Finite Group Databasebeta

← #14664358

Subgroups — #14664358

Order 2816.

464 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 73 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#13072919C211yesmaximal, characteristic
2#13068407C211yesmaximal, characteristic
3#13066953C211yesmaximal, characteristic
4#13066623C211yesmaximal, characteristic, complemented
5#13066622C211yesmaximal, characteristic, complemented
6#13066621C211yesmaximal, characteristic, complemented
7C11×#1346C211yesmaximal, characteristic, complemented
8C2×#66947—21no—
9C2×#66946C2211yescharacteristic
10C2×C4⋊C4×D11C411yescharacteristic
11C11×#398C2211yescharacteristic
12C2×#66887—21no—
13M16×Dic11—21no—
14#10622606C411yescharacteristic
15#10622596C2211yescharacteristic
16#10622585—21no—
17#10622339—21no—
18#10622287C411yescharacteristic
19#10622280—21no—
20#10622280C411yescharacteristic
21#10622277—21no—
22C11×#343C2211yescharacteristic
23C11×#324C2211yescharacteristic
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622106—21no—
27C22×D44D411yescharacteristic
28C22×C4×D11—21no—
29C22×C4×D11C2×C411yescharacteristic
30C22×C4×D11D411yescharacteristic
31C2×C11×M16—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4C2×C411yescharacteristic
39C2×(C2×D11)⋊C4D411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×C4×Dic11D411yescharacteristic
45C2×#4318—21no—
46C2×#4313—41no—
47#66947—42no—
48#66947—42no—
49#66946—41no—
50#66946—41no—
51C4⋊C4×D11—41no—
52C4⋊C4×D11—41no—
53C11×C22⋊C8—21no—
54C11×#95—21no—
55C11×#95C2×C411yescharacteristic
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95C2×C411yescharacteristic
60C22⋊(C11⋊C8)—21no—
61#66887—24no—
62(C2×D11)⋊C8—41no—
63#66879—41no—
64C8×Dic11—41no—
65#11780—111nomaximal, Sylow
66C23×D11C22⋊C411yescharacteristic
67C23×D11C22⋊C411yescharacteristic
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11C22⋊C411yescharacteristic
76C22×Dic11C22⋊C411yescharacteristic
77C2×D44—22no—
78C2×D44—21no—
79C2×D44—21no—
80C2×D44—41no—
81C2×C4×D11—21no—
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—42no—
86C2×C4×D11—42no—
87C2×C4×D11—42no—
88C2×C4×D11—42no—
89C2×C4×D11—42no—
90C11×M16—22no—
91C11×M16—41no—
92C2×C8×C11—41no—
93C2×C8×C11—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98(C2×D11)⋊C4—41no—
99(C2×D11)⋊C4—41no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—42no—
102(C2×D11)⋊C4—42no—
103C4⋊Dic11—41no—
104Dic11⋊C4—42no—
105Dic11⋊C4—41no—
106Dic11⋊C4—41no—
107Dic11⋊C4—41no—
108Dic11⋊C4—41no—
109C4×Dic11—21no—
110C4×Dic11—21no—
111#4318—22no—
112#4318—41no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115#4313—82no—
116#2486—111no—
117C4×#100—111no—
118#1465—111no—
119#1346—111no—
120#1346—111no—
121#1346—111no—
122#1346D1111yescharacteristic, complemented
123C23×C11C2×C22⋊C411yescharacteristic
124C22×D11—21no—
125C22×D11—21no—
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11—41no—
133C22×D11#10412yes—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
148C2×Dic11—22no—
149C2×Dic11—21no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11#9911yescharacteristic
158C2×Dic11#9911yescharacteristic
159D44—42no—
160D44—42no—
161C4×D11—42no—
162C4×D11—42no—
163C4×D11—42no—
164C4×D11—81no—
165C4×D11—84no—
166C8×C11—42no—
167C8×C11—81no—
168C11⋊C8—42no—
169C11⋊C8—81no—
170C2×#123—221no—
171C2×C4×D4—111no—
172C22×C4⋊C4—111no—
173C2×#100—221no—
174#407—221no—
175C4×M16—221no—
176#398—111no—
177#398C2×D1111yescharacteristic
178#397—111no—
179#397—111no—
180#389—221no—
181#381—221no—
182#380—111no—
183#380—221no—
184#343—111no—
185#343C2×D1111yescharacteristic
186#324—111no—
187#324C2×D1111yescharacteristic
188#323—221no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11C2×#9911yescharacteristic
192C22×C11#41811yescharacteristic
193C22×C11C2×#10411yescharacteristic
194C2×D11—22no—
195C2×D11—42no—
