Finite Group Databasebeta

← #14651519

Subgroups — #14651519

Order 2816.

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

normal subgroups only

This group has 554 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#13073109C211yesmaximal, characteristic
2#13071217C211yesmaximal, characteristic, complemented
3#13068694C211yesmaximal, characteristic, complemented
4#13067145C211yesmaximal, characteristic
5#13066470C211yesmaximal, characteristic, complemented
6#13066468C211yesmaximal, characteristic, complemented
7C11×#1510C211yesmaximal, characteristic
8C2×C11×#121C2211yescharacteristic
9C22×C4⋊Dic11C2211yescharacteristic
10C11×#407C2211yescharacteristic
11C11×#381C2211yescharacteristic
12#10622834C412yescomplemented
13#10622833—21no—
14#10622833—21no—
15#10622824C2211yescharacteristic
16C4×C22⋊Dic11C2211yescharacteristic
17#10622820C2211yescharacteristic
18#10622590C412yescomplemented
19#10622566—22no—
20#10622555—21no—
21C22⋊C4×Dic11—21no—
22#10622267—22no—
23#10622266—22no—
24C11×#327—22no—
25#10622192—22no—
26#10622175—22no—
27C22×D4×C11—21no—
28C22×D4×C11C2×C411yescharacteristic
29C23×C4×C11C2311yescharacteristic
30C23×Dic11D411yescharacteristic
31C23×Dic11D411yescharacteristic
32C2×C11×M16—21no—
33C11×#121—21no—
34C11×#121—21no—
35C11×#121—21no—
36C11×#121—21no—
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11—22no—
43C2×C22⋊Dic11—22no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11C2×C412yes—
49C2×C4⋊Dic11D412yes—
50C2×Dic11⋊C4—22no—
51C2×C4×Dic11—22no—
52C2×C4×Dic11C2×C412yes—
53C2×#4318—21no—
54C11×C22⋊C8—21no—
55C11×C22⋊C8—21no—
56C11×#95—21no—
57C11×#95D412yes—
58C11⋊#95—22no—
59C11⋊#95—22no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95—22no—
63C11⋊#95—22no—
64C11⋊#95D412yes—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—21no—
67#9465—111nomaximal, Sylow
68C24×C11—21no—
69C24×C11C2×D411yescharacteristic
70C2×D4×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11—42no—
73C2×D4×C11—44no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C22×C4×C11—21no—
77C22×C4×C11—22no—
78C22×C4×C11—42no—
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C22×Dic11—22no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—22no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—81no—
92C22×Dic11—81no—
93C22×Dic11C22⋊C412yes—
94C22×Dic11C22⋊C412yes—
95C11×M16—42no—
96C2×C8×C11—41no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C22⋊C4—42no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C22⋊Dic11—42no—
103C22⋊Dic11—42no—
104C22⋊Dic11—82no—
105C22⋊Dic11—82no—
106C4⋊Dic11—22no—
107C4⋊Dic11—22no—
108C4⋊Dic11—22no—
109C4⋊Dic11—22no—
110Dic11⋊C4—82no—
111C4×Dic11—42no—
112C4×Dic11—82no—
113#4318—42no—
114C2×C11⋊C8—41no—
115#2504—111no—
116#2313—111no—
117#1821—111no—
118#1510—111no—
119#1510D1111yescharacteristic
120#1284—111no—
121#1284—111no—
122C23×C11—22no—
123C23×C11—22no—
124C23×C11—41no—
125C23×C11—42no—
126C23×C11—42no—
127C23×C11—41no—
128C23×C11—42no—
129C23×C11C2×C22⋊C411yescharacteristic
130C23×C11#12011yescharacteristic
131C23×C11#12311yescharacteristic
132D4×C11—81no—
133D4×C11—81no—
134D4×C11—82no—
135D4×C11—82no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—41no—
146C2×C4×C11—42no—
147C2×C4×C11C4×D411yescharacteristic
148C2×C4×C11C4×D411yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×Dic11—22no—
152C2×Dic11—22no—
153C2×Dic11—42no—
154C2×Dic11—42no—
155C2×Dic11—42no—
156C2×Dic11—42no—
157C2×Dic11—42no—
158C2×Dic11—42no—
159C2×Dic11—42no—
160C2×Dic11—42no—
161C2×Dic11—42no—
162C2×Dic11—42no—
163C2×Dic11—81no—
164C2×Dic11—81no—
165C8×C11—81no—
166C11⋊C8—81no—
167C2×#121C2×D1111yescharacteristic
168C22×C4⋊C4—111no—
169#407—111no—
170#407C2×D1111yescharacteristic
171#397—222no—
172#390—112no—
173#387—222no—
174#387—222no—
175#386—221no—
176#386—221no—
177#382—112no—
178#381—111no—
179#381C2×D1111yescharacteristic
180#380—221no—
181C4×C22⋊C4—111no—
182C4×C22⋊C4—221no—
183#343—222no—
184#327—22no—
