Finite Group Databasebeta

← C2×#21434761 #29458554

Subgroups — C2×#21434761 #29458554

Order 15104.

1906 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838021C211yesmaximal, characteristic
2C2×#16838013C211yesmaximal, characteristic, complemented
3#21434761C2116yesmaximal, direct product factor
4C2×#16837811C211yesmaximal, characteristic, complemented
5C2×#16837756C211yesmaximal, characteristic, complemented
6C2×#16837752C211yesmaximal, characteristic, complemented
7C2×#16837657C211yesmaximal, characteristic, complemented
8C2×#16837645C211yesmaximal, characteristic
9C2×#16837640C211yesmaximal, characteristic, complemented
10C2×#16837628C211yesmaximal, characteristic
11C2×#16837509C211yesmaximal, characteristic, complemented
12C2×#16837503C211yesmaximal, characteristic, complemented
13C2×Q16×Dic59C211yesmaximal, characteristic, complemented
14C2×SD16×Dic59C211yesmaximal, characteristic, complemented
15C2×#16837359C211yesmaximal, characteristic, complemented
16C2×C59×#497C211yesmaximal, characteristic, complemented
17C22×#11745659C2211yescharacteristic
18C22×C8×D59C2211yescharacteristic
19#16838021—24no—
20#16838021C2218yes—
21#16838013—24no—
22#16838013C2218yescomplemented
23C2×#14273727C2211yescharacteristic
24C2×#14273722—21no—
25C2×#14273722—21no—
26C2×#14273720—21no—
27C2×#14273719C2211yescharacteristic
28C2×#14273717—21no—
29C2×#14273717—21no—
30C2×#14273713—21no—
31C2×#14273711—21no—
32C2×#14273704—21no—
33C2×#14273703C2211yescharacteristic
34C2×#14273703C2211yescharacteristic
35C2×#14273703C2211yescharacteristic
36C2×#14273698C2211yescharacteristic
37C2×Q8×Dic59C2211yescharacteristic
38C2×Q8×Dic59C2211yescharacteristic
39C2×Q8×Dic59C2211yescharacteristic
40C2×D4×Dic59C2211yescharacteristic
41C2×#14273684C2211yescharacteristic
42#16837811C2218yescomplemented
43#16837756C2218yescomplemented
44#16837752C2218yescomplemented
45#16837657C2218yescomplemented
46#16837645C2218yes—
47#16837640C2218yescomplemented
48#16837628C2218yes—
49#16837509C2218yescomplemented
50#16837503C2218yescomplemented
51Q16×Dic59C2218yescomplemented
52SD16×Dic59C2218yescomplemented
53C2×#14273661C2211yescharacteristic
54C2×#14273661C2211yescharacteristic
55C2×#14273659C2211yescharacteristic
56C2×#14273659C2211yescharacteristic
57C2×#14273651C2211yescharacteristic
58C2×#14273651C2211yescharacteristic
59C2×#14273651C2211yescharacteristic
60C2×#14273651C2211yescharacteristic
61C2×#14273651C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273648C2211yescharacteristic
64C2×#14273648C2211yescharacteristic
65#16837359C2218yescomplemented
66C2×#14273637C2211yescharacteristic
67C2×C4×C59⋊C8C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C22×Q16×C59C2211yescharacteristic
70C22×Q16×C59C2211yescharacteristic
71C22×SD16×C59C2211yescharacteristic
72C22×SD16×C59C2211yescharacteristic
