Finite Group Databasebeta

← #14652865

Subgroups — #14652865

Order 2816.

538 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
1#13077012C211yesmaximal, characteristic
2#13068732C211yesmaximal, characteristic
3#13068471C211yesmaximal, characteristic
4C2×#10622120C211yesmaximal, characteristic
5C2×#10622185C211yesmaximal, characteristic
6C2×#10622124C211yesmaximal, characteristic
7C2×C11×#332C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66997—21no—
10C2×#66997—21no—
11C2×#66922C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×#66879—21no—
15#10622589—22no—
16#10622589C414yes—
17C42×Dic11C2211yescharacteristic
18C2×C4⋊(C11⋊C8)C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C11×#332—22no—
21#10622188—21no—
22#10622188—22no—
23#10622185—22no—
24#10622124—22no—
25#10622120—22no—
26C22×Q8×C11—21no—
27C22×Dic22—21no—
28C22×C8×C11—21no—
29C22×C8×C11—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4C2×C412yes—
36C2×C42×C11C2311yescharacteristic
37#66997—42no—
38#66997—42no—
39#66997—42no—
40#66997—42no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11C2×C412yes—
43C2×Dic11⋊C4—24no—
44C2×Dic11⋊C4—24no—
45C2×C4×Dic11C2×C412yes—
46C2×C4×Dic11D411yescharacteristic
47C2×C4×Dic11D412yes—
48C2×C4×Dic11D411yescharacteristic
49C22×C11⋊C8—21no—
50C22×C11⋊C8—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8D412yes—
59#66879—42no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)D412yes—
64#9705—111nomaximal, Sylow
65C2×Q8×C11—41no—
66C2×Q8×C11—41no—
67C2×Q8×C11—41no—
68C2×Q8×C11—41no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C22×C4×C11—22no—
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×Dic11—22no—
76C22×Dic11C22⋊C412yes—
77C22×Dic11C22⋊C412yes—
78C2×Dic22—41no—
79C2×Dic22—41no—
80C2×Dic22—41no—
81C2×Dic22—41no—
82C2×Dic22—41no—
83C2×Dic22—41no—
84C2×C8×C11—22no—
85C2×C8×C11—41no—
86C2×C8×C11—41no—
87C2×C8×C11—41no—
88C2×C8×C11—42no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C42×C11C2×D411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11#4111yescharacteristic
96C42×C11#4111yescharacteristic
97C4⋊Dic11—22no—
98C4⋊Dic11—22no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101Dic11⋊C4—48no—
102Dic11⋊C4—48no—
103C4×Dic11—24no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11—22no—
107C4×Dic11—22no—
108C4×Dic11D812yes—
109C4×Dic11SD1612yes—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—42no—
115#2868—111no—
116#1831—111no—
117#1767—111no—
118C2×#332—111no—
119C2×#332—111no—
120C2×#332—111no—
121C2×#332D1111yescharacteristic
122C23×C11C2×C22⋊C411yescharacteristic
123Q8×C11—81no—
124Q8×C11—81no—
125Q8×C11—81no—
126Q8×C11—81no—
127C2×C4×C11—22no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11C4×D411yescharacteristic
132C2×C4×C11C4×D411yescharacteristic
133C2×C4×C11#12111yescharacteristic
134C2×C4×C11#12111yescharacteristic
135C2×C4×C11#12411yescharacteristic
136C2×C4×C11#12711yescharacteristic
137C2×C4×C11C2×D811yescharacteristic
138C2×C4×C11C2×SD1611yescharacteristic
139C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C11#13712yes—
142C2×C4×C11#13712yes—
143C2×Dic11—22no—
144C2×Dic11—22no—
145C2×Dic11—22no—
146C2×Dic11—22no—
147C2×Dic11—42no—
148C2×Dic11—42no—
149C2×Dic11—42no—
150C2×Dic11#10114yes—
151C2×Dic11#10214yes—
152Dic22—81no—
153Dic22—81no—
154Dic22—81no—
155Dic22—81no—
156C8×C11—42no—
157C8×C11—81no—
158C11⋊C8—42no—
159C11⋊C8—81no—
160C2×C4⋊Q8—111no—
161C2×C4⋊Q8—221no—
162C2×C4⋊Q8—221no—
163C2×C4⋊Q8C2×D1111yescharacteristic
164C2×C4⋊C8—111no—
165C2×C4⋊C8—111no—
166C2×C4⋊C8C2×D1111yescharacteristic
167C2×C4⋊C8C2×D1111yescharacteristic
168C2×#97—221no—
169#384—114no—
170#384—222no—
171C43—111no—
172#336—222no—
173#336—221no—
174#332—22no—
175#332—222no—
176#332—222no—
177#332—222no—
178C22×C11#39011yescharacteristic
179C22×C11C2×#10112yes—
180C22×C11C2×#10211yescharacteristic
181C22×C11#41811yescharacteristic
