Finite Group Databasebeta

← #28615003

Subgroups — #28615003

Order 15104.

860 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14273702C211yesmaximal, characteristic
2#21424894C211yesmaximal, characteristic, complemented
3#21424893C211yesmaximal, characteristic, complemented
4#21424709C211yesmaximal, characteristic, complemented
5#21424707C211yesmaximal, characteristic, complemented
6#21424662C211yesmaximal, characteristic, complemented
7#21424387C211yesmaximal, characteristic, complemented
8#21424387C211yesmaximal, characteristic, complemented
9#21424387C211yesmaximal, characteristic, complemented
10#21424387C211yesmaximal, characteristic, complemented
11#21424275C211yesmaximal, characteristic, complemented
12#21424272C211yesmaximal, characteristic, complemented
13#21424163C211yesmaximal, characteristic, complemented
14#21424075C211yesmaximal, characteristic, complemented
15C59×#1917C211yesmaximal, characteristic, complemented
16C22×C8×D59C2211yescharacteristic
17C22×C8×D59C2211yescharacteristic
18C2×#14273702C411yescharacteristic
19C2×C4×D236C2211yescharacteristic
20C2×C4×D236C2211yescharacteristic
21C2×C4×D236C2211yescharacteristic
22C2×C42×D59C2211yescharacteristic
23C2×C4⋊(C59⋊C8)C2211yescharacteristic
24C2×Dic59⋊C8C2211yescharacteristic
25C2×Dic59⋊C8C2211yescharacteristic
26C2×(C2×D59)⋊C8C2211yescharacteristic
27C2×(C2×D59)⋊C8C2211yescharacteristic
28C2×(C2×D59)⋊C8C2211yescharacteristic
29C2×(C2×D59)⋊C8C2211yescharacteristic
30C2×(C2×D59)⋊C8C2211yescharacteristic
31C2×(C2×D59)⋊C8C2211yescharacteristic
32C2×(C2×D59)⋊C8C2211yescharacteristic
33C2×(C2×D59)⋊C8C2211yescharacteristic
34C2×(C2×D59)⋊C8C2211yescharacteristic
35C2×(C2×D59)⋊C8C2211yescharacteristic
36C2×#14273638C2211yescharacteristic
37#16837303C411yescharacteristic
38#16837301C411yescharacteristic
39#16837294C411yescharacteristic
40#16837294C411yescharacteristic
41#16837280C411yescharacteristic
42#16837280C411yescharacteristic
43#16837259C411yescharacteristic
44C4×(C2×D59)⋊C4C2211yescharacteristic
45C4×(C2×D59)⋊C4C2211yescharacteristic
46#16837157C2211yescharacteristic
47#16837157C2211yescharacteristic
48#16837157C2211yescharacteristic
49#16837157C2211yescharacteristic
50#16837156C2211yescharacteristic
51#16837156C2211yescharacteristic
52C2×C4⋊C8×C59C2211yescharacteristic
53C2×#97×C59C2211yescharacteristic
54C4×C4⋊C4×C59C2211yescharacteristic
55C59×#336C2211yescharacteristic
56C59×#336C2211yescharacteristic
57C59×#336C2211yescharacteristic
58C59×#336C2211yescharacteristic
59C22×D236C2×C411yescharacteristic
60C22×D236C2×C411yescharacteristic
61C22×D236C2×C411yescharacteristic
62C22×C4×D59C2×C411yescharacteristic
63C22×C4×D59C2×C411yescharacteristic
64C22×C4×D59C2311yescharacteristic
65C22×C4×D59C2311yescharacteristic
66C22×C4×D59C2311yescharacteristic
67C22×C59⋊C8C2311yescharacteristic
68C22×C59⋊C8C2311yescharacteristic
69C22×C59⋊C8C2311yescharacteristic
