Finite Group Databasebeta

← #14909894

Subgroups — #14909894

Order 2816.

494 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079199C211yesmaximal, characteristic
2D11×#500C211yesmaximal, characteristic
3#13070897C212yesmaximal, complemented
4#13070842C212yesmaximal, complemented
5#13070815C212yesmaximal
6#13070812C212yesmaximal
7#13070759C211yesmaximal, characteristic, complemented
8#13070758C211yesmaximal, characteristic, complemented
9#13070755C211yesmaximal, characteristic, complemented
10#13070414C211yesmaximal, characteristic
11C11×#2225C211yesmaximal, characteristic, complemented
12D11×C4⋊Q8—21no—
13#10623109—21no—
14C11×#500C2211yescharacteristic
15C4×C11×Q16C2211yescharacteristic
16#10622801C2211yescharacteristic
17#10622794C2211yescharacteristic
18#10622691—21no—
19C4×#4326—21no—
20#10622500C2211yescharacteristic
21D11×#107—21no—
22D11×#107C2212yes—
23#10622487—21no—
24#10622487C2211yescharacteristic
25#10622487C2212yes—
26#10622426—21no—
27#10622405—21no—
28C4×Dic44C2211yescharacteristic
29C4×C8×D11C2211yescharacteristic
30#10622295C2211yescharacteristic
31C11×#367C2212yes—
32C11×C4⋊C16C2211yescharacteristic
33C11×#358C2212yes—
34#10622202C2212yes—
35(C2×D11)⋊C16C2212yes—
36#10622143C2212yes—
37#10622141C2212yes—
38C16×Dic11C2212yes—
39#10622130C2212yes—
40#10622128C2212yes—
41#10622128C2212yes—
42C4⋊(C11⋊C16)C2211yescharacteristic
43C2×Q8×D11—41no—
44C2×C11×Q16C2311yescharacteristic
45C11×C4⋊Q8—21no—
46C4×Q8×C11—21no—
47#66999—21no—
48#66997—21no—
49#66997—41no—
50C2×#4326—21no—
51C2×Dic44C2311yescharacteristic
52C2×C8×D11D411yescharacteristic
53C2×C8×D11C2311yescharacteristic
54#66950—21no—
55#66949—41no—
56C4⋊C4×D11—22no—
57C4⋊C4×D11—41no—
58#66942—41no—
59#66941—22no—
60#66941—21no—
61#66941—41no—
62#66925—41no—
63C42×D11D411yescharacteristic
64#66922—21no—
65C4×Dic22—21no—
66C4×Dic22—41no—
67C2×C11×C16C2312yes—
68C11×#107—21no—
69C11×#107C2312yes—
70C11×#107C2311yescharacteristic
71C11×#103—21no—
72C4×C8×C11C2311yescharacteristic
73#66899—21no—
74#66882—21no—
75#66882C2312yes—
76#66882C2311yescharacteristic
77#66880—21no—
78C8×Dic11D411yescharacteristic
79C8×Dic11C2311yescharacteristic
80C2×C11⋊C16C2312yes—
81#66874—21no—
82#66871—22no—
83#66871—22no—
84#66871—21no—
85C4×C11⋊C8D411yescharacteristic
86#33795—111nomaximal, Sylow
87C2×Q8×C11—21no—
88C2×Q8×C11—41no—
89Q8×D11—84no—
90C2×C4×D11—42no—
91C2×C4×D11D811yescharacteristic
92C2×C4×D11D811yescharacteristic
93C2×C4×D11C2×D411yescharacteristic
94C2×Dic22—21no—
95C2×Dic22—41no—
96C2×Dic22—42no—
97C2×Dic22—41no—
98C11×Q16—21no—
99C11×Q16—21no—
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2411yescharacteristic
102C11×C4⋊C4—22no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C42×C11—41no—
107C42×C11C2×D411yescharacteristic
108#4326—42no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—41no—
111C4⋊Dic11—22no—
