Finite Group Databasebeta

← #14642003

Subgroups — #14642003

Order 2816.

510 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 101 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#13071074C211yesmaximal, characteristic
2#13068468C211yesmaximal, characteristic, complemented
3#13068363C211yesmaximal, characteristic, complemented
4#13066439C211yesmaximal, characteristic, complemented
5#13066436C211yesmaximal, characteristic
6#13066436C211yesmaximal, characteristic
7C11×#1271C211yesmaximal, characteristic, complemented
8C2×#66946C411yescharacteristic
9C2×#66945—21no—
10C11×#389C2211yescharacteristic
11C2×#66879—21no—
12C2×#66879—21no—
13C2×Dic11⋊C8—21no—
14#10622603—21no—
15#10622601C411yescharacteristic
16#10622598C411yescharacteristic
17C4⋊C4×Dic11C411yescharacteristic
18#10622552C2211yescharacteristic
19C42×Dic11C2211yescharacteristic
20#10622283—21no—
21#10622279—21no—
22C11×#336C2211yescharacteristic
23C11×#336C2211yescharacteristic
24#10622188—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×D44C2×C411yescharacteristic
28C22×C4×D11—21no—
29C22×C8×C11—21no—
30C22×C8×C11—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C42×C11C2311yescharacteristic
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×C4⋊Dic11—21no—
41C2×C4⋊Dic11C2×C411yescharacteristic
42C2×C4×Dic11—21no—
43C2×C4×Dic11C2×C411yescharacteristic
44C2×C4×Dic11C2×C411yescharacteristic
45C2×C4×Dic11D411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48C2×C4×Dic11D411yescharacteristic
49C22×C11⋊C8—21no—
50C22×C11⋊C8—21no—
51#66946—22no—
52#66946—22no—
53#66945—42no—
54#66945—42no—
55C11×#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58#66879—24no—
59#66879—42no—
60Dic11⋊C8—24no—
61#7628—111nomaximal, Sylow
62C23×D11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11C22×C411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—21no—
69C22×Dic11C22⋊C411yescharacteristic
70C22×Dic11C22⋊C411yescharacteristic
71C22×Dic11C22⋊C411yescharacteristic
72C22×Dic11C22⋊C411yescharacteristic
73C2×D44—21no—
74C2×D44—41no—
75C2×D44—41no—
76C2×D44M1612yes—
77C2×C4×D11—24no—
78C2×C4×D11—42no—
79C2×C4×D11—42no—
80C2×C8×C11—22no—
81C2×C8×C11—22no—
82C2×C8×C11—41no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4M1612yes—
91C42×C11—41no—
92(C2×D11)⋊C4—24no—
93(C2×D11)⋊C4—42no—
94(C2×D11)⋊C4—42no—
95(C2×D11)⋊C4—41no—
96(C2×D11)⋊C4—41no—
97(C2×D11)⋊C4—41no—
98(C2×D11)⋊C4—41no—
99C4⋊Dic11—41no—
100C4⋊Dic11—42no—
101C4×Dic11—22no—
102C4×Dic11—22no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11—21no—
108C4×Dic11—21no—
109C4×Dic11—41no—
110C4×Dic11—42no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—41no—
117#2293—111no—
118#1767—111no—
119#1745—111no—
120#1271—111no—
121#1271D1111yescharacteristic, complemented
122#1270—111no—
123#1270—111no—
124C23×C11C2×C22⋊C411yescharacteristic
125C22×D11—22no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11—41no—
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—22no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11C2×M1611yescharacteristic
145C2×C4×C11C2×M1611yescharacteristic
146C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C11#13711yescharacteristic
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11#10412yes—
164C2×Dic11#10412yes—
165D44—42no—
166D44—42no—
167C4×D11—48no—
168C8×C11—42no—
169C8×C11—42no—
170C11⋊C8—42no—
171C11⋊C8—42no—
172C2×C4×D4—111no—
173C2×#117—221no—
174C2×C4⋊C8—221no—
175C2×#97—221no—
176C2×#97—221no—
177#390—111no—
178#390—111no—
179#389—111no—
180#389C2×D1111yescharacteristic
181#388—221no—
182#388—221no—
183C4×C4⋊C4—111no—
184C4×C22⋊C4—221no—
185C43—111no—
186#336—111no—
187#336—111no—
188#336—221no—
189#336C2×D1111yescharacteristic
190#336C2×D1111yescharacteristic
191C22×C11#40711yescharacteristic
192C22×C11#41011yescharacteristic
193C22×C11#41311yescharacteristic
194C22×C11#41711yescharacteristic
195C22×C11#41811yescharacteristic
196C22×C11C2×#10411yescharacteristic
197C22×C11C2×#10411yescharacteristic
198C2×D11—42no—
199C2×D11—42no—
200C2×D11—42no—
201C2×D11—81no—
202C2×D11—81no—
