Finite Group Databasebeta

← C2×#21436209 #29465281

Subgroups — C2×#21436209 #29465281

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×#16838109C211yesmaximal, characteristic, complemented
2C2×#16838061C211yesmaximal, characteristic
3#21436209C2116yesmaximal, direct product factor
4C2×#16837762C211yesmaximal, characteristic, complemented
5C2×#16837721C211yesmaximal, characteristic, complemented
6C2×#16837733C211yesmaximal, characteristic, complemented
7C2×#16837688C211yesmaximal, characteristic, complemented
8C2×#16837660C211yesmaximal, characteristic, complemented
9C2×#16837631C211yesmaximal, characteristic, complemented
10C2×#16837625C211yesmaximal, characteristic, complemented
11C2×#16837566C211yesmaximal, characteristic, complemented
12C2×#16837560C211yesmaximal, characteristic, complemented
13C2×#16837510C211yesmaximal, characteristic, complemented
14C2×#16837404C211yesmaximal, characteristic, complemented
15C22×#14273652C211yesmaximal, characteristic, complemented
16C2×C59×#435C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C23×Dic118C2211yescharacteristic
19C22×Dic236C2211yescharacteristic
20C22×Dic236C2211yescharacteristic
21C22×#11745660C2211yescharacteristic
22#16838109—24no—
23#16838109C2218yescomplemented
24#16838061—24no—
25#16838061C2218yes—
26C2×#14273727C2211yescharacteristic
27C2×#14273718—21no—
28C2×#14273715C2211yescharacteristic
29C2×#14273713—21no—
30C2×#14273706C2211yescharacteristic
31C2×#14273706C2211yescharacteristic
32C2×#14273706C2211yescharacteristic
33C2×#14273705—21no—
34C2×#14273704—21no—
35C2×#14273704—21no—
36C2×#14273701C2211yescharacteristic
37C2×#14273699—21no—
38C2×C4×Dic118C2211yescharacteristic
39C2×C4×Dic118C2211yescharacteristic
40C2×D4×Dic59—21no—
41C2×(C22⋊D59)⋊C4—21no—
42C22×C4⋊Dic59C2211yescharacteristic
43C22×C4⋊Dic59C2211yescharacteristic
44#16837762C2218yescomplemented
45#16837733C2218yescomplemented
46#16837721C2218yescomplemented
47#16837688C2218yescomplemented
48#16837660C2218yescomplemented
49#16837631C2218yescomplemented
50#16837625C2218yescomplemented
51#16837566C2218yescomplemented
52#16837560C2218yescomplemented
53#16837510C2218yescomplemented
54C2×#14273659C2211yescharacteristic
55C2×#14273659C2211yescharacteristic
56C2×#14273659C2211yescharacteristic
57#16837404C2218yescomplemented
58C2×#14273652C2211yescharacteristic
59C2×#14273652C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273652C2211yescharacteristic
62C2×#14273652C2211yescharacteristic
63C2×#14273652C2211yescharacteristic
64C2×#14273652C2211yescharacteristic
65C2×#14273652C2218yescomplemented
66C2×#14273649C2211yescharacteristic
67C2×#14273649C2211yescharacteristic
