Finite Group Databasebeta

← C2×#20287172 #28262641

Subgroups — C2×#20287172 #28262641

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
2C2×#16811313C211yesmaximal, characteristic
3#20287172C2116yesmaximal, direct product factor
4C2×#16811032C211yesmaximal, characteristic, complemented
5C2×#16810959C211yesmaximal, characteristic, complemented
6C2×#16810965C211yesmaximal, characteristic, complemented
7C2×#16810954C211yesmaximal, characteristic, complemented
8C2×#16810954C211yesmaximal, characteristic, complemented
9C2×#16810931C211yesmaximal, characteristic, complemented
10C2×#16810909C211yesmaximal, characteristic, complemented
11C2×#16810881C211yesmaximal, characteristic, complemented
12C2×#16810864C211yesmaximal, characteristic, complemented
13C2×#16810731C211yesmaximal, characteristic, complemented
14C2×#16810665C211yesmaximal, characteristic, complemented
15C22×#13133149C211yesmaximal, characteristic, complemented
16C2×C53×#435C211yesmaximal, characteristic
17C22×Dic212C2211yescharacteristic
18#16811330—24no—
19#16811330C2218yes—
20#16811313—24no—
21#16811313C2218yes—
22C2×#13133217C2211yescharacteristic
23C2×#13133210—21no—
24C2×#13133209C2211yescharacteristic
25C2×#13133208—21no—
26C2×#13133207—21no—
27C2×#13133198—21no—
28C2×#13133196C2211yescharacteristic
29C2×#13133196C2211yescharacteristic
30C2×#13133196C2211yescharacteristic
31C2×#13133196C2211yescharacteristic
32C2×#13133194—21no—
33C2×#13133194—21no—
34C2×C4×Dic106C2211yescharacteristic
35C2×C4×Dic106C2211yescharacteristic
36C2×D4×Dic53—21no—
37C2×#13133176C2211yescharacteristic
38C2×#13133173—21no—
39C22×C4⋊Dic53C2211yescharacteristic
40C22×C4⋊Dic53C2211yescharacteristic
41C22×C4⋊Dic53C2211yescharacteristic
42#16811032C2218yescomplemented
43#16810965C2218yescomplemented
44#16810959C2218yescomplemented
45#16810954C2218yescomplemented
46#16810954C2218yescomplemented
47#16810931C2218yescomplemented
48#16810909C2218yescomplemented
49#16810881C2218yescomplemented
50#16810864C2218yescomplemented
51#16810731C2218yescomplemented
52#16810665C2218yescomplemented
53C2×#13133151C2211yescharacteristic
54C2×#13133151C2211yescharacteristic
55C2×#13133151C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57C2×#13133149C2211yescharacteristic
58C2×#13133149C2211yescharacteristic
59C2×#13133149C2211yescharacteristic
60C2×#13133149C2211yescharacteristic
61C2×#13133149C2211yescharacteristic
62C2×#13133149C2218yescomplemented
63C2×#13133142C2211yescharacteristic
64C2×#13133142C2211yescharacteristic
65C2×#13133142C2211yescharacteristic
66C2×#13133142C2211yescharacteristic
67C2×#13133142C2211yescharacteristic
68C2×#13133142C2211yescharacteristic
69C22×M16×C53C2211yescharacteristic
70C23×C8×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C53×#435C2218yes—
73C2×C4⋊C8×C53C2211yescharacteristic
74C2×C22⋊C8×C53C2211yescharacteristic
75C2×C22⋊C8×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C22×Dic106C2311yescharacteristic
80C23×Dic53—21no—
81C23×Dic53—21no—
82C23×Dic53—21no—
83C2×Dic212—24no—
84C2×Dic212C2314yes—
85#13133217—22no—
86#13133217C2314yes—
87#13133210—28no—
