Finite Group Databasebeta

← #14764172

Subgroups — #14764172

Order 2816.

874 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
1C2×#10622731C211yesmaximal, characteristic
2#13071018C212yesmaximal
3#13069378C212yesmaximal, complemented
4#13069376C212yesmaximal, complemented
5#13069373C212yesmaximal, complemented
6#13069371C212yesmaximal, complemented
7#13068649C211yesmaximal, characteristic
8#13068647C212yesmaximal
9C11×#1809C211yesmaximal, characteristic
10C22×C11×M16C2211yescharacteristic
11C22×C4×Dic11C2211yescharacteristic
12C22×#4318C2211yescharacteristic
13C2×#66930—22no—
14C2×C11×#107C2211yescharacteristic
15C2×C11×#106C2211yescharacteristic
16C11×#380C2212yes—
17#10622825C2212yes—
18#10622731C418yescomplemented
19C2×#66882C2211yescharacteristic
20C2×#66881C2211yescharacteristic
21C2×Dic11⋊C8C2212yes—
22C2×Dic11⋊C8C2212yes—
23#10622589C2212yes—
24#10622589C2212yes—
25C4⋊C4×Dic11C2212yes—
26C4⋊C4×Dic11C2212yes—
27C2×#66872C2212yes—
28C2×#66871C2212yes—
29#10622555—22no—
30#10622263—22no—
31#10622262—22no—
32C11×#340C2212yes—
33#10622189C2212yes—
34#10622167C2212yes—
35#10622167C2212yes—
36C23×C4×C11C2311yescharacteristic
37C23×Dic11D412yes—
38C2×C11×M16—41no—
39C2×C11×M16—41no—
40C2×C11×M16C2×C414yes—
41C22×C8×C11C2311yescharacteristic
42C22×C8×C11C2311yescharacteristic
43C2×C11×C4⋊C4C2312yes—
44C2×C11×C4⋊C4C2312yes—
45C2×C11×C22⋊C4—22no—
46C2×C22⋊Dic11—22no—
47C2×C4⋊Dic11C2312yes—
48C2×C4⋊Dic11C2312yes—
49C2×Dic11⋊C4—22no—
50C2×Dic11⋊C4—22no—
51C2×Dic11⋊C4—22no—
52C2×Dic11⋊C4—22no—
53C2×C4×Dic11—22no—
54C2×C4×Dic11—22no—
55C2×C4×Dic11C2×C414yes—
56C2×C4×Dic11D411yescharacteristic
57C2×C4×Dic11D411yescharacteristic
58C2×C4×Dic11Q814yes—
59C2×C4×Dic11C2312yes—
60C2×#4318—41no—
61C2×#4318—41no—
62C2×#4318C2×C414yes—
63C22×C11⋊C8C2312yes—
64#66930—48no—
65C11×#107—41no—
66C11×#106—41no—
67C11×#95—22no—
68C11⋊#95—22no—
69C11⋊#95—22no—
70C11⋊#95—22no—
71#66882—41no—
72#66881—41no—
73Dic11⋊C8C2×C418yes—
74Dic11⋊C8C2×C418yes—
75#66872—42no—
76#66871—42no—
77#21964—111nomaximal, Sylow
78C24×C11C2×D411yescharacteristic
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11C22×C412yes—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×Q812yes—
88C22×C4×C11C2411yescharacteristic
89C22×Dic11—24no—
90C22×Dic11—24no—
91C22×Dic11—22no—
92C22×Dic11—22no—
93C22×Dic11C4⋊C418yes—
94C22×Dic11C2×D412yes—
95C22×Dic11C2×D412yes—
96C11×M16—44no—
97C2×C8×C11—21no—
98C2×C8×C11—21no—
99C2×C8×C11—21no—
100C2×C8×C11—21no—
101C2×C8×C11C22×C412yes—
102C2×C8×C11C22×C412yes—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C22⋊C4—44no—
108C22⋊Dic11—44no—
109C4⋊Dic11—22no—
110C4⋊Dic11—22no—
111C4⋊Dic11—22no—
112C4⋊Dic11—22no—
113Dic11⋊C4—44no—
114Dic11⋊C4—44no—
115Dic11⋊C4—44no—
116Dic11⋊C4—44no—
117C4×Dic11—44no—
118C4×Dic11—44no—
