Finite Group Databasebeta

← C2×#21434930 #29459311

Subgroups — C2×#21434930 #29459311

Order 15104.

2342 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837914C211yesmaximal, characteristic
2C2×C22⋊Q8×D59C211yesmaximal, characteristic, complemented
3#21434930C2116yesmaximal, direct product factor
4C2×#16837739C211yesmaximal, characteristic, complemented
5C2×#16837722C211yesmaximal, characteristic, complemented
6C2×#16837743C211yesmaximal, characteristic, complemented
7C2×#16837661C211yesmaximal, characteristic, complemented
8C2×#16837659C211yesmaximal, characteristic, complemented
9C2×#16837651C211yesmaximal, characteristic, complemented
10C2×#16837649C211yesmaximal, characteristic, complemented
11C2×#16837566C211yesmaximal, characteristic, complemented
12C2×#16837562C211yesmaximal, characteristic, complemented
13C2×#16837559C211yesmaximal, characteristic, complemented
14C2×#16837542C211yesmaximal, characteristic, complemented
15C2×#16837364C211yesmaximal, characteristic, complemented
16C2×C59×#485C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C22×Q8×D59C2211yescharacteristic
19C23×C4×D59C2211yescharacteristic
20C22×Dic236C2211yescharacteristic, complemented
21C22×#11745672C2211yescharacteristic, complemented
22C22×#11745660C2211yescharacteristic, complemented
23C22×#11745671C2211yescharacteristic, complemented
24C22×#11745659C2211yescharacteristic
25C22×#11745659C2211yescharacteristic
26#16837914—24no—
27#16837914C2218yes—
28C2×#14273711—21no—
29C2×#14273707C2211yescharacteristic
30C2×#14273707C2211yescharacteristic
31C2×#14273707C2211yescharacteristic
32C2×#14273706C2211yescharacteristic
33C2×#14273705—21no—
34C2×#14273704—21no—
35C2×#14273703C2211yescharacteristic
36C22⋊Q8×D59—24no—
37C22⋊Q8×D59C2218yescomplemented
38C2×#14273702C2211yescharacteristic
39C2×#14273702C2211yescharacteristic
40C2×#14273697—21no—
41C2×C4×D236—21no—
42C2×C4×D236—21no—
43C2×C4⋊C4×D59—21no—
44C2×C4⋊C4×D59C2211yescharacteristic
45C2×C22⋊C4×D59—21no—
46#16837743C2218yescomplemented
47#16837739C2218yescomplemented
48#16837722C2218yescomplemented
49#16837661C2218yescomplemented
50#16837659C2218yescomplemented
51#16837651C2218yescomplemented
52#16837649C2218yescomplemented
53#16837566C2218yescomplemented
54#16837562C2218yescomplemented
55#16837559C2218yescomplemented
56#16837542C2218yescomplemented
57C2×#14273660C2211yescharacteristic, complemented
58C2×#14273658C2211yescharacteristic, complemented
59C2×#14273652C2211yescharacteristic, complemented
60C2×#14273650C2211yescharacteristic, complemented
61C2×#14273650C2211yescharacteristic, complemented
62C2×#14273650C2211yescharacteristic, complemented
