Finite Group Databasebeta

← C2×#21433077 #29453148

Subgroups — C2×#21433077 #29453148

Order 15104.

1970 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837930C211yesmaximal, characteristic
2#21433077C2116yesmaximal, direct product factor
3C2×#16837532C211yesmaximal, characteristic, complemented
4C2×#16837530C211yesmaximal, characteristic, complemented
5C2×#16837481C211yesmaximal, characteristic, complemented
6C2×#16837478C211yesmaximal, characteristic, complemented
7C2×#16837475C211yesmaximal, characteristic, complemented
8C2×#16837473C211yesmaximal, characteristic, complemented
9C2×#16837473C211yesmaximal, characteristic, complemented
10C2×#16837471C211yesmaximal, characteristic, complemented
11C2×#16837464C211yesmaximal, characteristic, complemented
12C2×#16837463C211yesmaximal, characteristic, complemented
13C2×#16837457C211yesmaximal, characteristic, complemented
14C2×#16837356C211yesmaximal, characteristic, complemented
15C2×C4×#11745659C211yesmaximal, characteristic, complemented
16C2×C59×#405C211yesmaximal, characteristic, complemented
17C22×#11745659C2211yescharacteristic
18C22×#11745659C2211yescharacteristic
19C22×#11745659C2211yescharacteristic
20C22×C8×D59C2211yescharacteristic
21#16837930C418yes—
22#16837930C2218yes—
23C2×#14273722C411yescharacteristic
24C2×#14273720C411yescharacteristic
25C2×#14273717C411yescharacteristic
26C2×#14273713C411yescharacteristic
27C2×#14273712C411yescharacteristic
28C2×#14273709C411yescharacteristic
29C2×#14273705C411yescharacteristic
30C2×#14273700C411yescharacteristic
31C2×C4×Dic118C2211yescharacteristic
32C2×C4×D236C2211yescharacteristic
33C2×C4×C22⋊D59C2211yescharacteristic
34C2×C4×C22⋊D59C2211yescharacteristic
35C2×#14273684C2211yescharacteristic
36C2×C42×D59C2211yescharacteristic
37#16837532C2218yescomplemented
38#16837530C2218yescomplemented
39#16837481C2218yescomplemented
40#16837478C2218yescomplemented
41#16837475C2218yescomplemented
42#16837473C2218yescomplemented
43#16837473C2218yescomplemented
44#16837471C2218yescomplemented
45#16837464C2218yescomplemented
46#16837463C2218yescomplemented
47#16837457C2218yescomplemented
48C2×C4⋊(C59⋊C8)C2211yescharacteristic
49C2×C4⋊(C59⋊C8)C2211yescharacteristic
50C2×Dic59⋊C8C2211yescharacteristic
51C2×Dic59⋊C8C2211yescharacteristic
52C2×Dic59⋊C8C2211yescharacteristic
53C2×Dic59⋊C8C2211yescharacteristic
54C2×C22⋊(C59⋊C8)C2211yescharacteristic
55C2×C22⋊(C59⋊C8)C2211yescharacteristic
56C2×(C2×D59)⋊C8C2211yescharacteristic
57C2×(C2×D59)⋊C8C2211yescharacteristic
58C2×(C2×D59)⋊C8C2211yescharacteristic
59C2×(C2×D59)⋊C8C2211yescharacteristic
60#16837356C2218yescomplemented
61C4×#11745659C2218yescomplemented
62C2×#14273638C2211yescharacteristic
