Finite Group Databasebeta

← C2×#21436481 #29467142

Subgroups — C2×#21436481 #29467142

Order 15104.

1930 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838104C211yesmaximal, characteristic
2C2×#16838094C211yesmaximal, characteristic, complemented
3#21436481C2116yesmaximal, direct product factor
4C2×#16837802C211yesmaximal, characteristic, complemented
5C2×#16837735C211yesmaximal, characteristic, complemented
6C2×#16837741C211yesmaximal, characteristic, complemented
7C2×#16837725C211yesmaximal, characteristic, complemented
8C2×#16837713C211yesmaximal, characteristic, complemented
9C2×#16837707C211yesmaximal, characteristic, complemented
10C2×#16837704C211yesmaximal, characteristic, complemented
11C2×#16837628C211yesmaximal, characteristic, complemented
12C2×SD16×Dic59C211yesmaximal, characteristic, complemented
13C2×C8×C22⋊D59C211yesmaximal, characteristic, complemented
14C2×#16837437C211yesmaximal, characteristic, complemented
15C22×#14273659C211yesmaximal, characteristic, complemented
16C2×C59×#465C211yesmaximal, characteristic, complemented
17C22×C8×D59C2211yescharacteristic
18#16838104—24no—
19#16838104C2218yes—
20#16838094—24no—
21#16838094C2218yescomplemented
22C2×#14273722—21no—
23C2×#14273720—21no—
24C2×#14273718—21no—
25C2×#14273718C2211yescharacteristic
26C2×#14273718C2211yescharacteristic
27C2×#14273711—21no—
28C2×#14273711—21no—
29C2×#14273703C2211yescharacteristic
30C2×#14273699—21no—
31C2×#14273698C2211yescharacteristic
32C2×Q8×Dic59C2211yescharacteristic
33C2×D4×Dic59—21no—
34C2×D4×Dic59C2211yescharacteristic
35C2×C4×C22⋊D59C2211yescharacteristic
36C2×#14273685C2211yescharacteristic
37C2×#14273685C2211yescharacteristic
38C2×#14273683—21no—
39C22×C4⋊Dic59C2211yescharacteristic
40C22×C4⋊Dic59C2211yescharacteristic
41#16837802C2218yescomplemented
42#16837741C2218yescomplemented
43#16837735C2218yescomplemented
44#16837725C2218yescomplemented
45#16837713C2218yescomplemented
46#16837707C2218yescomplemented
47#16837704C2218yescomplemented
48#16837628C2218yescomplemented
49SD16×Dic59C2218yescomplemented
50C8×C22⋊D59C2218yescomplemented
51#16837437C2218yescomplemented
52C2×#14273660C2211yescharacteristic
53C2×#14273660C2211yescharacteristic
54C2×#14273660C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×#14273659C2211yescharacteristic
57C2×#14273659C2211yescharacteristic
58C2×#14273659C2211yescharacteristic
59C2×#14273659C2211yescharacteristic
60C2×#14273659C2218yescomplemented
61C2×Dic59⋊C8C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273651C2211yescharacteristic
64C2×#14273648C2211yescharacteristic
65C2×#14273648C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C22×SD16×C59C2211yescharacteristic
70C23×C8×C59C2211yescharacteristic
71C2×C22⋊Q8×C59C2211yescharacteristic
72C2×#121×C59C2211yescharacteristic
73C59×#465C2218yescomplemented
74C2×#106×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C22×C22⋊D59—21no—
