Finite Group Databasebeta

← C2×#24921286 #36312884

Subgroups — C2×#24921286 #36312884

Order 21248.

6958 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921286C2132yesmaximal, direct product factor
2C2×#19128428C212yesmaximal, complemented
3C2×#19128426C212yesmaximal, complemented
4C2×#19128412C212yesmaximal, complemented
5C2×#19128409C214yesmaximal, complemented
6C2×#19128407C212yesmaximal, complemented
7C2×#19128405C214yesmaximal, complemented
8C2×#19128331C212yesmaximal, complemented
9C2×#19128329C211yesmaximal, characteristic, complemented
10C2×#19128328C212yesmaximal, complemented
11C2×#19128256C212yesmaximal, complemented
12C2×#19128254C211yesmaximal, characteristic, complemented
13C22×#14581783C211yesmaximal, characteristic, complemented
14C2×#125×D83C212yesmaximal, complemented
15C2×#19128182C211yesmaximal, characteristic
16C2×#19128181C211yesmaximal, characteristic
17C2×#19128169C211yesmaximal, characteristic
18C2×#544×C83C211yesmaximal, characteristic, complemented
19C22×#13050590C2211yescharacteristic
20#19128428C22132yescomplemented
21#19128426C22132yescomplemented
22#19128412C22132yescomplemented
23#19128409C22164yescomplemented
24#19128407C22132yescomplemented
25#19128405C22164yescomplemented
26#19128331C22132yescomplemented
27#19128329C22116yescomplemented
28#19128328C22132yescomplemented
29#19128256C22132yescomplemented
30#19128254C22116yescomplemented
31C2×#14581792C2212yes—
32C2×#14581791C2211yescharacteristic
33C2×#14581791C2212yes—
34C2×#14581791C2211yescharacteristic
35C2×#14581791C2214yes—
36C2×#14581790C2214yes—
37C2×#14581784C2212yes—
38C2×#14581783C2212yes—
39C2×#14581783C2212yes—
40C2×#14581783C2211yescharacteristic
41C2×#14581783C2212yes—
42C2×#14581783C2212yes—
43C2×#14581783C2212yes—
44C2×#14581783C2211yescharacteristic
45C2×#14581783C22116yescomplemented
46C2×#14581782C2214yes—
47C2×#14581782C2214yes—
48C2×#14581782C2214yes—
49C2×#14581782C2214yes—
50#125×D83C22132yescomplemented
51C2×#14581772C2214yes—
52C2×#14581772C2214yes—
53C2×#14581770C2214yes—
54C2×#14581770C2214yes—
55C2×#14581769C2214yes—
56C2×#14581769C2212yes—
57C2×#14581769C2212yes—
58C2×#14581768C2214yes—
59C2×#14581768C2214yes—
60#19128182C22116yes—
61#19128181C22116yes—
62#19128169C22116yes—
63C2×Q8×Dic83C2214yes—
64C2×C4×Dic166C2212yes—
65C2×C4×Dic166C2212yes—
66C2×C4×Dic166C2212yes—
67C2×#14581757C2211yescharacteristic
68C2×#14581757C2211yescharacteristic
69C2×#14581757C2212yes—
70C2×#14581757C2214yes—
71C2×C4×D332C2212yes—
72C2×#14581754C2211yescharacteristic