63C2×#14273649C2211yescharacteristic, complemented
64C2×#14273647C2211yescharacteristic, complemented
65#16837364C2218yescomplemented
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×(C2×D59)⋊C8C2211yescharacteristic
69C2×C22⋊Q8×C59C2211yescharacteristic
70C2×#117×C59C2211yescharacteristic
71C59×#485C2218yescomplemented
72C2×#107×C59C2211yescharacteristic, complemented
73C2×#106×C59C2211yescharacteristic, complemented
74C2×#103×C59C2211yescharacteristic, complemented
75C2×#103×C59C2211yescharacteristic, complemented
76C2×C22⋊C8×C59C2211yescharacteristic
77C24×D59D411yescharacteristic
78C2×#11745685—22no—
79C2×#11745685—42no—
80C2×#11745685—42no—
81C2×#11745685C2314yes—
82C22×Dic118—21no—
83C22×Dic118C2311yescharacteristic
84C22×Dic118C2311yescharacteristic
85C2×Q8×D59—22no—
86C2×Q8×D59—42no—
87C2×Q8×D59—42no—
88C2×Q8×D59C2314yes—
89C22×D236—21no—
90C22×D236—21no—
91C22×D236C2311yescharacteristic
92C22×C22⋊D59—21no—
93C23×Dic59D411yescharacteristic
94C22×C4×D59—21no—
95C22×C4×D59—21no—
96C22×C4×D59—21no—
97C22×C4×D59—42no—
98C22×C4×D59—42no—
99C22×C4×D59D414yes—
100C22×C4×D59D411yescharacteristic
101C22×C4×D59D411yescharacteristic
102C22×C4×D59C2311yescharacteristic
103C22×C4×D59C2311yescharacteristic
104C22×C4×D59C2314yes—
105C2×Dic236—42no—
106C2×Dic236C2314yescomplemented
107C2×#11745672—42no—
108C2×#11745672C2314yescomplemented
109C2×#11745660—42no—
110C2×#11745660C2314yescomplemented
111C2×#11745671—42no—
112C2×#11745671C2314yescomplemented
113C2×#11745659—42no—
114C2×#11745659—42no—
115C2×#11745659C2314yes—
116C2×#11745659C2314yes—
117C22×C59⋊C8C2311yescharacteristic
118C22×C59⋊C8C2311yescharacteristic
119#14273711—28no—
120#14273707—22no—
121#14273707—22no—
122#14273707—22no—
123#14273707C2314yes—
124#14273707C2314yes—
125#14273707C2314yes—
126#14273706—22no—
127#14273706C2314yes—
128#14273705—28no—
129#14273704—28no—
130#14273703—22no—
131#14273703C2314yes—
132#14273702—22no—
133#14273702—22no—
134#14273702C2314yes—
135#14273702C2314yes—
136#14273697—28no—
137C4×D236—28no—
138C4×D236—28no—
139C2×C4⋊Dic59—21no—
140C2×C4⋊Dic59—21no—
141C2×C4⋊Dic59—21no—
142C2×C4⋊Dic59C2311yescharacteristic
143C2×Dic59⋊C4—21no—
144C2×Dic59⋊C4—21no—
145C2×Dic59⋊C4—21no—
146C4⋊C4×D59—22no—
147C4⋊C4×D59—28no—
148C4⋊C4×D59C2314yes—
149C2×C22⋊Dic59—21no—
150C2×(C2×D59)⋊C4—21no—
151C2×(C2×D59)⋊C4—21no—
152C2×(C2×D59)⋊C4—21no—
153C2×(C2×D59)⋊C4—21no—
154C2×(C2×D59)⋊C4—21no—
155C2×(C2×D59)⋊C4—21no—
156C22⋊C4×D59—28no—
157#14273660C2314yescomplemented
158#14273658C2314yescomplemented
159#14273652C2314yescomplemented
160#14273650C2314yescomplemented
161#14273650C2314yescomplemented
