Finite Group Databasebeta

← C2×#21433961 #29456285

Subgroups — C2×#21433961 #29456285

Order 15104.

2094 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838032C211yesmaximal, characteristic, complemented
2C2×#16837884C211yesmaximal, characteristic
3#21433961C2116yesmaximal, direct product factor
4C2×#16837707C211yesmaximal, characteristic, complemented
5C2×#16837687C211yesmaximal, characteristic, complemented
6C2×#16837685C211yesmaximal, characteristic, complemented
7C2×#16837705C211yesmaximal, characteristic, complemented
8C2×#16837699C211yesmaximal, characteristic, complemented
9C2×#16837693C211yesmaximal, characteristic, complemented
10C2×#16837691C211yesmaximal, characteristic, complemented
11C2×#16837443C211yesmaximal, characteristic, complemented
12C2×#106×D59C211yesmaximal, characteristic, complemented
13C2×#16837427C211yesmaximal, characteristic, complemented
14C2×#16837402C211yesmaximal, characteristic
15C2×#16837397C211yesmaximal, characteristic
16C2×C59×#479C211yesmaximal, characteristic, complemented
17C22×#11745689C2211yescharacteristic
18C22×#11745659C2211yescharacteristic
19C22×C8×D59C2211yescharacteristic
20#16838032—24no—
21#16838032C2218yescomplemented
22C2×#14273727C2211yescharacteristic
23C2×#14273726—21no—
24C2×#14273726C2211yescharacteristic
25C2×#14273718C2211yescharacteristic
26C2×#14273717—21no—
27C2×#14273707—21no—
28C2×#14273705—21no—
29#16837884—24no—
30#16837884C2218yes—
31C2×Q8×Dic59C2211yescharacteristic
32C2×C4×D236—21no—
33C2×C4×D236C2211yescharacteristic
34C2×#14273689—21no—
35C2×#14273689C2211yescharacteristic
36C2×#14273685C2211yescharacteristic
37C2×#14273684—21no—
38C2×#14273684C2211yescharacteristic
39C2×C4⋊C4×D59—21no—
40C2×C4⋊C4×D59C2211yescharacteristic
41C2×C4⋊C4×D59C2211yescharacteristic
42#16837707C2218yescomplemented
43#16837705C2218yescomplemented
44#16837699C2218yescomplemented
45#16837693C2218yescomplemented
46#16837691C2218yescomplemented
47#16837687C2218yescomplemented
48#16837685C2218yescomplemented
49#16837443C2218yescomplemented
50C2×#14273660C2211yescharacteristic
51C2×#14273659C2211yescharacteristic
52C2×#14273659C2211yescharacteristic
53C2×#14273658C2211yescharacteristic
54C2×#14273658C2211yescharacteristic
55C2×#14273658C2211yescharacteristic
56#106×D59C2218yescomplemented
57#16837427C2218yescomplemented
58C2×C4⋊(C59⋊C8)C2211yescharacteristic
59C2×Dic59⋊C8C2211yescharacteristic
60C2×Dic59⋊C8C2211yescharacteristic
61#16837402C2218yes—
62#16837397C2218yes—
63C2×#14273651C2211yescharacteristic
64C2×#14273651C2211yescharacteristic
65C2×#14273649C2211yescharacteristic
66C2×#14273649C2211yescharacteristic
67C2×#14273647C2211yescharacteristic
68C2×#14273647C2211yescharacteristic
69C2×#125×C59C2211yescharacteristic
70C2×C4×Q8×C59C2211yescharacteristic
71C59×#479C2218yescomplemented
