Finite Group Databasebeta

← #14724464

Subgroups — #14724464

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079186C211yesmaximal, characteristic
2#13077767C212yesmaximal, complemented
3#13067520C212yesmaximal, complemented
4#13067514C211yesmaximal, characteristic, complemented
5#13067502C211yesmaximal, characteristic, complemented
6#13067430C212yesmaximal, complemented
7C8×Dic44C211yesmaximal, characteristic, complemented
8C8×D88C211yesmaximal, characteristic, complemented
9#13067375C211yesmaximal, characteristic, complemented
10#13067082C212yesmaximal, complemented
11C11×#1450C211yesmaximal, characteristic, complemented
12#10623010C2212yes—
13C11×#431C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C2×C4×C8×C11C2211yescharacteristic
16#10622729C411yescharacteristic
17#10622728C411yescharacteristic
18#10622727C412yes—
19#10622537C2212yes—
20#10622453—22no—
21#10622452—22no—
22#10622342—22no—
23#10622341—22no—
24C4×Dic44C2211yescharacteristic
25#10622310C412yes—
26#10622309C411yescharacteristic
27C4×D88C2211yescharacteristic
28C4×#4314C2212yes—
29#10622301C2212yes—
30C8×D44C2212yes—
31#10622296C411yescharacteristic
32#10622292C2212yes—
33C8×Dic22C2212yes—
34C11×#322C2211yescharacteristic
35C11×#322C2211yescharacteristic
36C82×C11C2211yescharacteristic
37C82×C11C2211yescharacteristic
38#10622097C2212yes—
39#10622097C2212yes—
40#10622096C2212yes—
41#10622096C2211yescharacteristic
42#10622096C2211yescharacteristic
43#10622094C2212yes—
44#10622094C2212yes—
45C22×C8×C11C2×C411yescharacteristic
46C22×C8×C11C2×C411yescharacteristic
47C2×C42×C11C2311yescharacteristic
48#66983C2×C412yes—
49#66982—22no—
50C4×C22⋊D11—22no—
51#66977C2×C412yes—
52C2×#4318—22no—
53C2×Dic44C2×C411yescharacteristic
54C2×D88C2×C411yescharacteristic
55C2×#4314C2×C412yes—
56C2×#4313—22no—
57C2×C8×D11—22no—
58#66929—22no—
59#66928C2×C412yes—
60C4×D44C2312yes—
61#66925—22no—
62#66923C2×C412yes—
63C4×Dic22C2312yes—
64C11×C4⋊C8—21no—
65C11×C4⋊C8D411yescharacteristic
66C11×C4⋊C8D411yescharacteristic
67C11×C22⋊C8—21no—
68C11×C22⋊C8D411yescharacteristic
69C11×C22⋊C8D411yescharacteristic
70C4×C8×C11C2×C411yescharacteristic
71C4×C8×C11C2×C411yescharacteristic
72C4×C8×C11C2311yescharacteristic
73C4×C8×C11C2311yescharacteristic
74C4×C8×C11C2311yescharacteristic
75C4×C8×C11C2311yescharacteristic
76C4×C8×C11C2311yescharacteristic
77C4×C8×C11C2311yescharacteristic
78#66885C2×C412yes—
79#66885C2×C412yes—
80(C2×D11)⋊C8—22no—
81(C2×D11)⋊C8—22no—
82#66882C2×C411yescharacteristic
83#66882C2×C411yescharacteristic
84#66881C2×C412yes—
85#66880C2×C412yes—
86#66880C2×C412yes—
87#66879—22no—
88Dic11⋊C8—22no—
89Dic11⋊C8—22no—
90C8×Dic11—22no—
91C4⋊(C11⋊C8)—22no—
92C4⋊(C11⋊C8)C2312yes—
93C4⋊(C11⋊C8)C2312yes—
94#17973—111nomaximal, Sylow
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C2×C22⋊D11—22no—
99C2×D44C22×C412yes—
100C2×C4×D11—22no—
101C2×Dic22C22×C412yes—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—21no—
105C2×C8×C11—21no—
106C2×C8×C11C22×C411yescharacteristic
107C2×C8×C11C22×C411yescharacteristic
108C2×C8×C11C22×C411yescharacteristic
109C2×C8×C11C22×C411yescharacteristic
110C2×C8×C11C2×D411yescharacteristic
111C2×C8×C11C2×D411yescharacteristic
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11C2×D411yescharacteristic
