Finite Group Databasebeta

← C2×#19148298 #26004533

Subgroups — C2×#19148298 #26004533

Order 11008.

7910 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148298C2132yesmaximal, direct product factor
2C2×#14583609C212yesmaximal, complemented
3C2×#14583604C212yesmaximal, complemented
4C2×#14583599C212yesmaximal, complemented
5C2×#14583593C212yesmaximal, complemented
6C2×#14583590C212yesmaximal, complemented
7C2×#14583588C212yesmaximal, complemented
8C2×#14583554C212yesmaximal, complemented
9C2×#14583550C212yesmaximal, complemented
10C2×#14583527C211yesmaximal, characteristic, complemented
11C2×#14583491C214yesmaximal, complemented
12C2×#14583477C211yesmaximal, characteristic, complemented
13C2×#14583411C211yesmaximal, characteristic, complemented
14C2×#14583408C214yesmaximal, complemented
15C2×#14583406C211yesmaximal, characteristic, complemented
16C2×#14583380C211yesmaximal, characteristic, complemented
17C22×C4⋊C4×D43C211yesmaximal, characteristic, complemented
18C2×C43×#520C211yesmaximal, characteristic, complemented
19C22×#10621898C2211yescharacteristic
20C22×#10621898C2214yes—
21C23×C4×D43C2211yescharacteristic
22C23×C4×D43C2212yes—
23#14583609C22132yescomplemented
24#14583604C22132yescomplemented
25#14583599C22132yescomplemented
26#14583593C22132yescomplemented
27#14583590C22132yescomplemented
28#14583588C22132yescomplemented
29#14583554C22132yescomplemented
30#14583550C22132yescomplemented
31#14583527C22116yescomplemented
32#14583491C22164yescomplemented
33#14583477C22116yescomplemented
34C2×#13063325C2212yescomplemented
35C2×#13063324C2212yescomplemented
36C2×#13063319C2214yescomplemented
37C2×#13063318C2214yescomplemented
38C2×#13063317C2214yescomplemented
39C2×#13063317C2212yescomplemented
40C2×#13063316C2212yescomplemented
41C2×#13063315C2214yescomplemented
42#14583411C22116yescomplemented
43#14583408C22164yescomplemented
44#14583406C22116yescomplemented
45C2×#13063310C2214yes—
46C2×#13063309C2212yes—
47C2×#13063308C2214yescomplemented
48C2×#13063307C2214yes—
49C2×#13063307C2214yescomplemented
50C2×#13063306C2212yes—
51C2×#13063305C2211yescharacteristic
52C2×#13063305C2211yescharacteristic
53C2×#13063304C2214yescomplemented
54C2×#13063304C2212yescomplemented
55C2×#13063303C2214yes—
56C2×#13063303C2214yescomplemented
57C2×#13063302C2214yes—
58C2×#13063301C2211yescharacteristic
59C2×#13063301C2211yescharacteristic
60C2×#13063301C2212yescomplemented
61C2×#13063300C2211yescharacteristic
62C2×#13063300C2211yescharacteristic
63C2×#13063299C2212yescomplemented
64C2×#13063298C2214yes—
65C2×#13063297C2214yes—
66C2×#13063296C2211yescharacteristic
67C2×#13063296C2211yescharacteristic
68C2×#13063296C2212yescomplemented
69C2×#13063295C2212yes—
70C2×#13063293C2212yes—
71#14583380C22116yescomplemented
72C2×#13063290C2212yescomplemented
73C2×C4×D172C2212yes—
74C2×C4×D172C2214yes—
75C2×C4×D172C2212yes—
76C2×#13063287C2212yescomplemented
77C2×C4×C22⋊D43C2214yes—
78C2×C4×C22⋊D43C2212yes—
79C2×C4×C22⋊D43C2212yes—
80C2×C4×C22⋊D43C2214yes—
81C2×#13063284C2211yescharacteristic
82C2×#13063283C2212yescomplemented
