Finite Group Databasebeta

← #14657486

Subgroups — #14657486

Order 2816.

406 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 97 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#13078413C211yesmaximal, characteristic
2#13067374C211yesmaximal, characteristic, complemented
3#13067307C211yesmaximal, characteristic, complemented
4#13067070C211yesmaximal, characteristic, complemented
5C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic
6#13066490C211yesmaximal, characteristic, complemented
7C11×#1800C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×C11×#100—21no—
13#10622828—21no—
14#10622622—22no—
15#10622621—21no—
16#10622620—21no—
17#10622577—21no—
18#10622537C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21C11×#343—21no—
22D4⋊(C11⋊C8)—21no—
23D4⋊(C11⋊C8)—21no—
24#10622124—21no—
25#10622122—21no—
26#10622122—21no—
27#10622119—21no—
28#10622117—22no—
29C22×D4×C11D411yescharacteristic
30C23×C4×C11—21no—
31C2×C11×M16—21no—
32C2×C11×M16—21no—
33C4×D4×C11—21no—
34C4×D4×C11—21no—
35C4×D4×C11—21no—
36C4×D4×C11—21no—
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C11×C22⋊C4—21no—
39C2×C42×C11C2311yescharacteristic
40#66979—21no—
41#66977—21no—
42#66977—21no—
43C2×#4318—21no—
44C22×C11⋊C8—21no—
45C22×C11⋊C8—21no—
46#66923—21no—
47#66922D411yescharacteristic
48#66922D411yescharacteristic
49C4×Dic22—21no—
50C4×Dic22—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×#100—42no—
56#66896—22no—
57#66896—22no—
58#66872—22no—
59#66871—22no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)D412yes—
64C4×C11⋊C8—21no—
65C4×C11⋊C8D411yescharacteristic
66C4×C11⋊C8D411yescharacteristic
67#10461—111nomaximal, Sylow
68C24×C11—21no—
69C2×D4×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11Q1612yes—
75C22×C4×C11—21no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11—81no—
79C22×C4×C11—81no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11#4111yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C2×Dic22—21no—
84C2×Dic22—21no—
85C11×M16—41no—
86C11×M16—41no—
87C11×M16—41no—
88C11×M16—41no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C42×C11C2×D411yescharacteristic
96C42×C11C2×D411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11#4111yescharacteristic
99C22⋊Dic11—41no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104Dic11⋊C4—41no—
105Dic11⋊C4—41no—
106C4×Dic11—41no—
107#4318—41no—
108#4318—41no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—21no—
111C2×C11⋊C8—21no—
112C2×C11⋊C8—42no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—81no—
115#3077—111no—
116#1800D1111yescharacteristic
117#1567—111no—
118#1550—111no—
119#1493—111no—
120C2×D4⋊C8—111no—
121#1292—111no—
122C23×C11—22no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—81no—
126C23×C11—81no—
127C23×C11#12311yescharacteristic
128D4×C11—22no—
129D4×C11—22no—
130D4×C11—41no—
131D4×C11—41no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—82no—
137C2×C4×C11—81no—
138C2×C4×C11—81no—
139C2×C4×C11—81no—
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12311yescharacteristic
145C2×C4×C11#12411yescharacteristic
146C2×C4×C11C2×Q1611yescharacteristic
147C2×C4×C11#13511yescharacteristic
148C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C11#13711yescharacteristic
150C2×Dic11—41no—
151C2×Dic11—41no—
152Dic22—41no—
153Dic22—41no—
154Dic22—81no—
155C8×C11—81no—
156C8×C11—81no—
157C11⋊C8—22no—
158C11⋊C8—41no—
159C11⋊C8—42no—
160C11⋊C8—81no—
161#533—111no—
162C2×C4×D4C2×D1111yescharacteristic
163#478—222no—
164#476—221no—
165#474—221no—
166#428—221no—
167#423—111no—
168#423C2×D1111yescharacteristic
169#423C2×D1111yescharacteristic
170C2×C4⋊C8—111no—
171#418—221no—
172C2×#100—21no—
173C2×C4×C8—111no—
174#343—21no—
175#335—222no—
176#333—221no—
177#332—221no—
178Q8⋊C8—221no—
179Q8⋊C8—221no—
180D4⋊C8—221no—
181D4⋊C8—221no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—42no—
185C22×C11—82no—
186C22×C11—82no—
187C22×C11—81no—
