Finite Group Databasebeta

← #28622857

Subgroups — #28622857

Order 15104.

1090 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837706C211yesmaximal, characteristic, complemented
2C2×#16837507C211yesmaximal, characteristic, complemented
3#21429018C211yesmaximal, characteristic
4#21425296C211yesmaximal, characteristic, complemented
5#21425289C211yesmaximal, characteristic, complemented
6#21425104C211yesmaximal, characteristic, complemented
7#21425104C211yesmaximal, characteristic, complemented
8#21425066C211yesmaximal, characteristic, complemented
9#21424895C211yesmaximal, characteristic
10#21424408C211yesmaximal, characteristic, complemented
11#21424403C211yesmaximal, characteristic, complemented
12#21424295C211yesmaximal, characteristic, complemented
13#21424289C211yesmaximal, characteristic, complemented
14#21424101C211yesmaximal, characteristic, complemented
15C2×C59×#552C211yesmaximal, characteristic
16C22×#11745672C2211yescharacteristic
17C2×#14273706C2211yescharacteristic
18C2×#14273706C2211yescharacteristic
19C2×C4×Dic118C2211yescharacteristic
20#16837706—24no—
21#16837507—24no—
22C2×#14273660C2211yescharacteristic
23C2×#14273658C2211yescharacteristic
24C2×#14273658C2211yescharacteristic
25C2×C4⋊(C59⋊C8)C2211yescharacteristic
26C2×#14273651C2211yescharacteristic
27C2×#14273651C2211yescharacteristic
28C2×#14273651C2211yescharacteristic
29C2×#14273650C2211yescharacteristic
30C2×#14273650C2211yescharacteristic
31C2×#14273650C2211yescharacteristic
32C2×C22⋊(C59⋊C8)C2211yescharacteristic
33C2×C22⋊(C59⋊C8)C2211yescharacteristic
34C2×C22⋊(C59⋊C8)C2211yescharacteristic
35C2×C22⋊(C59⋊C8)C2211yescharacteristic
36C2×#14273638C2211yescharacteristic
37#16837325—21no—
38#16837325—21no—
39#16837305—21no—
40#16837298—21no—
41#16837272C2211yescharacteristic
42#16837262C2211yescharacteristic
43#16837262C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50C59×#552—24no—
51C59×#552—24no—
52C2×#126×C59—21no—
53C2×#125×C59—21no—
54C2×#125×C59C2211yescharacteristic
55C2×#123×C59—21no—
56C2×C22⋊Q8×C59C2211yescharacteristic
57C2×C22⋊Q8×C59C2211yescharacteristic
58C2×C4×Q8×C59C2211yescharacteristic
59C2×C4×D4×C59C2211yescharacteristic
60C2×#117×C59—21no—
61C2×#117×C59C2211yescharacteristic
62C22×C4⋊C4×C59C2211yescharacteristic
63C22×Dic118C2311yescharacteristic
64C2×#11745672—22no—
65C2×#11745672—22no—
66C2×#11745672—22no—
67C22×C59⋊C8C2311yescharacteristic
68C22×C59⋊C8C2311yescharacteristic
69C22×C59⋊C8C2311yescharacteristic
70C22×C59⋊C8C2311yescharacteristic
71#14273706—22no—
72#14273706—22no—
73#14273706—41no—
74#14273706—41no—
75C4×Dic118—22no—
76C4×Dic118—22no—
77C2×C4⋊Dic59—21no—
78C2×C4⋊Dic59—21no—
79C2×C4⋊Dic59C2311yescharacteristic
80C2×C4⋊Dic59C2311yescharacteristic
81C2×C4⋊Dic59C2311yescharacteristic
82C2×Dic59⋊C4—21no—
83C2×Dic59⋊C4—21no—
84C2×Dic59⋊C4—21no—
85C2×C22⋊Dic59—21no—
86C2×C22⋊Dic59—21no—
87C2×C22⋊Dic59—21no—
88C2×C22⋊Dic59—21no—
89C2×C4×Dic59—21no—
90#14273660—22no—
91#14273658—22no—
92#14273658—22no—
93C4⋊(C59⋊C8)—22no—
94#14273651—22no—
95#14273651—41no—
96#14273651—41no—
97#14273650—22no—
