Finite Group Databasebeta

← C2×#19148409 #26004926

Subgroups — C2×#19148409 #26004926

Order 11008.

7478 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148409C2132yesmaximal, direct product factor
2C2×Q8×Dic86C211yesmaximal, characteristic, complemented
3C2×#14583629C211yesmaximal, characteristic, complemented
4C2×#14583626C212yesmaximal, complemented
5C2×#14583607C212yesmaximal, complemented
6C2×#14583606C211yesmaximal, characteristic, complemented
7C2×#14583604C212yesmaximal, complemented
8C2×D4×Dic86C212yesmaximal, complemented
9C2×#14583562C214yesmaximal, complemented
10C2×#14583529C212yesmaximal, complemented
11C2×#14583528C214yesmaximal, complemented
12C2×#14583453C211yesmaximal, characteristic, complemented
13C2×#14583451C212yesmaximal, complemented
14C22×#13063324C212yesmaximal, complemented
15C2×C4⋊Q8×D43C211yesmaximal, characteristic, complemented
16C2×#14583378C212yesmaximal
17C2×C4×#10621900C211yesmaximal, characteristic
18C2×C43×#554C211yesmaximal, characteristic, complemented
19C22×#10621900C2211yescharacteristic
20C23×Dic86C2214yes—
21C22×Q8×D43C2212yes—
22Q8×Dic86C22116yescomplemented
23#14583629C22116yescomplemented
24#14583626C22132yescomplemented
25#14583607C22132yescomplemented
26#14583606C22116yescomplemented
27#14583604C22132yescomplemented
28D4×Dic86C22132yescomplemented
29#14583562C22164yescomplemented
30#14583529C22132yescomplemented
31#14583528C22164yescomplemented
32#14583453C22116yescomplemented
33#14583451C22132yescomplemented
34C2×#13063325C2212yes—
35C2×#13063325C2211yescharacteristic
36C2×#13063324C2214yes—
37C2×#13063324C2214yes—
38C2×#13063324C2212yes—
39C2×#13063324C2212yes—
40C2×#13063324C2212yes—
41C2×#13063324C2212yes—
42C2×#13063324C2211yescharacteristic
43C2×#13063324C2212yes—
44C2×#13063324C2214yes—
45C2×#13063324C22132yescomplemented
46C2×#13063323C2214yes—
47C2×#13063323C2212yes—
48C2×#13063323C2211yescharacteristic
49C4⋊Q8×D43C22116yescomplemented
50C2×#13063316C2212yes—
51C2×#13063315C2214yes—
52C2×#13063315C2214yes—
53C2×#13063315C2214yes—
54C2×#13063315C2212yes—
55C2×#13063305C2214yes—
56C2×#13063305C2211yescharacteristic
57C2×#13063304C2214yes—
58C2×#13063304C2212yes—
59C2×#13063303C2212yes—
60C2×#13063303C2214yes—
61C2×#13063302C2214yes—
62C2×#13063302C2214yes—
63C2×#13063302C2214yes—
64C2×#13063301C2211yescharacteristic
65#14583378C22132yes—
66C4×#10621900C22116yes—
67C2×Q8×Dic43C2212yes—
68C2×C4×Dic86C2212yes—
69C2×C4×Dic86C2212yes—
70C2×C4×Dic86C2211yescharacteristic
71C2×C4×Dic86C2211yescharacteristic
72C2×#13063290C2212yes—
73C2×#13063290C2214yes—
74C2×#13063290C2212yes—
75C2×#13063290C2211yescharacteristic
76C2×D4×Dic43C2212yes—
