Finite Group Databasebeta

← #14910712

Subgroups — #14910712

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081039C211yesmaximal, characteristic, complemented
2#13080338C211yesmaximal, characteristic, complemented
3#13070844C211yesmaximal, characteristic, complemented
4#13070825C212yesmaximal, complemented
5#13070764C211yesmaximal, characteristic, complemented
6#13070712C212yesmaximal, complemented
7#13070662C211yesmaximal, characteristic, complemented
8#13070541C212yesmaximal, complemented
9C4×D176C211yesmaximal, characteristic, complemented
10#13070324C212yesmaximal, complemented
11D4×C11×C16C211yesmaximal, characteristic, complemented
12C2×#66957C2212yes—
13#10623094—21no—
14#10623082—21no—
15C22×C11×C16C2212yes—
16C8×D4×C11C2211yescharacteristic
17#10622729C2212yes—
18#10622728C2212yes—
19#10622719C2212yes—
20C2×#66864C2212yes—
21C2×D176C2211yescharacteristic
22#10622455—21no—
23#10622454—21no—
24#10622350—22no—
25#10622346—22no—
26#10622312C2211yescharacteristic
27C4×D88C2211yescharacteristic
28C4×D88C2211yescharacteristic
29#10622295C2211yescharacteristic
30C11×C4⋊C16C2211yescharacteristic
31C11×C22⋊C16C2212yes—
32C4×C11×C16C2211yescharacteristic
33#10622147C2211yescharacteristic
34#10622147C2211yescharacteristic
35#10622147C2212yes—
36#10622143C2212yes—
37#10622142C2211yescharacteristic
38#10622141C2212yes—
39#10622141C2212yes—
40#10622141C2212yes—
41C2×#4339—22no—
42C22×C8×C11C2312yes—
43C4×D4×C11D411yescharacteristic
44#66991—41no—
45#66991—41no—
46#66983—22no—
47#66979—22no—
48#66977—22no—
49C2×Dic44—21no—
50C2×Dic44C2312yes—
51#66957—24no—
52#66957—42no—
53C2×D88C2311yescharacteristic
54C2×D88C2311yescharacteristic
55C2×#4314—22no—
56#66945—41no—
57C4⋊C4×D11—41no—
58#66938—42no—
59#66936—42no—
60C4×D44—21no—
61C4×D44—21no—
62#66922—21no—
63#66922—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—21no—
73#66885—21no—
74#66882—21no—
75#66882C2312yes—
76#66882C2311yescharacteristic
77#66882C2311yescharacteristic
78#66881—22no—
79#66880—22no—
80#66864—42no—
81D176—22no—
82#33870—111nomaximal, Sylow
83C2×D4×C11D811yescharacteristic
84C22×C4×C11C2×D412yes—
85C2×C22⋊D11—42no—
86C2×C22⋊D11—42no—
87#4339—44no—
88#4339—82no—
89C2×D44—21no—
90C2×D44—21no—
91C2×C4×D11—41no—
92C2×C4×D11—41no—
93C2×C4×D11—42no—
94C2×Dic22—22no—
95C2×Dic22—41no—
96C2×C8×C11—22no—
97C2×C8×C11—22no—
98C2×C8×C11C2×D412yes—
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11C2411yescharacteristic
101C11×C4⋊C4D811yescharacteristic
102C11×C22⋊C4D812yes—
103C42×C11C2×D411yescharacteristic
104C22⋊Dic11—42no—
105C22⋊Dic11—42no—
106(C2×D11)⋊C4—41no—
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—42no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—22no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115Dic11⋊C4—42no—
116C4×Dic11—42no—
117Dic44—22no—
118Dic44—22no—
119Dic44—81no—
120D88—21no—
121D88—21no—
122D88—21no—
123D88#4112yes—
124#4314—44no—
125C11×C16—21no—
126C11×C16—22no—
127C11×C16—21no—
128#3341—111no—
129#3283—111no—
130#2241—111no—
131#2237—112no—
132#2226—111no—
133#2217—112no—
134#2208—111no—
135#2186—112no—
136C4×D16—111no—
137D4×C16D1111yescharacteristic, complemented
138#2138—112no—
139C23×C11C2×D812yes—
140C22×D11—41no—
141C22×D11—41no—
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—
151C2×Dic11—41no—
152C2×Dic11—42no—
153C2×Dic11—41no—
154C2×Dic11—42no—
155D44—22no—
156D44—41no—
157D44—41no—
158D44—41no—
159C4×D11—84no—
160C4×D11—82no—
161C4×D11—82no—
162Dic22—42no—
163Dic22—42no—
164Dic22—161no—
165C8×C11—22no—
166C8×C11—21no—
167C8×C11C2×#4111yescharacteristic
168C8×C11H(5,𝔽2)11yescharacteristic
169C2×#135—112no—
170#555—221no—
171#547—221no—
172C2×SD32—112no—
173C2×D16—111no—
174C22×C16C2×D1112yes—
175#500—111no—
176#494—111no—
177#482—222no—
178#476—221no—
179#467—112no—
180#466—112no—
181#461—221no—
182#452—222no—
183C4×D8—111no—
184C4×D8—111no—
185C8×D4C2×D1111yescharacteristic
186#427—112no—
187#367—112no—
188#366—111no—
189C4⋊C16C2×D1111yescharacteristic
