Finite Group Databasebeta

← C2×#20257787 #27124074

Subgroups — C2×#20257787 #27124074

Order 12032.

7810 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257787C2132yesmaximal, direct product factor
2C2×#15689869C214yesmaximal, complemented
3C2×#15689834C211yesmaximal, characteristic, complemented
4C2×#15689829C212yesmaximal, complemented
5C2×#15689795C211yesmaximal, characteristic, complemented
6C2×#15689794C211yesmaximal, characteristic, complemented
7C2×#15689794C212yesmaximal, complemented
8C2×#15689775C212yesmaximal, complemented
9C2×#15689774C212yesmaximal, complemented
10C2×#15689729C212yesmaximal, complemented
11C2×#15689724C212yesmaximal, complemented
12C2×#15689704C212yesmaximal, complemented
13C2×#15689703C212yesmaximal, complemented
14C2×#15689703C214yesmaximal, complemented
15C2×#15689677C211yesmaximal, characteristic, complemented
16C2×#15689674C211yesmaximal, characteristic, complemented
17C2×#15689670C211yesmaximal, characteristic, complemented
18C2×C47×#554C211yesmaximal, characteristic, complemented
19C22×#10625354C2212yes—
20C22×#10625354C2212yes—
21C22×#10625350C2214yes—
22C22×#10625350C2212yes—
23C22×#10625350C2212yes—
24#15689869C22164yescomplemented
25#15689834C22116yescomplemented
26#15689829C22132yescomplemented
27#15689795C22116yescomplemented
28#15689794C22116yescomplemented
29#15689794C22132yescomplemented
30#15689775C22132yescomplemented
31#15689774C22132yescomplemented
32#15689729C22132yescomplemented
33#15689724C22132yescomplemented
34#15689704C22132yescomplemented
35#15689703C22132yescomplemented
36#15689703C22164yescomplemented
37#15689677C22116yescomplemented
38#15689674C22116yescomplemented
39#15689670C22116yescomplemented
40C2×#13094023C2211yescharacteristic
41C2×#13094023C2211yescharacteristic
42C2×#13094022C2211yescharacteristic
43C2×#13094021C2211yescharacteristic
44C2×#13094021C2212yes—
45C2×#13094020C2211yescharacteristic
46C2×#13094020C2212yes—
47C2×#13094015C2212yes—
48C2×#13094014C2212yes—
49C2×#13094013C2212yes—
50C2×#13094010C2212yes—
51C2×#13094009C2214yes—
52C2×#13094009C2214yes—
53C2×#13094007C2214yes—
54C2×#13094006C2214yes—
55C2×#13094004C2212yes—
56C2×#13094004C2214yes—
57C2×#13094004C2211yescharacteristic
58C2×#13094002C2214yes—
59C2×#13094002C2214yes—
60C2×#13094002C2212yes—
61C2×#13094000C2214yes—
62C2×#13094000C2211yescharacteristic
63C2×#13093999C2212yes—
64C2×#13093999C2214yes—
65C2×#13093999C2211yescharacteristic
66C2×#13093999C2212yes—
67C2×#13093999C2212yes—
68C2×#13093999C2214yes—
69C2×#13093999C2214yes—
70C2×#13093998C2212yes—
71C2×#13093998C2214yes—
72C2×#13093998C2214yes—
73C2×#13093997C2214yes—
74C2×#13093997C2214yes—
75C2×#13093997C2214yes—
76C2×#13093997C2212yes—
