Finite Group Databasebeta

← #14655603

Subgroups — #14655603

Order 2816.

514 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079734C211yesmaximal, characteristic
2C2×#10622694C211yesmaximal, characteristic, complemented
3#13069460C211yesmaximal, characteristic, complemented
4#13067301C211yesmaximal, characteristic, complemented
5#13067067C211yesmaximal, characteristic
6#13066454C211yesmaximal, characteristic, complemented
7C11×#3141C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#489—22no—
12C11×#487—21no—
13C11×#486—21no—
14C11×#417—22no—
15C4×C11×M16C2211yescharacteristic
16C2×#66899—22no—
17C2×#66888—22no—
18#10622694—22no—
19#10622694—22no—
20#10622691—21no—
21#10622683—21no—
22#10622646—22no—
23#10622620—22no—
24#10622538C2211yescharacteristic
25#10622537C2211yescharacteristic
26C2×C4×C11⋊C8C2211yescharacteristic
27#10622185—22no—
28D4⋊(C11⋊C8)—22no—
29C2×C11×#41—21no—
30C22×Q8×C11—21no—
31C22×Dic22—21no—
32C2×C11×M16D412yes—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8D412yes—
37C11×C4⋊Q8D411yescharacteristic
38C11×#127D411yescharacteristic
39C11×#124—21no—
40C11×#121—21no—
41C11×#121—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C42×C11C2311yescharacteristic
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11D412yes—
49C2×#4318—21no—
50C22×C11⋊C8—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55C11×#103—24no—
56C11×#102—24no—
57C11×#97—21no—
58C4×C8×C11—21no—
59#66899—28no—
60#66896—24no—
61C22⋊(C11⋊C8)—21no—
62#66888—44no—
63#66871—24no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)D412yes—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8D412yes—
70#10158—111nomaximal, Sylow
71C11×#41—42no—
72C11×#41—42no—
73C2×Q8×C11—22no—
74C2×Q8×C11—21no—
75C2×Q8×C11—44no—
76C2×Q8×C11—41no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C22×Dic11—22no—
87C2×Dic22—41no—
88C2×Dic22—41no—
89C2×Dic22—42no—
90C2×Dic22—42no—
91C11×M16—22no—
92C11×M16—22no—
93C2×C8×C11—22no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C4⋊Dic11—22no—
107C4⋊Dic11—22no—
108C4⋊Dic11—41no—
109C4⋊Dic11—41no—
110#4318—42no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—42no—
114C2×C11⋊C8—41no—
115#3226—111no—
116#3141D1111yescharacteristic
117C2×#487—111no—
118#1966—111no—
119#1549—111no—
120#1492—111no—
121#1278—111no—
122C23×C11—41no—
123C23×C11#12111yescharacteristic
124Q8×C11—44no—
125Q8×C11—42no—
126Q8×C11—82no—
127D4×C11—42no—
128D4×C11—42no—
129D4×C11—42no—
130D4×C11—82no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—41no—
134C2×C4×C11—42no—
135C2×C4×C11—82no—
136C2×C4×C11—81no—
137C2×C4×C11—81no—
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12711yescharacteristic
144C2×C4×C11#13512yes—
145C2×C4×C11AGL(1,ℤ/8)12yes—
146C2×Dic11—42no—
147C2×Dic11—44no—
148Dic22—82no—
149Dic22—81no—
150Dic22—81no—
151C8×C11—42no—
152C11⋊C8—42no—
153C11⋊C8—42no—
154C11⋊C8—81no—
155#532C2×D1111yescharacteristic
156C2×C4⋊Q8—111no—
157C2×C4⋊Q8C2×D1111yescharacteristic
158#500—221no—
159#489—22no—
160#487—21no—
161#487—222no—
162#487—222no—
163#486—21no—
164#486—221no—
165#480—222no—
166#474—222no—
167#431—111no—
168#423—111no—
169#417—22no—
170C2×#103—222no—
171C2×#101—222no—
172C4×M16C2×D1111yescharacteristic
173C2×C4×C8—111no—
174#332—222no—
175D4⋊C8—222no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—81no—
179C22×C11—81no—
180C22×C11—81no—
181C22×C11#39211yescharacteristic
182C22×C11#46312yes—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—82no—
