Finite Group Databasebeta

← #14913240

Subgroups — #14913240

Order 2816.

2446 conjugacy classes of subgroups.

The subgroup lattice has 402 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#13071487C213yesmaximal
5#13071483C213yesmaximal
6Q8×C22⋊Dic11C211yesmaximal, characteristic
7#13071091C216yesmaximal, complemented
8#13071011C213yesmaximal
9C4×Q8×Dic11C212yesmaximal, complemented
10C4×#66930C213yesmaximal
11Q8×C11×C22⋊C4C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C2×C4×Q8×C11C2212yes—
14C2×Q8×Dic11C4116yescomplemented
15C2×Q8×Dic11C2212yes—
16C2×Q8×Dic11C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×Q8×Dic11C2213yes—
19C2×Q8×Dic11C2213yes—
20C22×C4⋊Dic11C2213yes—
21C22×C4×Dic11C2213yes—
22C2×#66930C2213yes—
23C2×#66930C2213yes—
24C11×#391C2216yes—
25C11×#380C2213yes—
26C4×C11×C22⋊C4C2213yes—
27#10622843C2216yes—
28#10622825C2213yes—
29C4×C22⋊Dic11C2213yes—
30#10622590C2216yes—
31C4⋊C4×Dic11C2216yes—
32C4⋊C4×Dic11C2216yes—
33#10622586C2216yes—
34#10622556C2216yes—
35C22⋊C4×Dic11C2211yescharacteristic
36C22⋊C4×Dic11C2213yes—
37C4×C4⋊Dic11C2216yes—
38C4×Dic11⋊C4C2216yes—
39C42×Dic11C2216yes—
40#10622541C2216yes—
41#10622267C22112yes—
42#10622266C22112yes—
43#10622264C2216yes—
44#10622262C2216yes—
45#10622261C2216yes—
46#10622261C2216yes—
47C22×Q8×C11—28no—
48C22×Q8×C11C2×C418yes—
49C22×Q8×C11C2313yes—
50C22×Q8×C11C2311yescharacteristic
51C23×C4×C11C2313yes—
52C23×Dic11C2313yes—
53C23×Dic11C2311yescharacteristic
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×Dic11C2316yes—
76C2×C4×Dic11C2316yes—
77C2×C4×Dic11C2312yes—
78C2×C4×Dic11C2316yes—
79C2×C4×Dic11C2313yes—
80C2×C4×Dic11C2313yes—
81C2×C4×Dic11C2313yes—
82C2×C4×Dic11C2313yes—
83#66930—212no—
84#66930—212no—
85C11×#95C2316yes—
86C11×#95C2316yes—
87C11⋊#95C2312yes—
88C11⋊#95C2316yes—
89C11⋊#95C2316yes—
90C11⋊#95C2316yes—
91C11⋊#95C23112yes—
92C11⋊#95C23112yes—
93#34128—111nomaximal, Sylow
94C24×C11C2411yescharacteristic
95C2×Q8×C11—232no—
96C2×Q8×C11—212no—
97C2×Q8×C11C22×C4112yes—
98C2×Q8×C11C22×C414yes—
99C2×Q8×C11#4118yes—
100C22×C4×C11—212no—
101C22×C4×C11C22×C4112yes—
102C22×C4×C11C2416yes—
103C22×C4×C11C2413yes—
104C22×C4×C11C2412yes—
105C22×C4×C11C2413yes—
106C22×Dic11—24no—
107C22×Dic11—26no—
108C22×Dic11—26no—
109C22×Dic11C22×C414yes—
110C22×Dic11C22×C4112yes—
111C22×Dic11C2416yes—
112C22×Dic11C2411yescharacteristic
113C22×Dic11C2413yes—
114C22×Dic11C2413yes—
115C22×Dic11C2412yes—
116C22×Dic11C2411yescharacteristic
117C11×C4⋊C4—212no—
118C11×C22⋊C4—26no—
119C11×C22⋊C4#4114yes—
120C42×C11—212no—
121C22⋊Dic11—26no—
122C22⋊Dic11#4114yes—
123C4⋊Dic11—212no—
124C4⋊Dic11C22×C4124yes—
125C4⋊Dic11C22×C4112yes—
126C4⋊Dic11C22×C4112yes—
127Dic11⋊C4—212no—
128Dic11⋊C4—212no—
129C4×Dic11—212no—
130C4×Dic11—24no—
131C4×Dic11—212no—
132C4×Dic11—212no—
133C4×Dic11—212no—
134C4×Dic11C22×C4112yes—
135C4×Dic11C22×C4112yes—
