Finite Group Databasebeta

← #11889131

Subgroups — #11889131

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
1C3×#5581C211yesmaximal, characteristic, complemented
2D122C211yesmaximal, characteristic
3#10592726C211yesmaximal, characteristic, complemented
4C3×#5026C211yesmaximal, characteristic, complemented
5#10591651C211yesmaximal, characteristic, complemented
6#10591651C211yesmaximal, characteristic, complemented
7#10591589C211yesmaximal, characteristic, complemented
8#10591585C211yesmaximal, characteristic, complemented
9#10590592C211yesmaximal, characteristic, complemented
10D3×#809C211yesmaximal, characteristic, complemented
11#10590424C211yesmaximal, characteristic, complemented
12#10590422C211yesmaximal, characteristic, complemented
13#10590326C211yesmaximal, characteristic, complemented
14#10590282C211yesmaximal, characteristic, complemented
15#10590270C211yesmaximal, characteristic, complemented
16#83599—31nomaximal
17#79800—31nomaximal
18C2×D3×D12—21no—
19C2×D3×D12C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic, complemented
22C2×#3755C2211yescharacteristic, complemented
23C2×#3755C2211yescharacteristic, complemented
24#64083C2211yescharacteristic
25C3×#946C2211yescharacteristic, complemented
26C3×#946C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C3×#894—21no—
29C3×#892C2211yescharacteristic, complemented
30C3×D3×C4⋊C4C2211yescharacteristic, complemented
31C3×#889—21no—
32C3×#876—21no—
33C3×C4×D12C2211yescharacteristic
34C3×C4×D12C2211yescharacteristic
35C3×#872—21no—
36C3×#870C2211yescharacteristic, complemented
37#63923—21no—
38#63923—21no—
39#63909—21no—
40#63909C2211yescharacteristic
41#63909C2211yescharacteristic
42C2×#3711C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63636C2211yescharacteristic, complemented
45#63636C2211yescharacteristic, complemented
46C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic
49C3×#807C2211yescharacteristic, complemented
50C3×#803C2211yescharacteristic, complemented
51#63576C2211yescharacteristic, complemented
52#63574C2211yescharacteristic, complemented
53#63564C2211yescharacteristic, complemented
54#63564C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#552—31no—
62#5581D311yescharacteristic, complemented
63D4×D12—31no—
64D4×D12—31no—
65C3×#440—31no—
66#5169—31no—
67#5169—31no—
68#5067—31no—
69#5066—31no—
70#5049—31no—
71#5048—31no—
72#5046—31no—
73#5046—31no—
74#5027—31no—
75#5027—31no—
76#5027—61no—
77#5026D311yescharacteristic, complemented
78#5011—31no—
79#5009—31no—
80#5003—31no—
81#5001—31no—
82#4967—31no—
83C2×#809—31no—
84#4885—31no—
85#4882—31no—
86#4812—31no—
87#4807—31no—
88#4770—31no—
89D3×#102—31no—
90#4713—31no—
91#4706—31no—
92C22×D32—21no—
93C22×D32—21no—
94C2×C32×Q8C2311yescharacteristic
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C3×D12D411yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×#626—21no—
106C2×#626—21no—
107C2×#626—21no—
108C2×#626—21no—
109D3×D12—22no—
110D3×D12—22no—
111D3×D12—41no—
112D3×D12—41no—
113D3×D12—44no—
114C32×C4⋊C4—21no—
115C32×C4⋊C4C2311yescharacteristic
116C32×C42—21no—
117C32×C42C2311yescharacteristic
118#3755—41no—
119#3755—41no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#215—22no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×C4⋊Dic3D411yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×C4×Dic3—21no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3722—21no—
142#3722—21no—
143#3711—41no—
144D3×C3⋊C8—41no—
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×SD16—31no—
153C3×#126—61no—
154C3×#125—31no—
155C3×#125—61no—
156C3×#123—61no—
157C3×C22⋊Q8—31no—
158C3×C22⋊Q8—31no—
159C3×C4×Q8—21no—
