Finite Group Databasebeta

← C2×#21434367 #29457014

Subgroups — C2×#21434367 #29457014

Order 15104.

2134 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837882C211yesmaximal, characteristic, complemented
2#21434367C2116yesmaximal, direct product factor
3C2×#16837718C211yesmaximal, characteristic, complemented
4C2×#16837730C211yesmaximal, characteristic, complemented
5C2×#16837684C211yesmaximal, characteristic, complemented
6C2×#16837689C211yesmaximal, characteristic, complemented
7C2×#16837621C211yesmaximal, characteristic, complemented
8C2×#16837614C211yesmaximal, characteristic, complemented
9C2×#16837562C211yesmaximal, characteristic, complemented
10C2×#16837545C211yesmaximal, characteristic
11C2×#16837512C211yesmaximal, characteristic, complemented
12C2×#16837507C211yesmaximal, characteristic, complemented
13C2×C4×#11745671C211yesmaximal, characteristic, complemented
14C2×C4×#11745670C211yesmaximal, characteristic, complemented
15C2×#16837463C211yesmaximal, characteristic, complemented
16C2×C59×#542C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C22×#11745672C2211yescharacteristic
19C22×#11745670C2211yescharacteristic
20C22×#11745671C2211yescharacteristic
21C22×#11745669C2211yescharacteristic
22#16837882—24no—
23#16837882C2218yescomplemented
24C2×C4×Dic118C2211yescharacteristic
25C2×C4×Dic118C2211yescharacteristic
26C2×C4×D236C2211yescharacteristic
27C2×C4×D236C2211yescharacteristic
28C2×(C22⋊D59)⋊C4—21no—
29C2×(C22⋊D59)⋊C4—21no—
30C2×#14273685—21no—
31C22×C4⋊Dic59C2211yescharacteristic
32C2×C4⋊C4×D59—21no—
33#16837730C2218yescomplemented
34#16837718C2218yescomplemented
35#16837689C2218yescomplemented
36#16837684C2218yescomplemented
37#16837621C2218yescomplemented
38#16837614C2218yescomplemented
39#16837562C2218yescomplemented
40#16837545C2218yes—
41#16837512C2218yescomplemented
42#16837507C2218yescomplemented
43C4×#11745671C2218yescomplemented
44C4×#11745670C2218yescomplemented
45#16837463C2218yescomplemented
46C2×#14273658C2211yescharacteristic
47C2×#14273658C2211yescharacteristic
48C2×#14273658C2211yescharacteristic
49C2×#14273658C2211yescharacteristic
50C2×C4⋊(C59⋊C8)C2211yescharacteristic
51C2×C4⋊(C59⋊C8)C2211yescharacteristic
52C2×#14273651C2211yescharacteristic
53C2×#14273651C2211yescharacteristic
54C2×#14273650C2211yescharacteristic
55C2×#14273650C2211yescharacteristic
56C2×#14273648C2211yescharacteristic
57C2×#14273648C2211yescharacteristic
58C2×#14273647C2211yescharacteristic
59C2×#14273647C2211yescharacteristic
60C2×C22⋊(C59⋊C8)C2211yescharacteristic
