of subgroups.

The subgroup lattice has 861 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596165C211yesmaximal, characteristic, complemented
2#10594004C211yesmaximal, characteristic
3C3×#5067C211yesmaximal, characteristic, complemented
4C3×#5066C211yesmaximal, characteristic, complemented
5#10590597C211yesmaximal, characteristic, complemented
6#10590597C211yesmaximal, characteristic, complemented
7#10590594C211yesmaximal, characteristic, complemented
8#10590593C211yesmaximal, characteristic, complemented
9#10590513C211yesmaximal, characteristic, complemented
10#10590510C211yesmaximal, characteristic, complemented
11#10590507C211yesmaximal, characteristic, complemented
12#10590506C211yesmaximal, characteristic, complemented
13#10590377C211yesmaximal, characteristic, complemented
14#10590360C211yesmaximal, characteristic, complemented
15#10590328C211yesmaximal, characteristic, complemented
16#81725—31nomaximal
17#81189—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×#3802C2211yescharacteristic
20C2×D3×D12—21no—
21C32×#125C2211yescharacteristic, complemented
22#64107—21no—
23#64106C2211yescharacteristic, complemented
24#64106C2211yescharacteristic, complemented
25#64103—21no—
26#64101—21no—
27#64101C2211yescharacteristic, complemented
28C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
29#64099—21no—
30C4×C4⋊(C3⋊D3)C2211yescharacteristic
31C4×#634C2211yescharacteristic, complemented
32C3×#874C2211yescharacteristic
33C3×C4×D12C2211yescharacteristic
34#63922—21no—
35#63922—21no—
36#63916C2211yescharacteristic
37#63916C2211yescharacteristic
38#63908—21no—
39C2×#3716C2211yescharacteristic
40C2×#3716C2211yescharacteristic, complemented
41C2×#3716C2211yescharacteristic, complemented
42C2×#3712C2211yescharacteristic, complemented
43C2×#3710C2211yescharacteristic, complemented
44C3×#809C2211yescharacteristic
45C3×#809C2211yescharacteristic
46C3×#809C2211yescharacteristic, complemented
47C3×#809C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic, complemented
50C3×#808C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
53C3×#803C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic, complemented
58#63563C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60#63557C2211yescharacteristic, complemented
61#5717—31no—
62#5694—31no—
63#5694—31no—
64#5694—61no—
65D4×D12—31no—
66C3×#490—31no—
67C3×#478—31no—
68#5075—31no—
69#5067D311yescharacteristic, complemented
70#5066D311yescharacteristic, complemented
71#5018—31no—
72#4886—31no—
73#4882—31no—
74#4866—31no—
75#4864—31no—
76#4848—31no—
77#4836—31no—
78#4784—31no—
79#4780—31no—
80#4778—31no—
81#4776—31no—
82#4776—31no—
83#4776—31no—
84#4776—31no—
85#4774—31no—
86#4770—31no—
87#4770—31no—
88D3×#102—31no—
89D3×#102—31no—
90#4710—31no—
91#4706—31no—
92C22×D32—21no—
93C22×D32—21no—
94C2×C4⋊(C3⋊D3)D411yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C2×C3×D12—21no—
100C2×C3×D12—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×#626—21no—
106C2×#626—21no—
