Finite Group Databasebeta

← #28610801

Subgroups — #28610801

Order 15104.

1084 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837475C211yesmaximal, characteristic, complemented
2C2×#16837470C211yesmaximal, characteristic, complemented
3C2×(C22⋊D59)⋊C8C211yesmaximal, characteristic, complemented
4C2×#16837424C211yesmaximal, characteristic, complemented
5C4×#14273700C211yesmaximal, characteristic
6#21424888C211yesmaximal, characteristic, complemented
7#21424813C211yesmaximal, characteristic, complemented
8#21424710C211yesmaximal, characteristic, complemented
9#21424392C211yesmaximal, characteristic, complemented
10#21424390C211yesmaximal, characteristic, complemented
11#21424276C211yesmaximal, characteristic, complemented
12#21424272C211yesmaximal, characteristic, complemented
13#21423964C211yesmaximal, characteristic, complemented
14#21423853C211yesmaximal, characteristic, complemented
15C59×#1924C211yesmaximal, characteristic, complemented
16C22×#11745659C2211yescharacteristic
17C22×#11745659C2211yescharacteristic
18C23×C59⋊C8C2211yescharacteristic
19C22×C8×D59C2211yescharacteristic
20C2×#14273700C411yescharacteristic
21C2×C4×D236C2211yescharacteristic
22C2×C4×C22⋊D59C2211yescharacteristic
23C2×C4×C22⋊D59C2211yescharacteristic
24C2×C42×D59C2211yescharacteristic
25#16837475—24no—
26#16837470—24no—
27(C22⋊D59)⋊C8—24no—
28#16837424—24no—
29C2×C4⋊(C59⋊C8)C2211yescharacteristic
30C2×C4⋊(C59⋊C8)C2211yescharacteristic
31C2×Dic59⋊C8C2211yescharacteristic
32C2×Dic59⋊C8C2211yescharacteristic
33C2×Dic59⋊C8C2211yescharacteristic
34C2×C22⋊(C59⋊C8)C2211yescharacteristic
35C2×(C2×D59)⋊C8C2211yescharacteristic
36C2×(C2×D59)⋊C8C2211yescharacteristic
37C2×(C2×D59)⋊C8C2211yescharacteristic
38C2×(C2×D59)⋊C8C2211yescharacteristic
39C2×(C2×D59)⋊C8C2211yescharacteristic
40C2×#14273637C2211yescharacteristic
41C2×C8×Dic59C2211yescharacteristic
42C2×C8×Dic59C2211yescharacteristic
43#16837302C411yescharacteristic
44#16837299C411yescharacteristic
45#16837295C411yescharacteristic
46#16837291C411yescharacteristic
47#16837280C411yescharacteristic
48#16837278C411yescharacteristic
49#16837261C411yescharacteristic
50C4×Dic59⋊C4C2211yescharacteristic
51C4×(C2×D59)⋊C4C2211yescharacteristic
52#16837157C2211yescharacteristic
53#16837157C2211yescharacteristic
54#16837156C2211yescharacteristic
55#16837156C2211yescharacteristic
56C2×C4⋊C8×C59C2211yescharacteristic
57C2×C22⋊C8×C59C2211yescharacteristic
58C2×C22⋊C8×C59C2211yescharacteristic
59C2×#97×C59C2211yescharacteristic
60C4×C22⋊C4×C59C2211yescharacteristic
61C59×#336C2211yescharacteristic
62C59×#336C2211yescharacteristic
63C22×D236C2×C411yescharacteristic
64C22×C22⋊D59C2×C411yescharacteristic
65C22×C22⋊D59C2×C411yescharacteristic
66C22×C4×D59C2×C411yescharacteristic
67C22×C4×D59C2×C411yescharacteristic
68C22×C4×D59C2311yescharacteristic
69C22×C4×D59C2311yescharacteristic
70C2×#11745659—22no—
71C2×#11745659—22no—
72C2×#11745659—22no—
73C2×#11745659—22no—
74C2×#11745659—41no—