160C3×C4×Q8C2×D311yescharacteristic, complemented
161C3×C4×Q8C2×D311yescharacteristic, complemented
162C3×C4×D4—31no—
163C3×C4×D4—31no—
164C3×#117—31no—
165C3×#117—61no—
166C2×C3×C4⋊C4—31no—
167#946C2×D311yescharacteristic, complemented
168#946C2×D311yescharacteristic, complemented
169C2×#215—31no—
170C2×#215—31no—
171C2×#215—31no—
172C2×#215—31no—
173C2×#215—61no—
174C2×#215—61no—
175C2×#215C2×D311yescharacteristic
176#930—31no—
177#930—31no—
178#930—61no—
179C2×#208—31no—
180C22×C3⋊C8—31no—
181C2×ΓL(1,𝔽25)—31no—
182C2×D3×C8—31no—
183#895—31no—
184#895—31no—
185#895—61no—
186#894—21no—
187#892C2×D311yescharacteristic, complemented
188D3×C4⋊C4C2×D311yescharacteristic, complemented
189#889—21no—
190#882—61no—
191#882—61no—
192#882—61no—
193#882—61no—
194#876—21no—
195#874—31no—
196#874—31no—
197#874—61no—
198C4×D12C2×D311yescharacteristic
199C4×D12C2×D311yescharacteristic
200#872—21no—
201#870C2×D311yescharacteristic, complemented
202C3×#107—31no—
203C3×#103—31no—
204C3×#102—31no—
205C3×#97—31no—
206#835C2×D311yescharacteristic, complemented
207#832—31no—
208#832—31no—
209#830—31no—
210#830—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8—31no—
217#809—31no—
218#809—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—61no—
228#809—61no—
229#809C2×D311yescharacteristic
230#808—31no—
231#808—31no—
232#807—31no—
233#807—31no—
234#807C2×D311yescharacteristic, complemented
235C4⋊(C3⋊C8)—31no—
236C4⋊(C3⋊C8)—31no—
237C4⋊(C3⋊C8)—61no—
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—
250C32×Q8—21no—
251C32×Q8—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2411yescharacteristic
257C4⋊(C3⋊D3)—21no—
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)—21no—
260C4⋊(C3⋊D3)—21no—
261C4⋊(C3⋊D3)—42no—
262C4⋊(C3⋊D3)—81no—
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—
276C3×C4×D3—42no—
277#626—42no—
278#626—42no—
279#626—42no—
280#626—42no—
281C3⋊(C3⋊C8)—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#552—31no—
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—31no—
297#435—91no—
298#418—91no—
299C2×#102—91no—
300C23×D3—61no—
301C23×D3—61no—
302C23×D3—61no—
303C23×D3—61no—
304C2×C3×Q8—21no—
305C2×C3×Q8C22×D311yescharacteristic
306C2×C3×Q8C22×D311yescharacteristic
307C2×C3×D4—31no—
308C2×C3×D4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317D3×D4—62no—
318D3×D4—62no—
319D3×D4—121no—
320D3×D4—121no—
321D3×D4—124no—
322C2×D12—31no—
323C2×D12—31no—
324C2×D12—31no—
325C2×D12—31no—
326C2×D12—61no—
327C2×D12—61no—
328C2×D12—62no—
329C2×D12—62no—
330C2×D12—61no—
331C2×D12—61no—
332C2×D12—61no—
333C2×D12—61no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12—61no—
337C2×D12—61no—
338C2×D12—121no—
339C2×D12—121no—
340C2×D12—121no—
341C2×D12—121no—
342C2×D12—124no—
343C2×D12#6711yescharacteristic
344C2×D12C22×D311yescharacteristic
345C2×C4×D3—21no—
346C2×C4×D3—21no—
347C2×C4×D3C22×D311yescharacteristic
348C2×C4×D3C22×D311yescharacteristic
349C3×SD16—62no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—41no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C4⋊C4C22×D311yescharacteristic
367C3×C22⋊C4—31no—
368C3×C22⋊C4—31no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C42—21no—
374C3×C42—21no—
375C3×C42—21no—
376C3×C42—41no—
377C3×C42—61no—
378C3×C42C22×D311yescharacteristic
379C3×C42C22×D311yescharacteristic
380#215—22no—
381#215—121no—
382#215—121no—
383#215—121no—
384#215—121no—
385#215—122no—
386#215—122no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—61no—
395(C2×D3)⋊C4#6711yescharacteristic
396(C2×D3)⋊C4#6711yescharacteristic
397C4⋊Dic3#6711yescharacteristic
398C4⋊Dic3C22×D311yescharacteristic
399C4⋊Dic3C22×D311yescharacteristic
