Finite Group Databasebeta

← C2×#19148507 #26004961

Subgroups — C2×#19148507 #26004961

Order 11008.

7758 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148507C2132yesmaximal, direct product factor
2C2×#14583621C212yesmaximal, complemented
3C2×#14583612C212yesmaximal, complemented
4C2×#14583605C212yesmaximal, complemented
5C2×#14583602C212yesmaximal, complemented
6C2×#14583593C212yesmaximal, complemented
7C2×#14583561C212yesmaximal, complemented
8C2×#14583559C212yesmaximal, complemented
9C2×#14583551C212yesmaximal, complemented
10C2×#14583522C212yesmaximal, complemented
11C2×#14583521C212yesmaximal, complemented
12C2×#14583479C212yesmaximal, complemented
13C2×#14583454C211yesmaximal, characteristic, complemented
14C2×#14583450C211yesmaximal, characteristic, complemented
15C2×#14583450C211yesmaximal, characteristic, complemented
16C2×#14583449C211yesmaximal, characteristic, complemented
17C2×C4⋊Q8×D43C211yesmaximal, characteristic, complemented
18C2×#14583381C212yesmaximal, complemented
19C2×C4×#10621898C211yesmaximal, characteristic, complemented
20C2×C43×#533C211yesmaximal, characteristic, complemented
21C22×#10621902C2212yes—
22C22×#10621902C2212yes—
23C22×#10621898C2211yescharacteristic
24C22×#10621898C2212yes—
25C22×Q8×D43C2212yes—
26#14583621C22132yescomplemented
27#14583612C22132yescomplemented
28#14583605C22132yescomplemented
29#14583602C22132yescomplemented
30#14583593C22132yescomplemented
31#14583561C22132yescomplemented
32#14583559C22132yescomplemented
33#14583551C22132yescomplemented
34#14583522C22132yescomplemented
35#14583521C22132yescomplemented
36#14583479C22132yescomplemented
37#14583454C22116yescomplemented
38#14583450C22116yescomplemented
39#14583450C22116yescomplemented
40#14583449C22116yescomplemented
41C2×#13063325C2211yescharacteristic
42C2×#13063324C2212yes—
43C2×#13063324C2212yes—
44C2×#13063323C2212yes—
45C4⋊Q8×D43C22116yescomplemented
46C2×#13063322C2211yescharacteristic
47C2×#13063320C2214yes—
48C2×#13063319C2214yes—
49C2×#13063316C2212yes—
50C2×#13063314C2212yes—
51C2×#13063314C2212yes—
52C2×#13063313C2214yes—
53C2×#13063313C2212yes—
54C2×#13063311C2214yes—
55C2×#13063310C2214yes—
56C2×#13063307C2214yes—
57C2×#13063305C2212yes—
58C2×#13063305C2214yes—
59C2×#13063303C2214yes—
60C2×#13063303C2214yes—
61C2×#13063301C2212yes—
62C2×#13063300C2212yes—
63C2×#13063300C2214yes—
64C2×#13063300C2212yes—
65C2×#13063300C2212yes—
66C2×#13063300C2212yes—
67C2×#13063299C2212yes—
68C2×#13063299C2212yes—
69C2×#13063298C2214yes—
70C2×#13063298C2214yes—
71#14583381C22132yescomplemented
72C4×#10621898C22116yescomplemented
73C2×Q8×Dic43C2212yes—
74C2×C4×Dic86C2211yescharacteristic
75C2×C4×Dic86C2211yescharacteristic
76C2×#13063290C2212yes—
77C2×C4×D172C2214yes—
78C2×C4×D172C2212yes—
79C2×C4×D172C2211yescharacteristic
80C2×C4×D172C2211yescharacteristic
81C2×C4×D172C2212yes—
82C2×#13063287C2214yes—
83C2×#13063287C2212yes—
84C2×#13063287C2212yes—
85C2×#13063287C2212yes—
86C2×#13063287C2212yes—