77C2×D4×Dic43C2211yescharacteristic
78C2×C4×C22⋊D43C2214yes—
79C2×C4×C22⋊D43C2212yes—
80C2×(C22⋊D43)⋊C4C2214yes—
81C2×(C22⋊D43)⋊C4C2212yes—
82C2×#13063283C2211yescharacteristic
83C2×#13063282C2212yes—
84C2×#13063281C2214yes—
85C2×#13063281C2212yes—
86C22×C4⋊Dic43C2212yes—
87C22×Dic43⋊C4C2214yes—
88C2×C4⋊C4×D43C2212yes—
89C2×C4⋊C4×D43C2212yes—
90C22×C4×Dic43C2212yes—
91C2×C42×D43C2211yescharacteristic
92C43×#554C22116yescomplemented
93C2×C4⋊Q8×C43C2211yescharacteristic
94C2×#125×C43C2212yes—
95C2×C22⋊Q8×C43C2214yes—
96C2×C22⋊Q8×C43C2212yes—
97C2×C4×Q8×C43C2211yescharacteristic
98C2×C4×D4×C43C2212yes—
99C2×C4×D4×C43C2211yescharacteristic
100C22×C4⋊C4×C43C2212yes—
101C2×#10621900Q8116yescomplemented
102C2×#10621900C2318yes—
103C22×Dic86—416no—
104C22×Dic86C2311yescharacteristic
105C22×Dic86C2314yes—
106C22×Dic86C2312yes—
107C22×Dic86C23132yes—
108C22×Dic86C2312yes—
109C22×Dic86C2314yes—
110C22×Dic86C2314yes—
111C22×Dic86C2311yescharacteristic
112C2×Q8×D43—48no—
113C2×Q8×D43C23116yes—
114C22×C22⋊D43C2312yes—
115C23×Dic43C2312yes—
116C23×Dic43C2314yes—
117C23×Dic43C2312yes—
118C22×C4×D43C2311yescharacteristic
119C22×C4×D43C2311yescharacteristic
120C22×C4×D43C2314yes—
121C22×C4×D43C2311yescharacteristic
122#13063325C23116yes—
123#13063325C2318yes—
124#13063324C23132yes—
125#13063324C23132yes—
126#13063324C23116yes—
127#13063324C23116yes—
128#13063324C23116yes—
129#13063324C23116yes—
130#13063324C23116yes—
131#13063324C2318yes—
132#13063324C23132yes—
133#13063323C23132yes—
134#13063323C23116yes—
135#13063323C2318yes—
136#13063316C23116yes—
137#13063315C23132yes—
138#13063315C23132yes—
139#13063315C23132yes—
140#13063315C23116yes—
141#13063305C23132yes—
142#13063305C2318yes—
143#13063304C23132yes—
144#13063304C23116yes—
145#13063303C23116yes—
146#13063303C23132yes—
147#13063302C23132yes—
148#13063302C23132yes—
149#13063302C23132yes—
150#13063301C2318yes—
151Q8×Dic43C23116yes—
152C4×Dic86C23116yes—
153C4×Dic86C2318yes—
154C4×Dic86C2318yes—
155C4×Dic86C23116yes—
156#13063290C23132yes—
157#13063290C23116yes—
158#13063290C2318yes—
159#13063290C23116yes—
160D4×Dic43C2318yes—
161D4×Dic43C23116yes—
162C4×C22⋊D43C23132yes—
163C4×C22⋊D43C23116yes—
164(C22⋊D43)⋊C4C23116yes—
165(C22⋊D43)⋊C4C23132yes—
166#13063283C2318yes—
167#13063282C23116yes—
168#13063281C23116yes—
169#13063281C23132yes—
170C2×C4⋊Dic43C2312yes—
171C2×C4⋊Dic43C2312yes—
172C2×C4⋊Dic43C2311yescharacteristic
173C2×C4⋊Dic43C23116yes—
174C2×C4⋊Dic43C2314yes—
175C2×C4⋊Dic43C2311yescharacteristic
176C2×C4⋊Dic43C2312yes—
177C2×C4⋊Dic43C2314yes—
178C2×Dic43⋊C4C2314yes—
179C2×Dic43⋊C4C2314yes—
180C2×Dic43⋊C4C2312yes—
181C2×Dic43⋊C4C2314yes—
