Finite Group Databasebeta

← C2×#20287094 #28262539

Subgroups — C2×#20287094 #28262539

Order 13568.

1930 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811319C211yesmaximal, characteristic
2#20287094C2116yesmaximal, direct product factor
3C2×#16811022C211yesmaximal, characteristic, complemented
4C2×#16810956C211yesmaximal, characteristic, complemented
5C2×#16810961C211yesmaximal, characteristic, complemented
6C2×#16810947C211yesmaximal, characteristic, complemented
7C2×#16810936C211yesmaximal, characteristic, complemented
8C2×#16810930C211yesmaximal, characteristic, complemented
9C2×#16810920C211yesmaximal, characteristic, complemented
10C2×#16810854C211yesmaximal, characteristic, complemented
11C2×#16810854C211yesmaximal, characteristic, complemented
12C2×C4×#11719924C211yesmaximal, characteristic, complemented
13C2×D4×#88322C211yesmaximal, characteristic, complemented
14C2×#16810659C211yesmaximal, characteristic, complemented
15C22×#13133148C211yesmaximal, characteristic, complemented
16C2×C53×#552C211yesmaximal, characteristic, complemented
17C22×#11719924C2211yescharacteristic
18C23×#88322C2211yescharacteristic
19C23×#88322C2211yescharacteristic
20#16811319—24no—
21#16811319C2218yes—
22C2×#13133212—21no—
23C2×#13133209C2211yescharacteristic
24C2×#13133199—21no—
25C2×#13133191C2211yescharacteristic
26C2×#13133191C2211yescharacteristic
27C2×#13133189—21no—
28C2×C4×D212C2211yescharacteristic
29C2×#13133177—21no—
30C2×#13133176C2211yescharacteristic
31C22×C4⋊Dic53C2211yescharacteristic
32#16811022C2218yescomplemented
33#16810961C2218yescomplemented
34#16810956C2218yescomplemented
35#16810947C2218yescomplemented
36#16810936C2218yescomplemented
37#16810930C2218yescomplemented
38#16810920C2218yescomplemented
39#16810854C2218yescomplemented
40#16810854C2218yescomplemented
41C4×#11719924C2218yescomplemented
42D4×#88322C2218yescomplemented
43#16810659C2218yescomplemented
44C2×#13133150C2211yescharacteristic
45C2×#13133150C2211yescharacteristic
46C2×#13133150C2211yescharacteristic
47C2×#13133150C2211yescharacteristic
48C2×#13133148C2211yescharacteristic
49C2×#13133148C2211yescharacteristic
50C2×#13133148C2211yescharacteristic
51C2×#13133148C2211yescharacteristic
52C2×#13133148C2211yescharacteristic
53C2×#13133148C2218yescomplemented
54C2×C4⋊#88322C2211yescharacteristic
55C2×#13133141C2211yescharacteristic
56C2×#13133141C2211yescharacteristic
57C2×#13133141C2211yescharacteristic
58C2×#13133137C2211yescharacteristic
59C2×#13133137C2211yescharacteristic
60C2×#13133137C2211yescharacteristic
61C2×C22⋊#88322C2211yescharacteristic
62C2×C22⋊#88322C2211yescharacteristic
63C2×C4×#88322C2211yescharacteristic
64C53×#552—24no—
65C53×#552C2218yescomplemented
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×D212C2311yescharacteristic
78C22×C22⋊D53—21no—
79C22×C22⋊D53—21no—
80C23×Dic53—21no—
81C22×C4×D53—21no—
82C2×#11719924—24no—
83C2×#11719924C2314yes—
84C22×#88322—24no—
85C22×#88322—24no—
86C22×#88322C2311yescharacteristic
87C22×#88322C2311yescharacteristic
88C22×#88322C2311yescharacteristic
89C22×#88322C2314yes—
90C22×#88322C2314yes—
91C22×#88322C2311yescharacteristic
