Finite Group Databasebeta

← #14907196

Subgroups — #14907196

Order 2816.

642 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622807C211yesmaximal, characteristic
2#13077533C211yesmaximal, characteristic, complemented
3#13077532C211yesmaximal, characteristic, complemented
4#13070499C214yesmaximal, complemented
5#13070494C214yesmaximal, complemented
6C2×#10622131C211yesmaximal, characteristic, complemented
7#13070345C211yesmaximal, characteristic, complemented
8#13070215C211yesmaximal, characteristic, complemented
9C11×#2143C211yesmaximal, characteristic, complemented
10C2×C11×#135C2211yescharacteristic
11#10623350—21no—
12#10623276—21no—
13C2×#66957C2211yescharacteristic
14C2×C11×M32C2211yescharacteristic
15C2×C11×#108C2211yescharacteristic
16#10622849—21no—
17#10622810—22no—
18#10622809C2214yescomplemented
19#10622807C412yescomplemented
20#10622807C412yescomplemented
21#10622807C2212yes—
22#10622807C2212yes—
23C2×#66893C411yescharacteristic, complemented
24C2×#66892C411yescharacteristic, complemented
25C2×#66891C411yescharacteristic, complemented
26C2×#66890C411yescharacteristic, complemented
27#10622752—21no—
28C2×#66883C2211yescharacteristic
29#10622714C2211yescharacteristic
30C22×C11⋊C16C2211yescharacteristic
31#10622508C2214yescomplemented
32#10622507—22no—
33C11×#359C2214yescomplemented
34#10622148C2214yescomplemented
35#10622140C2212yescomplemented
36C16×Dic11C2212yescomplemented
37#10622131C2212yescomplemented
38#10622131C2212yescomplemented
39C2×C11×#41—21no—
40C2×#4339—21no—
41C11×#135—21no—
42C11×#135—21no—
43C11×#135C2×C412yes—
44C11×#135C2312yes—
45C2×C11×Q16C2×C411yescharacteristic
46C2×C11×SD16—21no—
47C2×C11×D8C2×C411yescharacteristic
48C2×C11×M16—21no—
49C22×C8×C11C2311yescharacteristic
50#67001—24no—
51#67001—42no—
52#66979D411yescharacteristic
53C2×#4318—21no—
54C2×#4318—42no—
55C2×#4318D411yescharacteristic
56#66960—24no—
57M16×D11—42no—
58C2×Dic44C2×C411yescharacteristic
59#66957—21no—
60#66957—21no—
61#66957C2×C412yes—
62#66957C2312yes—
63C2×D88C2×C411yescharacteristic
64C2×#4314—21no—
65#66954—42no—
66C11×M32—21no—
67C11×M32—21no—
68C2×C11×C16C2312yes—
69C11×#108—21no—
70C11×#108C2312yes—
71#66901—24no—
72#66893C2×C412yes—
73#66893C2×C412yes—
74#66892C2×C412yes—
75#66892C2×C412yes—
76#66891C2×C412yes—
77#66891C2×C412yes—
78#66890C2×C412yes—
79#66890C2×C412yes—
80#66889—24no—
81#66883—21no—
82#66883C2312yes—
83#66879D412yes—
84C8×Dic11C2312yes—
85C2×C11⋊C16C2×C411yescharacteristic
86C2×C11⋊C16C2×C411yescharacteristic
87C2×C11⋊C16C2×C411yescharacteristic
88C2×C11⋊C16C2×C411yescharacteristic
89C2×C11⋊C16C2311yescharacteristic
90C2×C11⋊C16C2311yescharacteristic
91#33465—111nomaximal, Sylow
92C11×#41—22no—
93C11×#41—22no—
94C11×#41—41no—
95C11×#41—41no—
96C2×Q8×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11C2×D411yescharacteristic
101C2×C22⋊D11—41no—
102#4339—22no—
103#4339—22no—
104#4339—41no—
105#4339—41no—
106C2×D44—21no—
107C2×C4×D11—41no—
108C2×Dic22—21no—
109C11×Q16—21no—
110C11×Q16C22×C412yes—
111C11×SD16—22no—
112C11×SD16—22no—
113C11×D8—21no—
114C11×D8C22×C412yes—
115C11×M16—22no—
116C11×M16—41no—
117C2×C8×C11—41no—
118C2×C8×C11C22×C411yescharacteristic
119C2×C8×C11C22×C411yescharacteristic
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11#4111yescharacteristic
122C2×C8×C11#4111yescharacteristic
123C2×C8×C11C2411yescharacteristic
124C22⋊Dic11—21no—
