Finite Group Databasebeta

← C2×#21436261 #29465305

Subgroups — C2×#21436261 #29465305

Order 15104.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic118C211yesmaximal, characteristic, complemented
2#21436261C2116yesmaximal, direct product factor
3C2×#16837772C211yesmaximal, characteristic, complemented
4C2×#16837737C211yesmaximal, characteristic, complemented
5C2×#16837743C211yesmaximal, characteristic, complemented
6C2×#16837706C211yesmaximal, characteristic, complemented
7C2×#16837646C211yesmaximal, characteristic, complemented
8C2×#16837629C211yesmaximal, characteristic, complemented
9C2×#16837607C211yesmaximal, characteristic, complemented
10C2×#16837540C211yesmaximal, characteristic, complemented
11C2×#16837540C211yesmaximal, characteristic, complemented
12C2×#16837502C211yesmaximal, characteristic, complemented
13C2×#16837474C211yesmaximal, characteristic, complemented
14C2×#16837410C211yesmaximal, characteristic, complemented
15C22×#14273650C211yesmaximal, characteristic, complemented
16C2×C59×#553C211yesmaximal, characteristic
17C23×Dic118C2211yescharacteristic
18C23×Dic118C2211yescharacteristic
19C22×#11745670C2211yescharacteristic
20C22×#11745670C2211yescharacteristic
21C22×#11745670C2211yescharacteristic
22C22×#11745664C2211yescharacteristic
23C23×C59⋊C8C2211yescharacteristic
24D4×Dic118—24no—
25D4×Dic118C2218yescomplemented
26C2×#14273727C2211yescharacteristic
27C2×#14273726—21no—
28C2×#14273706C2211yescharacteristic
29C2×#14273706C2211yescharacteristic
30C2×#14273704—21no—
31C2×#14273704—21no—
32C2×C4×Dic118C2211yescharacteristic
33C2×D4×Dic59—21no—
34#16837772C2218yescomplemented
35#16837743C2218yescomplemented
36#16837737C2218yescomplemented
37#16837706C2218yescomplemented
38#16837646C2218yescomplemented
39#16837629C2218yescomplemented
40#16837607C2218yescomplemented
41#16837540C2218yescomplemented
42#16837540C2218yescomplemented
43#16837502C2218yescomplemented
44#16837474C2218yescomplemented
45C2×#14273660C2211yescharacteristic
46C2×#14273660C2211yescharacteristic
47C2×#14273658C2211yescharacteristic
48C2×C4⋊(C59⋊C8)C2211yescharacteristic
49#16837410C2218yescomplemented
50C2×#14273650C2211yescharacteristic
51C2×#14273650C2211yescharacteristic
52C2×#14273650C2211yescharacteristic
53C2×#14273650C2211yescharacteristic
54C2×#14273650C2211yescharacteristic
55C2×#14273650C2211yescharacteristic
56C2×#14273650C2211yescharacteristic
57C2×#14273650C2211yescharacteristic
58C2×#14273650C2211yescharacteristic
59C2×#14273650C2218yescomplemented
60C2×#14273648C2211yescharacteristic
61C2×C22⋊(C59⋊C8)C2211yescharacteristic
62C2×C22⋊(C59⋊C8)C2211yescharacteristic
