Finite Group Databasebeta

← #14664497

Subgroups — #14664497

Order 2816.

382 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 69 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#13074436C211yesmaximal, characteristic
2#13068692C211yesmaximal, characteristic
3#13066947C211yesmaximal, characteristic
4#13066638C211yesmaximal, characteristic
5#13066637C211yesmaximal, characteristic
6#13066636C211yesmaximal, characteristic
7C11×#1351C211yesmaximal, characteristic
8C2×#66997C411yescharacteristic, complemented
9C2×#66930C2211yescharacteristic
10C11×#393C2211yescharacteristic
11#10622842C411yescharacteristic, complemented
12#10622562—21no—
13#10622560C2211yescharacteristic
14#10622556—21no—
15#10622555—21no—
16#10622332—21no—
17#10622271—21no—
18#10622269C411yescharacteristic, complemented
19#10622263C411yescharacteristic, complemented
20#10622260—21no—
21C11×#342C2211yescharacteristic
22C11×#323C2211yescharacteristic
23#10622165—21no—
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622107—21no—
27C22×Q8×C11C2×C411yescharacteristic
28C23×Dic11D411yescharacteristic
29C22×Dic22C2×C411yescharacteristic
30C2×C11×C22⋊C4—21no—
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4C2311yescharacteristic
33C2×C22⋊Dic11—21no—
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11D411yescharacteristic
36#66997—41no—
37#66997—41no—
38C2×C4⋊Dic11—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4C2×C411yescharacteristic
44C2×Dic11⋊C4D411yescharacteristic
45C2×C4×Dic11C2×C411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47#66930—41no—
48#66930—41no—
49C11×C22⋊C8—21no—
50C11×#95—21no—
51C11×#95C2×C411yescharacteristic
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—41no—
57C11⋊#95—41no—
58C11⋊#95C2×C411yescharacteristic
59C22⋊(C11⋊C8)—21no—
60#66879—41no—
61Dic11⋊C8—41no—
62#11812—111nomaximal, Sylow
63C24×C11C2×D411yescharacteristic
64C2×Q8×C11—41no—
65C2×Q8×C11—81no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—41no—
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—41no—
78C22×Dic11—41no—
79C22×Dic11C22⋊C411yescharacteristic
80C22×Dic11C22⋊C411yescharacteristic
81C22×Dic11C22⋊C411yescharacteristic
82C22×Dic11C22⋊C411yescharacteristic
83C2×Dic22—41no—
84C2×Dic22—81no—
85C2×C8×C11—41no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—81no—
90C22⋊Dic11—41no—
91C22⋊Dic11—41no—
92C22⋊Dic11—41no—
93C22⋊Dic11—81no—
94C4⋊Dic11—81no—
95Dic11⋊C4—41no—
96Dic11⋊C4—41no—
97Dic11⋊C4—42no—
98Dic11⋊C4—42no—
99Dic11⋊C4—41no—
100Dic11⋊C4—41no—
101Dic11⋊C4—81no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C2×C11⋊C8—41no—
107#2628—111no—
108#1820—111no—
109#1464—111no—
110#1351—111no—
111#1351—111no—
112#1351—111no—
113#1351D1111yescharacteristic
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11C2×C22⋊C411yescharacteristic
119C23×C11#13711yescharacteristic
120C23×C11#13711yescharacteristic
121Q8×C11—82no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—81no—
133C2×C4×C11—81no—
134C2×C4×C11—81no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—81no—
155C2×Dic11—81no—
156C2×Dic11—81no—
157C2×Dic11#9911yescharacteristic
158C2×Dic11#9911yescharacteristic
159Dic22—82no—
160C8×C11—81no—
161C11⋊C8—81no—
162C2×C4⋊Q8—111no—
163C2×#117—111no—
164#432—221no—
165#400—221no—
166#399—221no—
167#395—111no—
168#395—111no—
169#393—111no—
170#393C2×D1111yescharacteristic
171#389—221no—
172#382—111no—
173#381—221no—
174#380—221no—
175#342—111no—
176#342—221no—
177#342C2×D1111yescharacteristic
178#324—221no—
179#323—111no—
180#323C2×D1111yescharacteristic
