Finite Group Databasebeta

← #14664166

Subgroups — #14664166

Order 2816.

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

normal subgroups only

This group has 420 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#13074542C211yesmaximal, characteristic
2#13068407C211yesmaximal, characteristic
3#13066933C211yesmaximal, characteristic
4#13066646C211yesmaximal, characteristic, complemented
5#13066623C211yesmaximal, characteristic, complemented
6#13066621C211yesmaximal, characteristic, complemented
7C11×#1354C211yesmaximal, characteristic, complemented
8C2×#66999C411yescharacteristic
9C2×#66946C2211yescharacteristic
10C11×#395C2211yescharacteristic
11#10622844C411yescharacteristic
12C2×#66887—21no—
13M16×Dic11—21no—
14#10622606—21no—
15#10622602—21no—
16#10622596C2211yescharacteristic
17D11×C22⋊C8—21no—
18#10622287C411yescharacteristic
19#10622285—21no—
20#10622277C411yescharacteristic
21#10622265—21no—
22C11×#343C2211yescharacteristic
23C11×#324C2211yescharacteristic
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622106—21no—
27C22×Q8×C11C2×C411yescharacteristic
28C22×D44D411yescharacteristic
29C22×C4×D11C2×C411yescharacteristic
30C22×C4×D11D411yescharacteristic
31C2×C11×M16—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4C2311yescharacteristic
34#66999—41no—
35#66999—41no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4C2×C411yescharacteristic
41C2×(C2×D11)⋊C4D411yescharacteristic
42C2×C4⋊Dic11C2×C411yescharacteristic
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11D411yescharacteristic
46C2×#4318—21no—
47C2×C8×D11—41no—
48#66946—41no—
49#66946—41no—
50C11×C22⋊C8—21no—
51C11×#95—21no—
52C11×#95C2×C411yescharacteristic
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95C2×C411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59#66887—24no—
60(C2×D11)⋊C8—41no—
61#66879—41no—
62C8×Dic11—41no—
63#11739—111nomaximal, Sylow
64C23×D11C22⋊C411yescharacteristic
65C23×D11C22⋊C411yescharacteristic
66C2×Q8×C11—41no—
67C2×Q8×C11—81no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11C22⋊C411yescharacteristic
76C22×Dic11C22⋊C411yescharacteristic
77C2×D44—22no—
78C2×D44—21no—
79C2×D44—21no—
80C2×D44—41no—
81C2×C4×D11—21no—
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—81no—
86C2×C4×D11—81no—
87C11×M16—22no—
88C11×M16—41no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—81no—
93(C2×D11)⋊C4—41no—
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4—42no—
96(C2×D11)⋊C4—42no—
97(C2×D11)⋊C4—81no—
98(C2×D11)⋊C4—81no—
99C4⋊Dic11—41no—
100Dic11⋊C4—41no—
101Dic11⋊C4—41no—
102Dic11⋊C4—41no—
103Dic11⋊C4—41no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106#4318—22no—
107#4318—41no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110C8×D11—82no—
111#2638—111no—
112C4×#100—111no—
113#1459—111no—
114#1354—111no—
115#1354D1111yescharacteristic, complemented
116#1346—111no—
117#1346—111no—
118C23×C11C2×C22⋊C411yescharacteristic
119C22×D11—21no—
120C22×D11—21no—
121C22×D11—21no—
122C22×D11—21no—
123C22×D11—21no—
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11#10412yes—
129Q8×C11—82no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
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×C11#13511yescharacteristic
143C2×C4×C11#13511yescharacteristic
144C2×Dic11—21no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11#9911yescharacteristic
154C2×Dic11#9911yescharacteristic
155D44—42no—
156D44—42no—
157C4×D11—42no—
158C4×D11—81no—
159C4×D11—81no—
160C4×D11—81no—
161C8×C11—42no—
162C8×C11—81no—
163C11⋊C8—42no—
164C11⋊C8—81no—
165C2×C22⋊Q8—111no—
166C2×C4×D4—111no—
167C2×#100—221no—
168C2×C22⋊C8—221no—
169C4×M16—221no—
170#398—111no—
171#397—111no—
172#397—221no—
173#395C2×D1111yescharacteristic
174#394—221no—
175#393—111no—
176#387—221no—
177#385—221no—
178#381—111no—
179#343—111no—
180#343C2×D1111yescharacteristic
181#324—111no—