87C2×C4×C22⋊D43C2211yescharacteristic
88C2×C4×C22⋊D43C2211yescharacteristic
89C2×C4×C22⋊D43C2211yescharacteristic
90C2×C4×C22⋊D43C2211yescharacteristic
91C2×#13063284C2211yescharacteristic
92C2×#13063283C2212yes—
93C2×#13063282C2211yescharacteristic
94C2×#13063282C2214yes—
95C2×#13063282C2211yescharacteristic
96C2×C4⋊C4×D43C2214yes—
97C2×C4⋊C4×D43C2212yes—
98C2×C4⋊C4×D43C2212yes—
99C2×C42×D43C2211yescharacteristic
100C2×C42×D43C2211yescharacteristic
101C43×#533C22116yescomplemented
102C2×C4⋊Q8×C43C2211yescharacteristic
103C2×C4⋊Q8×C43C2211yescharacteristic
104C2×#125×C43C2212yes—
105C2×C22⋊Q8×C43C2212yes—
106C2×C22⋊Q8×C43C2212yes—
107C2×C4×Q8×C43C2212yes—
108C2×C4×Q8×C43C2212yes—
109C2×#117×C43C2212yes—
110C22×C42×C43C2211yescharacteristic
111C2×#10621902—216no—
112C2×#10621902—48no—
113C2×#10621902C23116yes—
114C2×#10621902C23116yes—
115C2×#10621898—28no—
116C2×#10621898—48no—
117C2×#10621898C2318yes—
118C2×#10621898C23116yes—
119C22×Dic86C2312yes—
120C22×Dic86C2311yescharacteristic
121C22×Dic86C2314yes—
122C2×Q8×D43—48no—
123C2×Q8×D43C23116yes—
124C22×D172C2312yes—
125C22×D172C2314yes—
126C22×D172C2312yes—
127C22×D172C2312yes—
128C22×D172C2311yescharacteristic
129C22×D172C2314yes—
130C22×C22⋊D43C2311yescharacteristic
131C22×C22⋊D43C2311yescharacteristic
132C22×C22⋊D43C2314yes—
133C22×C4×D43C2311yescharacteristic
134C22×C4×D43C2311yescharacteristic
135C22×C4×D43C2311yescharacteristic
136C22×C4×D43C2311yescharacteristic
137C22×C4×D43C2311yescharacteristic
138C22×C4×D43C2314yes—
139C22×C4×D43C2314yes—
140C22×C4×D43C2314yes—
141C22×C4×D43C2314yes—
142C22×C4×D43C2311yescharacteristic
143#13063325C2318yes—
144#13063324C23116yes—
145#13063324C23116yes—
146#13063323C23116yes—
147#13063322C2318yes—
148#13063320C23132yes—
149#13063319C23132yes—
150#13063316C23116yes—
151#13063314C23116yes—
152#13063314C23116yes—
153#13063313C23132yes—
154#13063313C23116yes—
155#13063311C23132yes—
156#13063310C23132yes—
157#13063307C23132yes—
158#13063305C23132yes—
159#13063305C23116yes—
160#13063303C23132yes—
161#13063303C23132yes—
162#13063301C23116yes—
163#13063300C23116yes—
164#13063300C23132yes—
165#13063300C23116yes—
166#13063300C23116yes—
167#13063300C23116yes—
168#13063299C23116yes—
169#13063299C23116yes—
170#13063298C23132yes—
171#13063298C23132yes—
172Q8×Dic43C23116yes—
173C4×Dic86C2318yes—
174C4×Dic86C2318yes—
175#13063290C23116yes—
176C4×D172C2318yes—
177C4×D172C23132yes—
178C4×D172C2318yes—
179C4×D172C23116yes—
180C4×D172C23116yes—
181#13063287C23132yes—
182#13063287C23116yes—
183#13063287C23116yes—
184#13063287C23116yes—
185#13063287C23116yes—
186C4×C22⋊D43C2318yes—
187C4×C22⋊D43C2318yes—
188C4×C22⋊D43C2318yes—
189C4×C22⋊D43C2318yes—
190#13063284C2318yes—
191#13063283C23116yes—
192#13063282C23132yes—
193#13063282C2318yes—
194#13063282C2318yes—
195C2×C4⋊Dic43C2312yes—
196C2×C4⋊Dic43C2312yes—
197C2×C4⋊Dic43C2314yes—
198C2×C4⋊Dic43C2311yescharacteristic
199C2×C4⋊Dic43C2311yescharacteristic
200C2×Dic43⋊C4C2311yescharacteristic
