Finite Group Databasebeta

← #14651624

Subgroups — #14651624

Order 2816.

542 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 113 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#13077696C211yesmaximal, characteristic, complemented
2#13073525C211yesmaximal, characteristic
3#13068609C211yesmaximal, characteristic, complemented
4#13067041C211yesmaximal, characteristic
5#13066476C211yesmaximal, characteristic, complemented
6#13066475C211yesmaximal, characteristic, complemented
7C11×#1486C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9C2×#66977—21no—
10C2×C4×Dic22C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13#10622835C412yes—
14#10622825—21no—
15C2×#66888—21no—
16#10622593C412yes—
17#10622557—22no—
18#10622549C2211yescharacteristic
19#10622538C2211yescharacteristic
20#10622537C2211yescharacteristic
21#10622443—22no—
22#10622331—22no—
23C8×Dic22—22no—
24C11×D4⋊C8—22no—
25#10622192—21no—
26D4⋊(C11⋊C8)—22no—
27C22×D4×C11C2×C411yescharacteristic
28C23×C4×C11—21no—
29C22×Dic22D411yescharacteristic
30C2×C11×M16—21no—
31C4×D4×C11—21no—
32C4×D4×C11—21no—
33C4×D4×C11—21no—
34C4×D4×C11—21no—
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C22⋊C4—21no—
37C2×C42×C11C2311yescharacteristic
38C2×C22⋊Dic11—22no—
39C2×C22⋊Dic11—22no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11D411yescharacteristic
42#66977—42no—
43#66977—42no—
44C2×Dic11⋊C4—22no—
45C2×Dic11⋊C4C2×C412yes—
46C2×C4×Dic11D412yes—
47C2×#4318—21no—
48C4×Dic22—21no—
49C4×Dic22—21no—
50C4×Dic22—21no—
51C4×Dic22—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×C22⋊C8—21no—
56C4×C8×C11D412yes—
57C11⋊#95—21no—
58C11⋊#95—22no—
59C11⋊#95C2×C412yes—
60C22⋊(C11⋊C8)—21no—
61#66888—42no—
62Dic11⋊C8—24no—
63C8×Dic11—24no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4×C11⋊C8D412yes—
68#9486—111nomaximal, Sylow
69C24×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11—42no—
73C22×C4×C11—21no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×Dic11—22no—
84C22×Dic11C22⋊C412yes—
85C22×Dic11C22⋊C412yes—
86C2×Dic22—21no—
87C2×Dic22—21no—
88C2×Dic22—21no—
89C2×Dic22—21no—
90C2×Dic22D812yes—
91C2×Dic22SD1612yes—
92C11×M16—41no—
93C11×M16—41no—
94C2×C8×C11—22no—
95C2×C8×C11—41no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11#4111yescharacteristic
103C42×C11#4111yescharacteristic
104C22⋊Dic11—44no—
105C22⋊Dic11—44no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108C4⋊Dic11—41no—
109C4⋊Dic11—41no—
110Dic11⋊C4—22no—
111Dic11⋊C4—22no—
112Dic11⋊C4—44no—
113C4×Dic11—22no—
114C4×Dic11—22no—
115#4318—41no—
116#4318—41no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—41no—
119#2982—111no—
120#2536—111no—
121#1801—111no—
122#1486—111no—
123#1486D1111yescharacteristic
124#1286—111no—
125#1286—111no—
126C23×C11—22no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11C2×C22⋊C411yescharacteristic
134D4×C11—22no—
135D4×C11—22no—
136D4×C11—41no—
137D4×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—81no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11—81no—
147C2×C4×C11C4×D411yescharacteristic
148C2×C4×C11C4×D411yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12311yescharacteristic
153C2×C4×C11C2×D811yescharacteristic
154C2×C4×C11C2×SD1611yescharacteristic
155C2×C4×C11#13511yescharacteristic
156C2×C4×C11#13511yescharacteristic
157C2×Dic11—22no—
158C2×Dic11—22no—
159C2×Dic11—22no—
160C2×Dic11—42no—
161C2×Dic11—42no—
162C2×Dic11—42no—
163C2×Dic11—42no—
164C2×Dic11#10214yes—
165Dic22—22no—
166Dic22—22no—
167Dic22—22no—
168Dic22—22no—
169C8×C11—42no—
170C8×C11—81no—
171C11⋊C8—42no—
172C11⋊C8—81no—
173C2×C22⋊Q8—221no—
174C2×C4×Q8—111no—
175C2×C4×D4C2×D1111yescharacteristic
176C8×Q8—222no—
177C8×Q8—222no—
178#431—111no—
179#431—222no—
180#431C2×D1111yescharacteristic
181#423—111no—
182#423C2×D1111yescharacteristic
183C2×#101—221no—
184#398—112no—
185#394—112no—
186#388—222no—
187#382—111no—
188#380—221no—
189#343—221no—
190D4⋊C8—22no—
191D4⋊C8—222no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—42no—
195C22×C11—42no—
