Finite Group Databasebeta

← #14657577

Subgroups — #14657577

Order 2816.

522 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622640C211yesmaximal, characteristic
2#13069553C211yesmaximal, characteristic, complemented
3#13069421C211yesmaximal, characteristic
4C2×#10622117C211yesmaximal, characteristic, complemented
5C2×#10622123C211yesmaximal, characteristic
6#13066499C211yesmaximal, characteristic, complemented
7C11×#1803C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C22×#4325—21no—
10C2×#66927C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×#103—21no—
13C11×#384C2211yescharacteristic
14#10622640—22no—
15#10622640—22no—
16C2×#66873—21no—
17C2×#66873—21no—
18C2×#66873—21no—
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C2×C4×C11⋊C8C2211yescharacteristic
22C11×#340—21no—
23#10622162—21no—
24#10622162—21no—
25#10622123—22no—
26#10622117—22no—
27C22×Q8×C11D411yescharacteristic
28C22×D44—21no—
29C22×D44—21no—
30C22×D44—21no—
31C22×C8×C11—21no—
32C4×Q8×C11—21no—
33C4×Q8×C11—21no—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4D411yescharacteristic
41C2×C42×C11—21no—
42C2×C42×C11C2311yescharacteristic
43C2×#4325—24no—
44C2×#4325—42no—
45C2×#4325—42no—
46C22×C11⋊C8—21no—
47C22×C11⋊C8—21no—
48C22×C11⋊C8D411yescharacteristic
49C22×C11⋊C8D411yescharacteristic
50#66927—21no—
51#66927—21no—
52#66927—21no—
53#66927D412yes—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×#103—42no—
57#66873—24no—
58#66873—42no—
59#66873—42no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)D412yes—
64C4×C11⋊C8—21no—
65C4×C11⋊C8—21no—
66#10474—111nomaximal, Sylow
67C23×D11—41no—
68C2×Q8×C11—21no—
69C2×Q8×C11—21no—
70C2×Q8×C11—21no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11D812yes—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—41no—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C2×D44—22no—
81C2×D44—22no—
82C2×D44—22no—
83C2×D44—41no—
84C2×D44—41no—
85C2×D44—41no—
86C2×D44—41no—
87C2×D44—41no—
88C2×D44—41no—
89C2×D44—41no—
90C2×D44—41no—
91C2×D44—41no—
92C2×D44—41no—
93C2×D44—41no—
94C2×D44—81no—
95C2×D44—81no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—81no—
108C42×C11—41no—
109C42×C11—41no—
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11#4111yescharacteristic
113C42×C11#4111yescharacteristic
114#4325—48no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—21no—
117C2×C11⋊C8—21no—
118C2×C11⋊C8—21no—
119C2×C11⋊C8—21no—
120C2×C11⋊C8—21no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—41no—
124C2×C11⋊C8—41no—
125C2×C11⋊C8—41no—
126C2×C11⋊C8SD1612yescomplemented
127C2×#460—111no—
128#1984—111no—
129#1957—111no—
130#1803D1111yescharacteristic, complemented
131C2×#335—111no—
132C2×#331—111no—
133#1296—111no—
134C23×C11#12111yescharacteristic
135C22×D11—42no—
136C22×D11—81no—
137C22×D11—81no—
138C22×D11—81no—
139C22×D11—81no—
140C22×D11—81no—
141C22×D11—81no—
142Q8×C11—22no—
143Q8×C11—22no—
144Q8×C11—41no—
145Q8×C11—41no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—22no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—81no—
155C2×C4×C11—81no—
156C2×C4×C11—81no—
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12311yescharacteristic
161C2×C4×C11#12311yescharacteristic
162C2×C4×C11#12411yescharacteristic
163C2×C4×C11C2×D811yescharacteristic
164C2×C4×C11C2×SD1611yescharacteristic
165C2×C4×C11#13511yescharacteristic
166C2×C4×C11#13511yescharacteristic
167C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C11#13711yescharacteristic
170C2×C4×C11#13711yescharacteristic
171D44—42no—
172D44—42no—
173D44—42no—
174D44—42no—
175D44—82no—
176D44—82no—
177D44—81no—
178D44—81no—
179D44—81no—
180D44—81no—
181C8×C11—81no—
182C11⋊C8—22no—
183C11⋊C8—42no—
184C11⋊C8—41no—
185C11⋊C8—81no—
186C22×SD16—221no—
187C2×#127—111no—
188C2×C4×Q8C2×D1111yescharacteristic
189#460—222no—
190#460—222no—
191C2×C4⋊C8—111no—
192C2×C4⋊C8—111no—
193C2×C4⋊C8C2×D1111yescharacteristic
194C2×#103—21no—
195C2×#102—221no—
196C2×#102—221no—
197C2×#102—221no—
198C2×C4×C8—111no—
199#384C2×D1111yescharacteristic
200#340—21no—
201#336—221no—
202#336—221no—
203#335—222no—
204#331—222no—
205C22×C11#39411yescharacteristic
206C22×C11#46011yescharacteristic
207C22×C11#46411yescharacteristic
208C22×C11#46611yescharacteristic
209C22×C11#46811yescharacteristic
210C22×C11#47111yescharacteristic
211C22×C11#47211yescharacteristic
212C2×D11—82no—
213C2×D11—82no—
214C2×D11—82no—
215C2×D11—161no—
216C2×D11—161no—
217C2×D11—161no—
218C2×D11—161no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—42no—
222C4×C11—81no—
223C4×C11—161no—
224C4×C11#44711yescharacteristic
