Finite Group Databasebeta

← #28320687

Subgroups — #28320687

Order 13568.

826 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20291193C211yesmaximal, characteristic
2#20291152C211yesmaximal, characteristic
3#20290828C211yesmaximal, characteristic, complemented
4#20290828C211yesmaximal, characteristic, complemented
5#20290827C211yesmaximal, characteristic, complemented
6#20290826C211yesmaximal, characteristic, complemented
7#20290666C211yesmaximal, characteristic
8#20290666C211yesmaximal, characteristic
9#20290665C211yesmaximal, characteristic
10#20290664C211yesmaximal, characteristic
11#20290529C211yesmaximal, characteristic, complemented
12#20290529C211yesmaximal, characteristic, complemented
13C4×#13133286C211yesmaximal, characteristic, complemented
14C4×#13133285C211yesmaximal, characteristic, complemented
15#433×D53C211yesmaximal, characteristic
16C2×#13133296C2211yescharacteristic
17C22×C4⋊#6157C2211yescharacteristic
18C2×#13133286C2211yescharacteristic
19C2×#13133286C2211yescharacteristic
20C2×#13133286C2211yescharacteristic
21C2×#13133286C2211yescharacteristic
22C2×#13133285C2211yescharacteristic
23C2×#13133285C2211yescharacteristic
24C2×#13133285C2211yescharacteristic
25C2×#13133285C2211yescharacteristic
26#16811573—21no—
27#16811573—21no—
28#16811572—21no—
29#16811572—21no—
30#16811569C2211yescharacteristic
31#16811567C2211yescharacteristic
32#16811565C2211yescharacteristic
33#16811565C2211yescharacteristic
34C4⋊C4×#6157—21no—
35C4⋊C4×#6157—21no—
36C4×C4⋊#6157C2211yescharacteristic
37C4×C4⋊#6157C2211yescharacteristic
38C4×C4⋊#6157C2211yescharacteristic
39C4×C4⋊#6157C2211yescharacteristic
40C4×C4⋊#6157C2211yescharacteristic
41C4×C4⋊#6157C2211yescharacteristic
42C22⋊C4×#6157—21no—
43C22⋊C4×#6157—21no—
44#16811497C2211yescharacteristic
45#16811497C2211yescharacteristic
46#16811497C2211yescharacteristic
47#16811497C2211yescharacteristic
48#16811497C2211yescharacteristic
49#16811497C2211yescharacteristic
50#16811497C2211yescharacteristic
51#16811497C2211yescharacteristic
52#117×D53C2211yescharacteristic
53#16810685C411yescharacteristic, complemented
54#16810684C411yescharacteristic, complemented
55#16810683C411yescharacteristic, complemented
56#16810683C411yescharacteristic, complemented
57#16810682C411yescharacteristic, complemented
58#16810681C411yescharacteristic, complemented
59#16810681C411yescharacteristic, complemented
60C4⋊C8×D53C2211yescharacteristic
61C4⋊C8×D53C2211yescharacteristic
62C22⋊C8×D53C2211yescharacteristic
63C22⋊C8×D53C2211yescharacteristic
64#97×D53C2211yescharacteristic
65C4×C8×D53C2211yescharacteristic
66C53×#433C411yescharacteristic, complemented
67C23×#6157—21no—
68#13133296—22no—
69#13133296—22no—
70C2×C4⋊#6157—21no—
71C2×C4⋊#6157—22no—
72C2×C4⋊#6157—22no—
