Finite Group Databasebeta

← C2×#19148498 #26004966

Subgroups — C2×#19148498 #26004966

Order 11008.

7758 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148498C2132yesmaximal, direct product factor
2C2×#14583617C212yesmaximal, complemented
3C2×#14583612C212yesmaximal, complemented
4C2×#14583604C212yesmaximal, complemented
5C2×#14583598C214yesmaximal, complemented
6C2×#14583558C214yesmaximal, complemented
7C2×#14583550C212yesmaximal, complemented
8C2×#14583521C212yesmaximal, complemented
9C2×#14583514C212yesmaximal, complemented
10C2×#14583480C211yesmaximal, characteristic, complemented
11C2×#14583477C211yesmaximal, characteristic, complemented
12C2×#14583453C212yesmaximal, complemented
13C2×#14583446C212yesmaximal, complemented
14C2×#14583445C211yesmaximal, characteristic, complemented
15C22×#13063324C211yesmaximal, characteristic, complemented
16C2×#14583379C211yesmaximal, characteristic, complemented
17C2×#14583367C211yesmaximal, characteristic, complemented
18C2×C43×#520C211yesmaximal, characteristic, complemented
19C22×#10621898C2211yescharacteristic
20C22×#10621898C2211yescharacteristic
21C22×#10621898C2214yes—
22C23×Dic86C2212yes—
23#14583617C22132yescomplemented
24#14583612C22132yescomplemented
25#14583604C22132yescomplemented
26#14583598C22164yescomplemented
27#14583558C22164yescomplemented
28#14583550C22132yescomplemented
29#14583521C22132yescomplemented
30#14583514C22132yescomplemented
31#14583480C22116yescomplemented
32#14583477C22116yescomplemented
33#14583453C22132yescomplemented
34#14583446C22132yescomplemented
35#14583445C22116yescomplemented
36C2×#13063324C2212yes—
37C2×#13063324C2212yes—
38C2×#13063324C2212yes—
39C2×#13063324C2212yes—
40C2×#13063324C22116yescomplemented
41C2×#13063323C2211yescharacteristic
42C2×#13063321C2211yescharacteristic
43C2×#13063319C2214yes—
44C2×#13063318C2214yes—
45C2×#13063315C2214yes—
46C2×#13063314C2211yescharacteristic
47C2×#13063313C2214yes—
48C2×#13063312C2211yescharacteristic
49C2×#13063311C2214yes—
50C2×#13063311C2214yes—
51C2×#13063310C2214yes—
52C2×#13063308C2214yes—
53C2×#13063305C2212yes—
54C2×#13063305C2212yes—
55C2×#13063304C2214yes—
56C2×#13063304C2212yes—
57C2×#13063303C2214yes—
58C2×#13063303C2214yes—
59C2×#13063301C2212yes—
60C2×#13063300C2212yes—
61C2×#13063300C2212yes—
62C2×#13063299C2212yes—
63C2×#13063299C2214yes—
64C2×#13063298C2214yes—
65C2×#13063297C2212yes—
66C2×#13063297C2214yes—
67C2×#13063297C2212yes—
68C2×#13063296C2212yes—
69#14583379C22116yescomplemented
70#14583367C22116yescomplemented
71C2×C4×Dic86C2212yes—
72C2×C4×Dic86C2214yes—
73C2×#13063290C2211yescharacteristic
74C2×#13063290C2211yescharacteristic
75C2×C4×D172C2212yes—
76C2×#13063287C2211yescharacteristic
77C2×#13063287C2211yescharacteristic
