Finite Group Databasebeta

← #14647259

Subgroups — #14647259

Order 2816.

450 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 87 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#13071096C211yesmaximal, characteristic
2#13066948C211yesmaximal, characteristic
3#13066948C211yesmaximal, characteristic
4#13066473C211yesmaximal, characteristic, complemented
5#13066472C211yesmaximal, characteristic, complemented
6#13066471C211yesmaximal, characteristic, complemented
7C11×#1285C211yesmaximal, characteristic, complemented
8C2×#66925C411yescharacteristic
9C2×#66925C2211yescharacteristic
10C2×C42×D11C411yescharacteristic
11C11×#432C2211yescharacteristic
12C11×#432C2211yescharacteristic
13C4×C11×C4⋊C4C2211yescharacteristic
14#10622602—21no—
15#10622585—21no—
16C4×C4⋊Dic11C2211yescharacteristic
17C4×Dic11⋊C4C411yescharacteristic
18C4×Dic11⋊C4C411yescharacteristic
19#10622539C2211yescharacteristic
20#10622539C2211yescharacteristic
21#10622281—21no—
22#10622260—21no—
23#10622107—21no—
24#10622107—21no—
25#10622106—21no—
26#10622106—21no—
27C22×C4×D11—21no—
28C22×C4×D11C2×C411yescharacteristic
29C2×C11×C4⋊C4—21no—
30C2×C42×C11C2×C411yescharacteristic
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33C2×(C2×D11)⋊C4—21no—
34C2×(C2×D11)⋊C4D411yescharacteristic
35C2×(C2×D11)⋊C4D411yescharacteristic
36C2×C4⋊Dic11—21no—
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4D411yescharacteristic
41C2×Dic11⋊C4D411yescharacteristic
42C2×C4×Dic11—21no—
43C2×C4×Dic11C2×C411yescharacteristic
44C2×C4×Dic11C2×C411yescharacteristic
45C2×C4×Dic11C2×C411yescharacteristic
46#66925—21no—
47#66925—21no—
48#66925—21no—
49#66925—21no—
50#66925—42no—
51C42×D11—42no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C22⋊C8—21no—
55C11×C22⋊C8—21no—
56C11×#97—21no—
57C11×#97—21no—
58C11×#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C22⋊(C11⋊C8)—21no—
63C22⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66#66867—21no—
67#66867—21no—
68#8742—111nomaximal, Sylow
69C23×D11C22⋊C411yescharacteristic
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11C22⋊C411yescharacteristic
78C22×Dic11C22⋊C411yescharacteristic
79C22×Dic11C22⋊C411yescharacteristic
80C2×C4×D11—22no—
81C2×C4×D11—22no—
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11—42no—
85C2×C4×D11—42no—
86C2×C4×D11—42no—
87C2×C8×C11—41no—
88C2×C8×C11—41no—
89C11×C4⋊C4—42no—
90C42×C11—41no—
91C42×C11—41no—
92C42×C11#4111yescharacteristic
93C42×C11#4111yescharacteristic
94C42×C11#4111yescharacteristic
95C42×C11#4111yescharacteristic
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4—42no—
101C4⋊Dic11—42no—
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106Dic11⋊C4—42no—
107Dic11⋊C4—42no—
108Dic11⋊C4—42no—
109C4×Dic11—21no—
110C4×Dic11—21no—
111C4×Dic11—41no—
112C4×Dic11—41no—
113C4×Dic11—42no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116#2296—111no—
117#1464—111no—
118#1464—111no—
119#1285—111no—
120#1285—111no—
121#1285—111no—
122#1285D1111yescharacteristic, complemented
123C23×C11C2×C22⋊C411yescharacteristic
124C22×D11—21no—
125C22×D11—21no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11#10012yes—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—22no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11#11711yescharacteristic
140C2×C4×C11#11711yescharacteristic
141C2×C4×C11#12311yescharacteristic
142C2×C4×C11#12311yescharacteristic
143C2×C4×C11#12311yescharacteristic
144C2×C4×C11#12311yescharacteristic
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—22no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11#10112yes—
158C4×D11—24no—
159C4×D11—24no—
160C4×D11—48no—
161C8×C11—81no—
162C8×C11—81no—
163C11⋊C8—81no—
164C11⋊C8—81no—
165C2×#117—111no—
166C2×#117—111no—
167C22×C42—111no—
168#432—111no—
169#432—111no—
170#432C2×D1111yescharacteristic
171#432C2×D1111yescharacteristic
172#389—221no—
173#389—221no—
174#385—221no—
175#385—221no—
176C4×C4⋊C4—111no—
177C4×C4⋊C4—111no—
178C4×C4⋊C4—111no—
179C4×C4⋊C4C2×D1111yescharacteristic
180#324—221no—
181#324—221no—