186C4×C11—81no—
187C4×C11#44912yes—
188C4×C11#45412yes—
189C4×C11#47312yes—
190C4×C11#49511yescharacteristic
191C4×C11#49611yescharacteristic
192Dic11—82no—
193C2×#41—21no—
194C22×Q8—21no—
195C22×Q8—221no—
196C2×M16—221no—
197C2×M16C22⋊D1112yes—
198C22×C8—221no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—221no—
203C4⋊Q8—221no—
204C4⋊Q8—221no—
205C4⋊Q8—221no—
206C4⋊Q8C22⋊D1112yes—
207C4⋊Q8C22⋊D1111yescharacteristic
208#127C22⋊D1111yescharacteristic
209#124—21no—
210#121—21no—
211#121—21no—
212C4×D4—21no—
213C4×D4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—112no—
217C2×C4⋊C4—221no—
218C2×C42C22×D1111yescharacteristic
219#107—224no—
220C4⋊C8—112no—
221C4⋊C8—221no—
222C4⋊C8—221no—
223#103—24no—
224#103—228no—
225#102—24no—
226#102—224no—
227#101—444no—
228C22⋊C8—221no—
229#97—21no—
230C4×C8—21no—
231C4×C8—112no—
232C4×C8—221no—
233C4×C8—221no—
234C2×C11—22no—
235C2×C11—161no—
236C2×C11#200311yescharacteristic
237C2×C11#201211yescharacteristic
238C2×C11#202011yescharacteristic
239#41—42no—
240#41—42no—
241C2×Q8—22no—
242C2×Q8—21no—
243C2×Q8—44no—
244C2×Q8—41no—
245C2×Q8—441no—
246C2×Q8—442no—
247C2×Q8—442no—
248C2×Q8—441no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—222no—
256C22×C4D4×D1111yescharacteristic
257C22×C4#434111yescharacteristic
258C22×C4C2×C22⋊D1111yescharacteristic
259M16—22no—
260M16—22no—
261M16—442no—
262C2×C8—22no—
263C2×C8—222no—
264C2×C8—222no—
265C2×C8—442no—
266C2×C8—441no—
267C4⋊C4—21no—
268C4⋊C4—22no—
269C4⋊C4—21no—
270C4⋊C4—22no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—222no—
274C4⋊C4—222no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C42D4×D1111yescharacteristic
280C42D4×D1111yescharacteristic
281C42C2×C22⋊D1111yescharacteristic
282C42C2×C22⋊D1111yescharacteristic
283C11#1015811yescharacteristic, complemented, Sylow
284C23—41no—
285C23#6699111yescharacteristic
286Q8—44no—
287Q8—42no—
288Q8—82no—
289Q8—882no—
290Q8—881no—
291Q8—881no—
292D4—42no—
293D4—42no—
294D4—42no—
295D4—82no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—82no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—442no—
304C2×C4—444no—
305C2×C4#6699011yescharacteristic
306C2×C4#6699011yescharacteristic
307C2×C4#6699211yescharacteristic
308C2×C4#6699211yescharacteristic
309C2×C4#6699311yescharacteristic
310C2×C4#6700212yes—
311C2×C4#6700312yes—
312C2×C4#6700611yescharacteristic
313C8—42no—
314C8—442no—
315C8—442no—
316C8—881no—
317C22—21no—
318C22—21no—
319C22—81no—
320C22—81no—
321C22—81no—
322C22#1062267012yes—
323C22#1062283611yescharacteristic
324C4—21no—
325C4—21no—
326C4—82no—
327C4—81no—
328C4—882no—
329C4#1062267111yescharacteristic
330C4#1062267211yescharacteristic
331C4#1062281412yes—
332C4#1062281712yes—
333C4#1062285112yes—
334C2—22no—
335C2—161no—
336C2#1306963511yescharacteristic
337C2#1306969311yescharacteristic
338C2#1306973411yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3141C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#3141D11
hypocenterC11#10158
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3141

Complements

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

NH ≅ G/Ntype
2. C2×#10622694C2semidirect
3. #13069460C2semidirect
4. #13067301C2semidirect
6. #13066454C2semidirect
283. C11#10158semidirect

Maximal subgroups

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

subgroupindex
#130797342
C2×#106226942
#130694602
#130673012
#130670672
#130664542
C11×#31412
#1015811