Finite Group Databasebeta

← #27400585

Subgroups — #27400585

Order 13568.

1148 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#11719917C211yesmaximal, characteristic, complemented
2#20277160C211yesmaximal, characteristic, complemented
3#20275697C211yesmaximal, characteristic, complemented
4#20275660C211yesmaximal, characteristic, complemented
5#20275164C211yesmaximal, characteristic, complemented
6#20275159C211yesmaximal, characteristic, complemented
7#20275018C211yesmaximal, characteristic, complemented
8#20275018C211yesmaximal, characteristic, complemented
9#20274814C211yesmaximal, characteristic, complemented
10#20274814C211yesmaximal, characteristic, complemented
11#20274735C211yesmaximal, characteristic, complemented
12#20274525C211yesmaximal, characteristic, complemented
13#20274424C211yesmaximal, characteristic, complemented
14C2×#16810382C211yesmaximal, characteristic, complemented
15C53×#3475C211yesmaximal, characteristic
16C22×#11719917C2211yescharacteristic
17C22×#11719917C2211yescharacteristic
18C2×#13133176C2211yescharacteristic
19C22×C4×Dic53C2211yescharacteristic
20#16810701—21no—
21#16810695—21no—
22#16810695—21no—
23D4×#88322—21no—
24#16810647C2211yescharacteristic
25C2×#13133144C2211yescharacteristic
26C2×#13133144C2211yescharacteristic
27C2×#13133144C2211yescharacteristic
28C2×#13133144C2211yescharacteristic
29#16810587C2211yescharacteristic
30#16810587C2211yescharacteristic
31C4×#11719917C2211yescharacteristic
32#16810516—21no—
33#16810509—21no—
34#16810503—21no—
35#16810498—21no—
36C4×C4⋊Dic53C2211yescharacteristic
37C4×C22⋊Dic53C2211yescharacteristic
38C4×C22⋊Dic53C2211yescharacteristic
39#16810469C2211yescharacteristic
40#16810382C2211yescharacteristic
41#16810382C2211yescharacteristic
42#16810382C2211yescharacteristic
43#16810382C2211yescharacteristic
44#16810382C2211yescharacteristic
45#16810382C2211yescharacteristic
46#16810382C2211yescharacteristic
47#16810382C2211yescharacteristic
48#16810382C2211yescharacteristic
49#16810382C2211yescharacteristic
50#16810382C2211yescharacteristic
51#16810382C2211yescharacteristic
52C53×#556C411yescharacteristic, complemented
53C53×#555C411yescharacteristic, complemented
54C53×#554C411yescharacteristic, complemented
55C53×#553C411yescharacteristic, complemented
56C53×#553C411yescharacteristic, complemented
57C53×#552—21no—
58C53×#552C411yescharacteristic, complemented
59C53×#552C411yescharacteristic, complemented
60C53×#551—21no—
61C53×#551—21no—
62C53×#547C411yescharacteristic, complemented
63C53×#546—21no—
64C53×#533C2211yescharacteristic
65C53×#529—21no—
66C53×#529—21no—
67C53×#529—21no—
68C53×#525C2211yescharacteristic
69C53×#525C2211yescharacteristic
70C4×#41×C53—21no—
71C4×#41×C53C2211yescharacteristic
72C2×C4×D4×C53C2211yescharacteristic
73C2×#117×C53C2211yescharacteristic
74C2×#117×C53C2211yescharacteristic
75C23×Dic53—21no—
76C2×#11719917—22no—
77C2×#11719917—22no—
78C2×#11719917—21no—
79C2×#11719917—21no—
80C2×#11719917—41no—
81C2×#11719917—41no—
82C2×#11719917C2311yescharacteristic
83C2×#11719917C2311yescharacteristic
84C2×#11719917C2311yescharacteristic
85C2×#11719917C2311yescharacteristic
86C22×#88322—21no—
87C22×#88322—21no—
88#13133176—22no—
89#13133176—41no—
90C2×C4⋊Dic53—21no—
91C2×C4⋊Dic53—21no—
92C2×C22⋊Dic53—21no—
