Finite Group Databasebeta

← C2×#21433937 #29456259

Subgroups — C2×#21433937 #29456259

Order 15104.

2018 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838032C211yesmaximal, characteristic
2C2×#16837878C211yesmaximal, characteristic
3#21433937C2116yesmaximal, direct product factor
4C2×#16837711C211yesmaximal, characteristic, complemented
5C2×#16837708C211yesmaximal, characteristic, complemented
6C2×#16837706C211yesmaximal, characteristic, complemented
7C2×#16837698C211yesmaximal, characteristic, complemented
8C2×#16837695C211yesmaximal, characteristic, complemented
9C2×#16837687C211yesmaximal, characteristic, complemented
10C2×#16837686C211yesmaximal, characteristic, complemented
11C2×#16837441C211yesmaximal, characteristic
12C2×#16837439C211yesmaximal, characteristic
13C2×#16837427C211yesmaximal, characteristic
14C2×#16837409C211yesmaximal, characteristic
15C2×#103×D59C211yesmaximal, characteristic
16C2×C59×#479C211yesmaximal, characteristic, complemented
17C22×Q8×D59C2211yescharacteristic
18C22×#11745659C2211yescharacteristic
19C22×C8×D59C2211yescharacteristic
20#16838032—24no—
21#16838032C2218yes—
22C2×#14273727C2211yescharacteristic
23C2×#14273726—21no—
24C2×#14273726C2211yescharacteristic
25C2×#14273718C2211yescharacteristic
26C2×#14273717—21no—
27C2×#14273707—21no—
28C2×#14273705—21no—
29#16837878—24no—
30#16837878C2218yes—
31C2×Q8×Dic59C2211yescharacteristic
32C2×C4×Dic118—21no—
33C2×C4×Dic118C2211yescharacteristic
34C2×#14273692—21no—
35C2×#14273692C2211yescharacteristic
36C2×#14273685—21no—
37C2×#14273685C2211yescharacteristic
38C2×#14273685C2211yescharacteristic
39C2×#14273684—21no—
40C2×#14273684C2211yescharacteristic
41C2×C4⋊C4×D59C2211yescharacteristic
42#16837711C2218yescomplemented
43#16837708C2218yescomplemented
44#16837706C2218yescomplemented
45#16837698C2218yescomplemented
46#16837695C2218yescomplemented
47#16837687C2218yescomplemented
48#16837686C2218yescomplemented
49#16837441C2218yes—
50#16837439C2218yes—
51C2×#14273661C2211yescharacteristic
52C2×#14273661C2211yescharacteristic
53C2×#14273660C2211yescharacteristic
54C2×#14273658C2211yescharacteristic
55C2×#14273658C2211yescharacteristic
56C2×#14273658C2211yescharacteristic
57#16837427C2218yes—
58C2×C4⋊(C59⋊C8)C2211yescharacteristic
59C2×Dic59⋊C8C2211yescharacteristic
60C2×Dic59⋊C8C2211yescharacteristic
61#16837409C2218yes—
62C2×#14273652C2211yescharacteristic
63C2×#14273652C2211yescharacteristic
64C2×#14273651C2211yescharacteristic
65C2×#14273651C2211yescharacteristic
66C2×#14273650C2211yescharacteristic
67C2×#14273650C2211yescharacteristic
68#103×D59C2218yes—
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
77C22×Dic118—21no—
78C22×Dic118—21no—
79C22×Dic118—21no—
80C22×Dic118C2311yescharacteristic
81C2×Q8×D59—22no—
82C2×Q8×D59—24no—
83C2×Q8×D59Q818yescomplemented
84C2×Q8×D59C2314yes—
85C22×C4×D59—21no—
86C22×C4×D59—21no—
87C22×C4×D59C2311yescharacteristic
88C2×#11745659—24no—
89C2×#11745659C2314yes—
90C22×C59⋊C8C2311yescharacteristic
