Finite Group Databasebeta

← #27351450

Subgroups — #27351450

Order 13568.

1470 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
1C22×C22⋊#88322C211yesmaximal, characteristic, complemented
2#20277098C211yesmaximal, characteristic, complemented
3#20273287C212yesmaximal, complemented
4#20273283C212yesmaximal, complemented
5#20273271C214yesmaximal, complemented
6#20273206C214yesmaximal, complemented
7C2×C53×#525C211yesmaximal, characteristic
8C23×#88322—21no—
9C2×#13133176—21no—
10C2×C22⋊#88322—21no—
11C2×C22⋊#88322—21no—
12C2×C22⋊#88322—21no—
13C2×C22⋊#88322C2212yes—
14C2×C22⋊#88322C2212yescomplemented
15C2×C22⋊#88322C2212yescomplemented
16#16810486C2212yescomplemented
17#16810483—21no—
18#16810483C2212yes—
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
43C22×#88322—22no—
44C22×#88322—22no—
45C22×#88322—22no—
46C22×#88322—44no—
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—24no—
133C24×C53—21no—
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—
236C2×#88322—24no—
237C2×#88322—44no—
238C2×#88322—44no—
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—22no—
251C23×C53—22no—
252C23×C53—22no—
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—416no—
262C23×C53—42no—
263C23×C53—42no—
264C23×C53—42no—
265C23×C53C2×C22⋊C411yescharacteristic
266C23×C53C2×C22⋊C411yescharacteristic
267C23×C53C2×C22⋊C411yescharacteristic
268C23×C53C2×C22⋊C411yescharacteristic
269C23×C53C2×C22⋊C411yescharacteristic
270C23×C53C2×C22⋊C411yescharacteristic
271C23×C53#13514yes—
272C23×C53C22×D411yescharacteristic
273Q8×C53—42no—
274Q8×C53—42no—
275D4×C53—42no—
276D4×C53—44no—
277D4×C53—44no—
278D4×C53—44no—
279D4×C53—44no—
280D4×C53—44no—
281D4×C53—44no—
282D4×C53—42no—
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—44no—
314C2×C4×C53—42no—
315C2×C4×C53—42no—
316C2×C4×C53—42no—
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#17572—531nomaximal, Sylow
332C22×C53—28no—
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—44no—
350C22×C53—44no—
351C22×C53—44no—
352C22×C53—44no—
353C22×C53—44no—
354C22×C53—44no—
355C22×C53—42no—
356C22×C53—42no—
357C22×C53—42no—
358C22×C53—84no—
359C22×C53C2×#9912yes—
360C22×C53#41612yes—
361C22×C53#41612yes—
362C22×C53#42112yes—
363C22×C53C22×C22⋊C411yescharacteristic
364C22×C53C2×#13512yes—
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
378C22×C22⋊C8—531no—
379#2280—531no—
380#1520—532no—
381#1519—532no—
382#1516—534no—
383#1501—534no—
384C2×C53—22no—
385C2×C53—22no—
386C2×C53—22no—
387C2×C53—22no—
388C2×C53—22no—
389C2×C53—41no—
390C2×C53—41no—
391C2×C53—82no—
392C2×C53C22×#9911yescharacteristic
393C2×C53C2×#41611yescharacteristic
394C2×C53C2×#42111yescharacteristic
395C22×#41Dic5311yescharacteristic, complemented
396C24×C4C2×D5311yescharacteristic
397C23×C8—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
416C2×C22⋊C8—532no—
417C2×C22⋊C8—532no—
418C2×C22⋊C8—532no—
419C2×C22⋊C8—1061no—
420C2×C22⋊C8—1061no—
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#1757211yescharacteristic, 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
458C22×C8—1062no—
459C22×C8—1062no—
460C22×C8—1062no—
461C22×C8—2124no—
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—24no—
521C24—21no—
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
599C2×C8—1064no—
600C2×C8—2124no—
601C2×C8—2124no—
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—22no—
639C23—22no—
640C23—22no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—416no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23C2×C22⋊Dic5311yescharacteristic
654C23C2×C22⋊Dic5311yescharacteristic
655C23C2×C22⋊Dic5311yescharacteristic
656C23C2×C22⋊Dic5311yescharacteristic
657C23C2×C22⋊Dic5311yescharacteristic
658C23C2×C22⋊Dic5311yescharacteristic
659C23#1313323714yes—
660C23C22×C22⋊D5311yescharacteristic
661Q8—42no—
662Q8—42no—
663D4—42no—
664D4—44no—
665D4—44no—
666D4—44no—
667D4—44no—
668D4—44no—
669D4—44no—
670D4—42no—
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—44no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
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—28no—
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—44no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—84no—
746C22C2×#1313313212yes—
747C22#1681061912yes—
748C22#1681061912yes—
749C22#1681064012yes—
750C22C22×C22⋊Dic5311yescharacteristic
751C22C2×#1313323712yes—
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—22no—
768C2—22no—
769C2—41no—
770C2—41no—
771C2—82no—
772C2C22×#1313313211yescharacteristic
773C2C2×#1681061911yescharacteristic
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#17572
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. C22×C22⋊#88322C2semidirect
2. #20277098C2semidirect
3. #20273287C2semidirect
4. #20273283C2semidirect
5. #20273271C2semidirect
6. #20273206C2semidirect
14. C2×C22⋊#88322C22semidirect
15. C2×C22⋊#88322C22semidirect
16. #16810486C22semidirect
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#17572semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊#883222
#202770982
#202732872
#202732832
#202732712
#202732062
C2×C53×#5252
#1757253