Finite Group Databasebeta

← #14663358

Subgroups — #14663358

Order 2816.

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

normal subgroups only

This group has 414 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#13073091C211yesmaximal, characteristic
2#13066944C211yesmaximal, characteristic
3D11×#324C211yesmaximal, characteristic
4#13066562C211yesmaximal, characteristic, complemented
5#13066549C211yesmaximal, characteristic, complemented
6#13066549C211yesmaximal, characteristic, complemented
7C11×#1325C211yesmaximal, characteristic, complemented
8C2×#66950C411yescharacteristic
9C2×C4⋊C4×D11C2211yescharacteristic
10C11×#384C2211yescharacteristic
11#10622602—21no—
12#10622602—21no—
13#10622597—21no—
14#10622597—21no—
15#10622589C411yescharacteristic
16#10622587C2211yescharacteristic
17C4×(C2×D11)⋊C4C411yescharacteristic
18#10622542C411yescharacteristic
19#10622339—21no—
20D11×C22⋊C8—21no—
21C11×#324C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622166C2211yescharacteristic
25#10622107—21no—
26#10622107—21no—
27C22×C4×D11C2×C411yescharacteristic
28C22×C4×D11D411yescharacteristic
29C22×C4×D11D411yescharacteristic
30C22×Dic22C2×C411yescharacteristic
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×C42×C11C2×C411yescharacteristic
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4D411yescharacteristic
43C2×Dic11⋊C4D411yescharacteristic
44C2×C4×Dic11C2×C411yescharacteristic
45C2×#4313—41no—
46C2×C8×D11—41no—
47#66950—41no—
48#66950—41no—
49C4⋊C4×D11—41no—
50C4⋊C4×D11—41no—
51C11×C22⋊C8—21no—
52C11×C22⋊C8—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60(C2×D11)⋊C8—41no—
61(C2×D11)⋊C8—41no—
62#11555—111nomaximal, Sylow
63C23×D11C22⋊C411yescharacteristic
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11C22⋊C411yescharacteristic
72C22×Dic11C22⋊C411yescharacteristic
73C22×Dic11C22⋊C411yescharacteristic
74C2×C4×D11—21no—
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11—21no—
79C2×C4×D11—21no—
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11—41no—
83C2×C4×D11—81no—
84C2×C4×D11—81no—
85C2×Dic22—21no—
86C2×Dic22—21no—
87C2×Dic22—41no—
88C2×Dic22—41no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—81no—
94C11×C4⋊C4—81no—
95C42×C11—21no—
96C42×C11—21no—
97(C2×D11)⋊C4—24no—
98(C2×D11)⋊C4—41no—
99(C2×D11)⋊C4—41no—
100C4⋊Dic11—41no—
101C4⋊Dic11—42no—
102Dic11⋊C4—41no—
103Dic11⋊C4—41no—
104Dic11⋊C4—81no—
105Dic11⋊C4—81no—
106C4×Dic11—41no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109#4313—82no—
110C8×D11—82no—
111#2502—111no—
112#1463—111no—
113C2×#324—111no—
114#1325—111no—
115#1325D1111yescharacteristic, complemented
116#1319—111no—
117#1319—111no—
118C23×C11C2×C22⋊C411yescharacteristic
119C22×D11—21no—
120C22×D11—21no—
121C22×D11—22no—
122C22×D11—41no—
123C22×D11#9911yescharacteristic
124C22×D11#9911yescharacteristic
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—22no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11#13111yescharacteristic
138C2×C4×C11#13111yescharacteristic
139C2×Dic11—22no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C4×D11—41no—
153C4×D11—41no—
154C4×D11—41no—
155C4×D11—41no—
156C4×D11—42no—
157C4×D11—42no—
158C4×D11—81no—
159C4×D11—81no—
160Dic22—81no—
161Dic22—81no—
162C8×C11—81no—
163C8×C11—81no—
164C11⋊C8—81no—
165C11⋊C8—81no—
166C2×C22⋊Q8—111no—
167C22×C4⋊C4—111no—
168#407—221no—
169C2×C22⋊C8—221no—
170#398—221no—
171#398—221no—
172#391—111no—
173#391—111no—
174#385—221no—
175#385—221no—
176#384—111no—
177#384C2×D1111yescharacteristic
178C4×C22⋊C4—111no—
179#324—111no—
180#324—111no—
181#324—221no—
182#324—221no—
183#324C2×D1111yescharacteristic
184#324C2×D1111yescharacteristic
185C22×C11—21no—
186C22×C11—21no—
