Finite Group Databasebeta

← #14909790

Subgroups — #14909790

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079186C211yesmaximal, characteristic, complemented
2#13079044C211yesmaximal, characteristic, complemented
3#13070887C211yesmaximal, characteristic, complemented
4#13070882C211yesmaximal, characteristic, complemented
5#13070862C211yesmaximal, characteristic, complemented
6#13070858C211yesmaximal, characteristic, complemented
7#13070679C212yesmaximal, complemented
8#13070672C212yesmaximal, complemented
9#13070558C212yesmaximal, complemented
10#13070541C212yesmaximal, complemented
11C11×#2163C211yesmaximal, characteristic, complemented
12C2×#66957—21no—
13C2×#66957C2212yes—
14#10623010—21no—
15#10623008—21no—
16C2×C4×C8×C11C2211yescharacteristic
17#10622729C2211yescharacteristic
18#10622728C2211yescharacteristic
19#10622727—21no—
20C2×Dic88C2212yes—
21C2×#66864C2212yes—
22C2×#66864C2212yes—
23C2×D176C2212yes—
24#10622312C2211yescharacteristic
25C4×Dic44C2211yescharacteristic
26#10622310—21no—
27#10622309—21no—
28#10622309C2212yes—
29#10622309C2211yescharacteristic
30#10622308C2211yescharacteristic
31#10622306—21no—
32C4×D88C2211yescharacteristic
33C4×#4314—21no—
34#10622296C2211yescharacteristic
35C11×C4⋊C16C2212yes—
36C11×C22⋊C16C2212yes—
37C11×#346C2211yescharacteristic
38C11×#346C2211yescharacteristic
39#10622147C2212yes—
40#10622147C2212yes—
41#10622141C2212yes—
42#10622141C2212yes—
43C2×#4339—22no—
44C22×C8×C11D411yescharacteristic
45C22×C8×C11C2311yescharacteristic
46C2×C42×C11D411yescharacteristic
47#66983—21no—
48#66983—41no—
49#66983—41no—
50#66982—41no—
51C4×C22⋊D11—41no—
52#66977—21no—
53C2×Dic44—21no—
54C2×Dic44C2311yescharacteristic
55C2×Dic44C2312yes—
56#66957—42no—
57#66957—42no—
58#66957—44no—
59C2×D88—21no—
60C2×D88C2311yescharacteristic
61C2×D88C2312yes—
62C2×#4314—21no—
63C2×#4314—22no—
64C2×#4314—22no—
65#66929—41no—
66#66928—22no—
67#66928—21no—
68#66927—21no—
69C4×D44—21no—
70C4×D44—41no—
71C4×D44—41no—
72#66925—41no—
73#66923—21no—
74#66922—21no—
75C4×Dic22—21no—
76C2×C11×C16C2312yes—
77C2×C11×C16C2312yes—
78C4×C8×C11D411yescharacteristic
79C4×C8×C11D411yescharacteristic
80C4×C8×C11C2311yescharacteristic
81C4×C8×C11C2311yescharacteristic
82#66885—21no—
83#66885—21no—
84#66882C2311yescharacteristic
85#66882C2311yescharacteristic
86#66881—21no—
87#66880—21no—
88#66880—21no—
89Dic88—42no—
90#66864—42no—
91#66864—42no—
92D176—42no—
93#33785—111nomaximal, Sylow
94C22×C4×C11D811yescharacteristic
95C22×C4×C11D811yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C2×C22⋊D11—41no—
98C2×C22⋊D11—42no—
99#4339—44no—
100#4339—44no—
101C2×D44—21no—
102C2×D44—22no—
103C2×D44—41no—
104C2×D44—41no—
105C2×C4×D11—41no—
106C2×C4×D11—42no—
107C2×Dic22—21no—
108C2×Dic22—22no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11C2×D411yescharacteristic
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11C2×D411yescharacteristic
114C2×C8×C11C2411yescharacteristic
115C42×C11D811yescharacteristic
116C42×C11D811yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C22⋊Dic11—41no—
120(C2×D11)⋊C4—41no—
121(C2×D11)⋊C4—41no—
122(C2×D11)⋊C4—41no—
