Finite Group Databasebeta

← #14769706

Subgroups — #14769706

Order 2816.

1338 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623283C211yesmaximal, characteristic
2#13077534C212yesmaximal, complemented
3#13077093C212yesmaximal, complemented
4#13069526C212yesmaximal, complemented
5#13069095C214yesmaximal, complemented
6#13068666C211yesmaximal, characteristic, complemented
7#13068584C212yesmaximal, complemented
8C11×#1757C211yesmaximal, characteristic, complemented
9C2×#67042C2212yes—
10C2×C11×#131C2211yescharacteristic
11#10623283—24no—
12#10623283—24no—
13C2×#66961C414yescomplemented
14C2×#66961C2212yes—
15#10623276C2214yescomplemented
16C2×#66957C412yescomplemented
17C2×#66957C2211yescharacteristic
18C22×D88C412yescomplemented
19C22×D88C2211yescharacteristic
20C11×#413C2211yescharacteristic
21C11×#410C2211yescharacteristic
22C11×#405C2212yescomplemented
23#10622850C2212yes—
24C2×#66887C2214yescomplemented
25C2×#66883C2212yescomplemented
26#10622618C2214yescomplemented
27#10622614C2214yescomplemented
28#10622364—24no—
29D11×#100—24no—
30#10622330—24no—
31#10622313—24no—
32C11×#344C2212yescomplemented
33C11⋊#338C2212yescomplemented
34C2×C11×#41C2311yescharacteristic
35#67042—28no—
36#67042—44no—
37C2×#4343—22no—
38C2×D4×D11—22no—
39C2×D4×D11—24no—
40C2×#4339C2×C414yes—
41C2×#4339C2312yes—
42C22×D44C2×C414yes—
43C22×D44C2312yes—
44C11×#131—22no—
45C11×#131—22no—
46C2×C11×M16C2×C412yes—
47C2×C11×M16C2312yes—
48C2×C11×M16C2311yescharacteristic
49C22×C8×C11C2×C412yes—
50C22×C8×C11C2311yescharacteristic
51C11×#117C2312yes—
52C2×#4318C2314yes—
53#66961—28no—
54#66961—216no—
55#66960—44no—
56M16×D11—28no—
57C2×Dic44C2×C411yescharacteristic
58#66957—24no—
59#66957—24no—
60#66957D414yes—
61#66957D414yes—
62C2×D88—22no—
63C2×D88—22no—
64C2×D88—24no—
65C2×D88—24no—
66C2×D88C2×C412yes—
67C2×D88C2×C414yes—
68C2×D88C2×C412yes—
69C2×D88C2×C411yescharacteristic
70C2×#4314C2×C414yes—
71C2×#4314C2×C412yes—
72#66954—28no—
73C11×#101D412yes—
74C11×#100D412yes—
75C11×#99—22no—
76C11×#97—22no—
77C4×C8×C11—22no—
78#66900—22no—
79#66897—22no—
80#66887—28no—
81#66883—22no—
82#66883—22no—
83#66873—44no—
84#66869—28no—
85#22458—111nomaximal, Sylow
86C23×D11—24no—
87C23×D11—22no—
88C11×#41—22no—
89C11×#41—22no—
90C2×Q8×C11C2×D411yescharacteristic
91C2×D4×C11C2×D411yescharacteristic
92C2×D4×C11#4112yes—
93C22×C4×C11C22×C412yes—
94C22×C4×C11C2411yescharacteristic
95C2×C22⋊D11—24no—
96C2×C22⋊D11—22no—
97#4343—48no—
98D4×D11—48no—
99D4×D11—416no—
100#4339—28no—
101#4339—24no—
102#4339—44no—
103#4339C2×D418yes—
104C2×D44—28no—
105C2×D44—24no—
106C2×D44—22no—
107C2×D44—24no—
108C2×D44—24no—
109C2×D44—44no—
110C2×D44C22×C414yes—
111C2×D44C22×C412yes—
112C2×C4×D11—24no—
113C2×C4×D11—22no—
114C2×Dic22C22×C412yes—
115C11×M16—24no—
116C11×M16—22no—
117C11×M16—22no—
118C11×M16C2×D414yes—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C2×C8×C11C22×C412yes—
123C2×C8×C11C22×C411yescharacteristic
124C2×C8×C11C22×C411yescharacteristic
125C2×C8×C11C2×D412yes—
126C2×C8×C11C2×D412yes—
127C11×C4⋊C4—22no—
128C11×C22⋊C4—22no—
129C42×C11—22no—
130#4318—24no—
131#4318—24no—
132C2×C11⋊C8—24no—
133Dic44C22⋊C412yes—