78C2×C4×C22⋊D43C2212yes—
79C2×C4×C22⋊D43C2214yes—
80C2×C4×C22⋊D43C2212yes—
81C2×(C22⋊D43)⋊C4C2214yes—
82C2×(C22⋊D43)⋊C4C2212yes—
83C2×(C22⋊D43)⋊C4C2212yes—
84C2×#13063283C2212yes—
85C2×#13063282C2214yes—
86C2×#13063282C2212yes—
87C22×C4⋊Dic43C2211yescharacteristic
88C22×Dic43⋊C4C2212yes—
89C2×C4⋊C4×D43C2212yes—
90C22×C4×Dic43C2211yescharacteristic
91C2×C42×D43C2212yes—
92C22×#41×C43C2211yescharacteristic
93C43×#520C22116yescomplemented
94C2×C4×Q8×C43C2212yes—
95C2×C4×D4×C43C2214yes—
96C2×C4×D4×C43C2212yes—
97C2×#117×C43C2211yescharacteristic
98C2×#117×C43C2212yes—
99C22×C4⋊C4×C43C2212yes—
100C22×C4⋊C4×C43C2211yescharacteristic
101C2×#10621898—28no—
102C2×#10621898—28no—
103C2×#10621898—416no—
104C2×#10621898C2318yes—
105C2×#10621898C2318yes—
106C2×#10621898C23132yes—
107C22×Dic86—48no—
108C22×Dic86C2311yescharacteristic
109C22×Dic86C2311yescharacteristic
110C22×Dic86C2314yes—
111C22×Dic86C23116yes—
112C22×Dic86C2314yes—
113C22×D172C2311yescharacteristic
114C22×D172C2311yescharacteristic
115C22×D172C2314yes—
116C22×C22⋊D43C2312yes—
117C22×C22⋊D43C2312yes—
118C22×C22⋊D43C2312yes—
119C22×C22⋊D43C2312yes—
120C22×C22⋊D43C2314yes—
121C23×Dic43C2311yescharacteristic
122C23×Dic43C2311yescharacteristic
123C23×Dic43C2312yes—
124C22×C4×D43C2312yes—
125C22×C4×D43C2312yes—
126C22×C4×D43C2312yes—
127C22×C4×D43C2312yes—
128C22×C4×D43C2314yes—
129#13063324C23116yes—
130#13063324C23116yes—
131#13063324C23116yes—
132#13063324C23116yes—
133#13063323C2318yes—
134#13063321C2318yes—
135#13063319C23132yes—
136#13063318C23132yes—
137#13063315C23132yes—
138#13063314C2318yes—
139#13063313C23132yes—
140#13063312C2318yes—
141#13063311C23132yes—
142#13063311C23132yes—
143#13063310C23132yes—
144#13063308C23132yes—
145#13063305C23116yes—
146#13063305C23116yes—
147#13063304C23132yes—
148#13063304C23116yes—
149#13063303C23132yes—
150#13063303C23132yes—
151#13063301C23116yes—
152#13063300C23116yes—
153#13063300C23116yes—
154#13063299C23132yes—
155#13063299C23116yes—
156#13063298C23132yes—
157#13063297C23116yes—
158#13063297C23132yes—
159#13063297C23116yes—
160#13063296C23116yes—
161C4×Dic86C23132yes—
162C4×Dic86C23116yes—
163#13063290C2318yes—
164#13063290C2318yes—
165C4×D172C23116yes—
166#13063287C2318yes—
167#13063287C2318yes—
168C4×C22⋊D43C23132yes—
169C4×C22⋊D43C23116yes—
170C4×C22⋊D43C23116yes—
171(C22⋊D43)⋊C4C23116yes—
172(C22⋊D43)⋊C4C23132yes—
173(C22⋊D43)⋊C4C23116yes—
174#13063283C23116yes—
175#13063282C23132yes—
176#13063282C23116yes—
177C2×C4⋊Dic43C2312yes—
178C2×C4⋊Dic43C2312yes—
179C2×C4⋊Dic43C2318yes—
180C2×C4⋊Dic43C2314yes—
181C2×Dic43⋊C4C23116yes—
182C2×Dic43⋊C4C2314yes—
183C2×Dic43⋊C4C2314yes—
184C2×Dic43⋊C4C2314yes—
185C2×Dic43⋊C4C2312yes—
186C2×Dic43⋊C4C2312yes—
187C2×Dic43⋊C4C2312yes—