201C2×Dic43⋊C4C2314yes—
202C2×Dic43⋊C4C2314yes—
203C2×Dic43⋊C4C2311yescharacteristic
204C2×Dic43⋊C4C2311yescharacteristic
205C2×Dic43⋊C4C2311yescharacteristic
206C2×Dic43⋊C4C2314yes—
207C4⋊C4×D43C23116yes—
208C4⋊C4×D43C23132yes—
209C4⋊C4×D43C23116yes—
210C2×C22⋊Dic43C2311yescharacteristic
211C2×C22⋊Dic43C2311yescharacteristic
212C2×(C2×D43)⋊C4C2311yescharacteristic
213C2×(C2×D43)⋊C4C2311yescharacteristic
214C2×(C2×D43)⋊C4C2311yescharacteristic
215C2×(C2×D43)⋊C4C2311yescharacteristic
216C2×(C2×D43)⋊C4C2314yes—
217C2×(C2×D43)⋊C4C2314yes—
218C2×(C2×D43)⋊C4C2314yes—
219C2×(C2×D43)⋊C4C2314yes—
220C2×(C2×D43)⋊C4C2314yes—
221C2×(C2×D43)⋊C4C2314yes—
222C2×(C2×D43)⋊C4C2314yes—
223C2×C4×Dic43C2311yescharacteristic
224C2×C4×Dic43C2311yescharacteristic
225C2×C4×Dic43C2311yescharacteristic
226C2×C4×Dic43C2311yescharacteristic
227C2×C4×Dic43C2311yescharacteristic
228C2×C4×Dic43C2311yescharacteristic
229C2×C4×Dic43C2314yes—
230C42×D43C2318yes—
231C42×D43C2318yes—
232C22×Q8×C43C2312yes—
233C22×Q8×C43C2312yes—
234C23×C4×C43C2311yescharacteristic
235C23×C4×C43C2311yescharacteristic
236C23×C4×C43C2311yescharacteristic
237C4⋊Q8×C43C2318yes—
238C4⋊Q8×C43C2318yes—
239#125×C43C23116yes—
240C22⋊Q8×C43C23116yes—
241C22⋊Q8×C43C23116yes—
242C4×Q8×C43C23116yes—
243C4×Q8×C43C23116yes—
244#117×C43C23116yes—
245C2×C4⋊C4×C43C2312yes—
246C2×C4⋊C4×C43C2312yes—
247C2×C4⋊C4×C43C2314yes—
248C2×C4⋊C4×C43C2314yes—
249C2×C4⋊C4×C43C2312yes—
250C2×C4⋊C4×C43C2312yes—
251C2×C22⋊C4×C43C2314yes—
252C2×C42×C43C2311yescharacteristic
253C2×C42×C43C2311yescharacteristic
254C2×C42×C43C2311yescharacteristic
255C2×C42×C43C2311yescharacteristic
256C2×C42×C43C2318yes—
257C2×C42×C43C2314yes—
258C24×C43C2411yescharacteristic
259C23×D43C2414yes—
260C23×D43C2411yescharacteristic
261C23×D43C2411yescharacteristic
262C2×Q8×C43—28no—
263C2×Q8×C43—28no—
264C2×Q8×C43C2418yes—
265C2×Q8×C43C2418yes—
266C22×C4×C43—24no—
267C22×C4×C43—24no—
268C22×C4×C43—24no—
269C22×C4×C43C2411yescharacteristic
270C22×C4×C43C2411yescharacteristic
271C22×C4×C43C2411yescharacteristic
272C22×C4×C43C2414yes—
273C22×C4×C43C2414yes—
274C22×C4×C43C2414yes—
275C22×C4×C43C2414yes—
276C22×C4×C43C2414yes—
277C22×C4×C43C2411yescharacteristic
278C22×C4×C43C2411yescharacteristic
279C22×C4×C43C2411yescharacteristic
280C2×C22⋊D43—24no—
281C2×C22⋊D43—24no—
282C2×C22⋊D43—48no—
283C2×C22⋊D43C2414yes—
284C2×C22⋊D43C2414yes—
285C2×C22⋊D43C24116yes—
286C22×Dic43C2411yescharacteristic
287C22×Dic43C2411yescharacteristic
288C22×Dic43C2411yescharacteristic
289C22×Dic43C2411yescharacteristic
290C22×Dic43C2411yescharacteristic
291C22×Dic43C2414yes—
292C22×Dic43C2411yescharacteristic
293#10621902—264no—
294#10621902—432no—
295Q8×D43—432no—
296#10621898—232no—
297#10621898—432no—
298C2×D172—28no—
299C2×D172—28no—
300C2×D172—28no—
301C2×D172—24no—
302C2×D172—216no—
303C2×D172—48no—
304C2×D172C2418yes—
305C2×D172C24116yes—
306C2×D172C2418yes—
307C2×D172C2418yes—
308C2×D172C2414yes—
309C2×D172C24116yes—
310C2×C4×D43—24no—
