Finite Group Databasebeta

← C2×#21436666 #29467378

Subgroups — C2×#21436666 #29467378

Order 15104.

1834 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838094C211yesmaximal, characteristic
2C2×#16838086C211yesmaximal, characteristic
3#21436666C2116yesmaximal, direct product factor
4C2×#16837802C211yesmaximal, characteristic, complemented
5C2×#16837736C211yesmaximal, characteristic, complemented
6C2×#16837735C211yesmaximal, characteristic, complemented
7C2×#16837741C211yesmaximal, characteristic, complemented
8C2×#16837740C211yesmaximal, characteristic, complemented
9C2×#16837711C211yesmaximal, characteristic, complemented
10C2×#16837707C211yesmaximal, characteristic, complemented
11C2×#16837657C211yesmaximal, characteristic, complemented
12C2×Q16×Dic59C211yesmaximal, characteristic, complemented
13C2×#16837478C211yesmaximal, characteristic
14C2×#16837444C211yesmaximal, characteristic, complemented
15C2×#16837441C211yesmaximal, characteristic, complemented
16C2×C59×#470C211yesmaximal, characteristic, complemented
17C22×#11745659C2211yescharacteristic
18#16838094—24no—
19#16838094C2218yes—
20#16838086—24no—
21#16838086C2218yes—
22C2×#14273722—21no—
23C2×#14273720—21no—
24C2×#14273718—21no—
25C2×#14273718C2211yescharacteristic
26C2×#14273718C2211yescharacteristic
27C2×#14273717—21no—
28C2×#14273711—21no—
29C2×#14273709—21no—
30C2×#14273703C2211yescharacteristic
31C2×#14273703C2211yescharacteristic
32C2×Q8×Dic59C2211yescharacteristic
33C2×Q8×Dic59C2211yescharacteristic
34C2×C4×C22⋊D59C2211yescharacteristic
35C2×#14273686C2211yescharacteristic
36C2×#14273685—21no—
37C2×#14273685C2211yescharacteristic
38C2×#14273683—21no—
39C22×C4⋊Dic59C2211yescharacteristic
40C2×C4⋊C4×D59C2211yescharacteristic
41#16837802C2218yescomplemented
42#16837741C2218yescomplemented
43#16837740C2218yescomplemented
44#16837736C2218yescomplemented
45#16837735C2218yescomplemented
46#16837711C2218yescomplemented
47#16837707C2218yescomplemented
48#16837657C2218yescomplemented
49Q16×Dic59C2218yescomplemented
50#16837478C2218yes—
51#16837444C2218yescomplemented
52#16837441C2218yescomplemented
53C2×#14273661C2211yescharacteristic
54C2×#14273661C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273660C2211yescharacteristic
58C2×#14273659C2211yescharacteristic
59C2×#14273659C2211yescharacteristic
60C2×#14273658C2211yescharacteristic
61C2×Dic59⋊C8C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273651C2211yescharacteristic
64C2×#14273651C2211yescharacteristic
65C2×#14273651C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C22×Q16×C59C2211yescharacteristic
70C22×M16×C59C2211yescharacteristic
71C2×C22⋊Q8×C59C2211yescharacteristic
72C2×C22⋊Q8×C59C2211yescharacteristic
