Finite Group Databasebeta

← C2×#21435358 #29460888

Subgroups — C2×#21435358 #29460888

Order 15104.

1678 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838030C211yesmaximal, characteristic
2#21435358C2116yesmaximal, direct product factor
3C2×#16837812C211yesmaximal, characteristic, complemented
4C2×#16837801C211yesmaximal, characteristic, complemented
5C2×#16837770C211yesmaximal, characteristic, complemented
6C2×#16837752C211yesmaximal, characteristic, complemented
7C2×#16837735C211yesmaximal, characteristic
8C2×#16837740C211yesmaximal, characteristic
9C2×#16837740C211yesmaximal, characteristic
10C2×#16837730C211yesmaximal, characteristic
11C2×#16837709C211yesmaximal, characteristic, complemented
12C2×#16837709C211yesmaximal, characteristic, complemented
13C2×#16837697C211yesmaximal, characteristic, complemented
14C2×#16837687C211yesmaximal, characteristic, complemented
15C2×#16837463C211yesmaximal, characteristic
16C2×C59×#541C211yesmaximal, characteristic
17#16838030—24no—
18#16838030C2218yes—
19C2×#14273727C2211yescharacteristic
20C2×#14273727C2211yescharacteristic
21C2×#14273726—21no—
22C2×#14273719C2211yescharacteristic
23C2×#14273719C2211yescharacteristic
24C2×#14273718—21no—
25C2×#14273704—21no—
26C2×#14273704—21no—
27C2×#14273686C2211yescharacteristic
28C22×C4⋊Dic59C2211yescharacteristic
29#16837812C2218yescomplemented
30#16837801C2218yescomplemented
31#16837770C2218yescomplemented
32#16837752C2218yescomplemented
33#16837740C2218yes—
34#16837740C2218yes—
35#16837735C2218yes—
36#16837730C2218yes—
37#16837709C2218yescomplemented
38#16837709C2218yescomplemented
39#16837697C2218yescomplemented
40#16837687C2218yescomplemented
41#16837463C2218yes—
42C2×#14273660C2211yescharacteristic
43C2×#14273660C2211yescharacteristic
44C2×#14273660C2211yescharacteristic
45C2×#14273660C2211yescharacteristic
46C2×#14273658C2211yescharacteristic
47C2×#14273658C2211yescharacteristic
48C2×#14273658C2211yescharacteristic
49C2×#14273658C2211yescharacteristic
50C2×C4⋊(C59⋊C8)C2211yescharacteristic
51C2×C4⋊(C59⋊C8)C2211yescharacteristic
52C2×#14273651C2211yescharacteristic
53C2×#14273651C2211yescharacteristic
54C2×#14273651C2211yescharacteristic
55C2×#14273651C2211yescharacteristic
56C2×#14273651C2211yescharacteristic
57C2×#14273651C2211yescharacteristic
58C2×#14273651C2211yescharacteristic
59C2×#14273651C2211yescharacteristic
60C2×C22⋊(C59⋊C8)C2211yescharacteristic
61C2×C22⋊(C59⋊C8)C2211yescharacteristic
62C2×#14273638C2211yescharacteristic
63C2×C4×C59⋊C8C2211yescharacteristic
64C59×#541—24no—
65C59×#541C2218yes—
66C2×C4⋊Q8×C59C2211yescharacteristic
67C2×#126×C59—21no—