77C2×#13093997C2214yes—
78C2×#13093995C2211yescharacteristic
79C2×C4×Dic94C2212yes—
80C2×C4×Dic94C2211yescharacteristic
81C2×C4×D188C2212yes—
82C2×C4×D188C2211yescharacteristic
83C2×#13093986C2212yes—
84C2×#13093986C2212yes—
85C2×#13093986C2212yes—
86C2×#13093986C2212yes—
87C2×C4×C22⋊D47C2212yes—
88C2×#13093981C2212yes—
89C2×C4⋊C4×D47C2212yes—
90C2×C4⋊C4×D47C2214yes—
91C2×C42×D47C2211yescharacteristic
92C47×#554C22116yescomplemented
93C2×C4⋊Q8×C47C2211yescharacteristic
94C2×#125×C47C2212yes—
95C2×C22⋊Q8×C47C2212yes—
96C2×C22⋊Q8×C47C2214yes—
97C2×C4×Q8×C47C2211yescharacteristic
98C2×C4×D4×C47C2211yescharacteristic
99C2×C4×D4×C47C2212yes—
100C22×C4⋊C4×C47C2212yes—
101C2×#10625354—48no—
102C2×#10625354—48no—
103C2×#10625354C23116yes—
104C2×#10625354C23116yes—
105C2×#10625350—416no—
106C2×#10625350—48no—
107C2×#10625350—48no—
108C2×#10625350C23132yes—
109C2×#10625350C23116yes—
110C2×#10625350C23116yes—
111C22×Dic94C2312yes—
112C22×Dic94C2311yescharacteristic
113C22×Dic94C2312yes—
114C22×D188C2312yes—
115C22×D188C2311yescharacteristic
116C22×D188C2312yes—
117C22×D188C2314yes—
118C22×D188C2312yes—
119C22×D188C2314yes—
120C22×D188C2312yes—
121C22×D188C2314yes—
122C22×C22⋊D47C2312yes—
123C22×C22⋊D47C2312yes—
124C22×C22⋊D47C2314yes—
125C22×C22⋊D47C2314yes—
126C22×C22⋊D47C2312yes—
127C22×C4×D47C2311yescharacteristic
128C22×C4×D47C2311yescharacteristic
129C22×C4×D47C2311yescharacteristic
130C22×C4×D47C2312yes—
131C22×C4×D47C2314yes—
132C22×C4×D47C2314yes—
133C22×C4×D47C2314yes—
134C22×C4×D47C2314yes—
135#13094023C2318yes—
136#13094023C2318yes—
137#13094022C2318yes—
138#13094021C23116yes—
139#13094021C2318yes—
140#13094020C2318yes—
141#13094020C23116yes—
142#13094015C23116yes—
143#13094014C23116yes—
144#13094013C23116yes—
145#13094010C23116yes—
146#13094009C23132yes—
147#13094009C23132yes—
148#13094007C23132yes—
149#13094006C23132yes—
150#13094004C23116yes—
151#13094004C23132yes—
152#13094004C2318yes—
153#13094002C23132yes—
154#13094002C23132yes—
155#13094002C23116yes—
156#13094000C23132yes—
157#13094000C2318yes—
158#13093999C2318yes—
159#13093999C23116yes—
160#13093999C23132yes—
161#13093999C23132yes—
162#13093999C23116yes—
163#13093999C23132yes—
164#13093999C23116yes—
165#13093998C23116yes—
166#13093998C23132yes—
167#13093998C23132yes—
168#13093997C23132yes—
169#13093997C23132yes—
170#13093997C23132yes—
171#13093997C23116yes—
172#13093997C23132yes—
173#13093995C2318yes—
174C4×Dic94C23116yes—
175C4×Dic94C2318yes—
176C4×D188C23116yes—
177C4×D188C2318yes—
178#13093986C23116yes—
179#13093986C23116yes—
180#13093986C23116yes—
181#13093986C23116yes—
182C4×C22⋊D47C23116yes—
183#13093981C23116yes—
184C2×C4⋊Dic47C2311yescharacteristic
185C2×C4⋊Dic47C2314yes—
