Finite Group Databasebeta

← #14911445

Subgroups — #14911445

Order 2816.

498 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081629C211yesmaximal, characteristic, complemented
2#13081484C211yesmaximal, characteristic, complemented
3#13070848C212yesmaximal, complemented
4#13070840C211yesmaximal, characteristic, complemented
5#13070774C212yesmaximal, complemented
6#13070769C211yesmaximal, characteristic, complemented
7#13070672C212yesmaximal, complemented
8#13070652C211yesmaximal, characteristic
9C4×#66864C211yesmaximal, characteristic, complemented
10C4×D176C212yesmaximal, complemented
11Q8×C11×C16C211yesmaximal, characteristic, complemented
12#10623116—21no—
13#10623110—21no—
14C8×Q8×C11C2211yescharacteristic
15C2×#66864C2211yescharacteristic
16C2×D176C2212yes—
17#10622461—21no—
18#10622460—22no—
19#10622457—22no—
20#10622455—21no—
21C4×Dic44C2211yescharacteristic
22#10622309C2212yes—
23#10622308C2211yescharacteristic
24C4×D88C2212yes—
25C4×D88C2211yescharacteristic
26C4×D88C2212yes—
27#10622296C2212yes—
28#10622295C2211yescharacteristic
29C11×C4⋊C16C2211yescharacteristic
30C11×C4⋊C16C2212yes—
31C4×C11×C16C2212yes—
32C4×C11×C16C2211yescharacteristic
33#10622147C2212yes—
34#10622147C2212yes—
35#10622147C2212yes—
36#10622147C2211yescharacteristic
37#10622143C2211yescharacteristic
38#10622142C2212yes—
39#10622141C2211yescharacteristic
40#10622141C2212yes—
41C4×Q8×C11D411yescharacteristic
42#67000—41no—
43#66999—41no—
44C2×Dic44C2311yescharacteristic
45C2×D88—21no—
46C2×D88C2312yes—
47C2×D88C2311yescharacteristic
48C2×#4314—22no—
49#66949—42no—
50#66947—42no—
51#66946—41no—
52C4⋊C4×D11—41no—
53#66928—22no—
54#66927—21no—
55C4×D44—21no—
56C4×D44—22no—
57C4×D44—22no—
58#66923—22no—
59#66922—21no—
60C4×Dic22—21no—
61C2×C11×C16C2311yescharacteristic
62C2×C11×C16C2312yes—
63C2×C11×C16C2311yescharacteristic
64C11×C4⋊C8D411yescharacteristic
65C11×C4⋊C8D412yes—
66C4×C8×C11C2311yescharacteristic
67C4×C8×C11C2312yes—
68#66885—22no—
69#66885—22no—
70#66885—21no—
71#66882—21no—
72#66882C2312yes—
73#66882C2311yescharacteristic
74#66882C2311yescharacteristic
75#66881—22no—
76#66880—21no—
77#66864—22no—
78D176—24no—
79#33928—111nomaximal, Sylow
80C2×Q8×C11D811yescharacteristic
81C2×D44—21no—
82C2×D44—22no—
83C2×D44—41no—
84C2×D44—41no—
85C2×C4×D11—41no—
86C2×C4×D11—42no—
87C2×C4×D11—42no—
88C2×Dic22—21no—
89C2×Dic22—41no—
90C2×C8×C11C2×D411yescharacteristic
91C2×C8×C11C2×D412yes—
92C2×C8×C11C2411yescharacteristic
93C11×C4⋊C4D811yescharacteristic
94C11×C4⋊C4D812yes—
95C42×C11C2×D411yescharacteristic
96C42×C11C2×D412yes—
97(C2×D11)⋊C4—42no—
98(C2×D11)⋊C4—41no—
99(C2×D11)⋊C4—42no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—42no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11—22no—
105C4⋊Dic11—41no—
106Dic11⋊C4—41no—
107Dic11⋊C4—42no—
108Dic11⋊C4—42no—
109C4×Dic11—41no—
110Dic44—21no—
111Dic44—21no—
112D88—22no—
113D88—21no—
114D88—22no—
115D88—81no—
116D88#4112yes—
117#4314—82no—
118C11×C16—22no—
119C11×C16—21no—
120C11×C16—21no—
121#3396—111no—
122#3380—111no—
123#2242—112no—
124#2240—111no—
125#2228—112no—
126#2227—111no—
127#2210—112no—
128#2206—111no—
129Q8×C16D1111yescharacteristic, complemented
130C4×SD32—111no—
131C4×D16—112no—
132C22×D11—41no—
133C22×D11—42no—
134Q8×C11—22no—
135C2×C4×C11C2×D812yes—
136C2×C4×C11C2×D811yescharacteristic
137C2×C4×C11C2×D812yes—
138C2×C4×C11C2×D811yescharacteristic
139C2×C4×C11C22×D411yescharacteristic
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—42no—
144D44—22no—
145D44—42no—
146D44—41no—
147D44—42no—
148D44—82no—
149D44—161no—
150C4×D11—82no—
151C4×D11—162no—
152C4×D11—162no—
153Dic22—41no—
154Dic22—41no—
155Dic22—161no—
156C8×C11—22no—
157C8×C11—21no—
158C8×C11C2×#4111yescharacteristic
159C8×C112−1+411yescharacteristic
160#559—221no—
161#554—221no—
162C2×SD32—111no—
163C2×D16—112no—
164#500—111no—
165#499—112no—
166#495—112no—
167#493—111no—
168#478—222no—
169#476—221no—
170#463—222no—
171#460—221no—
172C8×Q8C2×D1111yescharacteristic