91C22×C59⋊C8C2311yescharacteristic
92C2×C8×D59—24no—
93C2×C8×D59C2314yes—
94#14273727—22no—
95#14273727C2314yes—
96#14273726—28no—
97#14273726—22no—
98#14273726C2314yes—
99#14273718—22no—
100#14273718C2314yes—
101#14273717—28no—
102#14273707—28no—
103#14273705—28no—
104Q8×Dic59—22no—
105Q8×Dic59C2314yes—
106C4×Dic118—22no—
107C4×Dic118—28no—
108C4×Dic118C2314yes—
109#14273692—28no—
110#14273692—22no—
111#14273692C2314yes—
112#14273685—22no—
113#14273685—22no—
114#14273685—28no—
115#14273685C2314yes—
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⋊C4—21no—
131C2×Dic59⋊C4D411yescharacteristic
132C2×Dic59⋊C4D411yescharacteristic
133C4⋊C4×D59—22no—
134C4⋊C4×D59C2314yes—
135C2×(C2×D59)⋊C4—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4D411yescharacteristic
138C2×(C2×D59)⋊C4D411yescharacteristic
139C2×C4×Dic59—21no—
140C2×C4×Dic59—21no—
141C2×C4×Dic59—21no—
142C2×C4×Dic59—21no—
143C2×C4×Dic59—21no—
144C2×C4×Dic59C2311yescharacteristic
145#14273661C2314yes—
146#14273661C2314yes—
147#14273660C2314yes—
148#14273658C2314yes—
149#14273658C2314yes—
150#14273658C2314yes—
151C4⋊(C59⋊C8)C2314yes—
152Dic59⋊C8C2314yes—
153Dic59⋊C8C2314yes—
154#14273652C2314yes—
155#14273652C2314yes—
156#14273651C2314yes—
157#14273651C2314yes—
158#14273650C2314yes—
159#14273650C2314yes—
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×D59C2×D411yescharacteristic
181C2×Q8×C59—21no—
182C2×Q8×C59—22no—
183C2×Q8×C59C2×Q814yes—
184C2×Q8×C59C2412yes—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59C2×D411yescharacteristic
190C22×C4×C59C2×D411yescharacteristic
191C22×C4×C59C2411yescharacteristic
192C22×Dic59—21no—
193C22×Dic59—21no—
194C22×Dic59—21no—
195C22×Dic59—21no—
196C22×Dic59C2×D411yescharacteristic
197C22×Dic59C2×D411yescharacteristic
198C22×Dic59C2×D411yescharacteristic
199Q8×D59—216no—
200Q8×D59—28no—
201Q8×D59C2×Q8116yescomplemented
202C2×C4×D59—28no—
203C2×C4×D59—24no—
204C2×C4×D59—24no—
205C2×C4×D59—82no—
206C2×C4×D59C2×D412yes—
207C2×C4×D59C2×Q814yes—
208C2×C4×D59#4114yes—
209C2×C4×D59C2412yes—
210C2×Dic118—21no—
211C2×Dic118—22no—
212C2×Dic118—28no—
213C2×Dic118—24no—
214C2×Dic118—24no—
215C2×Dic118—24no—
216C2×Dic118—82no—
217C2×Dic118—82no—
218C2×Dic118C2×Q814yes—
219C2×Dic118C2412yes—
220C2×C8×C59—22no—
221C2×C8×C59—22no—
222C2×C8×C59C2412yes—
223C2×C8×C59C2412yes—
224C4⋊C4×C59—24no—
225C4⋊C4×C59—24no—
226C4⋊C4×C59—24no—
227C4⋊C4×C59—21no—
228C4⋊C4×C59—21no—
229C4⋊C4×C59—21no—
230C4⋊C4×C59C2412yes—
231C4⋊C4×C59C2412yes—
232C4⋊C4×C59C2412yes—
233C42×C59—24no—
234C42×C59C2×D412yes—
235C42×C59C2412yes—
236(C2×D59)⋊C4—24no—
237(C2×D59)⋊C4—24no—
238(C2×D59)⋊C4C2×D414yes—
239(C2×D59)⋊C4C2×D414yes—
240C4⋊Dic59—21no—
241C4⋊Dic59—24no—
242C4⋊Dic59—21no—
243C4⋊Dic59—21no—
244C4⋊Dic59—24no—
245C4⋊Dic59—24no—
246C4⋊Dic59C2412yes—
247C4⋊Dic59C2412yes—
248C4⋊Dic59C2412yes—
249Dic59⋊C4—24no—
250Dic59⋊C4—24no—
251Dic59⋊C4—24no—
252Dic59⋊C4—24no—
253Dic59⋊C4—24no—
254Dic59⋊C4C2×D414yes—
255Dic59⋊C4C2×D414yes—
256C4×Dic59—24no—
257C4×Dic59—24no—
258C4×Dic59—24no—
