Finite Group Databasebeta

← #14908444

Subgroups — #14908444

Order 2816.

574 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622487C211yesmaximal, characteristic, complemented
2#13077387C211yesmaximal, characteristic
3#13070767C212yesmaximal, complemented
4#13070762C212yesmaximal, complemented
5#13070757C212yesmaximal, complemented
6#13070752C212yesmaximal, complemented
7#13070405C211yesmaximal, characteristic, complemented
8#13070371C211yesmaximal, characteristic, complemented
9#13070329C211yesmaximal, characteristic
10#13070326C211yesmaximal, characteristic
11C11×#2159C211yesmaximal, characteristic, complemented
12C2×#66957C2211yescharacteristic
13#10623053—21no—
14C2×#66941—21no—
15C2×C11×M32C2211yescharacteristic
16C11×#427C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18C2×#66882C2211yescharacteristic
19C2×C8×Dic11C2211yescharacteristic
20C2×#66876C2211yescharacteristic
21#10622615—21no—
22C2×#66871—21no—
23#10622487—21no—
24#10622487—21no—
25#10622487C2212yes—
26#10622487C2212yes—
27#10622486C2211yescharacteristic
28#10622486C2211yescharacteristic
29#10622485C2211yescharacteristic
30#10622485C2211yescharacteristic
31#10622465—21no—
32#10622465—21no—
33C11×#367C2212yes—
34C11×#366C2212yes—
35#10622147C2212yes—
36#10622141C2212yes—
37Dic11⋊C16C2212yes—
38Dic11⋊C16C2212yes—
39#10622130C2212yes—
40#10622129C2212yes—
41#10622128C2212yes—
42#10622127C2212yes—
43C2×#4339—21no—
44C22×Dic22—41no—
45C22×C8×C11C2311yescharacteristic
46C11×#117—21no—
47C2×C11×C4⋊C4—21no—
48C2×C4⋊Dic11—21no—
49C2×Dic11⋊C4—41no—
50C2×C4×Dic11D411yescharacteristic
51C22×C11⋊C8D411yescharacteristic
52C2×Dic44C2311yescharacteristic
53#66957—22no—
54#66957Q814yescomplemented
55C2×D88C2311yescharacteristic
56C2×#4314—21no—
57#66946—21no—
58#66946—21no—
59#66941—22no—
60#66941—22no—
61#66941—41no—
62#66941—41no—
63#66940—21no—
64#66940—21no—
65(C22⋊D11)⋊C4—41no—
66(C22⋊D11)⋊C4—41no—
67#66925—41no—
68C42×D11—41no—
69C11×M32—22no—
70C2×C11×C16C2312yes—
71C11×#107—21no—
72C11×#107C2311yescharacteristic
73C11×#107C2311yescharacteristic
74C11×#107C2312yes—
75C11×#106—21no—
76#66882—21no—
77#66882C2312yes—
78C8×Dic11D411yescharacteristic
79C8×Dic11D411yescharacteristic
80C8×Dic11C2311yescharacteristic
81C8×Dic11C2311yescharacteristic
82#66876—22no—
83C2×C11⋊C16C2312yes—
84#66874—21no—
85#66874—21no—
86#66873—21no—
87#66873—21no—
88#66871—22no—
89#66871—22no—
90#33629—111nomaximal, Sylow
91C22×C4×C11—41no—
92C22×C4×C11C2×D411yescharacteristic
93C2×C22⋊D11—41no—
94C22×Dic11—41no—
95C22×Dic11D811yescharacteristic
96C22×Dic11D811yescharacteristic
97#4339—24no—
98#4339—42no—
99C2×D44—21no—
100C2×C4×D11—41no—
101C2×C4×D11—41no—
102C2×C4×D11—41no—
103C2×Dic22—21no—
104C2×Dic22—42no—
105C2×Dic22—42no—
106C2×Dic22—84no—
107C2×C8×C11C2×D411yescharacteristic
108C2×C8×C11C2×Q812yes—
109C2×C8×C11#4112yes—
110C2×C8×C11C2411yescharacteristic
111C11×C4⋊C4—22no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—41no—
115C11×C22⋊C4—41no—
116C42×C11—41no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—41no—
119C4⋊Dic11—22no—
