Finite Group Databasebeta

← C2×#21435959 #29465070

Subgroups — C2×#21435959 #29465070

Order 15104.

2374 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838065C211yesmaximal, characteristic, complemented
2C2×#16838053C211yesmaximal, characteristic
3#21435959C2116yesmaximal, direct product factor
4C2×#16837751C211yesmaximal, characteristic, complemented
5C2×#16837734C211yesmaximal, characteristic, complemented
6C2×#16837686C211yesmaximal, characteristic, complemented
7C2×#16837633C211yesmaximal, characteristic, complemented
8C2×#16837632C211yesmaximal, characteristic, complemented
9C2×#16837606C211yesmaximal, characteristic, complemented
10C2×#16837543C211yesmaximal, characteristic, complemented
11C2×#16837542C211yesmaximal, characteristic, complemented
12C2×#16837489C211yesmaximal, characteristic, complemented
13C2×(C22⋊D59)⋊C8C211yesmaximal, characteristic, complemented
14C22×#14273650C211yesmaximal, characteristic, complemented
15C2×#103×D59C211yesmaximal, characteristic, complemented
16C2×C59×#483C211yesmaximal, characteristic, complemented
17C22×#11745685—21no—
18C23×Dic118C2211yescharacteristic
19C22×Q8×D59C2211yescharacteristic
20C22×#11745660C2211yescharacteristic
21C22×#11745660C2211yescharacteristic
22C22×#11745671C2211yescharacteristic
23C23×C59⋊C8C2211yescharacteristic
24C22×C8×D59C2211yescharacteristic
25#16838065—24no—
26#16838065C2218yescomplemented
27#16838053—24no—
28#16838053C2218yes—
29C2×#14273726—21no—
30C2×#14273726C2211yescharacteristic
31C2×#14273725C2211yescharacteristic
32C2×#14273712—21no—
33C2×#14273710—21no—
34C2×#14273707C2211yescharacteristic
35C2×#14273705—21no—
36C2×#14273705—21no—
37C2×#14273704—21no—
38C2×#14273702C2211yescharacteristic
39C2×#14273701C2211yescharacteristic
40C2×#14273692C2211yescharacteristic
41C2×#14273689C2211yescharacteristic
42C2×C4×C22⋊D59C2211yescharacteristic
43C2×(C22⋊D59)⋊C4—21no—
44C2×C4⋊C4×D59C2211yescharacteristic
45#16837751C2218yescomplemented
46#16837734C2218yescomplemented
47#16837686C2218yescomplemented
48#16837633C2218yescomplemented
49#16837632C2218yescomplemented
50#16837606C2218yescomplemented
51#16837543C2218yescomplemented
52#16837542C2218yescomplemented
53#16837489C2218yescomplemented
54(C22⋊D59)⋊C8C2218yescomplemented
55C2×#14273658C2211yescharacteristic
56C2×Dic59⋊C8C2211yescharacteristic
57C2×#14273652C2211yescharacteristic
58C2×#14273652C2211yescharacteristic
59C2×#14273651C2211yescharacteristic
60C2×#14273650C2211yescharacteristic
61C2×#14273650C2211yescharacteristic
62C2×#14273650C2211yescharacteristic
63C2×#14273650C2211yescharacteristic
64C2×#14273650C2218yescomplemented
65#103×D59C2218yescomplemented
