Finite Group Databasebeta

← C2×#20287170 #28262639

Subgroups — C2×#20287170 #28262639

Order 13568.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811330C211yesmaximal, characteristic
2#20287170C2116yesmaximal, direct product factor
3C2×#16811033C211yesmaximal, characteristic, complemented
4C2×#16810956C211yesmaximal, characteristic, complemented
5C2×#16810964C211yesmaximal, characteristic, complemented
6C2×#16810953C211yesmaximal, characteristic, complemented
7C2×#16810951C211yesmaximal, characteristic, complemented
8C2×#16810927C211yesmaximal, characteristic, complemented
9C2×#16810908C211yesmaximal, characteristic, complemented
10C2×#16810879C211yesmaximal, characteristic, complemented
11C2×#16810862C211yesmaximal, characteristic, complemented
12C2×#16810728C211yesmaximal, characteristic, complemented
13C2×#16810695C211yesmaximal, characteristic
14C2×#16810666C211yesmaximal, characteristic, complemented
15C22×#13133148C211yesmaximal, characteristic, complemented
16C2×C53×#552C211yesmaximal, characteristic
17C22×#11719925C2211yescharacteristic
18C22×#11719917C2211yescharacteristic
19C23×#88322C2211yescharacteristic
20#16811330—24no—
21#16811330C2218yes—
22C2×#13133217C2211yescharacteristic
23C2×#13133208—21no—
24C2×#13133196C2211yescharacteristic
25C2×#13133196C2211yescharacteristic
26C2×#13133194—21no—
27C2×#13133194—21no—
28C2×C4×Dic106C2211yescharacteristic
29C2×D4×Dic53—21no—
30C22×C4⋊Dic53C2211yescharacteristic
31C22×C4⋊Dic53C2211yescharacteristic
32#16811033C2218yescomplemented
33#16810964C2218yescomplemented
34#16810956C2218yescomplemented
35#16810953C2218yescomplemented
36#16810951C2218yescomplemented
37#16810927C2218yescomplemented
38#16810908C2218yescomplemented
39#16810879C2218yescomplemented
40#16810862C2218yescomplemented
41#16810728C2218yescomplemented
42#16810695C2218yes—
43#16810666C2218yescomplemented
44C2×#13133150C2211yescharacteristic
45C2×#13133150C2211yescharacteristic
46C2×#13133150C2211yescharacteristic
47C2×#13133148C2211yescharacteristic
48C2×#13133148C2211yescharacteristic
49C2×#13133148C2211yescharacteristic
50C2×#13133148C2211yescharacteristic
51C2×#13133148C2211yescharacteristic
52C2×#13133148C2211yescharacteristic
53C2×#13133148C2218yescomplemented
54C2×C4⋊#88322C2211yescharacteristic
55C2×#13133141C2211yescharacteristic
56C2×#13133141C2211yescharacteristic
57C2×#13133141C2211yescharacteristic
58C2×#13133140C2211yescharacteristic
59C2×#13133140C2211yescharacteristic
60C2×#13133140C2211yescharacteristic
61C2×C22⋊#88322C2211yescharacteristic
62C2×C22⋊#88322C2211yescharacteristic
63C2×#13133128C2211yescharacteristic
64C53×#552—24no—
65C53×#552C2218yes—
66C2×#126×C53—21no—
67C2×#125×C53—21no—
68C2×#125×C53C2211yescharacteristic
69C2×#123×C53—21no—