92#13133212—28no—
93#13133209—22no—
94#13133209C2314yes—
95#13133199—28no—
96#13133191—22no—
97#13133191—22no—
98#13133191C2314yes—
99#13133191C2314yes—
100#13133189—28no—
101C4×D212—22no—
102C4×D212C2314yes—
103#13133177—28no—
104#13133176—22no—
105#13133176C2314yes—
106C2×C4⋊Dic53—22no—
107C2×C4⋊Dic53—21no—
108C2×C4⋊Dic53C2314yes—
109C2×C4⋊Dic53C2311yescharacteristic
110C2×C4⋊Dic53C2311yescharacteristic
111C2×C4⋊Dic53C2311yescharacteristic
112C2×#11719919—21no—
113C2×#11719919—21no—
114C2×C22⋊Dic53—21no—
115C2×#11719921—21no—
116C2×#11719921—21no—
117C2×#11719921—21no—
118C2×C4×Dic53—21no—
119#13133150C2314yes—
120#13133150C2314yes—
121#13133150C2314yes—
122#13133150C2314yes—
123#13133148C2314yes—
124#13133148C2314yes—
125#13133148C2314yes—
126#13133148C2314yes—
127#13133148C2314yes—
128C4⋊#88322C2314yes—
129#13133141C2314yes—
130#13133141C2314yes—
131#13133141C2314yes—
132#13133137C2314yes—
133#13133137C2314yes—
134#13133137C2314yes—
135C22⋊#88322C2314yes—
136C22⋊#88322C2314yes—
137C4×#88322C2314yes—
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
181C23×D53—21no—
182C2×Q8×C53—21no—
183C2×Q8×C53—22no—
184C2×Q8×C53—22no—
185C2×Q8×C53C2412yes—
186C2×D4×C53—24no—
187C2×D4×C53C2×D414yes—
188C22×C4×C53—22no—
189C22×C4×C53—22no—
190C22×C4×C53—22no—
191C22×C4×C53—22no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—24no—
197C22×C4×C53—44no—
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2×D412yes—
203C22×C4×C53C2×D412yes—
204C22×C4×C53C2412yes—
205C22×C4×C53C2412yes—
206C22×C4×C53C2411yescharacteristic
207C2×C22⋊D53—24no—
208C2×C22⋊D53—24no—
209C2×C22⋊D53—44no—
210C2×C22⋊D53—82no—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—24no—
215C22×Dic53—82no—
216C2×D212—22no—
217C2×D212—22no—
218C2×D212—21no—
219C2×D212C2412yes—
220C2×C4×D53—24no—
221C2×C4×D53—82no—
222C4⋊C4×C53—21no—
223C4⋊C4×C53—21no—
224C4⋊C4×C53—24no—
225C4⋊C4×C53—24no—
226C4⋊C4×C53—24no—
227C4⋊C4×C53—24no—
228C4⋊C4×C53—24no—
229C4⋊C4×C53—24no—
230C4⋊C4×C53—21no—
231C4⋊C4×C53C2×D414yes—
232C4⋊C4×C53C2412yes—
233C4⋊C4×C53C2412yes—
234C4⋊C4×C53C2412yes—
235C22⋊C4×C53—24no—
236C22⋊C4×C53—24no—
237C22⋊C4×C53—24no—
238C22⋊C4×C53C2×D414yes—
239C22⋊C4×C53C2×D414yes—
240C42×C53—24no—
241C42×C53—24no—
242C42×C53C2×D412yes—
243C42×C53C2412yes—
244C22⋊Dic53—24no—
245#11719924—28no—
246#11719921—24no—
247#11719921—24no—
248#11719921—24no—
249C4⋊Dic53—21no—
250C4⋊Dic53—21no—
251C4⋊Dic53—24no—
252C4⋊Dic53—21no—
253C4⋊Dic53C2412yes—
254C4⋊Dic53C2412yes—
255C4⋊Dic53C2412yes—
256#11719919—24no—
257#11719919—24no—
258C4×Dic53—24no—
259C2×#88322—22no—
260C2×#88322—22no—
261C2×#88322—22no—
262C2×#88322—28no—
263C2×#88322—28no—
264C2×#88322#4114yes—
265C2×#88322C2412yes—
266C2×#88322C2412yes—
267C2×#88322C2412yes—
268C2×#88322C2412yes—
269C23×C53—22no—
270C23×C53—22no—
271C23×C53—22no—
272C23×C53—22no—
273C23×C53—22no—
274C23×C53#13514yes—
275C23×C53C22×D412yes—
276C23×C53C22×D412yes—
277C23×C53C22×D411yescharacteristic
278C22×D53—22no—
279C22×D53—42no—
280C22×D53—42no—
281C22×D53—42no—
282Q8×C53—22no—
283Q8×C53—22no—
284Q8×C53—42no—
285D4×C53—28no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—24no—
