Finite Group Databasebeta

← C2×#20257300 #27124642

Subgroups — C2×#20257300 #27124642

Order 12032.

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#20257300C2132yesmaximal, direct product factor
2C2×#15689845C212yesmaximal, complemented
3C2×#15689836C212yesmaximal, complemented
4C2×#15689829C212yesmaximal, complemented
5C2×#15689826C212yesmaximal, complemented
6C2×#15689817C212yesmaximal, complemented
7C2×#15689785C212yesmaximal, complemented
8C2×#15689783C212yesmaximal, complemented
9C2×#15689775C212yesmaximal, complemented
10C2×#15689746C212yesmaximal, complemented
11C2×#15689745C212yesmaximal, complemented
12C2×#15689703C212yesmaximal, complemented
13C2×#15689678C211yesmaximal, characteristic, complemented
14C2×#15689674C211yesmaximal, characteristic, complemented
15C2×#15689674C211yesmaximal, characteristic, complemented
16C2×#15689673C211yesmaximal, characteristic, complemented
17C2×C4⋊Q8×D47C211yesmaximal, characteristic, complemented
18C2×#15689605C212yesmaximal, complemented
19C2×C4×#10625350C211yesmaximal, characteristic, complemented
20C2×C47×#533C211yesmaximal, characteristic, complemented
21C22×#10625354C2212yes—
22C22×#10625354C2212yes—
23C22×#10625350C2211yescharacteristic
24C22×#10625350C2212yes—
25C22×Q8×D47C2212yes—
26#15689845C22132yescomplemented
27#15689836C22132yescomplemented
28#15689829C22132yescomplemented
29#15689826C22132yescomplemented
30#15689817C22132yescomplemented
31#15689785C22132yescomplemented
32#15689783C22132yescomplemented
33#15689775C22132yescomplemented
34#15689746C22132yescomplemented
35#15689745C22132yescomplemented
36#15689703C22132yescomplemented
37#15689678C22116yescomplemented
38#15689674C22116yescomplemented
39#15689674C22116yescomplemented
40#15689673C22116yescomplemented
41C2×#13094024C2211yescharacteristic
42C2×#13094023C2212yes—
43C2×#13094023C2212yes—
44C2×#13094022C2212yes—
45C4⋊Q8×D47C22116yescomplemented
46C2×#13094021C2211yescharacteristic
47C2×#13094019C2214yes—
48C2×#13094018C2214yes—
49C2×#13094015C2212yes—
50C2×#13094013C2212yes—
51C2×#13094013C2212yes—
52C2×#13094012C2214yes—
53C2×#13094012C2212yes—
54C2×#13094010C2214yes—
55C2×#13094009C2214yes—
56C2×#13094006C2214yes—
57C2×#13094004C2214yes—
58C2×#13094004C2212yes—
59C2×#13094002C2214yes—
60C2×#13094002C2214yes—
61C2×#13094000C2212yes—
62C2×#13093999C2212yes—
63C2×#13093999C2214yes—
64C2×#13093999C2212yes—
65C2×#13093999C2212yes—
66C2×#13093999C2212yes—
67C2×#13093998C2212yes—
68C2×#13093998C2212yes—
69C2×#13093997C2214yes—
70C2×#13093997C2214yes—
71#15689605C22132yescomplemented
72C4×#10625350C22116yescomplemented
73C2×Q8×Dic47C2212yes—
74C2×C4×Dic94C2211yescharacteristic
75C2×C4×Dic94C2211yescharacteristic
76C2×#13093989C2212yes—
77C2×C4×D188C2211yescharacteristic
78C2×C4×D188C2211yescharacteristic
79C2×C4×D188C2214yes—
80C2×C4×D188C2212yes—
81C2×C4×D188C2212yes—
82C2×#13093986C2212yes—
83C2×#13093986C2214yes—
84C2×#13093986C2212yes—
85C2×#13093986C2212yes—
86C2×#13093986C2212yes—
