Finite Group Databasebeta

← C2×#21436507 #29467171

Subgroups — C2×#21436507 #29467171

Order 15104.

1918 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×#16838120C211yesmaximal, characteristic, complemented
2C2×#16838116C211yesmaximal, characteristic
3#21436507C2116yesmaximal, direct product factor
4C2×#16837799C211yesmaximal, characteristic, complemented
5C2×#16837746C211yesmaximal, characteristic, complemented
6C2×#16837744C211yesmaximal, characteristic, complemented
7C2×#16837725C211yesmaximal, characteristic, complemented
8C2×#16837696C211yesmaximal, characteristic, complemented
9C2×#16837680C211yesmaximal, characteristic, complemented
10C2×#16837630C211yesmaximal, characteristic, complemented
11C2×#16837629C211yesmaximal, characteristic, complemented
12C2×#16837493C211yesmaximal, characteristic, complemented
13C2×(C22⋊D59)⋊C8C211yesmaximal, characteristic, complemented
14C2×#16837439C211yesmaximal, characteristic, complemented
15C2×#16837438C211yesmaximal, characteristic, complemented
16C2×C59×#482C211yesmaximal, characteristic, complemented
17C22×#11745670C2211yescharacteristic
18C23×C59⋊C8C2211yescharacteristic
19C22×C8×D59C2211yescharacteristic
20#16838120—24no—
21#16838120C2218yescomplemented
22#16838116—24no—
23#16838116C2218yes—
24C2×#14273726C2211yescharacteristic
25C2×#14273726C2211yescharacteristic
26C2×#14273721—21no—
27C2×#14273720—21no—
28C2×#14273714—21no—
29C2×#14273713—21no—
30C2×#14273713—21no—
31C2×#14273707C2211yescharacteristic
32C2×#14273706C2211yescharacteristic
33C2×#14273699—21no—
34C2×#14273698C2211yescharacteristic
35C2×C4×Dic118—21no—
36C2×#14273692C2211yescharacteristic
37C2×D4×Dic59C2211yescharacteristic
38C2×C4×C22⋊D59C2211yescharacteristic
39C2×#14273686C2211yescharacteristic
40C2×#14273685C2211yescharacteristic
41C2×#14273685C2211yescharacteristic
42C2×#14273683—21no—
43#16837799C2218yescomplemented
44#16837746C2218yescomplemented
45#16837744C2218yescomplemented
46#16837725C2218yescomplemented
47#16837696C2218yescomplemented
48#16837680C2218yescomplemented
49#16837630C2218yescomplemented
50#16837629C2218yescomplemented
51#16837493C2218yescomplemented
52(C22⋊D59)⋊C8C2218yescomplemented
53#16837439C2218yescomplemented
54#16837438C2218yescomplemented
55C2×#14273661C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273660C2211yescharacteristic
58C2×#14273659C2211yescharacteristic
59C2×#14273658C2211yescharacteristic
60C2×#14273658C2211yescharacteristic
61C2×#14273658C2211yescharacteristic
62C2×Dic59⋊C8C2211yescharacteristic
63C2×#14273652C2211yescharacteristic
64C2×#14273652C2211yescharacteristic
65C2×#14273650C2211yescharacteristic
66C2×#14273648C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C2×#121×C59C2211yescharacteristic
70C2×#117×C59C2211yescharacteristic
71C59×#482C2218yescomplemented