73C2×#14581754C2211yescharacteristic
74C2×#14581754C2212yes—
75C2×C4×C22⋊D83C2214yes—
76C2×(C22⋊D83)⋊C4C2212yes—
77C2×(C22⋊D83)⋊C4C2212yes—
78C2×(C22⋊D83)⋊C4C2214yes—
79C2×#14581751C2211yescharacteristic
80C2×#14581750C2212yes—
81C2×#14581750C2212yes—
82C2×#14581749C2212yes—
83C22×C4⋊Dic83C2211yescharacteristic
84C22×C4⋊Dic83C2212yes—
85C22×Dic83⋊C4C2212yes—
86C2×C4⋊C4×D83C2212yes—
87C2×C4⋊C4×D83C2212yes—
88C2×C4⋊C4×D83C2214yes—
89C2×C4⋊C4×D83C2214yes—
90C22×C4×Dic83C2211yescharacteristic
91C2×C42×D83C2212yes—
92#544×C83C22116yescomplemented
93C2×C4⋊Q8×C83C2212yes—
94C2×C4⋊Q8×C83C2212yes—
95C2×#125×C83C2212yes—
96C2×#125×C83C2212yes—
97C2×C22⋊Q8×C83C2214yes—
98C2×#117×C83C2211yescharacteristic
99C2×#117×C83C2211yescharacteristic
100C22×C4⋊C4×C83C2211yescharacteristic
101C2×#13050590Q8116yescomplemented
102C2×#13050590C2318yes—
103C22×Dic166C2314yes—
104C22×Dic166C2312yes—
105C22×Dic166C2312yes—
106C22×Dic166C2311yescharacteristic
107C22×D332C2311yescharacteristic
108C22×C22⋊D83C2312yes—
109C23×Dic83C2311yescharacteristic
110C23×Dic83C2311yescharacteristic
111C23×Dic83C2312yes—
112C22×C4×D83C2312yes—
113C22×C4×D83C2312yes—
114C22×C4×D83C2314yes—
115C22×C4×D83C2314yes—
116C22×C4×D83C2312yes—
117#14581792C23116yes—
118#14581791C2318yes—
119#14581791C23116yes—
120#14581791C2318yes—
121#14581791C23132yes—
122#14581790C23132yes—
123#14581784C23116yes—
124#14581783C23116yes—
125#14581783C23116yes—
126#14581783C23116yes—
127#14581783C23116yes—
128#14581783C2318yes—
129#14581783C23116yes—
130#14581783C2318yes—
131#14581782C23132yes—
132#14581782C23132yes—
133#14581782C23132yes—
134#14581782C23132yes—
135#14581772C23132yes—
136#14581772C23132yes—
137#14581770C23132yes—
138#14581770C23132yes—
139#14581769C23132yes—
140#14581769C23116yes—
141#14581769C23116yes—
142#14581768C23132yes—
143#14581768C23132yes—
144Q8×Dic83C23132yes—
145C4×Dic166C23116yes—
146C4×Dic166C23116yes—
147C4×Dic166C23116yes—
148#14581757C23132yes—
149#14581757C2318yes—
150#14581757C2318yes—
151#14581757C23116yes—
152C4×D332C23116yes—
153#14581754C2318yes—
154#14581754C23116yes—
155#14581754C2318yes—
156C4×C22⋊D83C23132yes—
157(C22⋊D83)⋊C4C23116yes—
158(C22⋊D83)⋊C4C23132yes—
159(C22⋊D83)⋊C4C23116yes—
160#14581751C2318yes—
161#14581750C23116yes—
162#14581750C23116yes—
163#14581749C23116yes—
164C2×C4⋊Dic83C2318yes—
165C2×C4⋊Dic83C2311yescharacteristic
166C2×C4⋊Dic83C2312yes—
167C2×C4⋊Dic83C2312yes—
168C2×C4⋊Dic83C2314yes—
169C2×C4⋊Dic83C23116yes—
170C2×C4⋊Dic83C2312yes—
171C2×C4⋊Dic83C2314yes—
172C2×C4⋊Dic83C2311yescharacteristic
