Finite Group Databasebeta

← #14643092

Subgroups — #14643092

Order 2816.

438 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 81 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#13076560C211yesmaximal, characteristic
2#13070154C211yesmaximal, characteristic, complemented
3#13070153C211yesmaximal, characteristic, complemented
4#13070148C211yesmaximal, characteristic
5#13066441C211yesmaximal, characteristic, complemented
6#13066436C211yesmaximal, characteristic
7C11×#1272C211yesmaximal, characteristic, complemented
8C11×#391C2211yescharacteristic
9#10622844—21no—
10C2×#66899—21no—
11C2×#66885—21no—
12C2×#66882—21no—
13C2×#66881—21no—
14C2×#66880—21no—
15#10622602—21no—
16C2×#66871—21no—
17#10622552C2211yescharacteristic
18#10622548C2211yescharacteristic
19#10622542C2211yescharacteristic
20#10622286—21no—
21#10622281—21no—
22#10622278—21no—
23#10622273—21no—
24C11×#336C2211yescharacteristic
25C11×#336C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C22×D44D411yescharacteristic
29C22×C4×D11—21no—
30C22×Dic22D411yescharacteristic
31C22×C8×C11—21no—
32C22×C8×C11—21no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C42×C11C2311yescharacteristic
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11D411yescharacteristic
44C2×C4⋊Dic11D411yescharacteristic
45C2×Dic11⋊C4—21no—
46C22×C11⋊C8—21no—
47C11×#95—21no—
48C11×#95—21no—
49#66899—42no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55#66885—42no—
56#66882—42no—
57#66881—42no—
58#66880—42no—
59#66871—42no—
60#7833—111nomaximal, Sylow
61C23×D11—21no—
62C2×Q8×C11—21no—
63C2×Q8×C11—21no—
64C2×Q8×C11—41no—
65C2×Q8×C11—41no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—41no—
75C2×D44—21no—
76C2×D44—41no—
77C2×D44—41no—
78C2×D44Q1612yes—
79C2×C4×D11—81no—
80C2×C4×D11—81no—
81C2×C4×D11—81no—
82C2×Dic22—21no—
83C2×Dic22—21no—
84C2×Dic22—41no—
85C2×Dic22—41no—
86C2×C8×C11—22no—
87C2×C8×C11—22no—
88C2×C8×C11—41no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C2×C8×C11—41no—
92C11×C4⋊C4—41no—
93C42×C11—41no—
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4—41no—
96(C2×D11)⋊C4—41no—
97(C2×D11)⋊C4—41no—
98(C2×D11)⋊C4—81no—
99(C2×D11)⋊C4—81no—
100(C2×D11)⋊C4—81no—
101C4⋊Dic11—41no—
102C4⋊Dic11—41no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107C4⋊Dic11—41no—
108C4⋊Dic11—41no—
109Dic11⋊C4—81no—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113#2804—111no—
114#2095—111no—
115#2095—111no—
116#2094—111no—
117#1272—111no—
118#1272D1111yescharacteristic, complemented
119#1270—111no—
120C23×C11#12011yescharacteristic
121C22×D11—22no—
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128Q8×C11—42no—
129Q8×C11—81no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11C2×Q1611yescharacteristic
143C2×C4×C11#13511yescharacteristic
144C2×C4×C11#13511yescharacteristic
145C2×C4×C11#13711yescharacteristic
146C2×C4×C11#13711yescharacteristic
147C2×C4×C11#13711yescharacteristic
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—81no—
158C2×Dic11—81no—
159C2×Dic11—81no—
160D44—42no—
161D44—81no—
162C4×D11—84no—
163Dic22—42no—
164Dic22—81no—
165C8×C11—42no—
166C8×C11—42no—
167C11⋊C8—42no—
168C2×#107—221no—
169C2×#107—221no—
170C2×#106—221no—
171C2×#103—221no—
172C2×#103—221no—
173C2×#102—221no—
174#400—221no—
175#393—221no—
176#393—221no—
177#391—111no—
178#391C2×D1111yescharacteristic
179#390—111no—
180#386—221no—
181#385—221no—
182#385—221no—
183#384—111no—
184#336—111no—
185#336C2×D1111yescharacteristic
186#336C2×D1111yescharacteristic
187C22×C11#45111yescharacteristic
188C22×C11#45211yescharacteristic
189C22×C11#45211yescharacteristic
190C22×C11#45311yescharacteristic
191C22×C11#45311yescharacteristic
192C22×C11#45311yescharacteristic
193C22×C11#45811yescharacteristic