68C2×#126×C59—21no—
69C2×#125×C59—21no—
70C2×#125×C59—21no—
71C2×#125×C59C2211yescharacteristic
72C2×C22⋊Q8×C59C2211yescharacteristic
73C2×C22⋊Q8×C59C2211yescharacteristic
74C2×C4×Q8×C59C2211yescharacteristic
75C2×C4×Q8×C59C2211yescharacteristic
76C2×#117×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C23×Dic59—21no—
80C22×C59⋊C8C2311yescharacteristic
81C22×C59⋊C8C2311yescharacteristic
82C22×C59⋊C8C2311yescharacteristic
83C22×C59⋊C8C2311yescharacteristic
84#14273727—22no—
85#14273727—22no—
86#14273727C2314yes—
87#14273727C2314yes—
88#14273726—28no—
89#14273719—22no—
90#14273719—22no—
91#14273719C2314yes—
92#14273719C2314yes—
93#14273718—28no—
94#14273704—28no—
95#14273704—28no—
96#14273686—22no—
97#14273686C2314yes—
98C2×C4⋊Dic59—21no—
99C2×C4⋊Dic59—21no—
100C2×C4⋊Dic59—21no—
101C2×C4⋊Dic59—22no—
102C2×C4⋊Dic59C2311yescharacteristic
103C2×C4⋊Dic59C2311yescharacteristic
104C2×C4⋊Dic59C2311yescharacteristic
105C2×C4⋊Dic59C2311yescharacteristic
106C2×C4⋊Dic59C2314yes—
107C2×Dic59⋊C4—21no—
108C2×Dic59⋊C4—21no—
109C2×Dic59⋊C4—21no—
110C2×Dic59⋊C4—21no—
111C2×C22⋊Dic59—21no—
112C2×C4×Dic59—21no—
113#14273660C2314yes—
114#14273660C2314yes—
115#14273660C2314yes—
116#14273660C2314yes—
117#14273658C2314yes—
118#14273658C2314yes—
119#14273658C2314yes—
120#14273658C2314yes—
121C4⋊(C59⋊C8)C2314yes—
122C4⋊(C59⋊C8)C2314yes—
123#14273651C2314yes—
124#14273651C2314yes—
125#14273651C2314yes—
126#14273651C2314yes—
127#14273651C2314yes—
128#14273651C2314yes—
129#14273651C2314yes—
130#14273651C2314yes—
131C22⋊(C59⋊C8)C2314yes—
132C22⋊(C59⋊C8)C2314yes—
133#14273638C2314yes—
134C4×C59⋊C8C2314yes—
135C22×Q8×C59C2311yescharacteristic
136C22×Q8×C59C2311yescharacteristic
137C23×C4×C59C2311yescharacteristic
138C4⋊Q8×C59—22no—
139C4⋊Q8×C59C2314yes—
140#126×C59—28no—
141#126×C59—28no—
142#125×C59—28no—
143#125×C59—28no—
144#125×C59—22no—
145#125×C59C2314yes—
146C22⋊Q8×C59—22no—
147C22⋊Q8×C59—22no—
148C22⋊Q8×C59C2314yes—
149C22⋊Q8×C59C2314yes—
150C4×Q8×C59—22no—
151C4×Q8×C59—22no—
152C4×Q8×C59C2314yes—
153C4×Q8×C59C2314yes—
154#117×C59D414yes—
155#117×C59C2314yes—
156C2×C4⋊C4×C59—21no—
157C2×C4⋊C4×C59—21no—
158C2×C4⋊C4×C59—21no—
159C2×C4⋊C4×C59—21no—
160C2×C4⋊C4×C59—21no—
161C2×C4⋊C4×C59—21no—
162C2×C4⋊C4×C59—21no—
163C2×C4⋊C4×C59—21no—
164C2×C4⋊C4×C59D411yescharacteristic
165C2×C4⋊C4×C59D411yescharacteristic
166C2×C4⋊C4×C59C2311yescharacteristic
167C2×C4⋊C4×C59C2311yescharacteristic
168C2×C22⋊C4×C59—21no—
169C2×C22⋊C4×C59—21no—
170C2×C22⋊C4×C59D411yescharacteristic
171C2×C22⋊C4×C59D411yescharacteristic
172C2×C42×C59—21no—
173C2×C42×C59—21no—
174C2×C42×C59C2311yescharacteristic
