Finite Group Databasebeta

← #49134866

Subgroups — #49134866

Order 36224.

1242 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827197C211yesmaximal, characteristic, complemented
2#31827174C211yesmaximal, characteristic, complemented
3#31827173C211yesmaximal, characteristic, complemented
4#31827162C211yesmaximal, characteristic, complemented
5#31827161C211yesmaximal, characteristic, complemented
6#31827158C212yesmaximal, complemented
7#31827141C212yesmaximal, complemented
8#31827138C212yesmaximal, complemented
9#31827103C211yesmaximal, characteristic, complemented
10#31827102C212yesmaximal, complemented
11D4×C22⋊D283C211yesmaximal, characteristic, complemented
12#31827010C211yesmaximal, characteristic, complemented
13#31827001C211yesmaximal, characteristic, complemented
14#31826994C211yesmaximal, characteristic, complemented
15#31826992C212yesmaximal, complemented
16#31826975C212yesmaximal, complemented
17#31826971C212yesmaximal, complemented
18#41×Dic283C211yesmaximal, characteristic, complemented
19C4×#17985391C211yesmaximal, characteristic, complemented
20C2×D4×Dic283C211yesmaximal, characteristic, complemented
21C2×(C22⋊D283)⋊C4C212yesmaximal, complemented
22C4×D4×D283C211yesmaximal, characteristic, complemented
23#546×C283C211yesmaximal, characteristic, complemented
24C2×#17985391C2211yescharacteristic
25C2×#17985391C2212yescomplemented
26C22×C22⋊D283C2212yes—
27C2×D4×D283C2211yescharacteristic
28C23×Dic283C2212yescomplemented
29C22×C4×D283C2212yescomplemented
30#22583609C2211yescharacteristic, complemented
31#22583606C2211yescharacteristic
32#22583605C2212yescomplemented
33#22583605C2212yescomplemented
34#22583603C2212yescomplemented
35#22583603C2212yescomplemented
36#22583602C2211yescharacteristic, complemented
37#22583601C2211yescharacteristic, complemented
38#22583600C2212yescomplemented
39#22583599C2211yescharacteristic, complemented
40#22583596C2212yescomplemented
41#22583596C2212yescomplemented
42#22583594C2212yescomplemented
43#22583594C2212yescomplemented
44#22583593C2212yescomplemented
45#22583592C2212yescomplemented
46#22583592C2212yescomplemented
47#22583592C2212yescomplemented
48#22583591C2212yescomplemented
49#22583590C2212yescomplemented
50#22583589C2212yescomplemented
51#22583587C2212yescomplemented
52#22583587C2212yescomplemented
53#22583587C2212yescomplemented
54#22583586C2211yescharacteristic, complemented
55#22583584C2211yescharacteristic
56#22583584C2211yescharacteristic, complemented
57#22583582C2212yes—
58#22583582C2212yescomplemented
59#22583582C2212yescomplemented
60#22583582C2212yescomplemented
61#22583581C2211yescharacteristic
62#22583581C2212yescomplemented
63#22583579C2212yes—
64#22583578C2212yes—
65#22583578C2212yescomplemented
66Q8×Dic283C2211yescharacteristic, complemented
67Q8×Dic283C2211yescharacteristic, complemented
68C4×Dic566C2211yescharacteristic, complemented
69#22583575C2211yescharacteristic, complemented
70C4×D1132C2211yescharacteristic, complemented
