Finite Group Databasebeta

← C2×#19149037 #26004203

Subgroups — C2×#19149037 #26004203

Order 11008.

7086 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19149037C2132yesmaximal, direct product factor
2C2×#14583650C214yesmaximal, complemented
3C2×#14583627C211yesmaximal, characteristic, complemented
4C2×#14583623C211yesmaximal, characteristic, complemented
5C2×#14583610C212yesmaximal, complemented
6C2×#14583599C212yesmaximal, complemented
7C2×Q8×C22⋊D43C212yesmaximal, complemented
8C2×#14583559C212yesmaximal, complemented
9C2×#14583554C211yesmaximal, characteristic, complemented
10C2×#14583526C212yesmaximal, complemented
11C2×#14583514C212yesmaximal, complemented
12C2×#14583509C212yesmaximal, complemented
13C2×#14583495C214yesmaximal, complemented
14C2×#14583473C212yesmaximal, complemented
15C2×C4⋊Q8×D43C211yesmaximal, characteristic, complemented
16C2×#14583436C211yesmaximal, characteristic, complemented
17C2×#14583431C211yesmaximal, characteristic, complemented
18C2×D4×Q8×C43C211yesmaximal, characteristic, complemented
19C22×#10621898C2212yes—
20C22×Q8×D43C2212yes—
21#14583650C22164yescomplemented
22#14583627C22116yescomplemented
23#14583623C22116yescomplemented
24#14583610C22132yescomplemented
25#14583599C22132yescomplemented
26Q8×C22⋊D43C22132yescomplemented
27#14583559C22132yescomplemented
28#14583554C22116yescomplemented
29#14583526C22132yescomplemented
30#14583514C22132yescomplemented
31#14583509C22132yescomplemented
32#14583495C22164yescomplemented
33#14583473C22132yescomplemented
34C2×#13063325C2211yescharacteristic
35C2×#13063324C2212yes—
36C2×#13063324C2212yes—
37C2×#13063323C2212yes—
38C2×#13063323C2214yes—
39C2×#13063323C2212yes—
40C4⋊Q8×D43C22116yescomplemented
41#14583436C22116yescomplemented
42#14583431C22116yescomplemented
43C2×#13063320C2212yes—
44C2×#13063320C2214yes—
45C2×#13063318C2212yes—
46C2×#13063318C2214yes—
47C2×#13063318C2214yes—
48C2×#13063317C2212yes—
49C2×#13063316C2211yescharacteristic
50C2×#13063316C2211yescharacteristic
51C2×#13063316C2214yes—
52C2×#13063315C2214yes—
53C2×#13063315C2214yes—
54C2×#13063314C2212yes—
55C2×#13063314C2211yescharacteristic
56C2×#13063312C2211yescharacteristic
57C2×#13063311C2214yes—
58C2×#13063310C2212yes—
59C2×#13063308C2214yes—
60C2×#13063308C2214yes—
61C2×#13063307C2214yes—
62C2×#13063307C2212yes—
63C2×#13063305C2211yescharacteristic
64C2×#13063305C2212yes—
65C2×#13063304C2212yes—
66C2×#13063304C2214yes—
67C2×#13063303C2214yes—
68C2×#13063301C2211yescharacteristic
69C2×#13063301C2214yes—
70C2×#13063301C2214yes—
71C2×#13063301C2214yes—
