Finite Group Databasebeta

← #14669266

Subgroups — #14669266

Order 2816.

1098 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 1098 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622179C212yesmaximal, complemented
2C2×#10622183C212yesmaximal, complemented
3#13068534C212yesmaximal, complemented
4C2×C11×#532C211yesmaximal, characteristic
5C22×C11×#41C411yescharacteristic, complemented
6C22×C11×#41C2211yescharacteristic
7C11×#532—24no—
8C11×#532—24no—
9C2×C11×C4⋊Q8C411yescharacteristic, complemented
10C2×C11×#127C2211yescharacteristic
11C2×C11×#124C411yescharacteristic, complemented
12C2×C11×#124C2211yescharacteristic
13C2×C11×#121—22no—
14C2×C4×D4×C11—22no—
15C22×C42×C11C411yescharacteristic, complemented
16C2×#66898—22no—
17C2×#66898C2214yes—
18#10622824—22no—
19#10622183—24no—
20#10622179—24no—
21C2×C11×#41—22no—
22C2×C11×#41—22no—
23C2×C11×#41—22no—
24C2×C11×#41—22no—
25C2×C11×#41—42no—
26C2×C11×#41—42no—
27C2×C11×#41—42no—
28C2×C11×#41—42no—
29C22×Q8×C11C2×C411yescharacteristic
30C22×Q8×C11C2×C411yescharacteristic
31C22×D4×C11—21no—
32C22×D4×C11—22no—
33C22×D4×C11C2×C411yescharacteristic
34C22×D4×C11D412yes—
35C22×D4×C11C2311yescharacteristic
36C23×C4×C11—21no—
37C23×C4×C11—21no—
38C23×C4×C11C2×C411yescharacteristic
39C23×C4×C11D412yes—
40C11×C4⋊Q8—22no—
41C11×C4⋊Q8—22no—
42C11×#127—22no—
43C11×#127D414yes—
44C11×#124—22no—
45C11×#124—22no—
46C11×#124—22no—
47C11×#124D414yes—
48C11×#121—216no—
49C4×D4×C11—216no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4—22no—
53C2×C42×C11—21no—
54C2×C42×C11—22no—
55C2×C42×C11—22no—
56C2×C42×C11C2×C411yescharacteristic
57C2×C42×C11C2×C411yescharacteristic
58C2×C22⋊Dic11—24no—
59#66898—24no—
60#66898—24no—
61#66898—44no—
62C11⋊#95—44no—
63#12695—111nomaximal, Sylow
64C24×C11—21no—
65C24×C11C22⋊C411yescharacteristic
66C24×C11C2×D412yes—
67C11×#41—48no—
68C11×#41—48no—
69C11×#41—48no—
70C11×#41—48no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11—41no—
75C2×Q8×C11—41no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11C22⋊C412yes—
79C2×D4×C11—24no—
80C2×D4×C11—24no—
81C2×D4×C11—28no—
82C2×D4×C11—24no—
83C2×D4×C11—21no—
84C2×D4×C11—42no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—48no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—42no—
91C2×D4×C11—42no—
92C2×D4×C11C22⋊C412yes—
93C2×D4×C11C2×D412yes—
94C2×D4×C11C2×D412yes—
95C22×C4×C11—22no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—24no—
101C22×C4×C11—24no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—24no—
105C22×C4×C11—24no—
106C22×C4×C11—42no—
107C22×C4×C11—44no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11C22⋊C412yes—
111C22×C4×C11C22⋊C411yescharacteristic
112C22×C4×C11C22×C411yescharacteristic
113C22×Dic11—44no—
114C11×C4⋊C4—28no—
115C11×C22⋊C4—28no—
116C11×C22⋊C4—28no—
117C42×C11—24no—
118C42×C11—21no—
119C42×C11—21no—
120C42×C11C22⋊C412yes—
121C42×C11C22⋊C412yes—
122C22⋊Dic11—44no—
