Finite Group Databasebeta

← #11859338

Subgroups — #11859338

Order 1152.

1107 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
1C22×C3×D3×C8C211yesmaximal, characteristic, complemented
2#10595002C211yesmaximal, characteristic
3C2×#63803C211yesmaximal, characteristic, complemented
4C8×#638C211yesmaximal, characteristic, complemented
5C3×C8×#67C211yesmaximal, characteristic, complemented
6#10591157C211yesmaximal, characteristic, complemented
7#10591155C211yesmaximal, characteristic, complemented
8#10591154C211yesmaximal, characteristic, complemented
9#10590953C211yesmaximal, characteristic, complemented
10#10590727C211yesmaximal, characteristic, complemented
11#10590723C211yesmaximal, characteristic, complemented
12C8×#626C211yesmaximal, characteristic, complemented
13C8×#625C211yesmaximal, characteristic, complemented
14#10590694C211yesmaximal, characteristic, complemented
15#10590692C211yesmaximal, characteristic, complemented
16#83734—31nomaximal
17#79421—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C2×#3798C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21C4×#638C2211yescharacteristic
22C2×C8×C3⋊D3C2211yescharacteristic, complemented
23C3×C4×#67C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×C3×D3×C8—24no—
26C2×C3×D3×C8C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29C2×C3×D3×C8C2211yescharacteristic
30C2×C3×D3×C8C2211yescharacteristic, complemented
31#63978C411yescharacteristic
32#63977C411yescharacteristic
33#63976C411yescharacteristic
34#63964C411yescharacteristic
35#63906C411yescharacteristic
36#63905C411yescharacteristic
37C4×#626C2211yescharacteristic
38C4×#625C2211yescharacteristic
39#63855C2211yescharacteristic
40#63851C411yescharacteristic
41#63850C411yescharacteristic
42C2×#3712C2211yescharacteristic, complemented
43C2×#3711C2211yescharacteristic
44C2×#3711C2211yescharacteristic
45C2×#3711C2211yescharacteristic, complemented
46#63803—24no—
47#63657C2211yescharacteristic
48#63647C2211yescharacteristic, complemented
49#63641C2211yescharacteristic, complemented
50C8×C3⋊Dic3C2211yescharacteristic, complemented
51C3×#830C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×C8×Dic3C2211yescharacteristic, complemented
55#63572C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63557C2211yescharacteristic, complemented
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63555C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C23×C3×C8—31no—
64#5791—31no—
65C2×#901—31no—
66C2×#901—31no—
67C22×D3×C8D311yescharacteristic, complemented
68#5547—31no—
69C3×C8×D4—31no—
70#5207—31no—
71#5111—31no—
72#5111—31no—
73#5111—31no—
74#5111—31no—
75#5110—31no—
76C8×#67—31no—
77C8×#67—31no—
78C8×#67—31no—
79C8×#67—31no—
80C8×#67—31no—
81C8×#67—61no—
82C8×#67D311yescharacteristic, complemented
83#5102—31no—
84#5101—31no—
85#5011—31no—
86#4839—31no—
87#4836—31no—
88#4730—31no—
89#4728—31no—
90#4727—31no—
91#4726—31no—
92#4689—31no—
93C8×D12—31no—
94C23×C3×D3C2×C411yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×#638C2×C411yescharacteristic
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C3×#67C2×C411yescharacteristic
99C22×C3×Dic3C2×C411yescharacteristic
