Finite Group Databasebeta

← #14657484

Subgroups — #14657484

Order 2816.

406 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 95 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#13078409C211yesmaximal, characteristic
2#13068605C211yesmaximal, characteristic
3#13067374C211yesmaximal, characteristic, complemented
4#13067071C211yesmaximal, characteristic, complemented
5C2×#10622121C211yesmaximal, characteristic
6#13066491C211yesmaximal, characteristic, complemented
7C11×#1550C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C4×D44C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×#66887—21no—
13#10622700—21no—
14#10622697—21no—
15#10622679—22no—
16#10622614—21no—
17#10622608—21no—
18#10622537C2211yescharacteristic
19#10622537C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21C11×#333—21no—
22C11×#332—21no—
23#10622192—21no—
24Q8⋊(C11⋊C8)—21no—
25Q8⋊(C11⋊C8)—21no—
26#10622121—21no—
27#10622121—21no—
28#10622117—22no—
29C22×D44D411yescharacteristic
30C22×C4×D11—21no—
31C2×C11×M16—21no—
32C22×C8×C11—21no—
33C11×C4⋊Q8D411yescharacteristic
34C11×C4⋊Q8D411yescharacteristic
35C11×#125—21no—
36C11×C22⋊Q8—21no—
37C11×C22⋊Q8—21no—
38C4×Q8×C11—21no—
39C4×Q8×C11—21no—
40C11×#117—21no—
41C2×C42×C11C2311yescharacteristic
42C2×(C2×D11)⋊C4—21no—
43C2×C4⋊Dic11D411yescharacteristic
44C2×#4318—21no—
45C2×#4318—21no—
46C22×C11⋊C8—21no—
47C4×D44—21no—
48C4×D44—21no—
49C4×D44—21no—
50C4×D44—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55#66887—42no—
56#66873—22no—
57#66873—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
68C23×D11—21no—
69C2×Q8×C11—21no—
70C2×Q8×C11—21no—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11#4111yescharacteristic
73C22×C4×C11#4111yescharacteristic
74C22×Dic11—21no—
75C2×D44—21no—
76C2×D44—21no—
77C2×D44—21no—
78C2×D44—21no—
79C2×D44—21no—
80C2×D44Q1612yes—
81C2×C4×D11—41no—
82C2×C4×D11—41no—
83C2×C4×D11—81no—
84C2×C4×D11—81no—
85C11×M16—41no—
86C11×M16—41no—
87C2×C8×C11—41no—
88C2×C8×C11—41no—
89C2×C8×C11—81no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C22⋊C4—41no—
97C42×C11—41no—
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11#4111yescharacteristic
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—41no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106#4318—41no—
107#4318—41no—
108#4318—41no—
109#4318—41no—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—21no—
112C2×C11⋊C8—21no—
113C2×C11⋊C8—42no—
114C2×C11⋊C8—41no—
115#3077—111no—
116#1800—111no—
117#1567—111no—
118#1550D1111yescharacteristic, complemented
119#1493—111no—
120C2×D4⋊C8—111no—
121#1292—111no—
122C23×C11#12311yescharacteristic
123C22×D11—22no—
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—81no—
127C22×D11—81no—
128Q8×C11—41no—
129Q8×C11—41no—
130Q8×C11—81no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11#12011yescharacteristic
137C2×C4×C11#12111yescharacteristic
138C2×C4×C11#12111yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12311yescharacteristic
141C2×C4×C11#12411yescharacteristic
142C2×C4×C11C2×Q1611yescharacteristic
143C2×C4×C11#13511yescharacteristic
144C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C11#13711yescharacteristic
146C2×Dic11—41no—
147C2×Dic11—81no—
148D44—22no—
149D44—22no—
150D44—41no—
151D44—41no—
152C4×D11—82no—
153C4×D11—81no—
154C4×D11—81no—
155C8×C11—81no—
156C8×C11—81no—
157C11⋊C8—22no—
158C11⋊C8—41no—
159C11⋊C8—42no—
160C11⋊C8—81no—
161#533C2×D1111yescharacteristic
162C2×C4×D4—111no—
163#478—222no—
164#476—221no—
165#474—221no—
166#428—221no—
167#423—111no—
168#423—111no—
169#423C2×D1111yescharacteristic
170C2×C4⋊C8C2×D1111yescharacteristic
171#418—221no—
172C2×#100—221no—
173C2×C4×C8—111no—
174#343—221no—
175#335—222no—
176#333—21no—
177#332—21no—
178Q8⋊C8—221no—
179Q8⋊C8—221no—
180D4⋊C8—221no—
181D4⋊C8—221no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11#39411yescharacteristic
185C22×C11#48411yescharacteristic
