Finite Group Databasebeta

← C2×#21434013 #29456460

Subgroups — C2×#21434013 #29456460

Order 15104.

2378 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837914C211yesmaximal, characteristic
2C2×#117×D59C211yesmaximal, characteristic, complemented
3#21434013C2116yesmaximal, direct product factor
4C2×#16837739C211yesmaximal, characteristic, complemented
5C2×#16837722C211yesmaximal, characteristic, complemented
6C2×#16837746C211yesmaximal, characteristic, complemented
7C2×#16837745C211yesmaximal, characteristic, complemented
8C2×#16837729C211yesmaximal, characteristic, complemented
9C2×#16837728C211yesmaximal, characteristic, complemented
10C2×#16837734C211yesmaximal, characteristic, complemented
11C2×#16837717C211yesmaximal, characteristic, complemented
12C2×#16837438C211yesmaximal, characteristic, complemented
13C2×#16837399C211yesmaximal, characteristic, complemented
14C2×#16837396C211yesmaximal, characteristic, complemented
15C22×(C2×D59)⋊C8C211yesmaximal, characteristic, complemented
16C2×C59×#427C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C23×C4×D59C2211yescharacteristic
19C23×C59⋊C8C2211yescharacteristic
20#16837914—24no—
21#16837914C2218yes—
22C2×#14273711—21no—
23C2×#14273707C2211yescharacteristic
24C2×#14273707C2211yescharacteristic
25C2×#14273702C2211yescharacteristic
26C2×#14273702C2211yescharacteristic
27C2×#14273697—21no—
28C2×C4×D236—21no—
29C2×C4×D236—21no—
30C2×#14273686C2211yescharacteristic
31C2×#14273685C2211yescharacteristic
32C2×#14273685C2211yescharacteristic
33C2×#14273684—21no—
34C2×#14273683—21no—
35#117×D59—24no—
36#117×D59C2218yescomplemented
37C2×C4⋊C4×D59C2211yescharacteristic
38C2×C4⋊C4×D59C2211yescharacteristic
39C2×C22⋊C4×D59—21no—
40C2×C42×D59—21no—
41#16837746C2218yescomplemented
42#16837745C2218yescomplemented
43#16837739C2218yescomplemented
44#16837734C2218yescomplemented
45#16837729C2218yescomplemented
46#16837728C2218yescomplemented
47#16837722C2218yescomplemented
48#16837717C2218yescomplemented
49#16837438C2218yescomplemented
50C2×#14273660C2211yescharacteristic, complemented
51C2×#14273660C2211yescharacteristic, complemented
52C2×#14273658C2211yescharacteristic, complemented
53C2×#14273658C2211yescharacteristic, complemented
54#16837399C2218yescomplemented
55#16837396C2218yescomplemented
56C2×#14273652C2211yescharacteristic, complemented
57C2×#14273652C2211yescharacteristic, complemented
58C2×#14273650C2211yescharacteristic, complemented
59C2×#14273650C2211yescharacteristic, complemented
60C2×#14273649C2211yescharacteristic, complemented
61C2×#14273649C2211yescharacteristic, complemented
62C2×#14273647C2211yescharacteristic, complemented
63C2×#14273647C2211yescharacteristic, complemented
64C2×(C2×D59)⋊C8C2211yescharacteristic
65C2×(C2×D59)⋊C8C2211yescharacteristic
66C2×(C2×D59)⋊C8C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×(C2×D59)⋊C8C2218yescomplemented
