Finite Group Databasebeta

← #14726898

Subgroups — #14726898

Order 2816.

958 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 958 conjugacy classes of subgroups — too many to draw. Only its 187 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#13082426C211yesmaximal, characteristic, complemented
2#13078624C212yesmaximal
3#13067623C214yesmaximal, complemented
4#13067555C214yesmaximal
5#13067179C212yesmaximal, complemented
6#13066940C211yesmaximal, characteristic, complemented
7C11×#2536C211yesmaximal, characteristic
8C2×C11×C22⋊Q8—21no—
9C2×C4×Q8×C11C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11#10623343—21no—
12#10623101—22no—
13#10623100—24no—
14Q8×Dic22—22no—
15#10623031—21no—
16#10623031C2214yes—
17#10623001—22no—
18#10623001C2212yes—
19C11×#398C2212yes—
20C11×#394C2212yes—
21C11×#388—22no—
22C11×#382C2211yescharacteristic
23C11×#380—21no—
24#10622831C2214yes—
25#10622632—22no—
26C4×#4324—24no—
27#10622621—22no—
28#10622584C2214yes—
29#10622538C2212yes—
30#10622166C2214yes—
31#10622090C2218yes—
32C22×Q8×C11D411yescharacteristic
33C22×D4×C11C2311yescharacteristic
34C23×C4×C11—21no—
35C11×C22⋊Q8—44no—
36C4×Q8×C11—22no—
37C4×Q8×C11—22no—
38C4×D4×C11—22no—
39C4×D4×C11—22no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4D411yescharacteristic
43C2×C11×C4⋊C4C2311yescharacteristic
44C2×C11×C4⋊C4C2312yes—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—22no—
47C2×C11×C22⋊C4—22no—
48C2×C42×C11D412yes—
49C2×C42×C11C2311yescharacteristic
50Q8×Dic11—24no—
51Q8×Dic11—24no—
52C2×#4324—24no—
53#66979—24no—
54#66979—22no—
55#66977—22no—
56#66977—24no—
57#66977C2314yes—
58#66943—24no—
59#66943—28no—
60#66941—24no—
61#66941—28no—
62#66923—24no—
63#66923—22no—
64#66922—22no—
65#66922—22no—
66#66922D412yes—
67#66922D412yes—
68C4×Dic22—24no—
69C4×Dic22—24no—
70C4×Dic22—22no—
71C4×Dic22D414yes—
72C11×#95—22no—
73C11×#95—21no—
74C11×#95C2312yes—
75#66896—24no—
76C22⋊(C11⋊C8)C2314yes—
77#66874—24no—
78#66872—24no—
79C4⋊(C11⋊C8)—22no—
80C4×C11⋊C8—22no—
81#18220—111nomaximal, Sylow
82C24×C11—21no—
83C2×Q8×C11—22no—
84C2×Q8×C11—22no—
85C2×Q8×C11SD1614yescomplemented
86C2×D4×C11—22no—
87C2×D4×C11—42no—
88C22×C4×C11—22no—
89C22×C4×C11—21no—
90C22×C4×C11—42no—
91C22×C4×C11—42no—
92C22×C4×C11—42no—
93C22×C4×C11C2×D412yes—
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2411yescharacteristic
98C2×Dic22—24no—
99C2×Dic22—22no—
100C2×Dic22C2×D414yes—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—24no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—42no—
105C11×C4⋊C4—44no—
106C11×C22⋊C4—44no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—44no—
110C42×C11—22no—
111C42×C11—22no—
112C42×C11C2×D412yes—
113C42×C11C2×D412yes—
114C22⋊Dic11—24no—
115#4324—48no—
116C4⋊Dic11—24no—
117C4⋊Dic11—24no—
118C4⋊Dic11—24no—
119C4⋊Dic11—22no—
120C4⋊Dic11—22no—
121C4⋊Dic11—22no—
122C4⋊Dic11C2×D414yes—
123Dic11⋊C4—28no—
124Dic11⋊C4—24no—
125Dic11⋊C4—24no—
126C4×Dic11—28no—
127C4×Dic11—24no—
128C2×C11⋊C8—24no—
129#3502—111no—
130#3101—112no—
131#2536D1111yescharacteristic
132#1611—114no—
133#1599—114no—
134#1518—112no—
135#1461—111no—
136C23×C11—22no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11C22×D411yescharacteristic
144Q8×C11—28no—
145D4×C11—24no—
146D4×C11—42no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—84no—
160C2×C4×C11#12011yescharacteristic
161C2×C4×C11#12011yescharacteristic
162C2×C4×C11#12012yes—
163C2×C4×C11C2×SD1614yes—
164C2×C4×C11C2×SD1612yes—
165C2×C4×C11#13712yes—
166C2×C4×C11C22×D412yes—
167C2×Dic11—24no—
168C2×Dic11—24no—
169Dic22—44no—
170Dic22—44no—
171Dic22—84no—
172C11⋊C8—44no—
173Q82—222no—
174#557—224no—
175#557—222no—
176#544—114no—
177#544—221no—
178#533—112no—
179#533—222no—
180C2×C22⋊Q8—21no—
181#519—221no—
182C2×C4×Q8C2×D1111yescharacteristic
183C2×C4×D4C2×D1111yescharacteristic
184#483—114no—
185#476—222no—
186#461—222no—
187#450—114no—
188C4×SD16—224no—
189#431—112no—
190#398C2×D1112yes—
191#394C2×D1112yes—
192#388—22no—
193#382C2×D1111yescharacteristic
194#380—21no—