68C2×#14273649C2211yescharacteristic
69C22×M16×C59C2211yescharacteristic
70C23×C8×C59C2211yescharacteristic
71C2×C4×D4×C59C2211yescharacteristic
72C59×#435C2218yescomplemented
73C2×C4⋊C8×C59C2211yescharacteristic
74C2×C22⋊C8×C59C2211yescharacteristic
75C2×C22⋊C8×C59C2211yescharacteristic
76C2×#97×C59C2211yescharacteristic
77C2×#11745685—22no—
78C2×#11745685—24no—
79C2×#11745685—42no—
80C2×#11745685C2314yes—
81C22×Dic118—24no—
82C22×Dic118—21no—
83C22×Dic118—22no—
84C22×Dic118—21no—
85C22×Dic118—42no—
86C22×Dic118C2311yescharacteristic
87C22×Dic118C2311yescharacteristic
88C22×Dic118C2314yes—
89C22×Dic118C2311yescharacteristic
90C22×D236C2311yescharacteristic
91C22×C22⋊D59—21no—
92C22×C22⋊D59—21no—
93C23×Dic59—21no—
94C23×Dic59—21no—
95C23×Dic59—21no—
96C22×C4×D59—21no—
97C2×Dic236—24no—
98C2×Dic236—42no—
99C2×Dic236C2314yes—
100C2×Dic236C2314yes—
101C2×#11745660—42no—
102C2×#11745660C2314yes—
103#14273727—22no—
104#14273727C2314yes—
105#14273718—28no—
106#14273715—22no—
107#14273715C2314yes—
108#14273713—28no—
109#14273706—22no—
110#14273706—22no—
111#14273706—22no—
112#14273706C2314yes—
113#14273706C2314yes—
114#14273706C2314yes—
115#14273705—28no—
116#14273704—28no—
117#14273704—28no—
118#14273701—22no—
119#14273701C2314yes—
120#14273699—28no—
121C4×Dic118—22no—
122C4×Dic118—22no—
123C4×Dic118C2314yes—
124C4×Dic118C2314yes—
125D4×Dic59—28no—
126(C22⋊D59)⋊C4—28no—
127C2×C4⋊Dic59—21no—
128C2×C4⋊Dic59—21no—
129C2×C4⋊Dic59—21no—
130C2×C4⋊Dic59—22no—
131C2×C4⋊Dic59—22no—
132C2×C4⋊Dic59C2311yescharacteristic
133C2×C4⋊Dic59C2311yescharacteristic
134C2×C4⋊Dic59C2311yescharacteristic
135C2×C4⋊Dic59C2311yescharacteristic
136C2×C4⋊Dic59C2314yes—
137C2×C4⋊Dic59C2314yes—
138C2×Dic59⋊C4—21no—
139C2×Dic59⋊C4—21no—
140C2×Dic59⋊C4—21no—
141C2×Dic59⋊C4—21no—
142C2×Dic59⋊C4—21no—
143C2×C22⋊Dic59—21no—
144C2×C22⋊Dic59—21no—
145C2×C22⋊Dic59—21no—
146C2×(C2×D59)⋊C4—21no—
147C2×(C2×D59)⋊C4—21no—
148C2×(C2×D59)⋊C4—21no—
149C2×C4×Dic59—21no—
150C2×C4×Dic59—21no—
151#14273659C2314yes—
152#14273659C2314yes—
153#14273659C2314yes—
154#14273652C2314yes—
155#14273652C2314yes—
156#14273652C2314yes—
157#14273652C2314yes—
158#14273652C2314yes—
159#14273652C2314yes—
160#14273652C2314yes—
161#14273649C2314yes—
162#14273649C2314yes—
163#14273649C2314yes—
164C22×D4×C59D411yescharacteristic
165C23×C4×C59C2311yescharacteristic
166C23×C4×C59C2311yescharacteristic
167C2×M16×C59—42no—
168C2×M16×C59C2314yes—
169C22×C8×C59—42no—
170C22×C8×C59C2311yescharacteristic
171C22×C8×C59C2311yescharacteristic
172C22×C8×C59C2311yescharacteristic
173C22×C8×C59C2311yescharacteristic
174C22×C8×C59C2314yes—
175C4×D4×C59D414yes—
176C4×D4×C59C2314yes—
