Finite Group Databasebeta

← #28605426

Subgroups — #28605426

Order 15104.

1108 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×#16837939C211yesmaximal, characteristic
2C2×#16837533C211yesmaximal, characteristic, complemented
3#21424894C211yesmaximal, characteristic, complemented
4#21424894C211yesmaximal, characteristic, complemented
5#21424893C211yesmaximal, characteristic, complemented
6#21424893C211yesmaximal, characteristic, complemented
7#21424890C211yesmaximal, characteristic, complemented
8#21424889C211yesmaximal, characteristic, complemented
9#21424077C211yesmaximal, characteristic, complemented
10#21424077C211yesmaximal, characteristic, complemented
11#21424073C211yesmaximal, characteristic, complemented
12#21423865C211yesmaximal, characteristic, complemented
13#21423863C211yesmaximal, characteristic, complemented
14#21423859C211yesmaximal, characteristic, complemented
15C2×C59×#446C211yesmaximal, characteristic, complemented
16#16837939—24no—
17#16837939—24no—
18C2×#14273722C411yescharacteristic
19C2×#14273722C411yescharacteristic
20C2×#14273718C411yescharacteristic
21C2×#14273716C411yescharacteristic
22C2×#14273712C411yescharacteristic
23C2×#14273712C411yescharacteristic
24C2×#14273703C411yescharacteristic
25C2×#14273702C411yescharacteristic
26C2×C4×D236C2211yescharacteristic
27C2×C4×D236C2211yescharacteristic
28C2×C4×D236C2211yescharacteristic
29C2×#14273684C2211yescharacteristic
30C2×#14273684C2211yescharacteristic
31C2×C42×D59C2211yescharacteristic
32#16837533—24no—
33C2×C4⋊(C59⋊C8)C2211yescharacteristic
34C2×C4⋊(C59⋊C8)C2211yescharacteristic
35C2×C4⋊(C59⋊C8)C2211yescharacteristic
36C2×(C2×D59)⋊C8C2211yescharacteristic
37C2×(C2×D59)⋊C8C2211yescharacteristic
38C2×(C2×D59)⋊C8C2211yescharacteristic
39C2×(C2×D59)⋊C8C2211yescharacteristic
40C2×(C2×D59)⋊C8C2211yescharacteristic
41C2×(C2×D59)⋊C8C2211yescharacteristic
42C2×(C2×D59)⋊C8C2211yescharacteristic
43C2×(C2×D59)⋊C8C2211yescharacteristic
44C2×(C2×D59)⋊C8C2211yescharacteristic
45C2×(C2×D59)⋊C8C2211yescharacteristic
46C2×(C2×D59)⋊C8C2211yescharacteristic
47C2×(C2×D59)⋊C8C2211yescharacteristic
48C2×#14273638C2211yescharacteristic
49C2×#14273638C2211yescharacteristic
50C2×C4×C59⋊C8C2211yescharacteristic
51#16837156C2211yescharacteristic
52#16837156C2211yescharacteristic
53#16837156C2211yescharacteristic
54#16837156C2211yescharacteristic
55C2×C4×Q8×C59C2211yescharacteristic
56C59×#446—24no—
57C2×C4⋊C8×C59C2211yescharacteristic
58C2×C4⋊C8×C59C2211yescharacteristic
59C2×C4⋊C8×C59C2211yescharacteristic
60C2×#97×C59C2211yescharacteristic
61C2×#97×C59C2211yescharacteristic
62C2×C4×C8×C59C2211yescharacteristic
63C22×D236C2×C411yescharacteristic
64C22×D236C2×C411yescharacteristic
