Finite Group Databasebeta

← #14642869

Subgroups — #14642869

Order 2816.

478 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 87 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#13074987C211yesmaximal, characteristic
2#13070145C211yesmaximal, characteristic
3#13070088C211yesmaximal, characteristic, complemented
4#13066440C211yesmaximal, characteristic, complemented
5#13066439C211yesmaximal, characteristic, complemented
6#13066436C211yesmaximal, characteristic
7C11×#2083C211yesmaximal, characteristic, complemented
8C2×#66950—21no—
9C2×#66949—21no—
10C2×C11×#107—21no—
11C11×#389C2211yescharacteristic
12C11×#384C2211yescharacteristic
13#10622607—21no—
14#10622607—21no—
15C2×#66873—21no—
16C2×#66871—21no—
17C2×#66871—21no—
18#10622552C2211yescharacteristic
19#10622541C2211yescharacteristic
20#10622278—21no—
21#10622269—21no—
22C11×#340—21no—
23C11×#336C2211yescharacteristic
24#10622167—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×D44D411yescharacteristic
28C22×C4×D11—21no—
29C22×Dic22—21no—
30C22×C8×C11—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C42×C11C2311yescharacteristic
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11D411yescharacteristic
45C2×C4⋊Dic11D411yescharacteristic
46C2×C4⋊Dic11D411yescharacteristic
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C22×C11⋊C8—21no—
50C22×C11⋊C8—21no—
51#66950—42no—
52#66950—42no—
53#66949—42no—
54#66949—42no—
55C11×#107—42no—
56C11×#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59#66873—42no—
60#66871—42no—
61#66871—42no—
62#7797—111nomaximal, Sylow
63C23×D11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—41no—
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11—21no—
73C2×D44—21no—
74C2×D44—41no—
75C2×D44—41no—
76C2×D44Q1612yes—
77C2×C4×D11—42no—
78C2×C4×D11—42no—
79C2×C4×D11—81no—
80C2×Dic22—42no—
81C2×Dic22—42no—
82C2×Dic22—81no—
83C2×C8×C11—22no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4D812yes—
97C42×C11—41no—
98(C2×D11)⋊C4—42no—
99(C2×D11)⋊C4—42no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—41no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—81no—
105C4⋊Dic11—21no—
106C4⋊Dic11—41no—
107C4⋊Dic11—41no—
108C4⋊Dic11—42no—
109C4⋊Dic11D812yes—
110Dic11⋊C4—42no—
111Dic11⋊C4—41no—
112Dic11⋊C4—41no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—41no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8—41no—
119#2683—111no—
120#2093—111no—
121#2083—111no—
122#2083D1111yescharacteristic, complemented
123#1271—111no—
124#1271—111no—
125#1270—111no—
126C23×C11#12011yescharacteristic
127C22×D11—22no—
128C22×D11—41no—
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11—41no—
133C22×D11—41no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—22no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—81no—
147C2×C4×C11—81no—
148C2×C4×C11—81no—
149C2×C4×C11C2×D811yescharacteristic
150C2×C4×C11C2×D811yescharacteristic
151C2×C4×C11C2×Q1611yescharacteristic
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C11#13711yescharacteristic
155C2×Dic11—22no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164D44—42no—
165D44—81no—
166C4×D11—84no—
167Dic22—84no—
168C8×C11—42no—
169C11⋊C8—42no—
170C11⋊C8—42no—
171C2×C22⋊Q8—221no—
172C2×C22⋊Q8—221no—
173C2×#107—21no—
174C2×#107—221no—
175C2×#107—221no—
176C2×#102—221no—
177#396—221no—
178#396—221no—
179#395—221no—
180#390—111no—
181#389—111no—
182#389C2×D1111yescharacteristic
183#386—221no—
184#384C2×D1111yescharacteristic
185#340—21no—
186#340—221no—
187#336—111no—
188#336—111no—
189#336C2×D1111yescharacteristic
190C22×C11#44711yescharacteristic
191C22×C11#44711yescharacteristic
192C22×C11#45111yescharacteristic
193C22×C11#45311yescharacteristic
194C22×C11#45611yescharacteristic
195C22×C11#45611yescharacteristic
196C22×C11#45811yescharacteristic
197C2×D11—42no—
198C2×D11—42no—
199C2×D11—42no—
200C2×D11—81no—