134Dic44C22⋊C412yes—
135D88—28no—
136D88—22no—
137D88—22no—
138D88—24no—
139D88C22⋊C412yes—
140D88C22⋊C412yes—
141#4314—28no—
142#4314C22⋊C418yes—
143#4313—48no—
144C8×D11—48no—
145C2×#576—111no—
146#2957—112no—
147#2888—112no—
148#1978—112no—
149#1903—114no—
150#1813—111no—
151#1795—112no—
152#1757D1111yescharacteristic, complemented
153C23×C11C4×D412yes—
154C23×C11C2×#4111yescharacteristic
155C22×D11—22no—
156C22×D11—24no—
157C22×D11—48no—
158C22×D11—44no—
159C22×D11—164no—
160C22×D11—162no—
161Q8×C11—22no—
162D4×C11—24no—
163D4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—42no—
167C2×C4×C11C4×D412yes—
168C2×C4×C11C23×C411yescharacteristic
169C2×C4×C11C22×D411yescharacteristic
170C2×C4×C11C22×D412yes—
171C2×C4×C11H(5,𝔽2)12yes—
172C22⋊D11—28no—
173C22⋊D11—48no—
174C2×Dic11—22no—
175D44—24no—
176D44—22no—
177D44—24no—
178D44—48no—
179D44—44no—
180D44C2×C22⋊C414yes—
181C4×D11—28no—
182C4×D11—48no—
183Dic22—22no—
184Dic22C2×C22⋊C414yes—
185C8×C11—22no—
186C8×C11—24no—
187C8×C11C2×C22⋊C412yes—
188C8×C11C2×C22⋊C411yescharacteristic
189C8×C11C2×C22⋊C411yescharacteristic
190C11⋊C8—44no—
191C2×H(5,𝔽2)—112no—
192#576—224no—
193#576—224no—
194C2×AGL(1,ℤ/8)—112no—
195C2×AGL(1,ℤ/8)—114no—
196C2×#135—111no—
197C2×#135—112no—
198C22×D8—111no—
199C22×D8—112no—
200#568—114no—
201C2×#131C2×D1111yescharacteristic
202#444—224no—
203#443—224no—
204C2×#108—112no—
205#421—114no—
206#418—114no—
207#413—112no—
208#413—224no—
209#413C2×D1111yescharacteristic
210C2×#100—114no—
211C2×#100—224no—
212#410C2×D1111yescharacteristic
213#405C2×D1112yescomplemented
214#344C2×D1112yescomplemented
215#338—112no—
216C22×C11—22no—
217C22×C11—41no—
218C22×C11—42no—
219C22×C11C2×C4×D411yescharacteristic
220C22×C11#54612yes—
221C2×D11—24no—
222C2×D11—44no—
223C2×D11—82no—
224C2×D11—84no—
225C2×D11—168no—
226C2×D11—164no—
227C4×C11—22no—
228C4×C11—82no—
229C4×C11C22×C22⋊C411yescharacteristic
230C4×C11#51811yescharacteristic
231C4×C11D4212yes—
232Dic11—24no—
233H(5,𝔽2)—228no—
234H(5,𝔽2)—444no—
235C2×#41—114no—
236C2×#41—112no—
237C2×#41—222no—
238C2×#41C22×D1111yescharacteristic
239C22×D4—114no—
240C22×D4—112no—
241C22×D4—222no—
242C22×D4—224no—
243AGL(1,ℤ/8)—2216no—
244AGL(1,ℤ/8)—228no—
245#135—114no—
246#135—114no—
247#135—224no—
248#135—224no—
249C2×Q16—111no—
250C2×SD16—112no—
251C2×SD16—114no—
252C2×D8—111no—
253C2×D8—112no—
254C2×D8—114no—
255C2×D8—112no—
256C2×D8—224no—
257C2×D8—224no—
258C2×D8—222no—
259C2×D8—222no—
260#131—22no—
261#131—22no—
262#131—228no—
263#131—444no—
264C2×M16—114no—
265C2×M16—228no—
266C2×M16C4×D1112yes—
267C2×M16C22×D1112yes—
268C2×M16C22×D1111yescharacteristic
269C22×C8C4×D1112yes—
270C22×C8C22×D1111yescharacteristic
271#117C22×D1112yes—
272#108—222no—
273#108—222no—
274#104—228no—
275#102—444no—
276#101—222no—
277#101D4412yes—
278#100—222no—
279#100—228no—
280#100D4412yes—
281#99—22no—
282#97—22no—
283C4×C8—22no—
284C2×C11—22no—
285C2×C11—21no—
286C2×C11—42no—
287C2×C11D4×C22⋊C411yescharacteristic
288D11—44no—
289D11—84no—
290C24—224no—
291C24—222no—
292#41—22no—
293#41—22no—
294#41—118no—
295#41—228no—
296#41—224no—
297#41—444no—
298#41—448no—
299C2×Q8—112no—