93C2×C22⋊Dic53—21no—
94C2×C22⋊Dic53—21no—
95C2×C4×Dic53—21no—
96C2×C4×Dic53—22no—
97C2×C4×Dic53—41no—
98C2×C4×Dic53C2311yescharacteristic
99C2×C4×Dic53C2311yescharacteristic
100C2×C4×Dic53C2311yescharacteristic
101C2×C4×Dic53C2311yescharacteristic
102C4⋊#88322—21no—
103C4⋊#88322—21no—
104#13133144—22no—
105#13133144—22no—
106#13133144—41no—
107#13133144—41no—
108C22⋊#88322—21no—
109C22⋊#88322—21no—
110C22⋊#88322—21no—
111C22⋊#88322—21no—
112#13133128—21no—
113C4×#88322—21no—
114#13133124—21no—
115#13133124—21no—
116#13133124—21no—
117#13133124—21no—
118#13133124—21no—
119C2×#41×C53—21no—
120C2×#41×C53C2311yescharacteristic
121C22×D4×C53D411yescharacteristic
122C23×C4×C53C2311yescharacteristic
123C23×C4×C53C2311yescharacteristic
124C4⋊Q8×C53C2×C411yescharacteristic, complemented
125C4⋊Q8×C53C2×C411yescharacteristic, complemented
126#126×C53—21no—
127#126×C53—21no—
128#126×C53—21no—
129#126×C53—21no—
130#126×C53—21no—
131#126×C53—21no—
132#125×C53—21no—
133#125×C53—21no—
134#125×C53—21no—
135#125×C53C2×C411yescharacteristic, complemented
136#125×C53C2×C411yescharacteristic, complemented
137#124×C53—21no—
138#124×C53—21no—
139#124×C53—21no—
140#123×C53—21no—
141#123×C53—21no—
142#123×C53—21no—
143#123×C53—21no—
144#123×C53—21no—
145#123×C53—21no—
146#123×C53—21no—
147#123×C53—21no—
148C22⋊Q8×C53—21no—
149C22⋊Q8×C53—21no—
150C22⋊Q8×C53—21no—
151C22⋊Q8×C53—21no—
152C22⋊Q8×C53—21no—
153C22⋊Q8×C53C2×C411yescharacteristic
154C22⋊Q8×C53C2×C411yescharacteristic
155C22⋊Q8×C53C2×C411yescharacteristic, complemented
156C22⋊Q8×C53C2×C411yescharacteristic, complemented
157#121×C53—21no—
158#121×C53—21no—
159#121×C53—21no—
160#121×C53C2×C411yescharacteristic
161#121×C53C2×C411yescharacteristic
162#121×C53C2×C411yescharacteristic, complemented
163#121×C53C2×C411yescharacteristic, complemented
164#120×C53—21no—
165#120×C53—21no—
166C4×Q8×C53—21no—
167C4×Q8×C53—21no—
168C4×Q8×C53—21no—
169C4×Q8×C53C2×C411yescharacteristic, complemented
170C4×Q8×C53C2×C411yescharacteristic, complemented
171C4×D4×C53—21no—
172C4×D4×C53—21no—
173C4×D4×C53—21no—
174C4×D4×C53—21no—
175C4×D4×C53—21no—
176C4×D4×C53—21no—
177C4×D4×C53—21no—
178C4×D4×C53—21no—
179C4×D4×C53—21no—
180C4×D4×C53C2×C411yescharacteristic
181C4×D4×C53C2×C411yescharacteristic
182C4×D4×C53C2×C411yescharacteristic
183C4×D4×C53C2×C411yescharacteristic
184C4×D4×C53C2×C411yescharacteristic, complemented
185C4×D4×C53C2×C411yescharacteristic, complemented
186C4×D4×C53D411yescharacteristic
187C4×D4×C53D411yescharacteristic
188C4×D4×C53D411yescharacteristic
189C4×D4×C53D411yescharacteristic
190#117×C53—21no—
191#117×C53—21no—
192#117×C53—21no—
193#117×C53—21no—
194#117×C53—21no—
195#117×C53—21no—
196#117×C53—21no—
197#117×C53—21no—
198#117×C53C2×C411yescharacteristic
199#117×C53C2×C411yescharacteristic
200#117×C53C2×C411yescharacteristic, complemented
201#117×C53C2×C411yescharacteristic, complemented
202#117×C53C2311yescharacteristic
203#117×C53C2311yescharacteristic
204#117×C53C2311yescharacteristic
205C2×C4⋊C4×C53C2×C411yescharacteristic
206C2×C4⋊C4×C53C2×C411yescharacteristic
207C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
208C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
209C2×C4⋊C4×C53D411yescharacteristic
210C2×C22⋊C4×C53—21no—
211C2×C22⋊C4×C53—21no—