63C2×#14273637C2211yescharacteristic
64C2×#14273637C2211yescharacteristic
65C2×#14273637C2211yescharacteristic
66C2×C4×C59⋊C8C2211yescharacteristic
67C2×C8×Dic59C2211yescharacteristic
68C22×M16×C59C2211yescharacteristic
69C23×C8×C59C2211yescharacteristic
70C2×#117×C59C2211yescharacteristic
71C59×#405C2218yescomplemented
72C2×#97×C59C2211yescharacteristic
73C2×#97×C59C2211yescharacteristic
74C2×C4×C8×C59C2211yescharacteristic
75C2×C4×C8×C59C2211yescharacteristic
76C22×Dic118C2×C411yescharacteristic
77C22×D236C2×C411yescharacteristic
78C22×C22⋊D59C2×C411yescharacteristic
79C22×C22⋊D59C2×C411yescharacteristic
80C22×C4×D59C2×C411yescharacteristic
81C22×C4×D59C2×C411yescharacteristic
82C22×C4×D59C2311yescharacteristic
83C22×C4×D59C2311yescharacteristic
84C2×#11745659—24no—
85C2×#11745659—24no—
86C2×#11745659—24no—
87C2×#11745659C2314yes—
88C2×#11745659C2314yes—
89C2×#11745659C2314yes—
90C22×C59⋊C8C2311yescharacteristic
91C22×C59⋊C8C2311yescharacteristic
92C22×C59⋊C8C2311yescharacteristic
93C22×C59⋊C8C2311yescharacteristic
94C2×C8×D59—24no—
95C2×C8×D59C2314yes—
96#14273722C2×C418yes—
97#14273720C2×C418yes—
98#14273717C2×C418yes—
99#14273713C2×C418yes—
100#14273712C2×C418yes—
101#14273709C2×C418yes—
102#14273705C2×C418yes—
103#14273700C2×C418yes—
104C4×Dic118C2×C414yes—
105C4×Dic118C2314yes—
106C4×D236C2×C414yes—
107C4×D236C2314yes—
108C4×C22⋊D59C2×C414yes—
109C4×C22⋊D59C2×C414yes—
110C4×C22⋊D59C2314yes—
111C4×C22⋊D59C2314yes—
112#14273684C2×C414yes—
113#14273684C2314yes—
114C2×C4⋊Dic59C2×C411yescharacteristic
115C2×C4⋊Dic59C2×C411yescharacteristic
116C2×Dic59⋊C4C2×C411yescharacteristic
117C2×Dic59⋊C4C2×C411yescharacteristic
118C2×Dic59⋊C4C2×C411yescharacteristic
119C2×Dic59⋊C4C2×C411yescharacteristic
120C2×Dic59⋊C4C2×C411yescharacteristic
121C2×Dic59⋊C4C2×C411yescharacteristic
122C2×C22⋊Dic59C2×C411yescharacteristic
123C2×C22⋊Dic59C2×C411yescharacteristic
124C2×(C2×D59)⋊C4C2×C411yescharacteristic
125C2×(C2×D59)⋊C4C2×C411yescharacteristic
126C2×(C2×D59)⋊C4C2×C411yescharacteristic
127C2×(C2×D59)⋊C4C2×C411yescharacteristic
128C2×(C2×D59)⋊C4C2×C411yescharacteristic
129C2×(C2×D59)⋊C4C2×C411yescharacteristic
130C2×C4×Dic59C2×C411yescharacteristic
131C2×C4×Dic59C2×C411yescharacteristic
132C2×C4×Dic59C2311yescharacteristic
133C2×C4×Dic59C2311yescharacteristic
134C42×D59C2×C414yes—
135C42×D59C2314yes—
136C4⋊(C59⋊C8)C2314yes—
137C4⋊(C59⋊C8)C2314yes—
138Dic59⋊C8C2314yes—
139Dic59⋊C8C2314yes—
140Dic59⋊C8C2314yes—
141Dic59⋊C8C2314yes—
142C22⋊(C59⋊C8)C2314yes—
143C22⋊(C59⋊C8)C2314yes—
144(C2×D59)⋊C8C2314yes—
145(C2×D59)⋊C8C2314yes—
146(C2×D59)⋊C8C2314yes—
147(C2×D59)⋊C8C2314yes—
148#14273638C2314yes—
149#14273637C2314yes—
150#14273637C2314yes—