182C2×Dic43⋊C4C2314yes—
183C2×Dic43⋊C4C23132yes—
184C2×Dic43⋊C4C2312yes—
185C2×Dic43⋊C4C2312yes—
186C2×Dic43⋊C4C2312yes—
187C2×Dic43⋊C4C2312yes—
188C2×Dic43⋊C4C2314yes—
189C2×Dic43⋊C4C2314yes—
190C2×Dic43⋊C4C2312yes—
191C2×Dic43⋊C4C2312yes—
192C4⋊C4×D43C23116yes—
193C4⋊C4×D43C23116yes—
194C2×C22⋊Dic43C2314yes—
195C2×C22⋊Dic43C2312yes—
196C2×(C2×D43)⋊C4C2312yes—
197C2×(C2×D43)⋊C4C2312yes—
198C2×(C2×D43)⋊C4C2312yes—
199C2×C4×Dic43C2311yescharacteristic
200C2×C4×Dic43C2311yescharacteristic
201C2×C4×Dic43C2311yescharacteristic
202C2×C4×Dic43C2312yes—
203C2×C4×Dic43C2312yes—
204C2×C4×Dic43C2312yes—
205C2×C4×Dic43C23116yes—
206C2×C4×Dic43C2314yes—
207C2×C4×Dic43C2314yes—
208C2×C4×Dic43C2312yes—
209C42×D43C2318yes—
210C22×Q8×C43C2311yescharacteristic
211C22×Q8×C43C2312yes—
212C22×D4×C43C2311yescharacteristic
213C23×C4×C43C2312yes—
214C23×C4×C43C2314yes—
215C4⋊Q8×C43C2318yes—
216#125×C43C23116yes—
217C22⋊Q8×C43C23132yes—
218C22⋊Q8×C43C23116yes—
219C4×Q8×C43C2318yes—
220C4×D4×C43C23116yes—
221C4×D4×C43C2318yes—
222C2×C4⋊C4×C43C2311yescharacteristic
223C2×C4⋊C4×C43C2314yes—
224C2×C4⋊C4×C43C2312yes—
225C2×C4⋊C4×C43C23116yes—
226C2×C4⋊C4×C43C2311yescharacteristic
227C2×C4⋊C4×C43C2312yes—
228C2×C4⋊C4×C43C2312yes—
229C2×C4⋊C4×C43C2314yes—
230C2×C22⋊C4×C43C2314yes—
231C2×C22⋊C4×C43C2312yes—
232C2×C42×C43C2312yes—
233C2×C42×C43C2311yescharacteristic
234C24×C43C2412yes—
235C23×D43C2411yescharacteristic
236C2×Q8×C43—24no—
237C2×Q8×C43—44no—
238C2×Q8×C43C2414yes—
239C2×Q8×C43C2418yes—
240C2×D4×C43C2×Q818yescomplemented
241C2×D4×C43C2414yes—
242C22×C4×C43—28no—
243C22×C4×C43—48no—
244C22×C4×C43C2412yes—
245C22×C4×C43C2411yescharacteristic
246C22×C4×C43C2412yes—
247C22×C4×C43C2412yes—
248C22×C4×C43C2414yes—
249C22×C4×C43C2418yes—
250C22×C4×C43C24116yes—
251C22×C4×C43C2411yescharacteristic
252C22×C4×C43C2411yescharacteristic
253C2×C22⋊D43C2×Q8116yescomplemented
254C2×C22⋊D43C2418yes—
255C22×Dic43—28no—
256C22×Dic43—48no—
257C22×Dic43C2×Q8116yescomplemented
258C22×Dic43C2412yes—
259C22×Dic43C2412yes—
260C22×Dic43C2411yescharacteristic
261C22×Dic43C2418yes—
262C22×Dic43C2412yes—
263C22×Dic43C2414yes—
264C22×Dic43C24116yes—
265C22×Dic43C2412yes—
266C22×Dic43C2411yescharacteristic
267C22×Dic43C2418yes—
268C22×Dic43C2411yescharacteristic
269Q8×D43—432no—
270#10621900C2×Q8164yescomplemented
271C2×C4×D43—24no—
272C2×C4×D43—24no—
273C2×C4×D43—48no—
274C2×C4×D43C2×Q818yescomplemented
275C2×C4×D43C2414yes—
276C2×C4×D43C2414yes—
277C2×C4×D43C24116yes—
278C2×C4×D43C2414yes—
279C2×Dic86—24no—
280C2×Dic86—216no—
281C2×Dic86—28no—
282C2×Dic86—464no—
283C2×Dic86—44no—
284C2×Dic86—48no—
285C2×Dic86—48no—
286C2×Dic86C2×Q818yescomplemented
