Finite Group Databasebeta

← #14657482

Subgroups — #14657482

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#13078415C211yesmaximal, characteristic
2#13068605C211yesmaximal, characteristic
3#13067371C211yesmaximal, characteristic, complemented
4#13067304C211yesmaximal, characteristic, complemented
5#13067070C211yesmaximal, characteristic, complemented
6C2×#10622121C211yesmaximal, characteristic
7C11×#1292C211yesmaximal, characteristic, complemented
8C2×C4×D44C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13#10622744—21no—
14C2×#66887—21no—
15#10622734—21no—
16#10622537C2211yescharacteristic
17C2×C4×C11⋊C8C2211yescharacteristic
18#10622460—22no—
19#10622459—21no—
20#10622455—21no—
21#10622192—21no—
22#10622122—21no—
23#10622122—21no—
24#10622121—21no—
25#10622121—21no—
26#10622120—21no—
27#10622119—21no—
28#10622118—22no—
29C22×D44D411yescharacteristic
30C22×C4×D11—21no—
31C2×C11×M16—21no—
32C2×C11×M16—21no—
33C22×C8×C11—21no—
34C2×C42×C11C2311yescharacteristic
35C2×(C2×D11)⋊C4—21no—
36#66979—21no—
37C2×C4⋊Dic11D411yescharacteristic
38#66977—21no—
39#66977—21no—
40C2×#4318—21no—
41C22×C11⋊C8—21no—
42C4×D44—21no—
43C4×D44—21no—
44C4×D44—21no—
45C4×D44—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×C4⋊C8—21no—
56C11×C4⋊C8D412yes—
57#66887—42no—
58#66885—22no—
59#66885—22no—
60#66882—22no—
61#66881—22no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4×C11⋊C8—21no—
65C4×C11⋊C8D411yescharacteristic
66C4×C11⋊C8D411yescharacteristic
67#10460—111nomaximal, Sylow
68C23×D11—21no—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11#4111yescharacteristic
71C22×C4×C11#4111yescharacteristic
72C22×Dic11—21no—
73C2×D44—21no—
74C2×D44—21no—
75C2×D44—21no—
76C2×D44—21no—
77C2×D44—21no—
78C2×D44SD1612yes—
79C2×C4×D11—41no—
80C2×C4×D11—41no—
81C2×C4×D11—81no—
82C2×C4×D11—81no—
83C2×Dic22—21no—
84C2×Dic22—21no—
85C11×M16—41no—
86C11×M16—41no—
87C11×M16—41no—
88C11×M16—41no—
89C2×C8×C11—22no—
90C2×C8×C11—41no—
91C2×C8×C11—41no—
92C2×C8×C11—81no—
93C42×C11C2×D411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11C2×D411yescharacteristic
96C42×C11#4111yescharacteristic
97C22⋊Dic11—41no—
98(C2×D11)⋊C4—41no—
99(C2×D11)⋊C4—41no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106Dic11⋊C4—41no—
107Dic11⋊C4—41no—
108C4×Dic11—41no—
109#4318—41no—
110#4318—41no—
111C2×C11⋊C8—21no—
112C2×C11⋊C8—21no—
113C2×C11⋊C8—42no—
114C2×C11⋊C8—41no—
115#3077—111no—
116#1800—111no—
117#1566—111no—
118#1550—111no—
119#1493—111no—
120C2×D4⋊C8—111no—
121#1292D1111yescharacteristic, complemented
122C23×C11#12311yescharacteristic
123C22×D11—22no—
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—81no—
127C22×D11—81no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—41no—
131C2×C4×C11#12011yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11#12111yescharacteristic
134C2×C4×C11#12111yescharacteristic
135C2×C4×C11#12311yescharacteristic
136C2×C4×C11#12411yescharacteristic
137C2×C4×C11C2×SD1611yescharacteristic
138C2×C4×C11#13511yescharacteristic
139C2×C4×C11#13711yescharacteristic
140C2×C4×C11#13711yescharacteristic
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—81no—
145D44—22no—
146D44—22no—
147D44—41no—
148D44—41no—
149C4×D11—82no—
150C4×D11—81no—
151C4×D11—81no—
152Dic22—41no—
153Dic22—41no—
154Dic22—81no—
155C8×C11—42no—
156C8×C11—81no—
157C8×C11—81no—
158C11⋊C8—22no—
159C11⋊C8—41no—
160C11⋊C8—81no—
161#533—111no—
162C2×C4×D4—111no—
163#478—222no—
164#476—221no—
165#474—221no—
166#428—221no—
167#423—111no—
168#423C2×D1111yescharacteristic
169#423C2×D1111yescharacteristic
170C2×C4⋊C8C2×D1111yescharacteristic
