Finite Group Databasebeta

← #14913959

Subgroups — #14913959

Order 2816.

2250 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
1C22×Q8×Dic11C211yesmaximal, characteristic
2#13071580C216yesmaximal, complemented
3#13071534C212yesmaximal, complemented
4#13071495C213yesmaximal
5#13071491C213yesmaximal
6Q8×C22⋊Dic11C211yesmaximal, characteristic
7#13071261C216yesmaximal, complemented
8#13071011C213yesmaximal
9#13071010C213yesmaximal
10#13070981C212yesmaximal, complemented
11Q8×C11×C22⋊C4C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C2×C4×Q8×C11C2212yes—
14C2×Q8×Dic11C4116yescomplemented
15C2×Q8×Dic11C2212yes—
16C2×Q8×Dic11C2211yescharacteristic
17C2×Q8×Dic11C2213yes—
18C2×Q8×Dic11C2211yescharacteristic
19C2×Q8×Dic11C2213yes—
20C22×C4⋊Dic11C2213yes—
21C22×C4×Dic11C2213yes—
22C11×#391C2216yes—
23C11×#380C2213yes—
24C4×C11×C22⋊C4C2213yes—
25#10622843C2216yes—
26#10622825C2213yes—
27C4×C22⋊Dic11C2213yes—
28#10622590C2216yes—
29C4⋊C4×Dic11C2216yes—
30C4⋊C4×Dic11C2216yes—
31#10622586C2216yes—
32#10622556C2211yescharacteristic
33#10622556C2213yes—
34#10622555C2213yes—
35#10622555C2213yes—
36C22⋊C4×Dic11C2216yes—
37C4×C4⋊Dic11C2216yes—
38#10622545C2216yes—
39C4×Dic11⋊C4C2216yes—
40#10622541C2216yes—
41#10622267C22112yes—
42#10622266C22112yes—
43#10622264C2216yes—
44#10622264C2216yes—
45#10622263C2216yes—
46#10622261C2216yes—
47C22×Q8×C11—28no—
48C22×Q8×C11C2×C418yes—
49C22×Q8×C11C2313yes—
50C22×Q8×C11C2311yescharacteristic
51C23×C4×C11C2313yes—
52C23×Dic11C2311yescharacteristic
53C23×Dic11C2313yes—
54C4×Q8×C11—28no—
55C2×C11×C4⋊C4C2316yes—
56C2×C11×C22⋊C4C2313yes—
57C2×C11×C22⋊C4C2311yescharacteristic
58C2×C42×C11C2316yes—
59C2×C22⋊Dic11C2313yes—
60C2×C22⋊Dic11C2311yescharacteristic
61Q8×Dic11—28no—
62Q8×Dic11C2×C4124yes—
63Q8×Dic11C2×C4124yes—
64Q8×Dic11C2×C418yes—
65Q8×Dic11C2×C418yes—
66C2×C4⋊Dic11C2×C4124yes—
67C2×C4⋊Dic11C2316yes—
68C2×C4⋊Dic11C2316yes—
69C2×C4⋊Dic11C2313yes—
70C2×C4⋊Dic11C2313yes—
71C2×Dic11⋊C4C2316yes—
72C2×Dic11⋊C4C2316yes—
73C2×C4×Dic11C2×C4124yes—
74C2×C4×Dic11C2316yes—
75C2×C4×Dic11C23112yes—
76C2×C4×Dic11C2313yes—
77C2×C4×Dic11C2313yes—
78C2×C4×Dic11C2313yes—
79C2×C4×Dic11C2313yes—
80C11×#95C2316yes—
81C11×#95C2316yes—
82C11⋊#95C2316yes—
83C11⋊#95C2316yes—
84C11⋊#95C2312yes—
85C11⋊#95C2316yes—
86C11⋊#95C2316yes—
87C11⋊#95C2312yes—
88C11⋊#95C2316yes—
89C11⋊#95C23112yes—
90C11⋊#95C2316yes—
91#34192—111nomaximal, Sylow
92C24×C11C2411yescharacteristic
93C2×Q8×C11—232no—
94C2×Q8×C11—212no—
95C2×Q8×C11C22×C4112yes—
96C2×Q8×C11C22×C414yes—
97C2×Q8×C11#4118yes—
98C22×C4×C11—212no—
99C22×C4×C11C22×C4112yes—
100C22×C4×C11C2416yes—
101C22×C4×C11C2412yes—
102C22×C4×C11C2413yes—
103C22×C4×C11C2413yes—
104C22×Dic11—22no—
105C22×Dic11—22no—
106C22×Dic11—46no—
107C22×Dic11C22×C414yes—
108C22×Dic11C22×C4112yes—
109C22×Dic11C2412yes—
110C22×Dic11C2416yes—
111C22×Dic11C2411yescharacteristic
112C22×Dic11C2411yescharacteristic
113C22×Dic11C2413yes—
114C22×Dic11C2413yes—