287C2×Dic86C2414yes—
288C2×Dic86C24116yes—
289C2×Dic86C2418yes—
290C2×Dic86C2418yes—
291C2×Dic86C24116yes—
292C2×Dic86C24116yes—
293C2×Dic86C2414yes—
294C4⋊C4×C43C2414yes—
295C4⋊C4×C43C24116yes—
296C4⋊C4×C43C2418yes—
297C4⋊C4×C43C2414yes—
298C4⋊C4×C43C2418yes—
299C4⋊C4×C43C2418yes—
300C4⋊C4×C43C24116yes—
301C22⋊C4×C43C24116yes—
302C22⋊C4×C43C2418yes—
303C42×C43C2418yes—
304C42×C43C2414yes—
305C22⋊Dic43C24116yes—
306C22⋊Dic43C2418yes—
307(C2×D43)⋊C4C2418yes—
308(C2×D43)⋊C4C2418yes—
309(C2×D43)⋊C4C2418yes—
310C4⋊Dic43C2418yes—
311C4⋊Dic43C2418yes—
312C4⋊Dic43C2414yes—
313C4⋊Dic43C24116yes—
314C4⋊Dic43C2414yes—
315C4⋊Dic43C2418yes—
316C4⋊Dic43C24116yes—
317Dic43⋊C4C24116yes—
318Dic43⋊C4C24116yes—
319Dic43⋊C4C2418yes—
320Dic43⋊C4C24116yes—
321Dic43⋊C4C24116yes—
322Dic43⋊C4C2418yes—
323Dic43⋊C4C2418yes—
324Dic43⋊C4C2418yes—
325Dic43⋊C4C2418yes—
326Dic43⋊C4C24116yes—
327Dic43⋊C4C24116yes—
328Dic43⋊C4C2418yes—
329Dic43⋊C4C2418yes—
330C4×Dic43C2414yes—
331C4×Dic43C2414yes—
332C4×Dic43C2414yes—
333C4×Dic43C2418yes—
334C4×Dic43C2418yes—
335C4×Dic43C2418yes—
336C4×Dic43C24116yes—
337C4×Dic43C24116yes—
338C4×Dic43C2418yes—
339C23×C43—24no—
340C23×C43—24no—
341C23×C43C22×Q818yes—
342C23×C43C2514yes—
343C23×C43C2511yescharacteristic
344C22×D43—22no—
345C22×D43—22no—
346C22×D43C22×Q814yes—
347C22×D43C2512yes—
348Q8×C43—28no—
349Q8×C43—48no—
350D4×C43C22×Q8116yescomplemented
351C2×C4×C43—24no—
352C2×C4×C43—28no—
353C2×C4×C43—22no—
354C2×C4×C43—24no—
355C2×C4×C43—24no—
356C2×C4×C43—216no—
357C2×C4×C43—416no—
358C2×C4×C43C22×Q814yes—
359C2×C4×C432−1+414yes—
360C2×C4×C43C2514yes—
361C2×C4×C43C2514yes—
362C2×C4×C43C2512yes—
363C2×C4×C43C2518yes—
364C2×C4×C43C2514yes—
365C2×C4×C43C2512yes—
366C2×C4×C43C2512yes—
367C22⋊D43C22×Q8132yescomplemented
368C2×Dic43—28no—
369C2×Dic43—24no—
370C2×Dic43—24no—
371C2×Dic43—24no—
372C2×Dic43—22no—
373C2×Dic43—216no—
374C2×Dic43—416no—
375C2×Dic43C22×Q818yes—
376C2×Dic43C22×Q814yes—
377C2×Dic43C22×Q8132yescomplemented
378C2×Dic43H(5,𝔽2)14yes—
379C2×Dic43C2514yes—
380C2×Dic43C2512yes—
381C2×Dic43C2514yes—
382C2×Dic43C2514yes—
383C2×Dic43C2518yes—
384C2×Dic43C2514yes—
385C2×Dic43C2512yes—
386C2×Dic43C2512yes—
387C4×D43—28no—
388C4×D43—28no—
389C4×D43—416no—
390C4×D43C22×Q8116yescomplemented
391Dic86—28no—
392Dic86—216no—
393Dic86—232no—
394Dic86—416no—
395Dic86—416no—
396Dic86—48no—
397Dic86C22×Q8116yescomplemented
398C2×#3503—431nomaximal, Sylow
399C22×C43—24no—
400C22×C43—24no—
401C22×C43—216no—
402C22×C43C23×Q818yes—
403C22×C43C23×Q812yes—
404C22×C43C2×H(5,𝔽2)12yes—
405C22×C43C2×2−1+412yes—
406C22×C43C2611yescharacteristic
407C2×D43—22no—
408C2×D43—22no—
409C2×D43—28no—
