Finite Group Databasebeta

← #14909721

Subgroups — #14909721

Order 2816.

608 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079187C211yesmaximal, characteristic, complemented
2C2×#10622804C211yesmaximal, characteristic, complemented
3#13070878C212yesmaximal, complemented
4#13070849C212yesmaximal, complemented
5#13070680C212yesmaximal, complemented
6#13070674C212yesmaximal, complemented
7#13070544C211yesmaximal, characteristic, complemented
8#13070533C211yesmaximal, characteristic, complemented
9#13070530C211yesmaximal, characteristic
10#13070412C211yesmaximal, characteristic, complemented
11C11×#2188C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C2×#67000—21no—
14C22×#4325—21no—
15C22×D88C2211yescharacteristic
16#10623155—21no—
17C2×C11×Q32C2212yescomplemented
18C11×#467C2211yescharacteristic
19#10622804—21no—
20#10622804—21no—
21#10622804C2212yes—
22#10622804C2212yes—
23#10622804C2211yescharacteristic, complemented
24Q16×Dic11C2211yescharacteristic, complemented
25C2×#66892C2212yes—
26C2×#66892C2212yescomplemented
27#10622728C2211yescharacteristic
28C2×C8×Dic11C2211yescharacteristic
29#10622661—21no—
30C2×D176C2212yes—
31#10622491C2211yescharacteristic, complemented
32#10622485C2211yescharacteristic, complemented
33#10622413—21no—
34#10622401—21no—
35C11×#358C2212yescomplemented
36C11×C22⋊C16C2211yescharacteristic
37#10622202C2212yescomplemented
38C22⋊(C11⋊C16)C2211yescharacteristic
39#10622147C2212yes—
40Dic11⋊C16C2212yescomplemented
41C16×Dic11C2212yescomplemented
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—21no—
54#67000—41no—
55#67000—41no—
56Q8×Dic11—21no—
57C2×#4325—22no—
58C2×#4325—22no—
59C2×#4325—21no—
60C2×#4325—44no—
61#66983—21no—
62C2×(C2×D11)⋊C4—41no—
63C2×(C2×D11)⋊C4—41no—
64C2×C4×Dic11D411yescharacteristic
65C22×C11⋊C8D411yescharacteristic
66C2×D88—21no—
67C2×D88—42no—
68C2×D88C2311yescharacteristic
69C2×D88C2312yes—
70#66951—41no—
71#66946—21no—
72#66945—41no—
73#66943—21no—
74#66939—41no—
75(C22⋊D11)⋊C4—41no—
76C11×Q32—42no—
77C2×C11×C16C2312yes—
78C11×#107C2311yescharacteristic
79C11×#103—21no—
80#66899—21no—
81#66892—42no—
82#66892—42no—
83#66885—21no—
84#66882C2311yescharacteristic
85C8×Dic11D411yescharacteristic
86C8×Dic11D411yescharacteristic
87C8×Dic11C2311yescharacteristic
88C8×Dic11C2311yescharacteristic
89C2×C11⋊C16C2312yes—
90#66873—21no—
91#66872—21no—
92D176—42no—
93#33777—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
102C2×C22⋊D11—41no—
103C22×Dic11D811yescharacteristic
104C22×Dic11D811yescharacteristic
105C2×D44—21no—
106C2×D44—22no—
107C2×D44—42no—
108C2×D44—42no—
109C2×D44—41no—
110C2×C4×D11—41no—
111C11×Q16—22no—
112C11×Q16—22no—
113C11×Q16—22no—
114C11×Q16—42no—
115C2×C8×C11—22no—
116C2×C8×C11C2×D411yescharacteristic
117C2×C8×C11C2411yescharacteristic
118C11×C4⋊C4—21no—
119C11×C4⋊C4—41no—
120C11×C22⋊C4—41no—
121#4325—44no—
122#4325—42no—
123#4325—44no—
124(C2×D11)⋊C4—41no—
125(C2×D11)⋊C4—41no—
126(C2×D11)⋊C4—41no—
127(C2×D11)⋊C4—42no—
128(C2×D11)⋊C4—42no—
129(C2×D11)⋊C4—42no—
130(C2×D11)⋊C4—42no—
131(C2×D11)⋊C4—41no—
132C4⋊Dic11—21no—
133C4⋊Dic11—41no—
134C4⋊Dic11—41no—
