Finite Group Databasebeta

← #14647664

Subgroups — #14647664

Order 2816.

446 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077724C211yesmaximal, characteristic
2#13068733C211yesmaximal, characteristic, complemented
3C4×#66869C211yesmaximal, characteristic
4#13067369C211yesmaximal, characteristic, complemented
5#13067004C211yesmaximal, characteristic
6#13066465C211yesmaximal, characteristic, complemented
7C11×#1276C211yesmaximal, characteristic, complemented
8C4×#4339C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C43×C11C2211yescharacteristic
12C2×#66869C411yescharacteristic
13C2×#66869C411yescharacteristic
14C2×C4⋊(C11⋊C8)C2211yescharacteristic
15C2×C4⋊(C11⋊C8)C2211yescharacteristic
16C4×#4318C2211yescharacteristic
17#10622446—21no—
18D11×C4⋊C8—21no—
19(C22⋊D11)⋊C8—22no—
20C8×D44—21no—
21C8×Dic22—21no—
22#10622162—22no—
23#10622161C411yescharacteristic
24#10622161C411yescharacteristic
25#10622118—21no—
26#10622117—21no—
27#10622097—21no—
28#10622094—21no—
29C2×#4339C2×C411yescharacteristic
30C2×C42×C11—21no—
31C2×C42×C11—21no—
32C2×C42×C11C2×C411yescharacteristic
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11C2311yescharacteristic
35C4×C22⋊D11—21no—
36C4×C22⋊D11—21no—
37#66979C2×C411yescharacteristic
38C2×#4318C2×C411yescharacteristic
39C2×#4318C2×C411yescharacteristic
40C22×C11⋊C8—21no—
41C22×C11⋊C8D412yes—
42C2×C8×D11—22no—
43C4×D44D411yescharacteristic
44C4×D44Q811yescharacteristic
45#66925—21no—
46C42×D11—21no—
47C4×Dic22D411yescharacteristic
48C4×Dic22Q811yescharacteristic
49C11×C4⋊C8—21no—
50C11×C4⋊C8D411yescharacteristic
51C11×C4⋊C8D411yescharacteristic
52C11×C22⋊C8—21no—
53C11×C22⋊C8—21no—
54C4×C8×C11—21no—
55C4×C8×C11—21no—
56(C2×D11)⋊C8—22no—
57Dic11⋊C8—22no—
58C8×Dic11—22no—
59#66869—22no—
60#66869C814yescomplemented
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65#66867—21no—
66C4×C11⋊C8—21no—
67#8840—111nomaximal, Sylow
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11#4111yescharacteristic
73C2×C22⋊D11—21no—
74#4339—21no—
75#4339—21no—
76#4339C2×C812yes—
77#4339M1612yes—
78C2×D44C4⋊C411yescharacteristic
79C2×C4×D11—21no—
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×Dic22C4⋊C411yescharacteristic
83C2×C8×C11—21no—
84C2×C8×C11—21no—
85C2×C8×C11—41no—
86C42×C11—21no—
87C42×C11—21no—
88C42×C11—21no—
89C42×C11—41no—
90C42×C11—41no—
91C42×C11—42no—
92C42×C11C2×C812yescomplemented
93C42×C11C2×D411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11C2×Q811yescharacteristic
96C42×C11#4111yescharacteristic
97C22⋊Dic11—21no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4—21no—
100C4⋊Dic11C4⋊C411yescharacteristic
101C4⋊Dic11C4⋊C411yescharacteristic
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107#4318—21no—
108#4318—21no—
109#4318—21no—
110#4318C2×C812yescomplemented
111C2×C11⋊C8—21no—
112C2×C11⋊C8—21no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—42no—
115C2×C11⋊C8—42no—
116C2×C11⋊C8—41no—
117C8×D11—82no—
118#2988—111no—
119#1831—111no—
120C4×#104—111no—
121#1565—111no—
122#1477—111no—
123#1283—111no—
124#1276D1111yescharacteristic, complemented
125C23×C11C4×D411yescharacteristic
126C22×D11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11C2×C4⋊C411yescharacteristic
137C2×C4×C11C4×D411yescharacteristic
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11C22⋊Q811yescharacteristic
140C2×C4×C11C22⋊Q811yescharacteristic
141C2×C4×C11#12311yescharacteristic
142C2×C4×C11C22×C811yescharacteristic
143C2×C4×C11C2×M1611yescharacteristic
144C2×C4×C11#13111yescharacteristic
145C2×C4×C11#13111yescharacteristic
146C22⋊D11—22no—
147C22⋊D11—22no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151D44—21no—
152D44C4⋊C812yes—
153C4×D11—22no—
154C4×D11—22no—
155C4×D11—41no—
156C4×D11—41no—
157C4×D11—81no—
158Dic22—21no—
159Dic22C4⋊C812yes—
160C8×C11—41no—
161C8×C11—41no—
162C8×C11—81no—
163C11⋊C8—22no—
164C11⋊C8—41no—
165C11⋊C8—42no—
166C11⋊C8—81no—
167C4×#41—111no—
168C8×Q8—221no—
169C8×D4—221no—
170C8×D4—222no—
171#431—221no—
172#431C2×D1111yescharacteristic
173#431C2×D1111yescharacteristic
174C2×C4⋊C8—111no—
175C2×C4⋊C8—111no—
176C2×C4⋊C8—221no—
177C2×#104—111no—
178C2×#104—111no—
179C4×M16—111no—
180C43C2×D1111yescharacteristic
181#339—111no—
182#339—111no—
183#336—222no—
184#335—221no—
185#334—221no—
186Q8⋊C8—221no—