187C22×C11#40811yescharacteristic
188C22×C11C2×#9911yescharacteristic
189C22×C11#41311yescharacteristic
190C2×D11—21no—
191C2×D11—21no—
192C2×D11—21no—
193C2×D11—21no—
194C2×D11—21no—
195C2×D11—42no—
196C2×D11—42no—
197C2×D11#35612yes—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—42no—
201C4×C11—41no—
202C4×C11—41no—
203C4×C11—81no—
204Dic11—42no—
205Dic11—41no—
206Dic11—41no—
207Dic11—41no—
208Dic11—81no—
209C22×Q8—111no—
210C23×C4—111no—
211C23×C4—111no—
212C23×C4—111no—
213C2×M16—441no—
214C22×C8—441no—
215C22⋊Q8—441no—
216C22⋊Q8—441no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—111no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—111no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—441no—
226C2×C4⋊C4—441no—
227C2×C4⋊C4C4×D1111yescharacteristic
228C2×C4⋊C4C22×D1111yescharacteristic
229C2×C22⋊C4—221no—
230C2×C22⋊C4—221no—
231C2×C42—111no—
232C2×C42C4×D1111yescharacteristic
233C22⋊C8—21no—
234C22⋊C8—21no—
235C22⋊C8—221no—
236C22⋊C8—221no—
237C22⋊C8—441no—
238C22⋊C8—441no—
239#95—221no—
240#95—221no—
241#95—221no—
242#95—221no—
243#95—221no—
244C2×C11—21no—
245C2×C11—21no—
246C2×C11#146811yescharacteristic
247C2×C11#212711yescharacteristic
248C2×C11C2×#35611yescharacteristic
249D11—22no—
250D11—41no—
251C24—111no—
252C2×Q8—221no—
253C2×Q8—221no—
254C2×Q8—441no—
255C2×Q8—441no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—111no—
259C22×C4—111no—
260C22×C4—111no—
261C22×C4—221no—
262C22×C4—221no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—221no—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4—441no—
272C22×C4—881no—
273C22×C4—881no—
274C22×C4C2×C4×D1111yescharacteristic
275C22×C4D4×D1111yescharacteristic
276C22×C4D4×D1111yescharacteristic
277M16—882no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—441no—
281C2×C8—441no—
282C2×C8—882no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—81no—
286C4⋊C4—81no—
287C4⋊C4—441no—
288C4⋊C4—441no—
289C4⋊C4—441no—
290C4⋊C4—442no—
291C4⋊C4—881no—
292C4⋊C4—881no—
293C22⋊C4—224no—
294C22⋊C4—441no—
295C22⋊C4—441no—
296C42—21no—
297C42—21no—
298C42—441no—
299C11#1155511yescharacteristic, complemented, Sylow
300C23—111no—
301C23—111no—
302C23—222no—
303C23—221no—
304C23—221no—
305C23—441no—
306C23C22⋊C4×D1111yescharacteristic
307Q8—881no—
308Q8—881no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—222no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—442no—
332C2×C4—442no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—881no—
341C2×C4—881no—
342C2×C4#6695411yescharacteristic
343C2×C4#6696011yescharacteristic
344C8—81no—
345C8—81no—
346C8—881no—
347C8—881no—
348C22—21no—
349C22—21no—
350C22—112no—
351C22—221no—
352C22—221no—
353C22—221no—
354C22—221no—
355C22—221no—
356C22—442no—
357C22—442no—
358C22#1062234011yescharacteristic
359C22D11×#9911yescharacteristic
360C22#1062236411yescharacteristic
361C4—21no—
362C4—21no—
363C4—42no—
364C4—41no—
365C4—41no—
366C4—81no—
367C4—442no—
368C4—441no—
369C4—441no—
370C4—441no—
371C4—881no—
372C2—21no—
373C2—21no—
374C2—222no—
375C2—441no—
376C2#1306696311yescharacteristic
377C2#1307028211yescharacteristic
378C2D11×#35611yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1325C2
socleC22×C11C2×#99
prime radicalC23×D11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1325D11
hypocenterC11#11555
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
4. #13066562C2semidirect
5. #13066549C2semidirect
6. #13066549C2semidirect
7. C11×#1325C2semidirect
115. #1325D11semidirect
299. C11#11555semidirect

Maximal subgroups

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

subgroupindex
#130730912
#130669442
D11×#3242
#130665622
#130665492
C11×#13252
#1155511