Finite Group Databasebeta

← C2×#24921327 #36312482

Subgroups — C2×#24921327 #36312482

Order 21248.

7130 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921327C2132yesmaximal, direct product factor
2C2×#19128433C212yesmaximal, complemented
3C2×#19128426C212yesmaximal, complemented
4C2×#19128425C212yesmaximal, complemented
5C2×#19128422C212yesmaximal, complemented
6C2×#19128420C212yesmaximal, complemented
7C2×#19128409C212yesmaximal, complemented
8C2×#19128393C212yesmaximal, complemented
9C2×#19128385C212yesmaximal, complemented
10C2×#19128295C214yesmaximal, complemented
11C2×#19128275C211yesmaximal, characteristic, complemented
12C2×#19128254C211yesmaximal, characteristic, complemented
13C2×#19128247C211yesmaximal, characteristic
14C2×#19128228C214yesmaximal, complemented
15C2×#19128184C211yesmaximal, characteristic, complemented
16C2×#19128181C211yesmaximal, characteristic, complemented
17C22×Q8×Dic83C211yesmaximal, characteristic, complemented
18C2×#536×C83C211yesmaximal, characteristic, complemented
19C22×#13050590C2211yescharacteristic
20#19128433C22132yescomplemented
21#19128426C22132yescomplemented
22#19128425C22132yescomplemented
23#19128422C22132yescomplemented
24#19128420C22132yescomplemented
25#19128409C22132yescomplemented
26#19128393C22132yescomplemented
27#19128385C22132yescomplemented
28#19128295C22164yescomplemented
29#19128275C22116yescomplemented
30#19128254C22116yescomplemented
31#19128247C22116yes—
32C2×#14581791C2211yescharacteristic
33C2×#14581791C2211yescharacteristic
34C2×#14581790C2211yescharacteristic
35C2×#14581790C2212yes—
36C2×#14581788C2211yescharacteristic
37#19128228C22164yescomplemented
38C2×#14581787C2214yes—
39C2×#14581787C2214yes—
40C2×#14581785C2214yes—
41C2×#14581785C2214yes—
42C2×#14581783C2211yescharacteristic
43C2×#14581783C2211yescharacteristic
44C2×#14581783C2214yes—
45C2×#14581782C2214yes—
46C2×#14581782C2214yes—
47C2×#14581781C2211yescharacteristic
48C2×#14581781C2212yes—
49C2×#14581779C2211yescharacteristic
50C2×#14581778C2214yes—
51C2×#14581776C2214yes—
52C2×#14581775C2214yes—
53C2×#14581774C2214yes—
54C2×#14581772C2214yes—
55C2×#14581769C2212yes—
56C2×#14581769C2214yes—
57C2×#14581769C2212yes—
58C2×#14581768C2212yes—
59C2×#14581768C2212yes—
60C2×#14581764C2212yes—
61C2×#14581764C2212yes—
62#19128184C22116yescomplemented
63#19128181C22116yescomplemented
64C2×Q8×Dic83C2212yes—
65C2×Q8×Dic83C2212yes—
66C2×Q8×Dic83C2212yes—
67C2×Q8×Dic83C2212yes—
68C2×Q8×Dic83C2212yes—
69C2×Q8×Dic83C22116yescomplemented
70C2×C4×Dic166C2212yes—
71C2×C4×Dic166C2212yes—
72C2×C4×Dic166C2212yes—
73C2×#14581757C2214yes—
