Finite Group Databasebeta

← C2×#21436530 #29467214

Subgroups — C2×#21436530 #29467214

Order 15104.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838092C211yesmaximal, characteristic, complemented
2#21436530C2116yesmaximal, direct product factor
3C2×#16837808C211yesmaximal, characteristic, complemented
4C2×#16837737C211yesmaximal, characteristic, complemented
5C2×#16837723C211yesmaximal, characteristic, complemented
6C2×#16837732C211yesmaximal, characteristic, complemented
7C2×#16837713C211yesmaximal, characteristic, complemented
8C2×#16837694C211yesmaximal, characteristic, complemented
9C2×#16837702C211yesmaximal, characteristic, complemented
10C2×#16837646C211yesmaximal, characteristic, complemented
11C2×#16837629C211yesmaximal, characteristic, complemented
12C2×#16837502C211yesmaximal, characteristic, complemented
13C2×#16837474C211yesmaximal, characteristic, complemented
14C2×#16837442C211yesmaximal, characteristic, complemented
15C22×#14273660C211yesmaximal, characteristic, complemented
16C2×C59×#547C211yesmaximal, characteristic
17C22×#11745670C2211yescharacteristic
18C22×#11745664C2211yescharacteristic
19C23×C59⋊C8C2211yescharacteristic
20#16838092—24no—
21#16838092C2218yescomplemented
22C2×#14273720—21no—
23C2×#14273719C2211yescharacteristic
24C2×#14273717—21no—
25C2×#14273708—21no—
26C2×#14273706C2211yescharacteristic
27C2×#14273706C2211yescharacteristic
28C2×C4×Dic118C2211yescharacteristic
29C2×#14273686C2211yescharacteristic
30C2×#14273683—21no—
31C22×C4⋊Dic59C2211yescharacteristic
32#16837808C2218yescomplemented
33#16837737C2218yescomplemented
34#16837732C2218yescomplemented
35#16837723C2218yescomplemented
36#16837713C2218yescomplemented
37#16837702C2218yescomplemented
38#16837694C2218yescomplemented
39#16837646C2218yescomplemented
40#16837629C2218yescomplemented
41#16837502C2218yescomplemented
42#16837474C2218yescomplemented
43#16837442C2218yescomplemented
44C2×#14273660C2211yescharacteristic
45C2×#14273660C2211yescharacteristic
46C2×#14273660C2211yescharacteristic
47C2×#14273660C2211yescharacteristic
48C2×#14273660C2211yescharacteristic
49C2×#14273660C2211yescharacteristic
50C2×#14273660C2218yescomplemented
51C2×#14273658C2211yescharacteristic
52C2×#14273658C2211yescharacteristic
53C2×#14273658C2211yescharacteristic
54C2×C4⋊(C59⋊C8)C2211yescharacteristic
55C2×#14273650C2211yescharacteristic
56C2×#14273650C2211yescharacteristic
57C2×#14273650C2211yescharacteristic
58C2×#14273648C2211yescharacteristic
59C2×#14273648C2211yescharacteristic
60C2×#14273648C2211yescharacteristic
61C2×C22⋊(C59⋊C8)C2211yescharacteristic
62C2×C22⋊(C59⋊C8)C2211yescharacteristic
63C2×#14273638C2211yescharacteristic
64C22×#41×C59—21no—
65C59×#547—24no—
66C59×#547C2218yes—
67C2×C4⋊Q8×C59C2211yescharacteristic
68C2×#123×C59—21no—
69C2×#123×C59—21no—
70C2×C22⋊Q8×C59—21no—
71C2×#121×C59C2211yescharacteristic