69C23×C8×C59C2211yescharacteristic
70C2×#117×C59C2211yescharacteristic
71C2×#117×C59C2211yescharacteristic
72C59×#427C2218yescomplemented
73C2×#107×C59C2211yescharacteristic, complemented
74C2×#107×C59C2211yescharacteristic, complemented
75C2×#106×C59C2211yescharacteristic, complemented
76C2×#106×C59C2211yescharacteristic, complemented
77C24×D59D411yescharacteristic
78C2×#11745685—22no—
79C2×#11745685—24no—
80C2×#11745685—24no—
81C2×#11745685C2314yes—
82C22×Dic118C2311yescharacteristic
83C22×D236—21no—
84C22×D236—21no—
85C22×D236C2311yescharacteristic
86C22×C22⋊D59—21no—
87C23×Dic59D411yescharacteristic
88C22×C4×D59—24no—
89C22×C4×D59—24no—
90C22×C4×D59—21no—
91C22×C4×D59—21no—
92C22×C4×D59—21no—
93C22×C4×D59D414yes—
94C22×C4×D59D411yescharacteristic
95C22×C4×D59D411yescharacteristic
96C22×C4×D59C2311yescharacteristic
97C22×C4×D59C2311yescharacteristic
98C22×C4×D59C2314yes—
99C22×C59⋊C8—24no—
100C22×C59⋊C8C2311yescharacteristic
101C22×C59⋊C8C2311yescharacteristic
102C22×C59⋊C8C2314yes—
103#14273711—28no—
104#14273707—22no—
105#14273707—22no—
106#14273707C2314yes—
107#14273707C2314yes—
108#14273702—22no—
109#14273702—22no—
110#14273702C2314yes—
111#14273702C2314yes—
112#14273697—28no—
113C4×D236—28no—
114C4×D236—28no—
115#14273686—22no—
116#14273686C2314yes—
117#14273685—22no—
118#14273685—22no—
119#14273685C2314yes—
120#14273685C2314yes—
121#14273684—28no—
122#14273683—28no—
123C2×C4⋊Dic59—21no—
124C2×C4⋊Dic59—21no—
125C2×C4⋊Dic59C2311yescharacteristic
126C2×C4⋊Dic59C2311yescharacteristic
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C4⋊C4×D59—22no—
130C4⋊C4×D59—22no—
131C4⋊C4×D59C2314yes—
132C4⋊C4×D59C2314yes—
133C2×C22⋊Dic59—21no—
134C2×(C2×D59)⋊C4—21no—
135C2×(C2×D59)⋊C4—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4—21no—
140C22⋊C4×D59—28no—
141C2×C4×Dic59—21no—
142C2×C4×Dic59—21no—
143C2×C4×Dic59—21no—
144C42×D59—28no—
145#14273660C2314yescomplemented
146#14273660C2314yescomplemented
147#14273658C2314yescomplemented
148#14273658C2314yescomplemented
149#14273652C2314yescomplemented
150#14273652C2314yescomplemented
151#14273650C2314yescomplemented
152#14273650C2314yescomplemented
153#14273649C2314yescomplemented
154#14273649C2314yescomplemented
155#14273647C2314yescomplemented
156#14273647C2314yescomplemented
157(C2×D59)⋊C8C2314yes—
158(C2×D59)⋊C8C2314yes—
159(C2×D59)⋊C8C2314yes—
160(C2×D59)⋊C8C2314yes—
161C23×C4×C59C2311yescharacteristic
162C22×C8×C59—24no—
163C22×C8×C59C2311yescharacteristic
164C22×C8×C59C2311yescharacteristic
165C22×C8×C59C2314yes—
166#117×C59—22no—
167#117×C59—22no—
168#117×C59C2314yes—
169#117×C59C2314yes—
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C22⋊C4×C59—21no—
175C2×C22⋊C4×C59—21no—
176C2×C42×C59—21no—
177C2×C42×C59—21no—
178#107×C59C2314yescomplemented
179#107×C59C2314yescomplemented
180#106×C59C2314yescomplemented
181#106×C59C2314yescomplemented
182C24×C59C2×D411yescharacteristic
183C23×D59—24no—