100C2×C3×C4×D3—22no—
101C2×C3×C4×D3—22no—
102C2×C3×C4×D3C2×C411yescharacteristic
103C2×C3×C4×D3C2×C411yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×#627C2×C411yescharacteristic
108C2×#626C2×C411yescharacteristic
109C2×#626C2×C411yescharacteristic
110C2×#626C2×C411yescharacteristic
111C2×#625C2×C411yescharacteristic
112C2×#625C2×C411yescharacteristic
113#3798—22no—
114#3798—22no—
115C2×C32×C8—22no—
116C2×C32×C8C2311yescharacteristic
117C2×C32×C8C2311yescharacteristic
118#3757C2×C411yescharacteristic
119#3752C2×C411yescharacteristic
120#3750C2×C411yescharacteristic
121C4×C3⋊Dic3C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C8×C3⋊D3—22no—
125C3×#217C2×C411yescharacteristic
126C3×(C2×D3)⋊C4C2×C411yescharacteristic
127C3×Dic3⋊C4C2×C411yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8—22no—
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C3×D3×C8—22no—
135C3×D3×C8—22no—
136C3×D3×C8—22no—
137C3×D3×C8—22no—
138C3×D3×C8D414yescomplemented
139#3724C2×C411yescharacteristic
140Dic3⋊Dic3C2×C411yescharacteristic
141Dic3⋊Dic3C2×C411yescharacteristic
142Dic3⋊Dic3C2×C411yescharacteristic
143#3722C2×C411yescharacteristic
144(C2×D3)⋊Dic3C2×C411yescharacteristic
145(C2×D3)⋊Dic3C2×C411yescharacteristic
146(C2×D3)⋊Dic3C2×C411yescharacteristic
147(C2×D3)⋊Dic3C2×C411yescharacteristic
148(C2×D3)⋊Dic3C2×C411yescharacteristic
149#3712—22no—
150#3711—22no—
151#3711—22no—
152#3711—22no—
153#2929—91noSylow
154C23×C3×C4—31no—
155C2×#235—31no—
156C2×#235—31no—
157C22×C4×D3C2×D311yescharacteristic
158C22×C3×C8—21no—
159C22×C3×C8—31no—
160C22×C3×C8—31no—
161C22×C3×C8—31no—
162C22×C3×C8—31no—
163C22×C3×C8—31no—
164C22×C3×C8—31no—
165C22×C3×C8—64no—
166C22×C3×C8C2×D311yescharacteristic
167C22×C3×C8C2×D311yescharacteristic
168C3×C4×D4—31no—
169#953—31no—
170#953—31no—
171#939—31no—
172#937—31no—
173#930—31no—
174#930—31no—
175#929—31no—
176#929—31no—
177C4×#67—31no—
178C4×#67—31no—
179C4×#67—31no—
180C4×#67—31no—
181C4×#67—31no—
182C4×#67—61no—
183C4×#67C2×D311yescharacteristic
184#926—31no—
185#924—31no—
186#924—31no—
187C2×#208—31no—
188C2×#208—31no—
189C2×#208—31no—
190C22×C3⋊C8C2×D311yescharacteristic
191#901—64no—
192#901—64no—
193C2×ΓL(1,𝔽25)—31no—
194C2×ΓL(1,𝔽25)—31no—
195C2×ΓL(1,𝔽25)—31no—
196C2×ΓL(1,𝔽25)—31no—
197C2×ΓL(1,𝔽25)—31no—
198C2×D3×C8—24no—
199C2×D3×C8—31no—
200C2×D3×C8—31no—
201C2×D3×C8—61no—
202C2×D3×C8C2×D311yescharacteristic
203C2×D3×C8C2×D311yescharacteristic
204C2×D3×C8C2×D311yescharacteristic
205C2×D3×C8C2×D311yescharacteristic
206C2×D3×C8C2×D311yescharacteristic, complemented
207#896—31no—
208#894—31no—
209#884—31no—
210#883—31no—
211#882—31no—
212#878—31no—
213C4×D12—31no—
214#872—31no—
215C3×C4⋊C8—31no—
216C3×C22⋊C8—31no—
217C3×C22⋊C8—31no—
218C3×C4×C8—31no—
219#830—31no—
220#830—31no—
221#830—31no—
222#830—31no—
223#830—31no—
224#830—61no—
225#830C2×D311yescharacteristic
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—61no—
234(C2×D3)⋊C8C2×D311yescharacteristic, complemented
235#815—31no—
236#815—31no—
237#815—31no—
238Dic3⋊C8—31no—
239Dic3⋊C8—31no—
240Dic3⋊C8—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8—31no—
243Dic3⋊C8—61no—