65C22×D236C2×C411yescharacteristic
66C22×C4×D59C2×C411yescharacteristic
67C22×C4×D59C2×C411yescharacteristic
68C22×C4×D59C2311yescharacteristic
69C22×C4×D59C2311yescharacteristic
70C22×C4×D59C2311yescharacteristic
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73C22×C59⋊C8C2311yescharacteristic
74C22×C59⋊C8C2311yescharacteristic
75#14273722—24no—
76#14273722—24no—
77#14273718—24no—
78#14273716—24no—
79#14273712—24no—
80#14273712—24no—
81#14273703—24no—
82#14273702—24no—
83C4×D236—22no—
84C4×D236—22no—
85C4×D236—22no—
86C4×D236—22no—
87C4×D236—22no—
88C4×D236—22no—
89#14273684—22no—
90#14273684—22no—
91#14273684—22no—
92#14273684—22no—
93C2×C4⋊Dic59C2×C411yescharacteristic
94C2×C4⋊Dic59C2×C411yescharacteristic
95C2×C4⋊Dic59C2×C411yescharacteristic
96C2×Dic59⋊C4C2×C411yescharacteristic
97C2×Dic59⋊C4C2×C411yescharacteristic
98C2×Dic59⋊C4C2×C411yescharacteristic
99C2×Dic59⋊C4C2×C411yescharacteristic
100C2×(C2×D59)⋊C4C2×C411yescharacteristic
101C2×(C2×D59)⋊C4C2×C411yescharacteristic
102C2×(C2×D59)⋊C4C2×C411yescharacteristic
103C2×(C2×D59)⋊C4C2×C411yescharacteristic
104C2×(C2×D59)⋊C4C2×C411yescharacteristic
105C2×(C2×D59)⋊C4C2×C411yescharacteristic
106C2×(C2×D59)⋊C4C2×C411yescharacteristic
107C2×(C2×D59)⋊C4C2×C411yescharacteristic
108C2×(C2×D59)⋊C4C2×C411yescharacteristic
109C2×(C2×D59)⋊C4C2×C411yescharacteristic
110C2×C4×Dic59C2×C411yescharacteristic
111C2×C4×Dic59C2×C411yescharacteristic
112C2×C4×Dic59C2311yescharacteristic
113C42×D59—22no—
114C42×D59—22no—
115C4⋊(C59⋊C8)—22no—
116C4⋊(C59⋊C8)—22no—
117C4⋊(C59⋊C8)—22no—
118(C2×D59)⋊C8—22no—
119(C2×D59)⋊C8—22no—
120(C2×D59)⋊C8—22no—
121(C2×D59)⋊C8—22no—
122(C2×D59)⋊C8—22no—
123(C2×D59)⋊C8—22no—
124(C2×D59)⋊C8—41no—
125(C2×D59)⋊C8—41no—
126(C2×D59)⋊C8—41no—
127(C2×D59)⋊C8—41no—
128(C2×D59)⋊C8—41no—
129(C2×D59)⋊C8—41no—
130#14273638—22no—
131#14273638—22no—
132C4×C59⋊C8—22no—
133C22×Q8×C59C2×C411yescharacteristic
134C22×C8×C59C2311yescharacteristic
135C22×C8×C59C2311yescharacteristic
136C22×C8×C59C2311yescharacteristic
137C22×C8×C59C2311yescharacteristic
138C4×Q8×C59D414yes—
139C4×Q8×C59D414yes—
140C2×C4⋊C4×C59C2×C411yescharacteristic
141C2×C4⋊C4×C59C2×C411yescharacteristic
142C2×C4⋊C4×C59C2×C411yescharacteristic
143C2×C42×C59C2311yescharacteristic
144C2×C42×C59C2311yescharacteristic
145C2×C42×C59C2311yescharacteristic
146C4⋊C8×C59—22no—
147C4⋊C8×C59—22no—
148C4⋊C8×C59—22no—
149#97×C59—22no—
150#97×C59—22no—
151C4×C8×C59—22no—
152C23×D59C22×C411yescharacteristic
153C23×D59C22×C411yescharacteristic
154C23×D59C22×C411yescharacteristic
155C2×Q8×C59—41no—
156C2×Q8×C59—41no—
157C2×Q8×C59C22⋊C414yes—
158C22×C4×C59C22×C411yescharacteristic
159C22×C4×C59C22×C411yescharacteristic