151#14273637C2314yes—
152C4×C59⋊C8C2314yes—
153C8×Dic59C2314yes—
154C23×C4×C59C2311yescharacteristic
155C2×M16×C59—24no—
156C2×M16×C59C2314yes—
157C22×C8×C59—24no—
158C22×C8×C59C2311yescharacteristic
159C22×C8×C59C2311yescharacteristic
160C22×C8×C59C2314yes—
161C22×C8×C59C2311yescharacteristic
162C22×C8×C59C2311yescharacteristic
163#117×C59C2×C414yes—
164#117×C59C2314yes—
165C2×C4⋊C4×C59C2×C411yescharacteristic
166C2×C4⋊C4×C59C2×C411yescharacteristic
167C2×C22⋊C4×C59C2×C411yescharacteristic
168C2×C22⋊C4×C59C2×C411yescharacteristic
169C2×C42×C59C2311yescharacteristic
170C2×C42×C59C2311yescharacteristic
171#97×C59C2314yes—
172#97×C59C2314yes—
173C4×C8×C59C2314yes—
174C4×C8×C59C2314yes—
175C24×C59C22×C411yescharacteristic
176C23×D59C22×C411yescharacteristic
177C23×D59C22×C411yescharacteristic
178C22×C4×C59—22no—
179C22×C4×C59—22no—
180C22×C4×C59C22×C411yescharacteristic
181C22×C4×C59C22×C411yescharacteristic
182C22×C4×C59C22×C411yescharacteristic
183C22×C4×C59C22×C411yescharacteristic
184C22×C4×C59C22×C411yescharacteristic
185C22×C4×C59C22×C412yes—
186C22×C4×C59C2412yes—
187C22×C4×C59C2411yescharacteristic
188C2×C22⋊D59—42no—
189C2×C22⋊D59—42no—
190C2×C22⋊D59C22×C414yes—
191C2×C22⋊D59C22×C414yes—
192C22×Dic59C22×C411yescharacteristic
193C22×Dic59C22×C411yescharacteristic
194C22×Dic59C22×C411yescharacteristic
195C22×Dic59C22×C411yescharacteristic
196C22×Dic59C22×C411yescharacteristic
197C22×Dic59C22×C411yescharacteristic
198C2×D236—42no—
199C2×D236C22×C414yes—
200C2×C4×D59—22no—
201C2×C4×D59—22no—
202C2×C4×D59—22no—
203C2×C4×D59—22no—
204C2×C4×D59—42no—
205C2×C4×D59—42no—
206C2×C4×D59C22×C412yes—
207C2×C4×D59C22×C412yes—
208C2×C4×D59C22×C414yes—
209C2×C4×D59C22×C414yes—
210C2×C4×D59C2412yes—
211C2×C4×D59C2412yes—
212C2×Dic118—42no—
213C2×Dic118C22×C414yes—
214M16×C59—28no—
215C2×C8×C59—22no—
216C2×C8×C59—22no—
217C2×C8×C59—28no—
218C2×C8×C59#4114yes—
219C2×C8×C59#4114yes—
220C2×C8×C59C2412yes—
221C2×C8×C59C2412yes—
222C2×C8×C59C2412yes—
223C2×C8×C59C2412yes—
224C4⋊C4×C59C22×C414yes—
225C4⋊C4×C59C22×C414yes—
226C22⋊C4×C59C22×C414yes—
227C22⋊C4×C59C22×C414yes—
228C42×C59C22×C412yes—
229C42×C59C22×C412yes—
230C42×C59C2412yes—
231C42×C59C2412yes—
232C22⋊Dic59C22×C414yes—
233C22⋊Dic59C22×C414yes—
234(C2×D59)⋊C4C22×C414yes—
235(C2×D59)⋊C4C22×C414yes—
236(C2×D59)⋊C4C22×C414yes—
237(C2×D59)⋊C4C22×C414yes—
238(C2×D59)⋊C4C22×C414yes—
239(C2×D59)⋊C4C22×C414yes—
240C4⋊Dic59C22×C414yes—
241C4⋊Dic59C22×C414yes—
242Dic59⋊C4C22×C414yes—
243Dic59⋊C4C22×C414yes—
244Dic59⋊C4C22×C414yes—
245Dic59⋊C4C22×C414yes—
246Dic59⋊C4C22×C414yes—
247Dic59⋊C4C22×C414yes—
248C4×Dic59C22×C412yes—
249C4×Dic59C22×C414yes—
250C4×Dic59C22×C414yes—
251C4×Dic59C22×C412yes—