73C59×#470C2218yescomplemented
74C2×#106×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#103×C59C2211yescharacteristic
77C22×C22⋊D59D411yescharacteristic
78C23×Dic59—21no—
79C22×C4×D59—21no—
80C22×C4×D59C2311yescharacteristic
81C2×#11745659—24no—
82C2×#11745659C2314yes—
83C22×C59⋊C8C2311yescharacteristic
84C22×C59⋊C8C2311yescharacteristic
85#14273722—28no—
86#14273720—28no—
87#14273718—28no—
88#14273718—22no—
89#14273718—22no—
90#14273718C2314yes—
91#14273718C2314yes—
92#14273717—28no—
93#14273711—28no—
94#14273709—28no—
95#14273703—22no—
96#14273703—22no—
97#14273703C2314yes—
98#14273703C2314yes—
99Q8×Dic59—22no—
100Q8×Dic59—22no—
101Q8×Dic59C2314yes—
102Q8×Dic59C2314yes—
103C4×C22⋊D59D414yes—
104C4×C22⋊D59C2314yes—
105#14273686—22no—
106#14273686C2314yes—
107#14273685—22no—
108#14273685—28no—
109#14273685C2314yes—
110#14273683—28no—
111C2×C4⋊Dic59—21no—
112C2×C4⋊Dic59—22no—
113C2×C4⋊Dic59—21no—
114C2×C4⋊Dic59—21no—
115C2×C4⋊Dic59—21no—
116C2×C4⋊Dic59—21no—
117C2×C4⋊Dic59C2311yescharacteristic
118C2×C4⋊Dic59C2311yescharacteristic
119C2×C4⋊Dic59C2311yescharacteristic
120C2×C4⋊Dic59C2311yescharacteristic
121C2×C4⋊Dic59C2314yes—
122C2×Dic59⋊C4—21no—
123C2×Dic59⋊C4—21no—
124C2×Dic59⋊C4—21no—
125C2×Dic59⋊C4—21no—
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4D411yescharacteristic
128C4⋊C4×D59—22no—
129C4⋊C4×D59C2314yes—
130C2×C22⋊Dic59—21no—
131C2×C22⋊Dic59D411yescharacteristic
132C2×(C2×D59)⋊C4—21no—
133C2×(C2×D59)⋊C4—21no—
134C2×(C2×D59)⋊C4—21no—
135C2×(C2×D59)⋊C4D411yescharacteristic
136C2×C4×Dic59—21no—
137C2×C4×Dic59—21no—
138C2×C4×Dic59—21no—
139C2×C4×Dic59—21no—
140C2×C4×Dic59C2311yescharacteristic
141#14273661C2314yes—
142#14273661C2314yes—
143#14273660C2314yes—
144#14273660C2314yes—
145#14273660C2314yes—
146#14273659C2314yes—
147#14273659C2314yes—
148#14273658C2314yes—
149Dic59⋊C8C2314yes—
150#14273651C2314yes—
151#14273651C2314yes—
152#14273651C2314yes—
153#14273651C2314yes—
154C22⋊(C59⋊C8)C2314yes—
155(C2×D59)⋊C8C2314yes—
156C8×Dic59C2314yes—
157C22×Q8×C59C2311yescharacteristic
158C22×Q8×C59C2311yescharacteristic
159C23×C4×C59C2311yescharacteristic
160C2×Q16×C59—24no—
161C2×Q16×C59C2314yes—
162C2×M16×C59—24no—
163C2×M16×C59C2314yes—
164C22×C8×C59C2311yescharacteristic
165C22×C8×C59C2311yescharacteristic
166C22⋊Q8×C59—22no—
167C22⋊Q8×C59—22no—
168C22⋊Q8×C59C2314yes—
169C22⋊Q8×C59C2314yes—
170C2×C4⋊C4×C59—21no—
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#103×C59C2314yes—
179C24×C59C2×D411yescharacteristic
180C23×D59C2×D411yescharacteristic
181C2×Q8×C59—21no—
182C2×Q8×C59—21no—
183C2×Q8×C59—22no—
184C2×Q8×C59—22no—
185C2×Q8×C59—22no—
186C2×Q8×C59—22no—
187C2×Q8×C59C2412yes—
188C2×Q8×C59C2412yes—
189C22×C4×C59—22no—
190C22×C4×C59—22no—