63C2×#14273638C2211yescharacteristic
64C59×#553—24no—
65C59×#553C2218yes—
66C2×#126×C59—21no—
67C2×#125×C59C2211yescharacteristic
68C2×#123×C59—21no—
69C2×#121×C59—21no—
70C2×#121×C59C2211yescharacteristic
71C2×#121×C59C2211yescharacteristic
72C2×C4×D4×C59—21no—
73C2×C4×D4×C59C2211yescharacteristic
74C2×C4×D4×C59C2211yescharacteristic
75C2×#117×C59C2211yescharacteristic
76C22×C4⋊C4×C59C2211yescharacteristic
77C22×Dic118—24no—
78C22×Dic118—24no—
79C22×Dic118—21no—
80C22×Dic118—21no—
81C22×Dic118—22no—
82C22×Dic118—22no—
83C22×Dic118—42no—
84C22×Dic118—42no—
85C22×Dic118C2311yescharacteristic
86C22×Dic118C2311yescharacteristic
87C22×Dic118C2314yes—
88C22×Dic118C2314yes—
89C22×Dic118C2311yescharacteristic
90C23×Dic59—21no—
91C23×Dic59—21no—
92C2×#11745670—24no—
93C2×#11745670—42no—
94C2×#11745670—42no—
95C2×#11745670C2314yes—
96C2×#11745670C2314yes—
97C2×#11745670C2314yes—
98C2×#11745664—42no—
99C2×#11745664C2314yes—
100C22×C59⋊C8—42no—
101C22×C59⋊C8C2311yescharacteristic
102C22×C59⋊C8C2311yescharacteristic
103C22×C59⋊C8C2311yescharacteristic
104C22×C59⋊C8C2311yescharacteristic
105C22×C59⋊C8C2314yes—
106#14273727—22no—
107#14273727C2314yes—
108#14273726—28no—
109#14273706—22no—
110#14273706—22no—
111#14273706C2314yes—
112#14273706C2314yes—
113#14273704—28no—
114#14273704—28no—
115C4×Dic118—22no—
116C4×Dic118C2314yes—
117D4×Dic59—28no—
118C2×C4⋊Dic59—21no—
119C2×C4⋊Dic59—21no—
120C2×C4⋊Dic59C2311yescharacteristic
121C2×Dic59⋊C4—21no—
122C2×Dic59⋊C4—21no—
123C2×Dic59⋊C4—21no—
124C2×C22⋊Dic59—21no—
125C2×C22⋊Dic59—21no—
126C2×C4×Dic59—21no—
127#14273660C2314yes—
128#14273660C2314yes—
129#14273658C2314yes—
130C4⋊(C59⋊C8)C2314yes—
131#14273650C2314yes—
132#14273650C2314yes—
133#14273650C2314yes—
134#14273650C2314yes—
135#14273650C2314yes—
136#14273650C2314yes—
137#14273650C2314yes—
138#14273650C2314yes—
139#14273650C2314yes—
140#14273648C2314yes—
141C22⋊(C59⋊C8)C2314yes—
142C22⋊(C59⋊C8)C2314yes—
143#14273638C2314yes—
144C22×D4×C59—21no—
145C22×D4×C59—21no—
146C22×D4×C59D411yescharacteristic
147C22×D4×C59C2311yescharacteristic
148C23×C4×C59—21no—
149C23×C4×C59—21no—
150C23×C4×C59C2311yescharacteristic
151C23×C4×C59C2311yescharacteristic
152#126×C59—28no—
153#125×C59—22no—
154#125×C59C2314yes—
155#123×C59—28no—
156#121×C59—28no—
157#121×C59—22no—
158#121×C59—22no—
159#121×C59C2314yes—
160#121×C59C2314yes—
161C4×D4×C59—28no—
162C4×D4×C59—22no—
163C4×D4×C59D414yes—
164C4×D4×C59C2314yes—
165C4×D4×C59C2314yes—
166#117×C59—22no—
167#117×C59C2314yes—
168C2×C4⋊C4×C59—21no—
169C2×C4⋊C4×C59—22no—
170C2×C4⋊C4×C59—21no—
171C2×C4⋊C4×C59—21no—
172C2×C4⋊C4×C59D411yescharacteristic
