Finite Group Databasebeta

← #14907101

Subgroups — #14907101

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622522C211yesmaximal, characteristic
2#13077387C211yesmaximal, characteristic
3C2×#10622486C211yesmaximal, characteristic, complemented
4#13070486C212yesmaximal, complemented
5#13070479C212yesmaximal, complemented
6#13070474C212yesmaximal, complemented
7#13070467C212yesmaximal, complemented
8#13070335C211yesmaximal, characteristic, complemented
9#13070326C211yesmaximal, characteristic
10M32×Dic11C211yesmaximal, characteristic, complemented
11C11×#2159C211yesmaximal, characteristic, complemented
12C22×Dic44C2211yescharacteristic
13C2×#66957C2211yescharacteristic
14#10623053—21no—
15C2×#66940—21no—
16C2×C11×M32C2211yescharacteristic
17C11×#427C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19C2×C8×Dic11C2211yescharacteristic
20C2×#66876C2211yescharacteristic
21#10622615—21no—
22C2×#66874—21no—
23#10622522C418yescomplemented
24C2×Dic88C2212yes—
25C2×#66864C2212yes—
26#10622486—21no—
27#10622486—21no—
28#10622486C2212yes—
29#10622486C2212yes—
30#10622486C2211yescharacteristic
31#10622486C2211yescharacteristic
32#10622485C2211yescharacteristic
33#10622485C2211yescharacteristic
34#10622465—21no—
35#10622465—21no—
36C11×#367C2212yes—
37C11×#366C2212yes—
38#10622140C2212yes—
39C16×Dic11C2212yes—
40#10622130C2212yes—
41#10622130C2212yes—
42#10622130C2212yes—
43#10622129C2212yes—
44C2×#4339—21no—
45C22×Dic22—21no—
46C22×C8×C11C2311yescharacteristic
47C11×#117—21no—
48C2×C11×C4⋊C4—21no—
49C2×Dic11⋊C4—41no—
50C2×C4×Dic11—41no—
51C2×C4×Dic11D411yescharacteristic
52C22×C11⋊C8D411yescharacteristic
53C2×Dic44—21no—
54C2×Dic44—22no—
55C2×Dic44C2×C414yescomplemented
56C2×Dic44C2311yescharacteristic
57C2×Dic44C2312yes—
58#66957—22no—
59#66957C2×C414yes—
60C2×D88C2311yescharacteristic
61C2×#4314—21no—
62#66946—21no—
63#66946—21no—
64#66940—21no—
65#66940—21no—
66#66940—22no—
67#66940—22no—
68#66940—41no—
69#66940—41no—
70(C22⋊D11)⋊C4—41no—
71(C22⋊D11)⋊C4—41no—
72#66925—41no—
73C42×D11—41no—
74C11×M32C2×C414yescomplemented
75C2×C11×C16C2312yes—
76C11×#107—21no—
77C11×#107C2311yescharacteristic
78C11×#107C2311yescharacteristic
79C11×#107C2312yes—
80C11×#106—21no—
81C8×Dic11D411yescharacteristic
82C8×Dic11D411yescharacteristic
83C8×Dic11C2311yescharacteristic
84C8×Dic11C2311yescharacteristic
85#66876—22no—
86C2×C11⋊C16C2312yes—
87#66874—21no—
88#66874—21no—
89#66874—22no—
90#66874—22no—
91#66873—21no—
92#66873—21no—
93Dic88C2×C418yescomplemented
94#66864C2×C418yescomplemented
95C4×#510—111nomaximal, Sylow
96C22×C4×C11—41no—
97C22×C4×C11C2×D411yescharacteristic
98C2×C22⋊D11—41no—
99C22×Dic11—41no—
100C22×Dic11D811yescharacteristic
101C22×Dic11D811yescharacteristic
102#4339—24no—
103#4339—42no—
104C2×D44—21no—
105C2×C4×D11—41no—
106C2×C4×D11—41no—
107C2×C4×D11—41no—
108C2×Dic22—24no—
109C2×Dic22—21no—
110C2×Dic22—22no—
111C2×Dic22—41no—
112C2×Dic22—42no—
113C2×C8×C11C22×C412yes—
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11#4112yes—
116C2×C8×C11C2411yescharacteristic
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—41no—
121C11×C22⋊C4—41no—
122C42×C11—41no—
123(C2×D11)⋊C4—41no—
124(C2×D11)⋊C4—41no—
125Dic11⋊C4—41no—
126Dic11⋊C4—41no—
127Dic11⋊C4—42no—
128Dic11⋊C4—42no—
129C4×Dic11—41no—