252C4×Dic59C2412yes—
253C4×Dic59C2412yes—
254C2×C59⋊C8—22no—
255C2×C59⋊C8—22no—
256C2×C59⋊C8—22no—
257C2×C59⋊C8—22no—
258C2×C59⋊C8C2412yes—
259C2×C59⋊C8C2412yes—
260C2×C59⋊C8C2412yes—
261C2×C59⋊C8C2412yes—
262#11745659—28no—
263#11745659—28no—
264#11745659—28no—
265C8×D59—28no—
266C23×C59—22no—
267C23×C59—22no—
268C23×C59—22no—
269C23×C59C23×C412yes—
270C23×C59C23×C411yescharacteristic
271C22×D59—22no—
272C22×D59—22no—
273C22×D59—22no—
274C22×D59—22no—
275C22×D59—22no—
276C22×D59—22no—
277C22×D59C23×C412yes—
278C22×D59C23×C412yes—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—24no—
285C2×C4×C59—22no—
286C2×C4×C59—22no—
287C2×C4×C59C23×C412yes—
288C2×C4×C59C23×C412yes—
289C2×C4×C59C23×C412yes—
290C2×C4×C59C23×C412yes—
291C2×C4×C59C23×C412yes—
292C2×C4×C59C23×C411yescharacteristic
293C2×C4×C59C2×#4112yes—
294C2×C4×C59C2×#4112yes—
295C2×C4×C59C2511yescharacteristic
296C22⋊D59—44no—
297C22⋊D59—44no—
298C2×Dic59—22no—
299C2×Dic59—22no—
300C2×Dic59—22no—
301C2×Dic59—22no—
302C2×Dic59—22no—
303C2×Dic59—22no—
304C2×Dic59C23×C412yes—
305C2×Dic59C23×C412yes—
306C2×Dic59C23×C412yes—
307C2×Dic59C23×C412yes—
308C2×Dic59C23×C412yes—
309C2×Dic59C23×C412yes—
310D236—44no—
311C4×D59—24no—
312C4×D59—24no—
313C4×D59—22no—
314C4×D59—22no—
315C4×D59—22no—
316C4×D59—22no—
317C4×D59—44no—
318C4×D59—44no—
319Dic118—44no—
320C8×C59—22no—
321C8×C59—22no—
322C8×C59C2×#4114yes—
323C8×C59C2×#4114yes—
324C59⋊C8—22no—
325C59⋊C8—22no—
326C59⋊C8—22no—
327C59⋊C8—22no—
328C2×#2967—591nomaximal, Sylow
329C22×C59—22no—
330C22×C59—22no—
331C22×C59—22no—
332C22×C59—44no—
333C22×C59C4×#4112yes—
334C22×C59#56812yes—
335C22×C59#56812yes—
336C22×C59C24×C411yescharacteristic
337C2×D59—22no—
338C2×D59—22no—
339C2×D59—22no—
340C2×D59—22no—
341C2×D59—22no—
342C2×D59—22no—
343C2×D59—44no—
344C2×D59—44no—
345C4×C59—22no—
346C4×C59—22no—
347C4×C59—22no—
348C4×C59—22no—
349C4×C59—22no—
350C4×C59C4×#4112yes—
351C4×C59C22×#4111yescharacteristic
352C4×C59C22×#4111yescharacteristic
353Dic59—22no—
354Dic59—22no—
355Dic59—22no—
356Dic59—22no—
357Dic59—22no—
358Dic59—22no—
359C2×#529—591no—
360#2967—5916no—
361C2×#446—591no—
362C2×#446—591no—
363C2×#436—591no—
364C2×#436—591no—
365C2×#435—591no—
366C2×#435—591no—
367C2×#435—591no—
368C2×#435—591no—
369C2×#433—591no—
370C2×#433—591no—
371C2×#432—591no—
372C2×#405—591no—
373C2×#405D5911yescharacteristic, complemented
374C2×C4×M16—591no—
375C2×C59—42no—
376C2×C59#296714yescomplemented
377C2×C59C2×C4×#4111yescharacteristic
378C2×C59C2×#56811yescharacteristic
379C2×C59C2×#56811yescharacteristic
380D59—42no—
381D59—42no—
382C22×M16—591no—
383C22×M16—591no—
384C22×M16—591no—
385C22×M16C2×D5911yescharacteristic
386C23×C8—591no—