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C4⋊C4×C59C2311yescharacteristic
175C2×C4⋊C4×C59C2311yescharacteristic
176C2×C4⋊C4×C59C2314yes—
177C2×C22⋊C4×C59—21no—
178C2×C22⋊C4×C59—21no—
179C2×C22⋊C4×C59—21no—
180C2×C22⋊C4×C59—21no—
181C2×C22⋊C4×C59D411yescharacteristic
182C2×C22⋊C4×C59D411yescharacteristic
183C2×C42×C59—21no—
184C2×C42×C59C2311yescharacteristic
185C24×C59—21no—
186C24×C59C2×D411yescharacteristic
187C24×C59C2×D411yescharacteristic
188C2×D4×C59—24no—
189C2×D4×C59—24no—
190C2×D4×C59—24no—
191C2×D4×C59—21no—
192C2×D4×C59—22no—
193C2×D4×C59—22no—
194C2×D4×C59—44no—
195C2×D4×C59—82no—
196C2×D4×C59C2×D414yes—
197C2×D4×C59C2412yes—
198C22×C4×C59—22no—
199C22×C4×C59—22no—
200C22×C4×C59—22no—
201C22×C4×C59—22no—
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—24no—
206C22×C4×C59—24no—
207C22×C4×C59—82no—
208C22×C4×C59—82no—
209C22×C4×C59C2×D411yescharacteristic
210C22×C4×C59C2×D411yescharacteristic
211C22×C4×C59C2×D411yescharacteristic
212C22×C4×C59C2×D411yescharacteristic
213C22×C4×C59C2×D412yes—
214C22×C4×C59C2×D412yes—
215C22×C4×C59C2412yes—
216C22×C4×C59C2412yes—
217C22×C4×C59C2411yescharacteristic
218C22×Dic59—21no—
219C22×Dic59—21no—
220C22×Dic59—21no—
221C22×Dic59—21no—
222C22×Dic59—24no—
223C22×Dic59—24no—
224C22×Dic59—44no—
225C22×Dic59—44no—
226C2×Dic118—21no—
227C2×Dic118—22no—
228C2×Dic118—22no—
229C2×Dic118—22no—
230C2×Dic118—22no—
231C2×Dic118—22no—
232C2×Dic118—28no—
233C2×Dic118—28no—
234C2×Dic118—24no—
235C2×Dic118—24no—
236C2×Dic118—21no—
237C2×Dic118—21no—
238C2×Dic118—44no—
239C2×Dic118—44no—
240C2×Dic118—48no—
241C2×Dic118—48no—
242C2×Dic118—44no—
243C2×Dic118—44no—
244C2×Dic118#4114yes—
245C2×Dic118C2412yes—
246C2×Dic118C2412yes—
247C2×Dic118C2412yes—
248C4⋊C4×C59—21no—
249C4⋊C4×C59—21no—
250C4⋊C4×C59—24no—
251C4⋊C4×C59—24no—
252C4⋊C4×C59—24no—
253C4⋊C4×C59—21no—
254C4⋊C4×C59C2×D414yes—
255C4⋊C4×C59C2412yes—
256C4⋊C4×C59C2412yes—
257C4⋊C4×C59C2412yes—
258C22⋊C4×C59—24no—
259C22⋊C4×C59—24no—
260C22⋊C4×C59—24no—
261C22⋊C4×C59—24no—
262C22⋊C4×C59C2×D414yes—
263C22⋊C4×C59C2×D414yes—
264C42×C59—24no—
265C42×C59C2×D412yes—
266C42×C59C2412yes—
267C22⋊Dic59—24no—
268C22⋊Dic59—24no—
269#11745670—28no—
270#11745670—44no—
271#11745670—44no—
272C4⋊Dic59—24no—
273C4⋊Dic59—24no—
274C4⋊Dic59—21no—
275C4⋊Dic59C2412yes—
276Dic59⋊C4—24no—
277Dic59⋊C4—24no—
278Dic59⋊C4—24no—
279C4×Dic59—24no—
280#11745664—44no—
281C2×C59⋊C8—22no—
282C2×C59⋊C8—22no—
283C2×C59⋊C8—22no—
284C2×C59⋊C8—22no—
285C2×C59⋊C8—44no—
286C2×C59⋊C8C2412yes—
287C2×C59⋊C8C2412yes—
288C2×C59⋊C8C2412yes—
289C2×C59⋊C8C2412yes—
290C23×C59—22no—
291C23×C59—22no—