87C2×C4×C22⋊D47C2211yescharacteristic
88C2×C4×C22⋊D47C2211yescharacteristic
89C2×C4×C22⋊D47C2211yescharacteristic
90C2×C4×C22⋊D47C2211yescharacteristic
91C2×#13093983C2211yescharacteristic
92C2×#13093982C2212yes—
93C2×#13093981C2211yescharacteristic
94C2×#13093981C2211yescharacteristic
95C2×#13093981C2214yes—
96C2×C4⋊C4×D47C2214yes—
97C2×C4⋊C4×D47C2212yes—
98C2×C4⋊C4×D47C2212yes—
99C2×C42×D47C2211yescharacteristic
100C2×C42×D47C2211yescharacteristic
101C47×#533C22116yescomplemented
102C2×C4⋊Q8×C47C2211yescharacteristic
103C2×C4⋊Q8×C47C2211yescharacteristic
104C2×#125×C47C2212yes—
105C2×C22⋊Q8×C47C2212yes—
106C2×C22⋊Q8×C47C2212yes—
107C2×C4×Q8×C47C2212yes—
108C2×C4×Q8×C47C2212yes—
109C2×#117×C47C2212yes—
110C22×C42×C47C2211yescharacteristic
111C2×#10625354—216no—
112C2×#10625354—48no—
113C2×#10625354C23116yes—
114C2×#10625354C23116yes—
115C2×#10625350—28no—
116C2×#10625350—48no—
117C2×#10625350C2318yes—
118C2×#10625350C23116yes—
119C22×Dic94C2312yes—
120C22×Dic94C2311yescharacteristic
121C22×Dic94C2314yes—
122C2×Q8×D47—48no—
123C2×Q8×D47C23116yes—
124C22×D188C2312yes—
125C22×D188C2314yes—
126C22×D188C2312yes—
127C22×D188C2312yes—
128C22×D188C2311yescharacteristic
129C22×D188C2314yes—
130C22×C22⋊D47C2311yescharacteristic
131C22×C22⋊D47C2311yescharacteristic
132C22×C22⋊D47C2314yes—
133C22×C4×D47C2311yescharacteristic
134C22×C4×D47C2311yescharacteristic
135C22×C4×D47C2311yescharacteristic
136C22×C4×D47C2311yescharacteristic
137C22×C4×D47C2311yescharacteristic
138C22×C4×D47C2314yes—
139C22×C4×D47C2314yes—
140C22×C4×D47C2314yes—
141C22×C4×D47C2314yes—
142C22×C4×D47C2311yescharacteristic
143#13094024C2318yes—
144#13094023C23116yes—
145#13094023C23116yes—
146#13094022C23116yes—
147#13094021C2318yes—
148#13094019C23132yes—
149#13094018C23132yes—
150#13094015C23116yes—
151#13094013C23116yes—
152#13094013C23116yes—
153#13094012C23132yes—
154#13094012C23116yes—
155#13094010C23132yes—
156#13094009C23132yes—
157#13094006C23132yes—
158#13094004C23132yes—
159#13094004C23116yes—
160#13094002C23132yes—
161#13094002C23132yes—
162#13094000C23116yes—
163#13093999C23116yes—
164#13093999C23116yes—
165#13093999C23132yes—
166#13093999C23116yes—
167#13093999C23116yes—
168#13093998C23116yes—
169#13093998C23116yes—
170#13093997C23132yes—
171#13093997C23132yes—
172Q8×Dic47C23116yes—
173C4×Dic94C2318yes—
174C4×Dic94C2318yes—
175#13093989C23116yes—
176C4×D188C23116yes—
177C4×D188C2318yes—
178C4×D188C23132yes—
179C4×D188C2318yes—
180C4×D188C23116yes—
181#13093986C23116yes—
182#13093986C23116yes—
183#13093986C23132yes—
184#13093986C23116yes—
185#13093986C23116yes—
186C4×C22⋊D47C2318yes—
187C4×C22⋊D47C2318yes—
188C4×C22⋊D47C2318yes—
189C4×C22⋊D47C2318yes—
190#13093983C2318yes—
191#13093982C23116yes—
192#13093981C2318yes—
193#13093981C23132yes—
194#13093981C2318yes—
195C2×C4⋊Dic47C2312yes—
196C2×C4⋊Dic47C2312yes—
197C2×C4⋊Dic47C2314yes—
198C2×C4⋊Dic47C2311yescharacteristic
199C2×C4⋊Dic47C2311yescharacteristic
