Finite Group Databasebeta

← #14764058

Subgroups — #14764058

Order 2816.

1090 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×#10622820C211yesmaximal, characteristic
2#13070999C211yesmaximal, characteristic
3#13068815C214yesmaximal, complemented
4#13068813C214yesmaximal, complemented
5#13068647C214yesmaximal, complemented
6C11×#2280C211yesmaximal, characteristic
7C24×C4×C11C2211yescharacteristic
8C2×C11×#117C2212yes—
9C2×#66979C2212yes—
10C22×#4318C2212yes—
11C11×#381—21no—
12C11×#380C2212yes—
13C11×#380C2212yes—
14C11×#379—21no—
15C4×C11×C22⋊C4—21no—
16C4×C11×C22⋊C4—21no—
17#10622860—21no—
18#10622825C2212yes—
19#10622825C2212yes—
20#10622824—21no—
21C4×C22⋊Dic11—21no—
22C4×C22⋊Dic11—21no—
23#10622820C418yescomplemented
24C2×C22⋊(C11⋊C8)C2212yes—
25C2×C22⋊(C11⋊C8)C2212yes—
26C2×#66872C2214yescomplemented
27C2×#66871C2214yescomplemented
28#10622167C2218yescomplemented
29C25×C11D411yescharacteristic
30C23×C4×C11—42no—
31C23×C4×C11—42no—
32C23×C4×C11C2×C414yes—
33C23×C4×C11D411yescharacteristic
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11Q814yes—
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C11×#117—42no—
41C11×#117—42no—
42C2×C11×C4⋊C4C2314yes—
43C2×C11×C22⋊C4—22no—
44C2×C11×C22⋊C4—22no—
45C2×C11×C22⋊C4—22no—
46C2×C42×C11—22no—
47C2×C22⋊Dic11—22no—
48C2×C22⋊Dic11—22no—
49C2×C22⋊Dic11—22no—
50#66979—42no—
51#66979—42no—
52C2×C4⋊Dic11C2314yes—
53C2×C4×Dic11—22no—
54C2×#4318—42no—
55C2×#4318—42no—
56C2×#4318C2×C418yes—
57C22×C11⋊C8C2314yes—
58C11×#95—22no—
59C11×#95—22no—
60C11⋊#95—22no—
61C11⋊#95—22no—
62C22⋊(C11⋊C8)C2×C418yes—
63C22⋊(C11⋊C8)C2×C418yes—
64#66872—44no—
65#66871—44no—
66#21943—111nomaximal, Sylow
67C24×C11—42no—
68C24×C11—42no—
69C24×C11—42no—
70C24×C11C4⋊C414yes—
71C24×C11C2×D411yescharacteristic
72C24×C11C2×D411yescharacteristic
73C24×C11C2×D411yescharacteristic
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—24no—
81C22×C4×C11—48no—
82C22×C4×C11—44no—
83C22×C4×C11—44no—
84C22×C4×C11—42no—
85C22×C4×C11—42no—
86C22×C4×C11—42no—
87C22×C4×C11C4⋊C414yes—
88C22×C4×C11C4⋊C414yes—
89C22×C4×C11C4⋊C414yes—
90C22×C4×C11C22×C412yes—
91C22×C4×C11C22×C412yes—
92C22×C4×C11C22×C412yes—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×Q812yes—
97C22×C4×C11C2×Q812yes—
98C22×C4×C11C2×Q812yes—
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—24no—
101C11×C4⋊C4—24no—
102C11×C4⋊C4—24no—
103C11×C22⋊C4—44no—
104C11×C22⋊C4—44no—
105C11×C22⋊C4—44no—
106C42×C11—44no—
107C22⋊Dic11—44no—
108C22⋊Dic11—44no—
109C22⋊Dic11—44no—
110C4⋊Dic11—24no—
111C4⋊Dic11—24no—
112C4×Dic11—44no—
113#4318—48no—
114C2×C11⋊C8—24no—
115C2×C11⋊C8—24no—
116C2×C11⋊C8C22×C418yes—
117C2×#407—111no—
118#2280—111no—
119#2280D1111yescharacteristic
120#1854—114no—
121#1854—114no—
122#1809—114no—
123C23×C11—22no—
