Finite Group Databasebeta

← #14664416

Subgroups — #14664416

Order 2816.

444 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 71 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#13073797C211yesmaximal, characteristic
2#13068407C211yesmaximal, characteristic
3#13066953C211yesmaximal, characteristic
4#13066646C211yesmaximal, characteristic, complemented
5#13066644C211yesmaximal, characteristic, complemented
6#13066642C211yesmaximal, characteristic, complemented
7C11×#1354C211yesmaximal, characteristic, complemented
8C2×#66999C411yescharacteristic
9C2×#66946C2211yescharacteristic
10C11×#395C2211yescharacteristic
11#10622844C411yescharacteristic
12C2×#66887—21no—
13M16×Dic11—21no—
14#10622602—21no—
15#10622600—21no—
16#10622599C2211yescharacteristic
17#10622339—21no—
18#10622290C411yescharacteristic
19#10622278—21no—
20D11×#95C411yescharacteristic
21#10622267—21no—
22C11×#343C2211yescharacteristic
23C11×#324C2211yescharacteristic
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622106—21no—
27C22×Q8×C11C2×C411yescharacteristic
28C22×D44D411yescharacteristic
29C22×C4×D11—21no—
30C22×C4×D11C2×C411yescharacteristic
31C22×C4×D11D411yescharacteristic
32C2×C11×M16—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4C2311yescharacteristic
35#66999—41no—
36#66999—41no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4C2×C411yescharacteristic
41C2×(C2×D11)⋊C4D411yescharacteristic
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11C2×C411yescharacteristic
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11D411yescharacteristic
46C2×#4318—21no—
47C2×#4313—41no—
48#66946—41no—
49#66946—41no—
50C11×C22⋊C8—21no—
51C11×#95—21no—
52C11×#95C2×C411yescharacteristic
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95C2×C411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59#66887—24no—
60(C2×D11)⋊C8—41no—
61#66879—41no—
62C8×Dic11—41no—
63#11793—111nomaximal, Sylow
64C23×D11C22⋊C411yescharacteristic
65C23×D11C22⋊C411yescharacteristic
66C2×Q8×C11—41no—
67C2×Q8×C11—81no—
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—81no—
88C2×C4×D11—81no—
89C2×C4×D11—81no—
90C11×M16—22no—
91C11×M16—41no—
92C2×C8×C11—41no—
93C2×C8×C11—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—81no—
96(C2×D11)⋊C4—41no—
97(C2×D11)⋊C4—41no—
98(C2×D11)⋊C4—42no—
99(C2×D11)⋊C4—42no—
100(C2×D11)⋊C4—81no—
101C4⋊Dic11—41no—
102C4⋊Dic11—42no—
103Dic11⋊C4—41no—
104Dic11⋊C4—41no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107#4318—22no—
108#4318—41no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111#4313—82no—
112#2564—111no—
113C4×#100—111no—
114#1465—111no—
115#1354—111no—
116#1354D1111yescharacteristic, complemented
117#1353—111no—
118#1353—111no—
119C23×C11C2×C22⋊C411yescharacteristic
120C22×D11—21no—
121C22×D11—21no—
122C22×D11—21no—
123C22×D11—21no—
124C22×D11—21no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11—41no—
129C22×D11#10412yes—
130Q8×C11—82no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—22no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11#13711yescharacteristic
144C2×C4×C11#13711yescharacteristic
145C2×Dic11—21no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11#9911yescharacteristic
155C2×Dic11#9911yescharacteristic
156D44—42no—
157D44—42no—
158C4×D11—42no—
159C4×D11—81no—
160C4×D11—81no—
161C4×D11—81no—
162C4×D11—84no—
163C8×C11—42no—
164C8×C11—81no—
165C11⋊C8—42no—
166C11⋊C8—81no—
167C2×C22⋊Q8—111no—
168C2×C4×D4—111no—
169C2×#100—221no—
170#407—221no—
171C4×M16—221no—
172#400—111no—
173#399—111no—
174#395C2×D1111yescharacteristic
175#393—111no—
176#387—221no—
177#386—221no—
178#385—221no—
179#380—221no—
180C2×#95—111no—
181#343—111no—
182#343C2×D1111yescharacteristic
183#324—111no—
184#324C2×D1111yescharacteristic
