Finite Group Databasebeta

← #14782675

Subgroups — #14782675

Order 2816.

906 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
1C2×#10622719C211yesmaximal, characteristic, complemented
2#13077135C212yesmaximal
3#13070061C214yesmaximal, complemented
4#13070056C214yesmaximal, complemented
5#13068354C212yesmaximal, complemented
6C2×#10622190C211yesmaximal, characteristic, complemented
7C2×C11×#408C211yesmaximal, characteristic
8C22×C11×#41C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C23×C8×C11C2211yescharacteristic
11C2×#66979C2212yes—
12C22×#4318C2212yes—
13C11×#408—22no—
14C11×#408C2212yes—
15C11×#408C2212yes—
16C2×C11×C22⋊C8—22no—
17#10622846—24no—
18#10622845C2218yes—
19#10622838—22no—
20#10622828—22no—
21#10622719—22no—
22#10622719—22no—
23C2×#66882C2212yescomplemented
24C2×#66881C2212yescomplemented
25#10622192C2218yescomplemented
26#10622190C2212yescomplemented
27#10622190C2212yescomplemented
28C2×C11×#41—21no—
29C2×C11×#41—21no—
30C2×C11×#41—24no—
31C2×C11×#41—24no—
32C2×C11×#41D412yes—
33C2×C11×#41C2312yes—
34C22×Q8×C11D411yescharacteristic
35C22×D4×C11—21no—
36C22×D4×C11D411yescharacteristic
37C23×C4×C11—21no—
38C23×C4×C11C2311yescharacteristic
39C2×C11×M16—21no—
40C2×C11×M16—24no—
41C2×C11×M16C2312yes—
42C22×C8×C11—24no—
43C22×C8×C11—21no—
44C22×C8×C11D412yes—
45C22×C8×C11D412yes—
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C2×C22⋊Dic11—22no—
49#66979—22no—
50#66979—22no—
51#66979—22no—
52#66979—22no—
53C2×C4⋊Dic11C2314yes—
54C2×C4×Dic11—22no—
55C2×#4318—22no—
56C2×#4318—24no—
57C2×#4318—24no—
58C2×#4318C2314yes—
59C22×C11⋊C8—22no—
60C11×C22⋊C8—24no—
61C11×C22⋊C8—24no—
62#66899—28no—
63#66896—28no—
64#66882—24no—
65#66881—24no—
66#23646—111nomaximal, Sylow
67C24×C11—21no—
68C24×C11#4111yescharacteristic
69C11×#41—28no—
70C11×#41—24no—
71C11×#41—24no—
72C11×#41—42no—
73C11×#41—42no—
74C11×#41—44no—
75C2×Q8×C11—21no—
76C2×Q8×C11—24no—
77C2×Q8×C11C2×D412yes—
78C2×D4×C11—22no—
79C2×D4×C11—22no—
80C2×D4×C11—21no—
81C2×D4×C11—24no—
82C2×D4×C11—44no—
83C2×D4×C11C2×D412yes—
84C22×C4×C11—21no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—42no—
88C22×C4×C11—42no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C22×C4×C11#4114yes—
95C22×C4×C11#4114yes—
96C22×C4×C11C2411yescharacteristic
97C22×Dic11—24no—
98C11×M16—24no—
99C11×M16—42no—
100C2×C8×C11—24no—
101C2×C8×C11—24no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11—42no—
106C2×C8×C11C2×D412yes—
107C2×C8×C11C2×D412yes—
108C22⋊Dic11—42no—
109C22⋊Dic11—42no—
110C4⋊Dic11—24no—
111C4⋊Dic11—24no—
112C4×Dic11—42no—
113C4×Dic11—42no—
114#4318—24no—
115#4318—24no—
116#4318—44no—
117C2×C11⋊C8—24no—
118C2×C11⋊C8—44no—
119C2×#427—111no—
120#2896—112no—
121C2×#408D1111yescharacteristic
122#2079—114no—
123#2078—114no—
124#1742—112no—
125C2×#341—111no—
126C23×C11—22no—
127C23×C11—42no—
128C23×C11—44no—
129C23×C11—42no—
130C23×C11#12111yescharacteristic
131C23×C11#12111yescharacteristic
132C23×C11#12614yes—
133C23×C11C2×#4111yescharacteristic
134Q8×C11—24no—
135Q8×C11—42no—
136D4×C11—24no—
137D4×C11—44no—
138D4×C11—44no—
139D4×C11—42no—
140C2×C4×C11—22no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—44no—
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12314yes—
148C2×C4×C11#12314yes—
149C2×C4×C11#12312yes—
150C2×C4×C11#12312yes—
151C2×C4×C11#12412yes—
152C2×C4×C11#12412yes—
153C2×C4×C11#12614yes—
154C2×C4×C11C22×D411yescharacteristic
155C2×C4×C11C22×D411yescharacteristic
156C2×C4×C11C2×#4112yes—
157C2×C4×C11C2×#4112yes—
158C2×Dic11—44no—
159C2×Dic11—84no—
160C8×C11—22no—
161C8×C11—22no—
162C8×C11—42no—
163C11⋊C8—44no—
164C22×#41C2×D1111yescharacteristic
165C22×M16—112no—
166C22×M16C2×D1111yescharacteristic
167C23×C8C2×D1111yescharacteristic
168C2×#117—112no—
169#427—222no—
170#427—222no—
171C2×#107—112no—
172C2×#106—112no—
173#419—222no—
174#418—222no—
175#417—118no—
176#416—224no—
177#408—22no—
178#408C2×D1112yes—
179#408C2×D1112yes—
180C2×C22⋊C8—22no—
181#343—118no—
182#341—112no—
183#341—112no—
184C22×C11—22no—
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—44no—