73C2×C4⋊#6157—21no—
74C2×C4⋊#6157—21no—
75C2×C4⋊#6157C2311yescharacteristic
76C2×C4⋊#6157C2311yescharacteristic
77C2×C4⋊#6157C2311yescharacteristic
78C2×C4⋊#6157C2311yescharacteristic
79C2×C4⋊#6157C2311yescharacteristic
80C2×C4⋊#6157C2311yescharacteristic
81C2×C4⋊#6157C2311yescharacteristic
82C2×C4⋊#6157C2311yescharacteristic
83C2×C22⋊#6157—21no—
84C2×C22⋊#6157—21no—
85C2×C22⋊#6157—21no—
86C2×C4×#6157—21no—
87C2×C4×#6157—21no—
88C2×C4×#6157—21no—
89C2×C4×#6157—21no—
90C2×C4×#6157—21no—
91C2×C4×#6157—21no—
92C2×C4×#6157—21no—
93#13133286—22no—
94#13133286—22no—
95#13133286—22no—
96#13133286—22no—
97#13133285—22no—
98#13133285—22no—
99#13133285—22no—
100#13133285—22no—
101(C2×#6157)⋊C4—21no—
102(C2×#6157)⋊C4—21no—
103(C2×#6157)⋊C4—21no—
104(C2×#6157)⋊C4—21no—
105(C2×#6157)⋊C4—21no—
106(C2×#6157)⋊C4—21no—
107(C2×#6157)⋊C4—21no—
108(C2×#6157)⋊C4—21no—
109(C2×#6157)⋊C4—21no—
110(C2×#6157)⋊C4—21no—
111C22×C4×D53C2311yescharacteristic
112C2×C8×D53C2311yescharacteristic
113C2×C8×D53C2311yescharacteristic
114C2×C8×D53C2311yescharacteristic
115C2×C8×D53C2311yescharacteristic
116#13133176C2×C411yescharacteristic
117#13133175Q811yescharacteristic
118#13133175Q811yescharacteristic
119#13133174C2×C411yescharacteristic
120#13133174C2×C411yescharacteristic
121#13133173Q811yescharacteristic
122#13133173Q811yescharacteristic
123C4⋊C4×D53D411yescharacteristic
124C4⋊C4×D53D411yescharacteristic
125C22⋊C4×D53D411yescharacteristic
126C22⋊C4×D53D411yescharacteristic
127C42×D53C2311yescharacteristic
128C42×D53C2311yescharacteristic
129C4⋊#88322C2×C411yescharacteristic, complemented
130C4⋊#88322C2×C411yescharacteristic, complemented
131#13133146C2×C411yescharacteristic, complemented
132#13133146C2×C411yescharacteristic, complemented
133#13133146C2×C411yescharacteristic, complemented
134#13133146C2×C411yescharacteristic, complemented
135C22⋊#88322C2×C411yescharacteristic
136C22⋊#88322C2×C411yescharacteristic
137#13133129C2×C411yescharacteristic
138#13133129C2×C411yescharacteristic
139#13133129C2×C411yescharacteristic
140#13133129C2×C411yescharacteristic
141#13133128C2×C411yescharacteristic, complemented
142#13133127C2×C411yescharacteristic, complemented
143#13133127C2×C411yescharacteristic, complemented
144C4×#88322C2×C411yescharacteristic, complemented
145C8×Dic53C2×C411yescharacteristic, complemented
146C8×Dic53C2×C411yescharacteristic, complemented
147#117×C53C2×C411yescharacteristic
148C4⋊C8×C53C2×C411yescharacteristic, complemented
149C4⋊C8×C53C2×C411yescharacteristic, complemented
150C22⋊C8×C53C2×C411yescharacteristic
151C22⋊C8×C53C2×C411yescharacteristic
152#97×C53C2×C411yescharacteristic, complemented
153C4×C8×C53C2×C411yescharacteristic, complemented
154C23×D53C2×D411yescharacteristic
155C22×#6157—21no—
