Finite Group Databasebeta

← C2×#21435379 #29460910

Subgroups — C2×#21435379 #29460910

Order 15104.

1742 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838023C211yesmaximal, characteristic
2#21435379C2116yesmaximal, direct product factor
3C2×#16837812C211yesmaximal, characteristic, complemented
4C2×#16837805C211yesmaximal, characteristic, complemented
5C2×#16837764C211yesmaximal, characteristic, complemented
6C2×#16837759C211yesmaximal, characteristic, complemented
7C2×#16837737C211yesmaximal, characteristic, complemented
8C2×#16837743C211yesmaximal, characteristic, complemented
9C2×#16837726C211yesmaximal, characteristic
10C2×#16837715C211yesmaximal, characteristic
11C2×#16837706C211yesmaximal, characteristic, complemented
12C2×#16837694C211yesmaximal, characteristic, complemented
13C2×#16837699C211yesmaximal, characteristic, complemented
14C2×#16837679C211yesmaximal, characteristic, complemented
15C2×#16837463C211yesmaximal, characteristic, complemented
16C2×C59×#544C211yesmaximal, characteristic, complemented
17#16838023—24no—
18#16838023C2218yes—
19C2×#14273727C2211yescharacteristic
20C2×#14273722—21no—
21C2×#14273715C2211yescharacteristic
22C2×#14273713—21no—
23C2×#14273709—21no—
24C2×#14273706C2211yescharacteristic
25C2×#14273705—21no—
26C2×#14273701C2211yescharacteristic
27C2×C4×Dic118C2211yescharacteristic
28C2×C4×D236C2211yescharacteristic
29#16837812C2218yescomplemented
30#16837805C2218yescomplemented
31#16837764C2218yescomplemented
32#16837759C2218yescomplemented
33#16837743C2218yescomplemented
34#16837737C2218yescomplemented
35#16837726C2218yes—
36#16837715C2218yes—
37#16837706C2218yescomplemented
38#16837699C2218yescomplemented
39#16837694C2218yescomplemented
40#16837679C2218yescomplemented
41#16837463C2218yescomplemented
42C2×#14273660C2211yescharacteristic
43C2×#14273660C2211yescharacteristic
44C2×#14273660C2211yescharacteristic
45C2×#14273660C2211yescharacteristic
46C2×#14273660C2211yescharacteristic
47C2×#14273660C2211yescharacteristic
48C2×#14273658C2211yescharacteristic
49C2×#14273658C2211yescharacteristic
50C2×C4⋊(C59⋊C8)C2211yescharacteristic
51C2×C4⋊(C59⋊C8)C2211yescharacteristic
52C2×#14273650C2211yescharacteristic
53C2×#14273650C2211yescharacteristic
54C2×#14273650C2211yescharacteristic
55C2×#14273650C2211yescharacteristic
56C2×#14273647C2211yescharacteristic
57C2×#14273647C2211yescharacteristic
58C2×#14273647C2211yescharacteristic
59C2×#14273647C2211yescharacteristic
60C2×C22⋊(C59⋊C8)C2211yescharacteristic
61C2×C22⋊(C59⋊C8)C2211yescharacteristic
62C2×#14273638C2211yescharacteristic
63C2×C4×C59⋊C8C2211yescharacteristic
64C59×#544—24no—
65C59×#544C2218yescomplemented
66C2×C4⋊Q8×C59—21no—
67C2×C4⋊Q8×C59C2211yescharacteristic
68C2×C4⋊Q8×C59C2211yescharacteristic
