Finite Group Databasebeta

← C2×#24921459 #36312604

Subgroups — C2×#24921459 #36312604

Order 21248.

7130 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
1#24921459C2132yesmaximal, direct product factor
2C2×#19128424C213yesmaximal, complemented
3C2×#19128412C213yesmaximal, complemented
4C2×#19128404C213yesmaximal, complemented
5C2×#19128389C213yesmaximal, complemented
6C2×Q8×D332C211yesmaximal, characteristic, complemented
7C2×#19128363C211yesmaximal, characteristic, complemented
8C2×#19128363C211yesmaximal, characteristic, complemented
9C2×#19128325C213yesmaximal, complemented
10C2×#19128314C213yesmaximal, complemented
11C2×#19128238C213yesmaximal, complemented
12C2×#19128236C213yesmaximal, complemented
13C2×#19128183C211yesmaximal, characteristic, complemented
14C2×#19128177C211yesmaximal, characteristic, complemented
15C2×C4×Q8×D83C211yesmaximal, characteristic, complemented
16C2×#557×C83C211yesmaximal, characteristic, complemented
17C22×#13050591C2211yescharacteristic
18C22×Q8×D83C2211yescharacteristic
19C22×Q8×D83C2211yescharacteristic
20#19128424C22148yescomplemented
21#19128412C22148yescomplemented
22#19128404C22148yescomplemented
23#19128389C22148yescomplemented
24Q8×D332C22116yescomplemented
25#19128363C22116yescomplemented
26#19128363C22116yescomplemented
27#19128325C22148yescomplemented
28#19128314C22148yescomplemented
29C2×#14581792C2213yes—
30#19128238C22148yescomplemented
31#19128236C22148yescomplemented
32C2×#14581787C2216yes—
33C2×#14581787C2216yes—
34C2×#14581787C2213yes—
35C2×#14581787C2213yes—
36C2×#14581783C2213yes—
37C2×#14581783C2216yes—
38C2×#14581781C2213yes—
39C2×#14581780C2213yes—
40C2×#14581780C2213yes—
41C2×#14581777C2216yes—
42C2×#14581777C2213yes—
43C2×#14581777C2211yescharacteristic
44C2×#14581772C2213yes—
45C2×#14581772C2213yes—
46C2×#14581772C2213yes—
47C2×#14581772C2213yes—
48C2×#14581768C2216yes—
49C2×#14581768C2213yes—
50C2×#14581767C2213yes—
51C2×#14581767C2213yes—
52C2×#14581767C2213yes—
53#19128183C22116yescomplemented
54#19128177C22116yescomplemented
55C2×Q8×Dic83C2211yescharacteristic
56C2×C4×Dic166C2213yes—
57C2×C4×Dic166C2213yes—
58C2×#14581757C2213yes—
59C2×#14581757C2213yes—
60C4×Q8×D83C22116yescomplemented
61C2×C4×D332C2213yes—
62C2×C4×D332C2213yes—
63C2×C4×D332C2213yes—
64C2×C4×D332C2213yes—
65C2×#14581754C2213yes—
66C2×#14581754C2216yes—
67C2×#14581750C2213yes—
68C2×#14581750C2216yes—
69C2×#14581749C2213yes—
70C2×#14581749C2213yes—