135Dic11⋊C4—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
144D88—22no—
145D88—22no—
146D88—22no—
147D88—42no—
148C11×C16—22no—
149C11⋊C16—22no—
150#3168—111no—
151C2×#495—111no—
152#2249—112no—
153#2242—112no—
154#2211—112no—
155#2210—112no—
156#2188D1111yescharacteristic, complemented
157#2187—111no—
158#2185—111no—
159#2184—111no—
160#2162—111no—
161C23×C11C2×D811yescharacteristic
162C22×D11—41no—
163C22×D11—42no—
164C22×D11—82no—
165C22×D11—82no—
166C22×D11—82no—
167Q8×C11—42no—
168Q8×C11—41no—
169Q8×C11—42no—
170Q8×C11—41no—
171Q8×C11—82no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11—82no—
178C2×C4×C11C2×D811yescharacteristic
179C2×C4×C11C22×D411yescharacteristic
180C22⋊D11—82no—
181C2×Dic11—22no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11C2×D811yescharacteristic
185C2×Dic11C2×D811yescharacteristic
186C2×Dic11C2×D811yescharacteristic
187C2×Dic11C2×D811yescharacteristic
188D44—42no—
189D44—41no—
190D44—42no—
191D44—41no—
192D44—82no—
193C4×D11—82no—
194C8×C11—21no—
195C8×C11H(5,𝔽2)12yes—
196C11⋊C8—21no—
197C11⋊C8AGL(1,ℤ/8)12yes—
198C22×Q16C2×D1111yescharacteristic
199C22×SD16—221no—
200C22×D8—111no—
201#529—221no—
202C2×#124—221no—
203C2×Q32C2×D1112yescomplemented
204C2×SD32—112no—
205C2×SD32—112no—
206C2×D16—112no—
207#499—111no—
208#495—112no—
209#495—112no—
210#495—111no—
211#495—221no—
212#495—221no—
213#488—221no—
214#467C2×D1111yescharacteristic
215#466—111no—
216#465—221no—
217C4×Q16—111no—
218C4×SD16—221no—
219C4×D8—111no—
220C2×C4×C8—111no—
221C4⋊C16—112no—
222#358—112no—
223#358C2×D1112yescomplemented
224#357—112no—
225#357—112no—
226C22⋊C16—111no—
227C22⋊C16C2×D1111yescharacteristic
228C4×C16—112no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11#50812yes—
232C22×C11C22×D811yescharacteristic
233C2×D11—82no—
234C2×D11—81no—
235C2×D11—82no—
236C2×D11—81no—
237C2×D11—82no—
238C2×D11—81no—
239C2×D11—164no—
240C4×C11—21no—
241C4×C11—81no—
242C4×C11—82no—
243C4×C11—81no—
244C4×C11#53511yescharacteristic
245C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
246Dic11—21no—
247Dic11—21no—
248Dic11—21no—
249Dic11—21no—
250Dic11—81no—
251C22×Q8—21no—
252C22×D4—221no—
253C2×Q16—21no—
254C2×Q16—42no—
255C2×Q16C22×D1112yes—
256C2×Q16C22×D1111yescharacteristic
257C2×SD16—222no—
258C2×SD16—222no—
259C2×SD16—221no—
260C2×SD16—444no—
261C2×D8—112no—
262C2×D8—111no—
263C2×D8—221no—
264C2×D8—442no—
265C22×C8—111no—
266C22×C8C22×D1111yescharacteristic
267#126—441no—
268#125—221no—
269#124—222no—
270#124—222no—
271#124—221no—
272#124—441no—
273#124—441no—
274#123—441no—
275C22⋊Q8—21no—
276#121—221no—
277C4×Q8—221no—
278C4×D4—221no—
279C4×D4—441no—
280#117—441no—
281C2×C22⋊C4—441no—
282C2×C22⋊C4—441no—
283C2×C42—111no—
284Q32—42no—
285SD32—442no—
286SD32—442no—
287D16—442no—
288C2×C16—112no—
289C2×C16C22×D1112yes—
290#107—111no—
291#107C22×D1111yescharacteristic
292#106—221no—
293#103—21no—
294#103—221no—
295#102—221no—
296#102—221no—
297C4×C8—111no—
298C4×C8—111no—
299C4×C8—111no—
300C4×C8—111no—
301C2×C11—22no—
302C2×C11#320511yescharacteristic
303C2×C11C2×#50811yescharacteristic
304C2×C11#341411yescharacteristic
