Finite Group Databasebeta

← #14656203

Subgroups — #14656203

Order 2816.

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

normal subgroups only

This group has 604 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#13079564C211yesmaximal, characteristic, complemented
2#13078413C211yesmaximal, characteristic
3#13067297C211yesmaximal, characteristic, complemented
4#13067114C211yesmaximal, characteristic, complemented
5#13067007C211yesmaximal, characteristic
6#13066519C211yesmaximal, characteristic, complemented
7C11×#2542C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×C22⋊Q8—22no—
10C2×C4×D4×C11C2211yescharacteristic
11#10623001C2211yescharacteristic
12C11×#399—22no—
13C11×#390—21no—
14C11×#384—21no—
15C4×C11×C4⋊C4C2211yescharacteristic
16#10622841—22no—
17#10622828—21no—
18#10622705—21no—
19#10622703—22no—
20#10622694—21no—
21#10622622—22no—
22#10622621—21no—
23#10622620—21no—
24#10622577—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622184—22no—
29D4⋊(C11⋊C8)—22no—
30#10622090—22no—
31C22×Q8×C11D412yes—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C22⋊Q8—48no—
39C4×D4×C11—21no—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—24no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C11×C22⋊C4—24no—
49C2×C11×C22⋊C4—21no—
50C2×C42×C11—21no—
51C2×C42×C11C2311yescharacteristic
52C2×#4326—24no—
53#66979—21no—
54#66977—21no—
55#66977—21no—
56C2×#4318—21no—
57#66923—21no—
58#66922D411yescharacteristic
59#66922D411yescharacteristic
60C4×Dic22—21no—
61C4×Dic22—21no—
62C11×#95D412yes—
63#66899—24no—
64#66896—22no—
65#66896—22no—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)—21no—
68#66872—22no—
69#66871—22no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)D412yes—
73C4⋊(C11⋊C8)D412yes—
74C4×C11⋊C8—21no—
75C4×C11⋊C8—21no—
76#10248—111nomaximal, Sylow
77C24×C11—21no—
78C2×Q8×C11—22no—
79C2×Q8×C11—22no—
80C2×Q8×C11—44no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11Q1612yescomplemented
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—21no—
90C22×C4×C11—44no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C2×Dic22—21no—
97C2×Dic22—21no—
98C11×C4⋊C4—24no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—48no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C22⋊C4—48no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C42×C11—41no—
110C42×C11—41no—
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11#4111yescharacteristic
115C22⋊Dic11—41no—
116#4326—84no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121Dic11⋊C4—41no—
122Dic11⋊C4—41no—
123C4×Dic11—41no—
124#4318—41no—
125#4318—41no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—41no—
129#3209—111no—
130#3077—111no—
131#2542D1111yescharacteristic
132#1548—111no—
133#1503—111no—
134#1478—111no—
135#1303—111no—
136C23×C11—22no—
137C23×C11—42no—
138C23×C11—42no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11#12011yescharacteristic
142Q8×C11—44no—
143Q8×C11—82no—
144D4×C11—22no—
145D4×C11—22no—
146D4×C11—41no—
147D4×C11—41no—
148C2×C4×C11—22no—
149C2×C4×C11—24no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—44no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—82no—
158C2×C4×C11—82no—
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11#12011yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12711yescharacteristic
165C2×C4×C11C2×Q1611yescharacteristic
166C2×C4×C11#13511yescharacteristic
167C2×C4×C11#13711yescharacteristic
168C2×C4×C11#13711yescharacteristic
169C2×Dic11—41no—
170C2×Dic11—41no—
171Dic22—42no—
172Dic22—81no—
173C11⋊C8—42no—
174C11⋊C8—42no—
175C11⋊C8—81no—
176#533—111no—
177C2×C4⋊Q8C2×D1111yescharacteristic
178C2×C22⋊Q8—22no—
179C2×C4×D4C2×D1111yescharacteristic
180#494—221no—
181#487—221no—
182#478—222no—
183#476—221no—
184#474—221no—
185#462—222no—
186#451—222no—
187#431—111no—
188#431—111no—
189#428—221no—
190#423—111no—
191#418—221no—
192#399—22no—
193#390—21no—
194#384—21no—
195C4×C4⋊C4C2×D1111yescharacteristic
196#333—222no—
197#328—222no—
198D4⋊C8—222no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—44no—
202C22×C11—42no—
203C22×C11—82no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11#39211yescharacteristic
207C22×C11#45111yescharacteristic