173C4×Q16—111no—
174C4×D8—112no—
175C4×D8—111no—
176C4×D8—112no—
177#367—111no—
178#366—112no—
179C4⋊C16C2×D1111yescharacteristic
180C4⋊C16C2×D1112yes—
181#358—111no—
182#358—112no—
183#357—111no—
184#357—112no—
185#357—112no—
186#357—112no—
187C4×C16C2×D1112yes—
188C4×C16C2×D1111yescharacteristic
189C22×C11C22×D811yescharacteristic
190C2×D11—42no—
191C2×D11—81no—
192C2×D11—81no—
193C2×D11—82no—
194C2×D11—82no—
195C2×D11—82no—
196C4×C11—22no—
197C4×C11—21no—
198C4×C11—22no—
199C4×C11#50812yes—
200C4×C11#54811yescharacteristic
201C4×C11#57711yescharacteristic
202Dic11—81no—
203Dic11—81no—
204Dic11—82no—
205Dic11—81no—
206C2×Q16—111no—
207C2×SD16—222no—
208C2×D8—111no—
209C2×D8—112no—
210C2×D8—221no—
211C4⋊Q8—221no—
212#127—221no—
213#125—222no—
214#124—222no—
215#124—441no—
216#123—442no—
217C22⋊Q8—441no—
218C22⋊Q8—442no—
219C4×Q8—221no—
220C4×Q8D4411yescharacteristic
221C4×D4—221no—
222C4×D4—222no—
223C4×D4—222no—
224C4×D4—441no—
225C2×C4⋊C4—441no—
226SD32—222no—
227D16—224no—
228C2×C16C22×D1111yescharacteristic
229C2×C16C22×D1111yescharacteristic
230C2×C16C22×D1112yes—
231#107—112no—
232#107—111no—
233#107—111no—
234#107—221no—
235#106—222no—
236C4⋊C8D4411yescharacteristic
237C4⋊C8D4412yes—
238#103—221no—
239#102—222no—
240#102—222no—
241#102—221no—
242C4×C8C22×D1112yes—
243C4×C8C22×D1111yescharacteristic
244C2×C11#335811yescharacteristic
245C2×C11C2×#50811yescharacteristic
246C2×C11#341511yescharacteristic
247D11—82no—
248D11—162no—
249C2×Q8—221no—
250C2×Q8—441no—
251C2×Q8D8811yescharacteristic
252C2×D4—221no—
253C2×D4—222no—
254C2×D4—441no—
255C2×D4—441no—
256C22×C4—441no—
257C22×C4—442no—
258C22×C4—442no—
259Q16—221no—
260Q16—221no—
261SD16—882no—
262D8—112no—
263D8—221no—
264D8—222no—
265D8—222no—
266D8—881no—
267C2×C8C2×D4412yes—
268C2×C8C2×D4411yescharacteristic
269C2×C8C23×D1111yescharacteristic
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4—222no—
273C4⋊C4—442no—
274C4⋊C4—441no—
275C4⋊C4—441no—
276C4⋊C4—442no—
277C4⋊C4D8811yescharacteristic
278C4⋊C4D8812yes—
279C22⋊C4—441no—
280C22⋊C4—442no—
281C22⋊C4—442no—
282C22⋊C4—442no—
283C22⋊C4—442no—
284C42—441no—
285C42C2×D4412yes—
286C42C2×D4411yescharacteristic
287C16—21no—
288C16—22no—
289C16—21no—
290C11#3392811yescharacteristic, complemented, Sylow
291C23—441no—
292C23—442no—
293Q8—22no—
294Q8—441no—
295Q8—441no—
296Q8—1761no—
297D4—222no—
298D4—441no—
299D4—442no—
300D4—442no—
301D4—882no—
302D4—1761no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—442no—
307C2×C4—882no—
308C2×C4—1762no—
309C2×C4—1762no—
310C2×C4C2×D8812yes—
311C2×C4C2×D8812yes—
312C2×C4C2×D8811yescharacteristic
313C2×C4C2×D8811yescharacteristic
314C2×C4C22×D4411yescharacteristic
315C8—21no—
316C8—22no—
317C8#6704011yescharacteristic
318C8#41×D1111yescharacteristic
319C22—442no—
320C22—881no—
321C22—881no—
322C22—882no—
323C22—882no—
324C22—882no—
325C22C22×D8811yescharacteristic
326C4—22no—
327C4—22no—
328C4—21no—
329C4—881no—
330C4—881no—
331C4—882no—
332C4—881no—
333C4#1062251712yes—
334C4#1062310711yescharacteristic
335C4#1062328211yescharacteristic
336C2—882no—
337C2—1762no—
338C2#1308125211yescharacteristic
339C2C2×#1062251711yescharacteristic
340C2#1308175711yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingQ8×C11×C16C2
socleC22×C11C22×D8
prime radical#13070652C2
hypercenterQ8×C16D11
hypocenterC11#33928
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ Q8×C16

Complements

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

NH ≅ G/Ntype
1. #13081629C2semidirect
2. #13081484C2semidirect
3. #13070848C2semidirect
4. #13070840C2semidirect
5. #13070774C2semidirect
6. #13070769C2semidirect
7. #13070672C2semidirect
9. C4×#66864C2semidirect
10. C4×D176C2semidirect
11. Q8×C11×C16C2semidirect
129. Q8×C16D11semidirect
290. C11#33928semidirect

Maximal subgroups

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

subgroupindex
#130816292
#130814842
#130708482
#130708402
#130707742
#130707692
#130706722
#130706522
C4×#668642
C4×D1762
Q8×C11×C162
#3392811