Finite Group Databasebeta

← #14908419

Subgroups — #14908419

Order 2816.

546 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079130C211yesmaximal, characteristic, complemented
2#13070780C212yesmaximal, complemented
3#13070773C212yesmaximal, complemented
4#13070768C211yesmaximal, characteristic, complemented
5#13070763C211yesmaximal, characteristic, complemented
6#13070758C211yesmaximal, characteristic, complemented
7#13070753C211yesmaximal, characteristic, complemented
8#13070398C212yesmaximal, complemented
9C2×C4⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
10#13070323C212yesmaximal
11C4×C11×#135C211yesmaximal, characteristic
12C2×C11×#135C2211yescharacteristic
13C4×C11×#41—21no—
14#10623001—21no—
15C4×C11×Q16C2211yescharacteristic
16C4×C11×Q16C2211yescharacteristic
17C4×C11×SD16—21no—
18C4×C11×SD16—21no—
19C4×C11×D8C2211yescharacteristic
20C4×C11×D8C2211yescharacteristic
21C11×#427C2211yescharacteristic
22C11×#416—21no—
23C2×C4×C8×C11C2211yescharacteristic
24#10622719—21no—
25#10622719C2212yes—
26C22×C11⋊C16C2212yes—
27#10622296—21no—
28#10622296C2212yes—
29#10622295C2211yescharacteristic
30#10622295C2211yescharacteristic
31#10622293—21no—
32#10622202C2212yes—
33#10622202C2212yes—
34#10622200C2212yes—
35#10622200C2212yes—
36#10622128C2212yes—
37#10622128C2212yes—
38#10622127C2212yes—
39#10622127C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C4⋊(C11⋊C16)C2211yescharacteristic
42C4⋊(C11⋊C16)C2212yes—
43C2×C11×#41—21no—
44C11×#135—22no—
45C11×#135Q814yescomplemented
46C2×C11×Q16C2311yescharacteristic
47C2×C11×SD16—21no—
48C2×C11×D8C2311yescharacteristic
49C22×C8×C11D411yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C4×Q8×C11—21no—
52C4×Q8×C11—21no—
53C4×D4×C11—21no—
54C4×D4×C11—21no—
55C4×D4×C11—41no—
56C4×D4×C11—41no—
57C11×#117—21no—
58C11×#117—41no—
59C2×C42×C11—41no—
60C2×C42×C11D411yescharacteristic
61#66979—22no—
62#66977—41no—
63#66977—41no—
64#66923—22no—
65#66922—21no—
66#66922—21no—
67C4×Dic22—41no—
68C4×Dic22—41no—
69C11×#107C2311yescharacteristic
70C11×#107C2311yescharacteristic
71C11×#106—21no—
72C11×#103—21no—
73C11×#103—21no—
74C11×#102—21no—
75C11×#102—21no—
76C4×C8×C11D411yescharacteristic
77C4×C8×C11D411yescharacteristic
78C4×C8×C11C2311yescharacteristic
79C4×C8×C11C2311yescharacteristic
80#66882—21no—
81#66882—21no—
82#66882C2312yes—
83#66882C2312yes—
84#66881—22no—
85#66881—22no—
86C2×C11⋊C16—24no—
87C2×C11⋊C16C2312yes—
88C2×C11⋊C16C2312yes—
89#33626—111nomaximal, Sylow
90C11×#41—24no—
91C11×#41—42no—
92C2×Q8×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11D811yescharacteristic
99C22×C4×C11D811yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C2×Dic22—41no—
102C2×Dic22—41no—
103C11×Q16—21no—
104C11×Q16C2×Q812yes—
105C11×SD16—24no—
106C11×D8—21no—
107C11×D8C2×Q812yes—
108C2×C8×C11—22no—
109C2×C8×C11C2×D411yescharacteristic
110C2×C8×C11C2×D411yescharacteristic
111C2×C8×C11C2×D411yescharacteristic
112C2×C8×C11C2×Q812yes—
113C2×C8×C11#4112yes—
114C2×C8×C11C2411yescharacteristic
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C42×C11—41no—
123C42×C11—41no—
124C42×C11—41no—
125C42×C11D811yescharacteristic