175C2×C42×C59C2311yescharacteristic
176C24×C59C2×D411yescharacteristic
177C2×Q8×C59—21no—
178C2×Q8×C59—21no—
179C2×Q8×C59—22no—
180C2×Q8×C59—22no—
181C2×Q8×C59—22no—
182C2×Q8×C59—22no—
183C2×Q8×C59C2412yes—
184C2×Q8×C59C2412yes—
185C22×C4×C59—22no—
186C22×C4×C59—22no—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59—21no—
191C22×C4×C59C2×D411yescharacteristic
192C22×C4×C59C2×D411yescharacteristic
193C22×C4×C59C2×D411yescharacteristic
194C22×C4×C59C2×D411yescharacteristic
195C22×C4×C59C2×D411yescharacteristic
196C22×C4×C59C2×D412yes—
197C22×C4×C59C2412yes—
198C22×C4×C59C2411yescharacteristic
199C22×Dic59—21no—
200C22×Dic59—21no—
201C22×Dic59—21no—
202C22×Dic59—21no—
203C22×Dic59—24no—
204C22×Dic59—82no—
205C2×Dic118—24no—
206C2×Dic118—24no—
207C2×Dic118—82no—
208C2×Dic118—82no—
209C4⋊C4×C59—24no—
210C4⋊C4×C59—24no—
211C4⋊C4×C59—24no—
212C4⋊C4×C59—24no—
213C4⋊C4×C59—24no—
214C4⋊C4×C59—24no—
215C4⋊C4×C59—24no—
216C4⋊C4×C59—24no—
217C4⋊C4×C59—21no—
218C4⋊C4×C59—21no—
219C4⋊C4×C59C2×D414yes—
220C4⋊C4×C59C2×D414yes—
221C4⋊C4×C59C2412yes—
222C4⋊C4×C59C2412yes—
223C22⋊C4×C59—24no—
224C22⋊C4×C59—24no—
225C22⋊C4×C59C2×D414yes—
226C22⋊C4×C59C2×D414yes—
227C42×C59—24no—
228C42×C59—24no—
229C42×C59C2×D412yes—
230C42×C59C2×D412yes—
231C42×C59C2412yes—
232C42×C59C2412yes—
233C22⋊Dic59—24no—
234C4⋊Dic59—24no—
235C4⋊Dic59—21no—
236C4⋊Dic59—21no—
237C4⋊Dic59—24no—
238C4⋊Dic59—24no—
239C4⋊Dic59—21no—
240C4⋊Dic59—21no—
241C4⋊Dic59C2412yes—
242C4⋊Dic59C2412yes—
243C4⋊Dic59C2412yes—
244C4⋊Dic59C2412yes—
245Dic59⋊C4—24no—
246Dic59⋊C4—24no—
247Dic59⋊C4—24no—
248Dic59⋊C4—24no—
249C4×Dic59—24no—
250C2×C59⋊C8—22no—
251C2×C59⋊C8—22no—
252C2×C59⋊C8—22no—
253C2×C59⋊C8—22no—
254C2×C59⋊C8C2412yes—
255C2×C59⋊C8C2412yes—
256C2×C59⋊C8C2412yes—
257C2×C59⋊C8C2412yes—
258C23×C59—22no—
259C23×C59—22no—
260C23×C59—22no—
261C23×C59C22×D412yes—
262C23×C59C22×D411yescharacteristic
263Q8×C59—22no—
264Q8×C59—22no—
265Q8×C59—22no—
266Q8×C59—22no—
267Q8×C59—42no—
268Q8×C59—42no—
269C2×C4×C59—22no—
270C2×C4×C59—22no—
271C2×C4×C59—22no—
272C2×C4×C59—22no—
273C2×C4×C59—22no—
274C2×C4×C59—24no—
275C2×C4×C59—22no—
276C2×C4×C59—22no—
277C2×C4×C59—22no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—42no—
282C2×C4×C59—42no—
283C2×C4×C59—42no—
284C2×C4×C59—42no—
285C2×C4×C59C22×D412yes—
286C2×C4×C59C22×D412yes—
287C2×C4×C59C22×D412yes—
288C2×C4×C59C22×D412yes—
289C2×C4×C59C22×D412yes—
290C2×C4×C59C22×D411yescharacteristic
291C2×C4×C592−1+412yes—
292C2×C4×C592−1+412yes—
293C2×C4×C59C2511yescharacteristic
294C2×Dic59—22no—
295C2×Dic59—22no—
296C2×Dic59—22no—
297C2×Dic59—22no—
298C2×Dic59—42no—