292C23×C59—22no—
293C23×C59—22no—
294C23×C59—22no—
295C23×C59—22no—
296C23×C59—42no—
297C23×C59—42no—
298C23×C59—42no—
299C23×C59#13714yes—
300C23×C59C22×D412yes—
301C23×C59C22×D412yes—
302C23×C59C22×D411yescharacteristic
303D4×C59—28no—
304D4×C59—22no—
305D4×C59—22no—
306D4×C59—48no—
307D4×C59—42no—
308D4×C59—84no—
309C2×C4×C59—22no—
310C2×C4×C59—22no—
311C2×C4×C59—22no—
312C2×C4×C59—22no—
313C2×C4×C59—24no—
314C2×C4×C59—24no—
315C2×C4×C59—22no—
316C2×C4×C59—22no—
317C2×C4×C59—22no—
318C2×C4×C59—22no—
319C2×C4×C59—22no—
320C2×C4×C59—22no—
321C2×C4×C59—22no—
322C2×C4×C59—42no—
323C2×C4×C59—42no—
324C2×C4×C59—42no—
325C2×C4×C59—84no—
326C2×C4×C59—84no—
327C2×C4×C59C22×D412yes—
328C2×C4×C59C22×D412yes—
329C2×C4×C59C22×D412yes—
330C2×C4×C59C22×D412yes—
331C2×C4×C59C22×D411yescharacteristic
332C2×C4×C59C2×#4112yes—
333C2×C4×C59H(5,𝔽2)12yes—
334C2×C4×C59C2511yescharacteristic
335C2×Dic59—24no—
336C2×Dic59—22no—
337C2×Dic59—22no—
338C2×Dic59—22no—
339C2×Dic59—22no—
340C2×Dic59—48no—
341C2×Dic59—48no—
342C2×Dic59—42no—
343C2×Dic59—42no—
344C2×Dic59—42no—
345Dic118—24no—
346Dic118—22no—
347Dic118—22no—
348Dic118—22no—
349Dic118—22no—
350Dic118—22no—
351Dic118—48no—
352Dic118—48no—
353Dic118—42no—
354Dic118—42no—
355Dic118C2×#4114yes—
356C59⋊C8—22no—
357C59⋊C8—22no—
358C59⋊C8—22no—
359C59⋊C8—22no—
360C2×#3320—591nomaximal, Sylow
361C22×C59—22no—
362C22×C59—28no—
363C22×C59—22no—
364C22×C59—22no—
365C22×C59—22no—
366C22×C59—22no—
367C22×C59—44no—
368C22×C59—42no—
369C22×C59—42no—
370C22×C59—42no—
371C22×C59—84no—
372C22×C59#54612yes—
373C22×C59C2×#13714yes—
374C22×C59C2×#13712yes—
375C22×C59#57712yes—
376C22×C59C23×D411yescharacteristic
377C4×C59—22no—
378C4×C59—22no—
379C4×C59—22no—
380C4×C59—22no—
381C4×C59—42no—
382C4×C59—42no—
383C4×C59—42no—
384C4×C59#54612yes—
385C4×C59C22×#4111yescharacteristic
386C4×C59C2×H(5,𝔽2)11yescharacteristic
387Dic59—24no—
388Dic59—42no—
389Dic59—42no—
390Dic59—42no—
391C2×#553D5911yescharacteristic
392C2×D4×Q8—591no—
393#3320—5916no—
394C2×#491—591no—
395C2×#484—591no—
396C2×#485—591no—
397C2×#479—591no—
398C2×#468—591no—
399C2×#465—591no—
400C2×#461—591no—
401C2×#448—591no—
402C2×#448—591no—
403C2×#440—591no—
404C2×#435—591no—
405C2×#419—591no—
406C22×#103—591no—
407C2×C59—24no—
408C2×C59—42no—
409C2×C59—82no—
410C2×C59#332014yescomplemented
411C2×C59C2×#54611yescharacteristic
412C2×C59C22×#13711yescharacteristic
413C2×C59C2×#57711yescharacteristic
414C23×Q8—591no—
415C23×Q8—591no—
416C22×SD16—591no—
417C22×SD16—591no—
418C22×SD16—591no—
419C22×M16—591no—
420C23×C8—591no—
421#553—24no—
422#553C2×D5918yes—
423D4×Q8—598no—
424D4×Q8—1184no—
