Finite Group Databasebeta

← C2×#21436917 #29468448

Subgroups — C2×#21436917 #29468448

Order 15104.

1886 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838112C211yesmaximal, characteristic, complemented
2#21436917C2116yesmaximal, direct product factor
3C2×#16837770C211yesmaximal, characteristic, complemented
4C2×#16837761C211yesmaximal, characteristic, complemented
5C2×#16837756C211yesmaximal, characteristic, complemented
6C2×#16837709C211yesmaximal, characteristic, complemented
7C2×#16837687C211yesmaximal, characteristic, complemented
8C2×#16837702C211yesmaximal, characteristic, complemented
9C2×#16837614C211yesmaximal, characteristic
10C2×#16837614C211yesmaximal, characteristic
11C2×#16837604C211yesmaximal, characteristic, complemented
12C2×#16837533C211yesmaximal, characteristic, complemented
13C2×#16837512C211yesmaximal, characteristic
14C2×#16837500C211yesmaximal, characteristic, complemented
15C2×C4×#11745671C211yesmaximal, characteristic, complemented
16C2×C59×#556C211yesmaximal, characteristic, complemented
17C22×#11745671C2211yescharacteristic
18C22×#11745671C2211yescharacteristic
19C22×#11745669C2211yescharacteristic
20#16838112—24no—
21#16838112C2218yescomplemented
22C2×#14273727C2211yescharacteristic
23C2×#14273719C2211yescharacteristic
24C2×#14273719C2211yescharacteristic
25C2×#14273705—21no—
26C2×#14273705—21no—
27C2×#14273703—21no—
28C2×C4×D236C2211yescharacteristic
29C2×C4×D236C2211yescharacteristic
30C2×C4×D236C2211yescharacteristic
31C2×C4⋊C4×D59—21no—
32#16837770C2218yescomplemented
33#16837761C2218yescomplemented
34#16837756C2218yescomplemented
35#16837709C2218yescomplemented
36#16837702C2218yescomplemented
37#16837687C2218yescomplemented
38#16837614C2218yes—
39#16837614C2218yes—
40#16837604C2218yescomplemented
41#16837533C2218yescomplemented
42#16837512C2218yes—
43#16837500C2218yescomplemented
44C4×#11745671C2218yescomplemented
45C2×#14273660C2211yescharacteristic
46C2×#14273658C2211yescharacteristic
47C2×#14273658C2211yescharacteristic
48C2×C4⋊(C59⋊C8)C2211yescharacteristic
49C2×C4⋊(C59⋊C8)C2211yescharacteristic
50C2×C4⋊(C59⋊C8)C2211yescharacteristic
51C2×#14273651C2211yescharacteristic
52C2×#14273651C2211yescharacteristic
53C2×#14273651C2211yescharacteristic
54C2×#14273651C2211yescharacteristic
55C2×#14273651C2211yescharacteristic
56C2×#14273651C2211yescharacteristic
57C2×#14273648C2211yescharacteristic
58C2×#14273648C2211yescharacteristic
59C2×#14273648C2211yescharacteristic
60C2×#14273647C2211yescharacteristic
61C2×#14273638C2211yescharacteristic
62C2×#14273638C2211yescharacteristic
63C2×C4×C59⋊C8C2211yescharacteristic
64C59×#556—24no—
65C59×#556C2218yescomplemented
66C2×C4⋊Q8×C59C2211yescharacteristic
67C2×#126×C59—21no—
68C2×#126×C59—21no—
69C2×#124×C59C2211yescharacteristic
70C2×#124×C59C2211yescharacteristic