119C4×Dic11C4⋊C414yes—
120C4×Dic11C4⋊C414yes—
121C4×Dic11C22×C414yes—
122C4×Dic11C2×Q814yes—
123#4318—44no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8C22×C414yes—
127C2×#423—111no—
128#2285—112no—
129#1948—112no—
130#1948—112no—
131#1947—112no—
132#1947—112no—
133#1809—112no—
134#1809—111no—
135#1809D1111yescharacteristic
136C23×C11—21no—
137C23×C11—21no—
138C23×C11—22no—
139C23×C11—22no—
140C23×C11C2×C4⋊C412yes—
141C23×C11C22×D411yescharacteristic
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11C2×C4⋊C412yes—
155C2×C4×C11C23×C411yescharacteristic
156C2×C4×C11C22×Q811yescharacteristic
157C2×C4×C11H(5,𝔽2)11yescharacteristic
158C2×C4×C11H(5,𝔽2)11yescharacteristic
159C2×C4×C112−1+411yescharacteristic
160C2×C4×C112−1+411yescharacteristic
161C2×Dic11—22no—
162C2×Dic11—22no—
163C2×Dic11—216no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C2×Dic11—42no—
169C2×Dic11—42no—
170C2×Dic11C2×C4⋊C414yes—
171C2×Dic11C2×C4⋊C414yes—
172C2×Dic11AGL(1,ℤ/8)14yes—
173C2×Dic11#13714yes—
174C8×C11—22no—
175C8×C11—22no—
176C11⋊C8—24no—
177C22×M16—111no—
178C22×M16C2×D1111yescharacteristic
179C2×#117—222no—
180C22×C42—111no—
181C2×#107—111no—
182C2×#107—112no—
183C2×#107C2×D1111yescharacteristic
184C2×#106—111no—
185C2×#106—112no—
186C2×#106C2×D1111yescharacteristic
187#423—118no—
188C2×C4⋊C8—112no—
189C2×C4⋊C8—112no—
190#384—112no—
191#384—112no—
192#382—222no—
193#380—112no—
194#380—222no—
195#380C2×D1112yes—
196C4×C4⋊C4—112no—
197C4×C4⋊C4—112no—
198C4×C4⋊C4—222no—
199#340—112no—
200#340—112no—
201#340—112no—
202#340C2×D1112yes—
203C22×C11—22no—
204C22×C11—24no—
205C22×C11—41no—
206C22×C11—42no—
207C22×C11—41no—
208C22×C11C22×C4⋊C411yescharacteristic
209C22×C11#53711yescharacteristic
210C22×C11#53711yescharacteristic
211C22×C11C2×AGL(1,ℤ/8)12yes—
212C22×C11C2×#13712yes—
213C4×C11—22no—
214C4×C11—82no—
215C4×C11—82no—
216C4×C11#51811yescharacteristic
217C4×C11#51911yescharacteristic
218C4×C11#54411yescharacteristic
219C4×C11#54411yescharacteristic
220Dic11—24no—
221Dic11—82no—
222Dic11—82no—
223Dic11#42818yes—
224C23×C4—112no—
225C23×C4C22×D1111yescharacteristic
226C2×M16—41no—
227C2×M16—41no—
228C2×M16—114no—
229C2×M16—441no—
230C2×M16—441no—
231C2×M16C4×D1114yes—
232C22×C8—112no—
233C22×C8C22×D1111yescharacteristic
234C22×C8C22×D1111yescharacteristic
235#117—448no—
236C2×C4⋊C4—112no—
237C2×C4⋊C4—112no—
238C2×C4⋊C4—222no—
239C2×C4⋊C4—222no—
240C2×C4⋊C4—222no—
241C2×C4⋊C4—222no—
242C2×C4⋊C4C22×D1112yes—
243C2×C4⋊C4C22×D1112yes—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—222no—
246C2×C42—114no—
247C2×C42—111no—
248C2×C42—111no—
249C2×C42—114no—
250C2×C42—112no—
251C2×C42—222no—
252C2×C42—222no—
253#107—41no—
254#107—442no—
255#107—441no—
256#106—41no—
257#106—442no—
258#106—441no—
259C4⋊C8—118no—
260C4⋊C8—118no—
261#95—22no—