72C2×#107×C59C2211yescharacteristic
73C2×#106×C59C2211yescharacteristic
74C2×#102×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C22×Dic118C2311yescharacteristic
80C22×C22⋊D59—21no—
81C22×C22⋊D59D411yescharacteristic
82C23×Dic59—21no—
83C22×C4×D59C2311yescharacteristic
84C2×#11745670—24no—
85C2×#11745670C2314yes—
86C22×C59⋊C8—24no—
87C22×C59⋊C8C2311yescharacteristic
88C22×C59⋊C8C2314yes—
89C22×C59⋊C8C2311yescharacteristic
90C2×C8×D59—24no—
91C2×C8×D59C2314yes—
92#14273726—22no—
93#14273726—22no—
94#14273726C2314yes—
95#14273726C2314yes—
96#14273721—28no—
97#14273720—28no—
98#14273714—28no—
99#14273713—28no—
100#14273713—28no—
101#14273707—22no—
102#14273707C2314yes—
103#14273706—22no—
104#14273706C2314yes—
105#14273699—28no—
106#14273698—22no—
107#14273698C2314yes—
108C4×Dic118—28no—
109#14273692—22no—
110#14273692C2314yes—
111D4×Dic59—22no—
112D4×Dic59C2314yes—
113C4×C22⋊D59D414yes—
114C4×C22⋊D59C2314yes—
115#14273686—22no—
116#14273686C2314yes—
117#14273685—22no—
118#14273685—22no—
119#14273685C2314yes—
120#14273685C2314yes—
121#14273683—28no—
122C2×C4⋊Dic59—21no—
123C2×C4⋊Dic59C2311yescharacteristic
124C2×C4⋊Dic59C2311yescharacteristic
125C2×C4⋊Dic59C2311yescharacteristic
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4D411yescharacteristic
131C2×C22⋊Dic59—21no—
132C2×C22⋊Dic59—21no—
133C2×C22⋊Dic59—21no—
134C2×C22⋊Dic59—21no—
135C2×C22⋊Dic59D411yescharacteristic
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4D411yescharacteristic
140C2×C4×Dic59—21no—
141C2×C4×Dic59—21no—
142C2×C4×Dic59—21no—
143C2×C4×Dic59—21no—
144C2×C4×Dic59C2311yescharacteristic
145#14273661C2314yes—
146#14273660C2314yes—
147#14273660C2314yes—
148#14273659C2314yes—
149#14273658C2314yes—
150#14273658C2314yes—
151#14273658C2314yes—
152Dic59⋊C8C2314yes—
153#14273652C2314yes—
154#14273652C2314yes—
155#14273650C2314yes—
156#14273648C2314yes—
157(C2×D59)⋊C8C2314yes—
158C8×Dic59C2314yes—
159C22×D4×C59—21no—
160C22×D4×C59C2311yescharacteristic
161C23×C4×C59C2311yescharacteristic
162C22×C8×C59C2311yescharacteristic
163C22×C8×C59C2311yescharacteristic
164#121×C59—22no—
165#121×C59C2314yes—
166#117×C59—22no—
167#117×C59C2314yes—
168C2×C4⋊C4×C59C2311yescharacteristic
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C22⋊C4×C59—21no—
172C2×C22⋊C4×C59—21no—
173C2×C42×C59—21no—
174#107×C59C2314yes—
175#106×C59C2314yes—
176#102×C59C2314yes—
177#102×C59C2314yes—
178C22⋊C8×C59C2314yes—
179C24×C59—21no—
180C24×C59C2×D411yescharacteristic
181C23×D59C2×D411yescharacteristic
182C2×D4×C59—24no—
183C2×D4×C59—21no—
184C2×D4×C59—22no—
185C2×D4×C59—22no—
186C2×D4×C59—82no—
187C2×D4×C59C2412yes—
188C22×C4×C59—22no—
189C22×C4×C59—22no—
190C22×C4×C59—21no—
191C22×C4×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59C2×D411yescharacteristic