400C4⋊Dic3C22×D311yescharacteristic
401Dic3⋊C4—21no—
402Dic3⋊C4—21no—
403Dic3⋊C4—21no—
404Dic3⋊C4—21no—
405Dic3⋊C4—21no—
406C4×Dic3—21no—
407#208—121no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—31no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—61no—
413C2×C3⋊C8—61no—
414C2×C3⋊C8—121no—
415C2×C3⋊C8C22×D311yescharacteristic
416C2×C3⋊C8C22×D311yescharacteristic
417ΓL(1,𝔽25)—121no—
418D3×C8—121no—
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×C4—41no—
440C32×C4—41no—
441C32×C4C2×#4111yescharacteristic
442C32×C4H(5,𝔽2)11yescharacteristic
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—31no—
452C2×SD16—91no—
453C2×SD16—91no—
454C2×M16—91no—
455C22×C8—91no—
456#127—91no—
457#126—61no—
458#125—31no—
459#125—61no—
460#123—61no—
461C22⋊Q8—31no—
462C22⋊Q8—31no—
463#121—91no—
464#121—91no—
465#121—181no—
466#120—181no—
467#120—181no—
468C4×Q8D3211yescharacteristic, complemented
469C4×D4—31no—
470C4×D4—31no—
471#117—31no—
472#117—61no—
473C2×C4⋊C4—31no—
474#107—31no—
475#107—91no—
476#106—91no—
477C4⋊C8—91no—
478#103—31no—
479#102—31no—
480#102—91no—
481#102—91no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102—91no—
488C22⋊C8—91no—
489C22⋊C8—91no—
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×#6711yescharacteristic
514C22×D3C2×#6711yescharacteristic
515C3×Q8—22no—
516C3×Q8—21no—
517C3×Q8—21no—
518C3×Q8—21no—
519C3×Q8—21no—
520C3×Q8—41no—
521C3×D4—32no—
522C3×D4—62no—
523C3×D4—61no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—31no—
532C2×C3×C4—31no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—122no—
543C2×C3×C4—122no—
544C2×C3×C4D3×D411yescharacteristic
545C2×C3×C4D3×D411yescharacteristic
546C2×C3×C4C2×#6711yescharacteristic
547C2×C3×C4C2×#6711yescharacteristic
548C2×C3×C4C23×D311yescharacteristic
549C2×C3×C4C23×D311yescharacteristic
550#67—122no—
551#67—122no—
552#67—122no—
553#67—122no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3C2×#6711yescharacteristic
558C2×Dic3C2×#6711yescharacteristic
559D12—22no—
560D12—21no—
561D12—61no—
562D12—61no—
563D12—61no—
564D12—61no—
565D12—61no—
566D12—61no—
567D12—61no—
568D12—61no—
569D12—121no—
570D12—121no—
571D12—121no—
572D12—121no—
573D12—122no—
574D12—122no—
575D12—122no—
576D12—122no—
577D12—122no—
578D12—122no—
579D12—242no—
580D12—241no—
581D12—241no—
582D12—242no—
583D12#23512yes—
584C4×D3—21no—
585C4×D3—21no—
586C4×D3—21no—
587C4×D3—21no—
588C4×D3—42no—
589C4×D3—42no—
590C3×C8—61no—
591C3×C8—61no—
592C3⋊C8—21no—
593C3⋊C8—21no—
594C3⋊C8—61no—
595C3⋊C8—61no—
596C3⋊C8—61no—
597C3⋊C8—61no—
598C3⋊C8—121no—
599C3⋊C8—121no—
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×Q8C2×D3211yescharacteristic
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—61no—
630SD16—62no—
631SD16—361no—
632SD16—361no—
633M16—361no—
634C2×C8—31no—
635C2×C8—31no—
636C2×C8—91no—
637C2×C8—91no—
638C2×C8—361no—
639C4⋊C4—21no—
640C4⋊C4—31no—
641C4⋊C4—31no—
642C4⋊C4—31no—
643C4⋊C4—31no—
644C4⋊C4—61no—
645C4⋊C4—61no—
646C4⋊C4—61no—
647C4⋊C4—61no—
648C4⋊C4—61no—
649C4⋊C4C2×D3211yescharacteristic
650C22⋊C4—31no—
651C22⋊C4—31no—
652C22⋊C4—61no—
653C22⋊C4—61no—
654C22⋊C4—61no—
655C22⋊C4—61no—
656C22⋊C4—181no—
657C22⋊C4—181no—
658C42—21no—
659C42—61no—
660C42C2×D3211yescharacteristic
661C22×C3—21no—
662C22×C3—32no—
663C22×C3—61no—
664C22×C3—61no—
665C22×C3—61no—
666C22×C3—61no—
667C22×C3—61no—
668C22×C3—62no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3C2×D3×D411yescharacteristic
672C22×C3C22×#6711yescharacteristic
673C2×D3—21no—
674C2×D3—21no—
675C2×D3—22no—
676C2×D3—21no—
677C2×D3—21no—
678C2×D3—21no—
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#94912yes—
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—42no—