299C2×Dic59—42no—
300C2×Dic59—42no—
301C2×Dic59—42no—
302C2×Dic59—84no—
303Dic118—84no—
304Dic118—84no—
305C59⋊C8—22no—
306C59⋊C8—22no—
307C59⋊C8—22no—
308C59⋊C8—22no—
309C2×#3242—591nomaximal, Sylow
310C22×C59—22no—
311C22×C59—22no—
312C22×C59—22no—
313C22×C59—44no—
314C22×C59#53612yes—
315C22×C59#57712yes—
316C22×C59#57812yes—
317C22×C59C23×D411yescharacteristic
318C4×C59—22no—
319C4×C59—22no—
320C4×C59—22no—
321C4×C59—22no—
322C4×C59—22no—
323C4×C59—42no—
324C4×C59—42no—
325C4×C59—42no—
326C4×C59—42no—
327C4×C59#53612yes—
328C4×C59C2×2−1+411yescharacteristic
329C4×C59C2×2−1+411yescharacteristic
330Dic59—42no—
331Dic59—42no—
332Dic59—42no—
333Dic59—42no—
334C2×#544—591no—
335C2×#541D5911yescharacteristic
336#3242—5916no—
337C2×#501—591no—
338C2×#499—591no—
339C2×#491—591no—
340C2×#487—591no—
341C2×#484—591no—
342C2×#485—591no—
343C2×#485—591no—
344C2×#483—591no—
345C2×#479—591no—
346C2×#479—591no—
347C2×#477—591no—
348C2×#475—591no—
349C2×#433—591no—
350C2×C59—42no—
351C2×C59#324214yescomplemented
352C2×C59C2×#53611yescharacteristic
353C2×C59C2×#57711yescharacteristic
354C2×C59C2×#57811yescharacteristic
355#544—598no—
356#544—1184no—
357#541—24no—
358#541C2×D5918yes—
359C2×C4⋊Q8—591no—
360C2×C4⋊Q8—591no—
361C2×C4⋊Q8—1181no—
362C2×C4⋊Q8C2×D5911yescharacteristic
363C2×#126—21no—
364C2×#126—21no—
365C2×#125—21no—
366C2×#125—21no—
367C2×#125—591no—
368C2×#125—591no—
369C2×#125—1181no—
370C2×#125C2×D5911yescharacteristic
371C2×C22⋊Q8—1181no—
372C2×C22⋊Q8—1181no—
373C2×C22⋊Q8C2×D5911yescharacteristic
374C2×C22⋊Q8C2×D5911yescharacteristic
375C2×C4×Q8C2×D5911yescharacteristic
376C2×C4×Q8C2×D5911yescharacteristic
377C2×#117—591no—
378C2×#117C2×D5911yescharacteristic
379C22×C4⋊C4—591no—
380#501—598no—
381#499—598no—
382#491—598no—
383#487—598no—
384#485—598no—
385#485—598no—
386#484—598no—
387#483—598no—
388#479—598no—
389#479—598no—
390#477—598no—
391#475—598no—
392#433—598no—
393C2×#107—591no—
394C2×#107—591no—
395C2×#107—591no—
396C2×#107—591no—
397C2×#106—591no—
398C2×#106—591no—
399C2×#106—591no—
400C2×#106—591no—
401C2×C4⋊C8—591no—
402C2×C4⋊C8—591no—
403C2×#103—591no—
404C2×#103—591no—
405C2×#103—591no—
406C2×#103—591no—
407C2×#103—591no—
408C2×#103—591no—
409C2×#103—591no—
410C2×#103—591no—
411C2×C22⋊C8—591no—
412C2×C22⋊C8—591no—
413C2×#97—591no—
414C2×C4×C8—591no—
415C59C2×#324211yescharacteristic, complemented, Sylow
416C22×Q8—1181no—
417C22×Q8—1181no—
418C22×Q8C22×D5911yescharacteristic
419C22×Q8C22×D5911yescharacteristic
420C23×C4—1181no—
421C23×C4C22×D5911yescharacteristic
422C22×C8—591no—
423C22×C8—591no—
424C22×C8—591no—
425C22×C8—591no—
426C4⋊Q8—22no—