291C2×C4×C53—24no—
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—42no—
301C2×C4×C53—48no—
302C2×C4×C53—42no—
303C2×C4×C53—42no—
304C2×C4×C53—42no—
305C2×C4×C53C22×D412yes—
306C2×C4×C53C22×D412yes—
307C2×C4×C53C22×D412yes—
308C2×C4×C53C22×D412yes—
309C2×C4×C53C22×D411yescharacteristic
310C2×C4×C53C2×#4112yes—
311C2×C4×C532−1+412yes—
312C2×C4×C53C2511yescharacteristic
313C22⋊D53—48no—
314C22⋊D53—84no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—42no—
319C2×Dic53—42no—
320C2×Dic53—42no—
321C2×Dic53—84no—
322D212—22no—
323D212—22no—
324D212—42no—
325C4×D53—84no—
326#88322—22no—
327#88322—22no—
328#88322—22no—
329#88322C2×#4114yes—
330C2×#3337—531nomaximal, Sylow
331C22×C53—28no—
332C22×C53—22no—
333C22×C53—22no—
334C22×C53—22no—
335C22×C53—22no—
336C22×C53—22no—
337C22×C53—44no—
338C22×C53#54712yes—
339C22×C53C2×#13514yes—
340C22×C53C2×#13512yes—
341C22×C53#57712yes—
342C22×C53C23×D411yescharacteristic
343C2×D53—42no—
344C2×D53—42no—
345C2×D53—42no—
346C2×D53—84no—
347C4×C53—22no—
348C4×C53—22no—
349C4×C53—22no—
350C4×C53—22no—
351C4×C53—42no—
352C4×C53—42no—
353C4×C53—42no—
354C4×C53—42no—
355C4×C53#54712yes—
356C4×C53C22×#4111yescharacteristic
357C4×C53C2×2−1+411yescharacteristic
358Dic53—42no—
359Dic53—42no—
360Dic53—42no—
361C2×#553—531no—
362C2×#552D5311yescharacteristic, complemented
363#3337—5316no—
364C2×#499—531no—
365C2×#484—531no—
366C2×#485—531no—
367C2×#482—531no—
368C2×#480—531no—
369C2×#479—531no—
370C2×#478—531no—
371C2×#465—531no—
372C2×#465—531no—
373C2×C4×SD16—531no—
374C2×C8×D4—531no—
375C2×#427—531no—
376C22×#106—531no—
377C2×C53—24no—
378C2×C53—42no—
379C2×C53#333714yescomplemented
380C2×C53C2×#54711yescharacteristic
381C2×C53C22×#13511yescharacteristic
382C2×C53C2×#57711yescharacteristic
383D53—82no—
384C22×SD16—531no—
385C23×C8—531no—
386C23×C8—531no—
387#553—538no—
388#553—1064no—
389#552—24no—
390#552C2×D5318yescomplemented
391C2×#126—21no—
392C2×#126—1061no—
393C2×#125—21no—
394C2×#125—531no—
395C2×#125C2×D5311yescharacteristic
396C2×#123—21no—
397C2×#123—1061no—
398C2×C22⋊Q8C2×D5311yescharacteristic
399C2×C22⋊Q8C2×D5311yescharacteristic
400C2×#121—531no—
401C2×#121—531no—
402C2×#121—1061no—
403C2×C4×Q8C2×D5311yescharacteristic
404C2×C4×D4—531no—
405C2×C4×D4—1061no—
406C2×C4×D4C2×D5311yescharacteristic
407C2×#117—21no—
408C2×#117—531no—
409C2×#117C2×D5311yescharacteristic
410C22×C4⋊C4—531no—
411C22×C4⋊C4C2×D5311yescharacteristic
412#499—538no—
413#485—538no—
414#484—538no—
415#482—538no—
416#480—538no—
417#479—538no—
418#478—538no—
419#465—538no—
420#465—538no—
421C4×SD16—538no—
422C8×D4—538no—
423#427—538no—
424C2×#107—531no—
425C2×#107—531no—
426C2×#107—531no—
427C2×#107—531no—
428C2×#106—531no—
429C2×#106—531no—
430C2×#106—538no—
431C2×#106—531no—
432C2×#106—531no—
433C2×#106—531no—
434C2×C4⋊C8—531no—
435C2×#103—531no—
436C2×#103—531no—
437C2×#103—531no—
438C2×#102—531no—
439C2×#102—531no—
440C2×#102—531no—
441C2×C22⋊C8—531no—
442C2×C22⋊C8—531no—
443C2×C4×C8—531no—
444C53C2×#333711yescharacteristic, complemented, Sylow
445C22×Q8C22×D5311yescharacteristic
446C22×D4—531no—
447C22×D4—1061no—
