Finite Group Databasebeta

← #14908573

Subgroups — #14908573

Order 2816.

590 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078199C211yesmaximal, characteristic
2C2×#10622493C211yesmaximal, characteristic, complemented
3#13070822C212yesmaximal, complemented
4#13070816C211yesmaximal, characteristic, complemented
5#13070809C212yesmaximal, complemented
6#13070802C211yesmaximal, characteristic, complemented
7#13070796C211yesmaximal, characteristic, complemented
8#13070399C212yesmaximal, complemented
9#13070322C212yesmaximal, complemented
10D11×C22⋊C16C211yesmaximal, characteristic, complemented
11C11×#2235C211yesmaximal, characteristic, complemented
12C2×#66972C2211yescharacteristic
13C22×C8×D11C2211yescharacteristic
14#10623158—21no—
15C2×#66945—21no—
16C11×#467C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18#10622801C2211yescharacteristic
19#10622728C2211yescharacteristic
20C2×#66882C2211yescharacteristic
21#10622661—21no—
22C2×#66872—21no—
23C2×C16×D11C2212yes—
24#10622496C2211yescharacteristic
25#10622493—21no—
26#10622493—21no—
27#10622493C2211yescharacteristic
28#10622493C2212yes—
29#10622493C2212yes—
30#10622420—21no—
31#10622417—21no—
32C11×#367C2212yescomplemented
33C11×#358C2212yescomplemented
34C11×C22⋊C16C2211yescharacteristic
35#10622202C2212yescomplemented
36C22⋊(C11⋊C16)C2211yescharacteristic
37#10622147C2212yescomplemented
38(C2×D11)⋊C16C2212yes—
39#10622143C2212yescomplemented
40#10622129C2212yescomplemented
41#10622127C2212yescomplemented
42#10622127C2212yescomplemented
43C2×#4343—21no—
44C22×C4×D11D411yescharacteristic
45C2×C11×Q16C2311yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C11×C22⋊Q8—21no—
48C2×C11×C4⋊C4—21no—
49#66999—21no—
50C2×#4325—21no—
51#66983—21no—
52C2×(C2×D11)⋊C4—41no—
53C2×C4⋊Dic11—21no—
54C2×C4×Dic11—41no—
55C22×C11⋊C8D411yescharacteristic
56#66972—24no—
57C2×D88C2311yescharacteristic
58C2×C8×D11—24no—
59C2×C8×D11D411yescharacteristic
60C2×C8×D11D411yescharacteristic
61C2×C8×D11C2311yescharacteristic
62C2×C8×D11C2311yescharacteristic
63#66948—21no—
64#66947—41no—
65#66946—41no—
66#66945—22no—
67#66945—22no—
68#66945—21no—
69#66945—41no—
70#66945—41no—
71#66935—41no—
72(C22⋊D11)⋊C4—41no—
73C2×C11×C16C2312yes—
74C11×#107—21no—
75C11×#107C2312yes—
76C11×#107C2311yescharacteristic
77C11×#103—21no—
78#66899—21no—
79#66885—21no—
80#66882—21no—
81#66882C2311yescharacteristic
82#66882C2312yes—
83C2×C11⋊C16C2312yes—
84#66873—21no—
85#66872—22no—
86#66872—22no—
87#66872—21no—
88C16×D11—24no—
89#33645—111nomaximal, Sylow
90C23×D11D811yescharacteristic
91C2×Q8×C11—21no—
92C22×C4×C11—41no—
93C22×C4×C11C2×D411yescharacteristic
94C2×C22⋊D11—41no—
95C22×Dic11—41no—
96C22×Dic11D811yescharacteristic
97#4343—42no—
98#4343—42no—
99C2×D44—21no—
100C2×D44—41no—
101C2×D44—41no—
102C2×C4×D11—22no—
103C2×C4×D11—22no—
104C2×C4×D11—41no—
105C2×C4×D11D811yescharacteristic
106C2×C4×D11D811yescharacteristic
107C2×C4×D11C2×D411yescharacteristic
108C2×C4×D11C2×D411yescharacteristic
109C11×Q16—22no—
110C2×C8×C11—22no—
111C2×C8×C11C2×D411yescharacteristic
112C2×C8×C11C2411yescharacteristic
113C11×C4⋊C4—22no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C22⋊C4—41no—
118#4325—42no—
119(C2×D11)⋊C4—41no—
120(C2×D11)⋊C4—41no—
121(C2×D11)⋊C4—41no—
122(C2×D11)⋊C4—42no—
123(C2×D11)⋊C4—42no—