300C2×Q8C2×D4411yescharacteristic
301C2×D4—112no—
302C2×D4—114no—
303C2×D4—228no—
304C2×D4—222no—
305C2×D4—224no—
306C2×D4—224no—
307C2×D4—222no—
308C2×D4—224no—
309C2×D4—224no—
310C2×D4—444no—
311C2×D4—448no—
312C2×D4—4416no—
313C2×D4C2×D4411yescharacteristic
314C2×D4#433912yes—
315C22×C4—222no—
316C22×C4—224no—
317C22×C4C2×C4×D1112yes—
318C22×C4C23×D1111yescharacteristic
319Q16—112no—
320Q16—112no—
321SD16—118no—
322SD16—228no—
323D8—112no—
324D8—112no—
325D8—228no—
326D8—222no—
327D8—222no—
328D8—224no—
329M16—22no—
330M16—22no—
331M16—24no—
332M16—224no—
333M16—224no—
334M16—448no—
335M16C2×D4414yes—
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—22no—
339C2×C8—224no—
340C2×C8—448no—
341C2×C8C2×C4×D1112yes—
342C2×C8C2×C4×D1111yescharacteristic
343C2×C8C2×C4×D1111yescharacteristic
344C2×C8D4×D1112yes—
345C2×C8D4×D1112yes—
346C4⋊C4—22no—
347C22⋊C4—22no—
348C42—22no—
349C11#2245811yescharacteristic, complemented, Sylow
350C23—222no—
351C23—224no—
352C23—448no—
353C23—444no—
354C23—1762no—
355C23—1764no—
356C23C4×D4412yes—
357C23C2×#433911yescharacteristic
358Q8—22no—
359Q8—114no—
360Q8—222no—
361D4—24no—
362D4—22no—
363D4—114no—
364D4—228no—
365D4—224no—
366D4—222no—
367D4—224no—
368D4—448no—
369D4—448no—
370D4—444no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—42no—
374C2×C4—222no—
375C2×C4—228no—
376C2×C4—448no—
377C2×C4C4×D4412yes—
378C2×C4C22×C4×D1111yescharacteristic
379C2×C4C22×D4411yescharacteristic
380C2×C4C2×D4×D1112yes—
381C2×C4#6704212yes—
382C8—22no—
383C8—24no—
384C8—444no—
385C8C22⋊C4×D1111yescharacteristic
386C8C22⋊C4×D1111yescharacteristic
387C8C22⋊C4×D1112yes—
388C22—22no—
389C22—41no—
390C22—42no—
391C22—224no—
392C22—444no—
393C22—882no—
394C22—884no—
395C22—1764no—
396C22—1768no—
397C22C2×C4×D4411yescharacteristic
398C22#1062308112yes—
399C4—22no—
400C4—82no—
401C4—224no—
402C4C2×C22⋊C4×D1111yescharacteristic
403C4#1062305211yescharacteristic
404C4D4×D4412yes—
405C2—22no—
406C2—21no—
407C2—42no—
408C2—444no—
409C2—884no—
410C2C22⋊C4×D4411yescharacteristic
subgroupG/H
centerC2C22⋊C4×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1757C2
socleC2×C11D4×C22⋊C4
prime radicalC2×#10623283C2
cosocleC22×C4×C11C24
hypercenter#1757D11
hypocenterC11#22458
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #1757

Complements

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

NH ≅ G/Ntype
2. #13077534C2semidirect
3. #13077093C2semidirect
4. #13069526C2semidirect
5. #13069095C2semidirect
6. #13068666C2semidirect
7. #13068584C2semidirect
8. C11×#1757C2semidirect
13. C2×#66961C4semidirect
15. #10623276C22semidirect
16. C2×#66957C4semidirect
18. C22×D88C4semidirect
22. C11×#405C22semidirect
24. C2×#66887C22semidirect
25. C2×#66883C22semidirect
26. #10622618C22semidirect
27. #10622614C22semidirect
32. C11×#344C22semidirect
33. C11⋊#338C22semidirect
152. #1757D11semidirect
213. #405C2×D11semidirect
214. #344C2×D11semidirect
349. C11#22458semidirect

Maximal subgroups

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

subgroupindex
C2×#106232832
#130775342
#130770932
#130695262
#130690952
#130686662
#130685842
C11×#17572
#2245811