114C42×C11C22×C411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11#4111yescharacteristic
117C42×C11C2411yescharacteristic
118C22⋊Dic11—22no—
119(C2×D11)⋊C4—22no—
120(C2×D11)⋊C4—22no—
121(C2×D11)⋊C4—22no—
122(C2×D11)⋊C4—22no—
123C4⋊Dic11C22×C412yes—
124C4⋊Dic11C22×C412yes—
125Dic11⋊C4—22no—
126Dic11⋊C4—22no—
127Dic11⋊C4—22no—
128Dic11⋊C4—22no—
129C4×Dic11—22no—
130#4318—82no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133Dic44—22no—
134D88—22no—
135#4314—24no—
136#4313—82no—
137C8×D11—82no—
138#3168—111no—
139#2993—112no—
140#1592—112no—
141#1591—111no—
142#1589—111no—
143SD16⋊C8—112no—
144C8×Q16—111no—
145C8×D8—111no—
146#1567—111no—
147#1495—112no—
148#1450D1111yescharacteristic, complemented
149C23×C11C4×D411yescharacteristic
150C22×D11—22no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—41no—
156C2×C4×C11C4×D411yescharacteristic
157C2×C4×C11C4×D411yescharacteristic
158C2×C4×C11C4×D411yescharacteristic
159C2×C4×C11C23×C411yescharacteristic
160C2×C4×C11C22×D411yescharacteristic
161C2×C4×C11C2×#4111yescharacteristic
162C22⋊D11—82no—
163C2×Dic11—22no—
164C2×Dic11—22no—
165C2×Dic11—22no—
166D44—22no—
167D44—22no—
168C4×D11—42no—
169C4×D11—42no—
170Dic22—22no—
171Dic22—22no—
172C8×C11—21no—
173C8×C11—21no—
174C8×C11—21no—
175C8×C11—21no—
176C8×C11—21no—
177C8×C11—21no—
178C8×C11—41no—
179C8×C11—41no—
180C8×C11#13112yes—
181C8×C11#13112yes—
182C11⋊C8—42no—
183C11⋊C8—42no—
184#529—112no—
185#499—111no—
186#495—111no—
187#488—112no—
188#467—111no—
189#466—111no—
190#465—112no—
191#446—112no—
192C8×Q8—112no—
193C4×Q16—111no—
194C4×SD16—112no—
195C4×D8—111no—
196#436—112no—
197#436—222no—
198#435—222no—
199C8×D4—112no—
200#433—222no—
201#431C2×D1111yescharacteristic
202#431C2×D1111yescharacteristic
203#424—222no—
204#423—112no—
205C2×C4×C8C2×D1111yescharacteristic
206#335—111no—
207#335—111no—
208#335—112no—
209Q8⋊C8—112no—
210Q8⋊C8—112no—
211D4⋊C8—112no—
212D4⋊C8—112no—
213#322C2×D1111yescharacteristic
214#322C2×D1111yescharacteristic
215C82C2×D1111yescharacteristic
216C82C2×D1111yescharacteristic
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11C2×C4×D411yescharacteristic
221C2×D11—42no—
222C2×D11—42no—
223C2×D11—42no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11C2×#13111yescharacteristic
229C4×C11C2×#13111yescharacteristic
230C4×C11#57611yescharacteristic
231C4×C11#57811yescharacteristic
232Dic11—42no—
233Dic11—42no—
234Dic11—42no—
235C2×Q16—111no—
236C2×SD16—112no—
237C2×D8—111no—
238C2×M16—222no—
239C2×M16—222no—
240C22×C8—222no—
241C22×C8C4×D1111yescharacteristic
242C22×C8C4×D1111yescharacteristic
243#126—222no—
244#125—112no—
245#124—112no—
246#123—222no—
247C22⋊Q8—112no—
248#121—112no—
249C4×Q8—112no—
250C4×D4—112no—
251C4×D4—222no—
252#117—222no—
253C2×C42C22×D1111yescharacteristic
254#107—111no—
255#107—111no—
256#106—112no—
257C4⋊C8—21no—
258C4⋊C8—112no—
259C4⋊C8—112no—
260C4⋊C8—222no—
261C4⋊C8—222no—
262C4⋊C8—222no—
263C4⋊C8D4411yescharacteristic
264C4⋊C8D4411yescharacteristic
265#103—112no—
266#103—112no—
267#102—112no—
268#102—112no—
269C22⋊C8—21no—
270C22⋊C8—222no—
271C22⋊C8—222no—
272C22⋊C8D4411yescharacteristic
273C22⋊C8D4411yescharacteristic
274#97—222no—
275C4×C8—222no—
276C4×C8C4×D1111yescharacteristic