185#327—222no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—44no—
194C22×C11—84no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11#38611yescharacteristic
199C22×C11#41012yes—
200C22×C11#45412yes—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—82no—
206C4×C11—81no—
207Dic11—42no—
208Dic11—42no—
209Dic11—82no—
210Dic11—82no—
211C22×D4—21no—
212C22×D4C4×D1111yescharacteristic
213C23×C4—111no—
214C23×C4—111no—
215C23×C4C22×D1111yescharacteristic
216C2×M16—21no—
217C2×M16—221no—
218#121—21no—
219#121—21no—
220#121—21no—
221#121—21no—
222C2×C4⋊C4—112no—
223C2×C4⋊C4—112no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4—221no—
227C2×C4⋊C4—221no—
228C2×C4⋊C4—222no—
229C2×C4⋊C4C4×D1111yescharacteristic
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—221no—
233C2×C22⋊C4—221no—
234C2×C22⋊C4—222no—
235C2×C22⋊C4—222no—
236C2×C42—112no—
237C2×C42—222no—
238C22⋊C8—21no—
239C22⋊C8—21no—
240C22⋊C8—221no—
241C22⋊C8—221no—
242#95—21no—
243#95—112no—
244#95—222no—
245#95—222no—
246#95—222no—
247#95—222no—
248#95—221no—
249#95—221no—
250#95C22⋊D1112yes—
251C2×C11—22no—
252C2×C11—22no—
253C2×C11—41no—
254C2×C11—161no—
255C2×C11#188811yescharacteristic
256C2×C11#189911yescharacteristic
257C2×C11#191111yescharacteristic
258C24—21no—
259C24D4×D1111yescharacteristic
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—42no—
263C2×D4—44no—
264C2×D4—41no—
265C2×D4—41no—
266C22×C4—21no—
267C22×C4—22no—
268C22×C4—42no—
269C22×C4—112no—
270C22×C4—112no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4—221no—
274C22×C4—221no—
275C22×C4—222no—
276C22×C4—222no—
277C22×C4—881no—
278C22×C4—881no—
279C22×C4C2×C4×D1111yescharacteristic
280C22×C4#433911yescharacteristic
281C22×C4D4×D1111yescharacteristic
282C22×C4D4×D1111yescharacteristic
283C22×C4#434111yescharacteristic
284C22×C4C2×C22⋊D1111yescharacteristic
285M16—42no—
286M16—442no—
287C2×C8—41no—
288C2×C8—441no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—222no—
292C4⋊C4—222no—
293C4⋊C4—222no—
294C4⋊C4—222no—
295C4⋊C4—882no—
296C22⋊C4—42no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—442no—
300C22⋊C4—442no—
301C22⋊C4—882no—
302C22⋊C4—882no—
303C42—442no—
304C42—882no—
305C11#946511yescharacteristic, complemented, Sylow
306C23—22no—
307C23—22no—
308C23—41no—
309C23—42no—
310C23—42no—
311C23—41no—
312C23—42no—
313C23C22⋊C4×D1111yescharacteristic
314C23#6693611yescharacteristic
315C23#6699011yescharacteristic
316D4—81no—
317D4—81no—
318D4—82no—
319D4—82no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—222no—
332C2×C4—222no—
333C2×C4—442no—
334C2×C4—442no—
335C2×C4—442no—
336C2×C4—442no—
337C2×C4—442no—
338C2×C4—442no—
339C2×C4—442no—
340C2×C4—442no—
341C2×C4—442no—
342C2×C4—442no—
343C2×C4—881no—
344C2×C4—881no—
345C2×C4(C22⋊D11)⋊C411yescharacteristic
346C2×C4#6693711yescharacteristic
347C2×C4C4×C22⋊D1111yescharacteristic
348C2×C4#6699111yescharacteristic
349C8—81no—
350C8—881no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—44no—
359C22—84no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22#1062235312yes—
364C22#1062256911yescharacteristic
365C22#1062281412yes—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—82no—
371C4—81no—
372C4—442no—
373C4—442no—
374C4—882no—
375C4—882no—
376C2—22no—
377C2—22no—
378C2—41no—
379C2—161no—
380C2#1306901611yescharacteristic
381C2#1306907111yescharacteristic
382C2#1306914511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1510C2
socleC22×C11#386
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenter#1510D11
hypocenterC11#9465
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1510

Complements

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

NH ≅ G/Ntype
2. #13071217C2semidirect
3. #13068694C2semidirect
5. #13066470C2semidirect
6. #13066468C2semidirect
12. #10622834C4semidirect
18. #10622590C4semidirect
305. C11#9465semidirect

Maximal subgroups

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

subgroupindex
#130731092
#130712172
#130686942
#130671452
#130664702
#130664682
C11×#15102
#946511