200C2×Dic47⋊C4C2311yescharacteristic
201C2×Dic47⋊C4C2314yes—
202C2×Dic47⋊C4C2314yes—
203C2×Dic47⋊C4C2311yescharacteristic
204C2×Dic47⋊C4C2311yescharacteristic
205C2×Dic47⋊C4C2311yescharacteristic
206C2×Dic47⋊C4C2314yes—
207C4⋊C4×D47C23132yes—
208C4⋊C4×D47C23116yes—
209C4⋊C4×D47C23116yes—
210C2×C22⋊Dic47C2311yescharacteristic
211C2×C22⋊Dic47C2311yescharacteristic
212C2×(C2×D47)⋊C4C2311yescharacteristic
213C2×(C2×D47)⋊C4C2311yescharacteristic
214C2×(C2×D47)⋊C4C2311yescharacteristic
215C2×(C2×D47)⋊C4C2311yescharacteristic
216C2×(C2×D47)⋊C4C2314yes—
217C2×(C2×D47)⋊C4C2314yes—
218C2×(C2×D47)⋊C4C2314yes—
219C2×(C2×D47)⋊C4C2314yes—
220C2×(C2×D47)⋊C4C2314yes—
221C2×(C2×D47)⋊C4C2314yes—
222C2×(C2×D47)⋊C4C2314yes—
223C2×C4×Dic47C2311yescharacteristic
224C2×C4×Dic47C2311yescharacteristic
225C2×C4×Dic47C2311yescharacteristic
226C2×C4×Dic47C2311yescharacteristic
227C2×C4×Dic47C2311yescharacteristic
228C2×C4×Dic47C2311yescharacteristic
229C2×C4×Dic47C2314yes—
230C42×D47C2318yes—
231C42×D47C2318yes—
232C22×Q8×C47C2312yes—
233C22×Q8×C47C2312yes—
234C23×C4×C47C2311yescharacteristic
235C23×C4×C47C2311yescharacteristic
236C23×C4×C47C2311yescharacteristic
237C4⋊Q8×C47C2318yes—
238C4⋊Q8×C47C2318yes—
239#125×C47C23116yes—
240C22⋊Q8×C47C23116yes—
241C22⋊Q8×C47C23116yes—
242C4×Q8×C47C23116yes—
243C4×Q8×C47C23116yes—
244#117×C47C23116yes—
245C2×C4⋊C4×C47C2312yes—
246C2×C4⋊C4×C47C2312yes—
247C2×C4⋊C4×C47C2314yes—
248C2×C4⋊C4×C47C2314yes—
249C2×C4⋊C4×C47C2312yes—
250C2×C4⋊C4×C47C2312yes—
251C2×C22⋊C4×C47C2314yes—
252C2×C42×C47C2311yescharacteristic
253C2×C42×C47C2311yescharacteristic
254C2×C42×C47C2311yescharacteristic
255C2×C42×C47C2311yescharacteristic
256C2×C42×C47C2318yes—
257C2×C42×C47C2314yes—
258C24×C47C2411yescharacteristic
259C23×D47C2414yes—
260C23×D47C2411yescharacteristic
261C23×D47C2411yescharacteristic
262C2×Q8×C47—28no—
263C2×Q8×C47—28no—
264C2×Q8×C47C2418yes—
265C2×Q8×C47C2418yes—
266C22×C4×C47—24no—
267C22×C4×C47—24no—
268C22×C4×C47—24no—
269C22×C4×C47C2411yescharacteristic
270C22×C4×C47C2411yescharacteristic
271C22×C4×C47C2411yescharacteristic
272C22×C4×C47C2414yes—
273C22×C4×C47C2414yes—
274C22×C4×C47C2414yes—
275C22×C4×C47C2414yes—
276C22×C4×C47C2414yes—
277C22×C4×C47C2411yescharacteristic
278C22×C4×C47C2411yescharacteristic
279C22×C4×C47C2411yescharacteristic
280C2×C22⋊D47—24no—
281C2×C22⋊D47—24no—
282C2×C22⋊D47—48no—
283C2×C22⋊D47C2414yes—
284C2×C22⋊D47C2414yes—
285C2×C22⋊D47C24116yes—
286C22×Dic47C2411yescharacteristic
287C22×Dic47C2411yescharacteristic
288C22×Dic47C2411yescharacteristic
289C22×Dic47C2411yescharacteristic
290C22×Dic47C2411yescharacteristic
291C22×Dic47C2414yes—
292C22×Dic47C2411yescharacteristic
293#10625354—264no—
294#10625354—432no—
295Q8×D47—432no—
296#10625350—232no—
297#10625350—432no—
298C2×D188—24no—
299C2×D188—216no—
300C2×D188—28no—
301C2×D188—28no—
302C2×D188—28no—
303C2×D188—48no—
304C2×D188C2418yes—
305C2×D188C24116yes—
306C2×D188C2418yes—
307C2×D188C2418yes—
308C2×D188C2414yes—
309C2×D188C24116yes—
