Finite Group Databasebeta

← #27351371

Subgroups — #27351371

Order 13568.

1438 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810587C211yesmaximal, characteristic, complemented
2#20277098C211yesmaximal, characteristic, complemented
3#20273258C214yesmaximal, complemented
4#20273248C212yesmaximal, complemented
5#20273244C212yesmaximal, complemented
6#20273206C214yesmaximal, complemented
7C2×C53×#525C211yesmaximal, characteristic
8C22×#11719917—21no—
9C2×#13133176—21no—
10#16810587—21no—
11#16810587—21no—
12#16810587C2212yes—
13#16810587C2212yescomplemented
14C2×C22⋊#88322—21no—
15C2×C22⋊#88322C2212yescomplemented
16#16810486C2212yes—
17#16810483—21no—
18#16810483C2212yescomplemented
19#16810479—21no—
20C4×C22⋊Dic53—21no—
21C4×C22⋊Dic53C2212yescomplemented
22#16810360C2218yescomplemented
23#16810357C2218yescomplemented
24C22×#41×C53C411yescharacteristic, complemented
25C24×C4×C53C2211yescharacteristic
26C53×#525—21no—
27C53×#525—21no—
28C53×#525—21no—
29C53×#525—21no—
30C53×#525C412yescomplemented
31C53×#525C412yescomplemented
32C53×#525C2212yes—
33C53×#525C2212yes—
34C2×#123×C53—21no—
35C2×C22⋊Q8×C53C411yescharacteristic, complemented
36C2×C22⋊Q8×C53C2211yescharacteristic
37C2×#121×C53C411yescharacteristic, complemented
38C2×#121×C53C2211yescharacteristic
39C2×#120×C53—21no—
40C2×C4×D4×C53—21no—
41C2×C4×D4×C53—21no—
42C2×#117×C53C411yescharacteristic, complemented
43C2×#11719917—22no—
44C2×#11719917—22no—
45C2×#11719917—44no—
46C22×#88322—22no—
47#13133176—44no—
48C2×C4⋊Dic53—22no—
49C2×C22⋊Dic53—22no—
50C2×C22⋊Dic53—22no—
51C2×C22⋊Dic53—22no—
52C2×C4×Dic53—22no—
53C22⋊#88322—22no—
54C22⋊#88322—22no—
55C22⋊#88322—22no—
56C22⋊#88322C2314yes—
57#13133124—22no—
58#13133124C2314yes—
59C25×C53D411yescharacteristic
60C2×#41×C53—21no—
61C2×#41×C53—21no—
62C2×#41×C53—44no—
63C2×#41×C53C2×C412yes—
64C2×#41×C53C2×C412yes—
65C22×Q8×C53C2×C411yescharacteristic
66C22×D4×C53—21no—
67C22×D4×C53—21no—
68C22×D4×C53—21no—
69C22×D4×C53C2×C411yescharacteristic
70C23×C4×C53—21no—
71C23×C4×C53—44no—
72C23×C4×C53C2×C411yescharacteristic
73C23×C4×C53C2×C411yescharacteristic
74C23×C4×C53C2×C411yescharacteristic
75C23×C4×C53C2×C411yescharacteristic
76C23×C4×C53D411yescharacteristic
77C23×C4×C53D411yescharacteristic
78C23×C4×C53D411yescharacteristic
79C23×C4×C53D411yescharacteristic
80C23×C4×C53D411yescharacteristic
81C23×C4×C53D411yescharacteristic
82C23×C4×C53D411yescharacteristic
83C23×C4×C53C2311yescharacteristic
84C23×C4×C53C2311yescharacteristic
85C23×C4×C53C2311yescharacteristic
86#123×C53—22no—
87#123×C53—22no—
88#123×C53—22no—
89#123×C53—22no—
90C22⋊Q8×C53—21no—
91C22⋊Q8×C53—21no—
92C22⋊Q8×C53—21no—
93C22⋊Q8×C53—21no—
94C22⋊Q8×C53C2×C412yes—
