Finite Group Databasebeta

← #28604925

Subgroups — #28604925

Order 15104.

1258 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838107C211yesmaximal, characteristic
2C2×C8×C22⋊D59C211yesmaximal, characteristic
3C4⋊C4×C22⋊D59C211yesmaximal, characteristic
4#21425055C211yesmaximal, characteristic, complemented
5#21425042C211yesmaximal, characteristic, complemented
6#21424519C211yesmaximal, characteristic, complemented
7#21424518C211yesmaximal, characteristic, complemented
8#21424403C211yesmaximal, characteristic, complemented
9#21424402C211yesmaximal, characteristic, complemented
10#21424186C211yesmaximal, characteristic, complemented
11#21424185C211yesmaximal, characteristic, complemented
12#21424100C211yesmaximal, characteristic, complemented
13#21423915C211yesmaximal, characteristic, complemented
14#340×D59C211yesmaximal, characteristic, complemented
15C2×C59×#340C211yesmaximal, characteristic, complemented
16C22×C8×D59C2211yescharacteristic
17#16838107—24no—
18#16838107C418yescomplemented
19C2×#14273726C2211yescharacteristic
20C2×#14273717—21no—
21C2×#14273707C2211yescharacteristic
22C2×#14273706—21no—
23C2×#14273706C2211yescharacteristic
24C2×#14273705—21no—
25C2×#14273692C2211yescharacteristic
26C2×C4×C22⋊D59—21no—
27C2×C4×C22⋊D59—21no—
28C2×C4×C22⋊D59C2211yescharacteristic
29C2×C4⋊C4×D59C2211yescharacteristic
30C2×C4⋊C4×D59C2211yescharacteristic
31C8×C22⋊D59—24no—
32C2×Dic59⋊C8C2211yescharacteristic
33C2×#14273652C2211yescharacteristic
34C2×#14273652C2211yescharacteristic
35C2×#14273650C2211yescharacteristic
36C2×#14273650C2211yescharacteristic
37C2×C22⋊(C59⋊C8)C2211yescharacteristic
38C2×(C2×D59)⋊C8C2211yescharacteristic
39C2×C8×Dic59C2211yescharacteristic
40#16837297—21no—
41#16837275—21no—
42#16837273—21no—
43#16837271C2211yescharacteristic
44#16837262C2211yescharacteristic
45#16837259C2211yescharacteristic
46C4⋊C4×Dic59C2211yescharacteristic
47#16837165C2211yescharacteristic
48#16837165C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837164C2211yescharacteristic
51#16837164C2211yescharacteristic
52#16837164C2211yescharacteristic
53#16837164C2211yescharacteristic
54#16837164C2211yescharacteristic
55C23×C8×C59C2211yescharacteristic
56C22×C4⋊C4×C59C2211yescharacteristic
57C22×C4⋊C4×C59C2211yescharacteristic
58C59×#340C2211yescharacteristic
59C59×#340C2211yescharacteristic
60C59×#340C2211yescharacteristic
61C59×#340C2211yescharacteristic
62C22×Dic118—21no—
63C22×Dic118C2311yescharacteristic
64C22×C22⋊D59D411yescharacteristic
65C22×C4×D59—21no—
66C22×C4×D59—21no—
67C22×C4×D59C2311yescharacteristic
68C22×C59⋊C8C2311yescharacteristic
69C22×C59⋊C8C2311yescharacteristic
70C2×C8×D59—22no—
71C2×C8×D59—22no—
72C2×C8×D59—41no—
73#14273726—22no—
74#14273726C2×C414yescomplemented
75#14273717—28no—
76#14273707—22no—
77#14273707C2×C414yescomplemented