203C2×D11—81no—
204C2×D11—81no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—42no—
212C4×C11—81no—
213Dic11—22no—
214Dic11—22no—
215Dic11—41no—
216Dic11—41no—
217Dic11—81no—
218C22×D4—111no—
219C23×C4—221no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—221no—
223C22×C8—221no—
224C4×D4—222no—
225C4×D4—222no—
226#117—442no—
227#117—442no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—111no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4C4×D1111yescharacteristic
232C2×C4⋊C4C4×D1111yescharacteristic
233C2×C22⋊C4—221no—
234C2×C22⋊C4—221no—
235C2×C22⋊C4—221no—
236C2×C22⋊C4—221no—
237C2×C22⋊C4—221no—
238C2×C42—111no—
239C2×C42—111no—
240C2×C42—111no—
241C2×C42—111no—
242C2×C42—111no—
243C2×C42—111no—
244C2×C42—221no—
245C2×C42C22×D1111yescharacteristic
246C4⋊C8—224no—
247#97—224no—
248#97—442no—
249#95—21no—
250#95—221no—
251#95—221no—
252C2×C11#146411yescharacteristic
253C2×C11#148911yescharacteristic
254C2×C11#149011yescharacteristic
255C2×C11#150511yescharacteristic
256C2×C11#150911yescharacteristic
257C2×C11#152411yescharacteristic
258C2×C11#155711yescharacteristic
259D11—82no—
260C24—221no—
261C2×D4—112no—
262C2×D4—221no—
263C2×D4—441no—
264C2×D4—441no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—111no—
268C22×C4—111no—
269C22×C4—111no—
270C22×C4—111no—
271C22×C4—224no—
272C22×C4—221no—
273C22×C4—442no—
274C22×C4—442no—
275C22×C4C2×C4×D1111yescharacteristic
276C22×C4D4×D1111yescharacteristic
277C22×C4D4×D1111yescharacteristic
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—222no—
285C2×C8—222no—
286C2×C8—441no—
287C2×C8—441no—
288C2×C8—441no—
289C2×C8—441no—
290C4⋊C4—21no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—441no—
295C4⋊C4—442no—
296C4⋊C4#431312yes—
297C22⋊C4—224no—
298C22⋊C4—442no—
299C22⋊C4—442no—
300C22⋊C4—441no—
301C22⋊C4—441no—
302C22⋊C4—441no—
303C22⋊C4—441no—
304C42—41no—
305C42—222no—
306C42—222no—
307C42—221no—
308C42—221no—
309C42—221no—
310C42—221no—
311C42—221no—
312C42—221no—
313C42—441no—
314C42—442no—
315C11#762811yescharacteristic, complemented, Sylow
316C23—222no—
317C23—441no—
318C23—441no—
319C23—441no—
320C23—441no—
321C23—441no—
322C23—441no—
323C23C22⋊C4×D1111yescharacteristic
324D4—442no—
325D4—442no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—112no—
339C2×C4—112no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4—221no—
343C2×C4—221no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—221no—
347C2×C4—221no—
348C2×C4—221no—
349C2×C4—221no—
350C2×C4—448no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4C2×#431311yescharacteristic
355C2×C4M16×D1111yescharacteristic
356C2×C4#6696411yescharacteristic
357C2×C4#6696711yescharacteristic
358C2×C4#6696711yescharacteristic
359C2×C4#6697111yescharacteristic
360C8—42no—
361C8—42no—
362C8—442no—
363C8—442no—
364C22—442no—
365C22—442no—
366C22—442no—
367C22—881no—
368C22—881no—
369C22—881no—
370C22—881no—
371C22#1062233911yescharacteristic
372C22#1062235311yescharacteristic
373C22#1062236411yescharacteristic
374C22#1062238311yescharacteristic
375C22#1062241611yescharacteristic
376C22D11×#10411yescharacteristic
377C22D11×#10411yescharacteristic
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—42no—
385C4—81no—
386C4—222no—
387C4—222no—
388C4—441no—
389C4—441no—
390C4—881no—
391C2—882no—
392C2#1306694911yescharacteristic
393C2#1306705411yescharacteristic
394C2#1306705711yescharacteristic
395C2#1306712211yescharacteristic
396C2#1306714011yescharacteristic
397C2#1306720311yescharacteristic
398C2#1306733711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1271C2
socleC23×C11C2×C22⋊C4
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1271D11
hypocenterC11#7628
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
2. #13068468C2semidirect
3. #13068363C2semidirect
4. #13066439C2semidirect
7. C11×#1271C2semidirect
121. #1271D11semidirect
315. C11#7628semidirect

Maximal subgroups

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

subgroupindex
#130710742
#130684682
#130683632
#130664392
#130664362
C11×#12712
#762811