125C4⋊Dic11—21no—
126C4×Dic11C2×D412yes—
127#4318—22no—
128#4318—44no—
129#4318—41no—
130#4318D812yes—
131#4318D812yes—
132C2×C11⋊C8—44no—
133C2×C11⋊C8—41no—
134C2×C11⋊C8C2×D412yes—
135Dic44—21no—
136Dic44C22×C412yes—
137D88—21no—
138D88C22×C412yes—
139#4314—22no—
140#4314—22no—
141#4313—44no—
142C8×D11—44no—
143C11×C16—22no—
144C11⋊C16C22×C411yescharacteristic
145C11⋊C16C22×C411yescharacteristic
146C11⋊C16C22×C411yescharacteristic
147C11⋊C16C22×C411yescharacteristic
148C2×#508—111no—
149#2957—111no—
150#2957—111no—
151#2179—114no—
152#2178—114no—
153C2×#368—111no—
154#2143—111no—
155#2143D1111yescharacteristic, complemented
156#2108—111no—
157C23×C11—41no—
158C23×C11#13511yescharacteristic
159C22×D11—41no—
160Q8×C11—22no—
161Q8×C11—41no—
162D4×C11—22no—
163D4×C11—42no—
164D4×C11—42no—
165D4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11C4×D411yescharacteristic
170C2×C4×C11C4×D411yescharacteristic
171C2×C4×C11C2×D811yescharacteristic
172C2×C4×C11C2×D811yescharacteristic
173C2×C4×C11#13511yescharacteristic
174C2×C4×C11C22×D411yescharacteristic
175C22⋊D11—42no—
176C22⋊D11—42no—
177C2×Dic11—22no—
178C2×Dic11—41no—
179D44—22no—
180D44—41no—
181C4×D11—42no—
182C4×D11—42no—
183Dic22—22no—
184Dic22—41no—
185C8×C11—42no—
186C8×C11C4×D411yescharacteristic
187C8×C11C4×D411yescharacteristic
188C8×C11C23×C411yescharacteristic
189C8×C11C2×#4111yescharacteristic
190C11⋊C8—42no—
191C11⋊C8C2×D814yes—
192C2×#135—111no—
193C2×#135C2×D1111yescharacteristic
194#568—221no—
195#568—221no—
196#508—112no—
197#508—112no—
198#508—112no—
199#508—112no—
200C2×Q32—111no—
201C2×SD32—111no—
202C2×SD32—111no—
203C2×D16—111no—
204C2×M32C2×D1111yescharacteristic
205C22×C16—111no—
206#444—222no—
207#444—222no—
208#443—114no—
209#443—114no—
210C2×#108—111no—
211C2×#108C2×D1111yescharacteristic
212#421—221no—
213#421—221no—
214#405—111no—
215#368—112no—
216#368—112no—
217#359—114no—
218#359C2×D1114yescomplemented
219#346—112no—
220C4×C16—112no—
221C22×C11—41no—
222C22×C11—42no—
223C22×C11—161no—
224C22×C11C4×D811yescharacteristic
225C22×C11C4×D811yescharacteristic
226C22×C11C2×#13511yescharacteristic
227C2×D11—42no—
228C2×D11—161no—
229C4×C11—42no—
230C4×C11C4×D811yescharacteristic
231C4×C11C4×D811yescharacteristic
232C4×C11C2×C4×D411yescharacteristic
233C4×C11C22×D811yescharacteristic
234Dic11—42no—
235Dic11—42no—
236C2×#41—21no—
237C2×#41—221no—
238#135—21no—
239#135—21no—
240#135—112no—
241#135—112no—
242#135—221no—
243#135—221no—
244#135C4×D1112yes—
245#135C22×D1112yes—
246C2×Q16—111no—
247C2×Q16C4×D1111yescharacteristic
248C2×SD16—21no—
249C2×SD16—221no—
250C2×D8—111no—
251C2×D8C4×D1111yescharacteristic
252#131—224no—
253#131—224no—
254#131—442no—
255#131—442no—
256C2×M16—21no—
257C2×M16—111no—
258C2×M16—221no—
259C2×M16—442no—
260C2×M16—442no—
261C22×C8C22×D1111yescharacteristic
262#117—111no—
263Q32—112no—
264Q32—112no—
265SD32—112no—
266SD32—112no—
267SD32—112no—
268SD32—112no—
269D16—112no—
270D16—112no—
271M32—21no—
272M32—21no—
273C2×C16—111no—
274C2×C16—111no—
275C2×C16—111no—
276C2×C16—111no—
277C2×C16—111no—
278C2×C16—111no—
279C2×C16C22×D1112yes—
280#108—21no—
281#108—112no—
282#108—221no—
283#108C22×D1112yes—
284#104—224no—
285#104—224no—
286#97—112no—
287C4×C8—112no—
288C2×C11—21no—
289C2×C11—21no—
290C2×C11—21no—
291C2×C11—82no—
292C2×C11C2×C4×D811yescharacteristic
293D11—82no—
294#41—22no—
295#41—22no—