112C4⋊Dic11—21no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115Dic11⋊C4—41no—
116Dic11⋊C4—41no—
117Dic11⋊C4—41no—
118Dic11⋊C4—41no—
119Dic11⋊C4—42no—
120Dic11⋊C4—42no—
121Dic11⋊C4—41no—
122C4×Dic11—41no—
123C4×Dic11D811yescharacteristic
124C4×Dic11D811yescharacteristic
125C4×Dic11C2×D411yescharacteristic
126C2×C11⋊C8C2×D411yescharacteristic
127C2×C11⋊C8C2×D411yescharacteristic
128Dic44—21no—
129Dic44—21no—
130C8×D11—21no—
131C8×D11—21no—
132C8×D11—22no—
133C11×C16—22no—
134C11⋊C16—22no—
135#3170—111no—
136C2×#500—111no—
137#2254—112no—
138#2241—112no—
139#2235—112no—
140#2235—112no—
141#2225—111no—
142#2225—111no—
143#2225—111no—
144#2225D1111yescharacteristic, complemented
145#2162—111no—
146C22×D11C2×D811yescharacteristic
147Q8×C11—41no—
148Q8×C11—41no—
149Q8×C11—82no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—41no—
153C2×C4×C11C2×D811yescharacteristic
154C2×C4×C11C2×D811yescharacteristic
155C2×C4×C11C22×D411yescharacteristic
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—42no—
159C2×Dic11C2×D811yescharacteristic
160C2×Dic11C2×D811yescharacteristic
161C2×Dic11C2×D811yescharacteristic
162C4×D11—21no—
163C4×D11—21no—
164C4×D11—22no—
165C4×D11—84no—
166C4×D11SD3214yes—
167Dic22—41no—
168Dic22—41no—
169Dic22—82no—
170Dic22—84no—
171Dic22—82no—
172C8×C11—21no—
173C8×C112−1+411yescharacteristic
174C8×C112−1+411yescharacteristic
175C11⋊C8—21no—
176C11⋊C8#13712yes—
177#533—221no—
178C2×C4⋊Q8—221no—
179#500—112no—
180#500—111no—
181#500—111no—
182#500—221no—
183#500—221no—
184#500C2×D1111yescharacteristic
185#494—111no—
186#487—221no—
187#467—111no—
188#467—111no—
189#467—221no—
190C4×Q16—111no—
191C4×Q16—221no—
192C4×Q16C2×D1111yescharacteristic
193C2×#107—112no—
194C2×#107—221no—
195C2×C4×C8—111no—
196#367—112no—
197#367—112no—
198#367—112no—
199#367C2×D1112yes—
200C4⋊C16—111no—
201C4⋊C16C2×D1111yescharacteristic
202#358—112no—
203#358—112no—
204#358—112no—
205#358C2×D1112yes—
206C22⋊C16—112no—
207C4×C16—112no—
208C22×C11C22×D811yescharacteristic
209C2×D11—21no—
210C2×D11—21no—
211C2×D11C2×SD3212yes—
212C4×C11—21no—
213C4×C11—82no—
214C4×C11—81no—
215C4×C11—81no—
216C4×C11C2×SD3212yes—
217C4×C11#53611yescharacteristic
218C4×C11C2×#13711yescharacteristic
219Dic11—21no—
220Dic11—82no—
221Dic11—81no—
222Dic11—81no—
223Dic11C2×SD3212yes—
224Dic11#51012yes—
225C22×Q8—441no—
226C2×Q16—111no—
227C2×Q16—221no—
228C2×Q16C22×D1111yescharacteristic
229C22×C8—111no—
230C22×C8—111no—
231C4⋊Q8—21no—
232C4⋊Q8—222no—
233C4⋊Q8—221no—
234C4⋊Q8—221no—
235C4⋊Q8—221no—
236C4⋊Q8—441no—
237C4⋊Q8—441no—
238#125—441no—
239C22⋊Q8—221no—
240C22⋊Q8—221no—
241C22⋊Q8—441no—
242C4×Q8—21no—
243C4×Q8—221no—
244C4×Q8—441no—
245#117—441no—
246C2×C4⋊C4—222no—
247C2×C4⋊C4—441no—
248C2×C42—111no—
249C2×C16—112no—
250C2×C16C22×D1112yes—
251#107—21no—
252#107—112no—
253#107—111no—
254#107—222no—
255#107—222no—