74C2×C4×D332C2212yes—
75C2×D4×Dic83C2214yes—
76C2×D4×Dic83C2212yes—
77C2×C4×C22⋊D83C2212yes—
78C2×C4×C22⋊D83C2212yes—
79C2×(C22⋊D83)⋊C4C2214yes—
80C2×(C22⋊D83)⋊C4C2214yes—
81C2×#14581751C2212yes—
82C2×#14581751C2211yescharacteristic
83C2×#14581750C2212yes—
84C2×#14581750C2214yes—
85C2×#14581748C2214yes—
86C22×C4⋊Dic83C2211yescharacteristic
87C22×C4⋊Dic83C2212yes—
88C22×C4⋊Dic83C2212yes—
89C2×C4⋊C4×D83C2212yes—
90C22×C4×Dic83C2212yes—
91C22×C4×Dic83C2211yescharacteristic
92C22×#41×C83C2211yescharacteristic
93C23×Q8×C83C2211yescharacteristic
94#536×C83C22116yescomplemented
95C2×C4⋊Q8×C83C2212yes—
96C2×#124×C83C2212yes—
97C2×#123×C83C2214yes—
98C2×C22⋊Q8×C83C2212yes—
99C2×C22⋊Q8×C83C2212yes—
100C2×#117×C83C2211yescharacteristic
101C2×#13050590—28no—
102C2×#13050590C2318yes—
103C22×Dic166C2312yes—
104C22×Dic166C2311yescharacteristic
105C22×Dic166C2312yes—
106C22×D332C2311yescharacteristic
107C22×C22⋊D83C2312yes—
108C22×C22⋊D83C2312yes—
109C22×C22⋊D83C2312yes—
110C23×Dic83C2311yescharacteristic
111C23×Dic83C2312yes—
112C23×Dic83C2311yescharacteristic
113C23×Dic83C2314yes—
114C22×C4×D83C2312yes—
115C22×C4×D83C2314yes—
116#14581791C2318yes—
117#14581791C2318yes—
118#14581790C23116yes—
119#14581790C2318yes—
120#14581788C2318yes—
121#14581787C23132yes—
122#14581787C23132yes—
123#14581785C23132yes—
124#14581785C23132yes—
125#14581783C2318yes—
126#14581783C2318yes—
127#14581783C23132yes—
128#14581782C23132yes—
129#14581782C23132yes—
130#14581781C2318yes—
131#14581781C23116yes—
132#14581779C2318yes—
133#14581778C23132yes—
134#14581776C23132yes—
135#14581775C23132yes—
136#14581774C23132yes—
137#14581772C23132yes—
138#14581769C23132yes—
139#14581769C23116yes—
140#14581769C23116yes—
141#14581768C23116yes—
142#14581768C23116yes—
143#14581764C23116yes—
144#14581764C23116yes—
145Q8×Dic83C23116yes—
146Q8×Dic83C23116yes—
147Q8×Dic83C23116yes—
148Q8×Dic83C23116yes—
149Q8×Dic83C23116yes—
150C4×Dic166C23116yes—
151C4×Dic166C23116yes—
152C4×Dic166C23116yes—
153#14581757C23132yes—
154C4×D332C23116yes—
155D4×Dic83C23116yes—
156D4×Dic83C23132yes—
157C4×C22⋊D83C23116yes—
158C4×C22⋊D83C23116yes—
159(C22⋊D83)⋊C4C23132yes—
160(C22⋊D83)⋊C4C23132yes—
161#14581751C23116yes—
162#14581751C2318yes—
163#14581750C23132yes—
164#14581750C23116yes—
165#14581748C23132yes—
166C2×C4⋊Dic83C23116yes—
167C2×C4⋊Dic83C2312yes—
168C2×C4⋊Dic83C2311yescharacteristic
169C2×C4⋊Dic83C2312yes—
170C2×C4⋊Dic83C2314yes—
171C2×C4⋊Dic83C2314yes—
172C2×C4⋊Dic83C2314yes—
173C2×C4⋊Dic83C2318yes—
174C2×C4⋊Dic83C23116yes—
175C2×C4⋊Dic83C2312yes—
176C2×C4⋊Dic83C2311yescharacteristic
177C2×C4⋊Dic83C2312yes—
178C2×Dic83⋊C4C2314yes—
