Finite Group Databasebeta

← #14720159

Subgroups — #14720159

Order 2816.

1206 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#67043C211yesmaximal, characteristic
2#41×C11⋊C8C211yesmaximal, characteristic, complemented
3#13067010C213yesmaximal, complemented
4#13067001C213yesmaximal, complemented
5#13066996C213yesmaximal, complemented
6C2×#10622122C213yesmaximal, complemented
7C11×#2988C211yesmaximal, characteristic, complemented
8C2×#67043C411yescharacteristic
9C4×C11×#41C2211yescharacteristic
10#10623358C411yescharacteristic
11#10623103—21no—
12C4×Q8×D11—21no—
13#10623077—23no—
14C4×#4341—23no—
15#10623054C413yes—
16#10623047C413yes—
17C4×#4339C2213yes—
18C2×C4×Dic22C2213yes—
19C8×Q8×C11—21no—
20C8×D4×C11—23no—
21C11×#431C2213yes—
22C2×C11×C4⋊C8C2213yes—
23Q8×C11⋊C8—21no—
24D4×C11⋊C8—23no—
25#10622538C2213yes—
26C2×C4×C11⋊C8C2213yes—
27#10622122C2213yes—
28#10622122C2216yes—
29#10622122C2213yes—
30#10622121C2211yescharacteristic
31#10622121C2213yes—
32C2×C11×#41C2×C411yescharacteristic
33#67043—24no—
34#67043C818yescomplemented
35C2×Q8×D11—21no—
36C2×#4341—23no—
37C2×#4339C2×C413yes—
38C22×Dic22C2×C413yes—
39C22×C8×C11—23no—
40C4×Q8×C11D411yescharacteristic
41C4×Q8×C11D411yescharacteristic
42C4×D4×C11D413yes—
43C4×D4×C11D413yes—
44C11×#117C2×C413yes—
45C2×C42×C11C2313yes—
46Q8×Dic11—21no—
47D4×Dic11—23no—
48C4×C22⋊D11—23no—
49C4×C22⋊D11—23no—
50#66979C2×C413yes—
51C2×C4⋊Dic11C2×C413yes—
52C2×Dic11⋊C4—23no—
53C2×C4×Dic11—23no—
54C22×C11⋊C8—23no—
55#66945—23no—
56C4⋊C4×D11—23no—
57#66940—23no—
58#66940—23no—
59(C22⋊D11)⋊C4—26no—
60#66930—26no—
61C4×D44C2×C413yes—
62C4×D44C2311yescharacteristic
63#66925—23no—
64C42×D11—23no—
65C4×Dic22—23no—
66C4×Dic22—23no—
67C4×Dic22C2×C416yes—
68C4×Dic22C2×C413yes—
69C4×Dic22C2313yes—
70C11×C4⋊C8—23no—
71C11×C4⋊C8C2313yes—
72C11×C4⋊C8C2311yescharacteristic
73C11×C22⋊C8—23no—
74C4×C8×C11—23no—
75C22⋊(C11⋊C8)—23no—
76C4⋊(C11⋊C8)—23no—
77C4×C11⋊C8—23no—
78C4×C11⋊C8C2311yescharacteristic
79C4×C11⋊C8C2313yes—
80#17439—111nomaximal, Sylow
81C11×#41C2×C814yes—
82C11×#41M1614yes—
83C2×Q8×C11C22⋊C411yescharacteristic
84C2×D4×C11C22⋊C413yes—
85C22×C4×C11C22×C413yes—
86C22×C4×C11C2×D413yes—
87C22×C4×C11C2×D413yes—
88C2×C22⋊D11—23no—
89C22×Dic11—23no—
90C22×Dic11—23no—
91Q8×D11—28no—
92#4341—224no—
93#4339—26no—
94#4339C2×C8112yescomplemented
95C2×D44C22×C411yescharacteristic
96C2×C4×D11—23no—
97C2×C4×D11—23no—
98C2×C4×D11—21no—
99C2×Dic22—23no—
100C2×Dic22—26no—
101C2×Dic22C2×C8112yescomplemented
102C2×Dic22C22×C413yes—
103C2×C8×C11—21no—
104C2×C8×C11—23no—
105C2×C8×C11—83no—
106C11×C4⋊C4C22⋊C413yes—
107C11×C4⋊C4C22⋊C413yes—
108C11×C22⋊C4C22⋊C416yes—
109C42×C11C22×C413yes—
110C42×C11C2×D413yes—
111C42×C11C2×D413yes—
112C42×C11C2411yescharacteristic
113C22⋊Dic11—23no—
114(C2×D11)⋊C4—23no—
115(C2×D11)⋊C4—21no—
116C4⋊Dic11—23no—
117C4⋊Dic11C22×C411yescharacteristic
118C4⋊Dic11C22×C413yes—
119Dic11⋊C4—26no—
