Finite Group Databasebeta

← C2×#21435364 #29460894

Subgroups — C2×#21435364 #29460894

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×#16838014C211yesmaximal, characteristic
2#21435364C2116yesmaximal, direct product factor
3C2×#16837808C211yesmaximal, characteristic, complemented
4C2×#16837801C211yesmaximal, characteristic, complemented
5C2×#16837772C211yesmaximal, characteristic, complemented
6C2×#16837754C211yesmaximal, characteristic, complemented
7C2×#16837737C211yesmaximal, characteristic
8C2×#16837743C211yesmaximal, characteristic
9C2×#16837743C211yesmaximal, characteristic
10C2×#16837732C211yesmaximal, characteristic
11C2×#16837706C211yesmaximal, characteristic, complemented
12C2×#16837706C211yesmaximal, characteristic, complemented
13C2×#16837694C211yesmaximal, characteristic, complemented
14C2×#16837684C211yesmaximal, characteristic, complemented
15C2×#16837463C211yesmaximal, characteristic
16C2×C59×#544C211yesmaximal, characteristic
17#16838014—24no—
18#16838014C2218yes—
19C2×#14273727C2211yescharacteristic
20C2×#14273720—21no—
21C2×#14273720—21no—
22C2×#14273719C2211yescharacteristic
23C2×#14273717—21no—
24C2×#14273717—21no—
25C2×#14273706C2211yescharacteristic
26C2×#14273706C2211yescharacteristic
27C2×C4×Dic118C2211yescharacteristic
28C2×C4×Dic118C2211yescharacteristic
29#16837808C2218yescomplemented
30#16837801C2218yescomplemented
31#16837772C2218yescomplemented
32#16837754C2218yescomplemented
33#16837743C2218yes—
34#16837743C2218yes—
35#16837737C2218yes—
36#16837732C2218yes—
37#16837706C2218yescomplemented
38#16837706C2218yescomplemented
39#16837694C2218yescomplemented
40#16837684C2218yescomplemented
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×#14273650C2211yescharacteristic
53C2×#14273650C2211yescharacteristic
54C2×#14273650C2211yescharacteristic
55C2×#14273650C2211yescharacteristic
56C2×#14273650C2211yescharacteristic
57C2×#14273650C2211yescharacteristic
58C2×#14273650C2211yescharacteristic
59C2×#14273650C2211yescharacteristic
60C2×C22⋊(C59⋊C8)C2211yescharacteristic
61C2×C22⋊(C59⋊C8)C2211yescharacteristic
62C2×#14273638C2211yescharacteristic
63C2×C4×C59⋊C8C2211yescharacteristic
64C59×#544—24no—
65C59×#544C2218yes—
66C2×C4⋊Q8×C59—21no—
67C2×C4⋊Q8×C59C2211yescharacteristic
68C2×C4⋊Q8×C59C2211yescharacteristic
69C2×#125×C59—21no—
70C2×#125×C59C2211yescharacteristic
71C2×#125×C59C2211yescharacteristic
72C2×C22⋊Q8×C59—21no—
73C2×C22⋊Q8×C59—21no—
74C2×#117×C59C2211yescharacteristic
75C2×#117×C59C2211yescharacteristic
76C22×C4⋊C4×C59C2211yescharacteristic
77C22×Dic118C2311yescharacteristic
78C22×Dic118C2311yescharacteristic
79C22×C59⋊C8C2311yescharacteristic
80C22×C59⋊C8C2311yescharacteristic
81C22×C59⋊C8C2311yescharacteristic
82C22×C59⋊C8C2311yescharacteristic
83#14273727—22no—
84#14273727C2314yes—
85#14273720—28no—
86#14273720—28no—
87#14273719—22no—
88#14273719C2314yes—
89#14273717—28no—
90#14273717—28no—
91#14273706—22no—
92#14273706—22no—
93#14273706C2314yes—
94#14273706C2314yes—
95C4×Dic118—22no—
96C4×Dic118—22no—