70C2×C22⋊Q8×C53C2211yescharacteristic
71C2×C22⋊Q8×C53C2211yescharacteristic
72C2×C4×Q8×C53C2211yescharacteristic
73C2×C4×D4×C53C2211yescharacteristic
74C2×#117×C53—21no—
75C2×#117×C53C2211yescharacteristic
76C22×C4⋊C4×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C23×Dic53—21no—
80C23×Dic53—21no—
81C2×#11719925—24no—
82C2×#11719925C2314yes—
83C2×#11719917—24no—
84C2×#11719917C2314yes—
85C22×#88322—24no—
86C22×#88322C2311yescharacteristic
87C22×#88322C2311yescharacteristic
88C22×#88322C2311yescharacteristic
89C22×#88322C2314yes—
90C22×#88322C2311yescharacteristic
91#13133217—22no—
92#13133217C2314yes—
93#13133208—28no—
94#13133196—22no—
95#13133196—22no—
96#13133196C2314yes—
97#13133196C2314yes—
98#13133194—28no—
99#13133194—28no—
100C4×Dic106—22no—
101C4×Dic106C2314yes—
102D4×Dic53—28no—
103C2×C4⋊Dic53—22no—
104C2×C4⋊Dic53—22no—
105C2×C4⋊Dic53—21no—
106C2×C4⋊Dic53—21no—
107C2×C4⋊Dic53—21no—
108C2×C4⋊Dic53C2311yescharacteristic
109C2×C4⋊Dic53C2314yes—
110C2×C4⋊Dic53C2314yes—
111C2×C4⋊Dic53C2311yescharacteristic
112C2×C4⋊Dic53C2311yescharacteristic
113C2×#11719919—21no—
114C2×#11719919—21no—
115C2×#11719919—21no—
116C2×C22⋊Dic53—21no—
117C2×C22⋊Dic53—21no—
118C2×C4×Dic53—21no—
119#13133150C2314yes—
120#13133150C2314yes—
121#13133150C2314yes—
122#13133148C2314yes—
123#13133148C2314yes—
124#13133148C2314yes—
125#13133148C2314yes—
126#13133148C2314yes—
127#13133148C2314yes—
128C4⋊#88322C2314yes—
129#13133141C2314yes—
130#13133141C2314yes—
131#13133141C2314yes—
132#13133140C2314yes—
133#13133140C2314yes—
134#13133140C2314yes—
135C22⋊#88322C2314yes—
136C22⋊#88322C2314yes—
137#13133128C2314yes—
138C22×Q8×C53C2311yescharacteristic
139C22×D4×C53D411yescharacteristic
140C23×C4×C53—21no—
141C23×C4×C53C2311yescharacteristic
142C23×C4×C53C2311yescharacteristic
143#126×C53—28no—
144#125×C53—28no—
145#125×C53—22no—
146#125×C53C2314yes—
147#123×C53—28no—
148C22⋊Q8×C53—22no—
149C22⋊Q8×C53—22no—
150C22⋊Q8×C53C2314yes—
151C22⋊Q8×C53C2314yes—
152C4×Q8×C53—22no—
153C4×Q8×C53C2314yes—
154C4×D4×C53D414yes—
155C4×D4×C53C2314yes—
156#117×C53—28no—
157#117×C53—22no—
158#117×C53C2314yes—
159C2×C4⋊C4×C53—21no—
160C2×C4⋊C4×C53—22no—
161C2×C4⋊C4×C53—21no—
162C2×C4⋊C4×C53—21no—
163C2×C4⋊C4×C53—21no—
164C2×C4⋊C4×C53—21no—
165C2×C4⋊C4×C53—21no—
166C2×C4⋊C4×C53D411yescharacteristic
167C2×C4⋊C4×C53C2311yescharacteristic
168C2×C4⋊C4×C53C2311yescharacteristic
169C2×C4⋊C4×C53C2314yes—
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C22⋊C4×C53—21no—
172C2×C22⋊C4×C53—21no—
173C2×C22⋊C4×C53—21no—
174C2×C22⋊C4×C53D411yescharacteristic
175C2×C22⋊C4×C53D411yescharacteristic
176C2×C42×C53—21no—
177C2×C42×C53—21no—
178C2×C42×C53C2311yescharacteristic
179C24×C53C2×D411yescharacteristic
180C24×C53C2×D411yescharacteristic
