Finite Group Databasebeta

← C2×#24921457 #36312602

Subgroups — C2×#24921457 #36312602

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#24921457C2132yesmaximal, direct product factor
2C2×#19128427C211yesmaximal, characteristic, complemented
3C2×#19128425C213yesmaximal, complemented
4C2×#19128409C213yesmaximal, complemented
5C2×#19128397C213yesmaximal, complemented
6C2×#19128385C213yesmaximal, complemented
7C2×#19128362C211yesmaximal, characteristic, complemented
8C2×#19128362C211yesmaximal, characteristic, complemented
9C2×#19128324C213yesmaximal, complemented
10C2×#19128312C213yesmaximal, complemented
11C2×#19128237C213yesmaximal, complemented
12C2×#19128231C213yesmaximal, complemented
13C2×#19128183C211yesmaximal, characteristic, complemented
14C2×#19128179C211yesmaximal, characteristic, complemented
15C22×Q8×Dic83C211yesmaximal, characteristic, complemented
16C2×D4×Q8×C83C211yesmaximal, characteristic, complemented
17C22×#13050591C2211yescharacteristic
18#19128427C22116yescomplemented
19#19128425C22148yescomplemented
20#19128409C22148yescomplemented
21#19128397C22148yescomplemented
22#19128385C22148yescomplemented
23#19128362C22116yescomplemented
24#19128362C22116yescomplemented
25#19128324C22148yescomplemented
26#19128312C22148yescomplemented
27C2×#14581791C2213yes—
28#19128237C22148yescomplemented
29#19128231C22148yescomplemented
30C2×#14581787C2216yes—
31C2×#14581787C2213yes—
32C2×#14581787C2216yes—
33C2×#14581785C2213yes—
34C2×#14581784C2213yes—
35C2×#14581783C2213yes—
36C2×#14581782C2216yes—
37C2×#14581782C2213yes—
38C2×#14581781C2213yes—
39C2×#14581781C2213yes—
40C2×#14581778C2213yes—
41C2×#14581776C2213yes—
42C2×#14581774C2216yes—
43C2×#14581773C2211yescharacteristic
44C2×#14581772C2216yes—
45C2×#14581769C2213yes—
46C2×#14581768C2213yes—
47C2×#14581768C2213yes—
48C2×#14581766C2213yes—
49C2×#14581766C2213yes—
50C2×#14581764C2213yes—
51#19128183C22116yescomplemented
52#19128179C22116yescomplemented
53C2×Q8×Dic83C2213yes—
54C2×Q8×Dic83C2211yescharacteristic
55C2×Q8×Dic83C2211yescharacteristic
56C2×Q8×Dic83C2213yes—
57C2×Q8×Dic83C2211yescharacteristic
58C2×Q8×Dic83C2213yes—
59C2×Q8×Dic83C2213yes—
60C2×Q8×Dic83C22116yescomplemented
61C2×C4×Dic166C2213yes—
62C2×C4×D332C2213yes—
63C2×#14581754C2213yes—
64C2×C4×C22⋊D83C2213yes—
65C2×C4×C22⋊D83C2213yes—
66C2×(C22⋊D83)⋊C4C2216yes—
67C2×#14581751C2213yes—
68C2×#14581751C2213yes—
69C2×#14581750C2216yes—
70C2×#14581749C2213yes—
71C22×C4⋊Dic83C2213yes—
72C2×C4⋊C4×D83C2213yes—
73C22×C4×Dic83C2213yes—
74C23×Q8×C83C2211yescharacteristic
75C23×Q8×C83C2211yescharacteristic
76D4×Q8×C83C22116yescomplemented
77C2×C4⋊Q8×C83C2213yes—
78C2×C22⋊Q8×C83C2213yes—
79C2×C22⋊Q8×C83C2213yes—
80C2×C4×Q8×C83C2211yescharacteristic
81C2×C4×D4×C83C2213yes—
82C2×#13050591—28no—