156C22×#6157—21no—
157C22×#6157—21no—
158C22×#6157—21no—
159C22×#6157—24no—
160C22×#6157—21no—
161C22×#6157—21no—
162C22×#6157—21no—
163C22×#6157—21no—
164C22×#6157—81no—
165C22×#6157—81no—
166C22×C4×C53C22×C411yescharacteristic
167C22×Dic53C2×Q811yescharacteristic
168C2×C4×D53—21no—
169C2×C4×D53—21no—
170C2×C4×D53—21no—
171C2×C4×D53—21no—
172C2×C4×D53C22×C411yescharacteristic
173C2×C4×D53C2×D411yescharacteristic
174C2×C4×D53C2×D411yescharacteristic
175C2×C4×D53C2×D411yescharacteristic
176C2×C4×D53C2×D411yescharacteristic
177C2×C4×D53C2×D411yescharacteristic
178C2×C4×D53C2×Q811yescharacteristic
179C2×C4×D53C2411yescharacteristic
180C22⋊#6157—24no—
181C22⋊#6157—81no—
182C22⋊#6157—81no—
183C4⋊#6157—24no—
184C4⋊#6157—21no—
185C4⋊#6157—21no—
186C4⋊#6157—21no—
187C4⋊#6157—21no—
188C4⋊#6157—21no—
189C4⋊#6157—21no—
190C4⋊#6157—21no—
191C4⋊#6157—21no—
192C4⋊#6157—21no—
193C4⋊#6157—21no—
194C4⋊#6157—21no—
195C4⋊#6157—21no—
196C4⋊#6157—81no—
197C4⋊#6157—81no—
198C4⋊#6157#4112yes—
199C4⋊#6157#4112yes—
200C4⋊#6157#4112yes—
201C4⋊#6157#4112yes—
202C4×#6157—24no—
203C4×#6157—81no—
204C4×#6157—81no—
205C4×#6157—81no—
206C4×#6157—81no—
207C4×#6157—81no—
208C4×#6157—81no—
209C2×C8×C53C22×C411yescharacteristic
210C2×C8×C53C22×C411yescharacteristic
211C2×C8×C53C22×C411yescharacteristic
212C2×C8×C53C22×C411yescharacteristic
213C4⋊C4×C53C4⋊C411yescharacteristic
214C4⋊C4×C53C4⋊C411yescharacteristic
215C22⋊C4×C53C4⋊C411yescharacteristic
216C22⋊C4×C53C4⋊C411yescharacteristic
217C42×C53C22×C411yescharacteristic
218C42×C53C22×C411yescharacteristic
219C22⋊Dic53C4⋊C411yescharacteristic
220C22⋊Dic53C4⋊C411yescharacteristic
221#11719921C4⋊C411yescharacteristic
222#11719921C4⋊C411yescharacteristic
223#11719921C4⋊C411yescharacteristic
224#11719921C4⋊C411yescharacteristic
225C4⋊Dic53C4⋊C411yescharacteristic
226C4⋊Dic53C4⋊C411yescharacteristic
227#11719919C4⋊C411yescharacteristic
228#11719919C4⋊C411yescharacteristic
229#11719919C4⋊C411yescharacteristic
230#11719919C4⋊C411yescharacteristic
231C4×Dic53C22×C411yescharacteristic
232C4×Dic53C22×C411yescharacteristic
233C4×Dic53C2×Q811yescharacteristic
234C4×Dic53C2×Q811yescharacteristic
235C4×Dic53C2×Q811yescharacteristic
236C4×Dic53C2×Q811yescharacteristic
237C2×#88322C22×C411yescharacteristic
238C2×#88322C22×C411yescharacteristic
239C2×#88322C22×C411yescharacteristic
240C2×#88322C22×C411yescharacteristic
241C8×D53—21no—
242C8×D53—21no—
243C8×D53—21no—
244C8×D53—21no—
245C8×D53—21no—
246C8×D53—21no—
247C8×D53—21no—
248C8×D53—21no—
249C23×C53C2×C4⋊C411yescharacteristic
250C22×D53—21no—
251C22×D53—21no—
252C22×D53—21no—
253C22×D53—21no—
254C22×D53—21no—
255C22×D53—21no—
256C22×D53C2×C4⋊C411yescharacteristic
257C22×D53C22×D411yescharacteristic
258C2×#6157—22no—
259C2×#6157—22no—
