Finite Group Databasebeta

← #14655467

Subgroups — #14655467

Order 2816.

468 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 83 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#13079802C211yesmaximal, characteristic
2#13079538C211yesmaximal, characteristic
3C2×#10622315C211yesmaximal, characteristic, complemented
4#13067334C211yesmaximal, characteristic, complemented
5#13066973C211yesmaximal, characteristic, complemented
6#13066515C211yesmaximal, characteristic, complemented
7C11×#1530C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×#66923C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#432C2211yescharacteristic
12C2×C11×#97C2211yescharacteristic
13C2×#66882—21no—
14C2×#66881—21no—
15#10622706—21no—
16#10622693—21no—
17#10622689—21no—
18#10622684—21no—
19#10622653—22no—
20#10622647—21no—
21#10622646—21no—
22#10622632—22no—
23#10622622—22no—
24#10622539C2211yescharacteristic
25#10622538C2211yescharacteristic
26#10622315—22no—
27#10622315—22no—
28C11×#329—22no—
29#10622120—22no—
30#10622107—22no—
31C2×C11×#41—21no—
32C22×Dic22—21no—
33C22×C8×C11—21no—
34C11×C4⋊Q8D411yescharacteristic
35C11×#127D411yescharacteristic
36C11×#124—21no—
37C11×#121—21no—
38C11×#121—21no—
39C4×D4×C11—21no—
40C4×D4×C11—21no—
41C2×C42×C11C2311yescharacteristic
42C2×#4324—24no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11D411yescharacteristic
46C2×C4⋊Dic11D411yescharacteristic
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49#66923—21no—
50#66923—21no—
51#66923—21no—
52#66923—21no—
53#66922—21no—
54#66922—21no—
55#66922—21no—
56#66922D412yes—
57C11×C4⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×#97—21no—
60C11×#97—21no—
61C11×#97D412yes—
62#66896—22no—
63#66896—22no—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)D412yes—
66#66882—24no—
67#66881—24no—
68#66874—24no—
69#66872—22no—
70#66871—22no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)D412yes—
73#66867—21no—
74C4×C11⋊C8—21no—
75#10138—111nomaximal, Sylow
76C11×#41—82no—
77C2×Q8×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—41no—
89C2×Dic22—22no—
90C2×Dic22—41no—
91C2×Dic22—82no—
92C2×C8×C11—24no—
93C2×C8×C11—22no—
94C2×C8×C11—41no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103#4324—84no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107C4⋊Dic11—22no—
108C4⋊Dic11—21no—
109C4⋊Dic11—22no—
110C4⋊Dic11—41no—
111C4⋊Dic11—41no—
112Dic11⋊C4—41no—
113Dic11⋊C4—41no—
114Dic11⋊C4—41no—
115Dic11⋊C4—41no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—22no—
118#3234—111no—
119#3206—111no—
120C2×#501—111no—
121#1556—111no—
122#1530D1111yescharacteristic
123#1470—111no—
124#1302—111no—
125C23×C11—41no—
126C23×C11#12111yescharacteristic
127Q8×C11—81no—
128D4×C11—42no—
129D4×C11—42no—
130D4×C11—81no—
131D4×C11—82no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—82no—
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12711yescharacteristic
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147C2×Dic11—82no—
148C2×Dic11—81no—
149Dic22—44no—
150Dic22—82no—
151C8×C11—24no—
152C8×C11—81no—
153C11⋊C8—42no—
154C11⋊C8—42no—
155#532C2×D1111yescharacteristic
156C2×C4⋊Q8—111no—
157C2×#125—111no—
158#501—222no—
159#501—221no—
160#501—222no—
161#492—221no—
162#490—221no—
163#487—221no—
164#481—221no—
165#480—221no—
166#478—222no—
167#461—222no—
168#448—222no—
169#432—111no—
170#432C2×D1111yescharacteristic
171#431—111no—
172C2×#107—221no—
173C2×#106—221no—
174C2×#97C2×D1111yescharacteristic