73C2×C4⋊Q8×C59C2211yescharacteristic
74C2×#124×C59C2211yescharacteristic
75C59×#497C2218yescomplemented
76C2×#97×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×C22⋊D59—21no—
79C23×Dic59—21no—
80C22×C4×D59C2311yescharacteristic
81C2×#11745659—24no—
82C2×#11745659C2314yes—
83C22×C59⋊C8C2311yescharacteristic
84C22×C59⋊C8C2311yescharacteristic
85C2×C8×D59—24no—
86C2×C8×D59C2314yes—
87#14273727—22no—
88#14273727C2314yes—
89#14273722—28no—
90#14273722—28no—
91#14273720—28no—
92#14273719—22no—
93#14273719C2314yes—
94#14273717—28no—
95#14273717—28no—
96#14273713—28no—
97#14273711—28no—
98#14273704—28no—
99#14273703—22no—
100#14273703—22no—
101#14273703—22no—
102#14273703C2314yes—
103#14273703C2314yes—
104#14273703C2314yes—
105#14273698—22no—
106#14273698C2314yes—
107Q8×Dic59—22no—
108Q8×Dic59—22no—
109Q8×Dic59—22no—
110Q8×Dic59C2314yes—
111Q8×Dic59C2314yes—
112Q8×Dic59C2314yes—
113D4×Dic59—22no—
114D4×Dic59C2314yes—
115#14273684D414yes—
116#14273684C2314yes—
117C2×C4⋊Dic59—21no—
118C2×C4⋊Dic59—21no—
119C2×C4⋊Dic59—21no—
120C2×C4⋊Dic59—21no—
121C2×C4⋊Dic59C2311yescharacteristic
122C2×C4⋊Dic59C2311yescharacteristic
123C2×C4⋊Dic59C2311yescharacteristic
124C2×C4⋊Dic59C2311yescharacteristic
125C2×Dic59⋊C4—21no—
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4D411yescharacteristic
131C2×Dic59⋊C4D411yescharacteristic
132C2×C22⋊Dic59—21no—
133C2×C22⋊Dic59—21no—
134C2×(C2×D59)⋊C4—21no—
135C2×(C2×D59)⋊C4—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4D411yescharacteristic
138C2×(C2×D59)⋊C4D411yescharacteristic
139C2×C4×Dic59—21no—
140C2×C4×Dic59—21no—
141C2×C4×Dic59—21no—
142C2×C4×Dic59C2311yescharacteristic
143#14273661C2314yes—
144#14273661C2314yes—
145#14273659C2314yes—
146#14273659C2314yes—
147#14273651C2314yes—
148#14273651C2314yes—
149#14273651C2314yes—
150#14273651C2314yes—
151#14273651C2314yes—
152#14273651C2314yes—
153#14273648C2314yes—
154#14273648C2314yes—
155#14273637C2314yes—
156C4×C59⋊C8C2314yes—
157C8×Dic59C2314yes—
158C22×Q8×C59C2311yescharacteristic
159C22×Q8×C59C2311yescharacteristic
160C22×Q8×C59C2311yescharacteristic
161C22×D4×C59C2311yescharacteristic
162C2×Q16×C59—24no—
163C2×Q16×C59—24no—
164C2×Q16×C59C2314yes—
165C2×Q16×C59C2314yes—
166C2×SD16×C59—24no—
167C2×SD16×C59—24no—
168C2×SD16×C59C2314yes—
169C2×SD16×C59C2314yes—
170C22×C8×C59C2311yescharacteristic
171C22×C8×C59C2311yescharacteristic
172C4⋊Q8×C59—22no—
173C4⋊Q8×C59C2314yes—
174#124×C59—22no—
175#124×C59C2314yes—
176C2×C4⋊C4×C59—21no—
177C2×C4⋊C4×C59—21no—
178C2×C22⋊C4×C59—21no—
179C2×C22⋊C4×C59—21no—
180C2×C42×C59C2311yescharacteristic
181#97×C59C2314yes—
182C24×C59—21no—
183C23×D59C2×D411yescharacteristic
184C2×Q8×C59—21no—
185C2×Q8×C59—21no—
186C2×Q8×C59—21no—
187C2×Q8×C59—22no—
188C2×Q8×C59—22no—
189C2×Q8×C59—22no—
190C2×Q8×C59—22no—
191C2×Q8×C59—22no—
192C2×Q8×C59—22no—
193C2×Q8×C59C2412yes—