162#14273650C2314yescomplemented
163#14273649C2314yescomplemented
164#14273647C2314yescomplemented
165C22⋊(C59⋊C8)C2314yes—
166(C2×D59)⋊C8C2314yes—
167(C2×D59)⋊C8C2314yes—
168C22×Q8×C59C2311yescharacteristic
169C23×C4×C59C2311yescharacteristic
170C22×C8×C59C2311yescharacteristic
171C22×C8×C59C2311yescharacteristic
172C22⋊Q8×C59—22no—
173C22⋊Q8×C59C2314yes—
174#117×C59—22no—
175#117×C59C2314yes—
176C2×C4⋊C4×C59—21no—
177C2×C4⋊C4×C59C2311yescharacteristic
178C2×C4⋊C4×C59C2311yescharacteristic
179C2×C4⋊C4×C59C2311yescharacteristic
180C2×C22⋊C4×C59—21no—
181C2×C22⋊C4×C59—21no—
182C2×C42×C59—21no—
183#107×C59C2314yescomplemented
184#106×C59C2314yescomplemented
185#103×C59C2314yescomplemented
186#103×C59C2314yescomplemented
187C22⋊C8×C59C2314yes—
188C24×C59C2×D411yescharacteristic
189C23×D59—24no—
190C23×D59—21no—
191C23×D59—42no—
192C23×D59—42no—
193C23×D59C2×D411yescharacteristic
194C23×D59C2×D411yescharacteristic
195C23×D59C2×D414yes—
196C2×Q8×C59—21no—
197C2×Q8×C59—22no—
198C2×Q8×C59—22no—
199C2×Q8×C59C2412yes—
200C22×C4×C59—22no—
201C22×C4×C59—22no—
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59C2×D411yescharacteristic
207C22×C4×C59C2×D412yes—
208C22×C4×C59C2412yes—
209C22×C4×C59C2411yescharacteristic
210C2×C22⋊D59—24no—
211C2×C22⋊D59—44no—
212C22×Dic59—21no—
213C22×Dic59—21no—
214C22×Dic59—21no—
215C22×Dic59—42no—
216C22×Dic59C2×D411yescharacteristic
217C22×Dic59C2×D411yescharacteristic
218C22×Dic59C2×D414yes—
219Q8×D59—44no—
220Q8×D59—44no—
221Q8×D59—48no—
222#11745685—44no—
223#11745685—44no—
224#11745685—48no—
225C2×D236—22no—
226C2×D236—22no—
227C2×D236—24no—
228C2×D236—24no—
229C2×D236—21no—
230C2×D236—44no—
231C2×D236—44no—
232C2×D236C2412yes—
233C2×C4×D59—22no—
234C2×C4×D59—22no—
235C2×C4×D59—22no—
236C2×C4×D59—22no—
237C2×C4×D59—24no—
238C2×C4×D59—24no—
239C2×C4×D59—24no—
240C2×C4×D59—48no—
241C2×C4×D59—44no—
242C2×C4×D59—44no—
243C2×C4×D59—42no—
244C2×C4×D59—42no—
245C2×C4×D59—44no—
246C2×C4×D59—44no—
247C2×C4×D59—44no—
248C2×C4×D59C2×D412yes—
249C2×C4×D59C2×D412yes—
250C2×C4×D59C2×D414yes—
251C2×C4×D59C2×D414yes—
252C2×C4×D59C2412yes—
253C2×C4×D59C2412yes—
254C2×Dic118—22no—
255C2×Dic118—22no—
256C2×Dic118—22no—
257C2×Dic118—22no—
258C2×Dic118—21no—
259C2×Dic118—21no—
260C2×Dic118—24no—
261C2×Dic118—44no—
262C2×Dic118C2412yes—
263C2×Dic118C2412yes—
264C2×C8×C59—22no—
265C2×C8×C59—22no—
266C2×C8×C59C2412yes—
267C2×C8×C59C2412yes—
268C4⋊C4×C59—24no—
269C4⋊C4×C59—21no—
270C4⋊C4×C59—21no—
271C4⋊C4×C59—21no—
272C4⋊C4×C59C2412yes—
273C4⋊C4×C59C2412yes—
274C4⋊C4×C59C2412yes—
275C22⋊C4×C59—24no—
276C22⋊C4×C59—24no—
277C42×C59—24no—
278C22⋊Dic59—24no—
