Finite Group Databasebeta

← #14789025

Subgroups — #14789025

Order 2816.

1330 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078084C212yesmaximal, complemented
2C2×#10622859C212yesmaximal, complemented
3#13071332C211yesmaximal, characteristic, complemented
4#13069842C212yesmaximal, complemented
5#13069663C212yesmaximal, complemented
6#13069449C212yesmaximal, complemented
7#13068612C211yesmaximal, characteristic, complemented
8#13068575C212yesmaximal, complemented
9C11×#3497C211yesmaximal, characteristic
10C2×C11×2−1+4C2212yes—
11C11×#550—22no—
12D4×Q8×C11—22no—
13C11×#548—24no—
14C11×#537—22no—
15C11×#537C2212yes—
16C11×#532—22no—
17C11×#532C2212yes—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#67004C2214yes—
20C2×#66997C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22#10622859—28no—
23C2×#66901C2214yes—
24C2×#66901C2214yes—
25#10622845C2214yes—
26#10622843C2211yescharacteristic
27C2×#66900C2212yes—
28#10622703—22no—
29#10622688—22no—
30#10622667—24no—
31#10622591—22no—
32#10622590C2211yescharacteristic
33#10622587C2211yescharacteristic
34#10622546—22no—
35#10622545C2211yescharacteristic
36#10622537C2212yes—
37#10622168C2212yes—
38C11×2−1+4—24no—
39C11×2−1+4—24no—
40C11×2−1+4—44no—
41C2×C11×#41—24no—
42C2×C11×#41—24no—
43C2×C11×#41C2314yes—
44C22×Q8×C11—24no—
45C22×Q8×C11C2311yescharacteristic
46C22×Dic22C2311yescharacteristic
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8D412yes—
49C11×#127—22no—
50C11×#127D412yes—
51C11×#124—24no—
52C11×#124D414yes—
53C11×C22⋊Q8—28no—
54C11×C22⋊Q8—24no—
55C11×#121—28no—
56C11×#121—24no—
57C11×#121—22no—
58C11×#121—24no—
59C11×#121—22no—
60C4×Q8×C11—22no—
61C4×Q8×C11—22no—
62C4×D4×C11—24no—
63C4×D4×C11—24no—
64C4×D4×C11—22no—
65C4×D4×C11—22no—
66C2×C11×C4⋊C4D412yes—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C42×C11D412yes—
69C2×C42×C11C2311yescharacteristic
70#67004—28no—
71#67004—44no—
72#66997—22no—
73#66997D414yescomplemented
74C2×#4326—24no—
75C2×#4324—24no—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—21no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11C2311yescharacteristic
81C2×C4×Dic11C2311yescharacteristic
82C2×#4318C2314yes—
83C4×Dic22—22no—
84C4×Dic22—22no—
85#66901—28no—
86#66901—44no—
87#66900—24no—
88#66899—24no—
89#66896—24no—
90C11⋊#95—21no—
91C11⋊#95—21no—
92C11⋊#95—22no—
93C11⋊#95—22no—
94C11⋊#95—22no—
95C4⋊(C11⋊C8)—22no—
96C4⋊(C11⋊C8)—22no—
97#24229—111nomaximal, Sylow
98C11×#41—24no—
99C11×#41—24no—
100C11×#41—24no—
101C11×#41—24no—
102C11×#41—48no—
103C11×#41—48no—
104C11×#41—48no—
105C11×#41—48no—
106C2×Q8×C11—24no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—48no—
110C2×Q8×C11—48no—
111C2×Q8×C11C2×D414yes—
112C2×Q8×C11C2×D412yes—
113C2×Q8×C11#4112yes—
114C2×D4×C11—24no—
115C2×D4×C11—24no—
116C2×D4×C11—24no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11C2×D414yes—
120C22×C4×C11—28no—
121C22×C4×C11—24no—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C2×Dic22—22no—
132C2×Dic22—21no—
133C2×Dic22—22no—
134C2×Dic22C2×D412yes—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C22⋊C4—28no—
141C11×C22⋊C4—24no—
142C11×C22⋊C4—24no—
143C42×C11—22no—
144C42×C11—22no—
145C42×C11C2×D412yes—
146C42×C11C2×D412yes—
