Finite Group Databasebeta

← #14853489

Subgroups — #14853489

Order 2816.

706 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077003C211yesmaximal, characteristic, complemented
2#13070183C212yesmaximal, complemented
3#13069852C212yesmaximal
4#13069316C212yesmaximal
5#13069309C212yesmaximal, complemented
6#13068631C211yesmaximal, characteristic, complemented
7#13068631C211yesmaximal, characteristic, complemented
8#13068626C211yesmaximal, characteristic
9#13068626C211yesmaximal, characteristic
10#13068469C211yesmaximal, characteristic, complemented
11C4×C11×#124C211yesmaximal, characteristic
12C2×C11×#124C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C11×#391C2211yescharacteristic
16C11×#390C2211yescharacteristic
17C11×#388—22no—
18C11×#382C2211yescharacteristic
19C4×C11×C22⋊C4—22no—
20C43×C11C2211yescharacteristic
21C2×#66899C2212yes—
22C2×#66899C2212yes—
23C2×#66896C2212yes—
24C2×#66896C2212yes—
25#10622549C2211yescharacteristic
26#10622549C2211yescharacteristic
27#10622546—22no—
28#10622546—22no—
29#10622541C2212yes—
30#10622541C2212yes—
31C2×C4⋊(C11⋊C8)C2211yescharacteristic
32C2×C4⋊(C11⋊C8)C2211yescharacteristic
33C2×#66867C2212yes—
34#10622167C2212yes—
35#10622167C2212yes—
36#10622167C2212yes—
37#10622167C2212yes—
38#10622162C2212yes—
39C22×Q8×C11C2311yescharacteristic
40C22×D4×C11C2311yescharacteristic
41C23×C4×C11—21no—
42C11×#124—22no—
43C11×#124—22no—
44C4×Q8×C11—22no—
45C4×Q8×C11—22no—
46C4×D4×C11—22no—
47C4×D4×C11—22no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4C2311yescharacteristic
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4—21no—
54C2×C42×C11—21no—
55C2×C42×C11D412yes—
56C2×C42×C11D412yes—
57C2×C42×C11C2311yescharacteristic
58C2×C42×C11C2311yescharacteristic
59C2×C42×C11C2311yescharacteristic
60C2×C4⋊Dic11C2312yes—
61C2×C4⋊Dic11C2312yes—
62C2×Dic11⋊C4—22no—
63C2×Dic11⋊C4—22no—
64C22×C11⋊C8C2312yes—
65C22×C11⋊C8C2312yes—
66C11×#95—22no—
67C11×#95—22no—
68#66899—24no—
69#66899—42no—
70#66896—24no—
71#66896—42no—
72C11⋊#95—22no—
73C11⋊#95—22no—
74C11⋊#95—21no—
75C11⋊#95—21no—
76C11⋊#95—21no—
77C11⋊#95—21no—
78C4⋊(C11⋊C8)—22no—
79C4⋊(C11⋊C8)—22no—
80#66867—42no—
81#29128—111nomaximal, Sylow
82C24×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11#4112yes—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11#4112yes—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—44no—
99C22×C4×C11—42no—
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2411yescharacteristic
105C22×Dic11—22no—
106C22×Dic11—22no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—42no—
112C11×C22⋊C4—28no—
113C11×C22⋊C4—44no—
114C11×C22⋊C4—42no—
115C42×C11—21no—
116C42×C11—21no—
117C42×C11—21no—
118C42×C11—21no—
119C42×C11—42no—
120C42×C11—42no—
121C42×C11—42no—
122C42×C11#4112yes—
123C42×C11#4112yes—
124C4⋊Dic11—22no—
125C4⋊Dic11—22no—
126C4⋊Dic11—22no—
127C4⋊Dic11—22no—
128Dic11⋊C4—44no—
129Dic11⋊C4—44no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136#2864—111no—
137C4×#124D1111yescharacteristic
138#2101—112no—
139#2042—112no—
140#1936—112no—
141#1935—112no—
142#1805—111no—
143#1805—111no—
144#1804—111no—
145#1804—111no—
146#1767—111no—
147C23×C11—22no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—42no—
151C23×C11—42no—
152C23×C11C22×D411yescharacteristic
153Q8×C11—22no—
154Q8×C11—22no—
155Q8×C11—41no—
156Q8×C11—41no—
157D4×C11—22no—
158D4×C11—22no—
159D4×C11—41no—
160D4×C11—41no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—84no—
177C2×C4×C11#12412yes—
178C2×C4×C11#12412yes—
179C2×C4×C11C2×#4111yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181C2×C4×C11C2×#4111yescharacteristic
182C2×C4×C11C2×#4111yescharacteristic
183C2×C4×C11H(5,𝔽2)11yescharacteristic
184C2×C4×C112−1+411yescharacteristic
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C11⋊C8—42no—
192C11⋊C8—42no—
193C2×#124C2×D1111yescharacteristic
194C2×C4×Q8C2×D1111yescharacteristic
195C2×C4×D4C2×D1111yescharacteristic
196C2×C4⋊C8—111no—
197C2×C4⋊C8—111no—
198C2×#103—112no—
199C2×#103—112no—
200C2×#102—112no—
201C2×#102—112no—
202C2×#97—112no—
203#391C2×D1111yescharacteristic
204#390C2×D1111yescharacteristic
205#389—112no—
206#389—112no—
207#388—22no—
208#387—222no—
209#387—222no—
210#382—111no—
211#382—111no—
212#382C2×D1111yescharacteristic
213C4×C22⋊C4—22no—
214C43C2×D1111yescharacteristic
215#340—112no—
