Finite Group Databasebeta

← #14725783

Subgroups — #14725783

Order 2816.

606 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079186C211yesmaximal, characteristic
2#13077772C212yesmaximal, complemented
3#13067505C212yesmaximal, complemented
4#13067486C212yesmaximal, complemented
5#13067479C212yesmaximal, complemented
6#13067415C212yesmaximal, complemented
7#13067027C212yesmaximal, complemented
8C8×#4318C211yesmaximal, characteristic, complemented
9C2×C11×#334C211yesmaximal, characteristic, complemented
10#10623010C2212yes—
11C2×C11×C4⋊C8C2212yes—
12C2×C4×C8×C11C2211yescharacteristic
13#10622729C411yescharacteristic
14#10622728C411yescharacteristic
15#10622727C412yes—
16#10622724—22no—
17C8×C22⋊D11—22no—
18#10622538C2211yescharacteristic
19C4×#4318C2211yescharacteristic
20#10622453—22no—
21#10622452—22no—
22#10622451C2212yes—
23#10622447C2212yes—
24#10622444C2212yes—
25#10622443C2212yes—
26C4×Dic44C2211yescharacteristic
27#10622310C412yes—
28#10622309C411yescharacteristic
29C4×D88C2211yescharacteristic
30C4×#4314C2212yes—
31#10622296C411yescharacteristic
32C11×#334C2211yescharacteristic
33C11×#334C2212yes—
34C11×#334C2211yescharacteristic
35#10622122C2212yes—
36#10622122C2212yes—
37#10622121C2212yes—
38#10622121C2212yes—
39#10622092C2212yes—
40C8×C11⋊C8C2212yes—
41C22×C8×C11—22no—
42C22×C8×C11C2×C411yescharacteristic
43C22×C8×C11C2×C411yescharacteristic
44C2×C42×C11C2311yescharacteristic
45#66983C2×C412yes—
46#66982—22no—
47C4×C22⋊D11—22no—
48#66977C2×C412yes—
49C2×#4318—21no—
50C2×Dic44C2×C411yescharacteristic
51C2×D88C2×C411yescharacteristic
52C2×#4314C2×C412yes—
53C2×#4313—22no—
54C2×C8×D11—22no—
55#66929—22no—
56#66928C2×C412yes—
57C4×D44C2312yes—
58#66925—22no—
59#66923C2×C412yes—
60C4×Dic22C2312yes—
61C11×C4⋊C8—22no—
62C11×C4⋊C8C2312yes—
63C11×C4⋊C8C2312yes—
64C4×C8×C11C2×C411yescharacteristic
65C4×C8×C11C2×C411yescharacteristic
66C4×C8×C11C2311yescharacteristic
67C4×C8×C11C2311yescharacteristic
68C22⋊(C11⋊C8)D411yescharacteristic
69C22⋊(C11⋊C8)D411yescharacteristic
70#66885C2×C412yes—
71#66885C2×C412yes—
72(C2×D11)⋊C8—22no—
73(C2×D11)⋊C8—22no—
74#66882C2×C411yescharacteristic
75#66882C2×C411yescharacteristic
76#66881C2×C412yes—
77#66880C2×C412yes—
78#66880C2×C412yes—
79#66879—22no—
80Dic11⋊C8—22no—
81Dic11⋊C8—22no—
82C8×Dic11—22no—
83C4⋊(C11⋊C8)D412yes—
84#66867—21no—
85C4×C11⋊C8C2312yes—
86C4×C11⋊C8C2312yes—
87#18088—111nomaximal, Sylow
88C22×C4×C11C22×C411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C2×C22⋊D11—22no—
92C2×D44C22×C412yes—
93C2×C4×D11—22no—
94C2×Dic22C22×C412yes—
95C2×C8×C11—22no—
96C2×C8×C11—22no—
97C2×C8×C11—22no—
98C2×C8×C11—41no—
99C2×C8×C11—82no—
100C2×C8×C11C22×C411yescharacteristic
101C2×C8×C11C22×C411yescharacteristic
102C2×C8×C11C22×C411yescharacteristic
103C2×C8×C11C22×C411yescharacteristic
104C42×C11C22×C411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11#4111yescharacteristic