173C2×C4⋊Dic83C2312yes—
174C2×C4⋊Dic83C2314yes—
175C2×Dic83⋊C4C23116yes—
176C2×Dic83⋊C4C2312yes—
177C2×Dic83⋊C4C2314yes—
178C2×Dic83⋊C4C2314yes—
179C2×Dic83⋊C4C2314yes—
180C2×Dic83⋊C4C2314yes—
181C2×Dic83⋊C4C2314yes—
182C2×Dic83⋊C4C2314yes—
183C2×Dic83⋊C4C2312yes—
184C2×Dic83⋊C4C2312yes—
185C2×Dic83⋊C4C2312yes—
186C2×Dic83⋊C4C2312yes—
187C2×Dic83⋊C4C2312yes—
188C4⋊C4×D83C23116yes—
189C4⋊C4×D83C23116yes—
190C4⋊C4×D83C23132yes—
191C4⋊C4×D83C23132yes—
192C2×C22⋊Dic83C2312yes—
193C2×(C2×D83)⋊C4C2312yes—
194C2×(C2×D83)⋊C4C2312yes—
195C2×(C2×D83)⋊C4C2314yes—
196C2×(C2×D83)⋊C4C2314yes—
197C2×C4×Dic83C2311yescharacteristic
198C2×C4×Dic83C2312yes—
199C2×C4×Dic83C2312yes—
200C2×C4×Dic83C2311yescharacteristic
201C2×C4×Dic83C2311yescharacteristic
202C2×C4×Dic83C2311yescharacteristic
203C2×C4×Dic83C2318yes—
204C2×C4×Dic83C2314yes—
205C2×C4×Dic83C2314yes—
206C2×C4×Dic83C2312yes—
207C42×D83C23116yes—
208C22×Q8×C83C2314yes—
209C23×C4×C83C2312yes—
210C23×C4×C83C2311yescharacteristic
211C4⋊Q8×C83C23116yes—
212C4⋊Q8×C83C23116yes—
213#125×C83C23116yes—
214#125×C83C23116yes—
215C22⋊Q8×C83C23132yes—
216#117×C83C2318yes—
217#117×C83C2318yes—
218C2×C4⋊C4×C83C2312yes—
219C2×C4⋊C4×C83C2312yes—
220C2×C4⋊C4×C83C2318yes—
221C2×C4⋊C4×C83C2311yescharacteristic
222C2×C4⋊C4×C83C2311yescharacteristic
223C2×C4⋊C4×C83C2311yescharacteristic
224C2×C4⋊C4×C83C2311yescharacteristic
225C2×C4⋊C4×C83C2314yes—
226C2×C4⋊C4×C83C2314yes—
227C2×C4⋊C4×C83C2314yes—
228C2×C22⋊C4×C83C2312yes—
229C2×C22⋊C4×C83C2312yes—
230C2×C42×C83C2312yes—
231C2×C42×C83C2312yes—
232C23×D83C2412yes—
233#13050590C2×Q8164yescomplemented
234C2×Dic166—44no—
235C2×Dic166—48no—
236C2×Dic166—44no—
237C2×Dic166C2×Q818yes—
238C2×Dic166C2418yes—
239C2×Dic166C24116yes—
240C2×Dic166C2418yes—
241C2×Dic166C2414yes—
242C2×D332C2×Q818yes—
243C2×D332C2414yes—
244C2×C22⋊D83C2×Q8116yes—
245C2×C22⋊D83C2418yes—
246C22×Dic83—42no—
247C22×Dic83—42no—
248C22×Dic83—44no—
249C22×Dic83C2411yescharacteristic
250C22×Dic83C2411yescharacteristic
251C22×Dic83C2412yes—
252C22×Dic83C2414yes—
253C22×Dic83C2411yescharacteristic
254C22×Dic83C2411yescharacteristic
255C22×Dic83C2412yes—
256C22×Dic83C2414yes—
257C22×Dic83C2414yes—
258C22×Dic83C2418yes—
259C22×Dic83C2412yes—
260C2×C4×D83—44no—
261C2×C4×D83—44no—
262C2×C4×D83—48no—
263C2×C4×D83—48no—
264C2×C4×D83C2×Q8116yes—
265C2×C4×D83C2418yes—
266C2×C4×D83C24116yes—
267C2×C4×D83C24116yes—
268C2×C4×D83C2418yes—
269C2×C4×D83C2418yes—
270C4⋊Dic83C24116yes—
271C4⋊Dic83C24116yes—
272C4⋊Dic83C2418yes—
273C4⋊Dic83C2418yes—
274C4⋊Dic83C24116yes—