177C2×C4⋊C4×C59D411yescharacteristic
178C2×C22⋊C4×C59D411yescharacteristic
179C2×C22⋊C4×C59D411yescharacteristic
180C2×C42×C59C2311yescharacteristic
181C4⋊C8×C59C2314yes—
182C22⋊C8×C59C2314yes—
183C22⋊C8×C59C2314yes—
184#97×C59C2314yes—
185C24×C59C2×D411yescharacteristic
186C24×C59C2×D411yescharacteristic
187C23×D59—21no—
188C2×D4×C59—24no—
189C2×D4×C59C2×D414yes—
190C22×C4×C59—22no—
191C22×C4×C59—22no—
192C22×C4×C59—22no—
193C22×C4×C59—22no—
194C22×C4×C59C2×D411yescharacteristic
195C22×C4×C59C2×D411yescharacteristic
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2×D412yes—
199C22×C4×C59C2×D412yes—
200C22×C4×C59C2412yes—
201C22×C4×C59C2412yes—
202C22×C4×C59C2411yescharacteristic
203C2×C22⋊D59—24no—
204C2×C22⋊D59—24no—
205C2×C22⋊D59—44no—
206C2×C22⋊D59—44no—
207C22×Dic59—21no—
208C22×Dic59—21no—
209C22×Dic59—21no—
210C22×Dic59—21no—
211C22×Dic59—21no—
212C22×Dic59—21no—
213C22×Dic59—21no—
214C22×Dic59—24no—
215C22×Dic59—24no—
216C22×Dic59—24no—
217C22×Dic59—44no—
218C22×Dic59—82no—
219C22×Dic59—82no—
220#11745685—28no—
221#11745685—44no—
222#11745685—48no—
223C2×D236—22no—
224C2×D236—22no—
225C2×D236—21no—
226C2×D236C2412yes—
227C2×C4×D59—24no—
228C2×C4×D59—44no—
229C2×Dic118—21no—
230C2×Dic118—22no—
231C2×Dic118—22no—
232C2×Dic118—22no—
233C2×Dic118—22no—
234C2×Dic118—22no—
235C2×Dic118—28no—
236C2×Dic118—21no—
237C2×Dic118—24no—
238C2×Dic118—21no—
239C2×Dic118—24no—
240C2×Dic118—44no—
241C2×Dic118—48no—
242C2×Dic118—44no—
243C2×Dic118—82no—
244C2×Dic118#4114yes—
245C2×Dic118C2412yes—
246C2×Dic118C2412yes—
247C2×Dic118C2412yes—
248M16×C59—44no—
249C2×C8×C59—22no—
250C2×C8×C59—22no—
251C2×C8×C59—22no—
252C2×C8×C59—22no—
253C2×C8×C59—44no—
254C2×C8×C59C2412yes—
255C2×C8×C59C2412yes—
256C2×C8×C59C2412yes—
257C2×C8×C59C2412yes—
258C4⋊C4×C59C2×D414yes—
259C22⋊C4×C59C2×D414yes—
260C22⋊C4×C59C2×D414yes—
261C42×C59C2×D412yes—
262C42×C59C2412yes—
263C22⋊Dic59—24no—
264C22⋊Dic59—24no—
265C22⋊Dic59—24no—
266(C2×D59)⋊C4—24no—
267(C2×D59)⋊C4—24no—
268(C2×D59)⋊C4—24no—
269C4⋊Dic59—21no—
270C4⋊Dic59—24no—
271C4⋊Dic59—24no—
272C4⋊Dic59—21no—
273C4⋊Dic59—21no—
274C4⋊Dic59—24no—
275C4⋊Dic59—21no—
276C4⋊Dic59C2412yes—
277C4⋊Dic59C2412yes—
278C4⋊Dic59C2412yes—
279C4⋊Dic59C2412yes—
280Dic59⋊C4—24no—
281Dic59⋊C4—24no—
282Dic59⋊C4—24no—
283Dic59⋊C4—24no—
284Dic59⋊C4—24no—
285C4×Dic59—24no—
286C4×Dic59—24no—
287Dic236—28no—
288Dic236—44no—
289#11745660—44no—
290C23×C59—22no—
291C23×C59—22no—
292C23×C59—22no—
293C23×C59—22no—
294C23×C59—22no—
295C23×C59#13714yes—
296C23×C59C22×D412yes—
297C23×C59C22×D412yes—
298C23×C59C22×D411yescharacteristic
299C22×D59—22no—
300C22×D59—42no—
301C22×D59—42no—
