Finite Group Databasebeta

← C2×#21438075 #29496797

Subgroups — C2×#21438075 #29496797

Order 15104.

7142 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21438075C2132yesmaximal, direct product factor
2C2×#16838131C211yesmaximal, characteristic, complemented
3C2×#16838113C211yesmaximal, characteristic, complemented
4C2×#16838100C212yesmaximal, complemented
5C2×#16838094C214yesmaximal, complemented
6C2×#16838094C212yesmaximal, complemented
7C2×#16838090C212yesmaximal, complemented
8C2×#16838056C212yesmaximal, complemented
9C2×#16838056C211yesmaximal, characteristic, complemented
10C2×#16838015C212yesmaximal, complemented
11C2×#16838001C214yesmaximal, complemented
12C2×#16837957C211yesmaximal, characteristic, complemented
13C2×#16837939C211yesmaximal, characteristic, complemented
14C2×#16837938C212yesmaximal, complemented
15C22×#14273718C212yesmaximal, complemented
16C2×#16837881C212yesmaximal, complemented
17C2×C4×#11745687C211yesmaximal, characteristic, complemented
18C2×C59×#554C211yesmaximal, characteristic, complemented
19C22×#11745687C2211yescharacteristic
20C22×#11745687C2212yes—
21#16838131C22116yescomplemented
22#16838113C22116yescomplemented
23#16838100C22132yescomplemented
24#16838094C22132yescomplemented
25#16838094C22164yescomplemented
26#16838090C22132yescomplemented
27#16838056C22116yescomplemented
28#16838056C22132yescomplemented
29#16838015C22132yescomplemented
30#16838001C22164yescomplemented
31#16837957C22116yescomplemented
32C2×#14273727C2212yes—
33C2×#14273727C2211yescharacteristic
34#16837939C22116yescomplemented
35#16837938C22132yescomplemented
36C2×#14273722C2214yes—
37C2×#14273722C2214yes—
38C2×#14273722C2214yes—
39C2×#14273722C2212yes—
40C2×#14273718C2214yes—
41C2×#14273718C2214yes—
42C2×#14273718C2214yes—
43C2×#14273718C2211yescharacteristic
44C2×#14273718C2214yes—
45C2×#14273718C2212yes—
46C2×#14273718C2212yes—
47C2×#14273718C2212yes—
48C2×#14273718C22132yescomplemented
49C2×#14273716C2211yescharacteristic
50C2×#14273712C2212yes—
51C2×#14273712C2214yes—
52C2×#14273711C2214yes—
53C2×#14273711C2214yes—
54C2×#14273711C2214yes—
55C2×#14273707C2212yes—
56C2×#14273707C2212yes—
57C2×#14273707C2212yes—
58C2×#14273703C2212yes—
59C2×#14273703C2214yes—
60C2×#14273703C2211yescharacteristic
61C2×#14273702C2211yescharacteristic
62C2×#14273701C2214yes—
63C2×#14273701C2212yes—
64#16837881C22132yescomplemented
65C4×#11745687C22116yescomplemented
66C2×Q8×Dic59C2212yes—
67C2×Q8×Dic59C2212yes—
68C2×C4×Dic118C2211yescharacteristic
69C2×C4×Dic118C2212yes—
70C2×#14273692C2211yescharacteristic
71C2×#14273692C2212yes—
