Finite Group Databasebeta

← C2×#21437053 #29469229

Subgroups — C2×#21437053 #29469229

Order 15104.

1898 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838109C211yesmaximal, characteristic, complemented
2C2×#16838108C211yesmaximal, characteristic, complemented
3#21437053C2116yesmaximal, direct product factor
4C2×#16837812C211yesmaximal, characteristic, complemented
5C2×#16837809C211yesmaximal, characteristic, complemented
6C2×#16837803C211yesmaximal, characteristic, complemented
7C2×#16837705C211yesmaximal, characteristic, complemented
8C2×#16837701C211yesmaximal, characteristic, complemented
9C2×#16837700C211yesmaximal, characteristic, complemented
10C2×#16837683C211yesmaximal, characteristic, complemented
11C2×#16837680C211yesmaximal, characteristic, complemented
12C2×#16837531C211yesmaximal, characteristic, complemented
13C2×#16837512C211yesmaximal, characteristic
14C2×#16837511C211yesmaximal, characteristic
15C2×#16837482C211yesmaximal, characteristic
16C2×C59×#478C211yesmaximal, characteristic, complemented
17C22×#11745669C2211yescharacteristic
18#16838109—24no—
19#16838109C2218yescomplemented
20#16838108—24no—
21#16838108C2218yescomplemented
22C2×#14273727C2211yescharacteristic
23C2×#14273726C2211yescharacteristic
24C2×#14273718C2211yescharacteristic
25C2×#14273718C2211yescharacteristic
26C2×#14273718C2211yescharacteristic
27C2×#14273707—21no—
28C2×#14273706—21no—
29C2×#14273705—21no—
30C2×#14273705—21no—
31C2×#14273704—21no—
32C2×#14273704—21no—
33C2×C4×Dic118C2211yescharacteristic
34C2×C4×D236C2211yescharacteristic
35C2×D4×Dic59C2211yescharacteristic
36C2×D4×Dic59C2211yescharacteristic
37C2×#14273689C2211yescharacteristic
38C2×#14273689C2211yescharacteristic
39C22×C4⋊Dic59—21no—
40C2×C4⋊C4×D59—21no—
41#16837812C2218yescomplemented
42#16837809C2218yescomplemented
43#16837803C2218yescomplemented
44#16837705C2218yescomplemented
45#16837701C2218yescomplemented
46#16837700C2218yescomplemented
47#16837683C2218yescomplemented
48#16837680C2218yescomplemented
49#16837531C2218yescomplemented
50#16837512C2218yes—
51#16837511C2218yes—
52#16837482C2218yes—
53C2×#14273661C2211yescharacteristic
54C2×#14273661C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×#14273658C2211yescharacteristic
59C2×#14273658C2211yescharacteristic
60C2×Dic59⋊C8C2211yescharacteristic
61C2×Dic59⋊C8C2211yescharacteristic
62C2×#14273649C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273648C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×#14273638C2211yescharacteristic
67C2×#14273637C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C2×#125×C59C2211yescharacteristic
70C2×C4×D4×C59C2211yescharacteristic
71C59×#478C2218yescomplemented
72C2×#107×C59C2211yescharacteristic
