Finite Group Databasebeta

← C2×#21436536 #29467220

Subgroups — C2×#21436536 #29467220

Order 15104.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838056C211yesmaximal, characteristic
2#21436536C2116yesmaximal, direct product factor
3C2×#16837812C211yesmaximal, characteristic, complemented
4C2×#16837735C211yesmaximal, characteristic, complemented
5C2×#16837726C211yesmaximal, characteristic, complemented
6C2×#16837730C211yesmaximal, characteristic, complemented
7C2×#16837715C211yesmaximal, characteristic, complemented
8C2×#16837697C211yesmaximal, characteristic, complemented
9C2×#16837699C211yesmaximal, characteristic, complemented
10C2×#16837650C211yesmaximal, characteristic, complemented
11C2×#16837633C211yesmaximal, characteristic, complemented
12C2×#16837500C211yesmaximal, characteristic, complemented
13C2×#16837474C211yesmaximal, characteristic, complemented
14C2×#16837445C211yesmaximal, characteristic, complemented
15C22×#14273660C211yesmaximal, characteristic, complemented
16C2×C59×#552C211yesmaximal, characteristic, complemented
17C22×#11745687—21no—
18C22×#11745671C2211yescharacteristic
19C22×#11745664C2211yescharacteristic
20C23×C59⋊C8C2211yescharacteristic
21#16838056—24no—
22#16838056C2218yes—
23C2×#14273727C2211yescharacteristic
24C2×#14273711—21no—
25C2×#14273711—21no—
26C2×#14273707—21no—
27C2×#14273701C2211yescharacteristic
28C2×#14273701C2211yescharacteristic
29C2×C4×D236C2211yescharacteristic
30C22×C4⋊Dic59C2211yescharacteristic
31C22×C4⋊Dic59C2211yescharacteristic
32#16837812C2218yescomplemented
33#16837735C2218yescomplemented
34#16837730C2218yescomplemented
35#16837726C2218yescomplemented
36#16837715C2218yescomplemented
37#16837699C2218yescomplemented
38#16837697C2218yescomplemented
39#16837650C2218yescomplemented
40#16837633C2218yescomplemented
41#16837500C2218yescomplemented
42#16837474C2218yescomplemented
43#16837445C2218yescomplemented
44C2×#14273660C2211yescharacteristic
45C2×#14273660C2211yescharacteristic
46C2×#14273660C2211yescharacteristic
47C2×#14273660C2211yescharacteristic
48C2×#14273660C2211yescharacteristic
49C2×#14273660C2211yescharacteristic
50C2×#14273660C2218yescomplemented
51C2×#14273658C2211yescharacteristic
52C2×#14273658C2211yescharacteristic
53C2×#14273658C2211yescharacteristic
54C2×C4⋊(C59⋊C8)C2211yescharacteristic
55C2×#14273651C2211yescharacteristic
56C2×#14273651C2211yescharacteristic
57C2×#14273651C2211yescharacteristic
58C2×#14273647C2211yescharacteristic
59C2×#14273647C2211yescharacteristic
60C2×#14273647C2211yescharacteristic
61C2×C22⋊(C59⋊C8)C2211yescharacteristic
62C2×C22⋊(C59⋊C8)C2211yescharacteristic
63C2×#14273638C2211yescharacteristic
64C59×#552—24no—
65C59×#552C2218yescomplemented
66C2×#126×C59—21no—
67C2×#125×C59—21no—
68C2×#125×C59C2211yescharacteristic
69C2×#123×C59—21no—
70C2×C22⋊Q8×C59C2211yescharacteristic
71C2×C22⋊Q8×C59C2211yescharacteristic
72C2×C4×Q8×C59C2211yescharacteristic