387C23×C8C2×D5911yescharacteristic
388#529—598no—
389#529—598no—
390C2×#126—591no—
391C2×#126—591no—
392C2×#125—591no—
393C2×#124—591no—
394C2×#123—591no—
395C2×#123—591no—
396C2×C22⋊Q8—591no—
397C2×#121—591no—
398C2×C4×Q8—591no—
399C2×C4×D4—591no—
400C2×C4×D4—591no—
401C2×C4×D4—591no—
402C2×#117—591no—
403C2×#117C2×D5911yescharacteristic
404C22×C42—591no—
405#446—598no—
406#446—598no—
407#436—598no—
408#436—598no—
409#435—598no—
410#435—598no—
411#435—598no—
412#435—598no—
413#433—598no—
414#433—598no—
415#432—598no—
416C2×C4⋊C8—591no—
417C2×C4⋊C8—591no—
418C2×C4⋊C8—591no—
419C2×C4⋊C8—591no—
420C2×C4⋊C8—591no—
421C2×C4⋊C8—591no—
422C2×C22⋊C8—591no—
423C2×C22⋊C8—591no—
424C2×C22⋊C8—591no—
425C2×C22⋊C8—591no—
426C2×C22⋊C8—591no—
427C2×C22⋊C8—591no—
428#405—598no—
429#405C2×D5918yescomplemented
430C4×M16—598no—
431C2×#97—591no—
432C2×#97—591no—
433C2×#97—591no—
434C2×#97—591no—
435C2×#97C2×D5911yescharacteristic
436C2×#97C2×D5911yescharacteristic
437C2×C4×C8—591no—
438C2×C4×C8—591no—
439C2×C4×C8C2×D5911yescharacteristic
440C2×C4×C8C2×D5911yescharacteristic
441C59C2×#296711yescharacteristic, complemented, Sylow
442C22×Q8—591no—
443C22×D4—591no—
444C22×D4—591no—
445C22×D4—591no—
446C23×C4—591no—
447C23×C4—591no—
448C23×C4—591no—
449C23×C4—591no—
450C23×C4C22×D5911yescharacteristic
451C2×M16—24no—
452C2×M16—594no—
453C2×M16—594no—
454C2×M16—594no—
455C2×M16—1184no—
456C2×M16—1184no—
457C2×M16—1184no—
458C2×M16C22×D5914yes—
459C22×C8—24no—
460C22×C8—591no—
461C22×C8—591no—
462C22×C8—591no—
463C22×C8—591no—
464C22×C8—594no—
465C22×C8—1184no—
466C22×C8C22×D5914yes—
467C22×C8C22×D5911yescharacteristic
468C22×C8C22×D5911yescharacteristic
469C22×C8C22×D5911yescharacteristic
470C22×C8C22×D5911yescharacteristic
471#126—598no—
472#126—598no—
473#125—598no—
474#124—598no—
475#123—598no—
476#123—598no—
477C22⋊Q8—598no—
478#121—598no—
479C4×Q8—594no—
480C4×Q8—594no—
481C4×D4—594no—
482C4×D4—594no—
483C4×D4—594no—
484C4×D4—594no—
485C4×D4—594no—
486C4×D4—594no—
487#117—594no—
488#117—594no—
489#117C4×D5914yes—
490#117C22×D5914yes—
491C2×C4⋊C4—591no—
492C2×C4⋊C4—591no—
493C2×C4⋊C4—591no—
494C2×C4⋊C4—591no—
495C2×C4⋊C4—591no—
496C2×C4⋊C4—591no—
497C2×C4⋊C4—591no—
498C2×C4⋊C4—591no—
499C2×C4⋊C4C4×D5911yescharacteristic
500C2×C4⋊C4C4×D5911yescharacteristic
501C2×C22⋊C4—591no—
502C2×C22⋊C4—591no—
503C2×C22⋊C4—591no—
504C2×C22⋊C4—591no—
505C2×C22⋊C4—591no—
506C2×C22⋊C4—591no—
507C2×C22⋊C4—591no—
508C2×C22⋊C4—591no—
509C2×C22⋊C4C4×D5911yescharacteristic
510C2×C22⋊C4C4×D5911yescharacteristic
511C2×C42—591no—
512C2×C42—591no—
513C2×C42—591no—
514C2×C42—591no—
515C2×C42—594no—
516C2×C42—594no—
517C2×C42C22×D5911yescharacteristic
518C2×C42C22×D5911yescharacteristic