71D4×Dic283C2211yescharacteristic
72D4×Dic283C2211yescharacteristic
73D4×Dic283C2211yescharacteristic
74D4×Dic283C2211yescharacteristic, complemented
75D4×Dic283C2212yescomplemented
76D4×Dic283C2212yescomplemented
77D4×Dic283C2211yescharacteristic, complemented
78D4×Dic283C2212yescomplemented
79D4×Dic283C2212yescomplemented
80D4×Dic283C2211yescharacteristic, complemented
81#22583572C2211yescharacteristic, complemented
82C4×C22⋊D283C2211yescharacteristic
83C4×C22⋊D283C2211yescharacteristic, complemented
84C4×C22⋊D283C2212yescomplemented
85(C22⋊D283)⋊C4C2212yes—
86(C22⋊D283)⋊C4C2211yescharacteristic
87(C22⋊D283)⋊C4C2212yescomplemented
88(C22⋊D283)⋊C4C2212yescomplemented
89(C22⋊D283)⋊C4C2211yescharacteristic, complemented
90(C22⋊D283)⋊C4C2212yescomplemented
91(C22⋊D283)⋊C4C2212yescomplemented
92(C22⋊D283)⋊C4C2212yescomplemented
93(C22⋊D283)⋊C4C2212yescomplemented
94(C22⋊D283)⋊C4C2212yescomplemented
95#22583569C2212yescomplemented
96#22583569C2211yescharacteristic, complemented
97#22583568C2212yescomplemented
98#22583568C2211yescharacteristic, complemented
99#22583566C2212yescomplemented
100#22583566C2211yescharacteristic, complemented
101#22583566C2211yescharacteristic, complemented
102C2×C4⋊Dic283C2211yescharacteristic, complemented
103C2×Dic283⋊C4C2212yescomplemented
104C4⋊C4×D283C2211yescharacteristic, complemented
105C2×C22⋊Dic283C2212yescomplemented
106C2×(C2×D283)⋊C4C2212yescomplemented
107C22⋊C4×D283C2212yescomplemented
108C2×C4×Dic283C2212yescomplemented
109C2×C4×Dic283C2211yescharacteristic, complemented
110C2×C4×Dic283C2211yescharacteristic, complemented
111C42×D283C2211yescharacteristic, complemented
112C2×#41×C283C2211yescharacteristic
113C22×D4×C283C2211yescharacteristic
114#124×C283C2211yescharacteristic, complemented
115#123×C283C2212yescomplemented
116C22⋊Q8×C283C2211yescharacteristic, complemented
117#121×C283C2212yescomplemented
118#121×C283C2211yescharacteristic, complemented
119#120×C283C2212yescomplemented
120C4×D4×C283C2211yescharacteristic
121C4×D4×C283C2211yescharacteristic, complemented
122C2×C22⋊C4×C283C2212yescomplemented
123C23×D283C2312yes—
124#17985391—24no—
125#17985391—44no—
126C2×Dic566C2311yescharacteristic
127C2×Dic566C2312yes—
128C2×D1132C2311yescharacteristic
129C2×C22⋊D283—28no—
130C2×C22⋊D283C2312yes—
131C2×C22⋊D283C2312yes—
132C2×C22⋊D283C2312yes—
133C2×C22⋊D283C2311yescharacteristic
134C2×C22⋊D283C2312yes—
135C2×C22⋊D283C2312yes—
136C2×C22⋊D283C2312yes—
137C2×C22⋊D283C2311yescharacteristic
138D4×D283—24no—
139C22×Dic283—44no—
140C22×Dic283C2311yescharacteristic
141C22×Dic283C2312yes—
142C22×Dic283C2311yescharacteristic
143C22×Dic283C2311yescharacteristic
144C22×Dic283C2312yes—
145C22×Dic283C2311yescharacteristic
146C22×Dic283C2312yes—
147C22×Dic283C2312yes—
148C22×Dic283C2312yes—
149C22×Dic283C2312yes—
150C2×C4×D283—44no—
151C2×C4×D283C2311yescharacteristic
152C2×C4×D283C2311yescharacteristic
153C2×C4×D283C2311yescharacteristic
154C2×C4×D283C2312yes—
155C2×C4×D283C2312yes—
156C2×C4×D283C2312yes—
