Finite Group Databasebeta

← #14909753

Subgroups — #14909753

Order 2816.

598 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#13079197C211yesmaximal, characteristic, complemented
2C2×#10622804C211yesmaximal, characteristic
3#13070884C212yesmaximal, complemented
4#13070854C212yesmaximal, complemented
5#13070681C212yesmaximal, complemented
6#13070680C212yesmaximal, complemented
7#13070550C211yesmaximal, characteristic, complemented
8#13070547C211yesmaximal, characteristic
9#13070544C211yesmaximal, characteristic
10#13070416C211yesmaximal, characteristic, complemented
11C11×#2188C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C2×#67000—21no—
14C22×#4325—21no—
15C22×D88C2211yescharacteristic
16#10623153—21no—
17C2×C11×Q32C2212yescomplemented
18C11×#467C2211yescharacteristic
19#10622804—21no—
20#10622804—21no—
21#10622804C2212yes—
22#10622804C2212yes—
23Q16×Dic11C2211yescharacteristic, complemented
24#10622794C2211yescharacteristic, complemented
25C2×#66893C2212yescomplemented
26C2×#66892C2212yes—
27#10622729C2211yescharacteristic
28C2×C8×Dic11C2211yescharacteristic
29#10622664—21no—
30C2×#66864C2212yes—
31#10622487C2211yescharacteristic, complemented
32#10622486C2211yescharacteristic, complemented
33#10622405—21no—
34#10622403—21no—
35C11×#358C2212yescomplemented
36C11×C22⋊C16C2211yescharacteristic
37#10622202C2212yescomplemented
38C22⋊(C11⋊C16)C2211yescharacteristic
39#10622147C2212yes—
40#10622140C2212yescomplemented
41Dic11⋊C16C2212yescomplemented
42#10622129C2212yes—
43C22×Q8×C11—21no—
44C22×D44—21no—
45C2×C11×Q16—21no—
46C2×C11×Q16—42no—
47C2×C11×Q16C2311yescharacteristic
48C2×C11×Q16C2312yes—
49C22×C8×C11C2311yescharacteristic
50C11×C22⋊Q8—21no—
51#67000—22no—
52#67000—22no—
53#67000—41no—
54#67000—41no—
55Q8×Dic11—21no—
56#66997—21no—
57C2×#4326—21no—
58C2×#4325—22no—
59C2×#4325—22no—
60C2×#4325—44no—
61C2×(C2×D11)⋊C4—41no—
62C2×(C2×D11)⋊C4—41no—
63#66977—21no—
64C2×C4×Dic11D411yescharacteristic
65C22×C11⋊C8D411yescharacteristic
66C2×Dic44C2311yescharacteristic
67C2×D88—21no—
68C2×D88—42no—
69C2×D88C2312yes—
70#66942—41no—
71#66941—21no—
72#66940—21no—
73#66940—41no—
74#66931—41no—
75#66930—41no—
76C11×Q32—42no—
77C2×C11×C16C2312yes—
78C11×#107C2311yescharacteristic
79C11×#103—21no—
80#66899—21no—
81#66893—42no—
82#66892—42no—
83#66882C2311yescharacteristic
84#66880—21no—
85C8×Dic11D411yescharacteristic
86C8×Dic11D411yescharacteristic
87C8×Dic11C2311yescharacteristic
88C8×Dic11C2311yescharacteristic
89C2×C11⋊C16C2312yes—
90#66874—21no—
91#66871—21no—
92#66864—42no—
93#33781—111nomaximal, Sylow
94C23×D11—41no—
95C2×Q8×C11—21no—
96C2×Q8×C11—22no—
97C2×Q8×C11—42no—
98C2×Q8×C11—42no—
99C2×Q8×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11C2×D411yescharacteristic
102C22×Dic11D811yescharacteristic
103C22×Dic11D811yescharacteristic
104C2×D44—22no—
105C2×D44—42no—
106C2×D44—42no—
107C2×D44—41no—
108C2×Dic22—21no—
109C2×Dic22—41no—
110C11×Q16—22no—
111C11×Q16—22no—
112C11×Q16—22no—
113C11×Q16—42no—
114C2×C8×C11—22no—
115C2×C8×C11C2×D411yescharacteristic
116C2×C8×C11C2411yescharacteristic
117C11×C4⋊C4—21no—
118C11×C4⋊C4—41no—
119C11×C22⋊C4—41no—
120C22⋊Dic11—41no—
121#4326—42no—
122#4325—44no—
123#4325—44no—
124(C2×D11)⋊C4—42no—
125(C2×D11)⋊C4—42no—
