Finite Group Databasebeta

← #14738591

Subgroups — #14738591

Order 2816.

584 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079839C212yesmaximal
2C2×#10622295C211yesmaximal, characteristic, complemented
3#13077591C211yesmaximal, characteristic
4#13068145C212yesmaximal, complemented
5#13068140C212yesmaximal, complemented
6#13068021C212yesmaximal, complemented
7#13068016C212yesmaximal, complemented
8#13067341C212yesmaximal, complemented
9C11×#1568C211yesmaximal, characteristic, complemented
10#10623010C2211yescharacteristic
11C2×#66922C2212yes—
12C11×#432C2212yes—
13C2×C4×C8×C11C2211yescharacteristic
14#10622724—21no—
15C8×C22⋊D11—21no—
16C2×#66882—21no—
17C2×#66882—21no—
18#10622539C2211yescharacteristic
19#10622463C2214yes—
20#10622455C2214yes—
21#10622349—22no—
22#10622334—22no—
23#10622327—22no—
24#10622315—22no—
25#10622303—21no—
26#10622302—21no—
27#10622301C2211yescharacteristic
28C8×D44C2211yescharacteristic
29#10622295—21no—
30#10622295—21no—
31#10622295C2212yes—
32#10622295C2212yes—
33#10622292C2211yescharacteristic
34C8×Dic22C2211yescharacteristic
35C11×#335C2212yes—
36C11×#334C2212yes—
37#10622119C2214yes—
38#10622119C2214yes—
39C22×Dic22—22no—
40C22×C8×C11D411yescharacteristic
41C22×C8×C11D411yescharacteristic
42C2×C42×C11C2311yescharacteristic
43#66983D411yescharacteristic
44#66982—21no—
45C4×C22⋊D11—21no—
46C2×C4⋊Dic11—22no—
47C2×C4⋊Dic11—22no—
48#66977D411yescharacteristic
49C2×#4313—21no—
50C2×C8×D11—21no—
51#66929—21no—
52#66928D411yescharacteristic
53C4×D44C2311yescharacteristic
54#66925—21no—
55#66923D411yescharacteristic
56#66922—22no—
57#66922—22no—
58#66922—22no—
59#66922C2314yes—
60C4×Dic22C2311yescharacteristic
61C11×C4⋊C8C2314yes—
62C11×C22⋊C8—22no—
63C11×#97—22no—
64C4×C8×C11D411yescharacteristic
65C4×C8×C11D411yescharacteristic
66C4×C8×C11C2311yescharacteristic
67C4×C8×C11C2311yescharacteristic
68C22⋊(C11⋊C8)—21no—
69#66885—24no—
70(C2×D11)⋊C8—21no—
71(C2×D11)⋊C8—21no—
72#66882—22no—
73#66882—22no—
74#66882—22no—
75#66882—22no—
76#66882—24no—
77#66881—24no—
78#66880—24no—
79#66879—21no—
80Dic11⋊C8—21no—
81Dic11⋊C8—21no—
82C8×Dic11—21no—
83C4⋊(C11⋊C8)C2311yescharacteristic
84C4⋊(C11⋊C8)C2311yescharacteristic
85#66867—21no—
86#19359—111nomaximal, Sylow
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C2×C22⋊D11—21no—
91C22×Dic11—42no—
92C2×D44C2×D411yescharacteristic
93C2×C4×D11—21no—
94C2×Dic22—24no—
95C2×Dic22—42no—
96C2×Dic22—84no—
97C2×Dic22C2×D411yescharacteristic
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11—24no—
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11C2×D411yescharacteristic
104C2×C8×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11#4111yescharacteristic
108C42×C11C2411yescharacteristic
109C22⋊Dic11—21no—
110(C2×D11)⋊C4—21no—
111(C2×D11)⋊C4—21no—
112(C2×D11)⋊C4—21no—
113(C2×D11)⋊C4—21no—
114C4⋊Dic11—24no—
115C4⋊Dic11—24no—
116C4⋊Dic11—42no—
117C4⋊Dic11—42no—
118C4⋊Dic11C2×D411yescharacteristic
119C4⋊Dic11C2×D411yescharacteristic
120Dic11⋊C4—21no—
121Dic11⋊C4—21no—
122Dic11⋊C4—21no—
123Dic11⋊C4—21no—
124C4×Dic11—21no—
125C2×C11⋊C8—21no—
126C2×C11⋊C8—21no—
127#4313—42no—
128C8×D11—42no—
129#3238—112no—
130C2×#500—111no—
131#2966—111no—
132#1696—112no—
133#1695—112no—
134#1676—112no—
135#1675—112no—
136#1568D1111yescharacteristic, complemented
137#1558—112no—
138C23×C11#12111yescharacteristic
139C22×D11—21no—
140C2×C4×C11—22no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—22no—
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11C22×D411yescharacteristic
148C2×C4×C11C22×D411yescharacteristic
149C2×C4×C11C2×#4111yescharacteristic
150C22⋊D11—42no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—44no—
155C2×Dic11—84no—
156D44—22no—
157C4×D11—41no—
158C4×D11—41no—
159Dic22—22no—
160Dic22—84no—
161Dic22—84no—
162C8×C11—21no—
163C8×C11—21no—
164C8×C11—44no—
165C8×C11#13712yes—
166C8×C11#13712yes—
167C11⋊C8—41no—
168C11⋊C8—41no—
169C2×C4⋊Q8—112no—
170#529—111no—
171#501—222no—
172#500—112no—
173#500—112no—
174#500—221no—
175#500—221no—
176#489—222no—
177#483—222no—
178#480—222no—
179#477—114no—
180#476—114no—
181#446—111no—
182C8×Q8—111no—
183#436—111no—
184#435—221no—
185C8×D4—111no—
186C8×D4—221no—