66C2×#14273647C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C2×C22⋊Q8×C59C2211yescharacteristic
70C22×C4⋊C4×C59C2211yescharacteristic
71C59×#483C2218yescomplemented
72C2×#106×C59C2211yescharacteristic
73C2×#106×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic
77C2×#11745685—28no—
78C2×#11745685—48no—
79C22×Dic118—24no—
80C22×Dic118—21no—
81C22×Dic118—22no—
82C22×Dic118—21no—
83C22×Dic118—21no—
84C22×Dic118—42no—
85C22×Dic118C2311yescharacteristic
86C22×Dic118C2314yes—
87C22×Dic118C2311yescharacteristic
88C2×Q8×D59—22no—
89C2×Q8×D59—24no—
90C2×Q8×D59—42no—
91C2×Q8×D59C2314yes—
92C22×D236—21no—
93C22×D236C2311yescharacteristic
94C22×C22⋊D59—21no—
95C22×C22⋊D59D411yescharacteristic
96C23×Dic59—21no—
97C22×C4×D59—21no—
98C22×C4×D59—21no—
99C22×C4×D59—21no—
100C22×C4×D59C2311yescharacteristic
101C2×#11745660—24no—
102C2×#11745660—42no—
103C2×#11745660C2314yes—
104C2×#11745660C2314yes—
105C2×#11745671—42no—
106C2×#11745671C2314yes—
107C22×C59⋊C8—42no—
108C22×C59⋊C8C2311yescharacteristic
109C22×C59⋊C8C2311yescharacteristic
110C22×C59⋊C8C2314yes—
111C2×C8×D59—42no—
112C2×C8×D59C2314yes—
113#14273726—28no—
114#14273726—22no—
115#14273726C2314yes—
116#14273725—22no—
117#14273725C2314yes—
118#14273712—28no—
119#14273710—28no—
120#14273707—22no—
121#14273707C2314yes—
122#14273705—28no—
123#14273705—28no—
124#14273704—28no—
125#14273702—22no—
126#14273702C2314yes—
127#14273701—22no—
128#14273701C2314yes—
129#14273692—22no—
130#14273692C2314yes—
131#14273689—22no—
132#14273689C2314yes—
133C4×C22⋊D59D414yes—
134C4×C22⋊D59C2314yes—
135(C22⋊D59)⋊C4—28no—
136C2×C4⋊Dic59—21no—
137C2×C4⋊Dic59C2311yescharacteristic
138C2×Dic59⋊C4—21no—
139C2×Dic59⋊C4—21no—
140C2×Dic59⋊C4—21no—
141C2×Dic59⋊C4—21no—
142C2×Dic59⋊C4—21no—
143C2×Dic59⋊C4D411yescharacteristic
144C4⋊C4×D59—22no—
145C4⋊C4×D59C2314yes—
146C2×C22⋊Dic59D411yescharacteristic
147C2×(C2×D59)⋊C4—21no—
148C2×(C2×D59)⋊C4—21no—
149C2×(C2×D59)⋊C4—21no—
150C2×(C2×D59)⋊C4—21no—
151C2×(C2×D59)⋊C4D411yescharacteristic
152C2×C4×Dic59—21no—
153C2×C4×Dic59C2311yescharacteristic
154#14273658C2314yes—
155Dic59⋊C8C2314yes—
156#14273652C2314yes—
157#14273652C2314yes—
158#14273651C2314yes—
159#14273650C2314yes—
160#14273650C2314yes—
161#14273650C2314yes—
162#14273650C2314yes—
163#14273647C2314yes—
164(C2×D59)⋊C8C2314yes—
165C8×Dic59C2314yes—
166C22×Q8×C59C2311yescharacteristic
167C23×C4×C59—21no—
168C23×C4×C59C2311yescharacteristic
169C22×C8×C59C2311yescharacteristic
170C22×C8×C59C2311yescharacteristic
171C22⋊Q8×C59—22no—
172C22⋊Q8×C59C2314yes—
173C2×C4⋊C4×C59—21no—
174C2×C4⋊C4×C59—21no—
175C2×C4⋊C4×C59—22no—
176C2×C4⋊C4×C59C2311yescharacteristic
177C2×C4⋊C4×C59C2311yescharacteristic
178C2×C4⋊C4×C59C2311yescharacteristic
179C2×C4⋊C4×C59C2314yes—