194C22×C4×C59C2×D412yes—
195C22×C4×C59C2412yes—
196C22×C4×C59C2411yescharacteristic
197C2×C22⋊D59—24no—
198C2×C22⋊D59—24no—
199C2×C22⋊D59—82no—
200C2×C22⋊D59C2×D414yes—
201C22×Dic59—21no—
202C22×Dic59—21no—
203C22×Dic59—21no—
204C22×Dic59—21no—
205C22×Dic59—24no—
206C22×Dic59—44no—
207C22×Dic59C2×D411yescharacteristic
208C22×Dic59C2×D411yescharacteristic
209C22×Dic59C2×D411yescharacteristic
210C2×C4×D59—22no—
211C2×C4×D59—22no—
212C2×C4×D59C2×D412yes—
213C2×C4×D59C2412yes—
214C2×Dic118—22no—
215C2×Dic118—22no—
216C2×Dic118—21no—
217C2×Dic118—24no—
218C2×Dic118—24no—
219C2×Dic118—44no—
220C2×Dic118—82no—
221C2×Dic118C2412yes—
222C2×C8×C59—22no—
223C2×C8×C59—22no—
224C2×C8×C59C2412yes—
225C2×C8×C59C2412yes—
226C4⋊C4×C59—21no—
227C4⋊C4×C59—21no—
228C4⋊C4×C59—21no—
229C4⋊C4×C59C2412yes—
230C4⋊C4×C59C2412yes—
231C4⋊C4×C59C2412yes—
232C22⋊C4×C59—24no—
233C22⋊C4×C59—24no—
234C42×C59—24no—
235C22⋊Dic59—24no—
236C22⋊Dic59—24no—
237C22⋊Dic59—24no—
238C22⋊Dic59—24no—
239C22⋊Dic59C2×D414yes—
240#11745670—28no—
241(C2×D59)⋊C4—24no—
242(C2×D59)⋊C4—24no—
243(C2×D59)⋊C4—24no—
244(C2×D59)⋊C4C2×D414yes—
245C4⋊Dic59—21no—
246C4⋊Dic59—21no—
247C4⋊Dic59—21no—
248C4⋊Dic59—24no—
249C4⋊Dic59C2412yes—
250C4⋊Dic59C2412yes—
251C4⋊Dic59C2412yes—
252Dic59⋊C4—24no—
253Dic59⋊C4—24no—
254Dic59⋊C4—24no—
255Dic59⋊C4—24no—
256Dic59⋊C4C2×D414yes—
257C4×Dic59—24no—
258C4×Dic59—24no—
259C4×Dic59—24no—
260C4×Dic59—24no—
261C4×Dic59C2×D412yes—
262C4×Dic59C2412yes—
263C2×C59⋊C8—22no—
264C2×C59⋊C8—28no—
265C2×C59⋊C8#4114yes—
266C2×C59⋊C8C2412yes—
267C2×C59⋊C8C2412yes—
268C8×D59—28no—
269C23×C59—22no—
270C23×C59—22no—
271C23×C59—22no—
272C23×C59—22no—
273C23×C59—42no—
274C23×C59—42no—
275C23×C59—42no—
276C23×C59C22×D412yes—
277C23×C59C22×D411yescharacteristic
278C22×D59—22no—
279C22×D59—22no—
280C22×D59—22no—
281C22×D59C22×D412yes—
282D4×C59—22no—
283D4×C59—22no—
284D4×C59—42no—
285D4×C59—84no—
286C2×C4×C59—22no—
287C2×C4×C59—24no—
288C2×C4×C59—22no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—42no—
294C2×C4×C59—42no—
295C2×C4×C59—42no—
296C2×C4×C59C22×D412yes—
297C2×C4×C59C22×D411yescharacteristic
298C2×C4×C59C2×#4112yes—
299C2×C4×C592−1+412yes—
300C2×C4×C59C2511yescharacteristic
301C22⋊D59—28no—
302C22⋊D59—84no—
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—22no—
307C2×Dic59—22no—
308C2×Dic59—22no—
309C2×Dic59—42no—
310C2×Dic59—42no—
311C2×Dic59—42no—
312C2×Dic59—42no—
313C2×Dic59—48no—
314C2×Dic59#13514yes—
315C2×Dic59C22×D412yes—
316C2×Dic59C22×D412yes—
317C2×Dic59C22×D412yes—
318C4×D59—24no—
319C4×D59—22no—
320C4×D59—22no—
321Dic118—22no—
322Dic118—22no—
323Dic118—42no—
324Dic118—48no—
325Dic118—84no—
326C8×C59—22no—
327C8×C59—22no—
328C59⋊C8—22no—
329C59⋊C8C2×#4114yes—
330C2×#3340—591nomaximal, Sylow
331C22×C59—22no—
332C22×C59—22no—
333C22×C59—22no—
