Finite Group Databasebeta

← C2×#21436938 #29468486

Subgroups — C2×#21436938 #29468486

Order 15104.

1810 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838125C211yesmaximal, characteristic
2#21436938C2116yesmaximal, direct product factor
3C2×#16837772C211yesmaximal, characteristic, complemented
4C2×#16837764C211yesmaximal, characteristic
5C2×#16837759C211yesmaximal, characteristic
6C2×#16837706C211yesmaximal, characteristic, complemented
7C2×#16837694C211yesmaximal, characteristic, complemented
8C2×#16837699C211yesmaximal, characteristic
9C2×#16837624C211yesmaximal, characteristic
10C2×#16837624C211yesmaximal, characteristic
11C2×#16837612C211yesmaximal, characteristic, complemented
12C2×#16837533C211yesmaximal, characteristic, complemented
13C2×#16837507C211yesmaximal, characteristic, complemented
14C2×#16837500C211yesmaximal, characteristic
15C2×C4×#11745672C211yesmaximal, characteristic, complemented
16C2×C59×#557C211yesmaximal, characteristic, complemented
17C22×#11745672C2211yescharacteristic
18C22×#11745672C2211yescharacteristic
19C22×#11745671C2211yescharacteristic
20#16838125—24no—
21#16838125C2218yes—
22C2×#14273727C2211yescharacteristic
23C2×#14273722—21no—
24C2×#14273722—21no—
25C2×#14273715C2211yescharacteristic
26C2×#14273715C2211yescharacteristic
27C2×#14273703—21no—
28C2×C4×Dic118C2211yescharacteristic
29C2×C4×Dic118C2211yescharacteristic
30C2×C4×D236C2211yescharacteristic
31C2×#14273685—21no—
32#16837772C2218yescomplemented
33#16837764C2218yes—
34#16837759C2218yes—
35#16837706C2218yescomplemented
36#16837699C2218yes—
37#16837694C2218yescomplemented
38#16837624C2218yes—
39#16837624C2218yes—
40#16837612C2218yescomplemented
41#16837533C2218yescomplemented
42#16837507C2218yescomplemented
43#16837500C2218yes—
44C4×#11745672C2218yescomplemented
45C2×#14273660C2211yescharacteristic
46C2×#14273660C2211yescharacteristic
47C2×#14273658C2211yescharacteristic
48C2×C4⋊(C59⋊C8)C2211yescharacteristic
49C2×C4⋊(C59⋊C8)C2211yescharacteristic
50C2×C4⋊(C59⋊C8)C2211yescharacteristic
51C2×#14273651C2211yescharacteristic
52C2×#14273650C2211yescharacteristic
53C2×#14273650C2211yescharacteristic
54C2×#14273650C2211yescharacteristic
55C2×#14273650C2211yescharacteristic
56C2×#14273650C2211yescharacteristic
57C2×#14273650C2211yescharacteristic
58C2×#14273647C2211yescharacteristic
59C2×#14273647C2211yescharacteristic
60C2×#14273647C2211yescharacteristic
61C2×#14273638C2211yescharacteristic
62C2×#14273638C2211yescharacteristic
63C2×C4×C59⋊C8C2211yescharacteristic
64C59×#557—24no—
65C59×#557C2218yescomplemented
66C2×C4⋊Q8×C59—21no—
67C2×C4⋊Q8×C59C2211yescharacteristic
68C2×#125×C59—21no—
69C2×#125×C59—21no—