69C2×#125×C59—21no—
70C2×#125×C59C2211yescharacteristic
71C2×#125×C59C2211yescharacteristic
72C2×C22⋊Q8×C59—21no—
73C2×C22⋊Q8×C59—21no—
74C2×#117×C59C2211yescharacteristic
75C2×#117×C59C2211yescharacteristic
76C22×C4⋊C4×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118C2311yescharacteristic
79C22×D236C2311yescharacteristic
80C22×C22⋊D59—21no—
81C22×C4×D59—21no—
82C22×C59⋊C8C2311yescharacteristic
83C22×C59⋊C8C2311yescharacteristic
84C22×C59⋊C8C2311yescharacteristic
85C22×C59⋊C8C2311yescharacteristic
86#14273727—22no—
87#14273727C2314yes—
88#14273722—28no—
89#14273715—22no—
90#14273715C2314yes—
91#14273713—28no—
92#14273709—28no—
93#14273706—22no—
94#14273706C2314yes—
95#14273705—28no—
96#14273701—22no—
97#14273701C2314yes—
98C4×Dic118—22no—
99C4×Dic118C2314yes—
100C4×D236—22no—
101C4×D236C2314yes—
102C2×C4⋊Dic59—21no—
103C2×C4⋊Dic59C2311yescharacteristic
104C2×C4⋊Dic59C2311yescharacteristic
105C2×Dic59⋊C4—21no—
106C2×Dic59⋊C4—21no—
107C2×C22⋊Dic59—21no—
108C2×(C2×D59)⋊C4—21no—
109C2×(C2×D59)⋊C4—21no—
110C2×(C2×D59)⋊C4—21no—
111C2×(C2×D59)⋊C4—21no—
112C2×C4×Dic59—21no—
113#14273660C2314yes—
114#14273660C2314yes—
115#14273660C2314yes—
116#14273660C2314yes—
117#14273660C2314yes—
118#14273660C2314yes—
119#14273658C2314yes—
120#14273658C2314yes—
121C4⋊(C59⋊C8)C2314yes—
122C4⋊(C59⋊C8)C2314yes—
123#14273650C2314yes—
124#14273650C2314yes—
125#14273650C2314yes—
126#14273650C2314yes—
127#14273647C2314yes—
128#14273647C2314yes—
129#14273647C2314yes—
130#14273647C2314yes—
131C22⋊(C59⋊C8)C2314yes—
132C22⋊(C59⋊C8)C2314yes—
133#14273638C2314yes—
134C4×C59⋊C8C2314yes—
135C22×Q8×C59—21no—
136C22×Q8×C59—21no—
137C23×C4×C59—21no—
138C23×C4×C59C2311yescharacteristic
139C4⋊Q8×C59—28no—
140C4⋊Q8×C59—22no—
141C4⋊Q8×C59—22no—
142C4⋊Q8×C59C2314yes—
143C4⋊Q8×C59C2314yes—
144#125×C59—28no—
145#125×C59—22no—
146#125×C59—22no—
147#125×C59C2314yes—
148#125×C59C2314yes—
149C22⋊Q8×C59—28no—
150C22⋊Q8×C59—28no—
151#117×C59—22no—
152#117×C59D414yes—
153#117×C59C2314yes—
154#117×C59C2314yes—
155C2×C4⋊C4×C59—21no—
156C2×C4⋊C4×C59—22no—
157C2×C4⋊C4×C59—21no—
158C2×C4⋊C4×C59—21no—
159C2×C4⋊C4×C59—21no—
160C2×C4⋊C4×C59—21no—
161C2×C4⋊C4×C59—21no—
162C2×C4⋊C4×C59—21no—
163C2×C4⋊C4×C59D411yescharacteristic
164C2×C4⋊C4×C59D411yescharacteristic
165C2×C4⋊C4×C59C2311yescharacteristic
166C2×C4⋊C4×C59C2311yescharacteristic
167C2×C4⋊C4×C59C2311yescharacteristic
168C2×C4⋊C4×C59C2311yescharacteristic
169C2×C4⋊C4×C59C2314yes—
170C2×C22⋊C4×C59—21no—
171C2×C22⋊C4×C59D411yescharacteristic
172C2×C22⋊C4×C59D411yescharacteristic
173C2×C42×C59—21no—
174C2×C42×C59C2311yescharacteristic
175C2×C42×C59C2311yescharacteristic
176C24×C59C2×D411yescharacteristic
177C23×D59—21no—
178C2×Q8×C59—24no—
179C2×Q8×C59—24no—
180C2×Q8×C59—82no—
