Finite Group Databasebeta

← #28598336

Subgroups — #28598336

Order 15104.

1128 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837930C211yesmaximal, characteristic
2C2×#16837462C211yesmaximal, characteristic, complemented
3C2×#16837427C211yesmaximal, characteristic, complemented
4#21425034C211yesmaximal, characteristic, complemented
5#21425030C211yesmaximal, characteristic, complemented
6#21424892C211yesmaximal, characteristic, complemented
7#21424888C211yesmaximal, characteristic, complemented
8#21424392C211yesmaximal, characteristic, complemented
9#21424390C211yesmaximal, characteristic, complemented
10#21424387C211yesmaximal, characteristic, complemented
11#21424385C211yesmaximal, characteristic, complemented
12#21424080C211yesmaximal, characteristic, complemented
13#21424073C211yesmaximal, characteristic, complemented
14#21424073C211yesmaximal, characteristic, complemented
15C59×#1798C211yesmaximal, characteristic, complemented
16C22×#11745659C2211yescharacteristic
17C22×C8×D59C2211yescharacteristic
18#16837930—24no—
19#16837930—24no—
20C2×#14273722C411yescharacteristic
21C2×#14273720C411yescharacteristic
22C2×#14273717C411yescharacteristic
23C2×#14273713C411yescharacteristic
24C2×#14273712C411yescharacteristic
25C2×#14273709C411yescharacteristic
26C2×#14273705C411yescharacteristic
27C2×#14273700C411yescharacteristic
28C2×C4×Dic118C2211yescharacteristic
29C2×C4×D236C2211yescharacteristic
30C2×C4×C22⋊D59C2211yescharacteristic
31C2×C4×C22⋊D59C2211yescharacteristic
32C2×#14273684C2211yescharacteristic
33C2×C42×D59C2211yescharacteristic
34#16837462—24no—
35#16837427—24no—
36C2×C4⋊(C59⋊C8)C2211yescharacteristic
37C2×C4⋊(C59⋊C8)C2211yescharacteristic
38C2×Dic59⋊C8C2211yescharacteristic
39C2×Dic59⋊C8C2211yescharacteristic
40C2×C22⋊(C59⋊C8)C2211yescharacteristic
41C2×C22⋊(C59⋊C8)C2211yescharacteristic
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×#14273637C2211yescharacteristic
49C2×C8×Dic59C2211yescharacteristic
50#16837157C2211yescharacteristic
51#16837157C2211yescharacteristic
52#16837156C2211yescharacteristic
53#16837156C2211yescharacteristic
54#16837156C2211yescharacteristic
55#16837156C2211yescharacteristic
56C2×#117×C59C2211yescharacteristic
57C2×C4⋊C8×C59C2211yescharacteristic
58C2×C4⋊C8×C59C2211yescharacteristic
59C2×C22⋊C8×C59C2211yescharacteristic
60C2×C22⋊C8×C59C2211yescharacteristic
61C59×#336C2211yescharacteristic
62C59×#336C2211yescharacteristic
63C22×Dic118C2×C411yescharacteristic
64C22×D236C2×C411yescharacteristic
65C22×C22⋊D59C2×C411yescharacteristic
66C22×C22⋊D59C2×C411yescharacteristic
67C22×C4×D59C2×C411yescharacteristic
68C22×C4×D59C2×C411yescharacteristic
69C22×C4×D59C2311yescharacteristic
70C22×C4×D59C2311yescharacteristic
71C2×#11745659—22no—
72C2×#11745659—41no—
73C2×#11745659—41no—
74C22×C59⋊C8C2311yescharacteristic
75C22×C59⋊C8C2311yescharacteristic
76C22×C59⋊C8C2311yescharacteristic
77C22×C59⋊C8C2311yescharacteristic
