Finite Group Databasebeta

← C2×#21436992 #29469163

Subgroups — C2×#21436992 #29469163

Order 15104.

2082 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838108C211yesmaximal, characteristic, complemented
2C2×#16838067C211yesmaximal, characteristic, complemented
3#21436992C2116yesmaximal, direct product factor
4C2×#16837810C211yesmaximal, characteristic, complemented
5C2×#16837799C211yesmaximal, characteristic, complemented
6C2×#16837705C211yesmaximal, characteristic, complemented
7C2×#16837699C211yesmaximal, characteristic, complemented
8C2×#16837691C211yesmaximal, characteristic, complemented
9C2×#16837691C211yesmaximal, characteristic, complemented
10C2×#16837689C211yesmaximal, characteristic, complemented
11C2×#16837681C211yesmaximal, characteristic, complemented
12C2×#16837530C211yesmaximal, characteristic, complemented
13C2×#16837515C211yesmaximal, characteristic
14C2×#16837513C211yesmaximal, characteristic
15C2×#16837484C211yesmaximal, characteristic
16C2×C59×#501C211yesmaximal, characteristic, complemented
17C22×Q8×D59—21no—
18C22×D472C2211yescharacteristic
19#16838108—24no—
20#16838108C2218yescomplemented
21#16838067—24no—
22#16838067C2218yescomplemented
23C2×#14273726C2211yescharacteristic
24C2×#14273726C2211yescharacteristic
25C2×#14273726C2211yescharacteristic
26C2×#14273718C2211yescharacteristic
27C2×#14273707—21no—
28C2×#14273705—21no—
29C2×#14273705—21no—
30C2×#14273705—21no—
31C2×#14273705—21no—
32C2×#14273703—21no—
33C2×C4×Dic118C2211yescharacteristic
34C2×C4×D236C2211yescharacteristic
35C2×C4×D236C2211yescharacteristic
36C2×#14273689C2211yescharacteristic
37C2×#14273689C2211yescharacteristic
38C2×#14273689C2211yescharacteristic
39C2×#14273689C2211yescharacteristic
40C2×C4⋊C4×D59—21no—
41#16837810C2218yescomplemented
42#16837799C2218yescomplemented
43#16837705C2218yescomplemented
44#16837699C2218yescomplemented
45#16837691C2218yescomplemented
46#16837691C2218yescomplemented
47#16837689C2218yescomplemented
48#16837681C2218yescomplemented
49#16837530C2218yescomplemented
50#16837515C2218yes—
51#16837513C2218yes—
52#16837484C2218yes—
53C2×#14273660C2211yescharacteristic
54C2×#14273659C2211yescharacteristic
55C2×#14273658C2211yescharacteristic
56C2×#14273658C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×C4⋊(C59⋊C8)C2211yescharacteristic
59C2×Dic59⋊C8C2211yescharacteristic
60C2×Dic59⋊C8C2211yescharacteristic
61C2×#14273649C2211yescharacteristic
62C2×#14273649C2211yescharacteristic
63C2×#14273647C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×#14273647C2211yescharacteristic
67C2×#14273637C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C2×C4⋊Q8×C59C2211yescharacteristic
70C2×#125×C59C2211yescharacteristic
71C59×#501C2218yescomplemented
72C2×#107×C59C2211yescharacteristic
73C2×#107×C59C2211yescharacteristic
