Finite Group Databasebeta

← #27352986

Subgroups — #27352986

Order 13568.

926 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283840C211yesmaximal, characteristic, complemented
2#20283840C211yesmaximal, characteristic, complemented
3#20273445C211yesmaximal, characteristic, complemented
4#20273437C211yesmaximal, characteristic, complemented
5#20273432C211yesmaximal, characteristic, complemented
6#20273425C211yesmaximal, characteristic, complemented
7#20273420C211yesmaximal, characteristic, complemented
8#20273410C211yesmaximal, characteristic, complemented
9#20273410C211yesmaximal, characteristic, complemented
10#20273405C211yesmaximal, characteristic, complemented
11#20273392C211yesmaximal, characteristic, complemented
12#20273372C211yesmaximal, characteristic, complemented
13#20273364C211yesmaximal, characteristic, complemented
14C2×#16810369C211yesmaximal, characteristic, complemented
15C53×#3511C211yesmaximal, characteristic
16#16810754—21no—
17#16810754—21no—
18#16810695—21no—
19#16810695—21no—
20#16810695—21no—
21#16810695—21no—
22D4×#88322—21no—
23D4×#88322—21no—
24#16810680C2211yescharacteristic
25#16810680C2211yescharacteristic
26#16810680C2211yescharacteristic
27#16810680C2211yescharacteristic
28#16810676C2211yescharacteristic
29#16810676C2211yescharacteristic
30#16810647C2211yescharacteristic
31#16810647C2211yescharacteristic
32C2×C4⋊#88322C2211yescharacteristic
33C2×C4⋊#88322C2211yescharacteristic
34C2×C4⋊#88322C2211yescharacteristic
35C2×C4⋊#88322C2211yescharacteristic
36#16810372C2211yescharacteristic
37#16810372C2211yescharacteristic
38#16810372C2211yescharacteristic
39#16810372C2211yescharacteristic
40#16810369C2211yescharacteristic
41#16810369C2211yescharacteristic
42#16810369C2211yescharacteristic
43#16810369C2211yescharacteristic
44#16810369C2211yescharacteristic
45#16810369C2211yescharacteristic
46#16810369C2211yescharacteristic
47#16810369C2211yescharacteristic
48#16810367C2211yescharacteristic
49#16810367C2211yescharacteristic
50#16810367C2211yescharacteristic
51#16810367C2211yescharacteristic
52C53×#556—21no—
53C53×#555—21no—
54C53×#554—21no—
55C53×#553—21no—
56C53×#553—21no—
57C53×#548—21no—
58C53×#548—21no—
59C53×#547—21no—
60C53×#542C412yes—
61C53×#542C412yes—
62C53×#537C412yes—
63C53×#533C2211yescharacteristic
64C53×#533C2211yescharacteristic
65C53×#532C2211yescharacteristic
66C53×#532C2211yescharacteristic
67C53×#532C2211yescharacteristic
68C2×C4⋊Q8×C53C2211yescharacteristic
69C53×#520C412yes—
70C4×#41×C53C2211yescharacteristic
71C2×#11719917—21no—
72C2×#11719917—21no—
73C22×#88322—21no—
74C22×#88322—21no—
75C22×#88322—21no—
76C22×#88322—21no—
77C4⋊#88322—21no—
78C4⋊#88322—21no—
79C4⋊#88322—21no—
80C4⋊#88322—21no—
81C4⋊#88322—21no—
82C4⋊#88322—21no—
83C4⋊#88322C2311yescharacteristic
84C4⋊#88322C2311yescharacteristic
85C4⋊#88322C2311yescharacteristic
86C4⋊#88322C2311yescharacteristic
87C4⋊#88322C2311yescharacteristic