194C2×Q8×C59C2412yes—
195C2×Q8×C59C2412yes—
196C2×D4×C59—21no—
197C2×D4×C59—22no—
198C2×D4×C59—22no—
199C2×D4×C59C2412yes—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59C2×D411yescharacteristic
204C22×C4×C59C2×D411yescharacteristic
205C22×C4×C59C2411yescharacteristic
206C2×C22⋊D59—24no—
207C2×C22⋊D59—82no—
208C22×Dic59—21no—
209C22×Dic59—21no—
210C22×Dic59—21no—
211C22×Dic59—21no—
212C22×Dic59—24no—
213C22×Dic59—82no—
214C22×Dic59C2×D411yescharacteristic
215C22×Dic59C2×D411yescharacteristic
216C22×Dic59C2×D411yescharacteristic
217C2×C4×D59—22no—
218C2×C4×D59—22no—
219C2×C4×D59C2×D412yes—
220C2×C4×D59C2412yes—
221C2×Dic118—24no—
222C2×Dic118—82no—
223Q16×C59—28no—
224Q16×C59—28no—
225SD16×C59—28no—
226SD16×C59—28no—
227C2×C8×C59#4114yes—
228C2×C8×C59#4114yes—
229C2×C8×C59C2412yes—
230C2×C8×C59C2412yes—
231C4⋊C4×C59—24no—
232C4⋊C4×C59—24no—
233C22⋊C4×C59—24no—
234C22⋊C4×C59—24no—
235C42×C59C2×D412yes—
236C42×C59C2412yes—
237C22⋊Dic59—24no—
238C22⋊Dic59—24no—
239(C2×D59)⋊C4—24no—
240(C2×D59)⋊C4—24no—
241(C2×D59)⋊C4—24no—
242(C2×D59)⋊C4C2×D414yes—
243(C2×D59)⋊C4C2×D414yes—
244C4⋊Dic59—24no—
245C4⋊Dic59—21no—
246C4⋊Dic59—21no—
247C4⋊Dic59—21no—
248C4⋊Dic59—21no—
249C4⋊Dic59—24no—
250C4⋊Dic59—24no—
251C4⋊Dic59—24no—
252C4⋊Dic59C2412yes—
253C4⋊Dic59C2412yes—
254C4⋊Dic59C2412yes—
255C4⋊Dic59C2412yes—
256Dic59⋊C4—24no—
257Dic59⋊C4—24no—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261Dic59⋊C4C2×D414yes—
262Dic59⋊C4C2×D414yes—
263C4×Dic59—24no—
264C4×Dic59—24no—
265C4×Dic59—24no—
266C4×Dic59C2×D412yes—
267C4×Dic59C2412yes—
268C2×C59⋊C8—22no—
269C2×C59⋊C8—22no—
270C2×C59⋊C8C2412yes—
271C2×C59⋊C8C2412yes—
272#11745659—28no—
273C8×D59—28no—
274C23×C59—22no—
275C23×C59—42no—
276C23×C59—42no—
277C23×C59—42no—
278C23×C59C22×D411yescharacteristic
279C22×D59—22no—
280C22×D59—22no—
281C22×D59—22no—
282C22×D59C22×D412yes—
283Q8×C59—22no—
284Q8×C59—22no—
285Q8×C59—22no—
286Q8×C59—22no—
287Q8×C59—22no—
288Q8×C59—22no—
289Q8×C59—42no—
290Q8×C59—42no—
291Q8×C59—42no—
292D4×C59—22no—
293D4×C59—22no—
294D4×C59—42no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—42no—
301C2×C4×C59—42no—
302C2×C4×C59—42no—
303C2×C4×C59C22×D412yes—
304C2×C4×C59C22×D412yes—
305C2×C4×C59C22×D411yescharacteristic
306C2×C4×C59C2×#4112yes—
307C2×C4×C59C2×#4112yes—
308C2×C4×C59C2511yescharacteristic
309C22⋊D59—84no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—42no—
318C2×Dic59—42no—
319C2×Dic59—42no—
320C2×Dic59—42no—
321C2×Dic59—84no—
322C2×Dic59C22×D412yes—
323C2×Dic59C22×D412yes—
324C2×Dic59C22×D412yes—
325C4×D59—24no—
326C4×D59—22no—
327C4×D59—22no—
328Dic118—84no—
329C8×C59C2×#4114yes—
330C8×C59C2×#4114yes—
331C59⋊C8—22no—
332C59⋊C8—22no—
333C2×#3178—591nomaximal, Sylow
334C22×C59—42no—
335C22×C59—42no—
336C22×C59—42no—
337C22×C59—84no—
338C22×C59#53212yes—
339C22×C59#57712yes—
340C22×C59#57812yes—