201C2×D11—81no—
202C2×D11—81no—
203C2×D11—81no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—42no—
211C4×C11—81no—
212C4×C11—161no—
213Dic11—42no—
214Dic11—81no—
215Dic11—81no—
216C22×Q8—221no—
217C22×D4—111no—
218C23×C4—221no—
219C22×C8—21no—
220C22×C8—221no—
221C22×C8—221no—
222C22⋊Q8—442no—
223C22⋊Q8—442no—
224C22⋊Q8—442no—
225C22⋊Q8—442no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—111no—
231C2×C4⋊C4—111no—
232C2×C4⋊C4—111no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—221no—
235C2×C4⋊C4—221no—
236C2×C4⋊C4C22⋊D1111yescharacteristic
237C2×C4⋊C4C22⋊D1111yescharacteristic
238C2×C22⋊C4—221no—
239C2×C22⋊C4—221no—
240C2×C22⋊C4—221no—
241C2×C22⋊C4—221no—
242C2×C22⋊C4—221no—
243C2×C42C22×D1111yescharacteristic
244#107—42no—
245#107—442no—
246#107—442no—
247#102—442no—
248#95—21no—
249#95—221no—
250#95—221no—
251C2×C11#161011yescharacteristic
252C2×C11#161011yescharacteristic
253C2×C11#161411yescharacteristic
254C2×C11#161911yescharacteristic
255C2×C11#164911yescharacteristic
256C2×C11#164911yescharacteristic
257C2×C11#166011yescharacteristic
258D11—82no—
259C24—221no—
260C2×Q8—442no—
261C2×Q8—442no—
262C2×Q8—881no—
263C2×D4—112no—
264C2×D4—221no—
265C2×D4—441no—
266C2×D4—441no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—41no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4—442no—
274C22×C4—442no—
275C22×C4—881no—
276C22×C4D4×D1111yescharacteristic
277C22×C4D4×D1111yescharacteristic
278C22×C4C2×C22⋊D1111yescharacteristic
279C2×C8—22no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—222no—
283C2×C8—222no—
284C2×C8—441no—
285C2×C8—441no—
286C2×C8—441no—
287C2×C8—441no—
288C4⋊C4—21no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—112no—
299C4⋊C4—221no—
300C4⋊C4—441no—
301C4⋊C4—441no—
302C4⋊C4—442no—
303C4⋊C4—442no—
304C4⋊C4—441no—
305C4⋊C4—441no—
306C4⋊C4#432312yes—
307C22⋊C4—442no—
308C22⋊C4—442no—
309C22⋊C4—441no—
310C22⋊C4—441no—
311C22⋊C4—441no—
312C22⋊C4—441no—
313C22⋊C4—881no—
314C42—41no—
315C11#779711yescharacteristic, complemented, Sylow
316C23—222no—
317C23—441no—
318C23—441no—
319C23—441no—
320C23—441no—
321C23—441no—
322C23—441no—
323C23#6699011yescharacteristic
324Q8—884no—
325D4—442no—
326D4—881no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—222no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—884no—
352C2×C4D8×D1111yescharacteristic
353C2×C4#6696411yescharacteristic
354C2×C4Q16×D1111yescharacteristic
355C2×C4#6697111yescharacteristic
356C2×C4C2×#432311yescharacteristic
357C2×C4#6700211yescharacteristic
358C8—42no—
359C8—442no—
360C8—442no—
361C22—442no—
362C22—442no—
363C22—442no—
364C22—881no—
365C22—881no—
366C22—881no—
367C22—881no—
368C22#1062264911yescharacteristic
369C22#1062266611yescharacteristic
370C22#1062270811yescharacteristic
371C22#1062276911yescharacteristic
372C22#1062279911yescharacteristic
373C22#1062281111yescharacteristic
374C22#1062281811yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—42no—
382C4—81no—
383C4—161no—
384C4—442no—
385C4—881no—
386C4—881no—
387C2—882no—
388C2#1306761711yescharacteristic
389C2#1306761811yescharacteristic
390C2#1306763911yescharacteristic
391C2#1306766911yescharacteristic
392C2#1306786211yescharacteristic
393C2#1306786311yescharacteristic
394C2#1306792611yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2083C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenter#2083D11
hypocenterC11#7797
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2083

Complements

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

NH ≅ G/Ntype
3. #13070088C2semidirect
4. #13066440C2semidirect
5. #13066439C2semidirect
7. C11×#2083C2semidirect
122. #2083D11semidirect
315. C11#7797semidirect

Maximal subgroups

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

subgroupindex
#130749872
#130701452
#130700882
#130664402
#130664392
#130664362
C11×#20832
#779711