179C2×Dic83⋊C4C2312yes—
180C2×Dic83⋊C4C2314yes—
181C2×Dic83⋊C4C2312yes—
182C2×Dic83⋊C4C2312yes—
183C2×Dic83⋊C4C2312yes—
184C2×Dic83⋊C4C2314yes—
185C2×Dic83⋊C4C2312yes—
186C2×Dic83⋊C4C2312yes—
187C4⋊C4×D83C23116yes—
188C2×C22⋊Dic83C2312yes—
189C2×C22⋊Dic83C2312yes—
190C2×C22⋊Dic83C2314yes—
191C2×C22⋊Dic83C2312yes—
192C2×(C2×D83)⋊C4C2312yes—
193C2×(C2×D83)⋊C4C2314yes—
194C2×(C2×D83)⋊C4C2314yes—
195C2×(C2×D83)⋊C4C2314yes—
196C2×(C2×D83)⋊C4C2312yes—
197C2×C4×Dic83C2314yes—
198C2×C4×Dic83C2314yes—
199C2×C4×Dic83C2311yescharacteristic
200C2×C4×Dic83C2311yescharacteristic
201C2×C4×Dic83C2311yescharacteristic
202C2×C4×Dic83C2311yescharacteristic
203C2×C4×Dic83C23116yes—
204C2×C4×Dic83C2318yes—
205C2×C4×Dic83C2314yes—
206C2×C4×Dic83C2314yes—
207C2×C4×Dic83C2312yes—
208C2×#41×C83—28no—
209C2×#41×C83C2318yes—
210C22×Q8×C83—28no—
211C22×Q8×C83C2312yes—
212C22×Q8×C83C2312yes—
213C22×Q8×C83C2311yescharacteristic
214C22×Q8×C83C2318yes—
215C22×D4×C83C2312yes—
216C22×D4×C83C2311yescharacteristic
217C23×C4×C83C2312yes—
218C23×C4×C83C2312yes—
219C23×C4×C83C2311yescharacteristic
220C4⋊Q8×C83C23116yes—
221#124×C83C23116yes—
222#123×C83C23132yes—
223C22⋊Q8×C83C23116yes—
224C22⋊Q8×C83C23116yes—
225#117×C83C2318yes—
226C2×C4⋊C4×C83C2311yescharacteristic
227C2×C4⋊C4×C83C2311yescharacteristic
228C2×C4⋊C4×C83C2314yes—
229C2×C4⋊C4×C83C2314yes—
230C2×C22⋊C4×C83C2312yes—
231C2×C22⋊C4×C83C2314yes—
232C2×C22⋊C4×C83C2314yes—
233C2×C42×C83C2312yes—
234C23×D83C2412yes—
235#13050590—232no—
236C2×Dic166—24no—
237C2×Dic166—28no—
238C2×Dic166—44no—
239C2×Dic166C2418yes—
240C2×Dic166C2414yes—
241C2×Dic166C2418yes—
242C2×D332—24no—
243C2×D332C2414yes—
244C2×C22⋊D83—28no—
245C2×C22⋊D83—28no—
246C2×C22⋊D83—44no—
247C2×C22⋊D83C2418yes—
248C2×C22⋊D83C2418yes—
249C2×C22⋊D83C2418yes—
250C22×Dic83—24no—
251C22×Dic83—44no—
252C22×Dic83—48no—
253C22×Dic83—42no—
254C22×Dic83C2414yes—
255C22×Dic83C2414yes—
256C22×Dic83C2412yes—
257C22×Dic83C2412yes—
258C22×Dic83C2411yescharacteristic
259C22×Dic83C2411yescharacteristic
260C22×Dic83C2411yescharacteristic
261C22×Dic83C2412yes—
262C22×Dic83C2414yes—
263C22×Dic83C24116yes—
264C22×Dic83C2418yes—
265C22×Dic83C2411yescharacteristic
266C2×C4×D83—28no—
267C2×C4×D83—48no—
268C2×C4×D83C2418yes—
269C2×C4×D83C24116yes—
270C4⋊Dic83C2414yes—
271C4⋊Dic83C2414yes—
272C4⋊Dic83C24116yes—
273C4⋊Dic83C2418yes—
274C4⋊Dic83C2418yes—
275C4⋊Dic83C24116yes—
276C4⋊Dic83C24116yes—
277C4⋊Dic83C2418yes—
278C4⋊Dic83C2418yes—
279Dic83⋊C4C2418yes—
280Dic83⋊C4C2418yes—
281Dic83⋊C4C24116yes—
282Dic83⋊C4C24116yes—
283Dic83⋊C4C2418yes—
284Dic83⋊C4C24116yes—
285Dic83⋊C4C2418yes—