212C2×C22⋊C4×C53D411yescharacteristic
213C2×C22⋊C4×C53D411yescharacteristic
214C2×C42×C53—21no—
215C2×C42×C53—21no—
216C2×C42×C53—21no—
217C2×C42×C53C2311yescharacteristic
218C24×C53C2×D411yescharacteristic
219C24×C53C2×D411yescharacteristic
220#41×C53—21no—
221#41×C53—21no—
222#41×C53—21no—
223#41×C53—21no—
224#41×C53—44no—
225C2×Q8×C53—21no—
226C2×Q8×C53—21no—
227C2×Q8×C53C22×C411yescharacteristic
228C2×D4×C53—21no—
229C2×D4×C53—21no—
230C2×D4×C53—21no—
231C2×D4×C53—21no—
232C2×D4×C53—21no—
233C2×D4×C53—42no—
234C2×D4×C53C22⋊C411yescharacteristic
235C2×D4×C53C22⋊C411yescharacteristic
236C2×D4×C53C22⋊C411yescharacteristic
237C2×D4×C53C22⋊C411yescharacteristic
238C2×D4×C53C22×C411yescharacteristic
239C22×C4×C53—21no—
240C22×C4×C53—21no—
241C22×C4×C53—21no—
242C22×C4×C53—21no—
243C22×C4×C53—21no—
244C22×C4×C53—21no—
245C22×C4×C53—21no—
246C22×C4×C53—21no—
247C22×C4×C53—21no—
248C22×C4×C53—21no—
249C22×C4×C53—21no—
250C22×C4×C53—21no—
251C22×C4×C53—21no—
252C22×C4×C53—21no—
253C22×C4×C53—21no—
254C22×C4×C53C22×C411yescharacteristic
255C22×C4×C53C22×C411yescharacteristic
256C22×C4×C53C22×C411yescharacteristic
257C22×C4×C53C22×C411yescharacteristic
258C22×C4×C53C2×D411yescharacteristic
259C22×C4×C53C2×D411yescharacteristic
260C22×C4×C53C2×D411yescharacteristic
261C22×C4×C53C2×D411yescharacteristic
262C22×C4×C53C2×D411yescharacteristic
263C22×C4×C53C2×D411yescharacteristic
264C22×C4×C53C2×D411yescharacteristic
265C22×C4×C53C2×D411yescharacteristic
266C22×C4×C53C2411yescharacteristic
267C22×Dic53—21no—
268C22×Dic53—21no—
269C22×Dic53—21no—
270C22×Dic53—21no—
271C22×Dic53—42no—
272C22×Dic53—42no—
273C22×Dic53—42no—
274C4⋊C4×C53—21no—
275C4⋊C4×C53—21no—
276C4⋊C4×C53—21no—
277C4⋊C4×C53—21no—
278C4⋊C4×C53—21no—
279C4⋊C4×C53—21no—
280C4⋊C4×C53—21no—
281C4⋊C4×C53—21no—
282C4⋊C4×C53—21no—
283C4⋊C4×C53—21no—
284C4⋊C4×C53—21no—
285C4⋊C4×C53—21no—
286C4⋊C4×C53—21no—
287C4⋊C4×C53—21no—
288C4⋊C4×C53—21no—
289C4⋊C4×C53—21no—
290C4⋊C4×C53C22⋊C411yescharacteristic
291C4⋊C4×C53C22⋊C411yescharacteristic
292C4⋊C4×C53C22⋊C411yescharacteristic
293C4⋊C4×C53C22⋊C411yescharacteristic
294C4⋊C4×C53C22×C411yescharacteristic
295C4⋊C4×C53C22×C411yescharacteristic
296C4⋊C4×C53C22×C411yescharacteristic
297C4⋊C4×C53C22×C411yescharacteristic
298C4⋊C4×C53C22×C411yescharacteristic
299C4⋊C4×C53C22×C411yescharacteristic
300C22⋊C4×C53—21no—
301C22⋊C4×C53—21no—
302C22⋊C4×C53—21no—
303C22⋊C4×C53—21no—
304C22⋊C4×C53—21no—
305C22⋊C4×C53—21no—
306C22⋊C4×C53—21no—
307C22⋊C4×C53—21no—
308C22⋊C4×C53—21no—
309C22⋊C4×C53—21no—
310C22⋊C4×C53—21no—
311C22⋊C4×C53—21no—
312C22⋊C4×C53—21no—
313C22⋊C4×C53—21no—
314C22⋊C4×C53—21no—
315C22⋊C4×C53—21no—
316C22⋊C4×C53—21no—
317C22⋊C4×C53C22⋊C411yescharacteristic
318C22⋊C4×C53C22⋊C411yescharacteristic
319C22⋊C4×C53C22⋊C411yescharacteristic
320C22⋊C4×C53C22⋊C411yescharacteristic
321C22⋊C4×C53C22⋊C411yescharacteristic
322C22⋊C4×C53C22⋊C411yescharacteristic
323C22⋊C4×C53C22⋊C411yescharacteristic
324C22⋊C4×C53C22⋊C411yescharacteristic
325C42×C53—21no—
326C42×C53—21no—
327C42×C53—21no—
328C42×C53—21no—
329C42×C53—21no—
330C42×C53—21no—
331C42×C53—21no—
332C42×C53—21no—
333C42×C53—21no—
334C42×C53C22×C411yescharacteristic
335C42×C53C22×C411yescharacteristic
336C42×C53C2×D411yescharacteristic
337C42×C53C2×D411yescharacteristic
338C22⋊Dic53—42no—