88C4⋊#88322C2311yescharacteristic
89C4⋊#88322C2311yescharacteristic
90C4⋊#88322C2311yescharacteristic
91C22⋊#88322—21no—
92C22⋊#88322—21no—
93C22⋊#88322—21no—
94C22⋊#88322—21no—
95C22⋊#88322—21no—
96C22⋊#88322—21no—
97#13133128—21no—
98#13133128—21no—
99#13133128—21no—
100#13133128—21no—
101C4×#88322—21no—
102C4×#88322—21no—
103C2×#41×C53—21no—
104C2×#41×C53—21no—
105C2×#41×C53C2×C412yes—
106C2×#41×C53C2×C411yescharacteristic
107C22×Q8×C53—21no—
108C4⋊Q8×C53—21no—
109C4⋊Q8×C53—21no—
110C4⋊Q8×C53C2×C412yes—
111C4⋊Q8×C53C2311yescharacteristic
112C4⋊Q8×C53C2311yescharacteristic
113C4⋊Q8×C53C2311yescharacteristic
114#127×C53C2311yescharacteristic
115#126×C53—22no—
116#126×C53—22no—
117#125×C53—21no—
118#125×C53—21no—
119#124×C53—22no—
120#124×C53—22no—
121#124×C53—21no—
122#124×C53—21no—
123#124×C53C2×C412yes—
124#123×C53—22no—
125#123×C53—22no—
126C22⋊Q8×C53—22no—
127C22⋊Q8×C53—22no—
128C22⋊Q8×C53—22no—
129C22⋊Q8×C53—21no—
130C22⋊Q8×C53—21no—
131C22⋊Q8×C53C2×C412yes—
132C22⋊Q8×C53C2×C412yes—
133#121×C53—22no—
134#121×C53—22no—
135#121×C53—22no—
136#121×C53—21no—
137#121×C53—21no—
138#121×C53—21no—
139#121×C53—21no—
140#121×C53C2×C412yes—
141#121×C53C2×C412yes—
142C4×Q8×C53—21no—
143C4×Q8×C53—21no—
144C4×Q8×C53C2×C412yes—
145C4×Q8×C53C2×C412yes—
146C4×Q8×C53D411yescharacteristic
147C4×Q8×C53D411yescharacteristic
148C4×D4×C53—22no—
149C4×D4×C53—22no—
150C4×D4×C53—21no—
151C4×D4×C53—21no—
152C4×D4×C53—21no—
153C4×D4×C53—21no—
154C4×D4×C53C2×C412yes—
155C4×D4×C53C2×C412yes—
156C4×D4×C53D411yescharacteristic
157C4×D4×C53D411yescharacteristic
158C4×D4×C53D411yescharacteristic
159C4×D4×C53D411yescharacteristic
160C4×D4×C53D411yescharacteristic
161C4×D4×C53D411yescharacteristic
162#117×C53—22no—
163#117×C53—21no—
164#117×C53—21no—
165#117×C53C2×C411yescharacteristic
166#117×C53C2×C411yescharacteristic
167#117×C53C2×C411yescharacteristic
168C2×C4⋊C4×C53—22no—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53C2×C412yes—
171C2×C42×C53C2311yescharacteristic
172C2×C42×C53C2311yescharacteristic
173C2×C42×C53C2311yescharacteristic
174#41×C53—42no—
175#41×C53—44no—
176#41×C53—81no—
177#41×C53—81no—
178#41×C53—81no—
179#41×C53—81no—
180C2×Q8×C53—22no—
181C2×Q8×C53—21no—
182C2×Q8×C53—21no—
183C2×Q8×C53—81no—
184C2×Q8×C53—81no—
185C2×Q8×C53C22⋊C411yescharacteristic
186C2×Q8×C53C22×C412yes—
187C2×D4×C53—22no—
188C2×D4×C53—22no—
189C2×D4×C53—22no—
190C2×D4×C53—21no—
191C2×D4×C53—21no—
192C2×D4×C53C22⋊C411yescharacteristic
193C2×D4×C53C22⋊C411yescharacteristic
194C2×D4×C53C22⋊C411yescharacteristic
195C2×D4×C53C22×C412yes—
196C22×C4×C53—22no—
197C22×C4×C53—22no—
198C22×C4×C53—22no—
199C22×C4×C53—22no—
200C22×C4×C53C22×C411yescharacteristic
201C22×C4×C53C22×C411yescharacteristic
202C22×C4×C53C22×C411yescharacteristic
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2×D411yescharacteristic
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2×D411yescharacteristic
209C4⋊C4×C53—22no—
