Finite Group Databasebeta

← #14648855

Subgroups — #14648855

Order 2816.

516 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 103 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#13077701C211yesmaximal, characteristic, complemented
2#13071899C211yesmaximal, characteristic
3#13067060C212yesmaximal
4#13066510C212yesmaximal, complemented
5C4×C11×#101C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C11C2211yescharacteristic
7C2×C4×D44C2211yescharacteristic
8C2×C11×#101—21no—
9C4×C11×M16C2212yes—
10#10622844—21no—
11#10622637—24no—
12#10622606—21no—
13#10622604C411yescharacteristic
14#10622604C411yescharacteristic
15#10622599C411yescharacteristic
16#10622599C411yescharacteristic
17C4×(C2×D11)⋊C4—21no—
18C4×(C2×D11)⋊C4—21no—
19#10622545C2211yescharacteristic
20#10622539—21no—
21#10622539C2212yes—
22#10622538—21no—
23C11×#343—21no—
24#10622097—24no—
25C22×Q8×C11D411yescharacteristic
26C22×D44C2×C411yescharacteristic
27C22×C4×D11—21no—
28C2×C11×M16—22no—
29C4×Q8×C11—22no—
30C4×Q8×C11—22no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11C2311yescharacteristic
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×C4⋊Dic11C2×C411yescharacteristic
43C2×C4×Dic11—21no—
44C4×D44—22no—
45C4×D44—22no—
46C11×#101—24no—
47C11×#97—22no—
48C4×C8×C11—22no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95C2×C411yescharacteristic
55C11⋊#95C2×C411yescharacteristic
56C22⋊(C11⋊C8)—22no—
57C4⋊(C11⋊C8)—22no—
58C4⋊(C11⋊C8)—22no—
59C4⋊(C11⋊C8)D414yes—
60#66867—22no—
61#66867—22no—
62C4×C11⋊C8—22no—
63#9032—111nomaximal, Sylow
64C23×D11—21no—
65C2×Q8×C11—22no—
66C2×Q8×C11—22no—
67C2×Q8×C11—41no—
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C2×D44—22no—
79C2×D44—42no—
80C2×C4×D11—42no—
81C2×C4×D11—42no—
82C2×C4×D11—41no—
83C2×C4×D11—41no—
84C11×M16—24no—
85C11×M16—42no—
86C2×C8×C11—42no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—22no—
89C11×C4⋊C4—22no—
90C42×C11—21no—
91C42×C11—21no—
92C42×C11—21no—
93C42×C11—21no—
94C42×C11C2×D412yes—
95C42×C11#4112yes—
96(C2×D11)⋊C4—42no—
97(C2×D11)⋊C4—42no—
98(C2×D11)⋊C4—42no—
99(C2×D11)⋊C4—42no—
100(C2×D11)⋊C4—42no—
101C4⋊Dic11—22no—
102C4×Dic11—42no—
103C2×C11⋊C8—24no—
104#2983—111no—
105#2398—111no—
106C4×#101D1111yescharacteristic, complemented
107#1490—112no—
108#1300—112no—
109C23×C11C2×C22⋊C411yescharacteristic
110C22×D11—22no—
111C22×D11—41no—
112C22×D11—41no—
113C22×D11—41no—
114C22×D11—41no—
115C22×D11—41no—
116C22×D11—41no—
117Q8×C11—44no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—22no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11#10412yes—
132C2×C4×C11C4×D412yes—
133C2×C4×C11#12011yescharacteristic
134C2×C4×C11#12112yes—
135C2×C4×C11#12311yescharacteristic
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145D44—24no—
146D44—42no—
147C4×D11—82no—
148C4×D11—82no—
149C8×C11—44no—
150C11⋊C8—44no—
151C2×C4×Q8C2×D1111yescharacteristic
152C2×C4×D4—111no—
153#446—224no—
154#432—112no—
155#432—221no—
156#431—221no—
157C2×#101—21no—
158C4×M16C2×D1112yes—
159#400—111no—
160#400—111no—
161#397—221no—
162#394—111no—
163#394—111no—
164#393—221no—
165C4×C22⋊C4—221no—
166C4×C22⋊C4—221no—
167#376—111no—
168#343—21no—
169D4⋊C8—224no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11#38611yescharacteristic
173C22×C11C2×#10411yescharacteristic
174C22×C11#42111yescharacteristic
175C2×D11—42no—
176C2×D11—42no—
177C2×D11—42no—
178C2×D11—81no—
179C2×D11—81no—
180C2×D11—81no—