78#14273706—22no—
79#14273706—28no—
80#14273706C2×C414yescomplemented
81#14273705—28no—
82#14273692—22no—
83#14273692C2×C414yescomplemented
84C4×C22⋊D59—28no—
85C4×C22⋊D59—44no—
86C4×C22⋊D59C2×C414yes—
87C4×C22⋊D59D414yes—
88C2×C4⋊Dic59—21no—
89C2×C4⋊Dic59C2311yescharacteristic
90C2×C4⋊Dic59C2311yescharacteristic
91C2×C4⋊Dic59C2311yescharacteristic
92C2×Dic59⋊C4—21no—
93C2×Dic59⋊C4—21no—
94C2×Dic59⋊C4—21no—
95C2×Dic59⋊C4—21no—
96C2×Dic59⋊C4—21no—
97C2×Dic59⋊C4—21no—
98C2×Dic59⋊C4—21no—
99C2×Dic59⋊C4D411yescharacteristic
100C4⋊C4×D59—22no—
101C4⋊C4×D59—22no—
102C4⋊C4×D59—41no—
103C4⋊C4×D59C2×C414yescomplemented
104C2×C22⋊Dic59—21no—
105C2×C22⋊Dic59—21no—
106C2×C22⋊Dic59D411yescharacteristic
107C2×(C2×D59)⋊C4—21no—
108C2×(C2×D59)⋊C4—21no—
109C2×(C2×D59)⋊C4D411yescharacteristic
110C2×C4×Dic59—21no—
111C2×C4×Dic59—21no—
112C2×C4×Dic59C2311yescharacteristic
113Dic59⋊C8—22no—
114#14273652—22no—
115#14273652—41no—
116#14273650—22no—
117#14273650—41no—
118C22⋊(C59⋊C8)—22no—
119(C2×D59)⋊C8—22no—
120C8×Dic59—22no—
121C59⋊#95—21no—
122C59⋊#95—21no—
123C59⋊#95—21no—
124C23×C4×C59—21no—
125C23×C4×C59—21no—
126C23×C4×C59C2311yescharacteristic
127C22×C8×C59—22no—
128C22×C8×C59—22no—
129C22×C8×C59—41no—
130C22×C8×C59C2311yescharacteristic
131C22×C8×C59C2311yescharacteristic
132C2×C4⋊C4×C59—21no—
133C2×C4⋊C4×C59—22no—
134C2×C4⋊C4×C59—22no—
135C2×C4⋊C4×C59—21no—
136C2×C4⋊C4×C59—41no—
137C2×C4⋊C4×C59C2×C414yescomplemented
138C2×C4⋊C4×C59C2311yescharacteristic
139C2×C4⋊C4×C59C2311yescharacteristic
140C2×C4⋊C4×C59C2311yescharacteristic
141C2×C4⋊C4×C59C2311yescharacteristic
142C24×C59C2×D411yescharacteristic
143C23×D59C2×D411yescharacteristic
144C22×C4×C59—21no—
145C22×C4×C59—21no—
146C22×C4×C59—21no—
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—21no—
151C22×C4×C59—24no—
152C22×C4×C59—21no—
153C22×C4×C59—42no—
154C22×C4×C59—42no—
155C22×C4×C59—81no—
156C22×C4×C59—81no—
157C22×C4×C59—81no—
158C22×C4×C59C22×C412yes—
159C22×C4×C59C2×D411yescharacteristic
160C22×C4×C59C2×D412yes—
161C22×C4×C59C2411yescharacteristic
162C2×C22⋊D59C22⋊C414yes—
163C2×C22⋊D59SD1614yes—
164C2×C22⋊D59Q1614yes—
165C22×Dic59—21no—
166C22×Dic59—21no—
167C22×Dic59—21no—
168C22×Dic59—21no—
169C22×Dic59C2×D411yescharacteristic
170C22×Dic59C2×D411yescharacteristic
171C22×Dic59C2×D411yescharacteristic
172C2×C4×D59—21no—
173C2×C4×D59—21no—
174C2×C4×D59—21no—
175C2×C4×D59—21no—
176C2×C4×D59—24no—
177C2×C4×D59—42no—
178C2×C4×D59—42no—
179C2×C4×D59—81no—
180C2×C4×D59—81no—
181C2×C4×D59—81no—
182C2×C4×D59C22×C412yes—
183C2×C4×D59C2×D412yes—
184C2×Dic118—21no—
185C2×Dic118—21no—
186C2×Dic118—21no—
187C2×Dic118—21no—
188C2×Dic118—21no—
189C2×Dic118—24no—
190C2×Dic118—81no—
191C2×Dic118—81no—
192C2×Dic118C22×C412yes—
193C2×C8×C59—21no—
194C2×C8×C59—21no—
195C2×C8×C59—21no—
196C2×C8×C59—21no—