713C3×C4—41no—
714C3×C4—41no—
715C3×C4—41no—
716C3×C4—41no—
717C3×C4—61no—
718C3×C4—61no—
719C3×C4—81no—
720C3×C4—121no—
721C3×C4—121no—
722C3×C4—121no—
723C3×C4C2×#23511yescharacteristic
724C3×C4D3×#4111yescharacteristic
725C3×C4#100911yescharacteristic
726C3×C4#100911yescharacteristic
727Dic3—21no—
728Dic3—21no—
729Dic3—41no—
730Dic3—41no—
731Dic3—41no—
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—21no—
745Q8—21no—
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—21no—
760C2×C4—21no—
761C2×C4—31no—
762C2×C4—31no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—122no—
771C2×C4—122no—
772C2×C4D3×#6711yescharacteristic
773C2×C4D3×#6711yescharacteristic
774C2×C4C22×D3211yescharacteristic
775C8—61no—
776C8—61no—
777C8—181no—
778C8—181no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—62no—
783C2×C3—122no—
784C2×C3—121no—
785C2×C3#555011yescharacteristic
786C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
787C2×C3#577811yescharacteristic
788C2×C3C2×#94911yescharacteristic
789C2×C3#582911yescharacteristic
790C2×C3#583711yescharacteristic
791D3—22no—
792D3—41no—
793D3—42no—
794D3—241no—
795D3—241no—
796D3—241no—
797D3—241no—
798D3—481no—
799D3—481no—
800C22—32no—
801C22—61no—
802C22—61no—
803C22—61no—
804C22—61no—
805C22—61no—
806C22—62no—
807C22—121no—
808C22—121no—
809C22—361no—
810C22—361no—
811C22—361no—
812C22—361no—
813C22—361no—
814C22—361no—
815C22—724no—
816C22—724no—
817C22C2×D3×#6711yescharacteristic
818C4—21no—
819C4—21no—
820C4—41no—
821C4—41no—
822C4—61no—
823C4—61no—
824C4—121no—
825C4—121no—
826C4—121no—
827C4D3×#23511yescharacteristic
828C4#6430811yescharacteristic
829C3—21no—
830C3#7980011yescharacteristic, complemented
831C3#8359911yescharacteristic, complemented
832C2—62no—
833C2—121no—
834C2—122no—
835C2—721no—
836C2—721no—
837C2#1059506711yescharacteristic
838C2#1059531911yescharacteristic
839C2D3×#94911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalD122C2
hypercenterC4×Q8D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5581C2semidirect
3. #10592726C2semidirect
4. C3×#5026C2semidirect
5. #10591651C2semidirect
6. #10591651C2semidirect
7. #10591589C2semidirect
8. #10591585C2semidirect
9. #10590592C2semidirect
10. D3×#809C2semidirect
11. #10590424C2semidirect
12. #10590422C2semidirect
13. #10590326C2semidirect
14. #10590282C2semidirect
15. #10590270C2semidirect
21. C32×C4×Q8C22semidirect
22. C2×#3755C22semidirect
23. C2×#3755C22semidirect
25. C3×#946C22semidirect
26. C3×#946C22semidirect
29. C3×#892C22semidirect
30. C3×D3×C4⋊C4C22semidirect
36. C3×#870C22semidirect
42. C2×#3711C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63636C22semidirect
45. #63636C22semidirect
46. C4⋊(C3⋊(C3⋊C8))C22semidirect
47. C3×#835C22semidirect
49. C3×#807C22semidirect
50. C3×#803C22semidirect
51. #63576C22semidirect
52. #63574C22semidirect
53. #63564C22semidirect
54. #63564C22semidirect
55. #63564C22semidirect
56. #63564C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #5581D3semidirect
77. #5026D3semidirect
160. C3×C4×Q8C2×D3semidirect
161. C3×C4×Q8C2×D3semidirect
167. #946C2×D3semidirect
168. #946C2×D3semidirect
187. #892C2×D3semidirect
188. D3×C4⋊C4C2×D3semidirect
201. #870C2×D3semidirect
206. #835C2×D3semidirect
234. #807C2×D3semidirect
238. #803C2×D3semidirect
468. C4×Q8D32semidirect
732. C32#3310semidirect
830. C3#79800semidirect
831. C3#83599semidirect

Maximal subgroups

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

subgroupindex
C3×#55812
D1222
#105927262
C3×#50262
#105916512
#105915892
#105915852
#105905922
D3×#8092
#105904242
#105904222
#105903262
#105902822
#105902702
#835993
#798003