61C2×C22⋊(C59⋊C8)C2211yescharacteristic
62C2×#14273638C2211yescharacteristic
63C2×C4×C59⋊C8C2211yescharacteristic
64C59×#542—24no—
65C59×#542C2218yescomplemented
66C2×C4⋊Q8×C59C2211yescharacteristic
67C2×#126×C59—21no—
68C2×#124×C59—21no—
69C2×#124×C59C2211yescharacteristic
70C2×#123×C59—21no—
71C2×C22⋊Q8×C59—21no—
72C2×C22⋊Q8×C59C2211yescharacteristic
73C2×#121×C59C2211yescharacteristic
74C2×C4×Q8×C59C2211yescharacteristic
75C2×C4×D4×C59C2211yescharacteristic
76C2×#117×C59C2211yescharacteristic
77C2×#11745685—22no—
78C2×#11745685—24no—
79C2×#11745685—24no—
80C2×#11745685C2314yes—
81C22×Dic118C2311yescharacteristic
82C22×D236C2311yescharacteristic
83C22×C22⋊D59—21no—
84C23×Dic59—21no—
85C22×C4×D59—21no—
86C22×C4×D59—21no—
87C22×C4×D59—21no—
88C2×#11745672—24no—
89C2×#11745672C2314yes—
90C2×#11745670—24no—
91C2×#11745670C2314yes—
92C2×#11745671—24no—
93C2×#11745671C2314yes—
94C2×#11745669—24no—
95C2×#11745669C2314yes—
96C22×C59⋊C8C2311yescharacteristic
97C22×C59⋊C8C2311yescharacteristic
98C22×C59⋊C8C2311yescharacteristic
99C22×C59⋊C8C2311yescharacteristic
100C4×Dic118—22no—
101C4×Dic118—22no—
102C4×Dic118C2314yes—
103C4×Dic118C2314yes—
104C4×D236—22no—
105C4×D236—22no—
106C4×D236C2314yes—
107C4×D236C2314yes—
108(C22⋊D59)⋊C4—28no—
109(C22⋊D59)⋊C4—28no—
110#14273685—28no—
111C2×C4⋊Dic59—21no—
112C2×C4⋊Dic59—22no—
113C2×C4⋊Dic59C2311yescharacteristic
114C2×C4⋊Dic59C2311yescharacteristic
115C2×C4⋊Dic59C2314yes—
116C2×Dic59⋊C4—21no—
117C2×Dic59⋊C4—21no—
118C4⋊C4×D59—28no—
119C2×(C2×D59)⋊C4—21no—
120C2×(C2×D59)⋊C4—21no—
121C2×C4×Dic59—21no—
122C2×C4×Dic59—21no—
123#14273658C2314yes—
124#14273658C2314yes—
125#14273658C2314yes—
126#14273658C2314yes—
127C4⋊(C59⋊C8)C2314yes—
128C4⋊(C59⋊C8)C2314yes—
129#14273651C2314yes—
130#14273651C2314yes—
131#14273650C2314yes—
132#14273650C2314yes—
133#14273648C2314yes—
134#14273648C2314yes—
135#14273647C2314yes—
136#14273647C2314yes—
137C22⋊(C59⋊C8)C2314yes—
138C22⋊(C59⋊C8)C2314yes—
139#14273638C2314yes—
140C4×C59⋊C8C2314yes—
141C22×Q8×C59—21no—
142C22×Q8×C59C2311yescharacteristic
143C22×D4×C59—21no—
144C22×D4×C59C2311yescharacteristic
145C23×C4×C59—21no—
146C23×C4×C59C2311yescharacteristic
147C4⋊Q8×C59—22no—
148C4⋊Q8×C59C2314yes—
149#126×C59—28no—
150#124×C59—28no—
151#124×C59—22no—
152#124×C59C2314yes—
153#123×C59—28no—
154C22⋊Q8×C59—22no—
155C22⋊Q8×C59—28no—
156C22⋊Q8×C59C2314yes—
157#121×C59—22no—
158#121×C59C2314yes—
159C4×Q8×C59—22no—
160C4×Q8×C59C2314yes—
161C4×D4×C59—22no—
162C4×D4×C59C2314yes—
163#117×C59D414yes—
164#117×C59C2314yes—
165C2×C4⋊C4×C59—21no—
