Finite Group Databasebeta

← #14656202

Subgroups — #14656202

Order 2816.

604 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 101 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#13079561C211yesmaximal, characteristic, complemented
2#13078409C211yesmaximal, characteristic
3#13073565C211yesmaximal, characteristic
4#13067296C211yesmaximal, characteristic, complemented
5#13067008C211yesmaximal, characteristic
6#13066519C211yesmaximal, characteristic, complemented
7C11×#1503C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×#66950—22no—
10C2×C4×D44C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C4×C11×C4⋊C4C2211yescharacteristic
14#10622706—21no—
15#10622705—21no—
16#10622700—21no—
17#10622697—21no—
18#10622679—22no—
19#10622663—22no—
20#10622644—22no—
21#10622614—21no—
22#10622608—21no—
23#10622552—21no—
24#10622548—21no—
25#10622538C2211yescharacteristic
26#10622537C2211yescharacteristic
27#10622290—22no—
28C11×#328—22no—
29#10622119—22no—
30#10622097—22no—
31C22×D44D411yescharacteristic
32C22×C4×D11—21no—
33C22×Dic22D412yes—
34C11×C4⋊Q8D411yescharacteristic
35C11×C4⋊Q8D411yescharacteristic
36C11×#125—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C4×Q8×C11—21no—
40C4×Q8×C11—21no—
41C11×#117—21no—
42C2×C11×C4⋊C4—21no—
43C2×C42×C11—21no—
44C2×C42×C11C2311yescharacteristic
45C2×#4326—24no—
46C2×(C2×D11)⋊C4—24no—
47C2×(C2×D11)⋊C4—21no—
48C2×C4⋊Dic11—24no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11D411yescharacteristic
52C2×#4318—21no—
53#66950—48no—
54C4×D44—21no—
55C4×D44—21no—
56C4×D44—21no—
57C4×D44—21no—
58#66922—21no—
59#66922—21no—
60#66922—21no—
61#66922—21no—
62C11×C4⋊C8—21no—
63C11×C22⋊C8—21no—
64C4×C8×C11—21no—
65C11×#95D412yes—
66C22⋊(C11⋊C8)—21no—
67#66874—24no—
68#66873—22no—
69#66873—22no—
70#66872—22no—
71#66871—22no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)D412yes—
74C4⋊(C11⋊C8)D412yes—
75C4×C11⋊C8—21no—
76#10248—111nomaximal, Sylow
77C23×D11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C22×C4×C11—22no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×Dic11—21no—
85C22×Dic11—22no—
86C2×D44—21no—
87C2×D44—21no—
88C2×D44—21no—
89C2×D44—21no—
90C2×D44—21no—
91C2×D44Q1612yescomplemented
92C2×C4×D11—44no—
93C2×C4×D11—41no—
94C2×C4×D11—41no—
95C2×Dic22—22no—
96C2×Dic22—22no—
97C2×Dic22—44no—
98C2×C8×C11—41no—
99C11×C4⋊C4—24no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C22⋊C4—41no—
107C42×C11—41no—
108C42×C11—41no—
109C42×C11—41no—
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11#4111yescharacteristic
114#4326—84no—
115(C2×D11)⋊C4—48no—
116(C2×D11)⋊C4—41no—
117(C2×D11)⋊C4—41no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—48no—
121C4⋊Dic11—41no—
122C4⋊Dic11—41no—
123C4⋊Dic11—41no—
124C4⋊Dic11—41no—
125#4318—41no—
126#4318—41no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129#3209—111no—
130#3077—111no—
131#2542—111no—
132#1548—111no—
133#1503D1111yescharacteristic, complemented
134#1478—111no—
135#1303—111no—
136C23×C11#12011yescharacteristic
137C22×D11—22no—
138C22×D11—42no—
139C22×D11—42no—
140C22×D11—41no—
141C22×D11—41no—
142Q8×C11—42no—
143Q8×C11—81no—
144C2×C4×C11—22no—
145C2×C4×C11—24no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12711yescharacteristic
157C2×C4×C11C2×Q1611yescharacteristic
158C2×C4×C11#13511yescharacteristic
159C2×C4×C11#13711yescharacteristic
160C2×C4×C11#13711yescharacteristic
161C2×Dic11—42no—
162C2×Dic11—44no—
163C2×Dic11—41no—
164C2×Dic11—42no—
165D44—22no—
166D44—22no—
167D44—41no—
168D44—41no—
169C4×D11—82no—
170C4×D11—82no—
171Dic22—44no—
172Dic22—82no—
173C8×C11—81no—
174C11⋊C8—42no—
175C11⋊C8—42no—
176#533C2×D1111yescharacteristic
177C2×C4⋊Q8—111no—
178C2×C22⋊Q8—222no—
179C2×C4×D4—111no—
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#431C2×D1111yescharacteristic
189#428—221no—
190#423—111no—
191#418—221no—
192#399—222no—
193#390—221no—
194#384—221no—
195C4×C4⋊C4C2×D1111yescharacteristic
196#333—222no—
197#328—22no—
198D4⋊C8—222no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11#39211yescharacteristic
202C22×C11#45111yescharacteristic
203C22×C11#45211yescharacteristic
204C2×D11—44no—
205C2×D11—42no—