95C22⋊Q8×C53C2×C412yes—
96C22⋊Q8×C53C2×C412yes—
97C22⋊Q8×C53C2312yes—
98#121×C53—21no—
99#121×C53—21no—
100#121×C53—21no—
101#121×C53—21no—
102#121×C53C2×C412yes—
103#121×C53C2×C412yes—
104#121×C53C2×C412yes—
105#121×C53C2312yes—
106#120×C53—22no—
107#120×C53—22no—
108#120×C53—22no—
109#120×C53—22no—
110C4×D4×C53—22no—
111C4×D4×C53—22no—
112C4×D4×C53—22no—
113C4×D4×C53—22no—
114C4×D4×C53—22no—
115C4×D4×C53—22no—
116C4×D4×C53—22no—
117C4×D4×C53—22no—
118#117×C53—21no—
119#117×C53—21no—
120#117×C53C2×C412yes—
121#117×C53C2×C412yes—
122C2×C4⋊C4×C53—21no—
123C2×C4⋊C4×C53—21no—
124C2×C4⋊C4×C53C2×C411yescharacteristic
125C2×C4⋊C4×C53C2×C411yescharacteristic
126C2×C22⋊C4×C53—21no—
127C2×C22⋊C4×C53—21no—
128C2×C22⋊C4×C53—21no—
129C2×C22⋊C4×C53—21no—
130C2×C22⋊C4×C53—21no—
131C2×C42×C53—21no—
132C24×C53—21no—
133C24×C53—42no—
134C24×C53—42no—
135C24×C53—42no—
136C24×C53C22⋊C411yescharacteristic
137C24×C53C22⋊C411yescharacteristic
138C24×C53C22⋊C411yescharacteristic
139C24×C53C22⋊C411yescharacteristic
140C24×C53C2×D411yescharacteristic
141C24×C53C2×D411yescharacteristic
142C24×C53C2×D411yescharacteristic
143#41×C53—44no—
144#41×C53—44no—
145#41×C53—44no—
146#41×C53—44no—
147C2×Q8×C53—21no—
148C2×Q8×C53—42no—
149C2×Q8×C53C22×C412yes—
150C2×D4×C53—22no—
151C2×D4×C53—22no—
152C2×D4×C53—22no—
153C2×D4×C53—22no—
154C2×D4×C53—22no—
155C2×D4×C53—22no—
156C2×D4×C53—21no—
157C2×D4×C53—42no—
158C2×D4×C53—44no—
159C2×D4×C53—44no—
160C2×D4×C53—44no—
161C2×D4×C53C22×C412yes—
162C22×C4×C53—24no—
163C22×C4×C53—24no—
164C22×C4×C53—24no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—22no—
169C22×C4×C53—22no—
170C22×C4×C53—42no—
171C22×C4×C53—42no—
172C22×C4×C53—42no—
173C22×C4×C53—42no—
174C22×C4×C53—42no—
175C22×C4×C53—42no—
176C22×C4×C53—42no—
177C22×C4×C53—42no—
178C22×C4×C53—42no—
179C22×C4×C53—42no—
180C22×C4×C53—42no—
181C22×C4×C53—44no—
182C22×C4×C53C22⋊C411yescharacteristic
183C22×C4×C53C22⋊C411yescharacteristic
184C22×C4×C53C22⋊C411yescharacteristic
185C22×C4×C53C22⋊C411yescharacteristic
186C22×C4×C53C22⋊C411yescharacteristic
187C22×C4×C53C22⋊C411yescharacteristic
188C22×C4×C53C22⋊C411yescharacteristic
189C22×C4×C53C22⋊C411yescharacteristic
190C22×C4×C53C22⋊C411yescharacteristic
191C22×C4×C53C22⋊C411yescharacteristic
192C22×C4×C53C22⋊C411yescharacteristic
193C22×C4×C53C22⋊C411yescharacteristic
194C22×C4×C53C22×C411yescharacteristic
195C22×C4×C53C22×C411yescharacteristic
196C22×C4×C53C22×C411yescharacteristic
197C22×C4×C53C22×C411yescharacteristic
198C22×C4×C53C22×C411yescharacteristic
199C22×C4×C53C22×C411yescharacteristic
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2×D411yescharacteristic
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2×D411yescharacteristic