75C2×#11745659—41no—
76C22×C59⋊C8—22no—
77C22×C59⋊C8—22no—
78C22×C59⋊C8—41no—
79C22×C59⋊C8C2311yescharacteristic
80C22×C59⋊C8C2311yescharacteristic
81C22×C59⋊C8C2311yescharacteristic
82C22×C59⋊C8C2311yescharacteristic
83C2×C8×D59—22no—
84C2×C8×D59—22no—
85C2×C8×D59—41no—
86#14273700—24no—
87C4×D236—22no—
88C4×D236—22no—
89C4×C22⋊D59—22no—
90C4×C22⋊D59—22no—
91C4×C22⋊D59—22no—
92C4×C22⋊D59—22no—
93C2×C4⋊Dic59C2×C411yescharacteristic
94C2×Dic59⋊C4C2×C411yescharacteristic
95C2×Dic59⋊C4C2×C411yescharacteristic
96C2×Dic59⋊C4C2×C411yescharacteristic
97C2×Dic59⋊C4C2×C411yescharacteristic
98C2×C22⋊Dic59C2×C411yescharacteristic
99C2×C22⋊Dic59C2×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×C4×Dic59C2×C411yescharacteristic
107C2×C4×Dic59C2×C411yescharacteristic
108C2×C4×Dic59C2311yescharacteristic
109C2×C4×Dic59C2311yescharacteristic
110C42×D59—22no—
111C42×D59—22no—
112C4⋊(C59⋊C8)—22no—
113C4⋊(C59⋊C8)—22no—
114Dic59⋊C8—22no—
115Dic59⋊C8—22no—
116Dic59⋊C8D414yescomplemented
117C22⋊(C59⋊C8)—41no—
118(C2×D59)⋊C8—22no—
119(C2×D59)⋊C8—22no—
120(C2×D59)⋊C8—22no—
121(C2×D59)⋊C8—41no—
122(C2×D59)⋊C8D414yescomplemented
123#14273637—22no—
124C8×Dic59—22no—
125C8×Dic59—22no—
126C59⋊#95C2×C411yescharacteristic
127C59⋊#95C2×C411yescharacteristic
128C59⋊#95C2×C411yescharacteristic
129C59⋊#95C2×C411yescharacteristic
130C23×C4×C59C2311yescharacteristic
131C22×C8×C59C2311yescharacteristic
132C22×C8×C59C2311yescharacteristic
133C22×C8×C59C2311yescharacteristic
134C22×C8×C59C2311yescharacteristic
135C2×C22⋊C4×C59C2×C411yescharacteristic
136C2×C22⋊C4×C59C2×C411yescharacteristic
137C2×C42×C59C2311yescharacteristic
138C2×C42×C59C2311yescharacteristic
139C4⋊C8×C59—22no—
140C22⋊C8×C59—22no—
141C22⋊C8×C59—22no—
142#97×C59—22no—
143#95×C59C2×C411yescharacteristic
144#95×C59C2×C411yescharacteristic
145C24×C59C22×C411yescharacteristic
146C23×D59C22×C411yescharacteristic
147C23×D59C22×C411yescharacteristic
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59C22×C411yescharacteristic
155C22×C4×C59C22×C411yescharacteristic
156C22×C4×C59C22×C411yescharacteristic
157C22×C4×C59C22×C411yescharacteristic
158C22×C4×C59C22×C411yescharacteristic
159C22×C4×C59C2411yescharacteristic
160C2×C22⋊D59—22no—
161C2×C22⋊D59—22no—
162C2×C22⋊D59—22no—
163C2×C22⋊D59—22no—
164C2×C22⋊D59—41no—
165C2×C22⋊D59M1614yescomplemented
166C22×Dic59C22×C411yescharacteristic
167C22×Dic59C22×C411yescharacteristic
168C22×Dic59C22×C411yescharacteristic
169C22×Dic59C22×C411yescharacteristic
170C22×Dic59C22×C411yescharacteristic
171C22×Dic59C22×C411yescharacteristic
172C2×D236—22no—
173C2×D236—22no—
174C2×D236—41no—
175C2×C4×D59—21no—
176C2×C4×D59—21no—
177C2×C4×D59—21no—
178C2×C4×D59—21no—
179C2×C4×D59—22no—
180C2×C4×D59—21no—
181C2×C4×D59—21no—
182C2×C4×D59—21no—
183C2×C4×D59—21no—
184C2×C4×D59—21no—
185C2×C4×D59—21no—
186C2×C4×D59—22no—
187C2×C4×D59—22no—
188C2×C4×D59—22no—
189C2×C4×D59—22no—
190C2×C4×D59—41no—
191C2×C4×D59C2×D412yes—