78C2×C8×D59—22no—
79C2×C8×D59—41no—
80C2×C8×D59—41no—
81#14273722—24no—
82#14273720—24no—
83#14273717—24no—
84#14273713—24no—
85#14273712—24no—
86#14273709—24no—
87#14273705—24no—
88#14273700—24no—
89C4×Dic118—22no—
90C4×Dic118—22no—
91C4×D236—22no—
92C4×D236—22no—
93C4×C22⋊D59—22no—
94C4×C22⋊D59—22no—
95C4×C22⋊D59—22no—
96C4×C22⋊D59—22no—
97#14273684D414yes—
98#14273684D414yes—
99C2×C4⋊Dic59C2×C411yescharacteristic
100C2×C4⋊Dic59C2×C411yescharacteristic
101C2×Dic59⋊C4C2×C411yescharacteristic
102C2×Dic59⋊C4C2×C411yescharacteristic
103C2×Dic59⋊C4C2×C411yescharacteristic
104C2×Dic59⋊C4C2×C411yescharacteristic
105C2×Dic59⋊C4C2×C411yescharacteristic
106C2×Dic59⋊C4C2×C411yescharacteristic
107C2×C22⋊Dic59C2×C411yescharacteristic
108C2×C22⋊Dic59C2×C411yescharacteristic
109C2×(C2×D59)⋊C4C2×C411yescharacteristic
110C2×(C2×D59)⋊C4C2×C411yescharacteristic
111C2×(C2×D59)⋊C4C2×C411yescharacteristic
112C2×(C2×D59)⋊C4C2×C411yescharacteristic
113C2×(C2×D59)⋊C4C2×C411yescharacteristic
114C2×(C2×D59)⋊C4C2×C411yescharacteristic
115C2×C4×Dic59C2×C411yescharacteristic
116C2×C4×Dic59C2×C411yescharacteristic
117C2×C4×Dic59C2311yescharacteristic
118C2×C4×Dic59C2311yescharacteristic
119C42×D59—22no—
120C42×D59—22no—
121C4⋊(C59⋊C8)—22no—
122C4⋊(C59⋊C8)—22no—
123Dic59⋊C8—22no—
124Dic59⋊C8—22no—
125C22⋊(C59⋊C8)—41no—
126C22⋊(C59⋊C8)—41no—
127(C2×D59)⋊C8—22no—
128(C2×D59)⋊C8—22no—
129(C2×D59)⋊C8—41no—
130(C2×D59)⋊C8—41no—
131(C2×D59)⋊C8—41no—
132(C2×D59)⋊C8—41no—
133#14273637—22no—
134C8×Dic59—22no—
135C23×C4×C59C2311yescharacteristic
136C22×C8×C59C2311yescharacteristic
137C22×C8×C59C2311yescharacteristic
138C22×C8×C59C2311yescharacteristic
139C22×C8×C59C2311yescharacteristic
140#117×C59—22no—
141#117×C59—22no—
142C2×C4⋊C4×C59C2×C411yescharacteristic
143C2×C4⋊C4×C59C2×C411yescharacteristic
144C2×C22⋊C4×C59C2×C411yescharacteristic
145C2×C22⋊C4×C59C2×C411yescharacteristic
146C2×C42×C59C2311yescharacteristic
147C2×C42×C59C2311yescharacteristic
148C4⋊C8×C59—22no—
149C4⋊C8×C59—22no—
150C22⋊C8×C59—41no—
151C22⋊C8×C59—41no—
152C24×C59C22×C411yescharacteristic
153C23×D59C22×C411yescharacteristic
154C23×D59C22×C411yescharacteristic
155C22×C4×C59—21no—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59—21no—
159C22×C4×C59—21no—
160C22×C4×C59—21no—
161C22×C4×C59C22×C411yescharacteristic
162C22×C4×C59C22×C411yescharacteristic
163C22×C4×C59C22×C411yescharacteristic
164C22×C4×C59C22×C411yescharacteristic
165C22×C4×C59C22×C411yescharacteristic
166C22×C4×C59C2411yescharacteristic
167C2×C22⋊D59—22no—
168C2×C22⋊D59—22no—
169C2×C22⋊D59—22no—
170C2×C22⋊D59—22no—
171C2×C22⋊D59—41no—
172C2×C22⋊D59—41no—
173C22×Dic59C22×C411yescharacteristic
174C22×Dic59C22×C411yescharacteristic
175C22×Dic59C22×C411yescharacteristic
176C22×Dic59C22×C411yescharacteristic
177C22×Dic59C22×C411yescharacteristic
178C22×Dic59C22×C411yescharacteristic
179C2×D236—22no—
180C2×D236—22no—
181C2×D236—41no—