519C4⋊C8—594no—
520C4⋊C8—594no—
521C4⋊C8—594no—
522C4⋊C8—594no—
523C4⋊C8—594no—
524C4⋊C8—594no—
525C22⋊C8—594no—
526C22⋊C8—594no—
527C22⋊C8—594no—
528C22⋊C8—594no—
529C22⋊C8—594no—
530C22⋊C8—594no—
531#97—594no—
532#97—594no—
533#97—594no—
534#97—594no—
535#97C22×D5914yes—
536#97C22×D5914yes—
537C4×C8—594no—
538C4×C8—594no—
539C4×C8C22×D5914yes—
540C4×C8C22×D5914yes—
541C24—591no—
542C24—591no—
543C24C2×C4×D5911yescharacteristic
544C2×Q8—594no—
545C2×Q8—2362no—
546C2×D4—594no—
547C2×D4—594no—
548C2×D4—594no—
549C2×D4—2362no—
550C2×D4—2362no—
551C2×D4—2362no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—591no—
555C22×C4—591no—
556C22×C4—591no—
557C22×C4—591no—
558C22×C4—591no—
559C22×C4—591no—
560C22×C4—592no—
561C22×C4—592no—
562C22×C4—592no—
563C22×C4—592no—
564C22×C4—594no—
565C22×C4—594no—
566C22×C4—1182no—
567C22×C4—1182no—
568C22×C4—1182no—
569C22×C4—1182no—
570C22×C4—2362no—
571C22×C4—2362no—
572C22×C4C2×C4×D5911yescharacteristic
573C22×C4C2×C4×D5911yescharacteristic
574C22×C4C2×C4×D5911yescharacteristic
575C22×C4C2×C4×D5911yescharacteristic
576C22×C4C2×C4×D5911yescharacteristic
577C22×C4C2×C4×D5912yes—
578C22×C4C23×D5912yes—
579C22×C4C23×D5911yescharacteristic
580M16—28no—
581M16—1188no—
582M16—1188no—
583M16—1188no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—28no—
587C2×C8—592no—
588C2×C8—592no—
589C2×C8—592no—
590C2×C8—592no—
591C2×C8—1182no—
592C2×C8—1182no—
593C2×C8—1182no—
594C2×C8—1182no—
595C2×C8—1188no—
596C2×C8#1174568514yes—
597C2×C8#1174568514yes—
598C2×C8C23×D5912yes—
599C2×C8C23×D5912yes—
600C2×C8C23×D5912yes—
601C2×C8C23×D5912yes—
602C4⋊C4—594no—
603C4⋊C4—594no—
604C4⋊C4—594no—
605C4⋊C4—594no—
606C4⋊C4—594no—
607C4⋊C4—594no—
608C4⋊C4—594no—
609C4⋊C4—594no—
610C4⋊C4C2×C4×D5914yes—
611C4⋊C4C2×C4×D5914yes—
612C22⋊C4—594no—
613C22⋊C4—594no—
614C22⋊C4—594no—
615C22⋊C4—594no—
616C22⋊C4—594no—
617C22⋊C4—594no—
618C22⋊C4—594no—
619C22⋊C4—594no—
620C22⋊C4C2×C4×D5914yes—
621C22⋊C4C2×C4×D5914yes—
622C42—592no—
623C42—594no—
624C42—594no—
625C42—592no—
626C42—592no—
627C42—592no—
628C42C2×C4×D5912yes—
629C42C2×C4×D5912yes—
630C42C23×D5912yes—
631C42C23×D5912yes—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—592no—
636C23—592no—
637C23—1182no—
638C23—1182no—
639C23—1182no—
640C23—1182no—
641C23—1182no—
642C23—1182no—
643C23C22×C4×D5912yes—
644C23C22×C4×D5911yescharacteristic
645Q8—2364no—
646D4—2364no—
647D4—2364no—
648D4—2364no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—592no—
658C2×C4—592no—
659C2×C4—592no—
660C2×C4—592no—
661C2×C4—592no—
662C2×C4—592no—
663C2×C4—1182no—
664C2×C4—1182no—
665C2×C4—1182no—
666C2×C4—1182no—
667C2×C4—1182no—
668C2×C4—1182no—
669C2×C4—1182no—