180C2×C22⋊C4×C59—21no—
181#106×C59C2314yes—
182#106×C59C2314yes—
183#103×C59C2314yes—
184#103×C59C2314yes—
185C22⋊C8×C59C2314yes—
186C24×C59C2×D411yescharacteristic
187C23×D59—21no—
188C23×D59C2×D411yescharacteristic
189C2×Q8×C59—21no—
190C2×Q8×C59—22no—
191C2×Q8×C59—22no—
192C2×Q8×C59C2412yes—
193C22×C4×C59—22no—
194C22×C4×C59—22no—
195C22×C4×C59—21no—
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59—24no—
200C22×C4×C59—44no—
201C22×C4×C59C2×D411yescharacteristic
202C22×C4×C59C2×D412yes—
203C22×C4×C59C2412yes—
204C22×C4×C59C2411yescharacteristic
205C2×C22⋊D59—24no—
206C2×C22⋊D59—44no—
207C2×C22⋊D59SD1618yescomplemented
208C2×C22⋊D59C2×D414yes—
209C22×Dic59—21no—
210C22×Dic59—21no—
211C22×Dic59—21no—
212C22×Dic59—24no—
213C22×Dic59—44no—
214C22×Dic59C2×D411yescharacteristic
215C22×Dic59C2×D411yescharacteristic
216C22×Dic59C2×D411yescharacteristic
217Q8×D59—28no—
218Q8×D59—44no—
219Q8×D59—48no—
220#11745685—432no—
221C2×D236—22no—
222C2×D236—22no—
223C2×D236—24no—
224C2×D236—21no—
225C2×D236—44no—
226C2×D236C2412yes—
227C2×C4×D59—22no—
228C2×C4×D59—22no—
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×D412yes—
236C2×C4×D59C2412yes—
237C2×Dic118—21no—
238C2×Dic118—22no—
239C2×Dic118—22no—
240C2×Dic118—22no—
241C2×Dic118—28no—
242C2×Dic118—24no—
243C2×Dic118—21no—
244C2×Dic118—24no—
245C2×Dic118—24no—
246C2×Dic118—44no—
247C2×Dic118—48no—
248C2×Dic118—44no—
249C2×Dic118—44no—
250C2×Dic118—44no—
251C2×Dic118#4114yescomplemented
252C2×Dic118C2412yes—
253C2×Dic118C2412yes—
254C2×C8×C59—22no—
255C2×C8×C59—22no—
256C2×C8×C59C2412yes—
257C2×C8×C59C2412yes—
258C4⋊C4×C59—21no—
259C4⋊C4×C59—21no—
260C4⋊C4×C59—24no—
261C4⋊C4×C59—24no—
262C4⋊C4×C59—21no—
263C4⋊C4×C59C2412yes—
264C4⋊C4×C59C2412yes—
265C4⋊C4×C59C2412yes—
266C22⋊C4×C59—24no—
267C22⋊Dic59C2×D414yes—
268#11745671—44no—
269(C2×D59)⋊C4—24no—
270(C2×D59)⋊C4—24no—
271(C2×D59)⋊C4—24no—
272(C2×D59)⋊C4—24no—
273(C2×D59)⋊C4C2×D414yes—
274C4⋊Dic59—21no—
275C4⋊Dic59—24no—
276C4⋊Dic59C2412yes—
277Dic59⋊C4—24no—
278Dic59⋊C4—24no—
279Dic59⋊C4—24no—
280Dic59⋊C4—24no—
281Dic59⋊C4—24no—
282Dic59⋊C4C2×D414yes—
283C4×Dic59—24no—
284C4×Dic59C2×D412yes—
285C4×Dic59C2412yes—
286C2×C59⋊C8—22no—
287C2×C59⋊C8—22no—
288C2×C59⋊C8—44no—
289C2×C59⋊C8C2412yes—
290C2×C59⋊C8C2412yes—
291#11745660—28no—
292#11745660—44no—
293C8×D59—44no—
294C23×C59—22no—
295C23×C59—22no—
296C23×C59C2×SD1614yes—
297C23×C59C22×D412yes—
298C23×C59C22×D411yescharacteristic
299C22×D59—22no—
300C22×D59—22no—
301C22×D59—22no—
302C22×D59—42no—
303C22×D59—42no—
304C22×D59—42no—
305C22×D59C2×SD1614yes—
306C22×D59C22×D412yes—
307Q8×C59—22no—
308Q8×C59—22no—
309Q8×C59—42no—
310C2×C4×C59—22no—
311C2×C4×C59—24no—
312C2×C4×C59—22no—
313C2×C4×C59—22no—