73C2×C4×D4×C59C2211yescharacteristic
74C2×#117×C59—21no—
75C2×#117×C59C2211yescharacteristic
76C22×C4⋊C4×C59C2211yescharacteristic
77C2×#11745687—28no—
78C2×#11745687—48no—
79C22×Dic118—21no—
80C22×D236C2311yescharacteristic
81C22×C22⋊D59—21no—
82C22×C22⋊D59—21no—
83C23×Dic59—21no—
84C23×Dic59—21no—
85C22×C4×D59—21no—
86C2×#11745671—24no—
87C2×#11745671C2314yes—
88C2×#11745664—24no—
89C2×#11745664C2314yes—
90C22×C59⋊C8—24no—
91C22×C59⋊C8C2314yes—
92C22×C59⋊C8C2311yescharacteristic
93C22×C59⋊C8C2311yescharacteristic
94C22×C59⋊C8C2311yescharacteristic
95C22×C59⋊C8C2311yescharacteristic
96#14273727—22no—
97#14273727C2314yes—
98#14273711—28no—
99#14273711—28no—
100#14273707—28no—
101#14273701—22no—
102#14273701—22no—
103#14273701C2314yes—
104#14273701C2314yes—
105C4×D236—22no—
106C4×D236C2314yes—
107C2×C4⋊Dic59—21no—
108C2×C4⋊Dic59—21no—
109C2×C4⋊Dic59—21no—
110C2×C4⋊Dic59—22no—
111C2×C4⋊Dic59—22no—
112C2×C4⋊Dic59C2311yescharacteristic
113C2×C4⋊Dic59C2311yescharacteristic
114C2×C4⋊Dic59C2311yescharacteristic
115C2×C4⋊Dic59C2314yes—
116C2×C4⋊Dic59C2314yes—
117C2×(C2×D59)⋊C4—21no—
118C2×(C2×D59)⋊C4—21no—
119C2×(C2×D59)⋊C4—21no—
120#14273660C2314yes—
121#14273660C2314yes—
122#14273660C2314yes—
123#14273660C2314yes—
124#14273660C2314yes—
125#14273660C2314yes—
126#14273658C2314yes—
127#14273658C2314yes—
128#14273658C2314yes—
129C4⋊(C59⋊C8)C2314yes—
130#14273651C2314yes—
131#14273651C2314yes—
132#14273651C2314yes—
133#14273647C2314yes—
134#14273647C2314yes—
135#14273647C2314yes—
136C22⋊(C59⋊C8)C2314yes—
137C22⋊(C59⋊C8)C2314yes—
138#14273638C2314yes—
139C22×Q8×C59C2311yescharacteristic
140C22×D4×C59D411yescharacteristic
141C23×C4×C59—21no—
142C23×C4×C59C2311yescharacteristic
143C23×C4×C59C2311yescharacteristic
144#126×C59—28no—
145#125×C59—28no—
146#125×C59—22no—
147#125×C59C2314yes—
148#123×C59—28no—
149C22⋊Q8×C59—22no—
150C22⋊Q8×C59—22no—
151C22⋊Q8×C59C2314yes—
152C22⋊Q8×C59C2314yes—
153C4×Q8×C59—22no—
154C4×Q8×C59C2314yes—
155C4×D4×C59D414yes—
156C4×D4×C59C2314yes—
157#117×C59—22no—
158#117×C59—28no—
159#117×C59C2314yes—
160C2×C4⋊C4×C59—21no—
161C2×C4⋊C4×C59—22no—
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×C59C2311yescharacteristic
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2314yes—
172C2×C22⋊C4×C59—21no—
173C2×C22⋊C4×C59—21no—
174C2×C22⋊C4×C59—21no—
175C2×C22⋊C4×C59D411yescharacteristic
176C2×C22⋊C4×C59D411yescharacteristic
177C2×C42×C59—21no—
178C2×C42×C59—21no—
179C2×C42×C59C2311yescharacteristic
180C24×C59C2×D411yescharacteristic
181C24×C59C2×D411yescharacteristic
182C23×D59—21no—
183C2×Q8×C59—21no—
184C2×Q8×C59—22no—
185C2×Q8×C59—22no—
186C2×Q8×C59C2412yes—
187C2×D4×C59—24no—
188C2×D4×C59C2×D414yes—
189C22×C4×C59—22no—
190C22×C4×C59—22no—
191C22×C4×C59—22no—
192C22×C4×C59—22no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59—21no—
197C22×C4×C59—24no—
198C22×C4×C59—44no—
199C22×C4×C59C2×D411yescharacteristic
