Finite Group Databasebeta

← C2×#24917302 #36271972

Subgroups — C2×#24917302 #36271972

Order 21248.

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×#19128331C211yesmaximal, characteristic
2C2×#19128177C211yesmaximal, characteristic
3#24917302C2116yesmaximal, direct product factor
4C2×#19128011C211yesmaximal, characteristic, complemented
5C2×#19128006C211yesmaximal, characteristic, complemented
6C2×#19128005C211yesmaximal, characteristic, complemented
7C2×#19127996C211yesmaximal, characteristic, complemented
8C2×#19127995C211yesmaximal, characteristic, complemented
9C2×#19127987C211yesmaximal, characteristic, complemented
10C2×#19127984C211yesmaximal, characteristic, complemented
11C2×#19127742C211yesmaximal, characteristic
12C2×#19127736C211yesmaximal, characteristic
13C2×#19127726C211yesmaximal, characteristic
14C2×#19127708C211yesmaximal, characteristic
15C2×#103×D83C211yesmaximal, characteristic
16C2×#479×C83C211yesmaximal, characteristic, complemented
17C22×Q8×D83C2211yescharacteristic
18C22×#13050573C2211yescharacteristic
19C22×C8×D83C2211yescharacteristic
20#19128331—24no—
21#19128331C2218yes—
22C2×#14581792C2211yescharacteristic
23C2×#14581791—21no—
24C2×#14581791C2211yescharacteristic
25C2×#14581783C2211yescharacteristic
26C2×#14581782—21no—
27C2×#14581772—21no—
28C2×#14581770—21no—
29#19128177—24no—
30#19128177C2218yes—
31C2×Q8×Dic83C2211yescharacteristic
32C2×C4×Dic166—21no—
33C2×C4×Dic166C2211yescharacteristic
34C2×#14581757—21no—
35C2×#14581757C2211yescharacteristic
36C2×#14581750—21no—
37C2×#14581750C2211yescharacteristic
38C2×#14581750C2211yescharacteristic
39C2×#14581749—21no—
40C2×#14581749C2211yescharacteristic
41C2×C4⋊C4×D83C2211yescharacteristic
42#19128011C2218yescomplemented
43#19128006C2218yescomplemented
44#19128005C2218yescomplemented
45#19127996C2218yescomplemented
46#19127995C2218yescomplemented
47#19127987C2218yescomplemented
48#19127984C2218yescomplemented
49#19127742C2218yes—
50#19127736C2218yes—
51C2×#14581725C2211yescharacteristic
52C2×#14581725C2211yescharacteristic
53C2×#14581725C2211yescharacteristic
54C2×#14581724C2211yescharacteristic
55C2×#14581724C2211yescharacteristic
56C2×#14581723C2211yescharacteristic
57#19127726C2218yes—
58C2×C4⋊(C83⋊C8)C2211yescharacteristic
59C2×Dic83⋊C8C2211yescharacteristic
60C2×Dic83⋊C8C2211yescharacteristic
61#19127708C2218yes—
62C2×#14581717C2211yescharacteristic
63C2×#14581717C2211yescharacteristic
64C2×#14581716C2211yescharacteristic
65C2×#14581716C2211yescharacteristic
66C2×#14581715C2211yescharacteristic
67C2×#14581715C2211yescharacteristic
68#103×D83C2218yes—
69C2×#125×C83C2211yescharacteristic
70C2×C4×Q8×C83C2211yescharacteristic
71#479×C83C2218yescomplemented
72C2×#107×C83C2211yescharacteristic
73C2×#106×C83C2211yescharacteristic
