Finite Group Databasebeta

← #14664349

Subgroups — #14664349

Order 2816.

446 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 71 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#13073520C211yesmaximal, characteristic
2#13068411C211yesmaximal, characteristic, complemented
3#13066958C211yesmaximal, characteristic, complemented
4#13066623C211yesmaximal, characteristic, complemented
5#13066621C211yesmaximal, characteristic, complemented
6#13066619C211yesmaximal, characteristic
7C11×#1345C211yesmaximal, characteristic
8C2×D4×Dic11C411yescharacteristic
9C2×#66940C2211yescharacteristic
10C2×#66931—21no—
11C11×#394C2211yescharacteristic
12#10622835C411yescharacteristic
13C2×#66888—21no—
14M16×Dic11—21no—
15#10622596C2211yescharacteristic
16#10622564—21no—
17#10622558—21no—
18#10622555—21no—
19#10622332—21no—
20#10622274C411yescharacteristic
21#10622263C411yescharacteristic
22C11×#343C2211yescharacteristic
23C11×#324C2211yescharacteristic
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622107—21no—
27C22×D4×C11C2×C411yescharacteristic
28C23×Dic11—21no—
29C22×Dic22D411yescharacteristic
30C2×C11×M16—21no—
31C2×C11×C4⋊C4C2311yescharacteristic
32C2×C11×C22⋊C4—21no—
33C2×C11×C22⋊C4—21no—
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37D4×Dic11—41no—
38D4×Dic11—41no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4C2×C411yescharacteristic
44C2×Dic11⋊C4D411yescharacteristic
45C2×C4×Dic11C2×C411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48C2×#4318—21no—
49#66940—41no—
50#66940—41no—
51#66931—42no—
52#66931—42no—
53C11×C22⋊C8—21no—
54C11×#95C2×C411yescharacteristic
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95C2×C411yescharacteristic
59C22⋊(C11⋊C8)—21no—
60#66888—24no—
61#66879—41no—
62#66879—41no—
63Dic11⋊C8—41no—
64C8×Dic11—41no—
65#11778—111nomaximal, Sylow
66C24×C11—21no—
67C2×D4×C11—41no—
68C2×D4×C11—42no—
69C22×C4×C11—21no—
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—42no—
76C22×Dic11—42no—
77C22×Dic11—42no—
78C22×Dic11C22⋊C411yescharacteristic
79C22×Dic11C22⋊C411yescharacteristic
80C22×Dic11C22⋊C411yescharacteristic
81C22×Dic11C22⋊C411yescharacteristic
82C2×Dic22—22no—
83C2×Dic22—21no—
84C2×Dic22—21no—
85C2×Dic22—41no—
86C11×M16—22no—
87C11×M16—41no—
88C2×C8×C11—41no—
89C2×C8×C11—41no—
90C11×C4⋊C4—41no—
91C11×C22⋊C4—42no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C22⋊Dic11—42no—
95C22⋊Dic11—42no—
96C22⋊Dic11—41no—
97C22⋊Dic11—41no—
98C4⋊Dic11—41no—
99C4⋊Dic11—42no—
100Dic11⋊C4—41no—
101Dic11⋊C4—41no—
102Dic11⋊C4—42no—
103Dic11⋊C4—41no—
104Dic11⋊C4—41no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11—21no—
108C4×Dic11—21no—
109C4×Dic11—21no—
110C4×Dic11—21no—
111#4318—22no—
112#4318—41no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115#2536—111no—
116C4×#101—111no—
117#1467—111no—
118#1346—111no—
119#1346—111no—
120#1345—111no—
121#1345D1111yescharacteristic
122C23×C11—22no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11C2×C22⋊C411yescharacteristic
130D4×C11—42no—
131D4×C11—42no—
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×C11AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—21no—
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—84no—
158C2×Dic11#9911yescharacteristic
159C2×Dic11#9911yescharacteristic
160C2×Dic11#10412yes—
161Dic22—42no—
162Dic22—42no—
163C8×C11—42no—
164C8×C11—81no—
165C11⋊C8—42no—
166C11⋊C8—81no—
167C2×C22⋊Q8—221no—
168C2×C4×Q8—111no—
169C2×C4×D4—111no—
170#432—221no—
171C2×#101—221no—
172C4×M16—221no—
173#398—111no—
174#398—111no—
175#394—111no—
176#394C2×D1111yescharacteristic
177#388—221no—
178#388—221no—
179#382—111no—
180#380—221no—
181#343—111no—
182#343C2×D1111yescharacteristic
183#324—111no—
184#324—221no—
185#324C2×D1111yescharacteristic
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—42no—
