Finite Group Databasebeta

← #14660258

Subgroups — #14660258

Order 2816.

978 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
1C22×#66900C212yesmaximal
2C2×C4×#4318C211yesmaximal, characteristic
3C2×#10622168C212yesmaximal
4#13068310C211yesmaximal, characteristic
5C2×C11×#391C211yesmaximal, characteristic
6C23×Q8×C11C2211yescharacteristic
7C22×C11×C4⋊C4C2211yescharacteristic
8C22×C42×C11C2211yescharacteristic
9C22×#4318C2212yes—
10C22×#4318C2212yes—
11C11×#391—21no—
12C11×#391—21no—
13C11×#391—22no—
14C2×C11×#95C414yes—
15C2×#66900—24no—
16C2×#66900—24no—
17C2×#66900C418yescomplemented
18C4×#4318—24no—
19C2×#66867—21no—
20C2×C4×C11⋊C8—21no—
21#10622168—24no—
22#10622162—22no—
23C22×Q8×C11—22no—
24C22×Q8×C11—22no—
25C22×Q8×C11—21no—
26C22×Q8×C11—21no—
27C22×Q8×C11—22no—
28C22×Q8×C11—22no—
29C22×Q8×C11—22no—
30C22×Q8×C11C2×C414yes—
31C23×C4×C11C2×C412yes—
32C23×C4×C11C2×C412yes—
33C23×C4×C11C2×C412yes—
34C23×C4×C11C2311yescharacteristic
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—22no—
38C2×C11×C4⋊C4—22no—
39C2×C42×C11—22no—
40C2×C42×C11—22no—
41C2×C42×C11D411yescharacteristic
42C2×C42×C11D411yescharacteristic
43C2×C42×C11D412yes—
44C2×#4318—22no—
45C2×#4318—22no—
46C2×#4318—22no—
47C2×#4318—22no—
48C2×#4318—22no—
49C2×#4318—22no—
50C2×#4318—22no—
51C2×#4318—22no—
52C2×#4318C2×C414yes—
53C2×#4318C2×C414yes—
54C2×#4318D414yes—
55C2×#4318D414yes—
56C22×C11⋊C8—22no—
57C22×C11⋊C8—22no—
58C11×#95—24no—
59C11×#95—24no—
60#66900—216no—
61#66867—24no—
62C4×C11⋊C8—24no—
63#10963—111nomaximal, Sylow
64C24×C11C22×C411yescharacteristic
65C2×Q8×C11—24no—
66C2×Q8×C11—24no—
67C2×Q8×C11—24no—
68C2×Q8×C11—24no—
69C2×Q8×C11—24no—
70C2×Q8×C11—24no—
71C2×Q8×C11—41no—
72C2×Q8×C11—42no—
73C2×Q8×C11—42no—
74C2×Q8×C11—42no—
75C2×Q8×C11—41no—
76C2×Q8×C11—42no—
77C2×Q8×C11—42no—
78C2×Q8×C11—41no—
79C2×Q8×C11—42no—
80C2×Q8×C11—41no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—24no—
84C22×C4×C11—24no—
85C22×C4×C11—24no—
86C22×C4×C11—24no—
87C22×C4×C11—22no—
88C22×C4×C11—24no—
89C22×C4×C11—42no—
90C22×C4×C11—44no—
91C22×C4×C11C4214yes—
92C22×C4×C11C22⋊C412yes—
93C22×C4×C11C22⋊C412yes—
94C22×C4×C11C22×C412yes—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11#4112yes—
100C22×C4×C11#4112yes—
101C22×C4×C11#4112yes—
102C11×C4⋊C4—42no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C42×C11—21no—
106C42×C11—21no—
107C42×C11—24no—
108C42×C11—21no—
109C42×C11—21no—
110#4318—24no—
111#4318—24no—
112#4318—24no—
113#4318—24no—
114#4318—24no—
115#4318—42no—
116#4318—42no—
117#4318C22⋊C418yes—
118C2×C11⋊C8—24no—
119C2×C11⋊C8—24no—
120C2×C11⋊C8—24no—
121C2×C11⋊C8—24no—
122C2×C11⋊C8—42no—
123C2×C11⋊C8—42no—
124C22×#101—112no—
125C2×C4×M16—111no—
126C2×#391D1111yescharacteristic
127C2×#343—112no—
128#1728—111no—
129C23×C11—22no—
130C23×C11—22no—
131C23×C11C2×C4211yescharacteristic