72C2×#107×C59C2211yescharacteristic
73C2×#106×C59C2211yescharacteristic
74C2×C4⋊C8×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#103×C59C2211yescharacteristic
77C2×#11745689—22no—
78C2×#11745689—24no—
79C2×#11745689Q818yescomplemented
80C2×#11745689C2314yes—
81C22×Dic118—21no—
82C22×Dic118—21no—
83C22×D236—21no—
84C22×D236C2311yescharacteristic
85C22×C4×D59—21no—
86C22×C4×D59—21no—
87C22×C4×D59—21no—
88C22×C4×D59—21no—
89C22×C4×D59—21no—
90C22×C4×D59C2311yescharacteristic
91C2×#11745659—24no—
92C2×#11745659C2314yes—
93C22×C59⋊C8C2311yescharacteristic
94C22×C59⋊C8C2311yescharacteristic
95C2×C8×D59—24no—
96C2×C8×D59C2314yes—
97#14273727—22no—
98#14273727C2314yes—
99#14273726—28no—
100#14273726—22no—
101#14273726C2314yes—
102#14273718—22no—
103#14273718C2314yes—
104#14273717—28no—
105#14273707—28no—
106#14273705—28no—
107Q8×Dic59—22no—
108Q8×Dic59C2314yes—
109C4×D236—22no—
110C4×D236—28no—
111C4×D236C2314yes—
112#14273689—28no—
113#14273689—22no—
114#14273689C2314yes—
115#14273685—22no—
116#14273685C2314yes—
117#14273684—28no—
118#14273684D414yes—
119#14273684C2314yes—
120C2×C4⋊Dic59—21no—
121C2×C4⋊Dic59—21no—
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×Dic59⋊C4D411yescharacteristic
132C4⋊C4×D59—22no—
133C4⋊C4×D59—22no—
134C4⋊C4×D59—28no—
135C4⋊C4×D59C2314yes—
136C4⋊C4×D59C2314yes—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4D411yescharacteristic
141C2×(C2×D59)⋊C4D411yescharacteristic
142C2×C4×Dic59—21no—
143C2×C4×Dic59—21no—
144C2×C4×Dic59C2311yescharacteristic
145#14273660C2314yes—
146#14273659C2314yes—
147#14273659C2314yes—
148#14273658C2314yes—
149#14273658C2314yes—
150#14273658C2314yes—
151C4⋊(C59⋊C8)C2314yes—
152Dic59⋊C8C2314yes—
153Dic59⋊C8C2314yes—
154#14273651C2314yes—
155#14273651C2314yes—
156#14273649C2314yes—
157#14273649C2314yes—
158#14273647C2314yes—
159#14273647C2314yes—
160C22×Q8×C59C2311yescharacteristic
161C22×C8×C59C2311yescharacteristic
162C22×C8×C59C2311yescharacteristic
163#125×C59—22no—
164#125×C59C2314yes—
165C4×Q8×C59—22no—
166C4×Q8×C59C2314yes—
167C2×C4⋊C4×C59—21no—
168C2×C4⋊C4×C59—21no—
169C2×C4⋊C4×C59—21no—
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C42×C59—21no—
174C2×C42×C59C2311yescharacteristic
175#107×C59C2314yes—
176#106×C59C2314yes—
177C4⋊C8×C59C2314yes—
178#103×C59C2314yes—
179#103×C59C2314yes—
180C23×D59—21no—
181C23×D59C2×D411yescharacteristic
182C2×Q8×C59—21no—
183C2×Q8×C59—22no—
184C2×Q8×C59C2×Q814yes—
185C2×Q8×C59C2412yes—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59C2×D411yescharacteristic
191C22×C4×C59C2×D411yescharacteristic
192C22×C4×C59C2411yescharacteristic
193C22×Dic59—21no—
194C22×Dic59—21no—
195C22×Dic59—21no—
196C22×Dic59C2×D411yescharacteristic
197C22×Dic59C2×D411yescharacteristic
198C22×Dic59C2×D411yescharacteristic
199#11745689—216no—
