Finite Group Databasebeta

← #14657597

Subgroups — #14657597

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×#10622696C211yesmaximal, characteristic
2#13069410C211yesmaximal, characteristic
3#13068613C211yesmaximal, characteristic
4C2×#10622095C211yesmaximal, characteristic, complemented
5C2×#10622185C211yesmaximal, characteristic, complemented
6#13066499C211yesmaximal, characteristic, complemented
7C11×#1990C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C22×#4325—21no—
10C2×C4×D44C2211yescharacteristic
11C2×C4×C8×C11C2211yescharacteristic
12C11×#384C2211yescharacteristic
13C2×#66899—21no—
14C2×(C2×D11)⋊C8—21no—
15C2×(C2×D11)⋊C8—21no—
16#10622696—22no—
17#10622696—22no—
18C2×#66873—21no—
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C11×#340—21no—
23C11×#340—21no—
24#10622185—22no—
25#10622167—21no—
26#10622095—22no—
27C22×Q8×C11—21no—
28C22×D44D411yescharacteristic
29C22×C4×D11—21no—
30C22×C8×C11D411yescharacteristic
31C22×C8×C11D411yescharacteristic
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8D412yes—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C42×C11C2311yescharacteristic
42C2×#4325—24no—
43C2×#4325—42no—
44C2×#4325—42no—
45C2×(C2×D11)⋊C4—21no—
46C2×C4⋊Dic11D411yescharacteristic
47C22×C11⋊C8—21no—
48C22×C11⋊C8—21no—
49C22×C11⋊C8—21no—
50C4×D44—21no—
51C4×D44—21no—
52C4×D44—21no—
53C4×D44—21no—
54C4×C8×C11—21no—
55C4×C8×C11—21no—
56#66899—24no—
57(C2×D11)⋊C8—42no—
58(C2×D11)⋊C8—42no—
59#66873—42no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)D412yes—
66#10477—111nomaximal, Sylow
67C23×D11—21no—
68C2×Q8×C11—22no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C2×Q8×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C22×Dic11—21no—
80C2×D44—21no—
81C2×D44—21no—
82C2×D44—21no—
83C2×D44—21no—
84C2×D44—21no—
85C2×D44SD1612yes—
86C2×C4×D11—41no—
87C2×C4×D11—41no—
88C2×C4×D11—41no—
89C2×C4×D11—41no—
90C2×C4×D11—41no—
91C2×C4×D11—41no—
92C2×C8×C11—21no—
93C2×C8×C11—21no—
94C2×C8×C11—21no—
95C2×C8×C11—21no—
96C2×C8×C11—21no—
97C2×C8×C11SD1612yescomplemented
98C11×C4⋊C4—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—81no—
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11#4111yescharacteristic
110C42×C11#4111yescharacteristic
111#4325—48no—
112(C2×D11)⋊C4—41no—
113(C2×D11)⋊C4—41no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8—41no—
119C2×C11⋊C8—41no—
120C2×C11⋊C8—41no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—41no—
124C2×C11⋊C8—41no—
125C2×#461—111no—
126#1990D1111yescharacteristic, complemented
127#1954—111no—
128#1802—111no—
129C2×#334—111no—
130C2×#332—111no—
131#1296—111no—
132C23×C11#12111yescharacteristic
133C22×D11—22no—
134C22×D11—41no—
135C22×D11—41no—
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—41no—
140Q8×C11—42no—
141Q8×C11—42no—
142Q8×C11—81no—
143Q8×C11—81no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—42no—
147C2×C4×C11—81no—
148C2×C4×C11—81no—
149C2×C4×C11—81no—
150C2×C4×C11—81no—
151C2×C4×C11—81no—
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12311yescharacteristic
156C2×C4×C11#12311yescharacteristic
157C2×C4×C11#12411yescharacteristic
158C2×C4×C11C2×SD1611yescharacteristic
159C2×C4×C11C2×SD1611yescharacteristic
160C2×C4×C11#13511yescharacteristic
161C2×C4×C11#13511yescharacteristic
162C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C11#13711yescharacteristic
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169D44—22no—
170D44—22no—
171D44—41no—
172D44—41no—
173C4×D11—81no—
174C4×D11—81no—
175C4×D11—81no—
176C4×D11—81no—
177C8×C11—22no—
178C8×C11—41no—
179C11⋊C8—42no—
180C11⋊C8—81no—
181C11⋊C8—81no—
182C22×SD16—221no—
183C2×C4⋊Q8C2×D1111yescharacteristic
184C2×C4×D4—111no—
185#461—222no—
186#461—222no—
187C2×C4⋊C8—111no—
188C2×C4⋊C8—111no—
189C2×C4⋊C8—111no—
190C2×#103—221no—
191C2×#102—221no—
192C2×C22⋊C8—221no—
193C2×C22⋊C8—221no—
194C2×C4×C8C2×D1111yescharacteristic
195#384C2×D1111yescharacteristic
196#340—21no—
197#340—21no—
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—82no—
218C4×C11—161no—
219C4×C11#44911yescharacteristic
220C4×C11#45011yescharacteristic
221C4×C11#46011yescharacteristic
222C4×C11#46411yescharacteristic
223C4×C11#46511yescharacteristic
224C4×C11#46811yescharacteristic
