Finite Group Databasebeta

← #14656207

Subgroups — #14656207

Order 2816.

536 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 105 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#13073789C211yesmaximal, characteristic
3#13067302C211yesmaximal, characteristic, complemented
4#13067115C211yesmaximal, characteristic, complemented
5#13067007C211yesmaximal, characteristic
6#13066517C211yesmaximal, characteristic, complemented
7C11×#3077C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#478—22no—
12C11×#476—21no—
13C11×#474—21no—
14C11×#428—21no—
15C11×#423C2211yescharacteristic
16C11×#418—21no—
17#10622834—21no—
18#10622825—22no—
19#10622694—21no—
20#10622691—21no—
21#10622657—22no—
22#10622634—22no—
23#10622590—21no—
24#10622560—22no—
25C4×C4⋊Dic11C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622538C2211yescharacteristic
28#10622176—22no—
29D4⋊(C11⋊C8)—22no—
30#10622124—22no—
31C22×D4×C11D411yescharacteristic
32C23×C4×C11—21no—
33C22×Dic22—21no—
34C2×C11×M16—21no—
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D411yescharacteristic
37C11×#125—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C11×#117—21no—
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C11×C22⋊C4—21no—
49C2×C42×C11C2311yescharacteristic
50C2×C22⋊Dic11—24no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11D412yes—
54C2×C4×Dic11—21no—
55#66922—21no—
56#66922—21no—
57#66922—21no—
58#66922—21no—
59C11×#107—22no—
60C11×#106—22no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8D412yes—
63C11×#102—22no—
64C11×#102—22no—
65#66899—24no—
66C11⋊#95—24no—
67C11⋊#95D412yes—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70#66871—24no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)D412yes—
73C4×C11⋊C8—21no—
74C4×C11⋊C8—21no—
75#10249—111nomaximal, Sylow
76C24×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11Q1612yes—
85C22×C4×C11—21no—
86C22×C4×C11—44no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×Dic11—22no—
93C22×Dic11—22no—
94C2×Dic22—41no—
95C2×Dic22—41no—
96C2×Dic22—82no—
97C11×M16—41no—
98C11×M16—41no—
99C2×C8×C11—22no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C42×C11—41no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11#4111yescharacteristic
116C22⋊Dic11—84no—
117C4⋊Dic11—22no—
118C4⋊Dic11—22no—
119C4⋊Dic11—42no—
120C4⋊Dic11—41no—
121C4⋊Dic11—41no—
122C4×Dic11—41no—
123C4×Dic11—41no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—41no—
126#3230—111no—
127#3077D1111yescharacteristic
128#2563—111no—
129#1549—111no—
130#1503—111no—
131#1478—111no—
132#1303—111no—
133C23×C11—22no—
134C23×C11—42no—
135C23×C11—42no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11#12011yescharacteristic
139Q8×C11—42no—
140Q8×C11—81no—
141D4×C11—22no—
142D4×C11—22no—
143D4×C11—41no—
144D4×C11—41no—
145C2×C4×C11—22no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—82no—
152C2×C4×C11—82no—
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12711yescharacteristic
159C2×C4×C11C2×Q1611yescharacteristic
160C2×C4×C11#13511yescharacteristic
161C2×C4×C11#13711yescharacteristic
162C2×C4×C11#13711yescharacteristic
163C2×Dic11—42no—
164C2×Dic11—42no—
165C2×Dic11—44no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168Dic22—82no—
169Dic22—82no—
170C8×C11—42no—
171C11⋊C8—42no—
172C11⋊C8—81no—
173#533C2×D1111yescharacteristic
174C2×C4⋊Q8—111no—
175C2×C4×D4C2×D1111yescharacteristic
176#500—221no—
177#487—221no—
178#484—222no—
179#478—22no—
180#477—222no—
181#476—21no—
182#474—21no—
183#431—111no—
184#431—111no—
185#428—21no—
186#423C2×D1111yescharacteristic
187#418—21no—
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—44no—
199C22×C11—42no—
200C22×C11—82no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11#39211yescharacteristic
204C22×C11#45111yescharacteristic
205C22×C11#45211yescharacteristic
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—81no—
210C4×C11—81no—