72C2×C4×D236C2212yes—
73C2×C4×D236C2211yescharacteristic
74C2×D4×Dic59C2211yescharacteristic
75C2×#14273689C2212yes—
76C2×C4×C22⋊D59C2212yes—
77C2×C4×C22⋊D59C2214yes—
78C2×(C22⋊D59)⋊C4C2212yes—
79C2×(C22⋊D59)⋊C4C2214yes—
80C2×#14273685C2211yescharacteristic
81C2×#14273685C2214yes—
82C2×#14273685C2212yes—
83C2×#14273684C2212yes—
84C2×#14273683C2212yes—
85C2×#14273683C2214yes—
86C22×C4⋊Dic59C2212yes—
87C22×C4⋊Dic59C2214yes—
88C22×Dic59⋊C4C2214yes—
89C2×C4⋊C4×D59C2212yes—
90C22×C4×Dic59C2212yes—
91C2×C42×D59C2211yescharacteristic
92C59×#554C22116yescomplemented
93C2×C4⋊Q8×C59C2211yescharacteristic
94C2×#125×C59C2212yes—
95C2×C22⋊Q8×C59C2214yes—
96C2×C22⋊Q8×C59C2212yes—
97C2×C4×Q8×C59C2211yescharacteristic
98C2×C4×D4×C59C2211yescharacteristic
99C2×C4×D4×C59C2212yes—
100C22×C4⋊C4×C59C2212yes—
101C2×#11745687—28no—
102C2×#11745687—216no—
103C2×#11745687C2318yes—
104C2×#11745687C23116yes—
105C22×Dic118C2312yes—
106C22×Dic118C2311yescharacteristic
107C22×D236C2311yescharacteristic
108C22×D236C2312yes—
109C22×C22⋊D59C2312yes—
110C22×C22⋊D59C2314yes—
111C23×Dic59C2312yes—
112C23×Dic59C2314yes—
113C23×Dic59C2312yes—
114C22×C4×D59C2311yescharacteristic
115C22×C4×D59C2311yescharacteristic
116C22×C4×D59C2312yes—
117C22×C4×D59C2311yescharacteristic
118C22×C4×D59C2314yes—
119#14273727C2318yes—
120#14273727C23116yes—
121#14273722C23132yes—
122#14273722C23116yes—
123#14273722C23132yes—
124#14273722C23132yes—
125#14273718C2318yes—
126#14273718C23116yes—
127#14273718C23132yes—
128#14273718C23132yes—
129#14273718C23116yes—
130#14273718C23116yes—
131#14273718C23132yes—
132#14273718C23132yes—
133#14273716C2318yes—
134#14273712C23116yes—
135#14273712C23132yes—
136#14273711C23132yes—
137#14273711C23132yes—
138#14273711C23132yes—
139#14273707C23116yes—
140#14273707C23116yes—
141#14273707C23116yes—
142#14273703C2318yes—
143#14273703C23116yes—
144#14273703C23132yes—
145#14273702C2318yes—
146#14273701C23116yes—
147#14273701C23132yes—
148Q8×Dic59C23116yes—
149Q8×Dic59C23116yes—
150C4×Dic118C23116yes—
151C4×Dic118C2318yes—
152#14273692C23116yes—
153#14273692C2318yes—
154C4×D236C23116yes—
155C4×D236C2318yes—
156D4×Dic59C2318yes—
157#14273689C23116yes—
158C4×C22⋊D59C23116yes—
159C4×C22⋊D59C23132yes—
160(C22⋊D59)⋊C4C23132yes—
161(C22⋊D59)⋊C4C23116yes—
162#14273685C23132yes—
163#14273685C23116yes—
164#14273685C2318yes—
165#14273684C23116yes—
166#14273683C23116yes—
167#14273683C23132yes—
168C2×C4⋊Dic59C2314yes—
169C2×C4⋊Dic59C2312yes—
170C2×C4⋊Dic59C2314yes—
171C2×C4⋊Dic59C2312yes—
172C2×C4⋊Dic59C2311yescharacteristic
173C2×C4⋊Dic59C2314yes—
174C2×C4⋊Dic59C2314yes—
175C2×C4⋊Dic59C2314yes—