160C22×C4×C59C22×C411yescharacteristic
161C22×C4×C59C22×C411yescharacteristic
162C22×C4×C59C22×C411yescharacteristic
163C22×C4×C59C22×C411yescharacteristic
164C22×C4×C59C2411yescharacteristic
165C22×Dic59C22×C411yescharacteristic
166C22×Dic59C22×C411yescharacteristic
167C22×Dic59C22×C411yescharacteristic
168C22×Dic59C22×C411yescharacteristic
169C22×Dic59C22×C411yescharacteristic
170C2×D236—22no—
171C2×D236—22no—
172C2×D236—22no—
173C2×D236—22no—
174C2×D236—22no—
175C2×D236—41no—
176C2×D236—41no—
177C2×D236—41no—
178C2×D236—41no—
179C2×C4×D59—22no—
180C2×C4×D59—22no—
181C2×C4×D59—22no—
182C2×C4×D59—21no—
183C2×C4×D59—21no—
184C2×C4×D59—21no—
185C2×C4×D59—21no—
186C2×C4×D59—21no—
187C2×C4×D59—21no—
188C2×C4×D59—21no—
189C2×C4×D59—21no—
190C2×C4×D59—21no—
191C2×C4×D59—21no—
192C2×C4×D59—21no—
193C2×C4×D59—21no—
194C2×C4×D59—21no—
195C2×C4×D59—21no—
196C2×C4×D59—21no—
197C2×C4×D59—21no—
198C2×C4×D59—21no—
199C2×C4×D59—21no—
200C2×C4×D59—41no—
201C2×C4×D59—41no—
202C2×C4×D59—41no—
203C2×C8×C59—21no—
204C2×C8×C59—21no—
205C2×C8×C59—21no—
206C2×C8×C59—21no—
207C2×C8×C59—21no—
208C2×C8×C59—21no—
209C2×C8×C59—21no—
210C2×C8×C59—21no—
211C2×C8×C59—21no—
212C2×C8×C59—21no—
213C2×C8×C59—21no—
214C2×C8×C59#4112yes—
215C4⋊C4×C59C22⋊C414yes—
216C4⋊C4×C59C22⋊C414yes—
217C4⋊C4×C59C22⋊C414yes—
218C42×C59C2×D412yes—
219C42×C59C2×D412yes—
220C42×C59C2×D412yes—
221C42×C59C2×D412yes—
222C42×C59C2×D412yes—
223C42×C59C2×D412yes—
224(C2×D59)⋊C4—22no—
225(C2×D59)⋊C4—22no—
226(C2×D59)⋊C4—22no—
227(C2×D59)⋊C4—22no—
228(C2×D59)⋊C4—22no—
229(C2×D59)⋊C4—22no—
230(C2×D59)⋊C4—22no—
231(C2×D59)⋊C4—22no—
232(C2×D59)⋊C4—22no—
233(C2×D59)⋊C4—22no—
234C4⋊Dic59—22no—
235C4⋊Dic59—22no—
236C4⋊Dic59—22no—
237Dic59⋊C4—22no—
238Dic59⋊C4—22no—
239Dic59⋊C4—22no—
240Dic59⋊C4—22no—
241C4×Dic59—22no—
242C4×Dic59—22no—
243C4×Dic59—21no—
244C4×Dic59—21no—
245C2×C59⋊C8—21no—
246C2×C59⋊C8—21no—
247C2×C59⋊C8—21no—
248C2×C59⋊C8—21no—
249C2×C59⋊C8—21no—
250C2×C59⋊C8—21no—
251C2×C59⋊C8—21no—
252C2×C59⋊C8—21no—
253C2×C59⋊C8—21no—
254C2×C59⋊C8—21no—
255C2×C59⋊C8—21no—
256C2×C59⋊C8#4112yes—
257C23×C59C23×C411yescharacteristic
258C22×D59—21no—
259C22×D59—21no—
260C22×D59—21no—
261C22×D59—21no—
262C22×D59—21no—
263C22×D59—21no—
264C22×D59—21no—
265C22×D59—21no—
266C22×D59—21no—
267C22×D59—21no—
268C22×D59—21no—
269C22×D59—21no—
270C22×D59—21no—
271C22×D59—21no—
272C22×D59—21no—
273C22×D59—21no—
274C22×D59—21no—
275C22×D59—21no—
276C22×D59—21no—
277C22×D59—21no—
278C22×D59#13112yes—
279Q8×C59—44no—
280C2×C4×C59—21no—
281C2×C4×C59—21no—
282C2×C4×C59—21no—
283C2×C4×C59—21no—
284C2×C4×C59—21no—
285C2×C4×C59—21no—
286C2×C4×C59—21no—
287C2×C4×C59—21no—
288C2×C4×C59—21no—
289C2×C4×C59—21no—
