Finite Group Databasebeta

← #14726885

Subgroups — #14726885

Order 2816.

1222 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1222 conjugacy classes of subgroups — too many to draw. Only its 203 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
1#13078612C212yesmaximal, complemented
2#13073521C211yesmaximal, characteristic, complemented
3#13067619C214yesmaximal, complemented
4#13067551C214yesmaximal, complemented
5#13067176C212yesmaximal, complemented
6#13066940C211yesmaximal, characteristic, complemented
7C11×#3497C211yesmaximal, characteristic, complemented
8C2×C11×2−1+4—21no—
9C11×#550—22no—
10D4×Q8×C11—22no—
11C11×#548—24no—
12C11×#537—21no—
13C11×#537C2214yes—
14C11×#532—22no—
15C11×#532C2212yes—
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#66999—21no—
18C2×C4×D44C2211yescharacteristic
19#10622700—22no—
20#10622685—22no—
21#10622649C2214yes—
22#10622646C2214yes—
23C4×#4323—24no—
24#10622604C2212yes—
25#10622600—21no—
26#10622596C2212yes—
27#10622553—22no—
28#10622549C2211yescharacteristic
29#10622538C2212yes—
30#10622175C2218yes—
31#10622166C2214yes—
32C11×2−1+4—44no—
33C11×2−1+4—44no—
34C2×C11×#41—24no—
35C2×C11×#41—24no—
36C2×C11×#41—22no—
37C22×Q8×C11—24no—
38C22×Q8×C11D411yescharacteristic
39C22×D44C2311yescharacteristic
40C22×C4×D11—21no—
41C11×C4⋊Q8—22no—
42C11×C4⋊Q8D412yes—
43C11×#127—22no—
44C11×#127D412yes—
45C11×#124—24no—
46C11×#124—22no—
47C11×C22⋊Q8—24no—
48C11×C22⋊Q8—28no—
49C11×#121—24no—
50C11×#121—28no—
51C11×#121—22no—
52C11×#121—24no—
53C11×#121C2314yes—
54C4×Q8×C11—22no—
55C4×Q8×C11—22no—
56C4×D4×C11—24no—
57C4×D4×C11—24no—
58C4×D4×C11—22no—
59C4×D4×C11D414yes—
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C11×C4⋊C4C2312yes—
62C2×C42×C11D412yes—
63C2×C42×C11C2311yescharacteristic
64#66999—44no—
65C2×#4323—24no—
66C2×(C2×D11)⋊C4—21no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11C2311yescharacteristic
71C2×Dic11⋊C4—22no—
72C4×D44—22no—
73C4×D44—22no—
74#66896—24no—
75C11⋊#95—21no—
76C11⋊#95—22no—
77C11⋊#95C2312yes—
78C22⋊(C11⋊C8)C2314yes—
79#66873—24no—
80#66871—24no—
81C4⋊(C11⋊C8)—22no—
82C4×C11⋊C8—22no—
83#18218—111nomaximal, Sylow
84C23×D11—21no—
85C11×#41—48no—
86C11×#41—416no—
87C11×#41—48no—
88C11×#41—44no—
89C11×#41—44no—
90C2×Q8×C11—24no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11—416no—
95C2×Q8×C11D814yescomplemented
96C2×D4×C11—24no—
97C2×D4×C11—24no—
98C2×D4×C11—24no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11C2×D414yes—
102C22×C4×C11—28no—
103C22×C4×C11—24no—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2411yescharacteristic
109C22×Dic11—22no—
110C22×Dic11—21no—
111C2×D44—22no—
112C2×D44—42no—
113C2×C4×D11—42no—
114C2×C4×D11—42no—
115C2×C4×D11—42no—
116C11×C4⋊C4—24no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—24no—
120C11×C4⋊C4C2×D414yes—
121C11×C22⋊C4—28no—
122C11×C22⋊C4—24no—
123C11×C22⋊C4—24no—
124C42×C11—22no—
125C42×C11—22no—
126C42×C11C2×D412yes—
127C42×C11C2×D412yes—
128#4323—48no—
129(C2×D11)⋊C4—44no—
130(C2×D11)⋊C4—41no—
131(C2×D11)⋊C4—41no—