244Dic3⋊C8C2×D311yescharacteristic, complemented
245C8×Dic3—31no—
246C8×Dic3—31no—
247C8×Dic3—61no—
248C8×Dic3C2×D311yescharacteristic, complemented
249C4⋊(C3⋊C8)—31no—
250#803—31no—
251C23×C32C22×C411yescharacteristic
252C22×C3⋊D3C22×C411yescharacteristic
253C22×C3×D3—22no—
254C22×C3×D3—22no—
255C22×C3×D3—22no—
256C22×C3×D3C22×C411yescharacteristic
257C22×C3×D3C22×C411yescharacteristic
258C22×C3×D3C22×C411yescharacteristic
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4C22×C411yescharacteristic
262C2×C32×C4C2411yescharacteristic
263#638—22no—
264C2×C3⋊Dic3C22×C411yescharacteristic
265C2×C3⋊Dic3C22×C411yescharacteristic
266C2×C3⋊Dic3C22×C411yescharacteristic
267C4×C3⋊D3—21no—
268C4×C3⋊D3—21no—
269C3×#67—22no—
270C2×C3×Dic3—22no—
271C2×C3×Dic3C22×C411yescharacteristic
272C2×C3×Dic3C22×C411yescharacteristic
273C2×C3×Dic3C22×C411yescharacteristic
274C2×C3×Dic3C22×C411yescharacteristic
275C2×C3×Dic3C22×C411yescharacteristic
276C3×C4×D3—22no—
277C3×C4×D3—21no—
278C3×C4×D3—21no—
279C3×C4×D3—21no—
280C3×C4×D3—21no—
281C3×C4×D3—22no—
282C3×C4×D3C2×D412yes—
283C3×C4×D3#4112yes—
284#627—22no—
285#626—22no—
286#626—22no—
287#626—22no—
288#625—22no—
289#625—22no—
290C32×C8—21no—
291C32×C8C2×D412yes—
292C3⋊(C3⋊C8)—21no—
293C3⋊(C3⋊C8)—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C3×C3⋊C8—21no—
297C3×C3⋊C8C2×D412yes—
298C2×#131—91no—
299C23×C8—31no—
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—91no—
310#408—91no—
311#407—91no—
312#405—91no—
313C24×C3—31no—
314C23×D3C4×D311yescharacteristic
315C2×C3×D4—31no—
316C22×C3×C4—21no—
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—62no—
324C22×C3×C4—62no—
325C22×C3×C4C22×D311yescharacteristic
326C22×C3×C4C22×D311yescharacteristic
327C2×#67—31no—
328C2×#67—31no—
329C2×#67—31no—
330C2×#67—31no—
331C2×#67—31no—
332C2×#67—31no—
333C2×#67—31no—
334C2×#67—31no—
335C2×#67—31no—
336C2×#67—61no—
337C2×#67C4×D311yescharacteristic
338C22×Dic3C4×D311yescharacteristic
339#235—62no—
340#235—62no—
341#235—62no—
342#235—62no—
343C2×D12—31no—
344C2×D12—31no—
345C2×D12—31no—
346C2×C4×D3—22no—
347C2×C4×D3—22no—
348C2×C4×D3—31no—
349C2×C4×D3—31no—
350C2×C4×D3—61no—
351C2×C4×D3C4×D311yescharacteristic
352C2×C4×D3C4×D311yescharacteristic
353C2×C4×D3C22×D311yescharacteristic
354C2×C4×D3C22×D311yescharacteristic
355C2×C4×D3C22×D311yescharacteristic
356C2×Dic6—31no—
357C2×Dic6—31no—
358C2×C3×C8—22no—
359C2×C3×C8—22no—
360C2×C3×C8—21no—
361C2×C3×C8—21no—
362C2×C3×C8—31no—
363C2×C3×C8—34no—
364C2×C3×C8—31no—
365C2×C3×C8—31no—
366C2×C3×C8—31no—
367C2×C3×C8—42no—
368C2×C3×C8—62no—
369C2×C3×C8—62no—
370C2×C3×C8—62no—
371C2×C3×C8—62no—
372C2×C3×C8—62no—
373C2×C3×C8C22×D311yescharacteristic
374C2×C3×C8C22×D311yescharacteristic
375C2×C3×C8C22×D311yescharacteristic
376C2×C3×C8C22×D311yescharacteristic
377C3×C4⋊C4—31no—
378C3×C22⋊C4—31no—
379C3×C22⋊C4—31no—
380C3×C42—31no—
381#217—31no—
382#217—31no—
383#217—31no—
384#217—31no—
385#217—31no—
386#217—31no—
387#217—31no—
388#217—61no—
389#217C4×D311yescharacteristic
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—31no—
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—31no—
398(C2×D3)⋊C4—31no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4C4×D311yescharacteristic