191C22×C4×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59C2×D411yescharacteristic
196C22×C4×C59C2×D412yes—
197C22×C4×C59C2412yes—
198C22×C4×C59C2411yescharacteristic
199C2×C22⋊D59—42no—
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×D59—24no—
213C2×C4×D59—44no—
214C2×C4×D59C2×D412yes—
215C2×C4×D59C2412yes—
216Q16×C59—28no—
217M16×C59—28no—
218C2×C8×C59—22no—
219C2×C8×C59#4114yes—
220C2×C8×C59C2412yes—
221C2×C8×C59C2412yes—
222C4⋊C4×C59—24no—
223C4⋊C4×C59—24no—
224C4⋊C4×C59—21no—
225C4⋊C4×C59—21no—
226C4⋊C4×C59C2412yes—
227C4⋊C4×C59C2412yes—
228C22⋊C4×C59—24no—
229C22⋊C4×C59—24no—
230C22⋊Dic59—24no—
231C22⋊Dic59C2×D414yes—
232(C2×D59)⋊C4—24no—
233(C2×D59)⋊C4—24no—
234(C2×D59)⋊C4—24no—
235(C2×D59)⋊C4C2×D414yes—
236C4⋊Dic59—21no—
237C4⋊Dic59—21no—
238C4⋊Dic59—21no—
239C4⋊Dic59—24no—
240C4⋊Dic59—21no—
241C4⋊Dic59—24no—
242C4⋊Dic59—24no—
243C4⋊Dic59—24no—
244C4⋊Dic59—24no—
245C4⋊Dic59C2412yes—
246C4⋊Dic59C2412yes—
247C4⋊Dic59C2412yes—
248C4⋊Dic59C2412yes—
249Dic59⋊C4—24no—
250Dic59⋊C4—24no—
251Dic59⋊C4—24no—
252Dic59⋊C4—24no—
253Dic59⋊C4—24no—
254Dic59⋊C4C2×D414yes—
255C4×Dic59—24no—
256C4×Dic59—24no—
257C4×Dic59—24no—
258C4×Dic59—24no—
259C4×Dic59C2×D412yes—
260C4×Dic59C2412yes—
261C2×C59⋊C8—22no—
262C2×C59⋊C8—22no—
263C2×C59⋊C8C2412yes—
264C2×C59⋊C8C2412yes—
265#11745659—28no—
266C23×C59—22no—
267C23×C59—22no—
268C23×C59—22no—
269C23×C59C22×D412yes—
270C23×C59C22×D411yescharacteristic
271C22×D59—22no—
272C22×D59—22no—
273C22×D59—22no—
274C22×D59C22×D412yes—
275Q8×C59—22no—
276Q8×C59—22no—
277Q8×C59—22no—
278Q8×C59—22no—
279Q8×C59—42no—
280Q8×C59—42no—
281C2×C4×C59—22no—
282C2×C4×C59—24no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—22no—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—42no—
290C2×C4×C59—42no—
291C2×C4×C59—42no—
292C2×C4×C59—42no—
293C2×C4×C59C22×D412yes—
294C2×C4×C59C22×D411yescharacteristic
295C2×C4×C59C2×#4112yes—
296C2×C4×C592−1+412yes—
297C2×C4×C59C2511yescharacteristic
298C22⋊D59—44no—
299C2×Dic59—22no—
300C2×Dic59—22no—
301C2×Dic59—22no—
302C2×Dic59—22no—
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—48no—
307C2×Dic59—42no—
308C2×Dic59—42no—
309C2×Dic59—42no—
310C2×Dic59—42no—
311C2×Dic59C22×D412yes—
312C2×Dic59C22×D412yes—
313C2×Dic59C22×D412yes—
314C4×D59—24no—
315C4×D59—22no—
316C4×D59—22no—
317C4×D59—48no—
318C8×C59—22no—
319C8×C59C2×#4114yes—
320C59⋊C8—22no—
321C59⋊C8—22no—
322C2×#3352—591nomaximal, Sylow
323C22×C59—22no—
324C22×C59—22no—
325C22×C59—22no—
326C22×C59—44no—
327C22×C59#54712yes—
328C22×C59#57512yes—
329C22×C59#57812yes—
330C22×C59C23×D411yescharacteristic
331C2×D59—22no—
332C2×D59—22no—
333C2×D59—22no—
334C2×D59—44no—
335C4×C59—22no—
336C4×C59—42no—
337C4×C59—42no—
338C4×C59—42no—