194C2×D11—42no—
195C2×D11—42no—
196C2×D11—42no—
197C2×D11—81no—
198C2×D11—81no—
199C2×D11—81no—
200C2×D11—81no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—81no—
208C4×C11—81no—
209Dic11—81no—
210Dic11—81no—
211Dic11—81no—
212Dic11—161no—
213C22×Q8—111no—
214C22×Q8D4411yescharacteristic
215C22×D4—111no—
216C23×C4—221no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—221no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—111no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4D4411yescharacteristic
227C2×C22⋊C4—221no—
228C2×C22⋊C4—221no—
229C2×C22⋊C4—221no—
230C2×C22⋊C4—221no—
231C2×C22⋊C4—221no—
232C2×C42C22×D1111yescharacteristic
233#107—442no—
234#107—442no—
235#106—442no—
236#103—442no—
237#103—442no—
238#102—442no—
239#95—21no—
240#95—21no—
241#95—221no—
242#95—221no—
243#95—221no—
244#95—221no—
245#95—221no—
246C2×C11#161411yescharacteristic
247C2×C11#161811yescharacteristic
248C2×C11#161811yescharacteristic
249C2×C11#163011yescharacteristic
250C2×C11#163211yescharacteristic
251C2×C11#163211yescharacteristic
252C2×C11#165511yescharacteristic
253D11—82no—
254C24—221no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—221no—
260C2×Q8—221no—
261C2×Q8—441no—
262C2×Q8—441no—
263C2×D4—112no—
264C2×D4—221no—
265C2×D4—441no—
266C2×D4—441no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4—441no—
273C22×C4—881no—
274C22×C4—881no—
275C22×C4—881no—
276C22×C4C2×D4411yescharacteristic
277C22×C4D4×D1111yescharacteristic
278C22×C4D4×D1111yescharacteristic
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—222no—
286C2×C8—441no—
287C2×C8—441no—
288C4⋊C4—41no—
289C4⋊C4—441no—
290C4⋊C4—441no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C4⋊C4—441no—
294C4⋊C4—441no—
295C4⋊C4—441no—
296C4⋊C4—441no—
297C4⋊C4—881no—
298C22⋊C4—441no—
299C22⋊C4—441no—
300C22⋊C4—441no—
301C22⋊C4—441no—
302C22⋊C4—881no—
303C22⋊C4—881no—
304C22⋊C4—881no—
305C42—41no—
306C11#783311yescharacteristic, complemented, Sylow
307C23—222no—
308C23—441no—
309C23—441no—
310C23—441no—
311C23—441no—
312C23—441no—
313C23—441no—
314C23#6693511yescharacteristic
315Q8—42no—
316Q8—81no—
317Q8—442no—
318Q8—881no—
319D4—442no—
320D4—881no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—884no—
343C2×C4—881no—
344C2×C4—881no—
345C2×C4—881no—
346C2×C4#6695711yescharacteristic
347C2×C4#6696211yescharacteristic
348C2×C4#6696811yescharacteristic
349C2×C4#6696911yescharacteristic
350C2×C4Q16×D1111yescharacteristic
351C2×C4#6697111yescharacteristic
352C8—42no—
353C8—42no—
354C8—442no—
355C22—442no—
356C22—442no—
357C22—442no—
358C22—881no—
359C22—881no—
360C22—881no—
361C22—881no—
362C22#1062234611yescharacteristic
363C22#1062235511yescharacteristic
364C22#1062236011yescharacteristic
365C22#1062242111yescharacteristic
366C22#1062242311yescharacteristic
367C22#1062243511yescharacteristic
368C22#1062243511yescharacteristic
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—81no—
376C4—81no—
377C4—881no—
378C4—881no—
379C4—881no—
380C4—1761no—
381C2—882no—
382C2#1306764211yescharacteristic
383C2#1306766611yescharacteristic
384C2#1306766711yescharacteristic
385C2#1306773911yescharacteristic
386C2#1306775111yescharacteristic
387C2#1306775311yescharacteristic
388C2#1306790611yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1272C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenter#1272D11
hypocenterC11#7833
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
2. #13070154C2semidirect
3. #13070153C2semidirect
5. #13066441C2semidirect
7. C11×#1272C2semidirect
118. #1272D11semidirect
306. C11#7833semidirect

Maximal subgroups

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

subgroupindex
#130765602
#130701542
#130701532
#130701482
#130664412
#130664362
C11×#12722
#783311