72C2×#13063300C2211yescharacteristic
73C2×#13063298C2214yes—
74C2×#13063296C2212yes—
75C2×#13063296C2211yescharacteristic
76C2×Q8×Dic43C2212yes—
77C2×C4×Dic86C2211yescharacteristic
78C2×C4×Dic86C2212yes—
79C2×#13063290C2212yes—
80C2×C4×D172C2211yescharacteristic
81C2×C4×D172C2212yes—
82C2×#13063287C2214yes—
83C2×C4×C22⋊D43C2212yes—
84C2×C4×C22⋊D43C2214yes—
85C2×#13063284C2212yes—
86C2×#13063283C2212yes—
87C2×#13063282C2212yes—
88C2×C4⋊C4×D43C2212yes—
89C2×C4⋊C4×D43C2212yes—
90C2×C4⋊C4×D43C2212yes—
91C2×C42×D43C2211yescharacteristic
92C23×Q8×C43C2212yes—
93D4×Q8×C43C22116yescomplemented
94C2×C4⋊Q8×C43C2211yescharacteristic
95C2×C4⋊Q8×C43C2212yes—
96C2×C22⋊Q8×C43C2212yes—
97C2×C22⋊Q8×C43C2214yes—
98C2×C4×Q8×C43C2211yescharacteristic
99C2×C4×D4×C43C2211yescharacteristic
100C2×C4×D4×C43C2212yes—
101C2×#10621898—48no—
102C2×#10621898C23116yes—
103C22×Dic86C2312yes—
104C22×Dic86C2311yescharacteristic
105C22×Dic86C2314yes—
106C2×Q8×D43—48no—
107C2×Q8×D43C23116yes—
108C22×D172C2312yes—
109C22×D172C2311yescharacteristic
110C22×C22⋊D43C2312yes—
111C22×C22⋊D43C2314yes—
112C22×C4×D43C2311yescharacteristic
113C22×C4×D43C2311yescharacteristic
114C22×C4×D43C2311yescharacteristic
115C22×C4×D43C2312yes—
116C22×C4×D43C2314yes—
117C22×C4×D43C2314yes—
118#13063325C2318yes—
119#13063324C23116yes—
120#13063324C23116yes—
121#13063323C23116yes—
122#13063323C23132yes—
123#13063323C23116yes—
124#13063320C23132yes—
125#13063320C23116yes—
126#13063318C23132yes—
127#13063318C23116yes—
128#13063318C23132yes—
129#13063317C23116yes—
130#13063316C23132yes—
131#13063316C2318yes—
132#13063316C2318yes—
133#13063315C23132yes—
134#13063315C23132yes—
135#13063314C23116yes—
136#13063314C2318yes—
137#13063312C2318yes—
138#13063311C23132yes—
139#13063310C23116yes—
140#13063308C23132yes—
141#13063308C23132yes—
142#13063307C23132yes—
143#13063307C23116yes—
144#13063305C2318yes—
145#13063305C23116yes—
146#13063304C23116yes—
147#13063304C23132yes—
148#13063303C23132yes—
149#13063301C2318yes—
150#13063301C23132yes—
151#13063301C23132yes—
152#13063301C23132yes—
153#13063300C2318yes—
154#13063298C23132yes—
155#13063296C23116yes—
156#13063296C2318yes—
157Q8×Dic43C23116yes—
158C4×Dic86C23116yes—
159C4×Dic86C2318yes—
160#13063290C23116yes—
161C4×D172C2318yes—
162C4×D172C23116yes—
163#13063287C23132yes—
164C4×C22⋊D43C23116yes—
165C4×C22⋊D43C23132yes—
166#13063284C23116yes—
167#13063283C23116yes—
168#13063282C23116yes—
169C2×C4⋊Dic43C2312yes—
170C2×C4⋊Dic43C2312yes—
171C2×C4⋊Dic43C2311yescharacteristic
172C2×C4⋊Dic43C2312yes—
173C2×C4⋊Dic43C2312yes—
174C2×C4⋊Dic43C2311yescharacteristic