171#418—221no—
172C2×#100—221no—
173C2×C4×C8—111no—
174#343—221no—
175#334—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#39411yescharacteristic
185C22×C11#48311yescharacteristic
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#44811yescharacteristic
196C4×C11#45211yescharacteristic
197C4×C11#46511yescharacteristic
198C4×C11#47011yescharacteristic
199C4×C11#47111yescharacteristic
200C4×C11#47211yescharacteristic
201Dic11—81no—
202Dic11—81no—
203Dic11—81no—
204C22×D4—111no—
205C23×C4—221no—
206C2×M16—21no—
207C2×M16—21no—
208C2×M16—221no—
209C22×C8—21no—
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—221no—
219C4×D4—221no—
220C4×D4—221no—
221C4×D4—221no—
222#117—221no—
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—21no—
233C4⋊C8—221no—
234C4⋊C8—221no—
235C4⋊C8D4412yes—
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#203511yescharacteristic
245C2×C11#205011yescharacteristic
246C2×C11#205111yescharacteristic
247D11—82no—
248C24—221no—
249C2×Q8—221no—
250C2×Q8—221no—
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#434311yescharacteristic
265M16—41no—
266M16—41no—
267M16—41no—
268M16—41no—
269M16—441no—
270M16—441no—
271C2×C8—22no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—81no—
275C2×C8—221no—
276C2×C8—221no—
277C2×C8—442no—
278C2×C8—441no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4—441no—
286C4⋊C4—441no—
287C22⋊C4—441no—
288C22⋊C4—441no—
289C22⋊C4—441no—
290C42—441no—
291C42C2×D4411yescharacteristic
292C42#433911yescharacteristic
293C42D4×D1111yescharacteristic
294C42D4×D1111yescharacteristic
295C11#1046011yescharacteristic, complemented, Sylow
296C23—222no—
297C23—441no—
298C23—441no—
299C23—881no—
300C23—881no—
301C23#6694711yescharacteristic
302Q8—441no—
303Q8—441no—
304Q8—881no—
305D4—222no—
306D4—222no—
307D4—441no—
308D4—441no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—882no—
316C2×C4—881no—
317C2×C4—881no—
318C2×C4—881no—
319C2×C4#6692811yescharacteristic
320C2×C4#6693511yescharacteristic
321C2×C4#6693711yescharacteristic
322C2×C4#6693711yescharacteristic
323C2×C4#6694711yescharacteristic
324C2×C4#6694811yescharacteristic
325C2×C4#6696511yescharacteristic
326C2×C4SD16×D1111yescharacteristic
327C2×C4#6696811yescharacteristic
328C2×C4#6697111yescharacteristic
329C8—42no—
330C8—81no—
331C8—81no—
332C8—222no—
333C8—441no—
334C8—881no—
335C22—21no—
336C22—21no—
337C22—442no—
338C22—882no—
339C22—882no—
340C22—881no—
341C22—881no—
342C22#1062228511yescharacteristic
343C22#1062247511yescharacteristic
344C22#1062250111yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—881no—
349C4—881no—
350C4—881no—
351C4#1062236211yescharacteristic
352C4#1062236711yescharacteristic
353C4#1062239111yescharacteristic
354C4#1062239611yescharacteristic
355C4#1062241911yescharacteristic
356C4#1062242911yescharacteristic
357C2—21no—
358C2—21no—
359C2—882no—
360C2#1306981511yescharacteristic
361C2#1306990411yescharacteristic
362C2#1306991111yescharacteristic
subgroupG/H
centerC22#10622285
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1292C2
socleC22×C11#394
prime radicalC22×D44D4
hypercenter#1292D11
hypocenterC11#10460
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1292

Complements

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

NH ≅ G/Ntype
3. #13067371C2semidirect
4. #13067304C2semidirect
5. #13067070C2semidirect
7. C11×#1292C2semidirect
121. #1292D11semidirect
295. C11#10460semidirect

Maximal subgroups

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

subgroupindex
#130784152
#130686052
#130673712
#130673042
#130670702
C2×#106221212
C11×#12922
#1046011