181C2×Q8×C53—21no—
182C2×Q8×C53—22no—
183C2×Q8×C53—22no—
184C2×Q8×C53C2412yes—
185C2×D4×C53—24no—
186C2×D4×C53C2×D414yes—
187C22×C4×C53—22no—
188C22×C4×C53—22no—
189C22×C4×C53—22no—
190C22×C4×C53—22no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—24no—
196C22×C4×C53—44no—
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2×D412yes—
202C22×C4×C53C2×D412yes—
203C22×C4×C53C2412yes—
204C22×C4×C53C2412yes—
205C22×C4×C53C2411yescharacteristic
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—24no—
211C22×Dic53—24no—
212C22×Dic53—82no—
213C22×Dic53—82no—
214C2×Dic106—22no—
215C2×Dic106—22no—
216C2×Dic106—21no—
217C2×Dic106—24no—
218C2×Dic106—82no—
219C2×Dic106C2412yes—
220C4⋊C4×C53—21no—
221C4⋊C4×C53—21no—
222C4⋊C4×C53—24no—
223C4⋊C4×C53—24no—
224C4⋊C4×C53—24no—
225C4⋊C4×C53—24no—
226C4⋊C4×C53—24no—
227C4⋊C4×C53—24no—
228C4⋊C4×C53—21no—
229C4⋊C4×C53C2×D414yes—
230C4⋊C4×C53C2412yes—
231C4⋊C4×C53C2412yes—
232C4⋊C4×C53C2412yes—
233C22⋊C4×C53—24no—
234C22⋊C4×C53—24no—
235C22⋊C4×C53—24no—
236C22⋊C4×C53C2×D414yes—
237C22⋊C4×C53C2×D414yes—
238C42×C53—24no—
239C42×C53—24no—
240C42×C53C2×D412yes—
241C42×C53C2412yes—
242C22⋊Dic53—24no—
243C22⋊Dic53—24no—
244#11719925—28no—
245C4⋊Dic53—21no—
246C4⋊Dic53—24no—
247C4⋊Dic53—24no—
248C4⋊Dic53—21no—
249C4⋊Dic53—21no—
250C4⋊Dic53—24no—
251C4⋊Dic53C2412yes—
252C4⋊Dic53C2412yes—
253C4⋊Dic53C2412yes—
254#11719919—24no—
255#11719919—24no—
256#11719919—24no—
257C4×Dic53—24no—
258#11719917—28no—
259C2×#88322—22no—
260C2×#88322—22no—
261C2×#88322—22no—
262C2×#88322—28no—
263C2×#88322#4114yes—
264C2×#88322C2412yes—
265C2×#88322C2412yes—
266C2×#88322C2412yes—
267C2×#88322C2412yes—
268C23×C53—22no—
269C23×C53—22no—
270C23×C53—22no—
271C23×C53—22no—
272C23×C53—22no—
273C23×C53#13714yes—
274C23×C53C22×D412yes—
275C23×C53C22×D412yes—
276C23×C53C22×D411yescharacteristic
277Q8×C53—22no—
278Q8×C53—22no—
279Q8×C53—42no—
280D4×C53—28no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—24no—
286C2×C4×C53—24no—
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—42no—
296C2×C4×C53—48no—
297C2×C4×C53—42no—
298C2×C4×C53—42no—
299C2×C4×C53—42no—
300C2×C4×C53C22×D412yes—
301C2×C4×C53C22×D412yes—
302C2×C4×C53C22×D412yes—
303C2×C4×C53C22×D412yes—
304C2×C4×C53C22×D411yescharacteristic
305C2×C4×C53C2×#4112yes—
306C2×C4×C532−1+412yes—
307C2×C4×C53C2511yescharacteristic
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—42no—
313C2×Dic53—42no—
314C2×Dic53—42no—
315C2×Dic53—42no—
316C2×Dic53—84no—
317C2×Dic53—84no—
318Dic106—22no—
319Dic106—22no—
320Dic106—42no—
321Dic106—84no—
322#88322—22no—
323#88322—22no—
324#88322—22no—
325#88322C2×#4114yes—
326C2×#3344—531nomaximal, Sylow
327C22×C53—28no—
328C22×C53—22no—
329C22×C53—22no—
330C22×C53—22no—
331C22×C53—22no—
332C22×C53—22no—