107C2×#625—21no—
108C2×#625—21no—
109#3802—22no—
110#3802—22no—
111#3802—41no—
112#3802—41no—
113D3×D12—44no—
114C32×C4⋊C4—21no—
115C32×C4⋊C4—21no—
116C32×C4⋊C4C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C42C2311yescharacteristic
119#3752—21no—
120#3752—21no—
121#3752—21no—
122#3752D411yescharacteristic
123#3752D411yescharacteristic
124C4⋊(C3⋊Dic3)—21no—
125C4⋊(C3⋊Dic3)—21no—
126C4⋊(C3⋊Dic3)D411yescharacteristic
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128#3750—21no—
129#3750—21no—
130C4×C3⋊Dic3—21no—
131C4×C3⋊Dic3—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140#3716—22no—
141#3716—41no—
142#3716—41no—
143#3712—41no—
144#3710—41no—
145#3310—91noSylow
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C22×D12—61no—
152C3×#127—31no—
153C3×#125—21no—
154C3×#125C2×D311yescharacteristic, complemented
155C3×#125C2×D311yescharacteristic, complemented
156C3×C4×D4—31no—
157#938—31no—
158#938—31no—
159#938—61no—
160#937—61no—
161#937—61no—
162C2×#214—31no—
163C2×#214—31no—
164C2×#214—31no—
165#930—61no—
166C2×#204—31no—
167C2×#204—31no—
168C2×#204—31no—
169C2×ΓL(1,𝔽25)—31no—
170C2×ΓL(1,𝔽25)—31no—
171C2×D3×C8—31no—
172C2×D3×C8—31no—
173#898—61no—
174#898—61no—
175#898—62no—
176#897—31no—
177#897—31no—
178#897—31no—
179#897—31no—
180#897—61no—
181#897—61no—
182#895—31no—
183#895—31no—
184#894—61no—
185#894—61no—
186#894—62no—
187#892—31no—
188#892—31no—
189#892—61no—
190#892—61no—
191#892—61no—
192#892—62no—
193D3×C4⋊C4—31no—
194D3×C4⋊C4—31no—
195D3×C4⋊C4—61no—
196#890—61no—
197#890—61no—
198#890—62no—
199#882—61no—
200#882—61no—
201#874C2×D311yescharacteristic
202C4×D12—31no—
203C4×D12—31no—
204C4×D12—61no—
205C4×D12C2×D311yescharacteristic
206C4×Dic6—31no—
207C4×Dic6—31no—
208C4×Dic6—61no—
209C3×#107—31no—
210C3×#106—31no—
211C3×C4⋊C8—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×#102—31no—
217C3×#102—31no—
218C3×#97—31no—
219#832—31no—
220#832—31no—
221#832—31no—
222#821—31no—
223#821—31no—
224#821—31no—
225(C2×D3)⋊C8—31no—
226(C2×D3)⋊C8—31no—
227(C2×D3)⋊C8—31no—
228(C2×D3)⋊C8—31no—
229#818—31no—
230#816—31no—
231#810—31no—
232#809C2×D311yescharacteristic
233#809C2×D311yescharacteristic
234#809C2×D311yescharacteristic, complemented
235#809C2×D311yescharacteristic, complemented
236#809C2×D311yescharacteristic, complemented
237#809C2×D311yescharacteristic, complemented
238#808C2×D311yescharacteristic, complemented
239#807—31no—
240#807C2×D311yescharacteristic, complemented
241C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
242#803C2×D311yescharacteristic, complemented
243C22×C3⋊D3C2×D411yescharacteristic
244C22×C3⋊D3C2×D411yescharacteristic
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C2×D32—42no—
249C2×D32—42no—
250C2×D32—42no—
251C2×D32—42no—
252C2×D32—81no—
253C2×D32—81no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2411yescharacteristic
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3C2×D411yescharacteristic
262C2×C3⋊Dic3C2×D411yescharacteristic