120Dic11⋊C4—23no—
121Dic11⋊C4—23no—
122C4×Dic11—26no—
123C4×Dic11—23no—
124C4×Dic11—23no—
125C4×Dic11—23no—
126C2×C11⋊C8—21no—
127C2×C11⋊C8—23no—
128C2×C11⋊C8—46no—
129C4×2−1+4—111no—
130#2988D1111yescharacteristic, complemented
131C8×#41—111no—
132#1479—113no—
133#1477—113no—
134#1476—113no—
135C2×Q8⋊C8—113no—
136C23×C11C2×C22⋊C413yes—
137C22×D11—21no—
138Q8×C11C22⋊C814yes—
139D4×C11C22⋊C8112yes—
140C2×C4×C11—23no—
141C2×C4×C11—23no—
142C2×C4×C11—43no—
143C2×C4×C11C2×C22⋊C413yes—
144C2×C4×C11C2×C22⋊C413yes—
145C2×C4×C11C2×C22⋊C413yes—
146C2×C4×C11C22×C816yes—
147C2×C4×C11C2×M1616yes—
148C2×C4×C11C23×C411yescharacteristic
149C2×C4×C11C22×D411yescharacteristic
150C2×C4×C11C22×D411yescharacteristic
151C22⋊D11—212no—
152C2×Dic11—23no—
153C2×Dic11—212no—
154C2×Dic11—21no—
155C2×Dic11—23no—
156C2×Dic11—83no—
157D44—21no—
158D44C22×C812yes—
159C4×D11—212no—
160C4×D11—41no—
161C4×D11—41no—
162C4×D11—83no—
163Dic22—23no—
164Dic22—212no—
165Dic22C22×C816yes—
166C8×C11—43no—
167C8×C11—41no—
168C11⋊C8—22no—
169C11⋊C8—43no—
170C2×2−1+4—111no—
171#520—111no—
172#520—113no—
173#520—223no—
174#519—113no—
175#519—221no—
176C4×#41—113no—
177C4×#41—223no—
178C4×#41C2×D1111yescharacteristic
179C2×C4×Q8—113no—
180C2×C4×Q8—221no—
181C8×Q8—21no—
182C8×Q8—221no—
183C8×D4—23no—
184C8×D4—223no—
185#431—113no—
186#431C2×D1113yes—
187C2×C4⋊C8C2×D1113yes—
188C2×C4×C8—113no—
189Q8⋊C8—113no—
190Q8⋊C8—116no—
191Q8⋊C8—113no—
192D4⋊C8—111no—
193D4⋊C8—113no—
194C22×C11—23no—
195C22×C11—23no—
196C22×C11C2×C22⋊C816yes—
197C22×C11C22×C22⋊C411yescharacteristic
198C2×D11—22no—
199C2×D11—41no—
200C2×D11—41no—
201C4×C11—23no—
202C4×C11—21no—
203C4×C11—23no—
204C4×C11C2×C22⋊C816yes—
205C4×C11C23×C811yescharacteristic
206C4×C11C22×M1611yescharacteristic
207C4×C11#57711yescharacteristic
208C4×C11#57811yescharacteristic
209Dic11—26no—
210Dic11—41no—
211Dic11—43no—
2122−1+4—118no—
2132−1+4—224no—
214C2×#41—113no—
215C2×#41—223no—
216C2×#41C4×D1111yescharacteristic
217C22×Q8—113no—
218C22×Q8—221no—
219C22×C8—23no—
220C22×C8—223no—
221C4×Q8—116no—
222C4×Q8—113no—
223C4×Q8—113no—
224C4×Q8—221no—
225C4×Q8—223no—
226C4×Q8—223no—
227C4×Q8—223no—
228C4×Q8—223no—
229C4×Q8D4411yescharacteristic
230C4×Q8C22⋊D1111yescharacteristic
231C4×D4—113no—
232C4×D4—111no—
233C4×D4—223no—
234C4×D4—223no—
235C4×D4—223no—
236C4×D4—226no—
237C4×D4D4413yes—
238C4×D4C22⋊D1113yes—
239#117—113no—
240#117—223no—
241#117—226no—
242#117—223no—
243#117C4×D1113yes—
244C2×C4⋊C4—113no—
245C2×C4⋊C4—223no—
246C2×C4⋊C4—223no—
247C2×C42—223no—
248C2×C42—223no—
249C2×C42C22×D1113yes—
250C4⋊C8—23no—
251C4⋊C8—223no—
252C4⋊C8C22×D1113yes—
253C4⋊C8C22×D1111yescharacteristic
254C22⋊C8—23no—
255C22⋊C8—223no—
256C4×C8—23no—
257C4×C8—111no—
258C4×C8—113no—
259C4×C8—223no—
260C2×C11—26no—
261C2×C11C22×C22⋊C811yescharacteristic
262C2×C11#289811yescharacteristic
263C2×C11#290111yescharacteristic
264D11—42no—
265#41—1112no—
266#41—2224no—
