Finite Group Databasebeta

← #14907010

Subgroups — #14907010

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622520C211yesmaximal, characteristic, complemented
2C2×#10622753C211yesmaximal, characteristic, complemented
3#13077517C211yesmaximal, characteristic
4#13070455C214yesmaximal, complemented
5#13070450C214yesmaximal, complemented
6#13070381C211yesmaximal, characteristic, complemented
7#13070243C211yesmaximal, characteristic, complemented
8#13070215C211yesmaximal, characteristic, complemented
9C11×#2117C211yesmaximal, characteristic, complemented
10C2×C11×#131C2211yescharacteristic
11#10623353C411yescharacteristic
12C2×#66954C2211yescharacteristic
13C2×C11×M32C2211yescharacteristic
14C2×C11×M32C2211yescharacteristic
15#10622849C411yescharacteristic
16#10622758C414yes—
17#10622757C2214yes—
18#10622753—21no—
19#10622753—21no—
20#10622753C2212yescomplemented
21#10622753C2212yescomplemented
22#10622752C411yescharacteristic
23#10622737C411yescharacteristic
24#10622714C2211yescharacteristic
25C2×#66876—21no—
26C2×#66876C2211yescharacteristic
27C22×C11⋊C16—21no—
28C22×C11⋊C16C2211yescharacteristic
29#10622520—21no—
30#10622520—21no—
31#10622520C2212yescomplemented
32#10622520C2212yescomplemented
33C2×#66862—21no—
34C2×C16×D11—21no—
35C11×#350C2214yescomplemented
36#10622149C2214yescomplemented
37#10622146C2214yescomplemented
38#10622140C2212yescomplemented
39C16×Dic11C2212yescomplemented
40C2×C11×#41C2×C411yescharacteristic
41C2×#4339C2×C411yescharacteristic
42C11×#131—21no—
43C11×#131—21no—
44C11×#131C2×C412yes—
45C11×#131C2312yes—
46C2×C11×M16—21no—
47C2×C11×M16C2×C411yescharacteristic
48C22×C8×C11—21no—
49C22×C8×C11C2311yescharacteristic
50#67004C812yes—
51#67003C2×C414yes—
52#67002C812yes—
53#66995C812yes—
54#66985C812yes—
55#66979C2×C411yescharacteristic
56C2×#4318C2×C411yescharacteristic
57C2×#4318C2×C411yescharacteristic
58#66954—21no—
59#66954—21no—
60#66954C2×C412yes—
61#66954C2312yes—
62C2×#4313—21no—
63C2×C8×D11—21no—
64C11×M32—21no—
65C11×M32—21no—
66C11×M32—21no—
67C11×M32C2312yes—
68C2×C11×C16—21no—
69C2×C11×C16C2312yes—
70#66901C2×C414yes—
71#66889C2×C414yes—
72#66886C2×C414yes—
73#66879C2×C412yes—
74C8×Dic11C2312yes—
75#66876—21no—
76#66876—22no—
77#66876—22no—
78#66876C2312yes—
79C2×C11⋊C16—21no—
80C2×C11⋊C16—22no—
81C2×C11⋊C16—22no—
82C2×C11⋊C16D411yescharacteristic
83C2×C11⋊C16D411yescharacteristic
84C2×C11⋊C16D411yescharacteristic
85C2×C11⋊C16D411yescharacteristic
86C2×C11⋊C16C2311yescharacteristic
87C2×C11⋊C16C2311yescharacteristic
88#66862—22no—
89#66862—22no—
90C16×D11—22no—
91C16×D11—22no—
92#33441—111nomaximal, Sylow
93C11×#41—21no—
94C11×#41—21no—
95C11×#41C2×C812yes—
96C11×#41C22×C412yes—
97C2×Q8×C11C2×C811yescharacteristic
98C2×D4×C11—21no—
99C2×D4×C11C2×C811yescharacteristic
100C22×C4×C11—21no—
101C22×C4×C11C22×C411yescharacteristic
102C2×C22⋊D11—21no—
103#4339—21no—
104#4339—21no—
105#4339C2×C812yes—
106#4339C22×C412yes—
107C2×D44C2×C811yescharacteristic
108C2×C4×D11—21no—
109C2×Dic22C2×C811yescharacteristic
110C11×M16—22no—
111C11×M16—22no—
112C11×M16—21no—
113C11×M16C22×C412yes—
114C2×C8×C11—22no—
115C2×C8×C11—22no—
116C2×C8×C11—21no—
117C2×C8×C11C22×C411yescharacteristic
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11#4111yescharacteristic
121C2×C8×C11#4111yescharacteristic
122C2×C8×C11C2411yescharacteristic
123C22⋊Dic11—21no—
124#4326C2×C814yes—
125#4325C2×C814yes—