124(C2×D11)⋊C4—41no—
125C4⋊Dic11—22no—
126C4⋊Dic11—21no—
127C4⋊Dic11—41no—
128Dic11⋊C4—41no—
129C4×Dic11—41no—
130C4×Dic11—42no—
131C4×Dic11—42no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8C2×D411yescharacteristic
134C2×C11⋊C8C2×D411yescharacteristic
135D88—22no—
136C8×D11—22no—
137C8×D11—22no—
138C8×D11—22no—
139C8×D11#4114yes—
140C11×C16—22no—
141C11⋊C16—22no—
142#3050—111no—
143C2×#427—111no—
144#2237—112no—
145#2236—111no—
146#2235D1111yescharacteristic, complemented
147#2234—112no—
148#2233—111no—
149#2232—111no—
150#2158—112no—
151#2138—112no—
152C2×C22⋊C16—111no—
153C23×C11C2×D811yescharacteristic
154C22×D11—22no—
155C22×D11—22no—
156C22×D11—41no—
157C22×D11—41no—
158C22×D11C2×D811yescharacteristic
159C22×D11C2×D811yescharacteristic
160Q8×C11—41no—
161Q8×C11—41no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—42no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—82no—
168C2×C4×C11C2×D811yescharacteristic
169C2×C4×C11C22×D411yescharacteristic
170C22⋊D11—82no—
171C2×Dic11—22no—
172C2×Dic11—42no—
173C2×Dic11—41no—
174C2×Dic11—82no—
175C2×Dic11C2×D811yescharacteristic
176C2×Dic11C2×D811yescharacteristic
177D44—41no—
178D44—41no—
179D44—82no—
180D44—82no—
181C4×D11—22no—
182C4×D11—21no—
183C4×D11—21no—
184C4×D11—22no—
185C4×D11—82no—
186C4×D11#12312yes—
187C4×D11#13712yes—
188C8×C11—21no—
189C8×C11C2×#4112yes—
190C11⋊C8—21no—
191C11⋊C8#12312yes—
192C2×#135—111no—
193C23×C8—111no—
194#525—221no—
195C2×#117—221no—
196C22×C16—112no—
197#467—111no—
198#467C2×D1111yescharacteristic
199#466—111no—
200#466—111no—
201#465—221no—
202#465—221no—
203#427—112no—
204#427—112no—
205#427—111no—
206#427—221no—
207#427—221no—
208C2×#107—111no—
209C2×#107C2×D1111yescharacteristic
210C2×#106—221no—
211#416—221no—
212#367—112no—
213#367C2×D1112yescomplemented
214#366—112no—
215#366—112no—
216#358—112no—
217#358C2×D1112yescomplemented
218#357—112no—
219#357—112no—
220C22⋊C16—111no—
221C22⋊C16—112no—
222C22⋊C16C2×D1111yescharacteristic
223C22×C11—21no—
224C22×C11—21no—
225C22×C11#50812yes—
226C22×C11C22×D811yescharacteristic
227C2×D11—21no—
228C2×D11—21no—
229C2×D11—21no—
230C2×D11—21no—
231C2×D11—21no—
232C2×D11—44no—
233C2×D11—81no—
234C2×D11—81no—
235C2×D11—81no—
236C2×D11#48012yes—
237C4×C11—21no—
238C4×C11—81no—
239C4×C11—82no—
240C4×C11—81no—
241C4×C11C2×#12311yescharacteristic
242C4×C11C2×#13711yescharacteristic
243Dic11—21no—
244Dic11—81no—
245Dic11—82no—
246Dic11#48012yes—
247C2×#41—221no—
248C23×C4—111no—
249#135—224no—
250C2×Q16C22×D1111yescharacteristic
251C2×SD16—221no—
252C2×D8—111no—
253C22×C8—111no—
254C22×C8—111no—
255C22×C8—111no—
256C22×C8—111no—
257C22×C8—111no—
258C22×C8—224no—
259C22×C8C22×D1111yescharacteristic
260#123—441no—
261C22⋊Q8—21no—
262C22⋊Q8—221no—
263#121—221no—
264#121—221no—
265#120—441no—
266C4×D4—441no—
267C4×D4—441no—
268#117—222no—
269#117—222no—
270#117—221no—
271#117—441no—
272#117—441no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—221no—
275C2×C22⋊C4—441no—
276C2×C42—441no—
277C2×C16—112no—
278C2×C16—224no—
279C2×C16C22×D1112yes—
280#107—21no—
281#107—112no—
282#107—111no—
283#107—221no—
284#107C22×D1112yes—
285#107C22×D1111yescharacteristic
286#106—222no—
287#106—222no—
288#106—221no—
289#103—21no—
290#103—221no—
291#102—221no—
292#102—221no—
293C2×C11—22no—