185#323—221no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11C2×#9911yescharacteristic
189C22×C11#41911yescharacteristic
190C22×C11C2×#10411yescharacteristic
191C2×D11—22no—
192C2×D11—42no—
193C2×D11—41no—
194C2×D11—41no—
195C2×D11—42no—
196C2×D11—42no—
197C2×D11—41no—
198C2×D11—41no—
199C2×D11—41no—
200C2×D11—81no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—42no—
204C4×C11—41no—
205C4×C11—41no—
206C4×C11—81no—
207Dic11—21no—
208Dic11—21no—
209Dic11—41no—
210Dic11—81no—
211Dic11—81no—
212C22×Q8C4×D1111yescharacteristic
213C22×D4—111no—
214C23×C4—111no—
215C23×C4—111no—
216C23×C4—221no—
217C2×M16—21no—
218C2×M16—221no—
219C2×M16—441no—
220C22⋊Q8—441no—
221C22⋊Q8—441no—
222C4×D4—441no—
223C4×D4—441no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—221no—
227C2×C4⋊C4—221no—
228C2×C4⋊C4C22×D1111yescharacteristic
229C2×C22⋊C4—111no—
230C2×C22⋊C4—111no—
231C2×C22⋊C4—221no—
232C2×C22⋊C4—221no—
233C2×C22⋊C4—221no—
234C2×C42—111no—
235#100—224no—
236C22⋊C8—21no—
237C22⋊C8—221no—
238C22⋊C8—441no—
239#97—441no—
240C4×C8—441no—
241#95—21no—
242#95—111no—
243#95—221no—
244#95—221no—
245#95—221no—
246#95—221no—
247#95C4×D1111yescharacteristic
248C2×C11—21no—
249C2×C11—21no—
250C2×C11#150811yescharacteristic
251C2×C11#212111yescharacteristic
252C2×C11#213211yescharacteristic
253D11—42no—
254D11—81no—
255C24—111no—
256C24—111no—
257C2×Q8—41no—
258C2×Q8—81no—
259C2×D4—222no—
260C2×D4—221no—
261C2×D4—221no—
262C2×D4—441no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—111no—
266C22×C4—111no—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4—442no—
274C22×C4—442no—
275C22×C4—881no—
276C22×C4—881no—
277C22×C4—881no—
278C22×C4C2×C4×D1111yescharacteristic
279C22×C4D4×D1111yescharacteristic
280C22×C4D4×D1111yescharacteristic
281M16—22no—
282M16—41no—
283M16—222no—
284M16—441no—
285M16—882no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—441no—
289C2×C8—441no—
290C4⋊C4—41no—
291C4⋊C4—81no—
292C4⋊C4—441no—
293C4⋊C4—442no—
294C4⋊C4—441no—
295C4⋊C4—441no—
296C22⋊C4—441no—
297C22⋊C4—441no—
298C22⋊C4—442no—
299C22⋊C4—442no—
300C22⋊C4—881no—
301C42—221no—
302C42—221no—
303C11#1179311yescharacteristic, complemented, Sylow
304C23—112no—
305C23—221no—
306C23—221no—
307C23—221no—
308C23—221no—
309C23—221no—
310C23—441no—
311C23—441no—
312C23—441no—
313C23—441no—
314C23C22⋊C4×D1111yescharacteristic
315Q8—82no—
316D4—442no—
317D4—442no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—111no—
331C2×C4—111no—
332C2×C4—221no—
333C2×C4—442no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—881no—
343C2×C4—881no—
344C2×C4—881no—
345C2×C4—884no—
346C2×C4#6696811yescharacteristic
347C2×C4#6697111yescharacteristic
348C8—42no—
349C8—81no—
350C8—442no—
351C8—881no—
352C22—21no—
353C22—21no—
354C22—222no—
355C22—442no—
356C22—442no—
357C22—442no—
358C22—441no—
359C22—441no—
360C22—441no—
361C22—441no—
362C22—441no—
363C22—881no—
364C22D11×#9911yescharacteristic
365C22#1062241511yescharacteristic
366C22D11×#10411yescharacteristic
367C4—21no—
368C4—21no—
369C4—42no—
370C4—41no—
371C4—41no—
372C4—81no—
373C4—221no—
374C4—221no—
375C4—441no—
376C4—881no—
377C4—881no—
378C2—21no—
379C2—21no—
380C2—442no—
381C2—881no—
382C2#1306713411yescharacteristic
383C2#1307025911yescharacteristic
384C2#1307030011yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1354C2
socleC22×C11C2×#99
prime radicalC22×D44D4
cosocleC2×C11×C4⋊C4C23
hypercenter#1354D11
hypocenterC11#11793
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
4. #13066646C2semidirect
5. #13066644C2semidirect
6. #13066642C2semidirect
7. C11×#1354C2semidirect
116. #1354D11semidirect
303. C11#11793semidirect

Maximal subgroups

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

subgroupindex
#130737972
#130684072
#130669532
#130666462
#130666442
#130666422
C11×#13542
#1179311