98#14273650—22no—
99#14273650—22no—
100C22⋊(C59⋊C8)—22no—
101C22⋊(C59⋊C8)—22no—
102C22⋊(C59⋊C8)—41no—
103C22⋊(C59⋊C8)—41no—
104#14273638—22no—
105C59⋊#95—21no—
106C59⋊#95—21no—
107C22×Q8×C59C2311yescharacteristic
108C22×D4×C59D411yescharacteristic
109C23×C4×C59—21no—
110C23×C4×C59C2311yescharacteristic
111C23×C4×C59C2311yescharacteristic
112#126×C59—28no—
113#125×C59—28no—
114#125×C59—22no—
115#125×C59D414yes—
116#123×C59—28no—
117C22⋊Q8×C59—22no—
118C22⋊Q8×C59—22no—
119C22⋊Q8×C59—22no—
120C22⋊Q8×C59—22no—
121C4×Q8×C59—22no—
122C4×Q8×C59D414yes—
123C4×D4×C59—22no—
124C4×D4×C59—22no—
125#117×C59—28no—
126#117×C59—22no—
127#117×C59—22no—
128C2×C4⋊C4×C59—21no—
129C2×C4⋊C4×C59—21no—
130C2×C4⋊C4×C59—21no—
131C2×C4⋊C4×C59—21no—
132C2×C4⋊C4×C59—21no—
133C2×C4⋊C4×C59—21no—
134C2×C4⋊C4×C59—22no—
135C2×C4⋊C4×C59—22no—
136C2×C4⋊C4×C59D411yescharacteristic
137C2×C4⋊C4×C59C2311yescharacteristic
138C2×C4⋊C4×C59C2311yescharacteristic
139C2×C4⋊C4×C59C2311yescharacteristic
140C2×C22⋊C4×C59—21no—
141C2×C22⋊C4×C59—21no—
142C2×C22⋊C4×C59—21no—
143C2×C22⋊C4×C59D411yescharacteristic
144C2×C22⋊C4×C59D411yescharacteristic
145C2×C42×C59—21no—
146C2×C42×C59—21no—
147C2×C42×C59C2311yescharacteristic
148C24×C59C2×D411yescharacteristic
149C24×C59C2×D411yescharacteristic
150C2×Q8×C59—21no—
151C2×Q8×C59—21no—
152C2×Q8×C59—21no—
153C2×Q8×C59—21no—
154C2×Q8×C59—21no—
155C2×Q8×C59C2×D412yes—
156C2×D4×C59—22no—
157C2×D4×C59—22no—
158C2×D4×C59—41no—
159C22×C4×C59—24no—
160C22×C4×C59—21no—
161C22×C4×C59—21no—
162C22×C4×C59—21no—
163C22×C4×C59—21no—
164C22×C4×C59—21no—
165C22×C4×C59—21no—
166C22×C4×C59—21no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—21no—
172C22×C4×C59—21no—
173C22×C4×C59—21no—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—42no—
177C22×C4×C59—42no—
178C22×C4×C59C2×D411yescharacteristic
179C22×C4×C59C2×D411yescharacteristic
180C22×C4×C59C2×D411yescharacteristic
181C22×C4×C59C2×D411yescharacteristic
182C22×C4×C59C2411yescharacteristic
183C22×Dic59—21no—
184C22×Dic59—21no—
185C22×Dic59—21no—
186C22×Dic59—21no—
187C2×Dic118—21no—
188C2×Dic118—21no—
189C2×Dic118—21no—
190C2×Dic118—21no—
191C2×Dic118—21no—
192C2×Dic118#4112yes—
193C4⋊C4×C59—24no—
194C4⋊C4×C59—24no—
195C4⋊C4×C59—24no—
196C4⋊C4×C59—24no—
197C4⋊C4×C59—24no—
198C4⋊C4×C59—24no—
199C4⋊C4×C59—22no—
200C4⋊C4×C59—21no—
201C4⋊C4×C59—21no—
202C4⋊C4×C59—21no—
203C4⋊C4×C59C2×D412yes—
204C4⋊C4×C59C2×D412yes—
205C4⋊C4×C59C2×D412yes—
206C22⋊C4×C59—24no—
207C22⋊C4×C59—24no—
208C22⋊C4×C59—24no—
209C22⋊C4×C59—22no—
210C22⋊C4×C59—22no—
211C42×C59—24no—
212C42×C59—24no—
213C42×C59C2×D412yes—
214C42×C59C2×D412yes—
215C22⋊Dic59—42no—
216C22⋊Dic59—42no—
217C22⋊Dic59—81no—
218C22⋊Dic59—81no—
219#11745672—28no—
220C4⋊Dic59—21no—
221C4⋊Dic59—21no—
222C4⋊Dic59—21no—
223C4⋊Dic59—21no—
224C4⋊Dic59—21no—
225C4⋊Dic59—21no—
226C4⋊Dic59—42no—
227C4⋊Dic59—81no—
228Dic59⋊C4—42no—
229Dic59⋊C4—42no—
230Dic59⋊C4—42no—
231C4×Dic59—42no—
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—21no—
241C2×C59⋊C8—21no—
242C2×C59⋊C8—21no—
243C2×C59⋊C8#4112yes—
244C23×C59—21no—
245C23×C59—21no—
246C23×C59—21no—