401C4⋊Dic3—31no—
402C4⋊Dic3—31no—
403C4⋊Dic3—31no—
404Dic3⋊C4—31no—
405Dic3⋊C4—31no—
406Dic3⋊C4—31no—
407Dic3⋊C4—31no—
408Dic3⋊C4—31no—
409Dic3⋊C4—31no—
410Dic3⋊C4—31no—
411Dic3⋊C4—61no—
412Dic3⋊C4C4×D311yescharacteristic
413C4×Dic3—31no—
414C4×Dic3—31no—
415C4×Dic3—61no—
416C4×Dic3C22×D311yescharacteristic
417#208—62no—
418#208—62no—
419#208—62no—
420C2×C3⋊C8—22no—
421C2×C3⋊C8—31no—
422C2×C3⋊C8—31no—
423C2×C3⋊C8—31no—
424C2×C3⋊C8—31no—
425C2×C3⋊C8—61no—
426C2×C3⋊C8—61no—
427C2×C3⋊C8C22×D311yescharacteristic
428C2×C3⋊C8C22×D311yescharacteristic
429C2×C3⋊C8C22×D311yescharacteristic
430C2×C3⋊C8C22×D311yescharacteristic
431ΓL(1,𝔽25)—62no—
432ΓL(1,𝔽25)—62no—
433ΓL(1,𝔽25)—62no—
434ΓL(1,𝔽25)—62no—
435ΓL(1,𝔽25)—62no—
436D3×C8—22no—
437D3×C8—22no—
438D3×C8—22no—
439D3×C8—22no—
440D3×C8—62no—
441D3×C8—62no—
442D3×C8—122no—
443D3×C8#6714yescomplemented
444C22×C32—21no—
445C22×C32—21no—
446C22×C32#13112yescomplemented
447C22×C32C23×C411yescharacteristic
448C2×C3⋊D3—21no—
449C2×C3⋊D3—21no—
450C2×C3⋊D3—21no—
451C2×C3×D3—28no—
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×D3—21no—
459C2×C3×D3C4×D412yes—
460C2×C3×D3#13112yescomplemented
461C32×C4—21no—
462C32×C4C22×D411yescharacteristic
463C32×C4C2×#4111yescharacteristic
464C3⋊Dic3—21no—
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—31no—
474#131—184no—
475C2×M16—91no—
476C2×M16—91no—
477C2×M16—91no—
478C2×M16—91no—
479C22×C8—31no—
480C22×C8—31no—
481C22×C8—31no—
482C22×C8—31no—
483C22×C8—31no—
484C22×C8—31no—
485C22×C8—64no—
486C22×C8—91no—
487C22×C8D3211yescharacteristic
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—91no—
501C4⋊C8—31no—
502C4⋊C8—91no—
503C4⋊C8—91no—
504C4⋊C8—91no—
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—21no—
518C23×C3—31no—
519C23×C3—31no—
520C23×C3—31no—
521C23×C3—62no—
522C23×C3—62no—
523C23×C3—62no—
524C23×C3C2×C4×D311yescharacteristic
525C23×C3C2×C4×D311yescharacteristic
526C22×D3—22no—
527C22×D3—22no—
528C22×D3—22no—
529C22×D3—31no—
530C22×D3—31no—
531C22×D3—61no—
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—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—31no—
543C2×C3×C4—32no—
544C2×C3×C4—32no—
545C2×C3×C4—31no—
546C2×C3×C4—31no—
547C2×C3×C4—31no—
548C2×C3×C4—31no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—62no—
552C2×C3×C4—62no—
553C2×C3×C4—62no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4C2×C4×D311yescharacteristic
559C2×C3×C4C2×C4×D311yescharacteristic
560C2×C3×C4C23×D311yescharacteristic
561C2×C3×C4C23×D311yescharacteristic
562#67—22no—
563#67—62no—
564#67—62no—
565#67—62no—
566#67—62no—
567#67—64no—
568#67—62no—
569#67—62no—
570#67—62no—
571#67—62no—
572#67—62no—
573C2×Dic3—22no—
574C2×Dic3—31no—
575C2×Dic3—31no—
576C2×Dic3—31no—
577C2×Dic3—31no—
578C2×Dic3—31no—
579C2×Dic3—31no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3C2×C4×D311yescharacteristic
584C2×Dic3C2×C4×D311yescharacteristic
585C2×Dic3C2×C4×D311yescharacteristic
586C2×Dic3C2×C4×D311yescharacteristic
587C2×Dic3C2×C4×D311yescharacteristic
588D12—62no—
589D12—62no—
590D12—62no—
591C4×D3—22no—
592C4×D3—21no—
593C4×D3—21no—
594C4×D3—21no—