259C4×Dic59—24no—
260C4×Dic59—24no—
261C4×Dic59C2×D412yes—
262C4×Dic59C2412yes—
263C2×C59⋊C8—22no—
264C2×C59⋊C8—22no—
265C2×C59⋊C8C2412yes—
266C2×C59⋊C8C2412yes—
267#11745659—28no—
268C8×D59—28no—
269C23×C59C22×D411yescharacteristic
270C22×D59—22no—
271C22×D59—22no—
272C22×D59C22⋊Q814yes—
273C22×D59C22×D412yes—
274Q8×C59—24no—
275Q8×C59—22no—
276Q8×C59C22×Q814yes—
277C2×C4×C59—24no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—42no—
285C2×C4×C59—42no—
286C2×C4×C59—42no—
287C2×C4×C59C22×D412yes—
288C2×C4×C59C22×D412yes—
289C2×C4×C59C22×D411yescharacteristic
290C2×C4×C59C22×Q812yes—
291C2×C4×C59C2×#4112yes—
292C2×C4×C59C2511yescharacteristic
293C2×Dic59—24no—
294C2×Dic59—22no—
295C2×Dic59—22no—
296C2×Dic59—22no—
297C2×Dic59—22no—
298C2×Dic59—22no—
299C2×Dic59—22no—
300C2×Dic59—42no—
301C2×Dic59—42no—
302C2×Dic59—42no—
303C2×Dic59C22⋊Q814yes—
304C2×Dic59C22×D412yes—
305C2×Dic59C22×D412yes—
306C2×Dic59C22×D412yes—
307C4×D59—216no—
308C4×D59—84no—
309C4×D59C22⋊Q818yes—
310C4×D59C22×Q814yes—
311C4×D59C2×#4114yes—
312Dic118—24no—
313Dic118—22no—
314Dic118—216no—
315Dic118—84no—
316Dic118—84no—
317Dic118C22×Q814yes—
318C8×C59—22no—
319C8×C59—22no—
320C59⋊C8—22no—
321C59⋊C8—22no—
322C2×#3082—591nomaximal, Sylow
323C22×C59C2×C22⋊Q812yes—
324C22×C59#57712yes—
325C22×C59#57812yes—
326C22×C59C23×D411yescharacteristic
327C2×D59—28no—
328C2×D59—22no—
329C2×D59—22no—
330C2×D59C2×C22⋊Q814yes—
331C4×C59—24no—
332C4×C59—22no—
333C4×C59—22no—
334C4×C59—42no—
335C4×C59—42no—
336C4×C59—42no—
337C4×C59C2×C22⋊Q812yes—
338C4×C59C23×Q811yescharacteristic
339C4×C59C22×#4111yescharacteristic
340Dic59—24no—
341Dic59—22no—
342Dic59—22no—
343Dic59—42no—
344Dic59—42no—
345Dic59—42no—
346Dic59C2×C22⋊Q814yes—
347C2×#544—591no—
348C2×#519—591no—
349#3082—5916no—
350C2×#479—591no—
351C2×#479—591no—
352C2×#479—591no—
353C2×#479D5911yescharacteristic, complemented
354C2×#477—591no—
355C2×#477—591no—
356C2×#475—591no—
357C2×#475—591no—
358C2×#428—591no—
359C2×#427—591no—
360C2×#424—591no—
361C2×#419—591no—
362C22×#103—591no—
363C2×C59#308214yescomplemented
364C2×C59C22×C22⋊Q811yescharacteristic
365C2×C59C2×#57711yescharacteristic
366C2×C59C2×#57811yescharacteristic
367D59—24no—
368C23×Q8—591no—
369C22×M16—591no—
370C23×C8—591no—
371#544—598no—
372#544—1184no—
373C2×C4⋊Q8—591no—
374C2×C4⋊Q8—591no—
375C2×C4⋊Q8—1181no—
376C2×#125—591no—
377C2×#125—1181no—
378C2×#125C2×D5911yescharacteristic
379C2×C22⋊Q8—1181no—
380C2×C22⋊Q8—1181no—
381#519—598no—
382#519—1184no—
383C2×C4×Q8—591no—
384C2×C4×Q8—591no—
385C2×C4×Q8—591no—
386C2×C4×Q8—1181no—
387C2×C4×Q8—1181no—
388C2×C4×Q8C2×D5911yescharacteristic
389C2×#117—591no—
390C2×#117—591no—
391C2×#117—591no—
392C2×#117—1181no—
393C2×#117—1181no—
394C22×C4⋊C4—591no—
395#479—598no—
396#479—598no—
397#479—598no—
398#479C2×D5918yescomplemented
399#477—598no—
400#477—598no—
401#475—598no—
402#475—598no—
403#428—598no—
404#427—598no—
405C2×#107—591no—
406C2×#107—591no—
407C2×#107—591no—
408C2×#107C2×D5911yescharacteristic
409C2×#106—591no—
