Finite Group Databasebeta

← #14670695

Subgroups — #14670695

Order 2816.

466 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081718C211yesmaximal, characteristic, complemented
2#13077335C211yesmaximal, characteristic
3#13070245C211yesmaximal, characteristic, complemented
4#13070243C211yesmaximal, characteristic, complemented
5#13070236C211yesmaximal, characteristic, complemented
6#13066696C211yesmaximal, characteristic, complemented
7C11×#1375C211yesmaximal, characteristic, complemented
8C2×#66954C2211yescharacteristic
9C2×#66954C2211yescharacteristic
10#10623008C411yescharacteristic
11C2×C11×M32C2211yescharacteristic
12C2×C11×M32C2211yescharacteristic
13C2×C11×#97C2211yescharacteristic
14#10622723C411yescharacteristic
15#10622723C411yescharacteristic
16C2×#66876C2211yescharacteristic
17C2×#66876C2211yescharacteristic
18#10622537C411yescharacteristic
19#10622520—22no—
20D11×M32—22no—
21#10622514—22no—
22#10622319—22no—
23#10622319—22no—
24#10622153—22no—
25#10622152—22no—
26#10622146—22no—
27C2×#4339C2×C411yescharacteristic
28C2×#4339C2×C411yescharacteristic
29C22×C8×C11C2×C411yescharacteristic
30C22×C8×C11C2311yescharacteristic
31C2×C42×C11C2×C411yescharacteristic
32#66983—22no—
33C2×#4318C2×C411yescharacteristic
34C2×#4318C2×C411yescharacteristic
35#66954—21no—
36#66954—21no—
37#66954—21no—
38#66954—21no—
39#66954—21no—
40#66954—21no—
41#66954—21no—
42#66954—21no—
43C2×#4313—21no—
44C2×#4313D412yes—
45C2×C8×D11—21no—
46C2×C8×D11D412yes—
47#66928C811yescharacteristic
48#66928C811yescharacteristic
49#66927C811yescharacteristic
50C4×D44—22no—
51#66922C811yescharacteristic
52C11×M32—21no—
53C11×M32—21no—
54C11×M32—21no—
55C11×M32—21no—
56C2×C11×C16—21no—
57C2×C11×C16D412yescomplemented
58C11×#97—21no—
59C11×#97—21no—
60(C2×D11)⋊C8—22no—
61(C2×D11)⋊C8—22no—
62#66876—21no—
63#66876—21no—
64#66876—21no—
65#66876—21no—
66C2×C11⋊C16—21no—
67C2×C11⋊C16D412yescomplemented
68C4⋊(C11⋊C8)—22no—
69#66862—24no—
70C16×D11—24no—
71#12988—111nomaximal, Sylow
72C22×C4×C11—21no—
73C22×C4×C11C22×C411yescharacteristic
74C2×C22⋊D11—21no—
75C2×C22⋊D11M1612yes—
76#4339—21no—
77#4339—21no—
78#4339—21no—
79#4339—21no—
80#4339—21no—
81#4339—21no—
82#4339—21no—
83#4339—21no—
84C2×D44—22no—
85C2×D44C2×C811yescharacteristic
86C2×D44C2×C811yescharacteristic
87C2×C4×D11—21no—
88C2×C4×D11C22⋊C412yes—
89C2×Dic22C2×C811yescharacteristic
90C2×Dic22C2×C811yescharacteristic
91C2×C8×C11—21no—
92C2×C8×C11—21no—
93C2×C8×C11—21no—
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11#4111yescharacteristic
99C2×C8×C11#4111yescharacteristic
100C42×C11—21no—
101C42×C11C2×C811yescharacteristic
102C42×C11C2×C811yescharacteristic
103(C2×D11)⋊C4—22no—
104(C2×D11)⋊C4—22no—
105C4⋊Dic11—22no—
106#4318—21no—
107#4318—21no—
108#4318—21no—
109#4318—21no—
110C2×C11⋊C8—21no—
111C2×C11⋊C8C22⋊C412yes—
112#4313—22no—
113#4313—22no—
114#4313—41no—
115#4313—41no—
