Finite Group Databasebeta

← #14780217

Subgroups — #14780217

Order 2816.

700 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66977C211yesmaximal, characteristic
2#13069550C212yesmaximal, complemented
3#13069338C212yesmaximal, complemented
4#13069232C212yesmaximal
5#13069219C212yesmaximal
6#13069181C212yesmaximal, complemented
7#13069176C212yesmaximal, complemented
8#13068596C211yesmaximal, characteristic
9C11×#1817C211yesmaximal, characteristic
10C22×C42×C11C2211yescharacteristic
11C2×#66977C411yescharacteristic
12C2×C4×Dic22C2211yescharacteristic
13C2×C11×C22⋊C8C2212yes—
14#10622825C411yescharacteristic
15#10622823C412yes—
16C4×C22⋊Dic11C2212yes—
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19C2×#66879C2212yes—
20C2×Dic11⋊C8C2212yes—
21C2×Dic11⋊C8C2212yes—
22C2×C8×Dic11C2212yes—
23C4×C4⋊Dic11C2211yescharacteristic
24#10622546C412yes—
25C4×Dic11⋊C4C2212yes—
26#10622542C411yescharacteristic
27#10622541C411yescharacteristic
28C2×C4⋊(C11⋊C8)C2212yes—
29C11×#336C2211yescharacteristic
30C11×#336C2211yescharacteristic
31C11×#336C2212yes—
32#10622188C2212yes—
33#10622188C2212yes—
34#10622188C2212yes—
35#10622188C2212yes—
36#10622162C2212yes—
37C23×C4×C11C2×C411yescharacteristic
38C23×C4×C11C2×C411yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C22×Dic22C2×C411yescharacteristic
41C22×C8×C11C2312yes—
42C22×C8×C11C2312yes—
43C2×C42×C11—42no—
44C2×C42×C11C2×C411yescharacteristic
45C2×C42×C11C2×C411yescharacteristic
46C2×C42×C11C2311yescharacteristic
47C2×C42×C11C2311yescharacteristic
48C2×C22⋊Dic11C2×C412yes—
49C2×C22⋊Dic11C2×C412yes—
50C2×C4⋊Dic11C2×C411yescharacteristic
51C2×C4⋊Dic11C2×C411yescharacteristic
52C2×C4⋊Dic11C2×C411yescharacteristic
53#66977—24no—
54C2×Dic11⋊C4C2×C412yes—
55C2×Dic11⋊C4C2×C412yes—
56C2×Dic11⋊C4C2×C412yes—
57C2×C4×Dic11C2312yes—
58C2×C4×Dic11C2312yes—
59C22×C11⋊C8C2312yes—
60C22×C11⋊C8C2312yes—
61C4×Dic22—42no—
62C11×C22⋊C8—42no—
63C11⋊#95C2×C412yes—
64C11⋊#95C2×C412yes—
65C11⋊#95C2×C412yes—
66C11⋊#95C2×C412yes—
67C11⋊#95C2×C412yes—
68C22⋊(C11⋊C8)—41no—
69C22⋊(C11⋊C8)—41no—
70#66879—42no—
71Dic11⋊C8—42no—
72Dic11⋊C8—42no—
73C8×Dic11—42no—
74C4⋊(C11⋊C8)—42no—
75#23343—111nomaximal, Sylow
76C24×C11C22×C411yescharacteristic
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—21no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—21no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C22×C411yescharacteristic
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C22×C411yescharacteristic
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C2411yescharacteristic
93C22×Dic11C22×C412yes—
94C22×Dic11C22×C412yes—
95C22×Dic11C22×C412yes—
96C22×Dic11C22×C412yes—
97C2×Dic22—41no—
98C2×Dic22—41no—
99C2×Dic22M1614yes—
100C2×C8×C11—22no—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C42×C11—22no—
107C42×C11—22no—
108C42×C11—41no—
109C42×C11—41no—
110C22⋊Dic11—24no—
111C22⋊Dic11—24no—
112C4⋊Dic11—22no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115Dic11⋊C4—24no—
116Dic11⋊C4—24no—
117Dic11⋊C4—42no—