182#324C2×D1111yescharacteristic
183#323—221no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11C2×#9911yescharacteristic
187C22×C11#41611yescharacteristic
188C22×C11C2×#10411yescharacteristic
189C2×D11—22no—
190C2×D11—41no—
191C2×D11—41no—
192C2×D11—42no—
193C2×D11—41no—
194C2×D11—41no—
195C2×D11—41no—
196C2×D11—81no—
197C2×D11—81no—
198C2×D11—81no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—41no—
202C4×C11—41no—
203C4×C11—81no—
204C4×C11—81no—
205Dic11—21no—
206Dic11—21no—
207Dic11—41no—
208Dic11—81no—
209Dic11—81no—
210C22×Q8C4×D1111yescharacteristic
211C22×D4—111no—
212C23×C4—111no—
213C23×C4—111no—
214C2×M16—21no—
215C2×M16—221no—
216C22×C8—441no—
217C22⋊Q8—441no—
218C22⋊Q8—441no—
219C4×D4—441no—
220C4×D4—441no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—111no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4C22×D1111yescharacteristic
226C2×C22⋊C4—111no—
227C2×C22⋊C4—111no—
228C2×C22⋊C4—221no—
229C2×C22⋊C4—221no—
230C2×C22⋊C4—221no—
231C2×C22⋊C4—221no—
232C2×C42—111no—
233#100—224no—
234C22⋊C8—21no—
235C22⋊C8—221no—
236C22⋊C8—441no—
237#97—441no—
238C4×C8—441no—
239#95—21no—
240#95—111no—
241#95—221no—
242#95—221no—
243#95—221no—
244#95—221no—
245#95C4×D1111yescharacteristic
246C2×C11—21no—
247C2×C11—21no—
248C2×C11#150111yescharacteristic
249C2×C11#212111yescharacteristic
250C2×C11#213511yescharacteristic
251D11—42no—
252D11—81no—
253C24—111no—
254C24—111no—
255C2×Q8—41no—
256C2×Q8—81no—
257C2×D4—222no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4—441no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—111no—
264C22×C4—111no—
265C22×C4—221no—
266C22×C4—221no—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4—881no—
272C22×C4—881no—
273C22×C4C2×C4×D1111yescharacteristic
274C22×C4D4×D1111yescharacteristic
275C22×C4D4×D1111yescharacteristic
276M16—22no—
277M16—41no—
278M16—222no—
279M16—441no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—441no—
283C2×C8—441no—
284C2×C8—882no—
285C4⋊C4—41no—
286C4⋊C4—81no—
287C4⋊C4—441no—
288C4⋊C4—441no—
289C4⋊C4—441no—
290C4⋊C4—441no—
291C4⋊C4—441no—
292C22⋊C4—441no—
293C22⋊C4—441no—
294C22⋊C4—442no—
295C22⋊C4—442no—
296C22⋊C4—881no—
297C22⋊C4—881no—
298C42—221no—
299C42—221no—
300C11#1173911yescharacteristic, complemented, Sylow
301C23—112no—
302C23—221no—
303C23—221no—
304C23—221no—
305C23—221no—
306C23—221no—
307C23—441no—
308C23—441no—
309C23—441no—
310C23—441no—
311C23C22⋊C4×D1111yescharacteristic
312Q8—82no—
313D4—442no—
314D4—442no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—111no—
328C2×C4—111no—
329C2×C4—221no—
330C2×C4—442no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—881no—
340C2×C4—881no—
341C2×C4—881no—
342C2×C4#6696911yescharacteristic
343C2×C4#6697211yescharacteristic
344C8—42no—
345C8—81no—
346C8—442no—
347C8—881no—
348C22—21no—
349C22—21no—
350C22—222no—
351C22—442no—
352C22—441no—
353C22—441no—
354C22—441no—
355C22—441no—
356C22—441no—
357C22—881no—
358C22—881no—
359C22—881no—
360C22D11×#9911yescharacteristic
361C22#1062241711yescharacteristic
362C22D11×#10411yescharacteristic
363C4—21no—
364C4—21no—
365C4—41no—
366C4—41no—
367C4—81no—
368C4—81no—
369C4—221no—
370C4—221no—
371C4—441no—
372C4—881no—
373C4—881no—
374C2—21no—
375C2—21no—
376C2—442no—
377C2—881no—
378C2#1306710611yescharacteristic
379C2#1307025911yescharacteristic
380C2#1307030911yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1354C2
socleC22×C11C2×#99
prime radicalC22×D44D4
cosocleC2×C11×C4⋊C4C23
hypercenter#1354D11
hypocenterC11#11739
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
4. #13066646C2semidirect
5. #13066623C2semidirect
6. #13066621C2semidirect
7. C11×#1354C2semidirect
115. #1354D11semidirect
300. C11#11739semidirect

Maximal subgroups

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

subgroupindex
#130745422
#130684072
#130669332
#130666462
#130666232
#130666212
C11×#13542
#1173911