314C2×C4×C59—22no—
315C2×C4×C59—22no—
316C2×C4×C59—22no—
317C2×C4×C59—22no—
318C2×C4×C59—42no—
319C2×C4×C59—42no—
320C2×C4×C59—42no—
321C2×C4×C59—48no—
322C2×C4×C59—42no—
323C2×C4×C59C22×D412yes—
324C2×C4×C59C22×D411yescharacteristic
325C2×C4×C59C2×#4112yes—
326C2×C4×C59H(5,𝔽2)12yes—
327C2×C4×C59C2511yescharacteristic
328C22⋊D59—48no—
329C22⋊D59C2×SD16116yescomplemented
330C2×Dic59—24no—
331C2×Dic59—22no—
332C2×Dic59—22no—
333C2×Dic59—22no—
334C2×Dic59—22no—
335C2×Dic59—22no—
336C2×Dic59—48no—
337C2×Dic59—42no—
338C2×Dic59—42no—
339C2×Dic59C2×SD1614yes—
340C2×Dic59C22×D412yes—
341C2×Dic59C22×D412yes—
342C2×Dic59C22×D412yes—
343D236—22no—
344D236—22no—
345D236—48no—
346D236—42no—
347C4×D59—24no—
348C4×D59—22no—
349C4×D59—22no—
350C4×D59—48no—
351C4×D59—48no—
352C4×D59—48no—
353Dic118—24no—
354Dic118—22no—
355Dic118—22no—
356Dic118—22no—
357Dic118—48no—
358Dic118—48no—
359Dic118—42no—
360Dic118—48no—
361Dic118C2×#4114yescomplemented
362C8×C59—22no—
363C8×C59—22no—
364C59⋊C8—22no—
365C59⋊C8—22no—
366C2×#3298—591nomaximal, Sylow
367C22×C59—22no—
368C22×C59—28no—
369C22×C59—22no—
370C22×C59#54612yes—
371C22×C59C22×SD1614yes—
372C22×C59C22×SD1612yes—
373C22×C59#57812yes—
374C22×C59C23×D411yescharacteristic
375C2×D59—22no—
376C2×D59—28no—
377C2×D59—22no—
378C2×D59—42no—
379C2×D59—42no—
380C2×D59—42no—
381C2×D59—84no—
382C2×D59C22×SD1614yes—
383C4×C59—22no—
384C4×C59—42no—
385C4×C59—42no—
386C4×C59—42no—
387C4×C59—42no—
388C4×C59#54612yes—
389C4×C59C22×#4111yescharacteristic
390C4×C59C2×H(5,𝔽2)11yescharacteristic
391Dic59—24no—
392Dic59—22no—
393Dic59—22no—
394Dic59—42no—
395Dic59—42no—
396Dic59C22×SD1614yes—
397C2×D4×Q8—591no—
398C2×#547—591no—
399#3298—5916no—
400C2×#487—591no—
401C2×#483—591no—
402C2×#483D5911yescharacteristic, complemented
403C2×#475—591no—
404C2×#465—591no—
405C2×#465—591no—
406C2×#461—591no—
407C2×#448—591no—
408C2×#448—591no—
409C2×C4×SD16—591no—
410C2×C8×D4—591no—
411C22×#103—591no—
412C22×#103—591no—
413C2×C59—24no—
414C2×C59#329814yescomplemented
415C2×C59C2×#54611yescharacteristic
416C2×C59C23×SD1611yescharacteristic
417C2×C59C2×#57811yescharacteristic
418D59—24no—
419D59—82no—
420C22×#41—1181no—
421C23×Q8—591no—
422C23×Q8—591no—
423C22×SD16—591no—
424C22×SD16—591no—
425C22×SD16—591no—
426C23×C8—591no—
427C23×C8—591no—
428D4×Q8—598no—
429D4×Q8—1184no—
430#547—598no—
431#547—1184no—
432C2×C4⋊Q8—591no—
433C2×C4⋊Q8—591no—
434C2×C4⋊Q8—1181no—
435C2×#123—1181no—
436C2×#123—1181no—
437C2×C22⋊Q8—591no—
438C2×C22⋊Q8—1181no—
439C2×C22⋊Q8—1181no—
440C2×C22⋊Q8—1181no—
441C2×C22⋊Q8C2×D5911yescharacteristic
442C2×#121—591no—
443C2×#121—591no—
444C2×C4×Q8—591no—
445C2×C4×D4—591no—
446C2×C4×D4—591no—
447C2×C4×D4—1181no—
