Finite Group Databasebeta

← #14655719

Subgroups — #14655719

Order 2816.

578 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 107 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×#10622295C211yesmaximal, characteristic, complemented
3#13079076C211yesmaximal, characteristic
4#13069459C211yesmaximal, characteristic, complemented
5#13067289C211yesmaximal, characteristic, complemented
6#13066453C211yesmaximal, characteristic, complemented
7C11×#1492C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×#67004—22no—
10C2×#66922C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14C2×#66888—22no—
15C2×#66882—22no—
16#10622705—21no—
17#10622691—21no—
18#10622689—21no—
19#10622683—21no—
20#10622673—22no—
21#10622646—22no—
22#10622620—22no—
23#10622538C2211yescharacteristic
24C4×#4318C2211yescharacteristic
25#10622295—22no—
26#10622295—22no—
27C11×D4⋊C8—22no—
28#10622120—22no—
29C2×C11×#41—21no—
30C22×Dic22—21no—
31C22×Dic22—21no—
32C2×C11×M16—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
42#67004—44no—
43#67004—44no—
44C2×#4326—24no—
45C2×#4324—24no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11D412yes—
50C2×#4318D412yes—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55#66922—21no—
56#66922—21no—
57#66922—21no—
58#66922D412yes—
59C11×C4⋊C8—21no—
60C11×C4⋊C8—21no—
61C4×C8×C11—21no—
62C4×C8×C11D412yes—
63#66896—24no—
64C22⋊(C11⋊C8)—21no—
65#66888—44no—
66#66882—28no—
67#66871—24no—
68C4⋊(C11⋊C8)D412yes—
69#66867—21no—
70C4×C11⋊C8—21no—
71C4×C11⋊C8—21no—
72#10174—111nomaximal, Sylow
73C11×#41—42no—
74C11×#41—42no—
75C2×Q8×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C22×Dic11—22no—
85C22×Dic11—41no—
86C2×Dic22—22no—
87C2×Dic22—41no—
88C2×Dic22—41no—
89C2×Dic22—41no—
90C2×Dic22—42no—
91C2×Dic22—42no—
92C2×Dic22—42no—
93C2×Dic22—42no—
94C11×M16—42no—
95C2×C8×C11—24no—
96C2×C8×C11—22no—
97C2×C8×C11—41no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106#4326—48no—
107#4324—48no—
108C4⋊Dic11—22no—
109C4⋊Dic11—22no—
110C4⋊Dic11—22no—
111C4⋊Dic11—22no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115C4⋊Dic11—41no—
116#4318—22no—
117#4318D814yes—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—22no—
120#3226—111no—
121C2×#500—111no—
122#3152—111no—
123#1966—111no—
124#1546—111no—
125#1492D1111yescharacteristic
126#1278—111no—
127C23×C11—41no—
128C23×C11#12111yescharacteristic
129Q8×C11—42no—
130D4×C11—42no—
131D4×C11—42no—
132D4×C11—42no—
133D4×C11—82no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—41no—
137C2×C4×C11—81no—
138C2×C4×C11—81no—
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12711yescharacteristic
145C2×C4×C11C2×D812yes—
146C2×C4×C11AGL(1,ℤ/8)12yes—
147C2×Dic11—42no—
148C2×Dic11—42no—
149C2×Dic11—44no—
150C2×Dic11—82no—
151Dic22—44no—
152Dic22—82no—
153Dic22—81no—
154Dic22—81no—
155Dic22—81no—
156Dic22—81no—
157C8×C11—24no—
158C8×C11—81no—
159C11⋊C8—24no—
160C11⋊C8—42no—
161C2×#137—222no—
162#532C2×D1111yescharacteristic
163C2×C4⋊Q8—111no—
164C2×C4⋊Q8—111no—
165#500—222no—
166#500—221no—
167#500—222no—
168#497—222no—
169#494—221no—
170#492—221no—
171#486—221no—
172#480—222no—
173#474—222no—
174#431—111no—
175C2×#107—222no—
176#423C2×D1111yescharacteristic
177C2×#101—222no—
178C4×M16—111no—
179C2×C4×C8C2×D1111yescharacteristic
180#332—222no—
181D4⋊C8—22no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11#39211yescharacteristic
188C22×C11#45912yes—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—81no—
192C4×C11#44712yes—
193C4×C11#45612yes—
194C4×C11#47312yes—
