Finite Group Databasebeta

← #14650620

Subgroups — #14650620

Order 2816.

512 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078104C211yesmaximal, characteristic
2#13077724C211yesmaximal, characteristic
3#13069568C211yesmaximal, characteristic, complemented
4#13068637C211yesmaximal, characteristic
5#13067287C211yesmaximal, characteristic, complemented
6#13066490C211yesmaximal, characteristic, complemented
7C11×#1303C211yesmaximal, characteristic, complemented
8C2×#66962—21no—
9C4×#4339C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C4×C11×C4⋊C4C2211yescharacteristic
14#10622733—21no—
15C2×#66869—21no—
16#10622537C2211yescharacteristic
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18#10622462—21no—
19#10622462C412yescomplemented
20#10622454—21no—
21#10622454C412yescomplemented
22#10622446—21no—
23D11×C4⋊C8—21no—
24(C22⋊D11)⋊C8—22no—
25C8×D44—21no—
26C8×Dic22—21no—
27#10622167—22no—
28#10622161—21no—
29#10622124—21no—
30#10622124—21no—
31C2×#4339D411yescharacteristic
32C22×Dic22—21no—
33C2×C11×M16—21no—
34C2×C11×C4⋊C4—21no—
35C2×C42×C11—21no—
36C2×C42×C11C2311yescharacteristic
37C4×C22⋊D11—21no—
38C4×C22⋊D11—21no—
39#66979D411yescharacteristic
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×#4318—21no—
43C22×C11⋊C8D412yes—
44#66962—42no—
45#66962—42no—
46C2×Dic44—22no—
47C2×#4314—22no—
48C2×C8×D11—22no—
49C4×D44C2×C411yescharacteristic
50C4×D44D411yescharacteristic
51#66925—21no—
52C42×D11—21no—
53#66922—21no—
54#66922—21no—
55#66922—21no—
56#66922C2×C412yes—
57C4×Dic22C2×C411yescharacteristic
58C4×Dic22D411yescharacteristic
59C11×C4⋊C8—21no—
60C11×C4⋊C8C2×C412yes—
61C11×C4⋊C8D411yescharacteristic
62C11×C4⋊C8D411yescharacteristic
63C11×C22⋊C8—21no—
64C4×C8×C11—21no—
65C11×#95—21no—
66(C2×D11)⋊C8—22no—
67#66880—22no—
68#66880—22no—
69Dic11⋊C8—22no—
70C8×Dic11—22no—
71#66869—42no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)—21no—
76#9316—111nomaximal, Sylow
77C22×C4×C11—41no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C2×C22⋊D11—21no—
82C22×Dic11—41no—
83#4339—21no—
84#4339—21no—
85#4339D812yes—
86#4339SD1612yes—
87C2×D44C22⋊C411yescharacteristic
88C2×C4×D11—21no—
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×Dic22—22no—
92C2×Dic22—41no—
93C2×Dic22—41no—
94C2×Dic22—41no—
95C2×Dic22—41no—
96C2×Dic22—41no—
97C2×Dic22C22⋊C411yescharacteristic
98C11×M16—41no—
99C11×M16—41no—
100C2×C8×C11—22no—
101C2×C8×C11—21no—
102C2×C8×C11—21no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—41no—
105C42×C11—41no—
106C42×C11—41no—
107C42×C11C22×C411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11#4111yescharacteristic
111C22⋊Dic11—21no—
112(C2×D11)⋊C4—21no—
113(C2×D11)⋊C4—21no—
114C4⋊Dic11—22no—
115C4⋊Dic11—22no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118C4⋊Dic11C22⋊C411yescharacteristic
119C4⋊Dic11C22⋊C411yescharacteristic
120Dic11⋊C4—21no—
121Dic11⋊C4—21no—
122C4×Dic11—21no—
123C4×Dic11—21no—
124C4×Dic11—21no—
125#4318—41no—
126#4318—41no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—42no—