188C2×Dic43⋊C4C2312yes—
189C2×Dic43⋊C4C2314yes—
190C4⋊C4×D43C23116yes—
191C2×C22⋊Dic43C2314yes—
192C2×C22⋊Dic43C2312yes—
193C2×C22⋊Dic43C2312yes—
194C2×(C2×D43)⋊C4C2312yes—
195C2×(C2×D43)⋊C4C2312yes—
196C2×(C2×D43)⋊C4C2314yes—
197C2×(C2×D43)⋊C4C2314yes—
198C2×(C2×D43)⋊C4C2314yes—
199C2×(C2×D43)⋊C4C2312yes—
200C2×(C2×D43)⋊C4C2312yes—
201C2×(C2×D43)⋊C4C2314yes—
202C2×C4×Dic43C2311yescharacteristic
203C2×C4×Dic43C2312yes—
204C2×C4×Dic43C2312yes—
205C2×C4×Dic43C2311yescharacteristic
206C2×C4×Dic43C2311yescharacteristic
207C2×C4×Dic43C2311yescharacteristic
208C2×C4×Dic43C2318yes—
209C2×C4×Dic43C2314yes—
210C42×D43C23116yes—
211C2×#41×C43—28no—
212C2×#41×C43C2318yes—
213C22×Q8×C43C2311yescharacteristic
214C22×D4×C43C2311yescharacteristic
215C22×D4×C43C2312yes—
216C23×C4×C43C2312yes—
217C23×C4×C43C2312yes—
218C23×C4×C43C2314yes—
219C23×C4×C43C2311yescharacteristic
220C4×Q8×C43C23116yes—
221C4×D4×C43C23132yes—
222C4×D4×C43C23116yes—
223#117×C43C23116yes—
224#117×C43C2318yes—
225C2×C4⋊C4×C43C2311yescharacteristic
226C2×C4⋊C4×C43C2312yes—
227C2×C4⋊C4×C43C2312yes—
228C2×C4⋊C4×C43C2314yes—
229C2×C4⋊C4×C43C23116yes—
230C2×C4⋊C4×C43C2318yes—
231C2×C4⋊C4×C43C2311yescharacteristic
232C2×C22⋊C4×C43C2312yes—
233C2×C22⋊C4×C43C2314yes—
234C2×C42×C43C2312yes—
235C2×C42×C43C2314yes—
236C24×C43C2412yes—
237C24×C43C2411yescharacteristic
238C23×D43C2412yes—
239C23×D43C2412yes—
240#41×C43—232no—
241C2×Q8×C43—24no—
242C2×Q8×C43C2414yes—
243C2×D4×C43—24no—
244C2×D4×C43—28no—
245C2×D4×C43C2414yes—
246C2×D4×C43C2418yes—
247C22×C4×C43—28no—
248C22×C4×C43—44no—
249C22×C4×C43—48no—
250C22×C4×C43#4118yescomplemented
251C22×C4×C43C2412yes—
252C22×C4×C43C2412yes—
253C22×C4×C43C2412yes—
254C22×C4×C43C2414yes—
255C22×C4×C43C2418yes—
256C22×C4×C43C2418yes—
257C22×C4×C43C24116yes—
258C22×C4×C43C2411yescharacteristic
259C22×C4×C43C2411yescharacteristic
260C22×C4×C43C2414yes—
261C2×C22⋊D43—28no—
262C2×C22⋊D43—28no—
263C2×C22⋊D43—28no—
264C2×C22⋊D43—28no—
265C2×C22⋊D43—48no—
266C2×C22⋊D43C2418yes—
267C2×C22⋊D43C2418yes—
268C2×C22⋊D43C2418yes—
269C2×C22⋊D43C2418yes—
270C2×C22⋊D43C24116yes—
271C22×Dic43—24no—
272C22×Dic43—24no—
273C22×Dic43—44no—
274C22×Dic43C2411yescharacteristic
275C22×Dic43C2411yescharacteristic
276C22×Dic43C2412yes—
277C22×Dic43C2412yes—
278C22×Dic43C2414yes—
279C22×Dic43C2414yes—
280C22×Dic43C2414yes—
281C22×Dic43C2418yes—
282C22×Dic43C2411yescharacteristic
283C22×Dic43C2411yescharacteristic
284#10621898—232no—
285#10621898—232no—
286#10621898—464no—
287C2×D172—24no—
288C2×D172—24no—
289C2×D172—48no—
290C2×D172C2414yes—
291C2×D172C2414yes—
292C2×D172C24116yes—
293C2×C4×D43—28no—
294C2×C4×D43—28no—
295C2×C4×D43—28no—
296C2×C4×D43—28no—
297C2×C4×D43—48no—
298C2×C4×D43C2418yes—