73C2×#106×C59C2211yescharacteristic
74C2×C4⋊C8×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C22×Dic118D411yescharacteristic
80C22×D236C2311yescharacteristic
81C23×Dic59—21no—
82C23×Dic59—21no—
83C22×C4×D59—21no—
84C22×C4×D59—21no—
85C22×C4×D59—21no—
86C2×#11745669Q818yescomplemented
87C2×#11745669C2314yes—
88C22×C59⋊C8C2311yescharacteristic
89C22×C59⋊C8C2311yescharacteristic
90#14273727—22no—
91#14273727C2314yes—
92#14273726—22no—
93#14273726C2314yes—
94#14273718—22no—
95#14273718—22no—
96#14273718—22no—
97#14273718C2314yes—
98#14273718C2314yes—
99#14273718C2314yes—
100#14273707—28no—
101#14273706—28no—
102#14273705—28no—
103#14273705—28no—
104#14273704—28no—
105#14273704—28no—
106C4×Dic118D414yes—
107C4×Dic118C2314yes—
108C4×D236—22no—
109C4×D236C2314yes—
110D4×Dic59—22no—
111D4×Dic59—22no—
112D4×Dic59C2314yes—
113D4×Dic59C2314yes—
114#14273689—22no—
115#14273689—22no—
116#14273689C2314yes—
117#14273689C2314yes—
118C2×C4⋊Dic59—21no—
119C2×C4⋊Dic59—21no—
120C2×C4⋊Dic59—21no—
121C2×C4⋊Dic59—21no—
122C2×C4⋊Dic59—28no—
123C2×C4⋊Dic59D411yescharacteristic
124C2×C4⋊Dic59C2311yescharacteristic
125C2×C4⋊Dic59C2311yescharacteristic
126C2×C4⋊Dic59C2311yescharacteristic
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4D411yescharacteristic
132C2×Dic59⋊C4D411yescharacteristic
133C4⋊C4×D59—28no—
134C2×C22⋊Dic59—21no—
135C2×C22⋊Dic59—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4—21no—
139C2×C4×Dic59C2311yescharacteristic
140C2×C4×Dic59C2311yescharacteristic
141#14273661C2314yes—
142#14273661C2314yes—
143#14273660C2314yes—
144#14273660C2314yes—
145#14273658C2314yes—
146#14273658C2314yes—
147#14273658C2314yes—
148Dic59⋊C8C2314yes—
149Dic59⋊C8C2314yes—
150#14273649C2314yes—
151#14273649C2314yes—
152#14273648C2314yes—
153#14273647C2314yes—
154#14273638C2314yes—
155#14273637C2314yes—
156C8×Dic59C2314yes—
157C22×D4×C59C2311yescharacteristic
158C23×C4×C59—21no—
159C22×C8×C59C2311yescharacteristic
160C22×C8×C59C2311yescharacteristic
161#125×C59—22no—
162#125×C59C2314yes—
163C4×D4×C59—22no—
164C4×D4×C59C2314yes—
165C2×C4⋊C4×C59—21no—
166C2×C4⋊C4×C59—21no—
167C2×C4⋊C4×C59C2311yescharacteristic
168C2×C4⋊C4×C59C2311yescharacteristic
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C22⋊C4×C59—21no—
171C2×C42×C59C2311yescharacteristic
172#107×C59C2314yes—
173#106×C59C2314yes—
174C4⋊C8×C59C2314yes—
175#102×C59C2314yes—
176#102×C59C2314yes—
177C24×C59—21no—
178C23×D59—21no—
179C2×D4×C59—21no—
180C2×D4×C59—22no—
181C2×D4×C59C2×Q814yes—
182C2×D4×C59C2412yes—
183C22×C4×C59—21no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—24no—
187C22×C4×C59—44no—
188C22×C4×C59C2×D411yescharacteristic
189C22×C4×C59C2×D411yescharacteristic
190C22×C4×C59C2411yescharacteristic
191C22×Dic59—21no—
