Finite Group Databasebeta

← #14656209

Subgroups — #14656209

Order 2816.

536 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 101 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#13079764C211yesmaximal, characteristic, complemented
2#13078409C211yesmaximal, characteristic
3#13073785C211yesmaximal, characteristic
4#13067300C211yesmaximal, characteristic, complemented
5#13067008C211yesmaximal, characteristic
6#13066519C211yesmaximal, characteristic, complemented
7C11×#1503C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C4×D44C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13#10622700—21no—
14#10622697—21no—
15#10622694—21no—
16#10622691—21no—
17#10622679—22no—
18#10622657—22no—
19#10622634—22no—
20#10622614—21no—
21#10622608—21no—
22#10622600—22no—
23#10622552—21no—
24#10622549—21no—
25#10622538C2211yescharacteristic
26#10622537C2211yescharacteristic
27#10622286—22no—
28C11×#328—22no—
29#10622120—22no—
30#10622097—22no—
31C22×D44D411yescharacteristic
32C22×C4×D11—21no—
33C22×Dic22—21no—
34C11×C4⋊Q8D411yescharacteristic
35C11×C4⋊Q8D411yescharacteristic
36C11×#125—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C4×Q8×C11—21no—
40C4×Q8×C11—21no—
41C11×#117—21no—
42C2×C11×C4⋊C4—21no—
43C2×C42×C11—21no—
44C2×C42×C11C2311yescharacteristic
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—24no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11D412yes—
49C2×C4⋊Dic11D411yescharacteristic
50C2×#4318—21no—
51C4×D44—21no—
52C4×D44—21no—
53C4×D44—21no—
54C4×D44—21no—
55#66922—21no—
56#66922—21no—
57#66922—21no—
58#66922—21no—
59C11×C4⋊C8—21no—
60C11×C22⋊C8—21no—
61C4×C8×C11—21no—
62C11×#95D412yes—
63#66899—24no—
64C11⋊#95—24no—
65C22⋊(C11⋊C8)—21no—
66#66873—22no—
67#66873—22no—
68#66872—22no—
69#66871—22no—
70#66871—24no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)D412yes—
73C4⋊(C11⋊C8)D412yes—
74C4×C11⋊C8—21no—
75#10249—111nomaximal, Sylow
76C23×D11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C22×C4×C11—22no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×Dic11—21no—
84C22×Dic11—22no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44—21no—
88C2×D44—21no—
89C2×D44—21no—
90C2×D44Q1612yes—
91C2×C4×D11—44no—
92C2×C4×D11—41no—
93C2×C4×D11—41no—
94C2×Dic22—41no—
95C2×Dic22—41no—
96C2×Dic22—82no—
97C2×C8×C11—41no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—42no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C22⋊C4—41no—
106C42×C11—41no—
107C42×C11—41no—
108C42×C11—41no—
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11#4111yescharacteristic
113(C2×D11)⋊C4—41no—
114(C2×D11)⋊C4—41no—
115(C2×D11)⋊C4—84no—
116C4⋊Dic11—21no—
117C4⋊Dic11—22no—
118C4⋊Dic11—22no—
119C4⋊Dic11—21no—
120C4⋊Dic11—41no—
121C4⋊Dic11—41no—
122#4318—41no—
123#4318—41no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126#3230—111no—
127#3077—111no—
128#2563—111no—
129#1549—111no—
130#1503D1111yescharacteristic, complemented
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—
141C2×C4×C11—22no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12711yescharacteristic
154C2×C4×C11C2×Q1611yescharacteristic
155C2×C4×C11#13511yescharacteristic
156C2×C4×C11#13711yescharacteristic
157C2×C4×C11#13711yescharacteristic
158C2×Dic11—44no—
159C2×Dic11—42no—
160C2×Dic11—42no—
161C2×Dic11—41no—
162D44—22no—
163D44—22no—
164D44—41no—
165D44—41no—
166C4×D11—82no—
167C4×D11—82no—
168Dic22—82no—
169Dic22—82no—
170C8×C11—81no—
171C11⋊C8—42no—
172C11⋊C8—42no—
173#533C2×D1111yescharacteristic
174C2×C4⋊Q8—111no—
175C2×C4×D4—111no—
176#500—221no—
177#487—221no—
178#484—222no—
179#478—222no—
180#477—222no—