299C2×C4×D43C2418yes—
300C2×C4×D43C2418yes—
301C2×C4×D43C2418yes—
302C2×C4×D43C24116yes—
303C2×Dic86—24no—
304C2×Dic86—24no—
305C2×Dic86—216no—
306C2×Dic86—432no—
307C2×Dic86—48no—
308C2×Dic86C2414yes—
309C2×Dic86C2414yes—
310C2×Dic86C24116yes—
311C2×Dic86C24116yes—
312C4⋊C4×C43C2414yes—
313C4⋊C4×C43C2418yes—
314C4⋊C4×C43C2418yes—
315C4⋊C4×C43C24116yes—
316C4⋊C4×C43C2414yes—
317C22⋊C4×C43C2418yes—
318C22⋊C4×C43C24116yes—
319C42×C43C2418yes—
320C42×C43C24116yes—
321C22⋊Dic43C24116yes—
322C22⋊Dic43C2418yes—
323C22⋊Dic43C2418yes—
324(C2×D43)⋊C4C2418yes—
325(C2×D43)⋊C4C2418yes—
326(C2×D43)⋊C4C24116yes—
327(C2×D43)⋊C4C24116yes—
328(C2×D43)⋊C4C24116yes—
329(C2×D43)⋊C4C2418yes—
330(C2×D43)⋊C4C2418yes—
331(C2×D43)⋊C4C24116yes—
332C4⋊Dic43C2418yes—
333C4⋊Dic43C2418yes—
334C4⋊Dic43C24116yes—
335Dic43⋊C4C24116yes—
336Dic43⋊C4C24116yes—
337Dic43⋊C4C24116yes—
338Dic43⋊C4C2418yes—
339Dic43⋊C4C2418yes—
340Dic43⋊C4C2418yes—
341Dic43⋊C4C2418yes—
342Dic43⋊C4C24116yes—
343C4×Dic43C2414yes—
344C4×Dic43C2418yes—
345C4×Dic43C2418yes—
346C4×Dic43C2414yes—
347C4×Dic43C2414yes—
348C4×Dic43C2414yes—
349C4×Dic43C24116yes—
350C23×C43—22no—
351C23×C43—22no—
352C23×C43—24no—
353C23×C43—24no—
354C23×C43—24no—
355C23×C43C2×#4114yes—
356C23×C43C2514yes—
357C23×C43C2512yes—
358C23×C43C2511yescharacteristic
359C22×D43—24no—
360C22×D43—24no—
361C22×D43—24no—
362C22×D43—24no—
363C22×D43—24no—
364C22×D43—24no—
365C22×D43C2514yes—
366C22×D43C2514yes—
367Q8×C43—28no—
368D4×C43—216no—
369D4×C43—28no—
370C2×C4×C43—24no—
371C2×C4×C43—28no—
372C2×C4×C43—24no—
373C2×C4×C43—24no—
374C2×C4×C43—216no—
375C2×C4×C43—48no—
376C2×C4×C43—416no—
377C2×C4×C43C2×#4114yes—
378C2×C4×C43C2×#4114yes—
379C2×C4×C43C2×#41116yescomplemented
380C2×C4×C43C2514yes—
381C2×C4×C43C2514yes—
382C2×C4×C43C2514yes—
383C2×C4×C43C2518yes—
384C2×C4×C43C2512yes—
385C2×C4×C43C2512yes—
386C22⋊D43—216no—
387C22⋊D43—216no—
388C22⋊D43—216no—
389C22⋊D43—216no—
390C22⋊D43—416no—
391C2×Dic43—24no—
392C2×Dic43—24no—
393C2×Dic43—28no—
394C2×Dic43—22no—
395C2×Dic43—22no—
396C2×Dic43—28no—
397C2×Dic43—28no—
398C2×Dic43—48no—
399C2×Dic43H(5,𝔽2)14yes—
400C2×Dic432−1+414yes—
401C2×Dic43C2512yes—
402C2×Dic43C2514yes—
403C2×Dic43C2514yes—
404C2×Dic43C2512yes—
405C2×Dic43C2518yes—
406C2×Dic43C2512yes—
407C2×Dic43C2512yes—
408D172—28no—
409D172—28no—
410D172—416no—
411C4×D43—216no—
412C4×D43—216no—
413C4×D43—216no—
414C4×D43—216no—
415C4×D43—416no—
416Dic86—28no—
417Dic86—28no—
418Dic86—232no—
419Dic86—416no—
420C2×#3511—431nomaximal, Sylow
421C22×C43—22no—
422C22×C43—22no—
423C22×C43—28no—
424C22×C43—24no—
425C22×C43—24no—
426C22×C43—24no—
427C22×C43—48no—
428C22×C43C22×#4114yes—
429C22×C43C22×#4112yes—
430C22×C43C2×H(5,𝔽2)12yes—
431C22×C43C2×2−1+412yes—
432C22×C43C2611yescharacteristic