595C4×D3—21no—
596C4×D3—22no—
597C4×D3—61no—
598C4×D3—61no—
599C4×D3—61no—
600C4×D3—61no—
601C4×D3—121no—
602C4×D3—121no—
603C4×D3#23512yes—
604C4×D3C2×#6712yes—
605Dic6—62no—
606Dic6—62no—
607C3×C8—21no—
608C3×C8—21no—
609C3×C8—22no—
610C3×C8—32no—
611C3×C8—41no—
612C3×C8—61no—
613C3×C8—61no—
614C3×C8—61no—
615C3×C8D3×D412yes—
616C3×C8C2×#6712yes—
617C3⋊C8—21no—
618C3⋊C8—21no—
619C3⋊C8—21no—
620C3⋊C8—61no—
621C3⋊C8—61no—
622C3⋊C8—61no—
623C3⋊C8—61no—
624C3⋊C8—121no—
625C3⋊C8—121no—
626C3⋊C8C2×#6712yes—
627C2×C32—22no—
628C2×C32C2×C4×D411yescharacteristic
629C2×C32C2×#13111yescharacteristic
630C2×C32C2×#13111yescharacteristic
631C3⋊D3—41no—
632C3×D3—22no—
633C3×D3—22no—
634C3×D3—41no—
635C24—31no—
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—31no—
650C22×C4—31no—
651C22×C4—31no—
652C22×C4—62no—
653C22×C4—62no—
654C22×C4—91no—
655C22×C4C2×D3211yescharacteristic
656M16—182no—
657M16—182no—
658M16—182no—
659M16—182no—
660C2×C8—22no—
661C2×C8—31no—
662C2×C8—34no—
663C2×C8—31no—
664C2×C8—31no—
665C2×C8—31no—
666C2×C8—62no—
667C2×C8—62no—
668C2×C8—62no—
669C2×C8—62no—
670C2×C8—62no—
671C2×C8—91no—
672C2×C8—91no—
673C2×C8—182no—
674C2×C8C2×D3211yescharacteristic
675C2×C8C2×D3211yescharacteristic
676C4⋊C4—31no—
677C4⋊C4—91no—
678C4⋊C4—91no—
679C4⋊C4—91no—
680C4⋊C4—91no—
681C4⋊C4—91no—
682C22⋊C4—31no—
683C22⋊C4—31no—
684C22⋊C4—91no—
685C22⋊C4—91no—
686C22⋊C4—91no—
687C22⋊C4—91no—
688C22⋊C4—91no—
689C22⋊C4—91no—
690C22⋊C4—91no—
691C22⋊C4—91no—
692C42—31no—
693C42—91no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—22no—
700C22×C3—32no—
701C22×C3—32no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—68no—
705C22×C3—61no—
706C22×C3—61no—
707C22×C3—61no—
708C22×C3—61no—
709C22×C3—61no—
710C22×C3—61no—
711C22×C3—61no—
712C22×C3#90112yescomplemented
713C22×C3#90112yescomplemented
714C22×C3C22×C4×D311yescharacteristic
715C22×C3C22×C4×D311yescharacteristic
716C2×D3—28no—
717C2×D3—21no—
718C2×D3—21no—
719C2×D3—21no—
720C2×D3—21no—
721C2×D3—21no—
722C2×D3—21no—
723C2×D3—21no—
724C2×D3—62no—
725C2×D3—61no—
726C2×D3—61no—
727C2×D3—61no—
728C2×D3—61no—
729C2×D3—61no—
730C2×D3—61no—
731C2×D3—121no—
732C2×D3—121no—
733C2×D3#90112yescomplemented
734C2×D3C4×#6712yes—
735C3×C4—21no—
736C3×C4—21no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—32no—
740C3×C4—41no—
741C3×C4—61no—
742C3×C4—61no—
743C3×C4—61no—
744C3×C4—61no—
745C3×C4C2×#23511yescharacteristic
746C3×C4C2×D3×D411yescharacteristic
747C3×C4D3×#4111yescharacteristic
748C3×C4C22×#6711yescharacteristic
749Dic3—21no—
750Dic3—21no—
751Dic3—21no—
752Dic3—21no—
753Dic3—62no—
754Dic3—61no—
755Dic3—61no—
756Dic3—61no—
757Dic3—61no—
758Dic3—61no—
759Dic3—61no—
760Dic3—121no—
761Dic3—121no—
762Dic3C4×#6712yes—
763C32#292911yescharacteristic, complemented, Sylow
764C23—31no—
765C23—31no—
766C23—31no—
767C23—62no—
768C23—62no—
769C23—62no—
770C23—91no—
771C23C4×D3211yescharacteristic
772Q8—182no—
773D4—62no—
774D4—182no—
775D4—182no—
776D4—182no—
777D4—182no—
778D4—182no—
779D4—182no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—31no—
783C2×C4—32no—
784C2×C4—32no—
785C2×C4—31no—
786C2×C4—31no—
787C2×C4—31no—
788C2×C4—31no—
789C2×C4—62no—