123(C2×D11)⋊C4—42no—
124(C2×D11)⋊C4—42no—
125(C2×D11)⋊C4—41no—
126C4⋊Dic11—21no—
127C4⋊Dic11—21no—
128C4⋊Dic11—41no—
129C4⋊Dic11—41no—
130Dic11⋊C4—41no—
131Dic11⋊C4—41no—
132Dic11⋊C4—41no—
133Dic11⋊C4—41no—
134C4×Dic11—41no—
135Dic44—22no—
136Dic44—22no—
137Dic44—22no—
138Dic44—42no—
139D88—22no—
140D88—22no—
141D88—22no—
142D88—42no—
143#4314—44no—
144#4314—44no—
145#4314—42no—
146C11×C16—22no—
147C11×C16—22no—
148#3168—111no—
149#3147—111no—
150#2251—111no—
151#2250—111no—
152#2245—111no—
153#2244—111no—
154#2211—112no—
155#2210—112no—
156#2189—112no—
157#2186—112no—
158#2163D1111yescharacteristic, complemented
159C23×C11C2×D811yescharacteristic
160C22×D11—41no—
161C22×D11—42no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11C2×D811yescharacteristic
167C2×C4×C11C2×D811yescharacteristic
168C2×C4×C11C2×D811yescharacteristic
169C2×C4×C11C2×D811yescharacteristic
170C2×C4×C11C2×D811yescharacteristic
171C2×C4×C11C22×D411yescharacteristic
172C22⋊D11—84no—
173C22⋊D11—82no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—42no—
178D44—42no—
179D44—41no—
180D44—42no—
181D44—41no—
182D44—82no—
183D44—82no—
184C4×D11—82no—
185C4×D11—84no—
186Dic22—42no—
187Dic22—41no—
188Dic22—42no—
189Dic22—41no—
190C8×C11—21no—
191C8×C11—21no—
192C8×C11AGL(1,ℤ/8)12yes—
193C8×C11H(5,𝔽2)12yes—
194C2×#135—112no—
195C2×#135—221no—
196#532—221no—
197#529—221no—
198C2×Q32—112no—
199C2×SD32—112no—
200C2×SD32—112no—
201C2×D16—112no—
202#499—111no—
203#495—112no—
204#495—111no—
205#495—221no—
206#494—111no—
207#493—111no—
208#492—221no—
209#488—221no—
210#467—111no—
211#466—111no—
212#465—221no—
213C4×Q16—111no—
214C4×SD16—221no—
215C4×D8—111no—
216C2×C4×C8C2×D1111yescharacteristic
217C4⋊C16C2×D1112yes—
218#358—112no—
219#358—112no—
220#357—112no—
221#357—112no—
222C22⋊C16C2×D1112yes—
223#346C2×D1111yescharacteristic
224#346C2×D1111yescharacteristic
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11C22×D811yescharacteristic
229C2×D11—81no—
230C2×D11—82no—
231C2×D11—82no—
232C2×D11—81no—
233C2×D11—82no—
234C2×D11—81no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—21no—
240C4×C11#53511yescharacteristic
241C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
242Dic11—81no—
243Dic11—81no—
244Dic11—82no—
245Dic11—81no—
246C2×#41—222no—
247#135—442no—
248#135—442no—
249#135—444no—
250C2×Q16—112no—
251C2×Q16—111no—
252C2×Q16—221no—
253C2×SD16—222no—
254C2×SD16—222no—
255C2×SD16—221no—
256C2×D8—112no—
257C2×D8—111no—
258C2×D8—221no—
259C22×C8D4411yescharacteristic
260C22×C8C22×D1111yescharacteristic
261C4⋊Q8—221no—
262#127—221no—
263#126—441no—
264#125—221no—
265#124—221no—
266#124—222no—
267#123—441no—
268C22⋊Q8—221no—
269#121—221no—
270#121—441no—
271#121—441no—
272C4×Q8—221no—
273C4×D4—221no—
274C4×D4—441no—
275C4×D4—441no—
276C4×D4—441no—
277#117—441no—
278C2×C42D4411yescharacteristic
279Q32—442no—
280SD32—442no—
281SD32—442no—
282D16—442no—
283C2×C16C22×D1112yes—
284C2×C16C22×D1112yes—
285#107—111no—
286#107—111no—
287#106—221no—
288#103—221no—
289#103—221no—
290#102—221no—
291#102—221no—
292C4×C8D4411yescharacteristic
293C4×C8D4411yescharacteristic
294C4×C8C22×D1111yescharacteristic