132(C2×D11)⋊C4—44no—
133C4⋊Dic11—22no—
134C4⋊Dic11—42no—
135Dic11⋊C4—44no—
136C2×C11⋊C8—24no—
137#3497D1111yescharacteristic, complemented
138#3100—112no—
139#2536—111no—
140#1610—114no—
141#1598—114no—
142#1517—112no—
143#1461—111no—
144C23×C11—24no—
145C23×C11C22×D411yescharacteristic
146C22×D11—22no—
147C22×D11—41no—
148C22×D11—41no—
149C22×D11—41no—
150C22×D11—41no—
151C22×D11—41no—
152C22×D11—41no—
153Q8×C11—28no—
154Q8×C11—48no—
155Q8×C11—44no—
156D4×C11—44no—
157D4×C11—44no—
158D4×C11—48no—
159D4×C11—44no—
160D4×C11—44no—
161D4×C11—44no—
162D4×C11—84no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—24no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—416no—
170C2×C4×C11—48no—
171C2×C4×C11—42no—
172C2×C4×C11#12011yescharacteristic
173C2×C4×C11#12011yescharacteristic
174C2×C4×C11#12012yes—
175C2×C4×C11C2×D814yes—
176C2×C4×C11C2×D812yes—
177C2×C4×C11AGL(1,ℤ/8)12yes—
178C2×C4×C11C22×D412yes—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—42no—
184C2×Dic11—41no—
185D44—24no—
186D44—42no—
187C4×D11—84no—
188C11⋊C8—44no—
189C2×2−1+4—21no—
190#550—22no—
191D4×Q8—22no—
192#548—24no—
193#537—21no—
194#537C2×D1114yes—
195#532—22no—
196#532C2×D1112yes—
197C2×C22⋊Q8—221no—
198C2×C4×Q8C2×D1111yescharacteristic
199C2×C4×D4—111no—
200#480—114no—
201#474—222no—
202#459—222no—
203#447—114no—
204C4×D8—224no—
205#431—112no—
206#398—112no—
207#394—112no—
208#388—222no—
209#382—111no—
210#380—221no—
211#327—118no—
212#324—114no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—44no—
216C22×C11—44no—
217C22×C11—44no—
218C22×C11C2×#12011yescharacteristic
219C22×C11C22×D811yescharacteristic
220C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
221C2×D11—42no—
222C2×D11—42no—
223C2×D11—42no—
224C2×D11—81no—
225C2×D11—81no—
226C2×D11—81no—
227C2×D11—81no—
228C4×C11—24no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—22no—
232C4×C11—44no—
233C4×C11—42no—
234C4×C11#44714yes—
235Dic11—82no—
236Dic11—81no—
2372−1+4—44no—
2382−1+4—44no—
239C2×#41—24no—
240C2×#41—24no—
241C2×#41—22no—
242C22×Q8—24no—
243C22×Q8C22⋊D1111yescharacteristic
244C22×D4—111no—
245C23×C4—221no—
246C2×D8—224no—
247C4⋊Q8—22no—
248C4⋊Q8C22⋊D1112yes—
249#127—22no—
250#127C22⋊D1112yes—
251#124—24no—
252#124—22no—
253C22⋊Q8—24no—
254C22⋊Q8—28no—
255C22⋊Q8—444no—
256#121—24no—
257#121—28no—
258#121—22no—
259#121—24no—
260#121C22×D1114yes—
261C4×Q8—22no—
262C4×Q8—22no—
263C4×D4—24no—
264C4×D4—24no—
265C4×D4—22no—
266C4×D4—222no—
267C4×D4—222no—
268C4×D4C22⋊D1114yes—
269C2×C4⋊C4—111no—
270C2×C4⋊C4—221no—
271C2×C4⋊C4—222no—
272C2×C4⋊C4C22⋊D1111yescharacteristic
273C2×C4⋊C4C22×D1112yes—
274C2×C22⋊C4—221no—
275C2×C22⋊C4—222no—
276C2×C22⋊C4—222no—
277C2×C42C22⋊D1112yes—
278C2×C42C22×D1111yescharacteristic
279#107—224no—
280C4⋊C8—222no—
281#102—224no—
282#102—224no—
283C22⋊C8—114no—
284C4×C8—222no—
285#95—112no—
286#95—222no—
287#95—221no—
288C2×C11—21no—
289C2×C11—21no—
290C2×C11—84no—
291C2×C11C2×#44711yescharacteristic
292C2×C11#302011yescharacteristic
293C2×C11#302511yescharacteristic
294D11—82no—