176C2×C4⋊Dic59C2312yes—
177C2×C4⋊Dic59C23116yes—
178C2×C4⋊Dic59C23132yes—
179C2×C4⋊Dic59C2311yescharacteristic
180C2×Dic59⋊C4C2312yes—
181C2×Dic59⋊C4C2314yes—
182C2×Dic59⋊C4C2314yes—
183C2×Dic59⋊C4C2312yes—
184C2×Dic59⋊C4C2312yes—
185C2×Dic59⋊C4C2314yes—
186C2×Dic59⋊C4C2312yes—
187C2×Dic59⋊C4C23132yes—
188C4⋊C4×D59C23116yes—
189C2×C22⋊Dic59C2312yes—
190C2×(C2×D59)⋊C4C2314yes—
191C2×(C2×D59)⋊C4C2314yes—
192C2×(C2×D59)⋊C4C2314yes—
193C2×(C2×D59)⋊C4C2312yes—
194C2×(C2×D59)⋊C4C2312yes—
195C2×(C2×D59)⋊C4C2312yes—
196C2×(C2×D59)⋊C4C2312yes—
197C2×(C2×D59)⋊C4C2312yes—
198C2×(C2×D59)⋊C4C2312yes—
199C2×C4×Dic59C2311yescharacteristic
200C2×C4×Dic59C2312yes—
201C2×C4×Dic59C2312yes—
202C2×C4×Dic59C2312yes—
203C2×C4×Dic59C2314yes—
204C2×C4×Dic59C2314yes—
205C2×C4×Dic59C23116yes—
206C2×C4×Dic59C2311yescharacteristic
207C2×C4×Dic59C2311yescharacteristic
208C42×D59C2318yes—
209C22×Q8×C59C2311yescharacteristic
210C22×Q8×C59C2312yes—
211C22×D4×C59C2311yescharacteristic
212C23×C4×C59C2312yes—
213C23×C4×C59C2314yes—
214C4⋊Q8×C59C2318yes—
215#125×C59C23116yes—
216C22⋊Q8×C59C23116yes—
217C22⋊Q8×C59C23132yes—
218C4×Q8×C59C2318yes—
219C4×D4×C59C2318yes—
220C4×D4×C59C23116yes—
221C2×C4⋊C4×C59C2311yescharacteristic
222C2×C4⋊C4×C59C2311yescharacteristic
223C2×C4⋊C4×C59C2312yes—
224C2×C4⋊C4×C59C2314yes—
225C2×C4⋊C4×C59C2312yes—
226C2×C4⋊C4×C59C2312yes—
227C2×C4⋊C4×C59C2314yes—
228C2×C4⋊C4×C59C23116yes—
229C2×C22⋊C4×C59C2314yes—
230C2×C22⋊C4×C59C2312yes—
231C2×C42×C59C2312yes—
232C2×C42×C59C2311yescharacteristic
233C24×C59C2412yes—
234C23×D59C2411yescharacteristic
235C23×D59C2412yes—
236C2×Q8×C59—24no—
237C2×Q8×C59—44no—
238C2×Q8×C59C2414yes—
239C2×Q8×C59C2418yes—
240C2×D4×C59#4118yes—
241C2×D4×C59C2414yes—
242C22×C4×C59—28no—
243C22×C4×C59—48no—
244C22×C4×C59C2412yes—
245C22×C4×C59C2411yescharacteristic
246C22×C4×C59C2412yes—
247C22×C4×C59C2412yes—
248C22×C4×C59C2414yes—
249C22×C4×C59C2418yes—
250C22×C4×C59C24116yes—
251C22×C4×C59C2411yescharacteristic
252C22×C4×C59C2411yescharacteristic
253C2×C22⋊D59—28no—
254C2×C22⋊D59—216no—
255C2×C22⋊D59C24116yes—
256C2×C22⋊D59C2418yes—
257C22×Dic59—28no—
258C22×Dic59—216no—
259C22×Dic59—44no—
260C22×Dic59C2411yescharacteristic
261C22×Dic59C2411yescharacteristic
262C22×Dic59C2411yescharacteristic
263C22×Dic59C2412yes—
264C22×Dic59C2412yes—
265C22×Dic59C2414yes—
266C22×Dic59C2418yes—
267C22×Dic59C2412yes—
268C22×Dic59C24116yes—
269C22×Dic59C2418yes—
270#11745687—232no—
271#11745687—264no—
272C2×D236—24no—
273C2×D236—44no—
274C2×D236C2414yes—
275C2×D236C2418yes—
276C2×C4×D59—24no—
277C2×C4×D59—28no—
278C2×C4×D59—24no—