192C2×C4×D59#4112yes—
193C2×C8×C59—21no—
194C2×C8×C59—21no—
195C2×C8×C59—21no—
196C2×C8×C59—21no—
197C2×C8×C59—21no—
198C2×C8×C59—21no—
199C2×C8×C59—21no—
200C2×C8×C59—21no—
201C2×C8×C59—21no—
202C2×C8×C59—21no—
203C2×C8×C59C2×D412yes—
204C2×C8×C59C2×D412yes—
205C22⋊C4×C59—22no—
206C22⋊C4×C59—22no—
207C42×C59—21no—
208C42×C59—21no—
209C42×C59—21no—
210C42×C59—21no—
211C22⋊Dic59—22no—
212C22⋊Dic59—22no—
213(C2×D59)⋊C4—22no—
214(C2×D59)⋊C4—22no—
215(C2×D59)⋊C4—22no—
216(C2×D59)⋊C4—22no—
217(C2×D59)⋊C4—22no—
218(C2×D59)⋊C4—22no—
219C4⋊Dic59—22no—
220Dic59⋊C4—22no—
221Dic59⋊C4—22no—
222Dic59⋊C4—22no—
223Dic59⋊C4—22no—
224C4×Dic59—21no—
225C4×Dic59—21no—
226C4×Dic59—22no—
227C4×Dic59—22no—
228C4×Dic59C2×D412yes—
229C4×Dic59#4112yes—
230C2×C59⋊C8—21no—
231C2×C59⋊C8—21no—
232C2×C59⋊C8—21no—
233C2×C59⋊C8—21no—
234C2×C59⋊C8—21no—
235C2×C59⋊C8—21no—
236C2×C59⋊C8—21no—
237C2×C59⋊C8—21no—
238C2×C59⋊C8—21no—
239C2×C59⋊C8—21no—
240C2×C59⋊C8—44no—
241C2×C59⋊C8C2×D412yes—
242C2×C59⋊C8C2×D412yes—
243#11745659—44no—
244#11745659—44no—
245C8×D59—44no—
246C23×C59—21no—
247C23×C59—21no—
248C23×C59—21no—
249C23×C59—21no—
250C23×C59—21no—
251C23×C59—21no—
252C23×C59C2×M1612yes—
253C23×C59C23×C411yescharacteristic
254C22×D59—21no—
255C22×D59—21no—
256C22×D59—21no—
257C22×D59—21no—
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×D59C4×D412yes—
267C22×D59C2×M1612yes—
268C2×C4×C59—21no—
269C2×C4×C59—21no—
270C2×C4×C59—21no—
271C2×C4×C59—21no—
272C2×C4×C59—21no—
273C2×C4×C59—21no—
274C2×C4×C59—21no—
275C2×C4×C59—21no—
276C2×C4×C59—21no—
277C2×C4×C59—21no—
278C2×C4×C59—21no—
279C2×C4×C59—21no—
280C2×C4×C59—21no—
281C2×C4×C59—21no—
282C2×C4×C59—41no—
283C2×C4×C59—41no—
284C2×C4×C59—41no—
285C2×C4×C59—41no—
286C2×C4×C59#13112yes—
287C2×C4×C59C22×D411yescharacteristic
288C2×C4×C59C22×D411yescharacteristic
289C2×C4×C59C2×#4111yescharacteristic
290C2×C4×C59C2×#4111yescharacteristic
291C2×C4×C59H(5,𝔽2)11yescharacteristic
292C2×C4×C592−1+411yescharacteristic
293C22⋊D59—28no—
294C22⋊D59—44no—
295C2×Dic59—21no—
296C2×Dic59—21no—
297C2×Dic59—21no—
298C2×Dic59—21no—
299C2×Dic59—21no—
300C2×Dic59—21no—
301C2×Dic59—21no—
302C2×Dic59—21no—
303C2×Dic59—21no—
304C2×Dic59—21no—
305C2×Dic59—21no—
306C2×Dic59—21no—
307C2×Dic59—21no—
308C2×Dic59C4×D412yes—
309C2×Dic59C4×D412yes—
310C2×Dic59C4×D412yes—
311C2×Dic59C2×M1612yes—
312C2×Dic59#13112yes—
313D236—44no—
314C4×D59—22no—
315C4×D59—22no—
316C4×D59—22no—
317C4×D59—22no—
318C4×D59—44no—
319C4×D59—41no—
320C4×D59—41no—
321C4×D59—41no—
322C4×D59—41no—
323C4×D59—44no—
324C8×C59—22no—
325C8×C59—22no—
326C8×C59—41no—
327C8×C59—41no—
328C59⋊C8—22no—
329C59⋊C8—22no—
330C59⋊C8—41no—
331C59⋊C8—41no—
332#22986—591nomaximal, Sylow
333C22×C59—22no—
334C22×C59—22no—
335C22×C59—22no—
336C22×C59—41no—
337C22×C59—41no—
338C22×C59—41no—
339C22×C59—41no—
340C22×C59C2×C4×D411yescharacteristic
341C22×C59C2×C4×D411yescharacteristic
342C22×C59#52011yescharacteristic
343C22×C59C22×M1611yescharacteristic
