Finite Group Databasebeta

← #14909870

Subgroups — #14909870

Order 2816.

538 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079190C211yesmaximal, characteristic
2C2×#10622487C211yesmaximal, characteristic, complemented
3#13070890C212yesmaximal, complemented
4#13070838C212yesmaximal, complemented
5#13070797C211yesmaximal, characteristic, complemented
6#13070796C211yesmaximal, characteristic, complemented
7#13070794C211yesmaximal, characteristic, complemented
8#13070752C212yesmaximal, complemented
9#13070751C212yesmaximal, complemented
10#13070412C211yesmaximal, characteristic, complemented
11C11×#2232C211yesmaximal, characteristic, complemented
12#10623127—21no—
13C2×#66941—21no—
14C11×#466C2211yescharacteristic
15C2×C11×#107C2211yescharacteristic
16#10622764C2211yescharacteristic
17D8×Dic11C2211yescharacteristic
18#10622728C2211yescharacteristic
19C2×#66882C2211yescharacteristic
20C2×C8×Dic11C2211yescharacteristic
21#10622651—21no—
22C2×#66871—21no—
23#10622487—21no—
24#10622487—21no—
25#10622487C2211yescharacteristic
26#10622487C2212yes—
27#10622487C2212yes—
28#10622485C2211yescharacteristic
29#10622373—21no—
30#10622369—21no—
31C11×#366C2212yes—
32C11×#357C2212yes—
33C11×C22⋊C16C2211yescharacteristic
34#10622200C2212yes—
35C22⋊(C11⋊C16)C2211yescharacteristic
36#10622147C2212yes—
37#10622142C2212yes—
38Dic11⋊C16C2212yes—
39C16×Dic11C2212yes—
40#10622129C2212yes—
41#10622127C2212yes—
42#10622127C2212yes—
43C2×#4341—41no—
44C22×Dic22—41no—
45C2×C11×D8C2311yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C11×#121—21no—
48C2×C11×C4⋊C4—21no—
49#66993—21no—
50#66992—41no—
51D4×Dic11—21no—
52C2×#4323—21no—
53#66983—21no—
54C2×C4⋊Dic11—21no—
55C2×Dic11⋊C4—41no—
56C2×C4×Dic11D411yescharacteristic
57C22×C11⋊C8D411yescharacteristic
58C2×D88C2311yescharacteristic
59#66946—21no—
60#66941—22no—
61#66941—22no—
62#66941—21no—
63#66941—41no—
64#66941—41no—
65#66938—41no—
66(C22⋊D11)⋊C4—41no—
67C2×C11×C16C2312yes—
68C11×#107—21no—
69C11×#107C2311yescharacteristic
70C11×#107C2312yes—
71C11×#102—21no—
72#66896—21no—
73#66885—21no—
74#66882—21no—
75#66882C2311yescharacteristic
76#66882C2312yes—
77C8×Dic11D411yescharacteristic
78C8×Dic11D411yescharacteristic
79C8×Dic11C2311yescharacteristic
80C8×Dic11C2311yescharacteristic
81C2×C11⋊C16C2312yes—
82#66873—21no—
83#66871—22no—
84#66871—22no—
85#66871—21no—
86#33792—111nomaximal, Sylow
87C2×D4×C11—21no—
88C2×D4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11C2×D411yescharacteristic
91C2×C22⋊D11—41no—
92C2×C22⋊D11—41no—
93C2×C22⋊D11—41no—
94C22×Dic11—41no—
95C22×Dic11—41no—
96C22×Dic11D811yescharacteristic
97C22×Dic11D811yescharacteristic
98#4341—84no—
99C2×D44—21no—
100C2×C4×D11—41no—
101C2×Dic22—41no—
102C2×Dic22—42no—
103C2×Dic22—42no—
104C2×Dic22—84no—
105C11×D8—22no—
106C2×C8×C11—22no—
107C2×C8×C11C2×D411yescharacteristic
108C2×C8×C11C2411yescharacteristic
109C11×C4⋊C4—22no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—41no—
112C11×C22⋊C4—41no—
113C22⋊Dic11—41no—
114#4323—42no—