339C22⋊Dic53—42no—
340C22⋊Dic53—42no—
341C4⋊Dic53—42no—
342C4⋊Dic53—42no—
343C4×Dic53—21no—
344C4×Dic53—21no—
345C4×Dic53—21no—
346C4×Dic53—21no—
347C4×Dic53—21no—
348C4×Dic53—21no—
349C4×Dic53—21no—
350C4×Dic53—42no—
351C4×Dic53#4112yescomplemented
352#11719917—21no—
353#11719917—21no—
354#11719917—21no—
355#11719917—21no—
356#11719917—21no—
357#11719917—21no—
358#11719917—21no—
359#11719917—42no—
360#11719917—42no—
361#11719917#4112yescomplemented
362C2×#88322—21no—
363C2×#88322—21no—
364C2×#88322—21no—
365C2×#88322—21no—
366C2×#88322—42no—
367C2×#88322—42no—
368C23×C53—21no—
369C23×C53—21no—
370C23×C53—22no—
371C23×C53—21no—
372C23×C53—21no—
373C23×C53—21no—
374C23×C53—41no—
375C23×C53—41no—
376C23×C53—41no—
377C23×C53C2×C22⋊C411yescharacteristic
378C23×C53C2×C22⋊C411yescharacteristic
379C23×C53C2×C22⋊C411yescharacteristic
380C23×C53C2×C22⋊C411yescharacteristic
381C23×C53C22×D411yescharacteristic
382Q8×C53—21no—
383Q8×C53—21no—
384Q8×C53—42no—
385Q8×C53—81no—
386D4×C53—22no—
387D4×C53—22no—
388D4×C53—21no—
389D4×C53—21no—
390D4×C53—41no—
391D4×C53—41no—
392D4×C53—42no—
393D4×C53—41no—
394D4×C53—41no—
395D4×C53—42no—
396D4×C53—81no—
397D4×C53—81no—
398C2×C4×C53—21no—
399C2×C4×C53—21no—
400C2×C4×C53—21no—
401C2×C4×C53—21no—
402C2×C4×C53—21no—
403C2×C4×C53—21no—
404C2×C4×C53—21no—
405C2×C4×C53—21no—
406C2×C4×C53—21no—
407C2×C4×C53—21no—
408C2×C4×C53—21no—
409C2×C4×C53—21no—
410C2×C4×C53—21no—
411C2×C4×C53—21no—
412C2×C4×C53—21no—
413C2×C4×C53—21no—
414C2×C4×C53—21no—
415C2×C4×C53—21no—
416C2×C4×C53—21no—
417C2×C4×C53—21no—
418C2×C4×C53—21no—
419C2×C4×C53—21no—
420C2×C4×C53—21no—
421C2×C4×C53—21no—
422C2×C4×C53—21no—
423C2×C4×C53—21no—
424C2×C4×C53—21no—
425C2×C4×C53—41no—
426C2×C4×C53—41no—
427C2×C4×C53—42no—
428C2×C4×C53—42no—
429C2×C4×C53—42no—
430C2×C4×C53—41no—
431C2×C4×C53—41no—
432C2×C4×C53—81no—
433C2×C4×C53—81no—
434C2×C4×C53—81no—
435C2×C4×C53C2×C22⋊C411yescharacteristic
436C2×C4×C53C2×C22⋊C411yescharacteristic
437C2×C4×C53C2×C22⋊C411yescharacteristic
438C2×C4×C53C2×C22⋊C411yescharacteristic
439C2×C4×C53C2×C22⋊C411yescharacteristic
440C2×C4×C53C2×C22⋊C411yescharacteristic
441C2×C4×C53C2×C22⋊C411yescharacteristic
442C2×C4×C53C2×C22⋊C411yescharacteristic
443C2×C4×C53C23×C411yescharacteristic
444C2×C4×C53C22×D411yescharacteristic
445C2×C4×C53C2×#4111yescharacteristic
446C2×C4×C53C2×#4111yescharacteristic
447C2×C4×C53H(5,𝔽2)11yescharacteristic
448C2×C4×C532−1+411yescharacteristic
449C2×Dic53—22no—
450C2×Dic53—22no—
451C2×Dic53—41no—
452C2×Dic53—41no—
453C2×Dic53—41no—
454C2×Dic53—48no—
455C2×Dic53—41no—
456C2×Dic53—41no—
457C2×Dic53—41no—
458C2×Dic53—41no—
459C2×Dic53—41no—
460C2×Dic53—41no—
461C2×Dic53—41no—
462#88322—22no—
463#88322—41no—
464#88322—41no—
465#88322—41no—
466#22506—531nomaximal, Sylow
467C22×C53—21no—
468C22×C53—21no—
469C22×C53—21no—
470C22×C53—21no—
471C22×C53—21no—
472C22×C53—21no—
473C22×C53—21no—
474C22×C53—21no—
475C22×C53—21no—
476C22×C53—21no—
477C22×C53—21no—
478C22×C53—21no—
479C22×C53—21no—
480C22×C53—42no—
481C22×C53—42no—
482C22×C53—41no—
483C22×C53—41no—
484C22×C53—41no—
485C22×C53—81no—
486C22×C53—81no—
487C22×C53#42112yes—
488C22×C53C22×C22⋊C411yescharacteristic
489C22×C53#54611yescharacteristic
490C22×C53#54711yescharacteristic
491C4×C53—21no—
492C4×C53—21no—
493C4×C53—21no—
