Finite Group Databasebeta

← #11859365

Subgroups — #11859365

Order 1152.

1102 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63804C211yesmaximal, characteristic, complemented
2C2×D32×C8C211yesmaximal, characteristic, complemented
3#10593997C211yesmaximal, characteristic
4#10592535C211yesmaximal, characteristic, complemented
5C3×#4839C211yesmaximal, characteristic, complemented
6C3×#4834C211yesmaximal, characteristic, complemented
7#10590953C211yesmaximal, characteristic, complemented
8#10590936C211yesmaximal, characteristic, complemented
9#10590907C211yesmaximal, characteristic, complemented
10#10590737C211yesmaximal, characteristic, complemented
11#10590720C211yesmaximal, characteristic, complemented
12#10590720C211yesmaximal, characteristic, complemented
13#10590330C211yesmaximal, characteristic, complemented
14#10590327C211yesmaximal, characteristic, complemented
15#10590318C211yesmaximal, characteristic, complemented
16#79421—31nomaximal
17#79073—31nomaximal
18C2×C4×D32C2211yescharacteristic
19C2×#3798C2211yescharacteristic
20C2×#3743C2211yescharacteristic, complemented
21C2×C8×C3⋊D3C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic, complemented
27C3×C4×D12C2211yescharacteristic
28C3×#872C2211yescharacteristic
29#63923C411yescharacteristic
30#63922C411yescharacteristic
31#63910C411yescharacteristic
32C4×#626C2211yescharacteristic
33C4×#626C2211yescharacteristic
34#63895C411yescharacteristic
35#63893C411yescharacteristic
36#63891C411yescharacteristic
37#63890C411yescharacteristic
38#63886C411yescharacteristic
39C2×#3711C2211yescharacteristic
40C2×#3711C2211yescharacteristic, complemented
41C2×#3710C2211yescharacteristic
42C2×#3710C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic
45#63804—24no—
46D32×C8—24no—
47C32×C4⋊C8C2211yescharacteristic, complemented
48#63647C2211yescharacteristic
49#63647C2211yescharacteristic, complemented
50#63630C2211yescharacteristic, complemented
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×Dic3⋊C8C2211yescharacteristic, complemented
55C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
56C3×C4×C3⋊C8C2211yescharacteristic, complemented
57#63557C2211yescharacteristic
58#63557C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63554C2211yescharacteristic, complemented
62Dic3×C3⋊C8C2211yescharacteristic, complemented
63C2×#907—31no—
64C2×#901—31no—
65C22×D3×C8—31no—
66C22×D3×C8—31no—
67#5547—31no—
68#5524—31no—
69C3×C8×D4—31no—
70C3×#424—31no—
71#5126—31no—
72#5110—31no—
73C8×#67—31no—
74C8×#67—31no—
75#5011—31no—
76#4997—31no—
77#4839D311yescharacteristic, complemented
78#4836—31no—
79#4836—31no—
80#4836—31no—
81#4836—31no—
82#4836—31no—
83#4836—61no—
84#4834—31no—
85#4834—31no—
86#4834—31no—
87#4834D311yescharacteristic, complemented
88#4730—31no—
89#4728—31no—
90#4727—31no—
91#4726—31no—
92#4689—31no—