88#13133209—22no—
89#13133209C2314yes—
90#13133208—28no—
91#13133207—28no—
92#13133198—28no—
93#13133196—22no—
94#13133196—22no—
95#13133196—22no—
96#13133196—22no—
97#13133196C2314yes—
98#13133196C2314yes—
99#13133196C2314yes—
100#13133196C2314yes—
101#13133194—28no—
102#13133194—28no—
103C4×Dic106—22no—
104C4×Dic106—22no—
105C4×Dic106C2314yes—
106C4×Dic106C2314yes—
107D4×Dic53—28no—
108#13133176—22no—
109#13133176C2314yes—
110#13133173—28no—
111C2×C4⋊Dic53—22no—
112C2×C4⋊Dic53—22no—
113C2×C4⋊Dic53—22no—
114C2×C4⋊Dic53—21no—
115C2×C4⋊Dic53—21no—
116C2×C4⋊Dic53—21no—
117C2×C4⋊Dic53—21no—
118C2×C4⋊Dic53C2314yes—
119C2×C4⋊Dic53C2311yescharacteristic
120C2×C4⋊Dic53C2314yes—
121C2×C4⋊Dic53C2314yes—
122C2×C4⋊Dic53C2311yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×C22⋊Dic53—21no—
136C2×C22⋊Dic53—21no—
137C2×C22⋊Dic53—21no—
138C2×C22⋊Dic53—21no—
139C2×C22⋊Dic53—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53—21no—
142C2×C4×Dic53—21no—
143#13133151C2314yes—
144#13133151C2314yes—
145#13133151C2314yes—
146#13133149C2314yes—
147#13133149C2314yes—
148#13133149C2314yes—
149#13133149C2314yes—
150#13133149C2314yes—
151#13133149C2314yes—
152#13133142C2314yes—
153#13133142C2314yes—
154#13133142C2314yes—
155#13133142C2314yes—
156#13133142C2314yes—
157#13133142C2314yes—
158C22×D4×C53D411yescharacteristic
159C23×C4×C53C2311yescharacteristic
160C23×C4×C53C2311yescharacteristic
161C2×M16×C53—24no—
162C2×M16×C53C2314yes—
163C22×C8×C53—24no—
164C22×C8×C53C2314yes—
165C22×C8×C53C2311yescharacteristic
166C22×C8×C53C2311yescharacteristic
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C4×D4×C53D414yes—
170C4×D4×C53C2314yes—
171C2×C4⋊C4×C53D411yescharacteristic
172C2×C22⋊C4×C53D411yescharacteristic
173C2×C22⋊C4×C53D411yescharacteristic
174C2×C42×C53C2311yescharacteristic
175C4⋊C8×C53C2314yes—
176C22⋊C8×C53C2314yes—
177C22⋊C8×C53C2314yes—
178#97×C53C2314yes—
179C24×C53C2×D411yescharacteristic
180C24×C53C2×D411yescharacteristic
181C2×D4×C53—24no—
182C2×D4×C53C2×D414yes—
183C22×C4×C53—22no—
184C22×C4×C53—22no—
185C22×C4×C53—22no—
186C22×C4×C53—22no—
187C22×C4×C53C2×D411yescharacteristic
188C22×C4×C53C2×D411yescharacteristic
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53C2×D411yescharacteristic
191C22×C4×C53C2×D412yes—
192C22×C4×C53C2×D412yes—
193C22×C4×C53C2412yes—
194C22×C4×C53C2412yes—
195C22×C4×C53C2411yescharacteristic
196C22×Dic53—21no—
197C22×Dic53—21no—
198C22×Dic53—21no—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—24no—
205C22×Dic53—24no—
206C22×Dic53—24no—
207C22×Dic53—44no—
208C22×Dic53—82no—
209C22×Dic53—82no—
210C2×Dic106—22no—
211C2×Dic106—22no—
212C2×Dic106—22no—
213C2×Dic106—22no—
214C2×Dic106—21no—
215C2×Dic106—21no—
216C2×Dic106—24no—
217C2×Dic106—82no—
218C2×Dic106C2412yes—
219C2×Dic106C2412yes—
220M16×C53—28no—
221C2×C8×C53—22no—
222C2×C8×C53—22no—
223C2×C8×C53—22no—
224C2×C8×C53—28no—
225C2×C8×C53#4114yes—
226C2×C8×C53C2412yes—
227C2×C8×C53C2412yes—
228C2×C8×C53C2412yes—
229C2×C8×C53C2412yes—
230C4⋊C4×C53C2×D414yes—
231C22⋊C4×C53C2×D414yes—
232C22⋊C4×C53C2×D414yes—
233C42×C53C2×D412yes—