175C2×C4⋊Dic43C2312yes—
176C2×C4⋊Dic43C2314yes—
177C2×Dic43⋊C4C2314yes—
178C2×Dic43⋊C4C2314yes—
179C2×Dic43⋊C4C2314yes—
180C2×Dic43⋊C4C2312yes—
181C2×Dic43⋊C4C2312yes—
182C2×Dic43⋊C4C2314yes—
183C2×Dic43⋊C4C2312yes—
184C2×Dic43⋊C4C2314yes—
185C2×Dic43⋊C4C2314yes—
186C2×Dic43⋊C4C2312yes—
187C4⋊C4×D43C23116yes—
188C4⋊C4×D43C23116yes—
189C4⋊C4×D43C23116yes—
190C2×C22⋊Dic43C2312yes—
191C2×C22⋊Dic43C2312yes—
192C2×C22⋊Dic43C2314yes—
193C2×C22⋊Dic43C2312yes—
194C2×(C2×D43)⋊C4C2312yes—
195C2×(C2×D43)⋊C4C2312yes—
196C2×(C2×D43)⋊C4C2314yes—
197C2×(C2×D43)⋊C4C2312yes—
198C2×(C2×D43)⋊C4C2312yes—
199C2×(C2×D43)⋊C4C2314yes—
200C2×(C2×D43)⋊C4C2312yes—
201C2×(C2×D43)⋊C4C2312yes—
202C2×C4×Dic43C2311yescharacteristic
203C2×C4×Dic43C2311yescharacteristic
204C2×C4×Dic43C2311yescharacteristic
205C2×C4×Dic43C2314yes—
206C2×C4×Dic43C2312yes—
207C2×C4×Dic43C2314yes—
208C42×D43C2318yes—
209C22×Q8×C43—48no—
210C22×Q8×C43C2311yescharacteristic
211C22×Q8×C43C2312yes—
212C22×Q8×C43C23116yes—
213C22×Q8×C43C2314yes—
214C22×D4×C43C2311yescharacteristic
215C23×C4×C43C2312yes—
216C23×C4×C43C2314yes—
217C4⋊Q8×C43C23116yes—
218C4⋊Q8×C43C2318yes—
219C22⋊Q8×C43C23116yes—
220C22⋊Q8×C43C23132yes—
221C4×Q8×C43C2318yes—
222C4×D4×C43C2318yes—
223C4×D4×C43C23116yes—
224C2×C4⋊C4×C43C2311yescharacteristic
225C2×C4⋊C4×C43C2312yes—
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×C43C2311yescharacteristic
233C2×C42×C43C2312yes—
234C24×C43C2412yes—
235C23×D43C2412yes—
236C23×D43C2411yescharacteristic
237C2×Q8×C43—24no—
238C2×Q8×C43—28no—
239C2×Q8×C43—48no—
240C2×Q8×C43—432no—
241C2×Q8×C43C2414yes—
242C2×Q8×C43C2418yes—
243C2×Q8×C43C24116yes—
244C2×D4×C43—24no—
245C2×D4×C43C2414yes—
246C22×C4×C43—28no—
247C22×C4×C43—48no—
248C22×C4×C43C2412yes—
249C22×C4×C43C2411yescharacteristic
250C22×C4×C43C2412yes—
251C22×C4×C43C2414yes—
252C22×C4×C43C2412yes—
253C22×C4×C43C2418yes—
254C22×C4×C43C24116yes—
255C22×C4×C43C2411yescharacteristic
256C22×C4×C43C2411yescharacteristic
257C2×C22⋊D43—28no—
258C2×C22⋊D43—48no—
259C2×C22⋊D43C2418yes—
260C2×C22⋊D43C24116yes—
261C22×Dic43C2412yes—
262C22×Dic43C2412yes—
263C22×Dic43C2411yescharacteristic
264C22×Dic43C2411yescharacteristic
265C22×Dic43C2412yes—
266C22×Dic43C2411yescharacteristic
267C22×Dic43C2414yes—
268Q8×D43—432no—
269#10621898—432no—
270C2×D172—24no—
271C2×D172—28no—
272C2×D172C2418yes—
273C2×D172C2414yes—
274C2×C4×D43—24no—
275C2×C4×D43—24no—
276C2×C4×D43—28no—
277C2×C4×D43—24no—
278C2×C4×D43—48no—
279C2×C4×D43—48no—
280C2×C4×D43C2414yes—
281C2×C4×D43C2414yes—
282C2×C4×D43C2414yes—
283C2×C4×D43C2418yes—