93C8×D12—31no—
94C22×D32C2×C411yescharacteristic
95C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C3×D12C2×C411yescharacteristic
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×#627C2×C411yescharacteristic
103C2×#626C2×C411yescharacteristic
104C2×#626C2×C411yescharacteristic
105C2×#626C2×C411yescharacteristic
106C2×#626C2×C411yescharacteristic
107C2×#625C2×C411yescharacteristic
108C2×#624C2×C411yescharacteristic
109C2×D3×Dic3C2×C411yescharacteristic
110C2×D3×Dic3C2×C411yescharacteristic
111C4×D32—22no—
112C4×D32—22no—
113#3798—22no—
114#3798—22no—
115C2×C32×C8C2311yescharacteristic
116C2×C32×C8C2311yescharacteristic
117C32×C42C2311yescharacteristic
118#3752C2×C411yescharacteristic
119#3752C2×C411yescharacteristic
120C4⋊(C3⋊Dic3)C2×C411yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123#3743—22no—
124C8×C3⋊D3—22no—
125C3×(C2×D3)⋊C4C2×C411yescharacteristic
126C3×(C2×D3)⋊C4C2×C411yescharacteristic
127C3×(C2×D3)⋊C4C2×C411yescharacteristic
128C3×(C2×D3)⋊C4C2×C411yescharacteristic
129C3×C4⋊Dic3C2×C411yescharacteristic
130C3×Dic3⋊C4C2×C411yescharacteristic
131C3×Dic3⋊C4C2×C411yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×ΓL(1,𝔽25)—22no—
138C3×D3×C8—22no—
139C3×D3×C8—22no—
140C3×D3×C8—22no—
141Dic3⋊Dic3C2×C411yescharacteristic
142Dic3⋊Dic3C2×C411yescharacteristic
143#3722C2×C411yescharacteristic
144#3722C2×C411yescharacteristic
145(C2×D3)⋊Dic3C2×C411yescharacteristic
146(C2×D3)⋊Dic3C2×C411yescharacteristic
147#3711—22no—
148#3711—22no—
149#3710—22no—
150#3710—22no—
151D3×C3⋊C8—22no—
152D3×C3⋊C8D414yescomplemented
153#2929—91noSylow
154C2×#235—31no—
155C2×#235—31no—
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C2×C3×M16—31no—
159C22×C3×C8—31no—
160C22×C3×C8—31no—
161C22×C3×C8—31no—
162C3×C4×D4—31no—
163C3×#117—31no—
164#939—31no—
165#937—31no—
166C4×#67—31no—
167C4×#67—31no—
168C2×#208—31no—
169C2×#208—31no—
170C22×C3⋊C8—31no—
171C22×C3⋊C8—31no—
172#907—64no—
173#901—64no—
174C2×ΓL(1,𝔽25)—31no—
175C2×ΓL(1,𝔽25)—31no—
176C2×ΓL(1,𝔽25)—31no—
177C2×ΓL(1,𝔽25)—31no—
178C2×ΓL(1,𝔽25)—61no—
179C2×ΓL(1,𝔽25)C2×D311yescharacteristic
180C2×D3×C8—31no—
181C2×D3×C8—31no—
182C2×D3×C8—31no—
183C2×D3×C8—31no—
184C2×D3×C8—31no—
185C2×D3×C8—31no—
186C2×D3×C8—31no—
187C2×D3×C8—31no—
188C2×D3×C8—61no—
189C2×D3×C8—64no—
190C2×D3×C8—64no—
191C2×D3×C8C2×D311yescharacteristic
192C2×D3×C8C2×D311yescharacteristic
193C2×D3×C8C2×D311yescharacteristic, complemented
194#897—31no—
195#897—31no—
196#896—31no—
197#895—31no—
198#895—31no—
199#894—31no—
200#886—31no—
201#886—31no—
202#884—31no—
203#883—31no—
204#882—31no—
205#882—31no—
206#882—31no—
207#878—31no—
208C4×D12—31no—
209C4×D12—31no—
210C4×D12—31no—
211C4×D12—31no—
212C4×D12—61no—
213C4×D12C2×D311yescharacteristic
214#872C2×D311yescharacteristic
215C3×C4⋊C8—21no—
216C3×C4⋊C8—31no—
217C3×C4⋊C8—31no—
218C3×C4⋊C8—31no—