790C2×C4—62no—
791C2×C4—62no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—91no—
797C2×C4—91no—
798C2×C4—91no—
799C2×C4—181no—
800C2×C4—181no—
801C2×C4C4×D3211yescharacteristic
802C2×C4C22×D3211yescharacteristic
803C8—21no—
804C8—32no—
805C8—61no—
806C8—61no—
807C8—61no—
808C8—181no—
809C8—181no—
810C8D3×#6712yes—
811C2×C3—22no—
812C2×C3—22no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—42no—
817C2×C3—62no—
818C2×C3—62no—
819C2×C3—121no—
820C2×C3C4×D3×D411yescharacteristic
821C2×C3C2×#90111yescharacteristic
822C2×C3C2×#90111yescharacteristic
823C2×C3C2×#90111yescharacteristic
824C2×C3D3×#13111yescharacteristic
825C2×C3C2×C4×#6711yescharacteristic
826D3—22no—
827D3—22no—
828D3—41no—
829D3—122no—
830D3—121no—
831D3—121no—
832C22—21no—
833C22—21no—
834C22—32no—
835C22—32no—
836C22—68no—
837C22—61no—
838C22—61no—
839C22—61no—
840C22—61no—
841C22—61no—
842C22—61no—
843C22—61no—
844C22—181no—
845C22—181no—
846C22—181no—
847C22#6380312yescomplemented
848C22C2×C4×D3211yescharacteristic
849C4—21no—
850C4—32no—
851C4—61no—
852C4—61no—
853C4—61no—
854C4—61no—
855C4—181no—
856C4—181no—
857C4—181no—
858C4D3×#23511yescharacteristic
859C4C2×D3×#6711yescharacteristic
860C3—21no—
861C3#7942111yescharacteristic, complemented
862C3#8373411yescharacteristic, complemented
863C2—22no—
864C2—62no—
865C2—62no—
866C2—121no—
867C2—361no—
868C2D3×#90111yescharacteristic
869C2C2×#6380311yescharacteristic
870C2C4×D3×#6711yescharacteristic
subgroupG/H
centerC2×C8C2×D32
commutator, socleC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
prime radical#10595002C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2929
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×C8C2semidirect
3. C2×#63803C2semidirect
4. C8×#638C2semidirect
5. C3×C8×#67C2semidirect
6. #10591157C2semidirect
7. #10591155C2semidirect
8. #10591154C2semidirect
9. #10590953C2semidirect
10. #10590727C2semidirect
11. #10590723C2semidirect
12. C8×#626C2semidirect
13. C8×#625C2semidirect
14. #10590694C2semidirect
15. #10590692C2semidirect
22. C2×C8×C3⋊D3C22semidirect
30. C2×C3×D3×C8C22semidirect
42. C2×#3712C22semidirect
45. C2×#3711C22semidirect
48. #63647C22semidirect
49. #63641C22semidirect
50. C8×C3⋊Dic3C22semidirect
52. C3×(C2×D3)⋊C8C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. C3×C8×Dic3C22semidirect
55. #63572C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63557C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
61. #63555C22semidirect
62. #63554C22semidirect
67. C22×D3×C8D3semidirect
82. C8×#67D3semidirect
138. C3×D3×C8D4semidirect
206. C2×D3×C8C2×D3semidirect
234. (C2×D3)⋊C8C2×D3semidirect
244. Dic3⋊C8C2×D3semidirect
248. C8×Dic3C2×D3semidirect
443. D3×C8#67semidirect
446. C22×C32#131semidirect
460. C2×C3×D3#131semidirect
712. C22×C3#901semidirect
713. C22×C3#901semidirect
733. C2×D3#901semidirect
763. C32#2929semidirect
847. C22#63803semidirect
861. C3#79421semidirect
862. C3#83734semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×C82
#105950022
C2×#638032
C8×#6382
C3×C8×#672
#105911572
#105911552
#105911542
#105909532
#105907272
#105907232
C8×#6262
C8×#6252
#105906942
#105906922
#837343
#794213