Finite Group Databasebeta

← #14650326

Subgroups — #14650326

Order 2816.

492 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079559C211yesmaximal, characteristic
2#13077559C211yesmaximal, characteristic, complemented
3#13069455C211yesmaximal, characteristic
4#13067307C211yesmaximal, characteristic, complemented
5C2×#10622123C211yesmaximal, characteristic
6#13066465C211yesmaximal, characteristic, complemented
7C11×#1301C211yesmaximal, characteristic, complemented
8C2×#66927C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×#66887—21no—
14C2×#66887—21no—
15#10622715—21no—
16#10622714—21no—
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18C4×#4318C2211yescharacteristic
19#10622461—22no—
20#10622444—21no—
21#10622443—21no—
22#10622441—22no—
23#10622344C414yes—
24#10622307—21no—
25#10622306—21no—
26#10622124—21no—
27#10622123—21no—
28#10622123—21no—
29#10622119—21no—
30C22×D44—21no—
31C22×D44—21no—
32C22×D44C2×C412yes—
33C2×C11×M16—21no—
34C22×C8×C11—21no—
35C2×C42×C11C2311yescharacteristic
36#66979—21no—
37#66977—21no—
38#66977C2×C412yes—
39C2×#4318D411yescharacteristic
40C2×#4318D411yescharacteristic
41C22×C11⋊C8—21no—
42C2×#4314—24no—
43#66927—21no—
44#66927—21no—
45#66927—21no—
46#66927—21no—
47#66923—21no—
48#66922D411yescharacteristic
49#66922D411yescharacteristic
50C4×Dic22—21no—
51C4×Dic22D412yes—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8D411yescharacteristic
57C11×C4⋊C8D411yescharacteristic
58C11×C22⋊C8C2×C412yes—
59C4×C8×C11—21no—
60#66887—42no—
61#66887—42no—
62#66885—24no—
63#66879—22no—
64Dic11⋊C8—22no—
65Dic11⋊C8—22no—
66C8×Dic11—22no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69#66867—21no—
70C4×C11⋊C8—21no—
71#9274—111nomaximal, Sylow
72C23×D11—22no—
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11#4111yescharacteristic
76C2×D44—22no—
77C2×D44—22no—
78C2×D44—41no—
79C2×D44—41no—
80C2×D44—41no—
81C2×D44—41no—
82C2×D44—41no—
83C2×D44—41no—
84C2×D44—41no—
85C2×D44—41no—
86C2×D44—81no—
87C2×D44—81no—
88C2×D44—82no—
89C2×Dic22—21no—
90C2×Dic22C22⋊C412yes—
91C11×M16—41no—
92C11×M16—41no—
93C2×C8×C11—22no—
94C2×C8×C11—21no—
95C2×C8×C11—21no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11#4111yescharacteristic
103C22⋊Dic11—22no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107C4⋊Dic11C22⋊C412yes—
108Dic11⋊C4—22no—
109Dic11⋊C4—22no—
110C4×Dic11—22no—
111#4318—21no—
112#4318—21no—
113#4318—21no—
114#4318SD1612yescomplemented
115C2×C11⋊C8—21no—
116C2×C11⋊C8—21no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8—81no—
119#4314—84no—
120#3208—111no—
121#2962—111no—
122#1965—111no—
123#1550—111no—
124C2×#331—111no—
125#1301D1111yescharacteristic, complemented
126#1283—111no—
127C23×C11C4×D411yescharacteristic
128C22×D11—42no—
129C22×D11—42no—
130C22×D11—42no—
131C22×D11—82no—
132C22×D11—82no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—41no—
136C2×C4×C11C2×C22⋊C411yescharacteristic
137C2×C4×C11C4×D411yescharacteristic
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12311yescharacteristic
142C2×C4×C11C2×SD1611yescharacteristic
143C2×C4×C11#13511yescharacteristic
144C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C11#13711yescharacteristic
146C2×Dic11—22no—
147C2×Dic11—22no—
148D44—44no—
149D44—82no—
150D44—82no—
151D44—81no—
152D44—81no—
153D44—81no—
154D44—81no—
155D44—81no—
156D44—81no—
157Dic22—41no—
158Dic22—41no—
159Dic22—42no—
160C8×C11—42no—
161C8×C11—41no—
162C8×C11—41no—
163C8×C11—81no—
164C11⋊C8—22no—
165C11⋊C8—41no—
166C11⋊C8—81no—
167#533—111no—
168C2×#127—111no—
169#492—221no—
170#486—221no—
171#460—222no—
172#450—114no—
173#446—222no—
174#446—221no—
175C8×Q8—221no—
176#431C2×D1111yescharacteristic
177#424—221no—
178#423C2×D1111yescharacteristic
179C2×C4⋊C8—111no—
180C2×C4⋊C8C2×D1111yescharacteristic
181C2×#100—221no—
182C2×#100—221no—
183#405—221no—
184C4×M16—111no—
185#333—221no—
186#332—221no—
187#331—221no—
188#331—221no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11#38611yescharacteristic
192C22×C11C4×SD1611yescharacteristic
193C22×C11#44011yescharacteristic
