Finite Group Databasebeta

← #14739077

Subgroups — #14739077

Order 2816.

602 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079566C211yesmaximal, characteristic
2#13078423C211yesmaximal, characteristic
3C2×#10622464C211yesmaximal, characteristic
4#13077696C211yesmaximal, characteristic
5#13068075C214yesmaximal, complemented
6#13067987C214yesmaximal, complemented
7#13067302C211yesmaximal, characteristic
8#13067274C211yesmaximal, characteristic
9C11×#1571C211yesmaximal, characteristic
10#10623001C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C2×C4×Dic22C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C11×#423C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16#10622734—21no—
17#10622733—21no—
18C2×#66881—21no—
19C2×#66880—21no—
20#10622538C2211yescharacteristic
21#10622464—22no—
22#10622464C2214yes—
23#10622464C2212yes—
24#10622463C2212yes—
25#10622462—22no—
26#10622443—22no—
27#10622442—22no—
28#10622352—22no—
29#10622331—22no—
30#10622312C2212yes—
31#10622294C2212yes—
32C8×Dic22C2214yes—
33C11×#335C2214yes—
34#10622124C2212yes—
35#10622124C2214yes—
36#10622119C2212yes—
37C22×Dic22—21no—
38C22×Dic22D411yescharacteristic
39C2×C11×M16—21no—
40C22×C8×C11—21no—
41C2×C42×C11C2311yescharacteristic
42#66979—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11D411yescharacteristic
46#66977—21no—
47#66977—21no—
48C2×Dic11⋊C4—21no—
49C2×C4×Dic11—21no—
50C2×Dic44—24no—
51#66923—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55#66922C2312yes—
56#66922C2311yescharacteristic
57#66922C2311yescharacteristic
58C4×Dic22—21no—
59C4×Dic22—21no—
60C4×Dic22—21no—
61C4×Dic22—21no—
62C4×Dic22D412yes—
63C4×Dic22C2312yes—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8D412yes—
67C11×C4⋊C8C2312yes—
68C11×C4⋊C8C2312yes—
69C11×C22⋊C8D412yes—
70C4×C8×C11C2312yes—
71C22⋊(C11⋊C8)—21no—
72#66882—22no—
73#66881—24no—
74#66881—22no—
75#66880—24no—
76#66880—22no—
77#66880—22no—
78#66880—24no—
79Dic11⋊C8—24no—
80C8×Dic11—24no—
81C4⋊(C11⋊C8)C2312yes—
82C4×C11⋊C8—21no—
83#19399—111nomaximal, Sylow
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—41no—
90C2×Dic22—21no—
91C2×Dic22—22no—
92C2×Dic22—22no—
93C2×Dic22—21no—
94C2×Dic22—21no—
95C2×Dic22—41no—
96C2×Dic22—82no—
97C2×Dic22Q1614yescomplemented
98C2×Dic22C2×D412yes—
99C11×M16—42no—
100C2×C8×C11—22no—
101C2×C8×C11—22no—
102C2×C8×C11—42no—
103C2×C8×C11C2×D414yes—
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11#4111yescharacteristic
107C42×C11C2411yescharacteristic
108C22⋊Dic11—41no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—22no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—22no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118C4⋊Dic11C2×D412yes—
119Dic11⋊C4—22no—
120Dic11⋊C4—22no—
121Dic11⋊C4—41no—
122Dic11⋊C4—41no—
123C4×Dic11—22no—
124C4×Dic11—22no—
125C4×Dic11—41no—
126C2×C11⋊C8—22no—
127Dic44—84no—
128#3209—111no—
129#3078—111no—
130C2×#475—111no—
131#2982—111no—
132#1684—114no—
133#1670—114no—
134#1571D1111yescharacteristic
135#1549—111no—
136#1542—111no—
137C23×C11#12111yescharacteristic
138C2×C4×C11—22no—
139C2×C4×C11—41no—
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11C2×Q1612yes—
144C2×C4×C11#13512yes—
145C2×C4×C11C22×D411yescharacteristic
146C2×C4×C11C22×D411yescharacteristic
147C2×C4×C11C2×#4111yescharacteristic
148C2×Dic11—22no—
149C2×Dic11—24no—
150C2×Dic11—22no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—42no—
154C2×Dic11—81no—
155C2×Dic11—82no—
156Dic22—22no—
157Dic22—24no—
158Dic22—42no—
159Dic22—44no—
160Dic22—82no—
161Dic22—81no—
162Dic22C2×Q1614yes—
163C8×C11—24no—
164C8×C11—42no—
165C8×C11—42no—
166C11⋊C8—42no—
167#533—111no—
168C2×C4⋊Q8—111no—
169C2×C4×Q8—111no—
170#494—112no—
171#487—112no—
172#479—222no—
173#477—112no—
174#475—114no—
175#475—112no—
176#475—222no—
177#462—222no—
178#451—222no—
179C8×Q8—114no—
180C8×Q8—222no—
181#431—111no—
182#431—222no—
183#431C2×D1111yescharacteristic
184#428—221no—
185C2×#106—221no—
