Finite Group Databasebeta

← #14910701

Subgroups — #14910701

Order 2816.

546 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081047C211yesmaximal, characteristic, complemented
2#13080338C211yesmaximal, characteristic
3#13070844C211yesmaximal, characteristic, complemented
4#13070825C212yesmaximal, complemented
5#13070754C211yesmaximal, characteristic, complemented
6#13070707C212yesmaximal, complemented
7#13070667C211yesmaximal, characteristic, complemented
8#13070558C212yesmaximal, complemented
9C4×#66864C211yesmaximal, characteristic, complemented
10#13070324C212yesmaximal, complemented
11D4×C11×C16C211yesmaximal, characteristic, complemented
12C2×#66957C2212yes—
13#10623082—21no—
14#10623073—21no—
15C22×C11×C16C2212yes—
16C8×D4×C11C2211yescharacteristic
17#10622729C2212yes—
18#10622729C2212yes—
19#10622719C2212yes—
20C2×Dic88C2212yes—
21C2×#66864C2211yescharacteristic
22#10622464—21no—
23#10622454—21no—
24#10622346—22no—
25#10622336—22no—
26#10622312C2211yescharacteristic
27C4×Dic44C2211yescharacteristic
28C4×D88C2211yescharacteristic
29#10622295C2211yescharacteristic
30C11×C4⋊C16C2211yescharacteristic
31C11×C22⋊C16C2212yes—
32C4×C11×C16C2211yescharacteristic
33#10622147C2211yescharacteristic
34#10622147C2212yes—
35#10622143C2211yescharacteristic
36#10622142C2212yes—
37#10622141C2212yes—
38#10622141C2211yescharacteristic
39#10622141C2212yes—
40#10622141C2212yes—
41C2×#4339—22no—
42C22×C8×C11C2312yes—
43C4×D4×C11D411yescharacteristic
44#66991—41no—
45#66989—41no—
46#66979—22no—
47#66977—22no—
48#66977—22no—
49C2×Dic44—21no—
50C2×Dic44C2311yescharacteristic
51C2×Dic44C2312yes—
52#66957—24no—
53#66957—42no—
54C2×D88C2311yescharacteristic
55C2×#4314—22no—
56C4⋊C4×D11—41no—
57#66940—41no—
58#66936—42no—
59#66932—42no—
60C4×D44—21no—
61#66922—21no—
62#66922—21no—
63C4×Dic22—21no—
64C2×C11×C16—42no—
65C2×C11×C16C2311yescharacteristic
66C2×C11×C16C2312yes—
67C2×C11×C16C2311yescharacteristic
68C11×C4⋊C8D411yescharacteristic
69C11×C22⋊C8D412yes—
70C4×C8×C11C2311yescharacteristic
71#66885—21no—
72#66882—21no—
73#66882C2311yescharacteristic
74#66882C2312yes—
75#66882C2311yescharacteristic
76#66881—22no—
77#66880—22no—
78#66880—22no—
79#66880—21no—
80Dic88—42no—
81#66864—22no—
82#33869—111nomaximal, Sylow
83C2×D4×C11D811yescharacteristic
84C22×C4×C11C2×D412yes—
85C2×C22⋊D11—42no—
86#4339—44no—
87#4339—82no—
88C2×D44—21no—
89C2×C4×D11—41no—
90C2×C4×D11—42no—
91C2×Dic22—21no—
92C2×Dic22—22no—
93C2×Dic22—41no—
94C2×C8×C11—22no—
95C2×C8×C11—22no—
96C2×C8×C11C2×D412yes—
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11C2411yescharacteristic
99C11×C4⋊C4D811yescharacteristic
100C11×C22⋊C4D812yes—
101C42×C11C2×D411yescharacteristic
102C22⋊Dic11—42no—
103C22⋊Dic11—42no—
104C22⋊Dic11—42no—
105(C2×D11)⋊C4—41no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108C4⋊Dic11—22no—
109C4⋊Dic11—41no—
110C4⋊Dic11—41no—
111C4⋊Dic11—41no—
112Dic11⋊C4—41no—
113Dic11⋊C4—42no—
114Dic11⋊C4—42no—
115C4×Dic11—41no—
116C4×Dic11—42no—
117Dic44—21no—
118Dic44—22no—
119Dic44—21no—
120Dic44—22no—
121Dic44—81no—
122D88—21no—
123D88#4112yes—
124#4314—44no—
125C11×C16—21no—
126C11×C16—22no—
127C11×C16—21no—
128#3342—111no—
129#3283—111no—
130#2241—111no—
131#2237—112no—
132#2224—111no—
133#2216—112no—
134#2209—111no—
135#2189—112no—
136C4×SD32—111no—
137D4×C16D1111yescharacteristic, complemented
138#2138—112no—
139C23×C11C2×D812yes—
140C22×D11—41no—
141D4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11C2×D812yes—
145C2×C4×C11C2×D811yescharacteristic
146C2×C4×C11C2×D811yescharacteristic
147C2×C4×C11C22×D411yescharacteristic
148C22⋊D11—84no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—42no—
152C2×Dic11—41no—
153C2×Dic11—42no—
154D44—22no—
155D44—41no—
156C4×D11—84no—
157C4×D11—82no—
158Dic22—42no—
159Dic22—41no—
160Dic22—42no—
161Dic22—41no—
162Dic22—82no—
163C8×C11—22no—
164C8×C11—21no—
165C8×C11C2×#4111yescharacteristic
166C8×C11H(5,𝔽2)11yescharacteristic
167C2×#135—112no—
168#556—221no—
169#547—221no—
170C2×Q32—112no—
171C2×SD32—111no—
172C22×C16C2×D1112yes—
173#500—111no—
174#494—111no—
175#485—222no—
176#475—221no—
177#467—112no—
178#467—112no—
179#461—221no—
180#452—222no—