260C2×#6157—22no—
261C2×#6157—22no—
262C2×#6157—41no—
263C2×#6157—41no—
264C2×#6157—41no—
265C2×#6157—41no—
266C2×#6157—41no—
267C2×#6157—41no—
268C2×#6157—41no—
269C2×#6157—41no—
270C2×#6157—41no—
271C2×#6157—41no—
272C2×#6157—41no—
273C2×#6157—41no—
274C2×#6157—41no—
275C2×#6157—41no—
276C2×#6157—41no—
277C2×#6157—41no—
278C2×#6157—41no—
279C2×#6157—41no—
280C2×#6157—41no—
281C2×#6157—41no—
282C2×#6157—84no—
283C2×C4×C53—21no—
284C2×C4×C53—21no—
285C2×C4×C53C2×C4⋊C411yescharacteristic
286C2×C4×C53C2×C4⋊C411yescharacteristic
287C2×C4×C53C2×C4⋊C411yescharacteristic
288C2×C4×C53C2×C4⋊C411yescharacteristic
289C2×C4×C53C2×C4⋊C411yescharacteristic
290C2×C4×C53C23×C411yescharacteristic
291C2×Dic53—21no—
292C2×Dic53—21no—
293C2×Dic53C2×C4⋊C411yescharacteristic
294C2×Dic53C2×C4⋊C411yescharacteristic
295C2×Dic53C2×C4⋊C411yescharacteristic
296C2×Dic53C2×C4⋊C411yescharacteristic
297C2×Dic53C2×C4⋊C411yescharacteristic
298C2×Dic53C22×Q811yescharacteristic
299C4×D53—21no—
300C4×D53—21no—
301C4×D53—21no—
302C4×D53—21no—
303C4×D53—21no—
304C4×D53—21no—
305C4×D53—21no—
306C4×D53—21no—
307C4×D53—21no—
308C4×D53—21no—
309C4×D53—21no—
310C4×D53—21no—
311C4×D53—21no—
312C4×D53—21no—
313C4×D53C2×#4111yescharacteristic
314C4×D53C2×#4111yescharacteristic
315C4×D53C2×#4111yescharacteristic
316C4×D53C2×#4111yescharacteristic
317C8×C53—21no—
318C8×C53—21no—
319C8×C53—21no—
320C8×C53—21no—
321#88322—21no—
322#88322—21no—
323#88322—21no—
324#88322—21no—
325#21367—531nomaximal, Sylow
326C22×C53—21no—
327C22×C53—21no—
328C22×C53—21no—
329C22×C53C22×C4⋊C411yescharacteristic
330C2×D53—21no—
331C2×D53—21no—
332C2×D53—21no—
333C2×D53—41no—
334C2×D53—41no—
335C2×D53—41no—
336C2×D53—41no—
337C2×D53#52511yescharacteristic
338C2×D53#52511yescharacteristic
339C2×D53#57611yescharacteristic
340C2×D53#57711yescharacteristic
341C2×D53#57711yescharacteristic
342C2×D53#57811yescharacteristic
343#6157—42no—
344#6157—42no—
345#6157—42no—
346#6157—42no—
347#6157—81no—
348#6157—81no—
349#6157—81no—
350#6157—81no—
351C4×C53—21no—
352C4×C53—21no—
353C4×C53—21no—
354C4×C53—21no—
355C4×C53—21no—
356C4×C53C4×#4111yescharacteristic
357C4×C53C4×#4111yescharacteristic
358Dic53—21no—
359Dic53—21no—
360Dic53—21no—
361Dic53—21no—
362Dic53—21no—
363Dic53#53311yescharacteristic
364Dic53#53311yescharacteristic
365C2×#433—531no—
366#2314—531no—
367#2274—531no—
368#1949—531no—
369#1949—531no—
370#1948—531no—
371#1947—531no—
372#1854—531no—
373#1854—531no—
374#1853—531no—
375#1852—531no—
376#1776—531no—
377#1776—531no—
378C4×#107—531no—
379C4×#106—531no—
380C2×C53—41no—
381C2×C53#229611yescharacteristic
382C2×C53#291211yescharacteristic
383C2×C53#291311yescharacteristic
384D53—41no—
385D53#311811yescharacteristic
386D53#311911yescharacteristic