448C22×C4⋊C4—591no—
449C22×C4⋊C4C2×D5911yescharacteristic
450#487—598no—
451#483—598no—
452#483C2×D5918yescomplemented
453#475—598no—
454#465—598no—
455#465—598no—
456#461—598no—
457#448—598no—
458#448—598no—
459C4×SD16—598no—
460C8×D4—598no—
461C2×#106—591no—
462C2×#106C2×D5911yescharacteristic
463C2×#106C2×D5911yescharacteristic
464C2×C4⋊C8—591no—
465C2×#103—591no—
466C2×#103—591no—
467C2×#103—591no—
468C2×#103—591no—
469C2×#103—591no—
470C2×#103—591no—
471C2×#103—591no—
472C2×#103—598no—
473C2×#103—598no—
474C2×#103C2×D5911yescharacteristic
475C2×#103C2×D5911yescharacteristic
476C2×#102—591no—
477C2×C22⋊C8—591no—
478C2×C22⋊C8C2×D5911yescharacteristic
479C2×C4×C8—591no—
480C59C2×#329811yescharacteristic, complemented, Sylow
481C2×#41—1188no—
482C2×#41—2368no—
483C22×Q8—594no—
484C22×Q8—591no—
485C22×Q8—591no—
486C22×Q8—594no—
487C22×Q8—1181no—
488C22×Q8—1181no—
489C22×Q8—1184no—
490C22×Q8—1182no—
491C22×Q8—1181no—
492C22×Q8—1182no—
493C22×Q8—1184no—
494C22×Q8—2362no—
495C22×Q8—2362no—
496C22×Q8C22×D5911yescharacteristic
497C22×D4—591no—
498C22×D4—591no—
499C22×D4—1181no—
500C22×D4—1181no—
501C23×C4—21no—
502C23×C4—591no—
503C23×C4—1181no—
504C23×C4—1181no—
505C23×C4—1181no—
506C23×C4—1181no—
507C23×C4C22×D5911yescharacteristic
508C2×SD16—594no—
509C2×SD16—594no—
510C2×SD16—594no—
511C2×SD16—1184no—
512C2×SD16—2362no—
513C2×SD16—2362no—
514C22×C8—591no—
515C22×C8—591no—
516C22×C8—594no—
517C22×C8—594no—
518C22×C8—2362no—
519C22×C8—2362no—
520C22×C8C22×D5911yescharacteristic
521C22×C8C22×D5911yescharacteristic
522C4⋊Q8—594no—
523C4⋊Q8—594no—
524C4⋊Q8—1182no—
525C4⋊Q8—1182no—
526C4⋊Q8—1188no—
527#123—1188no—
528#123—1188no—
529C22⋊Q8—22no—
530C22⋊Q8—594no—
531C22⋊Q8—1188no—
532C22⋊Q8—1188no—
533C22⋊Q8—1188no—
534C22⋊Q8—1182no—
535C22⋊Q8C22×D5914yes—
536#121—594no—
537#121—594no—
538#121—1182no—
539#121—1182no—
540C4×Q8—594no—
541C4×Q8—1182no—
542C4×D4—594no—
543C4×D4—594no—
544C4×D4—594no—
545C4×D4—1182no—
546C4×D4—1188no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—22no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—591no—
551C2×C4⋊C4—591no—
552C2×C4⋊C4—594no—
553C2×C4⋊C4—1182no—
554C2×C4⋊C4—1181no—
555C2×C4⋊C4—1181no—
556C2×C4⋊C4—1181no—
557C2×C4⋊C4—1181no—
558C2×C4⋊C4—1181no—
559C2×C4⋊C4—1181no—
560C2×C4⋊C4C22×D5911yescharacteristic
561C2×C4⋊C4C22×D5911yescharacteristic
562C2×C4⋊C4C22×D5914yes—
563C2×C4⋊C4C22×D5911yescharacteristic
564C2×C22⋊C4—21no—
565C2×C22⋊C4—591no—
566C2×C22⋊C4—591no—
567C2×C22⋊C4—1181no—
568C2×C22⋊C4—1181no—
569C2×C22⋊C4—1181no—
570C2×C22⋊C4—1181no—
571C2×C42—591no—
572C2×C42—1181no—
573#106—594no—
574#106C22×D5914yes—
575#106C22×D5914yes—
576C4⋊C8—594no—
577#103—594no—
578#103—594no—
579#103—594no—