219C3×C4⋊C8C2×D311yescharacteristic, complemented
220C3×C4⋊C8C2×D311yescharacteristic, complemented
221C3×C22⋊C8—31no—
222C3×C22⋊C8—31no—
223C3×C4×C8—31no—
224#830—31no—
225#830—31no—
226(C2×D3)⋊C8—31no—
227(C2×D3)⋊C8—31no—
228(C2×D3)⋊C8—31no—
229(C2×D3)⋊C8—31no—
230(C2×D3)⋊C8—31no—
231(C2×D3)⋊C8—31no—
232(C2×D3)⋊C8—31no—
233(C2×D3)⋊C8—31no—
234(C2×D3)⋊C8—31no—
235(C2×D3)⋊C8—31no—
236(C2×D3)⋊C8—61no—
237(C2×D3)⋊C8—61no—
238(C2×D3)⋊C8C2×D311yescharacteristic
239(C2×D3)⋊C8C2×D311yescharacteristic, complemented
240#815—31no—
241Dic3⋊C8C2×D311yescharacteristic, complemented
242Dic3⋊C8C2×D311yescharacteristic, complemented
243C8×Dic3—31no—
244C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
245#803—31no—
246#803—31no—
247#803—31no—
248#803—61no—
249C4×C3⋊C8—31no—
250C4×C3⋊C8C2×D311yescharacteristic, complemented
251C22×C3⋊D3C22×C411yescharacteristic
252C22×C3⋊D3C22×C411yescharacteristic
253C22×C3×D3C22×C411yescharacteristic
254C22×C3×D3C22×C411yescharacteristic
255C22×C3×D3C22×C411yescharacteristic
256C2×D32—22no—
257C2×D32—22no—
258C2×D32—22no—
259C2×C32×C4C22×C411yescharacteristic
260C2×C32×C4C22×C411yescharacteristic
261C2×C32×C4C2411yescharacteristic
262C2×C3⋊Dic3C22×C411yescharacteristic
263C2×C3⋊Dic3C22×C411yescharacteristic
264C4⋊(C3⋊D3)—22no—
265C4×C3⋊D3—21no—
266C4×C3⋊D3—21no—
267C4×C3⋊D3—21no—
268C4×C3⋊D3—21no—
269C2×C3×Dic3C22×C411yescharacteristic
270C2×C3×Dic3C22×C411yescharacteristic
271C2×C3×Dic3C22×C411yescharacteristic
272C2×C3×Dic3C22×C411yescharacteristic
273C2×C3×Dic3C22×C411yescharacteristic
274C3×D12—22no—
275C3×C4×D3—21no—
276C3×C4×D3—21no—
277C3×C4×D3—21no—
278C3×C4×D3—21no—
279C3×C4×D3C2×D412yes—
280C3×C4×D3#4112yes—
281#627—22no—
282#626—22no—
283#626—22no—
284#626—22no—
285#626—22no—
286#625—22no—
287#624—22no—
288D3×Dic3—22no—
289D3×Dic3—22no—
290C32×C8—21no—
291C32×C8—21no—
292C3⋊(C3⋊C8)—21no—
293C3⋊(C3⋊C8)C2×D412yes—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C3×C3⋊C8—21no—
297C3×C3⋊C8C2×D412yes—
298C2×#131—91no—
299C23×C8—91no—
300#525—91no—
301#435—91no—
302#435—91no—
303#435—91no—
304#435—91no—
305C8×D4—31no—
306C8×D4—91no—
307C8×D4—91no—
308C8×D4—91no—
309#424—31no—
310#408—91no—
311#407—91no—
312#405—91no—
313C23×D3—31no—
314C23×D3—31no—
315C2×C3×D4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C2×#67—31no—
320C2×#67—31no—
321C2×#67—31no—
322C2×#67—31no—
323C2×#67—31no—
324C2×#67—31no—
325C22×Dic3—31no—
326C22×Dic3—31no—
327#235—62no—
328#235—62no—
329#235—62no—
330#235—62no—
331C2×D12—31no—
332C2×D12—31no—
333C2×D12—31no—
334C2×D12—31no—
335C2×D12—31no—
336C2×D12—31no—
337C2×D12—61no—
338C2×D12C4×D311yescharacteristic
339C2×C4×D3—31no—
340C2×C4×D3—31no—
341C2×C4×D3—31no—
342C2×C4×D3—31no—
343C2×C4×D3—31no—
344C2×C4×D3—31no—
345C2×C4×D3—31no—
346C2×C4×D3—31no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—62no—