279C2×C4×D59—48no—
280C2×C4×D59—42no—
281C2×C4×D59C2414yes—
282C2×C4×D59C2414yes—
283C2×C4×D59C2418yes—
284C2×C4×D59C2414yes—
285C2×C4×D59C24116yes—
286C2×Dic118—28no—
287C2×Dic118—24no—
288C2×Dic118C2418yes—
289C2×Dic118C2414yes—
290C4⋊C4×C59C2414yes—
291C4⋊C4×C59C24116yes—
292C4⋊C4×C59C2418yes—
293C4⋊C4×C59C2414yes—
294C4⋊C4×C59C2418yes—
295C4⋊C4×C59C2418yes—
296C4⋊C4×C59C24116yes—
297C22⋊C4×C59C24116yes—
298C22⋊C4×C59C2418yes—
299C42×C59C2418yes—
300C42×C59C2414yes—
301C22⋊Dic59C2418yes—
302(C2×D59)⋊C4C2418yes—
303(C2×D59)⋊C4C2418yes—
304(C2×D59)⋊C4C2418yes—
305(C2×D59)⋊C4C2418yes—
306(C2×D59)⋊C4C24116yes—
307(C2×D59)⋊C4C24116yes—
308(C2×D59)⋊C4C24116yes—
309(C2×D59)⋊C4C2418yes—
310(C2×D59)⋊C4C2418yes—
311C4⋊Dic59C2414yes—
312C4⋊Dic59C2414yes—
313C4⋊Dic59C2418yes—
314C4⋊Dic59C2418yes—
315C4⋊Dic59C24116yes—
316C4⋊Dic59C24116yes—
317C4⋊Dic59C24116yes—
318C4⋊Dic59C24116yes—
319C4⋊Dic59C2418yes—
320C4⋊Dic59C24116yes—
321Dic59⋊C4C24116yes—
322Dic59⋊C4C2418yes—
323Dic59⋊C4C24116yes—
324Dic59⋊C4C24116yes—
325Dic59⋊C4C2418yes—
326Dic59⋊C4C2418yes—
327Dic59⋊C4C2418yes—
328C4×Dic59C2414yes—
329C4×Dic59C2414yes—
330C4×Dic59C2414yes—
331C4×Dic59C2418yes—
332C4×Dic59C2418yes—
333C4×Dic59C2418yes—
334C4×Dic59C24116yes—
335C4×Dic59C24116yes—
336C23×C59—24no—
337C23×C59—24no—
338C23×C59C2×#4118yes—
339C23×C59C2514yes—
340C23×C59C2511yescharacteristic
341C22×D59—22no—
342C22×D59—24no—
343C22×D59—22no—
344C22×D59—24no—
345C22×D59—24no—
346C22×D59—22no—
347C22×D59C2512yes—
348C22×D59C2514yes—
349Q8×C59—28no—
350Q8×C59—48no—
351D4×C59C2×#41116yes—
352C2×C4×C59—24no—
353C2×C4×C59—24no—
354C2×C4×C59—28no—
355C2×C4×C59—22no—
356C2×C4×C59—24no—
357C2×C4×C59—216no—
358C2×C4×C59—416no—
359C2×C4×C59C2×#4114yes—
360C2×C4×C592−1+414yes—
361C2×C4×C59C2514yes—
362C2×C4×C59C2514yes—
363C2×C4×C59C2512yes—
364C2×C4×C59C2518yes—
365C2×C4×C59C2514yes—
366C2×C4×C59C2512yes—
367C2×C4×C59C2512yes—
368C22⋊D59—216no—
369C22⋊D59—232no—
370C2×Dic59—24no—
371C2×Dic59—28no—
372C2×Dic59—22no—
373C2×Dic59—24no—
374C2×Dic59—216no—
375C2×Dic59—232no—
376C2×Dic59—22no—
377C2×Dic59—24no—
378C2×Dic59—22no—
379C2×Dic59—48no—
380C2×Dic59C2512yes—
381C2×Dic59C2512yes—
382C2×Dic59C2514yes—
383C2×Dic59C2512yes—
384C2×Dic59C2514yes—
385C2×Dic59C2518yes—
386C2×Dic59C2514yes—
387D236—28no—
388D236—48no—
389C4×D59—28no—
390C4×D59—216no—
391C4×D59—28no—
392C4×D59—416no—
393C4×D59—44no—
394Dic118—216no—
395Dic118—28no—
396C2×#3515—591nomaximal, Sylow
397C22×C59—24no—
398C22×C59—24no—
399C22×C59—216no—
400C22×C59C22×#4118yes—
401C22×C59C22×#4112yes—
402C22×C59C2×2−1+412yes—
403C22×C59#58512yes—