290C2×C4×C59—21no—
291C2×C4×C59—21no—
292C2×C4×C59C2×C22⋊C412yes—
293C2×C4×C59C2×C22⋊C412yes—
294C2×C4×C59C2×C22⋊C412yes—
295C2×C4×C59C2×C22⋊C412yes—
296C2×C4×C59C2×C22⋊C412yes—
297C2×C4×C59C2×C22⋊C412yes—
298C2×C4×C59C22×D411yescharacteristic
299C2×C4×C59C22×D411yescharacteristic
300C2×C4×C59C2×#4111yescharacteristic
301C2×C4×C59C2×#4111yescharacteristic
302C2×C4×C59H(5,𝔽2)11yescharacteristic
303C2×C4×C592−1+411yescharacteristic
304C2×Dic59—21no—
305C2×Dic59—21no—
306C2×Dic59—21no—
307C2×Dic59—21no—
308C2×Dic59—21no—
309C2×Dic59—21no—
310C2×Dic59—21no—
311C2×Dic59—21no—
312C2×Dic59—21no—
313C2×Dic59—21no—
314C2×Dic59—21no—
315C2×Dic59—21no—
316C2×Dic59—21no—
317C2×Dic59—21no—
318C2×Dic59—21no—
319D236—44no—
320D236—44no—
321D236—44no—
322C4×D59—44no—
323C4×D59—44no—
324C4×D59—41no—
325C4×D59—41no—
326C4×D59—41no—
327C4×D59—41no—
328C4×D59—41no—
329C4×D59—41no—
330C4×D59—41no—
331C4×D59—41no—
332C4×D59—41no—
333C4×D59—41no—
334C4×D59—41no—
335C4×D59—41no—
336C8×C59—22no—
337C8×C59—41no—
338C8×C59—41no—
339C8×C59—41no—
340C59⋊C8—22no—
341C59⋊C8—41no—
342C59⋊C8—41no—
343C59⋊C8—41no—
344#22533—591nomaximal, Sylow
345C22×C59C22×C22⋊C411yescharacteristic
346C22×C59C4×#4111yescharacteristic
347C22×C59#52011yescharacteristic
348C22×C59C2×#13111yescharacteristic
349C22×C59#56811yescharacteristic
350C22×C59#56811yescharacteristic
351C22×C59#56811yescharacteristic
352C2×D59—22no—
353C2×D59—22no—
354C2×D59—22no—
355C2×D59—41no—
356C2×D59—41no—
357C2×D59—41no—
358C2×D59—41no—
359C2×D59—41no—
360C2×D59—41no—
361C2×D59—41no—
362C2×D59—41no—
363C2×D59—41no—
364C2×D59—41no—
365C2×D59—41no—
366C2×D59—41no—
367C2×D59—41no—
368C2×D59—41no—
369C2×D59—41no—
370C2×D59—41no—
371C2×D59—41no—
372C2×D59—41no—
373C4×C59—22no—
374C4×C59—22no—
375C4×C59—22no—
376C4×C59—22no—
377C4×C59—22no—
378C4×C59—22no—
379C4×C59#54811yescharacteristic
380C4×C59#54811yescharacteristic
381C4×C59#55011yescharacteristic
382C4×C59#55011yescharacteristic
383Dic59—41no—
384Dic59—41no—
385Dic59—41no—
386Dic59—41no—
387Dic59—41no—
388C2×#529—591no—
389C2×#446—591no—
390C2×#446D5911yescharacteristic, complemented
391#1955—591no—
392#1955—591no—
393#1955—591no—
394#1955—591no—
395#1954—591no—
396#1954—591no—
397#1798—591no—
398#1798—591no—
399#1797—591no—
400#1750—591no—
401#1750—591no—
402#1749—591no—
403C2×C59#234111yescharacteristic
404C2×C59#287911yescharacteristic
405C2×C59#288011yescharacteristic
406C2×C59#296711yescharacteristic
407C2×C59#296811yescharacteristic
408C2×C59#299211yescharacteristic
409C2×C59#299511yescharacteristic
410D59—42no—
411D59—81no—
412D59—81no—
413#529—1184no—
414#529—1184no—
415C2×#126—591no—
416C2×#126—591no—
417C2×#125—591no—
418C2×#124—591no—