279#11745672—44no—
280#11745671—44no—
281(C2×D59)⋊C4—24no—
282(C2×D59)⋊C4—24no—
283(C2×D59)⋊C4—24no—
284(C2×D59)⋊C4—24no—
285(C2×D59)⋊C4—24no—
286(C2×D59)⋊C4—24no—
287C4⋊Dic59—21no—
288C4⋊Dic59—24no—
289C4⋊Dic59—24no—
290C4⋊Dic59—24no—
291C4⋊Dic59C2412yes—
292Dic59⋊C4—24no—
293Dic59⋊C4—24no—
294Dic59⋊C4—24no—
295C2×C59⋊C8—22no—
296C2×C59⋊C8—22no—
297C2×C59⋊C8C2412yes—
298C2×C59⋊C8C2412yes—
299Dic236—44no—
300#11745660—44no—
301#11745659—44no—
302#11745659—44no—
303C23×C59—22no—
304C23×C59—22no—
305C23×C59—22no—
306C23×C59C22×D412yes—
307C23×C59C22×D411yescharacteristic
308C22×D59—22no—
309C22×D59—22no—
310C22×D59—22no—
311C22×D59—22no—
312C22×D59—22no—
313C22×D59—28no—
314C22×D59—22no—
315C22×D59—44no—
316C22×D59—44no—
317C22×D59—416no—
318C22×D59—42no—
319C22×D59—42no—
320C22×D59—42no—
321C22×D59#13714yes—
322C22×D59C22×D412yes—
323C22×D59C22×D412yes—
324Q8×C59—22no—
325Q8×C59—22no—
326Q8×C59—42no—
327C2×C4×C59—22no—
328C2×C4×C59—24no—
329C2×C4×C59—22no—
330C2×C4×C59—22no—
331C2×C4×C59—22no—
332C2×C4×C59—22no—
333C2×C4×C59—22no—
334C2×C4×C59—22no—
335C2×C4×C59—42no—
336C2×C4×C59—42no—
337C2×C4×C59—42no—
338C2×C4×C59—42no—
339C2×C4×C59C22×D412yes—
340C2×C4×C59C22×D411yescharacteristic
341C2×C4×C59H(5,𝔽2)12yes—
342C2×C4×C59H(5,𝔽2)12yes—
343C2×C4×C59C2511yescharacteristic
344C22⋊D59—48no—
345C2×Dic59—22no—
346C2×Dic59—22no—
347C2×Dic59—22no—
348C2×Dic59—22no—
349C2×Dic59—22no—
350C2×Dic59—44no—
351C2×Dic59—42no—
352C2×Dic59—42no—
353C2×Dic59—42no—
354C2×Dic59C22×D412yes—
355C2×Dic59C22×D412yes—
356D236—22no—
357D236—22no—
358D236—48no—
359D236—48no—
360D236—42no—
361C4×D59—24no—
362C4×D59—24no—
363C4×D59—22no—
364C4×D59—22no—
365C4×D59—22no—
366C4×D59—22no—
367C4×D59—44no—
368C4×D59—44no—
369C4×D59—48no—
370C4×D59—48no—
371C4×D59—48no—
372Dic118—22no—
373Dic118—22no—
374Dic118—22no—
375Dic118—22no—
376Dic118—48no—
377Dic118—42no—
378Dic118—42no—
379C8×C59—22no—
380C8×C59—22no—
381C59⋊C8—22no—
382C59⋊C8—22no—
383C2×#3196—591nomaximal, Sylow
384C22×C59—22no—
385C22×C59—22no—
386C22×C59—22no—
387C22×C59—44no—
388C22×C59#53412yes—
389C22×C59C2×#13712yes—
390C22×C59#57512yes—
391C22×C59C23×D411yescharacteristic
392C2×D59—22no—
393C2×D59—28no—
394C2×D59—22no—
395C2×D59—22no—
396C2×D59—22no—
397C2×D59—22no—
398C2×D59—416no—
399C2×D59—44no—
400C2×D59—42no—
401C2×D59—42no—
402C2×D59—42no—
403C2×D59—84no—
404C2×D59C2×#13714yes—
405C4×C59—22no—
406C4×C59—42no—
407C4×C59—42no—
408C4×C59—42no—
409C4×C59—42no—
410C4×C59#53412yes—
411C4×C59C2×H(5,𝔽2)11yescharacteristic
412C4×C59C2×H(5,𝔽2)11yescharacteristic
413Dic59—22no—
414Dic59—22no—
415Dic59—42no—
416Dic59—42no—
417Dic59—42no—