83C2×#13063282C2214yes—
84C22×C4⋊Dic43C2211yescharacteristic
85C22×Dic43⋊C4C2212yes—
86C2×C4⋊C4×D43C2212yes—
87C2×C4⋊C4×D43C2212yes—
88C2×C4⋊C4×D43C2212yes—
89C2×C4⋊C4×D43C2212yes—
90C2×C4⋊C4×D43C22116yescomplemented
91C2×C4⋊C4×D43C2212yescomplemented
92C22×#41×C43C2211yescharacteristic
93C43×#520C22116yescomplemented
94C2×C4×Q8×C43C2212yescomplemented
95C2×C4×D4×C43C2214yes—
96C2×C4×D4×C43C2212yescomplemented
97C2×#117×C43C2211yescharacteristic
98C2×#117×C43C2212yescomplemented
99C22×C4⋊C4×C43C2211yescharacteristic
100C22×C4⋊C4×C43C2212yescomplemented
101C24×D43C2311yescharacteristic
102C2×#10621898—28no—
103C2×#10621898—416no—
104C2×#10621898C2318yes—
105C2×#10621898C23132yes—
106C22×Dic86C2311yescharacteristic
107C22×Dic86C2314yes—
108C22×D172C2311yescharacteristic
109C22×D172C2312yes—
110C22×D172C2312yes—
111C22×C22⋊D43C2312yes—
112C22×C22⋊D43C2312yes—
113C22×C22⋊D43C2312yes—
114C22×C22⋊D43C2314yes—
115C23×Dic43C2311yescharacteristic
116C23×Dic43C2312yes—
117C22×C4×D43—28no—
118C22×C4×D43—48no—
119C22×C4×D43C2314yes—
120C22×C4×D43C2311yescharacteristic
121C22×C4×D43C2311yescharacteristic
122C22×C4×D43C2311yescharacteristic
123C22×C4×D43C2311yescharacteristic
124C22×C4×D43C2318yes—
125C22×C4×D43C2312yes—
126C22×C4×D43C2314yes—
127C22×C4×D43C23116yes—
128C22×C4×D43C2314yes—
129#13063325C23116yescomplemented
130#13063324C23116yescomplemented
131#13063319C23132yescomplemented
132#13063318C23132yescomplemented
133#13063317C23132yescomplemented
134#13063317C23116yescomplemented
135#13063316C23116yescomplemented
136#13063315C23132yescomplemented
137#13063310C23132yes—
138#13063309C23116yes—
139#13063308C23132yescomplemented
140#13063307C23132yes—
141#13063307C23132yescomplemented
142#13063306C23116yes—
143#13063305C2318yes—
144#13063305C2318yes—
145#13063304C23132yescomplemented
146#13063304C23116yescomplemented
147#13063303C23132yes—
148#13063303C23132yescomplemented
149#13063302C23132yes—
150#13063301C2318yes—
151#13063301C2318yes—
152#13063301C23116yescomplemented
153#13063300C2318yes—
154#13063300C2318yes—
155#13063299C23116yescomplemented
156#13063298C23132yes—
157#13063297C23132yes—
158#13063296C2318yes—
159#13063296C2318yes—
160#13063296C23116yescomplemented
161#13063295C23116yes—
162#13063293C23116yes—
163#13063290C23116yescomplemented
164C4×D172C23116yes—
165C4×D172C23132yes—
166C4×D172C23116yes—
167#13063287C23116yescomplemented
168C4×C22⋊D43C23116yes—
169C4×C22⋊D43C23116yes—
170C4×C22⋊D43C23132yes—
171C4×C22⋊D43C23132yes—
172#13063284C2318yes—
173#13063283C23116yescomplemented
174#13063282C23132yes—
175C2×C4⋊Dic43C2312yes—
176C2×C4⋊Dic43C2312yes—
177C2×C4⋊Dic43C2318yes—
178C2×C4⋊Dic43C2311yescharacteristic
179C2×C4⋊Dic43C2311yescharacteristic
180C2×C4⋊Dic43C2314yes—
181C2×C4⋊Dic43C2312yes—
182C2×C4⋊Dic43C2312yes—
183C2×Dic43⋊C4C2314yes—
184C2×Dic43⋊C4C2314yes—
185C2×Dic43⋊C4C23116yes—
186C2×Dic43⋊C4C2314yes—
187C2×Dic43⋊C4C2314yes—
188C2×Dic43⋊C4C2314yes—
189C2×Dic43⋊C4C2312yes—
190C2×Dic43⋊C4C2312yes—
191C2×Dic43⋊C4C2314yes—
192C4⋊C4×D43C23116yes—
193C4⋊C4×D43C23116yes—