166C2×C4⋊C4×C59—21no—
167C2×C4⋊C4×C59—21no—
168C2×C4⋊C4×C59D411yescharacteristic
169C2×C4⋊C4×C59D411yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C22⋊C4×C59—21no—
173C2×C22⋊C4×C59—21no—
174C2×C22⋊C4×C59—21no—
175C2×C22⋊C4×C59—21no—
176C2×C22⋊C4×C59—21no—
177C2×C22⋊C4×C59D411yescharacteristic
178C2×C22⋊C4×C59D411yescharacteristic
179C2×C42×C59—21no—
180C2×C42×C59C2311yescharacteristic
181C2×C42×C59C2311yescharacteristic
182C24×C59—21no—
183C24×C59C2×D411yescharacteristic
184C23×D59—21no—
185C2×Q8×C59—21no—
186C2×Q8×C59—24no—
187C2×Q8×C59—22no—
188C2×Q8×C59—22no—
189C2×Q8×C59—82no—
190C2×Q8×C59C2412yes—
191C2×D4×C59—24no—
192C2×D4×C59—21no—
193C2×D4×C59—22no—
194C2×D4×C59—22no—
195C2×D4×C59—82no—
196C2×D4×C59C2412yes—
197C22×C4×C59—22no—
198C22×C4×C59—22no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—24no—
203C22×C4×C59—82no—
204C22×C4×C59C2×D411yescharacteristic
205C22×C4×C59C2×D411yescharacteristic
206C22×C4×C59C2×D411yescharacteristic
207C22×C4×C59C2×D411yescharacteristic
208C22×C4×C59C2×D411yescharacteristic
209C22×C4×C59C2×D412yes—
210C22×C4×C59C2412yes—
211C22×C4×C59C2411yescharacteristic
212C2×C22⋊D59—28no—
213C2×C22⋊D59—24no—
214C22×Dic59—21no—
215C22×Dic59—21no—
216C22×Dic59—21no—
217C22×Dic59—24no—
218C22×Dic59—82no—
219#11745685—216no—
220#11745685—28no—
221#11745685—28no—
222C2×D236—21no—
223C2×D236—22no—
224C2×D236#4114yes—
225C2×D236C2412yes—
226C2×C4×D59—28no—
227C2×C4×D59—24no—
228C2×C4×D59—24no—
229C2×C4×D59—24no—
230C2×C4×D59—82no—
231C2×C4×D59—82no—
232C2×Dic118—21no—
233C2×Dic118—22no—
234C2×Dic118#4114yes—
235C2×Dic118C2412yes—
236C4⋊C4×C59—24no—
237C4⋊C4×C59—24no—
238C4⋊C4×C59—24no—
239C4⋊C4×C59—21no—
240C4⋊C4×C59—21no—
241C4⋊C4×C59C2×D414yes—
242C4⋊C4×C59C2×D414yes—
243C4⋊C4×C59C2412yes—
244C4⋊C4×C59C2412yes—
245C22⋊C4×C59—24no—
246C22⋊C4×C59—24no—
247C22⋊C4×C59—24no—
248C22⋊C4×C59—24no—
249C22⋊C4×C59—24no—
250C22⋊C4×C59C2×D414yes—
251C22⋊C4×C59C2×D414yes—
252C42×C59—24no—
253C42×C59C2×D412yes—
254C42×C59C2×D412yes—
255C42×C59C2412yes—
256C42×C59C2412yes—
257#11745672—28no—
258#11745671—28no—
259#11745670—28no—
260#11745669—28no—
261(C2×D59)⋊C4—24no—
262(C2×D59)⋊C4—24no—
263C4⋊Dic59—24no—
264C4⋊Dic59—21no—
265C4⋊Dic59—21no—
266C4⋊Dic59C2412yes—
267C4⋊Dic59C2412yes—
268Dic59⋊C4—24no—
269Dic59⋊C4—24no—
270C4×Dic59—24no—
271C4×Dic59—24no—
272C2×C59⋊C8—22no—
273C2×C59⋊C8—22no—
274C2×C59⋊C8—22no—
275C2×C59⋊C8—22no—
276C2×C59⋊C8C2412yes—
277C2×C59⋊C8C2412yes—
278C2×C59⋊C8C2412yes—
279C2×C59⋊C8C2412yes—
280C23×C59—22no—
281C23×C59—22no—
282C23×C59—22no—
283C23×C59—22no—