175#332—222no—
176#329—22no—
177#324—222no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—81no—
181C22×C11—81no—
182C22×C11—81no—
183C22×C11#39211yescharacteristic
184C22×C11#47112yes—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—81no—
191C4×C11#45612yes—
192Dic11—82no—
193Dic11—81no—
194Dic11—81no—
195C2×#41—21no—
196C22×Q8—221no—
197C2×SD16—224no—
198C22×C8—21no—
199C4⋊Q8—112no—
200C4⋊Q8—221no—
201C4⋊Q8—221no—
202C4⋊Q8—221no—
203C4⋊Q8D4411yescharacteristic
204#127D4411yescharacteristic
205#125—221no—
206#125—221no—
207#125—221no—
208#125—221no—
209#124—21no—
210#121—21no—
211#121—21no—
212C4×D4—21no—
213C4×D4—21no—
214C2×C4⋊C4—111no—
215C2×C4⋊C4—111no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4—221no—
219C2×C4⋊C4—221no—
220C2×C42C22×D1111yescharacteristic
221#107—222no—
222#107—224no—
223#106—222no—
224#106—224no—
225C4⋊C8—21no—
226C4⋊C8—112no—
227C4⋊C8—221no—
228#103—224no—
229#102—222no—
230#102—222no—
231C22⋊C8—21no—
232C22⋊C8—112no—
233C22⋊C8—221no—
234#97—21no—
235#97—21no—
236#97—221no—
237#97C22⋊D1112yes—
238C4×C8—221no—
239C2×C11—22no—
240C2×C11—161no—
241C2×C11#200511yescharacteristic
242C2×C11#200811yescharacteristic
243C2×C11#201911yescharacteristic
244#41—82no—
245C2×Q8—21no—
246C2×Q8—222no—
247C2×Q8—441no—
248C2×Q8—882no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—41no—
253C22×C4—41no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4—441no—
257C22×C4#433911yescharacteristic
258C22×C4D4×D1111yescharacteristic
259C22×C4D4×D1111yescharacteristic
260SD16—884no—
261C2×C8—24no—
262C2×C8—22no—
263C2×C8—41no—
264C2×C8—222no—
265C2×C8—222no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4—222no—
271C4⋊C4—221no—
272C4⋊C4—222no—
273C4⋊C4—221no—
274C4⋊C4—441no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C42C2×D4411yescharacteristic
283C42D4×D1111yescharacteristic
284C42D4×D1111yescharacteristic
285C42C2×C22⋊D1111yescharacteristic
286C11#1013811yescharacteristic, complemented, Sylow
287C23—41no—
288C23#6693711yescharacteristic
289Q8—81no—
290Q8—444no—
291Q8—882no—
292D4—42no—
293D4—42no—
294D4—81no—
295D4—82no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—82no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—442no—
304C2×C4—442no—
305C2×C4—882no—
306C2×C4—881no—
307C2×C4#6693511yescharacteristic
308C2×C4#6693511yescharacteristic
309C2×C4#6693711yescharacteristic
310C2×C4#6698311yescharacteristic
311C2×C4#6699011yescharacteristic
312C2×C4#6699311yescharacteristic
313C8—24no—
314C8—81no—
315C8—442no—
316C8—442no—
317C22—21no—
318C22—21no—
319C22—81no—
320C22—81no—
321C22—81no—
322C22#1062236112yes—
323C22#1062257311yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—81no—
330C4—882no—
331C4—881no—
332C4—881no—
333C4#1062243912yes—
334C2—22no—
335C2—161no—
336C2#1306965111yescharacteristic
337C2#1306967011yescharacteristic
338C2#1306973211yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1530C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#1530D11
hypocenterC11#10138
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1530

Complements

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

NH ≅ G/Ntype
3. C2×#10622315C2semidirect
4. #13067334C2semidirect
5. #13066973C2semidirect
6. #13066515C2semidirect
286. C11#10138semidirect

Maximal subgroups

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

subgroupindex
#130798022
#130795382
C2×#106223152
#130673342
#130669732
#130665152
C11×#15302
#1013811