284C2×C4×D43C24116yes—
285C2×C4×D43C24116yes—
286C2×Dic86—28no—
287C2×Dic86—24no—
288C2×Dic86—48no—
289C2×Dic86C2418yes—
290C2×Dic86C2414yes—
291C2×Dic86C24116yes—
292C4⋊C4×C43C2414yes—
293C4⋊C4×C43C2418yes—
294C4⋊C4×C43C2414yes—
295C4⋊C4×C43C2418yes—
296C4⋊C4×C43C2418yes—
297C4⋊C4×C43C24116yes—
298C22⋊C4×C43C24116yes—
299C22⋊C4×C43C2418yes—
300C42×C43C2414yes—
301C42×C43C2418yes—
302C22⋊Dic43C2418yes—
303C22⋊Dic43C2418yes—
304C22⋊Dic43C24116yes—
305C22⋊Dic43C2418yes—
306(C2×D43)⋊C4C2418yes—
307(C2×D43)⋊C4C2418yes—
308(C2×D43)⋊C4C24116yes—
309(C2×D43)⋊C4C2418yes—
310(C2×D43)⋊C4C2418yes—
311(C2×D43)⋊C4C24116yes—
312(C2×D43)⋊C4C2418yes—
313(C2×D43)⋊C4C2418yes—
314C4⋊Dic43C2418yes—
315C4⋊Dic43C2418yes—
316C4⋊Dic43C2414yes—
317C4⋊Dic43C2418yes—
318C4⋊Dic43C2418yes—
319C4⋊Dic43C2414yes—
320C4⋊Dic43C2418yes—
321C4⋊Dic43C24116yes—
322Dic43⋊C4C24116yes—
323Dic43⋊C4C24116yes—
324Dic43⋊C4C24116yes—
325Dic43⋊C4C2418yes—
326Dic43⋊C4C2418yes—
327Dic43⋊C4C24116yes—
328Dic43⋊C4C2418yes—
329Dic43⋊C4C24116yes—
330Dic43⋊C4C24116yes—
331Dic43⋊C4C2418yes—
332C4×Dic43C2414yes—
333C4×Dic43C2414yes—
334C4×Dic43C2414yes—
335C4×Dic43C24116yes—
336C4×Dic43C2418yes—
337C4×Dic43C24116yes—
338C23×C43—24no—
339C23×C43—24no—
340C23×C43—24no—
341C23×C43C2514yes—
342C23×C43C2511yescharacteristic
343C22×D43—22no—
344C22×D43—22no—
345C22×D43—24no—
346C22×D43—24no—
347C22×D43—24no—
348C22×D432−1+414yes—
349C22×D43C2514yes—
350C22×D43C2512yes—
351Q8×C43—216no—
352Q8×C43—28no—
353Q8×C43—416no—
354D4×C43—28no—
355C2×C4×C43—28no—
356C2×C4×C43—24no—
357C2×C4×C43—24no—
358C2×C4×C43—22no—
359C2×C4×C43—24no—
360C2×C4×C43—216no—
361C2×C4×C43—416no—
362C2×C4×C43H(5,𝔽2)14yes—
363C2×C4×C432−1+414yes—
364C2×C4×C43C2514yes—
365C2×C4×C43C2512yes—
366C2×C4×C43C2518yes—
367C2×C4×C43C2514yes—
368C2×C4×C43C2514yes—
369C2×C4×C43C2512yes—
370C2×C4×C43C2512yes—
371C22⋊D43—216no—
372C22⋊D43—416no—
373C2×Dic43—28no—
374C2×Dic43—22no—
375C2×Dic43—24no—
376C2×Dic43—22no—
377C2×Dic43—22no—
378C2×Dic43—24no—
379C2×Dic43—24no—
380C2×Dic43C2514yes—
381C2×Dic43C2514yes—
382C2×Dic43C2512yes—
383C2×Dic43C2512yes—
384C2×Dic43C2514yes—
385C2×Dic43C2512yes—
386C2×Dic43C2518yes—
387D172—216no—
388D172—28no—
389C4×D43—28no—
390C4×D43—28no—
391C4×D43—28no—
392C4×D43—216no—
393C4×D43—416no—
394C4×D43—416no—
395Dic86—216no—
396Dic86—28no—
397Dic86—416no—
398C2×#3552—431nomaximal, Sylow
399C22×C43—24no—
400C22×C43—24no—
401C22×C43—24no—
402C22×C43—48no—
403C22×C43C2×H(5,𝔽2)12yes—
404C22×C43C2×2−1+412yes—
405C22×C43C2×2−1+412yes—
406C22×C43C2611yescharacteristic
407C2×D43—22no—
408C2×D43—22no—
409C2×D43—28no—