70C2×#125×C59C2211yescharacteristic
71C2×#125×C59C2211yescharacteristic
72C2×C4×Q8×C59—21no—
73C2×C4×Q8×C59C2211yescharacteristic
74C2×C4×Q8×C59C2211yescharacteristic
75C2×C4×Q8×C59C2211yescharacteristic
76C2×C4×Q8×C59C2211yescharacteristic
77C22×Dic118C2311yescharacteristic
78C22×Dic118C2311yescharacteristic
79C22×D236C2311yescharacteristic
80C22×C4×D59—21no—
81C2×#11745672—24no—
82C2×#11745672—24no—
83C2×#11745672C2314yes—
84C2×#11745672C2314yes—
85C2×#11745671—24no—
86C2×#11745671C2314yes—
87C22×C59⋊C8C2311yescharacteristic
88C22×C59⋊C8C2311yescharacteristic
89C22×C59⋊C8C2311yescharacteristic
90C22×C59⋊C8C2311yescharacteristic
91#14273727—22no—
92#14273727C2314yes—
93#14273722—28no—
94#14273722—28no—
95#14273715—22no—
96#14273715—22no—
97#14273715C2314yes—
98#14273715C2314yes—
99#14273703—28no—
100C4×Dic118—22no—
101C4×Dic118—22no—
102C4×Dic118C2314yes—
103C4×Dic118C2314yes—
104C4×D236—22no—
105C4×D236C2314yes—
106#14273685—28no—
107C2×C4⋊Dic59—21no—
108C2×C4⋊Dic59—21no—
109C2×C4⋊Dic59C2311yescharacteristic
110C2×Dic59⋊C4—21no—
111C2×Dic59⋊C4—21no—
112C2×(C2×D59)⋊C4—21no—
113C2×(C2×D59)⋊C4—21no—
114C2×(C2×D59)⋊C4—21no—
115C2×(C2×D59)⋊C4—21no—
116C2×(C2×D59)⋊C4—21no—
117C2×C4×Dic59—21no—
118C2×C4×Dic59—21no—
119#14273660C2314yes—
120#14273660C2314yes—
121#14273658C2314yes—
122C4⋊(C59⋊C8)C2314yes—
123C4⋊(C59⋊C8)C2314yes—
124C4⋊(C59⋊C8)C2314yes—
125#14273651C2314yes—
126#14273650C2314yes—
127#14273650C2314yes—
128#14273650C2314yes—
129#14273650C2314yes—
130#14273650C2314yes—
131#14273650C2314yes—
132#14273647C2314yes—
133#14273647C2314yes—
134#14273647C2314yes—
135#14273638C2314yes—
136#14273638C2314yes—
137C4×C59⋊C8C2314yes—
138C22×Q8×C59—21no—
139C22×Q8×C59D411yescharacteristic
140C22×Q8×C59C2311yescharacteristic
141C4⋊Q8×C59—28no—
142C4⋊Q8×C59—22no—
143C4⋊Q8×C59C2314yes—
144#125×C59—28no—
145#125×C59—28no—
146#125×C59—22no—
147#125×C59—22no—
148#125×C59C2314yes—
149#125×C59C2314yes—
150C4×Q8×C59—28no—
151C4×Q8×C59—22no—
152C4×Q8×C59—22no—
153C4×Q8×C59—22no—
154C4×Q8×C59D414yes—
155C4×Q8×C59C2314yes—
156C4×Q8×C59C2314yes—
157C4×Q8×C59C2314yes—
158C4×Q8×C59C2314yes—
159C2×C4⋊C4×C59—21no—
160C2×C4⋊C4×C59—21no—
161C2×C4⋊C4×C59—21no—
162C2×C4⋊C4×C59—21no—
163C2×C4⋊C4×C59—21no—
164C2×C4⋊C4×C59—21no—
165C2×C4⋊C4×C59—21no—
166C2×C4⋊C4×C59—21no—
167C2×C4⋊C4×C59D411yescharacteristic
168C2×C4⋊C4×C59D411yescharacteristic
169C2×C4⋊C4×C59D411yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C42×C59—21no—
174C2×C42×C59—21no—
175C2×C42×C59—21no—
176C2×C42×C59C2311yescharacteristic
177C2×C42×C59C2311yescharacteristic
178C2×C42×C59C2311yescharacteristic
179C23×D59—21no—
180C2×Q8×C59—21no—
181C2×Q8×C59—24no—
182C2×Q8×C59—22no—
183C2×Q8×C59—42no—