126C42×C11D811yescharacteristic
127C42×C11C2×D411yescharacteristic
128C42×C11C2×D411yescharacteristic
129C22⋊Dic11—42no—
130C4⋊Dic11—22no—
131C4⋊Dic11—22no—
132C4⋊Dic11—41no—
133C4⋊Dic11—41no—
134Dic11⋊C4—42no—
135Dic11⋊C4—42no—
136C4×Dic11—42no—
137C11⋊C16—22no—
138C11⋊C16—22no—
139#3160—111no—
140C4×#135D1111yescharacteristic
141#2229—112no—
142#2228—112no—
143#2227—111no—
144#2226—111no—
145#2225—111no—
146#2224—111no—
147#2158—112no—
148C2×C4⋊C16—111no—
149#2138—112no—
150C23×C11—41no—
151C23×C11C2×D811yescharacteristic
152Q8×C11—22no—
153Q8×C11—41no—
154D4×C11—22no—
155D4×C11—44no—
156D4×C11—41no—
157C2×C4×C11—22no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—44no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—82no—
164C2×C4×C11—82no—
165C2×C4×C11C22⋊Q812yes—
166C2×C4×C11C2×D811yescharacteristic
167C2×C4×C11C2×D811yescharacteristic
168C2×C4×C11C2×D811yescharacteristic
169C2×C4×C11C2×D811yescharacteristic
170C2×C4×C11C2×D811yescharacteristic
171C2×C4×C11#13712yes—
172C2×C4×C11C22×D411yescharacteristic
173C2×Dic11—42no—
174C2×Dic11—42no—
175Dic22—82no—
176Dic22—82no—
177C8×C11—21no—
178C8×C11—21no—
179C8×C11C22⋊Q812yes—
180C8×C11C22×Q811yescharacteristic
181C8×C11C2×#4111yescharacteristic
182C2×#135C2×D1111yescharacteristic
183#533—221no—
184C4×#41—21no—
185C22×C16—112no—
186#500—111no—
187#500—111no—
188#499—112no—
189#499—221no—
190#498—221no—
191C4×Q16C2×D1111yescharacteristic
192C4×Q16C2×D1111yescharacteristic
193C4×SD16—21no—
194C4×SD16—21no—
195C4×D8C2×D1111yescharacteristic
196C4×D8C2×D1111yescharacteristic
197#427—112no—
198#427—221no—
199#427C2×D1111yescharacteristic
200#416—21no—
201C2×C4×C8C2×D1111yescharacteristic
202#367—112no—
203#367—112no—
204#366—112no—
205#366—112no—
206C4⋊C16—111no—
207C4⋊C16—111no—
208C4⋊C16—112no—
209#358—112no—
210#358—112no—
211#357—112no—
212#357—112no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—42no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11#47412yes—
219C22×C11C22×D811yescharacteristic
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—42no—
224C4×C11—81no—
225C4×C11—81no—
226C4×C11#47412yes—
227C4×C11#50812yes—
228C4×C11C2×C22⋊Q811yescharacteristic
229C4×C11C2×#13711yescharacteristic
230Dic11—82no—
231Dic11—82no—
232C2×#41—21no—
233#135—22no—
234#135Dic2214yescomplemented
235C2×Q16C22×D1111yescharacteristic
236C2×SD16—21no—
237C2×D8C22×D1111yescharacteristic
238C22×C8C22⋊D1111yescharacteristic
239C22×C8C22×D1111yescharacteristic
240C4⋊Q8—221no—
241C4⋊Q8—221no—
242#125—222no—
243C22⋊Q8—441no—
244C22⋊Q8—441no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×Q8—441no—
248C4×Q8—441no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4—41no—
252C4×D4—41no—
253#117—21no—
254#117—41no—
255#117—222no—
256C2×C42—41no—
257C2×C42C22⋊D1111yescharacteristic
258C2×C16—112no—
259C2×C16—112no—
260C2×C16—224no—
261#107—112no—
262#107—112no—
263#107—221no—
264#107—221no—
265#107C22×D1111yescharacteristic
266#107C22×D1111yescharacteristic
267#106—21no—
268#106—222no—
269#106—222no—
270#103—21no—
271#103—21no—
272#102—21no—
273#102—21no—
274C4×C8C22⋊D1111yescharacteristic