74C2×#106×C59C2211yescharacteristic
75C2×#106×C59C2211yescharacteristic
76C2×#97×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C22×Dic118—21no—
80C22×Dic118D411yescharacteristic
81C2×Q8×D59—28no—
82C2×Q8×D59—48no—
83C22×D236C2311yescharacteristic
84C22×D236C2311yescharacteristic
85C22×C4×D59—21no—
86C22×C4×D59—21no—
87C22×C4×D59—21no—
88C22×C4×D59—21no—
89C22×C4×D59—21no—
90C22×C4×D59—21no—
91C2×D472Q818yescomplemented
92C2×D472C2314yes—
93C22×C59⋊C8C2311yescharacteristic
94C22×C59⋊C8C2311yescharacteristic
95#14273726—22no—
96#14273726—22no—
97#14273726—22no—
98#14273726C2314yes—
99#14273726C2314yes—
100#14273726C2314yes—
101#14273718—22no—
102#14273718C2314yes—
103#14273707—28no—
104#14273705—28no—
105#14273705—28no—
106#14273705—28no—
107#14273705—28no—
108#14273703—28no—
109C4×Dic118D414yes—
110C4×Dic118C2314yes—
111C4×D236—22no—
112C4×D236—22no—
113C4×D236C2314yes—
114C4×D236C2314yes—
115#14273689—22no—
116#14273689—22no—
117#14273689—22no—
118#14273689—22no—
119#14273689C2314yes—
120#14273689C2314yes—
121#14273689C2314yes—
122#14273689C2314yes—
123C2×C4⋊Dic59—21no—
124C2×C4⋊Dic59D411yescharacteristic
125C2×C4⋊Dic59C2311yescharacteristic
126C2×C4⋊Dic59C2311yescharacteristic
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4D411yescharacteristic
132C2×Dic59⋊C4D411yescharacteristic
133C4⋊C4×D59—28no—
134C2×(C2×D59)⋊C4—21no—
135C2×(C2×D59)⋊C4—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×C4×Dic59C2311yescharacteristic
141C2×C4×Dic59C2311yescharacteristic
142#14273660C2314yes—
143#14273659C2314yes—
144#14273658C2314yes—
145#14273658C2314yes—
146#14273658C2314yes—
147C4⋊(C59⋊C8)C2314yes—
148Dic59⋊C8C2314yes—
149Dic59⋊C8C2314yes—
150#14273649C2314yes—
151#14273649C2314yes—
152#14273647C2314yes—
153#14273647C2314yes—
154#14273647C2314yes—
155#14273647C2314yes—
156#14273637C2314yes—
157C8×Dic59C2314yes—
158C22×Q8×C59—21no—
159C22×C8×C59C2311yescharacteristic
160C22×C8×C59C2311yescharacteristic
161C4⋊Q8×C59—22no—
162C4⋊Q8×C59C2314yes—
163#125×C59—22no—
164#125×C59C2314yes—
165C2×C4⋊C4×C59—21no—
166C2×C4⋊C4×C59—21no—
167C2×C4⋊C4×C59—21no—
168C2×C4⋊C4×C59C2311yescharacteristic
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C42×C59C2311yescharacteristic
173#107×C59C2314yes—
174#107×C59C2314yes—
175#106×C59C2314yes—
176#106×C59C2314yes—
177#97×C59C2314yes—
178C23×D59—21no—
179C23×D59—21no—
180C2×Q8×C59—24no—
181C2×Q8×C59—44no—
182C22×C4×C59—21no—
183C22×C4×C59—21no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59C2×D411yescharacteristic
187C22×C4×C59C2×D411yescharacteristic
188C22×C4×C59C2411yescharacteristic
189C22×Dic59—21no—
190C22×Dic59—21no—
191C22×Dic59C2×D411yescharacteristic
192C22×Dic59C2×D411yescharacteristic
193C22×Dic59C2×D411yescharacteristic
194C22×Dic59C2×D411yescharacteristic
195Q8×D59—432no—
196C2×D236—21no—
197C2×D236—21no—