275C4⋊Dic83C2418yes—
276C4⋊Dic83C2418yes—
277C4⋊Dic83C2414yes—
278C4⋊Dic83C2414yes—
279Dic83⋊C4C2418yes—
280Dic83⋊C4C2418yes—
281Dic83⋊C4C24116yes—
282Dic83⋊C4C24116yes—
283Dic83⋊C4C2418yes—
284Dic83⋊C4C24116yes—
285Dic83⋊C4C2418yes—
286Dic83⋊C4C24116yes—
287Dic83⋊C4C24116yes—
288Dic83⋊C4C24116yes—
289Dic83⋊C4C2418yes—
290Dic83⋊C4C2418yes—
291C22⋊Dic83C2418yes—
292(C2×D83)⋊C4C24116yes—
293(C2×D83)⋊C4C2418yes—
294(C2×D83)⋊C4C24116yes—
295(C2×D83)⋊C4C2418yes—
296C4×Dic83C2418yes—
297C4×Dic83C2418yes—
298C4×Dic83C24116yes—
299C4×Dic83C24116yes—
300C4×Dic83C2414yes—
301C4×Dic83C2414yes—
302C4×Dic83C2414yes—
303C4×Dic83C2414yes—
304C4×Dic83C2418yes—
305C24×C83C2411yescharacteristic
306C2×Q8×C83—48no—
307C2×Q8×C83C24116yes—
308C22×C4×C83—44no—
309C22×C4×C83C2×Q818yes—
310C22×C4×C83C2412yes—
311C22×C4×C83C2412yes—
312C22×C4×C83C2412yes—
313C22×C4×C83C2414yes—
314C22×C4×C83C2412yes—
315C22×C4×C83C2418yes—
316C22×C4×C83C2411yescharacteristic
317C22×C4×C83C2411yescharacteristic
318C22×C4×C83C2414yes—
319C4⋊C4×C83C24116yes—
320C4⋊C4×C83C24116yes—
321C4⋊C4×C83C24116yes—
322C4⋊C4×C83C2418yes—
323C4⋊C4×C83C2418yes—
324C4⋊C4×C83C2414yes—
325C4⋊C4×C83C2414yes—
326C4⋊C4×C83C2414yes—
327C4⋊C4×C83C2414yes—
328C22⋊C4×C83C2418yes—
329C22⋊C4×C83C2418yes—
330C42×C83C2418yes—
331C42×C83C2418yes—
332C23×C83—22no—
333C23×C83—22no—
334C23×C83C22×Q814yes—
335C23×C83C2512yes—
336C23×C83C2511yescharacteristic
337C22×D83—24no—
338C22×D83—24no—
339C22×D83C22×Q818yes—
340C22×D83C2514yes—
341Q8×C83—416no—
342C2×C4×C83—28no—
343C2×C4×C83—24no—
344C2×C4×C83—24no—
345C2×C4×C83—24no—
346C2×C4×C83—24no—
347C2×C4×C83—48no—
348C2×C4×C83C22×Q814yes—
349C2×C4×C83C22×Q814yes—
350C2×C4×C83C22×Q8116yes—
351C2×C4×C83C2514yes—
352C2×C4×C83C2514yes—
353C2×C4×C83C2514yes—
354C2×C4×C83C2514yes—
355C2×C4×C83C2518yes—
356C2×C4×C83C2512yes—
357C2×C4×C83C2512yes—
358C22⋊D83C22×Q8132yes—
359C2×Dic83—22no—
360C2×Dic83—22no—
361C2×Dic83—24no—
362C2×Dic83—28no—
363C2×Dic83—22no—
364C2×Dic83—22no—
365C2×Dic83—24no—
366C2×Dic83—44no—
367C2×Dic83—44no—
368C2×Dic83—48no—
369C2×Dic83C22×Q818yes—
370C2×Dic83C2512yes—
371C2×Dic83C2512yes—
372C2×Dic83C2514yes—
373C2×Dic83C2512yes—
374C2×Dic83C2512yes—
375C2×Dic83C2518yes—
376C2×Dic83C2514yes—
377C2×Dic83C2514yes—
378D332C22×Q8116yes—
379C4×D83—416no—
380C4×D83—416no—
381C4×D83—48no—
382C4×D83—48no—
383C4×D83C22×Q8132yes—
384Dic166—48no—
385Dic166—416no—
386Dic166—48no—
387Dic166C22×Q8116yes—
388C22×C83—22no—
389C22×C83—22no—
390C22×C83—28no—
391C22×C83C23×Q814yes—
392C22×C83C23×Q812yes—
