Finite Group Databasebeta

← #14656266

Subgroups — #14656266

Order 2816.

526 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079958C211yesmaximal, characteristic, complemented
2#13078413C211yesmaximal, characteristic
3#13069411C211yesmaximal, characteristic
4#13067071C211yesmaximal, characteristic, complemented
5#13067070C211yesmaximal, characteristic, complemented
6#13066490C211yesmaximal, characteristic, complemented
7C11×#3077C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#478—22no—
12C11×#476—21no—
13C11×#474—21no—
14C11×#428—21no—
15C11×#423C2211yescharacteristic
16C11×#418—21no—
17#10622828—21no—
18C2×C22⋊(C11⋊C8)—22no—
19#10622704—21no—
20#10622703—21no—
21#10622664—22no—
22#10622644—21no—
23#10622634—21no—
24#10622622—22no—
25#10622621—21no—
26#10622620—21no—
27#10622577—21no—
28#10622537C2211yescharacteristic
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30C2×C4×C11⋊C8C2211yescharacteristic
31Q8⋊(C11⋊C8)—22no—
32#10622122—22no—
33C22×D4×C11D411yescharacteristic
34C23×C4×C11—21no—
35C2×C11×M16—21no—
36C11×C4⋊Q8D411yescharacteristic
37C11×C4⋊Q8D411yescharacteristic
38C11×#125—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C11×#117—21no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C22⋊C4—21no—
50C2×C42×C11C2311yescharacteristic
51C2×#4326—22no—
52#66979—21no—
53#66977—21no—
54#66977—21no—
55C2×#4318—21no—
56C22×C11⋊C8—21no—
57C22×C11⋊C8D412yes—
58#66923—21no—
59#66922D411yescharacteristic
60#66922D411yescharacteristic
61C4×Dic22—21no—
62C4×Dic22—21no—
63C11×#107—22no—
64C11×#106—22no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8D412yes—
67C11×#102—22no—
68C11×#102—22no—
69#66899—22no—
70#66896—22no—
71#66896—22no—
72C22⋊(C11⋊C8)—44no—
73#66874—22no—
74#66872—22no—
75#66871—22no—
76#66871—22no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)D412yes—
81C4×C11⋊C8—21no—
82C4×C11⋊C8—21no—
83#10258—111nomaximal, Sylow
84C24×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11Q1612yescomplemented
93C22×C4×C11—21no—
94C22×C4×C11—42no—
95C22×C4×C11—42no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11#4111yescharacteristic
101C2×Dic22—21no—
102C2×Dic22—21no—
103C11×M16—41no—
104C11×M16—41no—
105C2×C8×C11—22no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C42×C11—41no—
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C22⋊Dic11—41no—
123#4326—82no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126C4⋊Dic11—21no—
127C4⋊Dic11—21no—
128Dic11⋊C4—41no—
129Dic11⋊C4—41no—
130C4×Dic11—41no—
131#4318—41no—
132#4318—41no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—42no—
137C2×C11⋊C8—41no—
138C2×C11⋊C8—41no—
139#3249—111no—
140#3077—111no—
141#3077D1111yescharacteristic
142#1954—111no—
143#1493—111no—
144#1493—111no—
145#1292—111no—
146C23×C11—22no—
147C23×C11—42no—
148C23×C11—42no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11#12111yescharacteristic
152Q8×C11—42no—
153Q8×C11—41no—
154Q8×C11—41no—
155D4×C11—22no—
156D4×C11—22no—
157D4×C11—41no—
158D4×C11—41no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—82no—
167C2×C4×C11—81no—
168C2×C4×C11—81no—
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11#12011yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12711yescharacteristic
175C2×C4×C11C2×Q1611yescharacteristic
176C2×C4×C11#13511yescharacteristic
177C2×C4×C11#13711yescharacteristic
178C2×C4×C11#13711yescharacteristic
179C2×Dic11—41no—
180C2×Dic11—41no—
181Dic22—42no—
182Dic22—41no—
183Dic22—41no—
184C8×C11—42no—
185C11⋊C8—42no—
186C11⋊C8—42no—
187C11⋊C8—42no—
188#533—111no—
189#533C2×D1111yescharacteristic
190C2×C4×D4C2×D1111yescharacteristic
191#478—22no—
192#478—222no—
193#477—221no—
194#477—221no—
195#476—21no—
196#476—221no—
197#474—21no—
198#474—221no—
199#467—222no—
200#462—221no—
201#462—221no—
202#428—21no—
203#428—221no—
204#423—111no—
205#423C2×D1111yescharacteristic
206C2×C4⋊C8—111no—
207#418—21no—
208#418—221no—
209C2×C22⋊C8—222no—
210C2×C4×C8—111no—
211Q8⋊C8—222no—
212Q8⋊C8—222no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—44no—
216C22×C11—42no—
217C22×C11—82no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11#39211yescharacteristic
221C22×C11#46711yescharacteristic
222C22×C11#47011yescharacteristic