350C2×C4×D3—62no—
351C2×C4×D3—62no—
352C2×C4×D3—62no—
353C2×C4×D3C22×D311yescharacteristic
354C2×C4×D3C22×D311yescharacteristic
355C2×C4×D3C22×D311yescharacteristic
356C2×Dic6—31no—
357C2×Dic6—31no—
358C3×M16—62no—
359C2×C3×C8—21no—
360C2×C3×C8—21no—
361C2×C3×C8—31no—
362C2×C3×C8—31no—
363C2×C3×C8—31no—
364C2×C3×C8—31no—
365C2×C3×C8—62no—
366C2×C3×C8—62no—
367C2×C3×C8—62no—
368C2×C3×C8C22×D311yescharacteristic
369C2×C3×C8C22×D311yescharacteristic
370C2×C3×C8C22×D311yescharacteristic
371C2×C3×C8C22×D311yescharacteristic
372C3×C4⋊C4—31no—
373C3×C4⋊C4—31no—
374C3×C4⋊C4—31no—
375C3×C22⋊C4—31no—
376C3×C22⋊C4—31no—
377C3×C22⋊C4—31no—
378C3×C22⋊C4—31no—
379C3×C42—21no—
380C3×C42—31no—
381C3×C42C22×D311yescharacteristic
382C3×C42C22×D311yescharacteristic
383#217—31no—
384#217—31no—
385(C2×D3)⋊C4—31no—
386(C2×D3)⋊C4—31no—
387(C2×D3)⋊C4—31no—
388(C2×D3)⋊C4—31no—
389(C2×D3)⋊C4—31no—
390(C2×D3)⋊C4—31no—
391(C2×D3)⋊C4—31no—
392(C2×D3)⋊C4—31no—
393(C2×D3)⋊C4—31no—
394(C2×D3)⋊C4—31no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4C4×D311yescharacteristic
398(C2×D3)⋊C4C4×D311yescharacteristic
399(C2×D3)⋊C4C4×D311yescharacteristic
400(C2×D3)⋊C4C4×D311yescharacteristic
401C4⋊Dic3—31no—
402C4⋊Dic3—31no—
403C4⋊Dic3—31no—
404C4⋊Dic3—31no—
405C4⋊Dic3—61no—
406C4⋊Dic3C4×D311yescharacteristic
407Dic3⋊C4—31no—
408Dic3⋊C4—31no—
409Dic3⋊C4C4×D311yescharacteristic
410Dic3⋊C4C4×D311yescharacteristic
411C4×Dic3C22×D311yescharacteristic
412#208—62no—
413#208—62no—
414C2×C3⋊C8—31no—
415C2×C3⋊C8—31no—
416C2×C3⋊C8—34no—
417C2×C3⋊C8—31no—
418C2×C3⋊C8—31no—
419C2×C3⋊C8—61no—
420C2×C3⋊C8—61no—
421C2×C3⋊C8—62no—
422C2×C3⋊C8C22×D311yescharacteristic
423C2×C3⋊C8C22×D311yescharacteristic
424C2×C3⋊C8C22×D311yescharacteristic
425C2×C3⋊C8C22×D311yescharacteristic
426ΓL(1,𝔽25)—22no—
427ΓL(1,𝔽25)—62no—
428ΓL(1,𝔽25)—62no—
429ΓL(1,𝔽25)—62no—
430ΓL(1,𝔽25)—62no—
431ΓL(1,𝔽25)—122no—
432D3×C8—22no—
433D3×C8—22no—
434D3×C8—22no—
435D3×C8—34no—
436D3×C8—62no—
437D3×C8—62no—
438D3×C8—62no—
439D3×C8—62no—
440D3×C8—62no—
441D3×C8—62no—
442D3×C8—62no—
443D3×C8—122no—
444C22×C32C23×C411yescharacteristic
445C2×C3⋊D3—21no—
446C2×C3⋊D3—21no—
447C2×C3⋊D3—21no—
448C2×C3⋊D3—21no—
449C2×C3⋊D3—21no—
450C2×C3⋊D3#13112yescomplemented
451C2×C3×D3—21no—
452C2×C3×D3—21no—
453C2×C3×D3—21no—
454C2×C3×D3—21no—
455C2×C3×D3—21no—
456C2×C3×D3—21no—
457C2×C3×D3—21no—
458C2×C3×D3C4×D412yes—
459C2×C3×D3#13112yescomplemented
460D32—28no—
461C32×C4—21no—
462C32×C4—21no—
463C32×C4C22×D411yescharacteristic
464C32×C4C2×#4111yescharacteristic
465C3⋊Dic3—21no—
466C3⋊Dic3—21no—
467C3×Dic3—21no—
468C3×Dic3—21no—
469C3×Dic3—21no—
470C3×Dic3—21no—
471C3×Dic3C4×D412yes—
472C2×#41—91no—
473C23×C4—91no—
474#131—184no—
475C2×M16—31no—
476C2×M16—91no—
477C2×M16—91no—
478C2×M16—91no—
479C22×C8—31no—
480C22×C8—31no—
481C22×C8—31no—
482C22×C8—91no—
483C22×C8—91no—
