Finite Group Databasebeta

← #14913243

Subgroups — #14913243

Order 2816.

2446 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D11C211yesmaximal, characteristic
2#13071577C216yesmaximal, complemented
3#13071534C212yesmaximal, complemented
4#13071481C216yesmaximal
5Q8×(C2×D11)⋊C4C212yesmaximal
6#13071093C213yesmaximal, complemented
7#13071090C213yesmaximal, complemented
8#13071012C213yesmaximal
9C4×Q8×Dic11C211yesmaximal, characteristic, complemented
10C4×#66925C213yesmaximal
11C42×Q8×C11C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2211yescharacteristic
13C2×C4×Q8×C11C2212yes—
14C2×C4×Q8×C11C2211yescharacteristic
15C2×Q8×Dic11C2212yes—
16C2×Q8×Dic11C2211yescharacteristic
17C4×Q8×D11C4116yescomplemented
18C2×C4⋊C4×D11C2213yes—
19C2×#66940C2213yes—
20C2×#66925C2216yes—
21C2×C42×D11C2213yes—
22C2×C4×Dic22C2213yes—
23C4×C11×C4⋊C4C2216yes—
24C4×C11×C4⋊C4C2213yes—
25C43×C11C2213yes—
26#10622600C2216yes—
27#10622590C2216yes—
28C4⋊C4×Dic11C2216yes—
29#10622587C2216yes—
30#10622586C2216yes—
31C4×(C2×D11)⋊C4C2216yes—
32C4×(C2×D11)⋊C4C2211yescharacteristic
33C4×(C2×D11)⋊C4C2213yes—
34C4×C4⋊Dic11C2213yes—
35#10622546C22112yes—
36#10622545C2216yes—
37#10622545C2216yes—
38C4×Dic11⋊C4C2216yes—
39C4×Dic11⋊C4C2213yes—
40C4×Dic11⋊C4C2213yes—
41C42×Dic11C2213yes—
42#10622542C2216yes—
43#10622541C2216yes—
44#10622277C2216yes—
45#10622265C22112yes—
46#10622264C2216yes—
47C22×Q8×C11C2311yescharacteristic
48C2×Q8×D11—28no—
49C2×Q8×D11C2×C418yes—
50C22×C4×D11C2311yescharacteristic
51C22×C4×D11C2313yes—
52C22×C4×D11C2313yes—
53C22×Dic22C2313yes—
54C4×Q8×C11—28no—
55C4×Q8×C11C2×C418yes—
56C2×C11×C4⋊C4C2316yes—
57C2×C11×C4⋊C4C2313yes—
58C2×C42×C11C2316yes—
59C2×C42×C11C2316yes—
60C2×C42×C11C2311yescharacteristic
61C2×C42×C11C2313yes—
62C2×C42×C11C2313yes—
63Q8×Dic11—28no—
64Q8×Dic11C2×C418yes—
65C2×(C2×D11)⋊C4C2316yes—
66C2×(C2×D11)⋊C4C2312yes—
67C2×C4⋊Dic11C2316yes—
68C2×C4⋊Dic11C2313yes—
69C2×Dic11⋊C4C2316yes—
70C2×Dic11⋊C4C2316yes—
71C2×Dic11⋊C4C2316yes—
72C2×C4×Dic11C2316yes—
73C2×C4×Dic11C2311yescharacteristic
74C2×C4×Dic11C2313yes—
75C2×C4×Dic11C2316yes—
76C2×C4×Dic11C2313yes—
77C2×C4×Dic11C2313yes—
78C2×C4×Dic11C2313yes—
79C4⋊C4×D11C2×C4124yes—
80#66940C2×C4124yes—
81#66925—224no—
82C42×D11C2×C4124yes—
83C4×Dic22C2×C4124yes—
84C11×#95C2316yes—
85C11⋊#95C2316yes—
86C11⋊#95C23112yes—
87C11⋊#95C2316yes—
88C11⋊#95C2316yes—
89C11⋊#95C23112yes—
90C11⋊#95C2316yes—
91C11⋊#95C2312yes—
92#34128—111nomaximal, Sylow
93C23×D11C2411yescharacteristic
94C2×Q8×C11C22×C414yes—
95C2×Q8×C11#4118yes—
96C22×C4×C11C2416yes—
97C22×C4×C11C2413yes—
98C22×C4×C11C2412yes—
99C22×C4×C11C2413yes—
100C22×C4×C11C2411yescharacteristic
101C22×Dic11C2416yes—
102C22×Dic11C2411yescharacteristic
103C22×Dic11C2413yes—
104C22×Dic11C2413yes—
105C22×Dic11C2412yes—
106Q8×D11—232no—
107C2×C4×D11—212no—
108C2×C4×D11—212no—
109C2×C4×D11—22no—
110C2×C4×D11—22no—
111C2×C4×D11C22×C414yes—
112C2×C4×D11C22×C4112yes—
113C2×C4×D11C22×C4112yes—
114C2×Dic22—212no—
115C2×Dic22C22×C4112yes—
116C11×C4⋊C4—212no—
117C11×C4⋊C4C22×C4112yes—
118C42×C11—212no—
119C42×C11—212no—
120C42×C11—22no—
121C42×C11—26no—