187D4⋊C8—221no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11#38511yescharacteristic
191C22×C11C8×D411yescharacteristic
192C22×C11#43511yescharacteristic
193C2×D11—22no—
194C2×D11—41no—
195C2×D11—41no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—42no—
200C4×C11—42no—
201C4×C11C2×C4⋊C811yescharacteristic
202C4×C11#42411yescharacteristic
203C4×C11C8×D411yescharacteristic
204C4×C11#43511yescharacteristic
205C4×C11#45411yescharacteristic
206C4×C11#45511yescharacteristic
207Dic11—22no—
208Dic11—41no—
209Dic11—41no—
210C2×#41—111no—
211C2×M16—111no—
212C2×M16—111no—
213C22×C8—112no—
214C22×C8—222no—
215C22×C8—221no—
216C4×Q8—111no—
217C4×Q8—111no—
218C4×D4—111no—
219C4×D4—111no—
220C4×D4—221no—
221C4×D4—221no—
222#117—111no—
223#117—221no—
224C2×C42—21no—
225C2×C42—21no—
226C2×C42—221no—
227C2×C42C4×D1111yescharacteristic
228C2×C42C4×D1111yescharacteristic
229C2×C42C22×D1111yescharacteristic
230C4⋊C8—21no—
231C4⋊C8—222no—
232C4⋊C8—221no—
233C4⋊C8—221no—
234C4⋊C8—221no—
235C4⋊C8—221no—
236C4⋊C8D4411yescharacteristic
237C4⋊C8D4411yescharacteristic
238#104—114no—
239#104—222no—
240C22⋊C8—21no—
241C22⋊C8—21no—
242C22⋊C8—222no—
243#97—221no—
244C4×C8—21no—
245C4×C8—21no—
246C4×C8—222no—
247C4×C8—221no—
248C2×C11—21no—
249C2×C11—21no—
250C2×C11#185011yescharacteristic
251C2×C11#186011yescharacteristic
252C2×C11#186111yescharacteristic
253D11—42no—
254#41—112no—
255#41—112no—
256#41—221no—
257#41—221no—
258C2×Q8—111no—
259C2×D4—111no—
260C2×D4—221no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4C2×C4×D1111yescharacteristic
267C22×C4D4×D1111yescharacteristic
268C22×C4#434111yescharacteristic
269M16—112no—
270M16—221no—
271M16—221no—
272M16—221no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—41no—
276C2×C8—221no—
277C2×C8—221no—
278C2×C8—222no—
279C2×C8—442no—
280C2×C8—442no—
281C2×C8—441no—
282C2×C8—882no—
283C4⋊C4—111no—
284C4⋊C4—111no—
285C4⋊C4—221no—
286C4⋊C4—221no—
287C22⋊C4—221no—
288C22⋊C4—221no—
289C22⋊C4—221no—
290C42—21no—
291C42—21no—
292C42—21no—
293C42—41no—
294C42—41no—
295C42—42no—
296C42—221no—
297C42—221no—
298C42—221no—
299C42C8×D1112yescomplemented
300C42C2×D4411yescharacteristic
301C42#433911yescharacteristic
302C42D4×D1111yescharacteristic
303C42Q8×D1111yescharacteristic
304C11#884011yescharacteristic, complemented, Sylow
305C23—221no—
306C23(C22⋊D11)⋊C411yescharacteristic
307Q8—112no—
308Q8—221no—
309D4—112no—
310D4—222no—
311D4—222no—
312D4—221no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—221no—
323C2×C4—222no—
324C2×C4—222no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—881no—
330C2×C4C4×D4411yescharacteristic
331C2×C4#6693511yescharacteristic
332C2×C4#6693611yescharacteristic
333C2×C4C4⋊C4×D1111yescharacteristic
334C2×C4#6694911yescharacteristic
335C2×C4#6695011yescharacteristic
336C2×C4C2×C8×D1111yescharacteristic
337C2×C4#6695411yescharacteristic
338C2×C4M16×D1111yescharacteristic
339C2×C4#6696011yescharacteristic
340C8—41no—
341C8—41no—
342C8—81no—
343C8—222no—
344C8—441no—
345C8—442no—
346C8—881no—
347C22—21no—
348C22—21no—
349C22—222no—
350C22—441no—
351C22—441no—
352C22#1062228111yescharacteristic
353C22(C22⋊D11)⋊C811yescharacteristic
354C22#1062234111yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—42no—
359C4—42no—
360C4—222no—
361C4—441no—
362C4—441no—
363C4C8×D4411yescharacteristic
364C4#1062231911yescharacteristic
365C4#1062243811yescharacteristic
366C4#1062244011yescharacteristic
367C4D11×C4⋊C811yescharacteristic
368C4#1062245211yescharacteristic
369C2—21no—
370C2—21no—
371C2—442no—
372C2#1306879511yescharacteristic
373C2#1306885011yescharacteristic
374C2#1306885711yescharacteristic
subgroupG/H
centerC2×C4#66935
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC11×#1276C2
socleC22×C11#385
prime radicalC2×#4339C2×C4
cosocleC2×C42×C11C23
hypercenter#1276D11
hypocenterC11#8840
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
2. #13068733C2semidirect
4. #13067369C2semidirect
6. #13066465C2semidirect
7. C11×#1276C2semidirect
60. #66869C8semidirect
92. C42×C11C2×C8semidirect
110. #4318C2×C8semidirect
124. #1276D11semidirect
299. C42C8×D11semidirect
304. C11#8840semidirect

Maximal subgroups

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

subgroupindex
#130777242
#130687332
C4×#668692
#130673692
#130670042
#130664652
C11×#12762
#884011