410C2×#106—591no—
411C2×#106—591no—
412C2×#106C2×D5911yescharacteristic
413#424—598no—
414C2×C4⋊C8—591no—
415C2×C4⋊C8—591no—
416C2×C4⋊C8—591no—
417C2×C4⋊C8C2×D5911yescharacteristic
418#419—598no—
419C2×#103—591no—
420C2×#103—591no—
421C2×#103—591no—
422C2×#103—591no—
423C2×#103—591no—
424C2×#103—591no—
425C2×#103—598no—
426C2×#103C2×D5911yescharacteristic
427C2×#103C2×D5911yescharacteristic
428C59C2×#308211yescharacteristic, complemented, Sylow
429C22×Q8—598no—
430C22×Q8—594no—
431C22×Q8—591no—
432C22×Q8—1181no—
433C22×Q8—1181no—
434C22×Q8—1182no—
435C22×Q8—1184no—
436C22×Q8—1181no—
437C22×Q8C22×D5911yescharacteristic
438C23×C4—591no—
439C23×C4—1181no—
440C23×C4—1181no—
441C2×M16—594no—
442C2×M16—1184no—
443C22×C8—591no—
444C22×C8—591no—
445C22×C8—594no—
446C22×C8—1184no—
447C22×C8C22×D5911yescharacteristic
448C22×C8C22×D5911yescharacteristic
449C4⋊Q8—594no—
450C4⋊Q8—594no—
451C4⋊Q8—1182no—
452C4⋊Q8—1188no—
453C4⋊Q8—1182no—
454#125—22no—
455#125—594no—
456#125—1182no—
457#125—1188no—
458#125C22×D5914yes—
459C22⋊Q8—1188no—
460C22⋊Q8—1188no—
461C4×Q8—22no—
462C4×Q8—594no—
463C4×Q8—594no—
464C4×Q8—594no—
465C4×Q8—1188no—
466C4×Q8—1182no—
467C4×Q8—1182no—
468C4×Q8—1188no—
469C4×Q8—1182no—
470C4×Q8C22×D5914yes—
471#117—594no—
472#117—594no—
473#117—594no—
474#117—594no—
475#117—1188no—
476#117—1188no—
477#117—1182no—
478#117—1182no—
479C2×C4⋊C4—21no—
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—594no—
488C2×C4⋊C4—1182no—
489C2×C4⋊C4—1181no—
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⋊C4C22×D5911yescharacteristic
498C2×C4⋊C4C22×D5911yescharacteristic
499C2×C4⋊C4C22×D5911yescharacteristic
500C2×C22⋊C4—591no—
501C2×C22⋊C4—591no—
502C2×C22⋊C4—1181no—
503C2×C22⋊C4—1181no—
504C2×C42—21no—
505C2×C42—591no—
506C2×C42—1181no—
507C2×C42—1181no—
508C2×C42—1181no—
509C2×C42—1181no—
510C2×C42—1181no—
511C2×C42C22×D5911yescharacteristic
512#107—594no—
513#107—594no—
514#107—594no—
515#107C22×D5914yes—
516#106—594no—
517#106—594no—
518#106—594no—
519#106C22×D5914yes—
520C4⋊C8—594no—
521C4⋊C8—594no—
522C4⋊C8—594no—
523C4⋊C8C22×D5914yes—
524#103—594no—
525#103—594no—
526#103—594no—
527#103—594no—
528#103—594no—
529#103—594no—
530#103C22×D5914yes—
531#103C22×D5914yes—
532C24—591no—
533C2×Q8—21no—
534C2×Q8—22no—
535C2×Q8—5916no—
536C2×Q8—594no—
537C2×Q8—592no—
538C2×Q8—1184no—
539C2×Q8—1188no—
540C2×Q8—1184no—
541C2×Q8—11816no—
542C2×Q8—1188no—
543C2×Q8—1181no—
544C2×Q8—1184no—
545C2×Q8—1182no—
546C2×Q8—4722no—
547C2×Q8—4722no—
548C2×Q8Q8×D5914yes—
549C2×Q8C23×D5912yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—591no—
555C22×C4—592no—
556C22×C4—594no—
557C22×C4—594no—
558C22×C4—592no—
559C22×C4—591no—
560C22×C4—591no—
561C22×C4—1184no—
562C22×C4—1188no—
563C22×C4—1184no—
564C22×C4—1181no—
565C22×C4—1181no—
566C22×C4—1181no—
567C22×C4—1181no—
568C22×C4—4722no—
569C22×C4D4×D5911yescharacteristic
570C22×C4D4×D5911yescharacteristic
571C22×C4C23×D5911yescharacteristic
572M16—1188no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—592no—