263C4⋊(C3⋊D3)—22no—
264C4×C3⋊D3—21no—
265C4×C3⋊D3—21no—
266C4×C3⋊D3—21no—
267C4×C3⋊D3—21no—
268C4×C3⋊D3—42no—
269#634—21no—
270#634—21no—
271C2×C3×Dic3—21no—
272C3×D12—21no—
273C3×D12—21no—
274C3×D12—21no—
275C3×D12—21no—
276C3×D12—21no—
277C3×D12—42no—
278C3×D12—81no—
279C3×D12#4112yes—
280C3×C4×D3—42no—
281#626—42no—
282#626—42no—
283#625—42no—
284#625—42no—
285C3×C3⋊C8—21no—
286C3×C3⋊C8—21no—
287C3×C3⋊C8—21no—
288C3×C3⋊C8—21no—
289#552—91no—
290D42—91no—
291#490—31no—
292#482—91no—
293#480—91no—
294#478—31no—
295#468—91no—
296#465—91no—
297#460—91no—
298#450—91no—
299#450—91no—
300#440—91no—
301#435—91no—
302#418—91no—
303C2×#102—91no—
304C23×D3—61no—
305C23×D3—61no—
306C23×D3—61no—
307C23×D3—61no—
308C2×C3×D4—31no—
309C2×C3×D4—31no—
310C2×C3×D4—31no—
311C2×C3×D4—61no—
312C2×C3×D4—61no—
313C22×C3×C4—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320D3×D4—62no—
321D3×D4—62no—
322D3×D4—62no—
323D3×D4—62no—
324D3×D4—124no—
325D3×D4—121no—
326D3×D4—121no—
327D3×D4—121no—
328D3×D4—121no—
329C2×D12—21no—
330C2×D12—21no—
331C2×D12—31no—
332C2×D12—31no—
333C2×D12—61no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12—124no—
337C2×D12C22×D311yescharacteristic
338C2×D12C22×D311yescharacteristic
339C2×D12C22×D311yescharacteristic
340C2×C4×D3—21no—
341C2×C4×D3—31no—
342C2×C4×D3—31no—
343C2×C4×D3—31no—
344C2×C4×D3—31no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—62no—
350C2×Dic6—31no—
351C2×Dic6—31no—
352C2×Dic6—61no—
353C2×C3×C8—31no—
354C2×C3×C8—31no—
355C2×C3×C8—31no—
356C2×C3×C8—31no—
357C3×C4⋊C4—22no—
358C3×C4⋊C4—22no—
359C3×C4⋊C4—21no—
360C3×C4⋊C4—21no—
361C3×C4⋊C4—21no—
362C3×C4⋊C4—21no—
363C3×C4⋊C4—21no—
364C3×C4⋊C4—21no—
365C3×C4⋊C4—31no—
366C3×C4⋊C4C22×D311yescharacteristic
367C3×C4⋊C4C22×D311yescharacteristic
368C3×C4⋊C4C22×D311yescharacteristic
369C3×C4⋊C4C22×D311yescharacteristic
370C3×C22⋊C4—61no—
371C3×C42—21no—
372C3×C42C22×D311yescharacteristic
373C3×C42C22×D311yescharacteristic
374#217—61no—
375#217—61no—
376#214—62no—
377#214—121no—
378#214—121no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—31no—
381(C2×D3)⋊C4—31no—
382(C2×D3)⋊C4—31no—
383(C2×D3)⋊C4—31no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—62no—
395(C2×D3)⋊C4—62no—
396(C2×D3)⋊C4—62no—
397C4⋊Dic3—31no—
398C4⋊Dic3—31no—
399C4⋊Dic3—31no—
400C4⋊Dic3—31no—
401C4⋊Dic3—61no—
402C4⋊Dic3—61no—
403C4⋊Dic3—61no—
404C4⋊Dic3—61no—
405C4⋊Dic3—61no—
406C4⋊Dic3—61no—
407C4⋊Dic3—62no—
408C4⋊Dic3—62no—
409C4⋊Dic3C22×D311yescharacteristic
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—62no—
413Dic3⋊C4—62no—
414Dic3⋊C4—61no—
415Dic3⋊C4—61no—
416C4×Dic3—61no—
417C4×Dic3—61no—
418C4×Dic3—62no—
419C4×Dic3—62no—
420C4×Dic3—61no—
421C4×Dic3—61no—
422C2×C3⋊C8C22×D311yescharacteristic
423C2×C3⋊C8C22×D311yescharacteristic
424C2×C3⋊C8C22×D311yescharacteristic
425C2×C3⋊C8C22×D311yescharacteristic
426#204—62no—
427#204—121no—
428#204—121no—
429ΓL(1,𝔽25)—121no—
430ΓL(1,𝔽25)—121no—
431D3×C8—121no—
432D3×C8—121no—
433C22×C32C22×D411yescharacteristic