197C2×C8×C59—21no—
198C2×C8×C59—44no—
199C2×C8×C59#4112yes—
200C4⋊C4×C59—24no—
201C4⋊C4×C59—21no—
202C4⋊C4×C59—21no—
203C4⋊C4×C59—21no—
204C4⋊C4×C59—21no—
205C4⋊C4×C59—21no—
206C4⋊C4×C59—42no—
207C4⋊C4×C59C22×C412yes—
208C4⋊C4×C59C22×C412yes—
209C4⋊C4×C59#4112yes—
210C22⋊Dic59—24no—
211C22⋊Dic59—42no—
212C22⋊Dic59C22⋊C414yes—
213(C2×D59)⋊C4—24no—
214(C2×D59)⋊C4—42no—
215(C2×D59)⋊C4C22⋊C414yes—
216C4⋊Dic59—21no—
217C4⋊Dic59—24no—
218C4⋊Dic59—21no—
219C4⋊Dic59—21no—
220C4⋊Dic59—21no—
221C4⋊Dic59—21no—
222C4⋊Dic59C22×C412yes—
223Dic59⋊C4—24no—
224Dic59⋊C4—24no—
225Dic59⋊C4—24no—
226Dic59⋊C4—24no—
227Dic59⋊C4—42no—
228Dic59⋊C4—42no—
229Dic59⋊C4—81no—
230Dic59⋊C4C22⋊C414yes—
231C4×Dic59—24no—
232C4×Dic59—42no—
233C4×Dic59C22×C412yes—
234C4×Dic59C2×D412yes—
235C2×C59⋊C8—21no—
236C2×C59⋊C8—21no—
237C2×C59⋊C8—21no—
238C2×C59⋊C8—21no—
239C2×C59⋊C8—21no—
240C2×C59⋊C8—21no—
241C8×D59—44no—
242C23×C59—21no—
243C23×C59—21no—
244C23×C59—21no—
245C23×C59—21no—
246C23×C59C2×C22⋊C412yes—
247C23×C59C2×SD1612yes—
248C23×C59C2×Q1612yes—
249C23×C59C22×D411yescharacteristic
250C22×D59—21no—
251C22×D59—21no—
252C22×D59—21no—
253C22×D59—21no—
254C22×D59C2×C22⋊C412yes—
255C22×D59C2×SD1612yes—
256C22×D59C2×Q1612yes—
257C2×C4×C59—21no—
258C2×C4×C59—21no—
259C2×C4×C59—22no—
260C2×C4×C59—22no—
261C2×C4×C59—22no—
262C2×C4×C59—22no—
263C2×C4×C59—22no—
264C2×C4×C59—22no—
265C2×C4×C59—22no—
266C2×C4×C59—41no—
267C2×C4×C59—41no—
268C2×C4×C59—41no—
269C2×C4×C59—41no—
270C2×C4×C59—41no—
271C2×C4×C59—41no—
272C2×C4×C59—41no—
273C2×C4×C59—41no—
274C2×C4×C59—41no—
275C2×C4×C59—84no—
276C2×C4×C59—84no—
277C2×C4×C59C2×C22⋊C412yes—
278C2×C4×C59C23×C411yescharacteristic
279C2×C4×C59C22×D411yescharacteristic
280C2×C4×C59C2×#4111yescharacteristic
281C2×C4×C59C2×#4111yescharacteristic
282C2×C4×C59H(5,𝔽2)11yescharacteristic
283C2×C4×C592−1+411yescharacteristic
284C22⋊D59#103116yescomplemented
285C2×Dic59—21no—
286C2×Dic59—21no—
287C2×Dic59—21no—
288C2×Dic59—21no—
289C2×Dic59—22no—
290C2×Dic59—22no—
291C2×Dic59—41no—
292C2×Dic59—41no—
293C2×Dic59—41no—
294C2×Dic59—41no—
295C2×Dic59—41no—
296C2×Dic59—41no—
297C2×Dic59—41no—
298C2×Dic59—41no—
299C2×Dic59—41no—
300C2×Dic59—41no—
301C2×Dic59C2×C22⋊C412yes—
302C2×Dic59C2×C22⋊C412yes—
303C2×Dic59C2×C22⋊C412yes—
304C2×Dic59C2×SD1612yes—
305C2×Dic59C2×Q1612yes—
306C4×D59—22no—
307C4×D59—22no—
308C4×D59—22no—
309C4×D59—22no—
310C4×D59—84no—
311C4×D59—84no—
312Dic118—22no—
313Dic118—22no—
314Dic118—41no—
315Dic118—41no—
316Dic118—84no—
317C8×C59—22no—
318C8×C59—41no—
319C59⋊C8—41no—
320C59⋊C8—41no—
321#22487—591nomaximal, Sylow
322C22×C59—22no—
323C22×C59—22no—
324C22×C59—22no—
325C22×C59—22no—
326C22×C59—22no—
327C22×C59—22no—
328C22×C59C2×#10314yes—
329C22×C59C22×C22⋊C411yescharacteristic
330C22×C59#54611yescharacteristic
331C22×C59#54711yescharacteristic