157C4⋊Dic283C2311yescharacteristic
158C4⋊Dic283C2311yescharacteristic
159C4⋊Dic283C2312yes—
160C4⋊Dic283C2311yescharacteristic
161C4⋊Dic283C2312yes—
162C4⋊Dic283C2311yescharacteristic
163C4⋊Dic283C2312yes—
164C4⋊Dic283C2312yes—
165Dic283⋊C4C2312yes—
166Dic283⋊C4C2311yescharacteristic
167Dic283⋊C4C2312yes—
168Dic283⋊C4C2312yes—
169Dic283⋊C4C2312yes—
170Dic283⋊C4C2311yescharacteristic
171Dic283⋊C4C2311yescharacteristic
172Dic283⋊C4C2311yescharacteristic
173Dic283⋊C4C2312yes—
174Dic283⋊C4C2312yes—
175C22⋊Dic283C2312yes—
176C22⋊Dic283C2312yes—
177C22⋊Dic283C2312yes—
178C22⋊Dic283C2312yes—
179C22⋊Dic283C2311yescharacteristic
180C22⋊Dic283C2311yescharacteristic
181C22⋊Dic283C2312yes—
182C22⋊Dic283C2312yes—
183C22⋊Dic283C2312yes—
184(C2×D283)⋊C4C2312yes—
185(C2×D283)⋊C4C2312yes—
186(C2×D283)⋊C4C2311yescharacteristic
187(C2×D283)⋊C4C2312yes—
188(C2×D283)⋊C4C2312yes—
189(C2×D283)⋊C4C2312yes—
190(C2×D283)⋊C4C2311yescharacteristic
191(C2×D283)⋊C4C2312yes—
192(C2×D283)⋊C4C2312yes—
193C4×Dic283C2311yescharacteristic
194C4×Dic283C2311yescharacteristic
195C4×Dic283C2311yescharacteristic
196C4×Dic283C2311yescharacteristic
197C4×Dic283C2311yescharacteristic
198C4×Dic283C2312yes—
199C4×Dic283C2311yescharacteristic
200C4×Dic283C2311yescharacteristic
201C4×Dic283C2312yes—
202C4×Dic283C2312yes—
203C4×Dic283C2311yescharacteristic
204C4×Dic283C2311yescharacteristic
205C24×C283C2312yes—
206#41×C283—24no—
207C2×Q8×C283C2311yescharacteristic
208C2×D4×C283—24no—
209C2×D4×C283C2312yes—
210C2×D4×C283C2312yes—
211C2×D4×C283C2311yescharacteristic
212C2×D4×C283C2311yescharacteristic
213C2×D4×C283C2312yes—
214C2×D4×C283C2311yescharacteristic
215C22×C4×C283C2312yes—
216C22×C4×C283C2311yescharacteristic
217C22×C4×C283C2311yescharacteristic
218C22×C4×C283C2312yes—
219C4⋊C4×C283C2311yescharacteristic
220C4⋊C4×C283C2311yescharacteristic
221C4⋊C4×C283C2312yes—
222C22⋊C4×C283C2312yes—
223C22⋊C4×C283C2311yescharacteristic
224C22⋊C4×C283C2311yescharacteristic
225C22⋊C4×C283C2312yes—
226C22⋊C4×C283C2312yes—
227C22⋊C4×C283C2312yes—
228C22⋊C4×C283C2312yes—
229C42×C283C2311yescharacteristic
230C22×D283—24no—
231C22×D283—24no—
232C22×D283—42no—
233C22×D283C2412yes—
234C22×D283C2411yescharacteristic
235Dic566—22no—
236Dic566—42no—
237D1132—22no—
238C22⋊D283—24no—
239C22⋊D283—24no—
240C22⋊D283—24no—
241C22⋊D283—22no—
242C22⋊D283—24no—
243C22⋊D283—42no—
244C22⋊D283—42no—
245C22⋊D283#4114yescomplemented
246C2×Dic283—22no—
247C2×Dic283—24no—
248C2×Dic283—22no—
249C2×Dic283—24no—
250C2×Dic283—22no—
251C2×Dic283—24no—
252C2×Dic283—22no—
253C2×Dic283—42no—
254C2×Dic283—42no—
255C2×Dic283—42no—
256C2×Dic283C2411yescharacteristic
257C2×Dic283C2411yescharacteristic
258C2×Dic283C2411yescharacteristic
259C2×Dic283C2412yes—
260C2×Dic283C2412yes—
261C2×Dic283C2411yescharacteristic
262C2×Dic283C2411yescharacteristic
263C2×Dic283C2412yes—
264C2×Dic283C2411yescharacteristic
265C2×Dic283C2411yescharacteristic
266C4×D283—22no—
267C4×D283—22no—
268C4×D283—22no—
269C4×D283—24no—