256#107—221no—
257#107—221no—
258#107C22×D1112yes—
259#107C22×D1111yescharacteristic
260#103—21no—
261#103—221no—
262#103—221no—
263#103—221no—
264C4×C8—111no—
265C4×C8—111no—
266C4×C8—111no—
267C4×C8C22×D1111yescharacteristic
268C2×C11#322611yescharacteristic
269C2×C11C22×SD3211yescharacteristic
270C2×C11C2×#51011yescharacteristic
271D11—22no—
272C2×Q8—21no—
273C2×Q8—41no—
274C2×Q8—221no—
275C2×Q8—441no—
276C2×Q8—442no—
277C2×Q8—441no—
278C2×Q8—884no—
279C22×C4—111no—
280C22×C4—111no—
281C22×C4—111no—
282C22×C4—442no—
283Q16—21no—
284Q16—21no—
285Q16—221no—
286Q16—221no—
287Q16—442no—
288C2×C8—111no—
289C2×C8—111no—
290C2×C8—222no—
291C2×C8—221no—
292C2×C8—221no—
293C2×C8D4×D1111yescharacteristic
294C2×C8C23×D1111yescharacteristic
295C4⋊C4—21no—
296C4⋊C4—22no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—221no—
300C4⋊C4—222no—
301C4⋊C4—442no—
302C4⋊C4—442no—
303C4⋊C4—441no—
304C4⋊C4—441no—
305C4⋊C4—441no—
306C4⋊C4—441no—
307C4⋊C4—441no—
308C4⋊C4—441no—
309C4⋊C4—441no—
310C22⋊C4—441no—
311C22⋊C4—441no—
312C42—41no—
313C42—111no—
314C42—111no—
315C42—111no—
316C42—441no—
317C42D4×D1111yescharacteristic
318C16—22no—
319C16—222no—
320C11#3379511yescharacteristic, complemented, Sylow
321C23—111no—
322Q8—41no—
323Q8—41no—
324Q8—82no—
325Q8—441no—
326Q8—441no—
327Q8—884no—
328Q8—882no—
329Q8—882no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—111no—
334C2×C4—111no—
335C2×C4—114no—
336C2×C4—111no—
337C2×C4—222no—
338C2×C4—221no—
339C2×C4—221no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—442no—
343C2×C4—884no—
344C2×C4D8×D1111yescharacteristic
345C2×C4D8×D1111yescharacteristic
346C2×C4C2×D4×D1111yescharacteristic
347C8—21no—
348C8—112no—
349C8—221no—
350C8#6704011yescharacteristic
351C8#6704311yescharacteristic
352C22—112no—
353C22—221no—
354C22—221no—
355C22C2×D8×D1111yescharacteristic
356C4—21no—
357C4—82no—
358C4—81no—
359C4—81no—
360C4—112no—
361C4—112no—
362C4—221no—
363C4—882no—
364C4—881no—
365C4—881no—
366C4D11×SD3212yes—
367C4#1062315911yescharacteristic
368C4D11×#13711yescharacteristic
369C2—222no—
370C2#1307973611yescharacteristic
371C2C2×D11×SD3211yescharacteristic
372C2D11×#51011yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2225C2
socleC22×C11C22×D8
prime radicalC22×D11C2×D8
hypercenter#2225D11
hypocenterC11#33795
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2225

Complements

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

NH ≅ G/Ntype
3. #13070897C2semidirect
4. #13070842C2semidirect
7. #13070759C2semidirect
8. #13070758C2semidirect
9. #13070755C2semidirect
11. C11×#2225C2semidirect
144. #2225D11semidirect
320. C11#33795semidirect

Maximal subgroups

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

subgroupindex
#130791992
D11×#5002
#130708972
#130708422
#130708152
#130708122
#130707592
#130707582
#130707552
#130704142
C11×#22252
#3379511