210C4⋊C4×C53—22no—
211C4⋊C4×C53—22no—
212C4⋊C4×C53—22no—
213C4⋊C4×C53—22no—
214C4⋊C4×C53—22no—
215C4⋊C4×C53—21no—
216C4⋊C4×C53—21no—
217C4⋊C4×C53—21no—
218C4⋊C4×C53—21no—
219C4⋊C4×C53C22⋊C411yescharacteristic
220C4⋊C4×C53C22⋊C411yescharacteristic
221C4⋊C4×C53C22⋊C411yescharacteristic
222C4⋊C4×C53C22⋊C411yescharacteristic
223C4⋊C4×C53C22⋊C411yescharacteristic
224C4⋊C4×C53C22⋊C411yescharacteristic
225C4⋊C4×C53C22×C412yes—
226C4⋊C4×C53C22×C412yes—
227C22⋊C4×C53—22no—
228C22⋊C4×C53—22no—
229C22⋊C4×C53—22no—
230C22⋊C4×C53—22no—
231C22⋊C4×C53—22no—
232C22⋊C4×C53—22no—
233C22⋊C4×C53—22no—
234C22⋊C4×C53—22no—
235C22⋊C4×C53C22⋊C411yescharacteristic
236C22⋊C4×C53C22⋊C411yescharacteristic
237C22⋊C4×C53C22⋊C411yescharacteristic
238C22⋊C4×C53C22⋊C411yescharacteristic
239C22⋊C4×C53C22⋊C411yescharacteristic
240C22⋊C4×C53C22⋊C411yescharacteristic
241C42×C53—22no—
242C42×C53—22no—
243C42×C53C22×C411yescharacteristic
244C42×C53C22×C411yescharacteristic
245C42×C53C22×C411yescharacteristic
246C42×C53C2×D411yescharacteristic
247C42×C53C2×D411yescharacteristic
248C42×C53C2×D411yescharacteristic
249C42×C53C2×D411yescharacteristic
250C42×C53C2×D411yescharacteristic
251C42×C53C2×D411yescharacteristic
252C42×C53C2411yescharacteristic
253#11719917—81no—
254#11719917—81no—
255C2×#88322—21no—
256C2×#88322—21no—
257C2×#88322—21no—
258C2×#88322—21no—
259C2×#88322—21no—
260C2×#88322—21no—
261C2×#88322—21no—
262C2×#88322—21no—
263C2×#88322—81no—
264C2×#88322—81no—
265C2×#88322—81no—
266C2×#88322—81no—
267C23×C53—22no—
268C23×C53C2×C22⋊C411yescharacteristic
269C23×C53C2×C22⋊C411yescharacteristic
270C23×C53C2×C22⋊C411yescharacteristic
271Q8×C53—41no—
272Q8×C53—42no—
273Q8×C53—41no—
274Q8×C53—41no—
275Q8×C53—41no—
276Q8×C53—41no—
277Q8×C53—82no—
278D4×C53—22no—
279D4×C53—22no—
280D4×C53—41no—
281D4×C53—42no—
282D4×C53—44no—
283D4×C53—41no—
284D4×C53—41no—
285D4×C53—41no—
286D4×C53—41no—
287D4×C53—82no—
288D4×C53—82no—
289C2×C4×C53—22no—
290C2×C4×C53—21no—
291C2×C4×C53—21no—
292C2×C4×C53—21no—
293C2×C4×C53—21no—
294C2×C4×C53—21no—
295C2×C4×C53—21no—
296C2×C4×C53—21no—
297C2×C4×C53—21no—
298C2×C4×C53—21no—
299C2×C4×C53—21no—
300C2×C4×C53—21no—
301C2×C4×C53—21no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—41no—
306C2×C4×C53—41no—
307C2×C4×C53—44no—
308C2×C4×C53—82no—
309C2×C4×C53—82no—
310C2×C4×C53—82no—
311C2×C4×C53C2×C22⋊C411yescharacteristic
312C2×C4×C53C2×C22⋊C411yescharacteristic
313C2×C4×C53C2×C22⋊C411yescharacteristic
314C2×C4×C53C2×C22⋊C411yescharacteristic
315C2×C4×C53C2×C22⋊C411yescharacteristic
316C2×C4×C53C2×C22⋊C411yescharacteristic
317C2×C4×C53C2×C22⋊C411yescharacteristic
318C2×C4×C53C2×C22⋊C411yescharacteristic
319C2×C4×C53C2×C22⋊C411yescharacteristic
320C2×C4×C53C23×C411yescharacteristic
321C2×C4×C53C22×D411yescharacteristic
322C2×C4×C53C22×D411yescharacteristic
323#88322—41no—
324#88322—41no—
325#88322—41no—
326#88322—41no—
327#88322—41no—
328#88322—41no—
329#88322—41no—