116C8×D11—22no—
117C8×D11—22no—
118C8×D11—41no—
119C8×D11—41no—
120C11×C16—22no—
121C11×C16—41no—
122C11⋊C16—22no—
123C11⋊C16—41no—
124#3407—111no—
125#2932—111no—
126#2117—111no—
127#2117—111no—
128#2115—111no—
129#1375—111no—
130#1375D1111yescharacteristic, complemented
131C23×C11C2×M1611yescharacteristic
132C22×D11—21no—
133C22×D11C22⋊C812yes—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—81no—
137C2×C4×C11C2×C22⋊C411yescharacteristic
138C2×C4×C11C4×D411yescharacteristic
139C2×C4×C11C4×D411yescharacteristic
140C2×C4×C11C22×C811yescharacteristic
141C2×C4×C11#13111yescharacteristic
142C2×C4×C11#13111yescharacteristic
143C22⋊D11—22no—
144C22⋊D11—22no—
145C22⋊D11—41no—
146C22⋊D11—41no—
147C2×Dic11—21no—
148C2×Dic11C22⋊C812yes—
149D44—21no—
150D44—21no—
151D44—21no—
152D44—21no—
153D44—82no—
154C4×D11—22no—
155C4×D11—22no—
156C4×D11—41no—
157C4×D11—41no—
158Dic22—21no—
159Dic22—21no—
160Dic22—21no—
161Dic22—21no—
162C8×C11—41no—
163C8×C11#12011yescharacteristic
164C8×C11#12111yescharacteristic
165C8×C11#12111yescharacteristic
166C8×C11#12311yescharacteristic
167C11⋊C8—22no—
168C11⋊C8—41no—
169C2×#131—111no—
170C2×#131—111no—
171#532—111no—
172#504—222no—
173#504—222no—
174C2×M32—111no—
175C2×M32—111no—
176C2×M32—222no—
177C2×M32C2×D1111yescharacteristic
178C2×M32C2×D1111yescharacteristic
179#435—222no—
180#435—222no—
181#423—111no—
182#408—111no—
183#408—111no—
184C2×#97C2×D1111yescharacteristic
185#350—222no—
186#350—222no—
187#349—222no—
188C22×C11—41no—
189C22×C11C2×C22⋊C811yescharacteristic
190C22×C11#43511yescharacteristic
191C22×C11#43511yescharacteristic
192C2×D11—22no—
193C2×D11—42no—
194C2×D11—42no—
195C2×D11—41no—
196C4×C11—41no—
197C4×C11—41no—
198C4×C11#38611yescharacteristic
199C4×C11#40811yescharacteristic
200C4×C11C8×D411yescharacteristic
201C4×C11C8×D411yescharacteristic
202Dic11—22no—
203Dic11—41no—
204C2×#41—111no—
205C2×#41—111no—
206#131—221no—
207#131—221no—
208#131—221no—
209#131—221no—
210#131—221no—
211#131—221no—
212#131—221no—
213#131—221no—
214C2×M16—111no—
215C2×M16—112no—
216C2×M16—111no—
217C2×M16—221no—
218C22×C8—112no—
219C22×C8—221no—
220C22×C8C4×D1111yescharacteristic
221C22×C8C22×D1111yescharacteristic
222C4⋊Q8—111no—
223#127—111no—
224#124—111no—
225#124—111no—
226#121—222no—
227C4×D4—222no—
228C2×C42C4×D1111yescharacteristic
229M32—21no—
230M32—21no—
231M32—21no—
232M32—21no—
233M32—224no—
234M32—221no—
235M32—221no—
236M32—221no—
237M32—221no—
238C2×C16—21no—
239C2×C16—112no—
240C2×C16—224no—
241C2×C16—221no—
242C2×C16D4412yescomplemented
243C4⋊C8—222no—
244C22⋊C8—222no—
245C22⋊C8—222no—
246#97—21no—
247#97—21no—
248C2×C11—21no—
249C2×C11—21no—
250C2×C11—21no—
251C2×C11#186911yescharacteristic
252D11—42no—
253D11—81no—
254#41—221no—
255#41—221no—
256#41—221no—
257#41—221no—
258#41—221no—
259#41—221no—
260#41—221no—
261#41—221no—
262C2×Q8—111no—
263C2×Q8—111no—
264C2×D4—112no—