434C2×C3⋊D3—21no—
435C2×C3⋊D3—21no—
436C2×C3⋊D3—21no—
437C2×C3⋊D3—21no—
438C2×C3⋊D3—21no—
439C2×C3⋊D3AGL(1,ℤ/8)12yes—
440C2×C3×D3—22no—
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×D3—41no—
448C2×C3×D3—41no—
449D32—84no—
450D32—84no—
451C32×C4—21no—
452C32×C4—21no—
453C32×C4—41no—
454C32×C4—41no—
455C32×C4C2×#4111yescharacteristic
456C32×C4H(5,𝔽2)11yescharacteristic
457C3⋊Dic3—21no—
458C3⋊Dic3—21no—
459C3⋊Dic3—41no—
460C3⋊Dic3—41no—
461C3×Dic3—41no—
462C22×D4—91no—
463C22×D4—91no—
464C22×D4—181no—
465C2×SD16—91no—
466C2×SD16—91no—
467C2×SD16—91no—
468C2×M16—91no—
469C22×C8—91no—
470#127—31no—
471#126—181no—
472#125—181no—
473#125D3211yescharacteristic, complemented
474#123—181no—
475C22⋊Q8—91no—
476C22⋊Q8—91no—
477#121—91no—
478#121—91no—
479#121—181no—
480#120—181no—
481#120—181no—
482C4×Q8—91no—
483C4×D4—31no—
484C4×D4—91no—
485#117—91no—
486#117—181no—
487C2×C4⋊C4—91no—
488#107—31no—
489#107—91no—
490#106—31no—
491C4⋊C8—31no—
492#103—91no—
493#102—31no—
494#102—31no—
495#102—31no—
496#102—31no—
497#102—31no—
498#102—31no—
499#102—91no—
500#102—91no—
501#102—91no—
502C22⋊C8—91no—
503C22⋊C8—91no—
504#97—31no—
505C23×C3—61no—
506C23×C3—61no—
507C23×C3—61no—
508C22×D3—21no—
509C22×D3—21no—
510C22×D3—21no—
511C22×D3—31no—
512C22×D3—31no—
513C22×D3—31no—
514C22×D3—31no—
515C22×D3—61no—
516C22×D3—61no—
517C22×D3—122no—
518C22×D3—122no—
519C22×D3—122no—
520C22×D3—122no—
521C22×D3—122no—
522C22×D3—122no—
523C22×D3—122no—
524C22×D3—122no—
525C22×D3—241no—
526C22×D3—241no—
527C22×D3—241no—
528C22×D3—241no—
529C3×D4—32no—
530C3×D4—61no—
531C3×D4—61no—
532C3×D4—61no—
533C3×D4—61no—
534C3×D4—61no—
535C3×D4—122no—
536C3×D4—241no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—61no—
547C2×C3×C4—122no—
548C2×C3×C4D3×D411yescharacteristic
549C2×C3×C4D3×D411yescharacteristic
550C2×C3×C4D3×D411yescharacteristic
551C2×C3×C4D3×D411yescharacteristic
552C2×C3×C4C23×D311yescharacteristic
553C2×C3×C4C23×D311yescharacteristic
554#67—122no—
555#67—122no—
556#67—122no—
557#67—122no—
558#67—122no—
559#67—122no—
560C2×Dic3—21no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—31no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—62no—
568C2×Dic3—62no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573D12—21no—
574D12—21no—
575D12—21no—
576D12—21no—
577D12—21no—
578D12—42no—
579D12—62no—
580D12—62no—
581D12—81no—
582D12—122no—
583D12—122no—
584D12—122no—
585D12#23912yes—
586C4×D3—42no—
587C4×D3—61no—
588C4×D3—61no—
589C4×D3—61no—
590C4×D3—61no—
591C4×D3—61no—
592C4×D3—61no—
593C4×D3—61no—
594C4×D3—61no—
595C4×D3—121no—
596C4×D3—121no—
597C4×D3—121no—
598C4×D3—121no—
599C4×D3—122no—
600C4×D3—122no—
601C4×D3—124no—
602Dic6—61no—
603Dic6—61no—
604Dic6—61no—
605Dic6—61no—
606Dic6—121no—
607Dic6—121no—
608C3×C8—61no—
609C3×C8—61no—
610C3×C8—61no—
611C3×C8—61no—
612C3⋊C8—21no—
613C3⋊C8—21no—
614C3⋊C8—21no—
615C3⋊C8—21no—
616C2×C32#54611yescharacteristic
617C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