83C2×#13050591C2318yes—
84C22×Dic166C2313yes—
85C22×D332C2313yes—
86C22×C22⋊D83C2313yes—
87C22×C22⋊D83C2313yes—
88C23×Dic83C2311yescharacteristic
89C23×Dic83C2313yes—
90C22×C4×D83C2313yes—
91C22×C4×D83C2316yes—
92#14581791C23124yes—
93#14581787C23148yes—
94#14581787C23148yes—
95#14581787C23124yes—
96#14581785C23124yes—
97#14581784C23124yes—
98#14581783C23124yes—
99#14581782C23148yes—
100#14581782C23124yes—
101#14581781C23124yes—
102#14581781C23124yes—
103#14581778C23124yes—
104#14581776C23124yes—
105#14581774C23148yes—
106#14581773C2318yes—
107#14581772C23148yes—
108#14581769C23124yes—
109#14581768C23124yes—
110#14581768C23124yes—
111#14581766C23124yes—
112#14581766C23124yes—
113#14581764C23124yes—
114Q8×Dic83C23124yes—
115Q8×Dic83C2318yes—
116Q8×Dic83C2318yes—
117Q8×Dic83C23124yes—
118Q8×Dic83C23124yes—
119Q8×Dic83C2318yes—
120Q8×Dic83C23124yes—
121C4×Dic166C23124yes—
122C4×D332C23124yes—
123#14581754C23124yes—
124C4×C22⋊D83C23124yes—
125C4×C22⋊D83C23124yes—
126(C22⋊D83)⋊C4C23148yes—
127#14581751C23124yes—
128#14581751C23124yes—
129#14581750C23148yes—
130#14581749C23124yes—
131C2×C4⋊Dic83C23124yes—
132C2×C4⋊Dic83C2313yes—
133C2×C4⋊Dic83C2313yes—
134C2×C4⋊Dic83C2316yes—
135C2×C4⋊Dic83C2313yes—
136C2×C4⋊Dic83C2313yes—
137C2×C4⋊Dic83C2313yes—
138C2×C4⋊Dic83C2313yes—
139C2×Dic83⋊C4C2313yes—
140C2×Dic83⋊C4C2311yescharacteristic
141C2×Dic83⋊C4C2316yes—
142C2×Dic83⋊C4C2313yes—
143C2×Dic83⋊C4C2313yes—
144C2×Dic83⋊C4C2311yescharacteristic
145C2×Dic83⋊C4C2313yes—
146C4⋊C4×D83C23124yes—
147C2×C22⋊Dic83C2313yes—
148C2×C22⋊Dic83C2311yescharacteristic
149C2×C22⋊Dic83C2311yescharacteristic
150C2×C22⋊Dic83C2311yescharacteristic
151C2×(C2×D83)⋊C4C2313yes—
152C2×(C2×D83)⋊C4C2313yes—
153C2×(C2×D83)⋊C4C2313yes—
154C2×(C2×D83)⋊C4C2316yes—
155C2×(C2×D83)⋊C4C2316yes—
156C2×(C2×D83)⋊C4C2313yes—
157C2×C4×Dic83C2313yes—
158C2×C4×Dic83C2313yes—
159C2×C4×Dic83C2313yes—
160C2×C4×Dic83C2313yes—
161C2×C4×Dic83C23124yes—
162C2×C4×Dic83C2316yes—
163C2×C4×Dic83C2313yes—
164C22×Q8×C83—28no—
165C22×Q8×C83—28no—
166C22×Q8×C83C2318yes—
167C22×Q8×C83C2318yes—
168C22×Q8×C83C2313yes—
169C22×Q8×C83C2313yes—
170C22×Q8×C83C2311yescharacteristic
171C22×D4×C83C2311yescharacteristic
172C23×C4×C83C2313yes—
173C23×C4×C83C2313yes—
174C4⋊Q8×C83C23124yes—
175C22⋊Q8×C83C23124yes—
176C22⋊Q8×C83C23124yes—
177C4×Q8×C83C2318yes—
178C4×D4×C83C23124yes—
179C2×C4⋊C4×C83C2313yes—
180C2×C4⋊C4×C83C2313yes—
181C2×C4⋊C4×C83C2316yes—
182C2×C22⋊C4×C83C2313yes—
183C2×C22⋊C4×C83C2313yes—
184C2×C42×C83C2313yes—
185C23×D83C2413yes—
186#13050591—232no—
187C2×Dic166—46no—
188C2×Dic166C24112yes—
189C2×D332—212no—
190C2×D332C24112yes—
191C2×C22⋊D83—212no—
192C2×C22⋊D83—46no—
193C2×C22⋊D83C24112yes—
194C2×C22⋊D83C24112yes—
195C22×Dic83—24no—
196C22×Dic83—46no—
197C22×Dic83C2414yes—
