Finite Group Databasebeta

← #14656208

Subgroups — #14656208

Order 2816.

536 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 103 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#13078409C211yesmaximal, characteristic
2#13073790C211yesmaximal, characteristic
3#13067301C211yesmaximal, characteristic, complemented
4#13067115C211yesmaximal, characteristic, complemented
5#13067006C211yesmaximal, characteristic
6#13066518C211yesmaximal, characteristic, complemented
7C11×#3230C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×D44C2211yescharacteristic
11C11×#500—21no—
12C11×#487—21no—
13C11×#484—22no—
14C11×#477—22no—
15C11×#431C2211yescharacteristic
16#10622844—22no—
17#10622700—21no—
18#10622697—21no—
19#10622679—22no—
20#10622614—21no—
21#10622608—21no—
22#10622601—21no—
23#10622600—22no—
24#10622590—21no—
25C4×C4⋊Dic11C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622185—22no—
29#10622176—22no—
30#10622121—22no—
31C22×Q8×C11—21no—
32C22×D44D411yescharacteristic
33C22×C4×D11—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8D411yescharacteristic
39C11×C4⋊Q8D411yescharacteristic
40C11×#125—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C11×#117—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4D412yes—
48C2×C42×C11C2311yescharacteristic
49C2×(C2×D11)⋊C4—21no—
50C2×(C2×D11)⋊C4—24no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11D411yescharacteristic
53C2×C4×Dic11—21no—
54C2×#4318—21no—
55C4×D44—21no—
56C4×D44—21no—
57C4×D44—21no—
58C4×D44—21no—
59C11×#107—24no—
60C11×C4⋊C8D412yes—
61C11×#103—24no—
62C11×C22⋊C8—21no—
63C4×C8×C11—21no—
64C11⋊#95—24no—
65C11⋊#95D412yes—
66C22⋊(C11⋊C8)—21no—
67#66873—22no—
68#66873—22no—
69#66872—22no—
70#66871—22no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)D412yes—
74C4×C11⋊C8—21no—
75#10249—111nomaximal, Sylow
76C23×D11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×Q8×C11—82no—
82C22×C4×C11—22no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×Dic11—21no—
87C22×Dic11—22no—
88C2×D44—21no—
89C2×D44—21no—
90C2×D44—21no—
91C2×D44—21no—
92C2×D44—21no—
93C2×D44Q1612yes—
94C2×C4×D11—44no—
95C2×C4×D11—41no—
96C2×C4×D11—41no—
97C2×C8×C11—22no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C22⋊C4—41no—
109C42×C11—41no—
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11#4111yescharacteristic
114(C2×D11)⋊C4—41no—
115(C2×D11)⋊C4—41no—
116(C2×D11)⋊C4—84no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—42no—
120C4×Dic11—41no—
121C4×Dic11—41no—
122#4318—41no—
123#4318—41no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—41no—
126#3230D1111yescharacteristic, complemented
127#3077—111no—
128#2563—111no—
129#1549—111no—
130#1503—111no—
131#1478—111no—
132#1303—111no—
133C23×C11#12011yescharacteristic
134C22×D11—22no—
135C22×D11—42no—
136C22×D11—42no—
137C22×D11—41no—
138C22×D11—41no—
139Q8×C11—42no—
140Q8×C11—81no—
141Q8×C11—82no—
142Q8×C11—82no—
143C2×C4×C11—22no—
144C2×C4×C11—41no—
145C2×C4×C11—44no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—42no—
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12711yescharacteristic
155C2×C4×C11C2×Q1611yescharacteristic
156C2×C4×C11#13511yescharacteristic
157C2×C4×C11#13711yescharacteristic
158C2×C4×C11#13711yescharacteristic
159C2×Dic11—42no—
160C2×Dic11—42no—
161C2×Dic11—42no—
162C2×Dic11—41no—
163C2×Dic11—42no—
164D44—22no—
165D44—22no—
166D44—41no—
167D44—41no—
168C4×D11—82no—
169C4×D11—82no—
170C8×C11—42no—
171C11⋊C8—42no—
172C11⋊C8—81no—
173#533C2×D1111yescharacteristic
174C2×C4⋊Q8C2×D1111yescharacteristic
175C2×C4×D4—111no—
176#500—21no—
177#487—21no—
178#484—22no—
179#478—222no—
180#477—22no—
181#476—221no—
182#474—221no—
183#431—111no—
184#431C2×D1111yescharacteristic
185#428—221no—
186#423—111no—
187#418—221no—
188#393—222no—
189#390—221no—
190#382—221no—
191#380—222no—
192C4×C4⋊C4—111no—
193#332—222no—
194#328—222no—
195D4⋊C8—222no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11#39211yescharacteristic
199C22×C11#45111yescharacteristic
200C22×C11#45211yescharacteristic
201C2×D11—44no—
202C2×D11—42no—
203C2×D11—82no—
204C2×D11—81no—