115C11×C4⋊C4—212no—
116C11×C22⋊C4—22no—
117C11×C22⋊C4—26no—
118C42×C11—212no—
119C22⋊Dic11—26no—
120C22⋊Dic11—22no—
121C4⋊Dic11—212no—
122C4⋊Dic11C22×C4124yes—
123C4⋊Dic11C22×C4112yes—
124C4⋊Dic11C22×C4112yes—
125Dic11⋊C4—46no—
126Dic11⋊C4—46no—
127C4×Dic11—212no—
128C4×Dic11—412no—
129C4×Dic11C22×C4112yes—
130C4×Dic11C22×C4112yes—
131C4×Dic11C22×C4112yes—
132C4×Dic11C22×C4112yes—
133C22×C4×Q8—111no—
134#2356—116no—
135#2351—112no—
136#2345—113no—
137#2345—113no—
138Q8×C22⋊C4—111no—
139Q8×C22⋊C4D1111yescharacteristic
140#2320—116no—
141#2283—113no—
142#2283—113no—
143#2276—112no—
144C23×C11—22no—
145C23×C11—22no—
146C23×C11C23×C412yes—
147C23×C112−1+412yes—
148C23×C112−1+412yes—
149C23×C11C2511yescharacteristic
150Q8×C11—224no—
151Q8×C11#117116yes—
152C2×C4×C11—26no—
153C2×C4×C11—224no—
154C2×C4×C11—22no—
155C2×C4×C11—26no—
156C2×C4×C11—22no—
157C2×C4×C11—26no—
158C2×C4×C11—26no—
159C2×C4×C11—22no—
160C2×C4×C11C23×C416yes—
161C2×C4×C11C23×C416yes—
162C2×C4×C11C2×#41112yes—
163C2×Dic11—28no—
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11—21no—
167C2×Dic11—21no—
168C2×Dic11—26no—
169C2×Dic11—26no—
170C2×Dic11—22no—
171C2×Dic11—26no—
172C2×Dic11—26no—
173C2×Dic11—22no—
174C2×Dic11—26no—
175C2×Dic11—22no—
176C2×Dic11—412no—
177C2×Dic11C23×C412yes—
178C2×Dic11C23×C412yes—
179C2×Dic11C23×C416yes—
180C2×Dic11C23×C416yes—
181C23×Q8C2×D1111yescharacteristic
182C2×C4×Q8—113no—
183C2×C4×Q8—111no—
184C2×C4×Q8—113no—
185C2×C4×Q8—111no—
186C2×C4×Q8—1116no—
187C2×C4×Q8—112no—
188C2×C4×Q8C2×D1112yes—
189C22×C4⋊C4—113no—
190C22×C42—113no—
191#391—116no—
192#391C2×D1116yes—
193#389—116no—
194#389—116no—
195#387—1112no—
196#387—1112no—
197#383—116no—
198#383—116no—
199#382—116no—
200#382—116no—
201#381—111no—
202#381—113no—
203#380—113no—
204#380—113no—
205#380—113no—
206#380C2×D1113yes—
207C4×C4⋊C4—116no—
208C4×C4⋊C4—116no—
209C4×C4⋊C4—116no—
210C4×C4⋊C4—116no—
211C4×C22⋊C4—113no—
212C4×C22⋊C4—116no—
213C4×C22⋊C4C2×D1113yes—
214#376—116no—
215#376—116no—
216C22×C11—22no—
217C22×C11—22no—
218C22×C11—24no—
219C22×C11—24no—
220C22×C11#51914yes—
221C22×C11C24×C411yescharacteristic
222C22×C11C22×#4112yes—
223C22×C11C2×2−1+411yescharacteristic
224C22×C11C2×2−1+411yescharacteristic
225C22×C11#58512yes—
226C4×C11—26no—
227C4×C11—46no—
228C4×C11—42no—
229C4×C11C2×#117112yes—
230Dic11—22no—
231Dic11—22no—
232Dic11—26no—
233Dic11—26no—
234Dic11—42no—
235Dic11—46no—
236C22×Q8—28no—
237C22×Q8C4×D1118yes—
238C22×Q8C22×D1113yes—
239C22×Q8C22×D1111yescharacteristic
240C23×C4—111no—
241C23×C4—113no—
242C23×C4C22×D1113yes—
243C4×Q8—28no—
244C4×Q8—1124no—
245C4×Q8—1124no—
246C4×Q8—118no—
247C4×Q8—118no—
248C4×Q8—228no—
249C2×C4⋊C4—1124no—
250C2×C4⋊C4—113no—
251C2×C4⋊C4—116no—
252C2×C4⋊C4—113no—
253C2×C4⋊C4—116no—
254C2×C4⋊C4—116no—
255C2×C4⋊C4—116no—
256C2×C4⋊C4C22×D1116yes—
257C2×C22⋊C4—113no—
258C2×C22⋊C4—111no—
259C2×C22⋊C4C22×D1113yes—
260C2×C22⋊C4C22×D1111yescharacteristic
261C2×C42—1124no—
262C2×C42—113no—