494C4×C53—21no—
495C4×C53—21no—
496C4×C53—21no—
497C4×C53—21no—
498C4×C53—21no—
499C4×C53—41no—
500C4×C53—41no—
501C4×C53—41no—
502C4×C53—41no—
503C4×C53—41no—
504C4×C53—41no—
505C4×C53—41no—
506C4×C53C4×#4111yescharacteristic
507C4×C53#52011yescharacteristic
508C4×C53#54611yescharacteristic
509C4×C53#54711yescharacteristic
510Dic53—42no—
511Dic53—42no—
512Dic53—81no—
513Dic53—81no—
514#3475D5311yescharacteristic
515D4×M16—531no—
516#2290—531no—
517#1995—531no—
518#1986—531no—
519#1897—531no—
520#1896—531no—
521#1871—531no—
522#1871—531no—
523#1826—531no—
524#1826—531no—
525#1806—531no—
526#1759—531no—
527#1733—531no—
528C2×#339—531no—
529C2×C53—21no—
530C2×C53—21no—
531C2×C53—22no—
532C2×C53—41no—
533C2×C53—41no—
534C2×C53—41no—
535C2×C53—81no—
536C2×C53#233911yescharacteristic
537C2×C53C2×#42111yescharacteristic
538C2×C53#290111yescharacteristic
539C22×M16—531no—
540C22×M16—531no—
541#556Dic5311yescharacteristic, complemented
542#555Dic5311yescharacteristic, complemented
543#554Dic5311yescharacteristic, complemented
544#553Dic5311yescharacteristic, complemented
545#553Dic5311yescharacteristic, complemented
546#552—21no—
547#552Dic5311yescharacteristic, complemented
548#552Dic5311yescharacteristic, complemented
549#551—21no—
550#551—21no—
551#547Dic5311yescharacteristic, complemented
552#546—21no—
553#533C2×D5311yescharacteristic
554#529—21no—
555#529—21no—
556#529—21no—
557#525C2×D5311yescharacteristic
558#525C2×D5311yescharacteristic
559C4×#41—21no—
560C4×#41C2×D5311yescharacteristic
561C2×C4×D4C2×D5311yescharacteristic
562C2×#117—531no—
563C2×#117C2×D5311yescharacteristic
564C2×#117C2×D5311yescharacteristic
565C22×C42—531no—
566#436—1061no—
567#435—1061no—
568#435—1061no—
569C8×D4—1061no—
570#423—531no—
571C2×#104—531no—
572C2×#104—531no—
573C2×#104—531no—
574C2×#104—531no—
575#407—531no—
576#407—531no—
577C4×M16—531no—
578#388—1061no—
579#387—1061no—
580#386—1061no—
581#385—1061no—
582C4×C4⋊C4—531no—
583C4×C22⋊C4—531no—
584C4×C22⋊C4—531no—
585#376—531no—
586#339—531no—
587#339—531no—
588#339—531no—
589#339—531no—
590#339—531no—
591#339—531no—
592#339—531no—
593#339—531no—
594#339—531no—
595#339—531no—
596#339—531no—
597#339—531no—
598C53#2250611yescharacteristic, complemented, Sylow
599C2×#41—21no—
600C2×#41C22×D5311yescharacteristic
601C22×D4C22⋊D5311yescharacteristic
602C23×C4—1061no—
603C23×C4C22×D5311yescharacteristic
604C23×C4C22×D5311yescharacteristic
605C2×M16—531no—
606C2×M16—531no—
607C2×M16—531no—
608C2×M16—531no—
609C2×M16—1061no—
610C2×M16—1061no—
611C2×M16—1062no—
612C2×M16—1062no—
613C2×M16—2121no—
614C2×M16—2121no—
615C22×C8—1061no—
616C22×C8—1061no—
617C4⋊Q8C2×Dic5311yescharacteristic, complemented
618C4⋊Q8C2×Dic5311yescharacteristic, complemented
619#126—21no—
620#126—21no—
621#126—21no—
622#126—21no—
623#126—21no—
624#126—21no—
625#125—21no—
626#125—21no—
627#125—21no—
628#125C2×Dic5311yescharacteristic, complemented
629#125C2×Dic5311yescharacteristic, complemented
630#124—21no—
631#124—21no—
632#124—21no—
633#123—21no—
634#123—21no—
635#123—21no—
636#123—21no—
637#123—21no—
638#123—21no—
639#123—21no—
640#123—21no—
641C22⋊Q8—21no—
642C22⋊Q8—21no—
643C22⋊Q8—21no—
644C22⋊Q8—21no—
645C22⋊Q8—21no—
646C22⋊Q8C2×Dic5311yescharacteristic
647C22⋊Q8C2×Dic5311yescharacteristic