330#88322—41no—
331#17775—531nomaximal, Sylow
332C22×C53—21no—
333C22×C53—21no—
334C22×C53—21no—
335C22×C53—21no—
336C22×C53—21no—
337C22×C53—21no—
338C22×C53—21no—
339C22×C53—21no—
340C22×C53—42no—
341C22×C53—42no—
342C22×C53—42no—
343C22×C53#41312yes—
344C22×C53C22×C22⋊C411yescharacteristic
345C4×C53—21no—
346C4×C53—21no—
347C4×C53—21no—
348C4×C53—21no—
349C4×C53—21no—
350C4×C53—21no—
351C4×C53—21no—
352C4×C53—21no—
353C4×C53—21no—
354C4×C53—21no—
355C4×C53—42no—
356C4×C53—42no—
357C4×C53—42no—
358C4×C53#57611yescharacteristic
359C4×C53#57711yescharacteristic
360C4×C53#57711yescharacteristic
361C4×C53#57811yescharacteristic
362#3511D5311yescharacteristic
363#2990—531no—
364#2990—531no—
365#1559—531no—
366#1557—531no—
367#1556—531no—
368#1554—531no—
369#1553—531no—
370#1551—531no—
371#1551—531no—
372#1550—531no—
373#1547—531no—
374#1542—531no—
375#1540—531no—
376C2×#332—531no—
377C2×C53—22no—
378C2×C53—41no—
379C2×C53—41no—
380C2×C53—82no—
381C2×C53C2×#41311yescharacteristic
382C2×C53#289711yescharacteristic
383C2×C53#289811yescharacteristic
384#556—21no—
385#555—21no—
386#554—21no—
387#553—21no—
388#553—21no—
389#548—21no—
390#548—21no—
391#547—21no—
392#542Dic5312yes—
393#542Dic5312yes—
394#537Dic5312yes—
395#533C2×D5311yescharacteristic
396#533C2×D5311yescharacteristic
397#532C2×D5311yescharacteristic
398#532C2×D5311yescharacteristic
399#532C2×D5311yescharacteristic
400C2×C4⋊Q8C2×D5311yescharacteristic
401#520Dic5312yes—
402C4×#41C2×D5311yescharacteristic
403#446—1061no—
404#446—1061no—
405#435—1061no—
406#435—1061no—
407#435—1061no—
408#435—1061no—
409C8×D4—1061no—
410C8×D4—1061no—
411#432—531no—
412#432—531no—
413#432—531no—
414#432—531no—
415#431—531no—
416#431—531no—
417#423—531no—
418#423—531no—
419C2×C4⋊C8—531no—
420C2×C4⋊C8—531no—
421C2×C4⋊C8—531no—
422C2×C4⋊C8—531no—
423#333—531no—
424#333—531no—
425#333—531no—
426#333—531no—
427#332—531no—
428#332—531no—
429#332—531no—
430#332—531no—
431#332—531no—
432#332—531no—
433#332—531no—
434#332—531no—
435#331—531no—
436#331—531no—
437#331—531no—
438#331—531no—
439C53#1777511yescharacteristic, complemented, Sylow
440C2×#41—21no—
441C2×#41—21no—
442C2×#41C2×Dic5312yes—
443C2×#41C2×Dic5311yescharacteristic
444C22×Q8—21no—
445C2×M16—1061no—
446C2×M16—1061no—
447C22×C8—1061no—
448C22×C8—1061no—
449C22×C8—1061no—
450C22×C8—1061no—
451C4⋊Q8—21no—
452C4⋊Q8—21no—
453C4⋊Q8C2×Dic5312yes—
454C4⋊Q8C22×D5311yescharacteristic
455C4⋊Q8C22×D5311yescharacteristic
456C4⋊Q8C22×D5311yescharacteristic
457#127C22×D5311yescharacteristic
458#126—22no—
459#126—22no—
460#125—21no—
461#125—21no—
462#124—22no—
463#124—22no—
464#124—21no—
465#124—21no—
466#124C2×Dic5312yes—
467#123—22no—
468#123—22no—
469C22⋊Q8—22no—
470C22⋊Q8—21no—
471C22⋊Q8—21no—
472C22⋊Q8—22no—
473C22⋊Q8—22no—
474C22⋊Q8C2×Dic5312yes—
475C22⋊Q8C2×Dic5312yes—
476#121—22no—
477#121—22no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—21no—
483#121C2×Dic5312yes—