267#41—226no—
268#41C8×D1114yes—
269#41#431314yes—
270C2×Q8—1112no—
271C2×Q8—113no—
272C2×Q8—228no—
273C2×Q8—226no—
274C2×Q8—223no—
275C2×Q8(C2×D11)⋊C411yescharacteristic
276C2×D4—111no—
277C2×D4—223no—
278C2×D4(C2×D11)⋊C413yes—
279C22×C4—223no—
280C22×C4—223no—
281C22×C4—223no—
282C22×C4—221no—
283C22×C4—223no—
284C22×C4C2×C4×D1113yes—
285C22×C4C2×D4413yes—
286C22×C4C2×C22⋊D1113yes—
287C2×C8—21no—
288C2×C8—23no—
289C2×C8—83no—
290C2×C8—221no—
291C2×C8—223no—
292C2×C8—446no—
293C4⋊C4—113no—
294C4⋊C4—111no—
295C4⋊C4—223no—
296C4⋊C4—226no—
297C4⋊C4—223no—
298C4⋊C4—223no—
299C4⋊C4(C2×D11)⋊C413yes—
300C4⋊C4(C2×D11)⋊C413yes—
301C22⋊C4—223no—
302C22⋊C4—223no—
303C22⋊C4—221no—
304C22⋊C4(C2×D11)⋊C416yes—
305C42—223no—
306C42—223no—
307C42—226no—
308C42—223no—
309C42C2×C4×D1113yes—
310C42C2×D4413yes—
311C42C2×C22⋊D1113yes—
312C42C23×D1111yescharacteristic
313C11#1743911yescharacteristic, complemented, Sylow
314C23—221no—
315C23C2×(C2×D11)⋊C413yes—
316Q8—116no—
317Q8—2212no—
318Q8—223no—
319Q8(C2×D11)⋊C814yes—
320D4—112no—
321D4—2212no—
322D4—221no—
323D4(C2×D11)⋊C8112yes—
324C2×C4—23no—
325C2×C4—23no—
326C2×C4—43no—
327C2×C4—2212no—
328C2×C4—223no—
329C2×C4—2212no—
330C2×C4—221no—
331C2×C4—223no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—883no—
335C2×C4—883no—
336C2×C4C2×C8×D1116yes—
337C2×C4C2×#431316yes—
338C2×C4C2×(C2×D11)⋊C413yes—
339C2×C4C2×(C2×D11)⋊C413yes—
340C2×C4C2×(C2×D11)⋊C413yes—
341C2×C4C22×C4×D1111yescharacteristic
342C2×C4C22×D4411yescharacteristic
343C2×C4C22×C22⋊D1111yescharacteristic
344C8—43no—
345C8—41no—
346C8—222no—
347C8—443no—
348C22—23no—
349C22—23no—
350C22—222no—
351C22—441no—
352C22—441no—
353C22C2×(C2×D11)⋊C816yes—
354C22C22×(C2×D11)⋊C411yescharacteristic
355C4—23no—
356C4—21no—
357C4—23no—
358C4—226no—
359C4—441no—
360C4—443no—
361C4C2×(C2×D11)⋊C816yes—
362C4C22×C8×D1111yescharacteristic
363C4C22×#431311yescharacteristic
364C4#1062336711yescharacteristic
365C4#1062336911yescharacteristic
366C2—26no—
367C2—442no—
368C2C22×(C2×D11)⋊C811yescharacteristic
369C2#1307714611yescharacteristic
370C2#1307716111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC4×C11C23×C8
FrattiniC42C23×D11
FittingC11×#2988C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#67043C4
cosocleC42×C11C24
hypercenter#2988D11
hypocenterC11#17439
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2988

Complements

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

NH ≅ G/Ntype
2. #41×C11⋊C8C2semidirect
3. #13067010C2semidirect
4. #13067001C2semidirect
5. #13066996C2semidirect
6. C2×#10622122C2semidirect
7. C11×#2988C2semidirect
34. #67043C8semidirect
94. #4339C2×C8semidirect
101. C2×Dic22C2×C8semidirect
130. #2988D11semidirect
313. C11#17439semidirect

Maximal subgroups

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

subgroupindex
C4×#670432
#41×C11⋊C82
#130670102
#130670012
#130669962
C2×#106221222
C11×#29882
#1743911