419C2×#123—591no—
420C2×#123—591no—
421C2×C22⋊Q8—591no—
422C2×#121—591no—
423C2×C4×Q8C2×D5911yescharacteristic
424C2×C4×D4—591no—
425C2×C4×D4—591no—
426C2×C4×D4—591no—
427C2×#117—591no—
428C2×#117—591no—
429C22×C42—591no—
430#446—24no—
431#446—1184no—
432C2×C4⋊C8—591no—
433C2×C4⋊C8—591no—
434C2×C4⋊C8—591no—
435C2×C4⋊C8C2×D5911yescharacteristic
436C2×C4⋊C8C2×D5911yescharacteristic
437C2×C4⋊C8C2×D5911yescharacteristic
438C2×C22⋊C8—591no—
439C2×C22⋊C8—591no—
440C2×C22⋊C8—591no—
441C2×C22⋊C8—591no—
442C2×C22⋊C8—591no—
443C2×C22⋊C8—591no—
444C2×C22⋊C8—591no—
445C2×C22⋊C8—591no—
446C2×C22⋊C8—591no—
447C2×C22⋊C8—591no—
448C2×C22⋊C8—591no—
449C2×C22⋊C8—591no—
450C2×#97—591no—
451C2×#97—591no—
452C2×#97C2×D5911yescharacteristic
453C2×#97C2×D5911yescharacteristic
454C2×C4×C8—591no—
455C2×C4×C8C2×D5911yescharacteristic
456#336—591no—
457#336—591no—
458#336—591no—
459#336—591no—
460C59#2253311yescharacteristic, complemented, Sylow
461C22×Q8C4×D5911yescharacteristic
462C22×D4—591no—
463C22×D4—591no—
464C22×D4—591no—
465C23×C4—591no—
466C23×C4—591no—
467C23×C4—591no—
468C23×C4—591no—
469C23×C4—591no—
470C22×C8—591no—
471C22×C8—591no—
472C22×C8—591no—
473C22×C8—591no—
474C22×C8C22×D5911yescharacteristic
475C22×C8C22×D5911yescharacteristic
476C22×C8C22×D5911yescharacteristic
477C22×C8C22×D5911yescharacteristic
478#126—1184no—
479#126—1184no—
480#125—1184no—
481#124—1184no—
482#123—1184no—
483#123—1184no—
484C22⋊Q8—1184no—
485#121—1184no—
486C4×Q8D23614yes—
487C4×Q8C22⋊D5914yes—
488C4×D4—1182no—
489C4×D4—1182no—
490C4×D4—1182no—
491C4×D4—1182no—
492C4×D4—1182no—
493C4×D4—1182no—
494#117—1182no—
495#117—1182no—
496#117—1182no—
497#117—1182no—
498C2×C4⋊C4—591no—
499C2×C4⋊C4—591no—
500C2×C4⋊C4—591no—
501C2×C4⋊C4—591no—
502C2×C4⋊C4—591no—
503C2×C4⋊C4—591no—
504C2×C4⋊C4—591no—
505C2×C4⋊C4C4×D5911yescharacteristic
506C2×C4⋊C4C4×D5911yescharacteristic
507C2×C4⋊C4C4×D5911yescharacteristic
508C2×C22⋊C4—591no—
509C2×C22⋊C4—591no—
510C2×C22⋊C4—591no—
511C2×C22⋊C4—591no—
512C2×C22⋊C4—591no—
513C2×C22⋊C4—591no—
514C2×C22⋊C4—591no—
515C2×C22⋊C4—591no—
516C2×C22⋊C4—591no—
517C2×C22⋊C4—591no—
518C2×C42—591no—
519C2×C42—591no—
520C2×C42—591no—
521C2×C42—1182no—
522C2×C42—1182no—
523C2×C42C22×D5911yescharacteristic
524C2×C42C22×D5911yescharacteristic
525C2×C42C22×D5911yescharacteristic
526C4⋊C8—22no—
527C4⋊C8—22no—
528C4⋊C8—22no—
529C4⋊C8—1182no—
530C4⋊C8—1182no—
531C4⋊C8—1182no—
532C22⋊C8—1182no—
533C22⋊C8—1182no—
534C22⋊C8—1182no—
535C22⋊C8—1182no—
536C22⋊C8—1182no—
537C22⋊C8—1182no—
538C22⋊C8—2361no—
539C22⋊C8—2361no—
540C22⋊C8—2361no—
541C22⋊C8—2361no—
542C22⋊C8—2361no—
543C22⋊C8—2361no—
544#97—22no—
545#97—22no—
546#97—1182no—
547#97—1182no—