196C22×C11—42no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11#38611yescharacteristic
202C22×C11C2×#10211yescharacteristic
203C22×C11#41611yescharacteristic
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—81no—
209C4×C11#46511yescharacteristic
210C4×C11#46511yescharacteristic
211C4×C11#46611yescharacteristic
212C4×C11#46611yescharacteristic
213Dic11—24no—
214Dic11—42no—
215Dic11—82no—
216C22×Q8—111no—
217C22×D4C4×D1111yescharacteristic
218C23×C4—21no—
219C2×M16—21no—
220C2×M16—221no—
221C22⋊Q8—442no—
222C22⋊Q8—442no—
223C4×Q8—221no—
224C4×Q8—221no—
225C4×Q8—221no—
226C4×Q8—221no—
227C4×D4—21no—
228C4×D4—21no—
229C4×D4—21no—
230C4×D4—21no—
231C2×C4⋊C4—112no—
232C2×C4⋊C4—111no—
233C2×C4⋊C4—222no—
234C2×C4⋊C4—221no—
235C2×C4⋊C4C4×D1111yescharacteristic
236C2×C22⋊C4—21no—
237C2×C22⋊C4—222no—
238C2×C22⋊C4—222no—
239C2×C42—112no—
240C2×C42C22×D1111yescharacteristic
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—224no—
245C4⋊C8—221no—
246C4⋊C8—221no—
247C4⋊C8—221no—
248#101—442no—
249C22⋊C8—21no—
250C22⋊C8—221no—
251C4×C8—112no—
252C4×C8—224no—
253C4×C8C22⋊D1112yes—
254#95—112no—
255#95—222no—
256#95—221no—
257C2×C11—21no—
258C2×C11—21no—
259C2×C11—82no—
260C2×C11#189111yescharacteristic
261C2×C11#189311yescharacteristic
262C2×C11#191211yescharacteristic
263C24—21no—
264C2×Q8—112no—
265C2×Q8—112no—
266C2×Q8—221no—
267C2×Q8—221no—
268C2×Q8—221no—
269C2×Q8—221no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—42no—
273C22×C4—21no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—112no—
281C22×C4—112no—
282C22×C4—222no—
283C22×C4C2×C4×D1111yescharacteristic
284C22×C4D4×D1111yescharacteristic
285C22×C4D4×D1111yescharacteristic
286M16—41no—
287M16—41no—
288M16—441no—
289M16—441no—
290C2×C8—22no—
291C2×C8—41no—
292C2×C8—222no—
293C2×C8—441no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—222no—
297C4⋊C4—221no—
298C4⋊C4—222no—
299C4⋊C4—221no—
300C4⋊C4—444no—
301C4⋊C4—441no—
302C4⋊C4—441no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—444no—
306C22⋊C4—444no—
307C42—222no—
308C42—222no—
309C42#433911yescharacteristic
310C42D4×D1111yescharacteristic
311C42#434111yescharacteristic
312C42C2×C22⋊D1111yescharacteristic
313C11#948611yescharacteristic, complemented, Sylow
314C23—22no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23C22⋊C4×D1111yescharacteristic
322Q8—222no—
323Q8—222no—
324Q8—222no—
325Q8—222no—
326D4—22no—
327D4—22no—
328D4—41no—
329D4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—114no—
340C2×C4—222no—
341C2×C4—222no—
342C2×C4—222no—
343C2×C4—442no—
344C2×C4—442no—
345C2×C4—442no—
346C2×C4—442no—
347C2×C4(C22⋊D11)⋊C411yescharacteristic
348C2×C4#6693611yescharacteristic
349C2×C4#6693711yescharacteristic
350C2×C4D8×D1111yescharacteristic
351C2×C4#6696511yescharacteristic
352C2×C4SD16×D1111yescharacteristic
353C2×C4#6696911yescharacteristic
354C2×C4C4×C22⋊D1111yescharacteristic
355C2×C4#6699011yescharacteristic
356C2×C4#6699111yescharacteristic
357C8—42no—
358C8—81no—
359C8—442no—
360C8—881no—
361C22—21no—
362C22—21no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22D11×#10211yescharacteristic
371C22#1062238511yescharacteristic
372C22#1062256911yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—81no—
378C4—224no—
379C4—442no—
380C4—882no—
381C4#1062238811yescharacteristic
382C4#1062239111yescharacteristic
383C4#1062277011yescharacteristic
384C4#1062278411yescharacteristic
385C2—21no—
386C2—21no—
387C2—82no—
388C2#1306903111yescharacteristic
389C2#1306904111yescharacteristic
390C2#1306915011yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1486C2
socleC22×C11#386
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenter#1486D11
hypocenterC11#9486
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
1. #13077696C2semidirect
3. #13068609C2semidirect
5. #13066476C2semidirect
6. #13066475C2semidirect
313. C11#9486semidirect

Maximal subgroups

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

subgroupindex
#130776962
#130735252
#130686092
#130670412
#130664762
#130664752
C11×#14862
#948611