181C2×Q8×C59—82no—
182C22×C4×C59—22no—
183C22×C4×C59—22no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—24no—
189C22×C4×C59—82no—
190C22×C4×C59C2×D411yescharacteristic
191C22×C4×C59C2×D411yescharacteristic
192C22×C4×C59C2×D411yescharacteristic
193C22×C4×C59C2×D411yescharacteristic
194C22×C4×C59C2×D411yescharacteristic
195C22×C4×C59C2×D412yes—
196C22×C4×C59C2412yes—
197C22×C4×C59C2411yescharacteristic
198C2×C22⋊D59—24no—
199C2×C22⋊D59—82no—
200C22×Dic59—21no—
201C22×Dic59—21no—
202C22×Dic59—21no—
203C2×D236—22no—
204C2×D236—22no—
205C2×D236—21no—
206C2×D236C2412yes—
207C2×C4×D59—24no—
208C2×C4×D59—82no—
209C2×Dic118—22no—
210C2×Dic118—22no—
211C2×Dic118—21no—
212C2×Dic118—24no—
213C2×Dic118—82no—
214C2×Dic118C2412yes—
215C4⋊C4×C59—24no—
216C4⋊C4×C59—21no—
217C4⋊C4×C59—21no—
218C4⋊C4×C59—24no—
219C4⋊C4×C59—24no—
220C4⋊C4×C59—24no—
221C4⋊C4×C59—24no—
222C4⋊C4×C59—24no—
223C4⋊C4×C59—24no—
224C4⋊C4×C59—21no—
225C4⋊C4×C59—21no—
226C4⋊C4×C59C2×D414yes—
227C4⋊C4×C59C2×D414yes—
228C4⋊C4×C59C2412yes—
229C4⋊C4×C59C2412yes—
230C4⋊C4×C59C2412yes—
231C4⋊C4×C59C2412yes—
232C22⋊C4×C59—24no—
233C22⋊C4×C59C2×D414yes—
234C22⋊C4×C59C2×D414yes—
235C42×C59—24no—
236C42×C59C2×D412yes—
237C42×C59C2×D412yes—
238C42×C59C2412yes—
239C42×C59C2412yes—
240C22⋊Dic59—24no—
241(C2×D59)⋊C4—24no—
242(C2×D59)⋊C4—24no—
243(C2×D59)⋊C4—24no—
244(C2×D59)⋊C4—24no—
245C4⋊Dic59—24no—
246C4⋊Dic59—21no—
247C4⋊Dic59—21no—
248C4⋊Dic59C2412yes—
249C4⋊Dic59C2412yes—
250Dic59⋊C4—24no—
251Dic59⋊C4—24no—
252C4×Dic59—24no—
253C2×C59⋊C8—22no—
254C2×C59⋊C8—22no—
255C2×C59⋊C8—22no—
256C2×C59⋊C8—22no—
257C2×C59⋊C8C2412yes—
258C2×C59⋊C8C2412yes—
259C2×C59⋊C8C2412yes—
260C2×C59⋊C8C2412yes—
261C23×C59—22no—
262C23×C59—22no—
263C23×C59—22no—
264C23×C59C22×D412yes—
265C23×C59C22×D411yescharacteristic
266C22×D59—22no—
267C22×D59—42no—
268C22×D59—42no—
269C22×D59—42no—
270Q8×C59—84no—
271Q8×C59—84no—
272C2×C4×C59—22no—
273C2×C4×C59—22no—
274C2×C4×C59—22no—
275C2×C4×C59—22no—
276C2×C4×C59—22no—
277C2×C4×C59—24no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—42no—
285C2×C4×C59—42no—
286C2×C4×C59—42no—
287C2×C4×C59—42no—
288C2×C4×C59—84no—
289C2×C4×C59C22×D412yes—
290C2×C4×C59C22×D412yes—
291C2×C4×C59C22×D412yes—
292C2×C4×C59C22×D412yes—
293C2×C4×C59C22×D412yes—
294C2×C4×C59C22×D411yescharacteristic
295C2×C4×C592−1+412yes—
296C2×C4×C592−1+412yes—
297C2×C4×C59C2511yescharacteristic
298C22⋊D59—84no—
299C2×Dic59—22no—
300C2×Dic59—22no—
301C2×Dic59—22no—
302C2×Dic59—42no—
303C2×Dic59—42no—
304C2×Dic59—42no—
305D236—22no—
306D236—22no—
307D236—42no—
308C4×D59—84no—
309Dic118—22no—
310Dic118—22no—
311Dic118—42no—
312Dic118—84no—
313C59⋊C8—22no—
314C59⋊C8—22no—
315C59⋊C8—22no—
316C59⋊C8—22no—
317C2×#3243—591nomaximal, Sylow