74C2×C4⋊C8×C83C2211yescharacteristic
75C2×#103×C83C2211yescharacteristic
76C2×#103×C83C2211yescharacteristic
77C22×Dic166—21no—
78C22×Dic166—21no—
79C22×Dic166—21no—
80C22×Dic166C2311yescharacteristic
81C2×Q8×D83—22no—
82C2×Q8×D83—24no—
83C2×Q8×D83Q818yescomplemented
84C2×Q8×D83C2314yes—
85C22×C4×D83—21no—
86C22×C4×D83—21no—
87C22×C4×D83C2311yescharacteristic
88C2×#13050573—24no—
89C2×#13050573C2314yes—
90C22×C83⋊C8C2311yescharacteristic
91C22×C83⋊C8C2311yescharacteristic
92C2×C8×D83—24no—
93C2×C8×D83C2314yes—
94#14581792—22no—
95#14581792C2314yes—
96#14581791—28no—
97#14581791—22no—
98#14581791C2314yes—
99#14581783—22no—
100#14581783C2314yes—
101#14581782—28no—
102#14581772—28no—
103#14581770—28no—
104Q8×Dic83—22no—
105Q8×Dic83C2314yes—
106C4×Dic166—28no—
107C4×Dic166—22no—
108C4×Dic166C2314yes—
109#14581757—28no—
110#14581757—22no—
111#14581757C2314yes—
112#14581750—22no—
113#14581750—22no—
114#14581750—28no—
115#14581750C2314yes—
116#14581750C2314yes—
117#14581749—28no—
118#14581749D414yes—
119#14581749C2314yes—
120C2×C4⋊Dic83—21no—
121C2×C4⋊Dic83—21no—
122C2×C4⋊Dic83—21no—
123C2×C4⋊Dic83C2311yescharacteristic
124C2×C4⋊Dic83C2311yescharacteristic
125C2×C4⋊Dic83C2311yescharacteristic
126C2×Dic83⋊C4—21no—
127C2×Dic83⋊C4—21no—
128C2×Dic83⋊C4—21no—
129C2×Dic83⋊C4—21no—
130C2×Dic83⋊C4—21no—
131C2×Dic83⋊C4D411yescharacteristic
132C2×Dic83⋊C4D411yescharacteristic
133C4⋊C4×D83—22no—
134C4⋊C4×D83C2314yes—
135C2×(C2×D83)⋊C4—21no—
136C2×(C2×D83)⋊C4—21no—
137C2×(C2×D83)⋊C4D411yescharacteristic
138C2×(C2×D83)⋊C4D411yescharacteristic
139C2×C4×Dic83—21no—
140C2×C4×Dic83—21no—
141C2×C4×Dic83—21no—
142C2×C4×Dic83—21no—
143C2×C4×Dic83—21no—
144C2×C4×Dic83C2311yescharacteristic
145#14581725C2314yes—
146#14581725C2314yes—
147#14581725C2314yes—
148#14581724C2314yes—
149#14581724C2314yes—
150#14581723C2314yes—
151C4⋊(C83⋊C8)C2314yes—
152Dic83⋊C8C2314yes—
153Dic83⋊C8C2314yes—
154#14581717C2314yes—
155#14581717C2314yes—
156#14581716C2314yes—
157#14581716C2314yes—
158#14581715C2314yes—
159#14581715C2314yes—
160C22×Q8×C83C2311yescharacteristic
161C22×C8×C83C2311yescharacteristic
162C22×C8×C83C2311yescharacteristic
163#125×C83—22no—
164#125×C83C2314yes—
165C4×Q8×C83—22no—
166C4×Q8×C83C2314yes—
167C2×C4⋊C4×C83—21no—
168C2×C4⋊C4×C83—21no—
169C2×C4⋊C4×C83—21no—
170C2×C4⋊C4×C83C2311yescharacteristic
171C2×C4⋊C4×C83C2311yescharacteristic
172C2×C4⋊C4×C83C2311yescharacteristic
173C2×C42×C83—21no—
174C2×C42×C83C2311yescharacteristic
175#107×C83C2314yes—
176#106×C83C2314yes—
177C4⋊C8×C83C2314yes—
178#103×C83C2314yes—
179#103×C83C2314yes—
180C23×D83C2×D411yescharacteristic
181C2×Dic166—21no—
182C2×Dic166—22no—
183C2×Dic166—28no—
184C2×Dic166—24no—
185C2×Dic166—24no—
186C2×Dic166—24no—
187C2×Dic166—82no—
188C2×Dic166—82no—
