Finite Group Databasebeta

← #14651098

Subgroups — #14651098

Order 2816.

548 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 115 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#13073792C211yesmaximal, characteristic
2#13068604C211yesmaximal, characteristic
3#13067189C212yesmaximal, complemented
4#13066496C212yesmaximal, complemented
5C11×#2973C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66977C2211yescharacteristic
8C11×#435—24no—
9C11×#432—21no—
10C11×#407—21no—
11C2×C11×C22⋊C8C2212yes—
12#10622833—21no—
13C2×#66898—21no—
14#10622825C2212yes—
15#10622823—21no—
16C2×C11⋊#95C2211yescharacteristic
17#10622599C411yescharacteristic, complemented
18#10622592C411yescharacteristic, complemented
19#10622562C411yescharacteristic, complemented
20#10622560C411yescharacteristic, complemented
21#10622555—21no—
22#10622546—21no—
23#10622164—21no—
24#10622105—24no—
25C22×D4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11C2311yescharacteristic
28C23×Dic11—21no—
29C22×Dic22C2×C411yescharacteristic
30C2×C11×M16—22no—
31C22×C8×C11—22no—
32C4×D4×C11—22no—
33C4×D4×C11—22no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C22⋊C4C2×C411yescharacteristic
36C2×C11×C22⋊C4D411yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—22no—
41C2×C22⋊Dic11—21no—
42C2×C4⋊Dic11—22no—
43C2×C4⋊Dic11C2×C411yescharacteristic
44#66977—22no—
45#66977—22no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C11×C4⋊C8—22no—
50C11×C22⋊C8—22no—
51C11×C22⋊C8—22no—
52C11×C22⋊C8D414yes—
53C11×#97—22no—
54#66898—42no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—22no—
61C11⋊#95C2×C411yescharacteristic
62C11⋊#95C2×C411yescharacteristic
63#9385—111nomaximal, Sylow
64C24×C11C22⋊C411yescharacteristic
65C24×C11C2×D411yescharacteristic
66C2×D4×C11—22no—
67C2×D4×C11—21no—
68C2×D4×C11—21no—
69C2×D4×C11—22no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—81no—
73C22×C4×C11—81no—
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D412yes—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11#4112yes—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C22×Dic11—42no—
86C22×Dic11—42no—
87C22×Dic11—41no—
88C22×Dic11—41no—
89C22×Dic11—81no—
90C2×Dic22—22no—
91C2×Dic22—81no—
92C11×M16—82no—
93C2×C8×C11—24no—
94C2×C8×C11—82no—
95C11×C4⋊C4—22no—
96C11×C22⋊C4—22no—
97C11×C22⋊C4—22no—
98C42×C11—21no—
99C42×C11—21no—
100C22⋊Dic11—42no—
101C22⋊Dic11—42no—
102C22⋊Dic11—42no—
103C22⋊Dic11—42no—
104C22⋊Dic11—81no—
105C4⋊Dic11—22no—
106C4⋊Dic11—82no—
107Dic11⋊C4—42no—
108Dic11⋊C4—41no—
109Dic11⋊C4—41no—
110Dic11⋊C4—81no—
111#2973D1111yescharacteristic
112#2564—111no—
113#1799—111no—
114#1520—112no—
115#1294—112no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11C2×C22⋊C411yescharacteristic
124C23×C11#12112yes—
125C23×C11AGL(1,ℤ/8)11yescharacteristic
126C23×C11#13711yescharacteristic
127C23×C11#13712yes—
128D4×C11—42no—
129D4×C11—42no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—42no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—81no—
143C2×C4×C11C4×D412yes—
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12311yescharacteristic
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—82no—
159C2×Dic11—82no—
160C2×Dic11—82no—
161C2×Dic11—82no—
162C2×Dic11—82no—
163Dic22—82no—
164C8×C11—44no—
165C2×C22⋊Q8—111no—
166C2×C4×D4C2×D1111yescharacteristic
167#435—24no—
168#432—21no—
169C2×#99—221no—
170#407—21no—
171C2×C22⋊C8C2×D1112yes—
172#400—111no—
173#399—111no—
174#395—111no—
175#393—111no—
176#387—221no—
177#386—221no—
178#385—221no—
179#380—112no—
180#380—221no—
181C2×#95—111no—
182#342—221no—
183#328—224no—
184C22×C11—21no—
185C22×C11—22no—
186C22×C11—21no—
187C22×C11—22no—
188C22×C11—41no—
189C22×C11—42no—
190C22×C11—41no—
191C22×C11—42no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—81no—
196C22×C11#38611yescharacteristic
197C22×C11#41711yescharacteristic
198C22×C11#41911yescharacteristic