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—81no—
227C4×C11—81no—
228C4×C11—81no—
229C4×C11#45111yescharacteristic
230C4×C11#45111yescharacteristic
231C4×C11#45211yescharacteristic
232C4×C11#45211yescharacteristic
233C4×C11#45311yescharacteristic
234C4×C11#45411yescharacteristic
235Dic11—81no—
236Dic11—81no—
237C22×D4C22⋊D1111yescharacteristic
238C23×C4—21no—
239C2×Q16—222no—
240C2×M16—21no—
241C2×M16—221no—
242C22×C8—112no—
243C22×C8—221no—
244C4⋊Q8—111no—
245C4⋊Q8—111no—
246C4⋊Q8C22⋊D1111yescharacteristic
247C4⋊Q8C22⋊D1111yescharacteristic
248#125—21no—
249#125—221no—
250C22⋊Q8—21no—
251C22⋊Q8—21no—
252C22⋊Q8—221no—
253C22⋊Q8—221no—
254C4×Q8—21no—
255C4×Q8—21no—
256C4×Q8—221no—
257C4×Q8—221no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4—21no—
261C4×D4—21no—
262#117—21no—
263#117—221no—
264C2×C4⋊C4C22⋊D1111yescharacteristic
265C2×C22⋊C4—21no—
266C2×C42C22×D1111yescharacteristic
267#107—22no—
268#107—222no—
269#107—222no—
270#106—22no—
271#106—222no—
272C4⋊C8—21no—
273C4⋊C8—112no—
274C4⋊C8—221no—
275C4⋊C8—221no—
276C4⋊C8—221no—
277C4⋊C8C22⋊D1112yes—
278#103—222no—
279#103—222no—
280#102—22no—
281#102—22no—
282#102—222no—
283#102—222no—
284C22⋊C8—444no—
285C4×C8—221no—
286C4×C8—221no—
287C2×C11—21no—
288C2×C11—21no—
289C2×C11—82no—
290C2×C11#200111yescharacteristic
291C2×C11#200611yescharacteristic
292C2×C11#201711yescharacteristic
293C24—21no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—221no—
297C2×Q8—221no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4#432612yescomplemented
304C22×C4—21no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4D4×D1111yescharacteristic
310C22×C4#434111yescharacteristic
311C22×C4C2×C22⋊D1111yescharacteristic
312Q16—882no—
313M16—41no—
314M16—41no—
315M16—441no—
316M16—441no—
317C2×C8—22no—
318C2×C8—222no—
319C2×C8—222no—
320C2×C8—222no—
321C2×C8—441no—
322C2×C8—441no—
323C2×C8—442no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—221no—
333C4⋊C4—221no—
334C4⋊C4—221no—
335C4⋊C4—221no—
336C4⋊C4—441no—
337C4⋊C4—441no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—441no—
342C42—41no—
343C42—441no—
344C42D4×D1111yescharacteristic
345C42D4×D1111yescharacteristic
346C42C2×C22⋊D1111yescharacteristic
347C42C2×C22⋊D1111yescharacteristic
348C11#1025811yescharacteristic, complemented, Sylow
349C23—22no—
350C23—42no—
351C23—42no—
352C23—41no—
353C23—41no—
354C23#6699211yescharacteristic
355Q8—42no—
356Q8—41no—
357Q8—41no—
358Q8—442no—
359Q8—441no—
360Q8—441no—
361D4—22no—
362D4—22no—
363D4—41no—
364D4—41no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—82no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—441no—
376C2×C4—441no—
377C2×C4#6699011yescharacteristic
378C2×C4#6699011yescharacteristic
379C2×C4#6699111yescharacteristic
380C2×C4#6699211yescharacteristic
381C2×C4#6699311yescharacteristic
382C2×C4#6699511yescharacteristic
383C2×C4C2×#432611yescharacteristic
384C2×C4#6700311yescharacteristic
385C2×C4#6700411yescharacteristic
386C2×C4#6700611yescharacteristic
387C8—42no—
388C8—442no—
389C8—442no—
390C8—442no—
391C22—21no—
392C22—21no—
393C22—44no—
394C22—42no—
395C22—82no—
396C22—81no—
397C22—81no—
398C22#1062266411yescharacteristic
399C22#1062266511yescharacteristic
400C22#1062283611yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—81no—
405C4—81no—
406C4—81no—
407C4—881no—
408C4—881no—
409C4#1062266011yescharacteristic
410C4#1062266311yescharacteristic
411C4#1062281111yescharacteristic
412C4#1062281411yescharacteristic
413C4#1062284111yescharacteristic
414C4#1062285211yescharacteristic
415C2—21no—
416C2—21no—
417C2—82no—
418C2#1306962411yescharacteristic
419C2#1306965611yescharacteristic
420C2#1306971911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3077C2
socleC22×C11#392
prime radicalC22×D4×C11D4
hypercenter#3077D11
hypocenterC11#10258
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
1. #13079958C2semidirect
4. #13067071C2semidirect
5. #13067070C2semidirect
6. #13066490C2semidirect
92. C2×D4×C11Q16semidirect
303. C2×D4#4326semidirect
348. C11#10258semidirect

Maximal subgroups

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

subgroupindex
#130799582
#130784132
#130694112
#130670712
#130670702
#130664902
C11×#30772
#1025811