344C22×C59C2×#13111yescharacteristic
345C22×C59C2×#13111yescharacteristic
346C22×C59#56811yescharacteristic
347C2×D59—22no—
348C2×D59—22no—
349C2×D59—22no—
350C2×D59—22no—
351C2×D59—22no—
352C2×D59—22no—
353C2×D59—41no—
354C2×D59—41no—
355C2×D59—41no—
356C2×D59—41no—
357C2×D59—41no—
358C2×D59—41no—
359C2×D59—41no—
360C2×D59—41no—
361C4×C59—22no—
362C4×C59—41no—
363C4×C59—41no—
364C4×C59—41no—
365C4×C59—41no—
366C4×C59D4211yescharacteristic
367C4×C59#54711yescharacteristic
368C4×C59#54811yescharacteristic
369C4×C59#55311yescharacteristic
370Dic59—22no—
371Dic59—22no—
372Dic59—41no—
373Dic59—41no—
374Dic59—41no—
375Dic59#43514yescomplemented
376C2×#435—591no—
377C2×#435—591no—
378C2×C8×D4—591no—
379C2×#423—591no—
380C4×#121—591no—
381#1954—591no—
382#1939—591no—
383#1924—591no—
384#1924D5911yescharacteristic, complemented
385#1870—591no—
386#1870—591no—
387#1850—591no—
388#1850—591no—
389#1770—591no—
390C4×C22⋊C8—591no—
391C2×C59—42no—
392C2×C59#236111yescharacteristic
393C2×C59C2×#43511yescharacteristic
394C2×C59#293111yescharacteristic
395C2×C59#293311yescharacteristic
396C2×C59D4×M1611yescharacteristic
397C2×C59#299011yescharacteristic
398C2×C59#299311yescharacteristic
399D59—42no—
400D59—42no—
401C22×M16—591no—
402C22×M16—591no—
403C23×C8—591no—
404C23×C8—591no—
405C2×#121—591no—
406C2×C4×D4—591no—
407C2×C4×D4—591no—
408C2×C4×D4—591no—
409C22×C42—591no—
410#435—1184no—
411#435—1184no—
412C8×D4—1184no—
413#423—1184no—
414C2×C4⋊C8—591no—
415C2×C4⋊C8—591no—
416C2×C4⋊C8—591no—
417C2×C4⋊C8—591no—
418C2×C4⋊C8—591no—
419C2×C4⋊C8C2×D5911yescharacteristic
420C2×C22⋊C8—591no—
421C2×C22⋊C8—591no—
422C2×C22⋊C8—591no—
423C2×C22⋊C8—591no—
424C2×C22⋊C8—591no—
425C2×C22⋊C8—591no—
426C2×C22⋊C8C2×D5911yescharacteristic
427C2×C22⋊C8C2×D5911yescharacteristic
428C2×#97—591no—
429C2×#97C2×D5911yescharacteristic
430C2×C4×C8—591no—
431C2×C4×C8—591no—
432#390—591no—
433#389—591no—
434#388—591no—
435#388—591no—
436#386—591no—
437#386—591no—
438#380—591no—
439C4×C4⋊C4—591no—
440C4×C22⋊C4—591no—
441C4×C22⋊C4C2×D5911yescharacteristic
442#336—591no—
443#336—591no—
444#336—591no—
445#336—591no—
446#336C2×D5911yescharacteristic
447#336C2×D5911yescharacteristic
448C59#2298611yescharacteristic, complemented, Sylow
449C22×D4—591no—
450C22×D4—591no—
451C22×D4—591no—
452C23×C4—591no—
453C23×C4—591no—
454C23×C4—591no—
455C23×C4—591no—
456C23×C4C22×D5911yescharacteristic
457C2×M16—1182no—
458C2×M16—1182no—
459C2×M16—1182no—
460C2×M16—1182no—
461C2×M16—2361no—
462C2×M16—2361no—
463C22×C8—591no—
464C22×C8—591no—
465C22×C8—591no—
466C22×C8—591no—
467C22×C8—1182no—
468C22×C8—1182no—
469C22×C8—1182no—
470C22×C8—1182no—
471C22×C8—2361no—
472C22×C8—2361no—
473C22×C8C22×D5911yescharacteristic
474C22×C8C22×D5911yescharacteristic
475C22×C8C22×D5911yescharacteristic
476C22×C8C22×D5911yescharacteristic
477#121—1184no—
478C4×D4—1182no—
479C4×D4—1182no—
480C4×D4—1182no—
481C4×D4—1182no—
482C4×D4—1182no—
483C4×D4—1182no—
484C2×C4⋊C4—591no—