410C2×D43C23×Q814yes—
411C4×C43—24no—
412C4×C43—28no—
413C4×C43—22no—
414C4×C43—24no—
415C4×C43—24no—
416C4×C43C23×Q814yes—
417C4×C43C2×2−1+414yes—
418Dic43—28no—
419Dic43—24no—
420Dic43—24no—
421Dic43—24no—
422Dic43—22no—
423Dic43C23×Q818yes—
424Dic43C23×Q814yes—
425Dic43C2×H(5,𝔽2)14yes—
426#3503—4332no—
427C2×Q82—431no—
428C2×Q82—431no—
429C2×#557—432no—
430C2×#554—432no—
431C2×#554—431no—
432C2×#554—432no—
433C2×#554D4311yescharacteristic, complemented
434C2×D4×Q8—434no—
435C2×D4×Q8—432no—
436C2×#544—432no—
437C2×#544—434no—
438C2×#533—432no—
439C2×#533—431no—
440C22×C4⋊Q8—431no—
441C22×C4⋊Q8—432no—
442C2×#520—432no—
443C2×C4×#41—431no—
444C2×C43—28no—
445C2×C43#350314yescomplemented
446C2×C43C24×Q811yescharacteristic
447C2×C43C22×H(5,𝔽2)11yescharacteristic
448C2×C43C22×2−1+411yescharacteristic
449D43—24no—
450C22×#41—431no—
451C23×Q8—432no—
452C23×Q8—434no—
453Q82—4316no—
454Q82—4316no—
455#557—4332no—
456#554—4332no—
457#554—4316no—
458#554—4332no—
459#554C2×D43116yescomplemented
460D4×Q8—4364no—
461D4×Q8—4332no—
462#544—4332no—
463#544—4364no—
464#533—4332no—
465#533—4316no—
466C2×C4⋊Q8—432no—
467C2×C4⋊Q8—431no—
468C2×C4⋊Q8—434no—
469C2×C4⋊Q8—4316no—
470C2×C4⋊Q8—432no—
471C2×C4⋊Q8—431no—
472C2×C4⋊Q8—434no—
473C2×C4⋊Q8—434no—
474C2×C4⋊Q8—432no—
475C2×C4⋊Q8—432no—
476C2×C4⋊Q8—432no—
477C2×C4⋊Q8—4332no—
478C2×C4⋊Q8—434no—
479C2×C4⋊Q8—432no—
480C2×C4⋊Q8—431no—
481C2×C4⋊Q8—432no—
482C2×C4⋊Q8C2×D4311yescharacteristic
483C2×#125—432no—
484C2×#125—434no—
485C2×#125—434no—
486C2×#125—434no—
487C2×#125—432no—
488C2×#125C2×D4312yes—
489C2×C22⋊Q8—431no—
490C2×C22⋊Q8—432no—
491C2×C22⋊Q8—434no—
492C2×C22⋊Q8—432no—
493C2×C22⋊Q8—434no—
494C2×C22⋊Q8—431no—
495C2×C22⋊Q8—434no—
496C2×C22⋊Q8—434no—
497C2×C22⋊Q8—434no—
498C2×C22⋊Q8—434no—
499C2×C22⋊Q8C2×D4312yes—
500C2×C22⋊Q8C2×D4314yes—
501#520—4332no—
502C4×#41—4316no—
503C2×C4×Q8—432no—
504C2×C4×Q8—431no—
505C2×C4×Q8—432no—
506C2×C4×Q8—434no—
507C2×C4×Q8—432no—
508C2×C4×Q8—431no—
509C2×C4×Q8—432no—
510C2×C4×Q8—432no—
511C2×C4×Q8—431no—
512C2×C4×Q8C2×D4311yescharacteristic
513C2×C4×D4—431no—
514C2×C4×D4—432no—
515C2×C4×D4—432no—
516C2×C4×D4—434no—
517C2×C4×D4—432no—
518C2×C4×D4—434no—
519C2×C4×D4C2×D4311yescharacteristic
520C2×C4×D4C2×D4312yes—
521C2×#117—431no—
522C2×#117—432no—
523C2×#117—434no—
524C2×#117—432no—
525C22×C4⋊C4—434no—
526C22×C4⋊C4—432no—
527C22×C4⋊C4—432no—
528C22×C4⋊C4—432no—
529C22×C4⋊C4C2×D4312yes—
530C22×C42—432no—
531C22×C42—431no—
532C43C2×#350311yescharacteristic, complemented, Sylow
533C2×#41—4316no—
534C2×#41—438no—
535C22×Q8—4316no—
536C22×Q8—431no—
537C22×Q8—431no—
538C22×Q8—434no—
539C22×Q8—432no—
540C22×Q8—434no—