225C4×C11#48111yescharacteristic
226C4×C11#48211yescharacteristic
227Dic11—81no—
228C22×Q8—21no—
229C22×D4—111no—
230C23×C4—221no—
231C2×SD16—224no—
232C2×SD16—442no—
233C2×SD16—442no—
234C22×C8—221no—
235C22×C8—221no—
236C22×C8—221no—
237C22×C8C22⋊D1111yescharacteristic
238C22×C8C22⋊D1111yescharacteristic
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8—21no—
242C4⋊Q8D4412yes—
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—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—111no—
253C2×C22⋊C4—221no—
254C2×C42C22×D1111yescharacteristic
255C4⋊C8—112no—
256C4⋊C8—221no—
257C4⋊C8—221no—
258C4⋊C8—221no—
259C4⋊C8—221no—
260C4⋊C8—221no—
261#103—224no—
262#102—442no—
263C22⋊C8—442no—
264C22⋊C8—442no—
265C4×C8—21no—
266C4×C8—21no—
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—22no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×D4—112no—
283C2×D4—221no—
284C2×D4—221no—
285C2×D4—221no—
286C2×D4—221no—
287C2×D4—221no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—221no—
291C22×C4—441no—
292C22×C4—441no—
293C22×C4—441no—
294C22×C4—441no—
295C22×C4—441no—
296C22×C4—441no—
297C22×C4D4×D1111yescharacteristic
298C22×C4#434111yescharacteristic
299C22×C4C2×C22⋊D1111yescharacteristic
300SD16—448no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—222no—
307C2×C8—441no—
308C2×C8—441no—
309C2×C8—441no—
310C2×C8—441no—
311C2×C8—441no—
312C2×C8—441no—
313C2×C8—441no—
314C2×C8—441no—
315C2×C8#432512yescomplemented
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—81no—
325C4⋊C4—221no—
326C4⋊C4—221no—
327C22⋊C4—441no—
328C22⋊C4—441no—
329C42C2×D4411yescharacteristic
330C42#433911yescharacteristic
331C42D4×D1111yescharacteristic
332C42#434111yescharacteristic
333C11#1047711yescharacteristic, complemented, Sylow
334C23—222no—
335C23—441no—
336C23—441no—
337C23—441no—
338C23—441no—
339C23—441no—
340C23—441no—
341C23#6699111yescharacteristic
342Q8—42no—
343Q8—42no—
344Q8—81no—
345Q8—81no—
346D4—222no—
347D4—222no—
348D4—441no—
349D4—441no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—881no—
362C2×C4—881no—
363C2×C4—881no—
364C2×C4—881no—
365C2×C4#6693511yescharacteristic
366C2×C4#6693611yescharacteristic
367C2×C4#6693811yescharacteristic
368C2×C4#6693911yescharacteristic
369C2×C4#6696411yescharacteristic
370C2×C4#6696411yescharacteristic
371C2×C4SD16×D1111yescharacteristic
372C2×C4#6696911yescharacteristic
373C2×C4#6698311yescharacteristic
374C2×C4#6699211yescharacteristic
375C2×C4C2×#432511yescharacteristic
376C2×C4#6699511yescharacteristic
377C2×C4#6700211yescharacteristic
378C2×C4#6700311yescharacteristic
379C8—22no—
380C8—41no—
381C8—442no—
382C8—881no—
383C8—881no—
384C22—442no—
385C22—442no—
386C22—442no—
387C22—881no—
388C22—881no—
389C22—881no—
390C22—881no—
391C22#1062257411yescharacteristic
392C22#1062267011yescharacteristic
393C22#1062269611yescharacteristic
394C22#1062277211yescharacteristic
395C22#1062278411yescharacteristic
396C22#1062279011yescharacteristic
397C22#1062280511yescharacteristic
398C4—21no—
399C4—21no—
400C4—82no—
401C4—161no—
402C4—881no—
403C4#1062238911yescharacteristic
404C4#1062239011yescharacteristic
405C4#1062239211yescharacteristic
406C4#1062239411yescharacteristic
407C4#1062264011yescharacteristic
408C4#1062264111yescharacteristic
409C4#1062266111yescharacteristic
410C4#1062266211yescharacteristic
411C2—882no—
412C2#1306798811yescharacteristic
413C2#1306803611yescharacteristic
414C2#1306812611yescharacteristic
415C2#1306817411yescharacteristic
416C2#1306980411yescharacteristic
417C2#1306991611yescharacteristic
418C2#1306993111yescharacteristic
subgroupG/H
centerC23#66991
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1990C2
socleC23×C11#121
prime radicalC22×D44D4
hypercenter#1990D11
hypocenterC11#10477
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
4. C2×#10622095C2semidirect
5. C2×#10622185C2semidirect
6. #13066499C2semidirect
7. C11×#1990C2semidirect
97. C2×C8×C11SD16semidirect
126. #1990D11semidirect
315. C2×C8#4325semidirect
333. C11#10477semidirect

Maximal subgroups

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

subgroupindex
C2×#106226962
#130694102
#130686132
C2×#106220952
C2×#106221852
#130664992
C11×#19902
#1047711