200#11745689—28no—
201#11745689C2×Q8116yescomplemented
202C2×D236—28no—
203C2×D236—24no—
204C2×D236—21no—
205C2×D236—22no—
206C2×D236C2×Q814yes—
207C2×D236C2412yes—
208C2×C4×D59—28no—
209C2×C4×D59—24no—
210C2×C4×D59—24no—
211C2×C4×D59—24no—
212C2×C4×D59—24no—
213C2×C4×D59—24no—
214C2×C4×D59—82no—
215C2×C4×D59—82no—
216C2×C4×D59—82no—
217C2×C4×D59—82no—
218C2×C4×D59C2×D412yes—
219C2×C4×D59C2×Q814yes—
220C2×C4×D59#4114yes—
221C2×C4×D59C2412yes—
222C2×Dic118—24no—
223C2×Dic118—24no—
224C2×Dic118—82no—
225C2×Dic118—82no—
226C2×C8×C59—22no—
227C2×C8×C59—22no—
228C2×C8×C59C2412yes—
229C2×C8×C59C2412yes—
230C4⋊C4×C59—24no—
231C4⋊C4×C59—24no—
232C4⋊C4×C59—24no—
233C4⋊C4×C59—21no—
234C4⋊C4×C59—21no—
235C4⋊C4×C59—21no—
236C4⋊C4×C59C2412yes—
237C4⋊C4×C59C2412yes—
238C4⋊C4×C59C2412yes—
239C42×C59—24no—
240C42×C59C2×D412yes—
241C42×C59C2412yes—
242(C2×D59)⋊C4—24no—
243(C2×D59)⋊C4—24no—
244(C2×D59)⋊C4—24no—
245(C2×D59)⋊C4C2×D414yes—
246(C2×D59)⋊C4C2×D414yes—
247C4⋊Dic59—21no—
248C4⋊Dic59—21no—
249C4⋊Dic59—24no—
250C4⋊Dic59—21no—
251C4⋊Dic59—24no—
252C4⋊Dic59—24no—
253C4⋊Dic59C2412yes—
254C4⋊Dic59C2412yes—
255C4⋊Dic59C2412yes—
256Dic59⋊C4—24no—
257Dic59⋊C4—24no—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260Dic59⋊C4C2×D414yes—
261Dic59⋊C4C2×D414yes—
262C4×Dic59—24no—
263C4×Dic59—24no—
264C4×Dic59C2×D412yes—
265C4×Dic59C2412yes—
266C2×C59⋊C8—22no—
267C2×C59⋊C8—22no—
268C2×C59⋊C8C2412yes—
269C2×C59⋊C8C2412yes—
270#11745659—28no—
271C8×D59—28no—
272C23×C59C22×D411yescharacteristic
273C22×D59—22no—
274C22×D59—22no—
275C22×D59—24no—
276C22×D59—22no—
277C22×D59—42no—
278C22×D59—42no—
279C22×D59C22⋊Q814yes—
280C22×D59C22×D412yes—
281Q8×C59—24no—
282Q8×C59—22no—
283Q8×C59C22×Q814yes—
284C2×C4×C59—24no—
285C2×C4×C59—22no—
286C2×C4×C59—22no—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—42no—
292C2×C4×C59—42no—
293C2×C4×C59—42no—
294C2×C4×C59C22×D412yes—
295C2×C4×C59C22×D412yes—
296C2×C4×C59C22×D411yescharacteristic
297C2×C4×C59C22×Q812yes—
298C2×C4×C59C2×#4112yes—
299C2×C4×C59C2511yescharacteristic
300C2×Dic59—22no—
301C2×Dic59—22no—
302C2×Dic59—22no—
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—42no—
306C2×Dic59—42no—
307C2×Dic59—42no—
308C2×Dic59C22⋊Q814yes—
309C2×Dic59C22×D412yes—
310C2×Dic59C22×D412yes—
311C2×Dic59C22×D412yes—
312D236—216no—
313D236—24no—
314D236—22no—
315D236C22×Q814yes—
316C4×D59—216no—
317C4×D59—84no—
318C4×D59—84no—
319C4×D59—84no—
320C4×D59—84no—
321C4×D59C22⋊Q818yes—
322C4×D59C22×Q814yes—
323C4×D59C2×#4114yes—
324Dic118—84no—
325Dic118—84no—
326C8×C59—22no—
327C8×C59—22no—
328C59⋊C8—22no—
329C59⋊C8—22no—
330C2×#3084—591nomaximal, Sylow
331C22×C59C2×C22⋊Q812yes—
332C22×C59#57712yes—
333C22×C59#57712yes—
334C22×C59C23×D411yescharacteristic
335C2×D59—28no—
336C2×D59—22no—
337C2×D59—22no—
338C2×D59—24no—
339C2×D59—48no—