334C22×C59—44no—
335C22×C59—42no—
336C22×C59—42no—
337C22×C59—42no—
338C22×C59—84no—
339C22×C59#54712yes—
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—42no—
357Dic59—42no—
358Dic59—42no—
359Dic59—42no—
360Dic59C2×#13514yes—
361C2×#556—591no—
362C2×#555—591no—
363#3340—5916no—
364C2×#498—591no—
365C2×#485—591no—
366C2×#485—591no—
367C2×#482—591no—
368C2×#482D5911yescharacteristic, complemented
369C2×#477—591no—
370C2×#474—591no—
371C2×#465—591no—
372C2×#465—591no—
373C2×C4×SD16—591no—
374C2×C8×D4—591no—
375C2×#427—591no—
376C2×#427—591no—
377C2×C59—42no—
378C2×C59—82no—
379C2×C59#334014yescomplemented
380C2×C59C2×#54711yescharacteristic
381C2×C59C22×#13511yescharacteristic
382C2×C59C2×#57711yescharacteristic
383D59—42no—
384C22×SD16—591no—
385C23×C8—591no—
386C23×C8—591no—
387#556—598no—
388#556—1184no—
389#555—598no—
390#555—1184no—
391C2×C4⋊Q8—591no—
392C2×C4⋊Q8—591no—
393C2×#126—1181no—
394C2×#126—1181no—
395C2×#124—1181no—
396C2×#124—1181no—
397C2×#124—1181no—
398C2×C22⋊Q8—591no—
399C2×C22⋊Q8—591no—
400C2×#121—591no—
401C2×#121—1181no—
402C2×#121C2×D5911yescharacteristic
403C2×C4×Q8—591no—
404C2×C4×Q8—1181no—
405C2×C4×D4—591no—
406C2×C4×D4—591no—
407C2×#117—591no—
408C2×#117—591no—
409C2×#117—591no—
410C2×#117—1181no—
411C2×#117C2×D5911yescharacteristic
412#498—598no—
413#485—598no—
414#485—598no—
415#482—598no—
416#482C2×D5918yescomplemented
417#477—598no—
418#474—598no—
419#465—598no—
420#465—598no—
421C4×SD16—598no—
422C8×D4—598no—
423#427—598no—
424#427—598no—
425C2×#107—591no—
426C2×#107—591no—
427C2×#107—591no—
428C2×#107C2×D5911yescharacteristic
429C2×#106—591no—
430C2×#106—591no—
431C2×#106—591no—
432C2×#106—591no—
433C2×#106C2×D5911yescharacteristic
434C2×C4⋊C8—591no—
435C2×#103—591no—
436C2×#103—591no—
437C2×#103—591no—
438C2×#102—591no—
439C2×#102C2×D5911yescharacteristic
440C2×#102C2×D5911yescharacteristic
441C2×C22⋊C8—591no—
442C2×C22⋊C8C2×D5911yescharacteristic
443C2×C4×C8—591no—
444C59C2×#334011yescharacteristic, complemented, Sylow
445C22×Q8—591no—
446C22×Q8—1181no—
447C22×Q8—1181no—
448C22×D4—21no—
449C22×D4—591no—
450C22×D4—1181no—
451C22×D4C22×D5911yescharacteristic
452C23×C4—591no—
453C23×C4—1181no—
454C23×C4C22×D5911yescharacteristic
455C2×SD16—594no—
456C2×SD16—1184no—
457C22×C8—591no—
458C22×C8—591no—
459C22×C8—594no—
460C22×C8—594no—
461C22×C8—1184no—
462C22×C8—1184no—
463C22×C8C22×D5911yescharacteristic
464C22×C8C22×D5911yescharacteristic
465C4⋊Q8—594no—
466C4⋊Q8—594no—
467C4⋊Q8—1182no—
468C4⋊Q8—1182no—
469#126—1188no—
470#126—1188no—
471#124—1188no—
472#124—1188no—
473#124—1188no—
474C22⋊Q8—594no—
475C22⋊Q8—594no—
476C22⋊Q8—1182no—
477C22⋊Q8—1182no—
478#121—22no—
479#121—594no—
480#121—1182no—
481#121—1188no—
482#121C22×D5914yes—
483C4×Q8—594no—
484C4×Q8—1188no—
485C4×Q8—1182no—
486C4×D4—594no—