118C4×Dic11—22no—
119C4×Dic11—22no—
120C4×Dic11—22no—
121C4×Dic11—22no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C4×C22⋊Q8—111no—
129#1984—112no—
130#1940—112no—
131#1924—112no—
132#1923—112no—
133#1917—112no—
134#1916—112no—
135#1817D1111yescharacteristic
136#1797—111no—
137C23×C11—21no—
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—21no—
141C23×C11—21no—
142C23×C11—21no—
143C23×C11#13112yes—
144C23×C11C23×C411yescharacteristic
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—44no—
159C2×C4×C11—44no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11C2×M1612yes—
163C2×C4×C11#13112yes—
164C2×C4×C11H(5,𝔽2)12yes—
165C2×C4×C11H(5,𝔽2)11yescharacteristic
166C2×C4×C112−1+412yes—
167C2×C4×C112−1+411yescharacteristic
168C2×Dic11—22no—
169C2×Dic11—22no—
170C2×Dic11—22no—
171C2×Dic11—22no—
172C2×Dic11—22no—
173C2×Dic11—22no—
174C2×Dic11—22no—
175C2×Dic11—22no—
176C2×Dic11—22no—
177C2×Dic11—22no—
178C2×Dic11—22no—
179C2×Dic11C2×M1614yes—
180Dic22—44no—
181C8×C11—42no—
182C8×C11—42no—
183C11⋊C8—42no—
184C11⋊C8—42no—
185C2×C22⋊Q8—111no—
186C2×C4×Q8—111no—
187C22×C42C2×D1111yescharacteristic
188C2×C4⋊C8—112no—
189C2×C4⋊C8—112no—
190C2×C4⋊C8—112no—
191C2×C22⋊C8—111no—
192C2×C22⋊C8—111no—
193C2×C22⋊C8C2×D1112yes—
194C2×#97—112no—
195C2×C4×C8—112no—
196#391—111no—
197#389—111no—
198#387—112no—
199#385—112no—
200#380—111no—
201C4×C4⋊C4—112no—
202C4×C4⋊C4—111no—
203C4×C22⋊C4—112no—
204#336—112no—
205#336—112no—
206#336—112no—
207#336—112no—
208#336—112no—
209#336C2×D1111yescharacteristic
210#336C2×D1112yes—
211#336C2×D1111yescharacteristic
212C22×C11—22no—
213C22×C11—22no—
214C22×C11—22no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11#51811yescharacteristic
220C22×C11#51911yescharacteristic
221C22×C11#52011yescharacteristic
222C22×C11C22×M1611yescharacteristic
223C22×C11C2×#13111yescharacteristic
224C22×C11C2×#13111yescharacteristic
225C22×C11#56811yescharacteristic
226C4×C11—22no—
227C4×C11—22no—
228C4×C11—41no—
229C4×C11—41no—
230C4×C11—41no—
231C4×C11#56212yes—
232C4×C11#56312yes—
233Dic11—24no—
234Dic11—42no—
235Dic11—42no—
236Dic11—42no—
237C22×Q8—111no—
238C23×C4C4×D1111yescharacteristic
239C23×C4C4×D1111yescharacteristic
240C23×C4C22×D1111yescharacteristic
241C22×C8—112no—
242C22×C8—112no—
243C22×C8C22×D1112yes—
244C22×C8C22×D1112yes—
245C22⋊Q8—224no—
246C4×Q8—442no—
247C2×C4⋊C4—112no—
248C2×C4⋊C4—111no—
249C2×C4⋊C4—112no—
250C2×C4⋊C4—111no—
251C2×C4⋊C4—112no—
252C2×C4⋊C4—111no—
253C2×C22⋊C4—112no—
254C2×C22⋊C4—112no—
255C2×C42—42no—
256C2×C42—112no—
257C2×C42—112no—
258C2×C42C4×D1111yescharacteristic
259C2×C42C4×D1111yescharacteristic
260C2×C42C22×D1111yescharacteristic
261C2×C42C22×D1111yescharacteristic
262C4⋊C8—442no—
263C4⋊C8—442no—
264C4⋊C8—442no—
265C22⋊C8—42no—
266C22⋊C8—441no—
267C22⋊C8—441no—
268#97—442no—
269C4×C8—442no—
270#95—112no—
271#95—112no—
272#95—112no—
273#95—112no—
274#95—112no—
275C2×C11—42no—
276C2×C11#237811yescharacteristic
277C2×C11#297311yescharacteristic
278C2×C11#297711yescharacteristic