71C2×C4⋊C4×D83C2213yes—
72C2×C4⋊C4×D83C2213yes—
73C2×C42×D83C2213yes—
74#557×C83C22116yescomplemented
75C2×C4⋊Q8×C83C2213yes—
76C2×#125×C83C2213yes—
77C2×#125×C83C2213yes—
78C2×C4×Q8×C83C2211yescharacteristic
79C2×C4×Q8×C83C2211yescharacteristic
80C2×C4×Q8×C83C2211yescharacteristic
81C2×C4×Q8×C83C2213yes—
82C2×#13050591—28no—
83C2×#13050591C2318yes—
84C22×Dic166C2313yes—
85C22×Dic166C2313yes—
86C2×Q8×D83—28no—
87C2×Q8×D83—28no—
88C2×Q8×D83C2318yes—
89C2×Q8×D83C2318yes—
90C22×D332C2313yes—
91C22×D332C2313yes—
92C22×D332C2311yescharacteristic
93C22×D332C2313yes—
94C22×C4×D83C2311yescharacteristic
95C22×C4×D83C2313yes—
96C22×C4×D83C2313yes—
97C22×C4×D83C2313yes—
98C22×C4×D83C2313yes—
99C22×C4×D83C2316yes—
100#14581792C23124yes—
101#14581787C23148yes—
102#14581787C23124yes—
103#14581787C23148yes—
104#14581787C23124yes—
105#14581783C23148yes—
106#14581783C23124yes—
107#14581781C23124yes—
108#14581780C23124yes—
109#14581780C23124yes—
110#14581777C23148yes—
111#14581777C23124yes—
112#14581777C2318yes—
113#14581772C23124yes—
114#14581772C23124yes—
115#14581772C23124yes—
116#14581772C23124yes—
117#14581768C23148yes—
118#14581768C23124yes—
119#14581767C23124yes—
120#14581767C23124yes—
121#14581767C23124yes—
122Q8×Dic83C2318yes—
123C4×Dic166C23124yes—
124C4×Dic166C23124yes—
125#14581757C23124yes—
126#14581757C23124yes—
127C4×D332C23124yes—
128C4×D332C23124yes—
129C4×D332C23124yes—
130C4×D332C23124yes—
131#14581754C23124yes—
132#14581754C23148yes—
133#14581750C23124yes—
134#14581750C23148yes—
135#14581749C23124yes—
136#14581749C23124yes—
137C2×C4⋊Dic83C2313yes—
138C2×C4⋊Dic83C2316yes—
139C2×C4⋊Dic83C2313yes—
140C2×C4⋊Dic83C2313yes—
141C2×C4⋊Dic83C2313yes—
142C2×Dic83⋊C4C2313yes—
143C2×Dic83⋊C4C2316yes—
144C2×Dic83⋊C4C2311yescharacteristic
145C2×Dic83⋊C4C2313yes—
146C2×Dic83⋊C4C2313yes—
147C4⋊C4×D83C23124yes—
148C4⋊C4×D83C23124yes—
149C2×(C2×D83)⋊C4C2311yescharacteristic
150C2×(C2×D83)⋊C4C2313yes—
151C2×(C2×D83)⋊C4C2313yes—
152C2×(C2×D83)⋊C4C2313yes—
153C2×(C2×D83)⋊C4C2313yes—
154C2×(C2×D83)⋊C4C2316yes—
155C2×(C2×D83)⋊C4C2313yes—
156C2×(C2×D83)⋊C4C2316yes—
157C2×(C2×D83)⋊C4C2311yescharacteristic
158C2×(C2×D83)⋊C4C2311yescharacteristic
159C2×(C2×D83)⋊C4C2313yes—
160C2×(C2×D83)⋊C4C2313yes—
161C2×C4×Dic83C2313yes—
162C2×C4×Dic83C2313yes—
163C2×C4×Dic83C2313yes—
164C2×C4×Dic83C2316yes—
165C42×D83C23124yes—
166C22×Q8×C83C2313yes—
167C22×Q8×C83C2311yescharacteristic
168C4⋊Q8×C83C23124yes—
