Finite Group Databasebeta

← #14910734

Subgroups — #14910734

Order 2816.

568 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081039C211yesmaximal, characteristic, complemented
2#13080376C211yesmaximal, characteristic, complemented
3#13070840C211yesmaximal, characteristic, complemented
4#13070808C212yesmaximal, complemented
5#13070769C211yesmaximal, characteristic, complemented
6#13070702C212yesmaximal, complemented
7#13070652C211yesmaximal, characteristic, complemented
8#13070541C212yesmaximal, complemented
9C4×#66864C211yesmaximal, characteristic, complemented
10#13070324C212yesmaximal, complemented
11D4×C11×C16C211yesmaximal, characteristic, complemented
12C2×#66957C2212yes—
13#10623094—21no—
14#10623084—21no—
15C22×C11×C16C2212yes—
16C8×D4×C11C2211yescharacteristic
17#10622728C2212yes—
18#10622728C2212yes—
19#10622719C2212yes—
20C2×#66864C2211yescharacteristic
21C2×D176C2212yes—
22#10622461—21no—
23#10622455—21no—
24#10622350—22no—
25#10622347—22no—
26C4×Dic44C2211yescharacteristic
27#10622308C2211yescharacteristic
28C4×D88C2211yescharacteristic
29#10622295C2211yescharacteristic
30C11×C4⋊C16C2211yescharacteristic
31C11×C22⋊C16C2212yes—
32C4×C11×C16C2211yescharacteristic
33#10622147C2212yes—
34#10622147C2211yescharacteristic
35#10622147C2212yes—
36#10622147C2212yes—
37#10622143C2211yescharacteristic
38#10622142C2212yes—
39#10622141C2211yescharacteristic
40#10622141C2212yes—
41C2×#4339—22no—
42C22×C8×C11C2312yes—
43C4×D4×C11D411yescharacteristic
44#66993—41no—
45#66991—41no—
46#66983—22no—
47#66983—22no—
48#66979—22no—
49C2×Dic44C2311yescharacteristic
50#66957—24no—
51#66957—42no—
52C2×D88—21no—
53C2×D88C2311yescharacteristic
54C2×D88C2312yes—
55C2×#4314—22no—
56#66946—41no—
57#66945—41no—
58#66938—42no—
59#66937—42no—
60#66927—21no—
61C4×D44—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—22no—
72#66885—22no—
73#66885—21no—
74#66882—21no—
75#66882C2311yescharacteristic
76#66882C2312yes—
77#66882C2311yescharacteristic
78#66881—22no—
79#66880—21no—
80#66864—22no—
81D176—42no—
82#33872—111nomaximal, Sylow
83C2×D4×C11D811yescharacteristic
84C22×C4×C11C2×D412yes—
85C2×C22⋊D11—42no—
86C2×C22⋊D11—42no—
87C2×C22⋊D11—42no—
88#4339—44no—
89#4339—82no—
90C2×D44—21no—
91C2×D44—22no—
92C2×D44—41no—
93C2×D44—41no—
94C2×C4×D11—41no—
95C2×C4×D11—42no—
96C2×Dic22—21no—
97C2×Dic22—41no—
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2×D412yes—
102C2×C8×C11C2411yescharacteristic
103C11×C4⋊C4D811yescharacteristic
104C11×C22⋊C4D812yes—
105C42×C11C2×D411yescharacteristic
106C22⋊Dic11—42no—
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—42no—
109(C2×D11)⋊C4—42no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112C4⋊Dic11—22no—
113C4⋊Dic11—41no—
114Dic11⋊C4—41no—
115C4×Dic11—41no—
116C4×Dic11—42no—
117Dic44—21no—
118Dic44#4112yes—
119D88—21no—
120D88—22no—
121D88—21no—
122D88—22no—
123D88—81no—
124#4314—44no—
125C11×C16—21no—
126C11×C16—22no—
127C11×C16—21no—
128#3341—111no—
129#3287—111no—
130#2240—111no—
131#2234—112no—
132#2227—111no—
133#2215—112no—
134#2206—111no—
135#2186—112no—
136C4×SD32—111no—
137D4×C16D1111yescharacteristic, complemented
138#2138—112no—
139C23×C11C2×D812yes—
140C22×D11—41no—
141C22×D11—42no—
142D4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11C2×D812yes—
146C2×C4×C11C2×D811yescharacteristic
147C2×C4×C11C2×D811yescharacteristic
148C2×C4×C11C22×D411yescharacteristic
149C22⋊D11—84no—
150C22⋊D11—162no—
151C22⋊D11—162no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—42no—
156D44—42no—
157D44—41no—
158D44—42no—
159D44—41no—
160D44—82no—
161D44—161no—
162C4×D11—84no—
163C4×D11—82no—
164Dic22—22no—
165Dic22—41no—
166Dic22—161no—
167C8×C11—22no—
168C8×C11—21no—
169C8×C11C2×#4111yescharacteristic
170C8×C11H(5,𝔽2)11yescharacteristic
171C2×#135—112no—
172#555—221no—
173#550—221no—
174C2×SD32—111no—
175C2×D16—112no—
176C22×C16C2×D1112yes—
177#500—111no—
178#493—111no—
179#482—222no—
180#476—221no—
181#466—112no—
182#466—112no—
183#460—221no—
184#449—222no—
185C4×Q16—111no—
186C4×D8—111no—
187C8×D4C2×D1111yescharacteristic