294C2×C11C2×#48011yescharacteristic
295C2×C11C2×#50811yescharacteristic
296C2×C11#341411yescharacteristic
297D11—22no—
298D11—41no—
299D11—161no—
300C24—111no—
301#41—442no—
302#41—442no—
303C2×Q8—21no—
304C2×D4—221no—
305C2×D4—441no—
306C2×D4—441no—
307C2×D4—441no—
308C22×C4—41no—
309C22×C4—111no—
310C22×C4—111no—
311C22×C4—111no—
312C22×C4—111no—
313C22×C4—111no—
314C22×C4—222no—
315C22×C4—222no—
316C22×C4—441no—
317C22×C4—441no—
318C22×C4D4×D1111yescharacteristic
319Q16—22no—
320SD16—442no—
321D8—222no—
322C2×C8—22no—
323C2×C8—111no—
324C2×C8—114no—
325C2×C8—111no—
326C2×C8—222no—
327C2×C8—222no—
328C2×C8—222no—
329C2×C8—222no—
330C2×C8D4×D1111yescharacteristic
331C2×C8C23×D1111yescharacteristic
332C4⋊C4—21no—
333C4⋊C4—22no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—221no—
337C4⋊C4—222no—
338C4⋊C4—441no—
339C4⋊C4—441no—
340C22⋊C4—41no—
341C22⋊C4—441no—
342C22⋊C4—442no—
343C22⋊C4—442no—
344C22⋊C4—441no—
345C22⋊C4—441no—
346C22⋊C4—441no—
347C42—442no—
348C42—442no—
349C42—441no—
350C16—22no—
351C16—222no—
352C11#3364511yescharacteristic, complemented, Sylow
353C23—111no—
354C23—111no—
355C23—222no—
356C23—222no—
357C23—441no—
358C23—441no—
359C23D8×D1111yescharacteristic
360Q8—41no—
361Q8—41no—
362D4—441no—
363D4—441no—
364D4—882no—
365D4—882no—
366D4—882no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—82no—
373C2×C4—111no—
374C2×C4—112no—
375C2×C4—112no—
376C2×C4—111no—
377C2×C4—222no—
378C2×C4—222no—
379C2×C4—222no—
380C2×C4—221no—
381C2×C4—221no—
382C2×C4—442no—
383C2×C4—441no—
384C2×C4—882no—
385C2×C4—882no—
386C2×C4D8×D1111yescharacteristic
387C2×C4C2×D4×D1111yescharacteristic
388C8—21no—
389C8—112no—
390C8—221no—
391C8#41×D1112yes—
392C22—21no—
393C22—21no—
394C22—112no—
395C22—221no—
396C22—221no—
397C22—221no—
398C22—221no—
399C22—221no—
400C22—444no—
401C22—881no—
402C22—881no—
403C22—881no—
404C22#1062252912yes—
405C22C2×D8×D1111yescharacteristic
406C4—21no—
407C4—82no—
408C4—81no—
409C4—81no—
410C4—112no—
411C4—221no—
412C4—881no—
413C4—882no—
414C4D11×#12311yescharacteristic
415C4D11×#13711yescharacteristic
416C2—22no—
417C2—222no—
418C2—441no—
419C2—1761no—
420C2D11×#48011yescharacteristic
421C2C2×#1062252911yescharacteristic
422C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2235C2
socleC22×C11C22×D8
prime radical#13078199C2
hypercenter#2235D11
hypocenterC11#33645
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2235

Complements

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

NH ≅ G/Ntype
2. C2×#10622493C2semidirect
3. #13070822C2semidirect
4. #13070816C2semidirect
5. #13070809C2semidirect
6. #13070802C2semidirect
7. #13070796C2semidirect
8. #13070399C2semidirect
9. #13070322C2semidirect
10. D11×C22⋊C16C2semidirect
11. C11×#2235C2semidirect
32. C11×#367C22semidirect
33. C11×#358C22semidirect
35. #10622202C22semidirect
37. #10622147C22semidirect
39. #10622143C22semidirect
40. #10622129C22semidirect
41. #10622127C22semidirect
42. #10622127C22semidirect
146. #2235D11semidirect
213. #367C2×D11semidirect
217. #358C2×D11semidirect
352. C11#33645semidirect

Maximal subgroups

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

subgroupindex
#130781992
C2×#106224932
#130708222
#130708162
#130708092
#130708022
#130707962
#130703992
#130703222
D11×C22⋊C162
C11×#22352
#3364511