186C2×C4⋊Dic47C2311yescharacteristic
187C2×C4⋊Dic47C2312yes—
188C2×Dic47⋊C4C2312yes—
189C2×Dic47⋊C4C2312yes—
190C2×Dic47⋊C4C2314yes—
191C2×Dic47⋊C4C2312yes—
192C2×Dic47⋊C4C2312yes—
193C2×Dic47⋊C4C2312yes—
194C2×Dic47⋊C4C2312yes—
195C4⋊C4×D47C23116yes—
196C4⋊C4×D47C23132yes—
197C2×C22⋊Dic47C2312yes—
198C2×(C2×D47)⋊C4C2312yes—
199C2×(C2×D47)⋊C4C2312yes—
200C2×(C2×D47)⋊C4C2312yes—
201C2×(C2×D47)⋊C4C2314yes—
202C2×(C2×D47)⋊C4C2314yes—
203C2×(C2×D47)⋊C4C2314yes—
204C2×(C2×D47)⋊C4C2314yes—
205C2×(C2×D47)⋊C4C2312yes—
206C2×(C2×D47)⋊C4C2314yes—
207C2×C4×Dic47C2311yescharacteristic
208C2×C4×Dic47C2311yescharacteristic
209C2×C4×Dic47C2311yescharacteristic
210C2×C4×Dic47C2312yes—
211C42×D47C2318yes—
212C22×Q8×C47C2311yescharacteristic
213C22×Q8×C47C2312yes—
214C22×D4×C47C2311yescharacteristic
215C23×C4×C47C2312yes—
216C23×C4×C47C2314yes—
217C4⋊Q8×C47C2318yes—
218#125×C47C23116yes—
219C22⋊Q8×C47C23116yes—
220C22⋊Q8×C47C23132yes—
221C4×Q8×C47C2318yes—
222C4×D4×C47C2318yes—
223C4×D4×C47C23116yes—
224C2×C4⋊C4×C47C23116yes—
225C2×C4⋊C4×C47C2311yescharacteristic
226C2×C4⋊C4×C47C2314yes—
227C2×C4⋊C4×C47C2312yes—
228C2×C4⋊C4×C47C2311yescharacteristic
229C2×C4⋊C4×C47C2312yes—
230C2×C4⋊C4×C47C2312yes—
231C2×C4⋊C4×C47C2314yes—
232C2×C22⋊C4×C47C2314yes—
233C2×C22⋊C4×C47C2312yes—
234C2×C42×C47C2312yes—
235C2×C42×C47C2311yescharacteristic
236C24×C47C2412yes—
237C23×D47C2411yescharacteristic
238C23×D47C2414yes—
239C23×D47C2412yes—
240C2×Q8×C47—24no—
241C2×Q8×C47—44no—
242C2×Q8×C47C2414yes—
243C2×Q8×C47C2418yes—
244C2×D4×C47—24no—
245C2×D4×C47C2414yes—
246C22×C4×C47—28no—
247C22×C4×C47—48no—
248C22×C4×C47C2412yes—
249C22×C4×C47C2411yescharacteristic
250C22×C4×C47C2412yes—
251C22×C4×C47C2412yes—
252C22×C4×C47C2414yes—
253C22×C4×C47C2418yes—
254C22×C4×C47C24116yes—
255C22×C4×C47C2411yescharacteristic
256C22×C4×C47C2411yescharacteristic
257C2×C22⋊D47—28no—
258C2×C22⋊D47—48no—
259C2×C22⋊D47—48no—
260C2×C22⋊D47—44no—
261C2×C22⋊D47—44no—
262C2×C22⋊D47C2418yes—
263C2×C22⋊D47C2418yes—
264C2×C22⋊D47C24116yes—
265C2×C22⋊D47C24116yes—
266C2×C22⋊D47C2418yes—
267C22×Dic47C2411yescharacteristic
268C22×Dic47C2411yescharacteristic
269C22×Dic47C2412yes—
270C22×Dic47C2412yes—
271C22×Dic47C2412yes—
272C22×Dic47C2411yescharacteristic
273#10625354—432no—
274#10625354—432no—
275#10625350—464no—
276#10625350—432no—
277#10625350—432no—
278C2×D188—28no—
279C2×D188—28no—
280C2×D188—24no—
281C2×D188—48no—
282C2×D188—44no—
283C2×D188—48no—
284C2×D188—44no—
285C2×D188—48no—
286C2×D188C2418yes—
287C2×D188C2414yes—
288C2×D188C2418yes—
289C2×D188C24116yes—
290C2×D188C2418yes—
291C2×D188C24116yes—
292C2×D188C2418yes—
293C2×D188C24116yes—
294C2×C4×D47—24no—
295C2×C4×D47—28no—
296C2×C4×D47—24no—
297C2×C4×D47—216no—