196C2×D11—41no—
197C2×D11—41no—
198C2×D11—42no—
199C2×D11—42no—
200C2×D11—41no—
201C2×D11—41no—
202C2×D11—41no—
203C2×D11—81no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—41no—
207C4×C11—41no—
208C4×C11—81no—
209C4×C11—81no—
210Dic11—21no—
211Dic11—41no—
212Dic11—81no—
213Dic11—81no—
214Dic11#35212yes—
215C22×D4—111no—
216C23×C4—111no—
217C23×C4—111no—
218C23×C4—221no—
219C2×M16—21no—
220C2×M16—221no—
221C2×M16—441no—
222#123—442no—
223#123—442no—
224C4×D4—441no—
225C4×D4—441no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—111no—
228C2×C4⋊C4—221no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4—441no—
232C2×C4⋊C4—441no—
233C2×C4⋊C4C4×D1111yescharacteristic
234C2×C4⋊C4C22×D1111yescharacteristic
235C2×C22⋊C4—111no—
236C2×C22⋊C4—111no—
237C2×C22⋊C4—221no—
238C2×C22⋊C4—221no—
239C2×C22⋊C4—221no—
240C2×C42—111no—
241#100—224no—
242C22⋊C8—21no—
243C22⋊C8—221no—
244C22⋊C8—441no—
245#97—441no—
246C4×C8—441no—
247#95—21no—
248#95—111no—
249#95—221no—
250#95—221no—
251#95—221no—
252#95C4×D1111yescharacteristic
253C2×C11—21no—
254C2×C11—21no—
255C2×C11#150711yescharacteristic
256C2×C11C2×#35211yescharacteristic
257C2×C11#213511yescharacteristic
258D11—42no—
259D11—81no—
260C24—111no—
261C24—111no—
262C2×D4—222no—
263C2×D4—221no—
264C2×D4—221no—
265C2×D4—441no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—111no—
269C22×C4—111no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4—221no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4—442no—
277C22×C4—442no—
278C22×C4—442no—
279C22×C4—442no—
280C22×C4—442no—
281C22×C4C2×C4×D1111yescharacteristic
282C22×C4D4×D1111yescharacteristic
283C22×C4D4×D1111yescharacteristic
284M16—22no—
285M16—41no—
286M16—222no—
287M16—441no—
288M16—882no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—441no—
292C2×C8—441no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—441no—
298C4⋊C4—441no—
299C4⋊C4—441no—
300C4⋊C4—442no—
301C4⋊C4—441no—
302C4⋊C4—441no—
303C22⋊C4—441no—
304C22⋊C4—441no—
305C22⋊C4—442no—
306C22⋊C4—442no—
307C22⋊C4—442no—
308C42—221no—
309C42—221no—
310C11#1178011yescharacteristic, complemented, Sylow
311C23—112no—
312C23—221no—
313C23—221no—
314C23—221no—
315C23—221no—
316C23—221no—
317C23—441no—
318C23—441no—
319C23—441no—
320C23—441no—
321C23C22⋊C4×D1111yescharacteristic
322D4—442no—
323D4—442no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—111no—
337C2×C4—111no—
338C2×C4—222no—
339C2×C4—221no—
340C2×C4—442no—
341C2×C4—442no—
342C2×C4—442no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—881no—
351C2×C4—884no—
352C2×C4#6696411yescharacteristic
353C2×C4#6696711yescharacteristic
354C8—42no—
355C8—81no—
356C8—442no—
357C8—881no—
358C22—21no—
359C22—21no—
360C22—222no—
361C22—442no—
362C22—442no—
363C22—442no—
364C22—441no—
365C22—441no—
366C22—441no—
367C22—441no—
368C22—441no—
369C22—881no—
370C22D11×#9911yescharacteristic
371C22#1062238311yescharacteristic
372C22D11×#10411yescharacteristic
373C4—21no—
374C4—21no—
375C4—41no—
376C4—41no—
377C4—81no—
378C4—81no—
379C4—112no—
380C4—221no—
381C4—441no—
382C4—881no—
383C4—881no—
384C2—21no—
385C2—21no—
386C2—442no—
387C2—881no—
388C2#1306713011yescharacteristic
389C2D11×#35211yescharacteristic
390C2#1307030911yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1346C2
socleC22×C11C2×#99
prime radicalC22×D44D4
cosocleC2×C11×C4⋊C4C23
hypercenter#1346D11
hypocenterC11#11780
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

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

NH ≅ G/Ntype
4. #13066623C2semidirect
5. #13066622C2semidirect
6. #13066621C2semidirect
7. C11×#1346C2semidirect
122. #1346D11semidirect
310. C11#11780semidirect

Maximal subgroups

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

subgroupindex
#130729192
#130684072
#130669532
#130666232
#130666222
#130666212
C11×#13462
#1178011