286Dic83⋊C4C2418yes—
287Dic83⋊C4C2418yes—
288C22⋊Dic83C2418yes—
289C22⋊Dic83C2418yes—
290C22⋊Dic83C2418yes—
291C22⋊Dic83C24116yes—
292(C2×D83)⋊C4C2418yes—
293(C2×D83)⋊C4C2418yes—
294(C2×D83)⋊C4C24116yes—
295(C2×D83)⋊C4C24116yes—
296(C2×D83)⋊C4C24116yes—
297C4×Dic83C24116yes—
298C4×Dic83C2414yes—
299C4×Dic83C2418yes—
300C4×Dic83C24116yes—
301C4×Dic83C2414yes—
302C4×Dic83C24116yes—
303C4×Dic83C24116yes—
304C4×Dic83C2414yes—
305C4×Dic83C2414yes—
306C24×C83C2412yes—
307C24×C83C2411yescharacteristic
308#41×C83—232no—
309C2×Q8×C83—28no—
310C2×Q8×C83—28no—
311C2×Q8×C83—232no—
312C2×Q8×C83—24no—
313C2×Q8×C83C2418yes—
314C2×Q8×C83C2418yes—
315C2×Q8×C83C2414yes—
316C2×D4×C83—28no—
317C2×D4×C83—24no—
318C2×D4×C83C2418yes—
319C2×D4×C83C2414yes—
320C22×C4×C83—28no—
321C22×C4×C83—28no—
322C22×C4×C83#4118yes—
323C22×C4×C83C2418yes—
324C22×C4×C83C2412yes—
325C22×C4×C83C2412yes—
326C22×C4×C83C2414yes—
327C22×C4×C83C2412yes—
328C22×C4×C83C2418yes—
329C22×C4×C83C2411yescharacteristic
330C22×C4×C83C2411yescharacteristic
331C22×C4×C83C2414yes—
332C4⋊C4×C83C24116yes—
333C4⋊C4×C83C24116yes—
334C4⋊C4×C83C2414yes—
335C4⋊C4×C83C2414yes—
336C22⋊C4×C83C2418yes—
337C22⋊C4×C83C24116yes—
338C22⋊C4×C83C24116yes—
339C42×C83C2418yes—
340C23×C83—22no—
341C23×C83—22no—
342C23×C83—24no—
343C23×C83—24no—
344C23×C83—24no—
345C23×C83C2×#4114yes—
346C23×C83C2514yes—
347C23×C83C2512yes—
348C23×C83C2511yescharacteristic
349C22×D83—24no—
350C22×D83—24no—
351C22×D83—24no—
352C22×D83C2514yes—
353Q8×C83—216no—
354Q8×C83—216no—
355Q8×C83—28no—
356D4×C83—216no—
357D4×C83—28no—
358C2×C4×C83—24no—
359C2×C4×C83—216no—
360C2×C4×C83—28no—
361C2×C4×C83—24no—
362C2×C4×C83—24no—
363C2×C4×C83—216no—
364C2×C4×C83C2×#4114yes—
365C2×C4×C83C2×#4114yes—
366C2×C4×C83C2×#41116yes—
367C2×C4×C83C2514yes—
368C2×C4×C83C2514yes—
369C2×C4×C83C2518yes—
370C2×C4×C83C2514yes—
371C2×C4×C83C2512yes—
372C2×C4×C83C2512yes—
373C22⋊D83—216no—
374C22⋊D83—216no—
375C22⋊D83—48no—
376C2×Dic83—24no—
377C2×Dic83—22no—
378C2×Dic83—24no—
379C2×Dic83—28no—
380C2×Dic83—24no—
381C2×Dic83—22no—
382C2×Dic83—22no—
383C2×Dic83—28no—
384C2×Dic83—44no—
385C2×Dic83—416no—
386C2×Dic83—48no—
387C2×Dic832−1+414yes—
388C2×Dic83C2512yes—
389C2×Dic83C2518yes—
390C2×Dic83C2514yes—
391C2×Dic83C2512yes—
392C2×Dic83C2514yes—
393C2×Dic83C2512yes—
394C2×Dic83C2514yes—
395C2×Dic83C2512yes—
396D332—28no—
397C4×D83—216no—
398C4×D83—416no—
399Dic166—28no—
400Dic166—216no—
401Dic166—48no—
402C22×C83—22no—
403C22×C83—22no—
404C22×C83—28no—
405C22×C83—24no—
406C22×C83—24no—
407C22×C83—24no—
408C22×C83—48no—
409C22×C83C22×#4114yes—
410C22×C83C22×#4112yes—
411C22×C83C2×2−1+412yes—