393C22×C83#58512yes—
394C22×C83#58512yes—
395C22×C83C2611yescharacteristic
396C2×D83—24no—
397C2×D83—24no—
398C2×D83—216no—
399C2×D83C23×Q818yes—
400C4×C83—24no—
401C4×C83—24no—
402C4×C83—24no—
403C4×C83—28no—
404C4×C83—24no—
405C4×C83C23×Q814yes—
406C4×C83C23×Q814yes—
407Dic83—24no—
408Dic83—22no—
409Dic83—22no—
410Dic83—24no—
411Dic83—28no—
412Dic83—22no—
413Dic83—22no—
414Dic83C23×Q818yes—
415C2×#3504—831nomaximal, Sylow
416C2×C83—24no—
417C2×C83#350414yescomplemented
418C2×C83C24×Q811yescharacteristic
419C2×C83C2×#58511yescharacteristic
420C2×C83C2×#58511yescharacteristic
421D83—28no—
422#3504—8332no—
423C2×#557—832no—
424C2×#557—832no—
425C2×#554—832no—
426C2×#554—832no—
427C2×#554—834no—
428C2×#554—834no—
429C2×#544—832no—
430C2×#544—832no—
431C2×#544—831no—
432C2×#544D8311yescharacteristic, complemented
433C2×#533—832no—
434C2×#533—831no—
435C22×#125—832no—
436C22×#125—831no—
437C2×#520—831no—
438C2×#520—831no—
439C2×C4×#41—831no—
440C83C2×#350411yescharacteristic, complemented, Sylow
441C22×#41—831no—
442#557—8332no—
443#557—8332no—
444#554—8332no—
445#554—8332no—
446#554—8364no—
447#554—8364no—
448#544—8332no—
449#544—8332no—
450#544—8316no—
451#544C2×D83116yescomplemented
452#533—8332no—
453#533—8316no—
454C2×C4⋊Q8—834no—
455C2×C4⋊Q8—831no—
456C2×C4⋊Q8—831no—
457C2×C4⋊Q8—834no—
458C2×C4⋊Q8—832no—
459C2×C4⋊Q8—832no—
460C2×C4⋊Q8C2×D8312yes—
461C2×C4⋊Q8C2×D8312yes—
462C2×#125—8332no—
463C2×#125—831no—
464C2×#125—832no—
465C2×#125—832no—
466C2×#125—834no—
467C2×#125—834no—
468C2×#125—832no—
469C2×#125—832no—
470C2×#125—8316no—
471C2×#125—831no—
472C2×#125—834no—
473C2×#125—834no—
474C2×#125—832no—
475C2×#125—832no—
476C2×#125C2×D8312yes—
477C2×#125C2×D8312yes—
478C2×C22⋊Q8—834no—
479C2×C22⋊Q8—834no—
480C2×C22⋊Q8—834no—
481C2×C22⋊Q8—834no—
482C2×C22⋊Q8—834no—
483C2×C22⋊Q8—834no—
484C2×C22⋊Q8—832no—
485C2×C22⋊Q8—832no—
486C2×C22⋊Q8—834no—
487C2×C22⋊Q8C2×D8314yes—
488#520—8316no—
489#520—8316no—
490C4×#41—8316no—
491C2×C4×Q8—834no—
492C2×C4×Q8—831no—
493C2×C4×Q8—831no—
494C2×C4×Q8—832no—
495C2×C4×Q8—834no—
496C2×C4×Q8—832no—
497C2×C4×Q8—832no—
498C2×C4×Q8—832no—
499C2×C4×D4—834no—
500C2×C4×D4—831no—
501C2×C4×D4—831no—
502C2×C4×D4—832no—
503C2×C4×D4—832no—
504C2×C4×D4—832no—
505C2×C4×D4—834no—
506C2×C4×D4—832no—
507C2×#117—831no—
508C2×#117—832no—
509C2×#117—832no—
510C2×#117—832no—
511C2×#117C2×D8311yescharacteristic
512C2×#117C2×D8311yescharacteristic
513C22×C4⋊C4—832no—
514C22×C4⋊C4—831no—
515C22×C4⋊C4—832no—
516C22×C4⋊C4—832no—
517C22×C4⋊C4—832no—
518C22×C4⋊C4—834no—