198C22×Dic83C2411yescharacteristic
199C22×Dic83C2413yes—
200C22×Dic83C2413yes—
201C22×Dic83C2411yescharacteristic
202C22×Dic83C2411yescharacteristic
203C22×Dic83C2413yes—
204C22×Dic83C2411yescharacteristic
205C22×Dic83C24112yes—
206C2×C4×D83—212no—
207C2×C4×D83—412no—
208C2×C4×D83C24112yes—
209C2×C4×D83C24124yes—
210C4⋊Dic83C24112yes—
211C4⋊Dic83C24112yes—
212C4⋊Dic83C24112yes—
213C4⋊Dic83C24124yes—
214C4⋊Dic83C24112yes—
215C4⋊Dic83C24112yes—
216C4⋊Dic83C24112yes—
217Dic83⋊C4C24112yes—
218Dic83⋊C4C24112yes—
219Dic83⋊C4C24112yes—
220Dic83⋊C4C24112yes—
221Dic83⋊C4C2414yes—
222Dic83⋊C4C2414yes—
223Dic83⋊C4C24124yes—
224C22⋊Dic83C24112yes—
225C22⋊Dic83C2414yes—
226C22⋊Dic83C2414yes—
227C22⋊Dic83C2414yes—
228(C2×D83)⋊C4C24112yes—
229(C2×D83)⋊C4C24124yes—
230(C2×D83)⋊C4C24124yes—
231(C2×D83)⋊C4C24112yes—
232(C2×D83)⋊C4C24112yes—
233(C2×D83)⋊C4C24112yes—
234C4×Dic83C24112yes—
235C4×Dic83C24112yes—
236C4×Dic83C24112yes—
237C4×Dic83C24124yes—
238C4×Dic83C24112yes—
239C4×Dic83C24112yes—
240C24×C83C2411yescharacteristic
241C24×C83C2411yescharacteristic
242C2×Q8×C83—232no—
243C2×Q8×C83—232no—
244C2×Q8×C83—212no—
245C2×Q8×C83—212no—
246C2×Q8×C83#4118yes—
247C2×Q8×C83C24112yes—
248C2×Q8×C83C24112yes—
249C2×Q8×C83C2414yes—
250C2×D4×C83—24no—
251C2×D4×C83C2414yes—
252C22×C4×C83—212no—
253C22×C4×C83—212no—
254C22×C4×C83C24112yes—
255C22×C4×C83C24112yes—
256C22×C4×C83C2413yes—
257C22×C4×C83C2411yescharacteristic
258C22×C4×C83C2413yes—
259C22×C4×C83C2413yes—
260C22×C4×C83C2413yes—
261C4⋊C4×C83C24124yes—
262C4⋊C4×C83C24112yes—
263C4⋊C4×C83C24112yes—
264C22⋊C4×C83C24112yes—
265C22⋊C4×C83C24112yes—
266C42×C83C24112yes—
267C23×C83—22no—
268C23×C83—22no—
269C23×C83—22no—
270C23×C83—22no—
271C23×C83—22no—
272C23×C832−1+414yes—
273C23×C83C2512yes—
274C23×C83C2512yes—
275C23×C83C2511yescharacteristic
276C22×D83—26no—
277C22×D83—26no—
278C22×D83—26no—
279C22×D83C2516yes—
280Q8×C83—224no—
281Q8×C83—224no—
282Q8×C83C2×#41116yes—
283D4×C83—28no—
284C2×C4×C83—26no—
285C2×C4×C83—26no—
286C2×C4×C83—22no—
287C2×C4×C83—26no—
288C2×C4×C83—224no—
289C2×C4×C83—224no—
290C2×C4×C83C2×#41112yes—
291C2×C4×C83C2512yes—
292C2×C4×C83C2516yes—
293C2×C4×C83C2516yes—
294C2×C4×C83C2516yes—
295C2×C4×C83C2516yes—
296C22⋊D83—224no—
297C22⋊D83—412no—
298C2×Dic83—22no—
299C2×Dic83—28no—
300C2×Dic83—22no—
301C2×Dic83—22no—
302C2×Dic83—26no—
303C2×Dic83—26no—
304C2×Dic83—26no—
305C2×Dic83—22no—
306C2×Dic83—412no—
307C2×Dic83C2512yes—
308C2×Dic83C2512yes—
309C2×Dic83C2516yes—
310C2×Dic83C2512yes—
311C2×Dic83C2516yes—
312C2×Dic83C2516yes—
313C2×Dic83C2512yes—
314D332—224no—
315C4×D83—224no—
316C4×D83—424no—
317Dic166—412no—
318C22×C83—22no—
319C22×C83—22no—
320C22×C83—28no—
321C22×C83—22no—
322C22×C83—22no—
323C22×C83—22no—
324C22×C83—44no—
325C22×C83C22×#4112yes—