310C2×C4×D47—24no—
311C2×C4×D47—24no—
312C2×C4×D47—24no—
313C2×C4×D47—24no—
314C2×C4×D47—24no—
315C2×C4×D47—216no—
316C2×C4×D47—48no—
317C2×C4×D47—48no—
318C2×C4×D47—48no—
319C2×C4×D47#4118yescomplemented
320C2×C4×D47C2414yes—
321C2×C4×D47C2414yes—
322C2×C4×D47C2414yes—
323C2×C4×D47C2414yes—
324C2×C4×D47C2414yes—
325C2×C4×D47C24116yes—
326C2×C4×D47C24116yes—
327C2×C4×D47C24116yes—
328C2×C4×D47C24116yes—
329C2×C4×D47C2414yes—
330C2×Dic94—28no—
331C2×Dic94—24no—
332C2×Dic94—48no—
333C2×Dic94C2418yes—
334C2×Dic94C2414yes—
335C2×Dic94C24116yes—
336C4⋊C4×C47C2418yes—
337C4⋊C4×C47C2418yes—
338C4⋊C4×C47C24116yes—
339C4⋊C4×C47C24116yes—
340C4⋊C4×C47C2418yes—
341C4⋊C4×C47C2418yes—
342C22⋊C4×C47C24116yes—
343C42×C47C2414yes—
344C42×C47C2414yes—
345C42×C47C2414yes—
346C42×C47C2414yes—
347C42×C47C24116yes—
348C22⋊Dic47C2414yes—
349C22⋊Dic47C2414yes—
350(C2×D47)⋊C4C2414yes—
351(C2×D47)⋊C4C2414yes—
352(C2×D47)⋊C4C2414yes—
353(C2×D47)⋊C4C2414yes—
354(C2×D47)⋊C4C24116yes—
355(C2×D47)⋊C4C24116yes—
356(C2×D47)⋊C4C24116yes—
357(C2×D47)⋊C4C24116yes—
358(C2×D47)⋊C4C24116yes—
359(C2×D47)⋊C4C24116yes—
360(C2×D47)⋊C4C24116yes—
361C4⋊Dic47C2418yes—
362C4⋊Dic47C2418yes—
363C4⋊Dic47C24116yes—
364C4⋊Dic47C2414yes—
365C4⋊Dic47C2414yes—
366Dic47⋊C4C2414yes—
367Dic47⋊C4C24116yes—
368Dic47⋊C4C24116yes—
369Dic47⋊C4C2414yes—
370Dic47⋊C4C2414yes—
371Dic47⋊C4C2414yes—
372Dic47⋊C4C24116yes—
373C4×Dic47C2414yes—
374C4×Dic47C2414yes—
375C4×Dic47C2414yes—
376C4×Dic47C2414yes—
377C4×Dic47C2414yes—
378C4×Dic47C2414yes—
379C4×Dic47C24116yes—
380C23×C47—22no—
381C23×C47—22no—
382C23×C47—22no—
383C23×C47C2512yes—
384C23×C47C2511yescharacteristic
385C22×D47—22no—
386C22×D47—22no—
387C22×D47—28no—
388C22×D47—22no—
389C22×D47—22no—
390C22×D47—28no—
391C22×D47—22no—
392C22×D47—28no—
393C22×D47C2×#4114yes—
394C22×D47C2518yes—
395C22×D47C2512yes—
396C22×D47C2512yes—
397Q8×C47—216no—
398Q8×C47—216no—
399C2×C4×C47—22no—
400C2×C4×C47—28no—
401C2×C4×C47—28no—
402C2×C4×C47—22no—
403C2×C4×C47—22no—
404C2×C4×C47—28no—
405C2×C4×C47—28no—
406C2×C4×C47—28no—
407C2×C4×C47C2×#4114yes—
408C2×C4×C47H(5,𝔽2)14yes—
409C2×C4×C472−1+414yes—
410C2×C4×C47C2518yes—
411C2×C4×C47C2512yes—
412C2×C4×C47C2512yes—
413C2×C4×C47C2518yes—
414C2×C4×C47C2512yes—
415C2×C4×C47C2512yes—
416C2×C4×C47C2512yes—
417C2×C4×C47C2512yes—
418C22⋊D47—28no—
419C22⋊D47—28no—
420C22⋊D47—416no—
421C2×Dic47—22no—
422C2×Dic47—28no—
423C2×Dic47—22no—
424C2×Dic47—22no—
425C2×Dic47—22no—
426C2×Dic47—22no—
427C2×Dic47C2×#4114yes—
428C2×Dic47C2512yes—
429C2×Dic47C2512yes—
430C2×Dic47C2512yes—
431C2×Dic47C2512yes—
432C2×Dic47C2512yes—
433C2×Dic47C2518yes—
434C2×Dic47C2512yes—
435D188—28no—
436D188—232no—
437D188—216no—
438D188—216no—
439D188—216no—
440D188—416no—
441C4×D47—28no—
442C4×D47—28no—
443C4×D47—28no—
444C4×D47—28no—
445C4×D47—28no—
446C4×D47—232no—
447C4×D47—416no—
448C4×D47—416no—
449C4×D47—416no—
450C4×D47C2×#41116yescomplemented
451Dic94—216no—
452Dic94—28no—
453Dic94—416no—