410C2×D43—24no—
411C2×D43—24no—
412C2×D43—24no—
413C2×D43—48no—
414C2×D43C2×2−1+414yes—
415C4×C43—28no—
416C4×C43—24no—
417C4×C43—24no—
418C4×C43—22no—
419C4×C43—24no—
420C4×C43C2×H(5,𝔽2)14yes—
421C4×C43C2×2−1+414yes—
422Dic43—28no—
423Dic43—22no—
424Dic43—24no—
425Dic43—22no—
426Dic43—22no—
427Dic43—24no—
428Dic43—24no—
429#3552—4332no—
430C2×#563—434no—
431C2×#557—431no—
432C2×#556—431no—
433C2×#554—432no—
434C2×#553—432no—
435C2×D4×Q8—432no—
436C2×D4×Q8D4311yescharacteristic, complemented
437C2×#548—432no—
438C2×#547—431no—
439C2×#544—432no—
440C2×#542—432no—
441C2×#541—432no—
442C2×#539—434no—
443C2×#536—432no—
444C22×C4⋊Q8—431no—
445C2×#529—431no—
446C2×#529—431no—
447C2×C43—44no—
448C2×C43#355214yescomplemented
449C2×C43C22×H(5,𝔽2)11yescharacteristic
450C2×C43C22×2−1+411yescharacteristic
451C2×C43C22×2−1+411yescharacteristic
452D43—24no—
453D43—44no—
454C22×#41—432no—
455C23×Q8—432no—
456C23×Q8C2×D4312yes—
457#563—4364no—
458#557—4316no—
459#556—4316no—
460#554—4332no—
461#553—4332no—
462D4×Q8—4332no—
463D4×Q8C2×D43116yescomplemented
464#548—4332no—
465#547—4316no—
466#544—4332no—
467#542—4332no—
468#541—4332no—
469#539—4364no—
470#536—4332no—
471C2×C4⋊Q8—432no—
472C2×C4⋊Q8—432no—
473C2×C4⋊Q8—434no—
474C2×C4⋊Q8—4316no—
475C2×C4⋊Q8—432no—
476C2×C4⋊Q8—432no—
477C2×C4⋊Q8—431no—
478C2×C4⋊Q8C2×D4311yescharacteristic
479C2×C4⋊Q8C2×D4312yes—
480#529—4316no—
481#529—4316no—
482C2×#126—432no—
483C2×#126—434no—
484C2×#126—432no—
485C2×#126—434no—
486C2×#126—434no—
487C2×#125—431no—
488C2×#125—431no—
489C2×#125—434no—
490C2×#125—434no—
491C2×#125—434no—
492C2×#125—432no—
493C2×#124—431no—
494C2×#124—432no—
495C2×#124—431no—
496C2×#124—434no—
497C2×#123—434no—
498C2×#123—434no—
499C2×#123—432no—
500C2×#123—432no—
501C2×#123—434no—
502C2×C22⋊Q8—431no—
503C2×C22⋊Q8—434no—
504C2×C22⋊Q8—434no—
505C2×C22⋊Q8—434no—
506C2×C22⋊Q8—432no—
507C2×C22⋊Q8—434no—
508C2×C22⋊Q8—434no—
509C2×C22⋊Q8—431no—
510C2×C22⋊Q8—432no—
511C2×C22⋊Q8C2×D4314yes—
512C2×C22⋊Q8C2×D4312yes—
513C2×#121—431no—
514C2×#121—432no—
515C2×#121—431no—
516C2×#121—434no—
517C2×C4×Q8—432no—
518C2×C4×Q8—432no—
519C2×C4×Q8—431no—
520C2×C4×Q8—432no—
521C2×C4×Q8C2×D4311yescharacteristic
522C2×C4×D4—432no—
523C2×C4×D4—434no—
524C2×C4×D4—434no—
525C2×C4×D4—431no—
526C2×C4×D4—432no—
527C2×C4×D4C2×D4311yescharacteristic
528C2×C4×D4C2×D4312yes—
529C2×#117—432no—
530C2×#117—432no—
531C2×#117—432no—
532C22×C4⋊C4—432no—
533C22×C4⋊C4—432no—
534C22×C4⋊C4—432no—
535C22×C42—431no—
536C43C2×#355211yescharacteristic, complemented, Sylow
537C2×#41—4316no—
538C2×#41—1728no—