332C22×C59C22×SD1611yescharacteristic
333C22×C59C22×Q1611yescharacteristic
334C22×C59#57611yescharacteristic
335C22×C59#57711yescharacteristic
336C2×D59—22no—
337C2×D59—22no—
338C2×D59—22no—
339C2×D59—22no—
340C2×D59—22no—
341C2×D59—22no—
342C2×D59C2×#10314yes—
343C4×C59—22no—
344C4×C59—42no—
345C4×C59—42no—
346C4×C59—42no—
347C4×C59—81no—
348C4×C59C4×#4111yescharacteristic
349C4×C59#52011yescharacteristic
350C4×C59#54611yescharacteristic
351C4×C59#54711yescharacteristic
352Dic59—22no—
353Dic59—22no—
354Dic59—42no—
355Dic59—42no—
356Dic59—81no—
357Dic59—81no—
358Dic59C2×#10314yes—
359C2×#554—591no—
360C2×C8×D4—591no—
361D4×C4⋊C4—591no—
362#1990—591no—
363#1987—591no—
364#1892—591no—
365#1892—591no—
366#1872—591no—
367#1872—591no—
368#1824—591no—
369#1824—591no—
370#1803—591no—
371C4×#103—591no—
372C2×#340—591no—
373C2×#340D5911yescharacteristic, complemented
374C2×C59—24no—
375C2×C59#233911yescharacteristic
376C2×C59C22×#10311yescharacteristic
377C2×C59#289711yescharacteristic
378C2×C59#329511yescharacteristic
379C2×C59#329911yescharacteristic
380C2×C59#333511yescharacteristic
381C2×C59#333811yescharacteristic
382D59—24no—
383C23×C8—591no—
384C23×C8C2×D5911yescharacteristic
385#554—598no—
386#554—1184no—
387C2×C4⋊Q8—591no—
388C2×#125—1181no—
389C2×C22⋊Q8—591no—
390C2×C22⋊Q8—591no—
391C2×C22⋊Q8—1181no—
392C2×C22⋊Q8—1181no—
393C2×C4×Q8—591no—
394C2×C4×D4—591no—
395C2×C4×D4—1181no—
396C2×C4×D4—1181no—
397C22×C4⋊C4—591no—
398C22×C4⋊C4—591no—
399C22×C4⋊C4C2×D5911yescharacteristic
400C22×C4⋊C4C2×D5911yescharacteristic
401C8×D4—1184no—
402C2×C4⋊C8—591no—
403C2×#103—591no—
404C2×#103—591no—
405C2×#103—591no—
406C2×#103—591no—
407C2×C22⋊C8—591no—
408C2×C22⋊C8—591no—
409C2×C4×C8—591no—
410#389—1181no—
411#385—1181no—
412#385—1181no—
413#384—591no—
414#380—591no—
415#380—591no—
416C4×C4⋊C4—591no—
417#340—591no—
418#340—591no—
419#340—591no—
420#340—591no—
421#340—591no—
422#340—591no—
423#340—591no—
424#340—591no—
425#340C2×D5911yescharacteristic
426#340C2×D5911yescharacteristic
427#340C2×D5911yescharacteristic
428#340C2×D5911yescharacteristic
429C59#2248711yescharacteristic, complemented, Sylow
430C22×Q8—591no—
431C22×Q8—1181no—
432C22×D4—591no—
433C23×C4—21no—
434C23×C4—21no—
435C23×C4—591no—
436C23×C4—1181no—
437C23×C4—1181no—
438C23×C4C22×D5911yescharacteristic
439C22×C8—22no—
440C22×C8—22no—
441C22×C8—41no—
442C22×C8—591no—
443C22×C8—591no—
444C22×C8—1182no—
445C22×C8—1182no—
446C22×C8—2361no—
447C22×C8C22×D5911yescharacteristic
448C22×C8C22×D5911yescharacteristic
449C4⋊Q8—594no—
450C4⋊Q8—1182no—
451#125—1188no—
452C22⋊Q8—594no—
453C22⋊Q8—594no—
454C22⋊Q8—1188no—
455C22⋊Q8—1188no—
456C22⋊Q8—1182no—
457C22⋊Q8—1182no—
458C4×Q8—594no—
459C4×Q8—1182no—
460C4×D4—594no—
461C4×D4—594no—
462C4×D4—1188no—
463C4×D4—2364no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—41no—