454C2×#3511—471nomaximal, Sylow
455C22×C47—22no—
456C22×C47—22no—
457C22×C47—22no—
458C22×C47—44no—
459C22×C47C22×#4112yes—
460C22×C47C2×H(5,𝔽2)12yes—
461C22×C47C2×2−1+412yes—
462C22×C47C2611yescharacteristic
463C2×D47—22no—
464C2×D47—22no—
465C2×D47—28no—
466C2×D47—28no—
467C2×D47—22no—
468C2×D47—22no—
469C2×D47—28no—
470C2×D47—22no—
471C2×D47—28no—
472C2×D47—416no—
473C2×D47—44no—
474C2×D47C22×#4114yes—
475C4×C47—22no—
476C4×C47—28no—
477C4×C47—28no—
478C4×C47—22no—
479C4×C47—22no—
480C4×C47C22×#4114yes—
481C4×C47C2×H(5,𝔽2)14yes—
482C4×C47C2×2−1+414yes—
483Dic47—22no—
484Dic47—28no—
485Dic47—22no—
486Dic47—22no—
487Dic47—22no—
488Dic47—22no—
489Dic47C22×#4114yes—
490#3511—4732no—
491C2×#556—472no—
492C2×#555—472no—
493C2×#554—472no—
494C2×#553—472no—
495C2×#553—472no—
496C2×#548—472no—
497C2×#548—472no—
498C2×#547—472no—
499C2×#542—472no—
500C2×#542—472no—
501C2×#537—472no—
502C2×#533—471no—
503C2×#533D4711yescharacteristic, complemented
504C2×#532—471no—
505C2×#532—471no—
506C2×#532—471no—
507C22×C4⋊Q8—471no—
508C2×#520—472no—
509C2×C4×#41—471no—
510C2×C47—42no—
511C2×C47#351114yescomplemented
512C2×C47C23×#4111yescharacteristic
513C2×C47C22×H(5,𝔽2)11yescharacteristic
514C2×C47C22×2−1+411yescharacteristic
515D47—24no—
516D47—48no—
517D47—42no—
518C22×#41—472no—
519C22×#41—472no—
520C22×#41—471no—
521C22×#41—472no—
522C23×Q8—472no—
523#556—4732no—
524#555—4732no—
525#554—4732no—
526#553—4732no—
527#553—4732no—
528#548—4732no—
529#548—4732no—
530#547—4732no—
531#542—4732no—
532#542—4732no—
533#537—4732no—
534#533—4716no—
535#533C2×D47116yescomplemented
536#532—4716no—
537#532—4716no—
538#532—4716no—
539C2×C4⋊Q8—472no—
540C2×C4⋊Q8—4716no—
541C2×C4⋊Q8—472no—
542C2×C4⋊Q8—472no—
543C2×C4⋊Q8—471no—
544C2×C4⋊Q8C2×D4711yescharacteristic
545C2×C4⋊Q8C2×D4711yescharacteristic
546C2×#127—471no—
547C2×#126—474no—
548C2×#126—474no—
549C2×#125—472no—
550C2×#125C2×D4712yes—
551C2×#124—472no—
552C2×#124—472no—
553C2×#124—474no—
554C2×#124—472no—
555C2×#124—474no—
556C2×#123—474no—
557C2×#123—474no—
558C2×C22⋊Q8—472no—
559C2×C22⋊Q8—472no—
560C2×C22⋊Q8—474no—
561C2×C22⋊Q8—474no—
562C2×C22⋊Q8—474no—
563C2×C22⋊Q8C2×D4712yes—
564C2×C22⋊Q8C2×D4712yes—
565C2×#121—472no—
566C2×#121—472no—
567C2×#121—472no—
568C2×#121—472no—
569C2×#121—472no—
570C2×#121—472no—
571C2×#121—474no—
572C2×#121—474no—
573C2×#121—474no—
574#520—4732no—
575C4×#41—4716no—
576C2×C4×Q8—472no—
577C2×C4×Q8—472no—
578C2×C4×Q8—471no—
579C2×C4×Q8—471no—
580C2×C4×Q8C2×D4712yes—
581C2×C4×Q8C2×D4712yes—
582C2×C4×D4—471no—
583C2×C4×D4—471no—
584C2×C4×D4—471no—
585C2×C4×D4—471no—
586C2×C4×D4—472no—
587C2×C4×D4—474no—
588C2×C4×D4—472no—
589C2×C4×D4—472no—
590C2×C4×D4—472no—
591C2×C4×D4—471no—
592C2×C4×D4—471no—
593C2×C4×D4—472no—
594C2×C4×D4—474no—
595C2×C4×D4—472no—
596C2×#117—471no—
597C2×#117—472no—
598C2×#117—471no—
599C2×#117—471no—
600C2×#117—474no—
601C2×#117C2×D4712yes—
602C22×C4⋊C4—472no—
603C22×C4⋊C4—474no—
604C22×C4⋊C4—472no—
605C22×C42—471no—
606C22×C42—471no—