194C4⋊C4×D43C23116yes—
195C4⋊C4×D43C23116yes—
196C4⋊C4×D43C23116yescomplemented
197C2×C22⋊Dic43C2312yes—
198C2×C22⋊Dic43C2312yes—
199C2×C22⋊Dic43C2312yes—
200C2×C22⋊Dic43C2314yes—
201C2×(C2×D43)⋊C4C2312yes—
202C2×(C2×D43)⋊C4C2312yes—
203C2×(C2×D43)⋊C4C2314yes—
204C2×(C2×D43)⋊C4C2312yes—
205C2×(C2×D43)⋊C4C2312yes—
206C2×(C2×D43)⋊C4C2314yes—
207C2×(C2×D43)⋊C4C2312yes—
208C2×(C2×D43)⋊C4C2312yes—
209C2×C4×Dic43C2314yes—
210C2×C4×Dic43C2312yes—
211C2×#41×C43—28no—
212C2×#41×C43C2318yes—
213C22×Q8×C43C2311yescharacteristic
214C22×D4×C43C2312yes—
215C22×D4×C43C2311yescharacteristic
216C23×C4×C43C2312yes—
217C23×C4×C43C2312yes—
218C23×C4×C43C2314yes—
219C23×C4×C43C2311yescharacteristic
220C4×Q8×C43C23116yescomplemented
221C4×D4×C43C23132yes—
222C4×D4×C43C23116yescomplemented
223#117×C43C2318yes—
224#117×C43C23116yescomplemented
225C2×C4⋊C4×C43C2312yes—
226C2×C4⋊C4×C43C2312yes—
227C2×C4⋊C4×C43C2318yes—
228C2×C4⋊C4×C43C2311yescharacteristic
229C2×C4⋊C4×C43C2314yes—
230C2×C4⋊C4×C43C2311yescharacteristic
231C2×C4⋊C4×C43C23116yescomplemented
232C2×C22⋊C4×C43C2312yes—
233C2×C22⋊C4×C43C2314yes—
234C2×C42×C43C2312yes—
235C2×C42×C43C2314yes—
236C24×C43C2412yes—
237C24×C43C2411yescharacteristic
238C23×D43—24no—
239C23×D43—24no—
240C23×D43—24no—
241C23×D43C2412yes—
242C23×D43C2414yes—
243C23×D43C2411yescharacteristic
244C23×D43C2411yescharacteristic
245#41×C43—232no—
246C2×Q8×C43—24no—
247C2×Q8×C43C2414yes—
248C2×D4×C43—24no—
249C2×D4×C43—28no—
250C2×D4×C43C2418yes—
251C2×D4×C43C2414yes—
252C22×C4×C43—28no—
253C22×C4×C43—44no—
254C22×C4×C43—48no—
255C22×C4×C43#4118yescomplemented
256C22×C4×C43C2412yes—
257C22×C4×C43C2412yes—
258C22×C4×C43C2414yes—
259C22×C4×C43C2412yes—
260C22×C4×C43C2418yes—
261C22×C4×C43C2418yes—
262C22×C4×C43C24116yes—
263C22×C4×C43C2411yescharacteristic
264C22×C4×C43C2411yescharacteristic
265C22×C4×C43C2414yes—
266C2×C22⋊D43—28no—
267C2×C22⋊D43—28no—
268C2×C22⋊D43—28no—
269C2×C22⋊D43—48no—
270C2×C22⋊D43C2418yes—
271C2×C22⋊D43C2418yes—
272C2×C22⋊D43C2418yes—
273C2×C22⋊D43C24116yes—
274C22×Dic43—24no—
275C22×Dic43—44no—
276C22×Dic43C2412yes—
277C22×Dic43C2412yes—
278C22×Dic43C2412yes—
279C22×Dic43C2411yescharacteristic
280C22×Dic43C2411yescharacteristic
281C22×Dic43C2414yes—
282C22×Dic43C2414yes—
283C22×Dic43C2418yes—
284#10621898—232no—
285#10621898—464no—
286C2×D172—24no—
287C2×D172—28no—
288C2×D172—28no—
289C2×D172C2414yes—
290C2×D172C2418yes—
291C2×D172C2418yes—
292C2×C4×D43—24no—
293C2×C4×D43—24no—
294C2×C4×D43—24no—
295C2×C4×D43—24no—
296C2×C4×D43—28no—
297C2×C4×D43—232no—
298C2×C4×D43—216no—
299C2×C4×D43—432no—
300C2×C4×D43—48no—
301C2×C4×D43—48no—
302C2×C4×D43C24116yes—
303C2×C4×D43C2414yes—
304C2×C4×D43C2414yes—
305C2×C4×D43C2414yes—
306C2×C4×D43C2414yes—
307C2×C4×D43C2418yes—
308C2×C4×D43C24116yes—
309C2×C4×D43C24116yes—
310C2×Dic86—24no—
311C2×Dic86—48no—
312C2×Dic86C2414yes—
313C2×Dic86C24116yes—
314C4⋊C4×C43C2418yes—
315C4⋊C4×C43C2418yes—
316C4⋊C4×C43C2414yes—
317C4⋊C4×C43C24116yes—
318C4⋊C4×C43C2414yes—
319C22⋊C4×C43C2418yes—
320C22⋊C4×C43C24116yes—
321C42×C43C2418yes—