72C2×#121×C59C2211yescharacteristic
73C2×C4×D4×C59C2211yescharacteristic
74C2×C4×D4×C59C2211yescharacteristic
75C22×C4⋊C4×C59C2211yescharacteristic
76C22×C4⋊C4×C59C2211yescharacteristic
77C22×Dic118C2311yescharacteristic
78C23×Dic59—21no—
79C2×#11745670—24no—
80C2×#11745670C2314yes—
81C2×#11745664—24no—
82C2×#11745664C2314yes—
83C22×C59⋊C8—24no—
84C22×C59⋊C8C2311yescharacteristic
85C22×C59⋊C8C2311yescharacteristic
86C22×C59⋊C8C2311yescharacteristic
87C22×C59⋊C8C2314yes—
88C22×C59⋊C8C2311yescharacteristic
89#14273720—28no—
90#14273719—22no—
91#14273719C2314yes—
92#14273717—28no—
93#14273708—28no—
94#14273706—22no—
95#14273706—22no—
96#14273706C2314yes—
97#14273706C2314yes—
98C4×Dic118—22no—
99C4×Dic118C2314yes—
100#14273686—22no—
101#14273686C2314yes—
102#14273683—28no—
103C2×C4⋊Dic59—21no—
104C2×C4⋊Dic59—22no—
105C2×C4⋊Dic59C2311yescharacteristic
106C2×C4⋊Dic59C2311yescharacteristic
107C2×C4⋊Dic59C2311yescharacteristic
108C2×C4⋊Dic59C2314yes—
109C2×Dic59⋊C4—21no—
110C2×Dic59⋊C4—21no—
111C2×Dic59⋊C4—21no—
112C2×Dic59⋊C4—21no—
113C2×Dic59⋊C4—21no—
114C2×C22⋊Dic59—21no—
115C2×C22⋊Dic59—21no—
116C2×C22⋊Dic59—21no—
117C2×C4×Dic59—21no—
118C2×C4×Dic59—21no—
119#14273660C2314yes—
120#14273660C2314yes—
121#14273660C2314yes—
122#14273660C2314yes—
123#14273660C2314yes—
124#14273660C2314yes—
125#14273658C2314yes—
126#14273658C2314yes—
127#14273658C2314yes—
128C4⋊(C59⋊C8)C2314yes—
129#14273650C2314yes—
130#14273650C2314yes—
131#14273650C2314yes—
132#14273648C2314yes—
133#14273648C2314yes—
134#14273648C2314yes—
135C22⋊(C59⋊C8)C2314yes—
136C22⋊(C59⋊C8)C2314yes—
137#14273638C2314yes—
138C2×#41×C59—28no—
139C2×#41×C59—48no—
140C22×Q8×C59—21no—
141C22×D4×C59—21no—
142C22×D4×C59—21no—
143C22×D4×C59D411yescharacteristic
144C22×D4×C59C2311yescharacteristic
145C23×C4×C59—21no—
146C23×C4×C59—21no—
147C23×C4×C59—21no—
148C23×C4×C59C2311yescharacteristic
149C23×C4×C59C2311yescharacteristic
150C4⋊Q8×C59—22no—
151C4⋊Q8×C59C2314yes—
152#123×C59—28no—
153#123×C59—28no—
154C22⋊Q8×C59—28no—
155#121×C59—22no—
156#121×C59—22no—
157#121×C59C2314yes—
158#121×C59C2314yes—
159C4×D4×C59—22no—
160C4×D4×C59D414yes—
161C4×D4×C59C2314yes—
162C4×D4×C59C2314yes—
163C2×C4⋊C4×C59—21no—
164C2×C4⋊C4×C59—21no—
165C2×C4⋊C4×C59—22no—
166C2×C4⋊C4×C59—22no—
167C2×C4⋊C4×C59—21no—
168C2×C4⋊C4×C59D411yescharacteristic
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C4⋊C4×C59C2314yes—
173C2×C4⋊C4×C59C2314yes—
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×C59C2311yescharacteristic
180C24×C59—21no—
181C24×C59C2×D411yescharacteristic
182C24×C59C2×D411yescharacteristic
183#41×C59—432no—
184C2×Q8×C59—24no—
185C2×Q8×C59—44no—
186C2×D4×C59—24no—
187C2×D4×C59—24no—
188C2×D4×C59—24no—
189C2×D4×C59—21no—
190C2×D4×C59—22no—
191C2×D4×C59—22no—
192C2×D4×C59—44no—
193C2×D4×C59—44no—
194C2×D4×C59C2×D414yes—
195C2×D4×C59C2412yes—
196C22×C4×C59—22no—
197C22×C4×C59—22no—
198C22×C4×C59—22no—