234C42×C53C2412yes—
235C22⋊Dic53—24no—
236C22⋊Dic53—24no—
237C22⋊Dic53—24no—
238C22⋊Dic53—24no—
239C22⋊Dic53—24no—
240C4⋊Dic53—21no—
241C4⋊Dic53—21no—
242C4⋊Dic53—24no—
243C4⋊Dic53—24no—
244C4⋊Dic53—21no—
245C4⋊Dic53—21no—
246C4⋊Dic53—21no—
247C4⋊Dic53—24no—
248C4⋊Dic53—24no—
249C4⋊Dic53—21no—
250C4⋊Dic53C2412yes—
251C4⋊Dic53C2412yes—
252C4⋊Dic53C2412yes—
253C4⋊Dic53C2412yes—
254C4⋊Dic53C2412yes—
255C4⋊Dic53C2412yes—
256#11719919—24no—
257#11719919—24no—
258#11719919—24no—
259#11719919—24no—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263#11719919—24no—
264C4×Dic53—24no—
265C4×Dic53—24no—
266C4×Dic53—24no—
267Dic212—28no—
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
277D4×C53—28no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—24no—
283C2×C4×C53—24no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53C22×D412yes—
289C2×C4×C53C22×D412yes—
290C2×C4×C53C22×D412yes—
291C2×C4×C53C22×D412yes—
292C2×C4×C53C22×D411yescharacteristic
293C2×C4×C53C2×#4112yes—
294C2×C4×C532−1+412yes—
295C2×C4×C53C2511yescharacteristic
296C2×Dic53—22no—
297C2×Dic53—22no—
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—42no—
305C2×Dic53—42no—
306C2×Dic53—48no—
307C2×Dic53—42no—
308C2×Dic53—42no—
309C2×Dic53—42no—
310C2×Dic53—42no—
311C2×Dic53—42no—
312C2×Dic53—42no—
313C2×Dic53—84no—
314C2×Dic53—84no—
315Dic106—22no—
316Dic106—22no—
317Dic106—22no—
318Dic106—22no—
319Dic106—42no—
320Dic106—42no—
321Dic106—84no—
322C8×C53—22no—
323C8×C53—22no—
324C8×C53—22no—
325C8×C53C2×#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#54712yes—
344C4×C53C22×#4111yescharacteristic
345C4×C53C2×2−1+411yescharacteristic
346Dic53—42no—
347Dic53—42no—
348Dic53—42no—
349Dic53—42no—
350Dic53—42no—
351Dic53—42no—
352Dic53—42no—
353Dic53—42no—
354C2×#554—531no—
355C2×#552—531no—
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×#435D5311yescharacteristic
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×M16C2×D5311yescharacteristic
378C23×C8C2×D5311yescharacteristic
379#554—538no—
380#554—1064no—
381#552—538no—
382#552—1064no—
383C2×C4⋊Q8—531no—
384C2×#126—1061no—
385C2×#125—531no—
386C2×#125—1061no—
387C2×#125—1061no—
388C2×#123—1061no—
389C2×C22⋊Q8—531no—
390C2×C22⋊Q8—531no—
391C2×C22⋊Q8—531no—
392C2×C22⋊Q8—531no—
393C2×C22⋊Q8—1061no—
394C2×C22⋊Q8—1061no—
395C2×C4×Q8—531no—
396C2×C4×Q8—531no—
397C2×C4×D4—1061no—
398C2×C4×D4C2×D5311yescharacteristic
399C2×#117—531no—
400C2×#117—1061no—
401C22×C4⋊C4—531no—
402C22×C4⋊C4—531no—
403C22×C4⋊C4—531no—
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#435C2×D5318yes—
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⋊C8C2×D5311yescharacteristic
427C2×#103—531no—
428C2×#103—531no—
429C2×#103—531no—
430C2×#103—531no—
431C2×#103—531no—
432C2×#103—531no—
433C2×C22⋊C8C2×D5311yescharacteristic
434C2×C22⋊C8C2×D5311yescharacteristic
435C2×#97C2×D5311yescharacteristic
436C53C2×#334411yescharacteristic, complemented, Sylow
437C22×Q8—531no—
438C22×Q8—531no—
439C22×Q8—1061no—
440C22×D4D21211yescharacteristic
441C23×C4—1061no—
442C23×C4—1061no—
443C23×C4—1061no—
444C23×C4C22×D5311yescharacteristic