270C4×D283—42no—
271C4×D283—42no—
272C23×C283—24no—
273C23×C283—24no—
274C23×C283—42no—
275C23×C283C2412yes—
276C23×C283C2411yescharacteristic
277C23×C283C2411yescharacteristic
278C23×C283C2412yes—
279Q8×C283—22no—
280D4×C283—24no—
281D4×C283—24no—
282D4×C283—22no—
283D4×C283—22no—
284D4×C283—42no—
285D4×C283#4114yescomplemented
286C2×C4×C283—24no—
287C2×C4×C283—22no—
288C2×C4×C283—22no—
289C2×C4×C283—42no—
290C2×C4×C283C2411yescharacteristic
291C2×C4×C283C2411yescharacteristic
292C2×C4×C283C2412yes—
293C2×C4×C283C2411yescharacteristic
294C2×C4×C283C2412yes—
295C2×C4×C283C2411yescharacteristic
296C2×C4×C283C2411yescharacteristic
297C22×C283—21no—
298C22×C283—22no—
299C22×C283—22no—
300C22×C283—21no—
301C22×C283—21no—
302C22×C283—22no—
303C22×C283—21no—
304C22×C283—22no—
305C22×C283—21no—
306C22×C283—22no—
307C22×C283—48no—
308C22×C283C2×#4112yes—
309C22×C283C2×#4114yes—
310C22×C283C2511yescharacteristic
311C2×D283—21no—
312C2×D283—21no—
313C2×D283—22no—
314C2×D283—22no—
315C2×D283—22no—
316C2×D283—48no—
317C2×D283C2×#4112yes—
318C4×C283—21no—
319C4×C283—21no—
320C4×C283—22no—
321C4×C283—21no—
322C4×C283—21no—
323C4×C283—22no—
324C4×C283C2×#4112yes—
325Dic283—21no—
326Dic283—21no—
327Dic283—22no—
328Dic283—21no—
329Dic283—22no—
330Dic283—21no—
331Dic283—22no—
332Dic283—21no—
333Dic283C2×#4112yes—
334Dic283H(5,𝔽2)12yes—
335C2×C283—24no—
336C2×C283—22no—
337C2×C283—41no—
338C2×C283—42no—
339C2×C283C22×#4111yescharacteristic
340C2×C283C22×#4111yescharacteristic
341C2×C283C2×H(5,𝔽2)11yescharacteristic
342D283—22no—
343D283—42no—
344C283#348111yescharacteristic, complemented, Sylow
345#3481—2831nomaximal, Sylow
346#559—2831no—
347#554—2831no—
348#554—2831no—
349#553—2832no—
350#553—2831no—
351#553—2831no—
352#551—2832no—
353#551—2832no—
354#546—2831no—
355#546—2832no—
356#546D28311yescharacteristic, complemented
357D42—2831no—
358#532—2831no—
359#529—2831no—
360#529—2832no—
361#529—2831no—
362#525—2832no—
363#525—2832no—
364C4×#41—2831no—
365C4×#41—2831no—
366C2×C4×D4—2831no—
367C2×C4×D4—2831no—
368C2×C4×D4—2832no—
369C2×#41—2831no—
370C2×#41—2832no—
371C2×#41C2×D28311yescharacteristic
372C22×D4—2832no—
373C22×D4—2831no—
374C22×D4C2×D28311yescharacteristic
375C23×C4—2832no—
376C23×C4—2832no—
377C4⋊Q8—2831no—
378#127—2831no—
379#126—2832no—
380#126—2832no—
381#126—2832no—
382#126—2832no—
383#125—2832no—
384#125—2831no—
385#125—2831no—
386#124—2831no—
387#124—2832no—
388#124—2832no—
389#124C2×D28311yescharacteristic, complemented
390#123—2832no—
391#123—2832no—
392#123—2832no—
393#123—2832no—
394#123—2832no—
395#123—2832no—
396#123—2832no—
397#123C2×D28312yescomplemented
398C22⋊Q8—2831no—
399C22⋊Q8—2832no—
400C22⋊Q8—2832no—
401C22⋊Q8—2832no—
402C22⋊Q8—2832no—
403C22⋊Q8—2832no—
404C22⋊Q8C2×D28311yescharacteristic, complemented
405#121—2832no—
406#121—2832no—
407#121—2832no—
408#121—2831no—
409#121—2832no—
410#121—2832no—
411#121—2831no—
412#121—2831no—
413#121C2×D28312yescomplemented
414#121C2×D28311yescharacteristic, complemented