189C2×Dic166C2×Q814yes—
190C2×Dic166C2412yes—
191Q8×D83—216no—
192Q8×D83—28no—
193Q8×D83C2×Q8116yescomplemented
194C22×Dic83—21no—
195C22×Dic83—21no—
196C22×Dic83—21no—
197C22×Dic83—21no—
198C22×Dic83C2×D411yescharacteristic
199C22×Dic83C2×D411yescharacteristic
200C22×Dic83C2×D411yescharacteristic
201C2×C4×D83—28no—
202C2×C4×D83—24no—
203C2×C4×D83—24no—
204C2×C4×D83—82no—
205C2×C4×D83C2×D412yes—
206C2×C4×D83C2×Q814yes—
207C2×C4×D83#4114yes—
208C2×C4×D83C2412yes—
209#13050573—28no—
210C2×C83⋊C8—22no—
211C2×C83⋊C8—22no—
212C2×C83⋊C8C2412yes—
213C2×C83⋊C8C2412yes—
214C8×D83—28no—
215C4⋊Dic83—24no—
216C4⋊Dic83—21no—
217C4⋊Dic83—21no—
218C4⋊Dic83—21no—
219C4⋊Dic83—24no—
220C4⋊Dic83—24no—
221C4⋊Dic83C2412yes—
222C4⋊Dic83C2412yes—
223C4⋊Dic83C2412yes—
224Dic83⋊C4—24no—
225Dic83⋊C4—24no—
226Dic83⋊C4—24no—
227Dic83⋊C4—24no—
228Dic83⋊C4—24no—
229Dic83⋊C4C2×D414yes—
230Dic83⋊C4C2×D414yes—
231(C2×D83)⋊C4—24no—
232(C2×D83)⋊C4—24no—
233(C2×D83)⋊C4C2×D414yes—
234(C2×D83)⋊C4C2×D414yes—
235C4×Dic83—24no—
236C4×Dic83—24no—
237C4×Dic83—24no—
238C4×Dic83—24no—
239C4×Dic83—24no—
240C4×Dic83C2×D412yes—
241C4×Dic83C2412yes—
242C2×Q8×C83—21no—
243C2×Q8×C83—22no—
244C2×Q8×C83C2×Q814yes—
245C2×Q8×C83C2412yes—
246C22×C4×C83—21no—
247C22×C4×C83—21no—
248C22×C4×C83—21no—
249C22×C4×C83—21no—
250C22×C4×C83C2×D411yescharacteristic
251C22×C4×C83C2×D411yescharacteristic
252C22×C4×C83C2411yescharacteristic
253C2×C8×C83—22no—
254C2×C8×C83—22no—
255C2×C8×C83C2412yes—
256C2×C8×C83C2412yes—
257C4⋊C4×C83—24no—
258C4⋊C4×C83—24no—
259C4⋊C4×C83—21no—
260C4⋊C4×C83—21no—
261C4⋊C4×C83—24no—
262C4⋊C4×C83—21no—
263C4⋊C4×C83C2412yes—
264C4⋊C4×C83C2412yes—
265C4⋊C4×C83C2412yes—
266C42×C83—24no—
267C42×C83C2×D412yes—
268C42×C83C2412yes—
269C23×C83C22×D411yescharacteristic
270C22×D83—22no—
271C22×D83—22no—
272C22×D83C22⋊Q814yes—
273C22×D83C22×D412yes—
274Q8×C83—24no—
275Q8×C83—22no—
276Q8×C83C22×Q814yes—
277C2×C4×C83—24no—
278C2×C4×C83—22no—
279C2×C4×C83—22no—
280C2×C4×C83—22no—
281C2×C4×C83—22no—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
284C2×C4×C83—42no—
285C2×C4×C83—42no—
286C2×C4×C83—42no—
287C2×C4×C83C22×D412yes—
288C2×C4×C83C22×D412yes—
289C2×C4×C83C22×D411yescharacteristic
290C2×C4×C83C22×Q812yes—
291C2×C4×C83C2×#4112yes—
292C2×C4×C83C2511yescharacteristic
293C2×Dic83—24no—
294C2×Dic83—22no—
295C2×Dic83—22no—
296C2×Dic83—22no—
297C2×Dic83—22no—
298C2×Dic83—22no—
299C2×Dic83—22no—
300C2×Dic83—42no—
301C2×Dic83—42no—
302C2×Dic83—42no—
303C2×Dic83C22⋊Q814yes—
304C2×Dic83C22×D412yes—
305C2×Dic83C22×D412yes—
306C2×Dic83C22×D412yes—
307C4×D83—216no—
308C4×D83—84no—
309C4×D83C22⋊Q818yes—
310C4×D83C22×Q814yes—
311C4×D83C2×#4114yes—
312Dic166—24no—
313Dic166—22no—
314Dic166—216no—
315Dic166—84no—
316Dic166—84no—
317Dic166C22×Q814yes—