404C22×C59C2611yescharacteristic
405C2×D59—22no—
406C2×D59—24no—
407C2×D59—22no—
408C2×D59—24no—
409C2×D59—24no—
410C2×D59—22no—
411C2×D59—44no—
412C2×D59—48no—
413C4×C59—24no—
414C4×C59—24no—
415C4×C59—28no—
416C4×C59—22no—
417C4×C59—24no—
418C4×C59C22×#4114yes—
419C4×C59C2×2−1+414yes—
420Dic59—24no—
421Dic59—28no—
422Dic59—22no—
423Dic59—24no—
424Dic59—22no—
425Dic59—24no—
426Dic59—22no—
427#3515—5932no—
428C2×#557—591no—
429C2×#554—591no—
430C2×#554D5911yescharacteristic, complemented
431C2×#553—592no—
432C2×#552—592no—
433C2×#552—594no—
434C2×#552—592no—
435C2×#547—592no—
436C2×#547—591no—
437C2×#541—592no—
438C2×#539—594no—
439C2×#533—591no—
440C2×#529—592no—
441C2×#529—591no—
442C22×#125—592no—
443C2×#520—592no—
444C2×C4×#41—591no—
445C2×C59—28no—
446C2×C59#351514yescomplemented
447C2×C59C23×#4111yescharacteristic
448C2×C59C22×2−1+411yescharacteristic
449C2×C59C2×#58511yescharacteristic
450D59—42no—
451D59—44no—
452C22×#41—591no—
453C22×#41—592no—
454#557—5916no—
455#554—5916no—
456#554C2×D59116yescomplemented
457#553—5932no—
458#552—5932no—
459#552—5964no—
460#552—5932no—
461#547—5932no—
462#547—5916no—
463#541—5932no—
464#539—5964no—
465#533—5916no—
466C2×C4⋊Q8—591no—
467C2×C4⋊Q8—592no—
468C2×C4⋊Q8C2×D5911yescharacteristic
469#529—5932no—
470#529—5916no—
471C2×#126—594no—
472C2×#126—592no—
473C2×#126—594no—
474C2×#126—594no—
475C2×#125—591no—
476C2×#125—592no—
477C2×#125—594no—
478C2×#125—594no—
479C2×#125—592no—
480C2×#125—592no—
481C2×#125—594no—
482C2×#125—594no—
483C2×#125—5932no—
484C2×#125C2×D5912yes—
485C2×#124—591no—
486C2×#123—592no—
487C2×#123—594no—
488C2×#123—594no—
489C2×#123—594no—
490C2×#123—594no—
491C2×C22⋊Q8—591no—
492C2×C22⋊Q8—592no—
493C2×C22⋊Q8—594no—
494C2×C22⋊Q8—592no—
495C2×C22⋊Q8—592no—
496C2×C22⋊Q8—592no—
497C2×C22⋊Q8C2×D5912yes—
498C2×C22⋊Q8C2×D5914yes—
499C2×#121—592no—
500C2×#121—594no—
501C2×#121—591no—
502#520—5932no—
503C4×#41—5916no—
504C2×C4×Q8—592no—
505C2×C4×Q8—592no—
506C2×C4×Q8—591no—
507C2×C4×Q8—592no—
508C2×C4×Q8—591no—
509C2×C4×Q8—592no—
510C2×C4×Q8C2×D5911yescharacteristic
511C2×C4×D4—591no—
512C2×C4×D4—592no—
513C2×C4×D4—594no—
514C2×C4×D4—592no—
515C2×C4×D4—592no—
516C2×C4×D4—594no—
517C2×C4×D4—592no—
518C2×C4×D4—591no—
519C2×C4×D4C2×D5911yescharacteristic
520C2×C4×D4C2×D5912yes—
521C2×#117—591no—
522C2×#117—594no—
523C2×#117—592no—
524C2×#117—592no—
525C2×#117—594no—
526C2×#117—592no—
527C22×C4⋊C4—594no—
528C22×C4⋊C4—592no—
529C22×C4⋊C4—594no—
530C22×C4⋊C4—592no—
531C22×C4⋊C4C2×D5912yes—
532C22×C42—592no—
533C22×C42—591no—
534C59C2×#351511yescharacteristic, complemented, Sylow
535C2×#41—598no—