181C4×Q16—111no—
182C4×D8—111no—
183C8×D4C2×D1111yescharacteristic
184#427—112no—
185#367—111no—
186#366—112no—
187C4⋊C16C2×D1111yescharacteristic
188#358—112no—
189#358—112no—
190#358—111no—
191#358—112no—
192#357—111no—
193#357—112no—
194C22⋊C16C2×D1112yes—
195C4×C16C2×D1111yescharacteristic
196C22×C11—22no—
197C22×C11—22no—
198C22×C11—22no—
199C22×C11C22×D811yescharacteristic
200C2×D11—42no—
201C2×D11—81no—
202C2×D11—81no—
203C4×C11—21no—
204C4×C11—22no—
205C4×C11#50812yes—
206C4×C11#54611yescharacteristic
207C4×C11#57711yescharacteristic
208Dic11—82no—
209Dic11—81no—
210Dic11—81no—
211Dic11—82no—
212Dic11—81no—
213C2×#41—222no—
214#135—224no—
215#135—442no—
216C2×Q16—112no—
217C2×Q16—111no—
218C2×Q16—221no—
219C2×SD16—222no—
220C2×D8—111no—
221C22×C8C22×D1112yes—
222C4⋊Q8—221no—
223C4⋊Q8—221no—
224#126—442no—
225#124—441no—
226#123—442no—
227C22⋊Q8—222no—
228C22⋊Q8—222no—
229#121—441no—
230C4×Q8—221no—
231C4×Q8—441no—
232C4×D4—221no—
233C4×D4D4411yescharacteristic
234#117—222no—
235C2×C4⋊C4—441no—
236Q32—442no—
237SD32—222no—
238C2×C16—42no—
239C2×C16C22×D1111yescharacteristic
240C2×C16C22×D1111yescharacteristic
241C2×C16C22×D1112yes—
242#107—112no—
243#107—111no—
244#107—111no—
245#107—221no—
246#106—222no—
247C4⋊C8D4411yescharacteristic
248#103—221no—
249#103—222no—
250#103—222no—
251#102—221no—
252C22⋊C8D4412yes—
253C4×C8C22×D1111yescharacteristic
254C2×C11—42no—
255C2×C11#329411yescharacteristic
256C2×C11C2×#50811yescharacteristic
257C2×C11#341711yescharacteristic
258D11—82no—
259#41—444no—
260#41—882no—
261C2×Q8—221no—
262C2×Q8—222no—
263C2×Q8—441no—
264C2×D4—221no—
265C2×D4—442no—
266C2×D4D8811yescharacteristic
267C22×C4—441no—
268C22×C4—442no—
269C22×C4C2×D4412yes—
270Q16—221no—
271Q16—222no—
272Q16—221no—
273Q16—222no—
274Q16—881no—
275SD16—444no—
276D8—112no—
277D8—221no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8C2×D4411yescharacteristic
281C2×C8C2×D4412yes—
282C2×C8C23×D1111yescharacteristic
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4—222no—
286C4⋊C4—441no—
287C4⋊C4—442no—
288C4⋊C4—441no—
289C4⋊C4—442no—
290C4⋊C4—441no—
291C4⋊C4—441no—
292C4⋊C4D8811yescharacteristic
293C22⋊C4—442no—
294C22⋊C4—442no—
295C22⋊C4—442no—
296C22⋊C4—441no—
297C22⋊C4D8812yes—
298C42—442no—
299C42—441no—
300C42C2×D4411yescharacteristic
301C16—21no—
302C16—22no—
303C16—21no—
304C11#3386911yescharacteristic, complemented, Sylow
305C23—441no—
306C23C2×D8812yes—
307Q8—442no—
308Q8—441no—
309Q8—442no—
310Q8—441no—
311Q8—882no—
312D4—22no—
313D4—222no—
314D4—441no—
315D4—884no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—441no—
319C2×C4—442no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—442no—
323C2×C4—884no—
324C2×C4—882no—
325C2×C4C2×D8812yes—
326C2×C4C2×D8811yescharacteristic
327C2×C4C2×D8811yescharacteristic
328C2×C4C22×D4411yescharacteristic
329C8—21no—
330C8—22no—
331C8#6703711yescharacteristic
332C8#41×D1111yescharacteristic
333C22—22no—
334C22—22no—
335C22—22no—
336C22—442no—
337C22—881no—
338C22—881no—
339C22C22×D8811yescharacteristic
340C4—22no—
341C4—21no—
342C4—882no—
343C4—881no—
344C4—881no—
345C4—882no—
346C4—881no—
347C4#1062251712yes—
348C4#1062308511yescharacteristic
349C4#1062328211yescharacteristic
350C2—42no—
351C2—882no—
352C2#1308043011yescharacteristic
353C2C2×#1062251711yescharacteristic
354C2#1308176911yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingD4×C11×C16C2
socleC22×C11C22×D8
prime radical#13080338C2
hypercenterD4×C16D11
hypocenterC11#33869
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×C16

Complements

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

NH ≅ G/Ntype
1. #13081047C2semidirect
3. #13070844C2semidirect
4. #13070825C2semidirect
5. #13070754C2semidirect
6. #13070707C2semidirect
7. #13070667C2semidirect
8. #13070558C2semidirect
9. C4×#66864C2semidirect
10. #13070324C2semidirect
11. D4×C11×C16C2semidirect
137. D4×C16D11semidirect
304. C11#33869semidirect

Maximal subgroups

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

subgroupindex
#130810472
#130803382
#130708442
#130708252
#130707542
#130707072
#130706672
#130705582
C4×#668642
#130703242
D4×C11×C162
#3386911