120C4⋊Dic11—41no—
121Dic11⋊C4—41no—
122Dic11⋊C4—41no—
123Dic11⋊C4—42no—
124Dic11⋊C4—42no—
125C4×Dic11—41no—
126C4×Dic11—41no—
127C4×Dic11D811yescharacteristic
128C4×Dic11D811yescharacteristic
129C4×Dic11C2×D411yescharacteristic
130C4×Dic11C2×D411yescharacteristic
131C2×C11⋊C8—22no—
132C2×C11⋊C8C2×D411yescharacteristic
133C2×C11⋊C8C2×D411yescharacteristic
134Dic44—21no—
135Dic44C2×Q812yescomplemented
136D88—21no—
137D88C2×Q812yescomplemented
138#4314—24no—
139C11×C16—22no—
140C11⋊C16—22no—
141C2×#500—111no—
142C4×#135—111no—
143#2227—112no—
144#2226—112no—
145#2225—112no—
146#2224—112no—
147#2159—111no—
148#2159D1111yescharacteristic, complemented
149#2150—111no—
150#2139—111no—
151#2139—111no—
152C23×C11C2×D811yescharacteristic
153C22×D11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—82no—
158C2×C4×C11C22⋊Q812yes—
159C2×C4×C11C2×D811yescharacteristic
160C2×C4×C11#13712yes—
161C2×C4×C11C22×D411yescharacteristic
162C22⋊D11—44no—
163C2×Dic11—22no—
164C2×Dic11—22no—
165C2×Dic11—41no—
166C2×Dic11—42no—
167C2×Dic11—82no—
168C2×Dic11C2×D811yescharacteristic
169C2×Dic11C2×D811yescharacteristic
170C2×Dic11C2×D811yescharacteristic
171C2×Dic11C2×D811yescharacteristic
172D44—22no—
173D44—41no—
174C4×D11—44no—
175C4×D11—82no—
176C4×D11—82no—
177Dic22—22no—
178Dic22—41no—
179Dic22—84no—
180Dic22—84no—
181C8×C11C22⋊Q812yes—
182C8×C11C22×Q811yescharacteristic
183C8×C11C2×#4111yescharacteristic
184C11⋊C8—21no—
185C11⋊C8—21no—
186C2×#135—111no—
187C2×C4⋊Q8—221no—
188C4×#41—221no—
189C2×M32—111no—
190C2×M32C2×D1111yescharacteristic
191#500—112no—
192#500—112no—
193#500—221no—
194#500—221no—
195C4×Q16—111no—
196C4×Q16—111no—
197C4×SD16—221no—
198C4×SD16—221no—
199C4×D8—111no—
200C4×D8—111no—
201#427C2×D1111yescharacteristic
202C2×#107—111no—
203C2×#107—221no—
204C2×#107C2×D1111yescharacteristic
205#416—221no—
206C2×C4×C8—111no—
207#367—112no—
208#367C2×D1112yes—
209#366—112no—
210#366C2×D1112yes—
211C4⋊C16—112no—
212C4⋊C16—112no—
213#358—112no—
214#358—112no—
215#357—112no—
216#357—112no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11#47412yes—
220C22×C11C22×D811yescharacteristic
221C2×D11—42no—
222C2×D11—81no—
223C2×D11—81no—
224C4×C11—82no—
225C4×C11—81no—
226C4×C11—81no—
227C4×C11#47412yes—
228C4×C11C2×C22⋊Q811yescharacteristic
229C4×C11C2×#13711yescharacteristic
230Dic11—21no—
231Dic11—21no—
232Dic11—42no—
233Dic11—82no—
234Dic11#50912yes—
235Dic11#51012yes—
236C2×#41—221no—
237C22×Q8—441no—
238#135—114no—
239#135—222no—
240C2×Q16—111no—
241C2×SD16—221no—
242C2×D8—111no—
243C22×C8—111no—
244C22×C8C22×D1111yescharacteristic
245C4⋊Q8—222no—
246C4⋊Q8—222no—
247C4⋊Q8—441no—
248C4⋊Q8—441no—
249C4×Q8—221no—
250C4×Q8—221no—
251C4×D4—221no—
252C4×D4—221no—
253C4×D4—441no—
254C4×D4—441no—
255#117—21no—
256#117—441no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—221no—
259C2×C4⋊C4—441no—
260C2×C42—111no—
261C2×C42—441no—
262M32—22no—
263M32—222no—
264C2×C16—112no—
265C2×C16C22×D1112yes—
266#107—21no—
267#107—112no—
268#107—222no—
269#107—222no—
270#107—221no—
271#107C22×D1112yes—
