Finite Group Databasebeta

← #14736923

Subgroups — #14736923

Order 2816.

662 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#13079739C211yesmaximal, characteristic
2#13079543C211yesmaximal, characteristic
3C2×#10622294C211yesmaximal, characteristic, complemented
4#13077329C211yesmaximal, characteristic
5#13068164C214yesmaximal, complemented
6#13068040C214yesmaximal, complemented
7#13067300C211yesmaximal, characteristic, complemented
8#13067287C211yesmaximal, characteristic, complemented
9C11×#1564C211yesmaximal, characteristic, complemented
10C2×#66954—21no—
11#10623008C2211yescharacteristic
12C2×#66922C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C11×#431C2211yescharacteristic
16C2×C4×C8×C11C2211yescharacteristic
17#10622723—21no—
18C2×#66880—21no—
19C2×#66880—21no—
20#10622537C2211yescharacteristic
21#10622459C2214yes—
22#10622454C2214yes—
23#10622351—22no—
24#10622349—22no—
25#10622307—21no—
26#10622306—21no—
27#10622301—21no—
28#10622301C2212yes—
29C8×D44—21no—
30C8×D44C2212yes—
31#10622295—21no—
32#10622294—21no—
33#10622294—21no—
34#10622294—21no—
35#10622294C2212yes—
36#10622294C2212yes—
37C11×#335C2212yes—
38C11×#334C2212yes—
39#10622124C2214yes—
40#10622120C2214yes—
41C2×#4339—21no—
42C22×Dic22—21no—
43C22×Dic22—21no—
44C22×C8×C11D411yescharacteristic
45C22×C8×C11D411yescharacteristic
46C2×C42×C11C2311yescharacteristic
47#66983—21no—
48#66983D412yes—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C2×#4318—21no—
54C2×#4314—24no—
55#66954—44no—
56C2×#4313—22no—
57C2×C8×D11—22no—
58#66928—21no—
59#66927D411yescharacteristic
60C4×D44—21no—
61C4×D44C2312yes—
62#66922—21no—
63#66922—21no—
64#66922—21no—
65#66922—21no—
66#66922—21no—
67#66922—21no—
68#66922D411yescharacteristic
69#66922C2312yes—
70#66922C2312yes—
71C11×C4⋊C8C2312yes—
72C11×C4⋊C8C2312yes—
73C11×C22⋊C8—21no—
74C11×C22⋊C8—21no—
75C4×C8×C11—21no—
76C4×C8×C11—21no—
77C4×C8×C11D411yescharacteristic
78C4×C8×C11D411yescharacteristic
79C4×C8×C11C2311yescharacteristic
80C4×C8×C11C2311yescharacteristic
81#66885—24no—
82(C2×D11)⋊C8—22no—
83(C2×D11)⋊C8—22no—
84#66882—24no—
85#66880—22no—
86#66880—22no—
87#66880—22no—
88#66880—22no—
89#66880—24no—
90C4⋊(C11⋊C8)—21no—
91C4⋊(C11⋊C8)C2312yes—
92#19197—111nomaximal, Sylow
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C2×C22⋊D11—22no—
97C22×Dic11—41no—
98C22×Dic11—41no—
99#4339—42no—
100#4339—42no—
101C2×D44—21no—
102C2×D44—21no—
103C2×D44C2×D412yes—
104C2×C4×D11—22no—
105C2×Dic22—21no—
106C2×Dic22—22no—
107C2×Dic22—22no—
108C2×Dic22—41no—
109C2×Dic22—41no—
110C2×Dic22—42no—
111C2×Dic22—42no—
112C2×Dic22—82no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11C2×D411yescharacteristic
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11#4111yescharacteristic
124C42×C11C2411yescharacteristic
125(C2×D11)⋊C4—22no—
126(C2×D11)⋊C4—22no—
127C4⋊Dic11—21no—
128C4⋊Dic11—22no—
129C4⋊Dic11—22no—
130C4⋊Dic11—22no—
131C4⋊Dic11—22no—
132C4⋊Dic11—41no—