284C23×C59—42no—
285C23×C59—42no—
286C23×C59—42no—
287C23×C59C22×D412yes—
288C23×C59C22×D411yescharacteristic
289C22×D59—24no—
290C22×D59—22no—
291C22×D59—42no—
292C22×D59—42no—
293Q8×C59—22no—
294Q8×C59—22no—
295Q8×C59—42no—
296Q8×C59—84no—
297D4×C59—22no—
298D4×C59—22no—
299D4×C59—42no—
300D4×C59—84no—
301C2×C4×C59—22no—
302C2×C4×C59—22no—
303C2×C4×C59—22no—
304C2×C4×C59—22no—
305C2×C4×C59—22no—
306C2×C4×C59—24no—
307C2×C4×C59—22no—
308C2×C4×C59—22no—
309C2×C4×C59—22no—
310C2×C4×C59—22no—
311C2×C4×C59—22no—
312C2×C4×C59—42no—
313C2×C4×C59—42no—
314C2×C4×C59—42no—
315C2×C4×C59—84no—
316C2×C4×C59C22×D412yes—
317C2×C4×C59C22×D412yes—
318C2×C4×C59C22×D412yes—
319C2×C4×C59C22×D412yes—
320C2×C4×C59C22×D412yes—
321C2×C4×C59C22×D411yescharacteristic
322C2×C4×C59C2×#4112yes—
323C2×C4×C59C2×#4112yes—
324C2×C4×C59C2511yescharacteristic
325C22⋊D59—216no—
326C2×Dic59—24no—
327C2×Dic59—22no—
328C2×Dic59—22no—
329C2×Dic59—22no—
330C2×Dic59—42no—
331C2×Dic59—42no—
332C2×Dic59—84no—
333D236—24no—
334D236—22no—
335D236C2×#4114yes—
336C4×D59—216no—
337C4×D59—84no—
338C4×D59—84no—
339Dic118—24no—
340Dic118—22no—
341Dic118C2×#4114yes—
342C59⋊C8—22no—
343C59⋊C8—22no—
344C59⋊C8—22no—
345C59⋊C8—22no—
346C2×#3125—591nomaximal, Sylow
347C22×C59—22no—
348C22×C59—22no—
349C22×C59—22no—
350C22×C59—44no—
351C22×C59—42no—
352C22×C59—42no—
353C22×C59—42no—
354C22×C59—84no—
355C22×C59#52512yes—
356C22×C59#57712yes—
357C22×C59#57712yes—
358C22×C59C23×D411yescharacteristic
359C2×D59—24no—
360C2×D59—48no—
361C2×D59—42no—
362C2×D59—42no—
363C4×C59—22no—
364C4×C59—22no—
365C4×C59—22no—
366C4×C59—22no—
367C4×C59—22no—
368C4×C59—42no—
369C4×C59—42no—
370C4×C59—42no—
371C4×C59#52512yes—
372C4×C59C22×#4111yescharacteristic
373C4×C59C22×#4111yescharacteristic
374Dic59—24no—
375Dic59—42no—
376Dic59—42no—
377C2×#542D5911yescharacteristic, complemented
378C2×#520—591no—
379#3125—5916no—
380C2×#481—591no—
381C2×#483—591no—
382C2×#475—591no—
383C2×#476—591no—
384C2×#464—591no—
385C2×#463—591no—
386C2×#452—591no—
387C2×#449—591no—
388C2×#442—591no—
389C2×#441—591no—
390C2×C4×SD16—591no—
391C2×C4×SD16—591no—
392C2×#433—591no—
393C2×C59—42no—
394C2×C59—82no—
395C2×C59#312514yescomplemented
396C2×C59C2×#52511yescharacteristic
397C2×C59C2×#57711yescharacteristic
398C2×C59C2×#57711yescharacteristic
399D59—44no—
400C22×#41—591no—
401C22×Q16—591no—
402C22×SD16—591no—
403C22×SD16—591no—
404C22×D8—591no—
405#542—24no—
406#542C2×D5918yescomplemented
407C2×C4⋊Q8C2×D5911yescharacteristic
408C2×#126—21no—
409C2×#124—21no—