484#121C2×Dic5312yes—
485C4×Q8—21no—
486C4×Q8—21no—
487C4×Q8C2×Dic5312yes—
488C4×Q8C2×Dic5312yes—
489C4×Q8C22⋊D5311yescharacteristic
490C4×Q8C22⋊D5311yescharacteristic
491C4×D4—22no—
492C4×D4—22no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4C2×Dic5312yes—
498C4×D4C2×Dic5312yes—
499C4×D4C22⋊D5311yescharacteristic
500C4×D4C22⋊D5311yescharacteristic
501C4×D4C22⋊D5311yescharacteristic
502C4×D4C22⋊D5311yescharacteristic
503C4×D4C22⋊D5311yescharacteristic
504C4×D4C22⋊D5311yescharacteristic
505#117—21no—
506#117—21no—
507#117—22no—
508#117C2×Dic5311yescharacteristic
509#117C2×Dic5311yescharacteristic
510#117C2×Dic5311yescharacteristic
511C2×C4⋊C4—21no—
512C2×C4⋊C4—22no—
513C2×C4⋊C4C2×Dic5312yes—
514C2×C42C22×D5311yescharacteristic
515C2×C42C22×D5311yescharacteristic
516C2×C42C22×D5311yescharacteristic
517C4⋊C8—531no—
518C4⋊C8—531no—
519C4⋊C8—531no—
520C4⋊C8—531no—
521C4⋊C8—531no—
522C4⋊C8—531no—
523C4⋊C8—531no—
524C4⋊C8—531no—
525C4⋊C8—1061no—
526C4⋊C8—1061no—
527C4⋊C8—1061no—
528C4⋊C8—1061no—
529C4⋊C8—1061no—
530C4⋊C8—1061no—
531C22⋊C8—1061no—
532C22⋊C8—1061no—
533C22⋊C8—1061no—
534C22⋊C8—1061no—
535C22⋊C8—1061no—
536C22⋊C8—1061no—
537#97—1061no—
538#97—1061no—
539#97—1061no—
540#97—1061no—
541C4×C8—1061no—
542C4×C8—1061no—
543#41—42no—
544#41—44no—
545#41—81no—
546#41—81no—
547#41—81no—
548#41—81no—
549C2×Q8—22no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—81no—
553C2×Q8—81no—
554C2×Q8C22⋊Dic5311yescharacteristic
555C2×Q8C22×Dic5312yes—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4C22⋊Dic5311yescharacteristic
562C2×D4C22⋊Dic5311yescharacteristic
563C2×D4C22⋊Dic5311yescharacteristic
564C2×D4C22×Dic5312yes—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4C22×Dic5311yescharacteristic
570C22×C4C22×Dic5311yescharacteristic
571C22×C4C22×Dic5311yescharacteristic
572C22×C4C2×C22⋊D5311yescharacteristic
573C22×C4C2×C22⋊D5311yescharacteristic
574C22×C4C2×C22⋊D5311yescharacteristic
575C22×C4C2×C22⋊D5311yescharacteristic
576C22×C4C2×C22⋊D5311yescharacteristic
577C22×C4C2×C22⋊D5311yescharacteristic
578M16—4241no—
579M16—4241no—
580C2×C8—1061no—
581C2×C8—1061no—
582C2×C8—1061no—
583C2×C8—1061no—
584C2×C8—1061no—
585C2×C8—1061no—
586C2×C8—1061no—
587C2×C8—1061no—
588C2×C8—4241no—
589C2×C8—4241no—
590C2×C8—4241no—
591C2×C8—4241no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4C22⋊Dic5311yescharacteristic
603C4⋊C4C22⋊Dic5311yescharacteristic
604C4⋊C4C22⋊Dic5311yescharacteristic
605C4⋊C4C22⋊Dic5311yescharacteristic
606C4⋊C4C22⋊Dic5311yescharacteristic
607C4⋊C4C22⋊Dic5311yescharacteristic
608C4⋊C4C22×Dic5312yes—
609C4⋊C4C22×Dic5312yes—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4C22⋊Dic5311yescharacteristic
619C22⋊C4C22⋊Dic5311yescharacteristic
620C22⋊C4C22⋊Dic5311yescharacteristic
621C22⋊C4C22⋊Dic5311yescharacteristic
622C22⋊C4C22⋊Dic5311yescharacteristic
623C22⋊C4C22⋊Dic5311yescharacteristic
624C42—22no—
625C42—22no—
