Finite Group Databasebeta

← #14672136

Subgroups — #14672136

Order 2816.

464 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 95 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#13078264C211yesmaximal, characteristic
2#13070307C212yesmaximal, complemented
3#13070267C212yesmaximal, complemented
4#13068416C211yesmaximal, characteristic, complemented
5C11×#1813C211yesmaximal, characteristic, complemented
6C2×C11×#131C2211yescharacteristic
7#10623361C2212yes—
8C22×D88C411yescharacteristic, complemented
9C2×C11×#108—21no—
10C11×#413C2212yes—
11#10622853C2211yescharacteristic
12#10622850C2211yescharacteristic
13#10622748—21no—
14#10622748—21no—
15#10622744C412yescomplemented
16#10622728—21no—
17#10622728—21no—
18#10622719C411yescharacteristic, complemented
19#10622714—21no—
20C11×#338—21no—
21#10622194—21no—
22#10622115—24no—
23#10622113—24no—
24C2×C11×#41C2311yescharacteristic
25C22×D44C2×C412yes—
26C11×#131—41no—
27C11×#131—41no—
28C2×C11×M16—22no—
29C2×C11×M16C2×C411yescharacteristic
30C2×C11×M16D411yescharacteristic
31C2×C11×M16D411yescharacteristic
32C22×C8×C11C2×C411yescharacteristic
33C22×C8×C11D411yescharacteristic
34C22×C8×C11D411yescharacteristic
35#67000—22no—
36#66993—22no—
37#66990—22no—
38#66990—22no—
39#66983—22no—
40#66983—22no—
41#66979—21no—
42#66979C2×C412yes—
43C2×#4318—21no—
44C2×D88—21no—
45C2×D88—21no—
46C2×D88—41no—
47C2×D88—41no—
48C11×#108—41no—
49C11×#108—41no—
50C11×#101—22no—
51C11×#100—22no—
52#66900D412yes—
53#66898—21no—
54#66898D412yes—
55#66897—21no—
56#66885—22no—
57#66885—22no—
58#66882—21no—
59#66881—21no—
60#66879—41no—
61C8×Dic11—41no—
62#13234—111nomaximal, Sylow
63C23×D11—22no—
64C11×#41—41no—
65C11×#41—41no—
66C2×Q8×C11C2×D411yescharacteristic
67C2×D4×C11C2×D411yescharacteristic
68C2×D4×C11#4111yescharacteristic
69C2×D4×C11#4111yescharacteristic
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C2×C22⋊D11—42no—
74C2×C22⋊D11—42no—
75C2×D44—22no—
76C2×D44—22no—
77C2×D44—42no—
78C2×D44—42no—
79C11×M16—41no—
80C11×M16—41no—
81C11×M16—41no—
82C11×M16—42no—
83C11×M16—42no—
84C2×C8×C11—21no—
85C2×C8×C11—21no—
86C2×C8×C11—21no—
87C2×C8×C11—21no—
88C2×C8×C11—21no—
89C2×C8×C11—21no—
90C2×C8×C11—42no—
91C2×C8×C11C22⋊C411yescharacteristic
92C2×C8×C11C22⋊C411yescharacteristic
93C2×C8×C11C22⋊C411yescharacteristic
94C2×C8×C11C22⋊C411yescharacteristic
95C22⋊Dic11—22no—
96C22⋊Dic11—22no—
97(C2×D11)⋊C4—42no—
98(C2×D11)⋊C4—42no—
99C4⋊Dic11—22no—
100C4⋊Dic11—41no—
101C4×Dic11—22no—
102C4×Dic11—41no—
103#4318—22no—
104#4318—41no—
105C2×C11⋊C8—41no—
106D88—42no—
107D88—41no—
108D88—41no—
109#3058—111no—
110#2134—112no—
111#2122—112no—
112#1813D1111yescharacteristic, complemented
113#1757—111no—
114C23×C11C4×D411yescharacteristic
115C23×C11#12111yescharacteristic
116C23×C11#12411yescharacteristic
117C22×D11—42no—
118C22×D11—82no—
119C22×D11—162no—
120Q8×C11—41no—
121D4×C11—41no—
122D4×C11—41no—
123D4×C11—41no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11C2×C22⋊C411yescharacteristic
131C2×C4×C11C4×D411yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11#12711yescharacteristic
134C22⋊D11—162no—
135C22⋊D11—162no—
136C2×Dic11—42no—
137C2×Dic11—42no—
138D44—42no—
139D44—42no—
140D44—82no—
141C8×C11—21no—
142C8×C11—21no—
143C8×C11—21no—
144C8×C11—82no—
145C8×C11#9911yescharacteristic
146C8×C11#9911yescharacteristic
147C11⋊C8—42no—
148C22×D8—111no—
149C2×#131C2×D1111yescharacteristic
150#535—112no—
151#469—221no—
152#469—221no—
153#466—221no—
154#466—221no—
155C2×#108—21no—
156#427—111no—
157#418—112no—
158#413—111no—
159#413C2×D1112yes—
160#410—111no—
161#405—221no—
162#355—224no—
163AΣL(1,𝔽16)—224no—
164#344—221no—
165#338—21no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11#39011yescharacteristic
