Finite Group Databasebeta

← #14650714

Subgroups — #14650714

Order 2816.

482 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 93 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#13078734C211yesmaximal, characteristic
2#13071268C211yesmaximal, characteristic, complemented
3#13069536C211yesmaximal, characteristic
4#13067062C211yesmaximal, characteristic, complemented
5#13066509C211yesmaximal, characteristic, complemented
6#13066471C211yesmaximal, characteristic, complemented
7C11×#1505C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C4×Dic22C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#376C2211yescharacteristic
12C2×#66901—22no—
13#10622704C412yescomplemented
14#10622688C412yescomplemented
15#10622653—21no—
16#10622646—21no—
17#10622631—22no—
18C4×C4⋊Dic11C2211yescharacteristic
19#10622542—21no—
20#10622541—21no—
21#10622539C2211yescharacteristic
22C4×#4318C2211yescharacteristic
23#10622265—22no—
24#10622264—21no—
25#10622263—21no—
26C11×#327—21no—
27C11×#327—21no—
28#10622122—22no—
29C2×C11×#41—21no—
30C22×Dic22D411yescharacteristic
31C11×C4⋊Q8C2×C411yescharacteristic
32C11×#127C2×C411yescharacteristic
33C11×#124—21no—
34C11×#121—21no—
35C11×#121—21no—
36C4×D4×C11—21no—
37C4×D4×C11—21no—
38C2×C42×C11—21no—
39C2×C42×C11C2311yescharacteristic
40C2×#4324—22no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11D411yescharacteristic
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—22no—
45C2×C4×Dic11—21no—
46C2×C4×Dic11D412yes—
47C2×#4318—21no—
48C4×Dic22—21no—
49C4×Dic22—21no—
50C4×Dic22C2×C412yes—
51C4×Dic22D412yes—
52C11×C4⋊C8—21no—
53C11×C22⋊C8—21no—
54C11×#97—21no—
55C11×#95—21no—
56C11×#95D411yescharacteristic
57C11×#95D411yescharacteristic
58#66901—44no—
59#66896—22no—
60C11⋊#95—22no—
61C11⋊#95—22no—
62C11⋊#95—22no—
63C11⋊#95—21no—
64C22⋊(C11⋊C8)—21no—
65#66874—22no—
66#66871—22no—
67C4⋊(C11⋊C8)C2×C412yes—
68#66867—21no—
69#66867—21no—
70C4×C11⋊C8—21no—
71#9330—111nomaximal, Sylow
72C11×#41—42no—
73C11×#41—42no—
74C2×Q8×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—41no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—41no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—22no—
88C2×Dic22—21no—
89C2×Dic22—42no—
90C2×Dic22C22⋊C412yes—
91C2×C8×C11—41no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C42×C11—42no—
97C42×C11C22×C411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11#4111yescharacteristic
100C42×C11#4111yescharacteristic
101#4324—44no—
102C4⋊Dic11—21no—
103C4⋊Dic11—42no—
104C4⋊Dic11C22⋊C412yes—
105Dic11⋊C4—22no—
106Dic11⋊C4—22no—
107Dic11⋊C4—82no—
108C4×Dic11—22no—
109C4×Dic11—22no—
110C4×Dic11—42no—
111#4318—22no—
112#4318—41no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—41no—
115#3112—111no—
116#2320—111no—
117#1980—111no—
118#1505D1111yescharacteristic
119#1491—111no—
120#1300—111no—
121#1285—111no—
122C23×C11—41no—
123C23×C11#12011yescharacteristic
124Q8×C11—42no—
125D4×C11—42no—
126D4×C11—42no—
127D4×C11—81no—
128D4×C11—81no—
129D4×C11—81no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—22no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—82no—
142C2×C4×C11C2×C22⋊C411yescharacteristic
143C2×C4×C11C4×D411yescharacteristic
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12311yescharacteristic
148C2×Dic11—22no—
149C2×Dic11—22no—
150C2×Dic11—42no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—42no—
154C2×Dic11—42no—
155C2×Dic11—42no—
156Dic22—22no—
157Dic22—22no—
158Dic22—42no—
159C8×C11—81no—
160C11⋊C8—42no—
161C11⋊C8—42no—
162#532C2×D1111yescharacteristic
163C2×C4×Q8—111no—
164#480—221no—
165#477—112no—
166#460—112no—
167#448—221no—
168#440—222no—
169#432—111no—
170#432C2×D1111yescharacteristic
171C2×#104—222no—
172C4×M16—111no—
173#391—221no—
174#389—221no—
175#387—222no—
176#383—221no—
177#382—221no—
178C4×C4⋊C4—111no—
179#376C2×D1111yescharacteristic
180#327—21no—
181#327—21no—