182#323—221no—
183#323—221no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11#38111yescharacteristic
187C22×C11C2×#10011yescharacteristic
188C22×C11C2×#10111yescharacteristic
189C2×D11—22no—
190C2×D11—42no—
191C2×D11—41no—
192C2×D11—41no—
193C2×D11—42no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—42no—
201C4×C11—81no—
202Dic11—22no—
203Dic11—42no—
204Dic11—41no—
205Dic11—41no—
206Dic11—81no—
207C23×C4—111no—
208C23×C4—221no—
209#117—221no—
210#117—221no—
211#117—221no—
212#117—221no—
213#117—442no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—111no—
216C2×C4⋊C4—111no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4—221no—
219C2×C4⋊C4—221no—
220C2×C4⋊C4—221no—
221C2×C22⋊C4—111no—
222C2×C22⋊C4—111no—
223C2×C22⋊C4—221no—
224C2×C42—111no—
225C2×C42—111no—
226C2×C42—111no—
227C2×C42—221no—
228C2×C42—442no—
229C2×C42C4×D1111yescharacteristic
230C2×C42C4×D1111yescharacteristic
231C2×C42C22×D1111yescharacteristic
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—221no—
235C4⋊C8—221no—
236C22⋊C8—21no—
237C22⋊C8—21no—
238C22⋊C8—221no—
239C22⋊C8—221no—
240#97—21no—
241#97—21no—
242#97—221no—
243#97—221no—
244#95—21no—
245#95—221no—
246#95—221no—
247#95—221no—
248C2×C11—21no—
249C2×C11—21no—
250C2×C11#182111yescharacteristic
251C2×C11#182711yescharacteristic
252C2×C11#182711yescharacteristic
253D11—42no—
254C24—111no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—111no—
258C22×C4—111no—
259C22×C4—111no—
260C22×C4—222no—
261C22×C4—222no—
262C22×C4—221no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—442no—
267C22×C4—442no—
268C22×C4—442no—
269C22×C4C2×C4×D1111yescharacteristic
270C22×C4D4×D1111yescharacteristic
271C22×C4D4×D1111yescharacteristic
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—441no—
275C2×C8—441no—
276C4⋊C4—42no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—442no—
282C4⋊C4—442no—
283C4⋊C4—442no—
284C4⋊C4—442no—
285C22⋊C4—221no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C22⋊C4—221no—
289C22⋊C4—442no—
290C42—41no—
291C42—41no—
292C42—221no—
293C42—221no—
294C42—441no—
295C42—441no—
296C42—442no—
297C42#433911yescharacteristic
298C42#433911yescharacteristic
299C42#434111yescharacteristic
300C42#434311yescharacteristic
301C11#874211yescharacteristic, complemented, Sylow
302C23—112no—
303C23—221no—
304C23—221no—
305C23—441no—
306C23—441no—
307C23C22⋊C4×D1111yescharacteristic
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—112no—
319C2×C4—224no—
320C2×C4—224no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—222no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—448no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4#6692511yescharacteristic
335C2×C4#6693611yescharacteristic
336C2×C4#6693611yescharacteristic
337C2×C4#6694511yescharacteristic
338C2×C4#6694711yescharacteristic
339C2×C4#6694711yescharacteristic
340C8—81no—
341C8—81no—
342C8—881no—
343C8—881no—
344C22—21no—
345C22—21no—
346C22—222no—
347C22—442no—
348C22—442no—
349C22—441no—
350C22—441no—
351C22#1062227711yescharacteristic
352C22D11×#10011yescharacteristic
353C22D11×#10111yescharacteristic
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—42no—
361C4—81no—
362C4—222no—
363C4—442no—
364C4—441no—
365C4—441no—
366C4—881no—
367C2—21no—
368C2—21no—
369C2—442no—
370C2#1306869511yescharacteristic
371C2#1306871811yescharacteristic
372C2#1306871911yescharacteristic
subgroupG/H
centerC22#10622277
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1285C2
socleC22×C11#381
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1285D11
hypocenterC11#8742
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1285

Complements

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

NH ≅ G/Ntype
4. #13066473C2semidirect
5. #13066472C2semidirect
6. #13066471C2semidirect
7. C11×#1285C2semidirect
122. #1285D11semidirect
301. C11#8742semidirect

Maximal subgroups

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

subgroupindex
#130710962
#130669482
#130664732
#130664722
#130664712
C11×#12852
#874211