78C22×C22⋊D59D411yescharacteristic
79C23×Dic59—21no—
80C23×Dic59—21no—
81C23×Dic59—21no—
82C22×C4×D59C2311yescharacteristic
83C22×C59⋊C8C2311yescharacteristic
84C22×C59⋊C8C2311yescharacteristic
85C2×C8×D59—24no—
86C2×C8×D59C2314yes—
87#14273722—28no—
88#14273720—28no—
89#14273718—28no—
90#14273718—22no—
91#14273718—22no—
92#14273718C2314yes—
93#14273718C2314yes—
94#14273711—28no—
95#14273711—28no—
96#14273703—22no—
97#14273703C2314yes—
98#14273699—28no—
99#14273698—22no—
100#14273698C2314yes—
101Q8×Dic59—22no—
102Q8×Dic59C2314yes—
103D4×Dic59—28no—
104D4×Dic59—22no—
105D4×Dic59C2314yes—
106C4×C22⋊D59D414yes—
107C4×C22⋊D59C2314yes—
108#14273685—22no—
109#14273685—22no—
110#14273685C2314yes—
111#14273685C2314yes—
112#14273683—28no—
113C2×C4⋊Dic59—21no—
114C2×C4⋊Dic59—21no—
115C2×C4⋊Dic59—22no—
116C2×C4⋊Dic59—22no—
117C2×C4⋊Dic59—21no—
118C2×C4⋊Dic59—21no—
119C2×C4⋊Dic59—21no—
120C2×C4⋊Dic59C2311yescharacteristic
121C2×C4⋊Dic59C2311yescharacteristic
122C2×C4⋊Dic59C2311yescharacteristic
123C2×C4⋊Dic59C2311yescharacteristic
124C2×C4⋊Dic59C2314yes—
125C2×C4⋊Dic59C2314yes—
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4D411yescharacteristic
130C2×C22⋊Dic59—21no—
131C2×C22⋊Dic59—21no—
132C2×C22⋊Dic59D411yescharacteristic
133C2×(C2×D59)⋊C4—21no—
134C2×(C2×D59)⋊C4—21no—
135C2×(C2×D59)⋊C4—21no—
136C2×(C2×D59)⋊C4D411yescharacteristic
137C2×C4×Dic59—21no—
138C2×C4×Dic59—21no—
139C2×C4×Dic59—21no—
140C2×C4×Dic59C2311yescharacteristic
141#14273660C2314yes—
142#14273660C2314yes—
143#14273660C2314yes—
144#14273660C2314yes—
145#14273659C2314yes—
146#14273659C2314yes—
147#14273659C2314yes—
148#14273659C2314yes—
149Dic59⋊C8C2314yes—
150#14273651C2314yes—
151#14273651C2314yes—
152#14273648C2314yes—
153#14273648C2314yes—
154C22⋊(C59⋊C8)C2314yes—
155(C2×D59)⋊C8C2314yes—
156C8×Dic59C2314yes—
157C22×Q8×C59C2311yescharacteristic
158C22×D4×C59—21no—
159C22×D4×C59C2311yescharacteristic
160C23×C4×C59C2311yescharacteristic
161C2×SD16×C59—24no—
162C2×SD16×C59C2314yes—
163C22×C8×C59—24no—
164C22×C8×C59C2311yescharacteristic
165C22×C8×C59C2314yes—
166C22×C8×C59C2311yescharacteristic
167C22⋊Q8×C59—22no—
168C22⋊Q8×C59C2314yes—
169#121×C59—22no—
170#121×C59C2314yes—
171C2×C4⋊C4×C59—21no—
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C22⋊C4×C59—21no—
175C2×C22⋊C4×C59—21no—
176#106×C59C2314yes—
177#103×C59C2314yes—
178#102×C59C2314yes—
179C24×C59—21no—
180C24×C59C2×D411yescharacteristic
181C23×D59C2×D411yescharacteristic
182C2×Q8×C59—21no—
183C2×Q8×C59—22no—
184C2×Q8×C59—22no—
185C2×Q8×C59C2412yes—
186C2×D4×C59—24no—
187C2×D4×C59—21no—
188C2×D4×C59—22no—
189C2×D4×C59—22no—
190C2×D4×C59—44no—
191C2×D4×C59C2412yes—
192C22×C4×C59—22no—
193C22×C4×C59—22no—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59—21no—
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2×D412yes—
199C22×C4×C59C2412yes—