132C23×C11C2×C22⋊C411yescharacteristic
133C23×C11#11711yescharacteristic
134C23×C11C4×D412yes—
135C23×C11C4×D412yes—
136Q8×C11—44no—
137Q8×C11—44no—
138Q8×C11—44no—
139Q8×C11—44no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—28no—
143C2×C4×C11—24no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—48no—
148C2×C4×C11—42no—
149C2×C4×C11—44no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—44no—
153C2×C4×C11—84no—
154C2×C4×C11#10114yescomplemented
155C2×C4×C11C2×C22⋊C412yes—
156C2×C4×C11#11712yes—
157C2×C4×C11C4×D412yes—
158C2×C4×C11C4×D412yes—
159C2×C4×C11C4×D412yes—
160C2×C4×C11C4×D412yes—
161C2×C4×C11#12011yescharacteristic
162C2×C4×C11#12112yes—
163C2×C4×C11#12112yes—
164C2×C4×C11#12112yes—
165C2×C4×C11#12312yes—
166C2×C4×C11#12311yescharacteristic
167C2×C4×C11#12412yes—
168C2×C4×C11#12411yescharacteristic
169C2×C4×C11#12612yes—
170C2×C4×C11#12711yescharacteristic
171C11⋊C8—28no—
172C11⋊C8—44no—
173C23×Q8C2×D1111yescharacteristic
174C22×M16—112no—
175C22×M16—112no—
176C22×C4⋊C4C2×D1111yescharacteristic
177C22×C42C2×D1111yescharacteristic
178C2×#101—118no—
179C2×#101—224no—
180C2×#101—224no—
181C4×M16—224no—
182C2×#97—221no—
183C2×C4×C8—221no—
184#391—22no—
185#391—21no—
186#391—21no—
187C2×#95Dic1114yes—
188#343—224no—
189#336—222no—
190C22×C11—24no—
191C22×C11—22no—
192C22×C11—22no—
193C22×C11—22no—
194C22×C11—22no—
195C22×C11C4×C22⋊C412yes—
196C22×C11C4×C22⋊C411yescharacteristic
197C22×C11#38611yescharacteristic
198C22×C11#38812yes—
199C22×C11#39011yescharacteristic
200C22×C11C2×#10112yes—
201C22×C11#41312yes—
202C4×C11—24no—
203C4×C11—42no—
204C4×C11—44no—
205C4×C11—82no—
206C4×C11#38612yes—
207C4×C11#38812yes—
208C4×C11#38812yes—
209C4×C11#39012yes—
210C22×Q8—22no—
211C22×Q8—22no—
212C22×Q8—22no—
213C22×Q8—22no—
214C22×Q8—22no—
215C22×Q8—21no—
216C22×Q8—21no—
217C22×Q8C4×D1114yes—
218C23×C4C2×Dic1112yes—
219C23×C4C2×Dic1112yes—
220C23×C4C2×Dic1112yes—
221C23×C4C22×D1111yescharacteristic
222C2×M16—114no—
223C2×M16—114no—
224C2×M16—114no—
225C2×M16—114no—
226C2×M16—222no—
227C2×M16—222no—
228C2×M16—222no—
229C2×M16—222no—
230C2×M16—222no—
231C2×M16—222no—
232C2×M16—222no—
233C2×M16—222no—
234C22×C8—222no—
235C22×C8—222no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C42—22no—
241C2×C42—22no—
242C2×C42C22⋊D1112yes—
243C2×C42C22⋊D1111yescharacteristic
244C2×C42C22⋊D1111yescharacteristic
245#101—2216no—
246#97—224no—
247C4×C8—224no—
248#95—24no—
249#95—24no—
250C2×C11—22no—
251C2×C11—22no—
252C2×C11#143711yescharacteristic
253C2×C11C4×#10112yes—
254C2×C11#190112yes—
255C2×C11#196611yescharacteristic
256C2×C11#196711yescharacteristic
257C24C22×Dic1111yescharacteristic
258C2×Q8—24no—
259C2×Q8—24no—
260C2×Q8—24no—
261C2×Q8—24no—
262C2×Q8—24no—
263C2×Q8—24no—
264C2×Q8—42no—
265C2×Q8—42no—
266C2×Q8—42no—
267C2×Q8—42no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—42no—
272C2×Q8—42no—