247C23×C59—21no—
248C23×C59—21no—
249C23×C59—21no—
250C23×C59—21no—
251C23×C59—21no—
252C23×C59—21no—
253C23×C59—21no—
254C23×C59—21no—
255C23×C59—21no—
256C23×C59—21no—
257C23×C59#13712yes—
258C23×C59C22×D411yescharacteristic
259Q8×C59—22no—
260Q8×C59—22no—
261Q8×C59—41no—
262Q8×C59—41no—
263D4×C59—44no—
264C2×C4×C59—21no—
265C2×C4×C59—21no—
266C2×C4×C59—21no—
267C2×C4×C59—21no—
268C2×C4×C59—21no—
269C2×C4×C59—22no—
270C2×C4×C59—22no—
271C2×C4×C59—22no—
272C2×C4×C59—21no—
273C2×C4×C59—22no—
274C2×C4×C59—21no—
275C2×C4×C59—21no—
276C2×C4×C59—21no—
277C2×C4×C59—21no—
278C2×C4×C59—48no—
279C2×C4×C59—41no—
280C2×C4×C59—41no—
281C2×C4×C59—41no—
282C2×C4×C59—41no—
283C2×C4×C59—41no—
284C2×C4×C59—41no—
285C2×C4×C59—41no—
286C2×C4×C59—41no—
287C2×C4×C59—41no—
288C2×C4×C59—41no—
289C2×C4×C59—41no—
290C2×C4×C59—41no—
291C2×C4×C59—41no—
292C2×C4×C59—41no—
293C2×C4×C59—41no—
294C2×C4×C59—41no—
295C2×C4×C59#12012yes—
296C2×C4×C59#12012yes—
297C2×C4×C59C22×D411yescharacteristic
298C2×C4×C59C22×D411yescharacteristic
299C2×C4×C59C2×#4111yescharacteristic
300C2×C4×C59C2×#4111yescharacteristic
301C2×C4×C59H(5,𝔽2)11yescharacteristic
302C2×C4×C592−1+411yescharacteristic
303C2×Dic59—22no—
304C2×Dic59—41no—
305C2×Dic59—41no—
306C2×Dic59—41no—
307C2×Dic59—41no—
308C2×Dic59—41no—
309C2×Dic59—41no—
310C2×Dic59—41no—
311C2×Dic59—41no—
312C2×Dic59—41no—
313C2×Dic59—41no—
314C2×Dic59—41no—
315Dic118—22no—
316Dic118—22no—
317Dic118—41no—
318Dic118—41no—
319C59⋊C8—22no—
320C59⋊C8—41no—
321C59⋊C8—41no—
322C59⋊C8—41no—
323#24139—591nomaximal, Sylow
324C22×C59—22no—
325C22×C59—22no—
326C22×C59—22no—
327C22×C59—41no—
328C22×C59—41no—
329C22×C59—41no—
330C22×C59—41no—
331C22×C59—41no—
332C22×C59—41no—
333C22×C59—41no—
334C22×C59—41no—
335C22×C59—41no—
336C22×C59—41no—
337C22×C59—41no—
338C22×C59C2×#12011yescharacteristic
339C22×C59#54611yescharacteristic
340C22×C59#54711yescharacteristic
341C22×C59C2×#13711yescharacteristic
342C22×C59#57511yescharacteristic
343C22×C59#57711yescharacteristic
344C22×C59#57811yescharacteristic
345C4×C59—22no—
346C4×C59—22no—
347C4×C59—41no—
348C4×C59—41no—
349C4×C59—42no—
350C4×C59—42no—
351C4×C59—42no—
352C4×C59—42no—
353C4×C59#52511yescharacteristic
354C4×C59#53711yescharacteristic
355C4×C59#54811yescharacteristic
356C4×C59#55011yescharacteristic
357Dic59—42no—
358Dic59—81no—
359Dic59—81no—
360Dic59—81no—
361C2×#552D5911yescharacteristic
362C2×#479—591no—
363C2×#441—591no—
364#2538—591no—
365#2036—591no—
366#2035—591no—
367#2001—591no—
368#2001—591no—
369#1992—591no—
370#1955—591no—
371#1873—591no—
372#1872—591no—
373#1854—591no—
374#1853—591no—
375#1803—591no—
376C2×C59—42no—
377C2×C59—81no—
378C2×C59#240711yescharacteristic
379C2×C59#300711yescharacteristic
380C2×C59#301311yescharacteristic
381C2×C59#331211yescharacteristic
382C2×C59#331711yescharacteristic
383C2×C59#334411yescharacteristic
384C2×C59#334911yescharacteristic
385C22×Q16—591no—
386#552—24no—
387#552—24no—
388C2×#126—21no—
389C2×#125—21no—
390C2×#125C2×D5911yescharacteristic
391C2×#123—21no—
392C2×C22⋊Q8—591no—
393C2×C22⋊Q8—591no—