445C23×C4C22×D5311yescharacteristic
446C2×Q16—534no—
447C2×Q16—1064no—
448C2×M16—24no—
449C2×M16C22×D5314yes—
450C22×C8—24no—
451C22×C8C22×D5311yescharacteristic
452C22×C8C22×D5314yes—
453C22×C8C22×D5311yescharacteristic
454C22×C8C22×D5311yescharacteristic
455C22×C8C22×D5311yescharacteristic
456C4⋊Q8—534no—
457C4⋊Q8—1062no—
458#126—1068no—
459#125—534no—
460#125—1068no—
461#125—1068no—
462#125—1062no—
463#123—1068no—
464C22⋊Q8—534no—
465C22⋊Q8—534no—
466C22⋊Q8—534no—
467C22⋊Q8—534no—
468C22⋊Q8—1062no—
469C22⋊Q8—1062no—
470C22⋊Q8—1062no—
471C22⋊Q8—1062no—
472C22⋊Q8—1068no—
473C22⋊Q8—1068no—
474C4×Q8—534no—
475C4×Q8—534no—
476C4×Q8—1062no—
477C4×Q8—1062no—
478C4×D4—1068no—
479C4×D4D21214yes—
480C4×D4C22×D5314yes—
481#117—534no—
482#117—1062no—
483#117—1068no—
484C2×C4⋊C4—531no—
485C2×C4⋊C4—531no—
486C2×C4⋊C4—531no—
487C2×C4⋊C4—531no—
488C2×C4⋊C4—531no—
489C2×C4⋊C4—534no—
490C2×C4⋊C4—534no—
491C2×C4⋊C4—534no—
492C2×C4⋊C4—531no—
493C2×C4⋊C4—1061no—
494C2×C4⋊C4—1061no—
495C2×C4⋊C4—1061no—
496C2×C4⋊C4—1062no—
497C2×C4⋊C4—1062no—
498C2×C4⋊C4—1062no—
499C2×C4⋊C4—1061no—
500C2×C4⋊C4—1061no—
501C2×C4⋊C4—1061no—
502C2×C4⋊C4—1061no—
503C2×C4⋊C4—1061no—
504C2×C4⋊C4—1061no—
505C2×C4⋊C4—1061no—
506C2×C4⋊C4—1061no—
507C2×C4⋊C4—1061no—
508C2×C4⋊C4D21211yescharacteristic
509C2×C22⋊C4—1061no—
510C2×C22⋊C4—1061no—
511C2×C22⋊C4—1061no—
512C2×C22⋊C4—1061no—
513C2×C22⋊C4—1061no—
514C2×C22⋊C4D21211yescharacteristic
515C2×C22⋊C4D21211yescharacteristic
516C2×C42—1061no—
517C2×C42—1061no—
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⋊C8C22×D5314yes—
530#103—534no—
531#103—534no—
532#103—534no—
533#103—534no—
534#103—534no—
535#103—534no—
536C22⋊C8C22×D5314yes—
537C22⋊C8C22×D5314yes—
538#97C22×D5314yes—
539C24C2×D21211yescharacteristic
540C24C2×D21211yescharacteristic
541C2×Q8—532no—
542C2×Q8—532no—
543C2×Q8—1064no—
544C2×Q8—1061no—
545C2×Q8—1061no—
546C2×Q8—1062no—
547C2×Q8—1062no—
548C2×Q8—1062no—
549C2×Q8—1062no—
550C2×Q8—4242no—
551C2×D4—24no—
552C2×D4C2×D21214yes—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—1064no—
558C22×C4—1064no—
559C22×C4—1064no—
560C22×C4—1061no—
561C22×C4—1061no—
562C22×C4—1061no—
563C22×C4—1061no—
564C22×C4—1061no—
565C22×C4—1061no—
566C22×C4—1061no—
567C22×C4—1061no—
568C22×C4—4242no—
569C22×C4—4242no—
570C22×C4—2124no—
571C22×C4C2×D21212yes—
572C22×C4C2×D21212yes—
573C22×C4C2×D21211yescharacteristic
574C22×C4C2×D21211yescharacteristic
575C22×C4C2×D21211yescharacteristic
576C22×C4C2×D21211yescharacteristic
577C22×C4C23×D5312yes—
578C22×C4C23×D5312yes—
579C22×C4C23×D5311yescharacteristic
580Q16—1068no—
581M16—28no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—28no—
586C2×C8#1171994714yes—
587C2×C8C23×D5312yes—
588C2×C8C23×D5312yes—
589C2×C8C23×D5312yes—
590C2×C8C23×D5312yes—
591C4⋊C4—532no—
592C4⋊C4—532no—
593C4⋊C4—532no—
594C4⋊C4—532no—
595C4⋊C4—532no—
596C4⋊C4—532no—
597C4⋊C4—1061no—
598C4⋊C4—1061no—
599C4⋊C4—1064no—
600C4⋊C4—1064no—
601C4⋊C4—1061no—
602C4⋊C4—1061no—
603C4⋊C4—1061no—
604C4⋊C4—1064no—
605C4⋊C4—1061no—
606C4⋊C4—1064no—
607C4⋊C4—1064no—
608C4⋊C4—1064no—
609C4⋊C4—1064no—
610C4⋊C4—1064no—