225C4×C11#45211yescharacteristic
226C4×C11#46111yescharacteristic
227C4×C11#46311yescharacteristic
228C4×C11#46511yescharacteristic
229C4×C11#46811yescharacteristic
230C4×C11#48011yescharacteristic
231C4×C11#48211yescharacteristic
232C22×Q8C22⋊D1111yescharacteristic
233C22×D4—221no—
234C22×D4—221no—
235C22×D4—221no—
236C2×SD16—224no—
237C2×SD16—442no—
238C2×SD16—442no—
239C22×C8—21no—
240C22×C8—111no—
241C22×C8—111no—
242C22×C8—221no—
243C22×C8—221no—
244#127—112no—
245#127—221no—
246#127—221no—
247#127—221no—
248C4×Q8—21no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4C22⋊D1111yescharacteristic
257C2×C42—21no—
258C2×C42C22×D1111yescharacteristic
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8—112no—
262C4⋊C8—221no—
263C4⋊C8—221no—
264C4⋊C8—221no—
265#103—42no—
266#102—224no—
267#102—442no—
268#102—442no—
269C4×C8—221no—
270C4×C8—221no—
271C2×C11#166811yescharacteristic
272C2×C11#168211yescharacteristic
273C2×C11#168611yescharacteristic
274C2×C11#169811yescharacteristic
275C2×C11#203311yescharacteristic
276C2×C11#205111yescharacteristic
277C2×C11#205511yescharacteristic
278D11—162no—
279C24—441no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8#432312yes—
286C2×D4—222no—
287C2×D4—222no—
288C2×D4—222no—
289C2×D4—441no—
290C2×D4—441no—
291C2×D4—441no—
292C2×D4—441no—
293C2×D4—441no—
294C2×D4—441no—
295C2×D4—441no—
296C2×D4—441no—
297C2×D4—441no—
298C2×D4—441no—
299C2×D4—441no—
300C2×D4—881no—
301C2×D4—881no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—41no—
305C22×C4D4×D1111yescharacteristic
306C22×C4#434111yescharacteristic
307C22×C4C2×C22⋊D1111yescharacteristic
308SD16—448no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—112no—
313C2×C8—221no—
314C2×C8—221no—
315C2×C8—221no—
316C2×C8—221no—
317C2×C8—221no—
318C2×C8—222no—
319C2×C8—441no—
320C2×C8—441no—
321C2×C8—441no—
322C2×C8—441no—
323C2×C8—441no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—81no—
333C42—41no—
334C42—41no—
335C42#433911yescharacteristic
336C42#433911yescharacteristic
337C42D4×D1111yescharacteristic
338C42D4×D1111yescharacteristic
339C11#1047411yescharacteristic, complemented, Sylow
340C23—442no—
341C23—881no—
342C23—881no—
343C23—881no—
344C23—881no—
345C23—881no—
346C23—881no—
347C23#6699211yescharacteristic
348Q8—22no—
349Q8—22no—
350Q8—41no—
351Q8—41no—
352D4—442no—
353D4—442no—
354D4—442no—
355D4—442no—
356D4—882no—
357D4—882no—
358D4—881no—
359D4—881no—
360D4—881no—
361D4—881no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4#6693611yescharacteristic
374C2×C4#6693711yescharacteristic
375C2×C4#6693711yescharacteristic
376C2×C4#6693811yescharacteristic
377C2×C4SD16×D1111yescharacteristic
378C2×C4#6696711yescharacteristic
379C2×C4#6697111yescharacteristic
380C2×C4#6697211yescharacteristic
381C2×C4#6698211yescharacteristic
382C2×C4C2×#432311yescharacteristic
383C2×C4#6699011yescharacteristic
384C2×C4#6699511yescharacteristic
385C2×C4#6700211yescharacteristic
386C2×C4#6700311yescharacteristic
387C8—81no—
388C8—222no—
389C8—442no—
390C8—441no—
391C8—881no—
392C22—882no—
393C22—882no—
394C22—882no—
395C22—1761no—
396C22—1761no—
397C22—1761no—
398C22—1761no—
399C22#1062257211yescharacteristic
400C22#1062265111yescharacteristic
401C22#1062266211yescharacteristic
402C22#1062277611yescharacteristic
403C22#1062279811yescharacteristic
404C22#1062281211yescharacteristic
405C22#1062281611yescharacteristic
406C4—21no—
407C4—21no—
408C4—42no—
409C4—81no—
410C4—161no—
411C4#1062242011yescharacteristic
412C4#1062242511yescharacteristic
413C4#1062243111yescharacteristic
414C4#1062243211yescharacteristic
415C4#1062258011yescharacteristic
416C4#1062261611yescharacteristic
417C4#1062264911yescharacteristic
418C4#1062266011yescharacteristic
419C2—1762no—
420C2#1306797411yescharacteristic
421C2#1306806211yescharacteristic
422C2#1306809011yescharacteristic
423C2#1306815811yescharacteristic
424C2#1306979811yescharacteristic
425C2#1306990611yescharacteristic
426C2#1306993011yescharacteristic
subgroupG/H
centerC23#66992
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1803C2
socleC23×C11#121
prime radicalC2×#66927C22
hypercenter#1803D11
hypocenterC11#10474
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
2. #13069553C2semidirect
4. C2×#10622117C2semidirect
6. #13066499C2semidirect
7. C11×#1803C2semidirect
126. C2×C11⋊C8SD16semidirect
130. #1803D11semidirect
339. C11#10474semidirect

Maximal subgroups

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

subgroupindex
C2×#106226402
#130695532
#130694212
C2×#106221172
C2×#106221232
#130664992
C11×#18032
#1047411