580#103—594no—
581#103—594no—
582#103—594no—
583#103—594no—
584#103C22×D5914yes—
585#103C22×D5914yes—
586#102—594no—
587C22⋊C8—594no—
588C22⋊C8C22×D5914yes—
589C4×C8—594no—
590C24—591no—
591C24—1181no—
592C24D4×D5911yescharacteristic
593#41—23632no—
594C2×Q8—21no—
595C2×Q8—22no—
596C2×Q8—22no—
597C2×Q8—594no—
598C2×Q8—592no—
599C2×Q8—592no—
600C2×Q8—1184no—
601C2×Q8—1184no—
602C2×Q8—1188no—
603C2×Q8—1181no—
604C2×Q8—1184no—
605C2×Q8—1181no—
606C2×Q8—1182no—
607C2×Q8—1188no—
608C2×Q8—1182no—
609C2×Q8—1182no—
610C2×Q8—2364no—
611C2×Q8—2364no—
612C2×Q8—2368no—
613C2×Q8—2364no—
614C2×Q8—2364no—
615C2×Q8—2364no—
616C2×Q8—2368no—
617C2×Q8C23×D5912yes—
618C2×D4—598no—
619C2×D4—594no—
620C2×D4—592no—
621C2×D4—1184no—
622C2×D4—1184no—
623C2×D4—1181no—
624C2×D4—1182no—
625C2×D4—1182no—
626C2×D4—2364no—
627C2×D4—2364no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—24no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—44no—
636C22×C4—591no—
637C22×C4—591no—
638C22×C4—591no—
639C22×C4—592no—
640C22×C4—592no—
641C22×C4—1184no—
642C22×C4—1184no—
643C22×C4—1184no—
644C22×C4—1181no—
645C22×C4—1182no—
646C22×C4—1182no—
647C22×C4—1184no—
648C22×C4—1181no—
649C22×C4—1181no—
650C22×C4—2364no—
651C22×C4—2364no—
652C22×C4—2364no—
653C22×C4—2364no—
654C22×C4D4×D5912yes—
655C22×C4D4×D5911yescharacteristic
656C22×C4C23×D5912yes—
657C22×C4C23×D5911yescharacteristic
658SD16—1188no—
659SD16—2364no—
660SD16—2364no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—592no—
664C2×C8—592no—
665C2×C8—1182no—
666C2×C8—1182no—
667C2×C8—2364no—
668C2×C8—2364no—
669C2×C8C23×D5912yes—
670C2×C8C23×D5912yes—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—21no—
676C4⋊C4—594no—
677C4⋊C4—592no—
678C4⋊C4—1184no—
679C4⋊C4—1184no—
680C4⋊C4—1184no—
681C4⋊C4—1184no—
682C4⋊C4—1184no—
683C4⋊C4—1184no—
684C4⋊C4—1181no—
685C4⋊C4C23×D5912yes—
686C4⋊C4C23×D5912yes—
687C4⋊C4C23×D5912yes—
688C22⋊C4—24no—
689C22⋊C4—594no—
690C22⋊C4—594no—
691C22⋊C4—1184no—
692C22⋊C4—1184no—
693C22⋊C4—1184no—
694C22⋊C4—1184no—
695C42—592no—
696C42—592no—
697C42—1184no—
698C23—22no—
699C23—22no—
700C23—594no—
701C23—592no—
702C23—1182no—
703C23—1182no—
704C23—1182no—
705C23—2362no—
706C23—2362no—
707C23—2362no—
708C23SD16×D5914yes—
709C23C2×D4×D5912yes—
710C23C2×D4×D5911yescharacteristic
711Q8—22no—
712Q8—22no—
713Q8—42no—
714Q8—594no—
715Q8—1182no—
716Q8—1184no—
717Q8—1182no—
718Q8—1182no—
719Q8—2368no—
720Q8—2368no—
721Q8—2368no—
722Q8—2362no—
723D4—5916no—
724D4—1182no—
725D4—1182no—
726D4—2368no—
727D4—2368no—
728D4—2362no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—48no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—594no—
743C2×C4—592no—
744C2×C4—592no—
745C2×C4—592no—