169#125×C83C23124yes—
170#125×C83C23124yes—
171C4×Q8×C83C2318yes—
172C4×Q8×C83C2318yes—
173C4×Q8×C83C2318yes—
174C4×Q8×C83C23124yes—
175C2×C4⋊C4×C83C2311yescharacteristic
176C2×C4⋊C4×C83C2313yes—
177C2×C4⋊C4×C83C2313yes—
178C2×C4⋊C4×C83C2313yes—
179C2×C4⋊C4×C83C2313yes—
180C2×C4⋊C4×C83C2313yes—
181C2×C4⋊C4×C83C2316yes—
182C2×C42×C83C2313yes—
183C2×C42×C83C2313yes—
184C2×C42×C83C2313yes—
185C23×D83C2411yescharacteristic
186C23×D83C2413yes—
187C23×D83C2411yescharacteristic
188#13050591—232no—
189C2×Dic166—212no—
190C2×Dic166—212no—
191C2×Dic166C24112yes—
192C2×Dic166C24112yes—
193Q8×D83—232no—
194Q8×D83—232no—
195C2×D332—212no—
196C2×D332—24no—
197C2×D332—212no—
198C2×D332—46no—
199C2×D332C24112yes—
200C2×D332C2414yes—
201C2×D332C24112yes—
202C2×D332C24112yes—
203C22×Dic83C2413yes—
204C22×Dic83C2411yescharacteristic
205C22×Dic83C2413yes—
206C22×Dic83C2413yes—
207C22×Dic83C2411yescharacteristic
208C2×C4×D83—24no—
209C2×C4×D83—212no—
210C2×C4×D83—212no—
211C2×C4×D83—212no—
212C2×C4×D83—412no—
213C2×C4×D83—46no—
214C2×C4×D83C24112yes—
215C2×C4×D83C24112yes—
216C2×C4×D83C24112yes—
217C2×C4×D83C2414yes—
218C2×C4×D83C24112yes—
219C2×C4×D83C24124yes—
220C4⋊Dic83C24112yes—
221C4⋊Dic83C24124yes—
222C4⋊Dic83C24112yes—
223C4⋊Dic83C24112yes—
224C4⋊Dic83C24112yes—
225Dic83⋊C4C24112yes—
226Dic83⋊C4C24124yes—
227Dic83⋊C4C24112yes—
228Dic83⋊C4C2414yes—
229Dic83⋊C4C24112yes—
230(C2×D83)⋊C4C24124yes—
231(C2×D83)⋊C4C24124yes—
232(C2×D83)⋊C4C24112yes—
233(C2×D83)⋊C4C24112yes—
234(C2×D83)⋊C4C2414yes—
235(C2×D83)⋊C4C24112yes—
236(C2×D83)⋊C4C24112yes—
237(C2×D83)⋊C4C24112yes—
238(C2×D83)⋊C4C24112yes—
239(C2×D83)⋊C4C2414yes—
240(C2×D83)⋊C4C24112yes—
241(C2×D83)⋊C4C2414yes—
242C4×Dic83C24112yes—
243C4×Dic83C24124yes—
244C4×Dic83C24112yes—
245C4×Dic83C24112yes—
246C2×Q8×C83—46no—
247C2×Q8×C83#4118yes—
248C2×Q8×C83C24112yes—
249C2×Q8×C83C2414yes—
250C22×C4×C83C2413yes—
251C22×C4×C83C2413yes—
252C22×C4×C83C2411yescharacteristic
253C22×C4×C83C2411yescharacteristic
254C22×C4×C83C2413yes—
255C22×C4×C83C2411yescharacteristic
256C22×C4×C83C2413yes—
257C4⋊C4×C83C24112yes—
258C4⋊C4×C83C24112yes—
259C4⋊C4×C83C24112yes—
260C4⋊C4×C83C24112yes—
261C4⋊C4×C83C24124yes—
262C4⋊C4×C83C2414yes—
263C4⋊C4×C83C24112yes—
264C42×C83C24112yes—
265C42×C83C24112yes—
266C42×C83C24112yes—
267C23×C83C2511yescharacteristic
268C22×D83—22no—
269C22×D83—22no—
270C22×D83—22no—
271C22×D83—26no—
272C22×D83—22no—
273C22×D83—26no—
274C22×D83—26no—