273C2×Q8—41no—
274C22×C4—22no—
275C22×C4—24no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—22no—
279C22×C4—24no—
280C22×C4—22no—
281C22×C4—24no—
282C22×C4—42no—
283C22×C4—44no—
284C22×C4C4×Dic1114yes—
285C22×C4C22⋊Dic1112yes—
286C22×C4C22⋊Dic1112yes—
287C22×C4C2×C4×D1112yes—
288C22×C4#433912yes—
289C22×C4D4×D1112yes—
290C22×C4D4×D1112yes—
291C22×C4#434112yes—
292C22×C4#434112yes—
293C22×C4C2×C22⋊D1111yescharacteristic
294C22×C4C2×C22⋊D1111yescharacteristic
295M16—118no—
296M16—224no—
297M16—224no—
298M16—224no—
299M16—224no—
300M16—224no—
301M16—442no—
302M16—442no—
303C2×C8—224no—
304C2×C8—224no—
305C2×C8—224no—
306C2×C8—224no—
307C2×C8—442no—
308C2×C8—442no—
309C4⋊C4—41no—
310C4⋊C4—42no—
311C4⋊C4—41no—
312C42—21no—
313C42—21no—
314C42—21no—
315C42—21no—
316C42—24no—
317C11#1096311yescharacteristic, complemented, Sylow
318C23—22no—
319C23—22no—
320C23C2×C4×Dic1111yescharacteristic
321C23#6697911yescharacteristic
322C23D4×Dic1112yes—
323C23D4×Dic1112yes—
324C23C2×C22⋊Dic1111yescharacteristic
325Q8—44no—
326Q8—44no—
327Q8—44no—
328Q8—44no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—28no—
332C2×C4—24no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—48no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—44no—
342C2×C4—84no—
343C2×C4#6690014yescomplemented
344C2×C4#6693012yes—
345C2×C4#6693212yes—
346C2×C4C22⋊C4×D1112yes—
347C2×C4(C22⋊D11)⋊C412yes—
348C2×C4(C22⋊D11)⋊C412yes—
349C2×C4#6693612yes—
350C2×C4#6693712yes—
351C2×C4#6693812yes—
352C2×C4C4×C22⋊D1112yes—
353C2×C4C4×C22⋊D1112yes—
354C2×C4#6698811yescharacteristic
355C2×C4#6698911yescharacteristic
356C2×C4#6699011yescharacteristic
357C2×C4#6699112yes—
358C2×C4#6699212yes—
359C2×C4#6699311yescharacteristic
360C8—228no—
361C8—444no—
362C22—24no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22C22⋊C4×Dic1112yes—
368C22#1062256412yes—
369C22C4×C22⋊Dic1111yescharacteristic
370C22#1062283311yescharacteristic
371C22#1062283411yescharacteristic
372C22C2×#6690012yes—
373C22#1062285012yes—
374C4—24no—
375C4—42no—
376C4—44no—
377C4—82no—
378C4#1062255712yes—
379C4#1062255812yes—
380C4#1062256912yes—
381C4#1062257012yes—
382C2—22no—
383C2—22no—
384C2#1306685311yescharacteristic
385C2C4×#6690012yes—
386C2#1306908512yes—
387C2#1306946111yescharacteristic
388C2#1306946611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC23×C11C2×C42
FrattiniC23×C4C22×D11
FittingC2×C11×#391C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22×C4
cosocleC23×C4×C11C23
hypercenterC2×#391D11
hypocenterC11#10963
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
17. C2×#66900C4semidirect
154. C2×C4×C11#101semidirect
317. C11#10963semidirect
343. C2×C4#66900semidirect

Maximal subgroups

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

subgroupindex
C22×#669002
C2×C4×#43182
C2×#106221682
#130683102
C2×C11×#3912
#1096311