199C22×C4×C59—22no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59—24no—
204C22×C4×C59—24no—
205C22×C4×C59—24no—
206C22×C4×C59—44no—
207C22×C4×C59—44no—
208C22×C4×C59—44no—
209C22×C4×C59C2×D411yescharacteristic
210C22×C4×C59C2×D411yescharacteristic
211C22×C4×C59C2×D411yescharacteristic
212C22×C4×C59C2×D411yescharacteristic
213C22×C4×C59C2×D412yes—
214C22×C4×C59C2×D412yes—
215C22×C4×C59C2412yes—
216C22×C4×C59C2412yes—
217C22×C4×C59C2411yescharacteristic
218C22×Dic59—21no—
219C22×Dic59—21no—
220C22×Dic59—21no—
221C22×Dic59—21no—
222C22×Dic59—24no—
223C22×Dic59—44no—
224C2×Dic118—22no—
225C2×Dic118—22no—
226C2×Dic118—21no—
227C2×Dic118C2412yes—
228C4⋊C4×C59—21no—
229C4⋊C4×C59—21no—
230C4⋊C4×C59—21no—
231C4⋊C4×C59—24no—
232C4⋊C4×C59—24no—
233C4⋊C4×C59—24no—
234C4⋊C4×C59C2×D414yes—
235C4⋊C4×C59C2412yes—
236C4⋊C4×C59C2412yes—
237C4⋊C4×C59C2412yes—
238C22⋊C4×C59—24no—
239C22⋊C4×C59—24no—
240C22⋊C4×C59—24no—
241C22⋊C4×C59C2×D414yes—
242C22⋊C4×C59C2×D414yes—
243C42×C59C2×D412yes—
244C42×C59C2412yes—
245C22⋊Dic59—24no—
246C22⋊Dic59—24no—
247C22⋊Dic59—24no—
248#11745670—28no—
249C4⋊Dic59—21no—
250C4⋊Dic59—21no—
251C4⋊Dic59—24no—
252C4⋊Dic59—21no—
253C4⋊Dic59C2412yes—
254C4⋊Dic59C2412yes—
255C4⋊Dic59C2412yes—
256Dic59⋊C4—24no—
257Dic59⋊C4—24no—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261C4×Dic59—24no—
262C4×Dic59—24no—
263#11745664—28no—
264C2×C59⋊C8—22no—
265C2×C59⋊C8—22no—
266C2×C59⋊C8—22no—
267C2×C59⋊C8—28no—
268C2×C59⋊C8#4114yescomplemented
269C2×C59⋊C8C2412yes—
270C2×C59⋊C8C2412yes—
271C2×C59⋊C8C2412yes—
272C2×C59⋊C8C2412yes—
273C23×C59—22no—
274C23×C59—22no—
275C23×C59—22no—
276C23×C59—22no—
277C23×C59—22no—
278C23×C59—22no—
279C23×C59—42no—
280C23×C59—42no—
281C23×C59—42no—
282C23×C59AGL(1,ℤ/8)14yes—
283C23×C59C22×D412yes—
284C23×C59C22×D412yes—
285C23×C59C22×D411yescharacteristic
286Q8×C59—48no—
287D4×C59—28no—
288D4×C59—22no—
289D4×C59—22no—
290D4×C59—48no—
291D4×C59—48no—
292D4×C59—42no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—24no—
298C2×C4×C59—24no—
299C2×C4×C59—22no—
300C2×C4×C59—22no—
301C2×C4×C59—22no—
302C2×C4×C59—22no—
303C2×C4×C59—22no—
304C2×C4×C59—22no—
305C2×C4×C59—22no—
306C2×C4×C59—48no—
307C2×C4×C59—48no—
308C2×C4×C59—42no—
309C2×C4×C59—42no—
310C2×C4×C59—42no—
311C2×C4×C59—48no—
312C2×C4×C59C22×D412yes—
313C2×C4×C59C22×D412yes—
314C2×C4×C59C22×D412yes—
315C2×C4×C59C22×D412yes—
316C2×C4×C59C22×D411yescharacteristic
317C2×C4×C59C2×#4112yes—
318C2×C4×C592−1+412yes—
319C2×C4×C59C2511yescharacteristic
320C2×Dic59—22no—
321C2×Dic59—22no—
322C2×Dic59—22no—
323C2×Dic59—22no—
324C2×Dic59—42no—
325C2×Dic59—48no—
326C2×Dic59—42no—
327C2×Dic59—42no—
328C2×Dic59—42no—
329Dic118—22no—
330Dic118—22no—
331Dic118—42no—
332C59⋊C8—22no—
333C59⋊C8—22no—
334C59⋊C8—22no—
335C59⋊C8C2×#4114yescomplemented
336C2×#3343—591nomaximal, Sylow
337C22×C59—28no—
338C22×C59—22no—
339C22×C59—22no—