71C2×C22⋊Q8×C59—21no—
72C2×C4×Q8×C59C2211yescharacteristic
73C2×C4×Q8×C59C2211yescharacteristic
74C2×C4×Q8×C59C2211yescharacteristic
75C2×C4×D4×C59C2211yescharacteristic
76C2×#117×C59—21no—
77C22×Dic118—21no—
78C22×D236C2311yescharacteristic
79C22×C4×D59—21no—
80C22×C4×D59—21no—
81C22×C4×D59—21no—
82C2×#11745671—24no—
83C2×#11745671—24no—
84C2×#11745671C2314yes—
85C2×#11745671C2314yes—
86C2×#11745669—24no—
87C2×#11745669C2314yes—
88C22×C59⋊C8C2311yescharacteristic
89C22×C59⋊C8C2311yescharacteristic
90C22×C59⋊C8C2311yescharacteristic
91C22×C59⋊C8C2311yescharacteristic
92#14273727—22no—
93#14273727C2314yes—
94#14273719—22no—
95#14273719—22no—
96#14273719C2314yes—
97#14273719C2314yes—
98#14273705—28no—
99#14273705—28no—
100#14273703—28no—
101C4×D236—22no—
102C4×D236—22no—
103C4×D236—22no—
104C4×D236C2314yes—
105C4×D236C2314yes—
106C4×D236C2314yes—
107C2×C4⋊Dic59—21no—
108C2×C4⋊Dic59C2311yescharacteristic
109C2×C4⋊Dic59C2311yescharacteristic
110C2×C4⋊Dic59C2311yescharacteristic
111C2×Dic59⋊C4—21no—
112C2×Dic59⋊C4—21no—
113C2×Dic59⋊C4—21no—
114C2×Dic59⋊C4—21no—
115C4⋊C4×D59—28no—
116C2×(C2×D59)⋊C4—21no—
117C2×(C2×D59)⋊C4—21no—
118C2×(C2×D59)⋊C4—21no—
119#14273660C2314yes—
120#14273658C2314yes—
121#14273658C2314yes—
122C4⋊(C59⋊C8)C2314yes—
123C4⋊(C59⋊C8)C2314yes—
124C4⋊(C59⋊C8)C2314yes—
125#14273651C2314yes—
126#14273651C2314yes—
127#14273651C2314yes—
128#14273651C2314yes—
129#14273651C2314yes—
130#14273651C2314yes—
131#14273648C2314yes—
132#14273648C2314yes—
133#14273648C2314yes—
134#14273647C2314yes—
135#14273638C2314yes—
136#14273638C2314yes—
137C4×C59⋊C8C2314yes—
138C22×Q8×C59D411yescharacteristic
139C22×Q8×C59C2311yescharacteristic
140C22×Q8×C59C2311yescharacteristic
141C22×D4×C59C2311yescharacteristic
142C23×C4×C59—21no—
143C4⋊Q8×C59—22no—
144C4⋊Q8×C59C2314yes—
145#126×C59—28no—
146#126×C59—28no—
147#124×C59—22no—
148#124×C59—22no—
149#124×C59C2314yes—
150#124×C59C2314yes—
151C22⋊Q8×C59—28no—
152C4×Q8×C59—22no—
153C4×Q8×C59—22no—
154C4×Q8×C59D414yes—
155C4×Q8×C59C2314yes—
156C4×Q8×C59C2314yes—
157C4×Q8×C59C2314yes—
158C4×D4×C59—22no—
159C4×D4×C59C2314yes—
160#117×C59—28no—
161C2×C4⋊C4×C59—21no—
162C2×C4⋊C4×C59—21no—
163C2×C4⋊C4×C59—21no—
164C2×C4⋊C4×C59—21no—
165C2×C4⋊C4×C59D411yescharacteristic
166C2×C4⋊C4×C59D411yescharacteristic
167C2×C4⋊C4×C59D411yescharacteristic
168C2×C4⋊C4×C59C2311yescharacteristic
169C2×C22⋊C4×C59—21no—
170C2×C22⋊C4×C59—21no—
171C2×C22⋊C4×C59—21no—
172C2×C22⋊C4×C59—21no—
173C2×C22⋊C4×C59—21no—
174C2×C42×C59—21no—
175C2×C42×C59—21no—
176C2×C42×C59C2311yescharacteristic
177C2×C42×C59C2311yescharacteristic
178C2×C42×C59C2311yescharacteristic
179C24×C59—21no—
180C23×D59—21no—
181C2×Q8×C59—21no—
182C2×Q8×C59—21no—
183C2×Q8×C59—22no—
184C2×Q8×C59—22no—
185C2×Q8×C59—22no—
186C2×Q8×C59—22no—
187C2×Q8×C59—42no—
188C2×Q8×C59C2×D414yes—
189C2×Q8×C59C2412yes—