184C2×Q8×C59—44no—
185C2×Q8×C59C2×D414yes—
186C2×Q8×C59#4114yes—
187C2×Q8×C59C2412yes—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59—21no—
191C22×C4×C59—21no—
192C22×C4×C59C2×D411yescharacteristic
193C22×C4×C59C2×D411yescharacteristic
194C22×C4×C59C2×D411yescharacteristic
195C22×C4×C59C2×D411yescharacteristic
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2411yescharacteristic
199C22×Dic59—21no—
200C22×Dic59—21no—
201C22×Dic59—21no—
202C2×D236—22no—
203C2×D236—22no—
204C2×D236—21no—
205C2×D236C2412yes—
206C2×C4×D59—24no—
207C2×C4×D59—44no—
208C2×Dic118—22no—
209C2×Dic118—22no—
210C2×Dic118—22no—
211C2×Dic118—22no—
212C2×Dic118—21no—
213C2×Dic118—21no—
214C2×Dic118C2412yes—
215C2×Dic118C2412yes—
216C4⋊C4×C59—24no—
217C4⋊C4×C59—24no—
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×C59—21no—
227C4⋊C4×C59C2×D414yes—
228C4⋊C4×C59C2×D414yes—
229C4⋊C4×C59C2×D414yes—
230C4⋊C4×C59C2412yes—
231C4⋊C4×C59C2412yes—
232C4⋊C4×C59C2412yes—
233C42×C59—24no—
234C42×C59—24no—
235C42×C59—24no—
236C42×C59C2×D412yes—
237C42×C59C2×D412yes—
238C42×C59C2×D412yes—
239C42×C59C2412yes—
240C42×C59C2412yes—
241C42×C59C2412yes—
242#11745672—28no—
243#11745672—28no—
244#11745671—28no—
245(C2×D59)⋊C4—24no—
246(C2×D59)⋊C4—24no—
247(C2×D59)⋊C4—24no—
248(C2×D59)⋊C4—24no—
249(C2×D59)⋊C4—24no—
250C4⋊Dic59—24no—
251C4⋊Dic59—24no—
252C4⋊Dic59—21no—
253C4⋊Dic59C2412yes—
254Dic59⋊C4—24no—
255Dic59⋊C4—24no—
256C4×Dic59—24no—
257C4×Dic59—24no—
258C2×C59⋊C8—22no—
259C2×C59⋊C8—22no—
260C2×C59⋊C8—22no—
261C2×C59⋊C8—22no—
262C2×C59⋊C8C2412yes—
263C2×C59⋊C8C2412yes—
264C2×C59⋊C8C2412yes—
265C2×C59⋊C8C2412yes—
266C23×C59C22×D411yescharacteristic
267C22×D59—22no—
268C22×D59—42no—
269C22×D59—42no—
270C22×D59—42no—
271Q8×C59—24no—
272Q8×C59—22no—
273Q8×C59—44no—
274Q8×C59—48no—
275Q8×C59C2×#4114yes—
276C2×C4×C59—24no—
277C2×C4×C59—22no—
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—22no—
285C2×C4×C59—22no—
286C2×C4×C59—22no—
287C2×C4×C59—42no—
288C2×C4×C59—42no—
289C2×C4×C59—42no—
290C2×C4×C59C22×D412yes—
291C2×C4×C59C22×D412yes—
292C2×C4×C59C22×D412yes—
293C2×C4×C59C22×D412yes—
294C2×C4×C59C22×D412yes—
295C2×C4×C59C22×D412yes—
296C2×C4×C59C22×D411yescharacteristic
297C2×C4×C59C2×#4112yes—
298C2×C4×C592−1+412yes—
299C2×C4×C59C2511yescharacteristic
300C2×Dic59—22no—
301C2×Dic59—22no—
302C2×Dic59—22no—
303C2×Dic59—42no—
304C2×Dic59—42no—
305C2×Dic59—42no—
306D236—22no—
307D236—22no—
308D236—42no—
309C4×D59—48no—
310Dic118—22no—
311Dic118—22no—
312Dic118—22no—
313Dic118—22no—
314Dic118—42no—
315Dic118—42no—
316C59⋊C8—22no—
317C59⋊C8—22no—
318C59⋊C8—22no—
319C59⋊C8—22no—
320C2×#3377—591nomaximal, Sylow
321C22×C59#54812yes—