298C2×C4×D47—24no—
299C2×C4×D47—48no—
300C2×C4×D47—48no—
301C2×C4×D47—48no—
302C2×C4×D47C2414yes—
303C2×C4×D47C2414yes—
304C2×C4×D47C2414yes—
305C2×C4×D47C2418yes—
306C2×C4×D47C24116yes—
307C2×C4×D47C24116yes—
308C2×C4×D47C24116yes—
309C2×C4×D47C24116yes—
310C2×Dic94—24no—
311C2×Dic94—28no—
312C2×Dic94—44no—
313C2×Dic94C2418yes—
314C2×Dic94C2414yes—
315C2×Dic94C2418yes—
316C4⋊C4×C47C2414yes—
317C4⋊C4×C47C24116yes—
318C4⋊C4×C47C2418yes—
319C4⋊C4×C47C2414yes—
320C4⋊C4×C47C2418yes—
321C4⋊C4×C47C2418yes—
322C4⋊C4×C47C24116yes—
323C22⋊C4×C47C24116yes—
324C22⋊C4×C47C2418yes—
325C42×C47C2418yes—
326C42×C47C2414yes—
327C22⋊Dic47C2418yes—
328(C2×D47)⋊C4C2418yes—
329(C2×D47)⋊C4C2418yes—
330(C2×D47)⋊C4C2418yes—
331(C2×D47)⋊C4C24116yes—
332(C2×D47)⋊C4C24116yes—
333(C2×D47)⋊C4C24116yes—
334(C2×D47)⋊C4C24116yes—
335(C2×D47)⋊C4C2418yes—
336(C2×D47)⋊C4C24116yes—
337C4⋊Dic47C2414yes—
338C4⋊Dic47C24116yes—
339C4⋊Dic47C2414yes—
340C4⋊Dic47C2418yes—
341Dic47⋊C4C2418yes—
342Dic47⋊C4C2418yes—
343Dic47⋊C4C24116yes—
344Dic47⋊C4C2418yes—
345Dic47⋊C4C2418yes—
346Dic47⋊C4C2418yes—
347Dic47⋊C4C2418yes—
348C4×Dic47C2414yes—
349C4×Dic47C2414yes—
350C4×Dic47C2414yes—
351C4×Dic47C2418yes—
352C23×C47—24no—
353C23×C47—24no—
354C23×C47—24no—
355C23×C47C2514yes—
356C23×C47C2511yescharacteristic
357C22×D47—22no—
358C22×D47—28no—
359C22×D47—24no—
360C22×D47—22no—
361C22×D47—28no—
362C22×D47—24no—
363C22×D47—22no—
364C22×D47—28no—
365C22×D47—24no—
366C22×D47C2512yes—
367C22×D47C2518yes—
368C22×D47C2514yes—
369Q8×C47—28no—
370Q8×C47—48no—
371D4×C47—28no—
372C2×C4×C47—24no—
373C2×C4×C47—24no—
374C2×C4×C47—28no—
375C2×C4×C47—22no—
376C2×C4×C47—24no—
377C2×C4×C47—216no—
378C2×C4×C47—416no—
379C2×C4×C47H(5,𝔽2)14yes—
380C2×C4×C472−1+414yes—
381C2×C4×C47C2512yes—
382C2×C4×C47C2514yes—
383C2×C4×C47C2514yes—
384C2×C4×C47C2518yes—
385C2×C4×C47C2514yes—
386C2×C4×C47C2512yes—
387C2×C4×C47C2512yes—
388C22⋊D47—216no—
389C22⋊D47—416no—
390C22⋊D47—416no—
391C22⋊D47—48no—
392C22⋊D47—48no—
393C2×Dic47—24no—
394C2×Dic47—24no—
395C2×Dic47—22no—
396C2×Dic47—24no—
397C2×Dic47—22no—
398C2×Dic47H(5,𝔽2)14yes—
399C2×Dic47C2512yes—
400C2×Dic47C2512yes—
401C2×Dic47C2514yes—
402C2×Dic47C2514yes—
403C2×Dic47C2514yes—
404C2×Dic47C2512yes—
405D188—216no—
406D188—216no—
407D188—28no—
408D188—416no—
409D188—48no—
410D188—416no—
411D188—48no—
412D188—416no—
413C4×D47—28no—
414C4×D47—216no—
415C4×D47—28no—
416C4×D47—232no—
417C4×D47—28no—
418C4×D47—416no—
419C4×D47—416no—
420C4×D47—416no—
421Dic94—28no—
422Dic94—216no—
423Dic94—48no—
424C2×#3548—471nomaximal, Sylow
425C22×C47—24no—
426C22×C47—24no—
427C22×C47—24no—
428C22×C47—48no—
429C22×C47C2×H(5,𝔽2)12yes—
430C22×C47C2×H(5,𝔽2)12yes—
431C22×C47C2×2−1+412yes—