265C2×D4—111no—
266C2×D4—111no—
267C2×D4—222no—
268C2×D4—221no—
269C22×C4—21no—
270C22×C4—112no—
271C22×C4—221no—
272C22×C4C2×C4×D1111yescharacteristic
273M16—221no—
274M16—221no—
275M16—222no—
276M16—222no—
277M16—221no—
278M16—221no—
279M16—441no—
280M16—441no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—112no—
285C2×C8—222no—
286C2×C8—222no—
287C2×C8—221no—
288C2×C8—441no—
289C2×C8—441no—
290C2×C8C2×D4411yescharacteristic
291C2×C8#433911yescharacteristic
292C2×C8D4×D1111yescharacteristic
293C2×C8D4×D1111yescharacteristic
294C2×C8D4×D1111yescharacteristic
295C2×C8#434311yescharacteristic
296C4⋊C4—222no—
297C22⋊C4—222no—
298C22⋊C4—222no—
299C42—21no—
300C42C8×D1111yescharacteristic
301C42C8×D1111yescharacteristic
302C16—22no—
303C16—41no—
304C16—222no—
305C16—441no—
306C11#1298811yescharacteristic, complemented, Sylow
307C23—112no—
308C23—221no—
309C23M16×D1111yescharacteristic
310Q8—221no—
311Q8—221no—
312Q8—221no—
313Q8—221no—
314D4—222no—
315D4—222no—
316D4—221no—
317D4—221no—
318D4—221no—
319D4—221no—
320D4—441no—
321D4—441no—
322D4—882no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—81no—
326C2×C4—112no—
327C2×C4—222no—
328C2×C4—222no—
329C2×C4—221no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4C4×D4411yescharacteristic
333C2×C4C22⋊C4×D1111yescharacteristic
334C2×C4#6694611yescharacteristic
335C2×C4C2×C8×D1111yescharacteristic
336C2×C4#6695411yescharacteristic
337C2×C4#6696011yescharacteristic
338C8—41no—
339C8—222no—
340C8—441no—
341C8#6693511yescharacteristic
342C8#6693711yescharacteristic
343C8#6694711yescharacteristic
344C8#6694811yescharacteristic
345C22—41no—
346C22—222no—
347C22—442no—
348C22—442no—
349C22—441no—
350C22#1062231911yescharacteristic
351C22D11×C22⋊C811yescharacteristic
352C22#1062244911yescharacteristic
353C4—41no—
354C4—41no—
355C4—222no—
356C4—441no—
357C4#1062227811yescharacteristic
358C4C8×D4411yescharacteristic
359C4#1062234011yescharacteristic
360C4#1062244711yescharacteristic
361C2—21no—
362C2—21no—
363C2—21no—
364C2—442no—
365C2—881no—
366C2#1306890711yescharacteristic
subgroupG/H
centerC4#10622278
commutatorC2×C4×C11C22×C8
FrattiniC22×C8C22×D11
FittingC11×#1375C2
socleC2×C11#1869
prime radical#10623008C4
cosocleC22×C8×C11C23
hypercenter#1375D11
hypocenterC11#12988
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C8 ◁ #1375

Complements

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

NH ≅ G/Ntype
1. #13081718C2semidirect
3. #13070245C2semidirect
4. #13070243C2semidirect
5. #13070236C2semidirect
6. #13066696C2semidirect
7. C11×#1375C2semidirect
57. C2×C11×C16D4semidirect
67. C2×C11⋊C16D4semidirect
130. #1375D11semidirect
242. C2×C16D44semidirect
306. C11#12988semidirect

Maximal subgroups

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

subgroupindex
#130817182
#130773352
#130702452
#130702432
#130702362
#130666962
C11×#13752
#1298811