539C22×Q8—48no—
540C22×Q8—4316no—
541C22×Q8—431no—
542C22×Q8—432no—
543C22×Q8—434no—
544C22×Q8—1728no—
545C22×Q8C22×D4312yes—
546C22×Q8C22×D4311yescharacteristic
547C22×Q8C22×D4314yes—
548C22×Q8C22×D43116yes—
549C22×D4—432no—
550C22×D4—434no—
551C22×D4—432no—
552C22×D4—431no—
553C22×D4C22×D4311yescharacteristic
554C23×C4—431no—
555C23×C4—431no—
556C23×C4—432no—
557C23×C4—431no—
558C23×C4—434no—
559C23×C4—434no—
560C23×C4C22×D4312yes—
561C23×C4C22×D4314yes—
562C4⋊Q8—4316no—
563C4⋊Q8—4316no—
564C4⋊Q8—4332no—
565C4⋊Q8—4316no—
566C4⋊Q8—4316no—
567C4⋊Q8—438no—
568C4⋊Q8C22×D4318yes—
569C4⋊Q8C22×D43116yes—
570#126—4316no—
571#126—4332no—
572#126—4316no—
573#126—4332no—
574#126—4332no—
575#125—438no—
576#125—438no—
577#125—4332no—
578#125—4332no—
579#125—4332no—
580#125—4316no—
581#124—438no—
582#124—4316no—
583#124—438no—
584#124—4332no—
585#123—4332no—
586#123—4332no—
587#123—4316no—
588#123—4316no—
589#123—4332no—
590C22⋊Q8—438no—
591C22⋊Q8—4332no—
592C22⋊Q8—4332no—
593C22⋊Q8—4332no—
594C22⋊Q8—4316no—
595C22⋊Q8—4332no—
596C22⋊Q8—438no—
597C22⋊Q8—4316no—
598C22⋊Q8—4332no—
599C22⋊Q8C22×D43132yes—
600C22⋊Q8C22×D43116yes—
601#121—438no—
602#121—4316no—
603#121—438no—
604#121—4332no—
605C4×Q8—4316no—
606C4×Q8—4316no—
607C4×Q8—438no—
608C4×Q8—4316no—
609C4×Q8C22×D4318yes—
610C4×D4—4316no—
611C4×D4—4332no—
612C4×D4—4332no—
613C4×D4—438no—
614C4×D4—4316no—
615C4×D4C22×D4318yes—
616C4×D4C22×D43116yes—
617#117—4316no—
618#117—4316no—
619#117—4316no—
620C2×C4⋊C4—432no—
621C2×C4⋊C4—434no—
622C2×C4⋊C4—434no—
623C2×C4⋊C4—434no—
624C2×C4⋊C4—432no—
625C2×C4⋊C4—431no—
626C2×C4⋊C4—432no—
627C2×C4⋊C4—432no—
628C2×C4⋊C4—432no—
629C2×C4⋊C4—432no—
630C2×C4⋊C4—431no—
631C2×C4⋊C4—432no—
632C2×C4⋊C4—434no—
633C2×C4⋊C4—432no—
634C2×C4⋊C4—434no—
635C2×C4⋊C4—434no—
636C2×C4⋊C4—434no—
637C2×C4⋊C4—432no—
638C2×C4⋊C4—4316no—
639C2×C4⋊C4—4316no—
640C2×C4⋊C4—4316no—
641C2×C4⋊C4C22×D4311yescharacteristic
642C2×C4⋊C4C22×D4312yes—
643C2×C4⋊C4C22×D4312yes—
644C2×C4⋊C4C22×D4314yes—
645C2×C4⋊C4C22×D4311yescharacteristic
646C2×C4⋊C4C22×D4312yes—
647C2×C22⋊C4—432no—
648C2×C22⋊C4—432no—
649C2×C22⋊C4—434no—
650C2×C22⋊C4—432no—
651C2×C22⋊C4—434no—
652C2×C22⋊C4—432no—
653C2×C22⋊C4—432no—
654C2×C22⋊C4—432no—
655C2×C22⋊C4—432no—
656C2×C22⋊C4—432no—
657C2×C22⋊C4—434no—
658C2×C22⋊C4—432no—
659C2×C22⋊C4C22×D4314yes—
660C2×C22⋊C4C22×D4312yes—
661C2×C42—431no—
662C2×C42—431no—
663C2×C42—432no—
664C2×C42—434no—
665C2×C42—434no—
666C2×C42—431no—
667C2×C42—438no—
668C2×C42C22×D4312yes—
669C2×C42C22×D4311yescharacteristic
670C24—431no—
671C24—432no—
672C24C23×D4312yes—
673#41—17232no—
