Finite Group Databasebeta

← #14643038

Subgroups — #14643038

Order 2816.

446 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 85 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#13075633C211yesmaximal, characteristic
2#13070180C211yesmaximal, characteristic, complemented
3#13070153C211yesmaximal, characteristic, complemented
4#13070149C211yesmaximal, characteristic
5#13066441C211yesmaximal, characteristic, complemented
6#13066440C211yesmaximal, characteristic, complemented
7C11×#1270C211yesmaximal, characteristic
8C2×#66931—21no—
9C11×#390C2211yescharacteristic
10#10622833—21no—
11C2×#66896—21no—
12C2×#66882—21no—
13C2×#66880—21no—
14#10622597—21no—
15C2×#66872—21no—
16#10622563—21no—
17#10622562—21no—
18#10622561—21no—
19#10622548C2211yescharacteristic
20#10622542C2211yescharacteristic
21#10622541C2211yescharacteristic
22C11×#336C2211yescharacteristic
23C11×#336C2211yescharacteristic
24#10622189—21no—
25#10622189—21no—
26#10622162C2211yescharacteristic
27C22×D4×C11D411yescharacteristic
28C23×Dic11—21no—
29C22×Dic22D411yescharacteristic
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—21no—
35C2×C42×C11C2311yescharacteristic
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11D411yescharacteristic
44C2×C4⋊Dic11D411yescharacteristic
45C2×C4⋊Dic11D411yescharacteristic
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C22×C11⋊C8—21no—
50#66931—42no—
51#66931—42no—
52#66896—42no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57#66882—42no—
58#66880—42no—
59#66872—42no—
60#7823—111nomaximal, Sylow
61C24×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11—41no—
64C2×D4×C11—41no—
65C2×D4×C11Q1612yes—
66C22×C4×C11—21no—
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—42no—
75C22×Dic11—41no—
76C22×Dic11—81no—
77C22×Dic11—81no—
78C2×Dic22—21no—
79C2×Dic22—41no—
80C2×Dic22—41no—
81C2×Dic22SD1612yes—
82C2×C8×C11—22no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C2×C8×C11—41no—
87C2×C8×C11—41no—
88C11×C4⋊C4—41no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C42×C11—41no—
94C22⋊Dic11—42no—
95C22⋊Dic11—81no—
96C22⋊Dic11—81no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102C4⋊Dic11—41no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105C4⋊Dic11—42no—
106C4⋊Dic11—42no—
107Dic11⋊C4—42no—
108Dic11⋊C4—41no—
109Dic11⋊C4—41no—
110Dic11⋊C4—81no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114#2732—111no—
115#2100—111no—
116#2095—111no—
117#2094—111no—
118#1272—111no—
119#1271—111no—
120#1270D1111yescharacteristic
121C23×C11—22no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11#12011yescharacteristic
129D4×C11—42no—
130D4×C11—81no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11C2×SD1611yescharacteristic
141C2×C4×C11C2×Q1611yescharacteristic
142C2×C4×C11#13511yescharacteristic
143C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C11#13711yescharacteristic
145C2×C4×C11#13711yescharacteristic
146C2×Dic11—22no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—84no—
159C2×Dic11—81no—
160C2×Dic11—81no—
161C2×Dic11—81no—
162Dic22—42no—
163Dic22—81no—
164C8×C11—42no—
165C8×C11—81no—
166C11⋊C8—42no—
167C2×C22⋊Q8—221no—
168C2×#107—221no—
169C2×#106—221no—
170C2×#103—221no—
171C2×#102—221no—
172#399—221no—
173#398—221no—
174#396—221no—
175#391—111no—
176#390C2×D1111yescharacteristic
177#389—111no—
178#386—221no—
179#385—221no—
180#384—111no—
181#340—221no—
182#340—221no—
183#336—111no—
184#336C2×D1111yescharacteristic
185#336C2×D1111yescharacteristic
186C22×C11—42no—
187C22×C11—42no—
188C22×C11—42no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11#45011yescharacteristic
194C22×C11#45111yescharacteristic
195C22×C11#45211yescharacteristic
196C22×C11#45311yescharacteristic
197C22×C11#45311yescharacteristic