107C42×C11C2411yescharacteristic
108C22⋊Dic11—22no—
109(C2×D11)⋊C4—22no—
110(C2×D11)⋊C4—22no—
111(C2×D11)⋊C4—22no—
112(C2×D11)⋊C4—22no—
113C4⋊Dic11C22×C412yes—
114C4⋊Dic11C22×C412yes—
115Dic11⋊C4—22no—
116Dic11⋊C4—22no—
117Dic11⋊C4—22no—
118Dic11⋊C4—22no—
119C4×Dic11—22no—
120#4318—24no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8C2×D412yes—
123C2×C11⋊C8C2×D412yes—
124Dic44—41no—
125D88—41no—
126#4314—24no—
127#4313—82no—
128C8×D11—82no—
129#3168—111no—
130#2994—112no—
131#1590—112no—
132#1587—112no—
133#1586—112no—
134C8×SD16—112no—
135C2×#334D1111yescharacteristic, complemented
136#1483—112no—
137C8×M16—111no—
138C23×C11C4×D411yescharacteristic
139C22×D11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—22no—
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11C4×D411yescharacteristic
146C2×C4×C11C4×D411yescharacteristic
147C2×C4×C11C23×C411yescharacteristic
148C2×C4×C11C22×D411yescharacteristic
149C2×C4×C11C2×#4111yescharacteristic
150C22⋊D11—44no—
151C2×Dic11—22no—
152C2×Dic11—22no—
153C2×Dic11—22no—
154D44—22no—
155D44—22no—
156C4×D11—42no—
157C4×D11—42no—
158Dic22—22no—
159Dic22—22no—
160C8×C11—21no—
161C8×C11—21no—
162C8×C11—21no—
163C8×C11—42no—
164C8×C11—42no—
165C8×C11#13112yes—
166C11⋊C8—24no—
167C11⋊C8—22no—
168C11⋊C8—22no—
169#529—112no—
170#499—111no—
171#495—111no—
172#488—112no—
173#467—111no—
174#466—111no—
175#465—112no—
176#446—112no—
177C8×Q8—112no—
178C4×Q16—111no—
179C4×SD16—112no—
180C4×D8—111no—
181#436—112no—
182#435—222no—
183C8×D4—112no—
184C8×D4—222no—
185#433—222no—
186#431—111no—
187#424—222no—
188C2×C4⋊C8C2×D1112yes—
189C4×M16—111no—
190C2×C4×C8C2×D1111yescharacteristic
191#334C2×D1111yescharacteristic
192#334C2×D1112yes—
193#334C2×D1111yescharacteristic
194Q8⋊C8—112no—
195Q8⋊C8—112no—
196D4⋊C8—112no—
197D4⋊C8—112no—
198#322—112no—
199C82—112no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11#44312yes—
203C22×C11C2×C4×D411yescharacteristic
204C2×D11—42no—
205C2×D11—42no—
206C2×D11—42no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11C2×#13111yescharacteristic
212C4×C11#56811yescharacteristic
213C4×C11#57712yes—
214Dic11—42no—
215Dic11—42no—
216Dic11—42no—
217C2×Q16—111no—
218C2×SD16—112no—
219C2×D8—111no—
220C2×M16—222no—
221C2×M16—221no—
222C22×C8—22no—
223C22×C8—222no—
224C22×C8C4×D1111yescharacteristic
225C22×C8C4×D1111yescharacteristic
226#126—222no—
227#125—112no—
228#124—112no—
229#123—222no—
230C22⋊Q8—112no—
231#121—112no—
232C4×Q8—112no—
233C4×D4—112no—
234C4×D4—222no—
235#117—222no—
236C2×C42C22×D1111yescharacteristic
237#107—111no—
238#107—111no—
239#106—112no—
240C4⋊C8—22no—
241C4⋊C8—112no—
242C4⋊C8—222no—
243C4⋊C8—222no—
244C4⋊C8C22×D1112yes—
245C4⋊C8C22×D1112yes—
246#103—112no—
247#103—112no—
248#102—112no—
249#102—112no—
250C22⋊C8—111no—
251C22⋊C8—111no—
252C22⋊C8—222no—
253C22⋊C8—222no—
254#97—222no—
255#97—221no—