670C2×C4—1182no—
671C2×C4—1182no—
672C2×C4—1182no—
673C2×C4—1184no—
674C2×C4—1184no—
675C2×C4—2364no—
676C2×C4—2364no—
677C2×C4C22×C4×D5912yes—
678C2×C4C22×C4×D5912yes—
679C2×C4C22×C4×D5912yes—
680C2×C4C22×C4×D5912yes—
681C2×C4C22×C4×D5912yes—
682C2×C4C22×C4×D5911yescharacteristic
683C2×C4C2×#1174568512yes—
684C2×C4C2×#1174568512yes—
685C2×C4C24×D5911yescharacteristic
686C8—22no—
687C8—22no—
688C8—1182no—
689C8—1182no—
690C8—1182no—
691C8—1182no—
692C8C2×#1174568514yes—
693C8C2×#1174568514yes—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—44no—
698C22—1182no—
699C22—1182no—
700C22—1182no—
701C22—1182no—
702C22—1182no—
703C22—1182no—
704C22—2364no—
705C22—2364no—
706C22C4×#1174568512yes—
707C22#1683816712yes—
708C22#1683816712yes—
709C22C23×C4×D5911yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—22no—
715C4—1182no—
716C4—1182no—
717C4—1182no—
718C4—1182no—
719C4—1182no—
720C4—1182no—
721C4C4×#1174568512yes—
722C4C22×#1174568511yescharacteristic
723C4C22×#1174568511yescharacteristic
724C2—42no—
725C2—2362no—
726C2—2362no—
727C2#2143307714yesdirect product factor
728C2C2×C4×#1174568511yescharacteristic
729C2C2×#1683816711yescharacteristic
730C2C2×#1683816711yescharacteristic
subgroupG/H
centerC22×C4C23×D59
commutatorC22×C59C24×C4
FrattiniC2×C4C24×D59
FittingC2×C59×#405C2
socleC23×C59C23×C4
prime radicalC2×#14273700C4
cosocleC2×C4×C59C25
hypercenterC2×#405D59
hypocenterC59C2×#2967
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
2. #21433077C2direct (N × H)
3. C2×#16837532C2semidirect
4. C2×#16837530C2semidirect
5. C2×#16837481C2semidirect
6. C2×#16837478C2semidirect
7. C2×#16837475C2semidirect
8. C2×#16837473C2semidirect
9. C2×#16837473C2semidirect
10. C2×#16837471C2semidirect
11. C2×#16837464C2semidirect
12. C2×#16837463C2semidirect
13. C2×#16837457C2semidirect
14. C2×#16837356C2semidirect
15. C2×C4×#11745659C2semidirect
16. C2×C59×#405C2semidirect
37. #16837532C22semidirect
38. #16837530C22semidirect
39. #16837481C22semidirect
40. #16837478C22semidirect
41. #16837475C22semidirect
42. #16837473C22semidirect
43. #16837473C22semidirect
44. #16837471C22semidirect
45. #16837464C22semidirect
46. #16837463C22semidirect
47. #16837457C22semidirect
60. #16837356C22semidirect
61. C4×#11745659C22semidirect
71. C59×#405C22semidirect
373. C2×#405D59semidirect
376. C2×C59#2967semidirect
429. #405C2×D59semidirect
441. C59C2×#2967semidirect
727. C2#21433077direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379302
#214330772
C2×#168375322
C2×#168375302
C2×#168374812
C2×#168374782
C2×#168374752
C2×#168374732
C2×#168374712
C2×#168374642
C2×#168374632
C2×#168374572
C2×#168373562
C2×C4×#117456592
C2×C59×#4052
C2×#296759