340C2×D59—42no—
341C2×D59—42no—
342C2×D59C2×C22⋊Q814yes—
343C4×C59—24no—
344C4×C59—22no—
345C4×C59—22no—
346C4×C59—42no—
347C4×C59—42no—
348C4×C59—42no—
349C4×C59C2×C22⋊Q812yes—
350C4×C59C23×Q811yescharacteristic
351C4×C59C22×#4111yescharacteristic
352Dic59—22no—
353Dic59—22no—
354Dic59—42no—
355Dic59—42no—
356Dic59—42no—
357Dic59C2×C22⋊Q814yes—
358C2×#544—591no—
359C2×#520—591no—
360#3084—5916no—
361C2×#479—591no—
362C2×#479D5911yescharacteristic, complemented
363C2×#475—591no—
364C2×#475—591no—
365C2×#478—591no—
366C2×#478—591no—
367C2×#476—591no—
368C2×#476—591no—
369C2×#428—591no—
370C22×#106—591no—
371C2×#424—591no—
372C2×#417—591no—
373C2×#416—591no—
374C2×C59#308414yescomplemented
375C2×C59C22×C22⋊Q811yescharacteristic
376C2×C59C2×#57711yescharacteristic
377C2×C59C2×#57711yescharacteristic
378D59—24no—
379D59—44no—
380C22×#41—591no—
381C22×M16—591no—
382C23×C8—591no—
383#544—598no—
384#544—1184no—
385C2×C4⋊Q8—591no—
386C2×C4⋊Q8—591no—
387C2×C4⋊Q8—1181no—
388C2×#125—591no—
389C2×#125—1181no—
390C2×#125C2×D5911yescharacteristic
391C2×C22⋊Q8—1181no—
392C2×C22⋊Q8—1181no—
393#520—598no—
394#520—1184no—
395C2×C4×Q8—591no—
396C2×C4×Q8C2×D5911yescharacteristic
397C2×C4×D4—591no—
398C2×C4×D4—591no—
399C2×C4×D4—1181no—
400C2×C4×D4—1181no—
401C2×#117—591no—
402C2×#117—591no—
403C2×#117—1181no—
404C22×C4⋊C4—591no—
405C22×C4⋊C4—591no—
406C22×C4⋊C4—1181no—
407#479—598no—
408#479C2×D5918yescomplemented
409#478—598no—
410#478—598no—
411#476—598no—
412#476—598no—
413#475—598no—
414#475—598no—
415#428—598no—
416C2×#107—591no—
417C2×#107C2×D5911yescharacteristic
418C2×#106—591no—
419C2×#106—591no—
420C2×#106—591no—
421C2×#106—591no—
422C2×#106—591no—
423C2×#106—598no—
424C2×#106C2×D5911yescharacteristic
425#424—598no—
426C2×C4⋊C8—591no—
427C2×C4⋊C8—591no—
428C2×C4⋊C8—591no—
429C2×C4⋊C8C2×D5911yescharacteristic
430#417—598no—
431#416—598no—
432C2×#103—591no—
433C2×#103—591no—
434C2×#103C2×D5911yescharacteristic
435C2×#103C2×D5911yescharacteristic
436C2×#102—591no—
437C2×#102—591no—
438C2×#102—591no—
439C2×#102—591no—
440C59C2×#308411yescharacteristic, complemented, Sylow
441C2×#41—598no—
442C2×#41—594no—
443C2×#41—1182no—
444C2×#41—1184no—
445C22×Q8—1181no—
446C22×Q8—1181no—
447C22×Q8C22×D5911yescharacteristic
448C22×D4—591no—
449C22×D4—1181no—
450C23×C4—591no—
451C23×C4—1181no—
452C23×C4—1181no—
453C23×C4—1181no—
454C23×C4—1181no—
455C23×C4—1181no—
456C2×M16—594no—
457C2×M16—1184no—
458C22×C8—591no—
459C22×C8—591no—
460C22×C8—594no—
461C22×C8—1184no—
462C22×C8C22×D5911yescharacteristic
463C22×C8C22×D5911yescharacteristic
464C4⋊Q8—594no—
465C4⋊Q8—594no—
466C4⋊Q8—1182no—
467C4⋊Q8—1188no—
468C4⋊Q8—1182no—
469#125—22no—
470#125—594no—
471#125—1182no—
472#125—1188no—
473#125C22×D5914yes—
474C22⋊Q8—1188no—
475C22⋊Q8—1188no—
476C4×Q8—22no—
477C4×Q8—594no—