256C4×C8—112no—
257C4×C8—112no—
258C4×C8—222no—
259C4×C8C4×D1111yescharacteristic
260C4×C8C4×D1111yescharacteristic
261C4×C8C22×D1111yescharacteristic
262C4×C8C22×D1111yescharacteristic
263C2×C11—22no—
264C2×C11#293511yescharacteristic
265C2×C11#295211yescharacteristic
266C2×C11C2×#44311yescharacteristic
267D11—82no—
268C2×Q8—112no—
269C2×D4—112no—
270C2×D4—222no—
271C22×C4—222no—
272C22×C4C2×C4×D1111yescharacteristic
273C22×C4D4×D1111yescharacteristic
274C22×C4#434311yescharacteristic
275Q16—441no—
276SD16—224no—
277D8—441no—
278M16—224no—
279M16—882no—
280C2×C8—22no—
281C2×C8—22no—
282C2×C8—22no—
283C2×C8—41no—
284C2×C8—82no—
285C2×C8—112no—
286C2×C8—112no—
287C2×C8—222no—
288C2×C8—882no—
289C2×C8C2×C4×D1111yescharacteristic
290C2×C8C2×C4×D1111yescharacteristic
291C2×C8C2×C4×D1111yescharacteristic
292C2×C8C2×C4×D1111yescharacteristic
293C4⋊C4—112no—
294C4⋊C4—112no—
295C4⋊C4—222no—
296C4⋊C4—222no—
297C4⋊C4—222no—
298C4⋊C4—222no—
299C22⋊C4—222no—
300C22⋊C4—222no—
301C22⋊C4—222no—
302C22⋊C4—222no—
303C22⋊C4—222no—
304C42—222no—
305C42C2×C4×D1111yescharacteristic
306C42D4×D1111yescharacteristic
307C42#434311yescharacteristic
308C42C23×D1111yescharacteristic
309C11#1808811yescharacteristic, complemented, Sylow
310C23—222no—
311C23#6694611yescharacteristic
312Q8—222no—
313Q8—222no—
314D4—222no—
315D4—222no—
316D4—444no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—222no—
322C2×C4—222no—
323C2×C4—222no—
324C2×C4—442no—
325C2×C4—442no—
326C2×C4#6694611yescharacteristic
327C2×C4#6694611yescharacteristic
328C2×C4#6694611yescharacteristic
329C2×C4C22×C4×D1111yescharacteristic
330C2×C4C2×D4×D1111yescharacteristic
331C2×C4C2×#434311yescharacteristic
332C8—21no—
333C8—21no—
334C8—21no—
335C8—42no—
336C8—42no—
337C8—224no—
338C8—222no—
339C8—222no—
340C8#6695412yes—
341C22—21no—
342C22—21no—
343C22—442no—
344C22—442no—
345C22—442no—
346C22#1062250812yes—
347C22C2×#6694611yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—442no—
353C4—442no—
354C4—442no—
355C4C2×#6695411yescharacteristic
356C4#1062327611yescharacteristic
357C4#1062329312yes—
358C2—22no—
359C2—882no—
360C2#1307735911yescharacteristic
361C2#1307749911yescharacteristic
362C2C2×#1062250811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC2×C11×#334C2
socleC22×C11C2×C4×D4
prime radical#10622728C4
cosocleC42×C11C24
hypercenterC2×#334D11
hypocenterC11#18088
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
2. #13077772C2semidirect
3. #13067505C2semidirect
4. #13067486C2semidirect
5. #13067479C2semidirect
6. #13067415C2semidirect
7. #13067027C2semidirect
8. C8×#4318C2semidirect
9. C2×C11×#334C2semidirect
135. C2×#334D11semidirect
309. C11#18088semidirect

Maximal subgroups

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

subgroupindex
#130791862
#130777722
#130675052
#130674862
#130674792
#130674152
#130670272
C8×#43182
C2×C11×#3342
#1808811