Finite Group Databasebeta

← #14652913

Subgroups — #14652913

Order 2816.

764 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068596C211yesmaximal, characteristic, complemented
2C2×#10622175C214yesmaximal, complemented
3#13066843C211yesmaximal, characteristic, complemented
4C11×#2856C211yesmaximal, characteristic
5C2×C11×#127C411yescharacteristic, complemented
6C2×C11×#121—21no—
7C2×C11×#121—21no—
8C2×C11×#121C2212yes—
9C22×C42×C11C2211yescharacteristic
10C11×#390—21no—
11C11×#390—21no—
12C11×#390C412yescomplemented
13C11×#384C411yescharacteristic, complemented
14C2×C11⋊#95—21no—
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2212yes—
17C2×C22⋊(C11⋊C8)C2212yes—
18C2×C4⋊(C11⋊C8)—21no—
19#10622175—28no—
20#10622162—21no—
21C22×D4×C11—22no—
22C22×D4×C11—21no—
23C22×D4×C11—21no—
24C22×D4×C11C2×C412yes—
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11C2311yescharacteristic
28C23×Dic11—22no—
29C11×#127—42no—
30C11×#121—24no—
31C11×#121—24no—
32C11×#121—44no—
33C11×#121—42no—
34C11×#121—42no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4C2×C412yes—
38C2×C11×C22⋊C4—22no—
39C2×C11×C22⋊C4—22no—
40C2×C11×C22⋊C4—22no—
41C2×C42×C11—42no—
42C2×C42×C11C2×C411yescharacteristic
43C2×C42×C11C2×C411yescharacteristic
44C2×C42×C11D411yescharacteristic
45C2×C42×C11D411yescharacteristic
46C22×C11⋊C8—22no—
47C11⋊#95—22no—
48C11⋊#95—42no—
49C11⋊#95—42no—
50C11⋊#95D414yescomplemented
51C22⋊(C11⋊C8)—24no—
52C4⋊(C11⋊C8)—42no—
53#9715—111nomaximal, Sylow
54C24×C11—22no—
55C24×C11C2×D411yescharacteristic
56C2×D4×C11—24no—
57C2×D4×C11—42no—
58C2×D4×C11—42no—
59C2×D4×C11—42no—
60C2×D4×C11—42no—
61C2×D4×C11—42no—
62C2×D4×C11—42no—
63C2×D4×C11—44no—
64C2×D4×C11—42no—
65C2×D4×C11—42no—
66C2×D4×C11—44no—
67C2×D4×C11—42no—
68C2×D4×C11—42no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11D812yes—
82C22×C4×C11SD1612yes—
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D412yes—
86C22×C4×C11#4112yes—
87C22×Dic11—24no—
88C22×Dic11—42no—
89C22×Dic11—42no—
90C22×Dic11—42no—
91C22×Dic11—42no—
92C22×Dic11—42no—
93C22×Dic11—42no—
94C11×C4⋊C4—24no—
95C11×C4⋊C4—42no—
96C11×C4⋊C4—42no—
97C11×C22⋊C4—44no—
98C11×C22⋊C4—44no—
99C11×C22⋊C4—42no—
100C11×C22⋊C4—42no—
101C42×C11—22no—
102C42×C11—22no—
103C42×C11—41no—
104C42×C11—41no—
105C2×C11⋊C8—42no—
106C2×C11⋊C8—42no—
107C2×C11⋊C8—42no—
108#2856D1111yescharacteristic
109#1797—111no—
110C2×#327—114no—
111#1434—111no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—42no—
117C23×C11—42no—
118C23×C11—42no—
119C23×C11—42no—
120C23×C11—42no—
121C23×C11—42no—
122C23×C11—42no—
123C23×C11C2×C22⋊C411yescharacteristic
124C23×C11#12112yes—
125C23×C11C2×D811yescharacteristic
126C23×C11C2×SD1611yescharacteristic
127C23×C11AGL(1,ℤ/8)12yes—
128D4×C11—84no—
129D4×C11—84no—
130D4×C11—84no—
131D4×C11—84no—
132D4×C11—84no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—44no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11#9912yes—
155C2×C4×C11#10212yes—
156C2×C4×C11#10212yes—
157C2×C4×C11C4×D412yes—
158C2×C4×C11#12411yescharacteristic
159C2×C4×C11#12711yescharacteristic
160C2×Dic11—44no—
161C2×Dic11—44no—
162C2×Dic11—44no—
163C2×Dic11—82no—
164C2×Dic11—82no—
165C2×Dic11—82no—
166C2×Dic11—82no—
167C11⋊C8—82no—
168C2×#127Dic1111yescharacteristic, complemented
169C2×#121—21no—
170C2×#121—21no—
171C2×#121C2×D1112yes—
172C22×C42C2×D1111yescharacteristic
173C2×C4⋊C8—221no—
174C2×C22⋊C8—112no—
175#390—21no—
176#390—21no—
177#390Dic1112yescomplemented
178#384Dic1111yescharacteristic, complemented
179C2×#95—112no—
180C2×#95—221no—
181C2×#95—221no—
182#336—221no—
183#327—228no—
184C22×C11—22no—
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—22no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—82no—
193C22×C11—82no—
194C22×C11—82no—
195C22×C11—82no—
196C22×C11—82no—
197C22×C11—82no—
198C22×C11—82no—
199C22×C11#39011yescharacteristic
200C22×C11C2×#9911yescharacteristic
201C22×C11#41011yescharacteristic
202C22×C11C2×#10211yescharacteristic
203C22×C11#41811yescharacteristic
204C22×C11#42111yescharacteristic
205C22×C11#42111yescharacteristic
206C22×C11#45912yes—
207C22×C11#46012yes—
208C4×C11—22no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—22no—
212C4×C11—22no—
213C4×C11—22no—
214C4×C11—41no—