387D53#312011yescharacteristic
388D53#312111yescharacteristic
389C2×#117—531no—
390C2×#117—531no—
391C22×C4⋊C4—531no—
392#433—531no—
393#433—531no—
394#433—531no—
395#433—531no—
396#433—531no—
397#433—531no—
398#433—531no—
399#433#615711yescharacteristic, complemented
400C2×#107—531no—
401C2×#107—531no—
402C2×#107—531no—
403C2×#107—531no—
404C2×#106—531no—
405C2×#106—531no—
406C2×#106—531no—
407C2×#106—531no—
408C2×C4⋊C8—531no—
409C2×C4⋊C8—531no—
410C2×C22⋊C8—531no—
411C2×C22⋊C8—531no—
412C2×#97—531no—
413C2×C4×C8—531no—
414#388—1061no—
415#388—1061no—
416#387—1061no—
417#387—1061no—
418#384—531no—
419#382—531no—
420#380—531no—
421#380—531no—
422C4×C4⋊C4—531no—
423C4×C4⋊C4—531no—
424C4×C4⋊C4—531no—
425C4×C4⋊C4—531no—
426C4×C4⋊C4—531no—
427C4×C4⋊C4—531no—
428C4×C4⋊C4—1061no—
429C4×C4⋊C4—1061no—
430C4×C22⋊C4—1061no—
431C4×C22⋊C4—1061no—
432#340—531no—
433#340—531no—
434#340—531no—
435#340—531no—
436#340—531no—
437#340—531no—
438#340—531no—
439#340—531no—
440C53#2136711yescharacteristic, complemented, Sylow
441C23×C4—531no—
442C23×C4—1061no—
443C22×C8—531no—
444C22×C8—531no—
445C22×C8—531no—
446C22×C8—531no—
447#117—531no—
448#117—531no—
449#117—531no—
450#117—531no—
451#117—531no—
452#117—531no—
453#117—531no—
454#117—1062no—
455#117—1062no—
456#117C2×#615711yescharacteristic
457C2×C4⋊C4—531no—
458C2×C4⋊C4—531no—
459C2×C4⋊C4—531no—
460C2×C4⋊C4—531no—
461C2×C4⋊C4—531no—
462C2×C4⋊C4—531no—
463C2×C4⋊C4—531no—
464C2×C4⋊C4—531no—
465C2×C4⋊C4—531no—
466C2×C4⋊C4—531no—
467C2×C4⋊C4—1062no—
468C2×C4⋊C4—1062no—
469C2×C4⋊C4—1061no—
470C2×C4⋊C4—1061no—
471C2×C4⋊C4—1061no—
472C2×C22⋊C4—531no—
473C2×C22⋊C4—531no—
474C2×C22⋊C4—1061no—
475C2×C22⋊C4—1061no—
476C2×C22⋊C4—1061no—
477C2×C42—531no—
478C2×C42—531no—
479C2×C42—1061no—
480C2×C42—1061no—
481C2×C42—1061no—
482C2×C42—1061no—
483C2×C42—1061no—
484C2×C42—1061no—
485C2×C42—1061no—
486#107—1062no—
487#107—1062no—
488#107—1062no—
489#107—1062no—
490#106—1062no—
491#106—1062no—
492#106—1062no—
493#106—1062no—
494C4⋊C8—531no—
495C4⋊C8—531no—
496C4⋊C8—531no—
497C4⋊C8—531no—
498C4⋊C8—531no—
499C4⋊C8—531no—
500C4⋊C8C2×#615711yescharacteristic, complemented
501C4⋊C8C2×#615711yescharacteristic, complemented
502C22⋊C8—531no—
503C22⋊C8—531no—
504C22⋊C8—531no—
505C22⋊C8—531no—
506C22⋊C8—531no—
507C22⋊C8—531no—
508C22⋊C8C2×#615711yescharacteristic
509C22⋊C8C2×#615711yescharacteristic
510#97—531no—
511#97—531no—
512#97—531no—
513#97C2×#615711yescharacteristic, complemented
514C4×C8—531no—
515C4×C8—531no—
516C4×C8—531no—
517C4×C8C2×#615711yescharacteristic, complemented
518#95—1061no—
519#95—1061no—
520#95—1061no—
521#95—1061no—
522#95—1061no—
523#95—1061no—
524#95—1061no—
525#95—1061no—
526#95—1061no—
527#95—1061no—
528C24—531no—
529C22×C4—531no—
530C22×C4—531no—