318C22×C59—22no—
319C22×C59—22no—
320C22×C59—22no—
321C22×C59—44no—
322C22×C59#53612yes—
323C22×C59#57612yes—
324C22×C59#57812yes—
325C22×C59C23×D411yescharacteristic
326C2×D59—42no—
327C2×D59—42no—
328C2×D59—42no—
329C2×D59—84no—
330C4×C59—22no—
331C4×C59—22no—
332C4×C59—22no—
333C4×C59—22no—
334C4×C59—22no—
335C4×C59—42no—
336C4×C59—42no—
337C4×C59—42no—
338C4×C59—42no—
339C4×C59#53612yes—
340C4×C59C2×2−1+411yescharacteristic
341C4×C59C2×2−1+411yescharacteristic
342Dic59—42no—
343Dic59—42no—
344Dic59—42no—
345C2×#544D5911yescharacteristic, complemented
346C2×#542—591no—
347#3243—5916no—
348C2×#501—591no—
349C2×#500—591no—
350C2×#489—591no—
351C2×#488—591no—
352C2×#484—591no—
353C2×#485—591no—
354C2×#482—591no—
355C2×#480—591no—
356C2×#479—591no—
357C2×#477—591no—
358C2×#478—591no—
359C2×#474—591no—
360C2×#433—591no—
361C2×C59—42no—
362C2×C59#324314yescomplemented
363C2×C59C2×#53611yescharacteristic
364C2×C59C2×#57611yescharacteristic
365C2×C59C2×#57811yescharacteristic
366D59—82no—
367#544—24no—
368#544C2×D5918yescomplemented
369#542—598no—
370#542—1184no—
371C2×C4⋊Q8—21no—
372C2×C4⋊Q8—591no—
373C2×C4⋊Q8C2×D5911yescharacteristic
374C2×C4⋊Q8C2×D5911yescharacteristic
375C2×#126—1181no—
376C2×#125—21no—
377C2×#125C2×D5911yescharacteristic
378C2×#125C2×D5911yescharacteristic
379C2×#124—591no—
380C2×#124—1181no—
381C2×#123—1181no—
382C2×C22⋊Q8—21no—
383C2×C22⋊Q8—21no—
384C2×C22⋊Q8—591no—
385C2×C22⋊Q8—1181no—
386C2×#121—591no—
387C2×C4×Q8—591no—
388C2×C4×D4—591no—
389C2×#117C2×D5911yescharacteristic
390C2×#117C2×D5911yescharacteristic
391C22×C4⋊C4C2×D5911yescharacteristic
392#501—598no—
393#500—598no—
394#489—598no—
395#488—598no—
396#485—598no—
397#484—598no—
398#482—598no—
399#480—598no—
400#479—598no—
401#478—598no—
402#477—598no—
403#474—598no—
404#433—598no—
405C2×#107—591no—
406C2×#107—591no—
407C2×#107—591no—
408C2×#107—591no—
409C2×#107—591no—
410C2×#107—591no—
411C2×#106—591no—
412C2×#106—591no—
413C2×C4⋊C8—591no—
414C2×C4⋊C8—591no—
415C2×#103—591no—
416C2×#103—591no—
417C2×#103—591no—
418C2×#103—591no—
419C2×#102—591no—
420C2×#102—591no—
421C2×#102—591no—
422C2×#102—591no—
423C2×C22⋊C8—591no—
424C2×C22⋊C8—591no—
425C2×#97—591no—
426C2×C4×C8—591no—
427C59C2×#324311yescharacteristic, complemented, Sylow
428C22×Q8—21no—
429C22×Q8—21no—
430C22×Q8—591no—
431C22×Q8—1181no—
432C22×D4—591no—
433C22×D4—1181no—
434C23×C4—21no—
435C23×C4—1181no—
436C23×C4C22×D5911yescharacteristic
437C22×C8—591no—
438C22×C8—591no—
439C22×C8—591no—
440C22×C8—591no—
441C4⋊Q8—28no—
442C4⋊Q8—22no—
443C4⋊Q8—22no—
444C4⋊Q8—594no—
445C4⋊Q8—1182no—
446C4⋊Q8C22×D5914yes—
447C4⋊Q8C22×D5914yes—
448#126—1188no—
449#125—28no—
450#125—22no—
451#125—22no—
452#125C22×D5914yes—
453#125C22×D5914yes—
454#124—594no—
455#124—1188no—