200C22×C4×C59C2×D411yescharacteristic
201C22×C4×C59C2×D411yescharacteristic
202C22×C4×C59C2×D411yescharacteristic
203C22×C4×C59C2×D412yes—
204C22×C4×C59C2×D412yes—
205C22×C4×C59C2412yes—
206C22×C4×C59C2412yes—
207C22×C4×C59C2411yescharacteristic
208C2×C22⋊D59—24no—
209C2×C22⋊D59—24no—
210C2×C22⋊D59—44no—
211C2×C22⋊D59—44no—
212C22×Dic59—21no—
213C22×Dic59—21no—
214C22×Dic59—21no—
215C22×Dic59—24no—
216C22×Dic59—24no—
217C22×Dic59—44no—
218C22×Dic59—44no—
219#11745687—432no—
220C2×D236—22no—
221C2×D236—22no—
222C2×D236—21no—
223C2×D236C2412yes—
224C2×C4×D59—24no—
225C2×C4×D59—44no—
226C2×Dic118—24no—
227C2×Dic118—44no—
228C4⋊C4×C59—21no—
229C4⋊C4×C59—21no—
230C4⋊C4×C59—24no—
231C4⋊C4×C59—24no—
232C4⋊C4×C59—24no—
233C4⋊C4×C59—24no—
234C4⋊C4×C59—24no—
235C4⋊C4×C59—24no—
236C4⋊C4×C59—21no—
237C4⋊C4×C59C2×D414yes—
238C4⋊C4×C59C2412yes—
239C4⋊C4×C59C2412yes—
240C4⋊C4×C59C2412yes—
241C22⋊C4×C59—24no—
242C22⋊C4×C59—24no—
243C22⋊C4×C59—24no—
244C22⋊C4×C59C2×D414yes—
245C22⋊C4×C59C2×D414yes—
246C42×C59—24no—
247C42×C59—24no—
248C42×C59C2×D412yes—
249C42×C59C2412yes—
250#11745671—28no—
251(C2×D59)⋊C4—24no—
252(C2×D59)⋊C4—24no—
253(C2×D59)⋊C4—24no—
254C4⋊Dic59—21no—
255C4⋊Dic59—21no—
256C4⋊Dic59—21no—
257C4⋊Dic59—24no—
258C4⋊Dic59—24no—
259C4⋊Dic59—24no—
260C4⋊Dic59C2412yes—
261C4⋊Dic59C2412yes—
262C4⋊Dic59C2412yes—
263#11745664—28no—
264C2×C59⋊C8—22no—
265C2×C59⋊C8—22no—
266C2×C59⋊C8—22no—
267C2×C59⋊C8—28no—
268C2×C59⋊C8#4114yescomplemented
269C2×C59⋊C8C2412yes—
270C2×C59⋊C8C2412yes—
271C2×C59⋊C8C2412yes—
272C2×C59⋊C8C2412yes—
273C23×C59—22no—
274C23×C59—22no—
275C23×C59—22no—
276C23×C59—22no—
277C23×C59—22no—
278C23×C59AGL(1,ℤ/8)14yes—
279C23×C59C22×D412yes—
280C23×C59C22×D412yes—
281C23×C59C22×D411yescharacteristic
282C22×D59—22no—
283C22×D59—42no—
284C22×D59—42no—
285C22×D59—42no—
286Q8×C59—22no—
287Q8×C59—22no—
288Q8×C59—42no—
289D4×C59—28no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—24no—
295C2×C4×C59—24no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—22no—
301C2×C4×C59—22no—
302C2×C4×C59—22no—
303C2×C4×C59—22no—
304C2×C4×C59—42no—
305C2×C4×C59—48no—
306C2×C4×C59—42no—
307C2×C4×C59—42no—
308C2×C4×C59—42no—
309C2×C4×C59C22×D412yes—
310C2×C4×C59C22×D412yes—
311C2×C4×C59C22×D412yes—
312C2×C4×C59C22×D412yes—
313C2×C4×C59C22×D411yescharacteristic
314C2×C4×C59C2×#4112yes—
315C2×C4×C592−1+412yes—
316C2×C4×C59C2511yescharacteristic
317C22⋊D59—48no—
318C22⋊D59—48no—
319C2×Dic59—22no—
320C2×Dic59—22no—
321C2×Dic59—22no—
322C2×Dic59—48no—
323C2×Dic59—42no—
324C2×Dic59—42no—
325C2×Dic59—42no—
326C2×Dic59—48no—
327D236—22no—
328D236—22no—
329D236—42no—
330C4×D59—48no—
331Dic118—48no—
332C59⋊C8—22no—
333C59⋊C8—22no—
334C59⋊C8—22no—
335C59⋊C8C2×#4114yescomplemented
336C2×#3343—591nomaximal, Sylow
337C22×C59—28no—
338C22×C59—22no—
339C22×C59—22no—
340C22×C59—22no—
341C22×C59—22no—
342C22×C59—22no—
343C22×C59—44no—
344C22×C59#54712yes—