318C8×C83—22no—
319C8×C83—22no—
320C83⋊C8—22no—
321C83⋊C8—22no—
322C22×C83C2×C22⋊Q812yes—
323C22×C83#57712yes—
324C22×C83#57812yes—
325C22×C83C23×D411yescharacteristic
326C2×D83—28no—
327C2×D83—22no—
328C2×D83—22no—
329C2×D83C2×C22⋊Q814yes—
330C4×C83—24no—
331C4×C83—22no—
332C4×C83—22no—
333C4×C83—42no—
334C4×C83—42no—
335C4×C83—42no—
336C4×C83C2×C22⋊Q812yes—
337C4×C83C23×Q811yescharacteristic
338C4×C83C22×#4111yescharacteristic
339Dic83—24no—
340Dic83—22no—
341Dic83—22no—
342Dic83—42no—
343Dic83—42no—
344Dic83—42no—
345Dic83C2×C22⋊Q814yes—
346C2×#3082—831nomaximal, Sylow
347C2×C83#308214yescomplemented
348C2×C83C22×C22⋊Q811yescharacteristic
349C2×C83C2×#57711yescharacteristic
350C2×C83C2×#57811yescharacteristic
351D83—24no—
352C2×#544—831no—
353C2×#519—831no—
354#3082—8316no—
355C2×#479—831no—
356C2×#479—831no—
357C2×#479—831no—
358C2×#479D8311yescharacteristic, complemented
359C2×#477—831no—
360C2×#477—831no—
361C2×#475—831no—
362C2×#475—831no—
363C2×#428—831no—
364C2×#427—831no—
365C2×#424—831no—
366C2×#419—831no—
367C22×#103—831no—
368C83C2×#308211yescharacteristic, complemented, Sylow
369C23×Q8—831no—
370C22×M16—831no—
371C23×C8—831no—
372#544—838no—
373#544—1664no—
374C2×C4⋊Q8—831no—
375C2×C4⋊Q8—831no—
376C2×C4⋊Q8—1661no—
377C2×#125—831no—
378C2×#125—1661no—
379C2×#125C2×D8311yescharacteristic
380C2×C22⋊Q8—1661no—
381C2×C22⋊Q8—1661no—
382#519—838no—
383#519—1664no—
384C2×C4×Q8—831no—
385C2×C4×Q8—831no—
386C2×C4×Q8—831no—
387C2×C4×Q8—1661no—
388C2×C4×Q8—1661no—
389C2×C4×Q8C2×D8311yescharacteristic
390C2×#117—831no—
391C2×#117—831no—
392C2×#117—831no—
393C2×#117—1661no—
394C2×#117—1661no—
395C22×C4⋊C4—831no—
396#479—838no—
397#479—838no—
398#479—838no—
399#479C2×D8318yescomplemented
400#477—838no—
401#477—838no—
402#475—838no—
403#475—838no—
404#428—838no—
405#427—838no—
406C2×#107—831no—
407C2×#107—831no—
408C2×#107—831no—
409C2×#107C2×D8311yescharacteristic
410C2×#106—831no—
411C2×#106—831no—
412C2×#106—831no—
413C2×#106C2×D8311yescharacteristic
414#424—838no—
415C2×C4⋊C8—831no—
416C2×C4⋊C8—831no—
417C2×C4⋊C8—831no—
418C2×C4⋊C8C2×D8311yescharacteristic
419#419—838no—
420C2×#103—831no—
421C2×#103—831no—
422C2×#103—831no—
423C2×#103—831no—
424C2×#103—831no—
425C2×#103—831no—
426C2×#103—838no—
427C2×#103C2×D8311yescharacteristic
428C2×#103C2×D8311yescharacteristic
429C22×Q8—838no—
430C22×Q8—834no—
431C22×Q8—831no—
432C22×Q8—1661no—
433C22×Q8—1661no—
434C22×Q8—1662no—
435C22×Q8—1664no—
436C22×Q8—1661no—
437C22×Q8C22×D8311yescharacteristic
438C23×C4—831no—
439C23×C4—1661no—
440C23×C4—1661no—
441C2×M16—834no—
442C2×M16—1664no—
443C22×C8—831no—
444C22×C8—831no—
445C22×C8—834no—
446C22×C8—1664no—
447C22×C8C22×D8311yescharacteristic
448C22×C8C22×D8311yescharacteristic
449C4⋊Q8—834no—
450C4⋊Q8—834no—