70C22×C59⋊C8C2311yescharacteristic
71C2×C8×D59—41no—
72C2×C8×D59—41no—
73C2×C8×D59—41no—
74C2×C8×D59—41no—
75C2×C8×D59—41no—
76C2×C8×D59—41no—
77#14273702—24no—
78C4×D236—41no—
79C4×D236—41no—
80C4×D236—41no—
81C4×D236—41no—
82C4×D236—41no—
83C4×D236—41no—
84C2×C4⋊Dic59C2×C411yescharacteristic
85C2×C4⋊Dic59C2×C411yescharacteristic
86C2×C4⋊Dic59C2×C411yescharacteristic
87C2×(C2×D59)⋊C4C2×C411yescharacteristic
88C2×(C2×D59)⋊C4C2×C411yescharacteristic
89C2×(C2×D59)⋊C4C2×C411yescharacteristic
90C2×(C2×D59)⋊C4C2×C411yescharacteristic
91C2×(C2×D59)⋊C4C2×C411yescharacteristic
92C2×(C2×D59)⋊C4C2×C411yescharacteristic
93C2×(C2×D59)⋊C4C2×C411yescharacteristic
94C2×(C2×D59)⋊C4C2×C411yescharacteristic
95C2×(C2×D59)⋊C4C2×C411yescharacteristic
96C2×(C2×D59)⋊C4C2×C411yescharacteristic
97C2×C4×Dic59C2×C411yescharacteristic
98C2×C4×Dic59C2×C411yescharacteristic
99C2×C4×Dic59C2311yescharacteristic
100C42×D59—41no—
101C42×D59—41no—
102C4⋊(C59⋊C8)—41no—
103Dic59⋊C8—41no—
104Dic59⋊C8—41no—
105(C2×D59)⋊C8—41no—
106(C2×D59)⋊C8—41no—
107(C2×D59)⋊C8—41no—
108(C2×D59)⋊C8—41no—
109(C2×D59)⋊C8—41no—
110(C2×D59)⋊C8—41no—
111(C2×D59)⋊C8—41no—
112(C2×D59)⋊C8—41no—
113(C2×D59)⋊C8—41no—
114(C2×D59)⋊C8—41no—
115#14273638—41no—
116C59⋊#95C2×C411yescharacteristic
117C59⋊#95C2×C411yescharacteristic
118C59⋊#95C2×C411yescharacteristic
119C59⋊#95C2×C411yescharacteristic
120C22×C8×C59C2311yescharacteristic
121C22×C8×C59C2311yescharacteristic
122C22×C8×C59C2311yescharacteristic
123C22×C8×C59C2311yescharacteristic
124C2×C4⋊C4×C59C2×C411yescharacteristic
125C2×C4⋊C4×C59C2×C411yescharacteristic
126C2×C42×C59C2311yescharacteristic
127C2×C42×C59C2311yescharacteristic
128C2×C42×C59C2311yescharacteristic
129C4⋊C8×C59—41no—
130#97×C59—41no—
131#95×C59C2×C411yescharacteristic
132#95×C59C2×C411yescharacteristic
133C23×D59C22×C411yescharacteristic
134C23×D59C22×C411yescharacteristic
135C23×D59C22×C411yescharacteristic
136C22×C4×C59C22×C411yescharacteristic
137C22×C4×C59C22×C411yescharacteristic
138C22×C4×C59C22×C411yescharacteristic
139C22×C4×C59C22×C411yescharacteristic
140C22×C4×C59C22×C411yescharacteristic
141C22×C4×C59C22×C411yescharacteristic
142C22×C4×C59C2411yescharacteristic
143C22×Dic59C22×C411yescharacteristic
144C22×Dic59C22×C411yescharacteristic
145C22×Dic59C22×C411yescharacteristic
146C22×Dic59C22×C411yescharacteristic
147C22×Dic59C22×C411yescharacteristic
148C2×D236—22no—
149C2×D236—22no—
150C2×D236—22no—
151C2×D236—22no—
152C2×D236—41no—
153C2×D236—41no—
154C2×D236—41no—
155C2×D236—41no—
156C2×D236M1614yes—
157C2×C4×D59—22no—
158C2×C4×D59—22no—
159C2×C4×D59—21no—
160C2×C4×D59—21no—
161C2×C4×D59—21no—
162C2×C4×D59—21no—
163C2×C4×D59—21no—
164C2×C4×D59—21no—
165C2×C4×D59—21no—
166C2×C4×D59—21no—
167C2×C4×D59—21no—
168C2×C4×D59—21no—
169C2×C4×D59—21no—
170C2×C4×D59—21no—
171C2×C4×D59—21no—
172C2×C4×D59—21no—
173C2×C4×D59—21no—
174C2×C4×D59—21no—
175C2×C4×D59—21no—
176C2×C4×D59—21no—
177C2×C4×D59—22no—