418C2×#525—591no—
419C22×C22⋊Q8—591no—
420#3196—5916no—
421C2×#484—591no—
422C2×#481—591no—
423C2×#485—591no—
424C2×#485D5911yescharacteristic, complemented
425C2×#470—591no—
426C2×#470—591no—
427C2×#468—591no—
428C2×#468—591no—
429C2×#452—591no—
430C2×#452—591no—
431C2×#451—591no—
432C2×#448—591no—
433C2×#407—591no—
434C2×C59—42no—
435C2×C59#319614yescomplemented
436C2×C59C2×#53411yescharacteristic
437C2×C59C22×#13711yescharacteristic
438C2×C59C2×#57511yescharacteristic
439D59—24no—
440D59—42no—
441D59—82no—
442C22×#41—591no—
443C23×Q8—591no—
444C24×C4—591no—
445C22×Q16—591no—
446C22×Q16—591no—
447C22×SD16—591no—
448C22×SD16—591no—
449C22×M16—591no—
450C22×M16—591no—
451#525—598no—
452#525—1184no—
453C2×#123—1181no—
454C2×C22⋊Q8—591no—
455C2×C22⋊Q8—591no—
456C2×C22⋊Q8—598no—
457C2×C22⋊Q8—591no—
458C2×C22⋊Q8—591no—
459C2×C22⋊Q8—591no—
460C2×C22⋊Q8—1181no—
461C2×C22⋊Q8—1181no—
462C2×C22⋊Q8—1184no—
463C2×C22⋊Q8C2×D5911yescharacteristic
464C2×#121—591no—
465C2×#121—591no—
466C2×#120—1181no—
467C2×C4×D4—1181no—
468C2×C4×D4—1181no—
469C2×#117C2×D5911yescharacteristic
470C22×C4⋊C4—591no—
471C22×C4⋊C4—1181no—
472C22×C22⋊C4—1181no—
473#485—598no—
474#485C2×D5918yescomplemented
475#484—598no—
476#481—598no—
477#470—598no—
478#470—598no—
479#468—598no—
480#468—598no—
481#452—598no—
482#452—598no—
483#451—598no—
484#448—598no—
485C2×#107—591no—
486C2×#107C2×D5911yescharacteristic, complemented
487C2×#106—591no—
488C2×#106C2×D5911yescharacteristic, complemented
489C2×#103—591no—
490C2×#103—591no—
491C2×#103—591no—
492C2×#103—591no—
493C2×#103C2×D5911yescharacteristic, complemented
494C2×#103C2×D5911yescharacteristic, complemented
495C2×#102—591no—
496C2×#102—591no—
497#407—598no—
498C2×C22⋊C8—591no—
499C2×C22⋊C8—591no—
500C2×C22⋊C8—591no—
501C2×C22⋊C8C2×D5911yescharacteristic
502C59C2×#319611yescharacteristic, complemented, Sylow
503C25—591no—
504C2×#41—594no—
505C2×#41—1182no—
506C2×#41—2362no—
507C2×#41—2362no—
508C22×Q8—594no—
509C22×Q8—591no—
510C22×Q8—591no—
511C22×Q8—1181no—
512C22×Q8—1182no—
513C22×Q8—2362no—
514C22×Q8—2362no—
515C22×Q8C22×D5911yescharacteristic
516C22×D4—591no—
517C22×D4—1181no—
518C22×D4—1181no—
519C22×D4—1181no—
520C23×C4—591no—
521C23×C4—591no—
522C23×C4—591no—
523C23×C4—591no—
524C23×C4—591no—
525C23×C4—594no—
526C23×C4—594no—
527C23×C4—1181no—
528C23×C4—1181no—
529C23×C4—1181no—
530C23×C4—2362no—
531C23×C4—2362no—
532C23×C4C22×D5911yescharacteristic
533C2×Q16—594no—
534C2×Q16—594no—
535C2×Q16—2362no—
536C2×Q16—2362no—
537C2×SD16—594no—
538C2×SD16—594no—
539C2×SD16—2362no—
540C2×SD16—2362no—
541C2×M16—594no—
542C2×M16—594no—
543C2×M16—2362no—
544C2×M16—2362no—