208C22×C11#45211yescharacteristic
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—44no—
213C4×C11—81no—
214C4×C11—82no—
215C4×C11#45111yescharacteristic
216C4×C11#45211yescharacteristic
217C4×C11#45312yes—
218C4×C11#46711yescharacteristic
219C4×C11#47011yescharacteristic
220Dic11—81no—
221Dic11—81no—
222C22×Q8C22⋊D1112yes—
223C22×D4C22⋊D1111yescharacteristic
224C23×C4—21no—
225C2×Q16—224no—
226C2×M16—221no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—111no—
232C4⋊Q8—111no—
233#125—221no—
234C22⋊Q8—48no—
235C22⋊Q8—221no—
236C22⋊Q8—221no—
237C4×Q8—221no—
238C4×Q8—221no—
239C4×D4—21no—
240C4×D4—21no—
241C4×D4—21no—
242C4×D4—21no—
243#117—221no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—24no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4C22⋊D1111yescharacteristic
249C2×C22⋊C4—24no—
250C2×C22⋊C4—21no—
251C2×C42—21no—
252C2×C42C22×D1111yescharacteristic
253#107—222no—
254#106—222no—
255C4⋊C8—112no—
256C4⋊C8—112no—
257C4⋊C8—221no—
258C4⋊C8—221no—
259#103—224no—
260#102—222no—
261#102—222no—
262C22⋊C8—221no—
263C22⋊C8—221no—
264C4×C8—221no—
265C4×C8—221no—
266#95C22⋊D1112yes—
267C2×C11—21no—
268C2×C11—21no—
269C2×C11—82no—
270C2×C11#200111yescharacteristic
271C2×C11#200211yescharacteristic
272C2×C11#200911yescharacteristic
273C24—21no—
274C2×Q8—22no—
275C2×Q8—22no—
276C2×Q8—44no—
277C2×Q8—221no—
278C2×Q8—221no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4#432612yescomplemented
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—21no—
288C22×C4—44no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4C2×C22⋊D1111yescharacteristic
292C22×C4C2×C22⋊D1111yescharacteristic
293C22×C4C2×C22⋊D1111yescharacteristic
294Q16—884no—
295M16—441no—
296M16—441no—
297C2×C8—222no—
298C2×C8—222no—
299C2×C8—441no—
300C4⋊C4—24no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—48no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—221no—
309C4⋊C4—221no—
310C4⋊C4—221no—
311C4⋊C4—221no—
312C4⋊C4—441no—
313C4⋊C4—441no—
314C22⋊C4—48no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—441no—
318C42—41no—
319C42—41no—
320C42—441no—
321C42D4×D1111yescharacteristic
322C42D4×D1111yescharacteristic
323C42D4×D1111yescharacteristic
324C42#434111yescharacteristic
325C11#1024811yescharacteristic, complemented, Sylow
326C23—22no—
327C23—42no—
328C23—42no—
329C23—41no—
330C23—41no—
331C23#6700611yescharacteristic
332Q8—44no—
333Q8—82no—
334Q8—442no—
335Q8—881no—
336D4—22no—
337D4—22no—
338D4—41no—
339D4—41no—
340C2×C4—22no—
341C2×C4—24no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—44no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4#6699011yescharacteristic
354C2×C4#6699011yescharacteristic
355C2×C4#6699111yescharacteristic
356C2×C4#6699211yescharacteristic
357C2×C4#6699211yescharacteristic
358C2×C4#6699311yescharacteristic
359C2×C4#6699511yescharacteristic
360C2×C4C2×#432611yescharacteristic
361C2×C4#6700311yescharacteristic
362C2×C4#6700411yescharacteristic
363C8—442no—
364C8—442no—
365C8—881no—
366C22—21no—
367C22—21no—
368C22—44no—
369C22—42no—
370C22—82no—
371C22—81no—
372C22—81no—
373C22#1062283611yescharacteristic
374C22#1062284111yescharacteristic
375C22#1062285211yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—44no—
380C4—81no—
381C4—82no—
382C4—881no—
383C4—881no—
384C4#1062266011yescharacteristic
385C4#1062266311yescharacteristic
386C4#1062266411yescharacteristic
387C4#1062266511yescharacteristic
388C4#1062269012yes—
389C2—21no—
390C2—21no—
391C2—82no—
392C2#1306962411yescharacteristic
393C2#1306963111yescharacteristic
394C2#1306967611yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2542C2
socleC22×C11#392
prime radicalC22×D4×C11D4
hypercenter#2542D11
hypocenterC11#10248
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2542

Complements

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

NH ≅ G/Ntype
1. #13079564C2semidirect
3. #13067297C2semidirect
4. #13067114C2semidirect
6. #13066519C2semidirect
86. C2×D4×C11Q16semidirect
284. C2×D4#4326semidirect
325. C11#10248semidirect

Maximal subgroups

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

subgroupindex
#130795642
#130784132
#130672972
#130671142
#130670072
#130665192
C11×#25422
#1024811