190#358—112no—
191#358—112no—
192#358—112no—
193#357—111no—
194#357—112no—
195#357—111no—
196C22⋊C16C2×D1112yes—
197C4×C16C2×D1111yescharacteristic
198C22×C11—22no—
199C22×C11—22no—
200C22×C11—22no—
201C22×C11C22×D811yescharacteristic
202C2×D11—42no—
203C2×D11—81no—
204C2×D11—81no—
205C2×D11—81no—
206C2×D11—81no—
207C2×D11—81no—
208C4×C11—21no—
209C4×C11—22no—
210C4×C11#50812yes—
211C4×C11#54611yescharacteristic
212C4×C11#57711yescharacteristic
213Dic11—81no—
214Dic11—81no—
215Dic11—82no—
216Dic11—82no—
217C2×#41—222no—
218#135—224no—
219#135—442no—
220C2×Q16—112no—
221C2×Q16—221no—
222C2×SD16—222no—
223C2×D8—111no—
224C2×D8—111no—
225C22×C8C22×D1112yes—
226C4⋊Q8—221no—
227C4⋊Q8—221no—
228#124—442no—
229#123—442no—
230C22⋊Q8—222no—
231#121—222no—
232#121—441no—
233#121—441no—
234C4×D4—221no—
235C4×D4—221no—
236C4×D4D4411yescharacteristic
237#117—222no—
238#117—441no—
239C2×C4⋊C4—441no—
240SD32—442no—
241D16—222no—
242C2×C16—42no—
243C2×C16C22×D1111yescharacteristic
244C2×C16C22×D1111yescharacteristic
245C2×C16C22×D1112yes—
246#107—111no—
247#107—112no—
248#107—111no—
249#107—221no—
250#106—222no—
251C4⋊C8D4411yescharacteristic
252#103—222no—
253#102—221no—
254#102—221no—
255#102—222no—
256C22⋊C8D4412yes—
257C4×C8C22×D1111yescharacteristic
258C2×C11—42no—
259C2×C11#329411yescharacteristic
260C2×C11C2×#50811yescharacteristic
261C2×C11#341611yescharacteristic
262D11—82no—
263D11—161no—
264#41—444no—
265#41—882no—
266C2×Q8—222no—
267C2×Q8—441no—
268C2×D4—221no—
269C2×D4—221no—
270C2×D4—442no—
271C2×D4—442no—
272C2×D4D8811yescharacteristic
273C22×C4—441no—
274C22×C4—442no—
275C22×C4—441no—
276C22×C4C2×D4412yes—
277Q16—222no—
278Q16—222no—
279Q16—881no—
280SD16—444no—
281D8—112no—
282D8—221no—
283D8—221no—
284D8—221no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8C2×D4411yescharacteristic
288C2×C8C2×D4412yes—
289C2×C8C23×D1111yescharacteristic
290C4⋊C4—221no—
291C4⋊C4—221no—
292C4⋊C4—222no—
293C4⋊C4—441no—
294C4⋊C4—442no—
295C4⋊C4—441no—
296C4⋊C4—441no—
297C4⋊C4D8811yescharacteristic
298C22⋊C4—442no—
299C22⋊C4—442no—
300C22⋊C4—442no—
301C22⋊C4—441no—
302C22⋊C4—441no—
303C22⋊C4D8812yes—
304C42—442no—
305C42C2×D4411yescharacteristic
306C16—21no—
307C16—22no—
308C16—21no—
309C11#3387011yescharacteristic, complemented, Sylow
310C23—441no—
311C23—441no—
312C23C2×D8812yes—
313Q8—442no—
314Q8—442no—
315Q8—1761no—
316D4—22no—
317D4—222no—
318D4—441no—
319D4—441no—
320D4—441no—
321D4—884no—
322D4—1762no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—441no—
326C2×C4—442no—
327C2×C4—441no—
328C2×C4—442no—
329C2×C4—884no—
330C2×C4—882no—
331C2×C4—882no—
332C2×C4C2×D8812yes—
333C2×C4C2×D8811yescharacteristic
334C2×C4C2×D8811yescharacteristic
335C2×C4C22×D4411yescharacteristic
336C8—21no—
337C8—22no—
338C8#6703711yescharacteristic
339C8#41×D1111yescharacteristic
340C22—22no—
341C22—22no—
342C22—22no—
343C22—442no—
344C22—881no—
345C22—881no—
346C22—881no—
347C22—881no—
348C22—881no—
349C22C22×D8811yescharacteristic
350C4—22no—
351C4—21no—
352C4—882no—
353C4—881no—
354C4—881no—
355C4—882no—
356C4#1062251712yes—
357C4#1062308511yescharacteristic
358C4#1062328211yescharacteristic
359C2—42no—
360C2—882no—
361C2—1761no—
362C2#1308043011yescharacteristic
363C2C2×#1062251711yescharacteristic
364C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingD4×C11×C16C2
socleC22×C11C22×D8
hypercenterD4×C16D11
hypocenterC11#33870
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. #13080338C2semidirect
3. #13070844C2semidirect
4. #13070825C2semidirect
5. #13070764C2semidirect
6. #13070712C2semidirect
7. #13070662C2semidirect
8. #13070541C2semidirect
9. C4×D176C2semidirect
10. #13070324C2semidirect
11. D4×C11×C16C2semidirect
137. D4×C16D11semidirect
309. C11#33870semidirect

Maximal subgroups

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

subgroupindex
#130810392
#130803382
#130708442
#130708252
#130707642
#130707122
#130706622
#130705412
C4×D1762
#130703242
D4×C11×C162
#3387011