648C22⋊Q8C2×Dic5311yescharacteristic, complemented
649C22⋊Q8C2×Dic5311yescharacteristic, complemented
650#121—21no—
651#121—21no—
652#121—21no—
653#121C2×Dic5311yescharacteristic
654#121C2×Dic5311yescharacteristic
655#121C2×Dic5311yescharacteristic, complemented
656#121C2×Dic5311yescharacteristic, complemented
657#120—21no—
658#120—21no—
659C4×Q8—21no—
660C4×Q8—21no—
661C4×Q8—21no—
662C4×Q8C2×Dic5311yescharacteristic, complemented
663C4×Q8C2×Dic5311yescharacteristic, complemented
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669C4×D4—21no—
670C4×D4—21no—
671C4×D4—21no—
672C4×D4—21no—
673C4×D4C2×Dic5311yescharacteristic
674C4×D4C2×Dic5311yescharacteristic
675C4×D4C2×Dic5311yescharacteristic
676C4×D4C2×Dic5311yescharacteristic
677C4×D4C2×Dic5311yescharacteristic, complemented
678C4×D4C2×Dic5311yescharacteristic, complemented
679C4×D4C22⋊D5311yescharacteristic
680C4×D4C22⋊D5311yescharacteristic
681C4×D4C22⋊D5311yescharacteristic
682C4×D4C22⋊D5311yescharacteristic
683#117—21no—
684#117—21no—
685#117—21no—
686#117—21no—
687#117—21no—
688#117—21no—
689#117—21no—
690#117—21no—
691#117—1062no—
692#117—2121no—
693#117C2×Dic5311yescharacteristic
694#117C2×Dic5311yescharacteristic
695#117C2×Dic5311yescharacteristic, complemented
696#117C2×Dic5311yescharacteristic, complemented
697#117C22×D5311yescharacteristic
698#117C22×D5311yescharacteristic
699#117C22×D5311yescharacteristic
700C2×C4⋊C4—1061no—
701C2×C4⋊C4—1061no—
702C2×C4⋊C4C2×Dic5311yescharacteristic
703C2×C4⋊C4C2×Dic5311yescharacteristic
704C2×C4⋊C4C2×Dic5311yescharacteristic, complemented
705C2×C4⋊C4C2×Dic5311yescharacteristic, complemented
706C2×C4⋊C4C22⋊D5311yescharacteristic
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—1061no—
710C2×C22⋊C4—1061no—
711C2×C22⋊C4—1061no—
712C2×C22⋊C4C22⋊D5311yescharacteristic
713C2×C22⋊C4C22⋊D5311yescharacteristic
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—531no—
718C2×C42—531no—
719C2×C42—531no—
720C2×C42—531no—
721C2×C42—1062no—
722C2×C42—1061no—
723C2×C42—2121no—
724C2×C42C22×D5311yescharacteristic
725C4⋊C8—1061no—
726C4⋊C8—1061no—
727#104—1062no—
728#104—1062no—
729#104—2121no—
730#104—2121no—
731C22⋊C8—1061no—
732C22⋊C8—1061no—
733C22⋊C8—1061no—
734C22⋊C8—1061no—
735#97—1061no—
736C4×C8—1061no—
737#95—1061no—
738#95—1061no—
739#95—1061no—
740#95—1061no—
741#95—1061no—
742C24C2×C22⋊D5311yescharacteristic
743C24C2×C22⋊D5311yescharacteristic
744#41—21no—
745#41—21no—
746#41—21no—
747#41—21no—
748#41—44no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8C22×Dic5311yescharacteristic
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—42no—
758C2×D4C22⋊Dic5311yescharacteristic
759C2×D4C22⋊Dic5311yescharacteristic
760C2×D4C22⋊Dic5311yescharacteristic
761C2×D4C22⋊Dic5311yescharacteristic
762C2×D4C22×Dic5311yescharacteristic
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—1061no—
779C22×C4—1061no—
780C22×C4—1061no—
781C22×C4—1061no—
782C22×C4—2122no—
783C22×C4—2122no—
784C22×C4—2122no—
785C22×C4C22×Dic5311yescharacteristic
786C22×C4C22×Dic5311yescharacteristic
787C22×C4C22×Dic5311yescharacteristic
788C22×C4C22×Dic5311yescharacteristic
789C22×C4C2×C22⋊D5311yescharacteristic
790C22×C4C2×C22⋊D5311yescharacteristic
791C22×C4C2×C22⋊D5311yescharacteristic
792C22×C4C2×C22⋊D5311yescharacteristic
793C22×C4C2×C22⋊D5311yescharacteristic