451C4⋊Q8—1662no—
452C4⋊Q8—1668no—
453C4⋊Q8—1662no—
454#125—22no—
455#125—834no—
456#125—1662no—
457#125—1668no—
458#125C22×D8314yes—
459C22⋊Q8—1668no—
460C22⋊Q8—1668no—
461C4×Q8—22no—
462C4×Q8—834no—
463C4×Q8—834no—
464C4×Q8—834no—
465C4×Q8—1668no—
466C4×Q8—1662no—
467C4×Q8—1662no—
468C4×Q8—1668no—
469C4×Q8—1662no—
470C4×Q8C22×D8314yes—
471#117—834no—
472#117—834no—
473#117—834no—
474#117—834no—
475#117—1668no—
476#117—1668no—
477#117—1662no—
478#117—1662no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—831no—
483C2×C4⋊C4—831no—
484C2×C4⋊C4—831no—
485C2×C4⋊C4—831no—
486C2×C4⋊C4—831no—
487C2×C4⋊C4—834no—
488C2×C4⋊C4—1662no—
489C2×C4⋊C4—1661no—
490C2×C4⋊C4—1661no—
491C2×C4⋊C4—1661no—
492C2×C4⋊C4—1661no—
493C2×C4⋊C4—1661no—
494C2×C4⋊C4—1661no—
495C2×C4⋊C4—1661no—
496C2×C4⋊C4—1661no—
497C2×C4⋊C4C22×D8311yescharacteristic
498C2×C4⋊C4C22×D8311yescharacteristic
499C2×C4⋊C4C22×D8311yescharacteristic
500C2×C22⋊C4—831no—
501C2×C22⋊C4—831no—
502C2×C22⋊C4—1661no—
503C2×C22⋊C4—1661no—
504C2×C42—21no—
505C2×C42—831no—
506C2×C42—1661no—
507C2×C42—1661no—
508C2×C42—1661no—
509C2×C42—1661no—
510C2×C42—1661no—
511C2×C42C22×D8311yescharacteristic
512#107—834no—
513#107—834no—
514#107—834no—
515#107C22×D8314yes—
516#106—834no—
517#106—834no—
518#106—834no—
519#106C22×D8314yes—
520C4⋊C8—834no—
521C4⋊C8—834no—
522C4⋊C8—834no—
523C4⋊C8C22×D8314yes—
524#103—834no—
525#103—834no—
526#103—834no—
527#103—834no—
528#103—834no—
529#103—834no—
530#103C22×D8314yes—
531#103C22×D8314yes—
532C24—831no—
533C2×Q8—21no—
534C2×Q8—22no—
535C2×Q8—8316no—
536C2×Q8—834no—
537C2×Q8—832no—
538C2×Q8—6642no—
539C2×Q8—6642no—
540C2×Q8—1664no—
541C2×Q8—1664no—
542C2×Q8—1668no—
543C2×Q8—16616no—
544C2×Q8—1668no—
545C2×Q8—1664no—
546C2×Q8—1661no—
547C2×Q8—1662no—
548C2×Q8Q8×D8314yes—
549C2×Q8C23×D8312yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—831no—
555C22×C4—832no—
556C22×C4—834no—
557C22×C4—834no—
558C22×C4—832no—
559C22×C4—831no—
560C22×C4—831no—
561C22×C4—6642no—
562C22×C4—1664no—
563C22×C4—1664no—
564C22×C4—1668no—
565C22×C4—1661no—
566C22×C4—1661no—
567C22×C4—1661no—
568C22×C4—1661no—
569C22×C4D4×D8311yescharacteristic
570C22×C4D4×D8311yescharacteristic
571C22×C4C23×D8311yescharacteristic
572M16—1668no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—832no—
576C2×C8—832no—
577C2×C8—1668no—
578C2×C8—1662no—
579C2×C8—1662no—
580C2×C8C23×D8312yes—
581C2×C8C23×D8312yes—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—834no—
589C4⋊C4—834no—
590C4⋊C4—832no—
591C4⋊C4—832no—
592C4⋊C4—832no—
593C4⋊C4—1664no—
594C4⋊C4—1664no—
595C4⋊C4—1664no—
596C4⋊C4—1664no—
597C4⋊C4—1664no—
598C4⋊C4—1664no—
599C4⋊C4—1661no—
600C4⋊C4—1661no—
601C4⋊C4—1661no—
602C4⋊C4—1664no—
603C4⋊C4—1664no—
604C4⋊C4C23×D8312yes—
605C4⋊C4C23×D8312yes—
