Finite Group Databasebeta

← #14656387

Subgroups — #14656387

Order 2816.

510 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622294C211yesmaximal, characteristic
2C2×#10622634C211yesmaximal, characteristic
3C2×#10622633C211yesmaximal, characteristic
4C2×#10622119C211yesmaximal, characteristic
5C2×#10622120C211yesmaximal, characteristic
6#13066451C211yesmaximal, characteristic
7C11×#1984C211yesmaximal, characteristic
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C4×C8×C11C2211yescharacteristic
13C2×#66899—21no—
14C2×#66899—21no—
15C2×#66880—22no—
16#10622634—22no—
17#10622634—22no—
18#10622633—22no—
19#10622633—22no—
20C2×#66872—21no—
21C2×#66871—21no—
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622294—22no—
25#10622294—22no—
26C11×#336—22no—
27#10622120—22no—
28#10622119—22no—
29C22×Q8×C11D411yescharacteristic
30C22×Dic22—21no—
31C22×Dic22—21no—
32C22×C8×C11—21no—
33C22×C8×C11D412yes—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C42×C11—21no—
41C2×C42×C11C2311yescharacteristic
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C22×C11⋊C8—21no—
47C22×C11⋊C8—21no—
48#66922—21no—
49#66922—21no—
50#66922—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922D412yes—
55#66922D412yes—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C4×C8×C11—21no—
59C4×C8×C11—21no—
60#66899—24no—
61#66899—24no—
62#66880—28no—
63#66872—24no—
64#66871—24no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)D412yes—
68C4⋊(C11⋊C8)D412yes—
69#10277—111nomaximal, Sylow
70C2×Q8×C11—21no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11—21no—
75C2×Q8×C11Q1612yes—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C22×Dic11—41no—
82C22×Dic11—41no—
83C2×Dic22—22no—
84C2×Dic22—22no—
85C2×Dic22—41no—
86C2×Dic22—41no—
87C2×Dic22—42no—
88C2×Dic22—42no—
89C2×Dic22—82no—
90C2×C8×C11—22no—
91C2×C8×C11—22no—
92C2×C8×C11—22no—
93C2×C8×C11—41no—
94C2×C8×C11—42no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C42×C11—41no—
100C42×C11—41no—
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C4⋊Dic11—22no—
106C4⋊Dic11—22no—
107C4⋊Dic11—22no—
108C4⋊Dic11—22no—
109C4⋊Dic11—41no—
110C4⋊Dic11—41no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—41no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8—41no—
119C2×#487—111no—
120C2×#477—111no—
121C2×#475—111no—
122#1984D1111yescharacteristic
123C2×#333—111no—
124C2×#332—111no—
125#1277—111no—
126C23×C11#12111yescharacteristic
127Q8×C11—22no—
128Q8×C11—22no—
129Q8×C11—41no—
130Q8×C11—41no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—42no—
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12711yescharacteristic
143C2×C4×C11C2×Q1611yescharacteristic
144C2×C4×C11#13511yescharacteristic
145C2×C4×C11#13512yes—
146C2×C4×C11#13711yescharacteristic
147C2×C4×C11#13711yescharacteristic
148C2×C4×C11#13712yes—
149C2×Dic11—42no—
150C2×Dic11—42no—
151C2×Dic11—82no—
152C2×Dic11—82no—
153Dic22—44no—
154Dic22—82no—
155Dic22—81no—
156Dic22—81no—
157Dic22—82no—
158C8×C11—42no—
159C8×C11—81no—
160C11⋊C8—42no—
161C11⋊C8—42no—
162C2×C4⋊Q8—111no—
163C2×C4⋊Q8—111no—
164C2×C4×Q8C2×D1111yescharacteristic
165#487—222no—
166#487—222no—
167#477—222no—
168#477—222no—
169#475—222no—
170#475—222no—
171C2×#107—221no—
172C2×#106—221no—
173C2×C4⋊C8—111no—
174C2×C4⋊C8—111no—
175C2×C4⋊C8C2×D1111yescharacteristic
176C2×#103—221no—
177C2×#103—221no—
178C2×#103—222no—
179C2×C4×C8C2×D1111yescharacteristic
180#336—22no—
181#333—222no—
182#332—222no—
183C22×C11#39211yescharacteristic
184C22×C11#46412yes—
185C22×C11#46711yescharacteristic
186C22×C11#47011yescharacteristic
187C22×C11#47112yes—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—42no—
191C4×C11—81no—
192C4×C11#45111yescharacteristic
193C4×C11#45111yescharacteristic