607C22×C42C2×D4711yescharacteristic
608C47C2×#351111yescharacteristic, complemented, Sylow
609C2×#41—4716no—
610C2×#41—4716no—
611C2×#41—478no—
612C2×#41—4716no—
613C2×#41—948no—
614C2×#41—9416no—
615C2×#41—1888no—
616C2×#41—1888no—
617C22×Q8—4716no—
618C22×Q8—471no—
619C22×Q8—472no—
620C22×Q8—474no—
621C22×Q8—1888no—
622C22×Q8C22×D4712yes—
623C22×Q8C22×D4712yes—
624C22×D4—471no—
625C22×D4—471no—
626C22×D4—474no—
627C22×D4—472no—
628C22×D4—474no—
629C22×D4—471no—
630C22×D4—472no—
631C22×D4—472no—
632C22×D4—474no—
633C23×C4—471no—
634C23×C4—471no—
635C23×C4—474no—
636C23×C4—471no—
637C23×C4—471no—
638C23×C4—471no—
639C23×C4—471no—
640C23×C4—474no—
641C23×C4—474no—
642C23×C4—474no—
643C23×C4C22×D4711yescharacteristic
644C23×C4C22×D4711yescharacteristic
645C23×C4C22×D4711yescharacteristic
646C4⋊Q8—4716no—
647C4⋊Q8—4716no—
648C4⋊Q8—4716no—
649C4⋊Q8—478no—
650C4⋊Q8C22×D4718yes—
651C4⋊Q8C22×D4718yes—
652#127—478no—
653#126—4732no—
654#126—4732no—
655#125—4716no—
656#125C22×D47116yes—
657#124—4716no—
658#124—4716no—
659#124—4732no—
660#124—4716no—
661#124—4732no—
662#123—4732no—
663#123—4732no—
664C22⋊Q8—4716no—
665C22⋊Q8—4716no—
666C22⋊Q8—4732no—
667C22⋊Q8—4732no—
668C22⋊Q8—4732no—
669C22⋊Q8C22×D47116yes—
670C22⋊Q8C22×D47116yes—
671#121—4716no—
672#121—4716no—
673#121—4716no—
674#121—4716no—
675#121—4716no—
676#121—4716no—
677#121—4732no—
678#121—4732no—
679#121—4732no—
680C4×Q8—4716no—
681C4×Q8—4716no—
682C4×Q8—478no—
683C4×Q8—478no—
684C4×Q8C22×D47116yes—
685C4×Q8C22×D47116yes—
686C4×D4—478no—
687C4×D4—478no—
688C4×D4—478no—
689C4×D4—478no—
690C4×D4—4716no—
691C4×D4—4732no—
692C4×D4—4716no—
693C4×D4—4716no—
694C4×D4—4716no—
695C4×D4—478no—
696C4×D4—478no—
697C4×D4—4716no—
698C4×D4—4732no—
699C4×D4—4716no—
700#117—478no—
701#117—4716no—
702#117—478no—
703#117—478no—
704#117—4732no—
705#117C22×D47116yes—
706C2×C4⋊C4—471no—
707C2×C4⋊C4—474no—
708C2×C4⋊C4—472no—
709C2×C4⋊C4—472no—
710C2×C4⋊C4—474no—
711C2×C4⋊C4—474no—
712C2×C4⋊C4—471no—
713C2×C4⋊C4—471no—
714C2×C4⋊C4—471no—
715C2×C4⋊C4—471no—
716C2×C4⋊C4—471no—
717C2×C4⋊C4—474no—
718C2×C4⋊C4—4716no—
719C2×C4⋊C4—4732no—
720C2×C4⋊C4—4716no—
721C2×C4⋊C4C22×D4712yes—
722C2×C4⋊C4C22×D4712yes—
723C2×C4⋊C4C22×D4714yes—
724C2×C4⋊C4C22×D4712yes—
725C2×C4⋊C4C22×D4712yes—
726C2×C4⋊C4C22×D4714yes—
727C2×C22⋊C4—471no—
728C2×C22⋊C4—471no—
729C2×C22⋊C4—471no—
730C2×C22⋊C4—471no—
731C2×C22⋊C4—474no—
732C2×C22⋊C4—474no—
733C2×C22⋊C4—471no—
734C2×C22⋊C4—471no—
735C2×C22⋊C4—474no—
736C2×C22⋊C4—474no—
737C2×C22⋊C4—474no—
738C2×C22⋊C4—474no—
739C2×C22⋊C4—474no—
740C2×C22⋊C4C22×D4714yes—
741C2×C42—471no—
742C2×C42—474no—
743C2×C42—471no—
744C2×C42—471no—
745C2×C42—471no—
746C2×C42—471no—
747C2×C42—471no—
748C2×C42—478no—
749C2×C42—478no—
750C2×C42C22×D4711yescharacteristic
751C2×C42C22×D4714yes—
752C2×C42C22×D4711yescharacteristic
753C2×C42C22×D4711yescharacteristic
754C2×C42C22×D4718yes—
755C2×C42C22×D4711yescharacteristic
756C24—471no—
757C24—471no—
758C24—474no—