178C2×C4×D59—41no—
179C2×C4×D59—41no—
180C2×C4×D59—41no—
181C2×C8×C59—21no—
182C2×C8×C59—21no—
183C2×C8×C59—21no—
184C2×C8×C59—21no—
185C2×C8×C59—21no—
186C2×C8×C59—21no—
187C2×C8×C59—21no—
188C2×C8×C59—21no—
189C2×C8×C59—21no—
190C2×C8×C59—21no—
191C2×C8×C59—21no—
192C2×C8×C59—21no—
193C4⋊C4×C59—22no—
194C4⋊C4×C59—41no—
195C42×C59—21no—
196C42×C59—21no—
197C42×C59—21no—
198C42×C59—21no—
199C42×C59—21no—
200C42×C59—21no—
201(C2×D59)⋊C4—22no—
202(C2×D59)⋊C4—22no—
203(C2×D59)⋊C4—22no—
204(C2×D59)⋊C4—22no—
205(C2×D59)⋊C4—41no—
206(C2×D59)⋊C4—41no—
207(C2×D59)⋊C4—41no—
208(C2×D59)⋊C4—41no—
209(C2×D59)⋊C4—41no—
210(C2×D59)⋊C4—41no—
211C4⋊Dic59—41no—
212C4⋊Dic59—41no—
213C4⋊Dic59—41no—
214C4×Dic59—21no—
215C4×Dic59—21no—
216C4×Dic59—41no—
217C4×Dic59—41no—
218C2×C59⋊C8—21no—
219C2×C59⋊C8—21no—
220C2×C59⋊C8—21no—
221C2×C59⋊C8—21no—
222C2×C59⋊C8—21no—
223C2×C59⋊C8—21no—
224C2×C59⋊C8—21no—
225C2×C59⋊C8—21no—
226C2×C59⋊C8—21no—
227C2×C59⋊C8—21no—
228C2×C59⋊C8—21no—
229C2×C59⋊C8—21no—
230C8×D59—44no—
231C8×D59—44no—
232C23×C59C23×C411yescharacteristic
233C22×D59—21no—
234C22×D59—21no—
235C22×D59—21no—
236C22×D59—21no—
237C22×D59—21no—
238C22×D59—21no—
239C22×D59—21no—
240C22×D59—21no—
241C22×D59—21no—
242C22×D59—21no—
243C22×D59—21no—
244C22×D59—21no—
245C22×D59—21no—
246C22×D59—21no—
247C22×D59—21no—
248C22×D59—21no—
249C22×D59—21no—
250C22×D59—21no—
251C22×D59C2×M1612yes—
252C22×D59C2×M1612yes—
253C22×D59#13112yes—
254C2×C4×C59—21no—
255C2×C4×C59—21no—
256C2×C4×C59—21no—
257C2×C4×C59—21no—
258C2×C4×C59—21no—
259C2×C4×C59—21no—
260C2×C4×C59—21no—
261C2×C4×C59—21no—
262C2×C4×C59—21no—
263C2×C4×C59—21no—
264C2×C4×C59—21no—
265C2×C4×C59—21no—
266C2×C4×C59—21no—
267C2×C4×C59—21no—
268C2×C4×C59—21no—
269C2×C4×C59—21no—
270C2×C4×C59—21no—
271C2×C4×C59C2×M1612yes—
272C2×C4×C59H(5,𝔽2)11yescharacteristic
273C2×C4×C59H(5,𝔽2)11yescharacteristic
274C2×C4×C59H(5,𝔽2)11yescharacteristic
275C2×C4×C59H(5,𝔽2)11yescharacteristic
276C2×C4×C59H(5,𝔽2)11yescharacteristic
277C2×C4×C592−1+411yescharacteristic
278C2×Dic59—21no—
279C2×Dic59—21no—
280C2×Dic59—21no—
281C2×Dic59—21no—
282C2×Dic59—21no—
283C2×Dic59—21no—
284C2×Dic59—21no—
285C2×Dic59—21no—
286C2×Dic59—21no—
287C2×Dic59—21no—
288C2×Dic59—21no—
289C2×Dic59—21no—
290C2×Dic59—21no—
291C2×Dic59—21no—
292C2×Dic59#13112yes—
293D236—44no—
294D236—44no—
295D236—44no—
296C4×D59—44no—
297C4×D59—44no—
298C4×D59—41no—
299C4×D59—41no—
300C4×D59—41no—
301C4×D59—41no—
302C4×D59—41no—
303C4×D59—41no—
304C4×D59—41no—
305C4×D59—41no—
306C4×D59—41no—
307C4×D59—41no—
308C4×D59—41no—
309C4×D59—41no—
310C8×C59—41no—
311C8×C59—41no—
312C8×C59—41no—
313C8×C59—41no—
314C59⋊C8—41no—
315C59⋊C8—41no—
316C59⋊C8—41no—
317C59⋊C8—41no—
318#23333—591nomaximal, Sylow
319C22×C59#51811yescharacteristic
320C22×C59#51811yescharacteristic
321C22×C59#52011yescharacteristic
322C22×C59C22×M1611yescharacteristic
323C22×C59C2×#13111yescharacteristic