746C2×C4—1182no—
747C2×C4—1182no—
748C2×C4—1182no—
749C2×C4—1184no—
750C2×C4—1182no—
751C2×C4—1182no—
752C2×C4—1184no—
753C2×C4—1182no—
754C2×C4—1182no—
755C2×C4—2368no—
756C2×C4—2368no—
757C2×C4—2368no—
758C2×C4—2368no—
759C2×C4—2362no—
760C2×C4—2362no—
761C2×C4C2×D4×D5912yes—
762C2×C4C2×D4×D5911yescharacteristic
763C2×C4#41×D5912yes—
764C2×C4#1427377312yes—
765C2×C4C24×D5911yescharacteristic
766C8—22no—
767C8—22no—
768C8—1182no—
769C8—1182no—
770C22—28no—
771C22—22no—
772C22—22no—
773C22—594no—
774C22—1188no—
775C22—1182no—
776C22—1182no—
777C22—4724no—
778C22—2362no—
779C22—2362no—
780C22—2362no—
781C22#1683804412yes—
782C22C2×SD16×D5914yes—
783C22C2×SD16×D5912yes—
784C22#1683821812yes—
785C22C22×D4×D5911yescharacteristic
786C4—22no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—42no—
791C4—594no—
792C4—1182no—
793C4—1184no—
794C4—1182no—
795C4—2362no—
796C4—2362no—
797C4#1683804412yes—
798C4C2×#41×D5911yescharacteristic
799C4C2×#1427377311yescharacteristic
800C2—24no—
801C2—1184no—
802C2—4722no—
803C2#2143595914yesdirect product factor
804C2C2×#1683804411yescharacteristic
805C2C22×SD16×D5911yescharacteristic
806C2C2×#1683821811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#483C2
socleC23×C59C22×D4
prime radicalC2×#16838053C2
hypercenterC2×#483D59
hypocenterC59C2×#3298
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
1. C2×#16838065C2semidirect
3. #21435959C2direct (N × H)
4. C2×#16837751C2semidirect
5. C2×#16837734C2semidirect
6. C2×#16837686C2semidirect
7. C2×#16837633C2semidirect
8. C2×#16837632C2semidirect
9. C2×#16837606C2semidirect
10. C2×#16837543C2semidirect
11. C2×#16837542C2semidirect
12. C2×#16837489C2semidirect
13. C2×(C22⋊D59)⋊C8C2semidirect
14. C22×#14273650C2semidirect
15. C2×#103×D59C2semidirect
16. C2×C59×#483C2semidirect
26. #16838065C22semidirect
45. #16837751C22semidirect
46. #16837734C22semidirect
47. #16837686C22semidirect
48. #16837633C22semidirect
49. #16837632C22semidirect
50. #16837606C22semidirect
51. #16837543C22semidirect
52. #16837542C22semidirect
53. #16837489C22semidirect
54. (C22⋊D59)⋊C8C22semidirect
64. C2×#14273650C22semidirect
65. #103×D59C22semidirect
71. C59×#483C22semidirect
207. C2×C22⋊D59SD16semidirect
251. C2×Dic118#41semidirect
329. C22⋊D59C2×SD16semidirect
361. Dic118C2×#41semidirect
402. C2×#483D59semidirect
414. C2×C59#3298semidirect
452. #483C2×D59semidirect
480. C59C2×#3298semidirect
803. C2#21435959direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380652
C2×#168380532
#214359592
C2×#168377512
C2×#168377342
C2×#168376862
C2×#168376332
C2×#168376322
C2×#168376062
C2×#168375432
C2×#168375422
C2×#168374892
C2×(C22⋊D59)⋊C82
C22×#142736502
C2×#103×D592
C2×C59×#4832
C2×#329859