618C2×C32#57711yescharacteristic
619C3⋊D3—22no—
620C3⋊D3—41no—
621C3×D3—42no—
622C3×D3—81no—
623C3×D3—81no—
624C24—181no—
625C24—181no—
626C2×Q8—91no—
627C2×D4—31no—
628C2×D4—31no—
629C2×D4—31no—
630C2×D4—61no—
631C2×D4—61no—
632C2×D4—91no—
633C2×D4—181no—
634C2×D4—181no—
635C2×D4—181no—
636C2×D4—181no—
637C2×D4—182no—
638C2×D4—182no—
639C2×D4—364no—
640C2×D4—361no—
641C2×D4—361no—
642C22×C4—61no—
643C22×C4—91no—
644C22×C4—91no—
645C22×C4—181no—
646SD16—182no—
647SD16—361no—
648SD16—361no—
649M16—361no—
650C2×C8—31no—
651C2×C8—31no—
652C2×C8—31no—
653C2×C8—31no—
654C2×C8—361no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—31no—
658C4⋊C4—91no—
659C4⋊C4—91no—
660C4⋊C4—181no—
661C4⋊C4—181no—
662C4⋊C4—181no—
663C4⋊C4—181no—
664C4⋊C4C2×D3211yescharacteristic
665C4⋊C4C2×D3211yescharacteristic
666C22⋊C4—61no—
667C22⋊C4—91no—
668C22⋊C4—91no—
669C22⋊C4—181no—
670C22⋊C4—181no—
671C22⋊C4—181no—
672C22⋊C4—181no—
673C22⋊C4—181no—
674C42—181no—
675C42—181no—
676C42C2×D3211yescharacteristic
677C22×C3—21no—
678C22×C3—62no—
679C22×C3—121no—
680C22×C3—121no—
681C22×C3—121no—
682C22×C3—121no—
683C22×C3—121no—
684C22×C3—121no—
685C22×C3—121no—
686C22×C3—121no—
687C22×C3C2×D3×D411yescharacteristic
688C22×C3C2×D3×D411yescharacteristic
689C2×D3—22no—
690C2×D3—32no—
691C2×D3—32no—
692C2×D3—41no—
693C2×D3—41no—
694C2×D3—41no—
695C2×D3—41no—
696C2×D3—41no—
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—62no—
701C2×D3—61no—
702C2×D3—61no—
703C2×D3—61no—
704C2×D3—61no—
705C2×D3—61no—
706C2×D3—61no—
707C2×D3—61no—
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—61no—
711C2×D3—121no—
712C2×D3—121no—
713C2×D3—121no—
714C2×D3—121no—
715C2×D3—121no—
716C2×D3—244no—
717C2×D3—244no—
718C2×D3—244no—
719C2×D3—244no—
720C3×C4—21no—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—21no—
726C3×C4—41no—
727C3×C4—41no—
728C3×C4—42no—
729C3×C4—42no—
730C3×C4—41no—
731C3×C4—41no—
732C3×C4—41no—
733C3×C4—41no—
734C3×C4—121no—
735C3×C4C2×#23911yescharacteristic
736C3×C4D3×#4111yescharacteristic
737C3×C4#100911yescharacteristic
738C3×C4#100911yescharacteristic
739Dic3—41no—
740Dic3—61no—
741Dic3—61no—
742Dic3—61no—
743Dic3—61no—
744Dic3—121no—
745Dic3—121no—
746Dic3—122no—
747Dic3—122no—
748Dic3—121no—
749Dic3—121no—
750Dic3—121no—
751Dic3—121no—
752C32#331011yescharacteristic, complemented, Sylow
753C23—61no—
754C23—61no—
755C23—61no—
756C23—91no—
757C23—91no—
758C23—362no—
759C23—362no—
760C23—362no—
761C23—362no—
762C23—721no—
763C23—721no—
764Q8—181no—
765Q8—181no—
766D4—32no—
767D4—61no—
768D4—61no—
769D4—61no—
770D4—61no—
771D4—61no—
772D4—122no—
773D4—182no—
774D4—241no—
775D4—362no—
776D4—362no—
777D4—362no—
778D4—362no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—61no—
782C2×C4—91no—
783C2×C4—91no—
784C2×C4—122no—
785C2×C4—181no—
786C2×C4—181no—
787C2×C4—181no—
788C2×C4—181no—
789C2×C4—181no—
790C2×C4—181no—
791C2×C4—362no—
792C2×C4#381111yescharacteristic
793C2×C4#381111yescharacteristic
794C2×C4C22×D3211yescharacteristic
795C8—61no—