469C2×C4⋊C4—591no—
470C2×C4⋊C4—591no—
471C2×C4⋊C4—594no—
472C2×C4⋊C4—591no—
473C2×C4⋊C4—591no—
474C2×C4⋊C4—1182no—
475C2×C4⋊C4—1181no—
476C2×C4⋊C4—1181no—
477C2×C4⋊C4—1181no—
478C2×C4⋊C4—1181no—
479C2×C4⋊C4—1181no—
480C2×C4⋊C4—1182no—
481C2×C4⋊C4—1181no—
482C2×C4⋊C4—1181no—
483C2×C4⋊C4—1181no—
484C2×C4⋊C4—2361no—
485C2×C4⋊C4C4×D5914yescomplemented
486C2×C4⋊C4C22×D5911yescharacteristic
487C2×C4⋊C4C22×D5911yescharacteristic
488C2×C4⋊C4C22×D5911yescharacteristic
489C2×C4⋊C4C22×D5911yescharacteristic
490C2×C22⋊C4—591no—
491C2×C22⋊C4—591no—
492C2×C22⋊C4—1181no—
493C2×C22⋊C4—1181no—
494C2×C22⋊C4—1181no—
495C2×C22⋊C4—1181no—
496C2×C42—591no—
497C2×C42—1181no—
498C2×C42—1181no—
499C4⋊C8—1182no—
500#103—1182no—
501#103—1182no—
502#103—2361no—
503#103—2361no—
504C22⋊C8—1182no—
505C22⋊C8—1182no—
506C4×C8—1182no—
507#95—1181no—
508#95—1181no—
509#95—1181no—
510C24—591no—
511C24D4×D5911yescharacteristic
512C2×Q8—592no—
513C2×Q8—1184no—
514C2×Q8—1181no—
515C2×Q8—1181no—
516C2×Q8—1181no—
517C2×Q8—1181no—
518C2×Q8—1181no—
519C2×Q8—4721no—
520C2×Q8—4721no—
521C2×D4—594no—
522C2×D4—594no—
523C2×D4—594no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—24no—
532C22×C4—21no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—81no—
536C22×C4—81no—
537C22×C4—81no—
538C22×C4—591no—
539C22×C4—591no—
540C22×C4—591no—
541C22×C4—592no—
542C22×C4—592no—
543C22×C4—1184no—
544C22×C4—1181no—
545C22×C4—1181no—
546C22×C4—1181no—
547C22×C4—1181no—
548C22×C4—1181no—
549C22×C4—1181no—
550C22×C4—1181no—
551C22×C4—1181no—
552C22×C4—4721no—
553C22×C4—4721no—
554C22×C4—4721no—
555C22×C4—2362no—
556C22×C4—2362no—
557C22×C4C2×C4×D5912yes—
558C22×C4D4×D5911yescharacteristic
559C22×C4D4×D5912yes—
560C22×C4C23×D5911yescharacteristic
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—44no—
567C2×C8—1181no—
568C2×C8—1181no—
569C2×C8—1181no—
570C2×C8—1181no—
571C2×C8—1181no—
572C2×C8—1181no—
573C2×C8—2364no—
574C2×C8#1174568512yes—
575C4⋊C4—24no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—42no—
582C4⋊C4—594no—
583C4⋊C4—592no—
584C4⋊C4—1184no—
585C4⋊C4—1184no—
586C4⋊C4—1184no—
587C4⋊C4—1184no—
588C4⋊C4—1184no—
589C4⋊C4—1181no—
590C4⋊C4—1181no—
591C4⋊C4—1181no—
592C4⋊C4—1181no—
593C4⋊C4—1181no—
594C4⋊C4—4721no—
595C4⋊C4—2362no—
596C4⋊C4—2362no—
597C4⋊C4C2×C4×D5912yes—
598C4⋊C4C2×C4×D5912yes—
599C4⋊C4#1174568512yes—
600C22⋊C4—594no—
601C22⋊C4—594no—
602C22⋊C4—1184no—
603C22⋊C4—1184no—
604C22⋊C4—2362no—
605C22⋊C4—2362no—
606C42—592no—
607C42—592no—
608C42—1184no—
609C42—2362no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—592no—
615C23—592no—
616C23—592no—
617C23—1181no—
618C23—1181no—
619C23—1181no—
620C23—1181no—
621C23C22⋊C4×D5912yes—
622C23SD16×D5912yes—
623C23Q16×D5912yes—
624C23C2×D4×D5911yescharacteristic
625Q8—1182no—
626Q8—1182no—
627Q8—4724no—
628Q8—2361no—