759C24C23×D4711yescharacteristic
760#41—9432no—
761#41—9464no—
762#41—18832no—
763#41—18832no—
764C2×Q8—28no—
765C2×Q8—28no—
766C2×Q8—474no—
767C2×Q8—478no—
768C2×Q8—4716no—
769C2×Q8—944no—
770C2×Q8—948no—
771C2×Q8—1888no—
772C2×Q8—18832no—
773C2×Q8C23×D4718yes—
774C2×Q8C23×D4718yes—
775C2×D4—474no—
776C2×D4—474no—
777C2×D4—4716no—
778C2×D4—478no—
779C2×D4—4716no—
780C2×D4—474no—
781C2×D4—478no—
782C2×D4—478no—
783C2×D4—4716no—
784C2×D4—944no—
785C2×D4—9416no—
786C2×D4—944no—
787C2×D4—944no—
788C2×D4—948no—
789C2×D4—948no—
790C2×D4—948no—
791C2×D4—1888no—
792C2×D4—1888no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—471no—
797C22×C4—478no—
798C22×C4—474no—
799C22×C4—471no—
800C22×C4—471no—
801C22×C4—471no—
802C22×C4—471no—
803C22×C4—471no—
804C22×C4—474no—
805C22×C4—474no—
806C22×C4—474no—
807C22×C4—474no—
808C22×C4—474no—
809C22×C4—474no—
810C22×C4—4716no—
811C22×C4—4716no—
812C22×C4—4716no—
813C22×C4—4716no—
814C22×C4—9416no—
815C22×C4—944no—
816C22×C4—944no—
817C22×C4—944no—
818C22×C4—944no—
819C22×C4—944no—
820C22×C4—1888no—
821C22×C4—1888no—
822C22×C4—1888no—
823C22×C4C23×D4714yes—
824C22×C4C23×D4714yes—
825C22×C4C23×D4714yes—
826C22×C4C23×D4714yes—
827C22×C4C23×D4711yescharacteristic
828C22×C4C23×D4711yescharacteristic
829C22×C4C23×D4711yescharacteristic
830C22×C4C23×D4714yes—
831C22×C4C23×D4711yescharacteristic
832C22×C4C23×D4711yescharacteristic
833C22×C4C23×D4711yescharacteristic
834C4⋊C4—474no—
835C4⋊C4—4716no—
836C4⋊C4—4716no—
837C4⋊C4—474no—
838C4⋊C4—474no—
839C4⋊C4—474no—
840C4⋊C4—4716no—
841C4⋊C4—478no—
842C4⋊C4—478no—
843C4⋊C4—4716no—
844C4⋊C4—474no—
845C4⋊C4—474no—
846C4⋊C4C23×D4718yes—
847C4⋊C4C23×D4718yes—
848C4⋊C4C23×D47116yes—
849C4⋊C4C23×D4718yes—
850C4⋊C4C23×D4718yes—
851C4⋊C4C23×D47116yes—
852C22⋊C4—474no—
853C22⋊C4—474no—
854C22⋊C4—474no—
855C22⋊C4—474no—
856C22⋊C4—4716no—
857C22⋊C4—4716no—
858C22⋊C4—474no—
859C22⋊C4—474no—
860C22⋊C4—4716no—
861C22⋊C4—4716no—
862C22⋊C4—4716no—
863C22⋊C4—4716no—
864C22⋊C4—4716no—
865C22⋊C4C23×D47116yes—
866C42—474no—
867C42—474no—
868C42—474no—
869C42—474no—
870C42—474no—
871C42—474no—
872C42—4716no—
873C42C23×D4714yes—
874C42C23×D4714yes—
875C42C23×D4714yes—
876C42C23×D4714yes—
877C42C23×D47116yes—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—474no—
882C23—472no—
883C23—472no—
884C23—478no—
885C23—942no—
886C23—942no—
887C23—948no—
888C23—942no—
889C23—942no—
890C23—948no—
891C23—942no—
892C23—948no—
893C23C24×D4712yes—
894C23C24×D4711yescharacteristic
895Q8—216no—
896Q8—216no—
897Q8—948no—
898Q8—9416no—
899Q8—18816no—
900D4—948no—
901D4—9432no—
902D4—948no—
903D4—948no—
904D4—9416no—
905D4—9416no—
906D4—9416no—
907D4—18816no—
908D4—18816no—
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—474no—
918C2×C4—472no—
919C2×C4—4716no—
920C2×C4—472no—
921C2×C4—472no—
922C2×C4—472no—
923C2×C4—472no—
924C2×C4—472no—
925C2×C4—478no—
926C2×C4—9432no—
927C2×C4—942no—
928C2×C4—942no—
929C2×C4—942no—
930C2×C4—948no—
931C2×C4—942no—
932C2×C4—942no—