448C22×D4—1061no—
449C22×D4C22⋊D5311yescharacteristic
450C23×C4—21no—
451C23×C4—1061no—
452C23×C4—1061no—
453C23×C4C22×D5311yescharacteristic
454C23×C4C22×D5311yescharacteristic
455C2×SD16—534no—
456C2×SD16—1064no—
457C22×C8—531no—
458C22×C8—531no—
459C22×C8—531no—
460C22×C8—534no—
461C22×C8—534no—
462C22×C8—531no—
463C22×C8—1064no—
464C22×C8—1064no—
465#126—28no—
466#126—1068no—
467#125—28no—
468#125—22no—
469#125—534no—
470#125—1062no—
471#125C22×D5314yes—
472#123—28no—
473#123—1068no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476C22⋊Q8C22×D5314yes—
477C22⋊Q8C22×D5314yes—
478#121—534no—
479#121—534no—
480#121—1068no—
481#121—1062no—
482#121—1062no—
483C4×Q8—22no—
484C4×Q8C22×D5314yes—
485C4×D4—534no—
486C4×D4—1068no—
487C4×D4—1062no—
488C4×D4C22⋊D5314yes—
489C4×D4C22×D5314yes—
490#117—22no—
491#117—28no—
492#117—534no—
493#117—1062no—
494#117C22×D5314yes—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—531no—
503C2×C4⋊C4—531no—
504C2×C4⋊C4—534no—
505C2×C4⋊C4—531no—
506C2×C4⋊C4—1061no—
507C2×C4⋊C4—1062no—
508C2×C4⋊C4—1061no—
509C2×C4⋊C4—1061no—
510C2×C4⋊C4C22⋊D5311yescharacteristic
511C2×C4⋊C4C22×D5311yescharacteristic
512C2×C4⋊C4C22×D5311yescharacteristic
513C2×C4⋊C4C22×D5314yes—
514C2×C4⋊C4C22×D5311yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—1061no—
519C2×C22⋊C4—1061no—
520C2×C22⋊C4—1061no—
521C2×C22⋊C4—1061no—
522C2×C22⋊C4C22⋊D5311yescharacteristic
523C2×C22⋊C4C22⋊D5311yescharacteristic
524C2×C42—21no—
525C2×C42—21no—
526C2×C42—1061no—
527C2×C42C22×D5311yescharacteristic
528#107—534no—
529#107—534no—
530#107—534no—
531#107—534no—
532#106—534no—
533#106—534no—
534#106—534no—
535#106—534no—
536#106—534no—
537C4⋊C8—534no—
538#103—534no—
539#103—534no—
540#103—534no—
541#102—534no—
542#102—534no—
543#102—534no—
544C22⋊C8—534no—
545C22⋊C8—534no—
546C4×C8—534no—
547C24—1061no—
548C24C2×C22⋊D5311yescharacteristic
549C24C2×C22⋊D5311yescharacteristic
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8C23×D5312yes—
554C2×D4—24no—
555C2×D4—532no—
556C2×D4—1064no—
557C2×D4—1064no—
558C2×D4—1061no—
559C2×D4—1062no—
560C2×D4—1062no—
561C2×D4—4242no—
562C2×D4—2124no—
563C2×D4C2×C22⋊D5314yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—44no—
574C22×C4—1064no—
575C22×C4—1061no—
576C22×C4—1061no—
577C22×C4—1061no—
578C22×C4—1064no—
579C22×C4—4242no—
580C22×C4—4242no—
581C22×C4C2×C22⋊D5312yes—
582C22×C4C2×C22⋊D5312yes—
583C22×C4C2×C22⋊D5311yescharacteristic
584C22×C4C2×C22⋊D5311yescharacteristic
585C22×C4C2×C22⋊D5311yescharacteristic
586C22×C4C2×C22⋊D5311yescharacteristic
587C22×C4C23×D5312yes—
588C22×C4C23×D5312yes—
589C22×C4C23×D5311yescharacteristic
590SD16—1068no—
591C2×C8—534no—
592C2×C8—532no—
593C2×C8—532no—
594C2×C8—532no—
595C2×C8—532no—
596C2×C8—1068no—
597C2×C8—1068no—
598C2×C8—1062no—
599C2×C8—1062no—
600C2×C8—1062no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—21no—
610C4⋊C4—532no—
611C4⋊C4—532no—
612C4⋊C4—532no—
613C4⋊C4—1061no—
614C4⋊C4—1061no—
615C4⋊C4—1064no—
616C4⋊C4—1061no—
617C4⋊C4—1064no—
618C4⋊C4—1064no—
619C4⋊C4C2×C22⋊D5314yes—
620C4⋊C4C23×D5312yes—
621C4⋊C4C23×D5312yes—