796C8—61no—
797C8—61no—
798C8—61no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—122no—
803C2×C3—241no—
804C2×C3—241no—
805C2×C3#563011yescharacteristic
806C2×C3#567611yescharacteristic
807C2×C3#577011yescharacteristic
808C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
809C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
810C2×C3#577511yescharacteristic
811D3—42no—
812D3—62no—
813D3—62no—
814D3—81no—
815D3—81no—
816D3—122no—
817D3—121no—
818D3—121no—
819D3—241no—
820C22—62no—
821C22—92no—
822C22—121no—
823C22—121no—
824C22—121no—
825C22—121no—
826C22—121no—
827C22—121no—
828C22—121no—
829C22—121no—
830C22—181no—
831C22—181no—
832C22—181no—
833C22—181no—
834C22—181no—
835C22—724no—
836C22—724no—
837C22C2×#381111yescharacteristic
838C4—21no—
839C4—21no—
840C4—41no—
841C4—41no—
842C4—121no—
843C4—181no—
844C4—181no—
845C4—361no—
846C4—361no—
847C4D3×#23911yescharacteristic
848C4#6432011yescharacteristic
849C3—21no—
850C3#8118911yescharacteristic, complemented
851C3#8172511yescharacteristic, complemented
852C2—122no—
853C2—182no—
854C2—241no—
855C2—241no—
856C2—361no—
857C2#1059543111yescharacteristic
858C2#1059545811yescharacteristic
859C2#1059546211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#125C22
socleC22×C32C22×D4
prime radical#10594004C2
hypercenter#125D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #10596165C2semidirect
3. C3×#5067C2semidirect
4. C3×#5066C2semidirect
5. #10590597C2semidirect
6. #10590597C2semidirect
7. #10590594C2semidirect
8. #10590593C2semidirect
9. #10590513C2semidirect
10. #10590510C2semidirect
11. #10590507C2semidirect
12. #10590506C2semidirect
13. #10590377C2semidirect
14. #10590360C2semidirect
15. #10590328C2semidirect
21. C32×#125C22semidirect
23. #64106C22semidirect
24. #64106C22semidirect
27. #64101C22semidirect
28. C4⋊C4×C3⋊D3C22semidirect
31. C4×#634C22semidirect
40. C2×#3716C22semidirect
41. C2×#3716C22semidirect
42. C2×#3712C22semidirect
43. C2×#3710C22semidirect
46. C3×#809C22semidirect
47. C3×#809C22semidirect
48. C3×#809C22semidirect
49. C3×#809C22semidirect
50. C3×#808C22semidirect
51. C3×#807C22semidirect
52. C3×C4⋊(C3⋊C8)C22semidirect
53. C3×#803C22semidirect
54. #63575C22semidirect
55. #63567C22semidirect
57. #63563C22semidirect
58. #63563C22semidirect
59. #63557C22semidirect
60. #63557C22semidirect
69. #5067D3semidirect
70. #5066D3semidirect
154. C3×#125C2×D3semidirect
155. C3×#125C2×D3semidirect
234. #809C2×D3semidirect
235. #809C2×D3semidirect
236. #809C2×D3semidirect
237. #809C2×D3semidirect
238. #808C2×D3semidirect
240. #807C2×D3semidirect
241. C4⋊(C3⋊C8)C2×D3semidirect
242. #803C2×D3semidirect
473. #125D32semidirect
752. C32#3310semidirect
850. C3#81189semidirect
851. C3#81725semidirect

Maximal subgroups

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

subgroupindex
#105961652
#105940042
C3×#50672
C3×#50662
#105905972
#105905942
#105905932
#105905132
#105905102
#105905072
#105905062
#105903772
#105903602
#105903282
#817253
#811893