415#120—2832no—
416#120—2832no—
417#120—2832no—
418#120C2×D28312yescomplemented
419C4×Q8—2831no—
420C4×Q8—2831no—
421C4×Q8—2831no—
422C4×Q8—2831no—
423C4×D4—2831no—
424C4×D4—2832no—
425C4×D4—2831no—
426C4×D4—2831no—
427C4×D4—2832no—
428C4×D4—2831no—
429C4×D4—2832no—
430C4×D4—2831no—
431C4×D4—2831no—
432C4×D4—2832no—
433C4×D4—2832no—
434C4×D4—2831no—
435C4×D4—2831no—
436C4×D4—2831no—
437C4×D4—2831no—
438C4×D4—2832no—
439C4×D4—2832no—
440C4×D4—2832no—
441C4×D4—2832no—
442C4×D4—2832no—
443C4×D4—2832no—
444C4×D4—2832no—
445C4×D4—2832no—
446C4×D4—2831no—
447C4×D4—2831no—
448C4×D4C2×D28311yescharacteristic
449C4×D4C2×D28311yescharacteristic, complemented
450#117—2832no—
451#117—2831no—
452#117—2831no—
453#117—2832no—
454#117—2831no—
455#117—2831no—
456#117—2832no—
457C2×C4⋊C4—2832no—
458C2×C4⋊C4—2831no—
459C2×C4⋊C4—2831no—
460C2×C22⋊C4—2832no—
461C2×C22⋊C4—2832no—
462C2×C22⋊C4—2832no—
463C2×C22⋊C4C2×D28312yescomplemented
464C2×C42—2831no—
465C2×C42—2832no—
466C2×C42—2831no—
467C2×C42—2831no—
468C24—2832no—
469C24C22×D28312yes—
470#41—24no—
471#41—5664no—
472#41—11324no—
473C2×Q8—2831no—
474C2×Q8—2832no—
475C2×Q8C22×D28311yescharacteristic
476C2×D4—24no—
477C2×D4—2831no—
478C2×D4—2831no—
479C2×D4—2832no—
480C2×D4—2832no—
481C2×D4—2832no—
482C2×D4—2832no—
483C2×D4—2832no—
484C2×D4—2832no—
485C2×D4—2831no—
486C2×D4—5668no—
487C2×D4—5664no—
488C2×D4C22×D28312yes—
489C2×D4C22×D28312yes—
490C2×D4C22×D28311yescharacteristic
491C2×D4C22×D28311yescharacteristic
492C2×D4C22×D28312yes—
493C2×D4C22×D28311yescharacteristic
494C22×C4—2831no—
495C22×C4—2832no—
496C22×C4—2831no—
497C22×C4—2831no—
498C22×C4—2832no—
499C22×C4—2831no—
500C22×C4—2832no—
501C22×C4—2832no—
502C22×C4—2832no—
503C22×C4—2832no—
504C22×C4—2831no—
505C22×C4—2831no—
506C22×C4—2831no—
507C22×C4—2832no—
508C22×C4—2832no—
509C22×C4—2832no—
510C22×C4—11324no—
511C22×C4—11324no—
512C22×C4C22×D28312yes—
513C22×C4C22×D28311yescharacteristic
514C22×C4C22×D28311yescharacteristic
515C22×C4C22×D28312yes—
516C4⋊C4—2831no—
517C4⋊C4—2832no—
518C4⋊C4—2832no—
519C4⋊C4—2832no—
520C4⋊C4—2832no—
521C4⋊C4—2831no—
522C4⋊C4—2831no—
523C4⋊C4—2831no—
524C4⋊C4—2832no—
525C4⋊C4—2832no—
526C4⋊C4—2831no—
527C4⋊C4—2831no—
528C4⋊C4—2832no—
529C4⋊C4—2831no—
530C4⋊C4—2832no—
531C4⋊C4—2831no—
532C4⋊C4—2832no—
533C4⋊C4—2832no—
534C4⋊C4C22×D28311yescharacteristic
535C4⋊C4C22×D28311yescharacteristic
536C4⋊C4C22×D28312yes—
537C22⋊C4—2832no—
538C22⋊C4—2832no—
539C22⋊C4—2832no—
540C22⋊C4—2832no—
541C22⋊C4—2831no—
542C22⋊C4—2832no—
543C22⋊C4—2831no—
544C22⋊C4—2832no—
545C22⋊C4—2832no—
546C22⋊C4—2831no—
547C22⋊C4—2832no—
548C22⋊C4—2832no—
549C22⋊C4—2832no—
550C22⋊C4—2832no—
551C22⋊C4—2832no—
552C22⋊C4—2831no—
553C22⋊C4—2832no—
554C22⋊C4—2832no—
555C22⋊C4C22×D28312yes—
556C22⋊C4C22×D28311yescharacteristic
557C22⋊C4C22×D28312yes—
558C22⋊C4C22×D28312yes—
559C22⋊C4C22×D28312yes—
560C22⋊C4C22×D28311yescharacteristic
561C22⋊C4C22×D28312yes—
562C42—2831no—
563C42—2831no—
564C42—2831no—
565C42—2831no—