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—21no—
190C2×C4×D59—21no—
191C2×C4×D59—21no—
192C2×C4×D59—21no—
193C2×C4×D59—21no—
194C2×C4×D59—21no—
195C2×C4×D59—22no—
196C2×C4×D59—41no—
197C2×C4×D59—41no—
198C2×C4×D59C2×D412yes—
199C2×C4×D59C2×D412yes—
200C2×Dic118—22no—
201C2×Dic118—22no—
202C2×Dic118—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—21no—
215C4⋊C4×C59—22no—
216C4⋊C4×C59—22no—
217C22⋊C4×C59—22no—
218C22⋊C4×C59—22no—
219C42×C59—21no—
220C42×C59—21no—
221C42×C59C2×D412yes—
222C42×C59C2×D412yes—
223C22⋊Dic59—22no—
224C22⋊Dic59—22no—
225(C2×D59)⋊C4—22no—
226(C2×D59)⋊C4—22no—
227(C2×D59)⋊C4—22no—
228(C2×D59)⋊C4—22no—
229(C2×D59)⋊C4C22⋊C414yes—
230(C2×D59)⋊C4C22⋊C414yes—
231C4⋊Dic59—22no—
232C4⋊Dic59—22no—
233Dic59⋊C4—22no—
234Dic59⋊C4—22no—
235Dic59⋊C4—22no—
236Dic59⋊C4—22no—
237Dic59⋊C4C22⋊C414yes—
238Dic59⋊C4C22⋊C414yes—
239C4×Dic59—22no—
240C4×Dic59—22no—
241C4×Dic59—21no—
242C4×Dic59—21no—
243C4×Dic59C2×D412yes—
244C4×Dic59C2×D412yes—
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—21no—
257#11745659—44no—
258C8×D59—44no—
259C23×C59—21no—
260C23×C59—21no—
261C23×C59—21no—
262C23×C59—21no—
263C23×C59—21no—
264C23×C59—21no—
265C23×C59—21no—
266C23×C59C23×C411yescharacteristic
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—21no—
279C22×D59C2×C22⋊C412yes—
280C22×D59#13112yes—
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×C59—21no—
293C2×C4×C59—21no—
294C2×C4×C59—41no—
295C2×C4×C59—41no—
296C2×C4×C59—41no—
297C2×C4×C59—41no—
298C2×C4×C59C2×C22⋊C412yes—
299C2×C4×C59C2×C22⋊C412yes—
300C2×C4×C59C22×D411yescharacteristic
301C2×C4×C59C22×D411yescharacteristic
302C2×C4×C59H(5,𝔽2)11yescharacteristic
303C2×C4×C59H(5,𝔽2)11yescharacteristic
304C2×C4×C592−1+411yescharacteristic
305C2×C4×C592−1+411yescharacteristic
306C22⋊D59—44no—
307C22⋊D59—44no—
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—
319C2×Dic59—21no—
320C2×Dic59—21no—
321C2×Dic59—21no—
322C2×Dic59C2×C22⋊C412yes—
323C2×Dic59C2×C22⋊C412yes—
324C2×Dic59C2×C22⋊C412yes—
325C2×Dic59#13112yes—
326D236—44no—
327C4×D59—22no—
328C4×D59—22no—
329C4×D59—22no—
330C4×D59—22no—
331C4×D59—44no—
332C4×D59—44no—
333C4×D59—41no—
334C4×D59—41no—
335C4×D59—41no—
336C4×D59—41no—
337Dic118—44no—
338C8×C59—41no—
339C8×C59—41no—
340C8×C59—41no—
341C8×C59—41no—
342C59⋊C8—41no—
343C59⋊C8—41no—
344C59⋊C8—41no—
345C59⋊C8—41no—
346#21855—591nomaximal, Sylow
347C22×C59—41no—
348C22×C59—41no—
349C22×C59—41no—
350C22×C59—41no—
351C22×C59—41no—
352C22×C59—41no—
353C22×C59—41no—
354C22×C59C22×C22⋊C411yescharacteristic
355C22×C59#52011yescharacteristic
356C22×C59#52011yescharacteristic
357C22×C59C2×#13111yescharacteristic
358C22×C59C2×#13111yescharacteristic
359C22×C59#56811yescharacteristic
360C22×C59#56811yescharacteristic
361C2×D59—22no—
362C2×D59—22no—
363C2×D59—22no—
364C2×D59—22no—
365C2×D59—22no—
366C2×D59—22no—
367C2×D59—41no—
368C2×D59—41no—
369C2×D59—41no—