339C4×C59—42no—
340C4×C59#54712yes—
341C4×C59C22×#4111yescharacteristic
342C4×C59C2×2−1+411yescharacteristic
343Dic59—22no—
344Dic59—22no—
345Dic59—22no—
346Dic59—42no—
347Dic59—42no—
348Dic59—42no—
349Dic59—42no—
350C2×#552—591no—
351C2×#552—591no—
352#3352—5916no—
353C2×#499—591no—
354C2×#484—591no—
355C2×#484—591no—
356C2×#485—591no—
357C2×#485—591no—
358C2×#479—591no—
359C2×#479—591no—
360C2×#470—591no—
361C2×#470D5911yescharacteristic, complemented
362C2×C4×Q16—591no—
363C2×#436—591no—
364C2×#428—591no—
365C2×#428—591no—
366C2×C59—42no—
367C2×C59#335214yescomplemented
368C2×C59C2×#54711yescharacteristic
369C2×C59C2×#57511yescharacteristic
370C2×C59C2×#57811yescharacteristic
371D59—42no—
372C22×Q16C2×D5911yescharacteristic
373C22×M16—591no—
374C22×M16C2×D5911yescharacteristic
375#552—598no—
376#552—598no—
377#552—1184no—
378#552—1184no—
379C2×#126—1181no—
380C2×#126—1181no—
381C2×#125—591no—
382C2×#125—591no—
383C2×#125—1181no—
384C2×#125—1181no—
385C2×#123—1181no—
386C2×#123—1181no—
387C2×C22⋊Q8—591no—
388C2×C22⋊Q8—591no—
389C2×C22⋊Q8C2×D5911yescharacteristic
390C2×C22⋊Q8C2×D5911yescharacteristic
391C2×C4×Q8—591no—
392C2×C4×Q8—591no—
393C2×C4×D4—591no—
394C2×#117—591no—
395C2×#117—591no—
396C2×#117—1181no—
397C2×#117—1181no—
398C22×C4⋊C4—591no—
399C22×C4⋊C4—591no—
400#499—598no—
401#485—598no—
402#485—598no—
403#484—598no—
404#484—598no—
405#479—598no—
406#479—598no—
407#470—598no—
408#470C2×D5918yescomplemented
409C4×Q16—598no—
410#436—598no—
411#428—598no—
412#428—598no—
413C2×#107—591no—
414C2×#107—591no—
415C2×#107—591no—
416C2×#107—591no—
417C2×#107—591no—
418C2×#106—591no—
419C2×#106—591no—
420C2×#106—591no—
421C2×#106C2×D5911yescharacteristic
422C2×C4⋊C8—591no—
423C2×#103—591no—
424C2×#103—591no—
425C2×#103—591no—
426C2×#103—591no—
427C2×#103C2×D5911yescharacteristic
428C2×#103C2×D5911yescharacteristic
429C2×C22⋊C8—591no—
430C2×C22⋊C8—591no—
431C2×C4×C8—591no—
432C59C2×#335211yescharacteristic, complemented, Sylow
433C22×Q8C22×D5911yescharacteristic
434C22×Q8C22×D5911yescharacteristic
435C22×D4—591no—
436C23×C4—591no—
437C23×C4—1181no—
438C23×C4—1181no—
439C23×C4C22×D5911yescharacteristic
440C2×Q16—24no—
441C2×Q16C22×D5914yes—
442C2×M16—24no—
443C2×M16—594no—
444C2×M16—1184no—
445C2×M16C22×D5914yes—
446C22×C8—591no—
447C22×C8—591no—
448C22×C8C22×D5911yescharacteristic
449C22×C8C22×D5911yescharacteristic
450#126—1188no—
451#126—1188no—
452#125—594no—
453#125—594no—
454#125—1182no—
455#125—1182no—
456#125—1188no—
457#125—1188no—
458#123—1188no—
459#123—1188no—
460C22⋊Q8—22no—
461C22⋊Q8—22no—
462C22⋊Q8—594no—
463C22⋊Q8—594no—
464C22⋊Q8—1182no—
465C22⋊Q8—1182no—
466C22⋊Q8C22×D5914yes—
467C22⋊Q8C22×D5914yes—
468C4×Q8—594no—
469C4×Q8—594no—