322C42×C43C24116yes—
323C22⋊Dic43C2418yes—
324C22⋊Dic43C2418yes—
325C22⋊Dic43C2418yes—
326C22⋊Dic43C24116yes—
327(C2×D43)⋊C4C2418yes—
328(C2×D43)⋊C4C2418yes—
329(C2×D43)⋊C4C24116yes—
330(C2×D43)⋊C4C2418yes—
331(C2×D43)⋊C4C2418yes—
332(C2×D43)⋊C4C24116yes—
333(C2×D43)⋊C4C2418yes—
334(C2×D43)⋊C4C2418yes—
335C4⋊Dic43C2418yes—
336C4⋊Dic43C2418yes—
337C4⋊Dic43C2414yes—
338C4⋊Dic43C2414yes—
339C4⋊Dic43C24116yes—
340C4⋊Dic43C2418yes—
341C4⋊Dic43C2418yes—
342Dic43⋊C4C24116yes—
343Dic43⋊C4C24116yes—
344Dic43⋊C4C24116yes—
345Dic43⋊C4C24116yes—
346Dic43⋊C4C24116yes—
347Dic43⋊C4C2418yes—
348Dic43⋊C4C2418yes—
349Dic43⋊C4C24116yes—
350C4×Dic43C24116yes—
351C4×Dic43C2418yes—
352C23×C43—22no—
353C23×C43—22no—
354C23×C43—24no—
355C23×C43—24no—
356C23×C43—24no—
357C23×C43C2×#4114yes—
358C23×C43C2514yes—
359C23×C43C2512yes—
360C23×C43C2511yescharacteristic
361C22×D43—232no—
362C22×D43—28no—
363C22×D43—22no—
364C22×D43—22no—
365C22×D43—22no—
366C22×D43—22no—
367C22×D43—28no—
368C22×D43—28no—
369C22×D43—24no—
370C22×D43—24no—
371C22×D43—24no—
372C22×D43H(5,𝔽2)14yes—
373C22×D432−1+414yes—
374C22×D43C2514yes—
375C22×D43C2512yes—
376C22×D43C2512yes—
377Q8×C43—28no—
378D4×C43—216no—
379D4×C43—28no—
380C2×C4×C43—24no—
381C2×C4×C43—24no—
382C2×C4×C43—28no—
383C2×C4×C43—24no—
384C2×C4×C43—216no—
385C2×C4×C43—48no—
386C2×C4×C43—416no—
387C2×C4×C43C2×#4114yes—
388C2×C4×C43C2×#4114yes—
389C2×C4×C43C2×#41116yescomplemented
390C2×C4×C43C2518yes—
391C2×C4×C43C2514yes—
392C2×C4×C43C2514yes—
393C2×C4×C43C2514yes—
394C2×C4×C43C2512yes—
395C2×C4×C43C2512yes—
396C22⋊D43—216no—
397C22⋊D43—216no—
398C22⋊D43—216no—
399C22⋊D43—416no—
400C2×Dic43—24no—
401C2×Dic43—28no—
402C2×Dic43—22no—
403C2×Dic43—22no—
404C2×Dic43—24no—
405C2×Dic43—28no—
406C2×Dic43—24no—
407C2×Dic43—48no—
408C2×Dic43C2514yes—
409C2×Dic43C2514yes—
410C2×Dic43C2514yes—
411C2×Dic43C2512yes—
412C2×Dic43C2512yes—
413C2×Dic43C2518yes—
414D172—216no—
415D172—216no—
416D172—28no—
417C4×D43—232no—
418C4×D43—28no—
419C4×D43—28no—
420C4×D43—28no—
421C4×D43—28no—
422C4×D43—216no—
423C4×D43—416no—
424C4×D43—416no—
425Dic86—28no—
426Dic86—416no—
427C2×#3492—431nomaximal, Sylow
428C22×C43—22no—
429C22×C43—22no—
430C22×C43—28no—
431C22×C43—24no—
432C22×C43—24no—
433C22×C43—24no—
434C22×C43—48no—
435C22×C43C22×#4114yes—
436C22×C43C22×#4112yes—
437C22×C43C2×H(5,𝔽2)12yes—
438C22×C43C2×2−1+412yes—
439C22×C43C2611yescharacteristic
440C2×D43—232no—
441C2×D43—22no—
442C2×D43—22no—
443C2×D43—22no—
444C2×D43—22no—
445C2×D43—28no—
446C2×D43—28no—
447C2×D43—24no—
448C2×D43—24no—
449C2×D43—24no—
450C2×D43—48no—
451C2×D43C2×H(5,𝔽2)14yes—
452C2×D43C2×2−1+414yes—
453C4×C43—24no—
454C4×C43—24no—
455C4×C43—28no—
456C4×C43—24no—
457C4×C43C22×#4114yes—
458C4×C43C22×#4114yes—
459Dic43—24no—
460Dic43—22no—
461Dic43—22no—
462Dic43—24no—
463Dic43—28no—
464Dic43—24no—
465#3492—4332no—
466C2×#554—432no—
467C2×#554—432no—
468C2×#553—432no—
469C2×#553—432no—
470C2×#552—432no—
471C2×#552—432no—
472C2×#547—432no—
473C2×#547—432no—
474C2×#544—431no—
475C2×#539—434no—
476C2×#537—431no—
477C2×#525—431no—
478C2×#525—434no—