333C22×C53—44no—
334C22×C53#54712yes—
335C22×C53C2×#13714yes—
336C22×C53C2×#13712yes—
337C22×C53#57712yes—
338C22×C53C23×D411yescharacteristic
339C4×C53—22no—
340C4×C53—22no—
341C4×C53—22no—
342C4×C53—22no—
343C4×C53—42no—
344C4×C53—42no—
345C4×C53—42no—
346C4×C53—42no—
347C4×C53#54712yes—
348C4×C53C22×#4111yescharacteristic
349C4×C53C2×2−1+411yescharacteristic
350Dic53—42no—
351Dic53—42no—
352Dic53—42no—
353Dic53—42no—
354C2×#554—531no—
355C2×#552D5311yescharacteristic
356#3344—5316no—
357C2×#501—531no—
358C2×#484—531no—
359C2×#485—531no—
360C2×#483—531no—
361C2×#483—531no—
362C2×#479—531no—
363C2×#475—531no—
364C2×#470—531no—
365C2×#467—531no—
366C2×#441—531no—
367C2×#435—531no—
368C2×#428—531no—
369C22×#106—531no—
370C2×C53—24no—
371C2×C53—42no—
372C2×C53#334414yescomplemented
373C2×C53C2×#54711yescharacteristic
374C2×C53C22×#13711yescharacteristic
375C2×C53C2×#57711yescharacteristic
376C22×Q16—531no—
377C22×M16—531no—
378C23×C8—531no—
379#554—538no—
380#554—1064no—
381#552—24no—
382#552C2×D5318yes—
383C2×C4⋊Q8—531no—
384C2×#126—21no—
385C2×#125—21no—
386C2×#125—1061no—
387C2×#125C2×D5311yescharacteristic
388C2×#123—21no—
389C2×C22⋊Q8—531no—
390C2×C22⋊Q8—531no—
391C2×C22⋊Q8—1061no—
392C2×C22⋊Q8—1061no—
393C2×C22⋊Q8C2×D5311yescharacteristic
394C2×C22⋊Q8C2×D5311yescharacteristic
395C2×C4×Q8—531no—
396C2×C4×Q8C2×D5311yescharacteristic
397C2×C4×D4—1061no—
398C2×C4×D4C2×D5311yescharacteristic
399C2×#117—21no—
400C2×#117C2×D5311yescharacteristic
401C22×C4⋊C4—531no—
402C22×C4⋊C4—531no—
403C22×C4⋊C4C2×D5311yescharacteristic
404#501—538no—
405#485—538no—
406#484—538no—
407#483—538no—
408#483—538no—
409#479—538no—
410#475—538no—
411#470—538no—
412#467—538no—
413#441—538no—
414#435—538no—
415#428—538no—
416C2×#107—531no—
417C2×#107—531no—
418C2×#107—531no—
419C2×#106—531no—
420C2×#106—531no—
421C2×#106—531no—
422C2×#106—531no—
423C2×#106—538no—
424C2×#106—531no—
425C2×#106—531no—
426C2×C4⋊C8—531no—
427C2×#103—531no—
428C2×#103—531no—
429C2×#103—531no—
430C2×#103—531no—
431C2×#103—531no—
432C2×#103—531no—
433C2×C22⋊C8—531no—
434C2×C22⋊C8—531no—
435C2×#97—531no—
436C53C2×#334411yescharacteristic, complemented, Sylow
437C22×Q8—531no—
438C22×Q8—1061no—
439C22×Q8C22×D5311yescharacteristic
440C22×D4C22⋊D5311yescharacteristic
441C23×C4—21no—
442C23×C4—1061no—
443C23×C4—1061no—
444C23×C4C22×D5311yescharacteristic
445C23×C4C22×D5311yescharacteristic
446C2×Q16—534no—
447C2×Q16—1064no—
448C2×M16—534no—
449C2×M16—1064no—
450C22×C8—531no—
451C22×C8—531no—
452C22×C8—534no—
453C22×C8—531no—
454C22×C8—531no—
455C22×C8—1064no—
456C4⋊Q8—534no—
457C4⋊Q8—1062no—
458#126—28no—
459#125—28no—
460#125—22no—
461#125—1068no—
462#125C22×D5314yes—
463#123—28no—
464C22⋊Q8—22no—
465C22⋊Q8—22no—
466C22⋊Q8—534no—