262#95—222no—
263#95—222no—
264#95—222no—
265C2×C11—42no—
266C2×C11#231611yescharacteristic
267C2×C11C2×#42812yes—
268C2×C11#325311yescharacteristic
269C2×C11#325412yes—
270C2×C11#325511yescharacteristic
271C24D4×D1111yescharacteristic
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—112no—
279C22×C4—118no—
280C22×C4—112no—
281C22×C4—224no—
282C22×C4—224no—
283C22×C4—222no—
284C22×C4—222no—
285C22×C4C2×C4×D1112yes—
286C22×C4D4×D1111yescharacteristic
287C22×C4Q8×D1112yes—
288C22×C4C23×D1111yescharacteristic
289M16—44no—
290M16—444no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—114no—
296C2×C8—222no—
297C2×C8—222no—
298C2×C8C2×C4×D1112yes—
299C2×C8C2×C4×D1112yes—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—222no—
305C4⋊C4—222no—
306C4⋊C4—222no—
307C4⋊C4—222no—
308C4⋊C4—444no—
309C4⋊C4—444no—
310C4⋊C4—444no—
311C4⋊C4—444no—
312C22⋊C4—44no—
313C22⋊C4—444no—
314C42—114no—
315C42—114no—
316C42—114no—
317C42—114no—
318C42—444no—
319C42—444no—
320C11#2196411yescharacteristic, complemented, Sylow
321C23—22no—
322C23—22no—
323C23—21no—
324C23—21no—
325C23C4⋊C4×D1112yes—
326C23C2×D4×D1111yescharacteristic
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—114no—
340C2×C4—114no—
341C2×C4—114no—
342C2×C4—114no—
343C2×C4—2216no—
344C2×C4—222no—
345C2×C4—222no—
346C2×C4—442no—
347C2×C4—442no—
348C2×C4—442no—
349C2×C4—442no—
350C2×C4—442no—
351C2×C4—442no—
352C2×C4C4⋊C4×D1112yes—
353C2×C4C22×C4×D1111yescharacteristic
354C2×C4#6703711yescharacteristic
355C2×C4#6703711yescharacteristic
356C2×C4C2×Q8×D1111yescharacteristic
357C2×C4#6704311yescharacteristic
358C2×C4#6704311yescharacteristic
359C8—22no—
360C8—22no—
361C8—224no—
362C22—22no—
363C22—24no—
364C22—41no—
365C22—42no—
366C22—41no—
367C22C2×C4⋊C4×D1111yescharacteristic
368C22#1062312811yescharacteristic
369C22#1062312811yescharacteristic
370C22D11×AGL(1,ℤ/8)12yes—
371C22D11×#13712yes—
372C4—22no—
373C4—82no—
374C4—82no—
375C4—118no—
376C4—224no—
377C4—882no—
378C4—882no—
379C4#1062301711yescharacteristic
380C4#1062304711yescharacteristic
381C4#1062315411yescharacteristic
382C4#1062315411yescharacteristic
383C2—42no—
384C2#1307123311yescharacteristic
385C2D11×#42812yes—
386C2#1307999311yescharacteristic
387C2#1307999812yes—
388C2#1308000611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1809C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1809D11
hypocenterC11#21964
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
3. #13069378C2semidirect
4. #13069376C2semidirect
5. #13069373C2semidirect
6. #13069371C2semidirect
18. #10622731C4semidirect
320. C11#21964semidirect

Maximal subgroups

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

subgroupindex
C2×#106227312
#130710182
#130693782
#130693762
#130693732
#130693712
#130686492
#130686472
C11×#18092
#2196411