194C4×C11#45211yescharacteristic
195C4×C11#45211yescharacteristic
196C4×C11#45212yes—
197C4×C11#49511yescharacteristic
198C4×C11#49711yescharacteristic
199Dic11—82no—
200Dic11—82no—
201C22×Q8—221no—
202C22×Q8—221no—
203C22×Q8D4411yescharacteristic
204C22×C8—21no—
205C22×C8—221no—
206C22×C8—221no—
207C22×C8C22⋊D1112yes—
208C4⋊Q8—112no—
209C4⋊Q8—112no—
210C4⋊Q8—221no—
211C4⋊Q8—221no—
212C4⋊Q8—221no—
213C4⋊Q8—221no—
214C4⋊Q8—221no—
215C4⋊Q8—221no—
216C4×Q8—21no—
217C4×Q8—21no—
218C4×Q8—21no—
219C4×Q8—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4D4411yescharacteristic
226C2×C42—21no—
227C2×C42C22×D1111yescharacteristic
228#107—224no—
229#106—224no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8—112no—
233C4⋊C8—112no—
234C4⋊C8—221no—
235C4⋊C8—221no—
236#103—228no—
237#103—224no—
238#103—224no—
239C4×C8—21no—
240C4×C8—21no—
241C2×C11#168412yes—
242C2×C11#170412yes—
243C2×C11#200111yescharacteristic
244C2×C11#201511yescharacteristic
245C2×C11#201911yescharacteristic
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—222no—
252C2×Q8—222no—
253C2×Q8—441no—
254C2×Q8—441no—
255C2×Q8—442no—
256C2×Q8—442no—
257C2×Q8—882no—
258C2×Q8Dic4412yes—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—441no—
262C22×C4—441no—
263C22×C4C2×D4411yescharacteristic
264C22×C4#433911yescharacteristic
265C22×C4C2×C22⋊D1111yescharacteristic
266C2×C8—22no—
267C2×C8—22no—
268C2×C8—22no—
269C2×C8—41no—
270C2×C8—42no—
271C2×C8—222no—
272C2×C8—222no—
273C2×C8—441no—
274C2×C8—441no—
275C2×C8—441no—
276C2×C8—441no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—222no—
282C4⋊C4—222no—
283C4⋊C4—222no—
284C4⋊C4—222no—
285C4⋊C4—441no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C4⋊C4—441no—
289C42—41no—
290C42—41no—
291C42D4×D1111yescharacteristic
292C42D4×D1111yescharacteristic
293C42D4×D1111yescharacteristic
294C42D4×D1111yescharacteristic
295C11#1027711yescharacteristic, complemented, Sylow
296C23#6698311yescharacteristic
297Q8—22no—
298Q8—22no—
299Q8—41no—
300Q8—41no—
301Q8—444no—
302Q8—882no—
303Q8—882no—
304Q8—881no—
305Q8—881no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—442no—
313C2×C4—442no—
314C2×C4—882no—
315C2×C4—882no—
316C2×C4#6693511yescharacteristic
317C2×C4#6693511yescharacteristic
318C2×C4#6693711yescharacteristic
319C2×C4#6693711yescharacteristic
320C2×C4#6695711yescharacteristic
321C2×C4C2×Dic4411yescharacteristic
322C2×C4#6696211yescharacteristic
323C2×C4#6696211yescharacteristic
324C2×C4#6699011yescharacteristic
325C2×C4#6699311yescharacteristic
326C2×C4#6699512yes—
327C2×C4#6700312yes—
328C8—42no—
329C8—81no—
330C8—442no—
331C8—442no—
332C22#1062257311yescharacteristic
333C22#1062264112yes—
334C22#1062272911yescharacteristic
335C22#1062275011yescharacteristic
336C22#1062275412yes—
337C4—21no—
338C4—21no—
339C4—42no—
340C4—81no—
341C4—882no—
342C4—882no—
343C4#1062234611yescharacteristic
344C4#1062234611yescharacteristic
345C4#1062235211yescharacteristic
346C4#1062235211yescharacteristic
347C4#1062266012yes—
348C4#1062267211yescharacteristic
349C4#1062269911yescharacteristic
350C2#1306807412yes—
351C2#1306819812yes—
352C2#1306962611yescharacteristic
353C2#1306970911yescharacteristic
354C2#1306973111yescharacteristic
subgroupG/H
centerC23#66983
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1984C2
socle, prime radicalC23×C11#121
hypercenter#1984D11
hypocenterC11#10277
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1984

Complements

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

NH ≅ G/Ntype
295. C11#10277semidirect

Maximal subgroups

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

subgroupindex
C2×#106222942
C2×#106226342
C2×#106226332
C2×#106221192
C2×#106221202
#130664512
C11×#19842
#1027711