326C22×C83C2×2−1+414yes—
327C22×C83C2×2−1+412yes—
328C22×C83#58512yes—
329C22×C83C2611yescharacteristic
330C2×D83—26no—
331C2×D83—26no—
332C2×D83—26no—
333C2×D83—412no—
334C4×C83—26no—
335C4×C83—26no—
336C4×C83—22no—
337C4×C83—26no—
338C4×C83C22×#41112yes—
339Dic83—22no—
340Dic83—22no—
341Dic83—22no—
342Dic83—26no—
343Dic83—22no—
344Dic83—26no—
345Dic83—26no—
346C2×#3516—831nomaximal, Sylow
347C2×C83—24no—
348C2×C83—42no—
349C2×C83#351614yescomplemented
350C2×C83C23×#4111yescharacteristic
351C2×C83C22×2−1+411yescharacteristic
352C2×C83C2×#58511yescharacteristic
353D83—46no—
354#3516—8332no—
355C2×#557—831no—
356C2×#556—833no—
357C2×#554—833no—
358C2×#553—833no—
359C2×#552—833no—
360C2×D4×Q8D8311yescharacteristic, complemented
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×Q8C2×D8311yescharacteristic
373C23×Q8C2×D8311yescharacteristic
374#557—8316no—
375#556—8348no—
376#554—8348no—
377#553—8348no—
378#552—8348no—
379D4×Q8C2×D83116yescomplemented
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—836no—
391C2×#126—833no—
392C2×#125—833no—
393C2×#125—833no—
394C2×#125—836no—
395C2×#125—833no—
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—833no—
404C2×C22⋊Q8—836no—
405C2×C22⋊Q8—833no—
406C2×C22⋊Q8C2×D8313yes—
407C2×C22⋊Q8C2×D8313yes—
408C2×#121—833no—
409C2×#121—833no—
410C2×#121—833no—
411#520—8316no—
412#519—8316no—
413C2×C4×Q8—831no—
414C2×C4×Q8—833no—
415C2×C4×Q8—831no—
416C2×C4×Q8—833no—
417C2×C4×Q8—8316no—
418C2×C4×Q8—833no—
419C2×C4×Q8—831no—
420C2×C4×Q8—833no—
421C2×C4×Q8—833no—
422C2×C4×Q8C2×D8311yescharacteristic
423C2×C4×D4—833no—
424C2×C4×D4—833no—
425C2×C4×D4—833no—
426C2×C4×D4—836no—
427C2×C4×D4—833no—
428C2×C4×D4C2×D8313yes—
429C2×#117—833no—
430C2×#117—833no—
431C2×#117—836no—
432C2×#117—833no—
433C22×C4⋊C4—833no—
434C22×C4⋊C4—833no—
435C22×C42—833no—
436C2×#41—838no—
437C2×#41—1668no—
438C22×Q8—28no—
439C22×Q8—28no—
440C22×Q8—833no—
441C22×Q8C22×D8313yes—
442C22×Q8C22×D8313yes—
443C22×Q8C22×D8318yes—
444C22×Q8C22×D8318yes—
445C22×Q8C22×D8311yescharacteristic
446C22×D4—833no—
447C22×D4—833no—
448C22×D4—833no—
449C22×D4C22×D8311yescharacteristic
450C23×C4—833no—
451C23×C4—836no—
452C23×C4—831no—
453C23×C4—833no—
454C23×C4C22×D8313yes—
455C23×C4C22×D8313yes—
456C4⋊Q8—8324no—
457C4⋊Q8C22×D83124yes—
458#126—8348no—
459#126—8324no—
460#126—8348no—
461#126—8324no—
462#125—8324no—
463#125—8324no—
464#125—8348no—
465#125—8324no—
466#124—8324no—
467#124—8324no—
468#124—8324no—
469#123—838no—
470#123—8348no—
471#123—8324no—
472C22⋊Q8—8324no—
473C22⋊Q8—8324no—
474C22⋊Q8—8348no—
475C22⋊Q8—8324no—
476C22⋊Q8C22×D83124yes—
477C22⋊Q8C22×D83124yes—
478#121—8324no—
479#121—8324no—
480#121—8324no—
481C4×Q8—838no—
482C4×Q8—8324no—
483C4×Q8—838no—
484C4×Q8—8324no—
485C4×Q8—8324no—