425C2×C4⋊Q8—591no—
426C2×C4⋊Q8—1181no—
427C2×#126—21no—
428C2×#125C2×D5911yescharacteristic
429C2×#123—21no—
430C2×C22⋊Q8—591no—
431C2×C22⋊Q8—591no—
432C2×C22⋊Q8—1181no—
433C2×C22⋊Q8—1181no—
434C2×#121—21no—
435C2×#121C2×D5911yescharacteristic
436C2×#121C2×D5911yescharacteristic
437C2×C4×Q8—591no—
438C2×C4×D4—21no—
439C2×C4×D4—1181no—
440C2×C4×D4C2×D5911yescharacteristic
441C2×C4×D4C2×D5911yescharacteristic
442C2×#117C2×D5911yescharacteristic
443C22×C4⋊C4C2×D5911yescharacteristic
444#491—598no—
445#485—598no—
446#484—598no—
447#479—598no—
448#468—598no—
449#465—598no—
450#461—598no—
451#448—598no—
452#448—598no—
453#440—598no—
454#435—598no—
455C2×#107—591no—
456C2×#107—591no—
457C2×#106—591no—
458C2×C4⋊C8—591no—
459#419—598no—
460C2×#103—591no—
461C2×#103—591no—
462C2×#103—591no—
463C2×#103—591no—
464C2×#103—591no—
465C2×#103—591no—
466C2×#103—591no—
467C2×#103—591no—
468C2×#103—591no—
469C2×#103—598no—
470C2×#102—591no—
471C2×C22⋊C8—591no—
472C2×C22⋊C8—591no—
473C2×#97—591no—
474C59C2×#332011yescharacteristic, complemented, Sylow
475C22×Q8—591no—
476C22×Q8—591no—
477C22×Q8—591no—
478C22×Q8—594no—
479C22×Q8—594no—
480C22×Q8—1184no—
481C22×Q8—1184no—
482C22×Q8—1181no—
483C22×Q8—1181no—
484C22×Q8—1182no—
485C22×Q8—1182no—
486C22×Q8—2362no—
487C22×Q8—2362no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4C22⋊D5911yescharacteristic
491C22×D4C22×D5911yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—1181no—
495C23×C4—1181no—
496C23×C4C22×D5911yescharacteristic
497C23×C4C22×D5911yescharacteristic
498C2×SD16—594no—
499C2×SD16—594no—
500C2×SD16—594no—
501C2×SD16—1184no—
502C2×SD16—2362no—
503C2×SD16—2362no—
504C2×M16—594no—
505C2×M16—2362no—
506C22×C8—591no—
507C22×C8—591no—
508C22×C8—591no—
509C22×C8—591no—
510C22×C8—594no—
511C22×C8—2362no—
512C4⋊Q8—594no—
513C4⋊Q8—1188no—
514C4⋊Q8—1182no—
515#126—28no—
516#125—22no—
517#125C22×D5914yes—
518#123—28no—
519C22⋊Q8—594no—
520C22⋊Q8—594no—
521C22⋊Q8—1182no—
522C22⋊Q8—1182no—
523C22⋊Q8—1188no—
524C22⋊Q8—1188no—
525#121—28no—
526#121—22no—
527#121—22no—
528#121C22×D5914yes—
529#121C22×D5914yes—
530C4×Q8—594no—
531C4×Q8—1182no—
532C4×D4—28no—
533C4×D4—22no—
534C4×D4—1188no—
535C4×D4C22⋊D5914yes—
536C4×D4C22×D5914yes—
537C4×D4C22×D5914yes—
538#117—22no—
539#117C22×D5914yes—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—591no—
545C2×C4⋊C4—1181no—
546C2×C4⋊C4—1181no—
547C2×C4⋊C4—1181no—
548C2×C4⋊C4—1181no—
549C2×C4⋊C4—1181no—
550C2×C4⋊C4C22⋊D5911yescharacteristic
551C2×C4⋊C4C22×D5911yescharacteristic
552C2×C4⋊C4C22×D5911yescharacteristic
553C2×C4⋊C4C22×D5914yes—
554C2×C4⋊C4C22×D5911yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—1181no—