126(C2×D11)⋊C4—42no—
127(C2×D11)⋊C4—42no—
128C4⋊Dic11—21no—
129C4⋊Dic11—41no—
130Dic11⋊C4—41no—
131Dic11⋊C4—41no—
132Dic11⋊C4—41no—
133Dic11⋊C4—41no—
134Dic11⋊C4—41no—
135C4×Dic11—41no—
136C4×Dic11—41no—
137C4×Dic11D811yescharacteristic
138C4×Dic11D811yescharacteristic
139C4×Dic11C2×D411yescharacteristic
140C4×Dic11C2×D411yescharacteristic
141C2×C11⋊C8—22no—
142C2×C11⋊C8C2×D411yescharacteristic
143C2×C11⋊C8C2×D411yescharacteristic
144Dic44—22no—
145D88—22no—
146D88—22no—
147D88—42no—
148C11×C16—22no—
149C11⋊C16—22no—
150#3170—111no—
151C2×#495—111no—
152#2251—112no—
153#2243—112no—
154#2211—112no—
155#2211—112no—
156#2188—111no—
157#2188D1111yescharacteristic, complemented
158#2187—111no—
159#2187—111no—
160#2163—111no—
161C23×C11C2×D811yescharacteristic
162C22×D11—42no—
163C22×D11—82no—
164C22×D11—82no—
165C22×D11—82no—
166Q8×C11—42no—
167Q8×C11—41no—
168Q8×C11—42no—
169Q8×C11—41no—
170Q8×C11—82no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—82no—
177C2×C4×C11C2×D811yescharacteristic
178C2×C4×C11C22×D411yescharacteristic
179C2×Dic11—22no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11C2×D811yescharacteristic
184C2×Dic11C2×D811yescharacteristic
185C2×Dic11C2×D811yescharacteristic
186C2×Dic11C2×D811yescharacteristic
187D44—42no—
188D44—42no—
189D44—82no—
190Dic22—41no—
191Dic22—41no—
192Dic22—82no—
193C8×C11—21no—
194C8×C11H(5,𝔽2)12yes—
195C11⋊C8—21no—
196C11⋊C8AGL(1,ℤ/8)12yes—
197C22×Q16C2×D1111yescharacteristic
198C22×SD16—221no—
199C22×D8—111no—
200#533—221no—
201C2×#124—221no—
202C2×Q32—112no—
203C2×Q32C2×D1112yescomplemented
204C2×SD32—112no—
205C2×SD32—112no—
206#500—111no—
207#495—112no—
208#495—112no—
209#495—221no—
210#495—221no—
211#494—111no—
212#487—221no—
213#467—111no—
214#467—221no—
215#467C2×D1111yescharacteristic
216C4×Q16—111no—
217C4×Q16—111no—
218C4×Q16—221no—
219C2×C4×C8—111no—
220C4⋊C16—112no—
221#358—112no—
222#358C2×D1112yescomplemented
223#357—112no—
224#357—112no—
225C22⋊C16—111no—
226C22⋊C16C2×D1111yescharacteristic
227#346—112no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11#51012yes—
231C22×C11C22×D811yescharacteristic
232C2×D11—82no—
233C2×D11—82no—
234C2×D11—82no—
235C2×D11—164no—
236C4×C11—21no—
237C4×C11—81no—
238C4×C11—82no—
239C4×C11—81no—
240C4×C11#53511yescharacteristic
241C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
242Dic11—21no—
243Dic11—21no—
244Dic11—21no—
245Dic11—21no—
246Dic11—81no—
247Dic11—81no—
248C22×Q8—21no—
249C22×D4—221no—
250C2×Q16—21no—
251C2×Q16—42no—
252C2×Q16—111no—
253C2×Q16—221no—
254C2×Q16C22×D1112yes—
255C2×Q16C22×D1111yescharacteristic
256C2×SD16—222no—
257C2×SD16—222no—
258C2×SD16—444no—
259C2×D8—112no—
260C2×D8—221no—
261C2×D8—442no—
262C22×C8—111no—
263C22×C8C22×D1111yescharacteristic
264C4⋊Q8—221no—
265C4⋊Q8—221no—
266#125—441no—
267#124—222no—
268#124—222no—
269#124—441no—
270#124—441no—
271C22⋊Q8—21no—
272C22⋊Q8—221no—
273C22⋊Q8—441no—
274C4×Q8—221no—
275C4×Q8—221no—
276C4×Q8—441no—
277#117—441no—
278C2×C22⋊C4—441no—
279C2×C22⋊C4—441no—
280C2×C42—111no—
281Q32—42no—
282Q32—442no—
283SD32—442no—
284SD32—442no—
285C2×C16—112no—
286C2×C16C22×D1112yes—
287#107—111no—
288#107—221no—
289#107C22×D1111yescharacteristic
290#103—21no—
291#103—221no—
292#103—221no—
293#103—221no—