200C22×C4×C59C2411yescharacteristic
201C2×C22⋊D59—24no—
202C2×C22⋊D59—24no—
203C2×C22⋊D59—82no—
204C2×C22⋊D59C2×D414yes—
205C22×Dic59—21no—
206C22×Dic59—21no—
207C22×Dic59—21no—
208C22×Dic59—21no—
209C22×Dic59—24no—
210C22×Dic59—24no—
211C22×Dic59—24no—
212C22×Dic59—44no—
213C22×Dic59—82no—
214C22×Dic59—82no—
215C22×Dic59C2×D411yescharacteristic
216C22×Dic59C2×D411yescharacteristic
217C22×Dic59C2×D411yescharacteristic
218C2×C4×D59—22no—
219C2×C4×D59—22no—
220C2×C4×D59C2×D412yes—
221C2×C4×D59C2412yes—
222SD16×C59—28no—
223C2×C8×C59—22no—
224C2×C8×C59—28no—
225C2×C8×C59#4114yes—
226C2×C8×C59C2412yes—
227C2×C8×C59C2412yes—
228C4⋊C4×C59—24no—
229C4⋊C4×C59—21no—
230C4⋊C4×C59—21no—
231C4⋊C4×C59C2412yes—
232C4⋊C4×C59C2412yes—
233C22⋊C4×C59—24no—
234C22⋊C4×C59—24no—
235C22⋊Dic59—24no—
236C22⋊Dic59—24no—
237C22⋊Dic59C2×D414yes—
238(C2×D59)⋊C4—24no—
239(C2×D59)⋊C4—24no—
240(C2×D59)⋊C4—24no—
241(C2×D59)⋊C4C2×D414yes—
242C4⋊Dic59—21no—
243C4⋊Dic59—21no—
244C4⋊Dic59—21no—
245C4⋊Dic59—21no—
246C4⋊Dic59—24no—
247C4⋊Dic59—24no—
248C4⋊Dic59—24no—
249C4⋊Dic59—24no—
250C4⋊Dic59—24no—
251C4⋊Dic59C2412yes—
252C4⋊Dic59C2412yes—
253C4⋊Dic59C2412yes—
254C4⋊Dic59C2412yes—
255Dic59⋊C4—24no—
256Dic59⋊C4—24no—
257Dic59⋊C4—24no—
258Dic59⋊C4C2×D414yes—
259C4×Dic59—24no—
260C4×Dic59—24no—
261C4×Dic59—24no—
262C4×Dic59C2×D412yes—
263C4×Dic59C2412yes—
264C2×C59⋊C8—22no—
265C2×C59⋊C8—22no—
266C2×C59⋊C8C2412yes—
267C2×C59⋊C8C2412yes—
268C8×D59—28no—
269C23×C59—22no—
270C23×C59—22no—
271C23×C59—22no—
272C23×C59—42no—
273C23×C59—42no—
274C23×C59—42no—
275C23×C59#13514yes—
276C23×C59C22×D412yes—
277C23×C59C22×D411yescharacteristic
278C22×D59—22no—
279C22×D59—22no—
280C22×D59—22no—
281C22×D59C22×D412yes—
282Q8×C59—22no—
283Q8×C59—22no—
284Q8×C59—42no—
285D4×C59—22no—
286D4×C59—22no—
287D4×C59—48no—
288D4×C59—42no—
289C2×C4×C59—22no—
290C2×C4×C59—24no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—42no—
297C2×C4×C59—42no—
298C2×C4×C59—42no—
299C2×C4×C59C22×D412yes—
300C2×C4×C59C22×D411yescharacteristic
301C2×C4×C59C2×#4112yes—
302C2×C4×C592−1+412yes—
303C2×C4×C59C2511yescharacteristic
304C22⋊D59—28no—
305C22⋊D59—84no—
306C2×Dic59—22no—
307C2×Dic59—22no—
308C2×Dic59—22no—
309C2×Dic59—22no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—48no—
314C2×Dic59—42no—
315C2×Dic59—42no—
316C2×Dic59—42no—
317C2×Dic59—42no—
318C2×Dic59—84no—
319C2×Dic59—84no—
320C2×Dic59C22×D412yes—
321C2×Dic59C22×D412yes—
322C2×Dic59C22×D412yes—
323C4×D59—24no—
324C4×D59—22no—
325C4×D59—22no—
326C8×C59—22no—
327C8×C59C2×#4114yes—
328C59⋊C8—22no—
329C59⋊C8—22no—
330C2×#3337—591nomaximal, Sylow
331C22×C59—28no—
332C22×C59—22no—
333C22×C59—22no—
334C22×C59—42no—
335C22×C59—42no—
336C22×C59—42no—
337C22×C59—84no—
338C22×C59#54712yes—
339C22×C59C2×#13514yes—
340C22×C59C2×#13512yes—
341C22×C59#57712yes—
342C22×C59C23×D411yescharacteristic
343C2×D59—22no—
344C2×D59—22no—