195C4×C11#49311yescharacteristic
196C4×C11#49611yescharacteristic
197Dic11—82no—
198Dic11—82no—
199C2×#41—21no—
200C22×Q8—221no—
201C22×Q8—221no—
202#137—444no—
203#137—444no—
204C2×Q16—224no—
205C2×SD16—224no—
206C2×M16—21no—
207C2×M16—112no—
208C22×C8—21no—
209C4⋊Q8—112no—
210C4⋊Q8—221no—
211C4⋊Q8—221no—
212C4⋊Q8—221no—
213C4⋊Q8—221no—
214C4⋊Q8—221no—
215C4⋊Q8—221no—
216C4⋊Q8—221no—
217C4⋊Q8D4411yescharacteristic
218#127D4411yescharacteristic
219#124—21no—
220#121—21no—
221#121—21no—
222C4×D4—21no—
223C4×D4—21no—
224C2×C4⋊C4—112no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4—221no—
227C2×C4⋊C4—221no—
228C2×C42C22×D1111yescharacteristic
229#107—224no—
230#107—228no—
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8—112no—
234#102—224no—
235#101—444no—
236C22⋊C8—221no—
237#97—221no—
238C4×C8—21no—
239C4×C8—221no—
240C4×C8—221no—
241C4×C8C22⋊D1112yes—
242C2×C11—22no—
243C2×C11—161no—
244C2×C11#200511yescharacteristic
245C2×C11#201111yescharacteristic
246C2×C11#202011yescharacteristic
247#41—42no—
248#41—42no—
249C2×Q8—21no—
250C2×Q8—222no—
251C2×Q8—441no—
252C2×Q8—442no—
253C2×Q8—442no—
254C2×Q8—441no—
255C2×Q8—441no—
256C2×Q8—442no—
257C2×Q8—442no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—41no—
262C22×C4—41no—
263C22×C4—222no—
264C22×C4—441no—
265C22×C4#433911yescharacteristic
266C22×C4D4×D1111yescharacteristic
267C22×C4D4×D1111yescharacteristic
268Q16—448no—
269SD16—448no—
270M16—42no—
271M16—114no—
272M16—222no—
273C2×C8—24no—
274C2×C8—22no—
275C2×C8—41no—
276C2×C8—222no—
277C2×C8—222no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—222no—
281C4⋊C4—222no—
282C4⋊C4—222no—
283C4⋊C4—222no—
284C4⋊C4—441no—
285C4⋊C4—441no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C42C2×D4411yescharacteristic
291C42D4×D1111yescharacteristic
292C42D4×D1111yescharacteristic
293C42C2×C22⋊D1111yescharacteristic
294C11#1017411yescharacteristic, complemented, Sylow
295C23—41no—
296C23#6693711yescharacteristic
297Q8—42no—
298Q8—444no—
299Q8—881no—
300Q8—881no—
301Q8—881no—
302Q8—881no—
303Q8—882no—
304D4—42no—
305D4—42no—
306D4—42no—
307D4—82no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—442no—
314C2×C4—442no—
315C2×C4—444no—
316C2×C4—882no—
317C2×C4#6693511yescharacteristic
318C2×C4#6693511yescharacteristic
319C2×C4#6693711yescharacteristic
320C2×C4D8×D1112yes—
321C2×C4#6696712yes—
322C2×C4#6698311yescharacteristic
323C2×C4#6699011yescharacteristic
324C2×C4#6699311yescharacteristic
325C8—24no—
326C8—81no—
327C8—224no—
328C8—442no—
329C22—21no—
330C22—21no—
331C22—81no—
332C22—81no—
333C22—81no—
334C22#1062239912yes—
335C22#1062257311yescharacteristic
336C4—21no—
337C4—21no—
338C4—81no—
339C4—882no—
340C4—882no—
341C4#1062238612yes—
342C4#1062243912yes—
343C4#1062275612yes—
344C4#1062276411yescharacteristic
345C4#1062278911yescharacteristic
346C2—22no—
347C2—161no—
348C2#1306965111yescharacteristic
349C2#1306968811yescharacteristic
350C2#1306973711yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1492C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#1492D11
hypocenterC11#10174
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1492

Complements

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

NH ≅ G/Ntype
2. C2×#10622295C2semidirect
4. #13069459C2semidirect
5. #13067289C2semidirect
6. #13066453C2semidirect
294. C11#10174semidirect

Maximal subgroups

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

subgroupindex
#130797342
C2×#106222952
#130790762
#130694592
#130672892
#130664532
C11×#14922
#1017411