215C4×C11—82no—
216Dic11—84no—
217C22×D4—22no—
218C22×D4—21no—
219C22×D4—21no—
220C22×D4C2×Dic1112yes—
221C23×C4—222no—
222C23×C4C22⋊D1111yescharacteristic
223C23×C4C22⋊D1111yescharacteristic
224C23×C4C22×D1111yescharacteristic
225C22×C8—222no—
226#127—42no—
227#121—24no—
228#121—24no—
229#121—44no—
230#121—42no—
231#121—42no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4C2×Dic1112yes—
235C2×C22⋊C4—22no—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—22no—
238C2×C42—42no—
239C2×C42C2×Dic1111yescharacteristic
240C2×C42C2×Dic1111yescharacteristic
241C2×C42C22⋊D1111yescharacteristic
242C2×C42C22⋊D1111yescharacteristic
243C4⋊C8—442no—
244C22⋊C8—224no—
245#95—114no—
246#95—222no—
247#95—442no—
248#95—442no—
249C2×C11—22no—
250C2×C11—22no—
251C2×C11—162no—
252C2×C11#151011yescharacteristic
253C2×C11#151411yescharacteristic
254C2×C11#151711yescharacteristic
255C2×C11#151911yescharacteristic
256C2×C11#196311yescharacteristic
257C2×C11#196411yescharacteristic
258C2×C11#198211yescharacteristic
259C24—22no—
260C24C2×C22⋊D1111yescharacteristic
261C2×D4—24no—
262C2×D4—42no—
263C2×D4—42no—
264C2×D4—42no—
265C2×D4—42no—
266C2×D4—42no—
267C2×D4—42no—
268C2×D4—42no—
269C2×D4—44no—
270C2×D4—42no—
271C2×D4—44no—
272C2×D4—42no—
273C2×D4—42no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—224no—
283C22×C4—442no—
284C22×C4—442no—
285C22×C4—442no—
286C22×C4—442no—
287C22×C4—442no—
288C22×C4—442no—
289C22×C4#432312yes—
290C22×C4#432412yes—
291C22×C4C22⋊Dic1111yescharacteristic
292C22×C4C22⋊Dic1111yescharacteristic
293C22×C4C22⋊Dic1111yescharacteristic
294C22×C4C22⋊Dic1111yescharacteristic
295C22×C4D4×D1112yes—
296C22×C4#434112yes—
297C22×C4C22×Dic1111yescharacteristic
298C22×C4C2×C22⋊D1111yescharacteristic
299C2×C8—442no—
300C2×C8—442no—
301C2×C8—442no—
302C4⋊C4—24no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C22⋊C4—44no—
306C22⋊C4—44no—
307C22⋊C4—42no—
308C22⋊C4—42no—
309C42—22no—
310C42—22no—
311C42—41no—
312C42—41no—
313C11#971511yescharacteristic, complemented, Sylow
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23—42no—
322C23—42no—
323C23—42no—
324C23—42no—
325C23C2×#432311yescharacteristic
326C23#6698512yes—
327C23C2×#432411yescharacteristic
328C23#6699112yes—
329C23C2×C22⋊Dic1111yescharacteristic
330D4—84no—
331D4—84no—
332D4—84no—
333D4—84no—
334D4—84no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—44no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—444no—
357C2×C4—444no—
358C2×C4—444no—
359C2×C4—882no—
360C2×C4—882no—
361C2×C4—882no—
362C2×C4—882no—
363C2×C4#6689612yes—
364C2×C4#6689612yes—
365C2×C4#6689812yes—
366C2×C4D4×Dic1112yes—
367C2×C4#6698911yescharacteristic
368C2×C4#6699311yescharacteristic
369C8—882no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—82no—
379C22—82no—
380C22—82no—
381C22—82no—
382C22—82no—
383C22—82no—
384C22—82no—
385C22#1062268512yes—
386C22#1062268812yes—
387C22C2×#6689611yescharacteristic
388C22#1062282811yescharacteristic
389C22C2×#6689811yescharacteristic
390C22#1062283411yescharacteristic
391C22#1062284911yescharacteristic
392C22#1062284911yescharacteristic
393C22#1062285311yescharacteristic
394C4—22no—
395C4—21no—
396C4—22no—
397C4—21no—
398C4—22no—
399C4—22no—
400C4—41no—
401C4—82no—
402C4—884no—
403C2—22no—
404C2—22no—
405C2—162no—
406C2#1306714511yescharacteristic
407C2#1306716311yescharacteristic
408C2#1306717611yescharacteristic
409C2#1306718411yescharacteristic
410C2#1306944911yescharacteristic
411C2#1306945311yescharacteristic
412C2#1306954411yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
Fitting, prime radicalC11×#2856C2
socleC23×C11C2×C22⋊C4
cosocleC23×C4×C11C23
hypercenter#2856D11
hypocenterC11#9715
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2856

Complements

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

NH ≅ G/Ntype
1. #13068596C2semidirect
2. C2×#10622175C2semidirect
3. #13066843C2semidirect
5. C2×C11×#127C4semidirect
12. C11×#390C4semidirect
13. C11×#384C4semidirect
50. C11⋊#95D4semidirect
168. C2×#127Dic11semidirect
177. #390Dic11semidirect
178. #384Dic11semidirect
313. C11#9715semidirect

Maximal subgroups

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

subgroupindex
#130685962
C2×#106221752
#130668432
C11×#28562
#971511