Finite Group Databasebeta

← #14645459

Subgroups — #14645459

Order 2816.

818 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623074C211yesmaximal, characteristic
2#13068707C212yesmaximal, complemented
3#13068604C211yesmaximal, characteristic
4#13067189C212yesmaximal, complemented
5C11×#1459C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×D4×Dic11—21no—
8C22×C4⋊Dic11C411yescharacteristic, complemented
9C22×C4⋊Dic11C2211yescharacteristic
10C2×#66977C411yescharacteristic, complemented
11C2×#66977C2211yescharacteristic
12#10623074—24no—
13#10623074—24no—
14C2×#66943—21no—
15C2×#66931—21no—
16C2×#66931—21no—
17C2×#66922C411yescharacteristic, complemented
18C2×C4×Dic22C411yescharacteristic, complemented
19C2×C11×C22⋊C8C2212yes—
20C2×#66898—21no—
21#10622825C2212yes—
22C11×#324—21no—
23C11×#323—21no—
24#10622189—24no—
25#10622164—21no—
26#10622105—24no—
27C22×D4×C11D411yescharacteristic
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11C2311yescharacteristic
30C23×Dic11—21no—
31C23×Dic11—21no—
32C22×Dic22—21no—
33C22×Dic22C2×C411yescharacteristic
34C22×C8×C11—22no—
35C4×D4×C11—22no—
36C4×D4×C11—22no—
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C11×C22⋊C4D411yescharacteristic
39C2×C11×C22⋊C4D411yescharacteristic
40C2×C42×C11C2×C411yescharacteristic
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11—21no—
43C2×C22⋊Dic11—22no—
44D4×Dic11—28no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—22no—
49C2×C4⋊Dic11—22no—
50C2×C4⋊Dic11—22no—
51C2×C4⋊Dic11—22no—
52C2×C4⋊Dic11C2×C411yescharacteristic
53C2×C4⋊Dic11C2×C411yescharacteristic
54C2×C4⋊Dic11C2×C411yescharacteristic
55C2×C4⋊Dic11D414yes—
56#66977—22no—
57#66977—22no—
58#66977—22no—
59#66977D414yes—
60C2×Dic11⋊C4—21no—
61C2×Dic11⋊C4—21no—
62C2×Dic11⋊C4—21no—
63C2×C4×Dic11—21no—
64#66943—28no—
65#66931—28no—
66#66931—28no—
67#66922—22no—
68#66922—22no—
69C4×Dic22—22no—
70C4×Dic22—22no—
71C11×C22⋊C8—22no—
72C11×C22⋊C8—22no—
73#66898—42no—
74C11⋊#95—22no—
75#8380—111nomaximal, Sylow
76C24×C11C22⋊C411yescharacteristic
77C24×C11C2×D411yescharacteristic
78C2×D4×C11—22no—
79C2×D4×C11—22no—
80C2×D4×C11SD1612yes—
81C2×D4×C11Q1612yes—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—42no—
85C22×C4×C11—42no—
86C22×C4×C11C22⋊C411yescharacteristic
87C22×C4×C11C22⋊C411yescharacteristic
88C22×C4×C11C22⋊C411yescharacteristic
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2×D411yescharacteristic
93C22×Dic11—24no—
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11—24no—
99C22×Dic11—42no—
100C22×Dic11—82no—
101C22×Dic11—82no—
102C2×Dic22—24no—
103C2×Dic22—21no—
104C2×Dic22—42no—
105C2×Dic22—82no—
106C2×Dic22C22⋊C412yes—
107C2×C8×C11—44no—
108C2×C8×C11—42no—
109C11×C4⋊C4—22no—
110C11×C22⋊C4—22no—
111C11×C22⋊C4—22no—
112C42×C11—21no—
113C42×C11—21no—
114C22⋊Dic11—24no—
115C22⋊Dic11—24no—
116C22⋊Dic11—42no—
117C22⋊Dic11—42no—
118C4⋊Dic11—24no—
119C4⋊Dic11—24no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C4⋊Dic11—24no—
124C4⋊Dic11—44no—
125C4⋊Dic11C22⋊C412yes—
126C4⋊Dic11C22⋊C412yes—
127C4⋊Dic11C22⋊C412yes—
128Dic11⋊C4—24no—
129Dic11⋊C4—24no—
130Dic11⋊C4—24no—
131C4×Dic11—24no—