192C22×Dic59—21no—
193C22×Dic59—21no—
194C22×Dic59—24no—
195C22×Dic59—24no—
196C22×Dic59—82no—
197C22×Dic59—82no—
198C22×Dic59C2×D411yescharacteristic
199C22×Dic59C2×D411yescharacteristic
200C22×Dic59C2×D411yescharacteristic
201C22×Dic59C2×D411yescharacteristic
202C2×D236—21no—
203C2×D236—22no—
204C2×D236C2×Q814yes—
205C2×D236C2412yes—
206C2×C4×D59—24no—
207C2×C4×D59—24no—
208C2×C4×D59—24no—
209C2×C4×D59—44no—
210C2×C4×D59—82no—
211C2×C4×D59—82no—
212C2×Dic118—24no—
213C2×Dic118—24no—
214C2×Dic118—42no—
215C2×Dic118—82no—
216C2×Dic118—82no—
217C2×Dic118C2×D414yes—
218C2×C8×C59—22no—
219C2×C8×C59—22no—
220C2×C8×C59C2412yes—
221C2×C8×C59C2412yes—
222C4⋊C4×C59—24no—
223C4⋊C4×C59—24no—
224C4⋊C4×C59—21no—
225C4⋊C4×C59—21no—
226C4⋊C4×C59—21no—
227C4⋊C4×C59C2412yes—
228C4⋊C4×C59C2412yes—
229C4⋊C4×C59C2412yes—
230C22⋊C4×C59—24no—
231C42×C59C2×D412yes—
232C42×C59C2412yes—
233C22⋊Dic59—24no—
234C22⋊Dic59—24no—
235#11745669C2×Q8116yescomplemented
236(C2×D59)⋊C4—24no—
237(C2×D59)⋊C4—24no—
238(C2×D59)⋊C4—24no—
239C4⋊Dic59—24no—
240C4⋊Dic59—21no—
241C4⋊Dic59—21no—
242C4⋊Dic59—21no—
243C4⋊Dic59—24no—
244C4⋊Dic59—24no—
245C4⋊Dic59—24no—
246C4⋊Dic59C2×D414yes—
247C4⋊Dic59C2412yes—
248C4⋊Dic59C2412yes—
249C4⋊Dic59C2412yes—
250Dic59⋊C4—24no—
251Dic59⋊C4—24no—
252Dic59⋊C4—24no—
253Dic59⋊C4—24no—
254Dic59⋊C4C2×D414yes—
255Dic59⋊C4C2×D414yes—
256C4×Dic59C2×D412yes—
257C4×Dic59C2×D412yes—
258C4×Dic59C2412yes—
259C4×Dic59C2412yes—
260C2×C59⋊C8—22no—
261C2×C59⋊C8C2×Q814yes—
262C2×C59⋊C8C2412yes—
263C2×C59⋊C8C2412yes—
264C23×C59—24no—
265C23×C59—22no—
266C23×C59—42no—
267C23×C59—42no—
268C23×C59C22×D411yescharacteristic
269C22×D59—24no—
270C22×D59—22no—
271C22×D59—42no—
272C22×D59—42no—
273D4×C59—24no—
274D4×C59—22no—
275D4×C59C22×Q814yes—
276C2×C4×C59—22no—
277C2×C4×C59—22no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—48no—
282C2×C4×C59—42no—
283C2×C4×C59—42no—
284C2×C4×C59—42no—
285C2×C4×C59C22×D412yes—
286C2×C4×C59C22×D412yes—
287C2×C4×C59C22×D411yescharacteristic
288C2×C4×C59C22×Q812yes—
289C2×C4×C592−1+412yes—
290C2×C4×C59C2511yescharacteristic
291C2×Dic59—22no—
292C2×Dic59—22no—
293C2×Dic59—22no—
294C2×Dic59—22no—
295C2×Dic59—22no—
296C2×Dic59—22no—
297C2×Dic59—22no—
298C2×Dic59—42no—
299C2×Dic59—42no—
300C2×Dic59—42no—
301C2×Dic59—84no—
302C2×Dic59—84no—
303C2×Dic59C22×D412yes—
304C2×Dic59C22×D412yes—
305C2×Dic59C22×D412yes—
306C2×Dic59C22×D412yes—
307D236—24no—
308D236—22no—
309D236C22×Q814yes—
310C4×D59—48no—
311C4×D59—84no—
312C4×D59—84no—
313Dic118—44no—
314Dic118—84no—
315Dic118—84no—
316C8×C59—22no—
317C8×C59—22no—
318C59⋊C8—22no—
319C59⋊C8C22×Q814yes—
320C2×#3389—591nomaximal, Sylow
321C22×C59—24no—
322C22×C59—48no—
323C22×C59—42no—
324C22×C59—42no—
325C22×C59D4×Q812yes—