186#423C2×D1111yescharacteristic
187C2×C4⋊C8C2×D1111yescharacteristic
188#419—221no—
189C2×#103—221no—
190#335C2×D1114yes—
191#333—112no—
192#332—112no—
193#332—114no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11#46712yes—
197C22×C11C2×#12111yescharacteristic
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11#46712yes—
202C4×C11C22×Q1611yescharacteristic
203C4×C11C2×#13511yescharacteristic
204C4×C11#57712yes—
205Dic11—24no—
206Dic11—42no—
207Dic11—82no—
208Dic11—81no—
209Dic11—81no—
210C22×Q8—111no—
211C22×Q8—221no—
212C2×Q16—224no—
213C2×M16—21no—
214C22×C8—21no—
215C4⋊Q8—112no—
216C4⋊Q8—111no—
217C4⋊Q8—111no—
218C4⋊Q8—221no—
219C4⋊Q8—221no—
220C4⋊Q8—221no—
221#125—221no—
222C22⋊Q8—221no—
223C22⋊Q8—221no—
224C4×Q8—112no—
225C4×Q8—112no—
226C4×Q8—221no—
227C4×Q8—221no—
228C4×Q8—221no—
229C4×Q8—221no—
230#117—221no—
231C2×C4⋊C4—111no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—221no—
235C2×C42—221no—
236C2×C42C22×D1111yescharacteristic
237#107—222no—
238#106—224no—
239#106—222no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—112no—
243C4⋊C8—224no—
244C4⋊C8D4412yes—
245C4⋊C8C22×D1112yes—
246C4⋊C8C22×D1112yes—
247#103—224no—
248#103—222no—
249#103—222no—
250#103—224no—
251C22⋊C8—221no—
252C22⋊C8D4412yes—
253C4×C8—224no—
254C4×C8—221no—
255C4×C8C22×D1112yes—
256C2×C11—22no—
257C2×C11#304311yescharacteristic
258C2×C11C2×#46711yescharacteristic
259C2×C11#306911yescharacteristic
260C2×Q8—114no—
261C2×Q8—112no—
262C2×Q8—221no—
263C2×Q8—222no—
264C2×Q8—222no—
265C2×Q8—221no—
266C2×Q8—221no—
267C2×Q8—441no—
268C2×Q8—882no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4—441no—
272C22×C4C2×D4411yescharacteristic
273C22×C4D4×D1111yescharacteristic
274C22×C4#434311yescharacteristic
275Q16—884no—
276M16—42no—
277C2×C8—22no—
278C2×C8—22no—
279C2×C8—42no—
280C2×C8—222no—
281C2×C8C2×D4414yes—
282C4⋊C4—112no—
283C4⋊C4—221no—
284C4⋊C4—222no—
285C4⋊C4—222no—
286C4⋊C4—221no—
287C4⋊C4—222no—
288C4⋊C4—221no—
289C4⋊C4—221no—
290C4⋊C4—222no—
291C4⋊C4—221no—
292C4⋊C4—441no—
293C4⋊C4—441no—
294C4⋊C4—441no—
295C4⋊C4—441no—
296C22⋊C4—441no—
297C42—222no—
298C42—222no—
299C42—441no—
300C42C2×D4411yescharacteristic
301C42D4×D1111yescharacteristic
302C42#434311yescharacteristic
303C42C23×D1111yescharacteristic
304C11#1939911yescharacteristic, complemented, Sylow
305C23#6694811yescharacteristic
306Q8—114no—
307Q8—224no—
308Q8—222no—
309Q8—442no—
310Q8—444no—
311Q8—881no—
312Q8—882no—
313C2×C4—22no—
314C2×C4—41no—
315C2×C4—224no—
316C2×C4—222no—
317C2×C4—222no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—442no—
321C2×C4—881no—
322C2×C4—882no—
323C2×C4#6694811yescharacteristic
324C2×C4#6694811yescharacteristic
325C2×C4#6694811yescharacteristic
326C2×C4#6696512yes—
327C2×C4Q16×D1112yes—
328C2×C4C22×D4411yescharacteristic
329C2×C4C2×D4×D1111yescharacteristic
330C2×C4C2×#434311yescharacteristic
331C8—24no—
332C8—42no—
333C8—42no—
334C8—442no—
335C22—21no—
336C22—21no—
337C22#1062250012yes—
338C22C2×#6694811yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—224no—
343C4—442no—
344C4—881no—
345C4—882no—
346C4—881no—
347C4#1062250012yes—
348C4#1062328212yes—
349C4C2×#6696511yescharacteristic
350C4C2×Q16×D1111yescharacteristic
351C2—22no—
352C2#1307813811yescharacteristic
353C2C2×#1062250011yescharacteristic
354C2#1307835411yescharacteristic
subgroupG/H
centerC22C2×#66948
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1571C2
socleC22×C11C2×#121
prime radicalC23×C11#121
hypercenter#1571D11
hypocenterC11#19399
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1571

Complements

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

NH ≅ G/Ntype
5. #13068075C2semidirect
6. #13067987C2semidirect
97. C2×Dic22Q16semidirect
304. C11#19399semidirect

Maximal subgroups

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

subgroupindex
#130795662
#130784232
C2×#106224642
#130776962
#130680752
#130679872
#130673022
#130672742
C11×#15712
#1939911