340C22×C59—22no—
341C22×C59—22no—
342C22×C59—22no—
343C22×C59—44no—
344C22×C59—42no—
345C22×C59—42no—
346C22×C59—42no—
347C22×C59—84no—
348C22×C59#54712yes—
349C22×C59C2×AGL(1,ℤ/8)14yes—
350C22×C59C2×AGL(1,ℤ/8)12yes—
351C22×C59#57812yes—
352C22×C59C23×D411yescharacteristic
353C4×C59—22no—
354C4×C59—22no—
355C4×C59—22no—
356C4×C59—22no—
357C4×C59—42no—
358C4×C59—42no—
359C4×C59—42no—
360C4×C59#54712yes—
361C4×C59C22×#4111yescharacteristic
362C4×C59C2×2−1+411yescharacteristic
363Dic59—42no—
364Dic59—42no—
365Dic59—42no—
366Dic59—42no—
367C2×#552—591no—
368C2×#547D5911yescharacteristic
369#3343—5916no—
370C2×#501—591no—
371C2×#484—591no—
372C2×#482—591no—
373C2×#483—591no—
374C2×#480—591no—
375C2×#477—591no—
376C2×#478—591no—
377C2×#468—591no—
378C2×#465—591no—
379C2×#440—591no—
380C2×#435—591no—
381C2×#428—591no—
382C22×#107—591no—
383C2×C59—24no—
384C2×C59—42no—
385C2×C59—82no—
386C2×C59#334314yescomplemented
387C2×C59C2×#54711yescharacteristic
388C2×C59C22×AGL(1,ℤ/8)11yescharacteristic
389C2×C59C2×#57811yescharacteristic
390C22×#41—21no—
391C22×SD16—591no—
392C22×M16—591no—
393C23×C8—591no—
394#552—598no—
395#552—1184no—
396#547—24no—
397#547C2×D5918yes—
398C2×C4⋊Q8C2×D5911yescharacteristic
399C2×#126—1181no—
400C2×#125—591no—
401C2×#125—1181no—
402C2×#123—21no—
403C2×#123—21no—
404C2×#123—1181no—
405C2×C22⋊Q8—21no—
406C2×C22⋊Q8—591no—
407C2×C22⋊Q8—591no—
408C2×#121C2×D5911yescharacteristic
409C2×#121C2×D5911yescharacteristic
410C2×C4×Q8—591no—
411C2×C4×D4C2×D5911yescharacteristic
412C2×C4×D4C2×D5911yescharacteristic
413C2×#117—591no—
414C2×#117—1181no—
415C22×C4⋊C4—591no—
416C22×C4⋊C4C2×D5911yescharacteristic
417C22×C4⋊C4C2×D5911yescharacteristic
418#501—598no—
419#484—598no—
420#483—598no—
421#482—598no—
422#480—598no—
423#478—598no—
424#477—598no—
425#468—598no—
426#465—598no—
427#440—598no—
428#435—598no—
429#428—598no—
430C2×#107—591no—
431C2×#107—591no—
432C2×#107—591no—
433C2×#107—591no—
434C2×#107—598no—
435C2×#107—591no—
436C2×#107—591no—
437C2×#106—591no—
438C2×#106—591no—
439C2×#106—591no—
440C2×C4⋊C8—591no—
441C2×#103—591no—
442C2×#103—591no—
443C2×#103—591no—
444C2×#102—591no—
445C2×#102—591no—
446C2×#102—591no—
447C2×C22⋊C8—591no—
448C2×C22⋊C8—591no—
449C2×#97—591no—
450C59C2×#334311yescharacteristic, complemented, Sylow
451C2×#41—28no—
452C2×#41—48no—
453C22×Q8—21no—
454C22×Q8—591no—
455C22×D4—21no—
456C22×D4—21no—
457C22×D4C22⋊D5911yescharacteristic
458C22×D4C22×D5911yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—21no—
462C23×C4—1181no—
463C23×C4C22×D5911yescharacteristic
464C23×C4C22×D5911yescharacteristic
465C2×SD16—594no—
466C2×SD16—1184no—
467C2×M16—594no—
468C2×M16—1184no—
469C22×C8—591no—
470C22×C8—591no—
471C22×C8—594no—
472C22×C8—591no—
473C22×C8—591no—
474C22×C8—1184no—
475C4⋊Q8—22no—
476C4⋊Q8C22×D5914yes—
477#126—1188no—
478#125—594no—
479#125—1188no—
480#125—1182no—
481#123—28no—