674C2×Q8—24no—
675C2×Q8—28no—
676C2×Q8—48no—
677C2×Q8—432no—
678C2×Q8—434no—
679C2×Q8—438no—
680C2×Q8—4316no—
681C2×Q8—868no—
682C2×Q8—864no—
683C2×Q8—1728no—
684C2×Q8—17232no—
685C2×Q8C23×D4318yes—
686C2×Q8C23×D4314yes—
687C2×Q8C23×D43116yes—
688C2×D4—24no—
689C2×D4—438no—
690C2×D4—4316no—
691C2×D4—438no—
692C2×D4—434no—
693C2×D4—868no—
694C2×D4—868no—
695C2×D4—864no—
696C2×D4—1728no—
697C2×D4C23×D4314yes—
698C22×C4—28no—
699C22×C4—48no—
700C22×C4—432no—
701C22×C4—432no—
702C22×C4—431no—
703C22×C4—431no—
704C22×C4—432no—
705C22×C4—431no—
706C22×C4—434no—
707C22×C4—434no—
708C22×C4—434no—
709C22×C4—434no—
710C22×C4—438no—
711C22×C4—4316no—
712C22×C4—4316no—
713C22×C4—864no—
714C22×C4—864no—
715C22×C4—864no—
716C22×C4—868no—
717C22×C4—1728no—
718C22×C4—1728no—
719C22×C4C23×D4318yes—
720C22×C4C23×D4312yes—
721C22×C4C23×D4311yescharacteristic
722C22×C4C23×D4314yes—
723C22×C4C23×D4312yes—
724C22×C4C23×D4312yes—
725C22×C4C23×D43116yes—
726C22×C4C23×D4311yescharacteristic
727C22×C4C23×D4311yescharacteristic
728C4⋊C4—438no—
729C4⋊C4—4316no—
730C4⋊C4—4316no—
731C4⋊C4—4316no—
732C4⋊C4—438no—
733C4⋊C4—434no—
734C4⋊C4—438no—
735C4⋊C4—438no—
736C4⋊C4—438no—
737C4⋊C4—438no—
738C4⋊C4—434no—
739C4⋊C4—438no—
740C4⋊C4—4316no—
741C4⋊C4—438no—
742C4⋊C4—4316no—
743C4⋊C4—4316no—
744C4⋊C4—4316no—
745C4⋊C4—438no—
746C4⋊C4C23×D4314yes—
747C4⋊C4C23×D4318yes—
748C4⋊C4C23×D4318yes—
749C4⋊C4C23×D43116yes—
750C4⋊C4C23×D4314yes—
751C4⋊C4C23×D4318yes—
752C22⋊C4—438no—
753C22⋊C4—438no—
754C22⋊C4—4316no—
755C22⋊C4—438no—
756C22⋊C4—4316no—
757C22⋊C4—438no—
758C22⋊C4—438no—
759C22⋊C4—438no—
760C22⋊C4—438no—
761C22⋊C4—438no—
762C22⋊C4—4316no—
763C22⋊C4—438no—
764C22⋊C4C23×D43116yes—
765C22⋊C4C23×D4318yes—
766C42—434no—
767C42—434no—
768C42—434no—
769C42—438no—
770C42—4316no—
771C42—4316no—
772C42C23×D4314yes—
773C42C23×D4318yes—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—434no—
778C23—432no—
779C23—434no—
780C23—862no—
781C23—862no—
782C23—864no—
783C23—864no—
784C23—864no—
785C23C24×D4314yes—
786C23C24×D4311yescharacteristic
787Q8—28no—
788Q8—216no—
789Q8—416no—
790Q8—8616no—
791Q8—868no—
792Q8—17216no—
793D4—28no—
794D4—8616no—
795D4—8616no—
796D4—868no—
797D4—17216no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—28no—
801C2×C4—22no—
802C2×C4—24no—
803C2×C4—216no—
804C2×C4—416no—
805C2×C4—434no—
806C2×C4—434no—
807C2×C4—432no—
808C2×C4—432no—
809C2×C4—434no—
810C2×C4—432no—
811C2×C4—438no—
812C2×C4—868no—
813C2×C4—862no—
814C2×C4—868no—
815C2×C4—862no—
816C2×C4—864no—
817C2×C4—862no—
818C2×C4—864no—
819C2×C4—864no—
820C2×C4—868no—