341C22×C59C23×D411yescharacteristic
342C2×D59—22no—
343C2×D59—22no—
344C2×D59—22no—
345C2×D59—44no—
346C4×C59—22no—
347C4×C59—22no—
348C4×C59—42no—
349C4×C59—42no—
350C4×C59—42no—
351C4×C59#53212yes—
352C4×C59C22×#4111yescharacteristic
353C4×C59C22×#4111yescharacteristic
354Dic59—22no—
355Dic59—22no—
356Dic59—22no—
357Dic59—42no—
358Dic59—42no—
359Dic59—42no—
360Dic59—42no—
361C2×#542—591no—
362C2×#541—591no—
363#3178—5916no—
364C2×#501—591no—
365C2×#497D5911yescharacteristic, complemented
366C2×#488—591no—
367C2×#487—591no—
368C2×#470—591no—
369C2×#468—591no—
370C2×#467—591no—
371C2×#465—591no—
372C2×#441—591no—
373C2×#440—591no—
374C2×C4×Q16—591no—
375C2×C4×SD16—591no—
376C2×#405—591no—
377C2×C59—82no—
378C2×C59#317814yescomplemented
379C2×C59C2×#53211yescharacteristic
380C2×C59C2×#57711yescharacteristic
381C2×C59C2×#57811yescharacteristic
382D59—42no—
383C22×Q16C2×D5911yescharacteristic
384C22×Q16C2×D5911yescharacteristic
385C22×SD16C2×D5911yescharacteristic
386C22×SD16C2×D5911yescharacteristic
387C22×M16—591no—
388C23×C8—591no—
389#542—598no—
390#542—1184no—
391#541—598no—
392#541—1184no—
393C2×C4⋊Q8—591no—
394C2×C4⋊Q8C2×D5911yescharacteristic
395C2×#126—1181no—
396C2×#126—1181no—
397C2×#126—1181no—
398C2×#125—591no—
399C2×#125—1181no—
400C2×#125—1181no—
401C2×#124—1181no—
402C2×#124C2×D5911yescharacteristic
403C2×#123—1181no—
404C2×C22⋊Q8—591no—
405C2×C22⋊Q8—591no—
406C2×C22⋊Q8—591no—
407C2×C22⋊Q8—1181no—
408C2×#121—591no—
409C2×C4×Q8—591no—
410C2×C4×Q8—591no—
411C2×C4×Q8—591no—
412C2×C4×D4—591no—
413C2×#117—591no—
414#501—598no—
415#497C2×D5918yescomplemented
416#488—598no—
417#487—598no—
418#470—598no—
419#468—598no—
420#467—598no—
421#465—598no—
422#441—598no—
423#440—598no—
424C4×Q16—598no—
425C4×SD16—598no—
426C2×#107—591no—
427C2×#107—591no—
428C2×#106—591no—
429C2×#106—591no—
430C2×#103—591no—
431C2×#103—591no—
432C2×#103—591no—
433C2×#103—591no—
434C2×#103—591no—
435C2×#103—591no—
436C2×#102—591no—
437C2×#102—591no—
438#405—598no—
439C2×#97—591no—
440C2×#97C2×D5911yescharacteristic
441C2×C4×C8—591no—
442C2×C4×C8—591no—
443C59C2×#317811yescharacteristic, complemented, Sylow
444C22×Q8—1181no—
445C22×Q8C22×D5911yescharacteristic
446C22×Q8C22×D5911yescharacteristic
447C22×Q8C22×D5911yescharacteristic
448C22×D4—1181no—
449C22×D4C22×D5911yescharacteristic
450C23×C4—591no—
451C23×C4—1181no—
452C2×Q16—24no—
453C2×Q16—24no—
454C2×Q16C22×D5914yes—
455C2×Q16C22×D5914yes—
456C2×SD16—24no—
457C2×SD16—24no—
458C2×SD16C22×D5914yes—
459C2×SD16C22×D5914yes—
460C2×M16—594no—
461C2×M16—1184no—
462C22×C8—591no—
463C22×C8—591no—
464C22×C8—594no—
465C22×C8—1184no—
466C22×C8C22×D5911yescharacteristic
467C22×C8C22×D5911yescharacteristic
468C4⋊Q8—22no—
469C4⋊Q8—594no—
470C4⋊Q8—1182no—
471C4⋊Q8C22×D5914yes—
472#126—1188no—
473#126—1188no—
474#126—1188no—
475#125—594no—
476#125—1188no—