311C2×C4×D43—24no—
312C2×C4×D43—24no—
313C2×C4×D43—24no—
314C2×C4×D43—24no—
315C2×C4×D43—216no—
316C2×C4×D43—48no—
317C2×C4×D43—48no—
318C2×C4×D43—48no—
319C2×C4×D43#4118yescomplemented
320C2×C4×D43C2414yes—
321C2×C4×D43C2414yes—
322C2×C4×D43C2414yes—
323C2×C4×D43C2414yes—
324C2×C4×D43C2414yes—
325C2×C4×D43C24116yes—
326C2×C4×D43C24116yes—
327C2×C4×D43C24116yes—
328C2×C4×D43C24116yes—
329C2×C4×D43C2414yes—
330C2×Dic86—28no—
331C2×Dic86—24no—
332C2×Dic86—48no—
333C2×Dic86C2418yes—
334C2×Dic86C2414yes—
335C2×Dic86C24116yes—
336C4⋊C4×C43C2418yes—
337C4⋊C4×C43C2418yes—
338C4⋊C4×C43C24116yes—
339C4⋊C4×C43C24116yes—
340C4⋊C4×C43C2418yes—
341C4⋊C4×C43C2418yes—
342C22⋊C4×C43C24116yes—
343C42×C43C2414yes—
344C42×C43C2414yes—
345C42×C43C2414yes—
346C42×C43C2414yes—
347C42×C43C24116yes—
348C22⋊Dic43C2414yes—
349C22⋊Dic43C2414yes—
350(C2×D43)⋊C4C2414yes—
351(C2×D43)⋊C4C2414yes—
352(C2×D43)⋊C4C2414yes—
353(C2×D43)⋊C4C2414yes—
354(C2×D43)⋊C4C24116yes—
355(C2×D43)⋊C4C24116yes—
356(C2×D43)⋊C4C24116yes—
357(C2×D43)⋊C4C24116yes—
358(C2×D43)⋊C4C24116yes—
359(C2×D43)⋊C4C24116yes—
360(C2×D43)⋊C4C24116yes—
361C4⋊Dic43C2418yes—
362C4⋊Dic43C2418yes—
363C4⋊Dic43C24116yes—
364C4⋊Dic43C2414yes—
365C4⋊Dic43C2414yes—
366Dic43⋊C4C2414yes—
367Dic43⋊C4C24116yes—
368Dic43⋊C4C24116yes—
369Dic43⋊C4C2414yes—
370Dic43⋊C4C2414yes—
371Dic43⋊C4C2414yes—
372Dic43⋊C4C24116yes—
373C4×Dic43C2414yes—
374C4×Dic43C2414yes—
375C4×Dic43C2414yes—
376C4×Dic43C2414yes—
377C4×Dic43C2414yes—
378C4×Dic43C2414yes—
379C4×Dic43C24116yes—
380C23×C43—22no—
381C23×C43—22no—
382C23×C43—22no—
383C23×C43C2512yes—
384C23×C43C2511yescharacteristic
385C22×D43—22no—
386C22×D43—22no—
387C22×D43—28no—
388C22×D43—22no—
389C22×D43—22no—
390C22×D43—28no—
391C22×D43—22no—
392C22×D43—28no—
393C22×D43C2×#4114yes—
394C22×D43C2518yes—
395C22×D43C2512yes—
396C22×D43C2512yes—
397Q8×C43—216no—
398Q8×C43—216no—
399C2×C4×C43—22no—
400C2×C4×C43—28no—
401C2×C4×C43—28no—
402C2×C4×C43—22no—
403C2×C4×C43—22no—
404C2×C4×C43—28no—
405C2×C4×C43—28no—
406C2×C4×C43—28no—
407C2×C4×C43C2×#4114yes—
408C2×C4×C43H(5,𝔽2)14yes—
409C2×C4×C432−1+414yes—
410C2×C4×C43C2518yes—
411C2×C4×C43C2512yes—
412C2×C4×C43C2512yes—
413C2×C4×C43C2518yes—
414C2×C4×C43C2512yes—
415C2×C4×C43C2512yes—
416C2×C4×C43C2512yes—
417C2×C4×C43C2512yes—
418C22⋊D43—28no—
419C22⋊D43—28no—
420C22⋊D43—416no—
421C2×Dic43—22no—
422C2×Dic43—28no—
423C2×Dic43—22no—
424C2×Dic43—22no—
425C2×Dic43—22no—
426C2×Dic43—22no—
427C2×Dic43C2×#4114yes—
428C2×Dic43C2512yes—
429C2×Dic43C2512yes—
430C2×Dic43C2512yes—
431C2×Dic43C2512yes—
432C2×Dic43C2512yes—
433C2×Dic43C2518yes—
434C2×Dic43C2512yes—
435D172—28no—
436D172—232no—
437D172—216no—
438D172—216no—
439D172—216no—
440D172—416no—
441C4×D43—28no—
442C4×D43—28no—
443C4×D43—28no—
444C4×D43—28no—
445C4×D43—28no—
446C4×D43—232no—
447C4×D43—416no—
448C4×D43—416no—
449C4×D43—416no—
450C4×D43C2×#41116yescomplemented
451Dic86—216no—
452Dic86—28no—
453Dic86—416no—
454C2×#3511—431nomaximal, Sylow
455C22×C43—22no—