115(C2×D11)⋊C4—41no—
116(C2×D11)⋊C4—41no—
117C4⋊Dic11—22no—
118C4⋊Dic11—21no—
119C4⋊Dic11—41no—
120Dic11⋊C4—41no—
121Dic11⋊C4—42no—
122Dic11⋊C4—42no—
123C4×Dic11D811yescharacteristic
124C4×Dic11D811yescharacteristic
125C4×Dic11C2×D411yescharacteristic
126C4×Dic11C2×D411yescharacteristic
127C2×C11⋊C8—22no—
128C2×C11⋊C8C2×D411yescharacteristic
129C2×C11⋊C8C2×D411yescharacteristic
130D88—22no—
131C11×C16—22no—
132C11⋊C16—22no—
133#3169—111no—
134C2×#500—111no—
135#2252—112no—
136#2240—112no—
137#2232—111no—
138#2232—111no—
139#2232—111no—
140#2232D1111yescharacteristic, complemented
141#2224—112no—
142#2224—112no—
143#2162—111no—
144C23×C11—41no—
145C23×C11C2×D811yescharacteristic
146C22×D11—41no—
147D4×C11—41no—
148D4×C11—41no—
149D4×C11—82no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—42no—
153C2×C4×C11—41no—
154C2×C4×C11—82no—
155C2×C4×C11C2×D811yescharacteristic
156C2×C4×C11C22×D411yescharacteristic
157C22⋊D11—82no—
158C22⋊D11—82no—
159C22⋊D11—82no—
160C2×Dic11—22no—
161C2×Dic11—42no—
162C2×Dic11—41no—
163C2×Dic11—82no—
164C2×Dic11—82no—
165C2×Dic11D1614yes—
166C2×Dic11C2×D811yescharacteristic
167C2×Dic11C2×D811yescharacteristic
168C2×Dic11C2×D811yescharacteristic
169C2×Dic11C2×D811yescharacteristic
170D44—41no—
171D44—41no—
172C4×D11—82no—
173Dic22—84no—
174Dic22—84no—
175Dic22—82no—
176C8×C11—21no—
177C8×C112−1+412yes—
178C11⋊C8—21no—
179C11⋊C8#13712yes—
180#532—221no—
181C2×C4⋊Q8—221no—
182#500—112no—
183#500—112no—
184#500—111no—
185#500—221no—
186#500—221no—
187#493—111no—
188#486—221no—
189#466—111no—
190#466—221no—
191#466C2×D1111yescharacteristic
192C4×D8—111no—
193C4×D8—111no—
194C4×D8—221no—
195C2×#107—111no—
196C2×#107—221no—
197C2×#107C2×D1111yescharacteristic
198C2×C4×C8—111no—
199#366—112no—
200#366—112no—
201#366—112no—
202#366C2×D1112yes—
203C4⋊C16—112no—
204#357—112no—
205#357—112no—
206#357—112no—
207#357C2×D1112yes—
208C22⋊C16—111no—
209C22⋊C16C2×D1111yescharacteristic
210C4×C16—112no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—81no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11C2×D1612yes—
217C22×C11C22×D811yescharacteristic
218C2×D11—81no—
219C2×D11—81no—
220C2×D11—81no—
221C4×C11—21no—
222C4×C11—82no—
223C4×C11—81no—
224C4×C11#53611yescharacteristic
225C4×C11C2×#13711yescharacteristic
226Dic11—21no—
227Dic11—82no—
228Dic11—81no—
229Dic11C2×D1612yes—
230Dic11C2×D1612yes—
231Dic11#51012yes—
232C2×#41—441no—
233C22×Q8—441no—
234C2×D8—111no—
235C2×D8—221no—
236C2×D8C22×D1111yescharacteristic
237C22×C8—111no—
238C22×C8C22×D1111yescharacteristic
239C4⋊Q8—222no—
240C4⋊Q8—222no—
241C4⋊Q8—221no—
242C4⋊Q8—441no—
243C4⋊Q8—441no—
244#127—221no—
245#124—441no—
246#121—21no—
247#121—221no—
248#121—441no—
249C4×D4—221no—
250C4×D4—221no—
251C4×D4—441no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—221no—
254C2×C4⋊C4—441no—
255C2×C42—111no—
256C2×C16—112no—
257C2×C16C22×D1112yes—
258#107—21no—
259#107—112no—
260#107—111no—
261#107—222no—
262#107—222no—
263#107—221no—
264#107—221no—
265#107C22×D1112yes—