484C22×C8—91no—
485C22×C8—91no—
486C22×C8—91no—
487C22×C8—184no—
488#123—91no—
489#123—91no—
490C22⋊Q8—91no—
491C22⋊Q8—91no—
492#121—91no—
493#121—91no—
494#120—91no—
495#120—91no—
496C4×D4—31no—
497C4×D4—91no—
498C4×D4—91no—
499C4×D4—91no—
500#117—31no—
501C4⋊C8—31no—
502C4⋊C8—31no—
503C4⋊C8—31no—
504C4⋊C8D3211yescharacteristic, complemented
505C22⋊C8—31no—
506C22⋊C8—31no—
507C22⋊C8—91no—
508C22⋊C8—91no—
509C22⋊C8—91no—
510C22⋊C8—91no—
511C22⋊C8—91no—
512C22⋊C8—91no—
513#97—91no—
514#97—91no—
515C4×C8—31no—
516C4×C8—91no—
517C23×C3—31no—
518C23×C3—31no—
519C23×C3—31no—
520C22×D3—31no—
521C22×D3—31no—
522C22×D3—31no—
523C22×D3—31no—
524C22×D3—61no—
525C22×D3—61no—
526C22×D3—62no—
527C22×D3—62no—
528C22×D3—62no—
529C22×D3—62no—
530C22×D3—62no—
531C22×D3—62no—
532C22×D3C2×C4×D311yescharacteristic
533C22×D3C2×C4×D311yescharacteristic
534C22×D3C2×C4×D311yescharacteristic
535C3×D4—62no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—31no—
540C2×C3×C4—32no—
541C2×C3×C4—32no—
542C2×C3×C4—31no—
543C2×C3×C4—31no—
544C2×C3×C4—31no—
545C2×C3×C4—31no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4C2×C4×D311yescharacteristic
551C2×C3×C4C2×C4×D311yescharacteristic
552C2×C3×C4C2×C4×D311yescharacteristic
553C2×C3×C4C2×C4×D311yescharacteristic
554C2×C3×C4C23×D311yescharacteristic
555C2×C3×C4C23×D311yescharacteristic
556#67—62no—
557#67—62no—
558#67—62no—
559#67—62no—
560#67—62no—
561#67—62no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—31no—
565C2×Dic3—31no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—62no—
569C2×Dic3—62no—
570C2×Dic3C2×C4×D311yescharacteristic
571C2×Dic3C2×C4×D311yescharacteristic
572C2×Dic3C2×C4×D311yescharacteristic
573C2×Dic3C2×C4×D311yescharacteristic
574C2×Dic3C2×C4×D311yescharacteristic
575D12—22no—
576D12—62no—
577D12—62no—
578D12—62no—
579D12—62no—
580D12—62no—
581D12—62no—
582D12—122no—
583C4×D3—21no—
584C4×D3—21no—
585C4×D3—21no—
586C4×D3—21no—
587C4×D3—62no—
588C4×D3—62no—
589C4×D3—62no—
590C4×D3—61no—
591C4×D3—61no—
592C4×D3—61no—
593C4×D3—61no—
594C4×D3—61no—
595C4×D3—61no—
596C4×D3—61no—
597C4×D3—61no—
598C4×D3—62no—
599C4×D3—121no—
600C4×D3—121no—
601C4×D3—121no—
602C4×D3—121no—
603C4×D3D3×D412yes—
604C4×D3#23912yes—
605Dic6—62no—
606Dic6—62no—
607C3×C8—21no—
608C3×C8—21no—
609C3×C8—21no—
610C3×C8—21no—
611C3×C8—32no—
612C3×C8—41no—
613C3×C8—41no—
614C3×C8—61no—
615C3×C8—61no—
616C3×C8—61no—
617C3⋊C8—21no—
618C3⋊C8—21no—
619C3⋊C8—21no—
620C3⋊C8—32no—
621C3⋊C8—32no—
622C3⋊C8—62no—
623C3⋊C8—61no—
624C3⋊C8—61no—
625C3⋊C8—121no—
626C3⋊C8D3×D412yes—
627C2×C32C2×C4×D411yescharacteristic
628C2×C32C2×#13111yescharacteristic
629C2×C32C2×#13111yescharacteristic
630C3⋊D3—22no—
631C3⋊D3—41no—
632C3×D3—22no—
633C3×D3—22no—
634C3×D3—41no—
635C24—91no—
636#41—182no—
637#41—182no—
638C2×Q8—91no—
639C2×D4—31no—
640C2×D4—91no—
641C2×D4—91no—