536C2×#41—5916no—
537C2×#41—1188no—
538C2×#41—11816no—
539C22×Q8—591no—
540C22×Q8—592no—
541C22×Q8C22×D5911yescharacteristic
542C22×Q8C22×D5912yes—
543C22×D4—592no—
544C22×D4—594no—
545C22×D4—591no—
546C22×D4—592no—
547C22×D4C22×D5911yescharacteristic
548C23×C4—594no—
549C23×C4—592no—
550C23×C4—592no—
551C23×C4—592no—
552C23×C4—591no—
553C23×C4—591no—
554C23×C4—594no—
555C23×C4—591no—
556C23×C4C22×D5912yes—
557C23×C4C22×D5914yes—
558C4⋊Q8—598no—
559C4⋊Q8—5916no—
560C4⋊Q8C22×D5918yes—
561#126—5932no—
562#126—5916no—
563#126—5932no—
564#126—5932no—
565#125—598no—
566#125—5916no—
567#125—5932no—
568#125—5932no—
569#125—5916no—
570#125—5916no—
571#125—5932no—
572#125—5932no—
573#125C22×D59116yes—
574#124—598no—
575#123—5916no—
576#123—5932no—
577#123—5932no—
578#123—5932no—
579#123—5932no—
580C22⋊Q8—598no—
581C22⋊Q8—5916no—
582C22⋊Q8—5932no—
583C22⋊Q8—5916no—
584C22⋊Q8—5916no—
585C22⋊Q8—5916no—
586C22⋊Q8C22×D59116yes—
587C22⋊Q8C22×D59132yes—
588#121—5916no—
589#121—5932no—
590#121—598no—
591C4×Q8—5916no—
592C4×Q8—5916no—
593C4×Q8—598no—
594C4×Q8—5916no—
595C4×Q8—598no—
596C4×Q8—5916no—
597C4×Q8C22×D5918yes—
598C4×D4—598no—
599C4×D4—5916no—
600C4×D4—5932no—
601C4×D4—5916no—
602C4×D4—5916no—
603C4×D4—5932no—
604C4×D4—5916no—
605C4×D4—598no—
606C4×D4C22×D5918yes—
607C4×D4C22×D59116yes—
608#117—598no—
609#117—5932no—
610#117—5916no—
611#117—5916no—
612#117—5932no—
613#117—5916no—
614C2×C4⋊C4—591no—
615C2×C4⋊C4—594no—
616C2×C4⋊C4—592no—
617C2×C4⋊C4—591no—
618C2×C4⋊C4—592no—
619C2×C4⋊C4—592no—
620C2×C4⋊C4—594no—
621C2×C4⋊C4—594no—
622C2×C4⋊C4—594no—
623C2×C4⋊C4—5932no—
624C2×C4⋊C4—594no—
625C2×C4⋊C4—594no—
626C2×C4⋊C4—594no—
627C2×C4⋊C4—5916no—
628C2×C4⋊C4—5932no—
629C2×C4⋊C4—592no—
630C2×C4⋊C4—592no—
631C2×C4⋊C4—592no—
632C2×C4⋊C4—592no—
633C2×C4⋊C4—594no—
634C2×C4⋊C4—5916no—
635C2×C4⋊C4C22×D5912yes—
636C2×C4⋊C4C22×D5911yescharacteristic
637C2×C4⋊C4C22×D5912yes—
638C2×C4⋊C4C22×D5914yes—
639C2×C4⋊C4C22×D59116yes—
640C2×C4⋊C4C22×D5911yescharacteristic
641C2×C4⋊C4C22×D5914yes—
642C2×C4⋊C4C22×D5912yes—
643C2×C22⋊C4—592no—
644C2×C22⋊C4—592no—
645C2×C22⋊C4—592no—
646C2×C22⋊C4—592no—
647C2×C22⋊C4—592no—
648C2×C22⋊C4—594no—
649C2×C22⋊C4—594no—
650C2×C22⋊C4—594no—
651C2×C22⋊C4—592no—
652C2×C22⋊C4—592no—
653C2×C22⋊C4C22×D5914yes—
654C2×C22⋊C4C22×D5912yes—
655C2×C42—592no—
656C2×C42—591no—
657C2×C42—594no—
658C2×C42—594no—
659C2×C42—591no—
660C2×C42—592no—
661C2×C42—592no—
662C2×C42—5916no—
663C2×C42—591no—
664C2×C42—598no—
665C2×C42C22×D5912yes—
666C2×C42C22×D5911yescharacteristic
667C24—591no—
668C24—592no—
669C24C23×D5912yes—
670#41—11832no—