187#433—221no—
188#432—111no—
189#432C2×D1112yes—
190C2×#107—221no—
191C2×#107—221no—
192#405—221no—
193C2×C4×C8C2×D1111yescharacteristic
194#335C2×D1112yes—
195#334C2×D1112yes—
196#333—114no—
197#333—114no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11#47212yes—
201C22×C11C2×#12111yescharacteristic
202C2×D11—41no—
203C2×D11—41no—
204C2×D11—41no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11C2×#13711yescharacteristic
210C4×C11C2×#13711yescharacteristic
211C4×C11#57812yes—
212Dic11—41no—
213Dic11—41no—
214Dic11—41no—
215Dic11—84no—
216C22×Q8—222no—
217C2×M16—221no—
218C22×C8—221no—
219C22×C8D4411yescharacteristic
220C22×C8D4411yescharacteristic
221C4⋊Q8—114no—
222C4⋊Q8—222no—
223C4⋊Q8—222no—
224C4⋊Q8—222no—
225#126—221no—
226#125—111no—
227#124—111no—
228#123—221no—
229C22⋊Q8—111no—
230#121—111no—
231C4×Q8—111no—
232C4×D4—111no—
233C4×D4—221no—
234#117—221no—
235C2×C4⋊C4—222no—
236C2×C4⋊C4—222no—
237C2×C42C22×D1111yescharacteristic
238#107—224no—
239#107—222no—
240#107—222no—
241#107—222no—
242#107—222no—
243#106—224no—
244C4⋊C8—111no—
245C4⋊C8—111no—
246C4⋊C8—221no—
247C4⋊C8—221no—
248C4⋊C8C22×D1114yes—
249#103—224no—
250#102—224no—
251C22⋊C8—22no—
252C22⋊C8—221no—
253C22⋊C8—221no—
254C22⋊C8—221no—
255#97—22no—
256#97—221no—
257#97—221no—
258C4×C8—221no—
259C4×C8D4411yescharacteristic
260C4×C8D4411yescharacteristic
261C4×C8C22×D1111yescharacteristic
262C4×C8C22×D1111yescharacteristic
263C2×C11—22no—
264C2×C11#303911yescharacteristic
265C2×C11#305911yescharacteristic
266C2×C11C2×#47211yescharacteristic
267D11—81no—
268C2×Q8—111no—
269C2×Q8—224no—
270C2×Q8—442no—
271C2×Q8—884no—
272C2×D4—111no—
273C2×D4—221no—
274C22×C4—221no—
275C22×C4—442no—
276C22×C4C2×D4411yescharacteristic
277C22×C4D4×D1111yescharacteristic
278C22×C4#434311yescharacteristic
279M16—442no—
280C2×C8—22no—
281C2×C8—22no—
282C2×C8—24no—
283C2×C8—221no—
284C2×C8—221no—
285C2×C8—442no—
286C2×C8C2×D4411yescharacteristic
287C2×C8C2×D4411yescharacteristic
288C2×C8C2×D4411yescharacteristic
289C2×C8C2×D4411yescharacteristic
290C4⋊C4—111no—
291C4⋊C4—111no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C4⋊C4—221no—
295C4⋊C4—221no—
296C4⋊C4—224no—
297C4⋊C4—224no—
298C4⋊C4—442no—
299C4⋊C4—442no—
300C22⋊C4—221no—
301C22⋊C4—221no—
302C22⋊C4—221no—
303C22⋊C4—221no—
304C22⋊C4—221no—
305C42—221no—
306C42C2×D4411yescharacteristic
307C42D4×D1111yescharacteristic
308C42#434311yescharacteristic
309C42C23×D1111yescharacteristic
310C11#1935911yescharacteristic, complemented, Sylow
311C23—221no—
312C23#6694811yescharacteristic
313Q8—222no—
314Q8—884no—
315Q8—884no—
316D4—222no—
317D4—442no—
318C2×C4—22no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—444no—
328C2×C4—884no—
329C2×C4#6694811yescharacteristic
330C2×C4#6694811yescharacteristic
331C2×C4#6694811yescharacteristic
332C2×C4C22×D4411yescharacteristic
333C2×C4C2×D4×D1111yescharacteristic
334C2×C4C2×#434311yescharacteristic
335C8—21no—
336C8—21no—
337C8—44no—
338C8—441no—
339C8—441no—
340C8#6696212yes—
341C8#6696212yes—
342C22—21no—
343C22—21no—
344C22—441no—
345C22—441no—
346C22—441no—
347C22#1062251012yes—
348C22C2×#6694811yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—441no—
354C4—441no—
355C4—441no—
356C4—884no—
357C4C2×#6696211yescharacteristic
358C4C2×#6696211yescharacteristic
359C4#1062330212yes—
360C2—22no—
361C2—881no—
362C2#1307810411yescharacteristic
363C2#1307827211yescharacteristic
364C2C2×#1062251011yescharacteristic
subgroupG/H
centerC22C2×#66948
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1568C2
socleC22×C11C2×#121
prime radical#66983D4
hypercenter#1568D11
hypocenterC11#19359
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1568

Complements

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

NH ≅ G/Ntype
2. C2×#10622295C2semidirect
4. #13068145C2semidirect
5. #13068140C2semidirect
6. #13068021C2semidirect
7. #13068016C2semidirect
8. #13067341C2semidirect
9. C11×#1568C2semidirect
136. #1568D11semidirect
310. C11#19359semidirect

Maximal subgroups

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

subgroupindex
#130798392
C2×#106222952
#130775912
#130681452
#130681402
#130680212
#130680162
#130673412
C11×#15682
#1935911