Finite Group Databasebeta

← #14673127

Subgroups — #14673127

Order 2816.

462 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622794C211yesmaximal, characteristic
2C2×#10622141C211yesmaximal, characteristic
3C2×#10622202C211yesmaximal, characteristic
4C2×#10622130C211yesmaximal, characteristic
5#13069347C211yesmaximal, characteristic
6#13066693C211yesmaximal, characteristic
7C2×C11×#358C211yesmaximal, characteristic
8C22×C11×Q16C2211yescharacteristic
9C2×#66997—21no—
10C22×#4326—21no—
11C22×Dic44C2211yescharacteristic
12C22×C11×C16C2211yescharacteristic
13C2×C11×#107C2211yescharacteristic
14#10622794—22no—
15#10622794—22no—
16C2×#66882C2211yescharacteristic
17C2×C8×Dic11C2211yescharacteristic
18C22×C11⋊C16C2211yescharacteristic
19#10622586—21no—
20C11×#358—22no—
21#10622202—22no—
22#10622167—21no—
23#10622141—22no—
24#10622130—22no—
25C22×Q8×C11—21no—
26C22×Dic22—21no—
27C2×C11×Q16—21no—
28C2×C11×Q16—21no—
29C2×C11×Q16—21no—
30C2×C11×Q16—21no—
31C2×C11×Q16—21no—
32C2×C11×Q16D412yes—
33C22×C8×C11C2311yescharacteristic
34C2×C11×C4⋊C4—21no—
35#66997—24no—
36#66997—42no—
37C2×#4326—24no—
38C2×#4326—42no—
39C2×#4326—42no—
40C2×C4⋊Dic11—21no—
41C2×Dic11⋊C4—41no—
42C2×Dic11⋊C4—41no—
43C2×Dic11⋊C4—41no—
44C2×C4×Dic11D411yescharacteristic
45C22×C11⋊C8D411yescharacteristic
46C2×Dic44—21no—
47C2×Dic44—21no—
48C2×Dic44—21no—
49C2×Dic44—21no—
50C2×Dic44—21no—
51C2×Dic44D412yes—
52C2×C11×C16—21no—
53C2×C11×C16—21no—
54C2×C11×C16—21no—
55C11×#107—21no—
56C11×#107—21no—
57C11⋊#95—41no—
58#66882—21no—
59#66882D412yes—
60C8×Dic11—21no—
61C8×Dic11—21no—
62C2×C11⋊C16—21no—
63C2×C11⋊C16—21no—
64C2×C11⋊C16—21no—
65#13409—111nomaximal, Sylow
66C2×Q8×C11—22no—
67C2×Q8×C11—41no—
68C2×Q8×C11—41no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C2×Q8×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11C2×D411yescharacteristic
75C22×Dic11—41no—
76C22×Dic11—41no—
77C22×Dic11D811yescharacteristic
78C22×Dic11D811yescharacteristic
79C2×Dic22—22no—
80C2×Dic22—41no—
81C2×Dic22—41no—
82C2×Dic22—41no—
83C2×Dic22—41no—
84C2×Dic22—41no—
85C11×Q16—22no—
86C11×Q16—22no—
87C11×Q16—41no—
88C11×Q16—41no—
89C2×C8×C11C2×D411yescharacteristic
90C2×C8×C11C2×D411yescharacteristic
91C2×C8×C11C2×D411yescharacteristic
92C2×C8×C11#4111yescharacteristic
93C2×C8×C11#4111yescharacteristic
94C2×C8×C11#4111yescharacteristic
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97#4326—48no—
98C4⋊Dic11—22no—
99C4⋊Dic11—41no—
100Dic11⋊C4—44no—
101Dic11⋊C4—44no—
102Dic11⋊C4—82no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8SD1612yes—
108Dic44—22no—
109Dic44—22no—
110Dic44—41no—
111Dic44—41no—
112C11×C16—41no—
113C11⋊C16—41no—
114C2×#494—111no—
115C2×#358—111no—
116C2×#358—111no—
117C2×#358—111no—
118C2×#358D1111yescharacteristic
119#1942—111no—
120#1374—111no—
121C23×C11C2×D811yescharacteristic
122Q8×C11—42no—
123Q8×C11—42no—
124Q8×C11—81no—
125Q8×C11—81no—
126C2×C4×C11—42no—
127C2×C4×C11—81no—
128C2×C4×C11—81no—
129C2×C4×C11—81no—
130C2×C4×C11—81no—
131C2×C4×C11—81no—
132C2×C4×C11#12011yescharacteristic
133C2×C4×C11#12111yescharacteristic
134C2×C4×C11#12411yescharacteristic
135C2×C4×C11C2×SD1611yescharacteristic
136C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—42no—
143C2×Dic11—42no—
144C2×Dic11—81no—
145C2×Dic11—81no—
146C2×Dic11—81no—
147C2×Dic11—81no—
148C2×Dic11SD3212yes—
149C2×Dic11Q3212yes—
150Dic22—42no—
151Dic22—42no—
152Dic22—81no—
153Dic22—81no—
154C8×C11#12111yescharacteristic
155C8×C11#12111yescharacteristic
156C8×C11#12311yescharacteristic
157C8×C11#12311yescharacteristic
158C11⋊C8—22no—
159C22×Q16—111no—
160C22×Q16—221no—
161C22×Q16C2×D1111yescharacteristic
162C2×C4⋊Q8—221no—
163C22×C16—111no—
164C22×C16C2×D1111yescharacteristic
165#494—222no—
166#494—222no—
167C2×#107—111no—
168C2×#107C2×D1111yescharacteristic
169C2×C4×C8—111no—
170#389—221no—
171#358—22no—
172#358—222no—
173#358—222no—
174#358—222no—
175#340—221no—
176C22×C11#44711yescharacteristic
177C22×C11#45911yescharacteristic
178C22×C11#48611yescharacteristic
179C22×C11C2×SD3211yescharacteristic