545C22×C8—591no—
546C22×C8—591no—
547C22×C8C22×D5911yescharacteristic
548C22×C8C22×D5911yescharacteristic
549#123—1188no—
550C22⋊Q8—22no—
551C22⋊Q8—594no—
552C22⋊Q8—594no—
553C22⋊Q8—594no—
554C22⋊Q8—594no—
555C22⋊Q8—594no—
556C22⋊Q8—1188no—
557C22⋊Q8—1188no—
558C22⋊Q8—1182no—
559C22⋊Q8—1182no—
560C22⋊Q8—1182no—
561C22⋊Q8—1182no—
562C22⋊Q8—1182no—
563C22⋊Q8C22×D5914yes—
564#121—594no—
565#121—594no—
566#121—1182no—
567#121—1182no—
568#120—1188no—
569C4×D4—1188no—
570C4×D4—1188no—
571#117—22no—
572#117C22×D5914yes—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—591no—
575C2×C4⋊C4—594no—
576C2×C4⋊C4—1182no—
577C2×C4⋊C4—1188no—
578C2×C4⋊C4—1181no—
579C2×C4⋊C4—1181no—
580C2×C4⋊C4—1181no—
581C2×C4⋊C4—1181no—
582C2×C4⋊C4—1181no—
583C2×C4⋊C4—1181no—
584C2×C4⋊C4C22×D5911yescharacteristic
585C2×C4⋊C4C22×D5911yescharacteristic
586C2×C4⋊C4C22×D5911yescharacteristic
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—1188no—
590C2×C22⋊C4—1181no—
591C2×C22⋊C4—1181no—
592C2×C22⋊C4—1181no—
593C2×C22⋊C4—1181no—
594C2×C22⋊C4—1181no—
595C2×C22⋊C4—1181no—
596C2×C22⋊C4—1181no—
597C2×C42—21no—
598#107—594no—
599#107C22×D5914yescomplemented
600#106—594no—
601#106C22×D5914yescomplemented
602#103—594no—
603#103—594no—
604#103—594no—
605#103—594no—
606#103C22×D5914yescomplemented
607#103C22×D5914yescomplemented
608#102—594no—
609#102—594no—
610C22⋊C8—594no—
611C22⋊C8—594no—
612C22⋊C8—594no—
613C22⋊C8C22×D5914yes—
614C24—591no—
615C24—591no—
616C24—594no—
617C24—1184no—
618C24—1181no—
619C24—2362no—
620C24—2362no—
621C24D4×D5911yescharacteristic
622#41—2364no—
623#41—2364no—
624#41—2368no—
625C2×Q8—21no—
626C2×Q8—22no—
627C2×Q8—22no—
628C2×Q8—592no—
629C2×Q8—592no—
630C2×Q8—1184no—
631C2×Q8—1181no—
632C2×Q8—1181no—
633C2×Q8—1182no—
634C2×Q8—1182no—
635C2×Q8—1182no—
636C2×Q8—1182no—
637C2×Q8—2364no—
638C2×Q8—2364no—
639C2×Q8—2364no—
640C2×Q8—2368no—
641C2×Q8C23×D5912yes—
642C2×D4—592no—
643C2×D4—1184no—
644C2×D4—1184no—
645C2×D4—1184no—
646C2×D4—1181no—
647C2×D4—1182no—
648C2×D4—1182no—
649C2×D4—2364no—
650C2×D4—2364no—
651C2×D4—2364no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—591no—
659C22×C4—591no—
660C22×C4—594no—
661C22×C4—592no—
662C22×C4—592no—
663C22×C4—592no—
664C22×C4—592no—
665C22×C4—594no—
666C22×C4—594no—
667C22×C4—1184no—
668C22×C4—1184no—
669C22×C4—1182no—
670C22×C4—1182no—
671C22×C4—1182no—
672C22×C4—1182no—
673C22×C4—1181no—
674C22×C4—1181no—
675C22×C4—1181no—
676C22×C4—1184no—
677C22×C4—2368no—
678C22×C4—2364no—
679C22×C4—2364no—
680C22×C4—2362no—
681C22×C4—2362no—
682C22×C4—2364no—
683C22×C4—2364no—
684C22×C4—2364no—
685C22×C4—2362no—
686C22×C4D4×D5912yes—