296#41—41no—
297#41—41no—
298#41—222no—
299#41—222no—
300#41—441no—
301#41—441no—
302C2×Q8—21no—
303C2×Q8—221no—
304C2×D4—21no—
305C2×D4—41no—
306C2×D4—221no—
307C2×D4—441no—
308C22×C4—41no—
309C22×C4—441no—
310C22×C4D4×D1111yescharacteristic
311Q16—21no—
312Q16—112no—
313Q16—221no—
314Q16C2×C4×D1112yes—
315SD16—22no—
316SD16—22no—
317SD16—222no—
318SD16—222no—
319D8—21no—
320D8—112no—
321D8—221no—
322D8C2×C4×D1112yes—
323M16—22no—
324M16—41no—
325M16—112no—
326M16—112no—
327M16—222no—
328M16—444no—
329M16—444no—
330M16—441no—
331C2×C8—41no—
332C2×C8—112no—
333C2×C8—444no—
334C2×C8—444no—
335C2×C8—441no—
336C2×C8C2×C4×D1111yescharacteristic
337C2×C8C2×C4×D1111yescharacteristic
338C2×C8D4×D1111yescharacteristic
339C2×C8#434111yescharacteristic
340C2×C8#434111yescharacteristic
341C2×C8C23×D1111yescharacteristic
342C4⋊C4—221no—
343C22⋊C4—221no—
344C42—112no—
345C16—22no—
346C16—111no—
347C16—111no—
348C16—111no—
349C16—111no—
350C11#3346511yescharacteristic, complemented, Sylow
351C23—41no—
352C23—441no—
353C23#6696911yescharacteristic
354Q8—22no—
355Q8—41no—
356Q8—222no—
357Q8—441no—
358D4—22no—
359D4—42no—
360D4—42no—
361D4—41no—
362D4—222no—
363D4—442no—
364D4—442no—
365D4—441no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—222no—
370C2×C4—441no—
371C2×C4—442no—
372C2×C4—442no—
373C2×C4(C22⋊D11)⋊C411yescharacteristic
374C2×C4(C22⋊D11)⋊C411yescharacteristic
375C2×C4D8×D1111yescharacteristic
376C2×C4D8×D1111yescharacteristic
377C2×C4#6696911yescharacteristic
378C2×C4C2×D4×D1111yescharacteristic
379C8—42no—
380C8—114no—
381C8—442no—
382C8(C22⋊D11)⋊C411yescharacteristic
383C8(C22⋊D11)⋊C411yescharacteristic
384C8C22×C4×D1111yescharacteristic
385C8C2×#434111yescharacteristic
386C22—41no—
387C22—42no—
388C22—161no—
389C22—442no—
390C22—1761no—
391C22#1062236911yescharacteristic
392C22#1062236911yescharacteristic
393C22C2×#6696911yescharacteristic
394C4—42no—
395C4—442no—
396C4—442no—
397C4#1062236911yescharacteristic
398C4#1062236911yescharacteristic
399C4C2×(C22⋊D11)⋊C411yescharacteristic
400C4C2×D8×D1111yescharacteristic
401C2—21no—
402C2—21no—
403C2—21no—
404C2—82no—
405C2—882no—
406C2C2×#1062236911yescharacteristic
subgroupG/H
centerC4C2×D8×D11
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC11×#2143C2
socleC2×C11C2×C4×D8
prime radicalC2×#10622807C2
cosocleC2×C8×C11C24
hypercenter#2143D11
hypocenterC11#33465
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #2143

Complements

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

NH ≅ G/Ntype
2. #13077533C2semidirect
3. #13077532C2semidirect
4. #13070499C2semidirect
5. #13070494C2semidirect
6. C2×#10622131C2semidirect
7. #13070345C2semidirect
8. #13070215C2semidirect
9. C11×#2143C2semidirect
18. #10622809C22semidirect
19. #10622807C4semidirect
20. #10622807C4semidirect
23. C2×#66893C4semidirect
24. C2×#66892C4semidirect
25. C2×#66891C4semidirect
26. C2×#66890C4semidirect
31. #10622508C22semidirect
33. C11×#359C22semidirect
34. #10622148C22semidirect
35. #10622140C22semidirect
36. C16×Dic11C22semidirect
37. #10622131C22semidirect
38. #10622131C22semidirect
155. #2143D11semidirect
218. #359C2×D11semidirect
350. C11#33465semidirect

Maximal subgroups

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

subgroupindex
C2×#106228072
#130775332
#130775322
#130704992
#130704942
C2×#106221312
#130703452
#130702152
C11×#21432
#3346511