182C22×C11#41912yes—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—82no—
186C4×C11#45911yescharacteristic
187C4×C11#45911yescharacteristic
188C4×C11#46011yescharacteristic
189C4×C11#46011yescharacteristic
190C4×C11#49112yes—
191C4×C11#49711yescharacteristic
192C4×C11#49711yescharacteristic
193Dic11—24no—
194Dic11—24no—
195Dic11—82no—
196C22×Q8—21no—
197C22×Q8—221no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—221no—
201C22×C8—221no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—221no—
207C4⋊Q8—221no—
208C4⋊Q8—221no—
209C4⋊Q8—221no—
210C4⋊Q8—442no—
211C4⋊Q8—442no—
212C4⋊Q8—442no—
213C4⋊Q8—442no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—112no—
216C2×C4⋊C4—224no—
217C2×C4⋊C4—224no—
218C2×C4⋊C4—221no—
219C2×C4⋊C4C4×D1112yes—
220C2×C42—111no—
221C2×C42—112no—
222C2×C42—111no—
223C2×C42—112no—
224C2×C42C22×D1111yescharacteristic
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—112no—
229C4⋊C8—221no—
230C4⋊C8—221no—
231C4⋊C8—221no—
232C4⋊C8C22⋊D1112yes—
233#97—442no—
234C2×C11#154612yes—
235C2×C11#155612yes—
236C2×C11#196011yescharacteristic
237C2×C11#196611yescharacteristic
238C2×C11#198211yescharacteristic
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—441no—
246C2×Q8—441no—
247C2×Q8—441no—
248C2×Q8—441no—
249C2×Q8—441no—
250C2×Q8—441no—
251C22×C4—22no—
252C22×C4—112no—
253C22×C4—112no—
254C22×C4—222no—
255C22×C4C2×C4×D1111yescharacteristic
256C22×C4D4×D1111yescharacteristic
257C22×C4D4×D1111yescharacteristic
258C2×C8—22no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—42no—
262C2×C8—41no—
263C2×C8—222no—
264C2×C8—441no—
265C2×C8—441no—
266C2×C8—442no—
267C2×C8—441no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—222no—
273C4⋊C4—222no—
274C4⋊C4—448no—
275C4⋊C4—448no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C42—112no—
279C42—112no—
280C42—224no—
281C42—221no—
282C42—221no—
283C42—222no—
284C42—222no—
285C42#433911yescharacteristic
286C42D4×D1111yescharacteristic
287C42#434111yescharacteristic
288C42C2×C22⋊D1111yescharacteristic
289C11#970511yescharacteristic, complemented, Sylow
290C23C22⋊C4×D1111yescharacteristic
291Q8—81no—
292Q8—81no—
293Q8—81no—
294Q8—81no—
295Q8—881no—
296Q8—881no—
297Q8—881no—
298Q8—881no—
299C2×C4—22no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—114no—
304C2×C4—114no—
305C2×C4—222no—
306C2×C4—222no—
307C2×C4—222no—
308C2×C4—222no—
309C2×C4—442no—
310C2×C4—442no—
311C2×C4—442no—
312C2×C4(C22⋊D11)⋊C411yescharacteristic
313C2×C4#6693711yescharacteristic
314C2×C4#6693811yescharacteristic
315C2×C4D8×D1111yescharacteristic
316C2×C4#6696411yescharacteristic
317C2×C4SD16×D1111yescharacteristic
318C2×C4#6696711yescharacteristic
319C2×C4#6696812yes—
320C2×C4#6697112yes—
321C2×C4C4×C22⋊D1111yescharacteristic
322C2×C4#6699211yescharacteristic
323C2×C4#6699311yescharacteristic
324C8—42no—
325C8—81no—
326C8—442no—
327C8—881no—
328C22D11×#10112yes—
329C22D11×#10211yescharacteristic
330C22#1062238311yescharacteristic
331C22#1062241512yes—
332C22#1062257011yescharacteristic
333C4—21no—
334C4—21no—
335C4—82no—
336C4—224no—
337C4—224no—
338C4—882no—
339C4#1062237511yescharacteristic
340C4#1062239911yescharacteristic
341C4#1062241012yes—
342C4#1062276311yescharacteristic
343C4#1062277611yescharacteristic
344C4#1062278011yescharacteristic
345C4#1062280311yescharacteristic
346C2#1306728612yes—
347C2#1306733112yes—
348C2#1306943411yescharacteristic
349C2#1306945811yescharacteristic
350C2#1306954111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#332C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenterC2×#332D11
hypocenterC11#9705
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
289. C11#9705semidirect

Maximal subgroups

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

subgroupindex
#130770122
#130687322
#130684712
C2×#106221202
C2×#106221852
C2×#106221242
C2×C11×#3322
#970511