671#41—11864no—
672C2×Q8—24no—
673C2×Q8—44no—
674C2×Q8—594no—
675C2×Q8—598no—
676C2×Q8—1184no—
677C2×Q8—1188no—
678C2×Q8C23×D5914yes—
679C2×Q8C23×D5918yes—
680C2×D4—598no—
681C2×D4—5916no—
682C2×D4—594no—
683C2×D4—598no—
684C2×D4—1188no—
685C2×D4—11816no—
686C2×D4—1184no—
687C2×D4—2364no—
688C2×D4#1174568918yes—
689C2×D4C23×D5914yes—
690C22×C4—28no—
691C22×C4—48no—
692C22×C4—598no—
693C22×C4—5916no—
694C22×C4—591no—
695C22×C4—591no—
696C22×C4—592no—
697C22×C4—591no—
698C22×C4—594no—
699C22×C4—592no—
700C22×C4—592no—
701C22×C4—598no—
702C22×C4—594no—
703C22×C4—594no—
704C22×C4—598no—
705C22×C4—594no—
706C22×C4—5916no—
707C22×C4—11816no—
708C22×C4—1188no—
709C22×C4—1188no—
710C22×C4—1184no—
711C22×C4—1184no—
712C22×C4—2368no—
713C22×C4—2362no—
714C22×C4—2364no—
715C22×C4C23×D5918yes—
716C22×C4C23×D5912yes—
717C22×C4C23×D5912yes—
718C22×C4C23×D5911yescharacteristic
719C22×C4C23×D5914yes—
720C22×C4C23×D5912yes—
721C22×C4C23×D59116yes—
722C22×C4C23×D5911yescharacteristic
723C22×C4C23×D5911yescharacteristic
724C4⋊C4—594no—
725C4⋊C4—5916no—
726C4⋊C4—598no—
727C4⋊C4—594no—
728C4⋊C4—598no—
729C4⋊C4—598no—
730C4⋊C4—5916no—
731C4⋊C4—5916no—
732C4⋊C4—5916no—
733C4⋊C4—5916no—
734C4⋊C4—5916no—
735C4⋊C4—5916no—
736C4⋊C4—598no—
737C4⋊C4—598no—
738C4⋊C4—598no—
739C4⋊C4—598no—
740C4⋊C4—5916no—
741C4⋊C4C23×D5918yes—
742C4⋊C4C23×D5914yes—
743C4⋊C4C23×D5918yes—
744C4⋊C4C23×D59116yes—
745C4⋊C4C23×D5914yes—
746C4⋊C4C23×D59116yes—
747C4⋊C4C23×D5918yes—
748C22⋊C4—598no—
749C22⋊C4—598no—
750C22⋊C4—598no—
751C22⋊C4—598no—
752C22⋊C4—598no—
753C22⋊C4—5916no—
754C22⋊C4—5916no—
755C22⋊C4—5916no—
756C22⋊C4—598no—
757C22⋊C4—598no—
758C22⋊C4C23×D59116yes—
759C22⋊C4C23×D5918yes—
760C42—594no—
761C42—598no—
762C42—594no—
763C42—594no—
764C42—598no—
765C42—598no—
766C42—5916no—
767C42—5916no—
768C42C23×D5914yes—
769C42C23×D5918yes—
770C23—24no—
771C23—24no—
772C23—592no—
773C23—594no—
774C23—1182no—
775C23—1184no—
776C23—1182no—
777C23—1184no—
778C23—1184no—
779C23—1182no—
780C23C2×#1174568918yes—
781C23C24×D5914yes—
782C23C24×D5911yescharacteristic
783Q8—28no—
784Q8—48no—
785Q8—1188no—
786Q8—11816no—
787D4—11816no—
788D4—11832no—
789D4—1188no—
790D4—2368no—
791D4C2×#11745689116yes—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—28no—
796C2×C4—22no—
797C2×C4—216no—
798C2×C4—416no—
799C2×C4—592no—
800C2×C4—592no—
801C2×C4—592no—
802C2×C4—594no—
803C2×C4—594no—
804C2×C4—598no—
805C2×C4—594no—
806C2×C4—1182no—
807C2×C4—1184no—
808C2×C4—1188no—
809C2×C4—1184no—
810C2×C4—11816no—
811C2×C4—11832no—
812C2×C4—1182no—
813C2×C4—1184no—
814C2×C4—1182no—
815C2×C4—1188no—
816C2×C4—11816no—