456C22×C43—22no—
457C22×C43—22no—
458C22×C43—44no—
459C22×C43C22×#4112yes—
460C22×C43C2×H(5,𝔽2)12yes—
461C22×C43C2×2−1+412yes—
462C22×C43C2611yescharacteristic
463C2×D43—22no—
464C2×D43—22no—
465C2×D43—28no—
466C2×D43—28no—
467C2×D43—22no—
468C2×D43—22no—
469C2×D43—28no—
470C2×D43—22no—
471C2×D43—28no—
472C2×D43—416no—
473C2×D43—44no—
474C2×D43C22×#4114yes—
475C4×C43—22no—
476C4×C43—28no—
477C4×C43—28no—
478C4×C43—22no—
479C4×C43—22no—
480C4×C43C22×#4114yes—
481C4×C43C2×H(5,𝔽2)14yes—
482C4×C43C2×2−1+414yes—
483Dic43—22no—
484Dic43—28no—
485Dic43—22no—
486Dic43—22no—
487Dic43—22no—
488Dic43—22no—
489Dic43C22×#4114yes—
490#3511—4332no—
491C2×#556—432no—
492C2×#555—432no—
493C2×#554—432no—
494C2×#553—432no—
495C2×#553—432no—
496C2×#548—432no—
497C2×#548—432no—
498C2×#547—432no—
499C2×#542—432no—
500C2×#542—432no—
501C2×#537—432no—
502C2×#533—431no—
503C2×#533D4311yescharacteristic, complemented
504C2×#532—431no—
505C2×#532—431no—
506C2×#532—431no—
507C22×C4⋊Q8—431no—
508C2×#520—432no—
509C2×C4×#41—431no—
510C2×C43—42no—
511C2×C43#351114yescomplemented
512C2×C43C23×#4111yescharacteristic
513C2×C43C22×H(5,𝔽2)11yescharacteristic
514C2×C43C22×2−1+411yescharacteristic
515D43—24no—
516D43—48no—
517D43—42no—
518C22×#41—432no—
519C22×#41—432no—
520C22×#41—431no—
521C22×#41—432no—
522C23×Q8—432no—
523#556—4332no—
524#555—4332no—
525#554—4332no—
526#553—4332no—
527#553—4332no—
528#548—4332no—
529#548—4332no—
530#547—4332no—
531#542—4332no—
532#542—4332no—
533#537—4332no—
534#533—4316no—
535#533C2×D43116yescomplemented
536#532—4316no—
537#532—4316no—
538#532—4316no—
539C2×C4⋊Q8—432no—
540C2×C4⋊Q8—4316no—
541C2×C4⋊Q8—432no—
542C2×C4⋊Q8—432no—
543C2×C4⋊Q8—431no—
544C2×C4⋊Q8C2×D4311yescharacteristic
545C2×C4⋊Q8C2×D4311yescharacteristic
546C2×#127—431no—
547C2×#126—434no—
548C2×#126—434no—
549C2×#125—432no—
550C2×#125C2×D4312yes—
551C2×#124—432no—
552C2×#124—432no—
553C2×#124—434no—
554C2×#124—432no—
555C2×#124—434no—
556C2×#123—434no—
557C2×#123—434no—
558C2×C22⋊Q8—432no—
559C2×C22⋊Q8—434no—
560C2×C22⋊Q8—434no—
561C2×C22⋊Q8—432no—
562C2×C22⋊Q8—434no—
563C2×C22⋊Q8C2×D4312yes—
564C2×C22⋊Q8C2×D4312yes—
565C2×#121—432no—
566C2×#121—432no—
567C2×#121—432no—
568C2×#121—432no—
569C2×#121—432no—
570C2×#121—432no—
571C2×#121—434no—
572C2×#121—434no—
573C2×#121—434no—
574#520—4332no—
575C4×#41—4316no—
576C2×C4×Q8—432no—
577C2×C4×Q8—432no—
578C2×C4×Q8—431no—
579C2×C4×Q8—431no—
580C2×C4×Q8C2×D4312yes—
581C2×C4×Q8C2×D4312yes—
582C2×C4×D4—431no—
583C2×C4×D4—431no—
584C2×C4×D4—431no—
585C2×C4×D4—431no—
586C2×C4×D4—432no—
587C2×C4×D4—434no—
588C2×C4×D4—432no—
589C2×C4×D4—432no—
590C2×C4×D4—432no—
591C2×C4×D4—431no—
592C2×C4×D4—431no—
593C2×C4×D4—432no—
594C2×C4×D4—434no—
595C2×C4×D4—432no—
596C2×#117—431no—
597C2×#117—432no—
598C2×#117—431no—
599C2×#117—431no—
600C2×#117—434no—
601C2×#117C2×D4312yes—
602C22×C4⋊C4—432no—
603C22×C4⋊C4—434no—
604C22×C4⋊C4—432no—
605C22×C42—431no—
606C22×C42—431no—
607C22×C42C2×D4311yescharacteristic
