Finite Group Databasebeta

← #14666813

Subgroups — #14666813

Order 2816.

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

normal subgroups only

This group has 388 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#13075745C211yesmaximal, characteristic
2#13067641C211yesmaximal, characteristic
3#13067573C211yesmaximal, characteristic
4#13066639C211yesmaximal, characteristic
5#13066636C211yesmaximal, characteristic
6#13066564C211yesmaximal, characteristic
7C11×#2062C211yesmaximal, characteristic
8C11×#543C2211yescharacteristic
9C11×#385—21no—
10C11×#385C2211yescharacteristic
11#10622825—21no—
12#10622663—21no—
13#10622657—21no—
14#10622599—21no—
15#10622598—21no—
16#10622564—21no—
17#10622562C2211yescharacteristic
18#10622560C2211yescharacteristic
19#10622269—21no—
20#10622267—21no—
21C11×#342—21no—
22C11×#342C2211yescharacteristic
23#10622176—21no—
24#10622176—21no—
25#10622163C2211yescharacteristic
26#10622163C2211yescharacteristic
27C23×C4×C11D411yescharacteristic
28C22×Dic22D411yescharacteristic
29C11×C22⋊Q8—21no—
30C11×C22⋊Q8—21no—
31C11×C22⋊Q8—41no—
32C11×C22⋊Q8—41no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—41no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4D411yescharacteristic
38C2×C11×C22⋊C4C2311yescharacteristic
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×#4326—41no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11D411yescharacteristic
46C2×Dic11⋊C4—21no—
47C2×C4×Dic11—21no—
48C11×#95—21no—
49C11×#95—41no—
50#66899—41no—
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#66871—41no—
62#12254—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—42no—
71C22×C4×C11—41no—
72C22×C4×C11—41no—
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—81no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—42no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—82no—
87C11×C22⋊C4—21no—
88C11×C22⋊C4—22no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4Q1612yescomplemented
94C22⋊Dic11—81no—
95C22⋊Dic11—81no—
96#4326—82no—
97C4⋊Dic11—41no—
98C4⋊Dic11—42no—
99C4⋊Dic11—81no—
100C4⋊Dic11—81no—
101Dic11⋊C4—81no—
102C4×Dic11—81no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105#2742—111no—
106#2062D1111yescharacteristic
107#1614—111no—
108#1602—111no—
109#1352—111no—
110#1351—111no—
111#1326—111no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—41no—
115C23×C11—41no—
116C23×C11#12011yescharacteristic
117C23×C11C2×Q1611yescharacteristic
118C23×C11#13711yescharacteristic
119Q8×C11—81no—
120Q8×C11—81no—
121C2×C4×C11—22no—
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—41no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—81no—
136C2×C4×C11—81no—
137C2×C4×C11—81no—
138C2×C4×C11—81no—
139C2×C4×C11—81no—
140C2×Dic11—41no—
141C2×Dic11—41no—
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—
152Dic22—42no—
153Dic22—81no—
154C11⋊C8—81no—
155C11⋊C8—81no—
156#543C2×D1111yescharacteristic
157#484—221no—
158#451—221no—
159#400—221no—
160#399—111no—
161#395—221no—
162#393—111no—
163#389—221no—
164#388—221no—
165#387—221no—
166#385—21no—
167#385C2×D1111yescharacteristic
168#380—221no—
169#342—21no—
170#342C2×D1111yescharacteristic
171#328—221no—
172#328—221no—
173#323—111no—
174#323—111no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—81no—
184C22×C11#45111yescharacteristic
185C22×C11#45611yescharacteristic
186C22×C11B(4,𝔽2)11yescharacteristic
187C4×C11—42no—
188C4×C11—42no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11—82no—
192C4×C11—81no—
193C4×C11—81no—
194Dic11—81no—
195Dic11—81no—
196Dic11—81no—
197Dic11—81no—
198C22×Q8—111no—
199C23×C4C22⋊D1111yescharacteristic
200C2×Q16—441no—
201C22⋊Q8—21no—
202C22⋊Q8—21no—
203C22⋊Q8—41no—
204C22⋊Q8—41no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—41no—
207C2×C4⋊C4—111no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4—221no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—221no—
215C2×C22⋊C4—221no—
216C2×C22⋊C4C22⋊D1111yescharacteristic
217C2×C22⋊C4C22×D1111yescharacteristic
218C2×C42—221no—
219#107—441no—
220#103—441no—
221#103—441no—
222C22⋊C8—221no—
223C22⋊C8—221no—
224#95—21no—
225#95—41no—
226#95—111no—
227#95—111no—
228#95—221no—
229#95—221no—
230#95—221no—
231#95—221no—
232#95—221no—
233C2×C11—21no—
234C2×C11—21no—
235C2×C11—41no—
236C2×C11—41no—
237C2×C11#160511yescharacteristic
238C2×C11#219711yescharacteristic
239C2×C11#220011yescharacteristic
240C24C2×C22⋊D1111yescharacteristic
241C2×Q8—21no—
242C2×Q8—21no—
243C2×Q8—441no—
244C2×Q8—881no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—42no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4D4×D1111yescharacteristic
257C22×C4D4×D1111yescharacteristic
258Q16—882no—
259C2×C8—441no—
260C2×C8—441no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—42no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—82no—
267C4⋊C4—441no—
268C4⋊C4—442no—
269C4⋊C4—881no—
270C4⋊C4—881no—
271C4⋊C4—881no—
272C22⋊C4—21no—
273C22⋊C4—22no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—881no—
279C22⋊C4—881no—
280C22⋊C4#432612yescomplemented
281C42—881no—
282C11#1225411yescharacteristic, complemented, Sylow
283C23—21no—
284C23—21no—
285C23—41no—
286C23—41no—
287C23#6699011yescharacteristic
288C23C2×#432611yescharacteristic
289C23#6700411yescharacteristic
290Q8—81no—
291Q8—81no—
292Q8—442no—
293Q8—881no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C8—881no—
326C8—881no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—81no—
336C22#1062264511yescharacteristic
337C22#1062266311yescharacteristic
338C22#1062270811yescharacteristic
339C4—42no—
340C4—41no—
341C4—42no—
342C4—41no—
343C4—82no—
344C4—81no—
345C4—81no—
346C4—881no—
347C4—881no—
348C4—881no—
349C4—881no—
350C2—21no—
351C2—21no—
352C2—41no—
353C2—41no—
354C2#1306758911yescharacteristic
355C2#1307060411yescharacteristic
356C2#1307062011yescharacteristic
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#12254
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
93. C11×C22⋊C4Q16semidirect
280. C22⋊C4#4326semidirect
282. C11#12254semidirect

Maximal subgroups

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

subgroupindex
#130757452
#130676412
#130675732
#130666392
#130666362
#130665642
C11×#20622
#1225411