345C22×C59C2×AGL(1,ℤ/8)14yes—
346C22×C59C2×AGL(1,ℤ/8)12yes—
347C22×C59#57812yes—
348C22×C59C23×D411yescharacteristic
349C2×D59—42no—
350C2×D59—42no—
351C2×D59—42no—
352C2×D59—84no—
353C4×C59—22no—
354C4×C59—22no—
355C4×C59—22no—
356C4×C59—22no—
357C4×C59—42no—
358C4×C59—42no—
359C4×C59—42no—
360C4×C59—42no—
361C4×C59#54712yes—
362C4×C59C22×#4111yescharacteristic
363C4×C59C2×2−1+411yescharacteristic
364Dic59—42no—
365Dic59—42no—
366Dic59—42no—
367C2×#552D5911yescharacteristic, complemented
368C2×#547—591no—
369#3343—5916no—
370C2×#501—591no—
371C2×#484—591no—
372C2×#482—591no—
373C2×#483—591no—
374C2×#480—591no—
375C2×#477—591no—
376C2×#478—591no—
377C2×#468—591no—
378C2×#465—591no—
379C2×#440—591no—
380C2×#435—591no—
381C2×#428—591no—
382C22×#107—591no—
383C2×C59—24no—
384C2×C59—42no—
385C2×C59#334314yescomplemented
386C2×C59C2×#54711yescharacteristic
387C2×C59C22×AGL(1,ℤ/8)11yescharacteristic
388C2×C59C2×#57811yescharacteristic
389D59—82no—
390C22×#41—1181no—
391C22×SD16—591no—
392C22×M16—591no—
393C23×C8—591no—
394#552—24no—
395#552C2×D5918yescomplemented
396#547—598no—
397#547—1184no—
398C2×C4⋊Q8—591no—
399C2×#126—21no—
400C2×#125—21no—
401C2×#125C2×D5911yescharacteristic
402C2×#123—21no—
403C2×#123—1181no—
404C2×#123—1181no—
405C2×C22⋊Q8—1181no—
406C2×C22⋊Q8C2×D5911yescharacteristic
407C2×C22⋊Q8C2×D5911yescharacteristic
408C2×#121—591no—
409C2×#121—591no—
410C2×C4×Q8C2×D5911yescharacteristic
411C2×C4×D4—591no—
412C2×C4×D4C2×D5911yescharacteristic
413C2×#117—21no—
414C2×#117C2×D5911yescharacteristic
415C22×C4⋊C4—591no—
416C22×C4⋊C4—591no—
417C22×C4⋊C4C2×D5911yescharacteristic
418#501—598no—
419#484—598no—
420#483—598no—
421#482—598no—
422#480—598no—
423#478—598no—
424#477—598no—
425#468—598no—
426#465—598no—
427#440—598no—
428#435—598no—
429#428—598no—
430C2×#107—591no—
431C2×#107—591no—
432C2×#107—591no—
433C2×#107—591no—
434C2×#107—598no—
435C2×#107—591no—
436C2×#107—591no—
437C2×#106—591no—
438C2×#106—591no—
439C2×#106—591no—
440C2×C4⋊C8—591no—
441C2×#103—591no—
442C2×#103—591no—
443C2×#103—591no—
444C2×#102—591no—
445C2×#102—591no—
446C2×#102—591no—
447C2×C22⋊C8—591no—
448C2×C22⋊C8—591no—
449C2×#97—591no—
450C59C2×#334311yescharacteristic, complemented, Sylow
451C2×#41—1188no—
452C2×#41—2368no—
453C22×Q8—1181no—
454C22×Q8C22×D5911yescharacteristic
455C22×D4—591no—
456C22×D4—1181no—
457C22×D4—1181no—
458C22×D4C22⋊D5911yescharacteristic
459C23×C4—21no—
460C23×C4—1181no—
461C23×C4—1181no—
462C23×C4—1181no—
463C23×C4C22×D5911yescharacteristic
464C23×C4C22×D5911yescharacteristic
465C2×SD16—594no—
466C2×SD16—1184no—
467C2×M16—594no—
468C2×M16—1184no—
469C22×C8—591no—
470C22×C8—591no—
471C22×C8—594no—
472C22×C8—591no—
473C22×C8—591no—
474C22×C8—1184no—
475C4⋊Q8—594no—
476C4⋊Q8—1182no—
477#126—28no—
478#125—28no—
479#125—22no—
480#125C22×D5914yes—
481#123—28no—
482#123—1188no—
483#123—1188no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—1188no—