275C22×D83—22no—
276C22×D832−1+414yes—
277C22×D83C2512yes—
278C22×D83C2516yes—
279C22×D83C2512yes—
280Q8×C83—412no—
281Q8×C83C2×#41116yes—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
284C2×C4×C83—26no—
285C2×C4×C83—22no—
286C2×C4×C83—26no—
287C2×C4×C83—26no—
288C2×C4×C83C2×#41112yes—
289C2×C4×C83C2512yes—
290C2×C4×C83C2512yes—
291C2×C4×C83C2512yes—
292C2×C4×C83C2516yes—
293C2×C4×C83C2516yes—
294C2×C4×C83C2516yes—
295C2×C4×C83C2516yes—
296C2×Dic83—22no—
297C2×Dic83—26no—
298C2×Dic83—26no—
299C2×Dic83—22no—
300C2×Dic83—26no—
301C2×Dic83C2512yes—
302C2×Dic83C2516yes—
303C2×Dic83C2516yes—
304C2×Dic83C2516yes—
305C2×Dic83C2512yes—
306D332—224no—
307D332—28no—
308D332—224no—
309D332—412no—
310C4×D83—28no—
311C4×D83—224no—
312C4×D83—224no—
313C4×D83—224no—
314C4×D83—424no—
315C4×D83—412no—
316Dic166—224no—
317Dic166—224no—
318C22×C83C22×#4112yes—
319C22×C83C2×2−1+412yes—
320C22×C83#58512yes—
321C22×C83C2611yescharacteristic
322C2×D83—22no—
323C2×D83—22no—
324C2×D83—28no—
325C2×D83—22no—
326C2×D83—26no—
327C2×D83—22no—
328C2×D83—26no—
329C2×D83—26no—
330C2×D83—22no—
331C2×D83—44no—
332C2×D83—412no—
333C2×D83C2×2−1+414yes—
334C4×C83—22no—
335C4×C83—22no—
336C4×C83—26no—
337C4×C83—26no—
338C4×C83—26no—
339C4×C83—22no—
340C4×C83C22×#41112yes—
341Dic83—26no—
342Dic83—26no—
343Dic83—22no—
344Dic83—22no—
345Dic83—26no—
346C2×#3516—831nomaximal, Sylow
347C2×C83#351614yescomplemented
348C2×C83C23×#4111yescharacteristic
349C2×C83C22×2−1+411yescharacteristic
350C2×C83C2×#58511yescharacteristic
351D83—24no—
352D83—42no—
353D83—46no—
354#3516—8332no—
355C2×#557D8311yescharacteristic, complemented
356C2×#556—833no—
357C2×#554—833no—
358C2×#553—833no—
359C2×#552—833no—
360C2×D4×Q8—831no—
361C2×#548—831no—
362C2×#548—831no—
363C2×#542—833no—
364C2×#541—833no—
365C2×#529—833no—
366C2×#529—833no—
367C2×#520—831no—
368C2×#519—831no—
369C22×C4×Q8—831no—
370C83C2×#351611yescharacteristic, complemented, Sylow
371C22×#41—831no—
372C23×Q8—831no—
373C23×Q8—831no—
374#557C2×D83116yescomplemented
375#556—8348no—
376#554—8348no—
377#553—8348no—
378#552—8348no—
379D4×Q8—8316no—
380#548—8316no—
381#548—8316no—
382#542—8348no—
383#541—8348no—
384C2×C4⋊Q8—833no—
385C2×C4⋊Q8C2×D8313yes—
386#529—8348no—
387#529—8348no—
388C2×#126—836no—
389C2×#126—833no—
390C2×#126—833no—
391C2×#126—836no—
392C2×#125—833no—
393C2×#125—836no—
394C2×#125C2×D8313yes—
395C2×#125C2×D8313yes—
396C2×#124—833no—
397C2×#124—833no—