629Q8—2361no—
630D4—5916no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—84no—
650C2×C4—84no—
651C2×C4—592no—
652C2×C4—592no—
653C2×C4—592no—
654C2×C4—592no—
655C2×C4—592no—
656C2×C4—1181no—
657C2×C4—1181no—
658C2×C4—1181no—
659C2×C4—1181no—
660C2×C4—1182no—
661C2×C4—1182no—
662C2×C4—1182no—
663C2×C4—1182no—
664C2×C4—1182no—
665C2×C4—1182no—
666C2×C4—4724no—
667C2×C4—4724no—
668C2×C4—2361no—
669C2×C4—2361no—
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×C4C22⋊C4×D5912yes—
679C2×C4C22×C4×D5911yescharacteristic
680C2×C4C2×D4×D5911yescharacteristic
681C2×C4C2×#1174568511yescharacteristic
682C2×C4C2×#1174568511yescharacteristic
683C2×C4#1427377211yescharacteristic
684C2×C4#1427377511yescharacteristic
685C8—22no—
686C8—41no—
687C8—2361no—
688C8—2361no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—594no—
696C22—1182no—
697C22—1182no—
698C22—1182no—
699C22—1182no—
700C22—1182no—
701C22—1182no—
702C22#103×D5914yes—
703C22C2×C22⋊C4×D5911yescharacteristic
704C22#1683804211yescharacteristic
705C22#1683805311yescharacteristic
706C22C2×SD16×D5911yescharacteristic
707C22C2×Q16×D5911yescharacteristic
708C22#1683820311yescharacteristic
709C22#1683820811yescharacteristic
710C4—22no—
711C4—42no—
712C4—42no—
713C4—42no—
714C4—81no—
715C4—594no—
716C4—1182no—
717C4—1182no—
718C4—4721no—
719C4—4721no—
720C4—2362no—
721C4—2362no—
722C4C4×#1174568511yescharacteristic
723C4#1683788311yescharacteristic
724C4#1683804211yescharacteristic
725C4#1683805311yescharacteristic
726C2—24no—
727C2—1184no—
728C2#2142692311yescharacteristic
729C2C2×#103×D5911yescharacteristic
730C2#2143261711yescharacteristic
731C2#2143591611yescharacteristic
732C2#2143596811yescharacteristic
733C2#2143644911yescharacteristic
734C2#2143648611yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C59×#340C2
socleC23×C59C22×D4
prime radicalC22×C22⋊D59D4
cosocleC22×C4×C59C24
hypercenterC2×#340D59
hypocenterC59#22487
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. #21425055C2semidirect
5. #21425042C2semidirect
6. #21424519C2semidirect
7. #21424518C2semidirect
8. #21424403C2semidirect
9. #21424402C2semidirect
10. #21424186C2semidirect
11. #21424185C2semidirect
12. #21424100C2semidirect
13. #21423915C2semidirect
14. #340×D59C2semidirect
15. C2×C59×#340C2semidirect
18. #16838107C4semidirect
74. #14273726C2×C4semidirect
77. #14273707C2×C4semidirect
80. #14273706C2×C4semidirect
83. #14273692C2×C4semidirect
103. C4⋊C4×D59C2×C4semidirect
137. C2×C4⋊C4×C59C2×C4semidirect
284. C22⋊D59#103semidirect
373. C2×#340D59semidirect
429. C59#22487semidirect
485. C2×C4⋊C4C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168381072
C2×C8×C22⋊D592
C4⋊C4×C22⋊D592
#214250552
#214250422
#214245192
#214245182
#214244032
#214244022
#214241862
#214241852
#214241002
#214239152
#340×D592
C2×C59×#3402
#2248759