622C4⋊C4C23×D5312yes—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—1064no—
627C22⋊C4—1064no—
628C22⋊C4—1064no—
629C22⋊C4—1064no—
630C22⋊C4C2×C22⋊D5314yes—
631C22⋊C4C2×C22⋊D5314yes—
632C42—24no—
633C42—24no—
634C42—1064no—
635C42C2×C22⋊D5312yes—
636C42C23×D5312yes—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—1062no—
643C23—2122no—
644C23—2122no—
645C23—2122no—
646C23#1313323714yes—
647C23C22×C22⋊D5312yes—
648C23C22×C22⋊D5312yes—
649C23C22×C22⋊D5311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653D4—28no—
654D4—1062no—
655D4—1062no—
656D4—4244no—
657D4—2128no—
658D4—2122no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—42no—
674C2×C4—48no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—1062no—
679C2×C4—1062no—
680C2×C4—1062no—
681C2×C4—4244no—
682C2×C4—4244no—
683C2×C4—2122no—
684C2×C4—2122no—
685C2×C4—2122no—
686C2×C4C22×C22⋊D5312yes—
687C2×C4C22×C22⋊D5312yes—
688C2×C4C22×C22⋊D5312yes—
689C2×C4C22×C22⋊D5312yes—
690C2×C4C22×C22⋊D5311yescharacteristic
691C2×C4#41×D5312yes—
692C2×C4#1313326412yes—
693C2×C4C24×D5311yescharacteristic
694C8—534no—
695C8—1062no—
696C8—1062no—
697C8—1062no—
698C22—28no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—4244no—
706C22—2122no—
707C22—2122no—
708C22—2122no—
709C22#1681127212yes—
710C22C2×#1313323714yes—
711C22C2×#1313323712yes—
712C22#1681143112yes—
713C22C23×C22⋊D5311yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—2122no—
723C4—2122no—
724C4—2122no—
725C4#1681127212yes—
726C4C2×#41×D5311yescharacteristic
727C4C2×#1313326411yescharacteristic
728C2—24no—
729C2—42no—
730C2—4242no—
731C2#2028709414yesdirect product factor
732C2C2×#1681127211yescharacteristic
733C2C22×#1313323711yescharacteristic
734C2C2×#1681143111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#552C2
socleC23×C53C22×D4
prime radicalC2×#16811319C2
hypercenterC2×#552D53
hypocenterC53C2×#3337
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. #20287094C2direct (N × H)
3. C2×#16811022C2semidirect
4. C2×#16810956C2semidirect
5. C2×#16810961C2semidirect
6. C2×#16810947C2semidirect
7. C2×#16810936C2semidirect
8. C2×#16810930C2semidirect
9. C2×#16810920C2semidirect
10. C2×#16810854C2semidirect
11. C2×#16810854C2semidirect
12. C2×C4×#11719924C2semidirect
13. C2×D4×#88322C2semidirect
14. C2×#16810659C2semidirect
15. C22×#13133148C2semidirect
16. C2×C53×#552C2semidirect
32. #16811022C22semidirect
33. #16810961C22semidirect
34. #16810956C22semidirect
35. #16810947C22semidirect
36. #16810936C22semidirect
37. #16810930C22semidirect
38. #16810920C22semidirect
39. #16810854C22semidirect
40. #16810854C22semidirect
41. C4×#11719924C22semidirect
42. D4×#88322C22semidirect
43. #16810659C22semidirect
53. C2×#13133148C22semidirect
65. C53×#552C22semidirect
362. C2×#552D53semidirect
379. C2×C53#3337semidirect
390. #552C2×D53semidirect
444. C53C2×#3337semidirect
731. C2#20287094direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113192
#202870942
C2×#168110222
C2×#168109562
C2×#168109612
C2×#168109472
C2×#168109362
C2×#168109302
C2×#168109202
C2×#168108542
C2×C4×#117199242
C2×D4×#883222
C2×#168106592
C22×#131331482
C2×C53×#5522
C2×#333753