Finite Group Databasebeta

← #14909871

Subgroups — #14909871

Order 2816.

538 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079192C211yesmaximal, characteristic
2D11×#500C211yesmaximal, characteristic, complemented
3#13070890C212yesmaximal, complemented
4#13070838C212yesmaximal, complemented
5#13070798C212yesmaximal, complemented
6#13070795C212yesmaximal, complemented
7#13070754C211yesmaximal, characteristic, complemented
8#13070753C211yesmaximal, characteristic, complemented
9#13070750C211yesmaximal, characteristic, complemented
10#13070414C211yesmaximal, characteristic, complemented
11C11×#2224C211yesmaximal, characteristic, complemented
12D11×C4⋊Q8—21no—
13#10623079—21no—
14C11×#500C2211yescharacteristic
15C4×C11×D8C2211yescharacteristic
16#10622770C2211yescharacteristic
17#10622764C2211yescharacteristic
18#10622691—21no—
19C4×#4323—21no—
20#10622496C2211yescharacteristic
21D11×#107—21no—
22D11×#107C2212yes—
23#10622487—21no—
24#10622487C2211yescharacteristic
25#10622487C2212yes—
26#10622388—21no—
27#10622373—21no—
28C4×D88C2211yescharacteristic
29C4×C8×D11C2211yescharacteristic
30#10622295C2211yescharacteristic
31C11×#366C2212yes—
32C11×C4⋊C16C2211yescharacteristic
33C11×#357C2212yes—
34#10622200C2212yes—
35#10622147C2212yes—
36(C2×D11)⋊C16C2212yes—
37#10622142C2212yes—
38C16×Dic11C2212yes—
39#10622129C2212yes—
40#10622127C2212yes—
41#10622127C2212yes—
42C4⋊(C11⋊C16)C2211yescharacteristic
43C2×Q8×D11—41no—
44C2×#4339—41no—
45C2×C11×D8C2311yescharacteristic
46C11×C4⋊Q8—21no—
47C4×D4×C11—21no—
48#66997—41no—
49#66993—21no—
50#66991—21no—
51C2×#4323—21no—
52C4×C22⋊D11—41no—
53C2×D88C2311yescharacteristic
54C2×C8×D11D411yescharacteristic
55C2×C8×D11C2311yescharacteristic
56#66948—21no—
57C4⋊C4×D11—22no—
58C4⋊C4×D11—41no—
59#66941—22no—
60#66941—21no—
61#66941—41no—
62#66938—41no—
63#66937—41no—
64C4×D44—21no—
65C42×D11D411yescharacteristic
66#66922—21no—
67C2×C11×C16C2312yes—
68C11×#107—21no—
69C11×#107C2312yes—
70C11×#107C2311yescharacteristic
71C11×#102—21no—
72C4×C8×C11C2311yescharacteristic
73#66896—21no—
74#66885—21no—
75#66882—21no—
76#66882C2312yes—
77#66882C2311yescharacteristic
78C8×Dic11D411yescharacteristic
79C8×Dic11C2311yescharacteristic
80C2×C11⋊C16C2312yes—
81#66873—21no—
82#66871—22no—
83#66871—22no—
84#66871—21no—
85C4×C11⋊C8D411yescharacteristic
86#33792—111nomaximal, Sylow
87C2×Q8×C11—41no—
88C2×D4×C11—21no—
89C22×C4×C11—41no—
90C2×C22⋊D11—41no—
91C2×C22⋊D11—41no—
92C2×C22⋊D11—41no—
93Q8×D11—84no—
94#4339—84no—
95C2×D44—21no—
96C2×D44—41no—
97C2×C4×D11—42no—
98C2×C4×D11—41no—
99C2×C4×D11D811yescharacteristic
100C2×C4×D11D811yescharacteristic
101C2×C4×D11C2×D411yescharacteristic
102C2×Dic22—41no—
103C2×Dic22—42no—
104C2×Dic22—41no—
105C11×D8—21no—
106C11×D8—21no—
107C2×C8×C11C2×D411yescharacteristic
108C2×C8×C11C2411yescharacteristic
109C11×C4⋊C4—22no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—41no—
112C11×C22⋊C4—41no—
113C42×C11C2×D411yescharacteristic
114C22⋊Dic11—41no—
115#4323—42no—
116(C2×D11)⋊C4—41no—
117(C2×D11)⋊C4—41no—