190C2×Q8×C59C2412yes—
191C2×D4×C59—21no—
192C2×D4×C59—22no—
193C2×D4×C59—22no—
194C2×D4×C59C2412yes—
195C22×C4×C59—21no—
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59—24no—
199C22×C4×C59—44no—
200C22×C4×C59C2×D411yescharacteristic
201C22×C4×C59C2×D411yescharacteristic
202C22×C4×C59C2×D411yescharacteristic
203C22×C4×C59C2×D411yescharacteristic
204C22×C4×C59C2×D411yescharacteristic
205C22×C4×C59C2×D411yescharacteristic
206C22×C4×C59C2411yescharacteristic
207C22×Dic59—21no—
208C22×Dic59—21no—
209C22×Dic59—21no—
210C2×D236—21no—
211C2×D236—22no—
212C2×D236#4114yes—
213C2×D236C2412yes—
214C2×C4×D59—24no—
215C2×C4×D59—24no—
216C2×C4×D59—24no—
217C2×C4×D59—44no—
218C2×C4×D59—82no—
219C2×C4×D59—82no—
220C2×Dic118—24no—
221C2×Dic118—82no—
222C4⋊C4×C59—24no—
223C4⋊C4×C59—24no—
224C4⋊C4×C59—24no—
225C4⋊C4×C59—24no—
226C4⋊C4×C59—21no—
227C4⋊C4×C59C2×D414yes—
228C4⋊C4×C59C2×D414yes—
229C4⋊C4×C59C2×D414yes—
230C4⋊C4×C59C2412yes—
231C22⋊C4×C59—24no—
232C22⋊C4×C59—24no—
233C22⋊C4×C59—24no—
234C22⋊C4×C59—24no—
235C22⋊C4×C59—24no—
236C42×C59—24no—
237C42×C59—24no—
238C42×C59C2×D412yes—
239C42×C59C2×D412yes—
240C42×C59C2×D412yes—
241C42×C59C2412yes—
242C42×C59C2412yes—
243C42×C59C2412yes—
244#11745671—28no—
245#11745671—28no—
246#11745669—28no—
247(C2×D59)⋊C4—24no—
248(C2×D59)⋊C4—24no—
249(C2×D59)⋊C4—24no—
250C4⋊Dic59—24no—
251C4⋊Dic59—21no—
252C4⋊Dic59—21no—
253C4⋊Dic59—21no—
254C4⋊Dic59C2412yes—
255C4⋊Dic59C2412yes—
256C4⋊Dic59C2412yes—
257Dic59⋊C4—24no—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261C2×C59⋊C8—22no—
262C2×C59⋊C8—22no—
263C2×C59⋊C8—22no—
264C2×C59⋊C8—22no—
265C2×C59⋊C8C2412yes—
266C2×C59⋊C8C2412yes—
267C2×C59⋊C8C2412yes—
268C2×C59⋊C8C2412yes—
269C23×C59—22no—
270C23×C59—42no—
271C23×C59—42no—
272C23×C59—42no—
273C23×C59C22×D411yescharacteristic
274C22×D59—24no—
275C22×D59—22no—
276C22×D59—42no—
277C22×D59—42no—
278Q8×C59—22no—
279Q8×C59—22no—
280Q8×C59—22no—
281Q8×C59—22no—
282Q8×C59—44no—
283Q8×C59—42no—
284Q8×C59—42no—
285D4×C59—22no—
286D4×C59—22no—
287D4×C59—42no—
288C2×C4×C59—22no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—48no—
298C2×C4×C59—42no—
299C2×C4×C59—42no—
300C2×C4×C59—42no—
301C2×C4×C59C22×D412yes—
302C2×C4×C59C22×D412yes—
303C2×C4×C59C22×D412yes—
304C2×C4×C59C22×D412yes—
305C2×C4×C59C22×D412yes—
306C2×C4×C59C22×D412yes—
307C2×C4×C59C22×D411yescharacteristic
308C2×C4×C59C2×#4112yes—
309C2×C4×C592−1+412yes—
310C2×C4×C59C2511yescharacteristic
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—42no—
315C2×Dic59—42no—
316C2×Dic59—42no—
317D236—24no—
318D236—22no—
319D236C2×#4114yes—
320C4×D59—48no—
321C4×D59—84no—
322C4×D59—84no—
323Dic118—84no—
324C59⋊C8—22no—
325C59⋊C8—22no—
326C59⋊C8—22no—
327C59⋊C8—22no—
328C2×#3376—591nomaximal, Sylow
329C22×C59—42no—
330C22×C59—42no—
331C22×C59—42no—
332C22×C59—84no—
