Finite Group Databasebeta

← #14657601

Subgroups — #14657601

Order 2816.

506 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
1C2×#10622454C211yesmaximal, characteristic
2#13069576C211yesmaximal, characteristic, complemented
3#13069409C211yesmaximal, characteristic
4#13068613C211yesmaximal, characteristic
5C2×#10622118C211yesmaximal, characteristic, complemented
6C2×#10622124C211yesmaximal, characteristic, complemented
7C11×#1296C211yesmaximal, characteristic, complemented
8C22×#4314—21no—
9C2×C4×D44C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C11×#384C2211yescharacteristic
14C2×(C2×D11)⋊C8—21no—
15C2×(C2×D11)⋊C8—21no—
16C2×#66880—21no—
17C2×#66873—21no—
18C2×C4⋊(C11⋊C8)C2211yescharacteristic
19C2×C4×C11⋊C8C2211yescharacteristic
20#10622454—22no—
21#10622454—22no—
22#10622167—21no—
23#10622167—21no—
24#10622167—21no—
25#10622124—22no—
26#10622118—22no—
27C22×D44D411yescharacteristic
28C22×C4×D11—21no—
29C22×Dic22—21no—
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C42×C11C2311yescharacteristic
36C2×(C2×D11)⋊C4—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11D411yescharacteristic
40C22×C11⋊C8—21no—
41C22×C11⋊C8D411yescharacteristic
42C22×C11⋊C8D411yescharacteristic
43C2×#4314—24no—
44C2×#4314—42no—
45C2×#4314—42no—
46C4×D44—21no—
47C4×D44—21no—
48C4×D44—21no—
49C4×D44—21no—
50#66922—21no—
51#66922—21no—
52#66922—21no—
53#66922D412yes—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8D412yes—
58(C2×D11)⋊C8—42no—
59(C2×D11)⋊C8—42no—
60#66880—24no—
61#66873—42no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4×C11⋊C8—21no—
65C4×C11⋊C8—21no—
66#10477—111nomaximal, Sylow
67C23×D11—21no—
68C22×C4×C11—41no—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11#4111yescharacteristic
72C22×Dic11—21no—
73C22×Dic11—41no—
74C2×D44—21no—
75C2×D44—21no—
76C2×D44—21no—
77C2×D44—21no—
78C2×D44—21no—
79C2×D44SD1612yes—
80C2×C4×D11—41no—
81C2×C4×D11—41no—
82C2×C4×D11—41no—
83C2×C4×D11—41no—
84C2×C4×D11—41no—
85C2×C4×D11—41no—
86C2×Dic22—22no—
87C2×Dic22—41no—
88C2×Dic22—41no—
89C2×Dic22—41no—
90C2×Dic22—41no—
91C2×Dic22—41no—
92C2×C8×C11—22no—
93C2×C8×C11—41no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—81no—
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11#4111yescharacteristic
106C42×C11#4111yescharacteristic
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—41no—
109C4⋊Dic11—21no—
110C4⋊Dic11—22no—
111C4⋊Dic11—22no—
112C4⋊Dic11—21no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115C2×C11⋊C8—21no—
116C2×C11⋊C8—21no—
117C2×C11⋊C8—21no—
118C2×C11⋊C8—21no—
119C2×C11⋊C8—21no—
120C2×C11⋊C8—41no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8SD1612yescomplemented
124#4314—48no—
125C2×#461—111no—
126#1990—111no—
127#1954—111no—
128#1802—111no—
129C2×#334—111no—
130C2×#332—111no—
131#1296D1111yescharacteristic, complemented
132C23×C11#12111yescharacteristic
133C22×D11—22no—
134C22×D11—41no—
135C22×D11—41no—
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—41no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—81no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12311yescharacteristic