188C22×C11—42no—
189C22×C11—44no—
190C22×C11—84no—
191C22×C11#39712yes—
192C22×C11#39712yes—
193C22×C11C2×#12111yescharacteristic
194C22×C11C2×#12612yes—
195C4×C11—42no—
196C4×C11#39712yes—
197C4×C11#39712yes—
198C4×C11C2×#12312yes—
199C4×C11C2×#12311yescharacteristic
200C4×C11C2×#12411yescharacteristic
201Dic11—84no—
202C2×#41—21no—
203C2×#41—21no—
204C2×#41—24no—
205C2×#41—24no—
206C2×#41D4412yes—
207C2×#41C22×D1112yes—
208C22×Q8D4411yescharacteristic
209C22×D4—21no—
210C22×D4D4411yescharacteristic
211C23×C4—21no—
212C23×C4C22×D1111yescharacteristic
213C2×M16—21no—
214C2×M16—24no—
215C2×M16—114no—
216C2×M16—222no—
217C2×M16—224no—
218C2×M16—224no—
219C2×M16C22×D1112yes—
220C22×C8—24no—
221C22×C8—21no—
222C22×C8—222no—
223C22×C8C22⋊D1112yes—
224C22×C8C22⋊D1112yes—
225C22×C8C22×D1111yescharacteristic
226C22×C8C22×D1111yescharacteristic
227#117—222no—
228#117—222no—
229#117—222no—
230#117—222no—
231C2×C4⋊C4—114no—
232C2×C22⋊C4—222no—
233C2×C42—222no—
234#107—224no—
235#106—224no—
236#103—228no—
237#102—228no—
238C22⋊C8—24no—
239C22⋊C8—24no—
240C2×C11—22no—
241C2×C11—22no—
242C2×C11—22no—
243C2×C11—82no—
244C2×C11C2×#39711yescharacteristic
245C2×C11#306712yes—
246C24—21no—
247C24#433911yescharacteristic
248#41—28no—
249#41—24no—
250#41—24no—
251#41—44no—
252#41—42no—
253#41—42no—
254C2×Q8—21no—
255C2×Q8—24no—
256C2×Q8C2×D4412yes—
257C2×D4—22no—
258C2×D4—22no—
259C2×D4—24no—
260C2×D4—21no—
261C2×D4—44no—
262C2×D4C2×D4412yes—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4—224no—
269C22×C4C2×D4411yescharacteristic
270C22×C4C2×D4411yescharacteristic
271C22×C4#433911yescharacteristic
272C22×C4#434114yes—
273C22×C4#434114yes—
274C22×C4C2×C22⋊D1111yescharacteristic
275C22×C4C2×C22⋊D1111yescharacteristic
276C22×C4C23×D1111yescharacteristic
277M16—24no—
278M16—42no—
279M16—224no—
280M16—224no—
281M16—444no—
282C2×C8—24no—
283C2×C8—24no—
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—42no—
288C2×C8—224no—
289C2×C8—444no—
290C2×C8C2×C22⋊D1112yes—
291C2×C8C2×C22⋊D1112yes—
292C4⋊C4—224no—
293C4⋊C4—224no—
294C22⋊C4—442no—
295C22⋊C4—442no—
296C42—442no—
297C42—442no—
298C11#2364611yescharacteristic, complemented, Sylow
299C23—22no—
300C23—42no—
301C23—44no—
302C23—42no—
303C23#6693214yes—
304C23#6698311yescharacteristic
305C23#6698311yescharacteristic
306C23C2×#433911yescharacteristic
307Q8—24no—
308Q8—42no—
309D4—24no—
310D4—44no—
311D4—44no—
312D4—42no—
313C2×C4—22no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—44no—
318C2×C4—444no—
319C2×C4—884no—
320C2×C4#6693214yes—
321C2×C4#6693914yes—
322C2×C4#6693914yes—
323C2×C4#6698311yescharacteristic
324C2×C4#6698311yescharacteristic
325C2×C4#6698812yes—
326C2×C4#6698812yes—
327C2×C4#6698912yes—
328C2×C4#6698912yes—
329C2×C4C22×D4411yescharacteristic
330C2×C4C2×#434112yes—
331C2×C4C2×#434112yes—
332C2×C4C22×C22⋊D1111yescharacteristic
333C8—22no—
334C8—22no—
335C8—42no—
336C8—444no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—44no—
341C22—44no—
342C22—42no—
343C22—84no—
344C22#1062256612yes—
345C22#1062256612yes—
346C22C2×#6693212yes—
347C22C2×#6698311yescharacteristic
348C4—42no—
349C4—884no—
350C4#1062256612yes—
351C4#1062256612yes—
352C4C2×#6693912yes—
353C4C2×#6698811yescharacteristic
354C4C2×#6698911yescharacteristic
355C2—22no—
356C2—22no—
357C2—22no—
358C2—82no—
359C2C2×#1062256611yescharacteristic
360C2#1307833612yes—
subgroupG/H
centerC2×C4#66983
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#408C2
socleC22×C11C2×#121
prime radicalC22×C11×#41C22
hypercenterC2×#408D11
hypocenterC11#23646
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
1. C2×#10622719C2semidirect
3. #13070061C2semidirect
4. #13070056C2semidirect
5. #13068354C2semidirect
6. C2×#10622190C2semidirect
23. C2×#66882C22semidirect
24. C2×#66881C22semidirect
25. #10622192C22semidirect
26. #10622190C22semidirect
27. #10622190C22semidirect
298. C11#23646semidirect

Maximal subgroups

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

subgroupindex
C2×#106227192
#130771352
#130700612
#130700562
#130683542
C2×#106221902
C2×C11×#4082
#2364611