305D11—161no—
306D11—162no—
307C24—441no—
308C2×Q8—21no—
309C2×Q8—22no—
310C2×Q8—42no—
311C2×Q8—42no—
312C2×Q8—41no—
313C2×D4—221no—
314C2×D4—222no—
315C2×D4—442no—
316C2×D4—442no—
317C2×D4—441no—
318C2×D4—441no—
319C22×C4—41no—
320C22×C4—111no—
321C22×C4—111no—
322C22×C4—441no—
323C22×C4D4×D1111yescharacteristic
324Q16—22no—
325Q16—22no—
326Q16—22no—
327Q16—42no—
328SD16—444no—
329SD16—442no—
330SD16—444no—
331D8—222no—
332D8—222no—
333D8—222no—
334D8—442no—
335C2×C8—22no—
336C2×C8—111no—
337C2×C8—111no—
338C2×C8—222no—
339C2×C8D4×D1111yescharacteristic
340C2×C8C23×D1111yescharacteristic
341C4⋊C4—21no—
342C4⋊C4—41no—
343C4⋊C4—221no—
344C4⋊C4—441no—
345C4⋊C4—441no—
346C4⋊C4—441no—
347C22⋊C4—41no—
348C22⋊C4—442no—
349C22⋊C4—442no—
350C22⋊C4—442no—
351C22⋊C4—442no—
352C22⋊C4—441no—
353C22⋊C4—441no—
354C22⋊C4—441no—
355C22⋊C4—441no—
356C42—111no—
357C42—111no—
358C42—111no—
359C42—111no—
360C42—441no—
361C16—22no—
362C16—222no—
363C11#3377711yescharacteristic, complemented, Sylow
364C23—441no—
365C23—442no—
366C23—882no—
367C23—882no—
368C23—882no—
369C23D8×D1111yescharacteristic
370Q8—42no—
371Q8—41no—
372Q8—42no—
373Q8—41no—
374Q8—82no—
375D4—442no—
376D4—441no—
377D4—442no—
378D4—441no—
379D4—882no—
380D4—882no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—82no—
387C2×C4—111no—
388C2×C4—111no—
389C2×C4—111no—
390C2×C4—111no—
391C2×C4—222no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—882no—
395C2×C4D8×D1111yescharacteristic
396C2×C4C2×D4×D1111yescharacteristic
397C8—21no—
398C8—112no—
399C8—221no—
400C8#6703712yes—
401C22—21no—
402C22—21no—
403C22—881no—
404C22—882no—
405C22—881no—
406C22—882no—
407C22—882no—
408C22—881no—
409C22—1764no—
410C22#1062253212yes—
411C22C2×D8×D1111yescharacteristic
412C4—21no—
413C4—81no—
414C4—82no—
415C4—81no—
416C4—221no—
417C4—221no—
418C4—221no—
419C4—221no—
420C4—881no—
421C4#1062312311yescharacteristic
422C4D11×AGL(1,ℤ/8)11yescharacteristic
423C2—22no—
424C2—1762no—
425C2—1761no—
426C2#1307953211yescharacteristic
427C2C2×#1062253211yescharacteristic
428C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2188C2
socleC22×C11C22×D8
prime radical#13070530C2
hypercenter#2188D11
hypocenterC11#33777
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. #13079187C2semidirect
2. C2×#10622804C2semidirect
3. #13070878C2semidirect
4. #13070849C2semidirect
5. #13070680C2semidirect
6. #13070674C2semidirect
7. #13070544C2semidirect
8. #13070533C2semidirect
10. #13070412C2semidirect
11. C11×#2188C2semidirect
17. C2×C11×Q32C22semidirect
23. #10622804C22semidirect
24. Q16×Dic11C22semidirect
26. C2×#66892C22semidirect
31. #10622491C22semidirect
32. #10622485C22semidirect
35. C11×#358C22semidirect
37. #10622202C22semidirect
40. Dic11⋊C16C22semidirect
41. C16×Dic11C22semidirect
156. #2188D11semidirect
203. C2×Q32C2×D11semidirect
223. #358C2×D11semidirect
363. C11#33777semidirect

Maximal subgroups

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

subgroupindex
#130791872
C2×#106228042
#130708782
#130708492
#130706802
#130706742
#130705442
#130705332
#130705302
#130704122
C11×#21882
#3377711