97C4×Dic118C2314yes—
98C4×Dic118C2314yes—
99C2×C4⋊Dic59—21no—
100C2×C4⋊Dic59—21no—
101C2×C4⋊Dic59C2311yescharacteristic
102C2×C4⋊Dic59C2311yescharacteristic
103C2×Dic59⋊C4—21no—
104C2×Dic59⋊C4—21no—
105C2×Dic59⋊C4—21no—
106C2×Dic59⋊C4—21no—
107C2×Dic59⋊C4—21no—
108C2×Dic59⋊C4—21no—
109C2×C22⋊Dic59—21no—
110C2×C22⋊Dic59—21no—
111C2×C4×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#14273650C2314yes—
124#14273650C2314yes—
125#14273650C2314yes—
126#14273650C2314yes—
127#14273650C2314yes—
128#14273650C2314yes—
129#14273650C2314yes—
130#14273650C2314yes—
131C22⋊(C59⋊C8)C2314yes—
132C22⋊(C59⋊C8)C2314yes—
133#14273638C2314yes—
134C4×C59⋊C8C2314yes—
135C22×Q8×C59—21no—
136C22×Q8×C59—21no—
137C23×C4×C59—21no—
138C23×C4×C59C2311yescharacteristic
139C4⋊Q8×C59—28no—
140C4⋊Q8×C59—22no—
141C4⋊Q8×C59—22no—
142C4⋊Q8×C59C2314yes—
143C4⋊Q8×C59C2314yes—
144#125×C59—28no—
145#125×C59—22no—
146#125×C59—22no—
147#125×C59C2314yes—
148#125×C59C2314yes—
149C22⋊Q8×C59—28no—
150C22⋊Q8×C59—28no—
151#117×C59—22no—
152#117×C59D414yes—
153#117×C59C2314yes—
154#117×C59C2314yes—
155C2×C4⋊C4×C59—21no—
156C2×C4⋊C4×C59—22no—
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×C59D411yescharacteristic
164C2×C4⋊C4×C59D411yescharacteristic
165C2×C4⋊C4×C59C2311yescharacteristic
166C2×C4⋊C4×C59C2311yescharacteristic
167C2×C4⋊C4×C59C2311yescharacteristic
168C2×C4⋊C4×C59C2311yescharacteristic
169C2×C4⋊C4×C59C2314yes—
170C2×C22⋊C4×C59—21no—
171C2×C22⋊C4×C59D411yescharacteristic
172C2×C22⋊C4×C59D411yescharacteristic
173C2×C42×C59—21no—
174C2×C42×C59C2311yescharacteristic
175C2×C42×C59C2311yescharacteristic
176C24×C59C2×D411yescharacteristic
177C2×Q8×C59—24no—
178C2×Q8×C59—24no—
179C2×Q8×C59—82no—
180C2×Q8×C59—82no—
181C22×C4×C59—22no—
182C22×C4×C59—22no—
183C22×C4×C59—21no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—24no—
188C22×C4×C59—82no—
189C22×C4×C59C2×D411yescharacteristic
190C22×C4×C59C2×D411yescharacteristic
191C22×C4×C59C2×D411yescharacteristic
192C22×C4×C59C2×D411yescharacteristic
193C22×C4×C59C2×D411yescharacteristic
194C22×C4×C59C2×D412yes—
195C22×C4×C59C2412yes—
196C22×C4×C59C2411yescharacteristic
197C22×Dic59—21no—
198C22×Dic59—21no—
199C22×Dic59—21no—
200C22×Dic59—21no—
201C2×Dic118—22no—
202C2×Dic118—22no—
203C2×Dic118—22no—
204C2×Dic118—22no—
205C2×Dic118—21no—
206C2×Dic118—21no—
207C2×Dic118C2412yes—
208C2×Dic118C2412yes—
209C4⋊C4×C59—24no—
210C4⋊C4×C59—21no—
211C4⋊C4×C59—21no—
212C4⋊C4×C59—24no—
213C4⋊C4×C59—24no—
214C4⋊C4×C59—24no—
215C4⋊C4×C59—24no—
216C4⋊C4×C59—24no—
217C4⋊C4×C59—24no—
218C4⋊C4×C59—21no—
219C4⋊C4×C59—21no—
220C4⋊C4×C59C2×D414yes—
221C4⋊C4×C59C2×D414yes—
222C4⋊C4×C59C2412yes—
223C4⋊C4×C59C2412yes—
224C4⋊C4×C59C2412yes—
225C4⋊C4×C59C2412yes—
226C22⋊C4×C59—24no—
227C22⋊C4×C59C2×D414yes—
228C22⋊C4×C59C2×D414yes—
229C42×C59—24no—
230C42×C59C2×D412yes—
231C42×C59C2×D412yes—
232C42×C59C2412yes—
233C42×C59C2412yes—
234C22⋊Dic59—24no—
235C22⋊Dic59—24no—
236C4⋊Dic59—24no—
237C4⋊Dic59—24no—
238C4⋊Dic59—21no—
239C4⋊Dic59—21no—
240C4⋊Dic59C2412yes—
241C4⋊Dic59C2412yes—