566C42—2832no—
567C42—2831no—
568C42—2831no—
569C42—2831no—
570C42—2832no—
571C42—2832no—
572C42—2831no—
573C42—2831no—
574C42C22×D28311yescharacteristic
575C23—24no—
576C23—24no—
577C23—42no—
578C23—2831no—
579C23—2832no—
580C23—5664no—
581C23—5664no—
582C23—11322no—
583C23C23×D28312yes—
584C23C23×D28311yescharacteristic
585C23C23×D28311yescharacteristic
586C23C23×D28312yes—
587Q8—22no—
588Q8—5662no—
589Q8—11322no—
590D4—22no—
591D4—24no—
592D4—24no—
593D4—22no—
594D4—42no—
595D4—2834no—
596D4—5664no—
597D4—5664no—
598D4—5662no—
599D4—5664no—
600D4—5664no—
601D4—5662no—
602D4—11322no—
603D4—11322no—
604D4#1798539114yescomplemented
605C2×C4—24no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—42no—
609C2×C4—2831no—
610C2×C4—2831no—
611C2×C4—2831no—
612C2×C4—2831no—
613C2×C4—2832no—
614C2×C4—2831no—
615C2×C4—2832no—
616C2×C4—2831no—
617C2×C4—2831no—
618C2×C4—2832no—
619C2×C4—5662no—
620C2×C4—5664no—
621C2×C4—5662no—
622C2×C4—5664no—
623C2×C4—5662no—
624C2×C4—5664no—
625C2×C4—5664no—
626C2×C4—5662no—
627C2×C4—5662no—
628C2×C4—5662no—
629C2×C4—5662no—
630C2×C4—11322no—
631C2×C4—11322no—
632C2×C4—11322no—
633C2×C4—11322no—
634C2×C4—11322no—
635C2×C4C23×D28311yescharacteristic
636C2×C4C23×D28312yes—
637C2×C4C23×D28311yescharacteristic
638C2×C4C23×D28311yescharacteristic
639C2×C4C23×D28311yescharacteristic
640C2×C4C23×D28312yes—
641C2×C4C23×D28311yescharacteristic
642C22—22no—
643C22—21no—
644C22—22no—
645C22—21no—
646C22—21no—
647C22—22no—
648C22—21no—
649C22—22no—
650C22—22no—
651C22—21no—
652C22—48no—
653C22—2832no—
654C22—5661no—
655C22—5661no—
656C22—5662no—
657C22—5662no—
658C22—5662no—
659C22—11328no—
660C22#41×D28312yes—
661C22C2×#1798539114yes—
662C22C24×D28311yescharacteristic
663C4—21no—
664C4—21no—
665C4—21no—
666C4—22no—
667C4—21no—
668C4—22no—
669C4—2832no—
670C4—2832no—
671C4—5661no—
672C4—5662no—
673C4—5661no—
674C4—5661no—
675C4—5662no—
676C4—5661no—
677C4—5662no—
678C4—5661no—
679C4C2×#1798539112yes—
680C2—22no—
681C2—24no—
682C2—42no—
683C2—41no—
684C2—5662no—
685C2—11322no—
686C2C2×#41×D28311yescharacteristic
687C2C22×#1798539111yescharacteristic
688C2H(5,𝔽2)×D28311yescharacteristic
subgroupG/H
center, FrattiniC22C24×D283
commutator, socle, cosocleC22×C283C25
Fitting#546×C283C2
hypercenter#546D283
hypocenterC283#3481
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #31827197C2semidirect
2. #31827174C2semidirect
3. #31827173C2semidirect
4. #31827162C2semidirect
5. #31827161C2semidirect
6. #31827158C2semidirect
7. #31827141C2semidirect
8. #31827138C2semidirect
9. #31827103C2semidirect
10. #31827102C2semidirect
11. D4×C22⋊D283C2semidirect
12. #31827010C2semidirect
13. #31827001C2semidirect
14. #31826994C2semidirect
15. #31826992C2semidirect
16. #31826975C2semidirect
17. #31826971C2semidirect
18. #41×Dic283C2semidirect
19. C4×#17985391C2semidirect
20. C2×D4×Dic283C2semidirect
21. C2×(C22⋊D283)⋊C4C2semidirect
22. C4×D4×D283C2semidirect
23. #546×C283C2semidirect
25. C2×#17985391C22semidirect