147#4326—48no—
148#4324—48no—
149C4⋊Dic11—22no—
150Dic11⋊C4—28no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153C4×Dic11—21no—
154C4×Dic11—22no—
155C4×Dic11—42no—
156C4×Dic11C2×D412yes—
157#4318—24no—
158#4318—24no—
159C2×C11⋊C8—24no—
160#3497D1111yescharacteristic
161#3037—112no—
162C2×#456—112no—
163#2327—111no—
164#2040—112no—
165#2007—112no—
166#1963—112no—
167#1801—111no—
168#1793—112no—
169C23×C11—24no—
170C23×C11C22×D411yescharacteristic
171Q8×C11—24no—
172Q8×C11—24no—
173Q8×C11—24no—
174Q8×C11—24no—
175Q8×C11—48no—
176D4×C11—24no—
177D4×C11—24no—
178D4×C11—44no—
179D4×C11—48no—
180D4×C11—44no—
181D4×C11—44no—
182D4×C11—82no—
183D4×C11—84no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—24no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—416no—
191C2×C4×C11—44no—
192C2×C4×C11—44no—
193C2×C4×C11—42no—
194C2×C4×C11#12012yes—
195C2×C4×C11#12011yescharacteristic
196C2×C4×C11#12011yescharacteristic
197C2×C4×C11#12114yes—
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C22×D412yes—
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C11H(5,𝔽2)12yes—
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—42no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213Dic22—24no—
214Dic22—42no—
215C11⋊C8—44no—
216C2×2−1+4C2×D1112yes—
217C2×#137—114no—
218#550—22no—
219D4×Q8—22no—
220#548—24no—
221#537—22no—
222#537C2×D1112yes—
223#532—22no—
224#532C2×D1112yes—
225C2×C4⋊Q8—111no—
226C2×C4×Q8—111no—
227C2×C4×Q8C2×D1111yescharacteristic
228#464—224no—
229#462—222no—
230#460—222no—
231#456—228no—
232#423—112no—
233C2×#104—114no—
234C2×#104—114no—
235#417—114no—
236C2×#101—112no—
237#391—111no—
238#391—111no—
239#387—222no—
240#387—222no—
241#382—111no—
242#376—111no—
243#343—112no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—44no—
247C22×C11—44no—
248C22×C11—44no—
249C22×C11C2×#12011yescharacteristic
250C22×C11C2×#12111yescharacteristic
251C22×C11#53511yescharacteristic
252C4×C11—24no—
253C4×C11—21no—
254C4×C11—21no—
255C4×C11—22no—
256C4×C11—44no—
257C4×C11—42no—
258C4×C11D4212yes—
259C4×C11#54612yes—
260Dic11—42no—
261Dic11—42no—
262Dic11—81no—
263Dic11—81no—
2642−1+4—24no—
2652−1+4—24no—
2662−1+4—44no—
267C2×#41—24no—
268C2×#41—24no—
269C2×#41C22×D1114yes—
270C22×Q8—24no—
271C22×Q8—111no—
272C22×Q8C22×D1111yescharacteristic
273#137—228no—
274#137—444no—
275C2×Q16—224no—
276C2×SD16—224no—
277C2×M16—114no—
278C4⋊Q8—22no—
279C4⋊Q8—114no—
280C4⋊Q8—222no—
281C4⋊Q8C22⋊D1112yes—
282#127—22no—
283#127C22⋊D1112yes—
284#124—24no—
285#124C22⋊D1114yes—
286C22⋊Q8—28no—
287C22⋊Q8—24no—
288#121—28no—
289#121—24no—
290#121—22no—
291#121—24no—
292#121—22no—
293C4×Q8—22no—
294C4×Q8—22no—
295C4×Q8—222no—
296C4×Q8—222no—
297C4×D4—24no—
298C4×D4—24no—
299C4×D4—22no—
300C4×D4—22no—
301C2×C4⋊C4—111no—
302C2×C4⋊C4—222no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4C22⋊D1112yes—
305C2×C4⋊C4C22×D1111yescharacteristic
306C2×C42—111no—
307C2×C42—111no—
308C2×C42—221no—
309C2×C42C22⋊D1112yes—
310C2×C42C22×D1111yescharacteristic
311C4⋊C8—222no—
312C4⋊C8—222no—
313#104—228no—
314#104—444no—
315#103—224no—
316#102—224no—
317#101—224no—
318#95—221no—
319#95—221no—
320#95—222no—
321#95—222no—
322#95—222no—
323C2×C11—21no—
324C2×C11—21no—