198C2×D236—22no—
199C2×D236—22no—
200C2×D236C2×Q814yes—
201C2×D236C2×Q814yescomplemented
202C2×D236C2412yes—
203C2×D236C2412yes—
204C2×C4×D59—24no—
205C2×C4×D59—24no—
206C2×C4×D59—24no—
207C2×C4×D59—24no—
208C2×C4×D59—24no—
209C2×C4×D59—24no—
210C2×C4×D59—44no—
211C2×C4×D59—44no—
212C2×C4×D59—44no—
213C2×C4×D59—44no—
214C2×C4×D59—82no—
215C2×C4×D59—82no—
216C2×Dic118—24no—
217C2×Dic118—24no—
218C2×Dic118—24no—
219C2×Dic118—24no—
220C2×Dic118—44no—
221C2×Dic118—44no—
222C2×Dic118—82no—
223C2×Dic118C2×D414yes—
224C2×C8×C59—22no—
225C2×C8×C59C2×Q814yescomplemented
226C2×C8×C59C2412yes—
227C2×C8×C59C2412yes—
228C4⋊C4×C59—24no—
229C4⋊C4×C59—24no—
230C4⋊C4×C59—24no—
231C4⋊C4×C59—21no—
232C4⋊C4×C59—21no—
233C4⋊C4×C59—21no—
234C4⋊C4×C59—21no—
235C4⋊C4×C59C2412yes—
236C4⋊C4×C59C2412yes—
237C4⋊C4×C59C2412yes—
238C4⋊C4×C59C2412yes—
239C42×C59C2×D412yes—
240C42×C59C2412yes—
241(C2×D59)⋊C4—24no—
242(C2×D59)⋊C4—24no—
243(C2×D59)⋊C4—24no—
244(C2×D59)⋊C4—24no—
245(C2×D59)⋊C4—24no—
246(C2×D59)⋊C4—24no—
247C4⋊Dic59—21no—
248C4⋊Dic59—21no—
249C4⋊Dic59—24no—
250C4⋊Dic59C2×D414yes—
251C4⋊Dic59C2412yes—
252C4⋊Dic59C2412yes—
253Dic59⋊C4—24no—
254Dic59⋊C4—24no—
255Dic59⋊C4—24no—
256Dic59⋊C4—24no—
257Dic59⋊C4C2×D414yes—
258Dic59⋊C4C2×D414yes—
259C4×Dic59C2×D412yes—
260C4×Dic59C2×D412yes—
261C4×Dic59C2412yes—
262C4×Dic59C2412yes—
263C2×C59⋊C8—22no—
264C2×C59⋊C8—22no—
265C2×C59⋊C8C2412yes—
266C2×C59⋊C8C2412yes—
267D472C2×Q8116yescomplemented
268C23×C59C22×D411yescharacteristic
269C22×D59—24no—
270C22×D59—24no—
271C22×D59—22no—
272C22×D59—22no—
273C22×D59—42no—
274C22×D59—42no—
275C22×D59—42no—
276C22×D59—42no—
277Q8×C59—48no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—42no—
285C2×C4×C59—42no—
286C2×C4×C59—42no—
287C2×C4×C59—42no—
288C2×C4×C59C22×D412yes—
289C2×C4×C59C22×D412yes—
290C2×C4×C59C22×D411yescharacteristic
291C2×C4×C59C22×Q812yes—
292C2×C4×C592−1+412yes—
293C2×C4×C59C2511yescharacteristic
294C2×Dic59—22no—
295C2×Dic59—22no—
296C2×Dic59—22no—
297C2×Dic59—22no—
298C2×Dic59—22no—
299C2×Dic59—42no—
300C2×Dic59—42no—
301C2×Dic59AGL(1,ℤ/8)14yes—
302C2×Dic59C22×D412yes—
303C2×Dic59C22×D412yes—
304C2×Dic59C22×D412yes—
305C2×Dic59C22×D412yes—
306D236—24no—
307D236—24no—
308D236—22no—
309D236—22no—
310D236C22×Q814yes—
311D236C22×Q814yescomplemented
312C4×D59—48no—
313C4×D59—48no—
314C4×D59—48no—
315C4×D59—48no—
316C4×D59—84no—
317C4×D59—84no—
318Dic118—28no—
319Dic118—48no—
320Dic118—48no—
321Dic118—84no—
322C8×C59—22no—
323C8×C59C22×Q814yescomplemented
324C59⋊C8—22no—
325C59⋊C8—22no—
326C2×#3384—591nomaximal, Sylow
327C22×C59D4×Q812yes—
328C22×C59C2×AGL(1,ℤ/8)12yes—
329C22×C59#57712yes—
330C22×C59C23×D411yescharacteristic
331C2×D59—24no—
332C2×D59—24no—
333C2×D59—48no—
334C2×D59—48no—
335C2×D59—42no—
336C2×D59—42no—
337C2×D59—42no—
338C2×D59—42no—
339C4×C59—22no—
340C4×C59—22no—