186C22×C11#48511yescharacteristic
187C2×D11—42no—
188C2×D11—82no—
189C2×D11—81no—
190C2×D11—81no—
191C2×D11—82no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11#44911yescharacteristic
198C4×C11#45111yescharacteristic
199C4×C11#46711yescharacteristic
200C4×C11#46811yescharacteristic
201C4×C11#47111yescharacteristic
202C4×C11#47211yescharacteristic
203Dic11—81no—
204C22×D4—111no—
205C23×C4—221no—
206C2×M16—21no—
207C2×M16—221no—
208C2×M16—221no—
209C22×C8—21no—
210C22×C8—221no—
211C4⋊Q8C22⋊D1111yescharacteristic
212C4⋊Q8C22⋊D1111yescharacteristic
213#125—21no—
214C22⋊Q8—21no—
215C22⋊Q8—21no—
216C4×Q8—21no—
217C4×Q8—21no—
218C4×D4—221no—
219C4×D4—221no—
220C4×D4—221no—
221C4×D4—221no—
222#117—21no—
223C2×C4⋊C4—111no—
224C2×C22⋊C4—221no—
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—442no—
239C4×C8—111no—
240C4×C8—111no—
241C4×C8—221no—
242C2×C11—21no—
243C2×C11—21no—
244C2×C11#203611yescharacteristic
245C2×C11#205011yescharacteristic
246C2×C11#205111yescharacteristic
247D11—82no—
248C24—221no—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×D4—112no—
252C2×D4—221no—
253C2×D4—221no—
254C2×D4—221no—
255C2×D4—221no—
256C2×D4—221no—
257C22×C4—221no—
258C22×C4—441no—
259C22×C4—441no—
260C22×C4—881no—
261C22×C4—881no—
262C22×C4#433911yescharacteristic
263C22×C4D4×D1111yescharacteristic
264C22×C4#434111yescharacteristic
265M16—41no—
266M16—41no—
267M16—441no—
268M16—441no—
269M16—441no—
270M16—441no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—81no—
274C2×C8—221no—
275C2×C8—221no—
276C2×C8—222no—
277C2×C8—442no—
278C2×C8—441no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—221no—
286C4⋊C4—221no—
287C22⋊C4—41no—
288C22⋊C4—441no—
289C22⋊C4—441no—
290C42—41no—
291C42#433911yescharacteristic
292C42D4×D1111yescharacteristic
293C42D4×D1111yescharacteristic
294C42C2×C22⋊D1111yescharacteristic
295C11#1046111yescharacteristic, complemented, Sylow
296C23—222no—
297C23—441no—
298C23—441no—
299C23—881no—
300C23—881no—
301C23#6693611yescharacteristic
302Q8—41no—
303Q8—41no—
304Q8—81no—
305D4—222no—
306D4—222no—
307D4—441no—
308D4—441no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—441no—
315C2×C4—882no—
316C2×C4—881no—
317C2×C4—881no—
318C2×C4—881no—
319C2×C4#6693711yescharacteristic
320C2×C4#6693711yescharacteristic
321C2×C4#6693811yescharacteristic
322C2×C4#6696711yescharacteristic
323C2×C4#6696911yescharacteristic
324C2×C4Q16×D1111yescharacteristic
325C2×C4#6697111yescharacteristic
326C2×C4#6698211yescharacteristic
327C2×C4#6699011yescharacteristic
328C2×C4#6699211yescharacteristic
329C8—81no—
330C8—81no—
331C8—222no—
332C8—441no—
333C8—442no—
334C8—881no—
335C22—21no—
336C22—21no—
337C22—442no—
338C22—882no—
339C22—882no—
340C22—881no—
341C22—881no—
342C22#1062242211yescharacteristic
343C22#1062242811yescharacteristic
344C22#1062257211yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—81no—
349C4—81no—
350C4—881no—
351C4#1062242511yescharacteristic
352C4#1062242611yescharacteristic
353C4#1062278511yescharacteristic
354C4#1062279911yescharacteristic
355C4#1062281211yescharacteristic
356C4#1062281611yescharacteristic
357C2—21no—
358C2—21no—
359C2—882no—
360C2#1306981711yescharacteristic
361C2#1306990111yescharacteristic
362C2#1306990611yescharacteristic
subgroupG/H
centerC22#10622572
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1550C2
socleC22×C11#394
prime radicalC22×D44D4
hypercenter#1550D11
hypocenterC11#10461
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1550

Complements

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

NH ≅ G/Ntype
3. #13067374C2semidirect
4. #13067071C2semidirect
6. #13066491C2semidirect
7. C11×#1550C2semidirect
118. #1550D11semidirect
295. C11#10461semidirect

Maximal subgroups

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

subgroupindex
#130784092
#130686052
#130673742
#130670712
C2×#106221212
#130664912
C11×#15502
#1046111