427C4⋊Q8—594no—
428C4⋊Q8—594no—
429C4⋊Q8—1188no—
430C4⋊Q8—1182no—
431C4⋊Q8—1182no—
432C4⋊Q8C22×D5914yes—
433#126—28no—
434#126—28no—
435#125—28no—
436#125—28no—
437#125—22no—
438#125—594no—
439#125—594no—
440#125—1188no—
441#125—1182no—
442#125—1182no—
443#125C22×D5914yes—
444C22⋊Q8—22no—
445C22⋊Q8—22no—
446C22⋊Q8—1188no—
447C22⋊Q8—1188no—
448C22⋊Q8C22×D5914yes—
449C22⋊Q8C22×D5914yes—
450C4×Q8—22no—
451C4×Q8—22no—
452C4×Q8C22×D5914yes—
453C4×Q8C22×D5914yes—
454#117—594no—
455#117—1182no—
456#117C22⋊D5914yes—
457#117C22×D5914yes—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—591no—
467C2×C4⋊C4—591no—
468C2×C4⋊C4—594no—
469C2×C4⋊C4—591no—
470C2×C4⋊C4—591no—
471C2×C4⋊C4—1181no—
472C2×C4⋊C4—1182no—
473C2×C4⋊C4—1181no—
474C2×C4⋊C4—1181no—
475C2×C4⋊C4—1181no—
476C2×C4⋊C4—1181no—
477C2×C4⋊C4—1181no—
478C2×C4⋊C4—1181no—
479C2×C4⋊C4C22⋊D5911yescharacteristic
480C2×C4⋊C4C22⋊D5911yescharacteristic
481C2×C4⋊C4C22×D5911yescharacteristic
482C2×C4⋊C4C22×D5911yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—1181no—
486C2×C22⋊C4C22⋊D5911yescharacteristic
487C2×C22⋊C4C22⋊D5911yescharacteristic
488C2×C42—21no—
489C2×C42—21no—
490C2×C42—1181no—
491C2×C42C22×D5911yescharacteristic
492C2×C42C22×D5911yescharacteristic
493#107—594no—
494#107—594no—
495#107—594no—
496#107—594no—
497#106—594no—
498#106—594no—
499#106—594no—
500#106—594no—
501C4⋊C8—594no—
502C4⋊C8—594no—
503#103—594no—
504#103—594no—
505#103—594no—
506#103—594no—
507#103—594no—
508#103—594no—
509#103—594no—
510#103—594no—
511C22⋊C8—594no—
512C22⋊C8—594no—
513#97—594no—
514C4×C8—594no—
515C24C2×C22⋊D5911yescharacteristic
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—1184no—
523C2×Q8—1184no—
524C2×Q8—4722no—
525C2×Q8—4722no—
526C2×Q8C23×D5912yes—
527C2×Q8C23×D5912yes—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—1184no—
535C22×C4—1181no—
536C22×C4—1181no—
537C22×C4—1181no—
538C22×C4—1181no—
539C22×C4—4722no—
540C22×C4C2×C22⋊D5912yes—
541C22×C4C2×C22⋊D5911yescharacteristic
542C22×C4C2×C22⋊D5911yescharacteristic
543C22×C4C2×C22⋊D5911yescharacteristic
544C22×C4C2×C22⋊D5911yescharacteristic
545C22×C4C2×C22⋊D5911yescharacteristic
546C22×C4C23×D5912yes—
547C22×C4C23×D5911yescharacteristic
548C2×C8—592no—
549C2×C8—592no—
550C2×C8—592no—
551C2×C8—592no—
552C2×C8—1182no—
553C2×C8—1182no—
554C2×C8—1182no—
555C2×C8—1182no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—592no—
567C4⋊C4—592no—
568C4⋊C4—592no—
569C4⋊C4—592no—
570C4⋊C4—1184no—
571C4⋊C4—1181no—
572C4⋊C4—1181no—
573C4⋊C4—1181no—
574C4⋊C4—1181no—
575C4⋊C4—1184no—
576C4⋊C4—1184no—
577C4⋊C4—1184no—
578C4⋊C4—1184no—
579C4⋊C4—1184no—