341C4×C59—42no—
342C4×C59—42no—
343C4×C59—42no—
344C4×C59—42no—
345C4×C59D4×Q812yes—
346C4×C59C23×Q811yescharacteristic
347C4×C59C2×2−1+411yescharacteristic
348Dic59—22no—
349Dic59—22no—
350Dic59—22no—
351Dic59—42no—
352Dic59—42no—
353Dic59C2×AGL(1,ℤ/8)14yes—
354C2×#554—591no—
355C2×D4×Q8—591no—
356#3384—5916no—
357C2×#501—591no—
358C2×#501D5911yescharacteristic, complemented
359C2×#498—591no—
360C2×#478—591no—
361C2×#478—591no—
362C2×#476—591no—
363C2×#476—591no—
364C2×#476—591no—
365C2×#474—591no—
366C2×#446—591no—
367C2×#442—591no—
368C2×#442—591no—
369C2×C4×D8—591no—
370C2×C59#338414yescomplemented
371C2×C59C2×D4×Q811yescharacteristic
372C2×C59C22×AGL(1,ℤ/8)11yescharacteristic
373C2×C59C2×#57711yescharacteristic
374D59—44no—
375D59—44no—
376C23×Q8—1181no—
377C22×D8—591no—
378#554—598no—
379#554—1184no—
380D4×Q8—598no—
381D4×Q8—1184no—
382C2×C4⋊Q8—591no—
383C2×C4⋊Q8—591no—
384C2×C4⋊Q8—591no—
385C2×C4⋊Q8C2×D5911yescharacteristic
386C2×#125—591no—
387C2×#125C2×D5911yescharacteristic
388C2×C22⋊Q8—1181no—
389C2×C22⋊Q8—1181no—
390C2×C22⋊Q8—1181no—
391C2×C22⋊Q8—1181no—
392C2×C22⋊Q8—1181no—
393C2×C22⋊Q8—1181no—
394C2×C4×Q8—591no—
395C2×C4×D4—591no—
396C2×C4×D4—591no—
397C2×C4×D4—591no—
398C2×C4×D4—591no—
399C2×C4×D4—591no—
400C2×C4×D4—591no—
401C22×C4⋊C4—1181no—
402#501—598no—
403#501C2×D5918yescomplemented
404#498—598no—
405#478—598no—
406#478—598no—
407#476—598no—
408#476—598no—
409#476—598no—
410#474—598no—
411#446—598no—
412#442—598no—
413#442—598no—
414C4×D8—598no—
415C2×#107—591no—
416C2×#107C2×D5911yescharacteristic
417C2×#107C2×D5911yescharacteristic
418C2×#106—591no—
419C2×#106—591no—
420C2×#106—591no—
421C2×#106—591no—
422C2×#106C2×D5911yescharacteristic
423C2×#106C2×D5911yescharacteristic
424C2×C4⋊C8—591no—
425C2×C4⋊C8—591no—
426C2×C4⋊C8—591no—
427C2×#102—591no—
428C2×#102—591no—
429C2×#102—591no—
430C2×#102—591no—
431C2×#102—591no—
432C2×#102—591no—
433C2×#97—591no—
434C2×#97C2×D5911yescharacteristic
435C2×C4×C8—591no—
436C59C2×#338411yescharacteristic, complemented, Sylow
437C22×Q8—21no—
438C22×Q8—591no—
439C22×Q8—1181no—
440C22×Q8—1181no—
441C22×Q8—1181no—
442C22×Q8—1188no—
443C22×Q8—2368no—
444C22×D4—591no—
445C22×D4—591no—
446C23×C4—1181no—
447C23×C4—1181no—
448C23×C4—1181no—
449C23×C4—1181no—
450C23×C4—1181no—
451C23×C4—1181no—
452C2×D8—598no—
453C2×D8—594no—
454C22×C8—591no—
455C22×C8—591no—
456C22×C8C22×D5911yescharacteristic
457C22×C8C22×D5911yescharacteristic
458C4⋊Q8—22no—
459C4⋊Q8—594no—
460C4⋊Q8—594no—
461C4⋊Q8—594no—
462C4⋊Q8—1182no—
463C4⋊Q8—1182no—
464C4⋊Q8—1182no—
465C4⋊Q8C22×D5914yes—
466#125—22no—
467#125—594no—
468#125—1182no—
469#125C22×D5914yes—
470C22⋊Q8—1188no—
471C22⋊Q8—1188no—
472C22⋊Q8—1188no—
473C22⋊Q8—1188no—
474C22⋊Q8—1188no—
475C22⋊Q8—1188no—
476C4×Q8—594no—
477C4×Q8—594no—
478C4×D4—594no—
479C4×D4—594no—