398C2×#124—833no—
399C2×#123—831no—
400C2×#123—833no—
401C2×#123—836no—
402C2×C22⋊Q8—833no—
403C2×C22⋊Q8—836no—
404C2×C22⋊Q8—833no—
405C2×C22⋊Q8—833no—
406C2×C22⋊Q8—833no—
407C2×C22⋊Q8—833no—
408C2×#121—833no—
409C2×#121—833no—
410C2×#121—833no—
411#520—8316no—
412#519—8316no—
413C2×C4×Q8—831no—
414C2×C4×Q8—8316no—
415C2×C4×Q8—833no—
416C2×C4×Q8—833no—
417C2×C4×Q8—833no—
418C2×C4×Q8—833no—
419C2×C4×Q8C2×D8311yescharacteristic
420C2×C4×Q8C2×D8311yescharacteristic
421C2×C4×Q8C2×D8311yescharacteristic
422C2×C4×Q8C2×D8313yes—
423C2×C4×D4—833no—
424C2×C4×D4—836no—
425C2×C4×D4—833no—
426C2×C4×D4—833no—
427C2×C4×D4—833no—
428C2×C4×D4—833no—
429C2×#117—833no—
430C2×#117—836no—
431C2×#117—833no—
432C2×#117—833no—
433C22×C4⋊C4—833no—
434C22×C4⋊C4—833no—
435C22×C42—833no—
436C2×#41—838no—
437C2×#41—1668no—
438C22×Q8—838no—
439C22×Q8—838no—
440C22×Q8—833no—
441C22×Q8—833no—
442C22×Q8—1668no—
443C22×Q8—1668no—
444C22×Q8C22×D8313yes—
445C22×Q8C22×D8311yescharacteristic
446C22×D4—833no—
447C22×D4—833no—
448C22×D4—831no—
449C22×D4—833no—
450C23×C4—833no—
451C23×C4—836no—
452C23×C4—833no—
453C23×C4—833no—
454C23×C4—833no—
455C23×C4—831no—
456C4⋊Q8—8324no—
457C4⋊Q8C22×D83124yes—
458#126—8348no—
459#126—8324no—
460#126—8324no—
461#126—8348no—
462#125—8324no—
463#125—8348no—
464#125C22×D83124yes—
465#125C22×D83124yes—
466#124—8324no—
467#124—8324no—
468#124—8324no—
469#123—838no—
470#123—8324no—
471#123—8348no—
472C22⋊Q8—8324no—
473C22⋊Q8—8348no—
474C22⋊Q8—8324no—
475C22⋊Q8—8324no—
476C22⋊Q8—8324no—
477C22⋊Q8—8324no—
478#121—8324no—
479#121—8324no—
480#121—8324no—
481C4×Q8—838no—
482C4×Q8—8324no—
483C4×Q8—8324no—
484C4×Q8—8324no—
485C4×Q8—8324no—
486C4×Q8C22×D8318yes—
487C4×Q8C22×D8318yes—
488C4×Q8C22×D8318yes—
489C4×Q8C22×D83124yes—
490C4×D4—8324no—
491C4×D4—8348no—
492C4×D4—8324no—
493C4×D4—8324no—
494C4×D4—8324no—
495C4×D4—8324no—
496#117—8324no—
497#117—8348no—
498#117—8324no—
499#117—8324no—
500C2×C4⋊C4—833no—
501C2×C4⋊C4—833no—
502C2×C4⋊C4—836no—
503C2×C4⋊C4—831no—
504C2×C4⋊C4—833no—
505C2×C4⋊C4—833no—
506C2×C4⋊C4—836no—
507C2×C4⋊C4—833no—
508C2×C4⋊C4—833no—
509C2×C4⋊C4—833no—
510C2×C4⋊C4—8324no—
511C2×C4⋊C4—8324no—
512C2×C4⋊C4C22×D8313yes—
513C2×C4⋊C4C22×D8313yes—
514C2×C4⋊C4C22×D8313yes—
515C2×C4⋊C4C22×D8313yes—
516C2×C4⋊C4C22×D8316yes—
517C2×C4⋊C4C22×D8311yescharacteristic
518C2×C4⋊C4C22×D8313yes—
519C2×C22⋊C4—833no—
520C2×C22⋊C4—831no—
521C2×C22⋊C4—833no—
522C2×C22⋊C4—833no—