122C42×C11C22×C4112yes—
123(C2×D11)⋊C4—212no—
124(C2×D11)⋊C4#4118yes—
125C4⋊Dic11—212no—
126C4⋊Dic11C22×C4112yes—
127Dic11⋊C4—212no—
128Dic11⋊C4—212no—
129Dic11⋊C4C22×C4124yes—
130C4×Dic11—212no—
131C4×Dic11—212no—
132C4×Dic11—26no—
133C4×Dic11—22no—
134C4×Dic11C22×C4112yes—
135C4×Dic11C22×C4112yes—
136C4×Dic11C22×C4112yes—
137C22×C4×Q8—111no—
138#2356—116no—
139#2351—112no—
140#2344—116no—
141Q8×C22⋊C4—112no—
142#2295—113no—
143#2295—113no—
144#2283—113no—
145C42×Q8—111no—
146C42×Q8D1111yescharacteristic, complemented
147C4×#117—113no—
148C23×C11C2511yescharacteristic
149C22×D11—22no—
150C22×D11—21no—
151C22×D11—21no—
152C22×D11C23×C412yes—
153C22×D11C2×#4114yes—
154Q8×C11#117116yescomplemented
155C2×C4×C11—26no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—26no—
159C2×C4×C11—26no—
160C2×C4×C11—26no—
161C2×C4×C11C23×C416yes—
162C2×C4×C11C23×C416yes—
163C2×C4×C11C23×C412yes—
164C2×C4×C11C2×#41112yes—
165C2×C4×C11C2×#4114yes—
166C2×C4×C112−1+412yes—
167C2×C4×C112−1+412yes—
168C2×Dic11—22no—
169C2×Dic11—26no—
170C2×Dic11—26no—
171C2×Dic11—22no—
172C2×Dic11—21no—
173C2×Dic11—21no—
174C2×Dic11—26no—
175C2×Dic11—26no—
176C2×Dic11—26no—
177C2×Dic11C23×C412yes—
178C2×Dic11C23×C416yes—
179C2×Dic11C23×C416yes—
180C2×Dic11C2×#4114yes—
181C4×D11—224no—
182C4×D11—224no—
183C4×D11—28no—
184Dic22—224no—
185C23×Q8—111no—
186C2×C4×Q8—111no—
187C2×C4×Q8—1116no—
188C2×C4×Q8—112no—
189C2×C4×Q8—113no—
190C2×C4×Q8—113no—
191C2×C4×Q8C2×D1112yes—
192C2×C4×Q8C2×D1111yescharacteristic
193C2×#117—116no—
194C22×C4⋊C4—113no—
195C22×C42—113no—
196#391—116no—
197#391—116no—
198#389—116no—
199#389—116no—
200#387—1112no—
201#387—1112no—
202#383—116no—
203#382—116no—
204#381—116no—
205#380—116no—
206C4×C4⋊C4—116no—
207C4×C4⋊C4—116no—
208C4×C4⋊C4—113no—
209C4×C4⋊C4—113no—
210C4×C4⋊C4—113no—
211C4×C4⋊C4C2×D1116yes—
212C4×C4⋊C4C2×D1113yes—
213C4×C22⋊C4—116no—
214C4×C22⋊C4—111no—
215C4×C22⋊C4—113no—
216#376—116no—
217#376—116no—
218C43—113no—
219C43C2×D1113yes—
220C22×C11C24×C411yescharacteristic
221C22×C11C22×#4112yes—
222C22×C11C22×#4112yes—
223C22×C11C2×2−1+411yescharacteristic
224C22×C11C2×2−1+411yescharacteristic
225C2×D11—22no—
226C2×D11—22no—
227C2×D11—24no—
228C2×D11—24no—
229C2×D11C4×#4114yes—
230C4×C11—26no—
231C4×C11—24no—
232C4×C11—46no—
233C4×C11C2×#117112yes—
234C4×C11#51914yes—
235Dic11—26no—
236Dic11—26no—
237Dic11—22no—
238Dic11—24no—
239Dic11—46no—
240C22×Q8—118no—
241C22×Q8—113no—
242C22×Q8—228no—
243C22×Q8C22×D1111yescharacteristic
244C23×C4—113no—
245C23×C4—113no—
246C23×C4—111no—
247C4×Q8—28no—
248C4×Q8—118no—
249C4×Q8—1124no—
250C4×Q8—1124no—
251C4×Q8—228no—
252C4×Q8C4×D1118yes—
253#117—2224no—
254C2×C4⋊C4—116no—
255C2×C4⋊C4—113no—
256C2×C4⋊C4—1124no—
257C2×C4⋊C4—116no—
258C2×C4⋊C4—116no—
259C2×C4⋊C4—116no—
260C2×C4⋊C4C22×D1116yes—
261C2×C4⋊C4C22×D1113yes—
262C2×C22⋊C4—112no—
263C2×C22⋊C4—116no—
264C2×C42—113no—
265C2×C42—113no—
266C2×C42—113no—
267C2×C42—1124no—
268C2×C42—116no—
269C2×C42—116no—
270C2×C42—111no—
271C2×C42—113no—
272C2×C42C22×D1116yes—
273C2×C42C22×D1116yes—
274C2×C42C22×D1111yescharacteristic
275C2×C42C22×D1113yes—
