Finite Group Databasebeta

← #14739122

Subgroups — #14739122

Order 2816.

676 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079737C211yesmaximal, characteristic
2#13078088C211yesmaximal, characteristic
3#13077697C211yesmaximal, characteristic, complemented
4#13068062C214yesmaximal, complemented
5#13068008C214yesmaximal, complemented
6#13067390C211yesmaximal, characteristic, complemented
7#13067288C211yesmaximal, characteristic, complemented
8#13067266C211yesmaximal, characteristic
9C2×C11×#462C211yesmaximal, characteristic, complemented
10C22×C11×Q16—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#66995—21no—
14#10623008C2211yescharacteristic
15C11×#462—22no—
16C11×#462C2214yes—
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#103—21no—
19#10622701C2212yes—
20#10622700—22no—
21#10622691C2212yes—
22#10622644C2212yes—
23#10622641—22no—
24#10622640C2212yes—
25Q8×C11⋊C8—22no—
26Q8×C11⋊C8C2214yes—
27#10622580—22no—
28#10622579—21no—
29#10622538—22no—
30#10622538C2211yescharacteristic
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622185C2214yes—
34#10622123C2212yes—
35#10622120C2212yes—
36#10622117C2214yes—
37C22×Q8×C11—21no—
38C22×Q8×C11D411yescharacteristic
39C2×#4339—21no—
40C2×C11×Q16—24no—
41C2×C11×Q16—44no—
42C22×C8×C11—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8C2312yes—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11D412yes—
50C4×Q8×C11C2312yes—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C42×C11—21no—
56C2×C42×C11C2311yescharacteristic
57C2×#4326—22no—
58#66995—44no—
59C2×#4325—22no—
60#66983—21no—
61#66983—21no—
62C2×#4318—21no—
63#66928—21no—
64#66927C2311yescharacteristic
65C4×D44—21no—
66C4×D44—21no—
67#66922C2311yescharacteristic
68C11×C4⋊C8—21no—
69C11×C4⋊C8C2312yes—
70C11×#103—24no—
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)D412yes—
73#66874—22no—
74#66873—22no—
75#66873—24no—
76#66871—24no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)—24no—
79C4⋊(C11⋊C8)D412yes—
80C4⋊(C11⋊C8)C2312yes—
81C4⋊(C11⋊C8)C2312yes—
82C4×C11⋊C8—21no—
83C4×C11⋊C8—24no—
84C4×C11⋊C8C2312yes—
85#19404—111nomaximal, Sylow
86C2×Q8×C11—21no—
87C2×Q8×C11—22no—
88C2×Q8×C11—22no—
89C2×Q8×C11—41no—
90C2×Q8×C11—42no—
91C2×Q8×C11—42no—
92C2×Q8×C11D814yes—
93C2×Q8×C11C2×D412yes—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—41no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11#4111yescharacteristic
100C2×C22⋊D11—41no—
101#4339—42no—
102#4339—42no—
103C2×D44—21no—
104C2×D44—21no—
105C2×D44—21no—
106C2×C4×D11—41no—
107C2×Dic22—21no—
108C11×Q16—48no—
109C2×C8×C11—22no—
110C2×C8×C11—42no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4C2×D412yes—
119C42×C11—22no—
120C42×C11—22no—
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11#4111yescharacteristic
124C42×C11C2411yescharacteristic
125#4326—44no—
126#4325—44no—
127(C2×D11)⋊C4—41no—
128(C2×D11)⋊C4—41no—
129C4⋊Dic11—21no—
130C4⋊Dic11—21no—
131#4318—42no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8C2×D414yes—
135#3226—111no—
136#3037—111no—
137C2×#462D1111yescharacteristic, complemented
138#2982—111no—
139#1682—114no—
140#1674—114no—
141#1571—111no—
142#1546—111no—
143#1540—111no—
144C23×C11#12111yescharacteristic
145C22×D11—41no—
146Q8×C11—22no—
147Q8×C11—24no—
148Q8×C11—42no—
149Q8×C11—42no—
150Q8×C11—82no—
151Q8×C11C2×D814yes—
152C2×C4×C11—22no—
153C2×C4×C11—24no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11—81no—
159C2×C4×C11—82no—
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11C2×D812yes—
164C2×C4×C11#13512yes—
165C2×C4×C11C22×D411yescharacteristic
166C2×C4×C11C22×D411yescharacteristic
167C2×C4×C11C2×#4111yescharacteristic
168C22⋊D11—82no—
169C2×Dic11—41no—
170D44—41no—
171D44—41no—
172D44—42no—
173D44—81no—
174C4×D11—82no—
175Dic22—41no—
176Dic22—41no—
177C8×C11—42no—
178C11⋊C8—24no—
179C11⋊C8—42no—
180C11⋊C8—42no—
181C2×#137—221no—
182C22×Q16—21no—
183#532—111no—
184C2×C4⋊Q8C2×D1111yescharacteristic
185C2×C4×Q8C2×D1111yescharacteristic
186#500—112no—
187#486—112no—
188#480—222no—
189#474—222no—
190#464—222no—
191#462—22no—
192#462—112no—
193#462C2×D1114yes—
194#460—112no—
195C8×Q8—114no—
196C8×Q8—222no—
197#431—111no—