523C2×C22⋊C4—833no—
524C2×C22⋊C4—836no—
525C2×C22⋊C4—833no—
526C2×C22⋊C4—831no—
527C2×C22⋊C4—831no—
528C2×C22⋊C4—836no—
529C2×C22⋊C4—833no—
530C2×C22⋊C4—833no—
531C2×C42—833no—
532C2×C42—836no—
533C2×C42—833no—
534C2×C42—833no—
535C2×C42—8324no—
536C2×C42C22×D8313yes—
537C2×C42C22×D8313yes—
538C2×C42C22×D8313yes—
539C24—831no—
540C24—831no—
541C24—833no—
542#41—16632no—
543C2×Q8—46no—
544C2×Q8—8312no—
545C2×Q8—8312no—
546C2×Q8—16632no—
547C2×Q8—16632no—
548C2×Q8—16612no—
549C2×Q8—16612no—
550C2×Q8#1305059118yes—
551C2×Q8C23×D83112yes—
552C2×Q8C23×D8314yes—
553C2×D4—3326no—
554C2×D4—8312no—
555C2×D4—8312no—
556C2×D4—834no—
557C2×D4—8312no—
558C2×D4—16612no—
559C2×D4—1664no—
560C2×D4—16612no—
561C22×C4—33212no—
562C22×C4—3326no—
563C22×C4—8312no—
564C22×C4—8324no—
565C22×C4—831no—
566C22×C4—833no—
567C22×C4—833no—
568C22×C4—833no—
569C22×C4—831no—
570C22×C4—834no—
571C22×C4—8312no—
572C22×C4—8312no—
573C22×C4—8312no—
574C22×C4—1664no—
575C22×C4—16612no—
576C22×C4—16612no—
577C22×C4—16612no—
578C22×C4C23×D8311yescharacteristic
579C22×C4C23×D8313yes—
580C22×C4C23×D8313yes—
581C22×C4C23×D8311yescharacteristic
582C22×C4C23×D8311yescharacteristic
583C22×C4C23×D8313yes—
584C22×C4C23×D8313yes—
585C4⋊C4—8312no—
586C4⋊C4—8312no—
587C4⋊C4—8324no—
588C4⋊C4—834no—
589C4⋊C4—8312no—
590C4⋊C4—8312no—
591C4⋊C4—8324no—
592C4⋊C4—8312no—
593C4⋊C4—8312no—
594C4⋊C4—8312no—
595C4⋊C4C23×D83112yes—
596C4⋊C4C23×D83112yes—
597C4⋊C4C23×D83112yes—
598C4⋊C4C23×D83112yes—
599C4⋊C4C23×D83124yes—
600C4⋊C4C23×D8314yes—
601C4⋊C4C23×D83112yes—
602C22⋊C4—8312no—
603C22⋊C4—834no—
604C22⋊C4—8312no—
605C22⋊C4—8312no—
606C22⋊C4—8312no—
607C22⋊C4—8324no—
608C22⋊C4—8312no—
609C22⋊C4—834no—
610C22⋊C4—834no—
611C22⋊C4—8324no—
612C22⋊C4—8312no—
613C22⋊C4—8312no—
614C42—8312no—
615C42—8312no—
616C42—8312no—
617C42—8324no—
618C42C23×D83112yes—
619C42C23×D83112yes—
620C42C23×D83112yes—
621C23—834no—
622C23—832no—
623C23—832no—
624C23—836no—
625C23—1662no—
626C23—1666no—
627C23—1662no—
628C23—1666no—
629C23—1666no—
630C23—1662no—
631C23—1662no—
632C23—1662no—
633C23C24×D8311yescharacteristic
634Q8—412no—
635Q8—16624no—
636Q8—16624no—
637Q8C2×#13050591116yes—
638D4—33212no—
639D4—16624no—
640D4—1668no—
641D4—16624no—
642C2×C4—22no—
643C2×C4—26no—
644C2×C4—22no—
645C2×C4—26no—
646C2×C4—26no—
647C2×C4—22no—
648C2×C4—33224no—
649C2×C4—33212no—
650C2×C4—832no—
651C2×C4—836no—
652C2×C4—836no—
653C2×C4—836no—
654C2×C4—832no—
655C2×C4—1668no—