184C23×D59—24no—
185C23×D59—21no—
186C23×D59—42no—
187C23×D59C2×D411yescharacteristic
188C23×D59C2×D414yes—
189C23×D59C2×D411yescharacteristic
190C22×C4×C59—21no—
191C22×C4×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59C2×D412yes—
195C22×C4×C59C2×D411yescharacteristic
196C22×C4×C59#4114yes—
197C22×C4×C59#4114yes—
198C22×C4×C59C2411yescharacteristic
199C22×C4×C59C2412yes—
200C2×C22⋊D59—24no—
201C2×C22⋊D59—44no—
202C22×Dic59—24no—
203C22×Dic59—21no—
204C22×Dic59—21no—
205C22×Dic59—21no—
206C22×Dic59C2×D411yescharacteristic
207C22×Dic59C2×D411yescharacteristic
208C22×Dic59C2×D414yes—
209#11745685—28no—
210#11745685—28no—
211#11745685—48no—
212C2×D236—22no—
213C2×D236—22no—
214C2×D236—24no—
215C2×D236—24no—
216C2×D236—21no—
217C2×D236—44no—
218C2×D236—44no—
219C2×D236C2412yes—
220C2×C4×D59—24no—
221C2×C4×D59—24no—
222C2×C4×D59—216no—
223C2×C4×D59—22no—
224C2×C4×D59—22no—
225C2×C4×D59—28no—
226C2×C4×D59—22no—
227C2×C4×D59—22no—
228C2×C4×D59—28no—
229C2×C4×D59—24no—
230C2×C4×D59—24no—
231C2×C4×D59—24no—
232C2×C4×D59—44no—
233C2×C4×D59—44no—
234C2×C4×D59—44no—
235C2×C4×D59C2×D414yes—
236C2×C4×D59C2×D412yes—
237C2×C4×D59C2×D414yes—
238C2×C4×D59C2×D412yes—
239C2×C4×D59C2412yes—
240C2×C4×D59C2412yes—
241C2×Dic118—22no—
242C2×Dic118—22no—
243C2×Dic118—21no—
244C2×Dic118C2412yes—
245C2×C8×C59—22no—
246C2×C8×C59—22no—
247C2×C8×C59—28no—
248C2×C8×C59C2412yes—
249C2×C8×C59C2412yes—
250C4⋊C4×C59—21no—
251C4⋊C4×C59—21no—
252C4⋊C4×C59—21no—
253C4⋊C4×C59—21no—
254C4⋊C4×C59C2412yes—
255C4⋊C4×C59C2412yes—
256C4⋊C4×C59C2412yes—
257C4⋊C4×C59C2412yes—
258C22⋊C4×C59—24no—
259C22⋊C4×C59—24no—
260C42×C59—24no—
261C42×C59—24no—
262C22⋊Dic59—24no—
263(C2×D59)⋊C4—24no—
264(C2×D59)⋊C4—24no—
265(C2×D59)⋊C4—24no—
266(C2×D59)⋊C4—24no—
267(C2×D59)⋊C4—24no—
268(C2×D59)⋊C4—24no—
269C4⋊Dic59—21no—
270C4⋊Dic59—21no—
271C4⋊Dic59—24no—
272C4⋊Dic59—24no—
273C4⋊Dic59C2412yes—
274C4⋊Dic59C2412yes—
275Dic59⋊C4—24no—
276Dic59⋊C4—24no—
277C4×Dic59—24no—
278C4×Dic59—24no—
279C4×Dic59—24no—
280C2×C59⋊C8—22no—
281C2×C59⋊C8—22no—
282C2×C59⋊C8—28no—
283C2×C59⋊C8C2412yes—
284C2×C59⋊C8C2412yes—
285C23×C59—22no—
286C23×C59—22no—
287C23×C59#12314yes—
288C23×C59C22×D412yes—
289C23×C59C22×D411yescharacteristic
290C22×D59—22no—
291C22×D59—22no—
292C22×D59—28no—
293C22×D59—22no—
294C22×D59—22no—
295C22×D59—22no—
296C22×D59—28no—
297C22×D59—22no—
298C22×D59—44no—
299C22×D59—416no—
300C22×D59—42no—
301C22×D59—42no—
302C22×D59—42no—
303C22×D59#13514yes—
304C22×D59C22×D412yes—
305C22×D59C22×D412yes—
306C2×C4×C59—22no—
307C2×C4×C59—22no—
308C2×C4×C59—22no—
309C2×C4×C59—22no—
310C2×C4×C59—42no—
311C2×C4×C59—42no—
312C2×C4×C59—42no—
313C2×C4×C59—42no—
314C2×C4×C59#12314yes—
315C2×C4×C59#12318yes—
316C2×C4×C59C22×D412yes—
317C2×C4×C59C22×D411yescharacteristic
318C2×C4×C59C2×#4112yes—
319C2×C4×C59C2×#4114yes—
320C2×C4×C59C2×#4112yes—
321C2×C4×C59C2×#4114yes—
322C2×C4×C59C2511yescharacteristic