302C22×D59—42no—
303D4×C59—28no—
304C2×C4×C59—22no—
305C2×C4×C59—22no—
306C2×C4×C59—22no—
307C2×C4×C59—22no—
308C2×C4×C59—24no—
309C2×C4×C59—24no—
310C2×C4×C59—22no—
311C2×C4×C59—22no—
312C2×C4×C59—22no—
313C2×C4×C59—22no—
314C2×C4×C59C22×D412yes—
315C2×C4×C59C22×D412yes—
316C2×C4×C59C22×D412yes—
317C2×C4×C59C22×D412yes—
318C2×C4×C59C22×D411yescharacteristic
319C2×C4×C59C2×#4112yes—
320C2×C4×C59H(5,𝔽2)12yes—
321C2×C4×C59C2511yescharacteristic
322C22⋊D59—48no—
323C22⋊D59—48no—
324C2×Dic59—24no—
325C2×Dic59—22no—
326C2×Dic59—22no—
327C2×Dic59—22no—
328C2×Dic59—22no—
329C2×Dic59—22no—
330C2×Dic59—22no—
331C2×Dic59—22no—
332C2×Dic59—48no—
333C2×Dic59—42no—
334C2×Dic59—42no—
335C2×Dic59—42no—
336C2×Dic59—42no—
337C2×Dic59—42no—
338C2×Dic59—42no—
339C2×Dic59—84no—
340C2×Dic59—84no—
341D236—22no—
342D236—22no—
343D236—42no—
344C4×D59—48no—
345Dic118—24no—
346Dic118—22no—
347Dic118—22no—
348Dic118—22no—
349Dic118—22no—
350Dic118—22no—
351Dic118—48no—
352Dic118—42no—
353Dic118—42no—
354Dic118—84no—
355Dic118C2×#4114yes—
356C8×C59—22no—
357C8×C59—22no—
358C8×C59—22no—
359C8×C59—22no—
360C2×#3316—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#54612yes—
369C22×C59C2×#13714yes—
370C22×C59C2×#13712yes—
371C22×C59#57712yes—
372C22×C59C23×D411yescharacteristic
373C2×D59—42no—
374C2×D59—42no—
375C2×D59—42no—
376C2×D59—84no—
377C4×C59—22no—
378C4×C59—22no—
379C4×C59—22no—
380C4×C59—22no—
381C4×C59#54612yes—
382C4×C59C22×#4111yescharacteristic
383C4×C59C2×H(5,𝔽2)11yescharacteristic
384Dic59—24no—
385Dic59—42no—
386Dic59—42no—
387Dic59—42no—
388Dic59—42no—
389Dic59—42no—
390Dic59—42no—
391C2×#554—591no—
392C2×#548—591no—
393#3316—5916no—
394C2×#489—591no—
395C2×#481—591no—
396C2×#483—591no—
397C2×#475—591no—
398C2×#470—591no—
399C2×#465—591no—
400C2×#464—591no—
401C2×#452—591no—
402C2×#451—591no—
403C2×#441—591no—
404C2×#435D5911yescharacteristic, complemented
405C2×#417—591no—
406C22×#103—591no—
407C2×C59—24no—
408C2×C59—42no—
409C2×C59#331614yescomplemented
410C2×C59C2×#54611yescharacteristic
411C2×C59C22×#13711yescharacteristic
412C2×C59C2×#57711yescharacteristic
413D59—82no—
414C22×#41—591no—
415C23×Q8—591no—
416C22×Q16—591no—
417C22×Q16—591no—
418C22×SD16—591no—
419C22×M16C2×D5911yescharacteristic
420C23×C8C2×D5911yescharacteristic
421#554—598no—
422#554—1184no—
423#548—598no—
424#548—1184no—
425C2×C4⋊Q8—591no—
426C2×#125—1181no—
427C2×#124—591no—
428C2×#124—1181no—
429C2×C22⋊Q8—591no—
430C2×C22⋊Q8—591no—
431C2×C22⋊Q8—591no—
432C2×C22⋊Q8—1181no—
433C2×C22⋊Q8—1181no—
434C2×C22⋊Q8—1181no—
435C2×#121—591no—
436C2×#121—1181no—
437C2×C4×Q8—591no—
438C2×C4×Q8—591no—
439C2×C4×D4—1181no—
440C2×C4×D4—1181no—