129C2×C11⋊C8—41no—
130Dic44—44no—
131#4314—44no—
132C8×D11—82no—
133#3039—111no—
134#2988—111no—
135#1988—111no—
136#1806—111no—
137#1546—111no—
138#1303D1111yescharacteristic, complemented
139#1292—111no—
140C23×C11#12111yescharacteristic
141C22×D11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—81no—
147C2×C4×C11—81no—
148C2×C4×C11C2×C22⋊C411yescharacteristic
149C2×C4×C11C4×D411yescharacteristic
150C2×C4×C11C4×D411yescharacteristic
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12311yescharacteristic
154C2×C4×C11C2×D811yescharacteristic
155C2×C4×C11C2×SD1611yescharacteristic
156C2×C4×C11#13511yescharacteristic
157C2×C4×C11#13511yescharacteristic
158C22⋊D11—22no—
159C22⋊D11—22no—
160C2×Dic11—21no—
161C2×Dic11—21no—
162C2×Dic11—21no—
163C2×Dic11—42no—
164C2×Dic11—81no—
165C2×Dic11—81no—
166D44—21no—
167D44#10212yes—
168C4×D11—22no—
169C4×D11—22no—
170C4×D11—41no—
171C4×D11—41no—
172C4×D11—81no—
173Dic22—21no—
174Dic22—42no—
175Dic22—42no—
176Dic22—81no—
177Dic22—81no—
178Dic22#10212yes—
179C8×C11—42no—
180C8×C11—41no—
181C8×C11—41no—
182C11⋊C8—42no—
183C11⋊C8—81no—
184C2×#137—221no—
185C2×C4⋊Q8—111no—
186C4×#41—111no—
187#462—112no—
188#462—221no—
189#461—112no—
190#461—221no—
191C8×Q8—221no—
192C8×D4—221no—
193C8×D4—222no—
194#431—221no—
195#431C2×D1111yescharacteristic
196#423—111no—
197#423C2×D1111yescharacteristic
198C2×C4⋊C8—111no—
199C2×C4⋊C8—221no—
200C2×#104—221no—
201#419—221no—
202C4×C4⋊C4C2×D1111yescharacteristic
203#340—222no—
204#339—221no—
205#332—221no—
206#332—221no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11#38611yescharacteristic
210C22×C11#46511yescharacteristic
211C22×C11#46611yescharacteristic
212C2×D11—22no—
213C2×D11—41no—
214C2×D11—41no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—82no—
219C4×C11C2×#10211yescharacteristic
220C4×C11#41611yescharacteristic
221C4×C11#45511yescharacteristic
222C4×C11#45611yescharacteristic
223C4×C11#46511yescharacteristic
224C4×C11#46611yescharacteristic
225Dic11—22no—
226Dic11—41no—
227Dic11—41no—
228Dic11—82no—
229C2×#41—111no—
230C22×Q8—221no—
231#137—442no—
232#137—442no—
233C2×Q16—222no—
234C2×SD16—222no—
235C2×M16—21no—
236C2×M16—221no—
237C22×C8—112no—
238C22×C8—222no—
239C4⋊Q8—112no—
240C4⋊Q8—221no—
241C4⋊Q8—221no—
242C4⋊Q8—221no—
243C4×Q8—111no—
244C4×Q8—111no—
245C4×D4—111no—
246C4×D4—111no—
247C4×D4—221no—
248C4×D4—221no—
249#117—111no—
250#117—221no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—221no—
253C2×C4⋊C4—221no—
254C2×C42—21no—
255C2×C42—221no—
256C2×C42C22×D1111yescharacteristic
257C4⋊C8—21no—
258C4⋊C8—222no—
259C4⋊C8—221no—
260C4⋊C8—221no—
261C4⋊C8—221no—
262C4⋊C8—221no—
263C4⋊C8C4×D1112yes—
264C4⋊C8D4411yescharacteristic
265C4⋊C8D4411yescharacteristic
266#104—442no—
267#103—222no—
268#103—222no—
269C22⋊C8—21no—
270C22⋊C8—222no—
271C4×C8—21no—
272C4×C8—222no—
273#95—21no—
274C2×C11—21no—
275C2×C11—21no—
276C2×C11#188211yescharacteristic
277C2×C11#189311yescharacteristic
278C2×C11#190211yescharacteristic
279D11—42no—
280#41—112no—
281#41—112no—
282#41—221no—