687C22×C4D4×D5911yescharacteristic
688C22×C4C23×D5912yes—
689C22×C4C23×D5911yescharacteristic
690Q16—2364no—
691Q16—2364no—
692SD16—2364no—
693SD16—2364no—
694M16—2364no—
695M16—2364no—
696C2×C8—22no—
697C2×C8—22no—
698C2×C8—592no—
699C2×C8—592no—
700C2×C8—1182no—
701C2×C8—1182no—
702C2×C8C23×D5912yes—
703C2×C8C23×D5912yes—
704C4⋊C4—24no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—592no—
709C4⋊C4—1184no—
710C4⋊C4—1184no—
711C4⋊C4—1184no—
712C4⋊C4—1184no—
713C4⋊C4—1184no—
714C4⋊C4—1181no—
715C4⋊C4—1184no—
716C4⋊C4C23×D5912yes—
717C4⋊C4C23×D5912yes—
718C4⋊C4C23×D5912yes—
719C22⋊C4—24no—
720C22⋊C4—24no—
721C22⋊C4—1184no—
722C22⋊C4—1184no—
723C22⋊C4—1184no—
724C22⋊C4—1184no—
725C22⋊C4—1184no—
726C22⋊C4—1184no—
727C22⋊C4—1184no—
728C42—24no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—594no—
733C23—592no—
734C23—592no—
735C23—1188no—
736C23—1182no—
737C23—1182no—
738C23—1182no—
739C23—1182no—
740C23—1182no—
741C23—1182no—
742C23—2364no—
743C23—2364no—
744C23—23616no—
745C23—2362no—
746C23—2362no—
747C23—2362no—
748C23C2×D4×D5912yes—
749C23C2×D4×D5911yescharacteristic
750Q8—22no—
751Q8—22no—
752Q8—42no—
753Q8—1182no—
754Q8—1182no—
755Q8—1182no—
756Q8—1182no—
757Q8—2368no—
758Q8—2362no—
759Q8—2362no—
760D4—1182no—
761D4—1182no—
762D4—2368no—
763D4—2368no—
764D4—2368no—
765D4—2362no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—592no—
779C2×C4—592no—
780C2×C4—1182no—
781C2×C4—1182no—
782C2×C4—1184no—
783C2×C4—1184no—
784C2×C4—1182no—
785C2×C4—1182no—
786C2×C4—1182no—
787C2×C4—1182no—
788C2×C4—1182no—
789C2×C4—1182no—
790C2×C4—1182no—
791C2×C4—2364no—
792C2×C4—2364no—
793C2×C4—2368no—
794C2×C4—2368no—
795C2×C4—2368no—
796C2×C4—2364no—
797C2×C4—2362no—
798C2×C4—2362no—
799C2×C4—2362no—
800C2×C4C2×D4×D5912yes—
801C2×C4C2×D4×D5911yescharacteristic
802C2×C4#1427377312yes—
803C2×C4#1427377312yes—
804C2×C4C24×D5911yescharacteristic
805C8—22no—
806C8—22no—
807C8—1182no—
808C8—1182no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—44no—
813C22—594no—
814C22—1188no—
815C22—1182no—
816C22—1182no—
817C22—1182no—
818C22—1182no—
819C22—1182no—
820C22—4724no—
821C22—23616no—
822C22—2362no—
823C22—2362no—
824C22—2362no—
825C22—2364no—
826C22#1683796312yes—
827C22#137×D5912yes—
828C22#1683819912yes—
829C22C22×D4×D5911yescharacteristic
830C4—22no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—1182no—
836C4—1182no—
837C4—2362no—
838C4—2362no—
839C4—2362no—
840C4#1683796312yes—
841C4C2×#1427377311yescharacteristic
842C4C2×#1427377311yescharacteristic
843C2—42no—
844C2—1184no—
845C2—4722no—
846C2—2362no—
847C2#2143493014yesdirect product factor
848C2C2×#1683796311yescharacteristic