441C2×C4×D4C2×D5911yescharacteristic
442C22×C4⋊C4—591no—
443C22×C4⋊C4—591no—
444#489—598no—
445#483—598no—
446#481—598no—
447#475—598no—
448#470—598no—
449#465—598no—
450#464—598no—
451#452—598no—
452#451—598no—
453#441—598no—
454#435C2×D5918yescomplemented
455C2×#106—591no—
456C2×#106—591no—
457C2×#106—591no—
458C2×C4⋊C8C2×D5911yescharacteristic
459#417—598no—
460C2×#103—591no—
461C2×#103—591no—
462C2×#103—591no—
463C2×#103—591no—
464C2×#103—591no—
465C2×#103—591no—
466C2×#103—591no—
467C2×#103—598no—
468C2×#102—591no—
469C2×#102—591no—
470C2×#102—591no—
471C2×C22⋊C8C2×D5911yescharacteristic
472C2×C22⋊C8C2×D5911yescharacteristic
473C2×#97C2×D5911yescharacteristic
474C59C2×#331611yescharacteristic, complemented, Sylow
475C2×#41—594no—
476C2×#41—1184no—
477C2×#41—1182no—
478C2×#41—2362no—
479C22×Q8—591no—
480C22×Q8—591no—
481C22×Q8—591no—
482C22×Q8—594no—
483C22×Q8—1184no—
484C22×Q8—1181no—
485C22×Q8—1181no—
486C22×Q8—1182no—
487C22×Q8—2362no—
488C22×D4—591no—
489C22×D4—1181no—
490C22×D4—1181no—
491C22×D4D23611yescharacteristic
492C23×C4—1181no—
493C23×C4—1181no—
494C23×C4—1181no—
495C23×C4—1181no—
496C23×C4C22×D5911yescharacteristic
497C23×C4C22×D5911yescharacteristic
498C2×Q16—594no—
499C2×Q16—594no—
500C2×Q16—1184no—
501C2×Q16—2362no—
502C2×SD16—594no—
503C2×SD16—2362no—
504C2×M16—42no—
505C2×M16C22×D5914yes—
506C22×C8—42no—
507C22×C8C22×D5911yescharacteristic
508C22×C8C22×D5911yescharacteristic
509C22×C8C22×D5911yescharacteristic
510C22×C8C22×D5911yescharacteristic
511C22×C8C22×D5914yes—
512C4⋊Q8—594no—
513C4⋊Q8—1182no—
514#125—1188no—
515#124—594no—
516#124—1188no—
517#124—1182no—
518C22⋊Q8—594no—
519C22⋊Q8—594no—
520C22⋊Q8—594no—
521C22⋊Q8—1182no—
522C22⋊Q8—1182no—
523C22⋊Q8—1182no—
524C22⋊Q8—1188no—
525C22⋊Q8—1188no—
526C22⋊Q8—1188no—
527#121—594no—
528#121—1188no—
529#121—1182no—
530C4×Q8—594no—
531C4×Q8—594no—
532C4×Q8—1182no—
533C4×Q8—1182no—
534C4×D4—1188no—
535C4×D4—1188no—
536C4×D4D23614yes—
537C4×D4C22×D5914yes—
538C2×C4⋊C4—591no—
539C2×C4⋊C4—591no—
540C2×C4⋊C4—591no—
541C2×C4⋊C4—594no—
542C2×C4⋊C4—594no—
543C2×C4⋊C4—591no—
544C2×C4⋊C4—1181no—
545C2×C4⋊C4—1181no—
546C2×C4⋊C4—1182no—
547C2×C4⋊C4—1182no—
548C2×C4⋊C4—1181no—
549C2×C4⋊C4—1181no—
550C2×C4⋊C4—1181no—
551C2×C4⋊C4—1181no—
552C2×C4⋊C4—1181no—
553C2×C4⋊C4—1181no—
554C2×C4⋊C4D23611yescharacteristic
555C2×C22⋊C4—1181no—
556C2×C22⋊C4—1181no—
557C2×C22⋊C4—1181no—
558C2×C22⋊C4—1181no—
559C2×C22⋊C4—1181no—
560C2×C22⋊C4—1181no—
561C2×C22⋊C4D23611yescharacteristic
562C2×C22⋊C4D23611yescharacteristic
563C2×C42—1181no—
564C2×C42—1181no—
565C2×C42C22×D5911yescharacteristic
566#106—594no—
567#106—594no—
568#106—594no—
569C4⋊C8C22×D5914yes—