28. C23×Dic283C22semidirect
29. C22×C4×D283C22semidirect
30. #22583609C22semidirect
32. #22583605C22semidirect
33. #22583605C22semidirect
34. #22583603C22semidirect
35. #22583603C22semidirect
36. #22583602C22semidirect
37. #22583601C22semidirect
38. #22583600C22semidirect
39. #22583599C22semidirect
40. #22583596C22semidirect
41. #22583596C22semidirect
42. #22583594C22semidirect
43. #22583594C22semidirect
44. #22583593C22semidirect
45. #22583592C22semidirect
46. #22583592C22semidirect
47. #22583592C22semidirect
48. #22583591C22semidirect
49. #22583590C22semidirect
50. #22583589C22semidirect
51. #22583587C22semidirect
52. #22583587C22semidirect
53. #22583587C22semidirect
54. #22583586C22semidirect
56. #22583584C22semidirect
58. #22583582C22semidirect
59. #22583582C22semidirect
60. #22583582C22semidirect
62. #22583581C22semidirect
65. #22583578C22semidirect
66. Q8×Dic283C22semidirect
67. Q8×Dic283C22semidirect
68. C4×Dic566C22semidirect
69. #22583575C22semidirect
70. C4×D1132C22semidirect
74. D4×Dic283C22semidirect
75. D4×Dic283C22semidirect
76. D4×Dic283C22semidirect
77. D4×Dic283C22semidirect
78. D4×Dic283C22semidirect
79. D4×Dic283C22semidirect
80. D4×Dic283C22semidirect
81. #22583572C22semidirect
83. C4×C22⋊D283C22semidirect
84. C4×C22⋊D283C22semidirect
87. (C22⋊D283)⋊C4C22semidirect
88. (C22⋊D283)⋊C4C22semidirect
89. (C22⋊D283)⋊C4C22semidirect
90. (C22⋊D283)⋊C4C22semidirect
91. (C22⋊D283)⋊C4C22semidirect
92. (C22⋊D283)⋊C4C22semidirect
93. (C22⋊D283)⋊C4C22semidirect
94. (C22⋊D283)⋊C4C22semidirect
95. #22583569C22semidirect
96. #22583569C22semidirect
97. #22583568C22semidirect
98. #22583568C22semidirect
99. #22583566C22semidirect
100. #22583566C22semidirect
101. #22583566C22semidirect
102. C2×C4⋊Dic283C22semidirect
103. C2×Dic283⋊C4C22semidirect
104. C4⋊C4×D283C22semidirect
105. C2×C22⋊Dic283C22semidirect
106. C2×(C2×D283)⋊C4C22semidirect
107. C22⋊C4×D283C22semidirect
108. C2×C4×Dic283C22semidirect
109. C2×C4×Dic283C22semidirect
110. C2×C4×Dic283C22semidirect
111. C42×D283C22semidirect
114. #124×C283C22semidirect
115. #123×C283C22semidirect
116. C22⋊Q8×C283C22semidirect
117. #121×C283C22semidirect
118. #121×C283C22semidirect
119. #120×C283C22semidirect
121. C4×D4×C283C22semidirect
122. C2×C22⋊C4×C283C22semidirect
245. C22⋊D283#41semidirect
285. D4×C283#41semidirect
344. C283#3481semidirect
356. #546D283semidirect
389. #124C2×D283semidirect
397. #123C2×D283semidirect
404. C22⋊Q8C2×D283semidirect
413. #121C2×D283semidirect
414. #121C2×D283semidirect
418. #120C2×D283semidirect
449. C4×D4C2×D283semidirect
463. C2×C22⋊C4C2×D283semidirect
604. D4#17985391semidirect

Maximal subgroups

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

subgroupindex
#318271972
#318271742
#318271732
#318271622
#318271612
#318271582
#318271412
#318271382
#318271032
#318271022
D4×C22⋊D2832
#318270102
#318270012
#318269942
#318269922
#318269752
#318269712
#41×Dic2832
C4×#179853912
C2×D4×Dic2832
C2×(C22⋊D283)⋊C42
C4×D4×D2832
#546×C2832
#3481283