794C22×C4C2×C22⋊D5311yescharacteristic
795C22×C4C2×C22⋊D5311yescharacteristic
796C22×C4C2×C22⋊D5311yescharacteristic
797C22×C4C23×D5311yescharacteristic
798M16—532no—
799M16—1061no—
800M16—1061no—
801M16—1061no—
802M16—1061no—
803M16—1061no—
804M16—1061no—
805M16—1061no—
806M16—2122no—
807M16—2122no—
808C2×C8—1061no—
809C2×C8—1061no—
810C2×C8—1061no—
811C2×C8—1061no—
812C2×C8—2122no—
813C2×C8—2122no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—2122no—
831C4⋊C4—2122no—
832C4⋊C4C22⋊Dic5311yescharacteristic
833C4⋊C4C22⋊Dic5311yescharacteristic
834C4⋊C4C22⋊Dic5311yescharacteristic
835C4⋊C4C22⋊Dic5311yescharacteristic
836C4⋊C4C22×Dic5311yescharacteristic
837C4⋊C4C22×Dic5311yescharacteristic
838C4⋊C4C22×Dic5311yescharacteristic
839C4⋊C4C22×Dic5311yescharacteristic
840C4⋊C4C22×Dic5311yescharacteristic
841C4⋊C4C22×Dic5311yescharacteristic
842C22⋊C4—21no—
843C22⋊C4—21no—
844C22⋊C4—21no—
845C22⋊C4—21no—
846C22⋊C4—21no—
847C22⋊C4—21no—
848C22⋊C4—21no—
849C22⋊C4—21no—
850C22⋊C4—21no—
851C22⋊C4—21no—
852C22⋊C4—21no—
853C22⋊C4—21no—
854C22⋊C4—21no—
855C22⋊C4—21no—
856C22⋊C4—21no—
857C22⋊C4—21no—
858C22⋊C4—21no—
859C22⋊C4—2122no—
860C22⋊C4—2122no—
861C22⋊C4—2122no—
862C22⋊C4C22⋊Dic5311yescharacteristic
863C22⋊C4C22⋊Dic5311yescharacteristic
864C22⋊C4C22⋊Dic5311yescharacteristic
865C22⋊C4C22⋊Dic5311yescharacteristic
866C22⋊C4C22⋊Dic5311yescharacteristic
867C22⋊C4C22⋊Dic5311yescharacteristic
868C22⋊C4C22⋊Dic5311yescharacteristic
869C22⋊C4C22⋊Dic5311yescharacteristic
870C42—21no—
871C42—21no—
872C42—21no—
873C42—21no—
874C42—21no—
875C42—21no—
876C42—21no—
877C42—21no—
878C42—21no—
879C42—532no—
880C42—1061no—
881C42—1061no—
882C42—1061no—
883C42—1061no—
884C42—1061no—
885C42—1061no—
886C42—1061no—
887C42—2122no—
888C42C22×Dic5311yescharacteristic
889C42C22×Dic5311yescharacteristic
890C42C2×C22⋊D5311yescharacteristic
891C42C2×C22⋊D5311yescharacteristic
892C23—21no—
893C23—22no—
894C23—21no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23C2×C22⋊Dic5311yescharacteristic
902C23C2×C22⋊Dic5311yescharacteristic
903C23C2×C22⋊Dic5311yescharacteristic
904C23C2×C22⋊Dic5311yescharacteristic
905C23C22×C22⋊D5311yescharacteristic
906Q8—21no—
907Q8—21no—
908Q8—42no—
909Q8—81no—
910D4—22no—
911D4—22no—
912D4—21no—
913D4—21no—
914D4—41no—
915D4—41no—
916D4—42no—
917D4—41no—
918D4—42no—
919D4—41no—
920D4—81no—
921D4—81no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—81no—
957C2×C4—81no—
958C2×C4—81no—
959C2×C4—1062no—
960C2×C4—1062no—
961C2×C4—2121no—
962C2×C4—2121no—
963C2×C4—2121no—
964C2×C4—2121no—
965C2×C4—2121no—
966C2×C4—2121no—
967C2×C4—2121no—
968C2×C4—2121no—
969C2×C4—2121no—
970C2×C4—2128no—
971C2×C4—2121no—
972C2×C4C2×C22⋊Dic5311yescharacteristic
973C2×C4C2×C22⋊Dic5311yescharacteristic
974C2×C4C2×C22⋊Dic5311yescharacteristic
975C2×C4C2×C22⋊Dic5311yescharacteristic
976C2×C4C2×C22⋊Dic5311yescharacteristic
977C2×C4C2×C22⋊Dic5311yescharacteristic
978C2×C4C2×C22⋊Dic5311yescharacteristic
979C2×C4C2×C22⋊Dic5311yescharacteristic
980C2×C4C23×Dic5311yescharacteristic
981C2×C4C22×C22⋊D5311yescharacteristic
982C2×C4#41×D5311yescharacteristic
983C2×C4#41×D5311yescharacteristic
984C2×C4#1313326311yescharacteristic
985C2×C4#1313326411yescharacteristic
986C8—1062no—
987C8—2121no—
988C8—2121no—
989C8—2121no—
990C22—21no—