479C2×#525—431no—
480C2×#520—431no—
481C2×#520D4311yescharacteristic, complemented
482C23×C4⋊C4—431no—
483C2×C43—24no—
484C2×C43—44no—
485C2×C43#349214yescomplemented
486C2×C43C23×#4111yescharacteristic
487C2×C43C22×H(5,𝔽2)11yescharacteristic
488C2×C43C22×2−1+411yescharacteristic
489D43—24no—
490D43—24no—
491D43—44no—
492C22×#41—431no—
493C22×#41—434no—
494C22×#41C2×D4311yescharacteristic
495C24×C4—431no—
496C24×C4—432no—
497#554—4332no—
498#554—4332no—
499#553—4332no—
500#553—4332no—
501#552—4332no—
502#552—4332no—
503#547—4332no—
504#547—4332no—
505#544—4316no—
506#539—4364no—
507#537—4316no—
508C2×C4⋊Q8—432no—
509C2×C4⋊Q8—432no—
510C2×#126—434no—
511C2×#126—434no—
512C2×#125—434no—
513C2×#125—432no—
514C2×#125—434no—
515C2×#125—432no—
516#525—4316no—
517#525—4364no—
518#525—4316no—
519C2×#123—432no—
520C2×#123—434no—
521C2×#123—434no—
522C2×#123—434no—
523C2×#123—434no—
524C2×#123—432no—
525C2×C22⋊Q8—431no—
526C2×C22⋊Q8—431no—
527C2×C22⋊Q8—432no—
528C2×C22⋊Q8—432no—
529C2×C22⋊Q8—434no—
530C2×C22⋊Q8—434no—
531C2×C22⋊Q8—434no—
532C2×C22⋊Q8—431no—
533C2×C22⋊Q8—431no—
534C2×C22⋊Q8—434no—
535C2×#121—431no—
536C2×#121—431no—
537C2×#121—432no—
538C2×#121—434no—
539C2×#121—432no—
540C2×#121—431no—
541C2×#121—431no—
542C2×#121—434no—
543C2×#120—432no—
544C2×#120—432no—
545#520—4316no—
546#520C2×D43116yescomplemented
547C2×C4×Q8—432no—
548C2×C4×Q8C2×D4312yescomplemented
549C2×C4×D4—434no—
550C2×C4×D4—432no—
551C2×C4×D4—434no—
552C2×C4×D4—432no—
553C2×C4×D4—432no—
554C2×C4×D4—432no—
555C2×C4×D4—434no—
556C2×C4×D4—432no—
557C2×C4×D4C2×D4314yes—
558C2×C4×D4C2×D4312yescomplemented
559C2×#117—431no—
560C2×#117—432no—
561C2×#117—434no—
562C2×#117C2×D4311yescharacteristic
563C2×#117C2×D4312yescomplemented
564C22×C4⋊C4—432no—
565C22×C4⋊C4—431no—
566C22×C4⋊C4—432no—
567C22×C4⋊C4—432no—
568C22×C4⋊C4—432no—
569C22×C4⋊C4—432no—
570C22×C4⋊C4—4316no—
571C22×C4⋊C4—432no—
572C22×C4⋊C4C2×D4311yescharacteristic
573C22×C4⋊C4C2×D4312yescomplemented
574C43C2×#349211yescharacteristic, complemented, Sylow
575C25—431no—
576C2×#41—28no—
577C2×#41—438no—
578C2×#41—4332no—
579C2×#41—868no—
580C2×#41—17216no—
581C2×#41C22×D4318yes—
582C22×Q8—431no—
583C22×Q8—434no—
584C22×Q8C22×D4311yescharacteristic
585C22×D4—432no—
586C22×D4—432no—
587C22×D4—432no—
588C22×D4—434no—
589C22×D4—432no—
590C22×D4—431no—
591C22×D4—432no—
592C22×D4C22×D4312yes—
593C22×D4C22×D4311yescharacteristic
594C23×C4—431no—
595C23×C4—432no—
596C23×C4—434no—
597C23×C4—431no—
598C23×C4—431no—
599C23×C4—431no—
600C23×C4—431no—
601C23×C4—438no—
602C23×C4—432no—
603C23×C4—434no—
604C23×C4—4316no—
605C23×C4—434no—
606C23×C4—868no—
607C23×C4—1728no—
608C23×C4C22×D4312yes—
609C23×C4C22×D4312yes—
610C23×C4C22×D4314yes—
611C23×C4C22×D4311yescharacteristic
612C4⋊Q8—4316no—
613C4⋊Q8—4316no—
614#126—4332no—
615#126—4332no—
616#125—4332no—
617#125—4316no—
618#125—4332no—
619#125—4316no—
620#123—4316no—
621#123—4332no—
622#123—4332no—
623#123—4316no—
624#123—4332no—
625#123—4332no—
626C22⋊Q8—438no—
627C22⋊Q8—438no—
628C22⋊Q8—4316no—
629C22⋊Q8—4316no—
630C22⋊Q8—4332no—