275C4×C8C22⋊D1111yescharacteristic
276C4×C8C22×D1111yescharacteristic
277C4×C8C22×D1111yescharacteristic
278C2×C11—22no—
279C2×C11—82no—
280C2×C11C2×#47411yescharacteristic
281C2×C11C2×#50811yescharacteristic
282C2×C11#341411yescharacteristic
283#41—24no—
284#41—42no—
285C2×Q8—21no—
286C2×Q8—441no—
287C2×Q8—441no—
288C2×D4—21no—
289C2×D4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4#432311yescharacteristic
294C22×C4#432311yescharacteristic
295C22×C4C2×C22⋊D1111yescharacteristic
296Q16—21no—
297Q16C2×Dic2212yes—
298SD16—24no—
299D8—21no—
300D8C2×Dic2212yes—
301C2×C8—22no—
302C2×C8C2×Dic2212yes—
303C2×C8#433912yes—
304C2×C8C2×C22⋊D1111yescharacteristic
305C2×C8C2×C22⋊D1111yescharacteristic
306C2×C8C2×C22⋊D1111yescharacteristic
307C2×C8C23×D1111yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—222no—
313C4⋊C4—222no—
314C4⋊C4—442no—
315C4⋊C4—442no—
316C4⋊C4—441no—
317C4⋊C4—441no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—442no—
322C42—41no—
323C42—41no—
324C42—41no—
325C42—442no—
326C42#432311yescharacteristic
327C42#432311yescharacteristic
328C42C2×C22⋊D1111yescharacteristic
329C42C2×C22⋊D1111yescharacteristic
330C16—222no—
331C16—222no—
332C11#3362611yescharacteristic, complemented, Sylow
333C23—41no—
334C23C2×#432311yescharacteristic
335Q8—22no—
336Q8—41no—
337Q8—882no—
338Q8—882no—
339D4—22no—
340D4—44no—
341D4—41no—
342C2×C4—22no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—44no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—82no—
349C2×C4—82no—
350C2×C4—442no—
351C2×C4—442no—
352C2×C4#6697712yes—
353C2×C4C2×#432311yescharacteristic
354C2×C4C2×#432311yescharacteristic
355C2×C4C2×#432311yescharacteristic
356C2×C4C2×#432311yescharacteristic
357C2×C4C2×#432311yescharacteristic
358C2×C4#6700412yes—
359C2×C4C22×C22⋊D1111yescharacteristic
360C8—21no—
361C8—21no—
362C8#6697712yes—
363C8C22×Dic2211yescharacteristic
364C8C2×#433911yescharacteristic
365C22—21no—
366C22—21no—
367C22—42no—
368C22—81no—
369C22—81no—
370C22#1062262012yes—
371C22C22×#432311yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—81no—
377C4—81no—
378C4—882no—
379C4—882no—
380C4#1062262012yes—
381C4#1062280712yes—
382C4C2×#6697711yescharacteristic
383C4C2×#6700411yescharacteristic
384C2—22no—
385C2—82no—
386C2C2×#1062262011yescharacteristic
387C2C2×#1062280711yescharacteristic
388C2#1308175011yescharacteristic
subgroupG/H
centerC2×C4C2×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×#135C2
socleC22×C11C22×D8
prime radicalC2×C11×#135C22
hypercenterC4×#135D11
hypocenterC11#33626
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
1. #13079130C2semidirect
2. #13070780C2semidirect
3. #13070773C2semidirect
4. #13070768C2semidirect
5. #13070763C2semidirect
6. #13070758C2semidirect
7. #13070753C2semidirect
8. #13070398C2semidirect
9. C2×C4⋊(C11⋊C16)C2semidirect
45. C11×#135Q8semidirect
234. #135Dic22semidirect
332. C11#33626semidirect

Maximal subgroups

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

subgroupindex
#130791302
#130707802
#130707732
#130707682
#130707632
#130707582
#130707532
#130703982
C2×C4⋊(C11⋊C16)2
#130703232
C4×C11×#1352
#3362611