541C22×Q8—434no—
542C22×Q8—432no—
543C22×Q8—4332no—
544C22×Q8—17216no—
545C22×Q8—1728no—
546C22×Q8C22×D4311yescharacteristic
547C22×Q8C22×D4312yes—
548C22×D4—432no—
549C22×D4C22×D4311yescharacteristic
550C23×C4—432no—
551C23×C4—431no—
552C23×C4—432no—
553C23×C4—434no—
554C23×C4—431no—
555C23×C4—431no—
556C23×C4—434no—
557C23×C4C22×D4312yes—
558C23×C4C22×D4314yes—
559C4⋊Q8—4316no—
560C4⋊Q8—438no—
561C4⋊Q8—4332no—
562C4⋊Q8—4316no—
563C4⋊Q8—438no—
564C4⋊Q8—4332no—
565C4⋊Q8—4332no—
566C4⋊Q8—4316no—
567C4⋊Q8—4316no—
568C4⋊Q8—4316no—
569C4⋊Q8—4332no—
570C4⋊Q8—4316no—
571C4⋊Q8—438no—
572C4⋊Q8—4316no—
573C4⋊Q8C22×D4318yes—
574#125—4316no—
575#125—4332no—
576#125—4332no—
577#125—4332no—
578#125—4316no—
579#125C22×D43116yes—
580C22⋊Q8—438no—
581C22⋊Q8—4316no—
582C22⋊Q8—4332no—
583C22⋊Q8—4316no—
584C22⋊Q8—438no—
585C22⋊Q8—4332no—
586C22⋊Q8—4332no—
587C22⋊Q8—4332no—
588C22⋊Q8—4332no—
589C22⋊Q8—4332no—
590C22⋊Q8C22×D43116yes—
591C22⋊Q8C22×D43132yes—
592C4×Q8—4316no—
593C4×Q8—438no—
594C4×Q8—4316no—
595C4×Q8—4332no—
596C4×Q8—4316no—
597C4×Q8—438no—
598C4×Q8—4316no—
599C4×Q8—4316no—
600C4×Q8—438no—
601C4×Q8C22×D4318yes—
602C4×D4—438no—
603C4×D4—4316no—
604C4×D4—4316no—
605C4×D4—4332no—
606C4×D4—4316no—
607C4×D4—4332no—
608C4×D4C22×D4318yes—
609C4×D4C22×D43116yes—
610#117—438no—
611#117—4316no—
612#117—4332no—
613#117—4316no—
614C2×C4⋊C4—434no—
615C2×C4⋊C4—432no—
616C2×C4⋊C4—431no—
617C2×C4⋊C4—432no—
618C2×C4⋊C4—434no—
619C2×C4⋊C4—434no—
620C2×C4⋊C4—432no—
621C2×C4⋊C4—4332no—
622C2×C4⋊C4—434no—
623C2×C4⋊C4—434no—
624C2×C4⋊C4—4316no—
625C2×C4⋊C4—432no—
626C2×C4⋊C4—432no—
627C2×C4⋊C4—432no—
628C2×C4⋊C4—431no—
629C2×C4⋊C4—432no—
630C2×C4⋊C4—434no—
631C2×C4⋊C4—432no—
632C2×C4⋊C4—432no—
633C2×C4⋊C4—434no—
634C2×C4⋊C4—432no—
635C2×C4⋊C4—434no—
636C2×C4⋊C4—4316no—
637C2×C4⋊C4—4316no—
638C2×C4⋊C4C22×D4312yes—
639C2×C4⋊C4C22×D4312yes—
640C2×C4⋊C4C22×D4311yescharacteristic
641C2×C4⋊C4C22×D4314yes—
642C2×C4⋊C4C22×D43116yes—
643C2×C4⋊C4C22×D4311yescharacteristic
644C2×C4⋊C4C22×D4314yes—
645C2×C4⋊C4C22×D4312yes—
646C2×C22⋊C4—434no—
647C2×C22⋊C4—432no—
648C2×C22⋊C4—432no—
649C2×C22⋊C4—432no—
650C2×C22⋊C4—432no—
651C2×C22⋊C4C22×D4314yes—
652C2×C22⋊C4C22×D4312yes—
653C2×C42—431no—
654C2×C42—432no—
655C2×C42—434no—
656C2×C42—434no—
657C2×C42—432no—
658C2×C42—432no—
659C2×C42—432no—
660C2×C42—431no—
661C2×C42—4316no—
662C2×C42—431no—
663C2×C42—438no—
664C2×C42C22×D4312yes—
665C2×C42C22×D4311yescharacteristic
666C24—431no—
667C24C23×D4312yes—
668#41—4364no—
669C2×Q8—24no—
670C2×Q8—44no—
671C2×Q8—438no—
672C2×Q8—434no—
673C2×Q8—434no—
674C2×Q8—4316no—
675C2×Q8—438no—
676C2×Q8—4316no—
677C2×Q8—4316no—
678C2×Q8—438no—
679C2×Q8—868no—