345C2×D59—22no—
346C2×D59—44no—
347C4×C59—22no—
348C4×C59—42no—
349C4×C59—42no—
350C4×C59—42no—
351C4×C59#54712yes—
352C4×C59C22×#4111yescharacteristic
353C4×C59C2×2−1+411yescharacteristic
354Dic59—22no—
355Dic59—22no—
356Dic59—22no—
357Dic59—42no—
358Dic59—42no—
359Dic59—42no—
360Dic59—42no—
361C2×#553—591no—
362C2×#552—591no—
363#3337—5916no—
364C2×#499—591no—
365C2×#484—591no—
366C2×#485—591no—
367C2×#482—591no—
368C2×#480—591no—
369C2×#479—591no—
370C2×#478—591no—
371C2×#465—591no—
372C2×#465D5911yescharacteristic, complemented
373C2×C4×SD16—591no—
374C2×C8×D4—591no—
375C2×#427—591no—
376C22×#106—591no—
377C2×C59—24no—
378C2×C59—82no—
379C2×C59#333714yescomplemented
380C2×C59C2×#54711yescharacteristic
381C2×C59C22×#13511yescharacteristic
382C2×C59C2×#57711yescharacteristic
383D59—42no—
384C22×SD16C2×D5911yescharacteristic
385C23×C8—591no—
386C23×C8C2×D5911yescharacteristic
387#553—598no—
388#553—1184no—
389#552—598no—
390#552—1184no—
391C2×#126—1181no—
392C2×#126—1181no—
393C2×#125—591no—
394C2×#125—591no—
395C2×#125—1181no—
396C2×#123—1181no—
397C2×#123—1181no—
398C2×C22⋊Q8—591no—
399C2×C22⋊Q8C2×D5911yescharacteristic
400C2×#121—591no—
401C2×#121—1181no—
402C2×#121C2×D5911yescharacteristic
403C2×C4×Q8—591no—
404C2×C4×D4—591no—
405C2×C4×D4—591no—
406C2×C4×D4—1181no—
407C2×#117—591no—
408C2×#117—591no—
409C2×#117—1181no—
410C22×C4⋊C4—591no—
411C22×C4⋊C4—591no—
412#499—598no—
413#485—598no—
414#484—598no—
415#482—598no—
416#480—598no—
417#479—598no—
418#478—598no—
419#465—598no—
420#465C2×D5918yescomplemented
421C4×SD16—598no—
422C8×D4—598no—
423#427—598no—
424C2×#107—591no—
425C2×#107—591no—
426C2×#107—591no—
427C2×#107—591no—
428C2×#106—591no—
429C2×#106—591no—
430C2×#106—598no—
431C2×#106—591no—
432C2×#106—591no—
433C2×#106C2×D5911yescharacteristic
434C2×C4⋊C8—591no—
435C2×#103—591no—
436C2×#103—591no—
437C2×#103C2×D5911yescharacteristic
438C2×#102—591no—
439C2×#102—591no—
440C2×#102C2×D5911yescharacteristic
441C2×C22⋊C8—591no—
442C2×C22⋊C8—591no—
443C2×C4×C8—591no—
444C59C2×#333711yescharacteristic, complemented, Sylow
445C22×Q8C22×D5911yescharacteristic
446C22×D4—21no—
447C22×D4—591no—
448C22×D4—1181no—
449C22×D4C22×D5911yescharacteristic
450C23×C4—591no—
451C23×C4—1181no—
452C23×C4—1181no—
453C23×C4—1181no—
454C23×C4C22×D5911yescharacteristic
455C2×SD16—24no—
456C2×SD16C22×D5914yes—
457C22×C8—24no—
458C22×C8—591no—
459C22×C8—591no—
460C22×C8—594no—
461C22×C8—1184no—
462C22×C8C22×D5911yescharacteristic
463C22×C8C22×D5914yes—
464C22×C8C22×D5911yescharacteristic
465#126—1188no—
466#126—1188no—
467#125—594no—
468#125—594no—
469#125—1182no—
470#125—1182no—
471#125—1188no—
472#123—1188no—
473#123—1188no—
474C22⋊Q8—22no—
475C22⋊Q8—594no—
476C22⋊Q8—1182no—
477C22⋊Q8C22×D5914yes—
478#121—22no—
479#121—594no—
480#121—1182no—
481#121—1188no—
482#121C22×D5914yes—
483C4×Q8—594no—
484C4×Q8—1182no—
485C4×D4—594no—
