Finite Group Databasebeta

← #14853526

Subgroups — #14853526

Order 2816.

710 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076979C211yesmaximal, characteristic
2#13070173C212yesmaximal
3#13069859C212yesmaximal
4#13069309C214yesmaximal
5#13068621C212yesmaximal
6#13068621C212yesmaximal
7#13068469C211yesmaximal, characteristic
8C4×C11×C4⋊Q8C211yesmaximal, characteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×Q8×C11C2212yes—
11C2×#66923—21no—
12C11×#391C2212yes—
13C11×#389—21no—
14C11×#389—21no—
15C11×#384C2211yescharacteristic
16C4×C11×C4⋊C4—21no—
17C4×C11×C4⋊C4—21no—
18C43×C11C2211yescharacteristic
19C2×#66899C2214yes—
20C2×#66899C2214yes—
21#10622549—21no—
22#10622548C2211yescharacteristic
23#10622548C2211yescharacteristic
24#10622541—21no—
25#10622541—21no—
26#10622541C2212yes—
27#10622541C2212yes—
28C2×C4⋊(C11⋊C8)C2212yes—
29C2×#66867C2212yes—
30#10622167C2214yes—
31#10622167C2214yes—
32#10622162C2212yes—
33C22×Q8×C11C2312yes—
34C11×C4⋊Q8—24no—
35C4×Q8×C11—24no—
36C4×Q8×C11—24no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4C2312yes—
43C2×C42×C11—22no—
44C2×C42×C11D411yescharacteristic
45C2×C42×C11D411yescharacteristic
46C2×C42×C11D411yescharacteristic
47C2×C42×C11D411yescharacteristic
48C2×C42×C11C2311yescharacteristic
49C2×C42×C11C2311yescharacteristic
50C2×C42×C11C2311yescharacteristic
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11C2312yes—
56C2×C4⋊Dic11C2312yes—
57C2×Dic11⋊C4—22no—
58C2×Dic11⋊C4—22no—
59C22×C11⋊C8C2314yes—
60#66923—44no—
61C11×#95—22no—
62C11×#95—22no—
63#66899—28no—
64#66899—44no—
65C11⋊#95—22no—
66C11⋊#95—22no—
67C4⋊(C11⋊C8)—24no—
68#66867—42no—
69#29132—111nomaximal, Sylow
70C2×Q8×C11—22no—
71C2×Q8×C11—22no—
72C2×Q8×C11—22no—
73C2×Q8×C11—22no—
74C2×Q8×C11—22no—
75C2×Q8×C11#4114yes—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2411yescharacteristic
85C22×Dic11—22no—
86C22×Dic11—22no—
87C11×C4⋊C4—24no—
88C11×C4⋊C4—24no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—44no—
92C11×C4⋊C4—42no—
93C11×C4⋊C4—42no—
94C42×C11—22no—
95C42×C11—22no—
96C42×C11—22no—
97C42×C11—22no—
98C42×C11—22no—
99C42×C11—21no—
100C42×C11—21no—
101C42×C11—44no—
102C42×C11#4114yes—
103C4⋊Dic11—24no—
104C4⋊Dic11—22no—
105C4⋊Dic11—22no—
106C4⋊Dic11—42no—
107C4⋊Dic11—42no—
108C4⋊Dic11—42no—
109C4⋊Dic11—42no—
110Dic11⋊C4—44no—
111Dic11⋊C4—44no—
112C2×C11⋊C8—24no—
113C2×C11⋊C8—24no—
114C2×C11⋊C8—24no—
115#2859—111no—
116C4×C4⋊Q8D1111yescharacteristic
117#2099—112no—
118#2043—112no—
119#1935—114no—
120#1803—112no—
121#1803—112no—
122#1767—111no—
123C23×C11C22×D411yescharacteristic
124Q8×C11—24no—
125Q8×C11—24no—
126Q8×C11—42no—
127Q8×C11—42no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—24no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11#12412yes—
147C2×C4×C11#12412yes—
148C2×C4×C11AGL(1,ℤ/8)12yes—
149C2×C4×C11#13712yes—
150C2×C4×C11#13712yes—
151C2×C4×C11#13712yes—
152C2×C4×C11C2×#4112yes—
153C2×C4×C11C2×#4112yes—
154C2×C4×C11H(5,𝔽2)11yescharacteristic
155C2×C4×C112−1+411yescharacteristic
156C2×Dic11—42no—
157C2×Dic11—42no—
158C2×Dic11—42no—
159C2×Dic11—42no—
160C2×Dic11—42no—
161C2×Dic11—42no—
162C11⋊C8—44no—
163C2×C4⋊Q8C2×D1111yescharacteristic
164C2×#125—221no—
165C2×C4×Q8C2×D1112yes—
166C2×C4⋊C8—112no—
167C2×#103—114no—
168C2×#103—114no—
169C2×#97—112no—
170#391C2×D1112yes—
171#389—21no—
172#389—21no—
173#389—112no—
174#389—112no—
175#389—221no—
176#389—221no—
177#384—111no—
178#384—111no—
179#384C2×D1111yescharacteristic
180#382—221no—
181C4×C4⋊C4—21no—
182C4×C4⋊C4—21no—
183C43C2×D1111yescharacteristic
184#340—114no—
185#340—114no—
186#336—112no—
187C22×C11#52511yescharacteristic
188C22×C11C2×#12411yescharacteristic
189C22×C11#53711yescharacteristic
190C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