133C4⋊Dic11—41no—
134C4⋊Dic11—41no—
135C4⋊Dic11—41no—
136C4⋊Dic11C2×D412yes—
137#4318—42no—
138C2×C11⋊C8—22no—
139#4314—84no—
140#4313—44no—
141C8×D11—44no—
142#3226—111no—
143#3206—111no—
144C2×#487—111no—
145#2931—111no—
146#1699—114no—
147#1679—114no—
148#1564D1111yescharacteristic, complemented
149#1549—111no—
150#1546—111no—
151C23×C11#12111yescharacteristic
152C22×D11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#13512yes—
159C2×C4×C11AGL(1,ℤ/8)12yes—
160C2×C4×C11C22×D411yescharacteristic
161C2×C4×C11C22×D411yescharacteristic
162C2×C4×C11C2×#4111yescharacteristic
163C22⋊D11—44no—
164C2×Dic11—22no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—82no—
168C2×Dic11—82no—
169D44—24no—
170D44—42no—
171D44—42no—
172C4×D11—42no—
173C4×D11—42no—
174Dic22—42no—
175Dic22—42no—
176Dic22—42no—
177Dic22—44no—
178Dic22—82no—
179Dic22—82no—
180C8×C11—21no—
181C8×C11—21no—
182C8×C11—21no—
183C8×C11—21no—
184C8×C11—42no—
185C8×C11—42no—
186C11⋊C8—42no—
187C2×#131—221no—
188#532—111no—
189C2×C4⋊Q8—111no—
190C2×C4⋊Q8—111no—
191#500—221no—
192#492—221no—
193#487—112no—
194#487—112no—
195#487—221no—
196#487—221no—
197#487—221no—
198#486—221no—
199#480—222no—
200#474—114no—
201#461—114no—
202#448—222no—
203#436—112no—
204#436—221no—
205C8×D4—112no—
206C8×D4—221no—
207#431C2×D1111yescharacteristic
208#431C2×D1111yescharacteristic
209#423—111no—
210C2×#103—221no—
211C2×#103—221no—
212#408—221no—
213C2×C4×C8C2×D1111yescharacteristic
214#335C2×D1112yes—
215#334C2×D1112yes—
216#332—114no—
217#332—114no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11#46312yes—
221C22×C11C2×#12111yescharacteristic
222C2×D11—42no—
223C2×D11—42no—
224C2×D11—42no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11#46312yes—
228C4×C11#47312yes—
229C4×C11C2×#13511yescharacteristic
230C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
231C4×C11#57712yes—
232Dic11—42no—
233Dic11—82no—
234Dic11—82no—
235C2×#41—221no—
236C22×Q8—221no—
237C22×Q8—221no—
238C2×SD16—224no—
239#131—444no—
240C2×M16—221no—
241C2×M16—222no—
242C22×C8—222no—
243C22×C8D4411yescharacteristic
244C22×C8D4411yescharacteristic
245C4⋊Q8—111no—
246C4⋊Q8—112no—
247C4⋊Q8—112no—
248C4⋊Q8—221no—
249C4⋊Q8—221no—
250C4⋊Q8—221no—
251C4⋊Q8—221no—
252C4⋊Q8—221no—
253C4⋊Q8—221no—
254#127—111no—
255#124—221no—
256#121—112no—
257#121—221no—
258C4×D4—112no—
259C4×D4—221no—
260C2×C4⋊C4—221no—
261C2×C4⋊C4—221no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4—221no—
264C2×C42C22×D1111yescharacteristic
265#107—224no—
266C4⋊C8—112no—
267C4⋊C8—221no—
268C4⋊C8C22×D1112yes—
269C4⋊C8C22×D1112yes—
270#103—224no—
271#103—222no—
272#103—222no—
273#103—222no—
274#103—222no—
275#102—224no—
276C22⋊C8—21no—
277C22⋊C8—21no—
278C22⋊C8—222no—
279C22⋊C8—222no—
280C4×C8—21no—
281C4×C8—21no—
282C4×C8D4411yescharacteristic
283C4×C8D4411yescharacteristic
284C4×C8C22×D1111yescharacteristic
285C4×C8C22×D1111yescharacteristic
286C2×C11—22no—
287C2×C11C2×#46311yescharacteristic