266#107C22×D1111yescharacteristic
267#102—21no—
268#102—221no—
269#102—221no—
270#102—221no—
271C4×C8—111no—
272C4×C8—111no—
273C4×C8—111no—
274C4×C8—111no—
275C2×C11—22no—
276C2×C11—161no—
277C2×C11#322611yescharacteristic
278C2×C11C22×D1611yescharacteristic
279C2×C11C2×#51011yescharacteristic
280D11—161no—
281#41—884no—
282C2×Q8—441no—
283C2×Q8—442no—
284C2×Q8—442no—
285C2×Q8—884no—
286C2×D4—21no—
287C2×D4—41no—
288C2×D4—221no—
289C2×D4—441no—
290C2×D4—441no—
291C2×D4—441no—
292C22×C4—41no—
293C22×C4—111no—
294C22×C4—111no—
295C22×C4—441no—
296C22×C4—441no—
297C22×C4—441no—
298C22×C4D4×D1111yescharacteristic
299D8—22no—
300D8—222no—
301D8—442no—
302C2×C8—22no—
303C2×C8—111no—
304C2×C8—111no—
305C2×C8—222no—
306C2×C8D4×D1111yescharacteristic
307C2×C8C23×D1111yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—22no—
310C4⋊C4—41no—
311C4⋊C4—221no—
312C4⋊C4—222no—
313C4⋊C4—442no—
314C4⋊C4—442no—
315C4⋊C4—441no—
316C4⋊C4—441no—
317C22⋊C4—41no—
318C22⋊C4—441no—
319C22⋊C4—441no—
320C22⋊C4—441no—
321C42—111no—
322C42—111no—
323C42—111no—
324C42—111no—
325C16—22no—
326C16—222no—
327C11#3379211yescharacteristic, complemented, Sylow
328C23—41no—
329C23—441no—
330C23D8×D1111yescharacteristic
331Q8—884no—
332Q8—884no—
333Q8—882no—
334D4—41no—
335D4—41no—
336D4—82no—
337D4—441no—
338D4—441no—
339D4—882no—
340D4—882no—
341D4—882no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—82no—
347C2×C4—111no—
348C2×C4—111no—
349C2×C4—111no—
350C2×C4—114no—
351C2×C4—111no—
352C2×C4—222no—
353C2×C4—441no—
354C2×C4—442no—
355C2×C4—882no—
356C2×C4—882no—
357C2×C4—882no—
358C2×C4D8×D1111yescharacteristic
359C2×C4C2×D4×D1111yescharacteristic
360C8—21no—
361C8—112no—
362C8—221no—
363C8#6704312yes—
364C22—21no—
365C22—21no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—881no—
370C22—881no—
371C22—881no—
372C22D11×D1612yes—
373C22C2×D8×D1111yescharacteristic
374C4—21no—
375C4—82no—
376C4—81no—
377C4—112no—
378C4—112no—
379C4—112no—
380C4—221no—
381C4—881no—
382C4—882no—
383C4#1062317911yescharacteristic
384C4D11×#13711yescharacteristic
385C2—22no—
386C2—161no—
387C2—1761no—
388C2#1307973511yescharacteristic
389C2C2×D11×D1611yescharacteristic
390C2D11×#51011yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2232C2
socleC22×C11C22×D8
prime radical#13079190C2
hypercenter#2232D11
hypocenterC11#33792
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2232

Complements

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

NH ≅ G/Ntype
2. C2×#10622487C2semidirect
3. #13070890C2semidirect
4. #13070838C2semidirect
5. #13070797C2semidirect
6. #13070796C2semidirect
7. #13070794C2semidirect
8. #13070752C2semidirect
9. #13070751C2semidirect
10. #13070412C2semidirect
11. C11×#2232C2semidirect
140. #2232D11semidirect
327. C11#33792semidirect

Maximal subgroups

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

subgroupindex
#130791902
C2×#106224872
#130708902
#130708382
#130707972
#130707962
#130707942
#130707522
#130707512
#130704122
C11×#22322
#3379211