Finite Group Databasebeta

← #14641997

Subgroups — #14641997

Order 2816.

594 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 109 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
1D11×#389C211yesmaximal, characteristic
2#13068377C211yesmaximal, characteristic
3#13068377C211yesmaximal, characteristic
4#13066440C211yesmaximal, characteristic, complemented
5#13066439C211yesmaximal, characteristic, complemented
6#13066438C211yesmaximal, characteristic, complemented
7C11×#1271C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×D11—21no—
9C2×C4⋊C4×D11C411yescharacteristic
10C2×C4⋊C4×D11C411yescharacteristic
11C2×C42×D11C2211yescharacteristic
12C11×#389C2211yescharacteristic
13C2×(C2×D11)⋊C8—21no—
14C2×(C2×D11)⋊C8—21no—
15C2×#66879—21no—
16C2×#66879—21no—
17#10622598C411yescharacteristic
18#10622586C411yescharacteristic
19#10622585—21no—
20#10622541C2211yescharacteristic
21D11×#95—21no—
22#10622260—21no—
23C11×#336C2211yescharacteristic
24C11×#336C2211yescharacteristic
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×C4×D11—21no—
28C22×C4×D11—21no—
29C22×C4×D11C2×C411yescharacteristic
30C22×C4×D11D411yescharacteristic
31C22×C4×D11D411yescharacteristic
32C22×C8×C11—21no—
33C22×C8×C11—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C42×C11C2311yescharacteristic
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11C2×C411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48C22×C11⋊C8—21no—
49C22×C11⋊C8—21no—
50C4⋊C4×D11—22no—
51C4⋊C4×D11—22no—
52C4⋊C4×D11—42no—
53C4⋊C4×D11—42no—
54C4⋊C4×D11—42no—
55C42×D11—42no—
56C11×#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60(C2×D11)⋊C8—24no—
61(C2×D11)⋊C8—24no—
62#66879—42no—
63#66879—42no—
64#7627—111nomaximal, Sylow
65C23×D11C22⋊C411yescharacteristic
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11C22⋊C411yescharacteristic
74C22×Dic11C22⋊C411yescharacteristic
75C22×Dic11C22⋊C411yescharacteristic
76C2×C4×D11—22no—
77C2×C4×D11—24no—
78C2×C4×D11—22no—
79C2×C4×D11—22no—
80C2×C4×D11—22no—
81C2×C4×D11—21no—
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—41no—
88C2×C4×D11—41no—
89C2×C4×D11—42no—
90C2×C4×D11—42no—
91C2×C4×D11—42no—
92C2×C4×D11—42no—
93C2×C4×D11—42no—
94C2×C8×C11—22no—
95C2×C8×C11—22no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
99C2×C8×C11—41no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4M1612yes—
105C42×C11—41no—
106C4⋊Dic11—21no—
107C4⋊Dic11—41no—
108C4⋊Dic11—42no—
109C4⋊Dic11M1612yes—
110Dic11⋊C4—24no—
111Dic11⋊C4—42no—
112Dic11⋊C4—42no—
113Dic11⋊C4—41no—
114Dic11⋊C4—41no—
115C4×Dic11—22no—
116C4×Dic11—22no—
117C4×Dic11—41no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—41no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—41no—
124C2×#389—111no—
125#1749—111no—
126#1749—111no—
127#1271—111no—
128#1271—111no—
129#1271—111no—
130#1271D1111yescharacteristic, complemented
131C23×C11C2×C22⋊C411yescharacteristic
132C22×D11—21no—
133C22×D11—21no—
134C22×D11—21no—
135C22×D11—21no—
136C22×D11#10112yes—
137C22×D11#10412yes—
138C22×D11#10412yes—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—22no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11C2×M1611yescharacteristic
152C2×C4×C11C2×M1611yescharacteristic
153C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C11#13711yescharacteristic
156C2×C4×C11#13711yescharacteristic
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—22no—
160C2×Dic11—21no—
161C2×Dic11—21no—
162C2×Dic11—21no—
163C2×Dic11—21no—
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11#9912yes—
172C4×D11—24no—
173C4×D11—24no—
174C4×D11—42no—
175C4×D11—42no—
176C4×D11—42no—
177C4×D11—42no—
178C4×D11—48no—
179C4×D11—84no—
180C8×C11—42no—
181C8×C11—42no—
182C11⋊C8—42no—
183C11⋊C8—42no—
184C22×C4⋊C4—111no—
185C22×C4⋊C4—111no—
186C22×C4⋊C4—221no—
187C22×C42—111no—
188C2×C22⋊C8—221no—
189C2×C22⋊C8—221no—
190C2×#97—221no—
191C2×#97—221no—
192#389—111no—
193#389—111no—
194#389—111no—
195#389—221no—
196#389—221no—
197#389C2×D1111yescharacteristic
198C2×#95—221no—
199#336—111no—
200#336—111no—
201#336C2×D1111yescharacteristic
202#336C2×D1111yescharacteristic
203C22×C11#40711yescharacteristic
204C22×C11C2×#9911yescharacteristic
205C22×C11C2×#10111yescharacteristic
206C22×C11#41811yescharacteristic
207C22×C11#41911yescharacteristic
208C22×C11C2×#10411yescharacteristic
209C22×C11C2×#10411yescharacteristic