326C22×C59#57512yes—
327C22×C59#57612yes—
328C22×C59C23×D411yescharacteristic
329C2×D59—24no—
330C2×D59—48no—
331C2×D59—42no—
332C2×D59—42no—
333C4×C59—22no—
334C4×C59—22no—
335C4×C59—42no—
336C4×C59—42no—
337C4×C59—42no—
338C4×C59D4×Q812yes—
339C4×C59C23×Q811yescharacteristic
340C4×C59C2×2−1+411yescharacteristic
341Dic59—22no—
342Dic59—22no—
343Dic59—22no—
344Dic59—22no—
345Dic59—42no—
346Dic59—42no—
347Dic59—42no—
348C2×#554—591no—
349C2×#554—591no—
350#3389—5916no—
351C2×#501—591no—
352C2×#501—591no—
353C2×#499—591no—
354C2×#478—591no—
355C2×#478—591no—
356C2×#478—591no—
357C2×#478D5911yescharacteristic, complemented
358C2×#474—591no—
359C2×#474—591no—
360C2×#446—591no—
361C2×#442—591no—
362C2×#442—591no—
363C2×C4×D8—591no—
364C2×C59—44no—
365C2×C59#338914yescomplemented
366C2×C59C2×D4×Q811yescharacteristic
367C2×C59C2×#57511yescharacteristic
368C2×C59C2×#57611yescharacteristic
369D59—44no—
370C22×D8—591no—
371#554—598no—
372#554—598no—
373#554—1184no—
374#554—1184no—
375C2×C4⋊Q8—591no—
376C2×C4⋊Q8—591no—
377C2×#125—591no—
378C2×#125—591no—
379C2×#125—591no—
380C2×#125C2×D5911yescharacteristic
381C2×C22⋊Q8—1181no—
382C2×C22⋊Q8—1181no—
383C2×C22⋊Q8—1181no—
384C2×C22⋊Q8—1181no—
385C2×C22⋊Q8—1181no—
386C2×C22⋊Q8—1181no—
387C2×C4×Q8—591no—
388C2×C4×D4—591no—
389C2×C4×D4—591no—
390C2×C4×D4—591no—
391C2×C4×D4—591no—
392C2×C4×D4—591no—
393C2×C4×D4C2×D5911yescharacteristic
394C22×C4⋊C4—1181no—
395C22×C4⋊C4—1181no—
396#501—598no—
397#501—598no—
398#499—598no—
399#478—598no—
400#478—598no—
401#478—598no—
402#478C2×D5918yescomplemented
403#474—598no—
404#474—598no—
405#446—598no—
406#442—598no—
407#442—598no—
408C4×D8—598no—
409C2×#107—591no—
410C2×#107—591no—
411C2×#107—591no—
412C2×#107—591no—
413C2×#107C2×D5911yescharacteristic
414C2×#106—591no—
415C2×#106—591no—
416C2×#106—591no—
417C2×#106C2×D5911yescharacteristic
418C2×C4⋊C8—591no—
419C2×C4⋊C8—591no—
420C2×C4⋊C8C2×D5911yescharacteristic
421C2×#102—591no—
422C2×#102—591no—
423C2×#102—591no—
424C2×#102—591no—
425C2×#102C2×D5911yescharacteristic
426C2×#102C2×D5911yescharacteristic
427C2×#97—591no—
428C2×#97—591no—
429C2×C4×C8—591no—
430C59C2×#338911yescharacteristic, complemented, Sylow
431C22×Q8—591no—
432C22×Q8—1181no—
433C22×Q8—1181no—
434C22×D4—591no—
435C22×D4C22×D5911yescharacteristic
436C23×C4—21no—
437C23×C4—1181no—
438C23×C4—1181no—
439C23×C4—1181no—
440C23×C4—1181no—
441C23×C4—1181no—
442C2×D8—598no—
443C2×D8—594no—
444C22×C8—591no—
445C22×C8—591no—
446C22×C8C22×D5911yescharacteristic
447C22×C8C22×D5911yescharacteristic
448C4⋊Q8—594no—
449C4⋊Q8—594no—
450C4⋊Q8—1182no—
451C4⋊Q8—1182no—
452#125—22no—
453#125—594no—
454#125—594no—
455#125—594no—
456#125—1182no—
457#125—1182no—
458#125—1182no—
459#125C22×D5914yes—