519C22×C4⋊C4—834no—
520C22×C4⋊C4C2×D8311yescharacteristic
521C22×C42—831no—
522C22×C42—832no—
523C2×#41—8316no—
524C2×#41—838no—
525C22×Q8—832no—
526C22×Q8—834no—
527C22×Q8—832no—
528C22×Q8—831no—
529C22×Q8C22×D8314yes—
530C22×D4—832no—
531C22×D4—831no—
532C23×C4—832no—
533C23×C4—831no—
534C23×C4—831no—
535C23×C4—834no—
536C23×C4—834no—
537C23×C4—832no—
538C23×C4—832no—
539C23×C4—832no—
540C23×C4C22×D8312yes—
541C23×C4C22×D8311yescharacteristic
542C4⋊Q8—8332no—
543C4⋊Q8—838no—
544C4⋊Q8—838no—
545C4⋊Q8—8332no—
546C4⋊Q8—8316no—
547C4⋊Q8—8316no—
548C4⋊Q8C22×D83116yes—
549C4⋊Q8C22×D83116yes—
550#125—838no—
551#125—8316no—
552#125—8332no—
553#125—8332no—
554#125—8316no—
555#125—8316no—
556#125—8316no—
557#125—838no—
558#125—8332no—
559#125—8332no—
560#125—8316no—
561#125—8316no—
562#125C22×D83116yes—
563#125C22×D83116yes—
564C22⋊Q8—8332no—
565C22⋊Q8—8332no—
566C22⋊Q8—8332no—
567C22⋊Q8—8332no—
568C22⋊Q8—8332no—
569C22⋊Q8—8332no—
570C22⋊Q8—8316no—
571C22⋊Q8—8316no—
572C22⋊Q8—8332no—
573C22⋊Q8C22×D83132yes—
574C4×Q8—8332no—
575C4×Q8—838no—
576C4×Q8—838no—
577C4×Q8—8316no—
578C4×Q8—8332no—
579C4×Q8—8316no—
580C4×Q8—8316no—
581C4×Q8—8316no—
582C4×D4—8332no—
583C4×D4—838no—
584C4×D4—838no—
585C4×D4—8316no—
586C4×D4—8316no—
587C4×D4—8316no—
588C4×D4—8332no—
589C4×D4—8316no—
590#117—838no—
591#117—8316no—
592#117—8316no—
593#117—8316no—
594#117C22×D8318yes—
595#117C22×D8318yes—
596C2×C4⋊C4—832no—
597C2×C4⋊C4—831no—
598C2×C4⋊C4—834no—
599C2×C4⋊C4—832no—
600C2×C4⋊C4—834no—
601C2×C4⋊C4—832no—
602C2×C4⋊C4—834no—
603C2×C4⋊C4—834no—
604C2×C4⋊C4—832no—
605C2×C4⋊C4—838no—
606C2×C4⋊C4—834no—
607C2×C4⋊C4—834no—
608C2×C4⋊C4—834no—
609C2×C4⋊C4—834no—
610C2×C4⋊C4—8316no—
611C2×C4⋊C4—8316no—
612C2×C4⋊C4—831no—
613C2×C4⋊C4—832no—
614C2×C4⋊C4—832no—
615C2×C4⋊C4—832no—
616C2×C4⋊C4—832no—
617C2×C4⋊C4—832no—
618C2×C4⋊C4—832no—
619C2×C4⋊C4—834no—
620C2×C4⋊C4—8316no—
621C2×C4⋊C4—8316no—
622C2×C4⋊C4—8332no—
623C2×C4⋊C4—8332no—
624C2×C4⋊C4C22×D8311yescharacteristic
625C2×C4⋊C4C22×D8312yes—
626C2×C4⋊C4C22×D8314yes—
627C2×C4⋊C4C22×D8314yes—
628C2×C4⋊C4C22×D8312yes—
629C2×C4⋊C4C22×D8318yes—
630C2×C4⋊C4C22×D8311yescharacteristic
631C2×C4⋊C4C22×D8311yescharacteristic
632C2×C4⋊C4C22×D8311yescharacteristic
633C2×C4⋊C4C22×D8314yes—
634C2×C22⋊C4—832no—
635C2×C22⋊C4—834no—
636C2×C22⋊C4—832no—
637C2×C22⋊C4—832no—
638C2×C22⋊C4—834no—
639C2×C22⋊C4C22×D8312yes—
640C2×C22⋊C4C22×D8312yes—
641C2×C42—831no—
642C2×C42—834no—
643C2×C42—834no—
644C2×C42—832no—
645C2×C42—832no—
646C2×C42—832no—
647C2×C42—831no—
648C2×C42—831no—