486C4×D4—594no—
487C4×D4—594no—
488C4×D4—1182no—
489C4×D4—1188no—
490#117—594no—
491#117—594no—
492#117—1188no—
493#117—1182no—
494#117—1182no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—591no—
497C2×C4⋊C4—591no—
498C2×C4⋊C4—591no—
499C2×C4⋊C4—591no—
500C2×C4⋊C4—591no—
501C2×C4⋊C4—594no—
502C2×C4⋊C4—594no—
503C2×C4⋊C4—1181no—
504C2×C4⋊C4—1181no—
505C2×C4⋊C4—1181no—
506C2×C4⋊C4—1181no—
507C2×C4⋊C4—1181no—
508C2×C4⋊C4—1181no—
509C2×C4⋊C4—1181no—
510C2×C4⋊C4—1181no—
511C2×C4⋊C4—1182no—
512C2×C4⋊C4—1182no—
513C2×C4⋊C4C22×D5911yescharacteristic
514C2×C4⋊C4C22×D5911yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—591no—
518C2×C22⋊C4—591no—
519C2×C22⋊C4—1181no—
520C2×C22⋊C4—1181no—
521C2×C22⋊C4—1181no—
522C2×C22⋊C4—1181no—
523C2×C22⋊C4—1181no—
524C2×C42—591no—
525C2×C42—1181no—
526C2×C42—1181no—
527C2×C42—1181no—
528#107—594no—
529#107—594no—
530#107—594no—
531#107—594no—
532#106—594no—
533#106—594no—
534#106—594no—
535#106—594no—
536#106C22×D5914yes—
537C4⋊C8—594no—
538#103—594no—
539#103—594no—
540#103C22×D5914yes—
541#102—594no—
542#102—594no—
543#102C22×D5914yes—
544C22⋊C8—594no—
545C22⋊C8—594no—
546C4×C8—594no—
547C24—21no—
548C24—591no—
549C24D4×D5911yescharacteristic
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8C23×D5912yes—
554C2×D4—24no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—44no—
559C2×D4—594no—
560C2×D4—1184no—
561C2×D4—1184no—
562C2×D4—4722no—
563C2×D4C23×D5912yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—591no—
570C22×C4—591no—
571C22×C4—591no—
572C22×C4—592no—
573C22×C4—592no—
574C22×C4—1184no—
575C22×C4—1182no—
576C22×C4—1182no—
577C22×C4—1184no—
578C22×C4—1184no—
579C22×C4—1181no—
580C22×C4—1181no—
581C22×C4—1181no—
582C22×C4—1181no—
583C22×C4—4722no—
584C22×C4—4722no—
585C22×C4—2364no—
586C22×C4D4×D5912yes—
587C22×C4D4×D5911yescharacteristic
588C22×C4C23×D5912yes—
589C22×C4C23×D5911yescharacteristic
590SD16—28no—
591C2×C8—22no—
592C2×C8—28no—
593C2×C8—592no—
594C2×C8—592no—
595C2×C8—1182no—
596C2×C8—1182no—
597C2×C8—1188no—
598C2×C8#1174568714yes—
599C2×C8C23×D5912yes—
600C2×C8C23×D5912yes—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—594no—
605C4⋊C4—592no—
606C4⋊C4—592no—
607C4⋊C4—592no—
608C4⋊C4—592no—
609C4⋊C4—1184no—
610C4⋊C4—1184no—
611C4⋊C4—1184no—
612C4⋊C4—1184no—
613C4⋊C4—1184no—
614C4⋊C4—1184no—
615C4⋊C4—1181no—
616C4⋊C4—1181no—
617C4⋊C4—1181no—
618C4⋊C4—1181no—
619C4⋊C4—1184no—
620C4⋊C4—1184no—
621C4⋊C4C23×D5912yes—
622C4⋊C4C23×D5912yes—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—594no—
626C22⋊C4—594no—
627C22⋊C4—1184no—
628C22⋊C4—1184no—
629C22⋊C4—1184no—
630C22⋊C4—1184no—
631C22⋊C4—1184no—
632C42—592no—
633C42—592no—
634C42—1184no—
635C42—1184no—
636C42—1184no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—592no—
644C23—1182no—
645C23—1182no—
646C23—1182no—
647C23#1427374814yes—
648C23C2×D4×D5912yes—