821C2×C4—868no—
822C2×C4—8616no—
823C2×C4—17216no—
824C2×C4—17216no—
825C2×C4#1306337014yes—
826C2×C4#1306337314yes—
827C2×C4C24×D4314yes—
828C2×C4C24×D4312yes—
829C2×C4C24×D4318yes—
830C2×C4C24×D4314yes—
831C2×C4C24×D4314yes—
832C2×C4C24×D4312yes—
833C2×C4C24×D4312yes—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—48no—
838C22—434no—
839C22—862no—
840C22—862no—
841C22—868no—
842C22—864no—
843C22—864no—
844C22—864no—
845C22—1728no—
846C22C2×#1306337012yes—
847C222−1+4×D4312yes—
848C22C2×#1306337312yes—
849C22C25×D4311yescharacteristic
850C4—24no—
851C4—24no—
852C4—28no—
853C4—22no—
854C4—24no—
855C4—862no—
856C4—868no—
857C4—862no—
858C4—864no—
859C4—862no—
860C4—864no—
861C4—864no—
862C4C2×#1306337014yes—
863C4C2×#1306337314yes—
864C2—44no—
865C2—864no—
866C2—1724no—
867C2#1914903714yesdirect product factor
868C2C22×#1306337011yescharacteristic
869C2C2×2−1+4×D4311yescharacteristic
870C2C22×#1306337311yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×D4×Q8×C43C2
socleC23×C43C25
hypercenterC2×D4×Q8D43
hypocenterC43C2×#3552
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #19149037C2direct (N × H)
2. C2×#14583650C2semidirect
3. C2×#14583627C2semidirect
4. C2×#14583623C2semidirect
5. C2×#14583610C2semidirect
6. C2×#14583599C2semidirect
7. C2×Q8×C22⋊D43C2semidirect
8. C2×#14583559C2semidirect
9. C2×#14583554C2semidirect
10. C2×#14583526C2semidirect
11. C2×#14583514C2semidirect
12. C2×#14583509C2semidirect
13. C2×#14583495C2semidirect
14. C2×#14583473C2semidirect
15. C2×C4⋊Q8×D43C2semidirect
16. C2×#14583436C2semidirect
17. C2×#14583431C2semidirect
18. C2×D4×Q8×C43C2semidirect
21. #14583650C22semidirect
22. #14583627C22semidirect
23. #14583623C22semidirect
24. #14583610C22semidirect
25. #14583599C22semidirect
26. Q8×C22⋊D43C22semidirect
27. #14583559C22semidirect
28. #14583554C22semidirect
29. #14583526C22semidirect
30. #14583514C22semidirect
31. #14583509C22semidirect
32. #14583495C22semidirect
33. #14583473C22semidirect
40. C4⋊Q8×D43C22semidirect
41. #14583436C22semidirect
42. #14583431C22semidirect
93. D4×Q8×C43C22semidirect
436. C2×D4×Q8D43semidirect
448. C2×C43#3552semidirect
463. D4×Q8C2×D43semidirect
536. C43C2×#3552semidirect
867. C2#19149037direct (N × H)

Maximal subgroups

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

subgroupindex
#191490372
C2×#145836502
C2×#145836272
C2×#145836232
C2×#145836102
C2×#145835992
C2×Q8×C22⋊D432
C2×#145835592
C2×#145835542
C2×#145835262
C2×#145835142
C2×#145835092
C2×#145834952
C2×#145834732
C2×C4⋊Q8×D432
C2×#145834362
C2×#145834312
C2×D4×Q8×C432
C2×#355243