Finite Group Databasebeta

← #14663353

Subgroups — #14663353

Order 2816.

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

normal subgroups only

This group has 408 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#13073075C211yesmaximal, characteristic
2#13066949C211yesmaximal, characteristic, complemented
3#13066929C211yesmaximal, characteristic, complemented
4#13066562C211yesmaximal, characteristic, complemented
5#13066547C211yesmaximal, characteristic, complemented
6#13066547C211yesmaximal, characteristic, complemented
7C11×#1325C211yesmaximal, characteristic, complemented
8C2×#66948C411yescharacteristic
9C2×#66945C2211yescharacteristic
10C11×#384C2211yescharacteristic
11#10622604—21no—
12#10622604—21no—
13#10622603—21no—
14#10622603—21no—
15#10622601C2211yescharacteristic
16#10622590C411yescharacteristic
17#10622552C411yescharacteristic
18C4×(C2×D11)⋊C4C411yescharacteristic
19#10622332—21no—
20#10622331—21no—
21C11×#324C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622166C2211yescharacteristic
25#10622106—21no—
26#10622106—21no—
27C22×D44—21no—
28C22×D44C2×C411yescharacteristic
29C22×C4×D11C2×C411yescharacteristic
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C4⋊C4C2311yescharacteristic
34C2×C42×C11C2×C411yescharacteristic
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4D411yescharacteristic
42C2×(C2×D11)⋊C4D411yescharacteristic
43C2×C4⋊Dic11C2×C411yescharacteristic
44C2×C4×Dic11C2×C411yescharacteristic
45C2×C4×Dic11D411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47#66948—41no—
48#66948—41no—
49#66945—41no—
50#66945—41no—
51C11×C22⋊C8—21no—
52C11×C22⋊C8—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C22⋊(C11⋊C8)—21no—
57C22⋊(C11⋊C8)—21no—
58#66879—41no—
59Dic11⋊C8—41no—
60Dic11⋊C8—41no—
61C8×Dic11—41no—
62#11554—111nomaximal, Sylow
63C23×D11—21no—
64C23×D11C22⋊C411yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×Dic11—21no—
71C22×Dic11C22⋊C411yescharacteristic
72C22×Dic11C22⋊C411yescharacteristic
73C22×Dic11C22⋊C411yescharacteristic
74C2×D44—21no—
75C2×D44—21no—
76C2×D44—41no—
77C2×D44—41no—
78C2×D44—42no—
79C2×D44—81no—
80C2×D44—81no—
81C2×C4×D11—21no—
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—41no—
86C2×C8×C11—41no—
87C2×C8×C11—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—81no—
91C11×C4⋊C4—81no—
92C42×C11—21no—
93C42×C11—21no—
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4—41no—
96(C2×D11)⋊C4—42no—
97(C2×D11)⋊C4—42no—
98(C2×D11)⋊C4—42no—
99(C2×D11)⋊C4—41no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—81no—
102(C2×D11)⋊C4—81no—
103C4⋊Dic11—41no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11—21no—
108C4×Dic11—41no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111#2500—111no—
112#1464—111no—
113#1458—111no—
114#1325—111no—
115#1325D1111yescharacteristic, complemented
116#1318—111no—
117#1318—111no—
118C23×C11C2×C22⋊C411yescharacteristic
119C22×D11—21no—
120C22×D11—21no—
121C22×D11—21no—
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11—41no—
129C22×D11—41no—
130C22×D11—41no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—22no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11#13111yescharacteristic
144C2×C4×C11#13111yescharacteristic
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11#9911yescharacteristic
155C2×Dic11#9911yescharacteristic
156D44—81no—
157D44—81no—
158D44—84no—
159C4×D11—41no—
160C4×D11—41no—
161C4×D11—41no—
162C4×D11—41no—
163C8×C11—81no—
164C8×C11—81no—
165C11⋊C8—81no—
166C11⋊C8—81no—
167C2×#121—111no—
168C2×#117—111no—
169#432—221no—
170#431—221no—
171#394—221no—
172#394—221no—
173#390—111no—
174#390—111no—
175#388—221no—
176#388—221no—
177#384C2×D1111yescharacteristic
178#382—111no—
179C4×C22⋊C4—111no—
180#324—111no—
181#324—111no—
182#324C2×D1111yescharacteristic
183#324C2×D1111yescharacteristic
184#323—221no—
185#323—221no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11#40811yescharacteristic