324C22×C59C2×#13111yescharacteristic
325C22×C59#56811yescharacteristic
326C2×D59—22no—
327C2×D59—22no—
328C2×D59—22no—
329C2×D59—22no—
330C2×D59—22no—
331C2×D59—22no—
332C2×D59—22no—
333C2×D59—22no—
334C2×D59—22no—
335C2×D59—41no—
336C2×D59—41no—
337C2×D59—41no—
338C2×D59—41no—
339C2×D59—41no—
340C2×D59—41no—
341C2×D59—41no—
342C2×D59—41no—
343C2×D59—41no—
344C2×D59—41no—
345C2×D59—41no—
346C2×D59—41no—
347C4×C59—22no—
348C4×C59—41no—
349C4×C59—41no—
350C4×C59—41no—
351C4×C59—41no—
352C4×C59—41no—
353C4×C59#56011yescharacteristic
354C4×C59#56011yescharacteristic
355C4×C59#56211yescharacteristic
356C4×C59#56211yescharacteristic
357Dic59—22no—
358Dic59—41no—
359Dic59—41no—
360Dic59—41no—
361Dic59—41no—
362C4×#121—591no—
363#1955—591no—
364#1955—591no—
365#1924—591no—
366#1924—591no—
367#1917—591no—
368#1917D5911yescharacteristic, complemented
369#1869—591no—
370#1869—591no—
371#1869—591no—
372#1869—591no—
373#1850—591no—
374#1850—591no—
375#1817—591no—
376#1797—591no—
377C2×C59#237711yescharacteristic
378C2×C59#297311yescharacteristic
379C2×C59#297411yescharacteristic
380C2×C59#297711yescharacteristic
381C2×C59#298111yescharacteristic
382C2×C59#299011yescharacteristic
383C2×C59#299211yescharacteristic
384D59—42no—
385D59—42no—
386D59—42no—
387C23×C8—591no—
388C23×C8—591no—
389C2×#121—591no—
390C2×C4×D4—591no—
391C2×C4×D4—591no—
392C2×C4×D4—591no—
393C22×C42—591no—
394C2×C4⋊C8—591no—
395C2×C4⋊C8—591no—
396C2×C4⋊C8—591no—
397C2×C4⋊C8C2×D5911yescharacteristic
398C2×C22⋊C8—591no—
399C2×C22⋊C8—591no—
400C2×C22⋊C8—591no—
401C2×C22⋊C8—591no—
402C2×C22⋊C8—591no—
403C2×C22⋊C8—591no—
404C2×C22⋊C8—591no—
405C2×C22⋊C8—591no—
406C2×C22⋊C8—591no—
407C2×C22⋊C8—591no—
408C2×#97—591no—
409C2×#97C2×D5911yescharacteristic
410#390—591no—
411#389—591no—
412#388—591no—
413#388—591no—
414#386—591no—
415#386—591no—
416#380—591no—
417C4×C4⋊C4C2×D5911yescharacteristic
418C4×C22⋊C4—591no—
419C4×C22⋊C4—591no—
420#336—591no—
421#336—591no—
422#336—591no—
423#336—591no—
424#336—591no—
425#336—591no—
426#336C2×D5911yescharacteristic
427#336C2×D5911yescharacteristic
428#336C2×D5911yescharacteristic
429#336C2×D5911yescharacteristic
430C59#2333311yescharacteristic, complemented, Sylow
431C22×D4—591no—
432C22×D4—591no—
433C22×D4—591no—
434C23×C4—591no—
435C23×C4—591no—
436C23×C4—591no—
437C23×C4—591no—
438C23×C4—591no—
439C22×C8—591no—
440C22×C8—591no—
441C22×C8—591no—
442C22×C8—591no—
443C22×C8—2361no—
444C22×C8—2361no—
445C22×C8—2361no—
446C22×C8—2361no—
447C22×C8—2361no—
448C22×C8—2361no—
449C22×C8C22×D5911yescharacteristic
450C22×C8C22×D5911yescharacteristic
451C22×C8C22×D5911yescharacteristic
452C22×C8C22×D5911yescharacteristic
453#121—1184no—
454C4×D4—2361no—
455C4×D4—2361no—
456C4×D4—2361no—
457C4×D4—2361no—
458C4×D4—2361no—
459C4×D4—2361no—
460C2×C4⋊C4—591no—
461C2×C4⋊C4—591no—
462C2×C4⋊C4—591no—
463C2×C4⋊C4C4×D5911yescharacteristic
464C2×C4⋊C4C4×D5911yescharacteristic