482#123—28no—
483#123—1188no—
484C22⋊Q8—28no—
485C22⋊Q8—594no—
486C22⋊Q8—594no—
487C22⋊Q8—1182no—
488C22⋊Q8—1182no—
489#121—22no—
490#121—22no—
491#121C22×D5914yes—
492#121C22×D5914yes—
493C4×Q8—594no—
494C4×Q8—1182no—
495C4×D4—22no—
496C4×D4C22⋊D5914yes—
497C4×D4C22×D5914yes—
498C4×D4C22×D5914yes—
499#117—594no—
500#117—1182no—
501#117—1188no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—591no—
508C2×C4⋊C4—591no—
509C2×C4⋊C4—594no—
510C2×C4⋊C4—591no—
511C2×C4⋊C4—1181no—
512C2×C4⋊C4—1182no—
513C2×C4⋊C4—1181no—
514C2×C4⋊C4—1181no—
515C2×C4⋊C4—1181no—
516C2×C4⋊C4—1181no—
517C2×C4⋊C4—1181no—
518C2×C4⋊C4C22⋊D5911yescharacteristic
519C2×C4⋊C4C22×D5911yescharacteristic
520C2×C4⋊C4C22×D5911yescharacteristic
521C2×C4⋊C4C22×D5911yescharacteristic
522C2×C4⋊C4C22×D5914yes—
523C2×C4⋊C4C22×D5914yes—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—1181no—
528C2×C22⋊C4—1181no—
529C2×C22⋊C4—1181no—
530C2×C22⋊C4C22⋊D5911yescharacteristic
531C2×C22⋊C4C22⋊D5911yescharacteristic
532C2×C42—1181no—
533C2×C42—1181no—
534C2×C42C22×D5911yescharacteristic
535#107—594no—
536#107—594no—
537#107—594no—
538#107—594no—
539#107—594no—
540#107—594no—
541#106—594no—
542#106—594no—
543#106—594no—
544C4⋊C8—594no—
545#103—594no—
546#103—594no—
547#103—594no—
548#102—594no—
549#102—594no—
550#102—594no—
551C22⋊C8—594no—
552C22⋊C8—594no—
553#97—594no—
554C24—21no—
555C24C2×C22⋊D5911yescharacteristic
556C24C2×C22⋊D5911yescharacteristic
557#41—432no—
558C2×Q8—24no—
559C2×Q8—44no—
560C2×Q8—592no—
561C2×Q8—1181no—
562C2×Q8—1182no—
563C2×Q8—1182no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—44no—
571C2×D4—44no—
572C2×D4C2×C22⋊D5914yes—
573C2×D4C23×D5912yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—24no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—1184no—
588C22×C4—1181no—
589C22×C4—1181no—
590C22×C4—1181no—
591C22×C4—1181no—
592C22×C4—2364no—
593C22×C4C2×C22⋊D5912yes—
594C22×C4C2×C22⋊D5912yes—
595C22×C4C2×C22⋊D5911yescharacteristic
596C22×C4C2×C22⋊D5911yescharacteristic
597C22×C4C2×C22⋊D5911yescharacteristic
598C22×C4C2×C22⋊D5911yescharacteristic
599C22×C4C23×D5912yes—
600C22×C4C23×D5912yes—
601C22×C4C23×D5911yescharacteristic
602SD16—1188no—
603M16—1188no—
604C2×C8—594no—
605C2×C8—592no—
606C2×C8—592no—
607C2×C8—592no—
608C2×C8—592no—
609C2×C8—1188no—
610C2×C8—1182no—
611C2×C8—1182no—
612C2×C8—1182no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—592no—
620C4⋊C4—592no—
621C4⋊C4—592no—
622C4⋊C4—1181no—
623C4⋊C4—1181no—
624C4⋊C4—1184no—
625C4⋊C4—1181no—
626C4⋊C4—1184no—
627C4⋊C4—1184no—
628C4⋊C4—1184no—
629C4⋊C4—1184no—
630C4⋊C4—1184no—
631C4⋊C4C2×C22⋊D5914yes—
632C4⋊C4C23×D5912yes—
633C4⋊C4C23×D5912yes—
634C4⋊C4C23×D5912yes—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—1184no—
639C22⋊C4—1184no—
640C22⋊C4—1184no—
641C22⋊C4C2×C22⋊D5914yes—
642C22⋊C4C2×C22⋊D5914yes—
643C42—1184no—
644C42—1184no—