370C2×D59—41no—
371C2×D59—41no—
372C2×D59—41no—
373C2×D59—41no—
374C2×D59—41no—
375C4×C59—22no—
376C4×C59—22no—
377C4×C59—41no—
378C4×C59—41no—
379C4×C59—41no—
380C4×C59#53511yescharacteristic
381C4×C59#53611yescharacteristic
382C4×C59#53711yescharacteristic
383C4×C59#53711yescharacteristic
384Dic59—22no—
385Dic59—22no—
386Dic59—22no—
387Dic59—22no—
388Dic59—41no—
389Dic59—41no—
390C2×#529—591no—
391C2×#433—591no—
392C2×#424—591no—
393#1985—591no—
394#1984—591no—
395#1955—591no—
396#1954—591no—
397#1870—591no—
398#1870—591no—
399#1869—591no—
400#1869—591no—
401#1798—591no—
402#1798D5911yescharacteristic, complemented
403#1797—591no—
404#1797—591no—
405C2×C59—81no—
406C2×C59#231111yescharacteristic
407C2×C59#288011yescharacteristic
408C2×C59#288011yescharacteristic
409C2×C59#299211yescharacteristic
410C2×C59#299311yescharacteristic
411C2×C59#299411yescharacteristic
412C2×C59#299511yescharacteristic
413D59—42no—
414D59—42no—
415C22×M16—591no—
416C23×C8—591no—
417#529—1184no—
418#529—1184no—
419C2×#126—591no—
420C2×#126—591no—
421C2×#125—591no—
422C2×#124—591no—
423C2×#123—591no—
424C2×#123—591no—
425C2×C22⋊Q8—591no—
426C2×#121—591no—
427C2×C4×Q8—591no—
428C2×C4×D4—591no—
429C2×C4×D4—591no—
430C2×C4×D4—591no—
431C2×#117—591no—
432C2×#117C2×D5911yescharacteristic
433C22×C42—591no—
434#433—1184no—
435#424—1184no—
436C2×C4⋊C8—591no—
437C2×C4⋊C8—591no—
438C2×C4⋊C8—591no—
439C2×C4⋊C8—591no—
440C2×C4⋊C8C2×D5911yescharacteristic
441C2×C4⋊C8C2×D5911yescharacteristic
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×C22⋊C8C2×D5911yescharacteristic
451C2×C22⋊C8C2×D5911yescharacteristic
452C2×#97—591no—
453C2×C4×C8—591no—
454#336—591no—
455#336—591no—
456#336—591no—
457#336—591no—
458#336—591no—
459#336—591no—
460#336C2×D5911yescharacteristic
461#336C2×D5911yescharacteristic
462C59#2185511yescharacteristic, complemented, Sylow
463C22×Q8—591no—
464C22×D4—591no—
465C22×D4—591no—
466C22×D4—591no—
467C23×C4—591no—
468C23×C4—591no—
469C23×C4—591no—
470C23×C4—591no—
471C23×C4C22×D5911yescharacteristic
472C2×M16—1182no—
473C2×M16—2361no—
474C2×M16—2361no—
475C22×C8—591no—
476C22×C8—591no—
477C22×C8—591no—
478C22×C8—591no—
479C22×C8—1182no—
480C22×C8—2361no—
481C22×C8—2361no—
482C22×C8C22×D5911yescharacteristic
483C22×C8C22×D5911yescharacteristic
484C22×C8C22×D5911yescharacteristic
485C22×C8C22×D5911yescharacteristic
486#126—1184no—
487#126—1184no—
488#125—1184no—
489#124—1184no—
490#123—1184no—
491#123—1184no—
492C22⋊Q8—1184no—
493#121—1184no—
494C4×Q8—1182no—
495C4×Q8—1182no—
496C4×D4—1182no—
497C4×D4—1182no—
498C4×D4—1182no—
499C4×D4—1182no—
500C4×D4—1182no—
501C4×D4—1182no—
502#117—22no—
503#117—22no—
504#117—594no—
505#117—594no—
506C2×C4⋊C4—591no—
507C2×C4⋊C4—591no—
508C2×C4⋊C4—591no—
509C2×C4⋊C4—591no—
510C2×C4⋊C4—591no—
511C2×C4⋊C4—591no—
512C2×C4⋊C4—591no—
513C2×C4⋊C4—591no—
514C2×C4⋊C4C4×D5911yescharacteristic
515C2×C4⋊C4C4×D5911yescharacteristic