656C2×C4—1662no—
657C2×C4—1666no—
658C2×C4—1666no—
659C2×C4—1662no—
660C2×C4—1666no—
661C2×C4—16624no—
662C2×C4—16624no—
663C2×C4—16624no—
664C2×C4C2×#13050591112yes—
665C2×C4C24×D8312yes—
666C2×C4C24×D8316yes—
667C2×C4C24×D8316yes—
668C2×C4C24×D8312yes—
669C2×C4C24×D8312yes—
670C2×C4C24×D8316yes—
671C2×C4C24×D8316yes—
672C22—3324no—
673C22—33212no—
674C22—834no—
675C22—1662no—
676C22—1666no—
677C22—1662no—
678C22—1666no—
679C22—1666no—
680C22—1662no—
681C22—1668no—
682C22—1662no—
683C22—1662no—
684C22C22×#1305059112yes—
685C222−1+4×D8312yes—
686C22#1912853712yes—
687C22C25×D8311yescharacteristic
688C4—22no—
689C4—26no—
690C4—22no—
691C4—26no—
692C4—26no—
693C4—22no—
694C4—1662no—
695C4—1666no—
696C4—1666no—
697C4—1662no—
698C4—1666no—
699C4C22×#13050591112yes—
700C2—3322no—
701C2—3326no—
702C2—1664no—
703C2#2492145914yesdirect product factor
704C2C23×#1305059111yescharacteristic
705C2C2×2−1+4×D8311yescharacteristic
706C2C2×#1912853711yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#557×C83C2
socleC23×C83C25
hypercenterC2×#557D83
hypocenterC83C2×#3516
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #24921459C2direct (N × H)
2. C2×#19128424C2semidirect
3. C2×#19128412C2semidirect
4. C2×#19128404C2semidirect
5. C2×#19128389C2semidirect
6. C2×Q8×D332C2semidirect
7. C2×#19128363C2semidirect
8. C2×#19128363C2semidirect
9. C2×#19128325C2semidirect
10. C2×#19128314C2semidirect
11. C2×#19128238C2semidirect
12. C2×#19128236C2semidirect
13. C2×#19128183C2semidirect
14. C2×#19128177C2semidirect
15. C2×C4×Q8×D83C2semidirect
16. C2×#557×C83C2semidirect
20. #19128424C22semidirect
21. #19128412C22semidirect
22. #19128404C22semidirect
23. #19128389C22semidirect
24. Q8×D332C22semidirect
25. #19128363C22semidirect
26. #19128363C22semidirect
27. #19128325C22semidirect
28. #19128314C22semidirect
30. #19128238C22semidirect
31. #19128236C22semidirect
53. #19128183C22semidirect
54. #19128177C22semidirect
60. C4×Q8×D83C22semidirect
74. #557×C83C22semidirect
347. C2×C83#3516semidirect
355. C2×#557D83semidirect
370. C83C2×#3516semidirect
374. #557C2×D83semidirect
703. C2#24921459direct (N × H)

Maximal subgroups

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

subgroupindex
#249214592
C2×#191284242
C2×#191284122
C2×#191284042
C2×#191283892
C2×Q8×D3322
C2×#191283632
C2×#191283252
C2×#191283142
C2×#191282382
C2×#191282362
C2×#191281832
C2×#191281772
C2×C4×Q8×D832
C2×#557×C832
C2×#351683