189C22×C11C2×#9911yescharacteristic
190C22×C11#41311yescharacteristic
191C2×D11—41no—
192C2×D11—41no—
193C2×D11—41no—
194C2×D11—81no—
195C2×D11—81no—
196C2×D11—81no—
197C2×D11—81no—
198C2×D11—81no—
199C2×D11—81no—
200C2×D11—81no—
201C2×D11—81no—
202C2×D11—81no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—42no—
206C4×C11—41no—
207C4×C11—41no—
208C4×C11—81no—
209Dic11—21no—
210Dic11—21no—
211Dic11—41no—
212Dic11—41no—
213Dic11—81no—
214C22×D4—111no—
215C22×D4—221no—
216C23×C4—111no—
217#121—441no—
218#121—441no—
219#117—441no—
220#117—441no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—111no—
224C2×C4⋊C4C4×D1111yescharacteristic
225C2×C4⋊C4C22×D1111yescharacteristic
226C2×C22⋊C4—111no—
227C2×C22⋊C4—111no—
228C2×C22⋊C4—221no—
229C2×C22⋊C4—221no—
230C2×C22⋊C4—221no—
231C2×C22⋊C4—221no—
232C2×C22⋊C4—221no—
233C2×C22⋊C4—221no—
234C2×C42—111no—
235C2×C42—111no—
236C2×C42—111no—
237C2×C42C4×D1111yescharacteristic
238C4⋊C8—441no—
239C4⋊C8—441no—
240C22⋊C8—21no—
241C22⋊C8—21no—
242C22⋊C8—221no—
243C22⋊C8—221no—
244#97—441no—
245C4×C8—441no—
246#95—221no—
247#95—221no—
248#95—221no—
249C2×C11—21no—
250C2×C11—21no—
251C2×C11#146811yescharacteristic
252C2×C11#212811yescharacteristic
253C2×C11#213211yescharacteristic
254D11—81no—
255D11—161no—
256C24—111no—
257C24—221no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4—441no—
261C2×D4—441no—
262C2×D4—442no—
263C2×D4—881no—
264C2×D4—881no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—111no—
268C22×C4—111no—
269C22×C4—111no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4—221no—
274C22×C4—221no—
275C22×C4—441no—
276C22×C4C2×C4×D1111yescharacteristic
277C22×C4D4×D1111yescharacteristic
278C22×C4D4×D1111yescharacteristic
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—441no—
282C2×C8—441no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—81no—
286C4⋊C4—81no—
287C4⋊C4—441no—
288C22⋊C4—441no—
289C22⋊C4—441no—
290C22⋊C4—442no—
291C22⋊C4—442no—
292C22⋊C4—442no—
293C22⋊C4—441no—
294C22⋊C4—441no—
295C22⋊C4—881no—
296C22⋊C4—881no—
297C42—21no—
298C42—21no—
299C42—221no—
300C42—221no—
301C42—221no—
302C42—221no—
303C42—441no—
304C11#1155411yescharacteristic, complemented, Sylow
305C23—221no—
306C23—221no—
307C23—221no—
308C23—441no—
309C23—441no—
310C23—441no—
311C23—441no—
312C23—441no—
313C23—441no—
314C23—441no—
315C23—441no—
316C23—441no—
317C23C22⋊C4×D1111yescharacteristic
318D4—881no—
319D4—881no—
320D4—884no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—22no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—111no—
334C2×C4—111no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—221no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4#6695411yescharacteristic
349C2×C4#6696011yescharacteristic
350C8—81no—
351C8—81no—
352C8—881no—
353C8—881no—
354C22—21no—
355C22—21no—
356C22—441no—
357C22—441no—
358C22—441no—
359C22—881no—
360C22—881no—
361C22—881no—
362C22—881no—
363C22—881no—
364C22—881no—
365C22—881no—
366C22—881no—
367C22—881no—
368C22#1062234011yescharacteristic
369C22D11×#9911yescharacteristic
370C22#1062236411yescharacteristic
371C4—21no—
372C4—21no—
373C4—42no—
374C4—41no—
375C4—41no—
376C4—81no—
377C4—221no—
378C4—221no—
379C4—441no—
380C4—441no—
381C4—881no—
382C2—21no—
383C2—21no—
384C2—881no—
385C2—1761no—
386C2#1306696311yescharacteristic
387C2#1307028611yescharacteristic
388C2#1307030011yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1325C2
socleC22×C11C2×#99
prime radicalC2×#66948C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1325D11
hypocenterC11#11554
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
2. #13066949C2semidirect
3. #13066929C2semidirect
4. #13066562C2semidirect
5. #13066547C2semidirect
6. #13066547C2semidirect
7. C11×#1325C2semidirect
115. #1325D11semidirect
304. C11#11554semidirect

Maximal subgroups

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

subgroupindex
#130730752
#130669492
#130669292
#130665622
#130665472
C11×#13252
#1155411