189C22×C11—42no—
190C22×C11—42no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11C2×#9911yescharacteristic
196C22×C11#41811yescharacteristic
197C22×C11C2×#10411yescharacteristic
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—41no—
201C4×C11—41no—
202C4×C11—81no—
203Dic11—21no—
204Dic11—21no—
205Dic11—22no—
206Dic11—41no—
207Dic11—41no—
208Dic11—81no—
209Dic11—81no—
210C22×Q8—111no—
211C22×D4C4×D1111yescharacteristic
212C23×C4—221no—
213C2×M16—21no—
214C2×M16—221no—
215C22⋊Q8—442no—
216C22⋊Q8—442no—
217C4×Q8—441no—
218C4×Q8—441no—
219C4×D4—441no—
220C4×D4—441no—
221C2×C4⋊C4—111no—
222C2×C4⋊C4—111no—
223C2×C4⋊C4—111no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4—221no—
227C2×C4⋊C4C22×D1111yescharacteristic
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—221no—
231C2×C22⋊C4—221no—
232C2×C22⋊C4—221no—
233C2×C42—111no—
234C2×C42—111no—
235C2×C42—111no—
236C4⋊C8—441no—
237#101—224no—
238C22⋊C8—21no—
239C22⋊C8—221no—
240#97—441no—
241#97—441no—
242C4×C8—441no—
243#95—111no—
244#95—221no—
245#95—221no—
246#95—221no—
247#95C4×D1111yescharacteristic
248C2×C11—21no—
249C2×C11—21no—
250C2×C11—82no—
251C2×C11#150711yescharacteristic
252C2×C11#212011yescharacteristic
253C2×C11#213311yescharacteristic
254C24—21no—
255C2×Q8—222no—
256C2×Q8—221no—
257C2×Q8—221no—
258C2×Q8—441no—
259C2×D4—41no—
260C2×D4—42no—
261C22×C4—21no—
262C22×C4—111no—
263C22×C4—111no—
264C22×C4—111no—
265C22×C4—111no—
266C22×C4—221no—
267C22×C4—221no—
268C22×C4—442no—
269C22×C4—442no—
270C22×C4—442no—
271C22×C4C2×C4×D1111yescharacteristic
272C22×C4D4×D1111yescharacteristic
273C22×C4D4×D1111yescharacteristic
274M16—22no—
275M16—41no—
276M16—222no—
277M16—441no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—441no—
281C2×C8—441no—
282C4⋊C4—41no—
283C4⋊C4—441no—
284C4⋊C4—441no—
285C4⋊C4—441no—
286C4⋊C4—442no—
287C4⋊C4—442no—
288C4⋊C4—441no—
289C4⋊C4—441no—
290C22⋊C4—42no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—441no—
294C22⋊C4—441no—
295C22⋊C4—442no—
296C22⋊C4—442no—
297C42—221no—
298C42—221no—
299C42—221no—
300C42—221no—
301C42—221no—
302C42—221no—
303C11#1177811yescharacteristic, complemented, Sylow
304C23—22no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23C22⋊C4×D1111yescharacteristic
312Q8—442no—
313Q8—442no—
314D4—42no—
315D4—42no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—111no—
326C2×C4—111no—
327C2×C4—112no—
328C2×C4—221no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—221no—
332C2×C4—221no—
333C2×C4—221no—
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#6696411yescharacteristic
344C2×C4#6696711yescharacteristic
345C8—42no—
346C8—81no—
347C8—442no—
348C8—881no—
349C22—21no—
350C22—21no—
351C22—42no—
352C22—42no—
353C22—42no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22D11×#9911yescharacteristic
359C22#1062238311yescharacteristic
360C22D11×#10411yescharacteristic
361C4—21no—
362C4—21no—
363C4—41no—
364C4—41no—
365C4—81no—
366C4—222no—
367C4—221no—
368C4—221no—
369C4—441no—
370C4—441no—
371C4—881no—
372C4—881no—
373C2—21no—
374C2—21no—
375C2—82no—
376C2#1306713011yescharacteristic
377C2#1307025411yescharacteristic
378C2#1307030211yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1345C2
socleC22×C11C2×#99
prime radicalC22×D4×C11C2×C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1345D11
hypocenterC11#11778
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1345

Complements

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

NH ≅ G/Ntype
2. #13068411C2semidirect
3. #13066958C2semidirect
4. #13066623C2semidirect
5. #13066621C2semidirect
303. C11#11778semidirect

Maximal subgroups

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

subgroupindex
#130735202
#130684112
#130669582
#130666232
#130666212
#130666192
C11×#13452
#1177811