516C2×C22⋊C4—591no—
517C2×C22⋊C4—591no—
518C2×C22⋊C4—591no—
519C2×C22⋊C4—591no—
520C2×C22⋊C4—591no—
521C2×C22⋊C4—591no—
522C2×C22⋊C4—591no—
523C2×C22⋊C4—591no—
524C2×C22⋊C4C4×D5911yescharacteristic
525C2×C22⋊C4C4×D5911yescharacteristic
526C2×C42—591no—
527C2×C42—591no—
528C2×C42—591no—
529C2×C42—591no—
530C2×C42—1182no—
531C2×C42—1182no—
532C2×C42C22×D5911yescharacteristic
533C2×C42C22×D5911yescharacteristic
534C4⋊C8—22no—
535C4⋊C8—22no—
536C4⋊C8—1182no—
537C4⋊C8—1182no—
538C4⋊C8—1182no—
539C4⋊C8—1182no—
540C22⋊C8—41no—
541C22⋊C8—41no—
542C22⋊C8—1182no—
543C22⋊C8—1182no—
544C22⋊C8—2361no—
545C22⋊C8—2361no—
546C22⋊C8—2361no—
547C22⋊C8—2361no—
548C22⋊C8—2361no—
549C22⋊C8—2361no—
550#97—1182no—
551C4×C8—1182no—
552C24—591no—
553C24—591no—
554C24C2×C4×D5911yescharacteristic
555C2×Q8—1182no—
556C2×Q8—1182no—
557C2×Q8—2361no—
558C2×D4—1182no—
559C2×D4—1182no—
560C2×D4—1182no—
561C2×D4—1182no—
562C2×D4—1182no—
563C2×D4—1182no—
564C2×D4—2361no—
565C2×D4—2361no—
566C2×D4—2361no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—591no—
574C22×C4—591no—
575C22×C4—591no—
576C22×C4—591no—
577C22×C4—592no—
578C22×C4—592no—
579C22×C4—591no—
580C22×C4—591no—
581C22×C4—1182no—
582C22×C4—1182no—
583C22×C4—1181no—
584C22×C4—1181no—
585C22×C4—1181no—
586C22×C4—1181no—
587C22×C4—1182no—
588C22×C4—1182no—
589C22×C4—1181no—
590C22×C4—1181no—
591C22×C4—1181no—
592C22×C4—1181no—
593C22×C4—1181no—
594C22×C4—1181no—
595C22×C4—2361no—
596C22×C4—2361no—
597C22×C4C2×C4×D5911yescharacteristic
598C22×C4C2×C4×D5911yescharacteristic
599C22×C4C2×C4×D5911yescharacteristic
600C22×C4C2×C4×D5911yescharacteristic
601C22×C4C2×C4×D5911yescharacteristic
602C22×C4C23×D5911yescharacteristic
603M16—2364no—
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—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
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—1181no—
625C2×C8—1181no—
626C2×C8—1181no—
627C2×C8—1181no—
628C2×C8—2364no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—594no—
632C4⋊C4—594no—
633C4⋊C4—1182no—
634C4⋊C4—1182no—
635C4⋊C4—1182no—
636C4⋊C4—1182no—
637C4⋊C4—1182no—
638C4⋊C4—1182no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—594no—
642C22⋊C4—594no—
643C22⋊C4—1182no—
644C22⋊C4—1182no—
645C22⋊C4—1182no—
646C22⋊C4—1182no—
647C22⋊C4—1182no—
648C22⋊C4—1182no—
649C42—21no—
650C42—21no—
651C42—592no—
652C42—592no—
653C42—1182no—
654C42—1182no—
655C42—1181no—
656C42—1181no—
657C42D4×D5912yes—
658C42D4×D5912yes—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—592no—
667C23—592no—
668C23—1181no—
669C23—1181no—
670C23—1181no—
671C23—1181no—
672C23—1181no—
673C23—1181no—
674C23—1181no—
675C23—1181no—
676C23—1181no—
677C23—1181no—
678C23—1181no—
679C23—1181no—
680C23C22×C4×D5911yescharacteristic
681Q8—2364no—
682D4—2364no—
683D4—2364no—
684D4—2364no—
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—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—592no—