181C2×D11—81no—
182C4×C11—22no—
183C4×C11—22no—
184C4×C11—21no—
185C4×C11—22no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11—41no—
189C4×C11#45412yes—
190Dic11—81no—
191Dic11—81no—
192Dic11—81no—
193C22×Q8C22⋊D1111yescharacteristic
194C22×D4—111no—
195C23×C4—221no—
196C2×M16—22no—
197C4×Q8—22no—
198C4×Q8—22no—
199C4×D4—222no—
200C4×D4—222no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4C4×D1111yescharacteristic
203C2×C4⋊C4C4×D1111yescharacteristic
204C2×C4⋊C4C22⋊D1111yescharacteristic
205C2×C22⋊C4—221no—
206C2×C22⋊C4—221no—
207C2×C22⋊C4—221no—
208C2×C22⋊C4—221no—
209C2×C22⋊C4—221no—
210C2×C42—221no—
211C2×C42D4411yescharacteristic
212C2×C42D4411yescharacteristic
213C2×C42C22×D1111yescharacteristic
214C4⋊C8—114no—
215C4⋊C8—222no—
216C4⋊C8—222no—
217#101—24no—
218C22⋊C8—222no—
219#97—22no—
220#97—222no—
221#97—222no—
222C4×C8—22no—
223C4×C8—222no—
224#95—111no—
225#95—111no—
226#95—221no—
227#95—221no—
228#95—221no—
229#95—221no—
230#95—221no—
231C2×C11—21no—
232C2×C11—21no—
233C2×C11#187111yescharacteristic
234C2×C11#188811yescharacteristic
235C2×C11#189111yescharacteristic
236D11—82no—
237C24—221no—
238C2×Q8—22no—
239C2×Q8—22no—
240C2×Q8—41no—
241C2×D4—222no—
242C2×D4—442no—
243C22×C4—221no—
244C22×C4—221no—
245C22×C4—221no—
246C22×C4—442no—
247C22×C4—442no—
248C22×C4—441no—
249C22×C4—441no—
250C22×C4(C2×D11)⋊C411yescharacteristic
251C22×C4(C2×D11)⋊C411yescharacteristic
252C22×C4(C2×D11)⋊C411yescharacteristic
253C22×C4(C2×D11)⋊C411yescharacteristic
254C22×C4C2×C4×D1111yescharacteristic
255C22×C4C2×D4411yescharacteristic
256C22×C4C2×C22⋊D1111yescharacteristic
257M16—24no—
258M16—42no—
259C2×C8—42no—
260C2×C8—224no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—222no—
265C22⋊C4—442no—
266C22⋊C4—442no—
267C22⋊C4—442no—
268C22⋊C4—442no—
269C22⋊C4—442no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42—442no—
275C42D4×D1112yes—
276C42#434112yes—
277C11#903211yescharacteristic, complemented, Sylow
278C23—222no—
279C23—441no—
280C23—441no—
281C23—441no—
282C23—441no—
283C23—441no—
284C23—441no—
285C23C2×(C2×D11)⋊C411yescharacteristic
286Q8—44no—
287D4—224no—
288D4—442no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—882no—
312C2×C4—882no—
313C2×C4#6686912yes—
314C2×C4(C22⋊D11)⋊C412yes—
315C2×C4#6693511yescharacteristic
316C2×C4#6693911yescharacteristic
317C2×C4#6699212yes—
318C8—44no—
319C8—444no—
320C22—21no—
321C22—21no—
322C22—442no—
323C22—442no—
324C22—442no—
325C22—881no—
326C22—881no—
327C22—881no—
328C22—881no—
329C22C2×#6686911yescharacteristic
330C22#1062257111yescharacteristic
331C22#1062261811yescharacteristic
332C4—22no—
333C4—22no—
334C4—21no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—881no—
340C4—881no—
341C4—881no—
342C4#1062236612yes—
343C2—21no—
344C2—21no—
345C2—882no—
346C2#1306891611yescharacteristic
347C2#1306901711yescharacteristic
348C2#1306903211yescharacteristic
subgroupG/H
centerC2×C4#66935
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC4×C11×#101C2
socleC22×C11#386
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenterC4×#101D11
hypocenterC11#9032
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
1. #13077701C2semidirect
4. #13066510C2semidirect
5. C4×C11×#101C2semidirect
106. C4×#101D11semidirect
277. C11#9032semidirect

Maximal subgroups

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

subgroupindex
#130777012
#130718992
#130670602
#130665102
C4×C11×#1012
#903211