487C4×D4—594no—
488C4×D4—594no—
489C4×D4—1182no—
490#117—22no—
491#117—594no—
492#117—594no—
493#117—594no—
494#117—1188no—
495#117—1182no—
496#117—1182no—
497#117—1182no—
498#117C22×D5914yes—
499C2×C4⋊C4—591no—
500C2×C4⋊C4—591no—
501C2×C4⋊C4—591no—
502C2×C4⋊C4—591no—
503C2×C4⋊C4—1181no—
504C2×C4⋊C4—1181no—
505C2×C4⋊C4—1181no—
506C2×C4⋊C4—1181no—
507C2×C4⋊C4—1181no—
508C2×C4⋊C4C22×D5911yescharacteristic
509C2×C4⋊C4C22×D5911yescharacteristic
510C2×C4⋊C4C22×D5911yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—591no—
514C2×C22⋊C4—591no—
515C2×C22⋊C4—1181no—
516C2×C22⋊C4—1181no—
517C2×C22⋊C4—1181no—
518C2×C22⋊C4—1181no—
519C2×C22⋊C4—1181no—
520C2×C22⋊C4—1181no—
521C2×C22⋊C4—1181no—
522C2×C42—21no—
523C2×C42—591no—
524C2×C42—1181no—
525C2×C42—1181no—
526C2×C42—1181no—
527C2×C42—1181no—
528#107—594no—
529#107—594no—
530#107—594no—
531#107C22×D5914yes—
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#103—594no—
541#102—594no—
542#102C22×D5914yes—
543#102C22×D5914yes—
544C22⋊C8—594no—
545C22⋊C8C22×D5914yes—
546C4×C8—594no—
547C24—21no—
548C24—591no—
549C24D4×D5911yescharacteristic
550C2×Q8—592no—
551C2×Q8—1184no—
552C2×Q8—1184no—
553C2×Q8—1181no—
554C2×Q8—1182no—
555C2×Q8—1182no—
556C2×Q8—4722no—
557C2×Q8—2364no—
558C2×D4—24no—
559C2×D4—21no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—82no—
563C2×D4—594no—
564C2×D4—1184no—
565C2×D4—1184no—
566C2×D4—4722no—
567C2×D4C23×D5912yes—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—591no—
574C22×C4—591no—
575C22×C4—591no—
576C22×C4—592no—
577C22×C4—592no—
578C22×C4—1184no—
579C22×C4—1182no—
580C22×C4—1182no—
581C22×C4—1181no—
582C22×C4—1181no—
583C22×C4—1181no—
584C22×C4—1181no—
585C22×C4—2364no—
586C22×C4D4×D5912yes—
587C22×C4D4×D5911yescharacteristic
588C22×C4C23×D5912yes—
589C22×C4C23×D5911yescharacteristic
590SD16—1188no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—594no—
594C2×C8—592no—
595C2×C8—592no—
596C2×C8—1188no—
597C2×C8—1188no—
598C2×C8—1182no—
599C2×C8C23×D5912yes—
600C2×C8C23×D5912yes—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—594no—
605C4⋊C4—592no—
606C4⋊C4—592no—
607C4⋊C4—592no—
608C4⋊C4—1184no—
609C4⋊C4—1184no—
610C4⋊C4—1184no—
611C4⋊C4—1184no—
612C4⋊C4—1181no—
613C4⋊C4—1181no—
614C4⋊C4—1181no—
615C4⋊C4—1184no—
616C4⋊C4C23×D5912yes—
617C4⋊C4C23×D5912yes—
618C4⋊C4C23×D5912yes—
619C22⋊C4—24no—
620C22⋊C4—24no—
621C22⋊C4—594no—
622C22⋊C4—594no—
623C22⋊C4—1184no—
624C22⋊C4—1184no—
625C22⋊C4—1184no—
626C22⋊C4—1184no—
627C22⋊C4—1184no—
628C22⋊C4—1184no—
629C22⋊C4—1184no—
630C42—24no—
631C42—592no—
632C42—592no—
633C42—1184no—
634C42—1184no—
635C42—1184no—
636C42—1184no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—592no—
645C23—1182no—
646C23—1182no—
647C23—1182no—
648C23C2×D4×D5912yes—
649C23C2×D4×D5911yescharacteristic
650Q8—1182no—