123C22⋊Dic11—44no—
124C2×#532D1111yescharacteristic
125C2×#354—112no—
126C2×#353—112no—
127#1782—112no—
128C23×C11—21no—
129C23×C11—22no—
130C23×C11—21no—
131C23×C11—22no—
132C23×C11—22no—
133C23×C11—42no—
134C23×C11—44no—
135C23×C11—44no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11#9912yes—
139C23×C11C2×C22⋊C411yescharacteristic
140C23×C11#12014yes—
141Q8×C11—42no—
142Q8×C11—42no—
143Q8×C11—42no—
144Q8×C11—42no—
145D4×C11—42no—
146D4×C11—42no—
147D4×C11—42no—
148D4×C11—416no—
149D4×C11—42no—
150D4×C11—48no—
151D4×C11—48no—
152C2×C4×C11—24no—
153C2×C4×C11—24no—
154C2×C4×C11—24no—
155C2×C4×C11—21no—
156C2×C4×C11—22no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—48no—
166C2×C4×C11—48no—
167C2×C4×C11—48no—
168C2×C4×C11—42no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11#9912yes—
172C2×C4×C11C2×C22⋊C411yescharacteristic
173C2×C4×C11C2×C22⋊C411yescharacteristic
174C2×Dic11—84no—
175C2×Dic11—88no—
176C22×#41Dic1111yescharacteristic, complemented
177C22×#41C2×D1111yescharacteristic
178#532—24no—
179#532—24no—
180C2×C4⋊Q8Dic1111yescharacteristic, complemented
181C2×#127C2×D1111yescharacteristic
182C2×#124Dic1111yescharacteristic, complemented
183C2×#124C2×D1111yescharacteristic
184C2×#121—22no—
185C2×C4×D4—22no—
186C22×C42Dic1111yescharacteristic, complemented
187C2×#99—114no—
188C2×#99—222no—
189#381—222no—
190#354—224no—
191#353—224no—
192C22×C11—22no—
193C22×C11—22no—
194C22×C11—24no—
195C22×C11—44no—
196C22×C11—42no—
197C22×C11—42no—
198C22×C11—44no—
199C22×C11—42no—
200C22×C11—44no—
201C22×C11—42no—
202C22×C11—82no—
203C22×C11—82no—
204C22×C11—82no—
205C22×C11#37911yescharacteristic
206C22×C11C2×#9911yescharacteristic
207C22×C11C2×#9911yescharacteristic
208C4×C11—24no—
209C4×C11—22no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—42no—
213C4×C11—42no—
214C4×C11—42no—
215Dic11—164no—
216C2×#41—22no—
217C2×#41—22no—
218C2×#41—22no—
219C2×#41—22no—
220C2×#41—42no—
221C2×#41—42no—
222C2×#41—42no—
223C2×#41—42no—
224C22×Q8C2×Dic1111yescharacteristic
225C22×Q8C2×Dic1111yescharacteristic
226C22×D4—21no—
227C22×D4—22no—
228C22×D4C2×Dic1111yescharacteristic
229C22×D4C22⋊D1112yes—
230C22×D4C22×D1111yescharacteristic
231C23×C4—21no—
232C23×C4—21no—
233C23×C4C2×Dic1111yescharacteristic
234C23×C4C22⋊D1112yes—
235C4⋊Q8—22no—
236C4⋊Q8—22no—
237#127—22no—
238#127C22⋊D1114yes—
239#124—22no—
240#124—22no—
241#124—22no—
242#124C22⋊D1114yes—
243#121—216no—
244C4×D4—216no—
245C2×C4⋊C4—22no—
246C2×C22⋊C4—22no—
247C2×C22⋊C4—22no—
248C2×C22⋊C4—224no—
249C2×C42—21no—
250C2×C42—22no—
251C2×C42—22no—
252C2×C42C2×Dic1111yescharacteristic
253C2×C42C2×Dic1111yescharacteristic
254#99—224no—
255#99—224no—
256#99—444no—
257#95—444no—
258C2×C11—21no—
259C2×C11—21no—
260C2×C11—44no—
261C2×C11—42no—
262C2×C11—82no—
263C2×C11#178111yescharacteristic
264C2×C11#212612yes—
265C24—21no—
266C24C22⋊Dic1111yescharacteristic
267C24C2×C22⋊D1112yes—