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—41no—
186C22×C11—41no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—81no—
190C22×C11C2×#9911yescharacteristic
191C22×C11#41911yescharacteristic
192C22×C11#42111yescharacteristic
193C4×C11—41no—
194C4×C11—41no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11—161no—
198Dic11—21no—
199Dic11—21no—
200Dic11—41no—
201Dic11—41no—
202Dic11—41no—
203Dic11—81no—
204Dic11—81no—
205Dic11—161no—
206C22×Q8—111no—
207C22×Q8C4×D1111yescharacteristic
208C23×C4—111no—
209C4⋊Q8—441no—
210C4⋊Q8—441no—
211#117—441no—
212#117—441no—
213C2×C4⋊C4—111no—
214C2×C4⋊C4—111no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4—221no—
219C2×C4⋊C4—221no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—111no—
223C2×C22⋊C4—221no—
224C2×C22⋊C4—221no—
225C2×C22⋊C4C22×D1111yescharacteristic
226C2×C42—111no—
227C2×C42—111no—
228C4⋊C8—441no—
229C22⋊C8—21no—
230C22⋊C8—221no—
231#97—441no—
232#95—21no—
233#95—111no—
234#95—221no—
235#95—221no—
236#95—221no—
237#95—221no—
238#95—441no—
239#95—441no—
240#95C4×D1111yescharacteristic
241C2×C11—21no—
242C2×C11—21no—
243C2×C11—41no—
244C2×C11—41no—
245C2×C11#151111yescharacteristic
246C2×C11#212211yescharacteristic
247C2×C11#212911yescharacteristic
248C24D4×D1111yescharacteristic
249C2×Q8—41no—
250C2×Q8—81no—
251C2×Q8—441no—
252C2×Q8—881no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—41no—
256C22×C4—111no—
257C22×C4—111no—
258C22×C4—111no—
259C22×C4—111no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4—221no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—441no—
267C22×C4—441no—
268C22×C4C2×C4×D1111yescharacteristic
269C22×C4D4×D1111yescharacteristic
270C2×C8—41no—
271C2×C8—441no—
272C4⋊C4—441no—
273C4⋊C4—441no—
274C4⋊C4—441no—
275C4⋊C4—441no—
276C4⋊C4—442no—
277C4⋊C4—442no—
278C4⋊C4—881no—
279C4⋊C4—881no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—81no—
284C22⋊C4—441no—
285C22⋊C4—441no—
286C22⋊C4—441no—
287C22⋊C4—881no—
288C42—221no—
289C42—221no—
290C42—221no—
291C42—221no—
292C11#1181211yescharacteristic, complemented, Sylow
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23C22⋊C4×D1111yescharacteristic
298C23#6696811yescharacteristic
299C23#6697111yescharacteristic
300Q8—82no—
301Q8—882no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—111no—
316C2×C4—111no—
317C2×C4—221no—
318C2×C4—221no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—881no—
337C2×C4—881no—
338C2×C4—881no—
339C8—81no—
340C8—881no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22D11×#9911yescharacteristic
351C22#1062241511yescharacteristic
352C22#1062243411yescharacteristic
353C4—41no—
354C4—41no—
355C4—81no—
356C4—81no—
357C4—161no—
358C4—221no—
359C4—221no—
360C4—441no—
361C4—441no—
362C4—441no—
363C4—881no—
364C4—881no—
365C4—1761no—
366C2—21no—
367C2—21no—
368C2—41no—
369C2—41no—
370C2#1306714711yescharacteristic
371C2#1307026411yescharacteristic
372C2#1307028911yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1351C2
socleC22×C11C2×#99
prime radicalC24×C11C2×D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1351D11
hypocenterC11#11812
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1351

Complements

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

NH ≅ G/Ntype
8. C2×#66997C4semidirect
11. #10622842C4semidirect
18. #10622269C4semidirect
19. #10622263C4semidirect
292. C11#11812semidirect

Maximal subgroups

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

subgroupindex
#130744362
#130686922
#130669472
#130666382
#130666372
#130666362
C11×#13512
#1181211