283#41—221no—
284C2×Q8—111no—
285C2×Q8—222no—
286C2×Q8—441no—
287C2×Q8—441no—
288C2×Q8—441no—
289C2×Q8—441no—
290C2×Q8—441no—
291C2×D4—111no—
292C2×D4—221no—
293C22×C4—41no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—221no—
297C22×C4—441no—
298C22×C4#433911yescharacteristic
299C22×C4D4×D1111yescharacteristic
300C22×C4D4×D1111yescharacteristic
301Q16—444no—
302SD16—444no—
303M16—41no—
304M16—41no—
305M16—441no—
306M16—441no—
307C2×C8—22no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—222no—
311C2×C8—442no—
312C2×C8—441no—
313C2×C8—882no—
314C4⋊C4—22no—
315C4⋊C4—41no—
316C4⋊C4—111no—
317C4⋊C4—111no—
318C4⋊C4—221no—
319C4⋊C4—221no—
320C4⋊C4—222no—
321C4⋊C4—222no—
322C4⋊C4—441no—
323C4⋊C4—441no—
324C22⋊C4—221no—
325C22⋊C4—221no—
326C22⋊C4—221no—
327C42—41no—
328C42—41no—
329C42—221no—
330C42—221no—
331C42—221no—
332C42C2×C4×D1111yescharacteristic
333C42C2×D4411yescharacteristic
334C42D4×D1111yescharacteristic
335C42#434311yescharacteristic
336C11#931611yescharacteristic, complemented, Sylow
337C23—221no—
338C23#6693711yescharacteristic
339Q8—112no—
340Q8—221no—
341Q8—442no—
342Q8—442no—
343Q8—881no—
344Q8—881no—
345D4—112no—
346D4—222no—
347D4—222no—
348D4—221no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—221no—
356C2×C4—222no—
357C2×C4—222no—
358C2×C4—221no—
359C2×C4—221no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—442no—
363C2×C4—881no—
364C2×C4—881no—
365C2×C4—881no—
366C2×C4C4×D4411yescharacteristic
367C2×C4C22⋊C4×D1111yescharacteristic
368C2×C4#6693511yescharacteristic
369C2×C4#6694611yescharacteristic
370C2×C4#6694711yescharacteristic
371C2×C4#6694811yescharacteristic
372C2×C4D8×D1111yescharacteristic
373C2×C4SD16×D1111yescharacteristic
374C2×C4#6696911yescharacteristic
375C2×C4#6697211yescharacteristic
376C8—42no—
377C8—41no—
378C8—41no—
379C8—442no—
380C8—881no—
381C22—21no—
382C22—21no—
383C22—222no—
384C22—441no—
385C22—441no—
386C22#1062227811yescharacteristic
387C22#1062238811yescharacteristic
388C22#1062242011yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—82no—
393C4—222no—
394C4—441no—
395C4—441no—
396C4—882no—
397C4D11×#10211yescharacteristic
398C4#1062241711yescharacteristic
399C4#1062243811yescharacteristic
400C4#1062243911yescharacteristic
401C4#1062247711yescharacteristic
402C4#1062249611yescharacteristic
403C2—21no—
404C2—21no—
405C2—442no—
406C2#1306898611yescharacteristic
407C2#1306904311yescharacteristic
408C2#1306908811yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1303C2
socleC22×C11#386
prime radicalC2×#4339D4
cosocleC2×C42×C11C23
hypercenter#1303D11
hypocenterC11#9316
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
3. #13069568C2semidirect
5. #13067287C2semidirect
6. #13066490C2semidirect
7. C11×#1303C2semidirect
19. #10622462C4semidirect
21. #10622454C4semidirect
138. #1303D11semidirect
336. C11#9316semidirect

Maximal subgroups

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

subgroupindex
#130781042
#130777242
#130695682
#130686372
#130672872
#130664902
C11×#13032
#931611