477#125—1188no—
478#125—1182no—
479#124—22no—
480#124—1188no—
481#124C22×D5914yes—
482#123—1188no—
483C22⋊Q8—594no—
484C22⋊Q8—594no—
485C22⋊Q8—594no—
486C22⋊Q8—1188no—
487C22⋊Q8—1182no—
488C22⋊Q8—1182no—
489C22⋊Q8—1182no—
490#121—594no—
491#121—1182no—
492C4×Q8—594no—
493C4×Q8—594no—
494C4×Q8—594no—
495C4×Q8—1182no—
496C4×Q8—1182no—
497C4×Q8—1182no—
498C4×D4—594no—
499C4×D4—1182no—
500#117—594no—
501#117—594no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—591no—
505C2×C4⋊C4—591no—
506C2×C4⋊C4—591no—
507C2×C4⋊C4—591no—
508C2×C4⋊C4—591no—
509C2×C4⋊C4—591no—
510C2×C4⋊C4—1181no—
511C2×C4⋊C4—1181no—
512C2×C4⋊C4—1181no—
513C2×C4⋊C4—1181no—
514C2×C4⋊C4—1181no—
515C2×C4⋊C4—1181no—
516C2×C4⋊C4—1181no—
517C2×C4⋊C4—1181no—
518C2×C4⋊C4—1181no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—591no—
522C2×C22⋊C4—591no—
523C2×C22⋊C4—1181no—
524C2×C22⋊C4—1181no—
525C2×C22⋊C4—1181no—
526C2×C22⋊C4—1181no—
527C2×C22⋊C4—1181no—
528C2×C42—591no—
529C2×C42—1181no—
530C2×C42—1181no—
531C2×C42—1181no—
532C2×C42C22×D5911yescharacteristic
533#107—594no—
534#107—594no—
535#106—594no—
536#106—594no—
537#103—594no—
538#103—594no—
539#103—594no—
540#103—594no—
541#103—594no—
542#103—594no—
543#102—594no—
544#102—594no—
545#97—594no—
546#97C22×D5914yes—
547C4×C8—594no—
548C4×C8—594no—
549C24—21no—
550C24—591no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—1184no—
561C2×Q8—4722no—
562C2×Q8C23×D5912yes—
563C2×Q8C23×D5912yes—
564C2×Q8C23×D5912yes—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—1184no—
569C2×D4—4722no—
570C2×D4C23×D5912yes—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—591no—
575C22×C4—591no—
576C22×C4—591no—
577C22×C4—592no—
578C22×C4—592no—
579C22×C4—1184no—
580C22×C4—1182no—
581C22×C4—1182no—
582C22×C4—1181no—
583C22×C4—1181no—
584C22×C4—1181no—
585C22×C4—1181no—
586C22×C4—4722no—
587C22×C4D4×D5911yescharacteristic
588C22×C4D4×D5911yescharacteristic
589C22×C4C23×D5911yescharacteristic
590Q16—28no—
591Q16—28no—
592SD16—28no—
593SD16—28no—
594M16—1188no—
595C2×C8—592no—
596C2×C8—592no—
597C2×C8—1182no—
598C2×C8—1182no—
599C2×C8—1188no—
600C2×C8#1174568714yes—
601C2×C8#1174568714yes—
602C2×C8C23×D5912yes—
603C2×C8C23×D5912yes—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—594no—
607C4⋊C4—594no—
608C4⋊C4—592no—
609C4⋊C4—592no—
610C4⋊C4—592no—
611C4⋊C4—592no—
612C4⋊C4—1184no—
613C4⋊C4—1184no—
614C4⋊C4—1184no—
615C4⋊C4—1184no—
616C4⋊C4—1184no—
617C4⋊C4—1184no—
618C4⋊C4—1181no—
619C4⋊C4—1181no—
620C4⋊C4—1181no—
621C4⋊C4—1181no—
622C4⋊C4—1184no—
623C4⋊C4—1184no—
624C4⋊C4—1184no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—594no—
628C22⋊C4—594no—
629C22⋊C4—1184no—
630C22⋊C4—1184no—
631C22⋊C4—1184no—
632C22⋊C4—1184no—
633C22⋊C4—1184no—
634C42—592no—
635C42—592no—
636C42—1184no—
637C42—1184no—
638C42—1184no—
639C42D4×D5912yes—
640C42C23×D5912yes—