531C22×C4—531no—
532C22×C4—531no—
533C22×C4—531no—
534C22×C4—531no—
535C22×C4—531no—
536C22×C4—531no—
537C22×C4—531no—
538C22×C4—1061no—
539C22×C4—1061no—
540C22×C4—1061no—
541C22×C4—1061no—
542C22×C4—1064no—
543C22×C4—1061no—
544C22×C4—1061no—
545C22×C4—1061no—
546C22×C4—1061no—
547C22×C4—1061no—
548C22×C4—1061no—
549C22×C4—1061no—
550C22×C4—1061no—
551C22×C4—4241no—
552C22×C4—4241no—
553C22×C4C22×#615711yescharacteristic
554C2×C8—531no—
555C2×C8—531no—
556C2×C8—531no—
557C2×C8—531no—
558C2×C8—1061no—
559C2×C8—1061no—
560C2×C8—1061no—
561C2×C8—1061no—
562C2×C8—1061no—
563C2×C8—1061no—
564C2×C8—1061no—
565C2×C8—1061no—
566C2×C8C22×#615711yescharacteristic
567C2×C8C22×#615711yescharacteristic
568C2×C8C22×#615711yescharacteristic
569C2×C8C22×#615711yescharacteristic
570C4⋊C4—531no—
571C4⋊C4—531no—
572C4⋊C4—531no—
573C4⋊C4—531no—
574C4⋊C4—531no—
575C4⋊C4—531no—
576C4⋊C4—532no—
577C4⋊C4—532no—
578C4⋊C4—532no—
579C4⋊C4—532no—
580C4⋊C4—1061no—
581C4⋊C4—1061no—
582C4⋊C4—1061no—
583C4⋊C4—1061no—
584C4⋊C4—1061no—
585C4⋊C4—1061no—
586C4⋊C4—1061no—
587C4⋊C4—1061no—
588C4⋊C4—1061no—
589C4⋊C4—1061no—
590C4⋊C4—1061no—
591C4⋊C4—1061no—
592C4⋊C4—1064no—
593C4⋊C4—4241no—
594C4⋊C4—4241no—
595C4⋊C4C4⋊#615711yescharacteristic
596C4⋊C4C4⋊#615711yescharacteristic
597C22⋊C4—531no—
598C22⋊C4—531no—
599C22⋊C4—531no—
600C22⋊C4—531no—
601C22⋊C4—531no—
602C22⋊C4—531no—
603C22⋊C4—1064no—
604C22⋊C4—4241no—
605C22⋊C4—4241no—
606C22⋊C4C4⋊#615711yescharacteristic
607C22⋊C4C4⋊#615711yescharacteristic
608C42—531no—
609C42—531no—
610C42—531no—
611C42—531no—
612C42—531no—
613C42—531no—
614C42—1064no—
615C42—4241no—
616C42—4241no—
617C42—4241no—
618C42—4241no—
619C42—4241no—
620C42—4241no—
621C42C22×#615711yescharacteristic
622C42C22×#615711yescharacteristic
623C23—531no—
624C23—531no—
625C23—1061no—
626C23—1061no—
627C23—1061no—
628C23—1061no—
629C23—1061no—
630C23—1061no—
631C23C2×C4⋊#615711yescharacteristic
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—531no—
635C2×C4—531no—
636C2×C4—531no—
637C2×C4—531no—
638C2×C4—531no—
639C2×C4—531no—
640C2×C4—531no—
641C2×C4—531no—
642C2×C4—531no—
643C2×C4—531no—
644C2×C4—1061no—
645C2×C4—1061no—
646C2×C4—1061no—
647C2×C4—1061no—
648C2×C4—1061no—
649C2×C4—1061no—
650C2×C4—1061no—
651C2×C4—1061no—
652C2×C4—1061no—
653C2×C4—1061no—
654C2×C4—1061no—
655C2×C4—1061no—
656C2×C4—1061no—
657C2×C4—1061no—
658C2×C4—1061no—
659C2×C4—1061no—
660C2×C4—1062no—
661C2×C4—1062no—
662C2×C4—1062no—
663C2×C4—1062no—
664C2×C4—4244no—
665C2×C4—2121no—
666C2×C4—2121no—
667C2×C4—2121no—
668C2×C4—2121no—
669C2×C4—2121no—
670C2×C4—2121no—
671C2×C4—2121no—
672C2×C4—2121no—
673C2×C4—2121no—
674C2×C4—2121no—
675C2×C4—2121no—
676C2×C4—2121no—
677C2×C4—2121no—
678C2×C4—2121no—
679C2×C4—2121no—
680C2×C4—2121no—