651Q8—1182no—
652Q8—4724no—
653Q8—2368no—
654Q8—2362no—
655D4—22no—
656D4—22no—
657D4—42no—
658D4—84no—
659D4—1188no—
660D4—4724no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—594no—
672C2×C4—592no—
673C2×C4—592no—
674C2×C4—592no—
675C2×C4—1182no—
676C2×C4—1182no—
677C2×C4—1182no—
678C2×C4—1182no—
679C2×C4—1184no—
680C2×C4—1182no—
681C2×C4—1182no—
682C2×C4—1182no—
683C2×C4—1182no—
684C2×C4—2368no—
685C2×C4—2362no—
686C2×C4—2362no—
687C2×C4—2362no—
688C2×C4—2362no—
689C2×C4C2×D4×D5912yes—
690C2×C4C2×D4×D5911yescharacteristic
691C2×C4#41×D5912yes—
692C2×C4#1427377412yes—
693C2×C4C24×D5911yescharacteristic
694C8—22no—
695C8—22no—
696C8—594no—
697C8—1182no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—44no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—84no—
706C22—1182no—
707C22—1182no—
708C22—1182no—
709C22—2364no—
710C22#1683805012yes—
711C22#135×D5912yes—
712C22#1683821212yes—
713C22C22×D4×D5911yescharacteristic
714C4—22no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—594no—
719C4—1182no—
720C4—1182no—
721C4—2362no—
722C4—2362no—
723C4—2362no—
724C4—2362no—
725C4#1683805012yes—
726C4C2×#41×D5911yescharacteristic
727C4C2×#1427377411yescharacteristic
728C2—42no—
729C2—82no—
730C2—2362no—
731C2#2143650714yesdirect product factor
732C2C2×#1683805011yescharacteristic
733C2C2×#135×D5911yescharacteristic
734C2C2×#1683821211yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#482C2
socleC23×C59C22×D4
prime radicalC2×#16838116C2
hypercenterC2×#482D59
hypocenterC59C2×#3340
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#16838120C2semidirect
3. #21436507C2direct (N × H)
4. C2×#16837799C2semidirect
5. C2×#16837746C2semidirect
6. C2×#16837744C2semidirect
7. C2×#16837725C2semidirect
8. C2×#16837696C2semidirect
9. C2×#16837680C2semidirect
10. C2×#16837630C2semidirect
11. C2×#16837629C2semidirect
12. C2×#16837493C2semidirect
13. C2×(C22⋊D59)⋊C8C2semidirect
14. C2×#16837439C2semidirect
15. C2×#16837438C2semidirect
16. C2×C59×#482C2semidirect
21. #16838120C22semidirect
43. #16837799C22semidirect
44. #16837746C22semidirect
45. #16837744C22semidirect
46. #16837725C22semidirect
47. #16837696C22semidirect
48. #16837680C22semidirect
49. #16837630C22semidirect
50. #16837629C22semidirect
51. #16837493C22semidirect
52. (C22⋊D59)⋊C8C22semidirect
53. #16837439C22semidirect
54. #16837438C22semidirect
71. C59×#482C22semidirect
368. C2×#482D59semidirect
379. C2×C59#3340semidirect
416. #482C2×D59semidirect
444. C59C2×#3340semidirect
731. C2#21436507direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381202
C2×#168381162
#214365072
C2×#168377992
C2×#168377462
C2×#168377442
C2×#168377252
C2×#168376962
C2×#168376802
C2×#168376302
C2×#168376292
C2×#168374932
C2×(C22⋊D59)⋊C82
C2×#168374392
C2×#168374382
C2×C59×#4822
C2×#334059