849C2C2×#137×D5911yescharacteristic
850C2C2×#1683819911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#485C2
socleC23×C59C22×D4
prime radicalC2×#16837914C2
hypercenterC2×#485D59
hypocenterC59C2×#3196
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊Q8×D59C2semidirect
3. #21434930C2direct (N × H)
4. C2×#16837739C2semidirect
5. C2×#16837722C2semidirect
6. C2×#16837743C2semidirect
7. C2×#16837661C2semidirect
8. C2×#16837659C2semidirect
9. C2×#16837651C2semidirect
10. C2×#16837649C2semidirect
11. C2×#16837566C2semidirect
12. C2×#16837562C2semidirect
13. C2×#16837559C2semidirect
14. C2×#16837542C2semidirect
15. C2×#16837364C2semidirect
16. C2×C59×#485C2semidirect
20. C22×Dic236C22semidirect
21. C22×#11745672C22semidirect
22. C22×#11745660C22semidirect
23. C22×#11745671C22semidirect
37. C22⋊Q8×D59C22semidirect
46. #16837743C22semidirect
47. #16837739C22semidirect
48. #16837722C22semidirect
49. #16837661C22semidirect
50. #16837659C22semidirect
51. #16837651C22semidirect
52. #16837649C22semidirect
53. #16837566C22semidirect
54. #16837562C22semidirect
55. #16837559C22semidirect
56. #16837542C22semidirect
57. C2×#14273660C22semidirect
58. C2×#14273658C22semidirect
59. C2×#14273652C22semidirect
60. C2×#14273650C22semidirect
61. C2×#14273650C22semidirect
62. C2×#14273650C22semidirect
63. C2×#14273649C22semidirect
64. C2×#14273647C22semidirect
65. #16837364C22semidirect
71. C59×#485C22semidirect
72. C2×#107×C59C22semidirect
73. C2×#106×C59C22semidirect
74. C2×#103×C59C22semidirect
75. C2×#103×C59C22semidirect
106. C2×Dic236C23semidirect
108. C2×#11745672C23semidirect
110. C2×#11745660C23semidirect
112. C2×#11745671C23semidirect
157. #14273660C23semidirect
158. #14273658C23semidirect
159. #14273652C23semidirect
160. #14273650C23semidirect
161. #14273650C23semidirect
162. #14273650C23semidirect
163. #14273649C23semidirect
164. #14273647C23semidirect
183. #107×C59C23semidirect
184. #106×C59C23semidirect
185. #103×C59C23semidirect
186. #103×C59C23semidirect
424. C2×#485D59semidirect
435. C2×C59#3196semidirect
474. #485C2×D59semidirect
486. C2×#107C2×D59semidirect
488. C2×#106C2×D59semidirect
493. C2×#103C2×D59semidirect
494. C2×#103C2×D59semidirect
502. C59C2×#3196semidirect
599. #107C22×D59semidirect
601. #106C22×D59semidirect
606. #103C22×D59semidirect
607. #103C22×D59semidirect
847. C2#21434930direct (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×C22⋊Q8×D592
#214349302
C2×#168377392
C2×#168377222
C2×#168377432
C2×#168376612
C2×#168376592
C2×#168376512
C2×#168376492
C2×#168375662
C2×#168375622
C2×#168375592
C2×#168375422
C2×#168373642
C2×C59×#4852
C2×#319659