149C2×C4×C11#12311yescharacteristic
150C2×C4×C11#12411yescharacteristic
151C2×C4×C11C2×SD1611yescharacteristic
152C2×C4×C11C2×SD1611yescharacteristic
153C2×C4×C11#13511yescharacteristic
154C2×C4×C11#13511yescharacteristic
155C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C11#13711yescharacteristic
159C2×Dic11—42no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—81no—
164C2×Dic11—81no—
165D44—22no—
166D44—22no—
167D44—41no—
168D44—41no—
169C4×D11—81no—
170C4×D11—81no—
171C4×D11—81no—
172C4×D11—81no—
173Dic22—42no—
174Dic22—42no—
175Dic22—81no—
176Dic22—81no—
177C8×C11—42no—
178C8×C11—81no—
179C11⋊C8—22no—
180C11⋊C8—41no—
181C11⋊C8—81no—
182C22×SD16—221no—
183C2×C4⋊Q8—111no—
184C2×C4×D4—111no—
185#461—222no—
186#461—222no—
187C2×C4⋊C8—111no—
188C2×C4⋊C8C2×D1111yescharacteristic
189C2×C4⋊C8C2×D1111yescharacteristic
190C2×#103—221no—
191C2×#102—221no—
192C2×C22⋊C8—221no—
193C2×C22⋊C8—221no—
194C2×C4×C8—111no—
195#384C2×D1111yescharacteristic
196#340—221no—
197#340—221no—
198#340—221no—
199#334—222no—
200#332—222no—
201C22×C11#39411yescharacteristic
202C22×C11#46111yescharacteristic
203C22×C11#46311yescharacteristic
204C22×C11#46511yescharacteristic
205C22×C11#46911yescharacteristic
206C22×C11#47111yescharacteristic
207C22×C11#47311yescharacteristic
208C2×D11—42no—
209C2×D11—42no—
210C2×D11—42no—
211C2×D11—81no—
212C2×D11—81no—
213C2×D11—81no—
214C2×D11—81no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—161no—
218C4×C11#44911yescharacteristic
219C4×C11#45011yescharacteristic
220C4×C11#46011yescharacteristic
221C4×C11#46411yescharacteristic
222C4×C11#46511yescharacteristic
223C4×C11#46811yescharacteristic
224C4×C11#48111yescharacteristic
225C4×C11#48211yescharacteristic
226Dic11—81no—
227Dic11—82no—
228C22×Q8—221no—
229C22×D4—111no—
230C23×C4—221no—
231C2×SD16—224no—
232C2×SD16—442no—
233C2×SD16—442no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—111no—
237C22×C8—111no—
238C22×C8—221no—
239C4⋊Q8—112no—
240C4⋊Q8—221no—
241C4⋊Q8—221no—
242C4⋊Q8—221no—
243C4×D4—221no—
244C4×D4—221no—
245C4×D4—221no—
246C4×D4—221no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—111no—
251C2×C4⋊C4—221no—
252C2×C4⋊C4—221no—
253C2×C22⋊C4—221no—
254C2×C42C22×D1111yescharacteristic
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—221no—
259C4⋊C8—221no—
260C4⋊C8D4412yes—
261#103—224no—
262#102—442no—
263C22⋊C8—442no—
264C22⋊C8—442no—
265C4×C8—221no—
266C4×C8—221no—
267C2×C11#167111yescharacteristic
268C2×C11#167911yescharacteristic
269C2×C11#169311yescharacteristic
270C2×C11#170111yescharacteristic
271C2×C11#203411yescharacteristic
272C2×C11#205211yescharacteristic
273C2×C11#205511yescharacteristic
274D11—82no—
275C24—221no—
276C2×Q8—222no—
277C2×Q8—441no—
278C2×Q8—441no—
279C2×Q8—441no—
280C2×Q8—441no—
281C2×Q8—441no—
282C2×D4—112no—
283C2×D4—221no—
284C2×D4—221no—
285C2×D4—221no—
286C2×D4—221no—
287C2×D4—221no—
288C22×C4—41no—
289C22×C4—221no—
290C22×C4—441no—
291C22×C4—441no—
292C22×C4—441no—
293C22×C4—441no—
294C22×C4—441no—
295C22×C4—441no—
296C22×C4—441no—
297C22×C4#433911yescharacteristic
298C22×C4D4×D1111yescharacteristic