210C2×D11—22no—
211C2×D11—22no—
212C2×D11—22no—
213C2×D11—22no—
214C2×D11—22no—
215C2×D11—22no—
216C2×D11#33014yes—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—42no—
224C4×C11—81no—
225Dic11—22no—
226Dic11—42no—
227Dic11—41no—
228Dic11—41no—
229Dic11—81no—
230C23×C4—111no—
231C23×C4—111no—
232C23×C4—111no—
233C23×C4—221no—
234C23×C4—221no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—221no—
238C22×C8—221no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—111no—
241C2×C4⋊C4—111no—
242C2×C4⋊C4—222no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4—222no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4—442no—
250C2×C4⋊C4—442no—
251C2×C4⋊C4—442no—
252C2×C4⋊C4C4×D1111yescharacteristic
253C2×C4⋊C4C4×D1111yescharacteristic
254C2×C42—111no—
255C2×C42—111no—
256C2×C42—111no—
257C2×C42—442no—
258C2×C42C22×D1111yescharacteristic
259C22⋊C8—224no—
260C22⋊C8—224no—
261#97—442no—
262#97—442no—
263#95—21no—
264#95—221no—
265#95—221no—
266#95—221no—
267C2×C11#146311yescharacteristic
268C2×C11#149011yescharacteristic
269C2×C11#149111yescharacteristic
270C2×C11#150711yescharacteristic
271C2×C11#150811yescharacteristic
272C2×C11C2×#33011yescharacteristic
273C2×C11#155611yescharacteristic
274D11—24no—
275C24—111no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—111no—
279C22×C4—111no—
280C22×C4—111no—
281C22×C4—222no—
282C22×C4—222no—
283C22×C4—222no—
284C22×C4—222no—
285C22×C4—224no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4—221no—
293C22×C4—221no—
294C22×C4—441no—
295C22×C4—441no—
296C22×C4—442no—
297C22×C4—442no—
298C22×C4—442no—
299C22×C4—442no—
300C22×C4—442no—
301C22×C4C2×C4×D1111yescharacteristic
302C22×C4D4×D1111yescharacteristic
303C22×C4D4×D1111yescharacteristic
304C2×C8—22no—
305C2×C8—22no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—222no—
311C2×C8—222no—
312C2×C8—441no—
313C2×C8—441no—
314C2×C8—441no—
315C2×C8—441no—
316C4⋊C4—21no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—112no—
321C4⋊C4—224no—
322C4⋊C4—221no—
323C4⋊C4—441no—
324C4⋊C4—442no—
325C4⋊C4—442no—
326C4⋊C4—442no—
327C4⋊C4—441no—
328C4⋊C4—441no—
329C4⋊C4#431312yes—
330C42—41no—
331C42—222no—
332C42—222no—
333C42—441no—
334C11#762711yescharacteristic, complemented, Sylow
335C23—112no—
336C23—112no—
337C23—112no—
338C23—221no—
339C23—221no—
340C23—221no—
341C23—221no—
342C23C22⋊C4×D1111yescharacteristic
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—22no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—112no—
356C2×C4—224no—
357C2×C4—224no—
358C2×C4—221no—
359C2×C4—221no—
360C2×C4—222no—
361C2×C4—221no—
362C2×C4—221no—
363C2×C4—221no—
364C2×C4—221no—
365C2×C4—221no—
366C2×C4—221no—
367C2×C4—442no—
368C2×C4—442no—
369C2×C4—442no—
370C2×C4—442no—
371C2×C4—448no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4—441no—
376C2×C4—441no—
377C2×C4—884no—
378C2×C4C2×#431311yescharacteristic
379C2×C4M16×D1111yescharacteristic
380C2×C4#6696411yescharacteristic
381C2×C4#6696711yescharacteristic
382C2×C4#6696811yescharacteristic
383C2×C4#6697111yescharacteristic
384C8—42no—
385C8—42no—
386C8—442no—
387C8—442no—
388C22—114no—
389C22—222no—
390C22—222no—
391C22—222no—
392C22—222no—
393C22—222no—
394C22—222no—
395C22#1062233911yescharacteristic
396C22D11×#9911yescharacteristic
397C22D11×#10111yescharacteristic
398C22#1062238311yescharacteristic
399C22#1062241511yescharacteristic
400C22D11×#10411yescharacteristic
401C22D11×#10411yescharacteristic
402C4—21no—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—42no—
409C4—81no—
410C4—222no—
411C4—442no—
412C4—441no—
413C4—441no—
414C4—881no—
415C2—224no—
416C2#1306694411yescharacteristic
417C2#1306705711yescharacteristic
418C2#1306706111yescharacteristic
419C2#1306713011yescharacteristic
420C2#1306713411yescharacteristic
421C2D11×#33011yescharacteristic
422C2#1306733111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1271C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1271D11
hypocenterC11#7627
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
4. #13066440C2semidirect
5. #13066439C2semidirect
6. #13066438C2semidirect
7. C11×#1271C2semidirect
130. #1271D11semidirect
334. C11#7627semidirect

Maximal subgroups

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

subgroupindex
D11×#3892
#130683772
#130664402
#130664392
#130664382
C11×#12712
#762711