130C4×Dic11—41no—
131C4×Dic11—42no—
132C4×Dic11—42no—
133C4×Dic11D811yescharacteristic
134C4×Dic11D811yescharacteristic
135C4×Dic11C2×D411yescharacteristic
136C4×Dic11C2×D411yescharacteristic
137C2×C11⋊C8—22no—
138C2×C11⋊C8C2×D411yescharacteristic
139C2×C11⋊C8C2×D411yescharacteristic
140Dic44—24no—
141Dic44—21no—
142Dic44—22no—
143Dic44C22×C414yes—
144Dic44C22×C412yes—
145D88—21no—
146D88C22×C412yes—
147#4314—24no—
148C11×C16C22×C414yes—
149C11⋊C16—22no—
150C2×#510—111no—
151C4×#135—111no—
152C2×C4×Q16—111no—
153#2176—112no—
154#2175—112no—
155C4×Q32—112no—
156C4×SD32—112no—
157#2159D1111yescharacteristic, complemented
158#2141—111no—
159#2139—111no—
160C4×M32—111no—
161C23×C11C2×D811yescharacteristic
162C22×D11—41no—
163C2×C4×C11—42no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—82no—
167C2×C4×C11C4×D412yes—
168C2×C4×C11C2×D811yescharacteristic
169C2×C4×C11#13512yes—
170C2×C4×C11C22×D411yescharacteristic
171C22⋊D11—44no—
172C2×Dic11—22no—
173C2×Dic11—41no—
174C2×Dic11—42no—
175C2×Dic11—41no—
176C2×Dic11—44no—
177C2×Dic11C2×D811yescharacteristic
178C2×Dic11C2×D811yescharacteristic
179C2×Dic11C2×D811yescharacteristic
180C2×Dic11C2×D811yescharacteristic
181D44—22no—
182D44—41no—
183C4×D11—44no—
184C4×D11—82no—
185C4×D11—82no—
186Dic22—22no—
187Dic22—24no—
188Dic22—42no—
189Dic22—41no—
190Dic22—44no—
191C8×C11C4×D412yes—
192C8×C11C23×C411yescharacteristic
193C8×C11C2×#4111yescharacteristic
194C11⋊C8—21no—
195C11⋊C8—21no—
196C2×#135—111no—
197C22×Q16—111no—
198C4×#41—221no—
199C2×C4×Q8—221no—
200#510—118no—
201C2×Q32—112no—
202C2×SD32—112no—
203C2×M32—111no—
204C2×M32C2×D1111yescharacteristic
205C4×Q16—112no—
206C4×Q16—112no—
207C4×Q16—111no—
208C4×Q16—111no—
209C4×Q16—221no—
210C4×Q16—221no—
211C4×SD16—221no—
212C4×SD16—221no—
213C4×D8—111no—
214C4×D8—111no—
215#427C2×D1111yescharacteristic
216C2×#107C2×D1111yescharacteristic
217#416—221no—
218C2×#103—221no—
219C2×C4×C8—111no—
220#367C2×D1112yes—
221#366C2×D1112yes—
222#358—112no—
223#358—112no—
224#358—112no—
225#357—112no—
226#346—112no—
227C4×C16—112no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11C4×D812yes—
231C22×C11C22×D811yescharacteristic
232C2×D11—42no—
233C2×D11—81no—
234C2×D11—81no—
235C4×C11—81no—
236C4×C11—82no—
237C4×C11—81no—
238C4×C11C4×D812yes—
239C4×C11C2×C4×D411yescharacteristic
240C4×C11C2×#13511yescharacteristic
241Dic11—21no—
242Dic11—21no—
243Dic11—21no—
244Dic11—44no—
245Dic11—42no—
246Dic11#51012yescomplemented
247C2×#41—221no—
248C22×Q8—221no—
249#135—114no—
250#135—222no—
251C2×Q16—114no—
252C2×Q16—112no—
253C2×Q16—111no—
254C2×Q16—221no—
255C2×Q16—222no—
256C2×SD16—221no—
257C2×D8—111no—
258C22×C8—111no—
259C22×C8C22×D1111yescharacteristic
260C4×Q8—222no—
261C4×Q8—222no—
262C4×Q8—221no—
263C4×Q8—221no—
264C4×Q8—441no—
265C4×Q8—441no—
266C4×D4—221no—
267C4×D4—221no—
268C4×D4—441no—
269C4×D4—441no—
270#117—21no—
271#117—441no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—441no—
274C2×C42—111no—
275C2×C42—441no—
276C2×C42—441no—
277Q32—118no—
278SD32—118no—
279M32—222no—
280M32C4×D1114yescomplemented
281C2×C16—112no—
282C2×C16C22×D1112yes—
283#107—21no—
284#107C22×D1112yes—
285#107C22×D1111yescharacteristic
286#107C22×D1111yescharacteristic
287#106—21no—
288#103—222no—
289#103—222no—
290#103—221no—