570#103—594no—
571#103—594no—
572#103—594no—
573#103—594no—
574#103—594no—
575#103—594no—
576#103—594no—
577#102—594no—
578#102—594no—
579#102—594no—
580C22⋊C8C22×D5914yes—
581C22⋊C8C22×D5914yes—
582#97C22×D5914yes—
583C24—1181no—
584C24C2×D23611yescharacteristic
585C24C2×D23611yescharacteristic
586#41—1188no—
587#41—2364no—
588#41—2368no—
589C2×Q8—594no—
590C2×Q8—592no—
591C2×Q8—592no—
592C2×Q8—592no—
593C2×Q8—1188no—
594C2×Q8—1181no—
595C2×Q8—1184no—
596C2×Q8—1181no—
597C2×Q8—1184no—
598C2×Q8—1181no—
599C2×Q8—1182no—
600C2×Q8—1182no—
601C2×Q8—1182no—
602C2×Q8—1182no—
603C2×Q8—1182no—
604C2×Q8—4722no—
605C2×Q8—2364no—
606C2×Q8—2364no—
607C2×Q8—2368no—
608C2×D4—24no—
609C2×D4—592no—
610C2×D4—1184no—
611C2×D4—1184no—
612C2×D4—1181no—
613C2×D4—1182no—
614C2×D4—1182no—
615C2×D4—2364no—
616C2×D4—2364no—
617C2×D4C2×D23614yes—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—1181no—
623C22×C4—1184no—
624C22×C4—1184no—
625C22×C4—1184no—
626C22×C4—1181no—
627C22×C4—1181no—
628C22×C4—1181no—
629C22×C4—1181no—
630C22×C4—1181no—
631C22×C4—1181no—
632C22×C4—1184no—
633C22×C4—4722no—
634C22×C4—4722no—
635C22×C4—2364no—
636C22×C4—2364no—
637C22×C4C2×D23612yes—
638C22×C4C2×D23612yes—
639C22×C4C2×D23611yescharacteristic
640C22×C4C2×D23611yescharacteristic
641C22×C4C2×D23611yescharacteristic
642C22×C4C2×D23611yescharacteristic
643C22×C4C23×D5912yes—
644C22×C4C23×D5912yes—
645C22×C4C23×D5911yescharacteristic
646Q16—1188no—
647Q16—2364no—
648SD16—2364no—
649M16—44no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—44no—
655C2×C8C23×D5912yes—
656C2×C8C23×D5912yes—
657C2×C8C23×D5912yes—
658C2×C8C23×D5912yes—
659C4⋊C4—592no—
660C4⋊C4—592no—
661C4⋊C4—592no—
662C4⋊C4—592no—
663C4⋊C4—1181no—
664C4⋊C4—1184no—
665C4⋊C4—1184no—
666C4⋊C4—1181no—
667C4⋊C4—1181no—
668C4⋊C4—1181no—
669C4⋊C4—1184no—
670C4⋊C4—1184no—
671C4⋊C4—1184no—
672C4⋊C4—1184no—
673C4⋊C4—1184no—
674C4⋊C4—1184no—
675C4⋊C4C2×D23614yes—
676C22⋊C4—1184no—
677C22⋊C4—1184no—
678C22⋊C4—1184no—
679C22⋊C4—1184no—
680C22⋊C4—1184no—
681C22⋊C4—1184no—
682C22⋊C4C2×D23614yes—
683C22⋊C4C2×D23614yes—
684C42—1184no—
685C42—1184no—
686C42C2×D23612yes—
687C42C23×D5912yes—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—1182no—
694C23—2362no—
695C23—2362no—
696C23—2362no—
697C23#1427376014yes—
698C23C22×D23612yes—
699C23C22×D23612yes—
700C23C22×D23611yescharacteristic
701Q8—594no—
702Q8—1182no—
703Q8—1184no—
704Q8—1182no—
705Q8—1182no—
706Q8—1182no—
707Q8—1182no—
708Q8—4724no—
709Q8—2368no—
710Q8—2362no—
711Q8—2362no—
712D4—28no—
713D4—1182no—
714D4—1182no—
715D4—2368no—
716D4—2368no—
717D4—2362no—
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—1182no—