480C4×D4—594no—
481C4×D4—594no—
482C4×D4—594no—
483C4×D4—594no—
484C4×D4—1182no—
485C4×D4—1182no—
486C4×D4—1182no—
487C4×D4—1182no—
488C4×D4—1182no—
489C4×D4—1182no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—591no—
494C2×C4⋊C4—591no—
495C2×C4⋊C4—591no—
496C2×C4⋊C4—591no—
497C2×C4⋊C4—591no—
498C2×C4⋊C4—1188no—
499C2×C4⋊C4—1181no—
500C2×C4⋊C4—1181no—
501C2×C4⋊C4—1181no—
502C2×C4⋊C4—1181no—
503C2×C4⋊C4—1181no—
504C2×C4⋊C4C22×D5911yescharacteristic
505C2×C4⋊C4C22×D5911yescharacteristic
506C2×C4⋊C4C22×D5911yescharacteristic
507C2×C4⋊C4C22×D5911yescharacteristic
508C2×C22⋊C4—1181no—
509C2×C22⋊C4—1181no—
510C2×C22⋊C4—1181no—
511C2×C22⋊C4—1181no—
512C2×C22⋊C4—1181no—
513C2×C22⋊C4—1181no—
514C2×C42—591no—
515C2×C42—591no—
516C2×C42C22×D5911yescharacteristic
517#107—594no—
518#107C22×D5914yes—
519#107C22×D5914yes—
520#106—594no—
521#106—594no—
522#106—594no—
523#106—594no—
524#106C22×D5914yes—
525#106C22×D5914yes—
526C4⋊C8—594no—
527C4⋊C8—594no—
528C4⋊C8—594no—
529#102—594no—
530#102—594no—
531#102—594no—
532#102—594no—
533#102—594no—
534#102—594no—
535#97—594no—
536#97C22×D5914yes—
537C4×C8—594no—
538C24—1181no—
539C24—1181no—
540C2×Q8—24no—
541C2×Q8—44no—
542C2×Q8—594no—
543C2×Q8—1184no—
544C2×Q8—1184no—
545C2×Q8—1184no—
546C2×Q8—1184no—
547C2×Q8—4722no—
548C2×Q8—2364no—
549C2×Q8—2364no—
550C2×Q8—23632no—
551C2×D4—594no—
552C2×D4—594no—
553C2×D4—592no—
554C2×D4—592no—
555C2×D4—1181no—
556C2×D4—1181no—
557C2×D4—1182no—
558C2×D4—1182no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—591no—
564C22×C4—591no—
565C22×C4—591no—
566C22×C4—591no—
567C22×C4—1184no—
568C22×C4—1184no—
569C22×C4—1184no—
570C22×C4—1184no—
571C22×C4—1181no—
572C22×C4—1181no—
573C22×C4—1184no—
574C22×C4—1184no—
575C22×C4—4722no—
576C22×C4—4722no—
577C22×C4—2364no—
578C22×C4—2364no—
579C22×C4—2364no—
580C22×C4—2364no—
581C22×C4D4×D5911yescharacteristic
582C22×C4D4×D5911yescharacteristic
583C22×C4C23×D5911yescharacteristic
584D8—5916no—
585C2×C8—22no—
586C2×C8—592no—
587C2×C8—592no—
588C2×C8—1182no—
589C2×C8—1182no—
590C2×C8Q8×D5914yescomplemented
591C2×C8C23×D5912yes—
592C2×C8C23×D5912yes—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—594no—
601C4⋊C4—594no—
602C4⋊C4—594no—
603C4⋊C4—592no—
604C4⋊C4—592no—
605C4⋊C4—1184no—
606C4⋊C4—1184no—
607C4⋊C4—1184no—
608C4⋊C4—1184no—
609C4⋊C4—1184no—
610C4⋊C4—1181no—
611C4⋊C4—1181no—
612C4⋊C4C23×D5912yes—
613C4⋊C4C23×D5912yes—
614C4⋊C4C23×D5912yes—
615C4⋊C4C23×D5912yes—
616C22⋊C4—1184no—
617C22⋊C4—1184no—
618C22⋊C4—1184no—
619C22⋊C4—1184no—
620C22⋊C4—1184no—
621C22⋊C4—1184no—
622C42—592no—
623C42—592no—
624C42—592no—
625C42—592no—
626C42D4×D5912yes—
627C42C23×D5912yes—
628C23—1182no—
629C23—1182no—
630C23—1184no—
631C23—1184no—
632C23—2362no—
633C23—2362no—
634C23—2362no—
635C23—2362no—
636C23C2×D4×D5911yescharacteristic
637Q8—48no—
638Q8—1188no—
