Finite Group Databasebeta

← #14664633

Subgroups — #14664633

Order 2816.

446 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 69 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#13074175C211yesmaximal, characteristic
2#13068692C211yesmaximal, characteristic, complemented
3#13066927C211yesmaximal, characteristic, complemented
4#13066641C211yesmaximal, characteristic, complemented
5#13066639C211yesmaximal, characteristic, complemented
6#13066613C211yesmaximal, characteristic
7C11×#1343C211yesmaximal, characteristic
8C2×D4×Dic11C411yescharacteristic, complemented
9C2×#66930C2211yescharacteristic
10C11×#392C2211yescharacteristic
11#10622835C411yescharacteristic, complemented
12#10622833—21no—
13#10622833—21no—
14#10622562C2211yescharacteristic
15#10622559—21no—
16#10622558—21no—
17#10622556—21no—
18#10622331—21no—
19#10622272C411yescharacteristic, complemented
20#10622264C411yescharacteristic, complemented
21C11×#342C2211yescharacteristic
22C11×#323C2211yescharacteristic
23#10622165—21no—
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622107—21no—
27C22×D4×C11—21no—
28C22×D4×C11C2×C411yescharacteristic
29C23×Dic11—21no—
30C23×Dic11D411yescharacteristic
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4—21no—
33C2×C11×C22⋊C4C2311yescharacteristic
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11D411yescharacteristic
40D4×Dic11—41no—
41D4×Dic11—41no—
42C2×C4⋊Dic11C2×C411yescharacteristic
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4C2×C411yescharacteristic
45C2×Dic11⋊C4D411yescharacteristic
46C2×C4×Dic11C2×C411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48#66930—41no—
49#66930—41no—
50C11×C22⋊C8—21no—
51C11×#95C2×C411yescharacteristic
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—41no—
57C11⋊#95—41no—
58C11⋊#95C2×C411yescharacteristic
59C22⋊(C11⋊C8)—21no—
60Dic11⋊C8—41no—
61C8×Dic11—41no—
62#11840—111nomaximal, Sylow
63C24×C11—21no—
64C24×C11C2×D411yescharacteristic
65C2×D4×C11—41no—
66C2×D4×C11—42no—
67C2×D4×C11—42no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—81no—
71C22×C4×C11—21no—
72C22×C4×C11—41no—
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—41no—
82C22×Dic11—41no—
83C22×Dic11—42no—
84C22×Dic11—81no—
85C22×Dic11—81no—
86C22×Dic11C22⋊C411yescharacteristic
87C22×Dic11C22⋊C411yescharacteristic
88C22×Dic11C22⋊C411yescharacteristic
89C22×Dic11C22⋊C411yescharacteristic
90C2×C8×C11—41no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—81no—
95C22⋊Dic11—41no—
96C22⋊Dic11—42no—
97C22⋊Dic11—41no—
98C22⋊Dic11—42no—
99C22⋊Dic11—41no—
100C22⋊Dic11—41no—
101C22⋊Dic11—41no—
102C22⋊Dic11—81no—
103C4⋊Dic11—41no—
104Dic11⋊C4—41no—
105Dic11⋊C4—41no—
106Dic11⋊C4—81no—
107C4×Dic11—21no—
108C4×Dic11—21no—
109C4×Dic11—21no—
110C4×Dic11—21no—
111C2×C11⋊C8—41no—
112#2598—111no—
113#1820—111no—
114#1458—111no—
115#1352—111no—
116#1352—111no—
117#1343—111no—
118#1343D1111yescharacteristic
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—22no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11C2×C22⋊C411yescharacteristic
131C23×C11#13511yescharacteristic
132C23×C11#13511yescharacteristic
133D4×C11—42no—
134D4×C11—42no—
135D4×C11—82no—
136D4×C11—82no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11—81no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—84no—
167C2×Dic11—81no—
168C2×Dic11—81no—
169C2×Dic11—81no—
170C2×Dic11#9911yescharacteristic
171C2×Dic11#9911yescharacteristic
172C8×C11—81no—
173C11⋊C8—81no—
174C2×C4×D4—111no—
175C2×#117—111no—
176#431—221no—
177#400—111no—
178#399—111no—
179#394—111no—
180#392C2×D1111yescharacteristic
181#388—221no—
182#386—221no—
183#386—221no—
184#385—221no—
185#383—111no—
186#381—221no—
187#342—111no—
188#342—221no—
189#342C2×D1111yescharacteristic
190#324—221no—
191#323—111no—
192#323C2×D1111yescharacteristic
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—42no—
200C22×C11—42no—
201C22×C11—41no—
202C22×C11—41no—