470C4×Q8—1182no—
471C4×Q8—1182no—
472C4×D4—594no—
473C4×D4—594no—
474#117—594no—
475#117—594no—
476#117—1188no—
477#117—1188no—
478#117—1182no—
479#117—1182no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—591no—
483C2×C4⋊C4—591no—
484C2×C4⋊C4—591no—
485C2×C4⋊C4—591no—
486C2×C4⋊C4—594no—
487C2×C4⋊C4—591no—
488C2×C4⋊C4—594no—
489C2×C4⋊C4—1182no—
490C2×C4⋊C4—1181no—
491C2×C4⋊C4—1181no—
492C2×C4⋊C4—1181no—
493C2×C4⋊C4—1181no—
494C2×C4⋊C4—1181no—
495C2×C4⋊C4—1181no—
496C2×C4⋊C4—1181no—
497C2×C4⋊C4—1181no—
498C2×C4⋊C4—1181no—
499C2×C4⋊C4—1181no—
500C2×C4⋊C4—1182no—
501C2×C4⋊C4C22×D5911yescharacteristic
502C2×C4⋊C4C22×D5911yescharacteristic
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—591no—
506C2×C22⋊C4—591no—
507C2×C22⋊C4—1181no—
508C2×C22⋊C4—1181no—
509C2×C22⋊C4—1181no—
510C2×C22⋊C4—1181no—
511C2×C42—591no—
512C2×C42—1181no—
513C2×C42—1181no—
514C2×C42—1181no—
515C2×C42—1181no—
516#107—594no—
517#107—594no—
518#107—594no—
519#107—594no—
520#107—594no—
521#106—594no—
522#106—594no—
523#106—594no—
524#106C22×D5914yes—
525C4⋊C8—594no—
526#103—594no—
527#103—594no—
528#103—594no—
529#103—594no—
530#103C22×D5914yes—
531#103C22×D5914yes—
532C22⋊C8—594no—
533C22⋊C8—594no—
534C4×C8—594no—
535C24—591no—
536C24D4×D5911yescharacteristic
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8C23×D5912yes—
544C2×Q8C23×D5912yes—
545C2×D4—594no—
546C2×D4—2362no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—591no—
554C22×C4—591no—
555C22×C4—591no—
556C22×C4—592no—
557C22×C4—592no—
558C22×C4—1184no—
559C22×C4—1182no—
560C22×C4—1182no—
561C22×C4—1184no—
562C22×C4—1181no—
563C22×C4—1181no—
564C22×C4—1181no—
565C22×C4—1181no—
566C22×C4—2364no—
567C22×C4—2364no—
568C22×C4D4×D5912yes—
569C22×C4D4×D5911yescharacteristic
570C22×C4C23×D5912yes—
571C22×C4C23×D5911yescharacteristic
572Q16—28no—
573M16—28no—
574M16—1188no—
575C2×C8—22no—
576C2×C8—592no—
577C2×C8—592no—
578C2×C8—1182no—
579C2×C8—1182no—
580C2×C8#1174568714yes—
581C2×C8C23×D5912yes—
582C2×C8C23×D5912yes—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—594no—
588C4⋊C4—592no—
589C4⋊C4—592no—
590C4⋊C4—592no—
591C4⋊C4—592no—
592C4⋊C4—1184no—
593C4⋊C4—1184no—
594C4⋊C4—1184no—
595C4⋊C4—1184no—
596C4⋊C4—1184no—
597C4⋊C4—1184no—
598C4⋊C4—1184no—
599C4⋊C4—1184no—
600C4⋊C4—1184no—
601C4⋊C4—1181no—
602C4⋊C4—1181no—
603C4⋊C4—1181no—
604C4⋊C4—1184no—
605C4⋊C4—1181no—
606C4⋊C4C23×D5912yes—
607C4⋊C4C23×D5912yes—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—594no—
611C22⋊C4—594no—
612C22⋊C4—1184no—
613C22⋊C4—1184no—
614C22⋊C4—1184no—
615C22⋊C4—1184no—
616C42—592no—
617C42—592no—
618C42—1184no—
619C42—1184no—
620C42—1184no—
621C42—1184no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—592no—