211C4×C11—81no—
212C4×C11#45111yescharacteristic
213C4×C11#45211yescharacteristic
214C4×C11#45412yes—
215C4×C11#46711yescharacteristic
216C4×C11#47011yescharacteristic
217Dic11—82no—
218Dic11—82no—
219C22×Q8—221no—
220C22×D4C22⋊D1111yescharacteristic
221C23×C4—21no—
222C2×M16—21no—
223C4⋊Q8—221no—
224C4⋊Q8—221no—
225C4⋊Q8—221no—
226C4⋊Q8—221no—
227C4⋊Q8C22⋊D1111yescharacteristic
228C4⋊Q8C22⋊D1111yescharacteristic
229#125—21no—
230C22⋊Q8—21no—
231C22⋊Q8—21no—
232C4×Q8—21no—
233C4×Q8—21no—
234C4×D4—21no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4—21no—
238#117—21no—
239C2×C4⋊C4—112no—
240C2×C4⋊C4—221no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4C22⋊D1111yescharacteristic
243C2×C22⋊C4—21no—
244C2×C22⋊C4—224no—
245C2×C42—221no—
246C2×C42C22×D1111yescharacteristic
247#107—22no—
248#107—224no—
249#106—22no—
250C4⋊C8—21no—
251C4⋊C8—112no—
252C4⋊C8—221no—
253C4⋊C8C22⋊D1112yes—
254#103—224no—
255#102—22no—
256#102—22no—
257C22⋊C8—221no—
258C22⋊C8—221no—
259C4×C8—221no—
260C4×C8—221no—
261#95—112no—
262#95—224no—
263C2×C11—21no—
264C2×C11—21no—
265C2×C11—82no—
266C2×C11#200111yescharacteristic
267C2×C11#200311yescharacteristic
268C2×C11#200811yescharacteristic
269C24—21no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—441no—
273C2×Q8—441no—
274C2×Q8—882no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4#432612yes—
281C22×C4—21no—
282C22×C4—44no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—222no—
286C22×C4—222no—
287C22×C4D4×D1111yescharacteristic
288C22×C4D4×D1111yescharacteristic
289C22×C4C2×C22⋊D1111yescharacteristic
290M16—41no—
291M16—41no—
292C2×C8—22no—
293C2×C8—222no—
294C2×C8—441no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—222no—
304C4⋊C4—222no—
305C4⋊C4—442no—
306C4⋊C4—441no—
307C4⋊C4—441no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—884no—
312C42—41no—
313C42—441no—
314C42—441no—
315C42D4×D1111yescharacteristic
316C42#434111yescharacteristic
317C42C2×C22⋊D1111yescharacteristic
318C42C2×C22⋊D1111yescharacteristic
319C11#1024911yescharacteristic, complemented, Sylow
320C23—22no—
321C23—42no—
322C23—42no—
323C23—41no—
324C23—41no—
325C23#6699011yescharacteristic
326Q8—42no—
327Q8—81no—
328Q8—882no—
329Q8—882no—
330D4—22no—
331D4—22no—
332D4—41no—
333D4—41no—
334C2×C4—22no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—82no—
341C2×C4—82no—
342C2×C4—442no—
343C2×C4—444no—
344C2×C4—442no—
345C2×C4—442no—
346C2×C4—442no—
347C2×C4#6699011yescharacteristic
348C2×C4#6699111yescharacteristic
349C2×C4#6699211yescharacteristic
350C2×C4#6699211yescharacteristic
351C2×C4#6699311yescharacteristic
352C2×C4#6699511yescharacteristic
353C2×C4C2×#432611yescharacteristic
354C2×C4#6700311yescharacteristic
355C2×C4#6700411yescharacteristic
356C2×C4#6700611yescharacteristic
357C8—42no—
358C8—442no—
359C8—881no—
360C22—21no—
361C22—21no—
362C22—44no—
363C22—42no—
364C22—82no—
365C22—81no—
366C22—81no—
367C22#1062266011yescharacteristic
368C22#1062266311yescharacteristic
369C22#1062283611yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—81no—
374C4—81no—
375C4—81no—
376C4—882no—
377C4—882no—
378C4#1062266411yescharacteristic
379C4#1062266511yescharacteristic
380C4#1062281412yes—
381C4#1062284111yescharacteristic
382C4#1062285211yescharacteristic
383C2—21no—
384C2—21no—
385C2—82no—
386C2#1306962411yescharacteristic
387C2#1306963511yescharacteristic
388C2#1306966611yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3077C2
socleC22×C11#392
prime radicalC22×D4×C11D4
hypercenter#3077D11
hypocenterC11#10249
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
1. #13079764C2semidirect
3. #13067302C2semidirect
4. #13067115C2semidirect
6. #13066517C2semidirect
319. C11#10249semidirect

Maximal subgroups

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

subgroupindex
#130797642
#130737892
#130673022
#130671152
#130670072
#130665172
C11×#30772
#1024911