608C43C2×#351111yescharacteristic, complemented, Sylow
609C2×#41—4316no—
610C2×#41—4316no—
611C2×#41—438no—
612C2×#41—4316no—
613C2×#41—868no—
614C2×#41—8616no—
615C2×#41—1728no—
616C2×#41—1728no—
617C22×Q8—4316no—
618C22×Q8—431no—
619C22×Q8—432no—
620C22×Q8—434no—
621C22×Q8—1728no—
622C22×Q8C22×D4312yes—
623C22×Q8C22×D4312yes—
624C22×D4—431no—
625C22×D4—431no—
626C22×D4—434no—
627C22×D4—432no—
628C22×D4—434no—
629C22×D4—431no—
630C22×D4—432no—
631C22×D4—432no—
632C22×D4—434no—
633C23×C4—431no—
634C23×C4—431no—
635C23×C4—434no—
636C23×C4—431no—
637C23×C4—431no—
638C23×C4—431no—
639C23×C4—431no—
640C23×C4—434no—
641C23×C4—434no—
642C23×C4—434no—
643C23×C4C22×D4311yescharacteristic
644C23×C4C22×D4311yescharacteristic
645C23×C4C22×D4311yescharacteristic
646C4⋊Q8—4316no—
647C4⋊Q8—4316no—
648C4⋊Q8—4316no—
649C4⋊Q8—438no—
650C4⋊Q8C22×D4318yes—
651C4⋊Q8C22×D4318yes—
652#127—438no—
653#126—4332no—
654#126—4332no—
655#125—4316no—
656#125C22×D43116yes—
657#124—4316no—
658#124—4316no—
659#124—4332no—
660#124—4316no—
661#124—4332no—
662#123—4332no—
663#123—4332no—
664C22⋊Q8—4316no—
665C22⋊Q8—4316no—
666C22⋊Q8—4332no—
667C22⋊Q8—4332no—
668C22⋊Q8—4332no—
669C22⋊Q8C22×D43116yes—
670C22⋊Q8C22×D43116yes—
671#121—4316no—
672#121—4316no—
673#121—4316no—
674#121—4316no—
675#121—4316no—
676#121—4316no—
677#121—4332no—
678#121—4332no—
679#121—4332no—
680C4×Q8—4316no—
681C4×Q8—4316no—
682C4×Q8—438no—
683C4×Q8—438no—
684C4×Q8C22×D43116yes—
685C4×Q8C22×D43116yes—
686C4×D4—438no—
687C4×D4—438no—
688C4×D4—438no—
689C4×D4—438no—
690C4×D4—4316no—
691C4×D4—4332no—
692C4×D4—4316no—
693C4×D4—4316no—
694C4×D4—4316no—
695C4×D4—438no—
696C4×D4—438no—
697C4×D4—4316no—
698C4×D4—4332no—
699C4×D4—4316no—
700#117—438no—
701#117—4316no—
702#117—438no—
703#117—438no—
704#117—4332no—
705#117C22×D43116yes—
706C2×C4⋊C4—431no—
707C2×C4⋊C4—434no—
708C2×C4⋊C4—432no—
709C2×C4⋊C4—432no—
710C2×C4⋊C4—434no—
711C2×C4⋊C4—434no—
712C2×C4⋊C4—431no—
713C2×C4⋊C4—431no—
714C2×C4⋊C4—431no—
715C2×C4⋊C4—431no—
716C2×C4⋊C4—431no—
717C2×C4⋊C4—434no—
718C2×C4⋊C4—4316no—
719C2×C4⋊C4—4332no—
720C2×C4⋊C4—4316no—
721C2×C4⋊C4C22×D4312yes—
722C2×C4⋊C4C22×D4312yes—
723C2×C4⋊C4C22×D4314yes—
724C2×C4⋊C4C22×D4312yes—
725C2×C4⋊C4C22×D4312yes—
726C2×C4⋊C4C22×D4314yes—
727C2×C22⋊C4—431no—
728C2×C22⋊C4—431no—
729C2×C22⋊C4—431no—
730C2×C22⋊C4—431no—
731C2×C22⋊C4—434no—
732C2×C22⋊C4—434no—
733C2×C22⋊C4—431no—
734C2×C22⋊C4—431no—
735C2×C22⋊C4—434no—
736C2×C22⋊C4—434no—
737C2×C22⋊C4—434no—
738C2×C22⋊C4—434no—
739C2×C22⋊C4—434no—
740C2×C22⋊C4C22×D4314yes—
741C2×C42—431no—
742C2×C42—434no—
743C2×C42—431no—
744C2×C42—431no—
745C2×C42—431no—
746C2×C42—431no—
747C2×C42—431no—
748C2×C42—438no—
749C2×C42—438no—
750C2×C42C22×D4311yescharacteristic
751C2×C42C22×D4314yes—
752C2×C42C22×D4311yescharacteristic
753C2×C42C22×D4311yescharacteristic
754C2×C42C22×D4318yes—
755C2×C42C22×D4311yescharacteristic
756C24—431no—
757C24—431no—
758C24—434no—
759C24C23×D4311yescharacteristic
760#41—8632no—
761#41—8664no—