198#431—111no—
199#431—222no—
200#423—111no—
201C2×C4⋊C8C2×D1111yescharacteristic
202#417—221no—
203C2×#103—21no—
204#335—114no—
205#332—114no—
206#332—112no—
207#331—112no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11#46612yes—
211C22×C11C2×#12111yescharacteristic
212C2×D11—81no—
213C2×D11—81no—
214C2×D11—81no—
215C4×C11—21no—
216C4×C11—24no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—42no—
220C4×C11—82no—
221C4×C11#46612yes—
222C4×C11C22×D811yescharacteristic
223C4×C11C2×#13511yescharacteristic
224C4×C11#57812yes—
225Dic11—81no—
226C2×#41—221no—
227C22×Q8—21no—
228C22×Q8C22⋊D1111yescharacteristic
229#137—444no—
230C2×Q16—24no—
231C2×Q16—44no—
232C2×Q16—222no—
233C2×SD16—222no—
234C2×M16—221no—
235C22×C8—21no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—111no—
240C4⋊Q8C22×D1112yes—
241#127—111no—
242#124—221no—
243#121—221no—
244#121—221no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×Q8C22⋊D1112yes—
248C4×Q8C22×D1112yes—
249C4×D4—221no—
250C4×D4—221no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4C22⋊D1111yescharacteristic
255C2×C42—21no—
256C2×C42C22×D1111yescharacteristic
257#107—224no—
258C4⋊C8—21no—
259C4⋊C8—112no—
260C4⋊C8—112no—
261C4⋊C8—112no—
262C4⋊C8—224no—
263C4⋊C8—221no—
264C4⋊C8C22×D1112yes—
265#103—24no—
266#103—222no—
267#102—224no—
268#102—222no—
269C22⋊C8—112no—
270C22⋊C8—221no—
271C4×C8—112no—
272C4×C8—224no—
273C4×C8—221no—
274C2×C11—22no—
275C2×C11#304411yescharacteristic
276C2×C11C2×#46611yescharacteristic
277C2×C11#306911yescharacteristic
278D11—161no—
279#41—442no—
280#41—442no—
281C2×Q8—21no—
282C2×Q8—22no—
283C2×Q8—22no—
284C2×Q8—41no—
285C2×Q8—42no—
286C2×Q8—42no—
287C2×Q8—221no—
288C2×Q8#432314yes—
289C2×Q8C2×C22⋊D1112yes—
290C2×D4—221no—
291C2×D4—221no—
292C2×D4—221no—
293C2×D4—441no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—41no—
297C22×C4—441no—
298C22×C4D4×D1111yescharacteristic
299C22×C4#434111yescharacteristic
300C22×C4C2×C22⋊D1111yescharacteristic
301Q16—48no—
302Q16—444no—
303SD16—444no—
304M16—442no—
305C2×C8—22no—
306C2×C8—42no—
307C2×C8—114no—
308C2×C8—222no—
309C2×C8—222no—
310C4⋊C4—22no—
311C4⋊C4—21no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—221no—
318C4⋊C4—221no—
319C4⋊C4C2×C22⋊D1112yes—
320C22⋊C4—441no—
321C22⋊C4—441no—
322C42—22no—
323C42—22no—
324C42D4×D1111yescharacteristic
325C42#434111yescharacteristic
326C42C2×C22⋊D1111yescharacteristic
327C42C23×D1111yescharacteristic
328C11#1940411yescharacteristic, complemented, Sylow
329C23—441no—
330C23#6699211yescharacteristic
331Q8—22no—
332Q8—24no—
333Q8—42no—
334Q8—42no—
335Q8—82no—
336Q8—441no—
337Q8—441no—
338Q8C2×#432314yes—
339D4—442no—
340D4—441no—
341D4—441no—
342D4—881no—
343D4—882no—
344C2×C4—22no—
345C2×C4—24no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—81no—
351C2×C4—82no—
352C2×C4—441no—
353C2×C4—882no—
354C2×C4C2×#432312yes—
355C2×C4#6699211yescharacteristic
356C2×C4#6699211yescharacteristic
357C2×C4#6699211yescharacteristic
358C2×C4#6700312yes—
359C2×C4C2×D4×D1111yescharacteristic
360C2×C4C2×#434111yescharacteristic
361C2×C4C22×C22⋊D1111yescharacteristic
362C8—42no—
363C8—224no—
364C8—442no—
365C8—442no—
366C22—21no—
367C22—21no—
368C22—881no—
369C22—881no—
370C22—881no—
371C22#1062265112yes—
372C22C2×#6699211yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—24no—
377C4—42no—
378C4—82no—
379C4—881no—
380C4#1062265112yes—
381C4#1062329712yes—
382C4C22×#432311yescharacteristic
383C4C2×#6700311yescharacteristic
384C2—22no—
385C2—1761no—
386C2#1307814311yescharacteristic
387C2C2×#1062265111yescharacteristic
388C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#462C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenterC2×#462D11
hypocenterC11#19404
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. #13077697C2semidirect
4. #13068062C2semidirect
5. #13068008C2semidirect
6. #13067390C2semidirect
7. #13067288C2semidirect
9. C2×C11×#462C2semidirect
137. C2×#462D11semidirect
328. C11#19404semidirect

Maximal subgroups

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

subgroupindex
#130797372
#130780882
#130776972
#130680622
#130680082
#130673902
#130672882
#130672662
C2×C11×#4622
#1940411