288C2×C11#305711yescharacteristic
289C2×C11C2×#47311yescharacteristic
290D11—82no—
291#41—442no—
292#41—442no—
293C2×Q8—221no—
294C2×Q8—222no—
295C2×Q8—222no—
296C2×Q8—441no—
297C2×Q8—441no—
298C2×Q8—442no—
299C2×Q8—442no—
300C2×Q8—882no—
301C2×D4—112no—
302C2×D4—222no—
303C2×D4—221no—
304C2×D4—221no—
305C22×C4—222no—
306C22×C4—441no—
307C22×C4—441no—
308C22×C4C2×D4411yescharacteristic
309C22×C4D4×D1111yescharacteristic
310C22×C4#434311yescharacteristic
311SD16—884no—
312M16—444no—
313M16—442no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—222no—
319C2×C8—444no—
320C2×C8C2×D4411yescharacteristic
321C2×C8C2×D4411yescharacteristic
322C2×C8C2×D4411yescharacteristic
323C2×C8C2×D4411yescharacteristic
324C4⋊C4—112no—
325C4⋊C4—221no—
326C4⋊C4—222no—
327C4⋊C4—222no—
328C4⋊C4—222no—
329C4⋊C4—222no—
330C4⋊C4—441no—
331C4⋊C4—441no—
332C4⋊C4—441no—
333C4⋊C4—441no—
334C22⋊C4—222no—
335C22⋊C4—222no—
336C42C2×D4411yescharacteristic
337C42D4×D1111yescharacteristic
338C42#434311yescharacteristic
339C42C23×D1111yescharacteristic
340C11#1919711yescharacteristic, complemented, Sylow
341C23—222no—
342C23#6694811yescharacteristic
343Q8—442no—
344Q8—442no—
345Q8—442no—
346Q8—444no—
347Q8—882no—
348Q8—882no—
349D4—224no—
350D4—444no—
351D4—442no—
352D4—442no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—222no—
356C2×C4—442no—
357C2×C4—442no—
358C2×C4—442no—
359C2×C4—442no—
360C2×C4—882no—
361C2×C4—882no—
362C2×C4#6694811yescharacteristic
363C2×C4#6694811yescharacteristic
364C2×C4#6694811yescharacteristic
365C2×C4#6695712yes—
366C2×C4#6696112yes—
367C2×C4C22×D4411yescharacteristic
368C2×C4C2×D4×D1111yescharacteristic
369C2×C4C2×#434311yescharacteristic
370C8—21no—
371C8—21no—
372C8—21no—
373C8—21no—
374C8—42no—
375C8—42no—
376C8—442no—
377C22—21no—
378C22—21no—
379C22—442no—
380C22—442no—
381C22—442no—
382C22#1062245712yes—
383C22C2×#6694811yescharacteristic
384C4—21no—
385C4—21no—
386C4—442no—
387C4—882no—
388C4—882no—
389C4#1062245712yes—
390C4#1062250912yes—
391C4C2×#6695711yescharacteristic
392C4C2×#6696111yescharacteristic
393C4#1062330112yes—
394C2—22no—
395C2—882no—
396C2C2×#1062245711yescharacteristic
397C2#1307825611yescharacteristic
398C2C2×#1062250911yescharacteristic
subgroupG/H
centerC22C2×#66948
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1564C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#1564D11
hypocenterC11#19197
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1564

Complements

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

NH ≅ G/Ntype
3. C2×#10622294C2semidirect
5. #13068164C2semidirect
6. #13068040C2semidirect
7. #13067300C2semidirect
8. #13067287C2semidirect
9. C11×#1564C2semidirect
148. #1564D11semidirect
340. C11#19197semidirect

Maximal subgroups

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

subgroupindex
#130797392
#130795432
C2×#106222942
#130773292
#130681642
#130680402
#130673002
#130672872
C11×#15642
#1919711