188C22×C11—81no—
189C22×C11#39411yescharacteristic
190C22×C11#48411yescharacteristic
191C22×C11#48511yescharacteristic
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—81no—
196C4×C11#44911yescharacteristic
197C4×C11#45111yescharacteristic
198C4×C11#46711yescharacteristic
199C4×C11#46811yescharacteristic
200C4×C11#47111yescharacteristic
201C4×C11#47211yescharacteristic
202Dic11—81no—
203Dic11—81no—
204C22×D4C22⋊D1111yescharacteristic
205C23×C4—21no—
206C2×M16—21no—
207C2×M16—21no—
208C2×M16—221no—
209C22×C8—221no—
210C22×C8—221no—
211C4⋊Q8—111no—
212C4⋊Q8—111no—
213#125—221no—
214C22⋊Q8—221no—
215C22⋊Q8—221no—
216C4×Q8—221no—
217C4×Q8—221no—
218C4×D4—21no—
219C4×D4—21no—
220C4×D4—21no—
221C4×D4—21no—
222#117—221no—
223C2×C4⋊C4C22⋊D1111yescharacteristic
224C2×C22⋊C4—21no—
225C2×C42C22×D1111yescharacteristic
226#107—222no—
227#106—222no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8—112no—
233C4⋊C8—221no—
234C4⋊C8—221no—
235C4⋊C8—221no—
236#102—222no—
237#102—222no—
238#100—42no—
239C4×C8—111no—
240C4×C8—111no—
241C4×C8—221no—
242C2×C11—21no—
243C2×C11—21no—
244C2×C11—82no—
245C2×C11#203611yescharacteristic
246C2×C11#205011yescharacteristic
247C2×C11#205111yescharacteristic
248C24—21no—
249C2×Q8—221no—
250C2×Q8—221no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4#432612yes—
257C22×C4—21no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—81no—
261C22×C4—81no—
262C22×C4#433911yescharacteristic
263C22×C4#433911yescharacteristic
264C22×C4C2×C22⋊D1111yescharacteristic
265M16—41no—
266M16—41no—
267M16—41no—
268M16—41no—
269M16—441no—
270M16—441no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—221no—
274C2×C8—221no—
275C2×C8—222no—
276C2×C8—442no—
277C2×C8—441no—
278C2×C8—881no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4—441no—
286C4⋊C4—441no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—441no—
290C42—441no—
291C42D4×D1111yescharacteristic
292C42D4×D1111yescharacteristic
293C42D4×D1111yescharacteristic
294C42#434111yescharacteristic
295C11#1046111yescharacteristic, complemented, Sylow
296C23—22no—
297C23—41no—
298C23—41no—
299C23—81no—
300C23—81no—
301C23#6698211yescharacteristic
302Q8—441no—
303Q8—441no—
304Q8—881no—
305D4—22no—
306D4—22no—
307D4—41no—
308D4—41no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—82no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4#6693611yescharacteristic
320C2×C4#6693711yescharacteristic
321C2×C4#6693711yescharacteristic
322C2×C4#6693811yescharacteristic
323C2×C4#6698511yescharacteristic
324C2×C4#6699011yescharacteristic
325C2×C4#6699211yescharacteristic
326C2×C4C2×#432611yescharacteristic
327C2×C4#6700311yescharacteristic
328C2×C4#6700411yescharacteristic
329C8—81no—
330C8—81no—
331C8—222no—
332C8—441no—
333C8—442no—
334C8—881no—
335C22—21no—
336C22—21no—
337C22—42no—
338C22—82no—
339C22—82no—
340C22—81no—
341C22—81no—
342C22#1062257211yescharacteristic
343C22#1062258311yescharacteristic
344C22#1062260911yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—81no—
349C4—881no—
350C4—881no—
351C4#1062236111yescharacteristic
352C4#1062236211yescharacteristic
353C4#1062265011yescharacteristic
354C4#1062265511yescharacteristic
355C4#1062266311yescharacteristic
356C4#1062266411yescharacteristic
357C2—21no—
358C2—21no—
359C2—82no—
360C2#1306981911yescharacteristic
361C2#1306990111yescharacteristic
362C2#1306990811yescharacteristic
subgroupG/H
centerC22#10622572
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1800C2
socleC22×C11#394
prime radicalC22×D4×C11D4
hypercenter#1800D11
hypocenterC11#10461
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
2. #13067374C2semidirect
3. #13067307C2semidirect
4. #13067070C2semidirect
6. #13066490C2semidirect
295. C11#10461semidirect

Maximal subgroups

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

subgroupindex
#130784132
#130673742
#130673072
#130670702
C2×D4⋊(C11⋊C8)2
#130664902
C11×#18002
#1046111