649C23C2×D4×D5911yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653D4—22no—
654D4—22no—
655D4—48no—
656D4—42no—
657D4—1188no—
658D4—4724no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—592no—
670C2×C4—592no—
671C2×C4—592no—
672C2×C4—1182no—
673C2×C4—1182no—
674C2×C4—1182no—
675C2×C4—1182no—
676C2×C4—1182no—
677C2×C4—1184no—
678C2×C4—1182no—
679C2×C4—1182no—
680C2×C4—1182no—
681C2×C4—1182no—
682C2×C4—4724no—
683C2×C4—4724no—
684C2×C4—2368no—
685C2×C4—2362no—
686C2×C4—2362no—
687C2×C4—2362no—
688C2×C4—2362no—
689C2×C4C2×D4×D5912yes—
690C2×C4C2×D4×D5911yescharacteristic
691C2×C4C2×#1174568712yes—
692C2×C4#1427377412yes—
693C2×C4C24×D5911yescharacteristic
694C8—22no—
695C8—1182no—
696C8—1182no—
697C8C2×#1174568714yes—
698C22—28no—
699C22—22no—
700C22—22no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—84no—
705C22—1182no—
706C22—1182no—
707C22—1182no—
708C22—2364no—
709C22#1683805212yes—
710C22C2×#1427374814yes—
711C22C2×#1427374812yes—
712C22#1683820912yes—
713C22C22×D4×D5911yescharacteristic
714C4—22no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—1182no—
719C4—1182no—
720C4—1182no—
721C4—2362no—
722C4—2362no—
723C4—2362no—
724C4—2362no—
725C4#1683805212yes—
726C4C22×#1174568711yescharacteristic
727C4C2×#1427377411yescharacteristic
728C2—24no—
729C2—82no—
730C2—2362no—
731C2#2143648114yesdirect product factor
732C2C2×#1683805211yescharacteristic
733C2C22×#1427374811yescharacteristic
734C2C2×#1683820911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#465C2
socleC23×C59C22×D4
prime radicalC2×#16838104C2
hypercenterC2×#465D59
hypocenterC59C2×#3337
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
2. C2×#16838094C2semidirect
3. #21436481C2direct (N × H)
4. C2×#16837802C2semidirect
5. C2×#16837735C2semidirect
6. C2×#16837741C2semidirect
7. C2×#16837725C2semidirect
8. C2×#16837713C2semidirect
9. C2×#16837707C2semidirect
10. C2×#16837704C2semidirect
11. C2×#16837628C2semidirect
12. C2×SD16×Dic59C2semidirect
13. C2×C8×C22⋊D59C2semidirect
14. C2×#16837437C2semidirect
15. C22×#14273659C2semidirect
16. C2×C59×#465C2semidirect
21. #16838094C22semidirect
41. #16837802C22semidirect
42. #16837741C22semidirect
43. #16837735C22semidirect
44. #16837725C22semidirect
45. #16837713C22semidirect
46. #16837707C22semidirect
47. #16837704C22semidirect
48. #16837628C22semidirect
49. SD16×Dic59C22semidirect
50. C8×C22⋊D59C22semidirect
51. #16837437C22semidirect
60. C2×#14273659C22semidirect
73. C59×#465C22semidirect
372. C2×#465D59semidirect
379. C2×C59#3337semidirect
420. #465C2×D59semidirect
444. C59C2×#3337semidirect
731. C2#21436481direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381042
C2×#168380942
#214364812
C2×#168378022
C2×#168377352
C2×#168377412
C2×#168377252
C2×#168377132
C2×#168377072
C2×#168377042
C2×#168376282
C2×SD16×Dic592
C2×C8×C22⋊D592
C2×#168374372
C22×#142736592
C2×C59×#4652
C2×#333759