487C22⋊Q8C22×D5914yes—
488C22⋊Q8C22×D5914yes—
489#121—594no—
490#121—594no—
491#121—1182no—
492#121—1182no—
493C4×Q8—22no—
494C4×Q8C22×D5914yes—
495C4×D4—594no—
496C4×D4—1182no—
497C4×D4C22⋊D5914yes—
498C4×D4C22×D5914yes—
499#117—22no—
500#117—28no—
501#117C22×D5914yes—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—591no—
510C2×C4⋊C4—591no—
511C2×C4⋊C4—591no—
512C2×C4⋊C4—594no—
513C2×C4⋊C4—594no—
514C2×C4⋊C4—1181no—
515C2×C4⋊C4—1181no—
516C2×C4⋊C4—1182no—
517C2×C4⋊C4—1182no—
518C2×C4⋊C4—1181no—
519C2×C4⋊C4C22⋊D5911yescharacteristic
520C2×C4⋊C4C22×D5911yescharacteristic
521C2×C4⋊C4C22×D5911yescharacteristic
522C2×C4⋊C4C22×D5914yes—
523C2×C4⋊C4C22×D5911yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—1181no—
528C2×C22⋊C4—1181no—
529C2×C22⋊C4—1181no—
530C2×C22⋊C4C22⋊D5911yescharacteristic
531C2×C22⋊C4C22⋊D5911yescharacteristic
532C2×C42—21no—
533C2×C42—21no—
534C2×C42C22×D5911yescharacteristic
535#107—594no—
536#107—594no—
537#107—594no—
538#107—594no—
539#107—594no—
540#107—594no—
541#106—594no—
542#106—594no—
543#106—594no—
544C4⋊C8—594no—
545#103—594no—
546#103—594no—
547#103—594no—
548#102—594no—
549#102—594no—
550#102—594no—
551C22⋊C8—594no—
552C22⋊C8—594no—
553#97—594no—
554C24—1181no—
555C24C2×C22⋊D5911yescharacteristic
556C24C2×C22⋊D5911yescharacteristic
557#41—23632no—
558C2×Q8—21no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—1184no—
562C2×Q8—2364no—
563C2×Q8C23×D5912yes—
564C2×D4—24no—
565C2×D4—592no—
566C2×D4—1184no—
567C2×D4—1184no—
568C2×D4—1181no—
569C2×D4—1182no—
570C2×D4—1182no—
571C2×D4—2364no—
572C2×D4—2364no—
573C2×D4C2×C22⋊D5914yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—44no—
584C22×C4—1184no—
585C22×C4—1184no—
586C22×C4—1181no—
587C22×C4—1181no—
588C22×C4—1181no—
589C22×C4—1184no—
590C22×C4—2364no—
591C22×C4—2364no—
592C22×C4—2364no—
593C22×C4C2×C22⋊D5912yes—
594C22×C4C2×C22⋊D5912yes—
595C22×C4C2×C22⋊D5911yescharacteristic
596C22×C4C2×C22⋊D5911yescharacteristic
597C22×C4C2×C22⋊D5911yescharacteristic
598C22×C4C2×C22⋊D5911yescharacteristic
599C22×C4C23×D5912yes—
600C22×C4C23×D5912yes—
601C22×C4C23×D5911yescharacteristic
602SD16—1188no—
603M16—1188no—
604C2×C8—594no—
605C2×C8—592no—
606C2×C8—592no—
607C2×C8—592no—
608C2×C8—592no—
609C2×C8—1188no—
610C2×C8—1182no—
611C2×C8—1182no—
612C2×C8—1182no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—21no—
622C4⋊C4—592no—
623C4⋊C4—592no—
624C4⋊C4—592no—
625C4⋊C4—1181no—
626C4⋊C4—1181no—
627C4⋊C4—1181no—
628C4⋊C4—1184no—
629C4⋊C4—1184no—
630C4⋊C4—1184no—
631C4⋊C4C2×C22⋊D5914yes—
632C4⋊C4C23×D5912yes—
633C4⋊C4C23×D5912yes—
634C4⋊C4C23×D5912yes—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—1184no—
639C22⋊C4—1184no—
640C22⋊C4—1184no—
641C22⋊C4C2×C22⋊D5914yes—
642C22⋊C4C2×C22⋊D5914yes—
643C42—24no—
644C42—24no—
645C42C2×C22⋊D5912yes—
646C42C23×D5912yes—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—1182no—