433C2×D43—24no—
434C2×D43—24no—
435C2×D43—24no—
436C2×D43—24no—
437C2×D43—24no—
438C2×D43—24no—
439C2×D43—48no—
440C2×D43—48no—
441C4×C43—24no—
442C4×C43—28no—
443C4×C43—24no—
444C4×C43—24no—
445C4×C43C22×#4114yes—
446C4×C43C22×#4114yes—
447Dic43—24no—
448Dic43—24no—
449Dic43—28no—
450Dic43—22no—
451Dic43—22no—
452Dic43C2×H(5,𝔽2)14yes—
453Dic43C2×2−1+414yes—
454#3511—4332no—
455C2×#556—432no—
456C2×#555—432no—
457C2×#554—432no—
458C2×#553—434no—
459C2×#548—434no—
460C2×#547—432no—
461C2×#542—432no—
462C2×#542—432no—
463C2×#537—431no—
464C2×#537—431no—
465C2×#533—432no—
466C2×#532—431no—
467C2×#532—432no—
468C22×C4⋊Q8—431no—
469C2×#520—431no—
470C2×#520D4311yescharacteristic, complemented
471C2×C4×#41—431no—
472C2×C43—24no—
473C2×C43—44no—
474C2×C43#351114yescomplemented
475C2×C43C23×#4111yescharacteristic
476C2×C43C22×H(5,𝔽2)11yescharacteristic
477C2×C43C22×2−1+411yescharacteristic
478D43—44no—
479D43—44no—
480C22×#41—431no—
481C22×#41—431no—
482C22×#41—434no—
483C22×#41C2×D4311yescharacteristic
484C23×Q8—432no—
485#556—4332no—
486#555—4332no—
487#554—4332no—
488#553—4364no—
489#548—4364no—
490#547—4332no—
491#542—4332no—
492#542—4332no—
493#537—4316no—
494#537—4316no—
495#533—4332no—
496#532—4316no—
497#532—4332no—
498C2×C4⋊Q8—431no—
499C2×C4⋊Q8—432no—
500C2×C4⋊Q8—432no—
501C2×C4⋊Q8—432no—
502C2×C4⋊Q8—432no—
503C2×C4⋊Q8—4316no—
504C2×#127—431no—
505C2×#126—434no—
506C2×#126—434no—
507C2×#125—434no—
508C2×#124—431no—
509C2×#124—431no—
510C2×#124—434no—
511C2×#124—434no—
512C2×#124—434no—
513C2×#123—434no—
514C2×#123—434no—
515C2×C22⋊Q8—432no—
516C2×C22⋊Q8—432no—
517C2×C22⋊Q8—434no—
518C2×C22⋊Q8—434no—
519C2×C22⋊Q8—434no—
520C2×C22⋊Q8—432no—
521C2×C22⋊Q8—432no—
522C2×#121—432no—
523C2×#121—432no—
524C2×#121—432no—
525C2×#121—434no—
526C2×#121—432no—
527C2×#121—434no—
528C2×#121—432no—
529C2×#121—432no—
530C2×#121—434no—
531#520—4316no—
532#520C2×D43116yescomplemented
533C4×#41—4316no—
534C2×C4×Q8—431no—
535C2×C4×Q8—431no—
536C2×C4×Q8—432no—
537C2×C4×Q8—434no—
538C2×C4×Q8C2×D4312yes—
539C2×C4×D4—432no—
540C2×C4×D4—434no—
541C2×C4×D4—432no—
542C2×C4×D4—431no—
543C2×C4×D4—431no—
544C2×C4×D4—432no—
545C2×C4×D4—432no—
546C2×C4×D4—434no—
547C2×C4×D4—432no—
548C2×C4×D4C2×D4312yes—
549C2×C4×D4C2×D4314yes—
550C2×#117—432no—
551C2×#117—432no—
552C2×#117—434no—
553C2×#117C2×D4311yescharacteristic
554C2×#117C2×D4312yes—
555C22×C4⋊C4—432no—
556C22×C4⋊C4—431no—
557C22×C4⋊C4—432no—
558C22×C4⋊C4C2×D4311yescharacteristic
559C22×C4⋊C4C2×D4312yes—
560C22×C42—431no—
561C22×C42—432no—
562C43C2×#351111yescharacteristic, complemented, Sylow
563C2×#41—28no—
564C2×#41—438no—
565C2×#41—438no—
566C2×#41—4332no—
567C2×#41—868no—
568C2×#41—868no—
569C2×#41—17216no—
570C2×#41C22×D4318yes—