333C22×C59#54812yes—
334C22×C59#57512yes—
335C22×C59#57712yes—
336C22×C59C23×D411yescharacteristic
337C2×D59—24no—
338C2×D59—48no—
339C2×D59—42no—
340C2×D59—42no—
341C4×C59—22no—
342C4×C59—22no—
343C4×C59—22no—
344C4×C59—22no—
345C4×C59—22no—
346C4×C59—22no—
347C4×C59—42no—
348C4×C59—42no—
349C4×C59—42no—
350C4×C59#54812yes—
351C4×C59C22×#4111yescharacteristic
352C4×C59C2×2−1+411yescharacteristic
353Dic59—42no—
354Dic59—42no—
355Dic59—42no—
356C2×#556D5911yescharacteristic, complemented
357C2×#554—591no—
358#3376—5916no—
359C2×#491—591no—
360C2×#489—591no—
361C2×#488—591no—
362C2×#479—591no—
363C2×#475—591no—
364C2×#478—591no—
365C2×#463—591no—
366C2×#463—591no—
367C2×#461—591no—
368C2×#446—591no—
369C2×#442—591no—
370C2×#440—591no—
371C2×C4×SD16—591no—
372C2×C59—82no—
373C2×C59#337614yescomplemented
374C2×C59C2×#54811yescharacteristic
375C2×C59C2×#57511yescharacteristic
376C2×C59C2×#57711yescharacteristic
377D59—44no—
378C22×SD16—591no—
379C22×SD16—591no—
380C22×D8—591no—
381#556—24no—
382#556C2×D5918yescomplemented
383#554—598no—
384#554—1184no—
385C2×C4⋊Q8—591no—
386C2×C4⋊Q8C2×D5911yescharacteristic
387C2×#126—21no—
388C2×#126—21no—
389C2×#125—591no—
390C2×#125—591no—
391C2×#124C2×D5911yescharacteristic
392C2×#124C2×D5911yescharacteristic
393C2×C22⋊Q8—21no—
394C2×C22⋊Q8—1181no—
395C2×C22⋊Q8—1181no—
396C2×C22⋊Q8—1181no—
397C2×C4×Q8C2×D5911yescharacteristic
398C2×C4×Q8C2×D5911yescharacteristic
399C2×C4×Q8C2×D5911yescharacteristic
400C2×C4×D4—591no—
401C2×C4×D4—591no—
402C2×C4×D4—591no—
403C2×C4×D4C2×D5911yescharacteristic
404C2×#117—21no—
405C22×C4⋊C4—1181no—
406#491—598no—
407#489—598no—
408#488—598no—
409#479—598no—
410#478—598no—
411#475—598no—
412#463—598no—
413#463—598no—
414#461—598no—
415#446—598no—
416#442—598no—
417#440—598no—
418C4×SD16—598no—
419C2×#107—591no—
420C2×#106—591no—
421C2×#106—591no—
422C2×C4⋊C8—591no—
423C2×C4⋊C8—591no—
424C2×C4⋊C8—591no—
425C2×#103—591no—
426C2×#103—591no—
427C2×#103—591no—
428C2×#103—591no—
429C2×#103—591no—
430C2×#103—591no—
431C2×#102—591no—
432C2×#102—591no—
433C2×#102—591no—
434C2×#102—591no—
435C2×#97—591no—
436C2×#97—591no—
437C2×C4×C8—591no—
438C59C2×#337611yescharacteristic, complemented, Sylow
439C22×Q8—1181no—
440C22×Q8C22⋊D5911yescharacteristic
441C22×Q8C22×D5911yescharacteristic
442C22×Q8C22×D5911yescharacteristic
443C22×D4—591no—
444C22×D4C22×D5911yescharacteristic
445C23×C4—21no—
446C23×C4—1181no—
447C23×C4—1181no—
448C23×C4—1181no—
449C2×SD16—594no—
450C2×SD16—594no—
451C2×SD16—1184no—
452C2×SD16—1184no—
453C2×D8—594no—
454C2×D8—1184no—
455C22×C8—591no—
456C22×C8—591no—
457C22×C8—591no—
458C22×C8—591no—
459C4⋊Q8—22no—
460C4⋊Q8—594no—
461C4⋊Q8—1182no—
462C4⋊Q8C22×D5914yes—
463#126—28no—
464#126—28no—
465#125—594no—
466#125—594no—
467#125—1182no—
468#125—1182no—
469#124—22no—
470#124—22no—