478C4×Q8—1182no—
479C4×Q8C22×D5914yes—
480C4×D4—594no—
481C4×D4—594no—
482C4×D4—1188no—
483C4×D4—1182no—
484C4×D4—1188no—
485C4×D4—1182no—
486#117—594no—
487#117—594no—
488#117—594no—
489#117—1188no—
490#117—1182no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—591no—
495C2×C4⋊C4—591no—
496C2×C4⋊C4—591no—
497C2×C4⋊C4—591no—
498C2×C4⋊C4—591no—
499C2×C4⋊C4—594no—
500C2×C4⋊C4—594no—
501C2×C4⋊C4—1188no—
502C2×C4⋊C4—1182no—
503C2×C4⋊C4—1182no—
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⋊C4C22×D5911yescharacteristic
512C2×C4⋊C4C22×D5911yescharacteristic
513C2×C4⋊C4C22×D5911yescharacteristic
514C2×C22⋊C4—591no—
515C2×C22⋊C4—591no—
516C2×C22⋊C4—1181no—
517C2×C22⋊C4—1181no—
518C2×C22⋊C4—1181no—
519C2×C42—21no—
520C2×C42—591no—
521C2×C42—1181no—
522C2×C42—1181no—
523C2×C42C22×D5911yescharacteristic
524#107—594no—
525#107C22×D5914yes—
526#106—594no—
527#106—594no—
528#106—594no—
529#106—594no—
530#106—594no—
531#106C22×D5914yes—
532C4⋊C8—594no—
533C4⋊C8—594no—
534C4⋊C8—594no—
535C4⋊C8C22×D5914yes—
536#103—594no—
537#103—594no—
538#103C22×D5914yes—
539#103C22×D5914yes—
540#102—594no—
541#102—594no—
542#102—594no—
543#102—594no—
544C24—591no—
545C24—1181no—
546#41—5916no—
547#41—11816no—
548#41—1188no—
549C2×Q8—21no—
550C2×Q8—22no—
551C2×Q8—1184no—
552C2×Q8—1184no—
553C2×Q8—4722no—
554C2×Q8—4722no—
555C2×Q8Q8×D5914yes—
556C2×Q8C23×D5912yes—
557C2×D4—594no—
558C2×D4—592no—
559C2×D4—1184no—
560C2×D4—1188no—
561C2×D4—1181no—
562C2×D4—1182no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—591no—
568C22×C4—592no—
569C22×C4—594no—
570C22×C4—594no—
571C22×C4—592no—
572C22×C4—591no—
573C22×C4—591no—
574C22×C4—1184no—
575C22×C4—1188no—
576C22×C4—1184no—
577C22×C4—1184no—
578C22×C4—1184no—
579C22×C4—1181no—
580C22×C4—1181no—
581C22×C4—1181no—
582C22×C4—1184no—
583C22×C4—4722no—
584C22×C4—4722no—
585C22×C4—4722no—
586C22×C4—4722no—
587C22×C4D4×D5911yescharacteristic
588C22×C4D4×D5911yescharacteristic
589C22×C4C23×D5911yescharacteristic
590M16—1188no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—592no—
594C2×C8—592no—
595C2×C8—1188no—
596C2×C8—1182no—
597C2×C8—1182no—
598C2×C8C23×D5912yes—
599C2×C8C23×D5912yes—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—594no—
607C4⋊C4—594no—
608C4⋊C4—592no—
609C4⋊C4—592no—
610C4⋊C4—592no—
611C4⋊C4—1184no—
612C4⋊C4—1184no—
613C4⋊C4—1184no—
614C4⋊C4—1184no—
615C4⋊C4—1184no—
616C4⋊C4—1184no—
617C4⋊C4—1181no—
618C4⋊C4—1181no—
619C4⋊C4—1181no—
620C4⋊C4—1184no—
621C4⋊C4C23×D5912yes—
622C4⋊C4C23×D5912yes—
623C4⋊C4C23×D5912yes—
624C22⋊C4—594no—
625C22⋊C4—594no—
626C22⋊C4—1184no—
627C22⋊C4—1184no—
628C22⋊C4—1184no—
629C42—24no—
630C42—592no—
631C42—592no—
632C42—1184no—
633C42—1184no—
634C42D4×D5912yes—
635C42C23×D5912yes—
636C23—594no—
637C23—592no—
638C23—1182no—
639C23—1182no—
640C23—1184no—
641C23—1182no—