611C4⋊C4—1064no—
612C4⋊C4—1064no—
613C4⋊C4—1064no—
614C4⋊C4—1064no—
615C4⋊C4C2×D21214yes—
616C22⋊C4—1064no—
617C22⋊C4—1064no—
618C22⋊C4—1064no—
619C22⋊C4—1064no—
620C22⋊C4—1064no—
621C22⋊C4C2×D21214yes—
622C22⋊C4C2×D21214yes—
623C42—1064no—
624C42—1064no—
625C42—1064no—
626C42C2×D21212yes—
627C42C23×D5312yes—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23#1313325014yes—
634C23C22×D21212yes—
635C23C22×D21212yes—
636C23C22×D21211yescharacteristic
637Q8—1062no—
638Q8—1062no—
639Q8—1062no—
640Q8—1062no—
641Q8—4244no—
642Q8—2122no—
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—1062no—
656C2×C4—1062no—
657C2×C4—1062no—
658C2×C4—1062no—
659C2×C4—1062no—
660C2×C4—1062no—
661C2×C4—1062no—
662C2×C4—1062no—
663C2×C4—4244no—
664C2×C4—4244no—
665C2×C4—2122no—
666C2×C4—2122no—
667C2×C4—2128no—
668C2×C4—2122no—
669C2×C4—2122no—
670C2×C4—2122no—
671C2×C4—2122no—
672C2×C4—2122no—
673C2×C4—2122no—
674C2×C4C22×D21212yes—
675C2×C4C22×D21212yes—
676C2×C4C22×D21212yes—
677C2×C4C22×D21212yes—
678C2×C4C22×D21211yescharacteristic
679C2×C4C2×#1171994712yes—
680C2×C4#1313326412yes—
681C2×C4C24×D5311yescharacteristic
682C8—22no—
683C8—22no—
684C8—22no—
685C8C2×#1171994714yes—
686C22—22no—
687C22—28no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—44no—
693C22#1681127712yes—
694C22C2×#1313325014yes—
695C22C2×#1313325012yes—
696C22#1681143512yes—
697C22C23×D21211yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—2122no—
703C4—2122no—
704C4—2122no—
705C4—2122no—
706C4—2122no—
707C4—2122no—
708C4—2122no—
709C4—2122no—
710C4#1681127712yes—
711C4C22×#1171994711yescharacteristic
712C4C2×#1313326411yescharacteristic
713C2—24no—
714C2—42no—
715C2#2028717214yesdirect product factor
716C2C2×#1681127711yescharacteristic
717C2C22×#1313325011yescharacteristic
718C2C2×#1681143511yescharacteristic
subgroupG/H
centerC23C22×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#435C2
socleC23×C53C22×D4
prime radicalC22×D4×C53D4
hypercenterC2×#435D53
hypocenterC53C2×#3344
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. #20287172C2direct (N × H)
4. C2×#16811032C2semidirect
5. C2×#16810959C2semidirect
6. C2×#16810965C2semidirect
7. C2×#16810954C2semidirect
8. C2×#16810954C2semidirect
9. C2×#16810931C2semidirect
10. C2×#16810909C2semidirect
11. C2×#16810881C2semidirect
12. C2×#16810864C2semidirect
13. C2×#16810731C2semidirect
14. C2×#16810665C2semidirect
15. C22×#13133149C2semidirect
42. #16811032C22semidirect
43. #16810965C22semidirect
44. #16810959C22semidirect
45. #16810954C22semidirect
46. #16810954C22semidirect
47. #16810931C22semidirect
48. #16810909C22semidirect
49. #16810881C22semidirect
50. #16810864C22semidirect
51. #16810731C22semidirect
52. #16810665C22semidirect
62. C2×#13133149C22semidirect
372. C2×C53#3344semidirect
436. C53C2×#3344semidirect
715. C2#20287172direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113302
C2×#168113132
#202871722
C2×#168110322
C2×#168109592
C2×#168109652
C2×#168109542
C2×#168109312
C2×#168109092
C2×#168108812
C2×#168108642
C2×#168107312
C2×#168106652
C22×#131331492
C2×C53×#4352
C2×#334453