118C4⋊Dic11—22no—
119C4⋊Dic11—21no—
120C4⋊Dic11—41no—
121Dic11⋊C4—41no—
122Dic11⋊C4—42no—
123Dic11⋊C4—42no—
124C4×Dic11D811yescharacteristic
125C4×Dic11D811yescharacteristic
126C4×Dic11C2×D411yescharacteristic
127C2×C11⋊C8C2×D411yescharacteristic
128C2×C11⋊C8C2×D411yescharacteristic
129D88—21no—
130D88—21no—
131C8×D11—21no—
132C8×D11—21no—
133C8×D11—22no—
134C11×C16—22no—
135C11⋊C16—22no—
136#3169—111no—
137C2×#500—111no—
138#2252—112no—
139#2240—112no—
140#2232—112no—
141#2232—112no—
142#2224—111no—
143#2224—111no—
144#2224—111no—
145#2224D1111yescharacteristic, complemented
146#2162—111no—
147C23×C11—41no—
148C22×D11—41no—
149C22×D11C2×D811yescharacteristic
150Q8×C11—82no—
151D4×C11—41no—
152D4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—41no—
155C2×C4×C11—82no—
156C2×C4×C11C2×D811yescharacteristic
157C2×C4×C11C2×D811yescharacteristic
158C2×C4×C11C22×D411yescharacteristic
159C22⋊D11—82no—
160C22⋊D11—82no—
161C22⋊D11—82no—
162C2×Dic11—42no—
163C2×Dic11—41no—
164C2×Dic11C2×D811yescharacteristic
165C2×Dic11C2×D811yescharacteristic
166C2×Dic11C2×D811yescharacteristic
167D44—41no—
168D44—41no—
169D44—82no—
170C4×D11—21no—
171C4×D11—21no—
172C4×D11—22no—
173C4×D11—84no—
174C4×D11—82no—
175C4×D11D1614yes—
176Dic22—82no—
177Dic22—82no—
178Dic22—84no—
179C8×C11—21no—
180C8×C112−1+411yescharacteristic
181C8×C112−1+411yescharacteristic
182C11⋊C8—21no—
183C11⋊C8#13712yes—
184#532—221no—
185C2×C4⋊Q8—221no—
186#500—112no—
187#500—111no—
188#500—111no—
189#500—221no—
190#500—221no—
191#500C2×D1111yescharacteristic
192#493—111no—
193#486—221no—
194#466—111no—
195#466—111no—
196#466—221no—
197C4×D8—111no—
198C4×D8—221no—
199C4×D8C2×D1111yescharacteristic
200C2×#107—112no—
201C2×#107—221no—
202C2×C4×C8—111no—
203#366—112no—
204#366—112no—
205#366—112no—
206#366C2×D1112yes—
207C4⋊C16—111no—
208C4⋊C16C2×D1111yescharacteristic
209#357—112no—
210#357—112no—
211#357—112no—
212#357C2×D1112yes—
213C22⋊C16—112no—
214C4×C16—112no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11C22×D811yescharacteristic
219C2×D11—21no—
220C2×D11—21no—
221C2×D11—81no—
222C2×D11—81no—
223C2×D11—81no—
224C2×D11C2×D1612yes—
225C4×C11—21no—
226C4×C11—81no—
227C4×C11—82no—
228C4×C11C2×D1612yes—
229C4×C11#53611yescharacteristic
230C4×C11C2×#13711yescharacteristic
231Dic11—21no—
232Dic11—82no—
233Dic11—81no—
234Dic11C2×D1612yes—
235Dic11#51012yes—
236C2×#41—441no—
237C22×Q8—441no—
238C2×D8—111no—
239C2×D8—221no—
240C2×D8C22×D1111yescharacteristic
241C22×C8—111no—
242C22×C8—111no—
243C4⋊Q8—21no—
244C4⋊Q8—222no—
245C4⋊Q8—221no—
246C4⋊Q8—221no—
247C4⋊Q8—441no—
248C4⋊Q8—441no—
249#127—221no—
250#124—441no—
251#121—221no—
252#121—221no—
253#121—441no—
254C4×D4—21no—
255C4×D4—221no—
256C4×D4—441no—
257C2×C4⋊C4—222no—
258C2×C4⋊C4—441no—
259C2×C42—111no—
260C2×C16—112no—
261C2×C16C22×D1112yes—
262#107—21no—
263#107—112no—
264#107—111no—
265#107—222no—
266#107—222no—
267#107—221no—
268#107—221no—
269#107C22×D1112yes—
270#107C22×D1111yescharacteristic
271#102—21no—
272#102—221no—
273#102—221no—