729C2×C4—1184no—
730C2×C4—1182no—
731C2×C4—1182no—
732C2×C4—1182no—
733C2×C4—1182no—
734C2×C4—1182no—
735C2×C4—1182no—
736C2×C4—4724no—
737C2×C4—4724no—
738C2×C4—2368no—
739C2×C4—2368no—
740C2×C4—2362no—
741C2×C4—2362no—
742C2×C4—2362no—
743C2×C4—2362no—
744C2×C4—2362no—
745C2×C4—2362no—
746C2×C4C22×D23612yes—
747C2×C4C22×D23612yes—
748C2×C4C22×D23612yes—
749C2×C4C22×D23612yes—
750C2×C4C22×D23611yescharacteristic
751C2×C4#41×D5912yes—
752C2×C4#1427377212yes—
753C2×C4C24×D5911yescharacteristic
754C8—22no—
755C8—22no—
756C8—22no—
757C8—22no—
758C22—28no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—4724no—
766C22—2362no—
767C22—2362no—
768C22—2362no—
769C22#1683804712yes—
770C22C2×#1427376014yes—
771C22C2×#1427376012yes—
772C22#1683821412yes—
773C22C23×D23611yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—1184no—
779C4—2362no—
780C4—2362no—
781C4—2362no—
782C4—2362no—
783C4—2362no—
784C4—2362no—
785C4#1683804712yes—
786C4C2×#41×D5911yescharacteristic
787C4C2×#1427377211yescharacteristic
788C2—24no—
789C2—42no—
790C2—4722no—
791C2#2143620914yesdirect product factor
792C2C2×#1683804711yescharacteristic
793C2C22×#1427376011yescharacteristic
794C2C2×#1683821411yescharacteristic
subgroupG/H
centerC23C22×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#435C2
socleC23×C59C22×D4
prime radicalC2×#16838061C2
hypercenterC2×#435D59
hypocenterC59C2×#3316
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#16838109C2semidirect
3. #21436209C2direct (N × H)
4. C2×#16837762C2semidirect
5. C2×#16837721C2semidirect
6. C2×#16837733C2semidirect
7. C2×#16837688C2semidirect
8. C2×#16837660C2semidirect
9. C2×#16837631C2semidirect
10. C2×#16837625C2semidirect
11. C2×#16837566C2semidirect
12. C2×#16837560C2semidirect
13. C2×#16837510C2semidirect
14. C2×#16837404C2semidirect
15. C22×#14273652C2semidirect
16. C2×C59×#435C2semidirect
23. #16838109C22semidirect
44. #16837762C22semidirect
45. #16837733C22semidirect
46. #16837721C22semidirect
47. #16837688C22semidirect
48. #16837660C22semidirect
49. #16837631C22semidirect
50. #16837625C22semidirect
51. #16837566C22semidirect
52. #16837560C22semidirect
53. #16837510C22semidirect
57. #16837404C22semidirect
65. C2×#14273652C22semidirect
72. C59×#435C22semidirect
404. C2×#435D59semidirect
409. C2×C59#3316semidirect
454. #435C2×D59semidirect
474. C59C2×#3316semidirect
791. C2#21436209direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381092
C2×#168380612
#214362092
C2×#168377622
C2×#168377212
C2×#168377332
C2×#168376882
C2×#168376602
C2×#168376312
C2×#168376252
C2×#168375662
C2×#168375602
C2×#168375102
C2×#168374042
C22×#142736522
C2×C59×#4352
C2×#331659