486C4×Q8—838no—
487C4×Q8—8324no—
488C4×Q8—8324no—
489C4×Q8C22×D8318yes—
490C4×D4—8324no—
491C4×D4—8324no—
492C4×D4—8324no—
493C4×D4—8348no—
494C4×D4—8324no—
495C4×D4C22×D83124yes—
496#117—8324no—
497#117—8324no—
498#117—8348no—
499#117—8324no—
500C2×C4⋊C4—833no—
501C2×C4⋊C4—833no—
502C2×C4⋊C4—833no—
503C2×C4⋊C4—836no—
504C2×C4⋊C4—8324no—
505C2×C4⋊C4—831no—
506C2×C4⋊C4—833no—
507C2×C4⋊C4—833no—
508C2×C4⋊C4—833no—
509C2×C4⋊C4—833no—
510C2×C4⋊C4—833no—
511C2×C4⋊C4—833no—
512C2×C4⋊C4—836no—
513C2×C4⋊C4—831no—
514C2×C4⋊C4—833no—
515C2×C4⋊C4—8324no—
516C2×C4⋊C4C22×D8313yes—
517C2×C4⋊C4C22×D8316yes—
518C2×C4⋊C4C22×D8313yes—
519C2×C22⋊C4—833no—
520C2×C22⋊C4—831no—
521C2×C22⋊C4—831no—
522C2×C22⋊C4—831no—
523C2×C22⋊C4—833no—
524C2×C22⋊C4—833no—
525C2×C22⋊C4—833no—
526C2×C22⋊C4—836no—
527C2×C22⋊C4—836no—
528C2×C22⋊C4—833no—
529C2×C22⋊C4C22×D8313yes—
530C2×C22⋊C4C22×D8313yes—
531C2×C42—833no—
532C2×C42—836no—
533C2×C42—833no—
534C2×C42—833no—
535C2×C42—833no—
536C2×C42—833no—
537C2×C42—8324no—
538C2×C42C22×D8313yes—
539C24—833no—
540C24C23×D8311yescharacteristic
541C24C23×D8311yescharacteristic
542#41—16632no—
543C2×Q8—232no—
544C2×Q8—232no—
545C2×Q8—212no—
546C2×Q8—212no—
547C2×Q8—3326no—
548C2×Q8—8312no—
549C2×Q8#1305058918yes—
550C2×Q8C23×D83112yes—
551C2×Q8C23×D83112yes—
552C2×Q8C23×D8314yes—
553C2×D4—24no—
554C2×D4—3326no—
555C2×D4—8312no—
556C2×D4—8312no—
557C2×D4—8312no—
558C2×D4—16612no—
559C2×D4—16612no—
560C2×D4C23×D8314yes—
561C22×C4—212no—
562C22×C4—212no—
563C22×C4—33212no—
564C22×C4—3326no—
565C22×C4—8312no—
566C22×C4—8324no—
567C22×C4—834no—
568C22×C4—831no—
569C22×C4—831no—
570C22×C4—833no—
571C22×C4—831no—
572C22×C4—833no—
573C22×C4—833no—
574C22×C4—831no—
575C22×C4—8312no—
576C22×C4—1664no—
577C22×C4—16612no—
578C22×C4C23×D83112yes—
579C22×C4C23×D83112yes—
580C22×C4C23×D8313yes—
581C22×C4C23×D8313yes—
582C22×C4C23×D8311yescharacteristic
583C22×C4C23×D8313yes—
584C22×C4C23×D8313yes—
585C4⋊C4—8312no—
586C4⋊C4—8312no—
587C4⋊C4—8312no—
588C4⋊C4—8324no—
589C4⋊C4—834no—
590C4⋊C4—8312no—
591C4⋊C4—8312no—
592C4⋊C4—8312no—
593C4⋊C4—8312no—
594C4⋊C4—8312no—
595C4⋊C4—8312no—
596C4⋊C4—8324no—
597C4⋊C4—834no—
598C4⋊C4—8312no—
599C4⋊C4C23×D83112yes—
600C4⋊C4C23×D83124yes—
601C4⋊C4C23×D83112yes—
602C22⋊C4—8312no—
603C22⋊C4—834no—
604C22⋊C4—834no—
605C22⋊C4—834no—
606C22⋊C4—8312no—
607C22⋊C4—8312no—
608C22⋊C4—8312no—
609C22⋊C4—8324no—
610C22⋊C4—8324no—
611C22⋊C4—8312no—
612C22⋊C4C23×D83112yes—
613C22⋊C4C23×D83112yes—
614C42—8312no—
615C42—8312no—
616C42—8312no—
617C42—8312no—
618C42—8324no—
619C42—8312no—
620C42C23×D83112yes—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—836no—
627C23—1666no—
628C23—1666no—
629C23—1666no—
630C23#1458184014yes—
631C23C24×D8312yes—
632C23C24×D8312yes—
633C23C24×D8311yescharacteristic