456#124—1182no—
457#123—1188no—
458C22⋊Q8—28no—
459C22⋊Q8—28no—
460C22⋊Q8—594no—
461C22⋊Q8—1182no—
462C22⋊Q8—1188no—
463#121—594no—
464#121—1182no—
465C4×Q8—594no—
466C4×Q8—1182no—
467C4×D4—594no—
468C4×D4—1182no—
469#117—22no—
470#117C22⋊D5914yes—
471#117C22×D5914yes—
472#117C22×D5914yes—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—591no—
482C2×C4⋊C4—591no—
483C2×C4⋊C4—1181no—
484C2×C4⋊C4—1181no—
485C2×C4⋊C4—1181no—
486C2×C4⋊C4C22⋊D5911yescharacteristic
487C2×C4⋊C4C22⋊D5911yescharacteristic
488C2×C4⋊C4C22×D5911yescharacteristic
489C2×C4⋊C4C22×D5911yescharacteristic
490C2×C4⋊C4C22×D5914yes—
491C2×C4⋊C4C22×D5911yescharacteristic
492C2×C4⋊C4C22×D5911yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—1181no—
495C2×C22⋊C4—1181no—
496C2×C22⋊C4—1181no—
497C2×C22⋊C4—1181no—
498C2×C22⋊C4—1181no—
499C2×C22⋊C4C22⋊D5911yescharacteristic
500C2×C22⋊C4C22⋊D5911yescharacteristic
501C2×C42—21no—
502C2×C42—1181no—
503C2×C42C22×D5911yescharacteristic
504C2×C42C22×D5911yescharacteristic
505#107—594no—
506#107—594no—
507#107—594no—
508#107—594no—
509#107—594no—
510#107—594no—
511#106—594no—
512#106—594no—
513C4⋊C8—594no—
514C4⋊C8—594no—
515#103—594no—
516#103—594no—
517#103—594no—
518#103—594no—
519#102—594no—
520#102—594no—
521#102—594no—
522#102—594no—
523C22⋊C8—594no—
524C22⋊C8—594no—
525#97—594no—
526C4×C8—594no—
527C24—1181no—
528C24C2×C22⋊D5911yescharacteristic
529C2×Q8—24no—
530C2×Q8—24no—
531C2×Q8—82no—
532C2×Q8—82no—
533C2×Q8—592no—
534C2×Q8—1184no—
535C2×Q8—1181no—
536C2×Q8—1182no—
537C2×Q8—1182no—
538C2×Q8—4722no—
539C2×D4—592no—
540C2×D4—1184no—
541C2×D4—1181no—
542C2×D4—1182no—
543C2×D4—1182no—
544C2×D4—4722no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—24no—
552C22×C4—82no—
553C22×C4—1181no—
554C22×C4—1181no—
555C22×C4—1181no—
556C22×C4—1184no—
557C22×C4—4722no—
558C22×C4C2×C22⋊D5912yes—
559C22×C4C2×C22⋊D5911yescharacteristic
560C22×C4C2×C22⋊D5911yescharacteristic
561C22×C4C2×C22⋊D5911yescharacteristic
562C22×C4C2×C22⋊D5911yescharacteristic
563C22×C4C2×C22⋊D5911yescharacteristic
564C22×C4C23×D5912yes—
565C22×C4C23×D5911yescharacteristic
566C2×C8—592no—
567C2×C8—592no—
568C2×C8—592no—
569C2×C8—592no—
570C2×C8—1182no—
571C2×C8—1182no—
572C2×C8—1182no—
573C2×C8—1182no—
574C4⋊C4—24no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—592no—
586C4⋊C4—592no—
587C4⋊C4—1181no—
588C4⋊C4—1181no—
589C4⋊C4—1184no—
590C4⋊C4—1184no—
591C4⋊C4—1184no—
592C4⋊C4C2×C22⋊D5914yes—
593C4⋊C4C2×C22⋊D5914yes—
594C4⋊C4C23×D5912yes—
595C4⋊C4C23×D5912yes—
596C4⋊C4C23×D5912yes—
597C4⋊C4C23×D5912yes—
598C22⋊C4—24no—
599C22⋊C4—1184no—
600C22⋊C4—1184no—
601C22⋊C4—1184no—
602C22⋊C4—1184no—
603C22⋊C4—1184no—
604C22⋊C4C2×C22⋊D5914yes—
605C22⋊C4C2×C22⋊D5914yes—
606C42—24no—
607C42—1184no—