268#41—48no—
269#41—48no—
270#41—48no—
271#41—48no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8C22⋊Dic1112yes—
280C2×D4—24no—
281C2×D4—24no—
282C2×D4—28no—
283C2×D4—24no—
284C2×D4—21no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—42no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—48no—
291C2×D4—42no—
292C2×D4—42no—
293C2×D4C22⋊Dic1112yes—
294C2×D4C2×C22⋊D1112yes—
295C2×D4C2×C22⋊D1112yes—
296C22×C4—22no—
297C22×C4—21no—
298C22×C4—22no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—24no—
302C22×C4—24no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—24no—
306C22×C4—24no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—44no—
310C22×C4—42no—
311C22×C4—444no—
312C22×C4C22⋊Dic1112yes—
313C22×C4C22⋊Dic1111yescharacteristic
314C22×C4C22×Dic1111yescharacteristic
315C4⋊C4—28no—
316C22⋊C4—28no—
317C22⋊C4—28no—
318C22⋊C4—444no—
319C22⋊C4—444no—
320C42—24no—
321C42—21no—
322C42—21no—
323C42C22⋊Dic1112yes—
324C42C22⋊Dic1112yes—
325C11#1269511yescharacteristic, complemented, Sylow
326C23—22no—
327C23—21no—
328C23—21no—
329C23—22no—
330C23—22no—
331C23—42no—
332C23—44no—
333C23—44no—
334C23—41no—
335C23—41no—
336C23#6689812yes—
337C23C2×C22⋊Dic1111yescharacteristic
338C23#6700614yes—
339Q8—42no—
340Q8—42no—
341Q8—42no—
342Q8—42no—
343D4—42no—
344D4—42no—
345D4—42no—
346D4—416no—
347D4—42no—
348D4—48no—
349D4—48no—
350C2×C4—24no—
351C2×C4—24no—
352C2×C4—24no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—48no—
364C2×C4—48no—
365C2×C4—48no—
366C2×C4—42no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—884no—
370C2×C4—888no—
371C2×C4#6689812yes—
372C2×C4C2×C22⋊Dic1111yescharacteristic
373C2×C4C2×C22⋊Dic1111yescharacteristic
374C22—22no—
375C22—22no—
376C22—24no—
377C22—44no—
378C22—42no—
379C22—42no—
380C22—44no—
381C22—44no—
382C22—42no—
383C22—42no—
384C22—82no—
385C22—82no—
386C22—82no—
387C22C2×#6689811yescharacteristic
388C22C2×#6689811yescharacteristic
389C22#1062286011yescharacteristic
390C4—24no—
391C4—22no—
392C4—21no—
393C4—21no—
394C4—42no—
395C4—42no—
396C4—42no—
397C4—1764no—
398C2—21no—
399C2—21no—
400C2—44no—
401C2—42no—
402C2—82no—
403C2#1306853111yescharacteristic
404C2#1307028112yes—
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC22×D4C22×D11
Fitting, prime radicalC2×C11×#532C2
socleC22×C11C2×#99
cosocleC22×D4×C11C23
hypercenterC2×#532D11
hypocenterC11#12695
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. C2×#10622179C2semidirect
2. C2×#10622183C2semidirect
3. #13068534C2semidirect
5. C22×C11×#41C4semidirect
9. C2×C11×C4⋊Q8C4semidirect
11. C2×C11×#124C4semidirect
15. C22×C42×C11C4semidirect
176. C22×#41Dic11semidirect
180. C2×C4⋊Q8Dic11semidirect
182. C2×#124Dic11semidirect
186. C22×C42Dic11semidirect
325. C11#12695semidirect

Maximal subgroups

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

subgroupindex
C2×#106221792
C2×#106221832
#130685342
C2×C11×#5322
#1269511