634Q8—224no—
635Q8—224no—
636Q8—33212no—
637Q8C2×#13050589116yes—
638D4—28no—
639D4—33212no—
640D4—16624no—
641D4—16624no—
642C2×C4—26no—
643C2×C4—26no—
644C2×C4—22no—
645C2×C4—26no—
646C2×C4—224no—
647C2×C4—224no—
648C2×C4—33224no—
649C2×C4—33212no—
650C2×C4—832no—
651C2×C4—832no—
652C2×C4—836no—
653C2×C4—832no—
654C2×C4—836no—
655C2×C4—836no—
656C2×C4—832no—
657C2×C4—1662no—
658C2×C4—1668no—
659C2×C4—1662no—
660C2×C4—1662no—
661C2×C4—1666no—
662C2×C4—1666no—
663C2×C4—1666no—
664C2×C4—1662no—
665C2×C4—16624no—
666C2×C4C2×#13050589112yes—
667C2×C4C24×D8316yes—
668C2×C4C24×D8316yes—
669C2×C4C24×D8312yes—
670C2×C4C24×D8316yes—
671C2×C4C24×D8316yes—
672C22—28no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—44no—
679C22—33212no—
680C22—1666no—
681C22—1666no—
682C22—1666no—
683C22C22×#1305058912yes—
684C22C2×#1458184014yes—
685C22C2×#1458184012yes—
686C22#1912853812yes—
687C22C25×D8311yescharacteristic
688C4—26no—
689C4—26no—
690C4—22no—
691C4—26no—
692C4—1662no—
693C4—1662no—
694C4—1662no—
695C4—1666no—
696C4—1666no—
697C4—1666no—
698C4—1662no—
699C4C22×#13050589112yes—
700C2—24no—
701C2—42no—
702C2—3326no—
703C2#2492145714yesdirect product factor
704C2C23×#1305058911yescharacteristic
705C2C22×#1458184011yescharacteristic
706C2C2×#1912853811yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×D4×Q8×C83C2
socleC23×C83C25
hypercenterC2×D4×Q8D83
hypocenterC83C2×#3516
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #24921457C2direct (N × H)
2. C2×#19128427C2semidirect
3. C2×#19128425C2semidirect
4. C2×#19128409C2semidirect
5. C2×#19128397C2semidirect
6. C2×#19128385C2semidirect
7. C2×#19128362C2semidirect
8. C2×#19128362C2semidirect
9. C2×#19128324C2semidirect
10. C2×#19128312C2semidirect
11. C2×#19128237C2semidirect
12. C2×#19128231C2semidirect
13. C2×#19128183C2semidirect
14. C2×#19128179C2semidirect
15. C22×Q8×Dic83C2semidirect
16. C2×D4×Q8×C83C2semidirect
18. #19128427C22semidirect
19. #19128425C22semidirect
20. #19128409C22semidirect
21. #19128397C22semidirect
22. #19128385C22semidirect
23. #19128362C22semidirect
24. #19128362C22semidirect
25. #19128324C22semidirect
26. #19128312C22semidirect
28. #19128237C22semidirect
29. #19128231C22semidirect
51. #19128183C22semidirect
52. #19128179C22semidirect
60. C2×Q8×Dic83C22semidirect
76. D4×Q8×C83C22semidirect
349. C2×C83#3516semidirect
360. C2×D4×Q8D83semidirect
370. C83C2×#3516semidirect
379. D4×Q8C2×D83semidirect
703. C2#24921457direct (N × H)

Maximal subgroups

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

subgroupindex
#249214572
C2×#191284272
C2×#191284252
C2×#191284092
C2×#191283972
C2×#191283852
C2×#191283622
C2×#191283242
C2×#191283122
C2×#191282372
C2×#191282312
C2×#191281832
C2×#191281792
C22×Q8×Dic832
C2×D4×Q8×C832
C2×#351683