206C2×D11—82no—
207C2×D11—81no—
208C2×D11—81no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—44no—
213C4×C11—81no—
214C4×C11—81no—
215C4×C11#45111yescharacteristic
216C4×C11#45211yescharacteristic
217C4×C11#45312yes—
218C4×C11#46711yescharacteristic
219C4×C11#47011yescharacteristic
220Dic11—82no—
221Dic11—81no—
222C22×Q8—112no—
223C22×D4—111no—
224C23×C4—221no—
225C2×Q16—224no—
226C2×M16—221no—
227C4⋊Q8—221no—
228C4⋊Q8—221no—
229C4⋊Q8—221no—
230C4⋊Q8—221no—
231C4⋊Q8D4411yescharacteristic
232C4⋊Q8D4411yescharacteristic
233#125—21no—
234C22⋊Q8—21no—
235C22⋊Q8—21no—
236C22⋊Q8—448no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×D4—221no—
240C4×D4—221no—
241C4×D4—221no—
242C4×D4—221no—
243#117—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—111no—
246C2×C4⋊C4—224no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4—221no—
249C2×C22⋊C4—224no—
250C2×C22⋊C4—221no—
251C2×C42—21no—
252C2×C42C22×D1111yescharacteristic
253#107—222no—
254#106—222no—
255C4⋊C8—21no—
256C4⋊C8—112no—
257C4⋊C8—112no—
258C4⋊C8—221no—
259#103—224no—
260#102—222no—
261#102—222no—
262C22⋊C8—21no—
263C22⋊C8—221no—
264C4×C8—21no—
265C4×C8—221no—
266#95C22⋊D1112yes—
267C2×C11—21no—
268C2×C11—21no—
269C2×C11#200111yescharacteristic
270C2×C11#200211yescharacteristic
271C2×C11#200911yescharacteristic
272D11—82no—
273C24—221no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—222no—
277C2×Q8—222no—
278C2×Q8—444no—
279C2×D4—112no—
280C2×D4—221no—
281C2×D4—221no—
282C2×D4—221no—
283C2×D4—221no—
284C2×D4—221no—
285C22×C4—22no—
286C22×C4—222no—
287C22×C4—221no—
288C22×C4—444no—
289C22×C4—441no—
290C22×C4—441no—
291C22×C4D4×D1111yescharacteristic
292C22×C4D4×D1111yescharacteristic
293C22×C4C2×C22⋊D1111yescharacteristic
294Q16—884no—
295M16—441no—
296M16—441no—
297C2×C8—41no—
298C2×C8—222no—
299C2×C8—222no—
300C4⋊C4—24no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—221no—
308C4⋊C4—221no—
309C4⋊C4—448no—
310C4⋊C4—441no—
311C4⋊C4—441no—
312C4⋊C4—441no—
313C4⋊C4—441no—
314C22⋊C4—41no—
315C22⋊C4—448no—
316C22⋊C4—441no—
317C22⋊C4—441no—
318C42—41no—
319C42—41no—
320C42—41no—
321C42C2×D4411yescharacteristic
322C42#433911yescharacteristic
323C42D4×D1111yescharacteristic
324C42D4×D1111yescharacteristic
325C11#1024811yescharacteristic, complemented, Sylow
326C23—222no—
327C23—442no—
328C23—442no—
329C23—441no—
330C23—441no—
331C23#6699011yescharacteristic
332Q8—42no—
333Q8—81no—
334Q8—444no—
335Q8—882no—
336D4—222no—
337D4—222no—
338D4—441no—
339D4—441no—
340C2×C4—22no—
341C2×C4—24no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—444no—
348C2×C4—442no—
349C2×C4—441no—
350C2×C4—442no—
351C2×C4—882no—
352C2×C4—882no—
353C2×C4#6693511yescharacteristic
354C2×C4#6693511yescharacteristic
355C2×C4#6693711yescharacteristic
356C2×C4#6693711yescharacteristic
357C2×C4#6696811yescharacteristic
358C2×C4#6696911yescharacteristic
359C2×C4Q16×D1111yescharacteristic
360C2×C4#6697111yescharacteristic
361C2×C4#6698311yescharacteristic
362C2×C4#6699311yescharacteristic
363C8—81no—
364C8—442no—
365C8—442no—
366C22—21no—
367C22—21no—
368C22—444no—
369C22—442no—
370C22—882no—
371C22—881no—
372C22—881no—
373C22#1062257311yescharacteristic
374C22#1062278611yescharacteristic
375C22#1062279911yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—44no—
380C4—81no—
381C4—81no—
382C4—881no—
383C4—882no—
384C4#1062242111yescharacteristic
385C4#1062242311yescharacteristic
386C4#1062242611yescharacteristic
387C4#1062242911yescharacteristic
388C4#1062243512yes—
389C2—21no—
390C2—21no—
391C2—882no—
392C2#1306962511yescharacteristic
393C2#1306963011yescharacteristic
394C2#1306967511yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1503C2
socleC22×C11#392
prime radicalC22×D44D4
hypercenter#1503D11
hypocenterC11#10248
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
1. #13079561C2semidirect
4. #13067296C2semidirect
6. #13066519C2semidirect
7. C11×#1503C2semidirect
91. C2×D44Q16semidirect
133. #1503D11semidirect
325. C11#10248semidirect

Maximal subgroups

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

subgroupindex
#130795612
#130784092
#130735652
#130672962
#130670082
#130665192
C11×#15032
#1024811