263C2×C42—113no—
264C2×C42—113no—
265C2×C42—113no—
266C2×C42—116no—
267C2×C42—1112no—
268C2×C42C22×D1116yes—
269#95—112no—
270#95—116no—
271#95—116no—
272#95—116no—
273#95—116no—
274#95—116no—
275#95—1112no—
276#95—116no—
277#95—112no—
278#95C22×D1116yes—
279#95C22×D1116yes—
280C2×C11—24no—
281C2×C11C22×#11711yescharacteristic
282C2×C11C2×#51911yescharacteristic
283C2×C11#342811yescharacteristic
284C2×C11#351612yes—
285C2×C11#351612yes—
286C24C23×D1111yescharacteristic
287C2×Q8—232no—
288C2×Q8—212no—
289C2×Q8C2×C4×D11112yes—
290C2×Q8C2×C4×D1114yes—
291C2×Q8#434118yes—
292C22×C4—212no—
293C22×C4—114no—
294C22×C4—111no—
295C22×C4—111no—
296C22×C4—113no—
297C22×C4—113no—
298C22×C4—1112no—
299C22×C4—112no—
300C22×C4—116no—
301C22×C4—222no—
302C22×C4—222no—
303C22×C4—446no—
304C22×C4C2×C4×D11112yes—
305C22×C4C23×D1116yes—
306C22×C4C23×D1112yes—
307C22×C4C23×D1113yes—
308C22×C4C23×D1113yes—
309C4⋊C4—212no—
310C4⋊C4—1124no—
311C4⋊C4—1112no—
312C4⋊C4—1112no—
313C4⋊C4—2212no—
314C4⋊C4—446no—
315C4⋊C4—446no—
316C22⋊C4—22no—
317C22⋊C4—26no—
318C22⋊C4—226no—
319C22⋊C4—222no—
320C42—212no—
321C42—1112no—
322C42—1112no—
323C42—1112no—
324C42—1112no—
325C42—2212no—
326C42—4412no—
327C11#3419211yescharacteristic, complemented, Sylow
328C23—22no—
329C23—22no—
330C23C22×C4×D1112yes—
331C23#6704012yes—
332C23#6704312yes—
333C23C24×D1111yescharacteristic
334Q8—224no—
335Q8#66930116yes—
336C2×C4—26no—
337C2×C4—224no—
338C2×C4—22no—
339C2×C4—26no—
340C2×C4—22no—
341C2×C4—26no—
342C2×C4—26no—
343C2×C4—22no—
344C2×C4—112no—
345C2×C4—112no—
346C2×C4—116no—
347C2×C4—116no—
348C2×C4—228no—
349C2×C4—221no—
350C2×C4—221no—
351C2×C4—221no—
352C2×C4—221no—
353C2×C4—226no—
354C2×C4—226no—
355C2×C4—222no—
356C2×C4—226no—
357C2×C4—226no—
358C2×C4—222no—
359C2×C4—226no—
360C2×C4—222no—
361C2×C4—4412no—
362C2×C4C22×C4×D1116yes—
363C2×C4C22×C4×D1116yes—
364C2×C4C2×#4341112yes—
365C22—22no—
366C22—22no—
367C22—24no—
368C22—24no—
369C22#1062310314yes—
370C22C23×C4×D1111yescharacteristic
371C22C22×#434112yes—
372C22C2×#6704011yescharacteristic
373C22C2×#6704311yescharacteristic
374C22#1062345712yes—
375C4—26no—
376C4—46no—
377C4—42no—
378C4—222no—
379C4—222no—
380C4—226no—
381C4—226no—
382C4—442no—
383C4—446no—
384C4C2×#66930112yes—
385C2—24no—
386C2C22×#6693011yescharacteristic
387C2C2×#1062310311yescharacteristic
388C2#1308181811yescharacteristic
389C2#1308259812yes—
390C2#1308261012yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingQ8×C11×C22⋊C4C2
socle, cosocleC23×C11C25
prime radicalC24×C11C24
hypercenterQ8×C22⋊C4D11
hypocenterC11#34192
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13071580C2semidirect
3. #13071534C2semidirect
7. #13071261C2semidirect
10. #13070981C2semidirect
14. C2×Q8×Dic11C4semidirect
327. C11#34192semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×Dic112
#130715802
#130715342
#130714952
#130714912
Q8×C22⋊Dic112
#130712612
#130710112
#130710102
#130709812
Q8×C11×C22⋊C42
#3419211