279C2×C11#298411yescharacteristic
280C2×C11#298511yescharacteristic
281C2×C11#299111yescharacteristic
282C2×C11#299211yescharacteristic
283C24C2×C4×D1111yescharacteristic
284C2×Q8—114no—
285C2×Q8—441no—
286C2×Q8—441no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—21no—
292C22×C4—22no—
293C22×C4—21no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—112no—
298C22×C4—112no—
299C22×C4—112no—
300C22×C4—112no—
301C22×C4C2×C4×D1111yescharacteristic
302C22×C4C2×C4×D1111yescharacteristic
303C22×C4C2×C4×D1111yescharacteristic
304C22×C4C2×C4×D1111yescharacteristic
305C22×C4C2×C4×D1111yescharacteristic
306C22×C4C23×D1111yescharacteristic
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—222no—
314C2×C8—222no—
315C2×C8—222no—
316C2×C8—222no—
317C2×C8—222no—
318C2×C8—222no—
319C4⋊C4—224no—
320C4⋊C4—224no—
321C4⋊C4—222no—
322C4⋊C4—442no—
323C4⋊C4—441no—
324C4⋊C4—441no—
325C22⋊C4—224no—
326C22⋊C4—224no—
327C42—22no—
328C42—22no—
329C42—41no—
330C42—41no—
331C42—222no—
332C42—222no—
333C42—222no—
334C42—222no—
335C11#2334311yescharacteristic, complemented, Sylow
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23#6696012yes—
343C23C22×C4×D1111yescharacteristic
344Q8—444no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—44no—
359C2×C4—44no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—114no—
363C2×C4—222no—
364C2×C4—222no—
365C2×C4—222no—
366C2×C4—222no—
367C2×C4—222no—
368C2×C4—222no—
369C2×C4—222no—
370C2×C4—222no—
371C2×C4—222no—
372C2×C4—222no—
373C2×C4—222no—
374C2×C4#6695412yes—
375C2×C4M16×D1112yes—
376C2×C4#6703712yes—
377C2×C4#6704211yescharacteristic
378C2×C4#6704311yescharacteristic
379C2×C4#6704312yes—
380C8—42no—
381C8—42no—
382C8—442no—
383C8—442no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22#1062301711yescharacteristic
392C22#1062304711yescharacteristic
393C22#1062305411yescharacteristic
394C22C2×#6695411yescharacteristic
395C22C2×M16×D1111yescharacteristic
396C22C2×#6696011yescharacteristic
397C22#1062327611yescharacteristic
398C4—22no—
399C4—22no—
400C4—41no—
401C4—41no—
402C4—41no—
403C4—224no—
404C4—442no—
405C4—442no—
406C4—442no—
407C4#1062318212yes—
408C4#1062319812yes—
409C2—42no—
410C2#1307178411yescharacteristic
411C2#1307764311yescharacteristic
412C2#1307767011yescharacteristic
413C2#1307770611yescharacteristic
414C2#1307771011yescharacteristic
415C2#1307774511yescharacteristic
416C2#1307775711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1817C2
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#1817D11
hypocenterC11#23343
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1817

Complements

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

NH ≅ G/Ntype
2. #13069550C2semidirect
3. #13069338C2semidirect
6. #13069181C2semidirect
7. #13069176C2semidirect
335. C11#23343semidirect

Maximal subgroups

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

subgroupindex
C4×#669772
#130695502
#130693382
#130692322
#130692192
#130691812
#130691762
#130685962
C11×#18172
#2334311