681C2×C4—2121no—
682C2×C4—2121no—
683C2×C4—2121no—
684C2×C4—2121no—
685C2×C4C2×C4⋊#615711yescharacteristic
686C2×C4C2×C4⋊#615711yescharacteristic
687C2×C4C2×C4⋊#615711yescharacteristic
688C2×C4C2×C4⋊#615711yescharacteristic
689C2×C4C2×C4⋊#615711yescharacteristic
690C2×C4C23×#615711yescharacteristic
691C8—21no—
692C8—21no—
693C8—21no—
694C8—21no—
695C8—1061no—
696C8—1061no—
697C8—1061no—
698C8—1061no—
699C22—21no—
700C22—21no—
701C22—21no—
702C22—531no—
703C22—531no—
704C22—531no—
705C22—531no—
706C22—531no—
707C22—531no—
708C22—1061no—
709C22—1061no—
710C22—1061no—
711C22—2121no—
712C22—2121no—
713C22—2121no—
714C22—2121no—
715C22C22×C4⋊#615711yescharacteristic
716C4—21no—
717C4—21no—
718C4—21no—
719C4—21no—
720C4—21no—
721C4—531no—
722C4—531no—
723C4—1061no—
724C4—1061no—
725C4—1061no—
726C4—1061no—
727C4—1061no—
728C4—4241no—
729C4—4241no—
730C4—4241no—
731C4—4241no—
732C4—2122no—
733C4—2122no—
734C4—2122no—
735C4—2122no—
736C4#41×#615711yescharacteristic
737C4#41×#615711yescharacteristic
738C2—41no—
739C2—531no—
740C2—531no—
741C2—531no—
742C2—531no—
743C2—2121no—
744C2#2029117511yescharacteristic
745C2#2029136911yescharacteristic
746C2#2029137011yescharacteristic
subgroupG/H
centerC22C22×C4⋊#6157
commutatorC2×C4×C53C23×C4
FrattiniC2×C4C23×#6157
FittingC53×#433C4
socleC22×C53C22×C4⋊C4
prime radicalC23×D53C2×D4
cosocleC2×C4×D53C24
hypercenter#433#6157
hypocenterC53#21367
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
3. #20290828C2semidirect
4. #20290828C2semidirect
5. #20290827C2semidirect
6. #20290826C2semidirect
11. #20290529C2semidirect
12. #20290529C2semidirect
13. C4×#13133286C2semidirect
14. C4×#13133285C2semidirect
53. #16810685C4semidirect
54. #16810684C4semidirect
55. #16810683C4semidirect
56. #16810683C4semidirect
57. #16810682C4semidirect
58. #16810681C4semidirect
59. #16810681C4semidirect
66. C53×#433C4semidirect
129. C4⋊#88322C2×C4semidirect
130. C4⋊#88322C2×C4semidirect
131. #13133146C2×C4semidirect
132. #13133146C2×C4semidirect
133. #13133146C2×C4semidirect
134. #13133146C2×C4semidirect
141. #13133128C2×C4semidirect
142. #13133127C2×C4semidirect
143. #13133127C2×C4semidirect
144. C4×#88322C2×C4semidirect
145. C8×Dic53C2×C4semidirect
146. C8×Dic53C2×C4semidirect
148. C4⋊C8×C53C2×C4semidirect
149. C4⋊C8×C53C2×C4semidirect
152. #97×C53C2×C4semidirect
153. C4×C8×C53C2×C4semidirect
399. #433#6157semidirect
440. C53#21367semidirect
500. C4⋊C8C2×#6157semidirect
501. C4⋊C8C2×#6157semidirect
513. #97C2×#6157semidirect
517. C4×C8C2×#6157semidirect

Maximal subgroups

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

subgroupindex
#202911932
#202911522
#202908282
#202908272
#202908262
#202906662
#202906652
#202906642
#202905292
C4×#131332862
C4×#131332852
#433×D532
#2136753