205C2×D11—81no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—81no—
210C4×C11—82no—
211C4×C11—81no—
212C4×C11#45111yescharacteristic
213C4×C11#45211yescharacteristic
214C4×C11#45412yes—
215C4×C11#46711yescharacteristic
216C4×C11#47011yescharacteristic
217Dic11—82no—
218Dic11—81no—
219C22×Q8—21no—
220C22×D4—111no—
221C23×C4—221no—
222C2×M16—221no—
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8C22⋊D1111yescharacteristic
228C4⋊Q8C22⋊D1111yescharacteristic
229#125—21no—
230C22⋊Q8—21no—
231C22⋊Q8—21no—
232C4×Q8—21no—
233C4×Q8—21no—
234C4×D4—221no—
235C4×D4—221no—
236C4×D4—221no—
237C4×D4—221no—
238#117—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—111no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4C22⋊D1112yes—
243C2×C22⋊C4—221no—
244C2×C22⋊C4—224no—
245C2×C42—221no—
246C2×C42C22×D1111yescharacteristic
247#107—24no—
248#107—222no—
249#106—222no—
250C4⋊C8—112no—
251C4⋊C8—221no—
252C4⋊C8—221no—
253C4⋊C8C22⋊D1112yes—
254#103—24no—
255#102—222no—
256#102—222no—
257C22⋊C8—21no—
258C22⋊C8—221no—
259C4×C8—21no—
260C4×C8—221no—
261#95—112no—
262#95—224no—
263C2×C11—21no—
264C2×C11—21no—
265C2×C11#200111yescharacteristic
266C2×C11#200311yescharacteristic
267C2×C11#200811yescharacteristic
268D11—82no—
269C24—221no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—82no—
275C2×D4—112no—
276C2×D4—221no—
277C2×D4—221no—
278C2×D4—221no—
279C2×D4—221no—
280C2×D4—221no—
281C22×C4—22no—
282C22×C4—222no—
283C22×C4—221no—
284C22×C4—444no—
285C22×C4—441no—
286C22×C4—441no—
287C22×C4D4×D1111yescharacteristic
288C22×C4D4×D1111yescharacteristic
289C22×C4C2×C22⋊D1111yescharacteristic
290M16—441no—
291M16—441no—
292C2×C8—22no—
293C2×C8—222no—
294C2×C8—441no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—22no—
298C4⋊C4—21no—
299C4⋊C4—22no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—221no—
306C4⋊C4—221no—
307C4⋊C4—442no—
308C22⋊C4—41no—
309C22⋊C4—441no—
310C22⋊C4—441no—
311C22⋊C4—884no—
312C42—41no—
313C42—441no—
314C42—441no—
315C42D4×D1111yescharacteristic
316C42#434111yescharacteristic
317C42C2×C22⋊D1111yescharacteristic
318C42C2×C22⋊D1111yescharacteristic
319C11#1024911yescharacteristic, complemented, Sylow
320C23—222no—
321C23—442no—
322C23—442no—
323C23—441no—
324C23—441no—
325C23#6699011yescharacteristic
326Q8—42no—
327Q8—81no—
328Q8—82no—
329Q8—82no—
330D4—222no—
331D4—222no—
332D4—441no—
333D4—441no—
334C2×C4—22no—
335C2×C4—41no—
336C2×C4—44no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—442no—
341C2×C4—442no—
342C2×C4—442no—
343C2×C4—442no—
344C2×C4—441no—
345C2×C4—882no—
346C2×C4—882no—
347C2×C4Q16×D1111yescharacteristic
348C2×C4#6697111yescharacteristic
349C2×C4#6697111yescharacteristic
350C2×C4#6697211yescharacteristic
351C2×C4#6699011yescharacteristic
352C2×C4#6699111yescharacteristic
353C2×C4#6699211yescharacteristic
354C2×C4#6699211yescharacteristic
355C2×C4#6699311yescharacteristic
356C2×C4#6700611yescharacteristic
357C8—42no—
358C8—442no—
359C8—881no—
360C22—21no—
361C22—21no—
362C22—444no—
363C22—442no—
364C22—882no—
365C22—881no—
366C22—881no—
367C22#1062279911yescharacteristic
368C22#1062280011yescharacteristic
369C22#1062283611yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—81no—
374C4—82no—
375C4—81no—
376C4—882no—
377C4—881no—
378C4#1062279911yescharacteristic
379C4#1062280011yescharacteristic
380C4#1062280111yescharacteristic
381C4#1062280211yescharacteristic
382C4#1062285812yes—
383C2—21no—
384C2—21no—
385C2—882no—
386C2#1306962311yescharacteristic
387C2#1306963611yescharacteristic
388C2#1306966711yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3230C2
socleC22×C11#392
prime radicalC22×D44D4
hypercenter#3230D11
hypocenterC11#10249
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3230

Complements

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

NH ≅ G/Ntype
3. #13067301C2semidirect
4. #13067115C2semidirect
6. #13066518C2semidirect
7. C11×#3230C2semidirect
126. #3230D11semidirect
319. C11#10249semidirect

Maximal subgroups

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

subgroupindex
#130784092
#130737902
#130673012
#130671152
#130670062
#130665182
C11×#32302
#1024911