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2×D411yescharacteristic
209C22×C4×C53C2411yescharacteristic
210C22×Dic53—24no—
211C4⋊C4×C53—22no—
212C4⋊C4×C53—22no—
213C4⋊C4×C53—22no—
214C4⋊C4×C53—21no—
215C4⋊C4×C53—21no—
216C4⋊C4×C53—22no—
217C4⋊C4×C53C22×C412yes—
218C4⋊C4×C53C22×C412yes—
219C22⋊C4×C53—22no—
220C22⋊C4×C53—22no—
221C22⋊C4×C53—22no—
222C22⋊C4×C53—22no—
223C22⋊C4×C53—22no—
224C22⋊C4×C53—22no—
225C22⋊C4×C53—22no—
226C22⋊C4×C53—22no—
227C22⋊C4×C53—22no—
228C22⋊C4×C53—22no—
229C42×C53—22no—
230C42×C53—22no—
231C22⋊Dic53—44no—
232C22⋊Dic53—44no—
233C22⋊Dic53—44no—
234C4⋊Dic53—44no—
235C4×Dic53—44no—
236#11719917—44no—
237#11719917—44no—
238C2×#88322—24no—
239C2×#88322—44no—
240C23×C53—22no—
241C23×C53—22no—
242C23×C53—22no—
243C23×C53—22no—
244C23×C53—22no—
245C23×C53—22no—
246C23×C53—22no—
247C23×C53—22no—
248C23×C53—22no—
249C23×C53—22no—
250C23×C53—41no—
251C23×C53—41no—
252C23×C53—41no—
253C23×C53—41no—
254C23×C53—41no—
255C23×C53—41no—
256C23×C53—41no—
257C23×C53—41no—
258C23×C53—41no—
259C23×C53—41no—
260C23×C53—41no—
261C23×C53—41no—
262C23×C53—42no—
263C23×C53—42no—
264C23×C53—416no—
265C23×C53—42no—
266C23×C53C2×C22⋊C411yescharacteristic
267C23×C53C2×C22⋊C411yescharacteristic
268C23×C53C2×C22⋊C411yescharacteristic
269C23×C53C2×C22⋊C411yescharacteristic
270C23×C53C2×C22⋊C411yescharacteristic
271C23×C53C2×C22⋊C411yescharacteristic
272C23×C53C22×D411yescharacteristic
273Q8×C53—42no—
274Q8×C53—42no—
275D4×C53—42no—
276D4×C53—42no—
277D4×C53—44no—
278D4×C53—44no—
279D4×C53—44no—
280D4×C53—44no—
281D4×C53—44no—
282D4×C53—44no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—41no—
302C2×C4×C53—41no—
303C2×C4×C53—41no—
304C2×C4×C53—41no—
305C2×C4×C53—41no—
306C2×C4×C53—41no—
307C2×C4×C53—41no—
308C2×C4×C53—41no—
309C2×C4×C53—41no—
310C2×C4×C53—41no—
311C2×C4×C53—41no—
312C2×C4×C53—41no—
313C2×C4×C53—42no—
314C2×C4×C53—42no—
315C2×C4×C53—42no—
316C2×C4×C53—44no—
317C2×C4×C53—44no—
318C2×C4×C53#9914yes—
319C2×C4×C53C2×C22⋊C411yescharacteristic
320C2×C4×C53C2×C22⋊C411yescharacteristic
321C2×C4×C53C2×C22⋊C411yescharacteristic
322C2×C4×C53C2×C22⋊C411yescharacteristic
323C2×C4×C53C2×C22⋊C411yescharacteristic
324C2×C4×C53C2×C22⋊C411yescharacteristic
325C2×C4×C53C23×C411yescharacteristic
326C2×C4×C53C22×D411yescharacteristic
327C2×Dic53—44no—
328C2×Dic53—44no—
329C2×Dic53—44no—
330#88322—44no—
331#17559—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—21no—
341C22×C53—21no—
342C22×C53—21no—
343C22×C53—21no—
344C22×C53—21no—
345C22×C53—21no—
346C22×C53—21no—
347C22×C53—21no—
348C22×C53—21no—
349C22×C53—21no—
350C22×C53—44no—
351C22×C53—44no—
352C22×C53—44no—
353C22×C53—44no—