412C22×C83#58512yes—
413C22×C83C2611yescharacteristic
414C2×D83—24no—
415C2×D83—24no—
416C2×D83—24no—
417C2×D83—48no—
418C4×C83—24no—
419C4×C83—28no—
420C4×C83—24no—
421C4×C83—24no—
422C4×C83C22×#4114yes—
423C4×C83C22×#4114yes—
424Dic83—24no—
425Dic83—24no—
426Dic83—22no—
427Dic83—22no—
428Dic83—24no—
429Dic83—28no—
430Dic83—22no—
431Dic83C2×2−1+414yes—
432C2×#3507—831nomaximal, Sylow
433C2×C83—24no—
434C2×C83—44no—
435C2×C83#350714yescomplemented
436C2×C83C23×#4111yescharacteristic
437C2×C83C22×2−1+411yescharacteristic
438C2×C83C2×#58511yescharacteristic
439D83—44no—
440#3507—8332no—
441C2×#559—832no—
442C2×#557—832no—
443C2×#556—832no—
444C2×#556—832no—
445C2×#556—832no—
446C2×#554—832no—
447C2×#552—832no—
448C2×#552—832no—
449C2×#539—834no—
450C2×#536—831no—
451C2×#536D8311yescharacteristic, complemented
452C2×#533—831no—
453C2×#532—831no—
454C2×#529—834no—
455C2×#520—831no—
456C2×#520—831no—
457C22×C4×Q8—831no—
458C83C2×#350711yescharacteristic, complemented, Sylow
459C22×#41—831no—
460C22×#41C2×D8311yescharacteristic
461C23×Q8C2×D8311yescharacteristic
462#559—8332no—
463#557—8332no—
464#556—8332no—
465#556—8332no—
466#556—8332no—
467#554—8332no—
468#552—8332no—
469#552—8332no—
470#539—8364no—
471#536—8316no—
472#536C2×D83116yescomplemented
473#533—8316no—
474#532—8316no—
475C2×C4⋊Q8—831no—
476C2×C4⋊Q8—832no—
477C2×C4⋊Q8—831no—
478C2×C4⋊Q8—831no—
479C2×C4⋊Q8C2×D8312yes—
480C2×#127—831no—
481#529—8364no—
482C2×#126—834no—
483C2×#126—834no—
484C2×#126—834no—
485C2×#126—834no—
486C2×#125—834no—
487C2×#125—831no—
488C2×#125—831no—
489C2×#125—834no—
490C2×#125—834no—
491C2×#124—831no—
492C2×#124—832no—
493C2×#124—831no—
494C2×#124—834no—
495C2×#124C2×D8312yes—
496C2×#123—834no—
497C2×#123—834no—
498C2×#123—834no—
499C2×#123C2×D8314yes—
500C2×C22⋊Q8—832no—
501C2×C22⋊Q8—832no—
502C2×C22⋊Q8—834no—
503C2×C22⋊Q8—832no—
504C2×C22⋊Q8—832no—
505C2×C22⋊Q8—834no—
506C2×C22⋊Q8C2×D8312yes—
507C2×C22⋊Q8C2×D8312yes—
508C2×#121—832no—
509C2×#121—832no—
510#520—8316no—
511#520—8316no—
512C2×C4×Q8—832no—
513C2×C4×Q8—832no—
514C2×C4×Q8—832no—
515C2×C4×Q8—832no—
516C2×C4×Q8—8316no—
517C2×C4×Q8—832no—
518C2×C4×Q8—834no—
519C2×C4×Q8—832no—
520C2×C4×Q8—832no—
521C2×C4×Q8—832no—
522C2×C4×D4—834no—
523C2×C4×D4—832no—
524C2×C4×D4—832no—
525C2×C4×D4—832no—
526C2×C4×D4—834no—
527C2×C4×D4—834no—
528C2×C4×D4—832no—
529C2×#117—831no—
530C2×#117—832no—
531C2×#117—832no—
532C2×#117—834no—
533C2×#117—834no—
534C2×#117C2×D8311yescharacteristic
535C22×C4⋊C4—831no—
536C22×C4⋊C4—832no—
537C22×C4⋊C4—832no—
538C22×C4⋊C4—832no—
539C22×C42—832no—
540C22×C42—831no—
541C2×#41—28no—