571C22×Q8—431no—
572C22×Q8—431no—
573C22×Q8—434no—
574C22×Q8—434no—
575C22×Q8—4316no—
576C22×Q8—1728no—
577C22×Q8C22×D4311yescharacteristic
578C22×D4—432no—
579C22×D4—432no—
580C22×D4—432no—
581C22×D4—432no—
582C22×D4—434no—
583C22×D4—431no—
584C22×D4—431no—
585C22×D4—434no—
586C22×D4C22×D4312yes—
587C22×D4C22×D4311yescharacteristic
588C23×C4—431no—
589C23×C4—431no—
590C23×C4—432no—
591C23×C4—432no—
592C23×C4—432no—
593C23×C4—432no—
594C23×C4—432no—
595C23×C4—434no—
596C23×C4C22×D4312yes—
597C23×C4C22×D4312yes—
598C23×C4C22×D4314yes—
599C23×C4C22×D4311yescharacteristic
600C4⋊Q8—438no—
601C4⋊Q8—4316no—
602C4⋊Q8—4316no—
603C4⋊Q8—4316no—
604C4⋊Q8—4316no—
605#127—438no—
606#126—4332no—
607#126—4332no—
608#125—4332no—
609#124—438no—
610#124—438no—
611#124—4332no—
612#124—4332no—
613#124—4332no—
614#123—4332no—
615#123—4332no—
616C22⋊Q8—4316no—
617C22⋊Q8—4316no—
618C22⋊Q8—4332no—
619C22⋊Q8—4316no—
620C22⋊Q8—4332no—
621C22⋊Q8—4316no—
622C22⋊Q8—4332no—
623#121—4316no—
624#121—4316no—
625#121—4316no—
626#121—4332no—
627#121—4316no—
628#121—4332no—
629#121—4316no—
630#121—4316no—
631#121—4332no—
632C4×Q8—438no—
633C4×Q8—438no—
634C4×Q8—4316no—
635C4×Q8—4332no—
636C4×Q8C22×D43116yes—
637C4×D4—4316no—
638C4×D4—4332no—
639C4×D4—4316no—
640C4×D4—438no—
641C4×D4—438no—
642C4×D4—4316no—
643C4×D4—4316no—
644C4×D4—4332no—
645C4×D4—4316no—
646C4×D4C22×D43116yes—
647C4×D4C22×D43132yes—
648#117—4316no—
649#117—4316no—
650#117—4332no—
651#117C22×D4318yes—
652#117C22×D43116yes—
653C2×C4⋊C4—432no—
654C2×C4⋊C4—434no—
655C2×C4⋊C4—432no—
656C2×C4⋊C4—434no—
657C2×C4⋊C4—438no—
658C2×C4⋊C4—434no—
659C2×C4⋊C4—4316no—
660C2×C4⋊C4—432no—
661C2×C4⋊C4—432no—
662C2×C4⋊C4—432no—
663C2×C4⋊C4—432no—
664C2×C4⋊C4—434no—
665C2×C4⋊C4—434no—
666C2×C4⋊C4—4316no—
667C2×C4⋊C4C22×D4311yescharacteristic
668C2×C4⋊C4C22×D4312yes—
669C2×C4⋊C4C22×D4312yes—
670C2×C4⋊C4C22×D4314yes—
671C2×C4⋊C4C22×D4318yes—
672C2×C4⋊C4C22×D43116yes—
673C2×C4⋊C4C22×D4311yescharacteristic
674C2×C22⋊C4—434no—
675C2×C22⋊C4—432no—
676C2×C22⋊C4—432no—
677C2×C22⋊C4—434no—
678C2×C22⋊C4—432no—
679C2×C22⋊C4—432no—
680C2×C22⋊C4—434no—
681C2×C22⋊C4—434no—
682C2×C22⋊C4—434no—
683C2×C22⋊C4—432no—
684C2×C22⋊C4—432no—
685C2×C22⋊C4C22×D4312yes—
686C2×C22⋊C4C22×D4314yes—
687C2×C42—434no—
688C2×C42—431no—
689C2×C42—432no—
690C2×C42—431no—
691C2×C42—431no—
692C2×C42—432no—
693C2×C42—438no—
694C2×C42—431no—
695C2×C42—4316no—
696C2×C42C22×D4312yes—
697C2×C42C22×D4314yes—
698C24—432no—
699C24—432no—
700C24C23×D4312yes—
701C24C23×D4311yescharacteristic
702#41—232no—
703#41—8632no—
704#41—8632no—
705#41—17264no—
706C2×Q8—24no—
707C2×Q8—434no—
708C2×Q8—434no—
709C2×Q8—4316no—
710C2×Q8—4316no—
711C2×Q8—8616no—
712C2×Q8—864no—
713C2×Q8—864no—
714C2×Q8—1728no—