126#4324C2×C814yes—
127#4323C2×C814yes—
128C4⋊Dic11—21no—
129C4×Dic11C22×C412yes—
130#4318—21no—
131#4318C2×C812yes—
132#4318C2×C812yes—
133#4318C22×C412yes—
134C2×C11⋊C8—21no—
135C2×C11⋊C8C22×C412yes—
136#4313—22no—
137#4313—22no—
138C8×D11—22no—
139C8×D11—22no—
140C11×C16—22no—
141C11×C16—22no—
142C11⋊C16—22no—
143C11⋊C16C2×D411yescharacteristic
144C11⋊C16C2×D411yescharacteristic
145C11⋊C16C2×D411yescharacteristic
146C11⋊C16C2×D411yescharacteristic
147C2×#504—111no—
148C2×#504—111no—
149#2955—111no—
150#2171—114no—
151#2170—114no—
152#2153—111no—
153#2117—111no—
154#2117D1111yescharacteristic, complemented
155#2108—111no—
156C23×C11—21no—
157C23×C11#13111yescharacteristic
158C22×D11—21no—
159Q8×C11—21no—
160Q8×C11C22×C812yes—
161D4×C11—22no—
162D4×C11—22no—
163D4×C11—21no—
164D4×C11C22×C812yes—
165C2×C4×C11—21no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11C4×D411yescharacteristic
169C2×C4×C11C4×D411yescharacteristic
170C2×C4×C11C22×C811yescharacteristic
171C2×C4×C11C22×C811yescharacteristic
172C2×C4×C11#13111yescharacteristic
173C2×C4×C11C23×C411yescharacteristic
174C22⋊D11—22no—
175C22⋊D11—22no—
176C2×Dic11—21no—
177C2×Dic11—22no—
178D44—21no—
179D44C22×C812yes—
180C4×D11—22no—
181C4×D11—22no—
182Dic22—21no—
183Dic22C22×C812yes—
184C8×C11—22no—
185C8×C11C4×D411yescharacteristic
186C8×C11C4×D411yescharacteristic
187C8×C11C22×D411yescharacteristic
188C8×C11C2×#4111yescharacteristic
189C11⋊C8—22no—
190C11⋊C8C22×C814yes—
191#575—111no—
192C2×#131—111no—
193C2×#131C2×D1111yescharacteristic
194#504—112no—
195#504—112no—
196#504—112no—
197#504—112no—
198#504—221no—
199#504—221no—
200#504—221no—
201#504—221no—
202C2×M32—111no—
203C2×M32—221no—
204C2×M32—221no—
205C2×M32C2×D1111yescharacteristic
206C2×M32C2×D1111yescharacteristic
207C22×C16—111no—
208C22×C16—221no—
209C22×C16—221no—
210#444—114no—
211#443—114no—
212#430—111no—
213#421—111no—
214#421—111no—
215#405—111no—
216#364—114no—
217#350—114no—
218#350C2×D1114yescomplemented
219#346—112no—
220C4×C16—112no—
221C22×C11—22no—
222C22×C11—41no—
223C22×C11—42no—
224C22×C11C8×D411yescharacteristic
225C22×C11C8×D411yescharacteristic
226C22×C11C2×#13111yescharacteristic
227C2×D11—22no—
228C2×D11—42no—
229C4×C11—22no—
230C4×C11C8×D411yescharacteristic
231C4×C11C8×D411yescharacteristic
232C4×C11C2×C4×D411yescharacteristic
233C4×C11C23×C811yescharacteristic
234Dic11—22no—
235Dic11—42no—
236C2×#41—111no—
237C2×#41C4×D1111yescharacteristic
238#137—112no—
239#137—112no—
240AGL(1,ℤ/8)—112no—
241AGL(1,ℤ/8)—112no—
242#135—114no—
243#131—21no—
244#131—21no—
245#131—112no—
246#131—112no—
247#131—221no—
248#131—221no—
249#131C4×D1112yes—
250#131C22×D1112yes—
251C2×M16—21no—
252C2×M16—111no—
253C2×M16—111no—
254C2×M16—221no—
255C2×M16C4×D1111yescharacteristic
256C22×C8—21no—
257C22×C8—221no—
258C22×C8C22×D1111yescharacteristic
259#117—111no—
260M32—21no—
261M32—21no—
262M32—21no—
263M32—112no—
264M32—222no—
265M32—222no—
266M32—222no—
267M32—222no—
268M32—221no—
269M32C22×D1112yes—
270C2×C16—21no—
271C2×C16—111no—
272C2×C16—111no—
273C2×C16—111no—
274C2×C16—111no—
275C2×C16—111no—
276C2×C16—111no—
277C2×C16—222no—
278C2×C16—222no—
279C2×C16—222no—
280C2×C16—222no—
281C2×C16—221no—
282C2×C16C22×D1112yes—
283#108—114no—
284#104—114no—
285#104—114no—
286#97—112no—
287C4×C8—112no—
288C2×C11—21no—
289C2×C11—21no—
290C2×C11—21no—
291C2×C11—42no—
292C2×C11C2×C8×D411yescharacteristic