542C2×#41—838no—
543C2×#41—1668no—
544C2×#41C22×D8318yes—
545C22×Q8—28no—
546C22×Q8—832no—
547C22×Q8—832no—
548C22×Q8—831no—
549C22×Q8C22×D8312yes—
550C22×Q8C22×D8312yes—
551C22×Q8C22×D8311yescharacteristic
552C22×Q8C22×D8318yes—
553C22×D4—832no—
554C22×D4—832no—
555C22×D4—832no—
556C22×D4—831no—
557C22×D4C22×D8312yes—
558C22×D4C22×D8311yescharacteristic
559C23×C4—832no—
560C23×C4—831no—
561C23×C4—834no—
562C23×C4—834no—
563C23×C4—831no—
564C23×C4—832no—
565C23×C4C22×D8312yes—
566C23×C4C22×D8312yes—
567C23×C4C22×D8311yescharacteristic
568C4⋊Q8—838no—
569C4⋊Q8—8316no—
570C4⋊Q8—838no—
571C4⋊Q8—838no—
572C4⋊Q8C22×D83116yes—
573#127—838no—
574#126—8332no—
575#126—8332no—
576#126—8332no—
577#126—8332no—
578#125—8332no—
579#125—838no—
580#125—838no—
581#125—8332no—
582#125—8332no—
583#124—838no—
584#124—8316no—
585#124—838no—
586#124—8332no—
587#124C22×D83116yes—
588#123—8332no—
589#123—8332no—
590#123—8332no—
591#123C22×D83132yes—
592C22⋊Q8—8316no—
593C22⋊Q8—8316no—
594C22⋊Q8—8332no—
595C22⋊Q8—8316no—
596C22⋊Q8—8316no—
597C22⋊Q8—8332no—
598C22⋊Q8C22×D83116yes—
599C22⋊Q8C22×D83116yes—
600#121—8316no—
601#121—8316no—
602C4×Q8—8316no—
603C4×Q8—8316no—
604C4×Q8—8316no—
605C4×Q8—8316no—
606C4×Q8—8316no—
607C4×Q8—8332no—
608C4×Q8—8316no—
609C4×Q8—8316no—
610C4×Q8—8316no—
611C4×D4—8332no—
612C4×D4—8316no—
613C4×D4—8316no—
614C4×D4—8316no—
615C4×D4—8332no—
616C4×D4—8332no—
617C4×D4—8316no—
618#117—838no—
619#117—8316no—
620#117—8316no—
621#117—8332no—
622#117—8332no—
623#117C22×D8318yes—
624C2×C4⋊C4—832no—
625C2×C4⋊C4—831no—
626C2×C4⋊C4—832no—
627C2×C4⋊C4—834no—
628C2×C4⋊C4—834no—
629C2×C4⋊C4—838no—
630C2×C4⋊C4—834no—
631C2×C4⋊C4—834no—
632C2×C4⋊C4—8316no—
633C2×C4⋊C4—8316no—
634C2×C4⋊C4—831no—
635C2×C4⋊C4—832no—
636C2×C4⋊C4—832no—
637C2×C4⋊C4—834no—
638C2×C4⋊C4—832no—
639C2×C4⋊C4—832no—
640C2×C4⋊C4—832no—
641C2×C4⋊C4—832no—
642C2×C4⋊C4—832no—
643C2×C4⋊C4—834no—
644C2×C4⋊C4—832no—
645C2×C4⋊C4—8316no—
646C2×C4⋊C4C22×D8311yescharacteristic
647C2×C4⋊C4C22×D8311yescharacteristic
648C2×C4⋊C4C22×D8314yes—
649C2×C4⋊C4C22×D8314yes—
650C2×C22⋊C4—832no—
651C2×C22⋊C4—832no—
652C2×C22⋊C4—834no—
653C2×C22⋊C4—832no—
654C2×C22⋊C4—832no—
655C2×C22⋊C4—834no—
656C2×C22⋊C4—834no—
657C2×C22⋊C4—832no—
658C2×C22⋊C4—834no—
659C2×C22⋊C4C22×D8314yes—
660C2×C22⋊C4C22×D8312yes—
661C2×C22⋊C4C22×D8314yes—
662C2×C42—834no—
663C2×C42—834no—
664C2×C42—834no—
665C2×C42—832no—
666C2×C42—831no—
667C2×C42—831no—
668C2×C42—834no—
669C2×C42—831no—
670C2×C42—831no—
671C2×C42—8316no—
672C2×C42—838no—
673C2×C42C22×D8312yes—
674C24—832no—
675C24C23×D8312yes—
676C24C23×D8311yescharacteristic
677#41—232no—