291#103—221no—
292#102—221no—
293#102—221no—
294C4×C8—111no—
295C4×C8—111no—
296C4×C8—111no—
297C4×C8—111no—
298C2×C11—22no—
299C2×C11C2×C4×D811yescharacteristic
300C2×C11C2×#51011yescharacteristic
301C2×C11#341411yescharacteristic
302D11—82no—
303#41—224no—
304#41—442no—
305C2×Q8—224no—
306C2×Q8—221no—
307C2×Q8—222no—
308C2×Q8—441no—
309C2×Q8—442no—
310C2×D4—221no—
311C2×D4—441no—
312C22×C4—41no—
313C22×C4—111no—
314C22×C4—111no—
315C22×C4—441no—
316C22×C4—441no—
317C22×C4—441no—
318C22×C4—441no—
319C22×C4D4×D1111yescharacteristic
320Q16—114no—
321Q16—112no—
322Q16—224no—
323Q16—222no—
324Q16—221no—
325SD16—224no—
326D8—112no—
327D8—221no—
328C2×C8—111no—
329C2×C8—111no—
330C2×C8—222no—
331C2×C8C2×C4×D1112yes—
332C2×C8D4×D1111yescharacteristic
333C2×C8#434312yes—
334C2×C8C23×D1111yescharacteristic
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—22no—
338C4⋊C4—41no—
339C4⋊C4—442no—
340C4⋊C4—442no—
341C4⋊C4—441no—
342C4⋊C4—441no—
343C22⋊C4—41no—
344C22⋊C4—441no—
345C22⋊C4—441no—
346C42—41no—
347C42—111no—
348C42—111no—
349C42—111no—
350C42—111no—
351C42—441no—
352C42—441no—
353C42—442no—
354C42—442no—
355C16—222no—
356C16C2×C4×D1114yes—
357C11C4×#51011yescharacteristic, complemented, Sylow
358C23—441no—
359C23D8×D1111yescharacteristic
360Q8—222no—
361Q8—224no—
362Q8—444no—
363Q8—442no—
364Q8—441no—
365D4—222no—
366D4—444no—
367D4—441no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—82no—
372C2×C4—111no—
373C2×C4—111no—
374C2×C4—111no—
375C2×C4—111no—
376C2×C4—222no—
377C2×C4—441no—
378C2×C4—444no—
379C2×C4—441no—
380C2×C4—442no—
381C2×C4—444no—
382C2×C4—882no—
383C2×C4—882no—
384C2×C4#6694612yes—
385C2×C4D8×D1111yescharacteristic
386C2×C4#6697212yes—
387C2×C4C2×D4×D1111yescharacteristic
388C8—221no—
389C8—221no—
390C8#6694612yes—
391C8C22×C4×D1111yescharacteristic
392C8C2×#434311yescharacteristic
393C22—21no—
394C22—21no—
395C22—442no—
396C22—881no—
397C22—881no—
398C22#1062248512yes—
399C22C2×D8×D1111yescharacteristic
400C4—81no—
401C4—82no—
402C4—81no—
403C4—112no—
404C4—221no—
405C4—221no—
406C4—221no—
407C4—442no—
408C4—444no—
409C4#1062248512yes—
410C4C2×#6694611yescharacteristic
411C4C2×#6697211yescharacteristic
412C2—22no—
413C2—882no—
414C2C2×#1062248511yescharacteristic
415C2D11×#51011yescharacteristic
416C2#1308174811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC11×#2159C2
socleC22×C11C22×D8
prime radicalC2×#66957C22
cosocleC2×C8×C11C24
hypercenter#2159D11
hypocenterC11C4×#510
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2159

Complements

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

NH ≅ G/Ntype
3. C2×#10622486C2semidirect
4. #13070486C2semidirect
5. #13070479C2semidirect
6. #13070474C2semidirect
7. #13070467C2semidirect
8. #13070335C2semidirect
10. M32×Dic11C2semidirect
11. C11×#2159C2semidirect
23. #10622522C4semidirect
55. C2×Dic44C2×C4semidirect
74. C11×M32C2×C4semidirect
93. Dic88C2×C4semidirect
94. #66864C2×C4semidirect
157. #2159D11semidirect
246. Dic11#510semidirect
280. M32C4×D11semidirect
357. C11C4×#510semidirect

Maximal subgroups

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

subgroupindex
C2×#106225222
#130773872
C2×#106224862
#130704862
#130704792
#130704742
#130704672
#130703352
#130703262
M32×Dic112
C11×#21592
C4×#51011