465C2×C22⋊C4—591no—
466C2×C22⋊C4—591no—
467C2×C22⋊C4—591no—
468C2×C22⋊C4—591no—
469C2×C22⋊C4—591no—
470C2×C22⋊C4—591no—
471C2×C22⋊C4—591no—
472C2×C22⋊C4—591no—
473C2×C22⋊C4—591no—
474C2×C22⋊C4—591no—
475C2×C42—591no—
476C2×C42—591no—
477C2×C42—591no—
478C2×C42—2361no—
479C2×C42—2361no—
480C2×C42C22×D5911yescharacteristic
481C2×C42C22×D5911yescharacteristic
482C2×C42C22×D5911yescharacteristic
483C4⋊C8—41no—
484C4⋊C8—2361no—
485C4⋊C8—2361no—
486C4⋊C8—2361no—
487C22⋊C8—2361no—
488C22⋊C8—2361no—
489C22⋊C8—2361no—
490C22⋊C8—2361no—
491C22⋊C8—2361no—
492C22⋊C8—2361no—
493C22⋊C8—2361no—
494C22⋊C8—2361no—
495C22⋊C8—2361no—
496C22⋊C8—2361no—
497#97—41no—
498#97—2361no—
499#95—591no—
500#95—591no—
501#95—591no—
502#95—591no—
503#95C4×D5911yescharacteristic
504#95C4×D5911yescharacteristic
505C24—591no—
506C24—591no—
507C24—591no—
508C2×D4—594no—
509C2×D4—1182no—
510C2×D4—1182no—
511C2×D4—1182no—
512C2×D4—1182no—
513C2×D4—2361no—
514C2×D4—2361no—
515C2×D4—2361no—
516C2×D4—2361no—
517C22×C4—591no—
518C22×C4—591no—
519C22×C4—591no—
520C22×C4—591no—
521C22×C4—591no—
522C22×C4—1182no—
523C22×C4—1182no—
524C22×C4—1182no—
525C22×C4—1181no—
526C22×C4—1181no—
527C22×C4—1181no—
528C22×C4—1181no—
529C22×C4—1181no—
530C22×C4—1181no—
531C22×C4—1181no—
532C22×C4—1181no—
533C22×C4—1181no—
534C22×C4—1181no—
535C22×C4—1181no—
536C22×C4—1181no—
537C22×C4—1181no—
538C22×C4—1181no—
539C22×C4—1181no—
540C22×C4—1181no—
541C22×C4—1181no—
542C22×C4—1181no—
543C22×C4—2361no—
544C22×C4—2361no—
545C22×C4—2361no—
546C22×C4C2×C4×D5911yescharacteristic
547C22×C4C2×C4×D5911yescharacteristic
548C22×C4C2×C4×D5911yescharacteristic
549C22×C4C2×C4×D5911yescharacteristic
550C22×C4C2×C4×D5911yescharacteristic
551C22×C4C2×C4×D5911yescharacteristic
552C22×C4C23×D5911yescharacteristic
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—1181no—
566C2×C8—1181no—
567C2×C8—1181no—
568C2×C8—1181no—
569C2×C8—1181no—
570C2×C8—1181no—
571C2×C8—1181no—
572C2×C8—1181no—
573C2×C8—1181no—
574C2×C8—1181no—
575C2×C8—1181no—
576C2×C8—1181no—
577C2×C8—2364no—
578C2×C8—2364no—
579C4⋊C4—22no—
580C4⋊C4—41no—
581C4⋊C4—2361no—
582C4⋊C4—2361no—
583C4⋊C4—2361no—
584C22⋊C4—1182no—
585C22⋊C4—1182no—
586C22⋊C4—1182no—
587C22⋊C4—1182no—
588C22⋊C4—2361no—
589C22⋊C4—2361no—
590C22⋊C4—2361no—
591C22⋊C4—2361no—
592C22⋊C4—2361no—
593C22⋊C4—2361no—
594C42—21no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—1181no—
601C42—1181no—
602C42—2361no—
603C42—2361no—
604C23—592no—
605C23—592no—
606C23—592no—
607C23—1181no—
608C23—1181no—
609C23—1181no—
610C23—1181no—
611C23—1181no—
612C23—1181no—
613C23—1181no—
614C23—1181no—
615C23—1181no—
616C23—1181no—
617C23—1181no—
618C23—1181no—
619C23—1181no—
620C23—1181no—
621C23—1181no—
622C23—1181no—
623C23—1181no—
624C23—1181no—
625C23C22×C4×D5911yescharacteristic
626D4—2364no—
627D4—2364no—
628D4—2364no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—592no—
647C2×C4—1181no—