323C22⋊D59—48no—
324C2×Dic59—28no—
325C2×Dic59—22no—
326C2×Dic59—22no—
327C2×Dic59—22no—
328C2×Dic59—22no—
329C2×Dic59—22no—
330C2×Dic59—42no—
331C2×Dic59—42no—
332C2×Dic59—42no—
333C2×Dic59C22×D412yes—
334C2×Dic59C22×D412yes—
335D236—22no—
336D236—22no—
337D236—48no—
338D236—48no—
339D236—42no—
340C4×D59—24no—
341C4×D59—24no—
342C4×D59—28no—
343C4×D59—28no—
344C4×D59—22no—
345C4×D59—22no—
346C4×D59—22no—
347C4×D59—22no—
348C4×D59—48no—
349C4×D59—48no—
350C4×D59—48no—
351Dic118—22no—
352Dic118—22no—
353Dic118—42no—
354C8×C59—22no—
355C8×C59—22no—
356C59⋊C8—22no—
357C59⋊C8—22no—
358C2×#3091—591nomaximal, Sylow
359C22×C59—28no—
360C22×C59—22no—
361C22×C59—22no—
362C22×C59C2×#12314yes—
363C22×C59C2×#12312yes—
364C22×C59C2×#13512yes—
365C22×C59#57512yes—
366C22×C59C23×D411yescharacteristic
367C2×D59—28no—
368C2×D59—22no—
369C2×D59—22no—
370C2×D59—22no—
371C2×D59—22no—
372C2×D59—22no—
373C2×D59—416no—
374C2×D59—44no—
375C2×D59—42no—
376C2×D59—42no—
377C2×D59—42no—
378C2×D59—84no—
379C2×D59C2×#13514yes—
380C4×C59—42no—
381C4×C59—42no—
382C4×C59—42no—
383C4×C59—42no—
384C4×C59C2×#12312yes—
385C4×C59C2×#12314yes—
386C4×C59C22×#4111yescharacteristic
387C4×C59C22×#4111yescharacteristic
388Dic59—22no—
389Dic59—22no—
390Dic59—42no—
391Dic59—42no—
392Dic59—42no—
393C2×#525—591no—
394C22×#117—591no—
395#3091—5916no—
396C2×#484—591no—
397C2×#481—591no—
398C2×#485—591no—
399C2×#485—591no—
400C2×#482—591no—
401C2×#482—591no—
402C2×#483—591no—
403C2×#480—591no—
404C2×#427—591no—
405C2×#427D5911yescharacteristic, complemented
406C2×#416—591no—
407C2×#416—591no—
408C22×C22⋊C8—591no—
409C2×C59—24no—
410C2×C59#309114yescomplemented
411C2×C59C22×#12311yescharacteristic
412C2×C59C22×#13511yescharacteristic
413C2×C59C2×#57511yescharacteristic
414D59—24no—
415D59—42no—
416D59—82no—
417C22×#41—591no—
418C24×C4—591no—
419C23×C8—591no—
420C23×C8C2×D5911yescharacteristic
421#525—598no—
422#525—1184no—
423C2×#123—1181no—
424C2×C22⋊Q8—591no—
425C2×C22⋊Q8—591no—
426C2×#121—591no—
427C2×#121—591no—
428C2×#120—1181no—
429C2×C4×D4—1181no—
430C2×C4×D4—1181no—
431C2×#117—591no—
432C2×#117—598no—
433C2×#117—591no—
434C2×#117—591no—
435C2×#117—1181no—
436C2×#117—1181no—
437C2×#117—1184no—
438C2×#117C2×D5911yescharacteristic
439C2×#117C2×D5911yescharacteristic
440C22×C4⋊C4—591no—
441C22×C4⋊C4—591no—
442C22×C22⋊C4—1181no—
443C22×C42—1181no—
444#485—598no—
445#485—598no—
446#484—598no—
447#483—598no—
448#482—598no—
449#482—598no—
450#481—598no—
451#480—598no—
452#427—598no—
453#427C2×D5918yescomplemented
454C2×#107—591no—
455C2×#107—591no—
456C2×#107C2×D5911yescharacteristic, complemented
457C2×#107C2×D5911yescharacteristic, complemented
458C2×#106—591no—
459C2×#106—591no—
460C2×#106C2×D5911yescharacteristic, complemented
461C2×#106C2×D5911yescharacteristic, complemented
462#416—598no—
463#416—598no—
464C2×#103—591no—
465C2×#103—591no—
466C2×#103—591no—
467C2×#103—591no—