631C22⋊Q8—438no—
632C22⋊Q8—4332no—
633C22⋊Q8—438no—
634C22⋊Q8—4332no—
635C22⋊Q8—4332no—
636#121—4332no—
637#121—438no—
638#121—438no—
639#121—4316no—
640#121—4316no—
641#121—438no—
642#121—438no—
643#121—4332no—
644#120—4316no—
645#120—4316no—
646C4×Q8—4316no—
647C4×Q8C22×D43116yescomplemented
648C4×D4—4332no—
649C4×D4—4316no—
650C4×D4—4332no—
651C4×D4—4316no—
652C4×D4—4316no—
653C4×D4—4316no—
654C4×D4—4332no—
655C4×D4—4316no—
656C4×D4C22×D43132yes—
657C4×D4C22×D43116yescomplemented
658#117—438no—
659#117—4316no—
660#117—4332no—
661#117C22×D4318yes—
662#117C22×D43116yescomplemented
663C2×C4⋊C4—432no—
664C2×C4⋊C4—432no—
665C2×C4⋊C4—434no—
666C2×C4⋊C4—434no—
667C2×C4⋊C4—438no—
668C2×C4⋊C4—4316no—
669C2×C4⋊C4—431no—
670C2×C4⋊C4—434no—
671C2×C4⋊C4—431no—
672C2×C4⋊C4—434no—
673C2×C4⋊C4—434no—
674C2×C4⋊C4—432no—
675C2×C4⋊C4—432no—
676C2×C4⋊C4—434no—
677C2×C4⋊C4—434no—
678C2×C4⋊C4—432no—
679C2×C4⋊C4—432no—
680C2×C4⋊C4—4316no—
681C2×C4⋊C4—4316no—
682C2×C4⋊C4—4316no—
683C2×C4⋊C4—4316no—
684C2×C4⋊C4—4316no—
685C2×C4⋊C4C22×D4312yes—
686C2×C4⋊C4C22×D4312yes—
687C2×C4⋊C4C22×D4318yes—
688C2×C4⋊C4C22×D4311yescharacteristic
689C2×C4⋊C4C22×D4314yes—
690C2×C4⋊C4C22×D4311yescharacteristic
691C2×C4⋊C4C22×D43116yescomplemented
692C2×C22⋊C4—432no—
693C2×C22⋊C4—434no—
694C2×C22⋊C4—432no—
695C2×C22⋊C4—432no—
696C2×C22⋊C4—432no—
697C2×C22⋊C4—432no—
698C2×C22⋊C4—434no—
699C2×C22⋊C4—432no—
700C2×C22⋊C4—432no—
701C2×C22⋊C4—434no—
702C2×C22⋊C4—432no—
703C2×C22⋊C4—432no—
704C2×C22⋊C4C22×D4312yes—
705C2×C22⋊C4C22×D4314yes—
706C2×C42—434no—
707C2×C42—432no—
708C2×C42C22×D4314yes—
709C2×C42C22×D4312yes—
710C24—431no—
711C24—431no—
712C24—434no—
713C24—432no—
714C24—864no—
715C24—864no—
716C24—864no—
717C24C23×D4312yes—
718C24C23×D4311yescharacteristic
719#41—232no—
720#41—8632no—
721#41—17264no—
722C2×Q8—24no—
723C2×Q8—434no—
724C2×Q8—4316no—
725C2×Q8—864no—
726C2×Q8—1728no—
727C2×Q8C23×D4314yes—
728C2×D4—28no—
729C2×D4—24no—
730C2×D4—438no—
731C2×D4—438no—
732C2×D4—438no—
733C2×D4—4316no—
734C2×D4—438no—
735C2×D4—434no—
736C2×D4—438no—
737C2×D4—868no—
738C2×D4—868no—
739C2×D4—868no—
740C2×D4—868no—
741C2×D4—868no—
742C2×D4—864no—
743C2×D4—1728no—
744C2×D4C23×D4318yes—
745C2×D4C23×D4314yes—
746C22×C4—28no—
747C22×C4—44no—
748C22×C4—48no—
749C22×C4—434no—
750C22×C4—432no—
751C22×C4—432no—
752C22×C4—432no—
753C22×C4—431no—
754C22×C4—431no—
755C22×C4—434no—
756C22×C4—438no—
757C22×C4—4316no—
758C22×C4—434no—
759C22×C4—434no—
760C22×C4—434no—
761C22×C4—434no—
762C22×C4—438no—
763C22×C4—4316no—
764C22×C4—4316no—
765C22×C4—8616no—
766C22×C4—864no—
767C22×C4—864no—
768C22×C4—864no—
769C22×C4—864no—
770C22×C4—864no—
771C22×C4—868no—
772C22×C4—8632no—
773C22×C4—1728no—
774C22×C4—1728no—
775C22×C4—17232no—
776C22×C4—1724no—
777C22×C4#1062189818yescomplemented
778C22×C4C23×D4318yes—
779C22×C4C23×D4314yes—
780C22×C4C23×D4312yes—
781C22×C4C23×D4312yes—
782C22×C4C23×D4312yes—
783C22×C4C23×D4318yes—
784C22×C4C23×D43116yes—
785C22×C4C23×D4311yescharacteristic
786C22×C4C23×D4311yescharacteristic
787C22×C4C23×D4314yes—
788C4⋊C4—438no—