188#427—112no—
189#367—111no—
190#366—112no—
191C4⋊C16C2×D1111yescharacteristic
192#358—111no—
193#358—112no—
194#357—112no—
195#357—112no—
196#357—111no—
197#357—112no—
198C22⋊C16C2×D1112yes—
199C4×C16C2×D1111yescharacteristic
200C22×C11—22no—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11C22×D811yescharacteristic
204C2×D11—81no—
205C2×D11—82no—
206C2×D11—82no—
207C2×D11—81no—
208C2×D11—82no—
209C2×D11—81no—
210C4×C11—21no—
211C4×C11—22no—
212C4×C11#50812yes—
213C4×C11#54611yescharacteristic
214C4×C11#57711yescharacteristic
215Dic11—42no—
216Dic11—81no—
217Dic11—82no—
218Dic11—81no—
219C2×#41—222no—
220#135—224no—
221#135—442no—
222C2×Q16—111no—
223C2×SD16—222no—
224C2×D8—112no—
225C2×D8—111no—
226C2×D8—221no—
227C22×C8C22×D1112yes—
228C4⋊Q8—221no—
229#127—221no—
230#127—441no—
231#124—442no—
232#121—222no—
233#121—222no—
234#121—441no—
235#121—442no—
236C4×Q8—221no—
237C4×D4—221no—
238C4×D4—441no—
239C4×D4D4411yescharacteristic
240#117—222no—
241#117—441no—
242SD32—222no—
243D16—442no—
244C2×C16—42no—
245C2×C16C22×D1111yescharacteristic
246C2×C16C22×D1111yescharacteristic
247C2×C16C22×D1112yes—
248#107—112no—
249#107—111no—
250#107—111no—
251#107—221no—
252#106—222no—
253C4⋊C8D4411yescharacteristic
254#103—221no—
255#102—221no—
256#102—222no—
257#102—222no—
258C22⋊C8D4412yes—
259C4×C8C22×D1111yescharacteristic
260C2×C11—42no—
261C2×C11#329411yescharacteristic
262C2×C11C2×#50811yescharacteristic
263C2×C11#341511yescharacteristic
264D11—161no—
265D11—162no—
266#41—444no—
267#41—882no—
268C2×Q8—221no—
269C2×Q8—441no—
270C2×D4—221no—
271C2×D4—222no—
272C2×D4—442no—
273C2×D4—442no—
274C2×D4—442no—
275C2×D4—441no—
276C2×D4—441no—
277C2×D4D8811yescharacteristic
278C22×C4—441no—
279C22×C4—442no—
280C22×C4C2×D4412yes—
281Q16—112no—
282Q16—221no—
283SD16—444no—
284D8—221no—
285D8—222no—
286D8—221no—
287D8—222no—
288D8—881no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8C2×D4411yescharacteristic
292C2×C8C2×D4412yes—
293C2×C8C23×D1111yescharacteristic
294C4⋊C4—221no—
295C4⋊C4—221no—
296C4⋊C4—222no—
297C4⋊C4—441no—
298C4⋊C4—441no—
299C4⋊C4D8811yescharacteristic
300C22⋊C4—442no—
301C22⋊C4—442no—
302C22⋊C4—441no—
303C22⋊C4—442no—
304C22⋊C4D8812yes—
305C42—442no—
306C42—441no—
307C42C2×D4411yescharacteristic
308C16—21no—
309C16—22no—
310C16—21no—
311C11#3387211yescharacteristic, complemented, Sylow
312C23—441no—
313C23—442no—
314C23C2×D8812yes—
315Q8—222no—
316Q8—441no—
317Q8—1761no—
318D4—22no—
319D4—442no—
320D4—441no—
321D4—442no—
322D4—441no—
323D4—884no—
324D4—882no—
325D4—1761no—
326D4—1762no—
327D4—1762no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—442no—
334C2×C4—884no—
335C2×C4—882no—
336C2×C4C2×D8812yes—
337C2×C4C2×D8811yescharacteristic
338C2×C4C2×D8811yescharacteristic
339C2×C4C22×D4411yescharacteristic
340C8—21no—
341C8—22no—
342C8#6703711yescharacteristic
343C8#41×D1111yescharacteristic
344C22—22no—
345C22—22no—
346C22—22no—
347C22—882no—
348C22—881no—
349C22—881no—
350C22—882no—
351C22—882no—
352C22—881no—
353C22C22×D8811yescharacteristic
354C4—22no—
355C4—21no—
356C4—442no—
357C4—881no—
358C4—881no—
359C4—882no—
360C4#1062251712yes—
361C4#1062308511yescharacteristic
362C4#1062328211yescharacteristic
363C2—42no—
364C2—1762no—
365C2—1761no—
366C2#1308043011yescharacteristic
367C2C2×#1062251711yescharacteristic
368C2#1308175711yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingD4×C11×C16C2
socleC22×C11C22×D8
hypercenterD4×C16D11
hypocenterC11#33872
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. #13081039C2semidirect
2. #13080376C2semidirect
3. #13070840C2semidirect
4. #13070808C2semidirect
5. #13070769C2semidirect
6. #13070702C2semidirect
7. #13070652C2semidirect
8. #13070541C2semidirect
9. C4×#66864C2semidirect
10. #13070324C2semidirect
11. D4×C11×C16C2semidirect
137. D4×C16D11semidirect
311. C11#33872semidirect

Maximal subgroups

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

subgroupindex
#130810392
#130803762
#130708402
#130708082
#130707692
#130707022
#130706522
#130705412
C4×#668642
#130703242
D4×C11×C162
#3387211