548C4×C8—22no—
549C4×C8—1182no—
550C24—591no—
551C24—591no—
552C24—591no—
553C2×Q8—41no—
554C2×Q8—41no—
555C2×Q8(C2×D59)⋊C414yes—
556C2×D4—1182no—
557C2×D4—1182no—
558C2×D4—1182no—
559C2×D4—1182no—
560C2×D4—1182no—
561C2×D4—2361no—
562C2×D4—2361no—
563C2×D4—2361no—
564C2×D4—2361no—
565C22×C4—591no—
566C22×C4—591no—
567C22×C4—591no—
568C22×C4—591no—
569C22×C4—591no—
570C22×C4—1182no—
571C22×C4—1182no—
572C22×C4—1182no—
573C22×C4—1181no—
574C22×C4—1181no—
575C22×C4—1181no—
576C22×C4—1181no—
577C22×C4—1181no—
578C22×C4—1181no—
579C22×C4—1181no—
580C22×C4—1181no—
581C22×C4—1181no—
582C22×C4—1181no—
583C22×C4—1181no—
584C22×C4—1181no—
585C22×C4—1181no—
586C22×C4—1181no—
587C22×C4—1181no—
588C22×C4—1181no—
589C22×C4—1181no—
590C22×C4—1181no—
591C22×C4—2361no—
592C22×C4—2361no—
593C22×C4—2361no—
594C22×C4C2×C4×D5911yescharacteristic
595C22×C4C2×C4×D5911yescharacteristic
596C22×C4C2×C4×D5911yescharacteristic
597C22×C4C2×C4×D5911yescharacteristic
598C22×C4C2×C4×D5911yescharacteristic
599C22×C4C2×C4×D5911yescharacteristic
600C22×C4C23×D5911yescharacteristic
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—592no—
613C2×C8—1181no—
614C2×C8—1181no—
615C2×C8—1181no—
616C2×C8—1181no—
617C2×C8—1181no—
618C2×C8—1181no—
619C2×C8—1181no—
620C2×C8—1181no—
621C2×C8—1181no—
622C2×C8—1181no—
623C2×C8—1181no—
624C2×C8#1174568912yes—
625C4⋊C4—1182no—
626C4⋊C4—1182no—
627C4⋊C4—1182no—
628C4⋊C4—1182no—
629C4⋊C4—1182no—
630C4⋊C4—1182no—
631C4⋊C4—1182no—
632C4⋊C4(C2×D59)⋊C414yes—
633C4⋊C4(C2×D59)⋊C414yes—
634C4⋊C4(C2×D59)⋊C414yes—
635C22⋊C4—1182no—
636C22⋊C4—1182no—
637C22⋊C4—1182no—
638C22⋊C4—1182no—
639C22⋊C4—1182no—
640C22⋊C4—1182no—
641C22⋊C4—1182no—
642C22⋊C4—1182no—
643C22⋊C4—1182no—
644C22⋊C4—1182no—
645C42—1182no—
646C42—1182no—
647C42—1181no—
648C42—1181no—
649C42C2×D23612yes—
650C42C2×D23612yes—
651C42C2×D23612yes—
652C42C2×C22⋊D5912yes—
653C42C2×C22⋊D5912yes—
654C42C2×C22⋊D5912yes—
655C23—592no—
656C23—1181no—
657C23—1181no—
658C23—1181no—
659C23—1181no—
660C23—1181no—
661C23—1181no—
662C23—1181no—
663C23—1181no—
664C23—1181no—
665C23—1181no—
666C23—1181no—
667C23—1181no—
668C23—1181no—
669C23—1181no—
670C23—1181no—
671C23—1181no—
672C23—1181no—
673C23—1181no—
674C23—1181no—
675C23—1181no—
676C23C22×C4×D5911yescharacteristic
677Q8—44no—
678D4—2364no—
679D4—2364no—
680D4—2364no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—1181no—
694C2×C4—1181no—
695C2×C4—1181no—
696C2×C4—1181no—
697C2×C4—1181no—
698C2×C4—1181no—
699C2×C4—1181no—
700C2×C4—1181no—
701C2×C4—1181no—
702C2×C4—1181no—
703C2×C4—1181no—
704C2×C4—1181no—
705C2×C4—1181no—
706C2×C4—1181no—
707C2×C4—1181no—
708C2×C4—2364no—
709C2×C4—2364no—
710C2×C4—2361no—
711C2×C4—2361no—