191C22×C11C2×#13711yescharacteristic
192C22×C11C2×#13711yescharacteristic
193C22×C11C2×#13711yescharacteristic
194C4×C11—22no—
195C4×C11—22no—
196C4×C11—22no—
197C4×C11—44no—
198C4×C11—41no—
199C4×C11—41no—
200C4×C11—82no—
201C4×C11#49114yes—
202C4×C11#55212yes—
203C4×C11#55312yes—
204Dic11—82no—
205Dic11—82no—
206C22×Q8C22×D1112yes—
207C22×C8—114no—
208C4⋊Q8—24no—
209#125—444no—
210C4×Q8—24no—
211C4×Q8—24no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—112no—
218C2×C4⋊C4—112no—
219C2×C4⋊C4—221no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—222no—
222C2×C4⋊C4—222no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4C22×D1112yes—
226C2×C42—22no—
227C2×C42C22⋊D1111yescharacteristic
228C2×C42C22⋊D1111yescharacteristic
229C2×C42C22⋊D1111yescharacteristic
230C2×C42C22⋊D1111yescharacteristic
231C2×C42C22×D1111yescharacteristic
232C2×C42C22×D1111yescharacteristic
233C2×C42C22×D1111yescharacteristic
234C4⋊C8—224no—
235#103—228no—
236#103—444no—
237#97—442no—
238#95—22no—
239#95—22no—
240#95—222no—
241#95—222no—
242C2×C11#256211yescharacteristic
243C2×C11#311211yescharacteristic
244C2×C11#311311yescharacteristic
245C2×C11C2×#49111yescharacteristic
246C2×C11#314111yescharacteristic
247C2×C11#325411yescharacteristic
248C2×C11#325511yescharacteristic
249C2×Q8—22no—
250C2×Q8—22no—
251C2×Q8—22no—
252C2×Q8—22no—
253C2×Q8—22no—
254C2×Q8#433914yes—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—222no—
258C22×C4—222no—
259C22×C4C2×C22⋊D1111yescharacteristic
260C22×C4C2×C22⋊D1111yescharacteristic
261C22×C4C2×C22⋊D1111yescharacteristic
262C22×C4C2×C22⋊D1111yescharacteristic
263C22×C4C2×C22⋊D1111yescharacteristic
264C22×C4C2×C22⋊D1111yescharacteristic
265C22×C4C23×D1111yescharacteristic
266C2×C8—224no—
267C2×C8—224no—
268C2×C8—224no—
269C4⋊C4—24no—
270C4⋊C4—24no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—44no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C4⋊C4—224no—
277C4⋊C4—222no—
278C4⋊C4—222no—
279C4⋊C4—444no—
280C4⋊C4—442no—
281C4⋊C4—442no—
282C4⋊C4—442no—
283C4⋊C4—442no—
284C4⋊C4—444no—
285C42—22no—
286C42—22no—
287C42—22no—
288C42—22no—
289C42—22no—
290C42—21no—
291C42—21no—
292C42—44no—
293C42#434114yes—
294C11#2913211yescharacteristic, complemented, Sylow
295C23C22×C22⋊D1111yescharacteristic
296Q8—24no—
297Q8—24no—
298Q8—42no—
299Q8—42no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—442no—
319C2×C4—442no—
320C2×C4—442no—
321C2×C4—442no—
322C2×C4—442no—
323C2×C4—442no—
324C2×C4#6698912yes—
325C2×C4#6698912yes—
326C2×C4#6699512yes—
327C2×C4#6699512yes—
328C2×C4#6700212yes—
329C2×C4#6700412yes—
330C2×C4C2×#433912yes—
331C2×C4C2×#434112yes—
332C2×C4#6704211yescharacteristic
333C2×C4#6704311yescharacteristic
334C8—444no—
335C22#1062332211yescharacteristic
336C22C2×#6698911yescharacteristic
337C22C2×#6699511yescharacteristic
338C22C2×#6699511yescharacteristic
339C22C2×#6700211yescharacteristic
340C22C2×#6700411yescharacteristic
341C22#1062336411yescharacteristic
342C4—22no—
343C4—22no—
344C4—22no—
345C4—44no—
346C4—41no—
347C4—41no—
348C4—82no—
349C4—882no—
350C4—882no—
351C4#1062269514yes—
352C4#1062307212yes—
353C4#1062309612yes—
354C2#1307378211yescharacteristic
355C2#1307873811yescharacteristic
356C2#1307874611yescharacteristic
357C2C2×#1062269511yescharacteristic
358C2#1307900911yescharacteristic
359C2#1307999911yescharacteristic
360C2#1308000711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×C4⋊Q8C2
socle, prime radicalC23×C11C22×D4
hypercenterC4×C4⋊Q8D11
hypocenterC11#29132
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
294. C11#29132semidirect

Maximal subgroups

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

subgroupindex
#130769792
#130701732
#130698592
#130693092
#130686212
#130684692
C4×C11×C4⋊Q82
#2913211