295C24—221no—
296#41—48no—
297#41—416no—
298#41—48no—
299#41—44no—
300#41—44no—
301C2×Q8—24no—
302C2×Q8—22no—
303C2×Q8—22no—
304C2×Q8—22no—
305C2×Q8—416no—
306C2×Q8#432314yescomplemented
307C2×D4—24no—
308C2×D4—24no—
309C2×D4—24no—
310C2×D4—22no—
311C2×D4—22no—
312C2×D4—222no—
313C2×D4—442no—
314C2×D4C2×C22⋊D1114yes—
315C22×C4—28no—
316C22×C4—24no—
317C22×C4—222no—
318C22×C4—221no—
319C22×C4—442no—
320C22×C4—442no—
321C22×C4—442no—
322C22×C4C2×C22⋊D1112yes—
323C22×C4C2×C22⋊D1112yes—
324C22×C4C2×C22⋊D1111yescharacteristic
325C22×C4C2×C22⋊D1111yescharacteristic
326C22×C4C23×D1111yescharacteristic
327D8—448no—
328C2×C8—224no—
329C4⋊C4—24no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—24no—
333C4⋊C4—222no—
334C4⋊C4—444no—
335C4⋊C4—442no—
336C4⋊C4C2×C22⋊D1114yes—
337C22⋊C4—28no—
338C22⋊C4—24no—
339C22⋊C4—24no—
340C22⋊C4—444no—
341C22⋊C4—444no—
342C22⋊C4—441no—
343C22⋊C4—441no—
344C42—22no—
345C42—22no—
346C42C2×C22⋊D1112yes—
347C42C2×C22⋊D1112yes—
348C11#1821811yescharacteristic, complemented, Sylow
349C23—24no—
350C23—222no—
351C23—441no—
352C23—441no—
353C23—441no—
354C23—441no—
355C23—441no—
356C23—441no—
357C23C22×C22⋊D1111yescharacteristic
358Q8—28no—
359Q8—48no—
360Q8—44no—
361D4—44no—
362D4—44no—
363D4—48no—
364D4—44no—
365D4—44no—
366D4—44no—
367D4—84no—
368D4—224no—
369D4—442no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—24no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—416no—
377C2×C4—48no—
378C2×C4—42no—
379C2×C4—442no—
380C2×C4—442no—
381C2×C4—442no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4—441no—
385C2×C4—884no—
386C2×C4C2×#432314yes—
387C2×C4C2×#432312yes—
388C2×C4#6698512yes—
389C2×C4#6700611yescharacteristic
390C2×C4#6700611yescharacteristic
391C2×C4#6700612yes—
392C2×C4C22×C22⋊D1112yes—
393C8—444no—
394C22—21no—
395C22—21no—
396C22—44no—
397C22—44no—
398C22—44no—
399C22—442no—
400C22—442no—
401C22—442no—
402C22—881no—
403C22—881no—
404C22—881no—
405C22—881no—
406C22C22×#432311yescharacteristic
407C22C2×#6698511yescharacteristic
408C22C2×#6700611yescharacteristic
409C4—24no—
410C4—21no—
411C4—21no—
412C4—22no—
413C4—44no—
414C4—42no—
415C4—882no—
416C4—881no—
417C4#1062283014yes—
418C2—21no—
419C2—21no—
420C2—84no—
421C2—882no—
422C2C2×#1062283011yescharacteristic
423C2#1307798011yescharacteristic
424C2#1307800811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3497C2
socleC22×C11C2×#120
hypercenter#3497D11
hypocenterC11#18218
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3497

Complements

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

NH ≅ G/Ntype
1. #13078612C2semidirect
2. #13073521C2semidirect
3. #13067619C2semidirect
4. #13067551C2semidirect
5. #13067176C2semidirect
6. #13066940C2semidirect
7. C11×#3497C2semidirect
95. C2×Q8×C11D8semidirect
137. #3497D11semidirect
306. C2×Q8#4323semidirect
348. C11#18218semidirect

Maximal subgroups

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

subgroupindex
#130786122
#130735212
#130676192
#130675512
#130671762
#130669402
C11×#34972
#1821811