678#41—16632no—
679C2×Q8—28no—
680C2×Q8—28no—
681C2×Q8—232no—
682C2×Q8—24no—
683C2×Q8—3324no—
684C2×Q8—838no—
685C2×Q8—838no—
686C2×Q8—834no—
687C2×Q8—1668no—
688C2×Q8—1664no—
689C2×Q8C23×D8318yes—
690C2×Q8C23×D8318yes—
691C2×Q8C23×D8314yes—
692C2×D4—28no—
693C2×D4—24no—
694C2×D4—3324no—
695C2×D4—838no—
696C2×D4—838no—
697C2×D4—838no—
698C2×D4—834no—
699C2×D4—1668no—
700C2×D4—1668no—
701C2×D4—1664no—
702C2×D4C23×D8318yes—
703C2×D4C23×D8314yes—
704C22×C4—28no—
705C22×C4—28no—
706C22×C4—3328no—
707C22×C4—3324no—
708C22×C4—3328no—
709C22×C4—3322no—
710C22×C4—838no—
711C22×C4—834no—
712C22×C4—8316no—
713C22×C4—8316no—
714C22×C4—831no—
715C22×C4—834no—
716C22×C4—831no—
717C22×C4—834no—
718C22×C4—832no—
719C22×C4—831no—
720C22×C4—832no—
721C22×C4—831no—
722C22×C4—832no—
723C22×C4—838no—
724C22×C4—1664no—
725C22×C4—1668no—
726C22×C4#1305058918yes—
727C22×C4C23×D8318yes—
728C22×C4C23×D8318yes—
729C22×C4C23×D8312yes—
730C22×C4C23×D8314yes—
731C22×C4C23×D8312yes—
732C22×C4C23×D8312yes—
733C22×C4C23×D8314yes—
734C22×C4C23×D8311yescharacteristic
735C22×C4C23×D8311yescharacteristic
736C4⋊C4—838no—
737C4⋊C4—834no—
738C4⋊C4—838no—
739C4⋊C4—8316no—
740C4⋊C4—8316no—
741C4⋊C4—8316no—
742C4⋊C4—8316no—
743C4⋊C4—834no—
744C4⋊C4—838no—
745C4⋊C4—838no—
746C4⋊C4—8316no—
747C4⋊C4—838no—
748C4⋊C4—838no—
749C4⋊C4—838no—
750C4⋊C4—838no—
751C4⋊C4—838no—
752C4⋊C4—8316no—
753C4⋊C4—838no—
754C4⋊C4C23×D8314yes—
755C4⋊C4C23×D8314yes—
756C4⋊C4C23×D83116yes—
757C4⋊C4C23×D83116yes—
758C22⋊C4—838no—
759C22⋊C4—838no—
760C22⋊C4—8316no—
761C22⋊C4—838no—
762C22⋊C4—838no—
763C22⋊C4—8316no—
764C22⋊C4—8316no—
765C22⋊C4—838no—
766C22⋊C4—8316no—
767C22⋊C4C23×D83116yes—
768C22⋊C4C23×D8318yes—
769C22⋊C4C23×D83116yes—
770C42—8316no—
771C42—834no—
772C42—834no—
773C42—8316no—
774C42—834no—
775C42—834no—
776C42—8316no—
777C42—8316no—
778C42—838no—
779C42C23×D8318yes—
780C23—22no—
781C23—22no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—834no—
786C23—1664no—
787C23—1664no—
788C23—1664no—
789C23C2×#1305058914yes—
790C23C24×D8314yes—
791C23C24×D8312yes—
792C23C24×D8311yescharacteristic
793Q8—216no—
794Q8—216no—
795Q8—28no—
796Q8—3328no—
797Q8—16616no—
798Q8—1668no—
799D4—216no—
800D4—28no—
801D4—3328no—
802D4—16616no—
803D4—16616no—
804D4—1668no—
805C2×C4—24no—
806C2×C4—216no—
807C2×C4—28no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—216no—
811C2×C4—33216no—
812C2×C4—3328no—
813C2×C4—33216no—
814C2×C4—3324no—
815C2×C4—834no—
816C2×C4—832no—
817C2×C4—832no—
818C2×C4—838no—
819C2×C4—834no—
820C2×C4—832no—
821C2×C4—834no—
822C2×C4—832no—
823C2×C4—834no—
824C2×C4—1668no—
825C2×C4—1664no—
826C2×C4—1662no—