294C4×C8—111no—
295C4×C8—111no—
296C4×C8—111no—
297C4×C8—111no—
298C2×C11—22no—
299C2×C11#320511yescharacteristic
300C2×C11C2×#51011yescharacteristic
301C2×C11#341411yescharacteristic
302D11—162no—
303C24—441no—
304C2×Q8—21no—
305C2×Q8—22no—
306C2×Q8—42no—
307C2×Q8—42no—
308C2×Q8—41no—
309C2×Q8—221no—
310C2×Q8—441no—
311C2×D4—222no—
312C2×D4—442no—
313C2×D4—442no—
314C2×D4—441no—
315C22×C4—41no—
316C22×C4—111no—
317C22×C4—111no—
318C22×C4D4×D1111yescharacteristic
319Q16—22no—
320Q16—22no—
321Q16—22no—
322Q16—42no—
323Q16—222no—
324Q16—442no—
325SD16—444no—
326SD16—444no—
327D8—222no—
328D8—222no—
329D8—442no—
330C2×C8—22no—
331C2×C8—111no—
332C2×C8—111no—
333C2×C8—222no—
334C2×C8D4×D1111yescharacteristic
335C2×C8C23×D1111yescharacteristic
336C4⋊C4—21no—
337C4⋊C4—41no—
338C4⋊C4—221no—
339C4⋊C4—441no—
340C4⋊C4—441no—
341C4⋊C4—441no—
342C4⋊C4—441no—
343C4⋊C4—441no—
344C4⋊C4—441no—
345C22⋊C4—41no—
346C22⋊C4—442no—
347C22⋊C4—442no—
348C22⋊C4—442no—
349C22⋊C4—442no—
350C22⋊C4—441no—
351C42—111no—
352C42—111no—
353C42—111no—
354C42—111no—
355C42—441no—
356C42—441no—
357C16—22no—
358C16—222no—
359C11#3378111yescharacteristic, complemented, Sylow
360C23—442no—
361C23—882no—
362C23—882no—
363C23—882no—
364C23D8×D1111yescharacteristic
365Q8—42no—
366Q8—41no—
367Q8—42no—
368Q8—41no—
369Q8—82no—
370Q8—441no—
371Q8—441no—
372Q8—882no—
373D4—442no—
374D4—442no—
375D4—882no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—82no—
382C2×C4—111no—
383C2×C4—111no—
384C2×C4—111no—
385C2×C4—111no—
386C2×C4—222no—
387C2×C4—441no—
388C2×C4—441no—
389C2×C4—441no—
390C2×C4D8×D1111yescharacteristic
391C2×C4C2×D4×D1111yescharacteristic
392C8—21no—
393C8—112no—
394C8—221no—
395C8#6703712yes—
396C22—21no—
397C22—21no—
398C22—882no—
399C22—882no—
400C22—882no—
401C22—1764no—
402C22#1062253112yes—
403C22C2×D8×D1111yescharacteristic
404C4—21no—
405C4—81no—
406C4—82no—
407C4—81no—
408C4—221no—
409C4—221no—
410C4—221no—
411C4—221no—
412C4—881no—
413C4—881no—
414C4#1062312311yescharacteristic
415C4D11×AGL(1,ℤ/8)11yescharacteristic
416C2—22no—
417C2—1762no—
418C2#1307953211yescharacteristic
419C2C2×#1062253111yescharacteristic
420C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2188C2
socleC22×C11C22×D8
prime radicalC22×D88C22
hypercenter#2188D11
hypocenterC11#33781
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2188

Complements

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

NH ≅ G/Ntype
1. #13079197C2semidirect
3. #13070884C2semidirect
4. #13070854C2semidirect
5. #13070681C2semidirect
6. #13070680C2semidirect
7. #13070550C2semidirect
10. #13070416C2semidirect
11. C11×#2188C2semidirect
17. C2×C11×Q32C22semidirect
23. Q16×Dic11C22semidirect
24. #10622794C22semidirect
25. C2×#66893C22semidirect
31. #10622487C22semidirect
32. #10622486C22semidirect
35. C11×#358C22semidirect
37. #10622202C22semidirect
40. #10622140C22semidirect
41. Dic11⋊C16C22semidirect
157. #2188D11semidirect
203. C2×Q32C2×D11semidirect
222. #358C2×D11semidirect
359. C11#33781semidirect

Maximal subgroups

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

subgroupindex
#130791972
C2×#106228042
#130708842
#130708542
#130706812
#130706802
#130705502
#130705472
#130705442
#130704162
C11×#21882
#3378111