606C4⋊C4C23×D8312yes—
607C22⋊C4—834no—
608C22⋊C4—834no—
609C22⋊C4—1664no—
610C22⋊C4—1664no—
611C42—24no—
612C42—832no—
613C42—832no—
614C42—1664no—
615C42—1664no—
616C42—1664no—
617C42—1664no—
618C42—1664no—
619C42D4×D8312yes—
620C42C23×D8312yes—
621C23—834no—
622C23—832no—
623C23—1662no—
624C23—1662no—
625C23C2×D4×D8311yescharacteristic
626Q8—24no—
627Q8—22no—
628Q8—834no—
629Q8—6644no—
630Q8—6644no—
631Q8—16616no—
632Q8—1664no—
633Q8—1662no—
634Q8C2×Q8×D8314yes—
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—3322no—
646C2×C4—3322no—
647C2×C4—3322no—
648C2×C4—834no—
649C2×C4—832no—
650C2×C4—838no—
651C2×C4—834no—
652C2×C4—834no—
653C2×C4—832no—
654C2×C4—832no—
655C2×C4—6644no—
656C2×C4—16616no—
657C2×C4—1662no—
658C2×C4—1662no—
659C2×C4—1662no—
660C2×C4—1664no—
661C2×C4—1662no—
662C2×C4—1662no—
663C2×C4—1662no—
664C2×C4C2×D4×D8312yes—
665C2×C4C2×D4×D8312yes—
666C2×C4C2×D4×D8311yescharacteristic
667C2×C4C2×Q8×D8312yes—
668C2×C4#41×D8312yes—
669C2×C4C24×D8311yescharacteristic
670C8—22no—
671C8—22no—
672C8—1662no—
673C8—1662no—
674C22—834no—
675C22—1668no—
676C22—1662no—
677C22—1662no—
678C22C22⋊Q8×D8312yes—
679C22#1912850812yes—
680C22#1912851712yes—
681C22C22×D4×D8311yescharacteristic
682C4—22no—
683C4—24no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—3322no—
689C4—3322no—
690C4—3322no—
691C4—834no—
692C4—1662no—
693C4—1664no—
694C4—1662no—
695C4C22⋊Q8×D8312yes—
696C4C22×Q8×D8311yescharacteristic
697C4C2×#41×D8311yescharacteristic
698C2—1664no—
699C2#2491730214yesdirect product factor
700C2C2×C22⋊Q8×D8311yescharacteristic
701C2C2×#1912850811yescharacteristic
702C2C2×#1912851711yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#479×C83C2
socleC23×C83C22×D4
prime radicalC23×D83C2×D4
hypercenterC2×#479D83
hypocenterC83C2×#3082
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
3. #24917302C2direct (N × H)
4. C2×#19128011C2semidirect
5. C2×#19128006C2semidirect
6. C2×#19128005C2semidirect
7. C2×#19127996C2semidirect
8. C2×#19127995C2semidirect
9. C2×#19127987C2semidirect
10. C2×#19127984C2semidirect
16. C2×#479×C83C2semidirect
42. #19128011C22semidirect
43. #19128006C22semidirect
44. #19128005C22semidirect
45. #19127996C22semidirect
46. #19127995C22semidirect
47. #19127987C22semidirect
48. #19127984C22semidirect
71. #479×C83C22semidirect
83. C2×Q8×D83Q8semidirect
193. Q8×D83C2×Q8semidirect
347. C2×C83#3082semidirect
358. C2×#479D83semidirect
368. C83C2×#3082semidirect
399. #479C2×D83semidirect
699. C2#24917302direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283312
C2×#191281772
#249173022
C2×#191280112
C2×#191280062
C2×#191280052
C2×#191279962
C2×#191279952
C2×#191279872
C2×#191279842
C2×#191277422
C2×#191277362
C2×#191277262
C2×#191277082
C2×#103×D832
C2×#479×C832
C2×#308283