991C22—21no—
992C22—21no—
993C22—21no—
994C22—21no—
995C22—21no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—42no—
1004C22—42no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—81no—
1009C22—81no—
1010C22#1681064012yes—
1011C22C22×C22⋊Dic5311yescharacteristic
1012C22#1681126111yescharacteristic
1013C22#1681127211yescharacteristic
1014C4—21no—
1015C4—21no—
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—21no—
1021C4—21no—
1022C4—41no—
1023C4—41no—
1024C4—41no—
1025C4—41no—
1026C4—41no—
1027C4—41no—
1028C4—41no—
1029C4—4241no—
1030C4—4241no—
1031C4—2122no—
1032C4—2122no—
1033C4#41×Dic5311yescharacteristic
1034C4#1681110611yescharacteristic
1035C4#1681126111yescharacteristic
1036C4#1681127211yescharacteristic
1037C2—21no—
1038C2—21no—
1039C2—22no—
1040C2—41no—
1041C2—41no—
1042C2—41no—
1043C2—81no—
1044C2#2027754511yescharacteristic
1045C2C2×#1681064011yescharacteristic
1046C2#2028326211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
Fitting, prime radicalC53×#3475C2
socleC22×C53C22×C22⋊C4
cosocleC22×C4×C53C24
hypercenter#3475D53
hypocenterC53#22506
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ #3475

Complements

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

NH ≅ G/Ntype
1. D4×#11719917C2semidirect
2. #20277160C2semidirect
3. #20275697C2semidirect
4. #20275660C2semidirect
5. #20275164C2semidirect
6. #20275159C2semidirect
7. #20275018C2semidirect
8. #20275018C2semidirect
9. #20274814C2semidirect
10. #20274814C2semidirect
11. #20274735C2semidirect
12. #20274525C2semidirect
13. #20274424C2semidirect
14. C2×#16810382C2semidirect
52. C53×#556C4semidirect
53. C53×#555C4semidirect
54. C53×#554C4semidirect
55. C53×#553C4semidirect
56. C53×#553C4semidirect
58. C53×#552C4semidirect
59. C53×#552C4semidirect
62. C53×#547C4semidirect
124. C4⋊Q8×C53C2×C4semidirect
125. C4⋊Q8×C53C2×C4semidirect
135. #125×C53C2×C4semidirect
136. #125×C53C2×C4semidirect
155. C22⋊Q8×C53C2×C4semidirect
156. C22⋊Q8×C53C2×C4semidirect
162. #121×C53C2×C4semidirect
163. #121×C53C2×C4semidirect
169. C4×Q8×C53C2×C4semidirect
170. C4×Q8×C53C2×C4semidirect
184. C4×D4×C53C2×C4semidirect
185. C4×D4×C53C2×C4semidirect
200. #117×C53C2×C4semidirect
201. #117×C53C2×C4semidirect
207. C2×C4⋊C4×C53C2×C4semidirect
208. C2×C4⋊C4×C53C2×C4semidirect
351. C4×Dic53#41semidirect
361. #11719917#41semidirect
541. #556Dic53semidirect
542. #555Dic53semidirect
543. #554Dic53semidirect
544. #553Dic53semidirect
545. #553Dic53semidirect
547. #552Dic53semidirect
548. #552Dic53semidirect
551. #547Dic53semidirect
598. C53#22506semidirect
617. C4⋊Q8C2×Dic53semidirect
618. C4⋊Q8C2×Dic53semidirect
628. #125C2×Dic53semidirect
629. #125C2×Dic53semidirect
648. C22⋊Q8C2×Dic53semidirect
649. C22⋊Q8C2×Dic53semidirect
655. #121C2×Dic53semidirect
656. #121C2×Dic53semidirect
662. C4×Q8C2×Dic53semidirect
663. C4×Q8C2×Dic53semidirect
677. C4×D4C2×Dic53semidirect
678. C4×D4C2×Dic53semidirect
695. #117C2×Dic53semidirect
696. #117C2×Dic53semidirect
704. C2×C4⋊C4C2×Dic53semidirect
705. C2×C4⋊C4C2×Dic53semidirect

Maximal subgroups

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

subgroupindex
D4×#117199172
#202771602
#202756972
#202756602
#202751642
#202751592
#202750182
#202748142
#202747352
#202745252
#202744242
C2×#168103822
C53×#34752
#2250653