242Dic59⋊C4—24no—
243Dic59⋊C4—24no—
244Dic59⋊C4—24no—
245Dic59⋊C4—24no—
246Dic59⋊C4—24no—
247Dic59⋊C4—24no—
248C4×Dic59—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—84no—
264Q8×C59—84no—
265C2×C4×C59—22no—
266C2×C4×C59—22no—
267C2×C4×C59—22no—
268C2×C4×C59—22no—
269C2×C4×C59—22no—
270C2×C4×C59—24no—
271C2×C4×C59—22no—
272C2×C4×C59—22no—
273C2×C4×C59—22no—
274C2×C4×C59—22no—
275C2×C4×C59—22no—
276C2×C4×C59—22no—
277C2×C4×C59—42no—
278C2×C4×C59—42no—
279C2×C4×C59—42no—
280C2×C4×C59—42no—
281C2×C4×C59—84no—
282C2×C4×C59C22×D412yes—
283C2×C4×C59C22×D412yes—
284C2×C4×C59C22×D412yes—
285C2×C4×C59C22×D412yes—
286C2×C4×C59C22×D412yes—
287C2×C4×C59C22×D411yescharacteristic
288C2×C4×C592−1+412yes—
289C2×C4×C592−1+412yes—
290C2×C4×C59C2511yescharacteristic
291C2×Dic59—22no—
292C2×Dic59—22no—
293C2×Dic59—22no—
294C2×Dic59—22no—
295C2×Dic59—42no—
296C2×Dic59—42no—
297C2×Dic59—42no—
298C2×Dic59—42no—
299Dic118—22no—
300Dic118—22no—
301Dic118—22no—
302Dic118—22no—
303Dic118—42no—
304Dic118—42no—
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×#544D5911yescharacteristic
335C2×#541—591no—
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—24no—
356#544C2×D5918yes—
357#541—598no—
358#541—1184no—
359C2×C4⋊Q8—21no—
360C2×C4⋊Q8—591no—
361C2×C4⋊Q8C2×D5911yescharacteristic
362C2×C4⋊Q8C2×D5911yescharacteristic
363C2×#126—1181no—
364C2×#126—1181no—
365C2×#125—21no—
366C2×#125—591no—
367C2×#125—1181no—
368C2×#125—1181no—
369C2×#125C2×D5911yescharacteristic
370C2×#125C2×D5911yescharacteristic
371C2×C22⋊Q8—21no—
372C2×C22⋊Q8—21no—
373C2×C22⋊Q8—591no—
374C2×C22⋊Q8—591no—
375C2×C4×Q8—591no—
376C2×C4×Q8—591no—
377C2×#117C2×D5911yescharacteristic
378C2×#117C2×D5911yescharacteristic
379C22×C4⋊C4C2×D5911yescharacteristic
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—21no—
417C22×Q8—21no—
418C22×Q8—591no—
419C22×Q8—591no—
420C23×C4—21no—
421C23×C4C22×D5911yescharacteristic
422C22×C8—591no—
423C22×C8—591no—
424C22×C8—591no—
425C22×C8—591no—
426C4⋊Q8—28no—
427C4⋊Q8—22no—
428C4⋊Q8—22no—
429C4⋊Q8—594no—
430C4⋊Q8—1182no—
431C4⋊Q8C22×D5914yes—
432C4⋊Q8C22×D5914yes—
433#126—1188no—
434#126—1188no—
435#125—28no—
436#125—22no—
437#125—22no—
438#125—594no—
439#125—1188no—
440#125—1188no—
441#125—1182no—
442#125C22×D5914yes—
443#125C22×D5914yes—
444C22⋊Q8—28no—
445C22⋊Q8—28no—
446C22⋊Q8—594no—
447C22⋊Q8—594no—
448C22⋊Q8—1182no—
449C22⋊Q8—1182no—
450C4×Q8—594no—
451C4×Q8—594no—
452C4×Q8—1182no—
453C4×Q8—1182no—
454#117—22no—
455#117C22⋊D5914yes—
456#117C22×D5914yes—
457#117C22×D5914yes—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—22no—
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—1181no—
469C2×C4⋊C4—1181no—
470C2×C4⋊C4—1181no—
471C2×C4⋊C4—1181no—
472C2×C4⋊C4—1181no—
473C2×C4⋊C4—1181no—
474C2×C4⋊C4—1181no—
475C2×C4⋊C4—1181no—
476C2×C4⋊C4C22⋊D5911yescharacteristic
477C2×C4⋊C4C22⋊D5911yescharacteristic
478C2×C4⋊C4C22×D5911yescharacteristic
479C2×C4⋊C4C22×D5911yescharacteristic
480C2×C4⋊C4C22×D5914yes—
481C2×C4⋊C4C22×D5911yescharacteristic