322C22×C59#57512yes—
323C22×C59#57812yes—
324C22×C59C23×D411yescharacteristic
325C2×D59—42no—
326C2×D59—42no—
327C2×D59—42no—
328C2×D59—84no—
329C4×C59—24no—
330C4×C59—22no—
331C4×C59—22no—
332C4×C59—22no—
333C4×C59—22no—
334C4×C59—22no—
335C4×C59—22no—
336C4×C59—42no—
337C4×C59—42no—
338C4×C59—42no—
339C4×C59#54812yes—
340C4×C59C22×#4111yescharacteristic
341C4×C59C2×2−1+411yescharacteristic
342Dic59—42no—
343Dic59—42no—
344Dic59—42no—
345C2×#557D5911yescharacteristic, complemented
346C2×#556—591no—
347#3377—5916no—
348C2×#491—591no—
349C2×#489—591no—
350C2×#488—591no—
351C2×#479—591no—
352C2×#477—591no—
353C2×#478—591no—
354C2×#464—591no—
355C2×#464—591no—
356C2×#462—591no—
357C2×#446—591no—
358C2×#441—591no—
359C2×#440—591no—
360C2×C4×Q16—591no—
361C2×C59#337714yescomplemented
362C2×C59C2×#54811yescharacteristic
363C2×C59C2×#57511yescharacteristic
364C2×C59C2×#57811yescharacteristic
365D59—82no—
366C22×Q16—591no—
367C22×Q16—591no—
368C22×SD16—591no—
369#557—24no—
370#557C2×D5918yescomplemented
371#556—598no—
372#556—1184no—
373C2×C4⋊Q8—21no—
374C2×C4⋊Q8—591no—
375C2×C4⋊Q8C2×D5911yescharacteristic
376C2×#126—1181no—
377C2×#126—1181no—
378C2×#125—21no—
379C2×#125—21no—
380C2×#125C2×D5911yescharacteristic
381C2×#125C2×D5911yescharacteristic
382C2×#124—591no—
383C2×#124—591no—
384C2×C22⋊Q8—1181no—
385C2×C4×Q8—21no—
386C2×C4×Q8—591no—
387C2×C4×Q8—591no—
388C2×C4×Q8C2×D5911yescharacteristic
389C2×C4×Q8C2×D5911yescharacteristic
390C2×C4×Q8C2×D5911yescharacteristic
391C2×C4×Q8C2×D5911yescharacteristic
392C2×C4×D4—591no—
393C2×#117—1181no—
394#491—598no—
395#489—598no—
396#488—598no—
397#479—598no—
398#478—598no—
399#477—598no—
400#464—598no—
401#464—598no—
402#462—598no—
403#446—598no—
404#441—598no—
405#440—598no—
406C4×Q16—598no—
407C2×#107—591no—
408C2×#107—591no—
409C2×#106—591no—
410C2×C4⋊C8—591no—
411C2×C4⋊C8—591no—
412C2×C4⋊C8—591no—
413C2×#103—591no—
414C2×#103—591no—
415C2×#103—591no—
416C2×#103—591no—
417C2×#103—591no—
418C2×#103—591no—
419C2×#103—591no—
420C2×#102—591no—
421C2×#102—591no—
422C2×#102—591no—
423C2×#97—591no—
424C2×#97—591no—
425C2×C4×C8—591no—
426C59C2×#337711yescharacteristic, complemented, Sylow
427C22×Q8—21no—
428C22×Q8—591no—
429C22×Q8—591no—
430C22×Q8C22⋊D5911yescharacteristic
431C22×Q8C22×D5911yescharacteristic
432C22×D4—591no—
433C23×C4—1181no—
434C2×Q16—594no—
435C2×Q16—594no—
436C2×Q16—1184no—
437C2×Q16—1184no—
438C2×SD16—594no—
439C2×SD16—1184no—
440C22×C8—591no—
441C22×C8—591no—
442C22×C8—591no—
443C22×C8—591no—
444C4⋊Q8—28no—
445C4⋊Q8—22no—
446C4⋊Q8—594no—
447C4⋊Q8—1182no—
448C4⋊Q8C22×D5914yes—
449#126—1188no—
450#126—1188no—
451#125—28no—
452#125—28no—
453#125—22no—
454#125—22no—
455#125C22×D5914yes—