468C2×#102—591no—
469C2×#102—591no—
470C2×#102—591no—
471C2×#102—591no—
472C2×C22⋊C8—591no—
473C2×C22⋊C8—591no—
474C2×C22⋊C8—591no—
475C2×C22⋊C8—591no—
476C2×C22⋊C8—598no—
477C59C2×#309111yescharacteristic, complemented, Sylow
478C25—591no—
479C2×#41—594no—
480C2×#41—1182no—
481C2×#41—1184no—
482C2×#41—1184no—
483C22×Q8—591no—
484C22×D4—591no—
485C22×D4—1181no—
486C22×D4—1181no—
487C22×D4—1181no—
488C23×C4—591no—
489C23×C4—594no—
490C23×C4—591no—
491C23×C4—591no—
492C23×C4—591no—
493C23×C4—591no—
494C23×C4—594no—
495C23×C4—1181no—
496C23×C4—1181no—
497C23×C4—1184no—
498C23×C4—1184no—
499C23×C4—1181no—
500C23×C4C22×D5911yescharacteristic
501C22×C8—24no—
502C22×C8—591no—
503C22×C8—591no—
504C22×C8—594no—
505C22×C8—1184no—
506C22×C8C22×D5911yescharacteristic
507C22×C8C22×D5911yescharacteristic
508C22×C8C22×D5914yes—
509#123—1188no—
510C22⋊Q8—594no—
511C22⋊Q8—594no—
512C22⋊Q8—1182no—
513C22⋊Q8—1182no—
514#121—594no—
515#121—594no—
516#121—1182no—
517#121—1182no—
518#120—1188no—
519C4×D4—1188no—
520C4×D4—1188no—
521#117—22no—
522#117—22no—
523#117—594no—
524#117—594no—
525#117—594no—
526#117—1188no—
527#117—1188no—
528#117—1182no—
529#117—1182no—
530#117—1182no—
531#117C22×D5914yes—
532#117C22×D5914yes—
533C2×C4⋊C4—591no—
534C2×C4⋊C4—591no—
535C2×C4⋊C4—594no—
536C2×C4⋊C4—594no—
537C2×C4⋊C4—1182no—
538C2×C4⋊C4—1182no—
539C2×C4⋊C4—1181no—
540C2×C4⋊C4—1181no—
541C2×C4⋊C4—1181no—
542C2×C4⋊C4—1181no—
543C2×C4⋊C4C22×D5911yescharacteristic
544C2×C4⋊C4C22×D5911yescharacteristic
545C2×C4⋊C4C22×D5911yescharacteristic
546C2×C4⋊C4C22×D5911yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—1188no—
550C2×C22⋊C4—1181no—
551C2×C22⋊C4—1181no—
552C2×C22⋊C4—1181no—
553C2×C22⋊C4—1181no—
554C2×C22⋊C4—1181no—
555C2×C22⋊C4—1181no—
556C2×C22⋊C4—1181no—
557C2×C42—21no—
558C2×C42—21no—
559C2×C42—1188no—
560C2×C42—1181no—
561C2×C42—1181no—
562C2×C42—1181no—
563#107—594no—
564#107—594no—
565#107C22×D5914yescomplemented
566#107C22×D5914yescomplemented
567#106—594no—
568#106—594no—
569#106C22×D5914yescomplemented
570#106C22×D5914yescomplemented
571#103—594no—
572#103—594no—
573#103—594no—
574#103—594no—
575#102—594no—
576#102—594no—
577#102—594no—
578#102—594no—
579C22⋊C8—594no—
580C22⋊C8—594no—
581C22⋊C8—594no—
582C22⋊C8—594no—
583C24—591no—
584C24—591no—
585C24—594no—
586C24—1184no—
587C24—1184no—
588C24—1181no—
589C24—2362no—
590C24D4×D5911yescharacteristic
591#41—1188no—
592#41—1188no—
593#41—2368no—
594C2×Q8—592no—
595C2×Q8—1181no—
596C2×Q8—1182no—
597C2×Q8—1182no—
598C2×D4—592no—
599C2×D4—1184no—
600C2×D4—1184no—
601C2×D4—1184no—
602C2×D4—1181no—
603C2×D4—1182no—
604C2×D4—1182no—
605C2×D4—2364no—
606C2×D4—2364no—
607C2×D4—2364no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—591no—
613C22×C4—591no—
614C22×C4—594no—
615C22×C4—594no—
616C22×C4—592no—
617C22×C4—594no—
618C22×C4—592no—
619C22×C4—592no—
620C22×C4—592no—
621C22×C4—1184no—
622C22×C4—1184no—
