Finite Group Databasebeta

← #14649639

Subgroups — #14649639

Order 2816.

478 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078432C211yesmaximal, characteristic
2#13077185C211yesmaximal, characteristic
3#13067302C211yesmaximal, characteristic, complemented
4C2×#10622119C211yesmaximal, characteristic, complemented
5#13067001C211yesmaximal, characteristic
6#13066511C211yesmaximal, characteristic, complemented
7C11×#1292C211yesmaximal, characteristic, complemented
8C2×#66960—21no—
9C4×#4339C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14#10622746—21no—
15#10622734—21no—
16#10622732—21no—
17#10622538C2211yescharacteristic
18C2×C4⋊(C11⋊C8)C2211yescharacteristic
19#10622464C412yes—
20#10622463—21no—
21#10622459C412yes—
22#10622455—21no—
23#10622452—22no—
24#10622450—21no—
25D11×C4⋊C8—21no—
26#10622124—22no—
27#10622122—21no—
28#10622121—21no—
29#10622119—21no—
30#10622119—21no—
31C2×#4339D411yescharacteristic
32C22×Dic22—21no—
33C2×C11×M16—21no—
34C2×C11×M16—21no—
35C22×C8×C11—21no—
36C2×C42×C11C2311yescharacteristic
37C4×C22⋊D11—21no—
38C4×C22⋊D11—21no—
39#66979D411yescharacteristic
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C22×C11⋊C8—21no—
43#66960—42no—
44#66960—42no—
45C2×#4313—22no—
46C2×C8×D11—22no—
47C4×D44C2×C411yescharacteristic
48C4×D44D411yescharacteristic
49#66925—21no—
50C42×D11—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922C2×C412yes—
55C4×Dic22C2×C411yescharacteristic
56C4×Dic22D411yescharacteristic
57C11×C4⋊C8—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8C2×C412yes—
62C11×C4⋊C8D412yes—
63C22⋊(C11⋊C8)—21no—
64#66885—22no—
65#66882—22no—
66#66881—22no—
67#66880—22no—
68Dic11⋊C8—22no—
69Dic11⋊C8—22no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)D411yescharacteristic
73C4⋊(C11⋊C8)D411yescharacteristic
74C4×C11⋊C8—21no—
75#9169—111nomaximal, Sylow
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C2×C22⋊D11—21no—
80C22×Dic11—41no—
81#4339—21no—
82#4339—21no—
83#4339SD1612yes—
84#4339Q1612yes—
85C2×D44C22⋊C411yescharacteristic
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×Dic22—22no—
90C2×Dic22—41no—
91C2×Dic22—82no—
92C2×Dic22C22⋊C411yescharacteristic
93C11×M16—41no—
94C11×M16—41no—
95C11×M16—41no—
96C11×M16—41no—
97C2×C8×C11—22no—
98C2×C8×C11—22no—
99C2×C8×C11—41no—
100C2×C8×C11—81no—
101C42×C11C22×C411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C22⋊Dic11—21no—
106(C2×D11)⋊C4—21no—
107(C2×D11)⋊C4—21no—
108C4⋊Dic11—22no—
109C4⋊Dic11—22no—
110C4⋊Dic11—41no—
111C4⋊Dic11—41no—
112C4⋊Dic11C22⋊C411yescharacteristic
113C4⋊Dic11C22⋊C411yescharacteristic
114Dic11⋊C4—21no—
115Dic11⋊C4—21no—
116C4×Dic11—21no—
117C4×Dic11—21no—
118C4×Dic11—21no—
119C2×C11⋊C8—21no—
120C2×C11⋊C8—21no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—41no—
124#4313—44no—
125C8×D11—44no—
126#3079—111no—
127#2906—111no—
128#1549—111no—
129C2×#333—111no—
130#1477—111no—
131#1301—111no—
132#1292D1111yescharacteristic, complemented
133C23×C11#12311yescharacteristic
134C22×D11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—41no—
138C2×C4×C11C2×C22⋊C411yescharacteristic
139C2×C4×C11C4×D411yescharacteristic
140C2×C4×C11C4×D411yescharacteristic
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11C2×SD1611yescharacteristic
145C2×C4×C11C2×Q1611yescharacteristic
146C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C11#13711yescharacteristic
148C22⋊D11—22no—
149C22⋊D11—22no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—42no—
154C2×Dic11—82no—
155D44—21no—
156D44#10312yes—
157C4×D11—22no—
158C4×D11—22no—
159C4×D11—41no—
160C4×D11—41no—
161C4×D11—81no—
162Dic22—21no—
163Dic22—82no—
164Dic22—82no—
165Dic22#10312yes—
166C8×C11—42no—
167C8×C11—42no—
168C8×C11—81no—
169C11⋊C8—41no—
170C11⋊C8—41no—
171C11⋊C8—81no—
172C2×#131—221no—
173C2×C4⋊Q8—111no—
174C4×#41—111no—
175#477—221no—
176#476—221no—
177#475—112no—
178#474—112no—
179#431—111no—
180#428—221no—
181#424—221no—
182#424—222no—
183#423—221no—
184#423C2×D1111yescharacteristic
185#423C2×D1111yescharacteristic
186C2×C4⋊C8—111no—
187C2×C4⋊C8—221no—
188C2×C4⋊C8C2×D1111yescharacteristic
189#417—221no—
190#333—221no—
191#333—221no—
192#332—222no—
193Q8⋊C8—221no—
194D4⋊C8—221no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11#38611yescharacteristic