203C22×C11—42no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11—81no—
209C22×C11C2×#9911yescharacteristic
210C22×C11#41611yescharacteristic
211C22×C11#42111yescharacteristic
212C4×C11—41no—
213C4×C11—41no—
214C4×C11—81no—
215C4×C11—161no—
216Dic11—21no—
217Dic11—21no—
218Dic11—41no—
219Dic11—41no—
220Dic11—41no—
221Dic11—81no—
222Dic11—81no—
223Dic11—161no—
224C22×D4—21no—
225C22×D4C4×D1111yescharacteristic
226C23×C4—111no—
227C23×C4—221no—
228C4×D4—441no—
229C4×D4—441no—
230#117—441no—
231#117—441no—
232C2×C4⋊C4—111no—
233C2×C4⋊C4—111no—
234C2×C4⋊C4—111no—
235C2×C4⋊C4—221no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—111no—
239C2×C22⋊C4—221no—
240C2×C22⋊C4—221no—
241C2×C22⋊C4—221no—
242C2×C22⋊C4—221no—
243C2×C22⋊C4—221no—
244C2×C22⋊C4C22×D1111yescharacteristic
245C2×C42—111no—
246C2×C42—111no—
247C4⋊C8—441no—
248C22⋊C8—21no—
249C22⋊C8—221no—
250C4×C8—441no—
251#95—111no—
252#95—221no—
253#95—221no—
254#95—221no—
255#95—221no—
256#95—441no—
257#95—441no—
258#95C4×D1111yescharacteristic
259C2×C11—21no—
260C2×C11—21no—
261C2×C11—41no—
262C2×C11—41no—
263C2×C11—82no—
264C2×C11#151611yescharacteristic
265C2×C11#212011yescharacteristic
266C2×C11#212811yescharacteristic
267C24—21no—
268C24D4×D1111yescharacteristic
269C2×D4—41no—
270C2×D4—42no—
271C2×D4—42no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—81no—
275C22×C4—21no—
276C22×C4—41no—
277C22×C4—111no—
278C22×C4—111no—
279C22×C4—111no—
280C22×C4—111no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—441no—
288C22×C4—442no—
289C22×C4—441no—
290C22×C4—881no—
291C22×C4—881no—
292C22×C4C2×C4×D1111yescharacteristic
293C22×C4D4×D1111yescharacteristic
294C2×C8—41no—
295C2×C8—441no—
296C4⋊C4—441no—
297C4⋊C4—441no—
298C4⋊C4—441no—
299C4⋊C4—881no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—81no—
304C22⋊C4—441no—
305C22⋊C4—441no—
306C22⋊C4—441no—
307C22⋊C4—442no—
308C22⋊C4—442no—
309C22⋊C4—441no—
310C22⋊C4—441no—
311C22⋊C4—881no—
312C42—221no—
313C42—221no—
314C42—221no—
315C42—221no—
316C11#1184011yescharacteristic, complemented, Sylow
317C23—21no—
318C23—21no—
319C23—22no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23C22⋊C4×D1111yescharacteristic
329C23#6696511yescharacteristic
330C23#6696911yescharacteristic
331D4—42no—
332D4—42no—
333D4—82no—
334D4—82no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—111no—
346C2×C4—111no—
347C2×C4—221no—
348C2×C4—221no—
349C2×C4—221no—
350C2×C4—221no—
351C2×C4—221no—
352C2×C4—221no—
353C2×C4—221no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—884no—
367C2×C4—881no—
368C2×C4—881no—
369C2×C4—881no—
370C8—81no—
371C8—881no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—41no—
377C22—41no—
378C22—42no—
379C22—42no—
380C22—41no—
381C22—41no—
382C22—42no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22D11×#9911yescharacteristic
389C22#1062238511yescharacteristic
390C22#1062243411yescharacteristic
391C4—41no—
392C4—41no—
393C4—81no—
394C4—161no—
395C4—221no—
396C4—221no—
397C4—441no—
398C4—441no—
399C4—441no—
400C4—881no—
401C4—881no—
402C4—1761no—
403C2—21no—
404C2—21no—
405C2—41no—
406C2—41no—
407C2—82no—
408C2#1306716911yescharacteristic
409C2#1307025411yescharacteristic
410C2#1307028611yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1343C2
socleC22×C11C2×#99
prime radicalC11×#392C22
cosocleC2×C11×C22⋊C4C23
hypercenter#1343D11
hypocenterC11#11840
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1343

Complements

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

NH ≅ G/Ntype
2. #13068692C2semidirect
3. #13066927C2semidirect
4. #13066641C2semidirect
5. #13066639C2semidirect
8. C2×D4×Dic11C4semidirect
11. #10622835C4semidirect
19. #10622272C4semidirect
20. #10622264C4semidirect
316. C11#11840semidirect

Maximal subgroups

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

subgroupindex
#130741752
#130686922
#130669272
#130666412
#130666392
#130666132
C11×#13432
#1184011