136C4×Dic11C22×C4112yes—
137C4×Dic11C22×C4112yes—
138C22×C4×Q8—111no—
139#2356—116no—
140#2351—112no—
141#2344—113no—
142#2344—113no—
143Q8×C22⋊C4—111no—
144Q8×C22⋊C4D1111yescharacteristic
145#2295—116no—
146#2283—113no—
147C42×Q8—112no—
148C4×#117—113no—
149C23×C11—22no—
150C23×C11—22no—
151C23×C11C23×C412yes—
152C23×C11C2×#4112yes—
153C23×C11C2×#4112yes—
154C23×C11C2511yescharacteristic
155Q8×C11—224no—
156Q8×C11#117116yescomplemented
157C2×C4×C11—22no—
158C2×C4×C11—26no—
159C2×C4×C11—22no—
160C2×C4×C11—224no—
161C2×C4×C11—26no—
162C2×C4×C11—26no—
163C2×C4×C11—26no—
164C2×C4×C11C23×C416yes—
165C2×C4×C11C23×C416yes—
166C2×C4×C11C2×#41112yes—
167C2×C4×C11C2×#4114yes—
168C2×Dic11—224no—
169C2×Dic11—22no—
170C2×Dic11—23no—
171C2×Dic11—23no—
172C2×Dic11—23no—
173C2×Dic11—23no—
174C2×Dic11—22no—
175C2×Dic11—22no—
176C2×Dic11—28no—
177C2×Dic11—26no—
178C2×Dic11—26no—
179C2×Dic11—26no—
180C2×Dic11C23×C412yes—
181C2×Dic11C23×C416yes—
182C2×Dic11C23×C416yes—
183C2×Dic11C23×C412yes—
184C2×Dic11C2×#4114yes—
185C2×Dic112−1+414yes—
186C23×Q8C2×D1111yescharacteristic
187C2×C4×Q8—111no—
188C2×C4×Q8—113no—
189C2×C4×Q8—111no—
190C2×C4×Q8—113no—
191C2×C4×Q8—1116no—
192C2×C4×Q8—112no—
193C2×C4×Q8C2×D1112yes—
194C2×#117—113no—
195C2×#117—113no—
196C22×C4⋊C4—113no—
197C22×C42—113no—
198#391—116no—
199#391C2×D1116yes—
200#389—116no—
201#389—116no—
202#387—1112no—
203#387—1112no—
204#383—116no—
205#382—116no—
206#381—116no—
207#380—113no—
208#380C2×D1113yes—
209C4×C4⋊C4—116no—
210C4×C4⋊C4—116no—
211C4×C4⋊C4—116no—
212C4×C4⋊C4—116no—
213C4×C4⋊C4—116no—
214C4×C22⋊C4—113no—
215C4×C22⋊C4—111no—
216C4×C22⋊C4—113no—
217C4×C22⋊C4C2×D1113yes—
218#376—116no—
219#376—116no—
220C43—116no—
221C22×C11—22no—
222C22×C11—22no—
223C22×C11—24no—
224C22×C11—24no—
225C22×C11C4×#4114yes—
226C22×C11C24×C411yescharacteristic
227C22×C11C22×#4112yes—
228C22×C11C22×#4111yescharacteristic
229C22×C11C22×#4111yescharacteristic
230C22×C11C2×2−1+412yes—
231C4×C11—26no—
232C4×C11—24no—
233C4×C11—46no—
234C4×C11C2×#117112yes—
235Dic11—26no—
236Dic11—26no—
237Dic11—22no—
238Dic11—24no—
239Dic11—46no—
240Dic11#51914yes—
241C22×Q8—28no—
242C22×Q8C4×D1118yes—
243C22×Q8C22×D1113yes—
244C22×Q8C22×D1111yescharacteristic
245C23×C4—113no—
246C23×C4—111no—
247C23×C4C22×D1113yes—
248C4×Q8—28no—
249C4×Q8—1124no—
250C4×Q8—1124no—
251C4×Q8—118no—
252C4×Q8—118no—
253C4×Q8—228no—
254#117—2212no—
255#117—2212no—
256C2×C4⋊C4—1124no—
257C2×C4⋊C4—113no—
258C2×C4⋊C4—116no—
259C2×C4⋊C4—113no—
260C2×C4⋊C4—116no—
261C2×C4⋊C4—116no—
262C2×C4⋊C4—116no—
263C2×C4⋊C4C22×D1116yes—
264C2×C22⋊C4—111no—
265C2×C22⋊C4—113no—
266C2×C22⋊C4C22×D1113yes—
267C2×C22⋊C4C22×D1111yescharacteristic
268C2×C42—1124no—
269C2×C42—113no—
270C2×C42—113no—
271C2×C42—113no—
272C2×C42—113no—
273C2×C42—116no—
274C2×C42—116no—
275C2×C42—116no—
276C2×C42—112no—
277C2×C42—116no—
278C2×C42C22×D1116yes—