394C2×C22⋊Q8C2×D5911yescharacteristic
395C2×C22⋊Q8C2×D5911yescharacteristic
396C2×C4×Q8—591no—
397C2×C4×Q8C2×D5911yescharacteristic
398C2×C4×D4C2×D5911yescharacteristic
399C2×#117—21no—
400C2×#117C2×D5911yescharacteristic
401C22×C4⋊C4C2×D5911yescharacteristic
402#479—1184no—
403#441—1184no—
404C2×#107—591no—
405C2×#106—591no—
406C2×#106—591no—
407C2×C4⋊C8—591no—
408C2×#103—591no—
409C2×#103—591no—
410C2×#103—591no—
411C2×#103—591no—
412C2×#103—591no—
413C2×#103—591no—
414C2×C22⋊C8—591no—
415C2×C22⋊C8—591no—
416C2×C22⋊C8—591no—
417C2×C22⋊C8—591no—
418C2×#97—591no—
419#396—1181no—
420#396—1181no—
421#390—1181no—
422#389—1181no—
423#384—591no—
424#380—591no—
425#380—591no—
426#340—591no—
427#340—591no—
428#340—591no—
429#340—591no—
430#340—591no—
431#340—591no—
432C59#2413911yescharacteristic, complemented, Sylow
433C22×Q8—591no—
434C22×Q8C22×D5911yescharacteristic
435C22×D4C22⋊D5911yescharacteristic
436C23×C4—21no—
437C23×C4C22×D5911yescharacteristic
438C23×C4C22×D5911yescharacteristic
439C2×Q16—1182no—
440C2×Q16—1182no—
441C2×Q16—1182no—
442C22×C8—591no—
443C22×C8—591no—
444C22×C8—591no—
445C22×C8—591no—
446#126—28no—
447#125—28no—
448#125—22no—
449#125C22⋊D5914yes—
450#123—28no—
451C22⋊Q8—22no—
452C22⋊Q8—22no—
453C22⋊Q8—22no—
454C22⋊Q8—22no—
455C22⋊Q8—1182no—
456C22⋊Q8—1182no—
457C22⋊Q8—2361no—
458C22⋊Q8—2361no—
459C4×Q8—22no—
460C4×Q8—1182no—
461C4×Q8—1182no—
462C4×Q8C22⋊D5914yes—
463C4×D4—22no—
464C4×D4—22no—
465#117—28no—
466#117—22no—
467#117—22no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—591no—
477C2×C4⋊C4—591no—
478C2×C4⋊C4—591no—
479C2×C4⋊C4—1181no—
480C2×C4⋊C4—1181no—
481C2×C4⋊C4—1181no—
482C2×C4⋊C4—1181no—
483C2×C4⋊C4—1181no—
484C2×C4⋊C4C22⋊D5911yescharacteristic
485C2×C4⋊C4C22×D5911yescharacteristic
486C2×C4⋊C4C22×D5911yescharacteristic
487C2×C4⋊C4C22×D5911yescharacteristic
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—1181no—
492C2×C22⋊C4—1181no—
493C2×C22⋊C4—1181no—
494C2×C22⋊C4—1181no—
495C2×C22⋊C4C22⋊D5911yescharacteristic
496C2×C22⋊C4C22⋊D5911yescharacteristic
497C2×C42—21no—
498C2×C42—21no—
499C2×C42—1181no—
500C2×C42C22×D5911yescharacteristic
501#107—1182no—
502#106—1182no—
503#106—1182no—
504C4⋊C8—1182no—
505#103—1182no—
506#103—1182no—
507#103—1182no—
508#103—1182no—
509#103—2361no—
510#103—2361no—
511C22⋊C8—1182no—
512C22⋊C8—1182no—
513C22⋊C8—2361no—
514C22⋊C8—2361no—
515#97—1182no—
516#95—1181no—
517#95—1181no—
518C24C2×C22⋊D5911yescharacteristic
519C24C2×C22⋊D5911yescharacteristic
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—592no—
526C2×Q8—1181no—
527C2×Q8—1181no—
528C2×Q8—1181no—
529C2×Q8—1181no—
530C2×Q8—1181no—
531C2×Q8C2×C22⋊D5912yes—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—41no—
535C22×C4—24no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—1181no—
555C22×C4—1181no—
556C22×C4—1181no—
557C22×C4—1181no—
558C22×C4C2×C22⋊D5911yescharacteristic
559C22×C4C2×C22⋊D5911yescharacteristic
560C22×C4C2×C22⋊D5911yescharacteristic
561C22×C4C2×C22⋊D5911yescharacteristic
562C22×C4C23×D5911yescharacteristic
563Q16—1188no—
564C2×C8—592no—