460C22⋊Q8—1188no—
461C22⋊Q8—1188no—
462C22⋊Q8—1188no—
463C22⋊Q8—1188no—
464C22⋊Q8—1188no—
465C22⋊Q8—1188no—
466C4×Q8—594no—
467C4×Q8—594no—
468C4×D4—22no—
469C4×D4—594no—
470C4×D4—594no—
471C4×D4—594no—
472C4×D4—594no—
473C4×D4—594no—
474C4×D4—1182no—
475C4×D4—1182no—
476C4×D4—1182no—
477C4×D4—1182no—
478C4×D4—1182no—
479C4×D4C22×D5914yes—
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—591no—
487C2×C4⋊C4—591no—
488C2×C4⋊C4—1188no—
489C2×C4⋊C4—1188no—
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⋊C4C22×D5911yescharacteristic
499C2×C4⋊C4C22×D5911yescharacteristic
500C2×C4⋊C4C22×D5911yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—1181no—
503C2×C22⋊C4—1181no—
504C2×C22⋊C4—1181no—
505C2×C22⋊C4—1181no—
506C2×C22⋊C4—1181no—
507C2×C42—591no—
508C2×C42—591no—
509C2×C42C22×D5911yescharacteristic
510#107—594no—
511#107—594no—
512#107—594no—
513#107—594no—
514#107C22×D5914yes—
515#106—594no—
516#106—594no—
517#106—594no—
518#106C22×D5914yes—
519C4⋊C8—594no—
520C4⋊C8—594no—
521C4⋊C8C22×D5914yes—
522#102—594no—
523#102—594no—
524#102—594no—
525#102—594no—
526#102C22×D5914yes—
527#102C22×D5914yes—
528#97—594no—
529#97—594no—
530C4×C8—594no—
531C24—21no—
532C24—1181no—
533C2×Q8—594no—
534C2×Q8—1184no—
535C2×Q8—1184no—
536C2×Q8—4722no—
537C2×Q8—4722no—
538C2×Q8—2362no—
539C2×D4—21no—
540C2×D4—22no—
541C2×D4—594no—
542C2×D4—592no—
543C2×D4—1181no—
544C2×D4—1182no—
545C2×D4Q8×D5914yes—
546C2×D4C23×D5912yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—44no—
552C22×C4—591no—
553C22×C4—591no—
554C22×C4—591no—
555C22×C4—591no—
556C22×C4—1184no—
557C22×C4—1184no—
558C22×C4—1184no—
559C22×C4—1184no—
560C22×C4—1181no—
561C22×C4—1181no—
562C22×C4—1181no—
563C22×C4—1184no—
564C22×C4—4722no—
565C22×C4—4722no—
566C22×C4—4722no—
567C22×C4—4722no—
568C22×C4—2364no—
569C22×C4D4×D5911yescharacteristic
570C22×C4D4×D5911yescharacteristic
571C22×C4C23×D5911yescharacteristic
572D8—5916no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—594no—
576C2×C8—592no—
577C2×C8—592no—
578C2×C8—1182no—
579C2×C8C23×D5912yes—
580C2×C8C23×D5912yes—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—594no—
587C4⋊C4—594no—
588C4⋊C4—594no—
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—1181no—
600C4⋊C4—1181no—
601C4⋊C4—1181no—
602C4⋊C4—1184no—
603C4⋊C4C23×D5912yes—
604C4⋊C4C23×D5912yes—
605C4⋊C4C23×D5912yes—
606C22⋊C4—24no—
607C22⋊C4—1184no—
608C22⋊C4—1184no—
609C22⋊C4—1184no—
610C22⋊C4—1184no—
611C22⋊C4—1184no—
612C42—592no—
613C42—592no—
614C42—592no—
615C42—592no—
616C42D4×D5912yes—
617C42C23×D5912yes—
618C23—22no—
619C23—24no—
620C23—42no—
621C23—42no—
622C23—1182no—
623C23—1184no—
624C23—2362no—
625C23—2362no—
626C23C2×D4×D5911yescharacteristic
627Q8—4724no—
628Q8—4724no—