295C4×C8C22×D1111yescharacteristic
296C2×C11—41no—
297C2×C11#320511yescharacteristic
298C2×C11#341411yescharacteristic
299C2×C11#341411yescharacteristic
300D11—161no—
301D11—162no—
302#41—444no—
303#41—444no—
304C2×Q8—221no—
305C2×Q8—222no—
306C2×D4—221no—
307C2×D4—222no—
308C2×D4—441no—
309C2×D4—442no—
310C2×D4—441no—
311C2×D4—441no—
312C22×C4—441no—
313C22×C4—442no—
314C22×C4D8811yescharacteristic
315C22×C4D8811yescharacteristic
316C22×C4C2×D4411yescharacteristic
317Q16—222no—
318Q16—222no—
319Q16—222no—
320Q16—442no—
321SD16—444no—
322SD16—444no—
323SD16—442no—
324D8—222no—
325D8—222no—
326D8—222no—
327D8—442no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8C2×D4411yescharacteristic
331C2×C8C2×D4411yescharacteristic
332C2×C8C2×D4411yescharacteristic
333C2×C8C23×D1111yescharacteristic
334C4⋊C4—221no—
335C4⋊C4—221no—
336C4⋊C4—441no—
337C4⋊C4—441no—
338C4⋊C4—441no—
339C4⋊C4—441no—
340C4⋊C4—441no—
341C4⋊C4—441no—
342C22⋊C4—441no—
343C22⋊C4—441no—
344C22⋊C4—441no—
345C22⋊C4—441no—
346C22⋊C4—442no—
347C22⋊C4—442no—
348C22⋊C4—441no—
349C42—441no—
350C42D8811yescharacteristic
351C42D8811yescharacteristic
352C42C2×D4411yescharacteristic
353C42C2×D4411yescharacteristic
354C16—22no—
355C16—22no—
356C11#3378511yescharacteristic, complemented, Sylow
357C23—441no—
358C23—442no—
359C23C2×D8811yescharacteristic
360Q8—442no—
361Q8—441no—
362Q8—442no—
363Q8—441no—
364D4—442no—
365D4—441no—
366D4—442no—
367D4—441no—
368D4—882no—
369D4—882no—
370D4—884no—
371D4—882no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4—441no—
379C2×C4—442no—
380C2×C4—884no—
381C2×C4—882no—
382C2×C4C2×D8811yescharacteristic
383C2×C4C2×D8811yescharacteristic
384C2×C4C2×D8811yescharacteristic
385C2×C4C2×D8811yescharacteristic
386C2×C4C2×D8811yescharacteristic
387C2×C4C22×D4411yescharacteristic
388C8—21no—
389C8—21no—
390C8#6696112yes—
391C8#6704212yes—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—881no—
396C22—882no—
397C22—882no—
398C22—881no—
399C22—882no—
400C22—881no—
401C22C22×D8811yescharacteristic
402C4—21no—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—881no—
408C4—881no—
409C4—882no—
410C4—881no—
411C4#1062305611yescharacteristic
412C4C2×#6696111yescharacteristic
413C2—41no—
414C2—1761no—
415C2—1762no—
416C2#1307953611yescharacteristic
417C2#1308175211yescharacteristic
418C2#1308175211yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2163C2
socleC22×C11C22×D8
hypercenter#2163D11
hypocenterC11#33785
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #2163

Complements

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

NH ≅ G/Ntype
1. #13079186C2semidirect
2. #13079044C2semidirect
3. #13070887C2semidirect
4. #13070882C2semidirect
5. #13070862C2semidirect
6. #13070858C2semidirect
7. #13070679C2semidirect
8. #13070672C2semidirect
9. #13070558C2semidirect
10. #13070541C2semidirect
11. C11×#2163C2semidirect
158. #2163D11semidirect
356. C11#33785semidirect

Maximal subgroups

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

subgroupindex
#130791862
#130790442
#130708872
#130708822
#130708622
#130708582
#130706792
#130706722
#130705582
#130705412
C11×#21632
#3378511