789C4⋊C4—438no—
790C4⋊C4—4316no—
791C4⋊C4—4316no—
792C4⋊C4—434no—
793C4⋊C4—4316no—
794C4⋊C4—434no—
795C4⋊C4—4316no—
796C4⋊C4—4316no—
797C4⋊C4—438no—
798C4⋊C4—438no—
799C4⋊C4—4316no—
800C4⋊C4—4316no—
801C4⋊C4—438no—
802C4⋊C4—438no—
803C4⋊C4C23×D4318yes—
804C4⋊C4C23×D4318yes—
805C4⋊C4C23×D4314yes—
806C4⋊C4C23×D43116yes—
807C4⋊C4C23×D4314yes—
808C22⋊C4—438no—
809C22⋊C4—4316no—
810C22⋊C4—438no—
811C22⋊C4—438no—
812C22⋊C4—438no—
813C22⋊C4—438no—
814C22⋊C4—4316no—
815C22⋊C4—438no—
816C22⋊C4—438no—
817C22⋊C4—4316no—
818C22⋊C4—438no—
819C22⋊C4—438no—
820C22⋊C4C23×D4318yes—
821C22⋊C4C23×D43116yes—
822C42—4316no—
823C42—438no—
824C42C23×D43116yes—
825C42C23×D4318yes—
826C23—22no—
827C23—22no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—434no—
832C23—434no—
833C23—432no—
834C23—432no—
835C23—434no—
836C23—868no—
837C23—868no—
838C23—8632no—
839C23—868no—
840C23—862no—
841C23—862no—
842C23—862no—
843C23—862no—
844C23—864no—
845C23—864no—
846C23—864no—
847C23C2×#1062189814yes—
848C23C24×D4314yes—
849C23C24×D4312yes—
850C23C24×D4311yescharacteristic
851Q8—28no—
852Q8—868no—
853Q8—17216no—
854D4—216no—
855D4—28no—
856D4—8616no—
857D4—8616no—
858D4—8616no—
859D4—8616no—
860D4—8616no—
861D4—868no—
862D4—17216no—
863C2×C4—24no—
864C2×C4—28no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—216no—
868C2×C4—48no—
869C2×C4—416no—
870C2×C4—434no—
871C2×C4—434no—
872C2×C4—434no—
873C2×C4—432no—
874C2×C4—432no—
875C2×C4—438no—
876C2×C4—8632no—
877C2×C4—868no—
878C2×C4—862no—
879C2×C4—862no—
880C2×C4—864no—
881C2×C4—868no—
882C2×C4—864no—
883C2×C4—864no—
884C2×C4—868no—
885C2×C4—868no—
886C2×C4—868no—
887C2×C4—868no—
888C2×C4—8616no—
889C2×C4—17216no—
890C2×C4—17216no—
891C2×C4—1728no—
892C2×C4C2×#1062189814yes—
893C2×C4C2×#1062189814yes—
894C2×C4C2×#10621898116yescomplemented
895C2×C4C24×D4318yes—
896C2×C4C24×D4314yes—
897C2×C4C24×D4314yes—
898C2×C4C24×D4314yes—
899C2×C4C24×D4312yes—
900C2×C4C24×D4312yes—
901C22—28no—
902C22—22no—
903C22—22no—
904C22—24no—
905C22—24no—
906C22—24no—
907C22—48no—
908C22—434no—
909C22—434no—
910C22—8632no—
911C22—868no—
912C22—868no—
913C22—862no—
914C22—862no—
915C22—862no—
916C22—862no—
917C22—864no—
918C22—864no—
919C22—864no—
920C22—1728no—
921C22C22×#1062189814yes—
922C22C22×#1062189812yes—
923C22H(5,𝔽2)×D4312yes—
924C222−1+4×D4312yes—
925C22C25×D4311yescharacteristic
926C4—24no—
927C4—28no—
928C4—24no—
929C4—24no—
930C4—862no—
931C4—862no—
932C4—864no—
933C4—868no—
934C4—864no—
935C4—864no—
936C4C22×#1062189814yes—
937C4C22×#1062189814yes—
938C2—24no—
939C2—44no—
940C2—864no—
941C2—864no—
942C2—1724no—
943C2#1914829814yesdirect product factor
944C2C23×#1062189811yescharacteristic
945C2C2×H(5,𝔽2)×D4311yescharacteristic
946C2C2×2−1+4×D4311yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#520C2
socleC23×C43C25
hypercenterC2×#520D43
hypocenterC43C2×#3492
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #19148298C2direct (N × H)
2. C2×#14583609C2semidirect
3. C2×#14583604C2semidirect
4. C2×#14583599C2semidirect
5. C2×#14583593C2semidirect
6. C2×#14583590C2semidirect