456#125C22×D5914yes—
457#124—594no—
458#124—594no—
459#124—1182no—
460#124—1182no—
461C22⋊Q8—1188no—
462C4×Q8—28no—
463C4×Q8—22no—
464C4×Q8—22no—
465C4×Q8—22no—
466C4×Q8—594no—
467C4×Q8—594no—
468C4×Q8—1182no—
469C4×Q8—1182no—
470C4×Q8C22⋊D5914yes—
471C4×Q8C22×D5914yes—
472C4×Q8C22×D5914yes—
473C4×Q8C22×D5914yes—
474C4×Q8C22×D5914yes—
475C4×D4—594no—
476C4×D4—1182no—
477#117—1188no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—591no—
487C2×C4⋊C4—1181no—
488C2×C4⋊C4—1181no—
489C2×C4⋊C4—1181no—
490C2×C4⋊C4—1181no—
491C2×C4⋊C4C22⋊D5911yescharacteristic
492C2×C4⋊C4C22⋊D5911yescharacteristic
493C2×C4⋊C4C22⋊D5911yescharacteristic
494C2×C4⋊C4C22×D5911yescharacteristic
495C2×C4⋊C4C22×D5911yescharacteristic
496C2×C4⋊C4C22×D5911yescharacteristic
497C2×C22⋊C4—1181no—
498C2×C22⋊C4—1181no—
499C2×C22⋊C4—1181no—
500C2×C22⋊C4—1181no—
501C2×C22⋊C4—1181no—
502C2×C42—21no—
503C2×C42—21no—
504C2×C42—21no—
505C2×C42—1181no—
506C2×C42—1181no—
507C2×C42C22×D5911yescharacteristic
508C2×C42C22×D5911yescharacteristic
509C2×C42C22×D5911yescharacteristic
510#107—594no—
511#107—594no—
512#106—594no—
513C4⋊C8—594no—
514C4⋊C8—594no—
515C4⋊C8—594no—
516#103—594no—
517#103—594no—
518#103—594no—
519#103—594no—
520#103—594no—
521#103—594no—
522#103—594no—
523#102—594no—
524#102—594no—
525#102—594no—
526#97—594no—
527#97—594no—
528C4×C8—594no—
529C24—1181no—
530C2×Q8—21no—
531C2×Q8—24no—
532C2×Q8—22no—
533C2×Q8—42no—
534C2×Q8—44no—
535C2×Q8—592no—
536C2×Q8—592no—
537C2×Q8—1181no—
538C2×Q8—1181no—
539C2×Q8—1182no—
540C2×Q8—1182no—
541C2×Q8—1182no—
542C2×Q8—1182no—
543C2×Q8#1174568914yes—
544C2×Q8C2×C22⋊D5914yes—
545C2×Q8C23×D5912yes—
546C2×D4—592no—
547C2×D4—1181no—
548C2×D4—1182no—
549C2×D4—1182no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—1181no—
555C22×C4—1181no—
556C22×C4—1181no—
557C22×C4—1184no—
558C22×C4—2364no—
559C22×C4C2×C22⋊D5911yescharacteristic
560C22×C4C2×C22⋊D5911yescharacteristic
561C22×C4C2×C22⋊D5911yescharacteristic
562C22×C4C2×C22⋊D5911yescharacteristic
563C22×C4C2×C22⋊D5911yescharacteristic
564C22×C4C2×C22⋊D5911yescharacteristic
565C22×C4C23×D5911yescharacteristic
566Q16—1188no—
567Q16—1188no—
568SD16—1188no—
569C2×C8—592no—
570C2×C8—592no—
571C2×C8—592no—
572C2×C8—592no—
573C2×C8—1182no—
574C2×C8—1182no—
575C2×C8—1182no—
576C2×C8—1182no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—592no—
589C4⋊C4—1181no—
590C4⋊C4—1184no—
591C4⋊C4—1184no—
592C4⋊C4—1184no—
593C4⋊C4—1184no—
594C4⋊C4C2×C22⋊D5914yes—
595C4⋊C4C2×C22⋊D5914yes—
596C4⋊C4C2×C22⋊D5914yes—
597C4⋊C4C23×D5912yes—
598C4⋊C4C23×D5912yes—
599C4⋊C4C23×D5912yes—
600C22⋊C4—1184no—
601C22⋊C4—1184no—
602C22⋊C4—1184no—
603C22⋊C4—1184no—
604C22⋊C4—1184no—