649C2×C42—838no—
650C2×C42—831no—
651C2×C42—8316no—
652C2×C42C22×D8312yes—
653C2×C42C22×D8312yes—
654C24—832no—
655C24C23×D8311yescharacteristic
656#41—8364no—
657C2×Q8—48no—
658C2×Q8—3324no—
659C2×Q8—3324no—
660C2×Q8—3328no—
661C2×Q8—838no—
662C2×Q8—838no—
663C2×Q8—8316no—
664C2×Q8—838no—
665C2×Q8—834no—
666C2×Q8C23×D83116yes—
667C2×D4—8316no—
668C2×D4—838no—
669C2×D4—838no—
670C2×D4—834no—
671C22×C4—44no—
672C22×C4—3328no—
673C22×C4—3324no—
674C22×C4—3328no—
675C22×C4—3324no—
676C22×C4—3322no—
677C22×C4—3322no—
678C22×C4—3324no—
679C22×C4—834no—
680C22×C4—834no—
681C22×C4—838no—
682C22×C4—838no—
683C22×C4—838no—
684C22×C4—8316no—
685C22×C4—8316no—
686C22×C4—832no—
687C22×C4—8316no—
688C22×C4—838no—
689C22×C4—831no—
690C22×C4—831no—
691C22×C4—832no—
692C22×C4—831no—
693C22×C4—831no—
694C22×C4—832no—
695C22×C4—834no—
696C22×C4Q8×D8318yes—
697C22×C4C23×D8312yes—
698C22×C4C23×D8312yes—
699C22×C4C23×D8312yes—
700C22×C4C23×D8314yes—
701C22×C4C23×D8312yes—
702C22×C4C23×D8318yes—
703C22×C4C23×D8314yes—
704C22×C4C23×D8311yescharacteristic
705C22×C4C23×D8311yescharacteristic
706C4⋊C4—838no—
707C4⋊C4—834no—
708C4⋊C4—8316no—
709C4⋊C4—838no—
710C4⋊C4—8316no—
711C4⋊C4—838no—
712C4⋊C4—8316no—
713C4⋊C4—8316no—
714C4⋊C4—838no—
715C4⋊C4—8316no—
716C4⋊C4—8316no—
717C4⋊C4—8316no—
718C4⋊C4—8316no—
719C4⋊C4—834no—
720C4⋊C4—838no—
721C4⋊C4—838no—
722C4⋊C4—838no—
723C4⋊C4—838no—
724C4⋊C4—838no—
725C4⋊C4—838no—
726C4⋊C4—8316no—
727C4⋊C4C23×D8314yes—
728C4⋊C4C23×D8318yes—
729C4⋊C4C23×D83116yes—
730C4⋊C4C23×D83116yes—
731C4⋊C4C23×D8318yes—
732C4⋊C4C23×D8314yes—
733C4⋊C4C23×D8314yes—
734C4⋊C4C23×D8314yes—
735C4⋊C4C23×D83116yes—
736C22⋊C4—838no—
737C22⋊C4—8316no—
738C22⋊C4—838no—
739C22⋊C4—838no—
740C22⋊C4—8316no—
741C22⋊C4C23×D8318yes—
742C22⋊C4C23×D8318yes—
743C42—834no—
744C42—834no—
745C42—838no—
746C42—838no—
747C42—834no—
748C42—834no—
749C42—8316no—
750C42—8316no—
751C42—838no—
752C42C23×D8318yes—
753C42C23×D8318yes—
754C23—22no—
755C23—22no—
756C23—838no—
757C23—834no—
758C23—1664no—
759C23—1664no—
760C23C2×Q8×D8314yes—
761C23C24×D8312yes—
762C23C24×D8311yescharacteristic
763Q8—416no—
764Q8—3328no—
765Q8—3328no—
766Q8—33216no—
767Q8—8316no—
768D4—8332no—
769D4—8316no—
770C2×C4—28no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—48no—
776C2×C4—33216no—
777C2×C4—3328no—
778C2×C4—33216no—
779C2×C4—3328no—
780C2×C4—3324no—
781C2×C4—3324no—
782C2×C4—3328no—
783C2×C4—838no—
784C2×C4—834no—
785C2×C4—8332no—
786C2×C4—832no—
787C2×C4—832no—
788C2×C4—834no—
789C2×C4—832no—
790C2×C4—832no—
791C2×C4—834no—