354C22×C53—44no—
355C22×C53—44no—
356C22×C53—44no—
357C22×C53—42no—
358C22×C53—42no—
359C22×C53—42no—
360C22×C53—84no—
361C22×C53C2×#9912yes—
362C22×C53#42112yes—
363C22×C53C22×C22⋊C411yescharacteristic
364C22×C53#57512yes—
365C4×C53—21no—
366C4×C53—21no—
367C4×C53—21no—
368C4×C53—21no—
369C4×C53—21no—
370C4×C53—21no—
371C4×C53—42no—
372C4×C53—42no—
373C4×C53—42no—
374C4×C53C2×#9912yes—
375C4×C53C2×#9912yes—
376Dic53—84no—
377C2×#525D5311yescharacteristic
378C2×#407—531no—
379#2280—531no—
380#1513—534no—
381#1511—532no—
382#1510—532no—
383#1501—534no—
384C2×C53—22no—
385C2×C53—22no—
386C2×C53—22no—
387C2×C53—41no—
388C2×C53—41no—
389C2×C53—41no—
390C2×C53—41no—
391C2×C53—82no—
392C2×C53C22×#9911yescharacteristic
393C2×C53#289611yescharacteristic
394C2×C53C2×#42111yescharacteristic
395C22×#41Dic5311yescharacteristic, complemented
396C24×C4C2×D5311yescharacteristic
397C22×M16—1061no—
398#525—21no—
399#525—21no—
400#525—21no—
401#525—21no—
402#525Dic5312yescomplemented
403#525Dic5312yescomplemented
404#525C2×D5312yes—
405#525C2×D5312yes—
406C2×#123—21no—
407C2×C22⋊Q8Dic5311yescharacteristic, complemented
408C2×C22⋊Q8C2×D5311yescharacteristic
409C2×#121Dic5311yescharacteristic, complemented
410C2×#121C2×D5311yescharacteristic
411C2×#120—21no—
412C2×C4×D4—21no—
413C2×C4×D4—21no—
414C2×#117—1061no—
415C2×#117Dic5311yescharacteristic, complemented
416#407—532no—
417#407—532no—
418#407—1061no—
419#407—1061no—
420C2×C22⋊C8—532no—
421C2×C22⋊C8—1061no—
422#381—532no—
423#380—532no—
424#380—1061no—
425#379—1061no—
426C4×C22⋊C4—532no—
427C4×C22⋊C4—1061no—
428#328—538no—
429#327—538no—
430C53#1755911yescharacteristic, complemented, Sylow
431C25C22⋊D5311yescharacteristic
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—44no—
435C2×#41C2×Dic5312yes—
436C2×#41C2×Dic5312yes—
437C22×Q8C2×Dic5311yescharacteristic
438C22×D4—21no—
439C22×D4—21no—
440C22×D4—21no—
441C22×D4C2×Dic5311yescharacteristic
442C23×C4—21no—
443C23×C4—44no—
444C23×C4C2×Dic5311yescharacteristic
445C23×C4C2×Dic5311yescharacteristic
446C23×C4C2×Dic5311yescharacteristic
447C23×C4C2×Dic5311yescharacteristic
448C23×C4C22⋊D5311yescharacteristic
449C23×C4C22⋊D5311yescharacteristic
450C23×C4C22⋊D5311yescharacteristic
451C23×C4C22⋊D5311yescharacteristic
452C23×C4C22⋊D5311yescharacteristic
453C23×C4C22⋊D5311yescharacteristic
454C23×C4C22⋊D5311yescharacteristic
455C23×C4C22×D5311yescharacteristic
456C23×C4C22×D5311yescharacteristic
457C23×C4C22×D5311yescharacteristic
458C2×M16—1062no—
459C2×M16—1062no—
460C2×M16—2124no—
461C22×C8—1062no—
462#123—22no—
463#123—22no—
464#123—22no—
465#123—22no—
466C22⋊Q8—21no—
467C22⋊Q8—21no—
468C22⋊Q8—21no—
469C22⋊Q8—21no—
470C22⋊Q8C2×Dic5312yes—
471C22⋊Q8C2×Dic5312yes—