817C2×C4—1188no—
818C2×C4—23616no—
819C2×C4—2364no—
820C2×C4—2368no—
821C2×C4C2×#1174568914yes—
822C2×C4#1427377414yes—
823C2×C4C24×D5914yes—
824C2×C4C24×D5914yes—
825C2×C4C24×D5912yes—
826C2×C4C24×D5918yes—
827C2×C4C24×D5914yes—
828C2×C4C24×D5912yes—
829C2×C4C24×D5912yes—
830C22—216no—
831C22—24no—
832C22—24no—
833C22—1182no—
834C22—1184no—
835C22—1182no—
836C22—1184no—
837C22—1184no—
838C22—1182no—
839C22—2364no—
840C22—2368no—
841C22C22×#1174568918yes—
842C22C22×#1174568912yes—
843C22C2×#1427377412yes—
844C22#1683823712yes—
845C22C25×D5911yescharacteristic
846C4—24no—
847C4—24no—
848C4—24no—
849C4—28no—
850C4—22no—
851C4—1182no—
852C4—1184no—
853C4—1184no—
854C4—1188no—
855C4—1182no—
856C4—1184no—
857C4—1182no—
858C4C22×#1174568914yes—
859C4C2×#1427377414yes—
860C2—28no—
861C2—2362no—
862C2—2364no—
863C2#2143807514yesdirect product factor
864C2C23×#1174568911yescharacteristic
865C2C22×#1427377411yescharacteristic
866C2C2×#1683823711yescharacteristic
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#554C2
socleC23×C59C25
hypercenterC2×#554D59
hypocenterC59C2×#3515
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #21438075C2direct (N × H)
2. C2×#16838131C2semidirect
3. C2×#16838113C2semidirect
4. C2×#16838100C2semidirect
5. C2×#16838094C2semidirect
6. C2×#16838094C2semidirect
7. C2×#16838090C2semidirect
8. C2×#16838056C2semidirect
9. C2×#16838056C2semidirect
10. C2×#16838015C2semidirect
11. C2×#16838001C2semidirect
12. C2×#16837957C2semidirect
13. C2×#16837939C2semidirect
14. C2×#16837938C2semidirect
15. C22×#14273718C2semidirect
16. C2×#16837881C2semidirect
17. C2×C4×#11745687C2semidirect
18. C2×C59×#554C2semidirect
21. #16838131C22semidirect
22. #16838113C22semidirect
23. #16838100C22semidirect
24. #16838094C22semidirect
25. #16838094C22semidirect
26. #16838090C22semidirect
27. #16838056C22semidirect
28. #16838056C22semidirect
29. #16838015C22semidirect
30. #16838001C22semidirect
31. #16837957C22semidirect
34. #16837939C22semidirect
35. #16837938C22semidirect
48. C2×#14273718C22semidirect
64. #16837881C22semidirect
65. C4×#11745687C22semidirect
92. C59×#554C22semidirect
430. C2×#554D59semidirect
446. C2×C59#3515semidirect
456. #554C2×D59semidirect
534. C59C2×#3515semidirect
863. C2#21438075direct (N × H)

Maximal subgroups

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

subgroupindex
#214380752
C2×#168381312
C2×#168381132
C2×#168381002
C2×#168380942
C2×#168380902
C2×#168380562
C2×#168380152
C2×#168380012
C2×#168379572
C2×#168379392
C2×#168379382
C22×#142737182
C2×#168378812
C2×C4×#117456872
C2×C59×#5542
C2×#351559