471#124C22×D5914yes—
472#124C22×D5914yes—
473C22⋊Q8—28no—
474C22⋊Q8—1188no—
475C22⋊Q8—1188no—
476C22⋊Q8—1188no—
477C4×Q8—22no—
478C4×Q8—22no—
479C4×Q8C22⋊D5914yes—
480C4×Q8C22×D5914yes—
481C4×Q8C22×D5914yes—
482C4×Q8C22×D5914yes—
483C4×D4—22no—
484C4×D4—594no—
485C4×D4—594no—
486C4×D4—594no—
487C4×D4—1182no—
488C4×D4—1182no—
489C4×D4—1182no—
490C4×D4C22×D5914yes—
491#117—28no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—591no—
497C2×C4⋊C4—591no—
498C2×C4⋊C4—591no—
499C2×C4⋊C4—1181no—
500C2×C4⋊C4—1181no—
501C2×C4⋊C4—1181no—
502C2×C4⋊C4—1181no—
503C2×C4⋊C4—1181no—
504C2×C4⋊C4—1188no—
505C2×C4⋊C4C22⋊D5911yescharacteristic
506C2×C4⋊C4C22⋊D5911yescharacteristic
507C2×C4⋊C4C22⋊D5911yescharacteristic
508C2×C4⋊C4C22×D5911yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—1181no—
515C2×C22⋊C4—1181no—
516C2×C22⋊C4—1181no—
517C2×C42—21no—
518C2×C42—21no—
519C2×C42C22×D5911yescharacteristic
520C2×C42C22×D5911yescharacteristic
521C2×C42C22×D5911yescharacteristic
522#107—594no—
523#106—594no—
524#106—594no—
525C4⋊C8—594no—
526C4⋊C8—594no—
527C4⋊C8—594no—
528#103—594no—
529#103—594no—
530#103—594no—
531#103—594no—
532#103—594no—
533#103—594no—
534#102—594no—
535#102—594no—
536#102—594no—
537#102—594no—
538#97—594no—
539#97—594no—
540C4×C8—594no—
541C24—21no—
542C24—1181no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—42no—
550C2×Q8—1184no—
551C2×Q8—4722no—
552C2×Q8C2×C22⋊D5914yes—
553C2×Q8C23×D5912yes—
554C2×Q8C23×D5912yes—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—594no—
559C2×D4—592no—
560C2×D4—1181no—
561C2×D4—1182no—
562C2×D4C23×D5912yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—44no—
568C22×C4—1181no—
569C22×C4—1181no—
570C22×C4—1181no—
571C22×C4—1184no—
572C22×C4—1184no—
573C22×C4—1184no—
574C22×C4—4722no—
575C22×C4—4722no—
576C22×C4—2364no—
577C22×C4C2×C22⋊D5911yescharacteristic
578C22×C4C2×C22⋊D5911yescharacteristic
579C22×C4C2×C22⋊D5911yescharacteristic
580C22×C4C2×C22⋊D5911yescharacteristic
581C22×C4C2×C22⋊D5911yescharacteristic
582C22×C4C2×C22⋊D5911yescharacteristic
583C22×C4C23×D5911yescharacteristic
584SD16—1188no—
585SD16—1188no—
586D8—1188no—
587C2×C8—592no—
588C2×C8—592no—
589C2×C8—592no—
590C2×C8—592no—
591C2×C8—1182no—
592C2×C8—1182no—
593C2×C8—1182no—
594C2×C8—1182no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—21no—
600C4⋊C4—592no—
601C4⋊C4—592no—
602C4⋊C4—592no—
603C4⋊C4—1181no—
604C4⋊C4—1181no—
605C4⋊C4—1181no—
606C4⋊C4—1184no—
607C4⋊C4—1184no—
608C4⋊C4—1184no—
609C4⋊C4—1184no—
610C4⋊C4—1184no—
611C4⋊C4C2×C22⋊D5914yes—
612C4⋊C4C2×C22⋊D5914yes—
613C4⋊C4C2×C22⋊D5914yes—
614C4⋊C4C23×D5912yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—24no—
619C22⋊C4—24no—
620C22⋊C4—1184no—
621C22⋊C4—1184no—
622C22⋊C4—1184no—
623C42—24no—
624C42—24no—
625C42C2×C22⋊D5912yes—
626C42C2×C22⋊D5912yes—
627C42C2×C22⋊D5912yes—
