Finite Group Databasebeta

← #14657621

Subgroups — #14657621

Order 2816.

474 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622455C211yesmaximal, characteristic
2#13069577C211yesmaximal, characteristic, complemented
3#13069410C211yesmaximal, characteristic
4#13068617C211yesmaximal, characteristic
5C2×#10622119C211yesmaximal, characteristic, complemented
6#13066500C211yesmaximal, characteristic, complemented
7C2×C11×#334C211yesmaximal, characteristic, complemented
8C2×C4×D44C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C4×C8×C11C2211yescharacteristic
13C2×#66885—21no—
14C2×#66885—21no—
15C2×(C2×D11)⋊C8—21no—
16C2×(C2×D11)⋊C8—21no—
17C2×#66881—21no—
18#10622548C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20#10622455—22no—
21#10622455—22no—
22C11×#334—22no—
23#10622189—21no—
24#10622189—21no—
25#10622189—21no—
26#10622119—22no—
27C22×D44D411yescharacteristic
28C22×C4×D11—21no—
29C22×Dic22—21no—
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C22×C8×C11D411yescharacteristic
33C22×C8×C11D411yescharacteristic
34C2×C42×C11C2311yescharacteristic
35C2×(C2×D11)⋊C4—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11D411yescharacteristic
42C22×C11⋊C8—21no—
43C4×D44—21no—
44C4×D44—21no—
45C4×D44—21no—
46C4×D44—21no—
47#66922—21no—
48#66922—21no—
49#66922—21no—
50#66922D412yes—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8D412yes—
55C4×C8×C11—21no—
56C4×C8×C11—21no—
57#66885—24no—
58#66885—42no—
59(C2×D11)⋊C8—42no—
60(C2×D11)⋊C8—42no—
61#66881—24no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64#10480—111nomaximal, Sylow
65C23×D11—21no—
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11#4111yescharacteristic
69C22×Dic11—21no—
70C22×Dic11—41no—
71C22×Dic11—41no—
72C2×D44—21no—
73C2×D44—21no—
74C2×D44—21no—
75C2×D44—21no—
76C2×D44—21no—
77C2×D44SD1612yes—
78C2×C4×D11—41no—
79C2×C4×D11—41no—
80C2×C4×D11—41no—
81C2×C4×D11—41no—
82C2×C4×D11—41no—
83C2×C4×D11—41no—
84C2×Dic22—22no—
85C2×Dic22—41no—
86C2×Dic22—81no—
87C2×Dic22—81no—
88C2×C8×C11—22no—
89C2×C8×C11—21no—
90C2×C8×C11—21no—
91C2×C8×C11—21no—
92C2×C8×C11—21no—
93C2×C8×C11—21no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
99C2×C8×C11SD1612yes—
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11#4111yescharacteristic
103C42×C11#4111yescharacteristic
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—41no—
106C4⋊Dic11—21no—
107C4⋊Dic11—22no—
108C4⋊Dic11—22no—
109C4⋊Dic11—21no—
110C4⋊Dic11—41no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115C4⋊Dic11—41no—
116C4⋊Dic11—81no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8—41no—
119C2×C11⋊C8—41no—
120C2×#476—111no—
121#1990—111no—
122#1954—111no—
123#1802—111no—
124C2×#334D1111yescharacteristic, complemented
125C2×#333—111no—
126#1296—111no—
127C23×C11#12111yescharacteristic
128C22×D11—22no—
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11—41no—
133C22×D11—41no—
134C22×D11—41no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12111yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12311yescharacteristic
141C2×C4×C11#12311yescharacteristic
142C2×C4×C11#12411yescharacteristic