629Q8—2364no—
630D4—22no—
631D4—24no—
632D4—594no—
633D4—1182no—
634D4—1184no—
635D4C2×Q8×D5914yes—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—48no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—592no—
646C2×C4—592no—
647C2×C4—592no—
648C2×C4—592no—
649C2×C4—1182no—
650C2×C4—1182no—
651C2×C4—1182no—
652C2×C4—1182no—
653C2×C4—1182no—
654C2×C4—1182no—
655C2×C4—1182no—
656C2×C4—4724no—
657C2×C4—4724no—
658C2×C4—4724no—
659C2×C4—4724no—
660C2×C4—2368no—
661C2×C4—2362no—
662C2×C4—2362no—
663C2×C4—2362no—
664C2×C4C2×D4×D5912yes—
665C2×C4C2×D4×D5912yes—
666C2×C4C2×D4×D5911yescharacteristic
667C2×C4C2×Q8×D5912yes—
668C2×C4#1427377412yes—
669C2×C4C24×D5911yescharacteristic
670C8—22no—
671C8—22no—
672C8—594no—
673C8—1182no—
674C22—24no—
675C22—42no—
676C22—48no—
677C22—42no—
678C22—1184no—
679C22—2362no—
680C22—2368no—
681C22—2362no—
682C22#1683806512yes—
683C22#1683819812yes—
684C22#1683820412yes—
685C22C22×D4×D5911yescharacteristic
686C4—22no—
687C4—22no—
688C4—42no—
689C4—42no—
690C4—42no—
691C4—1182no—
692C4—1182no—
693C4—1182no—
694C4—1182no—
695C4—2362no—
696C4—2362no—
697C4—2362no—
698C4#1683806512yes—
699C4C22×Q8×D5911yescharacteristic
700C4C2×#1427377411yescharacteristic
701C2—44no—
702C2—2364no—
703C2#2143705314yesdirect product factor
704C2C2×#1683806511yescharacteristic
705C2C2×#1683819811yescharacteristic
706C2C2×#1683820411yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#478C2
socleC23×C59C22×D4
prime radicalC22×#11745669C22
hypercenterC2×#478D59
hypocenterC59C2×#3389
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#16838109C2semidirect
2. C2×#16838108C2semidirect
3. #21437053C2direct (N × H)
4. C2×#16837812C2semidirect
5. C2×#16837809C2semidirect
6. C2×#16837803C2semidirect
7. C2×#16837705C2semidirect
8. C2×#16837701C2semidirect
9. C2×#16837700C2semidirect
10. C2×#16837683C2semidirect
11. C2×#16837680C2semidirect
12. C2×#16837531C2semidirect
16. C2×C59×#478C2semidirect
19. #16838109C22semidirect
21. #16838108C22semidirect
41. #16837812C22semidirect
42. #16837809C22semidirect
43. #16837803C22semidirect
44. #16837705C22semidirect
45. #16837701C22semidirect
46. #16837700C22semidirect
47. #16837683C22semidirect
48. #16837680C22semidirect
49. #16837531C22semidirect
71. C59×#478C22semidirect
86. C2×#11745669Q8semidirect
235. #11745669C2×Q8semidirect
357. C2×#478D59semidirect
365. C2×C59#3389semidirect
402. #478C2×D59semidirect
430. C59C2×#3389semidirect
703. C2#21437053direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381092
C2×#168381082
#214370532
C2×#168378122
C2×#168378092
C2×#168378032
C2×#168377052
C2×#168377012
C2×#168377002
C2×#168376832
C2×#168376802
C2×#168375312
C2×#168375122
C2×#168375112
C2×#168374822
C2×C59×#4782
C2×#338959