560C2×C22⋊C4—1181no—
561C2×C22⋊C4C22⋊D5911yescharacteristic
562C2×C22⋊C4C22⋊D5911yescharacteristic
563C2×C42—21no—
564C2×C42—1181no—
565C2×C42C22×D5911yescharacteristic
566#107—594no—
567#107—594no—
568#106—594no—
569C4⋊C8—594no—
570#103—594no—
571#103—594no—
572#103—594no—
573#103—594no—
574#103—594no—
575#103—594no—
576#103—594no—
577#103—594no—
578#103—594no—
579#102—594no—
580C22⋊C8—594no—
581C22⋊C8—594no—
582#97—594no—
583C24—21no—
584C24C2×C22⋊D5911yescharacteristic
585C24C2×C22⋊D5911yescharacteristic
586C2×Q8—594no—
587C2×Q8—592no—
588C2×Q8—592no—
589C2×Q8—592no—
590C2×Q8—1188no—
591C2×Q8—1188no—
592C2×Q8—1181no—
593C2×Q8—1184no—
594C2×Q8—1184no—
595C2×Q8—1181no—
596C2×Q8—1181no—
597C2×Q8—1182no—
598C2×Q8—1182no—
599C2×Q8—1182no—
600C2×Q8—1182no—
601C2×Q8—1182no—
602C2×Q8—2364no—
603C2×Q8—2364no—
604C2×Q8—2364no—
605C2×Q8—2364no—
606C2×Q8—2368no—
607C2×Q8—2368no—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—21no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—44no—
615C2×D4—82no—
616C2×D4C2×C22⋊D5914yes—
617C2×D4C23×D5912yes—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—24no—
626C22×C4—24no—
627C22×C4—82no—
628C22×C4—82no—
629C22×C4—1181no—
630C22×C4—1184no—
631C22×C4—1184no—
632C22×C4—1181no—
633C22×C4—1181no—
634C22×C4—1181no—
635C22×C4—2364no—
636C22×C4—2364no—
637C22×C4C2×C22⋊D5912yes—
638C22×C4C2×C22⋊D5912yes—
639C22×C4C2×C22⋊D5911yescharacteristic
640C22×C4C2×C22⋊D5911yescharacteristic
641C22×C4C2×C22⋊D5911yescharacteristic
642C22×C4C2×C22⋊D5911yescharacteristic
643C22×C4C23×D5912yes—
644C22×C4C23×D5912yes—
645C22×C4C23×D5911yescharacteristic
646SD16—1188no—
647SD16—2364no—
648SD16—2364no—
649M16—2364no—
650C2×C8—592no—
651C2×C8—592no—
652C2×C8—592no—
653C2×C8—592no—
654C2×C8—1182no—
655C2×C8—1182no—
656C2×C8—1182no—
657C2×C8—1182no—
658C2×C8—2364no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—24no—
662C4⋊C4—24no—
663C4⋊C4—24no—
664C4⋊C4—21no—
665C4⋊C4—592no—
666C4⋊C4—1181no—
667C4⋊C4—1184no—
668C4⋊C4—1184no—
669C4⋊C4—1184no—
670C4⋊C4—1184no—
671C4⋊C4—1184no—
672C4⋊C4C2×C22⋊D5914yes—
673C4⋊C4C23×D5912yes—
674C4⋊C4C23×D5912yes—
675C4⋊C4C23×D5912yes—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—24no—
679C22⋊C4—24no—
680C22⋊C4—1184no—
681C22⋊C4—1184no—
682C22⋊C4C2×C22⋊D5914yes—
683C22⋊C4C2×C22⋊D5914yes—
684C42—24no—
685C42—1184no—
686C42C2×C22⋊D5912yes—
687C42C23×D5912yes—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23#1427375714yes—
698C23C22×C22⋊D5912yes—
699C23C22×C22⋊D5912yes—
700C23C22×C22⋊D5911yescharacteristic
701Q8—594no—
702Q8—1182no—
703Q8—1184no—
704Q8—1182no—