143C2×C4×C11C2×SD1611yescharacteristic
144C2×C4×C11C2×SD1611yescharacteristic
145C2×C4×C11#13511yescharacteristic
146C2×C4×C11#13511yescharacteristic
147C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C11#13711yescharacteristic
149C2×C4×C11#13711yescharacteristic
150C2×C4×C11#13711yescharacteristic
151C2×Dic11—42no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—81no—
156C2×Dic11—81no—
157C2×Dic11—81no—
158C2×Dic11—81no—
159C2×Dic11—81no—
160D44—22no—
161D44—22no—
162D44—41no—
163D44—41no—
164C4×D11—81no—
165C4×D11—81no—
166C4×D11—81no—
167C4×D11—81no—
168Dic22—82no—
169Dic22—82no—
170C8×C11—22no—
171C8×C11—42no—
172C8×C11—41no—
173C8×C11—81no—
174C11⋊C8—81no—
175C2×C4⋊Q8—111no—
176C2×C4×D4—111no—
177#476—222no—
178#476—222no—
179C2×#106—221no—
180C2×C4⋊C8—111no—
181C2×C4⋊C8C2×D1111yescharacteristic
182C2×C4⋊C8C2×D1111yescharacteristic
183C2×#102—221no—
184C2×#102—221no—
185C2×C22⋊C8—221no—
186C2×C22⋊C8—221no—
187C2×C4×C8C2×D1111yescharacteristic
188#384—111no—
189#340—221no—
190#340—221no—
191#340—221no—
192#334—22no—
193#333—222no—
194C22×C11#39411yescharacteristic
195C22×C11#46111yescharacteristic
196C22×C11#46311yescharacteristic
197C22×C11#46511yescharacteristic
198C22×C11#47011yescharacteristic
199C22×C11#47111yescharacteristic
200C22×C11#47211yescharacteristic
201C2×D11—42no—
202C2×D11—42no—
203C2×D11—42no—
204C2×D11—81no—
205C2×D11—81no—
206C2×D11—81no—
207C2×D11—81no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11#44811yescharacteristic
211C4×C11#45211yescharacteristic
212C4×C11#46011yescharacteristic
213C4×C11#46411yescharacteristic
214C4×C11#46511yescharacteristic
215C4×C11#46811yescharacteristic
216C4×C11#48311yescharacteristic
217C4×C11#48511yescharacteristic
218Dic11—82no—
219Dic11—81no—
220Dic11—161no—
221C22×Q8—221no—
222C22×D4—111no—
223C23×C4—221no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—221no—
227C22×C8D4411yescharacteristic
228C22×C8D4411yescharacteristic
229C4⋊Q8—112no—
230C4⋊Q8—221no—
231C4⋊Q8—221no—
232C4⋊Q8—221no—
233C4×D4—221no—
234C4×D4—221no—
235C4×D4—221no—
236C4×D4—221no—
237C2×C4⋊C4—111no—
238C2×C4⋊C4—221no—
239C2×C4⋊C4—221no—
240C2×C4⋊C4—221no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4—221no—
243C2×C22⋊C4—221no—
244C2×C42C22×D1111yescharacteristic
245#106—224no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—221no—
250C4⋊C8—221no—
251C4⋊C8C22⋊D1112yes—
252#102—224no—
253#102—442no—
254C22⋊C8—442no—
255C22⋊C8—442no—
256C4×C8—21no—
257C4×C8—21no—
258C2×C11#167111yescharacteristic
259C2×C11#167711yescharacteristic
260C2×C11#169511yescharacteristic
261C2×C11#170311yescharacteristic
262C2×C11#203511yescharacteristic
263C2×C11#205111yescharacteristic
264C2×C11#205511yescharacteristic
265D11—82no—
266C24—221no—
267C2×Q8—222no—
268C2×Q8—441no—
269C2×Q8—881no—
270C2×Q8—881no—
271C2×D4—112no—
272C2×D4—221no—
273C2×D4—221no—
274C2×D4—221no—
275C2×D4—221no—
276C2×D4—221no—
277C22×C4—221no—
278C22×C4—441no—
279C22×C4—441no—
280C22×C4—441no—
281C22×C4—441no—
282C22×C4—441no—
283C22×C4—441no—
284C22×C4—441no—
285C22×C4—441no—
286C22×C4C2×D4411yescharacteristic
287C22×C4D4×D1111yescharacteristic