933C2×C4—948no—
934C2×C4—948no—
935C2×C4—948no—
936C2×C4—948no—
937C2×C4—948no—
938C2×C4—18816no—
939C2×C4—18816no—
940C2×C4—18816no—
941C2×C4#41×D4714yes—
942C2×C4#1309407014yes—
943C2×C4#1309407214yes—
944C2×C4C24×D4718yes—
945C2×C4C24×D4712yes—
946C2×C4C24×D4712yes—
947C2×C4C24×D4712yes—
948C2×C4C24×D4718yes—
949C2×C4C24×D4712yes—
950C2×C4C24×D4712yes—
951C2×C4C24×D4712yes—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—44no—
956C22—474no—
957C22—948no—
958C22—942no—
959C22—942no—
960C22—948no—
961C22—942no—
962C22—942no—
963C22—948no—
964C22—942no—
965C22—948no—
966C22—1884no—
967C22—18816no—
968C22C2×#41×D4712yes—
969C22C2×#1309407012yes—
970C22C2×#1309407212yes—
971C22C25×D4711yescharacteristic
972C4—22no—
973C4—28no—
974C4—22no—
975C4—28no—
976C4—22no—
977C4—474no—
978C4—942no—
979C4—942no—
980C4—942no—
981C4—948no—
982C4—942no—
983C4—942no—
984C4C2×#41×D4714yes—
985C4C2×#1309407014yes—
986C4C2×#1309407214yes—
987C2—42no—
988C2—944no—
989C2—1882no—
990C2—1888no—
991C2#2025730014yesdirect product factor
992C2C22×#41×D4711yescharacteristic
993C2C22×#1309407011yescharacteristic
994C2C22×#1309407211yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#533C2
socleC23×C47C25
hypercenterC2×#533D47
hypocenterC47C2×#3511
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #20257300C2direct (N × H)
2. C2×#15689845C2semidirect
3. C2×#15689836C2semidirect
4. C2×#15689829C2semidirect
5. C2×#15689826C2semidirect
6. C2×#15689817C2semidirect
7. C2×#15689785C2semidirect
8. C2×#15689783C2semidirect
9. C2×#15689775C2semidirect
10. C2×#15689746C2semidirect
11. C2×#15689745C2semidirect
12. C2×#15689703C2semidirect
13. C2×#15689678C2semidirect
14. C2×#15689674C2semidirect
15. C2×#15689674C2semidirect
16. C2×#15689673C2semidirect
17. C2×C4⋊Q8×D47C2semidirect
18. C2×#15689605C2semidirect
19. C2×C4×#10625350C2semidirect
20. C2×C47×#533C2semidirect
26. #15689845C22semidirect
27. #15689836C22semidirect
28. #15689829C22semidirect
29. #15689826C22semidirect
30. #15689817C22semidirect
31. #15689785C22semidirect
32. #15689783C22semidirect
33. #15689775C22semidirect
34. #15689746C22semidirect
35. #15689745C22semidirect
36. #15689703C22semidirect
37. #15689678C22semidirect
38. #15689674C22semidirect
39. #15689674C22semidirect
40. #15689673C22semidirect
45. C4⋊Q8×D47C22semidirect
71. #15689605C22semidirect
72. C4×#10625350C22semidirect
101. C47×#533C22semidirect
319. C2×C4×D47#41semidirect
450. C4×D47C2×#41semidirect
503. C2×#533D47semidirect
511. C2×C47#3511semidirect
535. #533C2×D47semidirect
608. C47C2×#3511semidirect
991. C2#20257300direct (N × H)

Maximal subgroups

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

subgroupindex
#202573002
C2×#156898452
C2×#156898362
C2×#156898292
C2×#156898262
C2×#156898172
C2×#156897852
C2×#156897832
C2×#156897752
C2×#156897462
C2×#156897452
C2×#156897032
C2×#156896782
C2×#156896742
C2×#156896732
C2×C4⋊Q8×D472
C2×#156896052
C2×C4×#106253502
C2×C47×#5332
C2×#351147