605C42—24no—
606C42—24no—
607C42—24no—
608C42—1184no—
609C42—1184no—
610C42C2×C22⋊D5912yes—
611C42C2×C22⋊D5912yes—
612C42C2×C22⋊D5912yes—
613C42C23×D5912yes—
614C42C23×D5912yes—
615C42C23×D5912yes—
616C23—1182no—
617C23—2362no—
618C23—2362no—
619C23—2362no—
620C23C22×C22⋊D5911yescharacteristic
621Q8—22no—
622Q8—24no—
623Q8—44no—
624Q8—48no—
625Q8—1182no—
626Q8—1182no—
627Q8—1182no—
628Q8—1182no—
629Q8—2362no—
630Q8—2362no—
631Q8C2×#1174568914yes—
632D4—1182no—
633D4—1182no—
634D4—2362no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—24no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—1182no—
650C2×C4—1182no—
651C2×C4—1182no—
652C2×C4—2368no—
653C2×C4—2362no—
654C2×C4—2362no—
655C2×C4—2362no—
656C2×C4C22×C22⋊D5912yes—
657C2×C4C22×C22⋊D5912yes—
658C2×C4C22×C22⋊D5912yes—
659C2×C4C22×C22⋊D5912yes—
660C2×C4C22×C22⋊D5912yes—
661C2×C4C22×C22⋊D5912yes—
662C2×C4C22×C22⋊D5911yescharacteristic
663C2×C4C2×#1174568912yes—
664C2×C4#1427377512yes—
665C2×C4C24×D5911yescharacteristic
666C8—1182no—
667C8—1182no—
668C8—1182no—
669C8—1182no—
670C22—4724no—
671C22—2362no—
672C22—2362no—
673C22—2362no—
674C22#1683806312yes—
675C22#1683820012yes—
676C22#1683821712yes—
677C22C23×C22⋊D5911yescharacteristic
678C4—22no—
679C4—22no—
680C4—22no—
681C4—24no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—2362no—
689C4—2362no—
690C4—2362no—
691C4#1683806312yes—
692C4C22×#1174568911yescharacteristic
693C4C2×#1427377511yescharacteristic
694C2—4722no—
695C2#2143693814yesdirect product factor
696C2C2×#1683806311yescharacteristic
697C2C2×#1683820011yescharacteristic
698C2C2×#1683821711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#557C2
socleC23×C59C22×D4
prime radicalC22×D236C23
hypercenterC2×#557D59
hypocenterC59C2×#3377
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #21436938C2direct (N × H)
3. C2×#16837772C2semidirect
6. C2×#16837706C2semidirect
7. C2×#16837694C2semidirect
11. C2×#16837612C2semidirect
12. C2×#16837533C2semidirect
13. C2×#16837507C2semidirect
15. C2×C4×#11745672C2semidirect
16. C2×C59×#557C2semidirect
32. #16837772C22semidirect
35. #16837706C22semidirect
37. #16837694C22semidirect
40. #16837612C22semidirect
41. #16837533C22semidirect
42. #16837507C22semidirect
44. C4×#11745672C22semidirect
65. C59×#557C22semidirect
345. C2×#557D59semidirect
361. C2×C59#3377semidirect
370. #557C2×D59semidirect
426. C59C2×#3377semidirect
695. C2#21436938direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381252
#214369382
C2×#168377722
C2×#168377642
C2×#168377592
C2×#168377062
C2×#168376942
C2×#168376992
C2×#168376242
C2×#168376122
C2×#168375332
C2×#168375072
C2×#168375002
C2×C4×#117456722
C2×C59×#5572
C2×#337759