7. C2×#14583588C2semidirect
8. C2×#14583554C2semidirect
9. C2×#14583550C2semidirect
10. C2×#14583527C2semidirect
11. C2×#14583491C2semidirect
12. C2×#14583477C2semidirect
13. C2×#14583411C2semidirect
14. C2×#14583408C2semidirect
15. C2×#14583406C2semidirect
16. C2×#14583380C2semidirect
17. C22×C4⋊C4×D43C2semidirect
18. C2×C43×#520C2semidirect
23. #14583609C22semidirect
24. #14583604C22semidirect
25. #14583599C22semidirect
26. #14583593C22semidirect
27. #14583590C22semidirect
28. #14583588C22semidirect
29. #14583554C22semidirect
30. #14583550C22semidirect
31. #14583527C22semidirect
32. #14583491C22semidirect
33. #14583477C22semidirect
34. C2×#13063325C22semidirect
35. C2×#13063324C22semidirect
36. C2×#13063319C22semidirect
37. C2×#13063318C22semidirect
38. C2×#13063317C22semidirect
39. C2×#13063317C22semidirect
40. C2×#13063316C22semidirect
41. C2×#13063315C22semidirect
42. #14583411C22semidirect
43. #14583408C22semidirect
44. #14583406C22semidirect
47. C2×#13063308C22semidirect
49. C2×#13063307C22semidirect
53. C2×#13063304C22semidirect
54. C2×#13063304C22semidirect
56. C2×#13063303C22semidirect
60. C2×#13063301C22semidirect
63. C2×#13063299C22semidirect
68. C2×#13063296C22semidirect
71. #14583380C22semidirect
72. C2×#13063290C22semidirect
76. C2×#13063287C22semidirect
82. C2×#13063283C22semidirect
90. C2×C4⋊C4×D43C22semidirect
91. C2×C4⋊C4×D43C22semidirect
93. C43×#520C22semidirect
94. C2×C4×Q8×C43C22semidirect
96. C2×C4×D4×C43C22semidirect
98. C2×#117×C43C22semidirect
100. C22×C4⋊C4×C43C22semidirect
129. #13063325C23semidirect
130. #13063324C23semidirect
131. #13063319C23semidirect
132. #13063318C23semidirect
133. #13063317C23semidirect
134. #13063317C23semidirect
135. #13063316C23semidirect
136. #13063315C23semidirect
139. #13063308C23semidirect
141. #13063307C23semidirect
145. #13063304C23semidirect
146. #13063304C23semidirect
148. #13063303C23semidirect
152. #13063301C23semidirect
155. #13063299C23semidirect
160. #13063296C23semidirect
163. #13063290C23semidirect
167. #13063287C23semidirect
173. #13063283C23semidirect
196. C4⋊C4×D43C23semidirect
220. C4×Q8×C43C23semidirect
222. C4×D4×C43C23semidirect
224. #117×C43C23semidirect
231. C2×C4⋊C4×C43C23semidirect
255. C22×C4×C43#41semidirect
389. C2×C4×C43C2×#41semidirect
481. C2×#520D43semidirect
485. C2×C43#3492semidirect
546. #520C2×D43semidirect
548. C2×C4×Q8C2×D43semidirect
558. C2×C4×D4C2×D43semidirect
563. C2×#117C2×D43semidirect
573. C22×C4⋊C4C2×D43semidirect
574. C43C2×#3492semidirect
647. C4×Q8C22×D43semidirect
657. C4×D4C22×D43semidirect
662. #117C22×D43semidirect
691. C2×C4⋊C4C22×D43semidirect
777. C22×C4#10621898semidirect
894. C2×C4C2×#10621898semidirect
943. C2#19148298direct (N × H)

Maximal subgroups

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

subgroupindex
#191482982
C2×#145836092
C2×#145836042
C2×#145835992
C2×#145835932
C2×#145835902
C2×#145835882
C2×#145835542
C2×#145835502
C2×#145835272
C2×#145834912
C2×#145834772
C2×#145834112
C2×#145834082
C2×#145834062
C2×#145833802
C22×C4⋊C4×D432
C2×C43×#5202
C2×#349243