124C23×C11—22no—
125C23×C11—22no—
126C23×C11—22no—
127C23×C11—22no—
128C23×C11—22no—
129C23×C11—22no—
130C23×C11—22no—
131C23×C11—22no—
132C23×C11—44no—
133C23×C11—44no—
134C23×C11—44no—
135C23×C11—416no—
136C23×C11C2×C4⋊C412yes—
137C23×C11C2×C4⋊C412yes—
138C23×C11C2×C4⋊C412yes—
139C23×C11C22×D411yescharacteristic
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—24no—
144C2×C4×C11—24no—
145C2×C4×C11—24no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—44no—
153C2×C4×C11—44no—
154C2×C4×C11—44no—
155C2×C4×C11—44no—
156C2×C4×C11—44no—
157C2×C4×C11—44no—
158C2×C4×C11C2×C4⋊C412yes—
159C2×C4×C11C2×C4⋊C412yes—
160C2×C4×C11C2×C4⋊C412yes—
161C2×C4×C11C23×C411yescharacteristic
162C2×C4×C11C22×Q811yescharacteristic
163C2×C4×C11H(5,𝔽2)12yes—
164C2×C4×C11H(5,𝔽2)12yes—
165C2×Dic11—44no—
166C2×Dic11—44no—
167C2×Dic11—44no—
168C11⋊C8—28no—
169C24×C4C2×D1111yescharacteristic
170C22×M16—112no—
171C2×#117—112no—
172C2×#117C2×D1112yes—
173C2×#107—114no—
174C2×#106—114no—
175#407—118no—
176C2×C22⋊C8—112no—
177C2×C22⋊C8—112no—
178#381—21no—
179#381—221no—
180#380—112no—
181#380—112no—
182#380C2×D1112yes—
183#380C2×D1112yes—
184#379—21no—
185#379—221no—
186C4×C22⋊C4—21no—
187C4×C22⋊C4—21no—
188C4×C22⋊C4—221no—
189C4×C22⋊C4—221no—
190#340—118no—
191C22×C11—22no—
192C22×C11—22no—
193C22×C11—22no—
194C22×C11—22no—
195C22×C11—22no—
196C22×C11—22no—
197C22×C11—22no—
198C22×C11—22no—
199C22×C11—22no—
200C22×C11—416no—
201C22×C11—44no—
202C22×C11—44no—
203C22×C11—44no—
204C22×C11C22×C4⋊C411yescharacteristic
205C22×C11#53412yes—
206C22×C11#57512yes—
207C22×C11#57512yes—
208C4×C11—22no—
209C4×C11—22no—
210C4×C11—22no—
211C4×C11—84no—
212C4×C11#51812yes—
213C4×C11#54311yescharacteristic
214C4×C11#54311yescharacteristic
215Dic11—84no—
216C25C22⋊D1111yescharacteristic
217C23×C4—42no—
218C23×C4—42no—
219C23×C4Dic2214yes—
220C23×C4C4×D1114yes—
221C23×C4C22⋊D1111yescharacteristic
222C23×C4C22⋊D1111yescharacteristic
223C23×C4C22⋊D1111yescharacteristic
224C23×C4C22×D1111yescharacteristic
225C23×C4C22×D1111yescharacteristic
226C23×C4C22×D1111yescharacteristic
227C2×M16—118no—
228C2×M16—442no—
229C2×M16—442no—
230C22×C8—114no—
231#117—42no—
232#117—42no—
233#117—442no—
234#117—442no—
235C2×C4⋊C4—114no—
236C2×C4⋊C4C22×D1114yes—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—22no—
240C2×C22⋊C4—222no—
241C2×C22⋊C4—222no—
242C2×C22⋊C4—222no—
243C2×C42—22no—
244C2×C42—222no—
245#107—444no—
246#106—444no—
247C22⋊C8—118no—
248C22⋊C8—118no—
249#95—22no—
250#95—22no—
251#95—222no—
252#95—222no—
253C2×C11—42no—
254C2×C11—42no—
255C2×C11—42no—
256C2×C11#231511yescharacteristic
257C2×C11#291111yescharacteristic
258C2×C11#291111yescharacteristic
259C2×C11#319714yes—
260C24—42no—
261C24—42no—
262C24—42no—
263C24Dic11⋊C414yes—
264C24C2×C22⋊D1111yescharacteristic