472C22⋊Q8C2×Dic5312yes—
473C22⋊Q8C22×D5312yes—
474#121—21no—
475#121—21no—
476#121—21no—
477#121—21no—
478#121C2×Dic5312yes—
479#121C2×Dic5312yes—
480#121C2×Dic5312yes—
481#121C22×D5312yes—
482#120—22no—
483#120—22no—
484#120—22no—
485#120—22no—
486C4×D4—22no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4—22no—
492C4×D4—22no—
493C4×D4—22no—
494#117—21no—
495#117—21no—
496#117—2124no—
497#117C2×Dic5312yes—
498#117C2×Dic5312yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—1062no—
502C2×C4⋊C4C2×Dic5311yescharacteristic
503C2×C4⋊C4C2×Dic5311yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—1062no—
510C2×C22⋊C4—1062no—
511C2×C22⋊C4—1062no—
512C2×C42—21no—
513C2×C42—1062no—
514C22⋊C8—534no—
515C22⋊C8—1062no—
516C22⋊C8—1062no—
517C22⋊C8—1062no—
518#95—534no—
519#95—1062no—
520C24—21no—
521C24—42no—
522C24—42no—
523C24—42no—
524C24C22⋊Dic5311yescharacteristic
525C24C22⋊Dic5311yescharacteristic
526C24C22⋊Dic5311yescharacteristic
527C24C22⋊Dic5311yescharacteristic
528C24C2×C22⋊D5311yescharacteristic
529C24C2×C22⋊D5311yescharacteristic
530C24C2×C22⋊D5311yescharacteristic
531#41—44no—
532#41—44no—
533#41—44no—
534#41—44no—
535C2×Q8—21no—
536C2×Q8—42no—
537C2×Q8C22×Dic5312yes—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—21no—
545C2×D4—42no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4C22×Dic5312yes—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—44no—
570C22×C4—1064no—
571C22×C4C22⋊Dic5311yescharacteristic
572C22×C4C22⋊Dic5311yescharacteristic
573C22×C4C22⋊Dic5311yescharacteristic
574C22×C4C22⋊Dic5311yescharacteristic
575C22×C4C22⋊Dic5311yescharacteristic
576C22×C4C22⋊Dic5311yescharacteristic
577C22×C4C22⋊Dic5311yescharacteristic
578C22×C4C22⋊Dic5311yescharacteristic
579C22×C4C22⋊Dic5311yescharacteristic
580C22×C4C22⋊Dic5311yescharacteristic
581C22×C4C22⋊Dic5311yescharacteristic
582C22×C4C22⋊Dic5311yescharacteristic
583C22×C4C22×Dic5311yescharacteristic
584C22×C4C22×Dic5311yescharacteristic
585C22×C4C22×Dic5311yescharacteristic
586C22×C4C22×Dic5311yescharacteristic
587C22×C4C22×Dic5311yescharacteristic
588C22×C4C22×Dic5311yescharacteristic
589C22×C4C2×C22⋊D5311yescharacteristic
590C22×C4C2×C22⋊D5311yescharacteristic
591C22×C4C2×C22⋊D5311yescharacteristic
592C22×C4C2×C22⋊D5311yescharacteristic
593C22×C4C2×C22⋊D5311yescharacteristic
594C22×C4C2×C22⋊D5311yescharacteristic
595C22×C4C2×C22⋊D5311yescharacteristic
596C22×C4C2×C22⋊D5311yescharacteristic
597C22×C4C2×C22⋊D5311yescharacteristic
598C22×C4C23×D5311yescharacteristic
599M16—2124no—
600M16—2124no—
601C2×C8—1064no—
602C2×C8—2124no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—22no—
609C4⋊C4—2124no—
610C4⋊C4C22×Dic5312yes—