180C22×C11C2×Q3211yescharacteristic
181C22×C11#51011yescharacteristic
182C22×C11#51011yescharacteristic
183C4×C11—82no—
184C4×C11—161no—
185C4×C11#39411yescharacteristic
186C4×C11#45011yescharacteristic
187C4×C11#46011yescharacteristic
188C4×C11#49011yescharacteristic
189Dic11—22no—
190Dic11—22no—
191Dic11—82no—
192Dic11—82no—
193C22×Q8—21no—
194C22×Q8—221no—
195C2×Q16—21no—
196C2×Q16—21no—
197C2×Q16—21no—
198C2×Q16—21no—
199C2×Q16—21no—
200C2×Q16—112no—
201C2×Q16—224no—
202C2×Q16—221no—
203C2×Q16—221no—
204C2×Q16—221no—
205C2×Q16—221no—
206C2×Q16—221no—
207C2×Q16—442no—
208C2×Q16—442no—
209C2×Q16C22⋊D1112yes—
210C22×C8—111no—
211C22×C8C22×D1111yescharacteristic
212C4⋊Q8—224no—
213C4⋊Q8—442no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—441no—
217C2×C4⋊C4—441no—
218C2×C4⋊C4—441no—
219C2×C42—111no—
220C2×C16—21no—
221C2×C16—21no—
222C2×C16—21no—
223C2×C16—221no—
224C2×C16—221no—
225C2×C16—221no—
226#107—21no—
227#107—21no—
228#107—112no—
229#107—221no—
230C4×C8—221no—
231C4×C8—221no—
232#95—441no—
233C2×C11#204111yescharacteristic
234C2×C11#218511yescharacteristic
235C2×C11#218811yescharacteristic
236C2×C11#220811yescharacteristic
237C2×C11#220911yescharacteristic
238C2×C11#224111yescharacteristic
239C2×C11#224511yescharacteristic
240C2×Q8—22no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—222no—
247C2×Q8—441no—
248C2×Q8—441no—
249C2×Q8—441no—
250C2×Q8—441no—
251C2×Q8—441no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—111no—
255C22×C4—111no—
256C22×C4—441no—
257C22×C4—441no—
258C22×C4D4×D1111yescharacteristic
259Q16—22no—
260Q16—22no—
261Q16—41no—
262Q16—41no—
263Q16—222no—
264Q16—222no—
265Q16—448no—
266Q16—441no—
267Q16—441no—
268C2×C8—112no—
269C2×C8—221no—
270C2×C8—221no—
271C2×C8#433911yescharacteristic
272C2×C8#433911yescharacteristic
273C2×C8D4×D1111yescharacteristic
274C2×C8D4×D1111yescharacteristic
275C2×C8#434111yescharacteristic
276C2×C8C2×C22⋊D1111yescharacteristic
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—222no—
280C4⋊C4—444no—
281C4⋊C4—444no—
282C4⋊C4—441no—
283C4⋊C4—882no—
284C42—221no—
285C42—221no—
286C16—41no—
287C16—441no—
288C11#1340911yescharacteristic, complemented, Sylow
289C23D8×D1111yescharacteristic
290Q8—42no—
291Q8—42no—
292Q8—81no—
293Q8—81no—
294Q8—442no—
295Q8—442no—
296Q8—881no—
297Q8—881no—
298C2×C4—42no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—112no—
305C2×C4—112no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—442no—
311C2×C4—442no—
312C2×C4—881no—
313C2×C4—881no—
314C2×C4—881no—
315C2×C4—881no—
316C2×C4#6693711yescharacteristic
317C2×C4#6693811yescharacteristic
318C2×C4#6696411yescharacteristic
319C2×C4SD16×D1111yescharacteristic
320C2×C4#6696711yescharacteristic
321C2×C4#6699011yescharacteristic
322C8—222no—
323C8#6693611yescharacteristic
324C8#6693711yescharacteristic
325C8#6698211yescharacteristic
326C8#6699211yescharacteristic
327C22#1062237311yescharacteristic
328C22#1062239911yescharacteristic
329C22D11×SD3211yescharacteristic
330C22#1062252811yescharacteristic
331C22D11×Q3211yescharacteristic
332C22#1062253111yescharacteristic
333C22#1062276911yescharacteristic
334C4—82no—
335C4—161no—
336C4—222no—
337C4—222no—
338C4—882no—
339C4—882no—
340C4#1062237511yescharacteristic
341C4#1062237711yescharacteristic
342C4#1062257211yescharacteristic
343C4#1062278211yescharacteristic
344C2#1306984811yescharacteristic
345C2#1307053111yescharacteristic
346C2#1307054811yescharacteristic
347C2#1307066011yescharacteristic
348C2#1307066511yescharacteristic
349C2#1307084211yescharacteristic
350C2#1307086011yescharacteristic
subgroupG/H
centerC23D8×D11
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC2×C11×#358C2
socle, prime radicalC23×C11C2×D8
hypercenterC2×#358D11
hypocenterC11#13409
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
288. C11#13409semidirect

Maximal subgroups

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

subgroupindex
C2×#106227942
C2×#106221412
C2×#106222022
C2×#106221302
#130693472
#130666932
C2×C11×#3582
#1340911