703C2×C4—592no—
704C2×C4—592no—
705C2×C4—592no—
706C2×C4—1181no—
707C2×C4—1181no—
708C2×C4—1181no—
709C2×C4—1181no—
710C2×C4—1181no—
711C2×C4—1181no—
712C2×C4—1181no—
713C2×C4—1181no—
714C2×C4—1182no—
715C2×C4—1182no—
716C2×C4—1182no—
717C2×C4—1182no—
718C2×C4—1181no—
719C2×C4—1181no—
720C2×C4—1181no—
721C2×C4—1181no—
722C2×C4—1181no—
723C2×C4—1181no—
724C2×C4—2364no—
725C2×C4—2364no—
726C2×C4—2361no—
727C2×C4—2361no—
728C2×C4—2361no—
729C2×C4—2361no—
730C2×C4C22⋊C4×D5912yes—
731C2×C4C22⋊C4×D5912yes—
732C2×C4C2×D4×D5911yescharacteristic
733C2×C4C2×D4×D5911yescharacteristic
734C2×C4#1427377211yescharacteristic
735C2×C4#1427377311yescharacteristic
736C2×C4#1427377411yescharacteristic
737C2×C4#1427377511yescharacteristic
738C8—41no—
739C8—41no—
740C8—41no—
741C8—41no—
742C8—2361no—
743C8—2361no—
744C8—2361no—
745C8—2361no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—1182no—
754C22—1182no—
755C22—1182no—
756C22—1182no—
757C22—1182no—
758C22—1182no—
759C22—2361no—
760C22—2361no—
761C22—2361no—
762C22—2361no—
763C22—2361no—
764C22—2361no—
765C22—2361no—
766C22—2361no—
767C22C2×C22⋊C4×D5911yescharacteristic
768C22#1683788211yescharacteristic
769C22#1683788311yescharacteristic
770C22#131×D5911yescharacteristic
771C22#131×D5911yescharacteristic
772C22#1683816711yescharacteristic
773C22#1683816711yescharacteristic
774C4—22no—
775C4—22no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—1182no—
780C4—1182no—
781C4—1182no—
782C4—1182no—
783C4—2361no—
784C4—2361no—
785C4#1683796811yescharacteristic
786C4#1683797511yescharacteristic
787C4#1683798111yescharacteristic
788C4#1683798211yescharacteristic
789C2—81no—
790C2—2362no—
791C2—2362no—
792C2#2142668511yescharacteristic
793C2#2143254411yescharacteristic
794C2#2143254411yescharacteristic
795C2#2143323011yescharacteristic
796C2#2143323911yescharacteristic
797C2#2143325411yescharacteristic
798C2#2143326411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D59
commutator, socleC23×C59C23×C4
FittingC59×#1798C2
prime radicalC2×#14273700C4
cosocleC22×C4×C59C24
hypercenter#1798D59
hypocenterC59#21855
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ #1798

Complements

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

NH ≅ G/Ntype
2. C2×#16837462C2semidirect
3. C2×#16837427C2semidirect
4. #21425034C2semidirect
5. #21425030C2semidirect
6. #21424892C2semidirect
7. #21424888C2semidirect
8. #21424392C2semidirect
9. #21424390C2semidirect
10. #21424387C2semidirect
11. #21424385C2semidirect
12. #21424080C2semidirect
13. #21424073C2semidirect
14. #21424073C2semidirect
15. C59×#1798C2semidirect
402. #1798D59semidirect
462. C59#21855semidirect

Maximal subgroups

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

subgroupindex
C2×#168379302
C2×#168374622
C2×#168374272
#214250342
#214250302
#214248922
#214248882
#214243922
#214243902
#214243872
#214243852
#214240802
#214240732
C59×#17982
#2185559