482C2×C4⋊C4C22×D5911yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—1181no—
485C2×C22⋊C4—1181no—
486C2×C22⋊C4C22⋊D5911yescharacteristic
487C2×C22⋊C4C22⋊D5911yescharacteristic
488C2×C42—21no—
489C2×C42—1181no—
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—24no—
517C2×Q8—24no—
518C2×Q8—82no—
519C2×Q8—82no—
520C2×Q8—592no—
521C2×Q8—592no—
522C2×Q8—1181no—
523C2×Q8—1181no—
524C2×Q8—1182no—
525C2×Q8—1182no—
526C2×Q8—1182no—
527C2×Q8—1182no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—24no—
535C22×C4—82no—
536C22×C4—1181no—
537C22×C4—1181no—
538C22×C4—1181no—
539C22×C4—1181no—
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—21no—
558C4⋊C4—21no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—592no—
568C4⋊C4—592no—
569C4⋊C4—1181no—
570C4⋊C4—1181no—
571C4⋊C4—1184no—
572C4⋊C4—1184no—
573C4⋊C4—1184no—
574C4⋊C4—1184no—
575C4⋊C4—1184no—
576C4⋊C4—1184no—
577C4⋊C4—1184no—
578C4⋊C4—1184no—
579C4⋊C4C2×C22⋊D5914yes—
580C4⋊C4C2×C22⋊D5914yes—
581C4⋊C4C23×D5912yes—
582C4⋊C4C23×D5912yes—
583C4⋊C4C23×D5912yes—
584C4⋊C4C23×D5912yes—
585C22⋊C4—24no—
586C22⋊C4—1184no—
587C22⋊C4—1184no—
588C22⋊C4C2×C22⋊D5914yes—
589C22⋊C4C2×C22⋊D5914yes—
590C42—24no—
591C42—1184no—
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—84no—
603Q8—84no—
604Q8—1182no—
605Q8—1182no—
606Q8—1182no—
607Q8—1182no—
608Q8—2362no—
609Q8—2362no—
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—84no—
627C2×C4—1182no—
628C2×C4—1182no—
629C2×C4—1182no—
630C2×C4—1182no—
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#1427377512yes—
642C2×C4#1427377512yes—
643C2×C4C24×D5911yescharacteristic
644C8—1182no—
645C8—1182no—
646C8—1182no—
647C8—1182no—
648C22—22no—
649C22—22no—
650C22—22no—
651C22—44no—
652C22#1683797612yes—
653C22#1683821312yes—
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#1683797612yes—
670C4C2×#1427377511yescharacteristic
671C4C2×#1427377511yescharacteristic
672C2—42no—
673C2#2143536414yesdirect product factor
674C2C2×#1683797611yescharacteristic
675C2C2×#1683821311yescharacteristic
676C2C2×#1683821711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#544C2
socleC23×C59C22×D4
prime radicalC24×C59C2×D4
hypercenterC2×#544D59
hypocenterC59C2×#3242
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #21435364C2direct (N × H)
3. C2×#16837808C2semidirect
4. C2×#16837801C2semidirect
5. C2×#16837772C2semidirect
6. C2×#16837754C2semidirect
11. C2×#16837706C2semidirect
12. C2×#16837706C2semidirect
13. C2×#16837694C2semidirect
14. C2×#16837684C2semidirect
29. #16837808C22semidirect
30. #16837801C22semidirect
31. #16837772C22semidirect
32. #16837754C22semidirect
37. #16837706C22semidirect
38. #16837706C22semidirect
39. #16837694C22semidirect
40. #16837684C22semidirect
351. C2×C59#3242semidirect
415. C59C2×#3242semidirect
673. C2#21435364direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380142
#214353642
C2×#168378082
C2×#168378012
C2×#168377722
C2×#168377542
C2×#168377372
C2×#168377432
C2×#168377322
C2×#168377062
C2×#168376942
C2×#168376842
C2×#168374632
C2×C59×#5442
C2×#324259