182Q8⋊C8—222no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11—81no—
188C22×C11#38611yescharacteristic
189C22×C11#45311yescharacteristic
190C22×C11#45411yescharacteristic
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—81no—
197C4×C11—81no—
198C4×C11—81no—
199C4×C11#42112yes—
200Dic11—42no—
201Dic11—42no—
202Dic11—82no—
203C2×#41—21no—
204C22×Q8—111no—
205C2×SD16—222no—
206C2×M16—221no—
207C4⋊Q8C4×D1111yescharacteristic
208#127C4×D1111yescharacteristic
209#124—21no—
210#121—21no—
211#121—21no—
212C4×Q8—112no—
213C4×Q8—112no—
214C4×Q8—221no—
215C4×Q8—221no—
216C4×D4—21no—
217C4×D4—21no—
218C2×C4⋊C4—111no—
219C2×C4⋊C4—221no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—222no—
222C2×C42—21no—
223C2×C42—112no—
224C2×C42—221no—
225C2×C42C22×D1111yescharacteristic
226#107—222no—
227C4⋊C8—21no—
228C4⋊C8—112no—
229#104—444no—
230#103—222no—
231#102—222no—
232C22⋊C8—21no—
233C22⋊C8—221no—
234#97—21no—
235#97—221no—
236#97—221no—
237C4×C8—221no—
238#95—21no—
239#95—222no—
240#95—222no—
241#95—222no—
242#95—221no—
243#95C22⋊D1111yescharacteristic
244#95C22⋊D1111yescharacteristic
245C2×C11—21no—
246C2×C11—21no—
247C2×C11—161no—
248C2×C11#188311yescharacteristic
249C2×C11#189711yescharacteristic
250C2×C11#190511yescharacteristic
251#41—42no—
252#41—42no—
253C2×Q8—21no—
254C2×Q8—112no—
255C2×Q8—221no—
256C2×Q8—442no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—41no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—41no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—222no—
267C22×C4D4×D1111yescharacteristic
268C22×C4D4×D1111yescharacteristic
269C22×C4C2×C22⋊D1111yescharacteristic
270SD16—444no—
271M16—222no—
272M16—441no—
273C2×C8—41no—
274C2×C8—222no—
275C2×C8—441no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—112no—
279C4⋊C4—222no—
280C4⋊C4—221no—
281C4⋊C4—222no—
282C4⋊C4—442no—
283C4⋊C4—882no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C42—42no—
287C42—222no—
288C42—222no—
289C42—442no—
290C42C2×C4×D1111yescharacteristic
291C42#433911yescharacteristic
292C42D4×D1111yescharacteristic
293C42#434111yescharacteristic
294C11#933011yescharacteristic, complemented, Sylow
295C23—41no—
296C23#6699011yescharacteristic
297Q8—42no—
298Q8—222no—
299Q8—222no—
300Q8—442no—
301D4—42no—
302D4—42no—
303D4—81no—
304D4—81no—
305D4—81no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—22no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—82no—
318C2×C4—222no—
319C2×C4—222no—
320C2×C4—442no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—442no—
324C2×C4—442no—
325C2×C4—442no—
326C2×C4C22⋊C4×D1111yescharacteristic
327C2×C4(C22⋊D11)⋊C411yescharacteristic
328C2×C4#6693611yescharacteristic
329C2×C4#6693711yescharacteristic
330C2×C4C4×C22⋊D1111yescharacteristic
331C2×C4#6699111yescharacteristic
332C8—81no—
333C8—442no—
334C8—442no—
335C22—21no—
336C22—21no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22#1062256911yescharacteristic
341C22#1062281111yescharacteristic
342C22#1062281411yescharacteristic
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—81no—
349C4—81no—
350C4—81no—
351C4—442no—
352C4—442no—
353C4—882no—
354C4#1062243412yes—
355C2—21no—
356C2—21no—
357C2—161no—
358C2#1306898911yescharacteristic
359C2#1306906111yescharacteristic
360C2#1306911311yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1505C2
socleC22×C11#386
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#1505D11
hypocenterC11#9330
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1505

Complements

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

NH ≅ G/Ntype
2. #13071268C2semidirect
4. #13067062C2semidirect
5. #13066509C2semidirect
6. #13066471C2semidirect
13. #10622704C4semidirect
14. #10622688C4semidirect
294. C11#9330semidirect

Maximal subgroups

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

subgroupindex
#130787342
#130712682
#130695362
#130670622
#130665092
#130664712
C11×#15052
#933011