410C2×#124C2×D5911yescharacteristic
411C2×#123—21no—
412C2×C22⋊Q8—21no—
413C2×C22⋊Q8C2×D5911yescharacteristic
414C2×#121C2×D5911yescharacteristic
415#520—598no—
416#520—1184no—
417C2×C4×Q8—591no—
418C2×C4×Q8—591no—
419C2×C4×Q8C2×D5911yescharacteristic
420C2×C4×D4—591no—
421C2×C4×D4—591no—
422C2×C4×D4—1181no—
423C2×C4×D4—1181no—
424C2×C4×D4C2×D5911yescharacteristic
425C2×#117—1181no—
426C2×#117C2×D5911yescharacteristic
427C22×C4⋊C4—591no—
428C22×C4⋊C4—1181no—
429#483—598no—
430#481—598no—
431#476—598no—
432#475—598no—
433#464—598no—
434#463—598no—
435#452—598no—
436#449—598no—
437#442—598no—
438#441—598no—
439C4×SD16—598no—
440C4×SD16—598no—
441#433—598no—
442C2×#106—591no—
443C2×#106—591no—
444C2×#106—591no—
445C2×#106—591no—
446C2×C4⋊C8—591no—
447C2×C4⋊C8—591no—
448C2×#103—591no—
449C2×#103—591no—
450C2×#103—591no—
451C2×#103—591no—
452C2×#102—591no—
453C2×#102—591no—
454C2×#102—591no—
455C2×#102—591no—
456C2×C22⋊C8—591no—
457C2×C22⋊C8—591no—
458C2×#97—591no—
459C2×C4×C8—591no—
460C59C2×#312511yescharacteristic, complemented, Sylow
461C2×#41—594no—
462C2×#41—1184no—
463C2×#41—1184no—
464C2×#41—1182no—
465C22×Q8—21no—
466C22×Q8—591no—
467C22×Q8C22×D5911yescharacteristic
468C22×D4—21no—
469C22×D4—591no—
470C22×D4—1181no—
471C22×D4C22×D5911yescharacteristic
472C23×C4—21no—
473C23×C4—1181no—
474C23×C4—1181no—
475C23×C4—1181no—
476C23×C4—1181no—
477C23×C4C22×D5911yescharacteristic
478C2×Q16—594no—
479C2×Q16—1184no—
480C2×SD16—594no—
481C2×SD16—594no—
482C2×SD16—1184no—
483C2×SD16—1184no—
484C2×D8—594no—
485C2×D8—1184no—
486C22×C8—591no—
487C22×C8—591no—
488C22×C8—591no—
489C22×C8—591no—
490C4⋊Q8—22no—
491C4⋊Q8C22×D5914yes—
492#126—28no—
493#124—28no—
494#124—22no—
495#124C22×D5914yes—
496#123—28no—
497C22⋊Q8—22no—
498C22⋊Q8—28no—
499C22⋊Q8C22×D5914yes—
500#121—22no—
501#121C22×D5914yes—
502C4×Q8—22no—
503C4×Q8—594no—
504C4×Q8—594no—
505C4×Q8—1182no—
506C4×Q8—1182no—
507C4×Q8C22×D5914yes—
508C4×D4—22no—
509C4×D4—594no—
510C4×D4—594no—
511C4×D4—1188no—
512C4×D4—1188no—
513C4×D4—1182no—
514C4×D4—1182no—
515C4×D4C22×D5914yes—
516#117—1188no—
517#117C22⋊D5914yes—
518#117C22×D5914yes—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—591no—
523C2×C4⋊C4—591no—
524C2×C4⋊C4—594no—
525C2×C4⋊C4—1181no—
526C2×C4⋊C4—1182no—
527C2×C4⋊C4—1181no—
528C2×C4⋊C4—1181no—
529C2×C4⋊C4—1188no—
530C2×C4⋊C4C22⋊D5911yescharacteristic
531C2×C4⋊C4C22⋊D5911yescharacteristic
532C2×C4⋊C4C22×D5911yescharacteristic
533C2×C4⋊C4C22×D5911yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—1181no—
540C2×C22⋊C4—1181no—
541C2×C22⋊C4C22⋊D5911yescharacteristic