467C22⋊Q8—534no—
468C22⋊Q8—1062no—
469C22⋊Q8—1062no—
470C22⋊Q8—1068no—
471C22⋊Q8—1068no—
472C22⋊Q8C22×D5314yes—
473C22⋊Q8C22×D5314yes—
474C4×Q8—22no—
475C4×Q8—534no—
476C4×Q8—1062no—
477C4×Q8C22×D5314yes—
478C4×D4—1068no—
479C4×D4C22⋊D5314yes—
480C4×D4C22×D5314yes—
481#117—22no—
482#117—28no—
483#117C22×D5314yes—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—531no—
492C2×C4⋊C4—531no—
493C2×C4⋊C4—531no—
494C2×C4⋊C4—534no—
495C2×C4⋊C4—534no—
496C2×C4⋊C4—1061no—
497C2×C4⋊C4—1061no—
498C2×C4⋊C4—1062no—
499C2×C4⋊C4—1062no—
500C2×C4⋊C4—1061no—
501C2×C4⋊C4—1061no—
502C2×C4⋊C4—1061no—
503C2×C4⋊C4—1061no—
504C2×C4⋊C4C22⋊D5311yescharacteristic
505C2×C4⋊C4C22×D5311yescharacteristic
506C2×C4⋊C4C22×D5311yescharacteristic
507C2×C4⋊C4C22×D5314yes—
508C2×C4⋊C4C22×D5311yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—1061no—
513C2×C22⋊C4—1061no—
514C2×C22⋊C4C22⋊D5311yescharacteristic
515C2×C22⋊C4C22⋊D5311yescharacteristic
516C2×C42—21no—
517C2×C42—21no—
518C2×C42—1061no—
519C2×C42C22×D5311yescharacteristic
520#107—534no—
521#107—534no—
522#107—534no—
523#106—534no—
524#106—534no—
525#106—534no—
526#106—534no—
527#106—534no—
528#106—534no—
529C4⋊C8—534no—
530#103—534no—
531#103—534no—
532#103—534no—
533#103—534no—
534#103—534no—
535#103—534no—
536C22⋊C8—534no—
537C22⋊C8—534no—
538#97—534no—
539C24C2×C22⋊D5311yescharacteristic
540C24C2×C22⋊D5311yescharacteristic
541C2×Q8—21no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—532no—
545C2×Q8—1064no—
546C2×Q8—1061no—
547C2×Q8—1062no—
548C2×Q8—1062no—
549C2×Q8—4242no—
550C2×Q8C23×D5312yes—
551C2×D4—24no—
552C2×D4C2×C22⋊D5314yes—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—44no—
563C22×C4—1064no—
564C22×C4—1064no—
565C22×C4—1061no—
566C22×C4—1061no—
567C22×C4—1061no—
568C22×C4—1061no—
569C22×C4—4242no—
570C22×C4—4242no—
571C22×C4C2×C22⋊D5312yes—
572C22×C4C2×C22⋊D5312yes—
573C22×C4C2×C22⋊D5311yescharacteristic
574C22×C4C2×C22⋊D5311yescharacteristic
575C22×C4C2×C22⋊D5311yescharacteristic
576C22×C4C2×C22⋊D5311yescharacteristic
577C22×C4C23×D5312yes—
578C22×C4C23×D5312yes—
579C22×C4C23×D5311yescharacteristic
580Q16—1068no—
581M16—1068no—
582C2×C8—534no—
583C2×C8—532no—
584C2×C8—532no—
585C2×C8—532no—
586C2×C8—532no—
587C2×C8—1068no—
588C2×C8—1062no—
589C2×C8—1062no—
590C2×C8—1062no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—21no—
600C4⋊C4—532no—
601C4⋊C4—532no—
602C4⋊C4—532no—
603C4⋊C4—1061no—
604C4⋊C4—1064no—
605C4⋊C4—1064no—
606C4⋊C4—1061no—
607C4⋊C4—1061no—
608C4⋊C4—1064no—
609C4⋊C4—1064no—
610C4⋊C4—1064no—
611C4⋊C4—1064no—
612C4⋊C4C2×C22⋊D5314yes—
613C4⋊C4C23×D5312yes—
614C4⋊C4C23×D5312yes—
615C4⋊C4C23×D5312yes—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—24no—
619C22⋊C4—1064no—
620C22⋊C4—1064no—
621C22⋊C4C2×C22⋊D5314yes—