623C22×C4—1184no—
624C22×C4—1184no—
625C22×C4—1184no—
626C22×C4—11816no—
627C22×C4—1182no—
628C22×C4—1182no—
629C22×C4—1188no—
630C22×C4—1182no—
631C22×C4—1182no—
632C22×C4—1188no—
633C22×C4—1181no—
634C22×C4—1181no—
635C22×C4—1181no—
636C22×C4—1184no—
637C22×C4—2364no—
638C22×C4—2364no—
639C22×C4—2364no—
640C22×C4#1174568514yes—
641C22×C4D4×D5912yes—
642C22×C4D4×D5911yescharacteristic
643C22×C4#1174568914yes—
644C22×C4C23×D5911yescharacteristic
645C22×C4C23×D5912yes—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—28no—
649C2×C8—592no—
650C2×C8—592no—
651C2×C8—1182no—
652C2×C8—1182no—
653C2×C8—1188no—
654C2×C8C23×D5912yes—
655C2×C8C23×D5912yes—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—592no—
661C4⋊C4—592no—
662C4⋊C4—1184no—
663C4⋊C4—1184no—
664C4⋊C4—1184no—
665C4⋊C4—1184no—
666C4⋊C4—1181no—
667C4⋊C4—1181no—
668C4⋊C4C23×D5912yes—
669C4⋊C4C23×D5912yes—
670C4⋊C4C23×D5912yes—
671C4⋊C4C23×D5912yes—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—1184no—
675C22⋊C4—1184no—
676C22⋊C4—1184no—
677C22⋊C4—1184no—
678C22⋊C4—1184no—
679C22⋊C4—1184no—
680C22⋊C4—1184no—
681C42—24no—
682C42—24no—
683C42—1184no—
684C42—1184no—
685C42—1184no—
686C23—22no—
687C23—22no—
688C23—594no—
689C23—592no—
690C23—592no—
691C23—1188no—
692C23—1182no—
693C23—1182no—
694C23—1188no—
695C23—1182no—
696C23—1182no—
697C23—1182no—
698C23—1182no—
699C23—2364no—
700C23—23616no—
701C23—2362no—
702C23—2362no—
703C23—2362no—
704C23#1427371214yes—
705C23C2×D4×D5912yes—
706C23C2×D4×D5911yescharacteristic
707Q8—1182no—
708Q8—1182no—
709Q8—2362no—
710D4—1182no—
711D4—1182no—
712D4—2368no—
713D4—2368no—
714D4—2368no—
715D4—2362no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—592no—
725C2×C4—592no—
726C2×C4—1188no—
727C2×C4—1182no—
728C2×C4—1182no—
729C2×C4—1188no—
730C2×C4—1188no—
731C2×C4—1184no—
732C2×C4—1184no—
733C2×C4—1182no—
734C2×C4—1182no—
735C2×C4—1182no—
736C2×C4—1182no—
737C2×C4—1182no—
738C2×C4—1182no—
739C2×C4—1182no—
740C2×C4—2368no—
741C2×C4—2368no—
742C2×C4—2362no—
743C2×C4—2362no—
744C2×C4—2362no—
745C2×C4—2368no—
746C2×C4#1427371214yes—
747C2×C4#1427371218yes—
748C2×C4C2×D4×D5912yes—
749C2×C4C2×D4×D5911yescharacteristic
750C2×C4C2×#1174568512yes—
751C2×C4C2×#1174568514yes—
752C2×C4C2×#1174568912yes—
753C2×C4C2×#1174568914yes—
754C2×C4C24×D5911yescharacteristic
755C8—22no—
756C8—22no—
757C8—1182no—
758C8—1182no—
759C22—22no—
760C22—22no—
761C22—28no—
762C22—594no—
763C22—1182no—
764C22—1182no—
765C22—1188no—
766C22—1182no—
767C22—1182no—
768C22—1182no—
769C22—4724no—
770C22—23616no—
771C22—2362no—
772C22—2362no—
773C22—2362no—
774C22—2364no—
775C22C2×#1427371214yes—
776C22C2×#1427371212yes—
777C22#135×D5912yes—
778C22#1683819912yes—
779C22C22×D4×D5911yescharacteristic
780C4—42no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—1182no—
785C4—1182no—
786C4—2362no—
787C4—2362no—
788C4—2362no—
789C4C2×#1427371214yes—