715C2×Q8—17232no—
716C2×Q8C23×D4314yes—
717C2×D4—28no—
718C2×D4—24no—
719C2×D4—438no—
720C2×D4—438no—
721C2×D4—438no—
722C2×D4—438no—
723C2×D4—4316no—
724C2×D4—434no—
725C2×D4—434no—
726C2×D4—4316no—
727C2×D4—868no—
728C2×D4—868no—
729C2×D4—868no—
730C2×D4—868no—
731C2×D4—864no—
732C2×D4—864no—
733C2×D4—1728no—
734C2×D4—1728no—
735C2×D4C23×D4318yes—
736C2×D4C23×D4314yes—
737C22×C4—28no—
738C22×C4—44no—
739C22×C4—48no—
740C22×C4—431no—
741C22×C4—431no—
742C22×C4—434no—
743C22×C4—434no—
744C22×C4—431no—
745C22×C4—431no—
746C22×C4—432no—
747C22×C4—432no—
748C22×C4—434no—
749C22×C4—438no—
750C22×C4—438no—
751C22×C4—438no—
752C22×C4—438no—
753C22×C4—438no—
754C22×C4—4316no—
755C22×C4—868no—
756C22×C4—868no—
757C22×C4—864no—
758C22×C4—864no—
759C22×C4—868no—
760C22×C4—868no—
761C22×C4—1728no—
762C22×C4—1724no—
763C22×C4#1062189818yescomplemented
764C22×C4C23×D4318yes—
765C22×C4C23×D4312yes—
766C22×C4C23×D4312yes—
767C22×C4C23×D4312yes—
768C22×C4C23×D4314yes—
769C22×C4C23×D4318yes—
770C22×C4C23×D43116yes—
771C22×C4C23×D4311yescharacteristic
772C22×C4C23×D4311yescharacteristic
773C22×C4C23×D4314yes—
774C4⋊C4—438no—
775C4⋊C4—4316no—
776C4⋊C4—438no—
777C4⋊C4—4316no—
778C4⋊C4—4316no—
779C4⋊C4—438no—
780C4⋊C4—438no—
781C4⋊C4—438no—
782C4⋊C4—438no—
783C4⋊C4—4316no—
784C4⋊C4—4316no—
785C4⋊C4C23×D4314yes—
786C4⋊C4C23×D4318yes—
787C4⋊C4C23×D4318yes—
788C4⋊C4C23×D43116yes—
789C4⋊C4C23×D4314yes—
790C22⋊C4—4316no—
791C22⋊C4—438no—
792C22⋊C4—438no—
793C22⋊C4—4316no—
794C22⋊C4—438no—
795C22⋊C4—438no—
796C22⋊C4—4316no—
797C22⋊C4—4316no—
798C22⋊C4—4316no—
799C22⋊C4—438no—
800C22⋊C4—438no—
801C22⋊C4C23×D4318yes—
802C22⋊C4C23×D43116yes—
803C42—434no—
804C42—434no—
805C42—438no—
806C42—434no—
807C42—434no—
808C42—438no—
809C42—4316no—
810C42C23×D4318yes—
811C42C23×D43116yes—
812C23—22no—
813C23—22no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—434no—
818C23—434no—
819C23—864no—
820C23—864no—
821C23—864no—
822C23—864no—
823C23—864no—
824C23—864no—
825C23C2×#1062189814yes—
826C23C24×D4314yes—
827C23C24×D4312yes—
828C23C24×D4311yescharacteristic
829Q8—28no—
830Q8—8632no—
831Q8—868no—
832Q8—868no—
833Q8—17216no—
834D4—216no—
835D4—28no—
836D4—8616no—
837D4—8616no—
838D4—8616no—
839D4—8616no—
840D4—868no—
841D4—868no—
842D4—17216no—
843D4—17216no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—28no—
847C2×C4—24no—
848C2×C4—216no—
849C2×C4—48no—
850C2×C4—416no—
851C2×C4—434no—
852C2×C4—434no—
853C2×C4—432no—
854C2×C4—432no—
855C2×C4—432no—
856C2×C4—432no—
857C2×C4—434no—
858C2×C4—434no—
859C2×C4—438no—
860C2×C4—8616no—
861C2×C4—8616no—
862C2×C4—868no—
863C2×C4—868no—
864C2×C4—864no—
865C2×C4—864no—
866C2×C4—862no—
867C2×C4—868no—
868C2×C4—862no—
869C2×C4—8616no—
870C2×C4—8616no—
871C2×C4—17216no—