639Q8—4724no—
640Q8—2368no—
641Q8—2368no—
642D4—594no—
643D4—594no—
644D4—1182no—
645D4—1182no—
646D4—1184no—
647D4—1184no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—594no—
659C2×C4—592no—
660C2×C4—592no—
661C2×C4—592no—
662C2×C4—592no—
663C2×C4—1182no—
664C2×C4—1182no—
665C2×C4—1182no—
666C2×C4—1182no—
667C2×C4—1182no—
668C2×C4—4724no—
669C2×C4—4724no—
670C2×C4—2368no—
671C2×C4—2368no—
672C2×C4—2368no—
673C2×C4—2368no—
674C2×C4—2362no—
675C2×C4—2362no—
676C2×C4C2×D4×D5912yes—
677C2×C4C2×D4×D5912yes—
678C2×C4C2×D4×D5911yescharacteristic
679C2×C4C2×Q8×D5912yes—
680C2×C4#1427377512yes—
681C2×C4C24×D5911yescharacteristic
682C8—22no—
683C8—1182no—
684C8—1182no—
685C8C2×Q8×D5914yescomplemented
686C22—1184no—
687C22—1184no—
688C22—2368no—
689C22—2368no—
690C22—2362no—
691C22—2362no—
692C22—2362no—
693C22—2362no—
694C22#1683806712yes—
695C22AGL(1,ℤ/8)×D5912yes—
696C22#1683821112yes—
697C22C22×D4×D5911yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—594no—
705C4—1182no—
706C4—1182no—
707C4—1182no—
708C4—2362no—
709C4—2362no—
710C4#1683806712yes—
711C4C22×Q8×D5911yescharacteristic
712C4C2×#1427377511yescharacteristic
713C2—2364no—
714C2—2364no—
715C2#2143699214yesdirect product factor
716C2C2×#1683806711yescharacteristic
717C2C2×AGL(1,ℤ/8)×D5911yescharacteristic
718C2C2×#1683821111yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#501C2
socleC23×C59C22×D4
prime radicalC22×D472C22
hypercenterC2×#501D59
hypocenterC59C2×#3384
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#16838108C2semidirect
2. C2×#16838067C2semidirect
3. #21436992C2direct (N × H)
4. C2×#16837810C2semidirect
5. C2×#16837799C2semidirect
6. C2×#16837705C2semidirect
7. C2×#16837699C2semidirect
8. C2×#16837691C2semidirect
9. C2×#16837691C2semidirect
10. C2×#16837689C2semidirect
11. C2×#16837681C2semidirect
12. C2×#16837530C2semidirect
16. C2×C59×#501C2semidirect
20. #16838108C22semidirect
22. #16838067C22semidirect
41. #16837810C22semidirect
42. #16837799C22semidirect
43. #16837705C22semidirect
44. #16837699C22semidirect
45. #16837691C22semidirect
46. #16837691C22semidirect
47. #16837689C22semidirect
48. #16837681C22semidirect
49. #16837530C22semidirect
71. C59×#501C22semidirect
91. C2×D472Q8semidirect
201. C2×D236C2×Q8semidirect
225. C2×C8×C59C2×Q8semidirect
267. D472C2×Q8semidirect
311. D236C22×Q8semidirect
323. C8×C59C22×Q8semidirect
358. C2×#501D59semidirect
370. C2×C59#3384semidirect
403. #501C2×D59semidirect
436. C59C2×#3384semidirect
590. C2×C8Q8×D59semidirect
685. C8C2×Q8×D59semidirect
715. C2#21436992direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381082
C2×#168380672
#214369922
C2×#168378102
C2×#168377992
C2×#168377052
C2×#168376992
C2×#168376912
C2×#168376892
C2×#168376812
C2×#168375302
C2×#168375152
C2×#168375132
C2×#168374842
C2×C59×#5012
C2×#338459