276C2×C42C22×D1113yes—
277#95—112no—
278#95—116no—
279#95—116no—
280#95—116no—
281#95—1112no—
282#95—1112no—
283#95—116no—
284#95C22×D1116yes—
285C2×C11C22×#11711yescharacteristic
286C2×C11C2×C4×#4111yescharacteristic
287C2×C11C2×#51911yescharacteristic
288C2×C11#348212yes—
289C2×C11#348212yes—
290D11—24no—
291C24—111no—
292C2×Q8—1112no—
293C2×Q8—2232no—
294C2×Q8—2212no—
295C2×Q8C2×C4×D1114yes—
296C2×Q8#433918yes—
297C22×C4—111no—
298C22×C4—113no—
299C22×C4—112no—
300C22×C4—113no—
301C22×C4—114no—
302C22×C4—1112no—
303C22×C4—1112no—
304C22×C4—116no—
305C22×C4—2212no—
306C22×C4—2212no—
307C22×C4—222no—
308C22×C4—222no—
309C22×C4C23×D1116yes—
310C22×C4C23×D1113yes—
311C22×C4C23×D1112yes—
312C22×C4C23×D1113yes—
313C22×C4C23×D1111yescharacteristic
314C4⋊C4—212no—
315C4⋊C4—1124no—
316C4⋊C4—1112no—
317C4⋊C4—2212no—
318C4⋊C4—2212no—
319C4⋊C4—2212no—
320C4⋊C4C2×C4×D11112yes—
321C22⋊C4—118no—
322C22⋊C4—2212no—
323C42—212no—
324C42—22no—
325C42—212no—
326C42—26no—
327C42—1112no—
328C42—1112no—
329C42—1112no—
330C42—2212no—
331C42—2212no—
332C42—226no—
333C42—222no—
334C42C2×C4×D11112yes—
335C11#3412811yescharacteristic, complemented, Sylow
336C23—112no—
337C23—114no—
338C23—222no—
339C23—221no—
340C23—221no—
341C23C24×D1111yescharacteristic
342Q8—2224no—
343Q8#66925116yescomplemented
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—26no—
347C2×C4—26no—
348C2×C4—26no—
349C2×C4—26no—
350C2×C4—112no—
351C2×C4—116no—
352C2×C4—116no—
353C2×C4—114no—
354C2×C4—2224no—
355C2×C4—222no—
356C2×C4—226no—
357C2×C4—221no—
358C2×C4—226no—
359C2×C4—222no—
360C2×C4—221no—
361C2×C4—2224no—
362C2×C4—228no—
363C2×C4—226no—
364C2×C4—226no—
365C2×C4—226no—
366C2×C4C22×C4×D1116yes—
367C2×C4C22×C4×D1116yes—
368C2×C4C22×C4×D1112yes—
369C2×C4C2×#4339112yes—
370C2×C4#6704012yes—
371C2×C4#41×D1114yes—
372C2×C4#6704312yes—
373C22—114no—
374C22—224no—
375C22—224no—
376C22—222no—
377C22—222no—
378C22C23×C4×D1111yescharacteristic
379C22C22×#433912yes—
380C22C2×#6704011yescharacteristic
381C22C2×#41×D1112yes—
382C22C2×#6704311yescharacteristic
383C4—24no—
384C4—26no—
385C4—46no—
386C4—224no—
387C4—226no—
388C4—226no—
389C4—222no—
390C4—446no—
391C4C2×#66925112yes—
392C4#1062310314yes—
393C2—224no—
394C2C22×#6692511yescharacteristic
395C2C4×#41×D1111yescharacteristic
396C2C2×#1062310311yescharacteristic
397C2#1308223312yes—
398C2#1308223812yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC42×Q8×C11C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenterC42×Q8D11
hypocenterC11#34128
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C42×Q8

Complements

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

NH ≅ G/Ntype
2. #13071577C2semidirect
3. #13071534C2semidirect
6. #13071093C2semidirect
7. #13071090C2semidirect
9. C4×Q8×Dic11C2semidirect
11. C42×Q8×C11C2semidirect
17. C4×Q8×D11C4semidirect
146. C42×Q8D11semidirect
154. Q8×C11#117semidirect
335. C11#34128semidirect
343. Q8#66925semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D112
#130715772
#130715342
#130714812
Q8×(C2×D11)⋊C42
#130710932
#130710902
#130710122
C4×Q8×Dic112
C4×#669252
C42×Q8×C112
#3412811