705Q8—1182no—
706Q8—1182no—
707Q8—1182no—
708Q8—2368no—
709Q8—2368no—
710Q8—2362no—
711Q8—2362no—
712D4—28no—
713D4—22no—
714D4—22no—
715D4—48no—
716D4—42no—
717D4—84no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—84no—
735C2×C4—84no—
736C2×C4—1182no—
737C2×C4—1184no—
738C2×C4—1182no—
739C2×C4—1182no—
740C2×C4—1182no—
741C2×C4—2368no—
742C2×C4—2368no—
743C2×C4—2362no—
744C2×C4—2362no—
745C2×C4—2362no—
746C2×C4C22×C22⋊D5912yes—
747C2×C4C22×C22⋊D5912yes—
748C2×C4C22×C22⋊D5912yes—
749C2×C4C22×C22⋊D5912yes—
750C2×C4C22×C22⋊D5911yescharacteristic
751C2×C4#41×D5912yes—
752C2×C4#1427377312yes—
753C2×C4C24×D5911yescharacteristic
754C8—1182no—
755C8—1182no—
756C8—1182no—
757C8—1182no—
758C22—22no—
759C22—28no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—84no—
769C22#1683804012yes—
770C22C2×#1427375714yes—
771C22C2×#1427375712yes—
772C22#1683821312yes—
773C22C23×C22⋊D5911yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—1184no—
782C4—2362no—
783C4—2362no—
784C4—2362no—
785C4#1683804012yes—
786C4C2×#41×D5911yescharacteristic
787C4C2×#1427377311yescharacteristic
788C2—24no—
789C2—42no—
790C2—82no—
791C2#2143626114yesdirect product factor
792C2C2×#1683804011yescharacteristic
793C2C22×#1427375711yescharacteristic
794C2C2×#1683821311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
Fitting, prime radicalC2×C59×#553C2
socleC23×C59C22×D4
hypercenterC2×#553D59
hypocenterC59C2×#3320
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic118C2semidirect
2. #21436261C2direct (N × H)
3. C2×#16837772C2semidirect
4. C2×#16837737C2semidirect
5. C2×#16837743C2semidirect
6. C2×#16837706C2semidirect
7. C2×#16837646C2semidirect
8. C2×#16837629C2semidirect
9. C2×#16837607C2semidirect
10. C2×#16837540C2semidirect
11. C2×#16837540C2semidirect
12. C2×#16837502C2semidirect
13. C2×#16837474C2semidirect
14. C2×#16837410C2semidirect
15. C22×#14273650C2semidirect
25. D4×Dic118C22semidirect
34. #16837772C22semidirect
35. #16837743C22semidirect
36. #16837737C22semidirect
37. #16837706C22semidirect
38. #16837646C22semidirect
39. #16837629C22semidirect
40. #16837607C22semidirect
41. #16837540C22semidirect
42. #16837540C22semidirect
43. #16837502C22semidirect
44. #16837474C22semidirect
49. #16837410C22semidirect
59. C2×#14273650C22semidirect
410. C2×C59#3320semidirect
474. C59C2×#3320semidirect
791. C2#21436261direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×Dic1182
#214362612
C2×#168377722
C2×#168377372
C2×#168377432
C2×#168377062
C2×#168376462
C2×#168376292
C2×#168376072
C2×#168375402
C2×#168375022
C2×#168374742
C2×#168374102
C22×#142736502
C2×C59×#5532
C2×#332059