132C2×#554—111no—
133#1824—112no—
134#1799—111no—
135#1520—112no—
136#1459D1111yescharacteristic
137C23×C11—21no—
138C23×C11—21no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11#10312yes—
144C23×C11C2×C22⋊C411yescharacteristic
145C23×C11#12012yes—
146C23×C11C2×SD1611yescharacteristic
147C23×C11C2×Q1611yescharacteristic
148C23×C11#13712yes—
149D4×C11—24no—
150D4×C11—24no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—24no—
154C2×C4×C11—22no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—42no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11#10312yes—
164C2×C4×C11C2×C22⋊C411yescharacteristic
165C2×C4×C11C2×C22⋊C411yescharacteristic
166C2×C4×C11#12012yes—
167C2×Dic11—22no—
168C2×Dic11—22no—
169C2×Dic11—22no—
170C2×Dic11—22no—
171C2×Dic11—42no—
172C2×Dic11—42no—
173C2×Dic11—42no—
174C2×Dic11—42no—
175C2×Dic11—84no—
176C2×Dic11—84no—
177C2×Dic11—82no—
178C2×Dic11—82no—
179C2×Dic11—82no—
180Dic22—42no—
181Dic22—42no—
182Dic22—84no—
183C8×C11—82no—
184#554—224no—
185#554—224no—
186C2×C4⋊Q8—111no—
187C2×#125—221no—
188C2×C22⋊Q8—111no—
189C2×C22⋊Q8—111no—
190C2×C22⋊Q8—221no—
191C2×C22⋊Q8—221no—
192C2×C4×Q8—111no—
193C2×C4×D4—221no—
194C2×C4×D4C2×D1111yescharacteristic
195C22×C4⋊C4—111no—
196C22×C4⋊C4—111no—
197C2×#99—221no—
198C2×C22⋊C8C2×D1112yes—
199#380—112no—
200#342—221no—
201#340—224no—
202#328—224no—
203#324—21no—
204#323—21no—
205C22×C11—21no—
206C22×C11—22no—
207C22×C11—21no—
208C22×C11—22no—
209C22×C11—22no—
210C22×C11—41no—
211C22×C11—41no—
212C22×C11—42no—
213C22×C11—42no—
214C22×C11—42no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11#37911yescharacteristic
218C22×C11C2×#10311yescharacteristic
219C22×C11#41911yescharacteristic
220C22×C11#44812yes—
221C22×C11#45112yes—
222C4×C11—21no—
223C4×C11—22no—
224C4×C11—22no—
225C4×C11—41no—
226C4×C11—41no—
227C4×C11#41012yes—
228Dic11—42no—
229Dic11—42no—
230Dic11—42no—
231Dic11—42no—
232Dic11—162no—
233C22×Q8—111no—
234C22×Q8—221no—
235C22×D4D4411yescharacteristic
236C23×C4—221no—
237C23×C4—221no—
238C23×C4C4×D1111yescharacteristic
239C23×C4C22×D1111yescharacteristic
240C22×C8—22no—
241C4⋊Q8—222no—
242C4⋊Q8—222no—
243#125—228no—
244C22⋊Q8—114no—
245C22⋊Q8—228no—
246C22⋊Q8—228no—
247C22⋊Q8—222no—
248C22⋊Q8—222no—
249C22⋊Q8—222no—
250C4×Q8—222no—
251C4×Q8—222no—
252C4×D4—22no—
253C4×D4—22no—
254C4×D4—228no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—111no—
258C2×C4⋊C4—114no—
259C2×C4⋊C4—222no—
260C2×C4⋊C4—222no—
261C2×C4⋊C4—221no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4—221no—
264C2×C4⋊C4—221no—
265C2×C4⋊C4—222no—
266C2×C4⋊C4—221no—
267C2×C4⋊C4—221no—
268C2×C4⋊C4—222no—
269C2×C4⋊C4C22⋊D1111yescharacteristic
270C2×C22⋊C4—221no—
271C2×C22⋊C4—221no—
272C2×C22⋊C4—222no—
273C2×C22⋊C4D4411yescharacteristic
274C2×C22⋊C4C22⋊D1111yescharacteristic
275C2×C42—221no—
276C2×C42C4×D1111yescharacteristic
277#99—442no—
278C22⋊C8—22no—
279C22⋊C8—22no—
280#95—222no—
281C2×C11—22no—
282C2×C11—21no—
283C2×C11—21no—
284C2×C11—22no—
285C2×C11—42no—
286C2×C11#178211yescharacteristic
287C2×C11#178711yescharacteristic
288C2×C11#179511yescharacteristic
289C24(C2×D11)⋊C411yescharacteristic