642C2×D4—91no—
643C2×D4—91no—
644C2×D4—91no—
645C2×D4—91no—
646C22×C4—31no—
647C22×C4—31no—
648C22×C4—31no—
649C22×C4—91no—
650C22×C4—91no—
651C22×C4—91no—
652C22×C4—91no—
653C22×C4—91no—
654C22×C4—182no—
655C22×C4—182no—
656M16—62no—
657M16—182no—
658M16—182no—
659M16—182no—
660C2×C8—31no—
661C2×C8—31no—
662C2×C8—31no—
663C2×C8—31no—
664C2×C8—62no—
665C2×C8—62no—
666C2×C8—62no—
667C2×C8—94no—
668C2×C8—91no—
669C2×C8—91no—
670C2×C8—182no—
671C2×C8—182no—
672C2×C8—182no—
673C2×C8—182no—
674C2×C8C2×D3211yescharacteristic
675C2×C8C2×D3211yescharacteristic
676C4⋊C4—31no—
677C4⋊C4—31no—
678C4⋊C4—31no—
679C4⋊C4—91no—
680C4⋊C4—91no—
681C4⋊C4—91no—
682C22⋊C4—31no—
683C22⋊C4—31no—
684C22⋊C4—31no—
685C22⋊C4—31no—
686C22⋊C4—91no—
687C22⋊C4—91no—
688C22⋊C4—91no—
689C22⋊C4—91no—
690C22⋊C4—91no—
691C22⋊C4—91no—
692C42—31no—
693C42C2×D3211yescharacteristic
694C22×C3—21no—
695C22×C3—32no—
696C22×C3—32no—
697C22×C3—61no—
698C22×C3—61no—
699C22×C3—61no—
700C22×C3—61no—
701C22×C3—61no—
702C22×C3—61no—
703C22×C3—61no—
704C22×C3C22×C4×D311yescharacteristic
705C22×C3C22×C4×D311yescharacteristic
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—21no—
709C2×D3—21no—
710C2×D3—21no—
711C2×D3—21no—
712C2×D3—21no—
713C2×D3—32no—
714C2×D3—32no—
715C2×D3—62no—
716C2×D3—68no—
717C2×D3—68no—
718C2×D3—61no—
719C2×D3—61no—
720C2×D3—61no—
721C2×D3—61no—
722C2×D3—61no—
723C2×D3—61no—
724C2×D3—61no—
725C2×D3—61no—
726C2×D3—61no—
727C2×D3—61no—
728C2×D3—121no—
729C2×D3—121no—
730C2×D3—121no—
731C2×D3—121no—
732C2×D3—121no—
733C2×D3#89312yes—
734C2×D3#90112yescomplemented
735C3×C4—21no—
736C3×C4—21no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—21no—
740C3×C4—21no—
741C3×C4—32no—
742C3×C4—41no—
743C3×C4—41no—
744C3×C4—61no—
745C3×C4—61no—
746C3×C4—61no—
747C3×C4—61no—
748C3×C4C2×D3×D411yescharacteristic
749C3×C4C2×D3×D411yescharacteristic
750C3×C4C2×#23911yescharacteristic
751C3×C4D3×#4111yescharacteristic
752Dic3—21no—
753Dic3—21no—
754Dic3—21no—
755Dic3—21no—
756Dic3—61no—
757Dic3—61no—
758Dic3—61no—
759Dic3—61no—
760Dic3—121no—
761Dic3—121no—
762Dic3#89312yes—
763C32#292911yescharacteristic, complemented, Sylow
764C23—31no—
765C23—31no—
766C23—31no—
767C23—91no—
768C23—91no—
769C23—182no—
770C23—182no—
771C23—182no—
772Q8—182no—
773D4—62no—
774D4—182no—
775D4—182no—
776D4—182no—
777D4—182no—
778D4—182no—
779D4—182no—
780C2×C4—31no—
781C2×C4—32no—
782C2×C4—32no—
783C2×C4—31no—
784C2×C4—31no—
785C2×C4—31no—
786C2×C4—31no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—91no—
792C2×C4—91no—
793C2×C4—182no—
794C2×C4—182no—
795C2×C4—182no—
796C2×C4—181no—
797C2×C4—181no—
798C2×C4—181no—
799C2×C4—181no—
800C2×C4C4×D3211yescharacteristic
801C2×C4C4×D3211yescharacteristic
802C2×C4C22×D3211yescharacteristic
803C8—21no—
804C8—21no—
805C8—32no—
806C8—61no—
807C8—61no—
808C8—61no—
809C8—92no—