622C22⋊C4C2×C22⋊D5314yes—
623C42—24no—
624C42—24no—
625C42—1064no—
626C42C2×C22⋊D5312yes—
627C42C23×D5312yes—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23#1313324714yes—
634C23C22×C22⋊D5312yes—
635C23C22×C22⋊D5312yes—
636C23C22×C22⋊D5311yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—42no—
640Q8—1062no—
641Q8—1062no—
642Q8—4244no—
643Q8—2122no—
644D4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—48no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—1062no—
665C2×C4—1062no—
666C2×C4—1062no—
667C2×C4—1062no—
668C2×C4—4244no—
669C2×C4—4244no—
670C2×C4—2122no—
671C2×C4—2122no—
672C2×C4—2122no—
673C2×C4—2122no—
674C2×C4C22×C22⋊D5312yes—
675C2×C4C22×C22⋊D5312yes—
676C2×C4C22×C22⋊D5312yes—
677C2×C4C22×C22⋊D5312yes—
678C2×C4C22×C22⋊D5311yescharacteristic
679C2×C4#41×D5312yes—
680C2×C4#1313326412yes—
681C2×C4C24×D5311yescharacteristic
682C8—534no—
683C8—1062no—
684C8—1062no—
685C8—1062no—
686C22—22no—
687C22—22no—
688C22—28no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—44no—
693C22#1681127212yes—
694C22C2×#1313324714yes—
695C22C2×#1313324712yes—
696C22#1681143112yes—
697C22C23×C22⋊D5311yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—2122no—
707C4—2122no—
708C4—2122no—
709C4—2122no—
710C4#1681127212yes—
711C4C2×#41×D5311yescharacteristic
712C4C2×#1313326411yescharacteristic
713C2—24no—
714C2—42no—
715C2#2028717014yesdirect product factor
716C2C2×#1681127211yescharacteristic
717C2C22×#1313324711yescharacteristic
718C2C2×#1681143111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#552C2
socleC23×C53C22×D4
prime radicalC22×D4×C53D4
hypercenterC2×#552D53
hypocenterC53C2×#3344
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #20287170C2direct (N × H)
3. C2×#16811033C2semidirect
4. C2×#16810956C2semidirect
5. C2×#16810964C2semidirect
6. C2×#16810953C2semidirect
7. C2×#16810951C2semidirect
8. C2×#16810927C2semidirect
9. C2×#16810908C2semidirect
10. C2×#16810879C2semidirect
11. C2×#16810862C2semidirect
12. C2×#16810728C2semidirect
14. C2×#16810666C2semidirect
15. C22×#13133148C2semidirect
32. #16811033C22semidirect
33. #16810964C22semidirect
34. #16810956C22semidirect
35. #16810953C22semidirect
36. #16810951C22semidirect
37. #16810927C22semidirect
38. #16810908C22semidirect
39. #16810879C22semidirect
40. #16810862C22semidirect
41. #16810728C22semidirect
43. #16810666C22semidirect
53. C2×#13133148C22semidirect
372. C2×C53#3344semidirect
436. C53C2×#3344semidirect
715. C2#20287170direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113302
#202871702
C2×#168110332
C2×#168109562
C2×#168109642
C2×#168109532
C2×#168109512
C2×#168109272
C2×#168109082
C2×#168108792
C2×#168108622
C2×#168107282
C2×#168106952
C2×#168106662
C22×#131331482
C2×C53×#5522
C2×#334453