762#41—17232no—
763#41—17232no—
764C2×Q8—28no—
765C2×Q8—28no—
766C2×Q8—434no—
767C2×Q8—438no—
768C2×Q8—4316no—
769C2×Q8—864no—
770C2×Q8—868no—
771C2×Q8—1728no—
772C2×Q8—17232no—
773C2×Q8C23×D4318yes—
774C2×Q8C23×D4318yes—
775C2×D4—434no—
776C2×D4—434no—
777C2×D4—4316no—
778C2×D4—438no—
779C2×D4—4316no—
780C2×D4—434no—
781C2×D4—438no—
782C2×D4—438no—
783C2×D4—4316no—
784C2×D4—864no—
785C2×D4—8616no—
786C2×D4—864no—
787C2×D4—864no—
788C2×D4—868no—
789C2×D4—868no—
790C2×D4—868no—
791C2×D4—1728no—
792C2×D4—1728no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—431no—
797C22×C4—438no—
798C22×C4—434no—
799C22×C4—431no—
800C22×C4—431no—
801C22×C4—431no—
802C22×C4—431no—
803C22×C4—431no—
804C22×C4—434no—
805C22×C4—434no—
806C22×C4—434no—
807C22×C4—434no—
808C22×C4—434no—
809C22×C4—434no—
810C22×C4—4316no—
811C22×C4—4316no—
812C22×C4—4316no—
813C22×C4—4316no—
814C22×C4—8616no—
815C22×C4—864no—
816C22×C4—864no—
817C22×C4—864no—
818C22×C4—864no—
819C22×C4—864no—
820C22×C4—1728no—
821C22×C4—1728no—
822C22×C4—1728no—
823C22×C4C23×D4314yes—
824C22×C4C23×D4314yes—
825C22×C4C23×D4314yes—
826C22×C4C23×D4314yes—
827C22×C4C23×D4311yescharacteristic
828C22×C4C23×D4311yescharacteristic
829C22×C4C23×D4311yescharacteristic
830C22×C4C23×D4314yes—
831C22×C4C23×D4311yescharacteristic
832C22×C4C23×D4311yescharacteristic
833C22×C4C23×D4311yescharacteristic
834C4⋊C4—434no—
835C4⋊C4—4316no—
836C4⋊C4—438no—
837C4⋊C4—438no—
838C4⋊C4—4316no—
839C4⋊C4—4316no—
840C4⋊C4—434no—
841C4⋊C4—434no—
842C4⋊C4—434no—
843C4⋊C4—434no—
844C4⋊C4—434no—
845C4⋊C4—4316no—
846C4⋊C4C23×D4318yes—
847C4⋊C4C23×D4318yes—
848C4⋊C4C23×D43116yes—
849C4⋊C4C23×D4318yes—
850C4⋊C4C23×D4318yes—
851C4⋊C4C23×D43116yes—
852C22⋊C4—434no—
853C22⋊C4—434no—
854C22⋊C4—434no—
855C22⋊C4—434no—
856C22⋊C4—4316no—
857C22⋊C4—4316no—
858C22⋊C4—434no—
859C22⋊C4—434no—
860C22⋊C4—4316no—
861C22⋊C4—4316no—
862C22⋊C4—4316no—
863C22⋊C4—4316no—
864C22⋊C4—4316no—
865C22⋊C4C23×D43116yes—
866C42—434no—
867C42—434no—
868C42—434no—
869C42—434no—
870C42—434no—
871C42—434no—
872C42—4316no—
873C42C23×D4314yes—
874C42C23×D4314yes—
875C42C23×D4314yes—
876C42C23×D4314yes—
877C42C23×D43116yes—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—434no—
882C23—432no—
883C23—432no—
884C23—438no—
885C23—862no—
886C23—862no—
887C23—868no—
888C23—862no—
889C23—862no—
890C23—868no—
891C23—862no—
892C23—868no—
893C23C24×D4312yes—
894C23C24×D4311yescharacteristic
895Q8—216no—
896Q8—216no—
897Q8—868no—
898Q8—8616no—
899Q8—17216no—
900D4—868no—
901D4—8632no—
902D4—868no—
903D4—868no—
904D4—8616no—
905D4—8616no—
906D4—8616no—
907D4—17216no—
908D4—17216no—
909C2×C4—22no—
910C2×C4—28no—
911C2×C4—22no—
912C2×C4—28no—
913C2×C4—22no—
914C2×C4—28no—
915C2×C4—28no—
916C2×C4—28no—
917C2×C4—434no—
918C2×C4—432no—
919C2×C4—4316no—
920C2×C4—432no—
921C2×C4—432no—
922C2×C4—432no—
923C2×C4—432no—
924C2×C4—432no—
925C2×C4—438no—
926C2×C4—8632no—
927C2×C4—862no—
928C2×C4—862no—
929C2×C4—862no—
930C2×C4—868no—
931C2×C4—862no—
