Finite Group Databasebeta

← #14664602

Subgroups — #14664602

Order 2816.

400 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 79 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#13074533C211yesmaximal, characteristic
2#13066954C211yesmaximal, characteristic
3#13066645C212yesmaximal, complemented
4#13066621C212yesmaximal, complemented
5C11×#1800C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66977C411yescharacteristic
8C11×#423—21no—
9C2×C11×#100—21no—
10#10622835—21no—
11#10622824C411yescharacteristic
12#10622823—21no—
13#10622820—21no—
14#10622596C2211yescharacteristic
15#10622592C2211yescharacteristic
16#10622566C411yescharacteristic
17#10622565—21no—
18#10622560C411yescharacteristic
19#10622546—21no—
20C11×#343C2212yes—
21#10622166C2212yes—
22#10622163—21no—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×Dic22C2×C411yescharacteristic
27C2×C11×M16—22no—
28C4×D4×C11—41no—
29C4×D4×C11—41no—
30C2×C11×C4⋊C4C2311yescharacteristic
31C2×C11×C22⋊C4C2×C411yescharacteristic
32C2×C11×C22⋊C4D411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C4⋊Dic11C2×C411yescharacteristic
39#66977—41no—
40#66977—41no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×#4318—41no—
45C11×C4⋊C8—41no—
46C11×C4⋊C8—41no—
47C11×#100—42no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95C2×C411yescharacteristic
54C11⋊#95C2×C411yescharacteristic
55C22⋊(C11⋊C8)—22no—
56C22⋊(C11⋊C8)—41no—
57#11834—111nomaximal, Sylow
58C24×C11C22⋊C411yescharacteristic
59C24×C11C22⋊C411yescharacteristic
60C2×D4×C11—21no—
61C2×D4×C11—21no—
62C2×D4×C11—41no—
63C2×D4×C11—41no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—81no—
69C22×C4×C11—81no—
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—
78C22×Dic11—21no—
79C2×Dic22—41no—
80C2×Dic22—81no—
81C11×M16—42no—
82C11×M16—42no—
83C2×C8×C11—42no—
84C11×C4⋊C4—41no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—41no—
87C42×C11—21no—
88C42×C11—21no—
89C22⋊Dic11—42no—
90C22⋊Dic11—42no—
91C22⋊Dic11—81no—
92C22⋊Dic11—81no—
93C4⋊Dic11—41no—
94Dic11⋊C4—41no—
95Dic11⋊C4—41no—
96Dic11⋊C4—41no—
97Dic11⋊C4—41no—
98Dic11⋊C4—81no—
99#4318—82no—
100C2×C11⋊C8—42no—
101#2638—111no—
102#1800D1111yescharacteristic
103#1465—111no—
104#1354—112no—
105#1346—112no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—41no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11—41no—
116C23×C11C2×C22⋊C411yescharacteristic
117D4×C11—42no—
118D4×C11—42no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—41no—
125C2×C4×C11—42no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—81no—
130C2×C4×C11—81no—
131C2×C4×C11—81no—
132C2×C4×C11#9911yescharacteristic
133C2×C4×C11#9911yescharacteristic
134C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C11#13711yescharacteristic
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—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148Dic22—82no—
149C8×C11—82no—
150C11⋊C8—82no—
151C2×C22⋊Q8—111no—
152C2×C4×D4C2×D1111yescharacteristic
153#423—21no—
154C2×#100—21no—
155#407—221no—
156#398—111no—
157#397—111no—
158#397—221no—
159#395—111no—
160#394—221no—
161#393—111no—
162#387—221no—
163#385—221no—
164#381—111no—
165#343C2×D1112yes—
166#324—112no—
167#323—221no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—42no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—81no—
178C22×C11—81no—
179C22×C11—81no—
180C22×C11C2×#9911yescharacteristic
181C22×C11#41711yescharacteristic
182C22×C11#42111yescharacteristic
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—41no—
188C4×C11—41no—
189C4×C11—41no—
190Dic11—81no—
191Dic11—81no—
192Dic11—81no—
193Dic11—81no—
194C22×Q8—111no—
195C22×D4C22⋊D1111yescharacteristic
196C23×C4C4×D1111yescharacteristic
197C23×C4D4411yescharacteristic
198C2×M16—22no—
199C2×M16—441no—
200C22⋊Q8—441no—
201C22⋊Q8—441no—
202C4×D4—41no—
203C4×D4—41no—
204C2×C4⋊C4—111no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4C22×D1111yescharacteristic
209C2×C22⋊C4—221no—
210C2×C22⋊C4—221no—
211C2×C22⋊C4—221no—
212C2×C22⋊C4—221no—
213C2×C22⋊C4C4×D1111yescharacteristic
214C2×C22⋊C4D4411yescharacteristic
215C2×C42C22⋊D1111yescharacteristic
216C4⋊C8—41no—
217C4⋊C8—41no—
218#100—42no—
219C22⋊C8—222no—
220C22⋊C8—441no—
221#95—111no—
222#95—111no—
223#95—221no—
224#95—221no—
225#95—221no—
226#95—221no—
227#95—221no—
228C2×C11—21no—
229C2×C11—21no—
230C2×C11—81no—
231C2×C11—81no—
232C2×C11#151311yescharacteristic
233C2×C11#212111yescharacteristic
234C2×C11#213511yescharacteristic
235C24(C2×D11)⋊C411yescharacteristic
236C24(C2×D11)⋊C411yescharacteristic
237C2×Q8—441no—
238C2×Q8—881no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—41no—
242C2×D4—41no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—81no—
248C22×C4—81no—
249C22×C4—221no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4(C2×D11)⋊C411yescharacteristic
254C22×C4(C2×D11)⋊C411yescharacteristic
255C22×C4C2×C4×D1111yescharacteristic
256C22×C4C2×D4411yescharacteristic
257C22×C4C2×C22⋊D1111yescharacteristic
258M16—42no—
259M16—42no—
260M16—882no—
261C2×C8—42no—
262C2×C8—442no—
263C4⋊C4—41no—
264C4⋊C4—441no—
265C4⋊C4—441no—
266C4⋊C4—441no—
267C4⋊C4—441no—
268C4⋊C4—441no—
269C4⋊C4—881no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—442no—
273C22⋊C4—442no—
274C22⋊C4—881no—
275C22⋊C4—881no—
276C42—21no—
277C42—21no—
278C11#1183411yescharacteristic, complemented, Sylow
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23C2×(C2×D11)⋊C411yescharacteristic
290Q8—882no—
291D4—42no—
292D4—42no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4#6687011yescharacteristic
319C2×C4#6687011yescharacteristic
320C2×C4#6698511yescharacteristic
321C2×C4#6699511yescharacteristic
322C8—82no—
323C8—882no—
324C22—21no—
325C22—21no—
326C22—42no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—81no—
334C22—81no—
335C22—81no—
336C22C2×#6687011yescharacteristic
337C22#1062257911yescharacteristic
338C22#1062261811yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—881no—
347C4—881no—
348C4—881no—
349C4—881no—
350C2—21no—
351C2—21no—
352C2—81no—
353C2—81no—
354C2#1306715711yescharacteristic
355C2#1307026311yescharacteristic
356C2#1307031011yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1800C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C4⋊C4C23
hypercenter#1800D11
hypocenterC11#11834
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1800

Complements

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

NH ≅ G/Ntype
3. #13066645C2semidirect
4. #13066621C2semidirect
278. C11#11834semidirect

Maximal subgroups

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

subgroupindex
#130745332
#130669542
#130666452
#130666212
C11×#18002
#1183411