325C2×C11—84no—
326C2×C11#240811yescharacteristic
327C2×C11#302011yescharacteristic
328C2×C11#302211yescharacteristic
329#41—24no—
330#41—24no—
331#41—24no—
332#41—24no—
333#41—48no—
334#41—48no—
335#41—48no—
336#41—48no—
337C2×Q8—24no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—48no—
341C2×Q8—48no—
342C2×Q8—112no—
343C2×Q8—221no—
344C2×Q8—222no—
345C2×Q8—222no—
346C2×Q8D4×D1112yes—
347C2×Q8#434112yes—
348C2×Q8C2×C22⋊D1114yes—
349C2×D4—24no—
350C2×D4—24no—
351C2×D4—24no—
352C2×D4—22no—
353C2×D4—22no—
354C2×D4C2×C22⋊D1114yes—
355C22×C4—28no—
356C22×C4—24no—
357C22×C4—221no—
358C22×C4—221no—
359C22×C4—221no—
360C22×C4—221no—
361C22×C4C2×C22⋊D1112yes—
362C22×C4C2×C22⋊D1112yes—
363C22×C4C2×C22⋊D1111yescharacteristic
364C22×C4C2×C22⋊D1111yescharacteristic
365C22×C4C23×D1111yescharacteristic
366Q16—448no—
367SD16—448no—
368M16—224no—
369M16—224no—
370C2×C8—224no—
371C4⋊C4—24no—
372C4⋊C4—24no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—228no—
377C4⋊C4—222no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C22⋊C4—28no—
381C22⋊C4—24no—
382C22⋊C4—24no—
383C42—22no—
384C42—22no—
385C42—112no—
386C42—221no—
387C42—222no—
388C42—442no—
389C42C2×C22⋊D1112yes—
390C42C2×C22⋊D1112yes—
391C11#2422911yescharacteristic, complemented, Sylow
392C23—24no—
393C23C22×C22⋊D1111yescharacteristic
394Q8—24no—
395Q8—24no—
396Q8—24no—
397Q8—24no—
398Q8—48no—
399Q8—224no—
400Q8—442no—
401D4—24no—
402D4—24no—
403D4—44no—
404D4—48no—
405D4—44no—
406D4—44no—
407D4—82no—
408D4—84no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—24no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—416no—
416C2×C4—44no—
417C2×C4—44no—
418C2×C4—42no—
419C2×C4—222no—
420C2×C4—222no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—442no—
428C2×C4—441no—
429C2×C4—441no—
430C2×C4#6699114yes—
431C2×C4#6700611yescharacteristic
432C2×C4#6700611yescharacteristic
433C2×C4#6700612yes—
434C2×C4C2×D4×D1111yescharacteristic
435C2×C4C2×#434111yescharacteristic
436C2×C4#6703712yes—
437C2×C4C22×C22⋊D1112yes—
438C8—444no—
439C22—21no—
440C22—21no—
441C22—44no—
442C22—44no—
443C22—44no—
444C22C2×#6699111yescharacteristic
445C22#1062333611yescharacteristic
446C22C2×#6700611yescharacteristic
447C4—24no—
448C4—21no—
449C4—21no—
450C4—22no—
451C4—44no—
452C4—42no—
453C4—442no—
454C4—442no—
455C4—881no—
456C4—881no—
457C4D4×C22⋊D1112yes—
458C4#1062333712yes—
459C2—21no—
460C2—21no—
461C2—84no—
462C2#1307196611yescharacteristic
463C2#1307798011yescharacteristic
464C2#1307799511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3497C2
socleC22×C11C2×#120
hypercenter#3497D11
hypocenterC11#24229
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3497

Complements

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

NH ≅ G/Ntype
1. #13078084C2semidirect
2. C2×#10622859C2semidirect
3. #13071332C2semidirect
4. #13069842C2semidirect
5. #13069663C2semidirect
6. #13069449C2semidirect
7. #13068612C2semidirect
8. #13068575C2semidirect
73. #66997D4semidirect
391. C11#24229semidirect

Maximal subgroups

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

subgroupindex
#130780842
C2×#106228592
#130713322
#130698422
#130696632
#130694492
#130686122
#130685752
C11×#34972
#2422911