432C22×C47C2611yescharacteristic
433C2×D47—22no—
434C2×D47—28no—
435C2×D47—24no—
436C2×D47—22no—
437C2×D47—28no—
438C2×D47—24no—
439C2×D47—22no—
440C2×D47—28no—
441C2×D47—24no—
442C2×D47—44no—
443C2×D47—416no—
444C2×D47—48no—
445C4×C47—24no—
446C4×C47—24no—
447C4×C47—28no—
448C4×C47—22no—
449C4×C47—24no—
450C4×C47C2×H(5,𝔽2)14yes—
451C4×C47C2×2−1+414yes—
452Dic47—24no—
453Dic47—24no—
454Dic47—22no—
455Dic47—24no—
456Dic47—22no—
457Dic47C2×H(5,𝔽2)14yes—
458#3548—4732no—
459C2×#562—474no—
460C2×#554—471no—
461C2×#554—472no—
462C2×#554D4711yescharacteristic, complemented
463C2×#550—471no—
464C2×#550—472no—
465C2×#550—471no—
466C2×#547—472no—
467C2×#547—472no—
468C2×#540—472no—
469C2×#540—472no—
470C2×#537—474no—
471C2×#537—472no—
472C2×#537—472no—
473C2×#533—471no—
474C2×#532—471no—
475C2×#532—471no—
476C2×C47—44no—
477C2×C47#354814yescomplemented
478C2×C47C22×H(5,𝔽2)11yescharacteristic
479C2×C47C22×H(5,𝔽2)11yescharacteristic
480C2×C47C22×2−1+411yescharacteristic
481D47—42no—
482D47—48no—
483D47—44no—
484C22×#41—472no—
485C22×#41—472no—
486C22×#41—472no—
487C22×#41—474no—
488C22×#41—472no—
489#562—4764no—
490#554—4716no—
491#554—4732no—
492#554C2×D47116yescomplemented
493#550—4716no—
494#550—4732no—
495#550—4716no—
496#547—4732no—
497#547—4732no—
498#540—4732no—
499#540—4732no—
500#537—4764no—
501#537—4732no—
502#537—4732no—
503#533—4716no—
504#532—4716no—
505#532—4716no—
506C2×C4⋊Q8—471no—
507C2×C4⋊Q8—471no—
508C2×C4⋊Q8—471no—
509C2×C4⋊Q8C2×D4711yescharacteristic
510C2×#127—471no—
511C2×#127—472no—
512C2×#127—471no—
513C2×#127—472no—
514C2×#125—472no—
515C2×#125—472no—
516C2×#125C2×D4712yes—
517C2×#124—472no—
518C2×#124—472no—
519C2×#123—474no—
520C2×#123—474no—
521C2×#123—474no—
522C2×#123—474no—
523C2×C22⋊Q8—471no—
524C2×C22⋊Q8—474no—
525C2×C22⋊Q8—472no—
526C2×C22⋊Q8—471no—
527C2×C22⋊Q8—474no—
528C2×C22⋊Q8—472no—
529C2×C22⋊Q8—474no—
530C2×C22⋊Q8—474no—
531C2×C22⋊Q8C2×D4712yes—
532C2×C22⋊Q8C2×D4714yes—
533C2×#121—471no—
534C2×#121—474no—
535C2×#121—472no—
536C2×#121—474no—
537C2×#121—472no—
538C2×#121—472no—
539C2×#121—471no—
540C2×#121—474no—
541C2×#121—474no—
542C2×#121—472no—
543C2×#121—474no—
544C2×#121—472no—
545C2×#121—474no—
546C2×#121—474no—
547C2×#121—474no—
548C2×#121—474no—
549C2×C4×Q8—471no—
550C2×C4×Q8—472no—
551C2×C4×Q8C2×D4711yescharacteristic
552C2×C4×D4—472no—
553C2×C4×D4—472no—
554C2×C4×D4—472no—
555C2×C4×D4—472no—
556C2×C4×D4—472no—
557C2×C4×D4—471no—
558C2×C4×D4—472no—
559C2×C4×D4C2×D4711yescharacteristic
560C2×C4×D4C2×D4712yes—
561C2×#117—472no—
562C22×C4⋊C4—474no—
563C22×C4⋊C4—472no—
564C22×C4⋊C4C2×D4712yes—
565C22×C42—471no—
566C47C2×#354811yescharacteristic, complemented, Sylow
567C2×#41—4716no—
568C2×#41—4716no—
569C2×#41—4716no—