648C2×C4—1181no—
649C2×C4—1181no—
650C2×C4—1181no—
651C2×C4—1181no—
652C2×C4—1181no—
653C2×C4—1181no—
654C2×C4—1181no—
655C2×C4—1181no—
656C2×C4—1181no—
657C2×C4—1181no—
658C2×C4—1181no—
659C2×C4—1181no—
660C2×C4—1181no—
661C2×C4—2364no—
662C2×C4—2364no—
663C2×C4—2361no—
664C2×C4—2361no—
665C2×C4—2361no—
666C2×C4—2361no—
667C2×C4—2361no—
668C2×C4—2361no—
669C2×C4—2361no—
670C2×C4—2361no—
671C2×C4—2361no—
672C2×C4—2361no—
673C2×C4—2361no—
674C2×C4—2361no—
675C2×C4M16×D5912yes—
676C2×C4#1427377211yescharacteristic
677C2×C4#1427377311yescharacteristic
678C2×C4#1427377311yescharacteristic
679C2×C4#1427377311yescharacteristic
680C2×C4#1427377311yescharacteristic
681C2×C4#1427377511yescharacteristic
682C8—41no—
683C8—41no—
684C8—41no—
685C8—41no—
686C8—2361no—
687C8—2361no—
688C8—2361no—
689C8—2361no—
690C22—1182no—
691C22—1182no—
692C22—1182no—
693C22—1182no—
694C22—1182no—
695C22—1182no—
696C22—1182no—
697C22—1182no—
698C22—1182no—
699C22—2361no—
700C22—2361no—
701C22—2361no—
702C22—2361no—
703C22—2361no—
704C22—2361no—
705C22—2361no—
706C22—2361no—
707C22—2361no—
708C22—2361no—
709C22—2361no—
710C22—2361no—
711C22#1683787411yescharacteristic
712C22#1683787611yescharacteristic
713C22#1683788411yescharacteristic
714C22C2×M16×D5911yescharacteristic
715C22#131×D5911yescharacteristic
716C22#131×D5911yescharacteristic
717C22#1683816811yescharacteristic
718C4—22no—
719C4—41no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—41no—
724C4—1182no—
725C4—2361no—
726C4—2361no—
727C4—2361no—
728C4—2361no—
729C4#1683814211yescharacteristic
730C4#1683814311yescharacteristic
731C4#1683814811yescharacteristic
732C4#1683815011yescharacteristic
733C2—2362no—
734C2—2362no—
735C2—2362no—
736C2#2142725111yescharacteristic
737C2#2143312411yescharacteristic
738C2#2143312811yescharacteristic
739C2#2143315111yescharacteristic
740C2#2143316811yescharacteristic
741C2#2143322011yescharacteristic
742C2#2143323411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D59
commutator, socleC23×C59C23×C4
FittingC59×#1917C2
prime radicalC2×#14273702C4
cosocleC22×C4×C59C24
hypercenter#1917D59
hypocenterC59#23333
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ #1917

Complements

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

NH ≅ G/Ntype
2. #21424894C2semidirect
3. #21424893C2semidirect
4. #21424709C2semidirect
5. #21424707C2semidirect
6. #21424662C2semidirect
7. #21424387C2semidirect
8. #21424387C2semidirect
9. #21424387C2semidirect
10. #21424387C2semidirect
11. #21424275C2semidirect
12. #21424272C2semidirect
13. #21424163C2semidirect
14. #21424075C2semidirect
15. C59×#1917C2semidirect
368. #1917D59semidirect
430. C59#23333semidirect

Maximal subgroups

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

subgroupindex
C4×#142737022
#214248942
#214248932
#214247092
#214247072
#214246622
#214243872
#214242752
#214242722
#214241632
#214240752
C59×#19172
#2333359