485C2×C4⋊C4—591no—
486C2×C4⋊C4—591no—
487C2×C4⋊C4—591no—
488C2×C4⋊C4—591no—
489C2×C22⋊C4—591no—
490C2×C22⋊C4—591no—
491C2×C22⋊C4—591no—
492C2×C22⋊C4—591no—
493C2×C22⋊C4—591no—
494C2×C22⋊C4—591no—
495C2×C22⋊C4—591no—
496C2×C22⋊C4—591no—
497C2×C22⋊C4C4×D5911yescharacteristic
498C2×C22⋊C4C4×D5911yescharacteristic
499C2×C42—591no—
500C2×C42—591no—
501C2×C42—591no—
502C2×C42—591no—
503C2×C42—1182no—
504C2×C42—1182no—
505C2×C42C22×D5911yescharacteristic
506C2×C42C22×D5911yescharacteristic
507C4⋊C8—22no—
508C4⋊C8—594no—
509C4⋊C8—1182no—
510C4⋊C8—1182no—
511C4⋊C8—1182no—
512C4⋊C8—1182no—
513C22⋊C8—22no—
514C22⋊C8—22no—
515C22⋊C8—594no—
516C22⋊C8—1182no—
517C22⋊C8—1182no—
518C22⋊C8—1182no—
519C22⋊C8—2361no—
520C22⋊C8—2361no—
521#97—22no—
522#97—1182no—
523C4×C8—1182no—
524C4×C8—1182no—
525#95—591no—
526#95—591no—
527#95—591no—
528#95—591no—
529#95C4×D5911yescharacteristic
530#95C4×D5911yescharacteristic
531C24—591no—
532C24—591no—
533C24C2×C4×D5911yescharacteristic
534C2×D4—594no—
535C2×D4—1182no—
536C2×D4—1182no—
537C2×D4—1182no—
538C2×D4—1182no—
539C2×D4—1182no—
540C2×D4—1182no—
541C2×D4—2361no—
542C2×D4—2361no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—591no—
550C22×C4—591no—
551C22×C4—591no—
552C22×C4—592no—
553C22×C4—592no—
554C22×C4—591no—
555C22×C4—591no—
556C22×C4—591no—
557C22×C4—1182no—
558C22×C4—1182no—
559C22×C4—1182no—
560C22×C4—1182no—
561C22×C4—1181no—
562C22×C4—1181no—
563C22×C4—1181no—
564C22×C4—1181no—
565C22×C4—1182no—
566C22×C4—1181no—
567C22×C4—1181no—
568C22×C4—1181no—
569C22×C4—1181no—
570C22×C4—1181no—
571C22×C4—1181no—
572C22×C4—2361no—
573C22×C4C2×C4×D5911yescharacteristic
574C22×C4C2×C4×D5911yescharacteristic
575C22×C4C2×C4×D5911yescharacteristic
576C22×C4C2×C4×D5911yescharacteristic
577C22×C4C2×C4×D5911yescharacteristic
578C22×C4C23×D5911yescharacteristic
579M16—2364no—
580M16—2364no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—592no—
592C2×C8—592no—
593C2×C8—1181no—
594C2×C8—1181no—
595C2×C8—1181no—
596C2×C8—1181no—
597C2×C8—1181no—
598C2×C8—1181no—
599C2×C8—1181no—
600C2×C8—1181no—
601C2×C8—1181no—
602C2×C8—1181no—
603C2×C8—2364no—
604C2×C8—2364no—
605C2×C8D4×D5912yes—
606C2×C8D4×D5912yes—
607C4⋊C4—1182no—
608C4⋊C4—1182no—
609C4⋊C4—1182no—
610C4⋊C4—1182no—
611C4⋊C4—1182no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—1182no—
615C22⋊C4—1182no—
616C22⋊C4—1182no—
617C22⋊C4—1182no—
618C22⋊C4—1182no—
619C22⋊C4—1182no—
620C22⋊C4—1182no—
621C22⋊C4—1182no—
622C42—21no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—592no—
627C42—592no—
628C42—1182no—
629C42—1182no—
630C42—1181no—
631C42—1181no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—592no—
639C23—592no—
640C23—1181no—
641C23—1181no—
642C23—1181no—
643C23—1181no—
644C23—1181no—
645C23—1181no—
646C23—1181no—
647C23—1181no—
648C23—1181no—
649C23—1181no—
650C23—1181no—
651C23—1181no—
652C23M16×D5912yes—
653C23C22×C4×D5911yescharacteristic
654D4—1188no—
655D4—2364no—