299C22×C4D4×D1111yescharacteristic
300SD16—448no—
301C2×C8—22no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—112no—
308C2×C8—221no—
309C2×C8—221no—
310C2×C8—221no—
311C2×C8—221no—
312C2×C8—221no—
313C2×C8—441no—
314C2×C8—441no—
315C2×C8—441no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—81no—
321C4⋊C4—221no—
322C4⋊C4—222no—
323C4⋊C4—221no—
324C4⋊C4—222no—
325C4⋊C4—441no—
326C4⋊C4—441no—
327C22⋊C4—441no—
328C22⋊C4—441no—
329C42C2×D4411yescharacteristic
330C42#433911yescharacteristic
331C42D4×D1111yescharacteristic
332C42#434311yescharacteristic
333C11#1047711yescharacteristic, complemented, Sylow
334C23—222no—
335C23—441no—
336C23—441no—
337C23—441no—
338C23—441no—
339C23—441no—
340C23—441no—
341C23#6693711yescharacteristic
342Q8—442no—
343Q8—442no—
344Q8—881no—
345Q8—881no—
346D4—222no—
347D4—222no—
348D4—441no—
349D4—441no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—441no—
356C2×C4—442no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—881no—
360C2×C4—881no—
361C2×C4—881no—
362C2×C4—881no—
363C2×C4—881no—
364C2×C4—881no—
365C2×C4#6692811yescharacteristic
366C2×C4#6693511yescharacteristic
367C2×C4#6693711yescharacteristic
368C2×C4#6694711yescharacteristic
369C2×C4#6694711yescharacteristic
370C2×C4#6694811yescharacteristic
371C2×C4#6696411yescharacteristic
372C2×C4#6696411yescharacteristic
373C2×C4SD16×D1111yescharacteristic
374C2×C4SD16×D1111yescharacteristic
375C2×C4#6696711yescharacteristic
376C2×C4#6696911yescharacteristic
377C2×C4#6697111yescharacteristic
378C2×C4#6697211yescharacteristic
379C8—42no—
380C8—81no—
381C8—222no—
382C8—441no—
383C8—881no—
384C22—442no—
385C22—442no—
386C22—442no—
387C22—881no—
388C22—881no—
389C22—881no—
390C22—881no—
391C22#1062228511yescharacteristic
392C22#1062236111yescharacteristic
393C22#1062236811yescharacteristic
394C22#1062239511yescharacteristic
395C22#1062240011yescharacteristic
396C22#1062242011yescharacteristic
397C22#1062243111yescharacteristic
398C4—21no—
399C4—21no—
400C4—161no—
401C4—881no—
402C4—882no—
403C4#1062237511yescharacteristic
404C4#1062238911yescharacteristic
405C4#1062241111yescharacteristic
406C4#1062242411yescharacteristic
407C4#1062247611yescharacteristic
408C4#1062247711yescharacteristic
409C4#1062249811yescharacteristic
410C4#1062249911yescharacteristic
411C2—882no—
412C2#1306799411yescharacteristic
413C2#1306803811yescharacteristic
414C2#1306812811yescharacteristic
415C2#1306817611yescharacteristic
416C2#1306980811yescharacteristic
417C2#1306991811yescharacteristic
418C2#1306993511yescharacteristic
subgroupG/H
centerC23#66937
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socleC23×C11#121
prime radicalC22×D44D4
hypercenter#1296D11
hypocenterC11#10477
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #13069576C2semidirect
5. C2×#10622118C2semidirect
6. C2×#10622124C2semidirect
7. C11×#1296C2semidirect
123. C2×C11⋊C8SD16semidirect
131. #1296D11semidirect
333. C11#10477semidirect

Maximal subgroups

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

subgroupindex
C2×#106224542
#130695762
#130694092
#130686132
C2×#106221182
C2×#106221242
C11×#12962
#1047711