Finite Group Databasebeta

← #14666806

Subgroups — #14666806

Order 2816.

398 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 59 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#13076030C211yesmaximal, characteristic
2#13067573C211yesmaximal, characteristic
3#13067573C211yesmaximal, characteristic
4#13066636C211yesmaximal, characteristic
5#13066636C211yesmaximal, characteristic
6#13066564C211yesmaximal, characteristic
7C11×#2062C211yesmaximal, characteristic
8C11×#543C2211yescharacteristic
9C11×#385—21no—
10C11×#385C2211yescharacteristic
11#10622823—21no—
12#10622663—21no—
13#10622663—21no—
14#10622592—21no—
15#10622590—21no—
16#10622564—21no—
17#10622560C2211yescharacteristic
18#10622560C2211yescharacteristic
19#10622273—21no—
20#10622259—21no—
21C11×#342—21no—
22C11×#342C2211yescharacteristic
23#10622176—21no—
24#10622176—21no—
25#10622163C2211yescharacteristic
26#10622163C2211yescharacteristic
27C23×C4×C11D411yescharacteristic
28C22×Dic22D411yescharacteristic
29C22×Dic22D411yescharacteristic
30C11×C22⋊Q8—21no—
31C11×C22⋊Q8—21no—
32C11×C22⋊Q8—41no—
33C11×C22⋊Q8—41no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—41no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4D411yescharacteristic
39C2×C11×C22⋊C4C2311yescharacteristic
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11—21no—
42C2×#4326—41no—
43C2×#4326—41no—
44C2×C4⋊Dic11—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×C4×Dic11—21no—
48C11×#95—21no—
49C11×#95—41no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95D411yescharacteristic
57C11⋊#95D411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60#66874—41no—
61#66874—41no—
62#12253—111nomaximal, Sylow
63C24×C11C2×D411yescharacteristic
64C2×Q8×C11—21no—
65C2×Q8×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11—81no—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C2×Dic22—41no—
80C2×Dic22—41no—
81C2×Dic22—42no—
82C2×Dic22—81no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—81no—
88C11×C4⋊C4—82no—
89C11×C22⋊C4—21no—
90C11×C22⋊C4—22no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4Q1612yescomplemented
96C22⋊Dic11—42no—
97C22⋊Dic11—81no—
98#4326—82no—
99#4326—82no—
100C4⋊Dic11—81no—
101Dic11⋊C4—81no—
102Dic11⋊C4—81no—
103C4×Dic11—42no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106#2763—111no—
107#2062D1111yescharacteristic
108#1602—111no—
109#1602—111no—
110#1351—111no—
111#1351—111no—
112#1326—111no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—41no—
116C23×C11—41no—
117C23×C11#12011yescharacteristic
118C23×C11C2×Q1611yescharacteristic
119C23×C11#13711yescharacteristic
120Q8×C11—81no—
121Q8×C11—81no—
122C2×C4×C11—22no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—42no—
131C2×C4×C11—41no—
132C2×C4×C11—42no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—81no—
137C2×C4×C11—81no—
138C2×C4×C11—81no—
139C2×C4×C11—81no—
140C2×C4×C11—81no—
141C2×Dic11—22no—
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—
153Dic22—42no—
154Dic22—42no—
155Dic22—81no—
156Dic22—81no—
157C11⋊C8—81no—
158C11⋊C8—81no—
159#543C2×D1111yescharacteristic
160#451—221no—
161#451—221no—
162#400—221no—
163#395—221no—
164#393—111no—
165#393—111no—
166#391—221no—
167#388—221no—
168#385—21no—
169#385—221no—
170#385C2×D1111yescharacteristic
171#382—221no—
172#342—21no—
173#342C2×D1111yescharacteristic
174#328—221no—
175#328—221no—
176#323—111no—
177#323—111no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11—81no—
187C22×C11#45111yescharacteristic
188C22×C11#45611yescharacteristic
189C22×C11B(4,𝔽2)11yescharacteristic
190C4×C11—42no—
191C4×C11—41no—
192C4×C11—41no—
193C4×C11—82no—
194C4×C11—81no—
195C4×C11—81no—
196C4×C11—81no—
197Dic11—42no—
198Dic11—81no—
199Dic11—81no—
200Dic11—81no—
201C22×Q8—111no—
202C22×Q8—111no—
203C23×C4C22⋊D1111yescharacteristic
204C2×Q16—441no—
205C2×Q16—441no—
206C22⋊Q8—21no—
207C22⋊Q8—21no—
208C22⋊Q8—41no—
209C22⋊Q8—41no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—41no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—221no—
218C2×C22⋊C4—221no—
219C2×C22⋊C4C22⋊D1111yescharacteristic
220C2×C22⋊C4C22×D1111yescharacteristic
221C2×C42—221no—
222#103—441no—
223#103—441no—
224C22⋊C8—221no—
225C22⋊C8—221no—
226#95—21no—
227#95—41no—
228#95—111no—
229#95—111no—
230#95—221no—
231#95—221no—
232#95—221no—
233#95—221no—
234#95—221no—
235#95—221no—
236C2×C11—21no—
237C2×C11—21no—
238C2×C11—41no—
239C2×C11—41no—
240C2×C11#160511yescharacteristic
241C2×C11#219711yescharacteristic
242C2×C11#219911yescharacteristic
243C24C2×C22⋊D1111yescharacteristic
244C2×Q8—21no—
245C2×Q8—21no—
246C2×Q8—441no—
247C2×Q8—441no—
248C2×Q8—442no—
249C2×Q8—881no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—81no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4D4×D1111yescharacteristic
262C22×C4D4×D1111yescharacteristic
263Q16—882no—
264Q16—882no—
265C2×C8—441no—
266C2×C8—441no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—81no—
272C4⋊C4—82no—
273C4⋊C4—881no—
274C4⋊C4—881no—
275C4⋊C4—881no—
276C22⋊C4—21no—
277C22⋊C4—22no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—442no—
283C22⋊C4—881no—
284C22⋊C4#432612yescomplemented
285C42—442no—
286C11#1225311yescharacteristic, complemented, Sylow
287C23—21no—
288C23—21no—
289C23—41no—
290C23—41no—
291C23#6699011yescharacteristic
292C23C2×#432611yescharacteristic
293C23#6700411yescharacteristic
294Q8—81no—
295Q8—81no—
296Q8—442no—
297Q8—442no—
298Q8—881no—
299Q8—881no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—222no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—441no—
331C8—881no—
332C8—881no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—81no—
342C22#1062264511yescharacteristic
343C22#1062266311yescharacteristic
344C22#1062270811yescharacteristic
345C4—42no—
346C4—41no—
347C4—41no—
348C4—82no—
349C4—81no—
350C4—81no—
351C4—81no—
352C4—442no—
353C4—881no—
354C4—881no—
355C4—881no—
356C2—21no—
357C2—21no—
358C2—41no—
359C2—41no—
360C2#1306758911yescharacteristic
361C2#1307060311yescharacteristic
362C2#1307061511yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2062C2
socleC22×C11B(4,𝔽2)
prime radicalC24×C11C2×D4
hypercenter#2062D11
hypocenterC11#12253
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2062

Complements

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

NH ≅ G/Ntype
95. C11×C22⋊C4Q16semidirect
284. C22⋊C4#4326semidirect
286. C11#12253semidirect

Maximal subgroups

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

subgroupindex
#130760302
#130675732
#130666362
#130665642
C11×#20622
#1225311