712C2×C4—2361no—
713C2×C4—2361no—
714C2×C4—2361no—
715C2×C4—2361no—
716C2×C4—2361no—
717C2×C4—2361no—
718C2×C4—2361no—
719C2×C4—2361no—
720C2×C4—2361no—
721C2×C4—2361no—
722C2×C4C2×(C2×D59)⋊C412yes—
723C2×C4C2×(C2×D59)⋊C412yes—
724C2×C4C2×(C2×D59)⋊C412yes—
725C2×C4C2×(C2×D59)⋊C412yes—
726C2×C4C2×(C2×D59)⋊C412yes—
727C2×C4C2×(C2×D59)⋊C412yes—
728C2×C4C22×C22⋊D5911yescharacteristic
729C2×C4C22×D23611yescharacteristic
730C2×C4#41×D5911yescharacteristic
731C2×C4C2×#1174568911yescharacteristic
732C2×C4#1427377311yescharacteristic
733C2×C4#1427377511yescharacteristic
734C8—22no—
735C8—41no—
736C8—41no—
737C8—41no—
738C8—1182no—
739C8—2361no—
740C8—2361no—
741C8—2361no—
742C22—1182no—
743C22—1182no—
744C22—1182no—
745C22—2361no—
746C22—2361no—
747C22—2361no—
748C22—2361no—
749C22—2361no—
750C22—2361no—
751C22—2361no—
752C22—2361no—
753C22—2361no—
754C22—2361no—
755C22—2361no—
756C22—2361no—
757C22—2361no—
758C22—2361no—
759C22—2361no—
760C22—2361no—
761C22—2361no—
762C22—2361no—
763C22C22×(C2×D59)⋊C411yescharacteristic
764C22C4×#1174568911yescharacteristic
765C22#1683788411yescharacteristic
766C22#131×D5911yescharacteristic
767C22#1683816711yescharacteristic
768C22#1683816811yescharacteristic
769C22#1683816811yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—22no—
774C4—22no—
775C4—22no—
776C4—2361no—
777C4—2361no—
778C4—2361no—
779C4—2361no—
780C4—2361no—
781C4#1683806311yescharacteristic
782C4#1683806411yescharacteristic
783C4#1683807111yescharacteristic
784C4#1683807411yescharacteristic
785C2—4721no—
786C2—4721no—
787C2—2362no—
788C2#2142693411yescharacteristic
789C2#2143254011yescharacteristic
790C2#2143254311yescharacteristic
791C2#2143308011yescharacteristic
792C2#2143308911yescharacteristic
793C2#2143323411yescharacteristic
794C2#2143326511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D59
commutator, socleC23×C59C23×C4
FittingC2×C59×#446C2
prime radicalC2×#14273702C4
cosocleC22×C4×C59C24
hypercenterC2×#446D59
hypocenterC59#22533
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. C2×#16837533C2semidirect
3. #21424894C2semidirect
4. #21424894C2semidirect
5. #21424893C2semidirect
6. #21424893C2semidirect
7. #21424890C2semidirect
8. #21424889C2semidirect
9. #21424077C2semidirect
10. #21424077C2semidirect
11. #21424073C2semidirect
12. #21423865C2semidirect
13. #21423863C2semidirect
14. #21423859C2semidirect
15. C2×C59×#446C2semidirect
390. C2×#446D59semidirect
460. C59#22533semidirect

Maximal subgroups

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

subgroupindex
C2×#168379392
C2×#168375332
#214248942
#214248932
#214248902
#214248892
#214240772
#214240732
#214238652
#214238632
#214238592
C2×C59×#4462
#2253359