542C2×C22⋊C4C22⋊D5911yescharacteristic
543C2×C42—21no—
544C2×C42—1181no—
545C2×C42—1181no—
546C2×C42C22×D5911yescharacteristic
547C2×C42C22×D5911yescharacteristic
548#106—594no—
549#106—594no—
550#106—594no—
551#106—594no—
552C4⋊C8—594no—
553C4⋊C8—594no—
554#103—594no—
555#103—594no—
556#103—594no—
557#103—594no—
558#102—594no—
559#102—594no—
560#102—594no—
561#102—594no—
562C22⋊C8—594no—
563C22⋊C8—594no—
564#97—594no—
565C4×C8—594no—
566C24—21no—
567C24—1181no—
568C24C2×C22⋊D5911yescharacteristic
569#41—1188no—
570#41—1188no—
571#41—11816no—
572C2×Q8—21no—
573C2×Q8—24no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—82no—
577C2×Q8—594no—
578C2×Q8—592no—
579C2×Q8—1181no—
580C2×Q8—1182no—
581C2×Q8C23×D5912yes—
582C2×D4—24no—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—82no—
587C2×D4—594no—
588C2×D4—592no—
589C2×D4—1188no—
590C2×D4—1184no—
591C2×D4—1181no—
592C2×D4—1182no—
593C2×D4C23×D5912yes—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—82no—
601C22×C4—1188no—
602C22×C4—1181no—
603C22×C4—1184no—
604C22×C4—1184no—
605C22×C4—1181no—
606C22×C4—1181no—
607C22×C4—1184no—
608C22×C4—1184no—
609C22×C4—4722no—
610C22×C4—4722no—
611C22×C4—4722no—
612C22×C4C2×C22⋊D5912yes—
613C22×C4C2×C22⋊D5911yescharacteristic
614C22×C4C2×C22⋊D5911yescharacteristic
615C22×C4C2×C22⋊D5911yescharacteristic
616C22×C4C2×C22⋊D5911yescharacteristic
617C22×C4C2×C22⋊D5911yescharacteristic
618C22×C4C23×D5912yes—
619C22×C4C23×D5911yescharacteristic
620Q16—1188no—
621SD16—1188no—
622SD16—1188no—
623D8—1188no—
624C2×C8—592no—
625C2×C8—592no—
626C2×C8—592no—
627C2×C8—592no—
628C2×C8—1182no—
629C2×C8—1182no—
630C2×C8—1182no—
631C2×C8—1182no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—592no—
638C4⋊C4—592no—
639C4⋊C4—1184no—
640C4⋊C4—1181no—
641C4⋊C4—1181no—
642C4⋊C4—1184no—
643C4⋊C4—1184no—
644C4⋊C4C2×C22⋊D5914yes—
645C4⋊C4C2×C22⋊D5914yes—
646C4⋊C4C23×D5912yes—
647C4⋊C4C23×D5912yes—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—1184no—
654C22⋊C4—1184no—
655C22⋊C4C2×C22⋊D5914yes—
656C22⋊C4C2×C22⋊D5914yes—
657C42—24no—
658C42—1184no—
659C42—1184no—
660C42C2×C22⋊D5912yes—
661C42C2×C22⋊D5912yes—
662C42C23×D5912yes—
663C42C23×D5912yes—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—1184no—
672C23—1182no—
673C23—2362no—
674C23—2362no—
675C23C22×C22⋊D5912yes—
676C23C22×C22⋊D5911yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—42no—
680Q8—84no—
681Q8—594no—
682Q8—1184no—
683Q8—1182no—
684D4—22no—
685D4—22no—
686D4—42no—
687D4—84no—
688D4—594no—
689D4—11816no—
690D4—1184no—