274#102—221no—
275C4×C8—111no—
276C4×C8—111no—
277C4×C8—111no—
278C4×C8C22×D1111yescharacteristic
279C2×C11—161no—
280C2×C11#322611yescharacteristic
281C2×C11C22×D1611yescharacteristic
282C2×C11C2×#51011yescharacteristic
283D11—22no—
284D11—161no—
285#41—884no—
286C2×Q8—41no—
287C2×Q8—441no—
288C2×Q8—442no—
289C2×Q8—441no—
290C2×Q8—884no—
291C2×D4—21no—
292C2×D4—221no—
293C2×D4—441no—
294C2×D4—441no—
295C2×D4—441no—
296C2×D4—441no—
297C22×C4—41no—
298C22×C4—111no—
299C22×C4—111no—
300C22×C4—111no—
301C22×C4—442no—
302C22×C4—441no—
303D8—21no—
304D8—21no—
305D8—221no—
306D8—221no—
307D8—442no—
308C2×C8—111no—
309C2×C8—111no—
310C2×C8—222no—
311C2×C8—221no—
312C2×C8—221no—
313C2×C8D4×D1111yescharacteristic
314C2×C8C23×D1111yescharacteristic
315C4⋊C4—21no—
316C4⋊C4—22no—
317C4⋊C4—41no—
318C4⋊C4—221no—
319C4⋊C4—222no—
320C4⋊C4—442no—
321C4⋊C4—442no—
322C4⋊C4—441no—
323C4⋊C4—441no—
324C22⋊C4—41no—
325C22⋊C4—441no—
326C22⋊C4—441no—
327C22⋊C4—441no—
328C42—111no—
329C42—111no—
330C42—111no—
331C42D4×D1111yescharacteristic
332C16—22no—
333C16—222no—
334C11#3379211yescharacteristic, complemented, Sylow
335C23—41no—
336C23—111no—
337C23—441no—
338Q8—82no—
339Q8—884no—
340Q8—882no—
341Q8—882no—
342D4—41no—
343D4—41no—
344D4—441no—
345D4—441no—
346D4—882no—
347D4—882no—
348D4—882no—
349D4—882no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—82no—
353C2×C4—111no—
354C2×C4—111no—
355C2×C4—114no—
356C2×C4—111no—
357C2×C4—222no—
358C2×C4—221no—
359C2×C4—221no—
360C2×C4—441no—
361C2×C4—442no—
362C2×C4—884no—
363C2×C4—882no—
364C2×C4D8×D1111yescharacteristic
365C2×C4D8×D1111yescharacteristic
366C2×C4C2×D4×D1111yescharacteristic
367C8—21no—
368C8—112no—
369C8—221no—
370C8#6704011yescharacteristic
371C8#6704311yescharacteristic
372C22—81no—
373C22—81no—
374C22—81no—
375C22—112no—
376C22—221no—
377C22—221no—
378C22—881no—
379C22—881no—
380C22—881no—
381C22C2×D8×D1111yescharacteristic
382C4—21no—
383C4—81no—
384C4—82no—
385C4—112no—
386C4—112no—
387C4—221no—
388C4—881no—
389C4—882no—
390C4D11×D1612yes—
391C4#1062315911yescharacteristic
392C4D11×#13711yescharacteristic
393C2—161no—
394C2—222no—
395C2—1761no—
396C2#1307973611yescharacteristic
397C2C2×D11×D1611yescharacteristic
398C2D11×#51011yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2224C2
socleC22×C11C22×D8
prime radical#13079192C2
hypercenter#2224D11
hypocenterC11#33792
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2224

Complements

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

NH ≅ G/Ntype
2. D11×#500C2semidirect
3. #13070890C2semidirect
4. #13070838C2semidirect
5. #13070798C2semidirect
6. #13070795C2semidirect
7. #13070754C2semidirect
8. #13070753C2semidirect
9. #13070750C2semidirect
10. #13070414C2semidirect
11. C11×#2224C2semidirect
145. #2224D11semidirect
334. C11#33792semidirect

Maximal subgroups

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

subgroupindex
#130791922
D11×#5002
#130708902
#130708382
#130707982
#130707952
#130707542
#130707532
#130707502
#130704142
C11×#22242
#3379211