792C2×C4—838no—
793C2×C4—1662no—
794C2×C4—1664no—
795C2×C4—1662no—
796C2×C4—1662no—
797C2×C4—1668no—
798C2×C4—1662no—
799C2×C4—1664no—
800C2×C4C2×Q8×D8314yes—
801C2×C4C2×Q8×D8314yes—
802C2×C4C2×Q8×D83116yes—
803C2×C4C24×D8314yes—
804C2×C4C24×D8314yes—
805C2×C4C24×D8314yes—
806C2×C4C24×D8318yes—
807C2×C4C24×D8314yes—
808C2×C4C24×D8312yes—
809C2×C4C24×D8312yes—
810C22—22no—
811C22—22no—
812C22—28no—
813C22—838no—
814C22—1664no—
815C22—1664no—
816C22—16616no—
817C22C22×Q8×D8314yes—
818C22C22×Q8×D8312yes—
819C22#1912853612yes—
820C22#1912853812yes—
821C22C25×D8311yescharacteristic
822C4—28no—
823C4—24no—
824C4—24no—
825C4—24no—
826C4—24no—
827C4—838no—
828C4—1662no—
829C4—1664no—
830C4—1662no—
831C4—1662no—
832C4—1668no—
833C4—1662no—
834C4—1664no—
835C4C22×Q8×D8314yes—
836C4C22×Q8×D8314yes—
837C2—24no—
838C2—1668no—
839C2#2492128614yesdirect product factor
840C2C23×Q8×D8311yescharacteristic
841C2C2×#1912853611yescharacteristic
842C2C2×#1912853811yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#544×C83C2
socleC23×C83C25
prime radicalC22×#13050590C22
hypercenterC2×#544D83
hypocenterC83C2×#3504
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. #24921286C2direct (N × H)
2. C2×#19128428C2semidirect
3. C2×#19128426C2semidirect
4. C2×#19128412C2semidirect
5. C2×#19128409C2semidirect
6. C2×#19128407C2semidirect
7. C2×#19128405C2semidirect
8. C2×#19128331C2semidirect
9. C2×#19128329C2semidirect
10. C2×#19128328C2semidirect
11. C2×#19128256C2semidirect
12. C2×#19128254C2semidirect
13. C22×#14581783C2semidirect
14. C2×#125×D83C2semidirect
18. C2×#544×C83C2semidirect
20. #19128428C22semidirect
21. #19128426C22semidirect
22. #19128412C22semidirect
23. #19128409C22semidirect
24. #19128407C22semidirect
25. #19128405C22semidirect
26. #19128331C22semidirect
27. #19128329C22semidirect
28. #19128328C22semidirect
29. #19128256C22semidirect
30. #19128254C22semidirect
45. C2×#14581783C22semidirect
50. #125×D83C22semidirect
92. #544×C83C22semidirect
101. C2×#13050590Q8semidirect
233. #13050590C2×Q8semidirect
417. C2×C83#3504semidirect
432. C2×#544D83semidirect
440. C83C2×#3504semidirect
451. #544C2×D83semidirect
839. C2#24921286direct (N × H)

Maximal subgroups

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

subgroupindex
#249212862
C2×#191284282
C2×#191284262
C2×#191284122
C2×#191284092
C2×#191284072
C2×#191284052
C2×#191283312
C2×#191283292
C2×#191283282
C2×#191282562
C2×#191282542
C22×#145817832
C2×#125×D832
C2×#191281822
C2×#191281812
C2×#191281692
C2×#544×C832
C2×#350483