277C4×C8C4×D1111yescharacteristic
278C4×C8C22×D1111yescharacteristic
279C4×C8C22×D1111yescharacteristic
280C4×C8C22×D1111yescharacteristic
281C4×C8C22×D1111yescharacteristic
282C4×C8C22×D1111yescharacteristic
283C4×C8C22×D1111yescharacteristic
284C2×C11—41no—
285C2×C11#293111yescharacteristic
286C2×C11#295111yescharacteristic
287C2×C11#295711yescharacteristic
288D11—82no—
289C2×Q8—112no—
290C2×D4—112no—
291C2×D4—222no—
292C22×C4—222no—
293C22×C4C2×C4×D1111yescharacteristic
294C22×C4C2×D4411yescharacteristic
295C22×C4#433911yescharacteristic
296Q16—222no—
297SD16—224no—
298D8—222no—
299M16—882no—
300M16—882no—
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—222no—
306C2×C8—222no—
307C2×C8—882no—
308C2×C8C2×C4×D1111yescharacteristic
309C2×C8C2×C4×D1111yescharacteristic
310C2×C8C2×C4×D1111yescharacteristic
311C2×C8C2×C4×D1111yescharacteristic
312C2×C8C2×D4411yescharacteristic
313C2×C8C2×D4411yescharacteristic
314C2×C8C2×D4411yescharacteristic
315C2×C8C2×D4411yescharacteristic
316C4⋊C4—112no—
317C4⋊C4—112no—
318C4⋊C4—222no—
319C4⋊C4—222no—
320C4⋊C4—222no—
321C4⋊C4—222no—
322C22⋊C4—222no—
323C22⋊C4—222no—
324C22⋊C4—222no—
325C22⋊C4—222no—
326C22⋊C4—222no—
327C42—222no—
328C42C2×C4×D1111yescharacteristic
329C42C2×D4411yescharacteristic
330C42#433911yescharacteristic
331C42C23×D1111yescharacteristic
332C11#1797311yescharacteristic, complemented, Sylow
333C23—222no—
334C23C4×D4411yescharacteristic
335Q8—222no—
336Q8—222no—
337D4—222no—
338D4—222no—
339D4—882no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—222no—
346C2×C4—222no—
347C2×C4—222no—
348C2×C4—442no—
349C2×C4—442no—
350C2×C4C4×D4411yescharacteristic
351C2×C4C4×D4411yescharacteristic
352C2×C4C4×D4411yescharacteristic
353C2×C4C22×C4×D1111yescharacteristic
354C2×C4C22×D4411yescharacteristic
355C2×C4C2×#433911yescharacteristic
356C8—21no—
357C8—21no—
358C8—21no—
359C8—21no—
360C8—21no—
361C8—21no—
362C8—41no—
363C8—41no—
364C8—442no—
365C8—442no—
366C8#6695412yes—
367C8#6695412yes—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—442no—
372C22—442no—
373C22—442no—
374C22C2×C4×D4411yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—442no—
380C4—442no—
381C4—442no—
382C4C2×#6695411yescharacteristic
383C4C2×#6695411yescharacteristic
384C4#1062328311yescharacteristic
385C4#1062328411yescharacteristic
386C2—41no—
387C2—882no—
388C2#1307732911yescharacteristic
389C2#1307749311yescharacteristic
390C2#1307753411yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1450C2
socleC22×C11C2×C4×D4
prime radical#10622728C4
cosocleC42×C11C24
hypercenter#1450D11
hypocenterC11#17973
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1450

Complements

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

NH ≅ G/Ntype
2. #13077767C2semidirect
3. #13067520C2semidirect
4. #13067514C2semidirect
5. #13067502C2semidirect
6. #13067430C2semidirect
7. C8×Dic44C2semidirect
8. C8×D88C2semidirect
9. #13067375C2semidirect
10. #13067082C2semidirect
11. C11×#1450C2semidirect
148. #1450D11semidirect
332. C11#17973semidirect

Maximal subgroups

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

subgroupindex
#130791862
#130777672
#130675202
#130675142
#130675022
#130674302
C8×Dic442
C8×D882
#130673752
#130670822
C11×#14502
#1797311