293D11—42no—
294#41—21no—
295#41—21no—
296#41—112no—
297#41—112no—
298#41—221no—
299#41—221no—
300#41C8×D1112yes—
301#41C2×C4×D1112yes—
302C2×Q8—111no—
303C2×Q8C8×D1111yescharacteristic
304C2×D4—21no—
305C2×D4—111no—
306C2×D4—221no—
307C2×D4C8×D1111yescharacteristic
308C22×C4—21no—
309C22×C4—221no—
310C22×C4C2×C4×D1111yescharacteristic
311Q16—114no—
312SD16—114no—
313SD16—114no—
314D8—114no—
315M16—21no—
316M16—22no—
317M16—22no—
318M16—112no—
319M16—112no—
320M16—112no—
321M16—221no—
322M16—222no—
323M16—222no—
324M16C2×C4×D1112yes—
325C2×C8—21no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—112no—
329C2×C8—221no—
330C2×C8—222no—
331C2×C8—222no—
332C2×C8C2×C4×D1111yescharacteristic
333C2×C8D4×D1111yescharacteristic
334C2×C8D4×D1111yescharacteristic
335C2×C8#434111yescharacteristic
336C2×C8#434111yescharacteristic
337C2×C8C23×D1111yescharacteristic
338C4⋊C4—221no—
339C22⋊C4—221no—
340C42—112no—
341C16—22no—
342C16—22no—
343C16—111no—
344C16—111no—
345C16—111no—
346C16—111no—
347C16—222no—
348C11#3344111yescharacteristic, complemented, Sylow
349C23—21no—
350C23—221no—
351C23#6696011yescharacteristic
352Q8—21no—
353Q8—112no—
354Q8—221no—
355Q8C2×C8×D1112yes—
356D4—22no—
357D4—22no—
358D4—21no—
359D4—112no—
360D4—222no—
361D4—222no—
362D4—221no—
363D4C2×C8×D1112yes—
364C2×C4—21no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—221no—
368C2×C4—222no—
369C2×C4—222no—
370C2×C4—222no—
371C2×C4(C22⋊D11)⋊C411yescharacteristic
372C2×C4(C22⋊D11)⋊C411yescharacteristic
373C2×C4C2×C8×D1111yescharacteristic
374C2×C4C2×C8×D1111yescharacteristic
375C2×C4#6696011yescharacteristic
376C2×C4C22×C4×D1111yescharacteristic
377C8—22no—
378C8—114no—
379C8—222no—
380C8(C22⋊D11)⋊C411yescharacteristic
381C8(C22⋊D11)⋊C411yescharacteristic
382C8C2×D4×D1111yescharacteristic
383C8C2×#434111yescharacteristic
384C22—22no—
385C22—41no—
386C22—42no—
387C22—222no—
388C22—442no—
389C22(C22⋊D11)⋊C811yescharacteristic
390C22(C22⋊D11)⋊C811yescharacteristic
391C22C2×#6696011yescharacteristic
392C4—22no—
393C4—222no—
394C4—442no—
395C4(C22⋊D11)⋊C811yescharacteristic
396C4(C22⋊D11)⋊C811yescharacteristic
397C4C2×(C22⋊D11)⋊C411yescharacteristic
398C4C22×C8×D1111yescharacteristic
399C2—21no—
400C2—21no—
401C2—21no—
402C2—42no—
403C2—442no—
404C2C2×(C22⋊D11)⋊C811yescharacteristic
subgroupG/H
centerC8C2×D4×D11
commutatorC4×C11C23×C8
FrattiniC2×C8C23×D11
FittingC11×#2117C2
socleC2×C11C2×C8×D4
prime radical#10623353C4
cosocleC2×C8×C11C24
hypercenter#2117D11
hypocenterC11#33441
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2117

Complements

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

NH ≅ G/Ntype
1. C2×#10622520C2semidirect
2. C2×#10622753C2semidirect
4. #13070455C2semidirect
5. #13070450C2semidirect
6. #13070381C2semidirect
7. #13070243C2semidirect
8. #13070215C2semidirect
9. C11×#2117C2semidirect
20. #10622753C22semidirect
21. #10622753C22semidirect
31. #10622520C22semidirect
32. #10622520C22semidirect
35. C11×#350C22semidirect
36. #10622149C22semidirect
37. #10622146C22semidirect
38. #10622140C22semidirect
39. C16×Dic11C22semidirect
154. #2117D11semidirect
218. #350C2×D11semidirect
348. C11#33441semidirect

Maximal subgroups

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

subgroupindex
C2×#106225202
C2×#106227532
#130775172
#130704552
#130704502
#130703812
#130702432
#130702152
C11×#21172
#3344111