872C2×C4—1728no—
873C2×C4C2×#1062189814yes—
874C2×C4C2×#1062189814yes—
875C2×C4C2×#10621898116yescomplemented
876C2×C4C24×D4314yes—
877C2×C4C24×D4314yes—
878C2×C4C24×D4314yes—
879C2×C4C24×D4318yes—
880C2×C4C24×D4312yes—
881C2×C4C24×D4312yes—
882C22—22no—
883C22—22no—
884C22—28no—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—48no—
889C22—864no—
890C22—864no—
891C22—864no—
892C22—864no—
893C22—864no—
894C22—864no—
895C22—1728no—
896C22—1728no—
897C22C22×#1062189814yes—
898C22C22×#1062189812yes—
899C22H(5,𝔽2)×D4312yes—
900C222−1+4×D4312yes—
901C22C25×D4311yescharacteristic
902C4—24no—
903C4—24no—
904C4—28no—
905C4—24no—
906C4—434no—
907C4—434no—
908C4—864no—
909C4—864no—
910C4—862no—
911C4—868no—
912C4—862no—
913C4C22×#1062189814yes—
914C4C22×#1062189814yes—
915C2—24no—
916C2—44no—
917C2—1724no—
918C2—1724no—
919C2#1914849814yesdirect product factor
920C2C23×#1062189811yescharacteristic
921C2C2×H(5,𝔽2)×D4311yescharacteristic
922C2C2×2−1+4×D4311yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#520C2
socleC23×C43C25
hypercenterC2×#520D43
hypocenterC43C2×#3511
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #19148498C2direct (N × H)
2. C2×#14583617C2semidirect
3. C2×#14583612C2semidirect
4. C2×#14583604C2semidirect
5. C2×#14583598C2semidirect
6. C2×#14583558C2semidirect
7. C2×#14583550C2semidirect
8. C2×#14583521C2semidirect
9. C2×#14583514C2semidirect
10. C2×#14583480C2semidirect
11. C2×#14583477C2semidirect
12. C2×#14583453C2semidirect
13. C2×#14583446C2semidirect
14. C2×#14583445C2semidirect
15. C22×#13063324C2semidirect
16. C2×#14583379C2semidirect
17. C2×#14583367C2semidirect
18. C2×C43×#520C2semidirect
23. #14583617C22semidirect
24. #14583612C22semidirect
25. #14583604C22semidirect
26. #14583598C22semidirect
27. #14583558C22semidirect
28. #14583550C22semidirect
29. #14583521C22semidirect
30. #14583514C22semidirect
31. #14583480C22semidirect
32. #14583477C22semidirect
33. #14583453C22semidirect
34. #14583446C22semidirect
35. #14583445C22semidirect
40. C2×#13063324C22semidirect
69. #14583379C22semidirect
70. #14583367C22semidirect
93. C43×#520C22semidirect
250. C22×C4×C43#41semidirect
379. C2×C4×C43C2×#41semidirect
470. C2×#520D43semidirect
474. C2×C43#3511semidirect
532. #520C2×D43semidirect
562. C43C2×#3511semidirect
763. C22×C4#10621898semidirect
875. C2×C4C2×#10621898semidirect
919. C2#19148498direct (N × H)

Maximal subgroups

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

subgroupindex
#191484982
C2×#145836172
C2×#145836122
C2×#145836042
C2×#145835982
C2×#145835582
C2×#145835502
C2×#145835212
C2×#145835142
C2×#145834802
C2×#145834772
C2×#145834532
C2×#145834462
C2×#145834452
C22×#130633242
C2×#145833792
C2×#145833672
C2×C43×#5202
C2×#351143