288C22×C4#434311yescharacteristic
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—22no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—441no—
301C2×C8—441no—
302C2×C8—441no—
303C2×C8#431412yes—
304C4⋊C4—221no—
305C4⋊C4—222no—
306C4⋊C4—222no—
307C4⋊C4—221no—
308C4⋊C4—441no—
309C4⋊C4—441no—
310C4⋊C4—441no—
311C4⋊C4—441no—
312C4⋊C4—441no—
313C4⋊C4—441no—
314C4⋊C4—881no—
315C22⋊C4—441no—
316C22⋊C4—441no—
317C42#433911yescharacteristic
318C42D4×D1111yescharacteristic
319C42#434311yescharacteristic
320C42C2×C22⋊D1111yescharacteristic
321C11#1048011yescharacteristic, complemented, Sylow
322C23—222no—
323C23—441no—
324C23—441no—
325C23—441no—
326C23—441no—
327C23—441no—
328C23—441no—
329C23#6694811yescharacteristic
330Q8—882no—
331Q8—882no—
332D4—222no—
333D4—222no—
334D4—441no—
335D4—441no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—441no—
339C2×C4—442no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—881no—
343C2×C4—881no—
344C2×C4—881no—
345C2×C4—881no—
346C2×C4—881no—
347C2×C4—881no—
348C2×C4—881no—
349C2×C4—881no—
350C2×C4—881no—
351C2×C4#6694711yescharacteristic
352C2×C4#6694711yescharacteristic
353C2×C4#6694811yescharacteristic
354C2×C4C2×#431411yescharacteristic
355C2×C4#6695711yescharacteristic
356C2×C4#6696111yescharacteristic
357C2×C4#6696211yescharacteristic
358C2×C4SD16×D1111yescharacteristic
359C2×C4#6696811yescharacteristic
360C2×C4#6696811yescharacteristic
361C2×C4#6696911yescharacteristic
362C2×C4#6698311yescharacteristic
363C2×C4#6699011yescharacteristic
364C2×C4#6700011yescharacteristic
365C8—22no—
366C8—41no—
367C8—42no—
368C8—81no—
369C8—881no—
370C22—442no—
371C22—442no—
372C22—442no—
373C22—881no—
374C22—881no—
375C22—881no—
376C22—881no—
377C22#1062245411yescharacteristic
378C22#1062245711yescharacteristic
379C22#1062247711yescharacteristic
380C22#1062248111yescharacteristic
381C22#1062251011yescharacteristic
382C22#1062251111yescharacteristic
383C22#1062260411yescharacteristic
384C4—21no—
385C4—21no—
386C4—882no—
387C4—881no—
388C4—1761no—
389C4#1062245811yescharacteristic
390C4#1062246111yescharacteristic
391C4#1062247511yescharacteristic
392C4#1062248011yescharacteristic
393C4#1062272711yescharacteristic
394C4#1062274711yescharacteristic
395C4#1062278311yescharacteristic
396C4#1062278611yescharacteristic
397C2—882no—
398C2#1306799211yescharacteristic
399C2#1306802611yescharacteristic
400C2#1306814011yescharacteristic
401C2#1306819211yescharacteristic
402C2#1306981411yescharacteristic
403C2#1306991011yescharacteristic
404C2#1306993411yescharacteristic
subgroupG/H
centerC23#66948
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#334C2
socleC23×C11#121
prime radicalC22×D44D4
hypercenterC2×#334D11
hypocenterC11#10480
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
2. #13069577C2semidirect
5. C2×#10622119C2semidirect
6. #13066500C2semidirect
7. C2×C11×#334C2semidirect
124. C2×#334D11semidirect
321. C11#10480semidirect

Maximal subgroups

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

subgroupindex
C2×#106224552
#130695772
#130694102
#130686172
C2×#106221192
#130665002
C2×C11×#3342
#1048011