576C2×C8—592no—
577C2×C8—1188no—
578C2×C8—1182no—
579C2×C8—1182no—
580C2×C8C23×D5912yes—
581C2×C8C23×D5912yes—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—594no—
589C4⋊C4—594no—
590C4⋊C4—592no—
591C4⋊C4—592no—
592C4⋊C4—592no—
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⋊C4—1184no—
604C4⋊C4C23×D5912yes—
605C4⋊C4C23×D5912yes—
606C4⋊C4C23×D5912yes—
607C22⋊C4—594no—
608C22⋊C4—594no—
609C22⋊C4—1184no—
610C22⋊C4—1184no—
611C42—24no—
612C42—592no—
613C42—592no—
614C42—1184no—
615C42—1184no—
616C42—1184no—
617C42—1184no—
618C42—1184no—
619C42D4×D5912yes—
620C42C23×D5912yes—
621C23—594no—
622C23—592no—
623C23—1182no—
624C23—1182no—
625C23C2×D4×D5911yescharacteristic
626Q8—24no—
627Q8—22no—
628Q8—594no—
629Q8—11816no—
630Q8—1184no—
631Q8—1182no—
632Q8—4724no—
633Q8—4724no—
634Q8C2×Q8×D5914yes—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—594no—
646C2×C4—592no—
647C2×C4—598no—
648C2×C4—594no—
649C2×C4—594no—
650C2×C4—592no—
651C2×C4—592no—
652C2×C4—11816no—
653C2×C4—1184no—
654C2×C4—1182no—
655C2×C4—1182no—
656C2×C4—1182no—
657C2×C4—1182no—
658C2×C4—1182no—
659C2×C4—1182no—
660C2×C4—4724no—
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#41×D5912yes—
669C2×C4C24×D5911yescharacteristic
670C8—22no—
671C8—22no—
672C8—1182no—
673C8—1182no—
674C22—594no—
675C22—1188no—
676C22—1182no—
677C22—1182no—
678C22C22⋊Q8×D5912yes—
679C22#1683821112yes—
680C22#1683821612yes—
681C22C22×D4×D5911yescharacteristic
682C4—22no—
683C4—24no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—594no—
689C4—1182no—
690C4—1184no—
691C4—1182no—
692C4—2362no—
693C4—2362no—
694C4—2362no—
695C4C22⋊Q8×D5912yes—
696C4C22×Q8×D5911yescharacteristic
697C4C2×#41×D5911yescharacteristic
698C2—1184no—
699C2#2143393714yesdirect product factor
700C2C2×C22⋊Q8×D5911yescharacteristic
701C2C2×#1683821111yescharacteristic
702C2C2×#1683821611yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#479C2
socleC23×C59C22×D4
prime radicalC23×D59C2×D4
hypercenterC2×#479D59
hypocenterC59C2×#3082
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
3. #21433937C2direct (N × H)
4. C2×#16837711C2semidirect
5. C2×#16837708C2semidirect
6. C2×#16837706C2semidirect
7. C2×#16837698C2semidirect
8. C2×#16837695C2semidirect
9. C2×#16837687C2semidirect
10. C2×#16837686C2semidirect
16. C2×C59×#479C2semidirect
42. #16837711C22semidirect
43. #16837708C22semidirect
44. #16837706C22semidirect
45. #16837698C22semidirect
46. #16837695C22semidirect
47. #16837687C22semidirect
48. #16837686C22semidirect
71. C59×#479C22semidirect
83. C2×Q8×D59Q8semidirect
201. Q8×D59C2×Q8semidirect
353. C2×#479D59semidirect
363. C2×C59#3082semidirect
398. #479C2×D59semidirect
428. C59C2×#3082semidirect
699. C2#21433937direct (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×#168378782
#214339372
C2×#168377112
C2×#168377082
C2×#168377062
C2×#168376982
C2×#168376952
C2×#168376872
C2×#168376862
C2×#168374412
C2×#168374392
C2×#168374272
C2×#168374092
C2×#103×D592
C2×C59×#4792
C2×#308259