272#107C22×D1111yescharacteristic
273#107C22×D1111yescharacteristic
274#106—21no—
275#103—221no—
276#103—221no—
277#102—221no—
278#102—221no—
279C4×C8—111no—
280C4×C8—111no—
281C4×C8—111no—
282C4×C8—111no—
283C2×C11—22no—
284C2×C11C2×#47411yescharacteristic
285C2×C11C2×#50911yescharacteristic
286C2×C11C2×#51011yescharacteristic
287D11—82no—
288#41—224no—
289#41—442no—
290C2×Q8—221no—
291C2×Q8—442no—
292C2×Q8—442no—
293C2×Q8—884no—
294C2×D4—221no—
295C2×D4—441no—
296C22×C4—41no—
297C22×C4—111no—
298C22×C4—111no—
299C22×C4—441no—
300C22×C4—441no—
301C22×C4—441no—
302C22×C4—441no—
303C22×C4D4×D1111yescharacteristic
304Q16—112no—
305Q16—221no—
306SD16—224no—
307D8—112no—
308D8—221no—
309C2×C8—111no—
310C2×C8—111no—
311C2×C8—222no—
312C2×C8#433912yes—
313C2×C8D4×D1111yescharacteristic
314C2×C8Q8×D1112yes—
315C2×C8C23×D1111yescharacteristic
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—22no—
319C4⋊C4—41no—
320C4⋊C4—222no—
321C4⋊C4—442no—
322C4⋊C4—442no—
323C4⋊C4—441no—
324C4⋊C4—441no—
325C4⋊C4—441no—
326C22⋊C4—41no—
327C22⋊C4—441no—
328C22⋊C4—441no—
329C42—41no—
330C42—111no—
331C42—111no—
332C42—111no—
333C42—111no—
334C42—441no—
335C42—441no—
336C16—22no—
337C16—222no—
338C11#3362911yescharacteristic, complemented, Sylow
339C23—441no—
340C23D8×D1111yescharacteristic
341Q8—222no—
342Q8—441no—
343Q8—884no—
344Q8—884no—
345D4—222no—
346D4—444no—
347D4—441no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—82no—
352C2×C4—111no—
353C2×C4—111no—
354C2×C4—111no—
355C2×C4—111no—
356C2×C4—222no—
357C2×C4—222no—
358C2×C4—441no—
359C2×C4—444no—
360C2×C4—442no—
361C2×C4—882no—
362C2×C4—882no—
363C2×C4—882no—
364C2×C4#6694912yes—
365C2×C4D8×D1111yescharacteristic
366C2×C4#6697112yes—
367C2×C4C2×D4×D1111yescharacteristic
368C8—221no—
369C8—221no—
370C8#6694912yes—
371C8C2×#433911yescharacteristic
372C8C2×Q8×D1111yescharacteristic
373C22—21no—
374C22—21no—
375C22—442no—
376C22—881no—
377C22—881no—
378C22#1062250312yes—
379C22C2×D8×D1111yescharacteristic
380C4—82no—
381C4—81no—
382C4—81no—
383C4—112no—
384C4—112no—
385C4—221no—
386C4—221no—
387C4—442no—
388C4—882no—
389C4#1062250312yes—
390C4C2×#6694911yescharacteristic
391C4C2×#6697111yescharacteristic
392C2—22no—
393C2—882no—
394C2C2×#1062250311yescharacteristic
395C2D11×#50911yescharacteristic
396C2D11×#51011yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2159C2
socleC22×C11C22×D8
prime radicalC2×#66957C22
hypercenter#2159D11
hypocenterC11#33629
LCSG ▷ C2×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
1. C2×#10622487C2semidirect
3. #13070767C2semidirect
4. #13070762C2semidirect
5. #13070757C2semidirect
6. #13070752C2semidirect
7. #13070405C2semidirect
8. #13070371C2semidirect
11. C11×#2159C2semidirect
54. #66957Q8semidirect
135. Dic44C2×Q8semidirect
137. D88C2×Q8semidirect
148. #2159D11semidirect
338. C11#33629semidirect

Maximal subgroups

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

subgroupindex
C2×#106224872
#130773872
#130707672
#130707622
#130707572
#130707522
#130704052
#130703712
#130703292
#130703262
C11×#21592
#3362911