279#95—112no—
280#95—116no—
281#95—116no—
282#95—116no—
283#95—1112no—
284#95—1112no—
285#95C22×D1116yes—
286#95C22×D1116yes—
287C2×C11—24no—
288C2×C11C22×#11711yescharacteristic
289C2×C11C2×C4×#4111yescharacteristic
290C2×C11C2×#51911yescharacteristic
291C2×C11#348212yes—
292C2×C11#348212yes—
293C24C23×D1111yescharacteristic
294C2×Q8—232no—
295C2×Q8—212no—
296C2×Q8C2×C4×D11112yes—
297C2×Q8C2×C4×D1114yes—
298C2×Q8#434118yes—
299C22×C4—212no—
300C22×C4—111no—
301C22×C4—114no—
302C22×C4—1112no—
303C22×C4—111no—
304C22×C4—112no—
305C22×C4—113no—
306C22×C4—113no—
307C22×C4—116no—
308C22×C4—224no—
309C22×C4—226no—
310C22×C4—226no—
311C22×C4C2×C4×D11112yes—
312C22×C4C23×D1116yes—
313C22×C4C23×D1113yes—
314C22×C4C23×D1112yes—
315C22×C4C23×D1113yes—
316C4⋊C4—212no—
317C4⋊C4—1124no—
318C4⋊C4—1112no—
319C4⋊C4—1112no—
320C4⋊C4—2212no—
321C4⋊C4—2212no—
322C4⋊C4—2212no—
323C22⋊C4—26no—
324C22⋊C4—114no—
325C22⋊C4—226no—
326C22⋊C4#434314yes—
327C42—212no—
328C42—1112no—
329C42—1112no—
330C42—1112no—
331C42—1112no—
332C42—2212no—
333C42—224no—
334C42—2212no—
335C42—2212no—
336C42—2212no—
337C11#3412811yescharacteristic, complemented, Sylow
338C23—22no—
339C23—22no—
340C23C22×C4×D1112yes—
341C23C2×#434312yes—
342C23#41×D1112yes—
343C23C24×D1111yescharacteristic
344Q8—224no—
345Q8#66930116yescomplemented
346C2×C4—22no—
347C2×C4—26no—
348C2×C4—22no—
349C2×C4—224no—
350C2×C4—26no—
351C2×C4—26no—
352C2×C4—26no—
353C2×C4—112no—
354C2×C4—114no—
355C2×C4—112no—
356C2×C4—116no—
357C2×C4—116no—
358C2×C4—114no—
359C2×C4—228no—
360C2×C4—2224no—
361C2×C4—222no—
362C2×C4—223no—
363C2×C4—223no—
364C2×C4—223no—
365C2×C4—223no—
366C2×C4—222no—
367C2×C4—222no—
368C2×C4—226no—
369C2×C4—226no—
370C2×C4—226no—
371C2×C4C22×C4×D1116yes—
372C2×C4C22×C4×D1116yes—
373C2×C4C2×#4341112yes—
374C2×C4C2×#434314yes—
375C22—24no—
376C22—24no—
377C22—22no—
378C22—22no—
379C22C4×#434314yes—
380C22C23×C4×D1111yescharacteristic
381C22C22×#434112yes—
382C22C22×#434311yescharacteristic
383C22C2×#41×D1111yescharacteristic
384C22D11×2−1+412yes—
385C4—24no—
386C4—26no—
387C4—46no—
388C4—114no—
389C4—224no—
390C4—226no—
391C4—226no—
392C4—222no—
393C4—446no—
394C4C2×#66930112yes—
395C2—24no—
396C2C22×#6693011yescharacteristic
397C2C2×C4×#434311yescharacteristic
398C2D11×#51911yescharacteristic
399C2#1308223212yes—
400C2#1308223712yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingQ8×C11×C22⋊C4C2
socle, cosocleC23×C11C25
prime radicalC24×C11C24
hypercenterQ8×C22⋊C4D11
hypocenterC11#34128
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. #13071091C2semidirect
9. C4×Q8×Dic11C2semidirect
14. C2×Q8×Dic11C4semidirect
156. Q8×C11#117semidirect
337. C11#34128semidirect
345. Q8#66930semidirect

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
#130714872
#130714832
Q8×C22⋊Dic112
#130710912
#130710112
C4×Q8×Dic112
C4×#669302
Q8×C11×C22⋊C42
#3412811