827C2×C4—1664no—
828C2×C4—1668no—
829C2×C4—1664no—
830C2×C4—1662no—
831C2×C4—1662no—
832C2×C4—16616no—
833C2×C4C2×#1305058914yes—
834C2×C4C2×#1305058914yes—
835C2×C4C2×#13050589116yes—
836C2×C4C24×D8314yes—
837C2×C4C24×D8318yes—
838C2×C4C24×D8314yes—
839C2×C4C24×D8314yes—
840C2×C4C24×D8312yes—
841C2×C4C24×D8312yes—
842C22—22no—
843C22—22no—
844C22—28no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—48no—
849C22—3328no—
850C22—1664no—
851C22—1664no—
852C22—1664no—
853C22C22×#1305058914yes—
854C22C22×#1305058912yes—
855C222−1+4×D8312yes—
856C22#1912853812yes—
857C22C25×D8311yescharacteristic
858C4—24no—
859C4—28no—
860C4—24no—
861C4—24no—
862C4—834no—
863C4—1664no—
864C4—1662no—
865C4—1664no—
866C4—1668no—
867C4—1664no—
868C4—1662no—
869C4—1662no—
870C4C22×#1305058914yes—
871C4C22×#1305058914yes—
872C2—24no—
873C2—44no—
874C2—3324no—
875C2#2492132714yesdirect product factor
876C2C23×#1305058911yescharacteristic
877C2C2×2−1+4×D8311yescharacteristic
878C2C2×#1912853811yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#536×C83C2
socleC23×C83C25
prime radicalC2×#19128247C2
hypercenterC2×#536D83
hypocenterC83C2×#3507
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. #24921327C2direct (N × H)
2. C2×#19128433C2semidirect
3. C2×#19128426C2semidirect
4. C2×#19128425C2semidirect
5. C2×#19128422C2semidirect
6. C2×#19128420C2semidirect
7. C2×#19128409C2semidirect
8. C2×#19128393C2semidirect
9. C2×#19128385C2semidirect
10. C2×#19128295C2semidirect
11. C2×#19128275C2semidirect
12. C2×#19128254C2semidirect
14. C2×#19128228C2semidirect
15. C2×#19128184C2semidirect
16. C2×#19128181C2semidirect
17. C22×Q8×Dic83C2semidirect
18. C2×#536×C83C2semidirect
20. #19128433C22semidirect
21. #19128426C22semidirect
22. #19128425C22semidirect
23. #19128422C22semidirect
24. #19128420C22semidirect
25. #19128409C22semidirect
26. #19128393C22semidirect
27. #19128385C22semidirect
28. #19128295C22semidirect
29. #19128275C22semidirect
30. #19128254C22semidirect
37. #19128228C22semidirect
62. #19128184C22semidirect
63. #19128181C22semidirect
69. C2×Q8×Dic83C22semidirect
94. #536×C83C22semidirect
435. C2×C83#3507semidirect
451. C2×#536D83semidirect
458. C83C2×#3507semidirect
472. #536C2×D83semidirect
875. C2#24921327direct (N × H)

Maximal subgroups

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

subgroupindex
#249213272
C2×#191284332
C2×#191284262
C2×#191284252
C2×#191284222
C2×#191284202
C2×#191284092
C2×#191283932
C2×#191283852
C2×#191282952
C2×#191282752
C2×#191282542
C2×#191282472
C2×#191282282
C2×#191281842
C2×#191281812
C22×Q8×Dic832
C2×#536×C832
C2×#350783