570C2×#41—4732no—
571C2×#41—4716no—
572C2×#41—1888no—
573C2×#41—1888no—
574C2×#41—18816no—
575C2×#41—1888no—
576C2×#41—1888no—
577C22×Q8—472no—
578C22×Q8—471no—
579C22×Q8—472no—
580C22×Q8C22×D4711yescharacteristic
581C22×Q8C22×D4712yes—
582C22×D4—472no—
583C22×D4—472no—
584C22×D4—474no—
585C22×D4—474no—
586C22×D4—472no—
587C22×D4—472no—
588C22×D4—471no—
589C22×D4—472no—
590C22×D4—474no—
591C22×D4—472no—
592C22×D4—474no—
593C22×D4—474no—
594C22×D4—472no—
595C22×D4C22×D4711yescharacteristic
596C23×C4—474no—
597C23×C4—472no—
598C23×C4—471no—
599C23×C4—471no—
600C23×C4—471no—
601C23×C4—474no—
602C23×C4—474no—
603C23×C4—474no—
604C23×C4C22×D4712yes—
605C23×C4C22×D4714yes—
606C4⋊Q8—478no—
607C4⋊Q8—478no—
608C4⋊Q8—478no—
609C4⋊Q8C22×D4718yes—
610#127—478no—
611#127—4716no—
612#127—478no—
613#127—4716no—
614#125—4716no—
615#125—4716no—
616#125C22×D47116yes—
617#124—4716no—
618#124—4716no—
619#123—4732no—
620#123—4732no—
621#123—4732no—
622#123—4732no—
623C22⋊Q8—478no—
624C22⋊Q8—4732no—
625C22⋊Q8—4716no—
626C22⋊Q8—478no—
627C22⋊Q8—4732no—
628C22⋊Q8—4716no—
629C22⋊Q8—4732no—
630C22⋊Q8—4732no—
631C22⋊Q8C22×D47116yes—
632C22⋊Q8C22×D47132yes—
633#121—478no—
634#121—4732no—
635#121—4716no—
636#121—4732no—
637#121—4716no—
638#121—4716no—
639#121—478no—
640#121—4732no—
641#121—4732no—
642#121—4716no—
643#121—4732no—
644#121—4716no—
645#121—4732no—
646#121—4732no—
647#121—4732no—
648#121—4732no—
649C4×Q8—4716no—
650C4×Q8—478no—
651C4×Q8C22×D4718yes—
652C4×D4—4716no—
653C4×D4—4716no—
654C4×D4—4716no—
655C4×D4—4716no—
656C4×D4—4716no—
657C4×D4—478no—
658C4×D4—4716no—
659C4×D4C22×D4718yes—
660C4×D4C22×D47116yes—
661#117—4716no—
662C2×C4⋊C4—472no—
663C2×C4⋊C4—472no—
664C2×C4⋊C4—471no—
665C2×C4⋊C4—474no—
666C2×C4⋊C4—474no—
667C2×C4⋊C4—472no—
668C2×C4⋊C4—472no—
669C2×C4⋊C4—471no—
670C2×C4⋊C4—472no—
671C2×C4⋊C4—472no—
672C2×C4⋊C4—472no—
673C2×C4⋊C4—4732no—
674C2×C4⋊C4—4716no—
675C2×C4⋊C4C22×D4712yes—
676C2×C4⋊C4C22×D4714yes—
677C2×C4⋊C4C22×D4711yescharacteristic
678C2×C4⋊C4C22×D4714yes—
679C2×C4⋊C4C22×D47116yes—
680C2×C4⋊C4C22×D4712yes—
681C2×C4⋊C4C22×D4711yescharacteristic
682C2×C4⋊C4C22×D4712yes—
683C2×C22⋊C4—472no—
684C2×C22⋊C4—472no—
685C2×C22⋊C4—472no—
686C2×C22⋊C4—474no—
687C2×C22⋊C4—474no—
688C2×C22⋊C4—474no—
689C2×C22⋊C4—474no—
690C2×C22⋊C4—472no—
691C2×C22⋊C4—474no—
692C2×C22⋊C4—472no—
693C2×C22⋊C4C22×D4714yes—
694C2×C22⋊C4C22×D4712yes—
695C2×C42—472no—
696C2×C42—471no—
697C2×C42—471no—
698C2×C42—471no—
699C2×C42—478no—
700C2×C42C22×D4712yes—
701C2×C42C22×D4711yescharacteristic
702C24—471no—
703C24—474no—
704C24—472no—
705C24C23×D4712yes—
706#41—18832no—
707#41—18832no—
708#41—18864no—
709#41—18832no—
710#41—18832no—
711C2×Q8—24no—
712C2×Q8—44no—
713C2×Q8—478no—