198C22×C11#45411yescharacteristic
199C22×C11#45811yescharacteristic
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—81no—
207Dic11—42no—
208Dic11—81no—
209Dic11—81no—
210Dic11—81no—
211Dic11—161no—
212C22×Q8—111no—
213C22×D4D4411yescharacteristic
214C23×C4—221no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—221no—
218C22⋊Q8—442no—
219C22⋊Q8—442no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—111no—
222C2×C4⋊C4—111no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4—221no—
227C2×C4⋊C4—221no—
228C2×C4⋊C4—221no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4D4411yescharacteristic
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—221no—
234C2×C22⋊C4—221no—
235C2×C22⋊C4—221no—
236C2×C42C22×D1111yescharacteristic
237#107—442no—
238#106—442no—
239#103—442no—
240#102—442no—
241#95—221no—
242#95—221no—
243#95—221no—
244#95—221no—
245C2×C11—82no—
246C2×C11#161311yescharacteristic
247C2×C11#161411yescharacteristic
248C2×C11#161511yescharacteristic
249C2×C11#163111yescharacteristic
250C2×C11#163211yescharacteristic
251C2×C11#163711yescharacteristic
252C2×C11#165611yescharacteristic
253C24—21no—
254C2×Q8—112no—
255C2×Q8—221no—
256C2×Q8—441no—
257C2×Q8—441no—
258C2×D4—21no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4Dic4412yes—
262C22×C4—21no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—221no—
267C22×C4—442no—
268C22×C4—441no—
269C22×C4—881no—
270C22×C4—881no—
271C22×C4C2×D4411yescharacteristic
272C22×C4D4×D1111yescharacteristic
273C22×C4D4×D1111yescharacteristic
274C2×C8—22no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—222no—
281C2×C8—441no—
282C2×C8—441no—
283C4⋊C4—41no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C4⋊C4—441no—
289C4⋊C4—441no—
290C4⋊C4—441no—
291C4⋊C4—441no—
292C4⋊C4—442no—
293C4⋊C4—442no—
294C4⋊C4—442no—
295C4⋊C4—441no—
296C4⋊C4—441no—
297C4⋊C4—881no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—442no—
303C22⋊C4—881no—
304C22⋊C4—881no—
305C42—41no—
306C11#782311yescharacteristic, complemented, Sylow
307C23—22no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23#6693511yescharacteristic
315Q8—442no—
316Q8—881no—
317D4—42no—
318D4—81no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—222no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—884no—
341C2×C4—881no—
342C2×C4—881no—
343C2×C4—881no—
344C2×C4C2×Dic4411yescharacteristic
345C2×C4#6696211yescharacteristic
346C2×C4#6696411yescharacteristic
347C2×C4#6696511yescharacteristic
348C2×C4SD16×D1111yescharacteristic
349C2×C4#6696811yescharacteristic
350C8—42no—
351C8—81no—
352C8—442no—
353C22—42no—
354C22—42no—
355C22—42no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22#1062235211yescharacteristic
361C22#1062235511yescharacteristic
362C22#1062236011yescharacteristic
363C22#1062238911yescharacteristic
364C22#1062239611yescharacteristic
365C22#1062243511yescharacteristic
366C22#1062244011yescharacteristic
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—81no—
374C4—442no—
375C4—881no—
376C4—881no—
377C4—881no—
378C4—1761no—
379C2—82no—
380C2#1306763711yescharacteristic
381C2#1306764311yescharacteristic
382C2#1306764811yescharacteristic
383C2#1306774411yescharacteristic
384C2#1306775211yescharacteristic
385C2#1306778411yescharacteristic
386C2#1306791011yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1270C2
socleC23×C11#120
prime radicalC22×D4×C11D4
hypercenter#1270D11
hypocenterC11#7823
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #13070180C2semidirect
3. #13070153C2semidirect
5. #13066441C2semidirect
6. #13066440C2semidirect
306. C11#7823semidirect

Maximal subgroups

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

subgroupindex
#130756332
#130701802
#130701532
#130701492
#130664412
#130664402
C11×#12702
#782311