199C22×C11#46812yes—
200C22×C11#47012yes—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—22no—
204C4×C11—41no—
205C4×C11—41no—
206C4×C11—41no—
207Dic11—42no—
208Dic11—81no—
209Dic11—81no—
210Dic11—81no—
211Dic11—162no—
212C22×Q8—111no—
213C22×D4D4411yescharacteristic
214C23×C4—221no—
215C23×C4C22⋊D1111yescharacteristic
216C23×C4C22×D1111yescharacteristic
217C2×M16—22no—
218C22×C8—22no—
219C22⋊Q8—222no—
220C22⋊Q8—222no—
221C4×D4—22no—
222C4×D4—22no—
223C2×C4⋊C4—111no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4—221no—
227C2×C4⋊C4—222no—
228C2×C4⋊C4C4×D1111yescharacteristic
229C2×C22⋊C4—221no—
230C2×C22⋊C4—221no—
231C2×C22⋊C4—222no—
232C2×C22⋊C4—221no—
233C2×C22⋊C4C4×D1111yescharacteristic
234C2×C22⋊C4D4411yescharacteristic
235C2×C42C22⋊D1111yescharacteristic
236C4⋊C8—22no—
237#99—442no—
238C22⋊C8—22no—
239C22⋊C8—22no—
240C22⋊C8C22⋊D1114yes—
241#97—22no—
242#95—111no—
243#95—111no—
244#95—221no—
245#95—221no—
246#95—221no—
247#95—221no—
248#95—221no—
249#95—222no—
250C2×C11—21no—
251C2×C11—22no—
252C2×C11—21no—
253C2×C11—22no—
254C2×C11—81no—
255C2×C11#188411yescharacteristic
256C2×C11#189411yescharacteristic
257C2×C11#191311yescharacteristic
258C24(C2×D11)⋊C411yescharacteristic
259C24C2×D4411yescharacteristic
260C2×Q8—222no—
261C2×Q8—881no—
262C2×D4—21no—
263C2×D4—22no—
264C2×D4—21no—
265C2×D4—22no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—81no—
269C22×C4—81no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4—221no—
274C22×C4—442no—
275C22×C4—441no—
276C22×C4—441no—
277C22×C4—442no—
278C22×C4—881no—
279C22×C4(C2×D11)⋊C411yescharacteristic
280C22×C4(C2×D11)⋊C411yescharacteristic
281C22×C4(C2×D11)⋊C411yescharacteristic
282C22×C4C2×C4×D1111yescharacteristic
283C22×C4#433912yes—
284C22×C4C2×C22⋊D1112yes—
285C22×C4C2×C22⋊D1111yescharacteristic
286M16—82no—
287C2×C8—24no—
288C2×C8—82no—
289C4⋊C4—22no—
290C4⋊C4—222no—
291C4⋊C4—442no—
292C4⋊C4—441no—
293C4⋊C4—441no—
294C4⋊C4—881no—
295C4⋊C4—882no—
296C22⋊C4—22no—
297C22⋊C4—22no—
298C22⋊C4—442no—
299C22⋊C4—442no—
300C22⋊C4—442no—
301C22⋊C4—442no—
302C22⋊C4—881no—
303C42—21no—
304C42—21no—
305C11#938511yescharacteristic, complemented, Sylow
306C23—21no—
307C23—21no—
308C23—21no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23#6696111yescharacteristic
314C23#6696212yes—
315C23#6696211yescharacteristic
316C23C2×(C2×D11)⋊C411yescharacteristic
317C23#6698312yes—
318Q8—882no—
319D4—42no—
320D4—42no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—222no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—882no—
347C2×C4—882no—
348C2×C4—882no—
349C2×C4—882no—
350C2×C4—882no—
351C2×C4C4×C22⋊D1112yes—
352C2×C4#6698211yescharacteristic
353C2×C4#6700611yescharacteristic
354C8—44no—
355C22—21no—
356C22—22no—
357C22—21no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—81no—
367C22#1062273311yescharacteristic
368C22#1062274611yescharacteristic
369C22#1062274712yes—
370C22#1062275012yes—
371C22#1062282611yescharacteristic
372C4—21no—
373C4—21no—
374C4—22no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—442no—
379C4—881no—
380C4—881no—
381C4—881no—
382C4—1762no—
383C2—21no—
384C2—22no—
385C2—21no—
386C2—22no—
387C2—81no—
388C2#1306899911yescharacteristic
389C2#1306904911yescharacteristic
390C2#1306915811yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2973C2
socleC22×C11#386
prime radicalC22×D4×C11D4
cosocleC23×C4×C11C23
hypercenter#2973D11
hypocenterC11#9385
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2973

Complements

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

NH ≅ G/Ntype
3. #13067189C2semidirect
4. #13066496C2semidirect
17. #10622599C4semidirect
18. #10622592C4semidirect
19. #10622562C4semidirect
20. #10622560C4semidirect
305. C11#9385semidirect

Maximal subgroups

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

subgroupindex
#130737922
#130686042
#130671892
#130664962
C11×#29732
#938511