173C2×D11—82no—
174C2×D11—82no—
175C2×D11—82no—
176C2×D11—164no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11C2×#9911yescharacteristic
181C4×C11#41011yescharacteristic
182Dic11—82no—
183Dic11—82no—
184C2×#41C22×D1111yescharacteristic
185C22×D4—112no—
186C2×D8—221no—
187C2×D8—221no—
188C2×D8—441no—
189C2×D8—441no—
190#131—41no—
191#131—41no—
192C2×M16—22no—
193C2×M16—221no—
194C2×M16C4×D1111yescharacteristic
195C2×M16D4411yescharacteristic
196C2×M16C22⋊D1111yescharacteristic
197C22×C8C4×D1111yescharacteristic
198C22×C8D4411yescharacteristic
199C22×C8C22⋊D1111yescharacteristic
200#127—222no—
201#124—222no—
202#121—222no—
203#121—222no—
204#120—222no—
205#120—222no—
206#117—112no—
207#117—221no—
208#108—41no—
209#108—41no—
210#107—221no—
211#106—221no—
212#102—222no—
213#102—222no—
214#101—22no—
215#101—112no—
216#100—22no—
217#100—221no—
218#99—112no—
219#99—221no—
220#97—441no—
221C4×C8—441no—
222C2×C11—21no—
223C2×C11—41no—
224C2×C11—41no—
225C2×C11—41no—
226C2×C11#196411yescharacteristic
227D11—162no—
228C24—222no—
229#41—41no—
230#41—41no—
231C2×Q8D4×D1111yescharacteristic
232C2×D4—222no—
233C2×D4—222no—
234C2×D4—442no—
235C2×D4—442no—
236C2×D4—442no—
237C2×D4—442no—
238C2×D4D4×D1111yescharacteristic
239C2×D4#434311yescharacteristic
240C2×D4#434311yescharacteristic
241C22×C4C2×C4×D1111yescharacteristic
242C22×C4C2×D4411yescharacteristic
243C22×C4C2×C22⋊D1111yescharacteristic
244D8—442no—
245D8—441no—
246D8—441no—
247M16—41no—
248M16—41no—
249M16—41no—
250M16—42no—
251M16—42no—
252M16—222no—
253M16—441no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—21no—
260C2×C8—42no—
261C2×C8—441no—
262C2×C8(C2×D11)⋊C411yescharacteristic
263C2×C8(C2×D11)⋊C411yescharacteristic
264C2×C8(C2×D11)⋊C411yescharacteristic
265C2×C8(C2×D11)⋊C411yescharacteristic
266C4⋊C4—222no—
267C4⋊C4—441no—
268C22⋊C4—222no—
269C22⋊C4—222no—
270C22⋊C4—442no—
271C22⋊C4—442no—
272C42—222no—
273C42—441no—
274C11#1323411yescharacteristic, complemented, Sylow
275C23—442no—
276C23—882no—
277C23—1762no—
278C23#6694611yescharacteristic
279C23#6694811yescharacteristic
280C23#6700011yescharacteristic
281Q8—41no—
282D4—41no—
283D4—41no—
284D4—41no—
285D4—442no—
286D4—442no—
287D4—882no—
288D4—1762no—
289D4—1762no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—442no—
297C2×C4—442no—
298C2×C4#6694611yescharacteristic
299C2×C4#6694811yescharacteristic
300C2×C4C2×(C2×D11)⋊C411yescharacteristic
301C2×C4#6699311yescharacteristic
302C8—21no—
303C8—21no—
304C8—21no—
305C8—82no—
306C8—442no—
307C8#6687011yescharacteristic
308C8#6687011yescharacteristic
309C22—21no—
310C22—21no—
311C22—21no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—882no—
316C22—882no—
317C22—882no—
318C22—1764no—
319C22#1062260111yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—882no—
324C4—882no—
325C4C2×#6687011yescharacteristic
326C4#1062261911yescharacteristic
327C2—21no—
328C2—41no—
329C2—41no—
330C2—41no—
331C2—1762no—
332C2#1306945111yescharacteristic
subgroupG/H
centerC2#13069451
commutatorC22×C4×C11C22×C4
FrattiniC2×#41C22×D11
FittingC11×#1813C2
socleC2×C11#1964
prime radical#13078264C2
cosocleC2×C11×#41C23
hypercenter#1813D11
hypocenterC11#13234
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#131 ◁ #1813

Complements

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

NH ≅ G/Ntype
2. #13070307C2semidirect
3. #13070267C2semidirect
4. #13068416C2semidirect
5. C11×#1813C2semidirect
8. C22×D88C4semidirect
15. #10622744C4semidirect
18. #10622719C4semidirect
112. #1813D11semidirect
274. C11#13234semidirect

Maximal subgroups

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

subgroupindex
#130782642
#130703072
#130702672
#130684162
C11×#18132
#1323411