194C2×D11—82no—
195C2×D11—82no—
196C2×D11—82no—
197C2×D11—162no—
198C2×D11—162no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11#44811yescharacteristic
203C4×C11#44911yescharacteristic
204C4×C11#46011yescharacteristic
205C4×C11#46411yescharacteristic
206C4×C11#47111yescharacteristic
207C4×C11#47211yescharacteristic
208Dic11—42no—
209Dic11—42no—
210C22×D4—112no—
211C22×D4—221no—
212C22×D4—221no—
213C2×SD16—224no—
214C2×M16—21no—
215C2×M16—111no—
216C2×M16—111no—
217C22×C8—21no—
218C22×C8—221no—
219C4⋊Q8—111no—
220C4⋊Q8—111no—
221#127—221no—
222#127—221no—
223#127—221no—
224#127—221no—
225#125—221no—
226C22⋊Q8—112no—
227C22⋊Q8—221no—
228C4×Q8—112no—
229C4×Q8—221no—
230#117—221no—
231C2×C42C22×D1111yescharacteristic
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—222no—
237C4⋊C8—222no—
238C4⋊C8—221no—
239C4⋊C8—221no—
240C4⋊C8D4411yescharacteristic
241C4⋊C8D4411yescharacteristic
242#102—224no—
243#100—442no—
244#100—442no—
245C22⋊C8C4×D1112yes—
246#97—222no—
247#97—221no—
248C4×C8—21no—
249C4×C8—222no—
250C4×C8—221no—
251C2×C11—21no—
252C2×C11—21no—
253C2×C11#188011yescharacteristic
254C2×C11#190711yescharacteristic
255C2×C11#191411yescharacteristic
256D11—162no—
257C24—222no—
258C2×Q8—112no—
259C2×Q8—221no—
260C2×D4—222no—
261C2×D4—222no—
262C2×D4—441no—
263C2×D4—441no—
264C2×D4—441no—
265C2×D4—441no—
266C2×D4—441no—
267C2×D4—441no—
268C2×D4—441no—
269C2×D4—441no—
270C2×D4—881no—
271C2×D4—881no—
272C2×D4—882no—
273C22×C4C2×C4×D1111yescharacteristic
274C22×C4D4×D1111yescharacteristic
275C22×C4#434311yescharacteristic
276SD16—884no—
277M16—41no—
278M16—41no—
279M16—112no—
280M16—221no—
281M16—221no—
282M16—221no—
283C2×C8—22no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—221no—
290C2×C8—221no—
291C2×C8—441no—
292C2×C8—881no—
293C4⋊C4—112no—
294C4⋊C4—222no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C4⋊C4—222no—
298C4⋊C4—221no—
299C22⋊C4—222no—
300C42—222no—
301C42C2×D4411yescharacteristic
302C42#433911yescharacteristic
303C42D4×D1111yescharacteristic
304C42D4×D1111yescharacteristic
305C11#927411yescharacteristic, complemented, Sylow
306C23—442no—
307C23—442no—
308C23—442no—
309C23—882no—
310C23—882no—
311C23#6694611yescharacteristic
312Q8—442no—
313Q8—441no—
314Q8—441no—
315D4—444no—
316D4—882no—
317D4—882no—
318D4—881no—
319D4—881no—
320D4—881no—
321D4—881no—
322D4—881no—
323D4—881no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—222no—
328C2×C4—222no—
329C2×C4C4×D4411yescharacteristic
330C2×C4C22⋊C4×D1111yescharacteristic
331C2×C4#6693511yescharacteristic
332C2×C4#6693711yescharacteristic
333C2×C4#6694711yescharacteristic
334C2×C4#6694811yescharacteristic
335C2×C4#6696411yescharacteristic
336C2×C4SD16×D1111yescharacteristic
337C2×C4#6696911yescharacteristic
338C2×C4#6697111yescharacteristic
339C8—42no—
340C8—41no—
341C8—41no—
342C8—81no—
343C8—222no—
344C8—441no—
345C8—881no—
346C22—21no—
347C22—21no—
348C22—882no—
349C22—882no—
350C22—882no—
351C22—1762no—
352C22—1762no—
353C22#1062227811yescharacteristic
354C22#1062246511yescharacteristic
355C22#1062250211yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—442no—
360C4—442no—
361C4#1062237511yescharacteristic
362C4#1062239411yescharacteristic
363C4#1062241111yescharacteristic
364C4#1062241911yescharacteristic
365C4#1062251011yescharacteristic
366C4#1062251111yescharacteristic
367C2—21no—
368C2—21no—
369C2—1762no—
370C2#1306897211yescharacteristic
371C2#1306912311yescharacteristic
372C2#1306916211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1301C2
socleC22×C11#386
prime radicalC2×#66927C22
cosocleC2×C42×C11C23
hypercenter#1301D11
hypocenterC11#9274
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
2. #13077559C2semidirect
4. #13067307C2semidirect
6. #13066465C2semidirect
7. C11×#1301C2semidirect
114. #4318SD16semidirect
125. #1301D11semidirect
305. C11#9274semidirect

Maximal subgroups

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

subgroupindex
#130795592
#130775592
#130694552
#130673072
C2×#106221232
#130664652
C11×#13012
#927411