691D4—1182no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—84no—
707C2×C4—11816no—
708C2×C4—1184no—
709C2×C4—1182no—
710C2×C4—1182no—
711C2×C4—1182no—
712C2×C4—4724no—
713C2×C4—4724no—
714C2×C4—4724no—
715C2×C4—2362no—
716C2×C4—2362no—
717C2×C4C22×C22⋊D5912yes—
718C2×C4C22×C22⋊D5912yes—
719C2×C4C22×C22⋊D5912yes—
720C2×C4C22×C22⋊D5912yes—
721C2×C4C22×C22⋊D5912yes—
722C2×C4C22×C22⋊D5911yescharacteristic
723C2×C4#41×D5912yes—
724C2×C4#41×D5912yes—
725C2×C4C24×D5911yescharacteristic
726C8—1182no—
727C8—1182no—
728C8—1182no—
729C8—1182no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—84no—
738C22—1184no—
739C22—2362no—
740C22—2362no—
741C22—2368no—
742C22#1683790912yes—
743C22#1683821012yes—
744C22#1683821312yes—
745C22C23×C22⋊D5911yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—1184no—
755C4—2362no—
756C4—2362no—
757C4#1683790912yes—
758C4C2×#41×D5911yescharacteristic
759C4C2×#41×D5911yescharacteristic
760C2—42no—
761C2—82no—
762C2—2364no—
763C2#2143436714yesdirect product factor
764C2C2×#1683790911yescharacteristic
765C2C2×#1683821011yescharacteristic
766C2C2×#1683821311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#542C2
socleC23×C59C22×D4
prime radicalC2×#16837545C2
hypercenterC2×#542D59
hypocenterC59C2×#3125
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#16837882C2semidirect
2. #21434367C2direct (N × H)
3. C2×#16837718C2semidirect
4. C2×#16837730C2semidirect
5. C2×#16837684C2semidirect
6. C2×#16837689C2semidirect
7. C2×#16837621C2semidirect
8. C2×#16837614C2semidirect
9. C2×#16837562C2semidirect
11. C2×#16837512C2semidirect
12. C2×#16837507C2semidirect
13. C2×C4×#11745671C2semidirect
14. C2×C4×#11745670C2semidirect
15. C2×#16837463C2semidirect
16. C2×C59×#542C2semidirect
23. #16837882C22semidirect
33. #16837730C22semidirect
34. #16837718C22semidirect
35. #16837689C22semidirect
36. #16837684C22semidirect
37. #16837621C22semidirect
38. #16837614C22semidirect
39. #16837562C22semidirect
41. #16837512C22semidirect
42. #16837507C22semidirect
43. C4×#11745671C22semidirect
44. C4×#11745670C22semidirect
45. #16837463C22semidirect
65. C59×#542C22semidirect
377. C2×#542D59semidirect
395. C2×C59#3125semidirect
406. #542C2×D59semidirect
460. C59C2×#3125semidirect
763. C2#21434367direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168378822
#214343672
C2×#168377182
C2×#168377302
C2×#168376842
C2×#168376892
C2×#168376212
C2×#168376142
C2×#168375622
C2×#168375452
C2×#168375122
C2×#168375072
C2×C4×#117456712
C2×C4×#117456702
C2×#168374632
C2×C59×#5422
C2×#312559