290C24C2×D4411yescharacteristic
291C2×Q8—112no—
292C2×Q8—224no—
293C2×Q8—221no—
294C2×Q8—442no—
295C2×Q8—882no—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4#431412yes—
299C2×D4Dic4412yes—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—221no—
305C22×C4—221no—
306C22×C4—221no—
307C22×C4—221no—
308C22×C4—224no—
309C22×C4—224no—
310C22×C4—442no—
311C22×C4—882no—
312C22×C4—882no—
313C22×C4(C2×D11)⋊C411yescharacteristic
314C22×C4(C2×D11)⋊C411yescharacteristic
315C22×C4(C2×D11)⋊C411yescharacteristic
316C22×C4C2×C4×D1111yescharacteristic
317C22×C4D4×D1112yes—
318C22×C4D4×D1112yes—
319C22×C4C2×C22⋊D1111yescharacteristic
320C2×C8—44no—
321C2×C8—42no—
322C4⋊C4—22no—
323C4⋊C4—112no—
324C4⋊C4—112no—
325C4⋊C4—112no—
326C4⋊C4—224no—
327C4⋊C4—224no—
328C4⋊C4—224no—
329C4⋊C4—224no—
330C4⋊C4—221no—
331C4⋊C4—221no—
332C4⋊C4—221no—
333C4⋊C4—224no—
334C4⋊C4—224no—
335C4⋊C4—444no—
336C22⋊C4—22no—
337C22⋊C4—22no—
338C22⋊C4—224no—
339C22⋊C4—224no—
340C22⋊C4—442no—
341C22⋊C4—442no—
342C42—21no—
343C42—21no—
344C42—224no—
345C11#838011yescharacteristic, complemented, Sylow
346C23—21no—
347C23—21no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23#6688012yes—
353C23#6693512yes—
354C23C2×#431411yescharacteristic
355C23C2×Dic4411yescharacteristic
356C23#6696212yes—
357C23C2×(C2×D11)⋊C411yescharacteristic
358Q8—442no—
359Q8—442no—
360Q8—884no—
361D4—24no—
362D4—24no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—24no—
366C2×C4—22no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—222no—
376C2×C4—222no—
377C2×C4—222no—
378C2×C4—222no—
379C2×C4—442no—
380C2×C4—442no—
381C2×C4—442no—
382C2×C4—442no—
383C2×C4—884no—
384C2×C4—884no—
385C2×C4—882no—
386C2×C4—882no—
387C2×C4—882no—
388C2×C4#6688012yes—
389C2×C4C22⋊C4×D1111yescharacteristic
390C2×C4C22⋊C4×D1111yescharacteristic
391C2×C4#6699012yes—
392C8—82no—
393C22—21no—
394C22—22no—
395C22—21no—
396C22—22no—
397C22—22no—
398C22—41no—
399C22—41no—
400C22—42no—
401C22—42no—
402C22—42no—
403C22—41no—
404C22—41no—
405C22#1062235112yes—
406C22#1062235212yes—
407C22#1062256811yescharacteristic
408C22C2×#6688011yescharacteristic
409C22#1062273311yescharacteristic
410C4—22no—
411C4—22no—
412C4—21no—
413C4—41no—
414C4—41no—
415C4—442no—
416C4—442no—
417C4—442no—
418C4—442no—
419C4—1762no—
420C4#1062235312yes—
421C2—22no—
422C2—21no—
423C2—21no—
424C2—22no—
425C2—42no—
426C2#1306853211yescharacteristic
427C2#1306855211yescharacteristic
428C2#1306858711yescharacteristic
subgroupG/H
centerC22#10622568
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1459C2
socleC22×C11#379
prime radicalC22×D4×C11D4
cosocleC23×C4×C11C23
hypercenter#1459D11
hypocenterC11#8380
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1459

Complements

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

NH ≅ G/Ntype
2. #13068707C2semidirect
4. #13067189C2semidirect
8. C22×C4⋊Dic11C4semidirect
10. C2×#66977C4semidirect
17. C2×#66922C4semidirect
18. C2×C4×Dic22C4semidirect
345. C11#8380semidirect

Maximal subgroups

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

subgroupindex
C2×#106230742
#130687072
#130686042
#130671892
C11×#14592
#838011