Finite Group Databasebeta

← #14664294

Subgroups — #14664294

Order 2816.

488 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#10622168C211yesmaximal, characteristic, complemented
2#13066946C211yesmaximal, characteristic, complemented
3#13066643C212yesmaximal, complemented
4#13066619C212yesmaximal, complemented
5C11×#2591C211yesmaximal, characteristic
6C2×C11×#121C411yescharacteristic
7C22×C11×C4⋊C4C2211yescharacteristic
8C22×#4318—21no—
9C11×#400C411yescharacteristic
10C11×#400C2211yescharacteristic
11C11×#394C411yescharacteristic
12C11×#394C2211yescharacteristic
13C11×#388—21no—
14C11×#388—21no—
15C11×#386—21no—
16C11×#386—21no—
17C4×C11×C22⋊C4C411yescharacteristic
18#10622820—21no—
19#10622168—21no—
20#10622168C2212yes—
21#10622166—21no—
22#10622166C2212yes—
23C22×D4×C11—21no—
24C22×D4×C11C2×C411yescharacteristic
25C23×C4×C11C2×C411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C11×#121—41no—
29C11×#121—41no—
30C2×C11×C4⋊C4—41no—
31C2×C11×C4⋊C4—41no—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C4⋊C4C2311yescharacteristic
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C42×C11—21no—
44C2×#4318—24no—
45C2×#4318—22no—
46C2×#4318—41no—
47C2×#4318—42no—
48C2×#4318—41no—
49C22×C11⋊C8—41no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95C2×C411yescharacteristic
55C11×#95C2×C411yescharacteristic
56C22⋊(C11⋊C8)—22no—
57C22⋊(C11⋊C8)—41no—
58#11766—111nomaximal, Sylow
59C24×C11—21no—
60C24×C11C22⋊C411yescharacteristic
61C2×D4×C11—41no—
62C2×D4×C11—42no—
63C2×D4×C11—42no—
64C2×D4×C11—41no—
65C2×D4×C11—41no—
66C2×D4×C11—81no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—22no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—81no—
80C22×C4×C11—81no—
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11C22⋊C411yescharacteristic
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C22⋊C4—42no—
93C11×C22⋊C4—42no—
94C11×C22⋊C4—42no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—81no—
98C11×C22⋊C4—81no—
99C42×C11—81no—
100#4318—24no—
101#4318—44no—
102#4318—42no—
103#4318—82no—
104C2×C11⋊C8—44no—
105C2×C11⋊C8—42no—
106C2×C11⋊C8—42no—
107#2591D1111yescharacteristic
108C2×#343—111no—
109#1463—111no—
110#1353—112no—
111#1345—112no—
112C23×C11—22no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—41no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11#9911yescharacteristic
124C23×C11#9911yescharacteristic
125C23×C11C2×C22⋊C411yescharacteristic
126D4×C11—82no—
127D4×C11—82no—
128D4×C11—82no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—21no—
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—21no—
141C2×C4×C11—42no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—81no—
156C2×C4×C11—81no—
157C2×C4×C11—81no—
158C2×C4×C11#10412yes—
159C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C11#13711yescharacteristic
161C11⋊C8—44no—
162C11⋊C8—82no—
163C22×M16—221no—
164C2×#121Dic1111yescharacteristic
165C22×C4⋊C4C2×D1111yescharacteristic
166#407—221no—
167#400Dic1111yescharacteristic
168#400C2×D1111yescharacteristic
169#394Dic1111yescharacteristic
170#394C2×D1111yescharacteristic
171#388—21no—
172#388—21no—
173#386—21no—
174#386—21no—
175C4×C22⋊C4Dic1111yescharacteristic
176#343—112no—
177#343—221no—
178#324—112no—
179#324—221no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—42no—
188C22×C11—42no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11#35512yes—
197C22×C11C2×#9911yescharacteristic