216#340—112no—
217#340—112no—
218#340—112no—
219#336—112no—
220C22×C11—42no—
221C22×C11—44no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11—82no—
225C22×C11#52511yescharacteristic
226C22×C11C2×#12411yescharacteristic
227C22×C11#53711yescharacteristic
228C22×C11#57512yes—
229C22×C11#57512yes—
230C4×C11—22no—
231C4×C11—22no—
232C4×C11—42no—
233C4×C11—42no—
234C4×C11—42no—
235C4×C11—81no—
236C4×C11—81no—
237C4×C11#55211yescharacteristic
238C4×C11#55211yescharacteristic
239C4×C11#55311yescharacteristic
240C4×C11#55311yescharacteristic
241Dic11—82no—
242Dic11—82no—
243C22×Q8C22×D1111yescharacteristic
244C22×D4C22×D1111yescharacteristic
245C23×C4—21no—
246C22×C8—112no—
247C22×C8—112no—
248#124—22no—
249#124—22no—
250C4×Q8—22no—
251C4×Q8—22no—
252C4×D4—22no—
253C4×D4—22no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—112no—
256C2×C4⋊C4—112no—
257C2×C4⋊C4—222no—
258C2×C4⋊C4—222no—
259C2×C4⋊C4C22×D1111yescharacteristic
260C2×C4⋊C4C22×D1111yescharacteristic
261C2×C22⋊C4—22no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—22no—
264C2×C42—21no—
265C2×C42C22⋊D1112yes—
266C2×C42C22⋊D1112yes—
267C2×C42C22×D1111yescharacteristic
268C2×C42C22×D1111yescharacteristic
269C2×C42C22×D1111yescharacteristic
270C4⋊C8—222no—
271C4⋊C8—222no—
272#103—224no—
273#103—442no—
274#102—224no—
275#102—442no—
276#97—442no—
277#95—22no—
278#95—22no—
279#95—221no—
280#95—221no—
281#95—221no—
282#95—221no—
283#95—222no—
284#95—222no—
285C2×C11—82no—
286C2×C11#256211yescharacteristic
287C2×C11#311112yes—
288C2×C11#313511yescharacteristic
289C2×C11#314011yescharacteristic
290C2×C11#325612yes—
291C24—21no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8#433912yes—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4#433912yes—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—44no—
308C22×C4—42no—
309C22×C4—222no—
310C22×C4—222no—
311C22×C4C2×C22⋊D1112yes—
312C22×C4C2×C22⋊D1112yes—
313C22×C4C2×C22⋊D1111yescharacteristic
314C22×C4C2×C22⋊D1111yescharacteristic
315C22×C4C23×D1111yescharacteristic
316C2×C8—222no—
317C2×C8—222no—
318C2×C8—222no—
319C2×C8—222no—
320C2×C8—222no—
321C2×C8—222no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—42no—
327C4⋊C4—222no—
328C4⋊C4—222no—
329C4⋊C4—222no—
330C4⋊C4—222no—
331C4⋊C4—444no—
332C4⋊C4—444no—
333C22⋊C4—28no—
334C22⋊C4—44no—
335C22⋊C4—42no—
336C42—21no—
337C42—21no—
338C42—21no—
339C42—21no—
340C42—42no—
341C42—42no—
342C42—42no—
343C42#434112yes—
344C42#434112yes—
345C11#2912811yescharacteristic, complemented, Sylow
346C23—22no—
347C23—41no—
348C23—42no—
349C23—42no—
350C23—41no—
351C23C22×C22⋊D1111yescharacteristic
352Q8—22no—
353Q8—22no—
354Q8—41no—
355Q8—41no—
356D4—22no—
357D4—22no—
358D4—41no—
359D4—41no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—84no—
376C2×C4—442no—
377C2×C4—442no—
378C2×C4—442no—
379C2×C4—442no—
380C2×C4—442no—
381C2×C4—442no—
382C2×C4#6698912yes—
383C2×C4#6698912yes—
384C2×C4C2×#433911yescharacteristic
385C2×C4C2×#433911yescharacteristic
386C2×C4C2×#434111yescharacteristic
387C2×C4C2×#434111yescharacteristic
388C2×C4#6704211yescharacteristic
389C2×C4#6704311yescharacteristic
390C8—442no—
391C8—442no—
392C22—42no—
393C22—44no—
394C22—81no—
395C22—82no—
396C22—81no—
397C22#1062332211yescharacteristic
398C22C2×#6698911yescharacteristic
399C22#1062335312yes—
400C22#1062335312yes—
401C22#1062336411yescharacteristic
402C4—22no—
403C4—22no—
404C4—42no—
405C4—42no—
406C4—42no—
407C4—81no—
408C4—81no—
409C4—882no—
410C4—882no—
411C4#1062307211yescharacteristic
412C4#1062307211yescharacteristic
413C4#1062309611yescharacteristic
414C4#1062309611yescharacteristic
415C2—82no—
416C2#1307378211yescharacteristic
417C2#1307872512yes—
418C2#1307896111yescharacteristic
419C2#1307900211yescharacteristic
420C2#1308001212yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#124C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC4×#124D11
hypocenterC11#29128
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
1. #13077003C2semidirect
2. #13070183C2semidirect
5. #13069309C2semidirect
6. #13068631C2semidirect
7. #13068631C2semidirect
10. #13068469C2semidirect
345. C11#29128semidirect

Maximal subgroups

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

subgroupindex
#130770032
#130701832
#130698522
#130693162
#130693092
#130686312
#130686262
#130684692
C4×C11×#1242
#2912811