626C23—1182no—
627C23—1182no—
628C23—1182no—
629C23C2×D4×D5912yes—
630C23C2×D4×D5911yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—22no—
634Q8—22no—
635Q8—42no—
636Q8—42no—
637D4—2364no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—592no—
651C2×C4—592no—
652C2×C4—592no—
653C2×C4—1182no—
654C2×C4—1182no—
655C2×C4—1182no—
656C2×C4—1182no—
657C2×C4—1182no—
658C2×C4—1184no—
659C2×C4—1182no—
660C2×C4—1182no—
661C2×C4—1182no—
662C2×C4—1182no—
663C2×C4—2368no—
664C2×C4—2368no—
665C2×C4—2362no—
666C2×C4—2362no—
667C2×C4—2362no—
668C2×C4—2362no—
669C2×C4C2×D4×D5912yes—
670C2×C4C2×D4×D5911yescharacteristic
671C2×C4C2×#1174568712yes—
672C2×C4#1427377412yes—
673C2×C4C24×D5911yescharacteristic
674C8—22no—
675C8—1182no—
676C8—1182no—
677C8C2×#1174568714yes—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—44no—
682C22—1182no—
683C22—1182no—
684C22—1182no—
685C22—2364no—
686C22#1683805212yes—
687C22#1683820112yes—
688C22#1683821812yes—
689C22C22×D4×D5911yescharacteristic
690C4—22no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—1182no—
696C4—1182no—
697C4—1182no—
698C4—2362no—
699C4—2362no—
700C4—2362no—
701C4—2362no—
702C4#1683805212yes—
703C4C22×#1174568711yescharacteristic
704C4C2×#1427377411yescharacteristic
705C2—42no—
706C2—2362no—
707C2#2143666614yesdirect product factor
708C2C2×#1683805211yescharacteristic
709C2C2×#1683820111yescharacteristic
710C2C2×#1683821811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#470C2
socleC23×C59C22×D4
prime radicalC22×C22⋊D59D4
hypercenterC2×#470D59
hypocenterC59C2×#3352
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
3. #21436666C2direct (N × H)
4. C2×#16837802C2semidirect
5. C2×#16837736C2semidirect
6. C2×#16837735C2semidirect
7. C2×#16837741C2semidirect
8. C2×#16837740C2semidirect
9. C2×#16837711C2semidirect
10. C2×#16837707C2semidirect
11. C2×#16837657C2semidirect
12. C2×Q16×Dic59C2semidirect
14. C2×#16837444C2semidirect
15. C2×#16837441C2semidirect
16. C2×C59×#470C2semidirect
41. #16837802C22semidirect
42. #16837741C22semidirect
43. #16837740C22semidirect
44. #16837736C22semidirect
45. #16837735C22semidirect
46. #16837711C22semidirect
47. #16837707C22semidirect
48. #16837657C22semidirect
49. Q16×Dic59C22semidirect
51. #16837444C22semidirect
52. #16837441C22semidirect
73. C59×#470C22semidirect
361. C2×#470D59semidirect
367. C2×C59#3352semidirect
408. #470C2×D59semidirect
432. C59C2×#3352semidirect
707. C2#21436666direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380942
C2×#168380862
#214366662
C2×#168378022
C2×#168377362
C2×#168377352
C2×#168377412
C2×#168377402
C2×#168377112
C2×#168377072
C2×#168376572
C2×Q16×Dic592
C2×#168374782
C2×#168374442
C2×#168374412
C2×C59×#4702
C2×#335259