580C4⋊C4—1184no—
581C4⋊C4C2×C22⋊D5914yes—
582C4⋊C4C2×C22⋊D5914yes—
583C4⋊C4C23×D5912yes—
584C4⋊C4C23×D5912yes—
585C22⋊C4—24no—
586C22⋊C4—24no—
587C22⋊C4—1184no—
588C22⋊C4C2×C22⋊D5914yes—
589C22⋊C4C2×C22⋊D5914yes—
590C42—24no—
591C42—24no—
592C42—1184no—
593C42C2×C22⋊D5912yes—
594C42C2×C22⋊D5912yes—
595C42C23×D5912yes—
596C42C23×D5912yes—
597C23—22no—
598C23—22no—
599C23—22no—
600C23C22×C22⋊D5912yes—
601C23C22×C22⋊D5911yescharacteristic
602Q8—22no—
603Q8—22no—
604Q8—22no—
605Q8—22no—
606Q8—42no—
607Q8—42no—
608Q8—4724no—
609Q8—4724no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—1182no—
627C2×C4—1182no—
628C2×C4—1182no—
629C2×C4—1182no—
630C2×C4—4724no—
631C2×C4—2362no—
632C2×C4—2362no—
633C2×C4—2362no—
634C2×C4—2362no—
635C2×C4C22×C22⋊D5912yes—
636C2×C4C22×C22⋊D5912yes—
637C2×C4C22×C22⋊D5912yes—
638C2×C4C22×C22⋊D5912yes—
639C2×C4C22×C22⋊D5912yes—
640C2×C4C22×C22⋊D5911yescharacteristic
641C2×C4#1427377412yes—
642C2×C4#1427377412yes—
643C2×C4C24×D5911yescharacteristic
644C8—1182no—
645C8—1182no—
646C8—1182no—
647C8—1182no—
648C22—22no—
649C22—22no—
650C22—22no—
651C22—44no—
652C22#1683797312yes—
653C22#1683821012yes—
654C22#1683821712yes—
655C22C23×C22⋊D5911yescharacteristic
656C4—22no—
657C4—22no—
658C4—22no—
659C4—22no—
660C4—22no—
661C4—42no—
662C4—42no—
663C4—42no—
664C4—42no—
665C4—2362no—
666C4—2362no—
667C4—2362no—
668C4—2362no—
669C4#1683797312yes—
670C4C2×#1427377411yescharacteristic
671C4C2×#1427377411yescharacteristic
672C2—42no—
673C2#2143535814yesdirect product factor
674C2C2×#1683797311yescharacteristic
675C2C2×#1683821011yescharacteristic
676C2C2×#1683821711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#541C2
socleC23×C59C22×D4
prime radicalC24×C59C2×D4
hypercenterC2×#541D59
hypocenterC59C2×#3242
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
2. #21435358C2direct (N × H)
3. C2×#16837812C2semidirect
4. C2×#16837801C2semidirect
5. C2×#16837770C2semidirect
6. C2×#16837752C2semidirect
11. C2×#16837709C2semidirect
12. C2×#16837709C2semidirect
13. C2×#16837697C2semidirect
14. C2×#16837687C2semidirect
29. #16837812C22semidirect
30. #16837801C22semidirect
31. #16837770C22semidirect
32. #16837752C22semidirect
37. #16837709C22semidirect
38. #16837709C22semidirect
39. #16837697C22semidirect
40. #16837687C22semidirect
351. C2×C59#3242semidirect
415. C59C2×#3242semidirect
673. C2#21435358direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380302
#214353582
C2×#168378122
C2×#168378012
C2×#168377702
C2×#168377522
C2×#168377352
C2×#168377402
C2×#168377302
C2×#168377092
C2×#168376972
C2×#168376872
C2×#168374632
C2×C59×#5412
C2×#324259