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—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—22no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—1181no—
587C4⋊C4—1181no—
588C4⋊C4—1181no—
589C4⋊C4—1181no—
590C4⋊C4—1181no—
591C4⋊C4—1181no—
592C4⋊C4—4721no—
593C4⋊C4—2362no—
594C4⋊C4—2362no—
595C4⋊C4—2362no—
596C4⋊C4—2362no—
597C4⋊C4C2×C22⋊D5912yes—
598C4⋊C4C2×C22⋊D5912yes—
599C4⋊C4C2×C22⋊D5912yes—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—4721no—
606C22⋊C4—4721no—
607C22⋊C4—2362no—
608C22⋊C4—2362no—
609C42—24no—
610C42—24no—
611C42—2362no—
612C42C2×C22⋊D5912yes—
613C42C2×C22⋊D5912yes—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23#1427375712yes—
628C23C22×C22⋊D5911yescharacteristic
629Q8—22no—
630Q8—22no—
631Q8—41no—
632Q8—41no—
633Q8—1182no—
634Q8—1182no—
635Q8—2361no—
636Q8—2361no—
637D4—44no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—48no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—1182no—
670C2×C4—2361no—
671C2×C4—2361no—
672C2×C4—2361no—
673C2×C4—2361no—
674C2×C4—2361no—
675C2×C4—2361no—
676C2×C4—2361no—
677C2×C4—2361no—
678C2×C4—2361no—
679C2×C4—2361no—
680C2×C4—2361no—
681C2×C4#1427369612yes—
682C2×C4#1427369612yes—
683C2×C4C22×C22⋊D5911yescharacteristic
684C2×C4C22×C22⋊D5911yescharacteristic
685C2×C4#41×D5911yescharacteristic
686C2×C4#41×D5911yescharacteristic
687C2×C4#1427377311yescharacteristic
688C2×C4#1427377411yescharacteristic
689C8—1182no—
690C8—2361no—
691C8—2361no—
692C8—2361no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22C2×#1427369611yescharacteristic
708C22#1683804011yescharacteristic
709C22#1683805111yescharacteristic
710C22C2×#1427375711yescharacteristic
711C22#1683820011yescharacteristic
712C22#1683821011yescharacteristic
713C22#1683821711yescharacteristic
714C4—22no—
715C4—22no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—41no—
720C4—41no—
721C4—42no—
722C4—4721no—
723C4—4721no—
724C4—4721no—
725C4—2362no—
726C4#1683790911yescharacteristic
727C4#1683798011yescharacteristic
728C4#1683805911yescharacteristic
729C4#1683807111yescharacteristic
730C2—42no—
731C2—81no—
732C2#2142743511yescharacteristic
733C2#2143335611yescharacteristic
734C2#2143341111yescharacteristic
735C2#2143614111yescharacteristic
736C2#2143621611yescharacteristic
737C2#2143655111yescharacteristic
738C2#2143662611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×C59×#552C2
socleC23×C59C22×D4
prime radicalC22×D4×C59D4
hypercenterC2×#552D59
hypocenterC59#24139
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×#16837706C2semidirect
2. C2×#16837507C2semidirect
4. #21425296C2semidirect
5. #21425289C2semidirect
6. #21425104C2semidirect
7. #21425104C2semidirect
8. #21425066C2semidirect
10. #21424408C2semidirect
11. #21424403C2semidirect
12. #21424295C2semidirect
13. #21424289C2semidirect
14. #21424101C2semidirect
432. C59#24139semidirect

Maximal subgroups

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

subgroupindex
C2×#168377062
C2×#168375072
#214290182
#214252962
#214252892
#214251042
#214250662
#214248952
#214244082
#214244032
#214242952
#214242892
#214241012
C2×C59×#5522
#2413959