611C4⋊C4C22×Dic5312yes—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—2124no—
623C22⋊C4—2124no—
624C22⋊C4—2124no—
625C42—22no—
626C42—22no—
627C42—2124no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—42no—
651C23—42no—
652C23—416no—
653C23—42no—
654C23C2×C22⋊Dic5311yescharacteristic
655C23C2×C22⋊Dic5311yescharacteristic
656C23C2×C22⋊Dic5311yescharacteristic
657C23C2×C22⋊Dic5311yescharacteristic
658C23C2×C22⋊Dic5311yescharacteristic
659C23C2×C22⋊Dic5311yescharacteristic
660C23C22×C22⋊D5311yescharacteristic
661Q8—42no—
662Q8—42no—
663D4—42no—
664D4—42no—
665D4—44no—
666D4—44no—
667D4—44no—
668D4—44no—
669D4—44no—
670D4—44no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—2124no—
707C2×C4—2124no—
708C2×C4—2124no—
709C2×C4#1313313214yes—
710C2×C4C2×C22⋊Dic5311yescharacteristic
711C2×C4C2×C22⋊Dic5311yescharacteristic
712C2×C4C2×C22⋊Dic5311yescharacteristic
713C2×C4C2×C22⋊Dic5311yescharacteristic
714C2×C4C2×C22⋊Dic5311yescharacteristic
715C2×C4C2×C22⋊Dic5311yescharacteristic
716C2×C4C23×Dic5311yescharacteristic
717C2×C4C22×C22⋊D5311yescharacteristic
718C8—2124no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—84no—
748C22C2×#1313313212yes—
749C22#1681064012yes—
750C22C22×C22⋊Dic5311yescharacteristic
751C22#1681142112yes—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—4244no—
762C4C2×#1313313212yes—
763C4C2×#1313313212yes—
764C2—22no—
765C2—22no—
766C2—22no—
767C2—41no—
768C2—41no—
769C2—41no—
770C2—41no—
771C2—82no—
772C2C22×#1313313211yescharacteristic
773C2#2028323411yescharacteristic
774C2C2×#1681064011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊Dic53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
Fitting, prime radicalC2×C53×#525C2
socleC22×C53C22×C22⋊C4
cosocleC22×C4×C53C24
hypercenterC2×#525D53
hypocenterC53#17559
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#16810587C2semidirect
2. #20277098C2semidirect
3. #20273258C2semidirect
4. #20273248C2semidirect
5. #20273244C2semidirect
6. #20273206C2semidirect
13. #16810587C22semidirect
15. C2×C22⋊#88322C22semidirect
18. #16810483C22semidirect
21. C4×C22⋊Dic53C22semidirect
22. #16810360C22semidirect
23. #16810357C22semidirect
24. C22×#41×C53C4semidirect
30. C53×#525C4semidirect
31. C53×#525C4semidirect
35. C2×C22⋊Q8×C53C4semidirect
37. C2×#121×C53C4semidirect
42. C2×#117×C53C4semidirect
395. C22×#41Dic53semidirect
402. #525Dic53semidirect
403. #525Dic53semidirect
407. C2×C22⋊Q8Dic53semidirect
409. C2×#121Dic53semidirect
415. C2×#117Dic53semidirect
430. C53#17559semidirect

Maximal subgroups

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

subgroupindex
C2×#168105872
#202770982
#202732582
#202732482
#202732442
#202732062
C2×C53×#5252
#1755953