642C23—2362no—
643C23—2362no—
644C23C2×D4×D5911yescharacteristic
645Q8—24no—
646Q8—22no—
647Q8—4724no—
648Q8—4724no—
649Q8C2×Q8×D5914yes—
650D4—594no—
651D4—11816no—
652D4—1184no—
653D4—1182no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—594no—
665C2×C4—592no—
666C2×C4—598no—
667C2×C4—594no—
668C2×C4—594no—
669C2×C4—592no—
670C2×C4—592no—
671C2×C4—11816no—
672C2×C4—1182no—
673C2×C4—1182no—
674C2×C4—1182no—
675C2×C4—1182no—
676C2×C4—1182no—
677C2×C4—4724no—
678C2×C4—4724no—
679C2×C4—4724no—
680C2×C4—4724no—
681C2×C4—2362no—
682C2×C4—2362no—
683C2×C4—2362no—
684C2×C4C2×D4×D5912yes—
685C2×C4C2×D4×D5912yes—
686C2×C4C2×D4×D5911yescharacteristic
687C2×C4C2×Q8×D5912yes—
688C2×C4#41×D5912yes—
689C2×C4C24×D5911yescharacteristic
690C8—22no—
691C8—22no—
692C8—1182no—
693C8—1182no—
694C22—594no—
695C22—1188no—
696C22—1182no—
697C22—1182no—
698C22—1184no—
699C22—2368no—
700C22—2362no—
701C22—2362no—
702C22C22⋊Q8×D5912yes—
703C22#1683820912yes—
704C22#1683821112yes—
705C22C22×D4×D5911yescharacteristic
706C4—22no—
707C4—22no—
708C4—24no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—594no—
713C4—1182no—
714C4—1182no—
715C4—2362no—
716C4—2362no—
717C4—2362no—
718C4C22⋊Q8×D5912yes—
719C4C22×Q8×D5911yescharacteristic
720C4C2×#41×D5911yescharacteristic
721C2—1184no—
722C2—2364no—
723C2#2143396114yesdirect product factor
724C2C2×C22⋊Q8×D5911yescharacteristic
725C2C2×#1683820911yescharacteristic
726C2C2×#1683821111yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#479C2
socleC23×C59C22×D4
prime radicalC22×#11745689C22
hypercenterC2×#479D59
hypocenterC59C2×#3084
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
1. C2×#16838032C2semidirect
3. #21433961C2direct (N × H)
4. C2×#16837707C2semidirect
5. C2×#16837687C2semidirect
6. C2×#16837685C2semidirect
7. C2×#16837705C2semidirect
8. C2×#16837699C2semidirect
9. C2×#16837693C2semidirect
10. C2×#16837691C2semidirect
11. C2×#16837443C2semidirect
12. C2×#106×D59C2semidirect
13. C2×#16837427C2semidirect
16. C2×C59×#479C2semidirect
21. #16838032C22semidirect
42. #16837707C22semidirect
43. #16837705C22semidirect
44. #16837699C22semidirect
45. #16837693C22semidirect
46. #16837691C22semidirect
47. #16837687C22semidirect
48. #16837685C22semidirect
49. #16837443C22semidirect
56. #106×D59C22semidirect
57. #16837427C22semidirect
71. C59×#479C22semidirect
79. C2×#11745689Q8semidirect
201. #11745689C2×Q8semidirect
362. C2×#479D59semidirect
374. C2×C59#3084semidirect
408. #479C2×D59semidirect
440. C59C2×#3084semidirect
723. C2#21433961direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380322
C2×#168378842
#214339612
C2×#168377072
C2×#168376872
C2×#168376852
C2×#168377052
C2×#168376992
C2×#168376932
C2×#168376912
C2×#168374432
C2×#106×D592
C2×#168374272
C2×#168374022
C2×#168373972
C2×C59×#4792
C2×#308459