195#328—118no—
196#324—114no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—42no—
200C22×C11—42no—
201C22×C11—42no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11C2×#12011yescharacteristic
207C22×C11C22×SD1611yescharacteristic
208C22×C11C2×#13711yescharacteristic
209C4×C11—24no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—22no—
213C4×C11—42no—
214C4×C11—82no—
215C4×C11—81no—
216C4×C11#44814yes—
217Dic11—44no—
218Dic11—44no—
219C22×Q8C22⋊D1111yescharacteristic
220C22×D4C22×D1111yescharacteristic
221C23×C4—21no—
222C2×SD16—224no—
223C4⋊Q8—112no—
224C4⋊Q8—112no—
225C4⋊Q8—222no—
226C4⋊Q8—222no—
227C4⋊Q8—228no—
228C4⋊Q8—224no—
229#125—224no—
230#125—228no—
231#125—224no—
232#125—222no—
233C22⋊Q8—44no—
234C22⋊Q8—114no—
235C22⋊Q8—222no—
236C22⋊Q8—224no—
237C4×Q8—22no—
238C4×Q8—22no—
239C4×Q8—114no—
240C4×Q8—224no—
241C4×Q8—224no—
242C4×Q8—224no—
243C4×Q8—224no—
244C4×Q8—222no—
245C4×D4—22no—
246C4×D4—22no—
247#117—222no—
248#117—224no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4C22⋊D1111yescharacteristic
252C2×C4⋊C4C22×D1111yescharacteristic
253C2×C4⋊C4C22×D1112yes—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—22no—
256C2×C22⋊C4—22no—
257C2×C42C22⋊D1112yes—
258C2×C42C22×D1111yescharacteristic
259#106—224no—
260C4⋊C8—222no—
261#103—224no—
262#102—224no—
263C22⋊C8—114no—
264C4×C8—222no—
265#95—22no—
266#95—21no—
267#95C22×D1112yes—
268C2×C11—21no—
269C2×C11—21no—
270C2×C11—82no—
271C2×C11C2×#44811yescharacteristic
272C2×C11#302011yescharacteristic
273C2×C11#302511yescharacteristic
274C24—21no—
275C2×Q8—22no—
276C2×Q8—22no—
277C2×Q8—114no—
278C2×Q8—224no—
279C2×Q8—222no—
280C2×Q8#432414yescomplemented
281C2×D4—22no—
282C2×D4—42no—
283C22×C4—22no—
284C22×C4—21no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4C2×C22⋊D1112yes—
289C22×C4C2×C22⋊D1112yes—
290C22×C4C2×C22⋊D1111yescharacteristic
291C22×C4C2×C22⋊D1111yescharacteristic
292C22×C4C23×D1111yescharacteristic
293SD16—448no—
294C2×C8—224no—
295C4⋊C4—22no—
296C4⋊C4—24no—
297C4⋊C4—22no—
298C4⋊C4—42no—
299C4⋊C4—44no—
300C4⋊C4—114no—
301C4⋊C4—224no—
302C4⋊C4—224no—
303C4⋊C4—224no—
304C4⋊C4—228no—
305C4⋊C4—222no—
306C4⋊C4—222no—
307C4⋊C4—224no—
308C4⋊C4—222no—
309C4⋊C4—224no—
310C22⋊C4—44no—
311C22⋊C4—44no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—224no—
315C42—22no—
316C42—22no—
317C42—228no—
318C42—224no—
319C42D4×D1112yes—
320C42D4×D1112yes—
321C11#1822011yescharacteristic, complemented, Sylow
322C23—22no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23C22×C22⋊D1111yescharacteristic
330Q8—28no—
331Q8—444no—
332Q8—444no—
333Q8—884no—
334D4—24no—
335D4—42no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—84no—
349C2×C4—224no—
350C2×C4—224no—
351C2×C4C2×#432414yes—
352C2×C4C2×#432412yes—
353C2×C4#6699011yescharacteristic
354C2×C4#6699011yescharacteristic
355C2×C4#6699012yes—
356C2×C4#6700412yes—
357C2×C4C2×D4×D1112yes—
358C8—444no—
359C22—21no—
360C22—21no—
361C22—42no—
362C22—42no—
363C22—42no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22C22×#432411yescharacteristic
369C22C2×#6699011yescharacteristic
370C22C2×#6700411yescharacteristic
371C4—24no—
372C4—21no—
373C4—21no—
374C4—22no—
375C4—42no—
376C4—82no—
377C4—81no—
378C4—444no—
379C4—444no—
380C4#1062265314yes—
381C2—21no—
382C2—21no—
383C2—82no—
384C2C2×#1062265311yescharacteristic
385C2#1307797911yescharacteristic
386C2#1307800711yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2536C2
socleC22×C11C2×#120
prime radicalC22×D4×C11C23
hypercenter#2536D11
hypocenterC11#18220
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2536

Complements

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

NH ≅ G/Ntype
1. #13082426C2semidirect
3. #13067623C2semidirect
5. #13067179C2semidirect
6. #13066940C2semidirect
85. C2×Q8×C11SD16semidirect
280. C2×Q8#4324semidirect
321. C11#18220semidirect

Maximal subgroups

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

subgroupindex
#130824262
#130786242
#130676232
#130675552
#130671792
#130669402
C11×#25362
#1822011