680C2×Q8—8616no—
681C2×Q8—864no—
682C2×Q8—1728no—
683C2×Q8—1728no—
684C2×Q8—1724no—
685C2×Q8—17264no—
686C2×Q8—17232no—
687C2×Q8C23×D4314yes—
688C2×Q8C23×D4318yes—
689C2×D4—4316no—
690C2×D4—438no—
691C2×D4Q8×D4318yescomplemented
692C2×D4C23×D4314yes—
693C22×C4—28no—
694C22×C4—48no—
695C22×C4—4316no—
696C22×C4—438no—
697C22×C4—432no—
698C22×C4—431no—
699C22×C4—431no—
700C22×C4—438no—
701C22×C4—434no—
702C22×C4—438no—
703C22×C4—432no—
704C22×C4—431no—
705C22×C4—432no—
706C22×C4—434no—
707C22×C4—432no—
708C22×C4—4316no—
709C22×C4—434no—
710C22×C4—434no—
711C22×C4—4316no—
712C22×C4—864no—
713C22×C4—868no—
714C22×C4—864no—
715C22×C4—1728no—
716C22×C4—1728no—
717C22×C4C23×D4318yes—
718C22×C4C23×D4312yes—
719C22×C4C23×D4312yes—
720C22×C4C23×D4311yescharacteristic
721C22×C4C23×D4314yes—
722C22×C4C23×D4312yes—
723C22×C4C23×D43116yes—
724C22×C4C23×D4311yescharacteristic
725C22×C4C23×D4311yescharacteristic
726C4⋊C4—4316no—
727C4⋊C4—438no—
728C4⋊C4—434no—
729C4⋊C4—438no—
730C4⋊C4—4316no—
731C4⋊C4—4316no—
732C4⋊C4—438no—
733C4⋊C4—4316no—
734C4⋊C4—4316no—
735C4⋊C4—438no—
736C4⋊C4—438no—
737C4⋊C4—438no—
738C4⋊C4—434no—
739C4⋊C4—438no—
740C4⋊C4—4316no—
741C4⋊C4—438no—
742C4⋊C4—438no—
743C4⋊C4—4316no—
744C4⋊C4—438no—
745C4⋊C4—4316no—
746C4⋊C4C23×D4318yes—
747C4⋊C4C23×D4318yes—
748C4⋊C4C23×D4314yes—
749C4⋊C4C23×D43116yes—
750C4⋊C4C23×D4314yes—
751C4⋊C4C23×D43116yes—
752C4⋊C4C23×D4318yes—
753C22⋊C4—4316no—
754C22⋊C4—438no—
755C22⋊C4—438no—
756C22⋊C4—438no—
757C22⋊C4—438no—
758C22⋊C4C23×D43116yes—
759C22⋊C4C23×D4318yes—
760C42—434no—
761C42—434no—
762C42—438no—
763C42—438no—
764C42—438no—
765C42—434no—
766C42—4316no—
767C42—4316no—
768C42—438no—
769C42C23×D4314yes—
770C42C23×D4318yes—
771C23—24no—
772C23—24no—
773C23—434no—
774C23—432no—
775C23—862no—
776C23—862no—
777C23C2×Q8×D4318yes—
778C23C24×D4314yes—
779C23C24×D4311yescharacteristic
780Q8—28no—
781Q8—48no—
782Q8—4316no—
783Q8—8616no—
784Q8—8632no—
785Q8—868no—
786Q8—17216no—
787Q8—17216no—
788Q8—1728no—
789D4—4332no—
790D4C2×Q8×D43116yescomplemented
791C2×C4—24no—
792C2×C4—28no—
793C2×C4—22no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—216no—
797C2×C4—416no—
798C2×C4—434no—
799C2×C4—438no—
800C2×C4—4332no—
801C2×C4—434no—
802C2×C4—434no—
803C2×C4—432no—
804C2×C4—432no—
805C2×C4—4316no—
806C2×C4—434no—
807C2×C4—432no—
808C2×C4—434no—
809C2×C4—438no—
810C2×C4—434no—
811C2×C4—868no—
812C2×C4—8616no—
813C2×C4—864no—
814C2×C4—868no—
815C2×C4—864no—
816C2×C4—862no—
817C2×C4—864no—
818C2×C4—868no—
819C2×C4—17216no—
820C2×C4—17216no—
821C2×C4C2×Q8×D4314yes—
822C2×C4#1306337214yes—
823C2×C4C24×D4314yes—
824C2×C4C24×D4314yes—
825C2×C4C24×D4312yes—