608C42C2×C22⋊D5912yes—
609C42C2×C22⋊D5912yes—
610C42C23×D5912yes—
611C42C23×D5912yes—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—1182no—
616C23—2362no—
617C23—2362no—
618C23—2362no—
619C23C22×C22⋊D5912yes—
620C23C22×C22⋊D5911yescharacteristic
621Q8—84no—
622Q8—84no—
623Q8—1182no—
624Q8—1182no—
625Q8—4724no—
626Q8—2362no—
627D4—1182no—
628D4—1182no—
629D4—4724no—
630D4—2362no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—84no—
648C2×C4—1182no—
649C2×C4—1182no—
650C2×C4—1182no—
651C2×C4—4724no—
652C2×C4—2362no—
653C2×C4—2362no—
654C2×C4—2362no—
655C2×C4C22×C22⋊D5912yes—
656C2×C4C22×C22⋊D5912yes—
657C2×C4C22×C22⋊D5912yes—
658C2×C4C22×C22⋊D5912yes—
659C2×C4C22×C22⋊D5912yes—
660C2×C4C22×C22⋊D5911yescharacteristic
661C2×C4#1427377512yes—
662C2×C4#1427377512yes—
663C2×C4C24×D5911yescharacteristic
664C8—1182no—
665C8—1182no—
666C8—1182no—
667C8—1182no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—44no—
672C22—4724no—
673C22—2362no—
674C22—2362no—
675C22—2362no—
676C22#1683797612yes—
677C22#1683820512yes—
678C22#1683821712yes—
679C22C23×C22⋊D5911yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—42no—
689C4—2362no—
690C4—2362no—
691C4—2362no—
692C4#1683797612yes—
693C4C2×#1427377511yescharacteristic
694C4C2×#1427377511yescharacteristic
695C2—42no—
696C2—4722no—
697C2#2143537914yesdirect product factor
698C2C2×#1683797611yescharacteristic
699C2C2×#1683820511yescharacteristic
700C2C2×#1683821711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#544C2
socleC23×C59C22×D4
prime radicalC2×#14273701C22
hypercenterC2×#544D59
hypocenterC59C2×#3243
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #21435379C2direct (N × H)
3. C2×#16837812C2semidirect
4. C2×#16837805C2semidirect
5. C2×#16837764C2semidirect
6. C2×#16837759C2semidirect
7. C2×#16837737C2semidirect
8. C2×#16837743C2semidirect
11. C2×#16837706C2semidirect
12. C2×#16837694C2semidirect
13. C2×#16837699C2semidirect
14. C2×#16837679C2semidirect
15. C2×#16837463C2semidirect
16. C2×C59×#544C2semidirect
29. #16837812C22semidirect
30. #16837805C22semidirect
31. #16837764C22semidirect
32. #16837759C22semidirect
33. #16837743C22semidirect
34. #16837737C22semidirect
37. #16837706C22semidirect
38. #16837699C22semidirect
39. #16837694C22semidirect
40. #16837679C22semidirect
41. #16837463C22semidirect
65. C59×#544C22semidirect
345. C2×#544D59semidirect
362. C2×C59#3243semidirect
368. #544C2×D59semidirect
427. C59C2×#3243semidirect
697. C2#21435379direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380232
#214353792
C2×#168378122
C2×#168378052
C2×#168377642
C2×#168377592
C2×#168377372
C2×#168377432
C2×#168377262
C2×#168377152
C2×#168377062
C2×#168376942
C2×#168376992
C2×#168376792
C2×#168374632
C2×C59×#5442
C2×#324359