198C22×C11#48311yescharacteristic
199C22×C11#48411yescharacteristic
200C2×D11—22no—
201C2×D11—41no—
202C2×D11—41no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11C2×#10311yescharacteristic
207C4×C11#41711yescharacteristic
208C4×C11#45011yescharacteristic
209C4×C11#45111yescharacteristic
210C4×C11#47111yescharacteristic
211C4×C11#47311yescharacteristic
212Dic11—22no—
213Dic11—41no—
214Dic11—41no—
215Dic11—82no—
216C2×#41—111no—
217C22×Q8—221no—
218#131—442no—
219#131—442no—
220C2×M16—21no—
221C2×M16—21no—
222C2×M16—222no—
223C22×C8—21no—
224C22×C8—222no—
225C22×C8—221no—
226C4⋊Q8—112no—
227C4⋊Q8—221no—
228C4⋊Q8—221no—
229C4⋊Q8—221no—
230C4×Q8—111no—
231C4×Q8—111no—
232C4×D4—111no—
233C4×D4—111no—
234C4×D4—221no—
235C4×D4—221no—
236#117—111no—
237#117—221no—
238C2×C4⋊C4—221no—
239C2×C4⋊C4—221no—
240C2×C42—221no—
241C2×C42C22×D1111yescharacteristic
242#107—222no—
243#106—222no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—111no—
249C4⋊C8—111no—
250C4⋊C8—222no—
251C4⋊C8—222no—
252C4⋊C8—221no—
253C4⋊C8—221no—
254C4⋊C8C4×D1112yes—
255C4⋊C8D4412yes—
256#103—222no—
257#102—222no—
258C22⋊C8—221no—
259C4×C8—221no—
260C2×C11—21no—
261C2×C11—21no—
262C2×C11#187211yescharacteristic
263C2×C11#190311yescharacteristic
264C2×C11#190811yescharacteristic
265D11—42no—
266#41—112no—
267#41—112no—
268#41—221no—
269#41—221no—
270C2×Q8—111no—
271C2×Q8—222no—
272C2×Q8—441no—
273C2×Q8—882no—
274C2×D4—111no—
275C2×D4—221no—
276C22×C4—221no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—441no—
280C22×C4#433911yescharacteristic
281C22×C4D4×D1111yescharacteristic
282C22×C4#434311yescharacteristic
283M16—41no—
284M16—41no—
285M16—41no—
286M16—41no—
287M16—444no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—41no—
291C2×C8—81no—
292C2×C8—221no—
293C2×C8—221no—
294C2×C8—444no—
295C2×C8—441no—
296C2×C8—441no—
297C2×C8—441no—
298C4⋊C4—111no—
299C4⋊C4—111no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—222no—
303C4⋊C4—222no—
304C4⋊C4—441no—
305C4⋊C4—441no—
306C22⋊C4—221no—
307C22⋊C4—221no—
308C22⋊C4—221no—
309C42—221no—
310C42—221no—
311C42—221no—
312C42C2×C4×D1111yescharacteristic
313C42C2×D4411yescharacteristic
314C42D4×D1111yescharacteristic
315C42D4×D1111yescharacteristic
316C11#916911yescharacteristic, complemented, Sylow
317C23—221no—
318C23#6694711yescharacteristic
319Q8—112no—
320Q8—221no—
321Q8—882no—
322Q8—882no—
323D4—112no—
324D4—222no—
325D4—222no—
326D4—221no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—41no—
330C2×C4—221no—
331C2×C4—222no—
332C2×C4—222no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—442no—
338C2×C4—881no—
339C2×C4—882no—
340C2×C4C4×D4411yescharacteristic
341C2×C4C22⋊C4×D1111yescharacteristic
342C2×C4#6693511yescharacteristic
343C2×C4#6693711yescharacteristic
344C2×C4#6694611yescharacteristic
345C2×C4#6694811yescharacteristic
346C2×C4#6696411yescharacteristic
347C2×C4SD16×D1111yescharacteristic
348C2×C4#6696811yescharacteristic
349C2×C4Q16×D1111yescharacteristic
350C8—42no—
351C8—42no—
352C8—81no—
353C8—441no—
354C8—441no—
355C8—881no—
356C22—21no—
357C22—21no—
358C22—222no—
359C22—441no—
360C22—441no—
361C22#1062227811yescharacteristic
362C22#1062247511yescharacteristic
363C22#1062249711yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—222no—
368C4—441no—
369C4—441no—
370C4—882no—
371C4#1062236111yescharacteristic
372C4#1062236811yescharacteristic
373C4#1062238411yescharacteristic
374C4#1062238911yescharacteristic
375C4D11×#10311yescharacteristic
376C4#1062242111yescharacteristic
377C2—21no—
378C2—21no—
379C2—442no—
380C2#1306892211yescharacteristic
381C2#1306909711yescharacteristic
382C2#1306913211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1292C2
socleC22×C11#386
prime radicalC2×#4339D4
cosocleC2×C42×C11C23
hypercenter#1292D11
hypocenterC11#9169
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1292

Complements

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

NH ≅ G/Ntype
3. #13067302C2semidirect
4. C2×#10622119C2semidirect
6. #13066511C2semidirect
7. C11×#1292C2semidirect
132. #1292D11semidirect
316. C11#9169semidirect

Maximal subgroups

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

subgroupindex
#130784322
#130771852
#130673022
C2×#106221192
#130670012
#130665112
C11×#12922
#916911