790C4C2×#1427371212yes—
791C4C22×#1174568511yescharacteristic
792C4C22×#1174568911yescharacteristic
793C2—24no—
794C2—1184no—
795C2—4722no—
796C2—2362no—
797C2#2143401314yesdirect product factor
798C2C22×#1427371211yescharacteristic
799C2C2×#135×D5911yescharacteristic
800C2C2×#1683819911yescharacteristic
subgroupG/H
centerC22×C4D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#427C2
socleC23×C59C22×D4
prime radicalC2×#16837914C2
hypercenterC2×#427D59
hypocenterC59C2×#3091
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
2. C2×#117×D59C2semidirect
3. #21434013C2direct (N × H)
4. C2×#16837739C2semidirect
5. C2×#16837722C2semidirect
6. C2×#16837746C2semidirect
7. C2×#16837745C2semidirect
8. C2×#16837729C2semidirect
9. C2×#16837728C2semidirect
10. C2×#16837734C2semidirect
11. C2×#16837717C2semidirect
12. C2×#16837438C2semidirect
13. C2×#16837399C2semidirect
14. C2×#16837396C2semidirect
15. C22×(C2×D59)⋊C8C2semidirect
16. C2×C59×#427C2semidirect
36. #117×D59C22semidirect
41. #16837746C22semidirect
42. #16837745C22semidirect
43. #16837739C22semidirect
44. #16837734C22semidirect
45. #16837729C22semidirect
46. #16837728C22semidirect
47. #16837722C22semidirect
48. #16837717C22semidirect
49. #16837438C22semidirect
50. C2×#14273660C22semidirect
51. C2×#14273660C22semidirect
52. C2×#14273658C22semidirect
53. C2×#14273658C22semidirect
54. #16837399C22semidirect
55. #16837396C22semidirect
56. C2×#14273652C22semidirect
57. C2×#14273652C22semidirect
58. C2×#14273650C22semidirect
59. C2×#14273650C22semidirect
60. C2×#14273649C22semidirect
61. C2×#14273649C22semidirect
62. C2×#14273647C22semidirect
63. C2×#14273647C22semidirect
68. C2×(C2×D59)⋊C8C22semidirect
72. C59×#427C22semidirect
73. C2×#107×C59C22semidirect
74. C2×#107×C59C22semidirect
75. C2×#106×C59C22semidirect
76. C2×#106×C59C22semidirect
145. #14273660C23semidirect
146. #14273660C23semidirect
147. #14273658C23semidirect
148. #14273658C23semidirect
149. #14273652C23semidirect
150. #14273652C23semidirect
151. #14273650C23semidirect
152. #14273650C23semidirect
153. #14273649C23semidirect
154. #14273649C23semidirect
155. #14273647C23semidirect
156. #14273647C23semidirect
178. #107×C59C23semidirect
179. #107×C59C23semidirect
180. #106×C59C23semidirect
181. #106×C59C23semidirect
405. C2×#427D59semidirect
410. C2×C59#3091semidirect
453. #427C2×D59semidirect
456. C2×#107C2×D59semidirect
457. C2×#107C2×D59semidirect
460. C2×#106C2×D59semidirect
461. C2×#106C2×D59semidirect
477. C59C2×#3091semidirect
565. #107C22×D59semidirect
566. #107C22×D59semidirect
569. #106C22×D59semidirect
570. #106C22×D59semidirect
797. C2#21434013direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379142
C2×#117×D592
#214340132
C2×#168377392
C2×#168377222
C2×#168377462
C2×#168377452
C2×#168377292
C2×#168377282
C2×#168377342
C2×#168377172
C2×#168374382
C2×#168373992
C2×#168373962
C22×(C2×D59)⋊C82
C2×C59×#4272
C2×#309159