645C42C2×C22⋊D5912yes—
646C42C23×D5912yes—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23#1427375314yes—
657C23C22×C22⋊D5912yes—
658C23C22×C22⋊D5912yes—
659C23C22×C22⋊D5911yescharacteristic
660Q8—48no—
661Q8—1182no—
662Q8—1182no—
663Q8—2362no—
664D4—28no—
665D4—22no—
666D4—22no—
667D4—48no—
668D4—48no—
669D4—42no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—48no—
684C2×C4—48no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—48no—
689C2×C4—1182no—
690C2×C4—1182no—
691C2×C4—1182no—
692C2×C4—1182no—
693C2×C4—2368no—
694C2×C4—2362no—
695C2×C4—2362no—
696C2×C4—2362no—
697C2×C4—2362no—
698C2×C4C22×C22⋊D5912yes—
699C2×C4C22×C22⋊D5912yes—
700C2×C4C22×C22⋊D5912yes—
701C2×C4C22×C22⋊D5912yes—
702C2×C4C22×C22⋊D5911yescharacteristic
703C2×C4#41×D5912yes—
704C2×C4#1427377412yes—
705C2×C4C24×D5911yescharacteristic
706C8—594no—
707C8—1182no—
708C8—1182no—
709C8—1182no—
710C22—22no—
711C22—28no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—84no—
721C22#1683805112yes—
722C22C2×#1427375314yes—
723C22C2×#1427375312yes—
724C22#1683821712yes—
725C22C23×C22⋊D5911yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—2362no—
734C4—2362no—
735C4—2362no—
736C4—2362no—
737C4#1683805112yes—
738C4C2×#41×D5911yescharacteristic
739C4C2×#1427377411yescharacteristic
740C2—24no—
741C2—42no—
742C2—82no—
743C2#2143653014yesdirect product factor
744C2C2×#1683805111yescharacteristic
745C2C22×#1427375311yescharacteristic
746C2C2×#1683821711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
Fitting, prime radicalC2×C59×#547C2
socleC23×C59C22×D4
hypercenterC2×#547D59
hypocenterC59C2×#3343
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#16838092C2semidirect
2. #21436530C2direct (N × H)
3. C2×#16837808C2semidirect
4. C2×#16837737C2semidirect
5. C2×#16837723C2semidirect
6. C2×#16837732C2semidirect
7. C2×#16837713C2semidirect
8. C2×#16837694C2semidirect
9. C2×#16837702C2semidirect
10. C2×#16837646C2semidirect
11. C2×#16837629C2semidirect
12. C2×#16837502C2semidirect
13. C2×#16837474C2semidirect
14. C2×#16837442C2semidirect
15. C22×#14273660C2semidirect
21. #16838092C22semidirect
32. #16837808C22semidirect
33. #16837737C22semidirect
34. #16837732C22semidirect
35. #16837723C22semidirect
36. #16837713C22semidirect
37. #16837702C22semidirect
38. #16837694C22semidirect
39. #16837646C22semidirect
40. #16837629C22semidirect
41. #16837502C22semidirect
42. #16837474C22semidirect
43. #16837442C22semidirect
50. C2×#14273660C22semidirect
268. C2×C59⋊C8#41semidirect
335. C59⋊C8C2×#41semidirect
386. C2×C59#3343semidirect
450. C59C2×#3343semidirect
743. C2#21436530direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380922
#214365302
C2×#168378082
C2×#168377372
C2×#168377232
C2×#168377322
C2×#168377132
C2×#168376942
C2×#168377022
C2×#168376462
C2×#168376292
C2×#168375022
C2×#168374742
C2×#168374422
C22×#142736602
C2×C59×#5472
C2×#334359