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⋊C4C2×D1111yescharacteristic
193#332—222no—
194#328—22no—
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—82no—
210C4×C11—81no—
211C4×C11—81no—
212C4×C11#45111yescharacteristic
213C4×C11#45211yescharacteristic
214C4×C11#45412yes—
215C4×C11#46711yescharacteristic
216C4×C11#47011yescharacteristic
217Dic11—81no—
218Dic11—82no—
219C22×Q8—221no—
220C22×D4—111no—
221C23×C4—221no—
222C2×M16—221no—
223C4⋊Q8—221no—
224C4⋊Q8—221no—
225C4⋊Q8—221no—
226C4⋊Q8—221no—
227C4⋊Q8D4411yescharacteristic
228C4⋊Q8D4411yescharacteristic
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—112no—
242C2×C4⋊C4—221no—
243C2×C22⋊C4—221no—
244C2×C22⋊C4—224no—
245C2×C42—21no—
246C2×C42C22×D1111yescharacteristic
247#107—222no—
248#107—224no—
249#106—222no—
250C4⋊C8—21no—
251C4⋊C8—112no—
252C4⋊C8—112no—
253C4⋊C8—221no—
254#103—224no—
255#102—222no—
256#102—222no—
257C22⋊C8—21no—
258C22⋊C8—221no—
259C4×C8—21no—
260C4×C8—221no—
261#95—224no—
262#95C22⋊D1112yes—
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—441no—
273C2×Q8—441no—
274C2×Q8—882no—
275C2×D4—112no—
276C2×D4—221no—
277C2×D4—221no—
278C2×D4—221no—
279C2×D4—221no—
280C2×D4—221no—
281C22×C4—22no—
282C22×C4—221no—
283C22×C4—222no—
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—41no—
293C2×C8—222no—
294C2×C8—222no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—42no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—222no—
303C4⋊C4—221no—
304C4⋊C4—221no—
305C4⋊C4—222no—
306C4⋊C4—441no—
307C4⋊C4—441no—
308C22⋊C4—41no—
309C22⋊C4—441no—
310C22⋊C4—441no—
311C22⋊C4—884no—
312C42—41no—
313C42—41no—
314C42—41no—
315C42C2×D4411yescharacteristic
316C42#433911yescharacteristic
317C42D4×D1111yescharacteristic
318C42D4×D1111yescharacteristic
319C11#1024911yescharacteristic, complemented, Sylow
320C23—222no—
321C23—442no—
322C23—442no—
323C23—441no—
324C23—441no—
325C23#6699011yescharacteristic
326Q8—42no—
327Q8—81no—
328Q8—882no—
329Q8—882no—
330D4—222no—
331D4—222no—
332D4—441no—
333D4—441no—
334C2×C4—22no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—444no—
342C2×C4—442no—
343C2×C4—441no—
344C2×C4—442no—
345C2×C4—882no—
346C2×C4—882no—
347C2×C4#6693511yescharacteristic
348C2×C4#6693511yescharacteristic
349C2×C4#6693711yescharacteristic
350C2×C4#6693711yescharacteristic
351C2×C4#6696811yescharacteristic
352C2×C4#6696911yescharacteristic
353C2×C4Q16×D1111yescharacteristic
354C2×C4#6697111yescharacteristic
355C2×C4#6698311yescharacteristic
356C2×C4#6699311yescharacteristic
357C8—81no—
358C8—442no—
359C8—442no—
360C22—21no—
361C22—21no—
362C22—444no—
363C22—442no—
364C22—882no—
365C22—881no—
366C22—881no—
367C22#1062257311yescharacteristic
368C22#1062278611yescharacteristic
369C22#1062279911yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—82no—
374C4—81no—
375C4—81no—
376C4—881no—
377C4—882no—
378C4#1062242111yescharacteristic
379C4#1062242311yescharacteristic
380C4#1062242611yescharacteristic
381C4#1062242911yescharacteristic
382C4#1062244012yes—
383C2—21no—
384C2—21no—
385C2—882no—
386C2#1306962511yescharacteristic
387C2#1306963711yescharacteristic
388C2#1306966811yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1503C2
socleC22×C11#392
prime radicalC22×D44D4
hypercenter#1503D11
hypocenterC11#10249
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
1. #13079764C2semidirect
4. #13067300C2semidirect
6. #13066519C2semidirect
7. C11×#1503C2semidirect
130. #1503D11semidirect
319. C11#10249semidirect

Maximal subgroups

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

subgroupindex
#130797642
#130784092
#130737852
#130673002
#130670082
#130665192
C11×#15032
#1024911