656D4—2364no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—592no—
676C2×C4—592no—
677C2×C4—592no—
678C2×C4—592no—
679C2×C4—592no—
680C2×C4—1181no—
681C2×C4—1181no—
682C2×C4—1181no—
683C2×C4—1181no—
684C2×C4—1182no—
685C2×C4—1182no—
686C2×C4—1182no—
687C2×C4—1182no—
688C2×C4—1181no—
689C2×C4—1181no—
690C2×C4—1181no—
691C2×C4—1181no—
692C2×C4—1181no—
693C2×C4—1181no—
694C2×C4—1181no—
695C2×C4—1181no—
696C2×C4—1181no—
697C2×C4—2364no—
698C2×C4—2364no—
699C2×C4—2361no—
700C2×C4—2361no—
701C2×C4—2361no—
702C2×C4—2361no—
703C2×C4#1427373512yes—
704C2×C4C2×D4×D5911yescharacteristic
705C2×C4C2×D4×D5911yescharacteristic
706C2×C4#41×D5911yescharacteristic
707C2×C4#41×D5911yescharacteristic
708C2×C4#1427377311yescharacteristic
709C2×C4#1427377411yescharacteristic
710C8—22no—
711C8—22no—
712C8—41no—
713C8—41no—
714C8—1182no—
715C8—1182no—
716C8—2361no—
717C8—2361no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—1182no—
726C22—1182no—
727C22—1182no—
728C22—1182no—
729C22—1182no—
730C22—1182no—
731C22—2361no—
732C22—2361no—
733C22—2361no—
734C22—2361no—
735C22—2361no—
736C22—2361no—
737C22—2361no—
738C22—2361no—
739C22C4×D4×D5911yescharacteristic
740C22C4×D4×D5911yescharacteristic
741C22#1683788211yescharacteristic
742C22C2×M16×D5911yescharacteristic
743C22#131×D5911yescharacteristic
744C22C2×#1427373511yescharacteristic
745C22#1683816711yescharacteristic
746C4—22no—
747C4—41no—
748C4—41no—
749C4—41no—
750C4—41no—
751C4—594no—
752C4—1182no—
753C4—1182no—
754C4—2361no—
755C4—2361no—
756C4—2361no—
757C4#1683803611yescharacteristic
758C4#1683805011yescharacteristic
759C4#1683806011yescharacteristic
760C4#1683810311yescharacteristic
761C2—42no—
762C2—2362no—
763C2—2362no—
764C2#2142710911yescharacteristic
765C2#435×D5911yescharacteristic
766C2#2143280511yescharacteristic
767C2#2143282211yescharacteristic
768C2#2143282911yescharacteristic
769C2#2143322311yescharacteristic
770C2#2143323911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D59
commutator, socleC23×C59C23×C4
FittingC59×#1924C2
prime radicalC2×#14273700C4
cosocleC22×C4×C59C24
hypercenter#1924D59
hypocenterC59#22986
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
1. C2×#16837475C2semidirect
2. C2×#16837470C2semidirect
3. C2×(C22⋊D59)⋊C8C2semidirect
4. C2×#16837424C2semidirect
6. #21424888C2semidirect
7. #21424813C2semidirect
8. #21424710C2semidirect
9. #21424392C2semidirect
10. #21424390C2semidirect
11. #21424276C2semidirect
12. #21424272C2semidirect
13. #21423964C2semidirect
14. #21423853C2semidirect
15. C59×#1924C2semidirect
116. Dic59⋊C8D4semidirect
122. (C2×D59)⋊C8D4semidirect
165. C2×C22⋊D59M16semidirect
375. Dic59#435semidirect
384. #1924D59semidirect
448. C59#22986semidirect

Maximal subgroups

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

subgroupindex
C2×#168374752
C2×#168374702
C2×(C22⋊D59)⋊C82
C2×#168374242
C4×#142737002
#214248882
#214248132
#214247102
#214243922
#214243902
#214242762
#214242722
#214239642
#214238532
C59×#19242
#2298659