641C23—22no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—592no—
646C23—1182no—
647C23—1182no—
648C23—1182no—
649C23C2×D4×D5911yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8—42no—
657Q8—42no—
658Q8—42no—
659Q8—4724no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—4724no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—592no—
673C2×C4—592no—
674C2×C4—592no—
675C2×C4—1182no—
676C2×C4—1182no—
677C2×C4—1182no—
678C2×C4—1184no—
679C2×C4—1182no—
680C2×C4—1182no—
681C2×C4—1182no—
682C2×C4—1182no—
683C2×C4—1182no—
684C2×C4—1182no—
685C2×C4—4724no—
686C2×C4—2362no—
687C2×C4—2362no—
688C2×C4—2362no—
689C2×C4—2362no—
690C2×C4C2×D4×D5912yes—
691C2×C4C2×D4×D5912yes—
692C2×C4C2×D4×D5911yescharacteristic
693C2×C4C2×#1174568712yes—
694C2×C4C2×#1174568712yes—
695C2×C4C24×D5911yescharacteristic
696C8—1182no—
697C8—1182no—
698C8C2×#1174568714yes—
699C8C2×#1174568714yes—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—84no—
704C22—1182no—
705C22—1182no—
706C22—1182no—
707C22—2364no—
708C22#1683795012yes—
709C22#1683821112yes—
710C22#1683821812yes—
711C22C22×D4×D5911yescharacteristic
712C4—22no—
713C4—22no—
714C4—42no—
715C4—42no—
716C4—42no—
717C4—1182no—
718C4—1182no—
719C4—1182no—
720C4—2362no—
721C4—2362no—
722C4—2362no—
723C4—2362no—
724C4#1683795012yes—
725C4C22×#1174568711yescharacteristic
726C4C22×#1174568711yescharacteristic
727C2—82no—
728C2—2362no—
729C2#2143476114yesdirect product factor
730C2C2×#1683795011yescharacteristic
731C2C2×#1683821111yescharacteristic
732C2C2×#1683821811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#497C2
socleC23×C59C22×D4
prime radicalC2×#14273698C22
hypercenterC2×#497D59
hypocenterC59C2×#3178
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
2. C2×#16838013C2semidirect
3. #21434761C2direct (N × H)
4. C2×#16837811C2semidirect
5. C2×#16837756C2semidirect
6. C2×#16837752C2semidirect
7. C2×#16837657C2semidirect
9. C2×#16837640C2semidirect
11. C2×#16837509C2semidirect
12. C2×#16837503C2semidirect
13. C2×Q16×Dic59C2semidirect
14. C2×SD16×Dic59C2semidirect
15. C2×#16837359C2semidirect
16. C2×C59×#497C2semidirect
22. #16838013C22semidirect
42. #16837811C22semidirect
43. #16837756C22semidirect
44. #16837752C22semidirect
45. #16837657C22semidirect
47. #16837640C22semidirect
49. #16837509C22semidirect
50. #16837503C22semidirect
51. Q16×Dic59C22semidirect
52. SD16×Dic59C22semidirect
65. #16837359C22semidirect
75. C59×#497C22semidirect
365. C2×#497D59semidirect
378. C2×C59#3178semidirect
415. #497C2×D59semidirect
443. C59C2×#3178semidirect
729. C2#21434761direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380212
C2×#168380132
#214347612
C2×#168378112
C2×#168377562
C2×#168377522
C2×#168376572
C2×#168376452
C2×#168376402
C2×#168376282
C2×#168375092
C2×#168375032
C2×Q16×Dic592
C2×SD16×Dic592
C2×#168373592
C2×C59×#4972
C2×#317859