714C2×Q8—474no—
715C2×Q8—478no—
716C2×Q8—948no—
717C2×Q8—944no—
718C2×Q8—1884no—
719C2×Q8C23×D4714yes—
720C2×Q8C23×D4718yes—
721C2×D4—24no—
722C2×D4—478no—
723C2×D4—478no—
724C2×D4—4716no—
725C2×D4—4716no—
726C2×D4—478no—
727C2×D4—478no—
728C2×D4—474no—
729C2×D4—478no—
730C2×D4—4716no—
731C2×D4—478no—
732C2×D4—4716no—
733C2×D4—4716no—
734C2×D4—478no—
735C2×D4—948no—
736C2×D4—948no—
737C2×D4—948no—
738C2×D4—944no—
739C2×D4—1888no—
740C2×D4—1888no—
741C2×D4—1884no—
742C2×D4—1884no—
743C2×D4—1888no—
744C2×D4—1888no—
745C2×D4—1884no—
746C2×D4—1884no—
747C2×D4—1888no—
748C2×D4C23×D4714yes—
749C22×C4—28no—
750C22×C4—48no—
751C22×C4—471no—
752C22×C4—471no—
753C22×C4—471no—
754C22×C4—472no—
755C22×C4—472no—
756C22×C4—472no—
757C22×C4—474no—
758C22×C4—474no—
759C22×C4—474no—
760C22×C4—4716no—
761C22×C4—478no—
762C22×C4—4716no—
763C22×C4—4716no—
764C22×C4—4716no—
765C22×C4—9416no—
766C22×C4—944no—
767C22×C4—948no—
768C22×C4—944no—
769C22×C4—944no—
770C22×C4—1888no—
771C22×C4—1888no—
772C22×C4—1888no—
773C22×C4C23×D4718yes—
774C22×C4C23×D4711yescharacteristic
775C22×C4C23×D4712yes—
776C22×C4C23×D4712yes—
777C22×C4C23×D4714yes—
778C22×C4C23×D4712yes—
779C22×C4C23×D47116yes—
780C22×C4C23×D4711yescharacteristic
781C22×C4C23×D4711yescharacteristic
782C4⋊C4—478no—
783C4⋊C4—478no—
784C4⋊C4—4716no—
785C4⋊C4—478no—
786C4⋊C4—478no—
787C4⋊C4—478no—
788C4⋊C4—478no—
789C4⋊C4—474no—
790C4⋊C4—4716no—
791C4⋊C4—474no—
792C4⋊C4—478no—
793C4⋊C4C23×D4718yes—
794C4⋊C4C23×D47116yes—
795C4⋊C4C23×D4714yes—
796C4⋊C4C23×D47116yes—
797C4⋊C4C23×D4718yes—
798C4⋊C4C23×D4714yes—
799C4⋊C4C23×D4718yes—
800C22⋊C4—478no—
801C22⋊C4—478no—
802C22⋊C4—478no—
803C22⋊C4—4716no—
804C22⋊C4—4716no—
805C22⋊C4—4716no—
806C22⋊C4—4716no—
807C22⋊C4—478no—
808C22⋊C4—4716no—
809C22⋊C4—478no—
810C22⋊C4C23×D47116yes—
811C22⋊C4C23×D4718yes—
812C42—474no—
813C42—474no—
814C42—474no—
815C42—478no—
816C42C23×D4714yes—
817C42C23×D4718yes—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—472no—
822C23—478no—
823C23—474no—
824C23—942no—
825C23—948no—
826C23—944no—
827C23—944no—
828C23—942no—
829C23—948no—
830C23—942no—
831C23—948no—
832C23—944no—
833C23C24×D4714yes—
834C23C24×D4711yescharacteristic
835Q8—28no—
836Q8—48no—
837Q8—9416no—
838Q8—948no—
839Q8—1888no—
840D4—28no—
841D4—9416no—
842D4—9416no—
843D4—9416no—
844D4—948no—
845D4—18816no—
846D4—18816no—
847D4—1888no—
848D4—1888no—
849D4—18816no—
850D4—18816no—
851D4—1888no—
852D4—1888no—
853D4—18816no—
854C2×C4—24no—
855C2×C4—28no—
856C2×C4—22no—
857C2×C4—24no—
858C2×C4—24no—
859C2×C4—216no—
860C2×C4—416no—
861C2×C4—474no—
862C2×C4—472no—
863C2×C4—472no—
864C2×C4—472no—
865C2×C4—474no—
866C2×C4—474no—
867C2×C4—474no—
868C2×C4—9432no—
869C2×C4—948no—