826C2×C4C24×D4318yes—
827C2×C4C24×D4314yes—
828C2×C4C24×D4312yes—
829C2×C4C24×D4312yes—
830C22—24no—
831C22—24no—
832C22—216no—
833C22—434no—
834C22—862no—
835C22—862no—
836C22—868no—
837C22C22×Q8×D4318yes—
838C22C22×Q8×D4312yes—
839C22H(5,𝔽2)×D4312yes—
840C22C2×#1306337212yes—
841C22C25×D4311yescharacteristic
842C4—24no—
843C4—28no—
844C4—22no—
845C4—24no—
846C4—24no—
847C4—434no—
848C4—438no—
849C4—434no—
850C4—864no—
851C4—868no—
852C4—864no—
853C4—862no—
854C4—864no—
855C4C22×Q8×D4314yes—
856C4C2×#1306337214yes—
857C2—28no—
858C2—864no—
859C2#1914840914yesdirect product factor
860C2C23×Q8×D4311yescharacteristic
861C2C2×H(5,𝔽2)×D4311yescharacteristic
862C2C22×#1306337211yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#554C2
socleC23×C43C25
prime radicalC22×#10621900C22
hypercenterC2×#554D43
hypocenterC43C2×#3503
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #19148409C2direct (N × H)
2. C2×Q8×Dic86C2semidirect
3. C2×#14583629C2semidirect
4. C2×#14583626C2semidirect
5. C2×#14583607C2semidirect
6. C2×#14583606C2semidirect
7. C2×#14583604C2semidirect
8. C2×D4×Dic86C2semidirect
9. C2×#14583562C2semidirect
10. C2×#14583529C2semidirect
11. C2×#14583528C2semidirect
12. C2×#14583453C2semidirect
13. C2×#14583451C2semidirect
14. C22×#13063324C2semidirect
15. C2×C4⋊Q8×D43C2semidirect
18. C2×C43×#554C2semidirect
22. Q8×Dic86C22semidirect
23. #14583629C22semidirect
24. #14583626C22semidirect
25. #14583607C22semidirect
26. #14583606C22semidirect
27. #14583604C22semidirect
28. D4×Dic86C22semidirect
29. #14583562C22semidirect
30. #14583529C22semidirect
31. #14583528C22semidirect
32. #14583453C22semidirect
33. #14583451C22semidirect
45. C2×#13063324C22semidirect
49. C4⋊Q8×D43C22semidirect
92. C43×#554C22semidirect
101. C2×#10621900Q8semidirect
240. C2×D4×C43C2×Q8semidirect
253. C2×C22⋊D43C2×Q8semidirect
257. C22×Dic43C2×Q8semidirect
270. #10621900C2×Q8semidirect
274. C2×C4×D43C2×Q8semidirect
286. C2×Dic86C2×Q8semidirect
350. D4×C43C22×Q8semidirect
367. C22⋊D43C22×Q8semidirect
377. C2×Dic43C22×Q8semidirect
390. C4×D43C22×Q8semidirect
397. Dic86C22×Q8semidirect
433. C2×#554D43semidirect
445. C2×C43#3503semidirect
459. #554C2×D43semidirect
532. C43C2×#3503semidirect
691. C2×D4Q8×D43semidirect
790. D4C2×Q8×D43semidirect
859. C2#19148409direct (N × H)

Maximal subgroups

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

subgroupindex
#191484092
C2×Q8×Dic862
C2×#145836292
C2×#145836262
C2×#145836072
C2×#145836062
C2×#145836042
C2×D4×Dic862
C2×#145835622
C2×#145835292
C2×#145835282
C2×#145834532
C2×#145834512
C22×#130633242
C2×C4⋊Q8×D432
C2×#145833782
C2×C4×#106219002
C2×C43×#5542
C2×#350343