932C2×C4—862no—
933C2×C4—868no—
934C2×C4—868no—
935C2×C4—868no—
936C2×C4—868no—
937C2×C4—868no—
938C2×C4—17216no—
939C2×C4—17216no—
940C2×C4—17216no—
941C2×C4#41×D4314yes—
942C2×C4#1306337114yes—
943C2×C4#1306337314yes—
944C2×C4C24×D4318yes—
945C2×C4C24×D4312yes—
946C2×C4C24×D4312yes—
947C2×C4C24×D4312yes—
948C2×C4C24×D4318yes—
949C2×C4C24×D4312yes—
950C2×C4C24×D4312yes—
951C2×C4C24×D4312yes—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—44no—
956C22—434no—
957C22—862no—
958C22—862no—
959C22—868no—
960C22—868no—
961C22—862no—
962C22—862no—
963C22—868no—
964C22—862no—
965C22—868no—
966C22—1724no—
967C22—17216no—
968C22C2×#41×D4312yes—
969C22C2×#1306337112yes—
970C22C2×#1306337312yes—
971C22C25×D4311yescharacteristic
972C4—22no—
973C4—28no—
974C4—22no—
975C4—28no—
976C4—22no—
977C4—434no—
978C4—862no—
979C4—862no—
980C4—862no—
981C4—868no—
982C4—862no—
983C4—862no—
984C4C2×#41×D4314yes—
985C4C2×#1306337114yes—
986C4C2×#1306337314yes—
987C2—42no—
988C2—864no—
989C2—1722no—
990C2—1728no—
991C2#1914850714yesdirect product factor
992C2C22×#41×D4311yescharacteristic
993C2C22×#1306337111yescharacteristic
994C2C22×#1306337311yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#533C2
socleC23×C43C25
hypercenterC2×#533D43
hypocenterC43C2×#3511
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #19148507C2direct (N × H)
2. C2×#14583621C2semidirect
3. C2×#14583612C2semidirect
4. C2×#14583605C2semidirect
5. C2×#14583602C2semidirect
6. C2×#14583593C2semidirect
7. C2×#14583561C2semidirect
8. C2×#14583559C2semidirect
9. C2×#14583551C2semidirect
10. C2×#14583522C2semidirect
11. C2×#14583521C2semidirect
12. C2×#14583479C2semidirect
13. C2×#14583454C2semidirect
14. C2×#14583450C2semidirect
15. C2×#14583450C2semidirect
16. C2×#14583449C2semidirect
17. C2×C4⋊Q8×D43C2semidirect
18. C2×#14583381C2semidirect
19. C2×C4×#10621898C2semidirect
20. C2×C43×#533C2semidirect
26. #14583621C22semidirect
27. #14583612C22semidirect
28. #14583605C22semidirect
29. #14583602C22semidirect
30. #14583593C22semidirect
31. #14583561C22semidirect
32. #14583559C22semidirect
33. #14583551C22semidirect
34. #14583522C22semidirect
35. #14583521C22semidirect
36. #14583479C22semidirect
37. #14583454C22semidirect
38. #14583450C22semidirect
39. #14583450C22semidirect
40. #14583449C22semidirect
45. C4⋊Q8×D43C22semidirect
71. #14583381C22semidirect
72. C4×#10621898C22semidirect
101. C43×#533C22semidirect
319. C2×C4×D43#41semidirect
450. C4×D43C2×#41semidirect
503. C2×#533D43semidirect
511. C2×C43#3511semidirect
535. #533C2×D43semidirect
608. C43C2×#3511semidirect
991. C2#19148507direct (N × H)

Maximal subgroups

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

subgroupindex
#191485072
C2×#145836212
C2×#145836122
C2×#145836052
C2×#145836022
C2×#145835932
C2×#145835612
C2×#145835592
C2×#145835512
C2×#145835222
C2×#145835212
C2×#145834792
C2×#145834542
C2×#145834502
C2×#145834492
C2×C4⋊Q8×D432
C2×#145833812
C2×C4×#106218982
C2×C43×#5332
C2×#351143