810C8—181no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—62no—
815C2×C3—62no—
816C2×C3—121no—
817C2×C3C2×#89311yescharacteristic
818C2×C3C4×D3×D411yescharacteristic
819C2×C3C2×#90111yescharacteristic
820C2×C3D3×#13111yescharacteristic
821C2×C3D3×#13111yescharacteristic
822C2×C3D3×#13111yescharacteristic
823D3—22no—
824D3—22no—
825D3—41no—
826D3—62no—
827D3—62no—
828D3—122no—
829D3—121no—
830D3—121no—
831D3—241no—
832C22—32no—
833C22—32no—
834C22—61no—
835C22—61no—
836C22—61no—
837C22—61no—
838C22—61no—
839C22—61no—
840C22—61no—
841C22—92no—
842C22—188no—
843C22—181no—
844C22—181no—
845C22—181no—
846C22—181no—
847C22—181no—
848C22C2×C4×D3211yescharacteristic
849C4—21no—
850C4—21no—
851C4—32no—
852C4—61no—
853C4—61no—
854C4—61no—
855C4—61no—
856C4—181no—
857C4—181no—
858C4D32×D411yescharacteristic
859C4D3×#23911yescharacteristic
860C3—21no—
861C3#7907311yescharacteristic, complemented
862C3#7942111yescharacteristic, complemented
863C2—62no—
864C2—62no—
865C2—121no—
866C2—182no—
867C2—361no—
868C2D3×#89311yescharacteristic
869C2D3×#90111yescharacteristic
870C2#1059470711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4⋊C8C22
prime radical#10593997C2
cosocleC2×C32×C4C24
hypercenterC4⋊C8D32
hypocenterC32#2929
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#63804C2semidirect
2. C2×D32×C8C2semidirect
4. #10592535C2semidirect
5. C3×#4839C2semidirect
6. C3×#4834C2semidirect
7. #10590953C2semidirect
8. #10590936C2semidirect
9. #10590907C2semidirect
10. #10590737C2semidirect
11. #10590720C2semidirect
12. #10590720C2semidirect
13. #10590330C2semidirect
14. #10590327C2semidirect
15. #10590318C2semidirect
20. C2×#3743C22semidirect
26. C2×C3×D3×C8C22semidirect
40. C2×#3711C22semidirect
42. C2×#3710C22semidirect
47. C32×C4⋊C8C22semidirect
49. #63647C22semidirect
50. #63630C22semidirect
52. C3×(C2×D3)⋊C8C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. C3×Dic3⋊C8C22semidirect
55. C3×C4⋊(C3⋊C8)C22semidirect
56. C3×C4×C3⋊C8C22semidirect
58. #63557C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
61. #63554C22semidirect
62. Dic3×C3⋊C8C22semidirect
77. #4839D3semidirect
87. #4834D3semidirect
152. D3×C3⋊C8D4semidirect
193. C2×D3×C8C2×D3semidirect
219. C3×C4⋊C8C2×D3semidirect
220. C3×C4⋊C8C2×D3semidirect
239. (C2×D3)⋊C8C2×D3semidirect
241. Dic3⋊C8C2×D3semidirect
242. Dic3⋊C8C2×D3semidirect
244. C4⋊(C3⋊C8)C2×D3semidirect
250. C4×C3⋊C8C2×D3semidirect
450. C2×C3⋊D3#131semidirect
459. C2×C3×D3#131semidirect
504. C4⋊C8D32semidirect
734. C2×D3#901semidirect
763. C32#2929semidirect
861. C3#79073semidirect
862. C3#79421semidirect

Maximal subgroups

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

subgroupindex
C2×#638042
C2×D32×C82
#105939972
#105925352
C3×#48392
C3×#48342
#105909532
#105909362
#105909072
#105907372
#105907202
#105903302
#105903272
#105903182
#794213
#790733