626C42C22×Dic5311yescharacteristic
627C42C22×Dic5311yescharacteristic
628C42C22×Dic5311yescharacteristic
629C42C2×C22⋊D5311yescharacteristic
630C42C2×C22⋊D5311yescharacteristic
631C42C2×C22⋊D5311yescharacteristic
632C42C2×C22⋊D5311yescharacteristic
633C42C2×C22⋊D5311yescharacteristic
634C42C2×C22⋊D5311yescharacteristic
635C42C23×D5311yescharacteristic
636C23—22no—
637C23C2×C22⋊Dic5311yescharacteristic
638C23C2×C22⋊Dic5311yescharacteristic
639C23C2×C22⋊Dic5311yescharacteristic
640Q8—41no—
641Q8—42no—
642Q8—41no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—82no—
647D4—22no—
648D4—22no—
649D4—41no—
650D4—42no—
651D4—44no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—82no—
657D4—82no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—44no—
677C2×C4—82no—
678C2×C4—82no—
679C2×C4—82no—
680C2×C4C2×C22⋊Dic5311yescharacteristic
681C2×C4C2×C22⋊Dic5311yescharacteristic
682C2×C4C2×C22⋊Dic5311yescharacteristic
683C2×C4C2×C22⋊Dic5311yescharacteristic
684C2×C4C2×C22⋊Dic5311yescharacteristic
685C2×C4C2×C22⋊Dic5311yescharacteristic
686C2×C4C2×C22⋊Dic5311yescharacteristic
687C2×C4C2×C22⋊Dic5311yescharacteristic
688C2×C4C2×C22⋊Dic5311yescharacteristic
689C2×C4C23×Dic5311yescharacteristic
690C2×C4C22×C22⋊D5311yescharacteristic
691C2×C4C22×C22⋊D5311yescharacteristic
692C8—2121no—
693C8—2121no—
694C8—2121no—
695C8—2121no—
696C8—2121no—
697C8—2121no—
698C8—2121no—
699C8—2121no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22#1681060712yes—
712C22C22×C22⋊Dic5311yescharacteristic
713C4—21no—
714C4—21no—
715C4—21no—
716C4—21no—
717C4—21no—
718C4—21no—
719C4—21no—
720C4—21no—
721C4—21no—
722C4—21no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4#1681142611yescharacteristic
727C4#1681143111yescharacteristic
728C4#1681143411yescharacteristic
729C4#1681143811yescharacteristic
730C2—22no—
731C2—41no—
732C2—41no—
733C2—82no—
734C2C2×#1681060711yescharacteristic
735C2#2028324111yescharacteristic
736C2#2028324811yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic53
commutatorC2×C4×C53C23×C4
FrattiniC42C23×D53
Fitting, prime radicalC53×#3511C2
socleC22×C53C22×C22⋊C4
cosocleC42×C53C24
hypercenter#3511D53
hypocenterC53#17775
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3511

Complements

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

NH ≅ G/Ntype
1. #20283840C2semidirect
2. #20283840C2semidirect
3. #20273445C2semidirect
4. #20273437C2semidirect
5. #20273432C2semidirect
6. #20273425C2semidirect
7. #20273420C2semidirect
8. #20273410C2semidirect
9. #20273410C2semidirect
10. #20273405C2semidirect
11. #20273392C2semidirect
12. #20273372C2semidirect
13. #20273364C2semidirect
14. C2×#16810369C2semidirect
439. C53#17775semidirect

Maximal subgroups

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

subgroupindex
#202838402
#202734452
#202734372
#202734322
#202734252
#202734202
#202734102
#202734052
#202733922
#202733722
#202733642
C2×#168103692
C53×#35112
#1777553