198C22×C11#41711yescharacteristic
199C22×C11C2×#10411yescharacteristic
200C4×C11—22no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—41no—
204C4×C11—41no—
205C4×C11—41no—
206C4×C11—41no—
207C4×C11—81no—
208C4×C11—81no—
209C4×C11—81no—
210C22×D4—21no—
211C22×D4C2×Dic1111yescharacteristic
212C23×C4C2×Dic1111yescharacteristic
213C23×C4C22⋊D1111yescharacteristic
214C23×C4C22⋊D1111yescharacteristic
215C2×M16—224no—
216C2×M16—222no—
217C2×M16—441no—
218C2×M16—442no—
219C2×M16—441no—
220C22×C8—441no—
221#121—41no—
222#121—41no—
223C2×C4⋊C4—41no—
224C2×C4⋊C4—41no—
225C2×C4⋊C4C2×Dic1111yescharacteristic
226C2×C4⋊C4C2×Dic1111yescharacteristic
227C2×C4⋊C4C22⋊D1111yescharacteristic
228C2×C4⋊C4C22⋊D1111yescharacteristic
229C2×C4⋊C4C22×D1111yescharacteristic
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C42—21no—
237C22⋊C8—222no—
238C22⋊C8—441no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95C2×Dic1111yescharacteristic
244#95C2×Dic1111yescharacteristic
245C2×C11—21no—
246C2×C11—21no—
247C2×C11—22no—
248C2×C11—41no—
249C2×C11—161no—
250C2×C11#150411yescharacteristic
251C2×C11#212111yescharacteristic
252C2×C11C2×#35511yescharacteristic
253C24—21no—
254C24C22⋊Dic1111yescharacteristic
255C2×D4—41no—
256C2×D4—42no—
257C2×D4—42no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—81no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—81no—
274C22×C4—81no—
275C22×C4C22⋊Dic1111yescharacteristic
276C22×C4C22⋊Dic1111yescharacteristic
277C22×C4C22⋊Dic1111yescharacteristic
278C22×C4C22×Dic1111yescharacteristic
279C22×C4C2×C22⋊D1111yescharacteristic
280C22×C4C2×C22⋊D1111yescharacteristic
281M16—224no—
282M16—444no—
283M16—442no—
284M16—882no—
285C2×C8—444no—
286C2×C8—442no—
287C2×C8—442no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C22⋊C4—42no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—81no—
299C22⋊C4—81no—
300C42—81no—
301C11#1176611yescharacteristic, complemented, Sylow
302C23—21no—
303C23—21no—
304C23—22no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23#6689811yescharacteristic
314C23#6689811yescharacteristic
315C23C2×C22⋊Dic1111yescharacteristic
316D4—82no—
317D4—82no—
318D4—82no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4#6690112yes—
349C2×C4#6700211yescharacteristic
350C2×C4#6700411yescharacteristic
351C8—444no—
352C8—882no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—42no—
361C22—42no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22#1062218012yes—
370C22C2×#6689811yescharacteristic
371C22#1062284511yescharacteristic
372C22C2×#6690111yescharacteristic
373C4—21no—
374C4—22no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—81no—
381C4—81no—
382C4—81no—
383C2—21no—
384C2—21no—
385C2—22no—
386C2—41no—
387C2—161no—
388C2#1306712011yescharacteristic
389C2#1307026211yescharacteristic
390C2C2×#1062218011yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2591C2
socleC22×C11C2×#99
prime radicalC2×C11×#121C4
cosocleC2×C11×C4⋊C4C23
hypercenter#2591D11
hypocenterC11#11766
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2591

Complements

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

NH ≅ G/Ntype
1. C2×#10622168C2semidirect
2. #13066946C2semidirect
3. #13066643C2semidirect
4. #13066619C2semidirect
301. C11#11766semidirect

Maximal subgroups

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

subgroupindex
C2×#106221682
#130669462
#130666432
#130666192
C11×#25912
#1176611