628C42C23×D5912yes—
629C42C23×D5912yes—
630C42C23×D5912yes—
631C23—22no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—1182no—
636C23—1184no—
637C23—2362no—
638C23—2362no—
639C23C22×C22⋊D5911yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—22no—
644Q8—44no—
645Q8—42no—
646Q8—42no—
647Q8—4724no—
648D4—22no—
649D4—22no—
650D4—42no—
651D4—594no—
652D4—1182no—
653D4—1184no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—48no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—1182no—
668C2×C4—1182no—
669C2×C4—1182no—
670C2×C4—4724no—
671C2×C4—4724no—
672C2×C4—2368no—
673C2×C4—2362no—
674C2×C4—2362no—
675C2×C4—2362no—
676C2×C4C22×C22⋊D5912yes—
677C2×C4C22×C22⋊D5912yes—
678C2×C4C22×C22⋊D5912yes—
679C2×C4C22×C22⋊D5912yes—
680C2×C4C22×C22⋊D5912yes—
681C2×C4C22×C22⋊D5912yes—
682C2×C4C22×C22⋊D5911yescharacteristic
683C2×C4#41×D5912yes—
684C2×C4#1427377412yes—
685C2×C4C24×D5911yescharacteristic
686C8—1182no—
687C8—1182no—
688C8—1182no—
689C8—1182no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—84no—
694C22—1184no—
695C22—2362no—
696C22—2362no—
697C22—2368no—
698C22#1683805912yes—
699C22#1683820012yes—
700C22#1683821012yes—
701C22C23×C22⋊D5911yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—2362no—
712C4—2362no—
713C4—2362no—
714C4#1683805912yes—
715C4C2×#41×D5911yescharacteristic
716C4C2×#1427377411yescharacteristic
717C2—82no—
718C2—2364no—
719C2#2143691714yesdirect product factor
720C2C2×#1683805911yescharacteristic
721C2C2×#1683820011yescharacteristic
722C2C2×#1683821011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#556C2
socleC23×C59C22×D4
prime radicalC22×#11745669C22
hypercenterC2×#556D59
hypocenterC59C2×#3376
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#16838112C2semidirect
2. #21436917C2direct (N × H)
3. C2×#16837770C2semidirect
4. C2×#16837761C2semidirect
5. C2×#16837756C2semidirect
6. C2×#16837709C2semidirect
7. C2×#16837687C2semidirect
8. C2×#16837702C2semidirect
11. C2×#16837604C2semidirect
12. C2×#16837533C2semidirect
14. C2×#16837500C2semidirect
15. C2×C4×#11745671C2semidirect
16. C2×C59×#556C2semidirect
21. #16838112C22semidirect
32. #16837770C22semidirect
33. #16837761C22semidirect
34. #16837756C22semidirect
35. #16837709C22semidirect
36. #16837702C22semidirect
37. #16837687C22semidirect
40. #16837604C22semidirect
41. #16837533C22semidirect
43. #16837500C22semidirect
44. C4×#11745671C22semidirect
65. C59×#556C22semidirect
356. C2×#556D59semidirect
373. C2×C59#3376semidirect
382. #556C2×D59semidirect
438. C59C2×#3376semidirect
719. C2#21436917direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381122
#214369172
C2×#168377702
C2×#168377612
C2×#168377562
C2×#168377092
C2×#168376872
C2×#168377022
C2×#168376142
C2×#168376042
C2×#168375332
C2×#168375122
C2×#168375002
C2×C4×#117456712
C2×C59×#5562
C2×#337659