265C24C2×C22⋊D1111yescharacteristic
266C24C2×C22⋊D1111yescharacteristic
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—24no—
274C22×C4—44no—
275C22×C4—44no—
276C22×C4—48no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—224no—
281C22×C4Dic11⋊C414yes—
282C22×C4Dic11⋊C414yes—
283C22×C4Dic11⋊C414yes—
284C22×C4C2×Dic2212yes—
285C22×C4C2×Dic2212yes—
286C22×C4C2×Dic2212yes—
287C22×C4C2×C4×D1112yes—
288C22×C4C2×C4×D1112yes—
289C22×C4C2×C4×D1112yes—
290C22×C4C2×C22⋊D1111yescharacteristic
291C22×C4C2×C22⋊D1111yescharacteristic
292C22×C4C2×C22⋊D1111yescharacteristic
293C22×C4C23×D1111yescharacteristic
294M16—448no—
295C2×C8—118no—
296C2×C8—224no—
297C2×C8—224no—
298C4⋊C4—24no—
299C4⋊C4—24no—
300C4⋊C4—224no—
301C4⋊C4—224no—
302C22⋊C4—44no—
303C22⋊C4—44no—
304C22⋊C4—44no—
305C22⋊C4—444no—
306C22⋊C4—444no—
307C22⋊C4—444no—
308C42—44no—
309C42—444no—
310C11#2194311yescharacteristic, complemented, Sylow
311C23—22no—
312C23—22no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—22no—
317C23—22no—
318C23—22no—
319C23—22no—
320C23—44no—
321C23—44no—
322C23—44no—
323C23—416no—
324C23C2×Dic11⋊C412yes—
325C23C2×Dic11⋊C412yes—
326C23C2×Dic11⋊C412yes—
327C23C22×C22⋊D1111yescharacteristic
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—24no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—44no—
341C2×C4—44no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—444no—
347C2×C4—444no—
348C2×C4—444no—
349C2×C4C2×Dic11⋊C412yes—
350C2×C4C2×Dic11⋊C412yes—
351C2×C4C2×Dic11⋊C412yes—
352C2×C4C22×Dic2211yescharacteristic
353C2×C4C22×C4×D1111yescharacteristic
354C2×C4#6703712yes—
355C2×C4#6703712yes—
356C8—228no—
357C22—22no—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—416no—
367C22—44no—
368C22—44no—
369C22—44no—
370C22C22×Dic11⋊C411yescharacteristic
371C22#1062333512yes—
372C22#1062335312yes—
373C22#1062335312yes—
374C4—22no—
375C4—22no—
376C4—22no—
377C4—84no—
378C4—884no—
379C4#1062301411yescharacteristic
380C4#1062301411yescharacteristic
381C4#1062301712yes—
382C2—42no—
383C2—42no—
384C2—42no—
385C2#1307122811yescharacteristic
386C2#1307720511yescharacteristic
387C2#1307720511yescharacteristic
388C2#1307945314yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2280C2
socleC23×C11C22×D4
prime radicalC25×C11D4
cosocleC22×C4×C11C24
hypercenter#2280D11
hypocenterC11#21943
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
3. #13068815C2semidirect
4. #13068813C2semidirect
5. #13068647C2semidirect
23. #10622820C4semidirect
26. C2×#66872C22semidirect
27. C2×#66871C22semidirect
28. #10622167C22semidirect
310. C11#21943semidirect

Maximal subgroups

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

subgroupindex
C2×#106228202
#130709992
#130688152
#130688132
#130686472
C11×#22802
#2194311