653C23—2362no—
654C23—2362no—
655C23—2362no—
656C23#1427375214yes—
657C23C22×C22⋊D5912yes—
658C23C22×C22⋊D5912yes—
659C23C22×C22⋊D5911yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—2368no—
664D4—28no—
665D4—1182no—
666D4—1182no—
667D4—2368no—
668D4—2368no—
669D4—2362no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—48no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—1182no—
690C2×C4—1182no—
691C2×C4—1182no—
692C2×C4—2368no—
693C2×C4—2368no—
694C2×C4—2362no—
695C2×C4—2362no—
696C2×C4—2362no—
697C2×C4—2368no—
698C2×C4C22×C22⋊D5912yes—
699C2×C4C22×C22⋊D5912yes—
700C2×C4C22×C22⋊D5912yes—
701C2×C4C22×C22⋊D5912yes—
702C2×C4C22×C22⋊D5911yescharacteristic
703C2×C4#41×D5912yes—
704C2×C4#1427377412yes—
705C2×C4C24×D5911yescharacteristic
706C8—594no—
707C8—1182no—
708C8—1182no—
709C8—1182no—
710C22—22no—
711C22—28no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—4724no—
718C22—2362no—
719C22—2362no—
720C22—2362no—
721C22#1683805112yes—
722C22C2×#1427375214yes—
723C22C2×#1427375212yes—
724C22#1683821712yes—
725C22C23×C22⋊D5911yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—2362no—
735C4—2362no—
736C4—2362no—
737C4#1683805112yes—
738C4C2×#41×D5911yescharacteristic
739C4C2×#1427377411yescharacteristic
740C2—24no—
741C2—42no—
742C2—4722no—
743C2#2143653614yesdirect product factor
744C2C2×#1683805111yescharacteristic
745C2C22×#1427375211yescharacteristic
746C2C2×#1683821711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#552C2
socleC23×C59C22×D4
prime radicalC2×#16838056C2
hypercenterC2×#552D59
hypocenterC59C2×#3343
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #21436536C2direct (N × H)
3. C2×#16837812C2semidirect
4. C2×#16837735C2semidirect
5. C2×#16837726C2semidirect
6. C2×#16837730C2semidirect
7. C2×#16837715C2semidirect
8. C2×#16837697C2semidirect
9. C2×#16837699C2semidirect
10. C2×#16837650C2semidirect
11. C2×#16837633C2semidirect
12. C2×#16837500C2semidirect
13. C2×#16837474C2semidirect
14. C2×#16837445C2semidirect
15. C22×#14273660C2semidirect
16. C2×C59×#552C2semidirect
32. #16837812C22semidirect
33. #16837735C22semidirect
34. #16837730C22semidirect
35. #16837726C22semidirect
36. #16837715C22semidirect
37. #16837699C22semidirect
38. #16837697C22semidirect
39. #16837650C22semidirect
40. #16837633C22semidirect
41. #16837500C22semidirect
42. #16837474C22semidirect
43. #16837445C22semidirect
50. C2×#14273660C22semidirect
65. C59×#552C22semidirect
268. C2×C59⋊C8#41semidirect
335. C59⋊C8C2×#41semidirect
367. C2×#552D59semidirect
385. C2×C59#3343semidirect
395. #552C2×D59semidirect
450. C59C2×#3343semidirect
743. C2#21436536direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380562
#214365362
C2×#168378122
C2×#168377352
C2×#168377262
C2×#168377302
C2×#168377152
C2×#168376972
C2×#168376992
C2×#168376502
C2×#168376332
C2×#168375002
C2×#168374742
C2×#168374452
C22×#142736602
C2×C59×#5522
C2×#334359