870C2×C4—944no—
871C2×C4—944no—
872C2×C4—942no—
873C2×C4—944no—
874C2×C4—942no—
875C2×C4—9416no—
876C2×C4—948no—
877C2×C4—948no—
878C2×C4—18816no—
879C2×C4—18816no—
880C2×C4—18816no—
881C2×C4#1309407014yes—
882C2×C4#1309407214yes—
883C2×C4C24×D4712yes—
884C2×C4C24×D4714yes—
885C2×C4C24×D4714yes—
886C2×C4C24×D4718yes—
887C2×C4C24×D4714yes—
888C2×C4C24×D4712yes—
889C2×C4C24×D4712yes—
890C22—24no—
891C22—24no—
892C22—24no—
893C22—48no—
894C22—942no—
895C22—948no—
896C22—944no—
897C22—944no—
898C22—942no—
899C22—948no—
900C22—942no—
901C22—948no—
902C22—944no—
903C22—1884no—
904C22—18816no—
905C22—1888no—
906C22H(5,𝔽2)×D4712yes—
907C22C2×#1309407012yes—
908C22C2×#1309407212yes—
909C22C25×D4711yescharacteristic
910C4—24no—
911C4—28no—
912C4—22no—
913C4—24no—
914C4—24no—
915C4—474no—
916C4—944no—
917C4—944no—
918C4—942no—
919C4—944no—
920C4—942no—
921C4C2×#1309407014yes—
922C4C2×#1309407214yes—
923C2—44no—
924C2—1882no—
925C2—1888no—
926C2—1884no—
927C2#2025778714yesdirect product factor
928C2C2×H(5,𝔽2)×D4711yescharacteristic
929C2C22×#1309407011yescharacteristic
930C2C22×#1309407211yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#554C2
socleC23×C47C25
hypercenterC2×#554D47
hypocenterC47C2×#3548
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #20257787C2direct (N × H)
2. C2×#15689869C2semidirect
3. C2×#15689834C2semidirect
4. C2×#15689829C2semidirect
5. C2×#15689795C2semidirect
6. C2×#15689794C2semidirect
7. C2×#15689794C2semidirect
8. C2×#15689775C2semidirect
9. C2×#15689774C2semidirect
10. C2×#15689729C2semidirect
11. C2×#15689724C2semidirect
12. C2×#15689704C2semidirect
13. C2×#15689703C2semidirect
14. C2×#15689703C2semidirect
15. C2×#15689677C2semidirect
16. C2×#15689674C2semidirect
17. C2×#15689670C2semidirect
18. C2×C47×#554C2semidirect
24. #15689869C22semidirect
25. #15689834C22semidirect
26. #15689829C22semidirect
27. #15689795C22semidirect
28. #15689794C22semidirect
29. #15689794C22semidirect
30. #15689775C22semidirect
31. #15689774C22semidirect
32. #15689729C22semidirect
33. #15689724C22semidirect
34. #15689704C22semidirect
35. #15689703C22semidirect
36. #15689703C22semidirect
37. #15689677C22semidirect
38. #15689674C22semidirect
39. #15689670C22semidirect
92. C47×#554C22semidirect
462. C2×#554D47semidirect
477. C2×C47#3548semidirect
492. #554C2×D47semidirect
566. C47C2×#3548semidirect
927. C2#20257787direct (N × H)

Maximal subgroups

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

subgroupindex
#202577872
C2×#156898692
C2×#156898342
C2×#156898292
C2×#156897952
C2×#156897942
C2×#156897752
C2×#156897742
C2×#156897292
C2×#156897242
C2×#156897042
C2×#156897032
C2×#156896772
C2×#156896742
C2×#156896702
C2×C47×#5542
C2×#354847