Finite Group Databasebeta

← #14656317

Subgroups — #14656317

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622701C211yesmaximal, characteristic, complemented
2C2×#10622628C211yesmaximal, characteristic
3#13069411C211yesmaximal, characteristic, complemented
4C2×#10622184C211yesmaximal, characteristic, complemented
5C2×#10622123C211yesmaximal, characteristic, complemented
6#13066450C211yesmaximal, characteristic, complemented
7C2×C11×#476C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10C22×#4323—21no—
11C2×#66927C2211yescharacteristic
12C11×#476—22no—
13C11×#476—22no—
14C2×C11×#106—21no—
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×#102—21no—
17C2×C22⋊(C11⋊C8)—22no—
18#10622701—22no—
19#10622701—22no—
20#10622628—22no—
21#10622628—22no—
22C2×#66873—21no—
23C2×#66873—22no—
24C2×C4⋊(C11⋊C8)C2211yescharacteristic
25C2×C4⋊(C11⋊C8)C2211yescharacteristic
26C2×C4×C11⋊C8C2211yescharacteristic
27#10622184—22no—
28#10622123—22no—
29C22×Q8×C11—21no—
30C22×D4×C11D411yescharacteristic
31C23×C4×C11—21no—
32C22×D44—21no—
33C22×D44—21no—
34C22×D44—21no—
35C22×C8×C11—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8D412yes—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C22⋊C4—21no—
48C2×C42×C11C2311yescharacteristic
49C2×#4323—24no—
50C2×#4323—42no—
51C2×#4323—42no—
52C22×C11⋊C8—21no—
53C22×C11⋊C8—21no—
54C22×C11⋊C8D412yes—
55#66927—21no—
56#66927—21no—
57#66927—21no—
58#66927D412yes—
59C11×#106—24no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8D412yes—
62C11×#102—24no—
63C22⋊(C11⋊C8)—44no—
64#66873—24no—
65#66873—28no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)D412yes—
70C4×C11⋊C8—21no—
71C4×C11⋊C8—21no—
72#10267—111nomaximal, Sylow
73C24×C11—21no—
74C23×D11—41no—
75C2×Q8×C11—22no—
76C2×Q8×C11—41no—
77C2×Q8×C11—82no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11SD1612yes—
84C22×C4×C11—21no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—42no—
89C22×C4×C11—42no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C2×D44—22no—
94C2×D44—22no—
95C2×D44—22no—
96C2×D44—41no—
97C2×D44—41no—
98C2×D44—41no—
99C2×D44—41no—
100C2×D44—42no—
101C2×D44—41no—
102C2×D44—41no—
103C2×D44—42no—
104C2×D44—41no—
105C2×D44—82no—
106C2×C8×C11—22no—
107C2×C8×C11—41no—
108C2×C8×C11—41no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121#4323—48no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—41no—
127C2×C11⋊C8—41no—
128C2×C11⋊C8—41no—
129C2×C11⋊C8—42no—
130C2×#486—111no—
131C2×#476D1111yescharacteristic, complemented
132C2×#459—111no—
133#1954—111no—
134C2×#333—111no—
135C2×#331—111no—
136#1277—111no—
137C23×C11—22no—
138C23×C11—41no—
139C23×C11—42no—
140C23×C11—41no—
141C23×C11—42no—
142C23×C11#12111yescharacteristic
143C22×D11—42no—
144C22×D11—82no—
145C22×D11—81no—
146C22×D11—81no—
147C22×D11—82no—
148Q8×C11—82no—
149Q8×C11—82no—
150D4×C11—22no—
151D4×C11—22no—
152D4×C11—41no—
153D4×C11—41no—
154C2×C4×C11—22no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—82no—
159C2×C4×C11—82no—
160C2×C4×C11—81no—
161C2×C4×C11—81no—
162C2×C4×C11#12011yescharacteristic
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12711yescharacteristic
168C2×C4×C11C2×SD1611yescharacteristic
169C2×C4×C11#13512yes—
170C2×C4×C11#13511yescharacteristic
171C2×C4×C11AGL(1,ℤ/8)12yes—
172C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C11#13711yescharacteristic
174D44—44no—
175D44—42no—
176D44—42no—
177D44—82no—
178D44—82no—
179D44—81no—
180D44—81no—
181D44—81no—
182D44—81no—
183C8×C11—42no—
184C11⋊C8—42no—
185C11⋊C8—42no—
186C11⋊C8—81no—
187C22×D8—221no—
188C2×C4⋊Q8C2×D1111yescharacteristic
189C2×#127—111no—
190C2×C4×D4C2×D1111yescharacteristic
191#486—222no—
192#486—222no—
193#476—22no—
194#476—22no—
195#459—222no—
196#459—222no—
197C2×#106—21no—
198C2×C4⋊C8—111no—
199C2×C4⋊C8—111no—
200C2×C4⋊C8C2×D1111yescharacteristic
201C2×#102—21no—
202C2×#102—222no—
203C2×#102—221no—
204C2×C22⋊C8—222no—
205C2×C4×C8—111no—
206#333—222no—
207#331—222no—
208C22×C11—44no—
209C22×C11—42no—
210C22×C11—82no—
211C22×C11—81no—
212C22×C11—81no—
213C22×C11#39211yescharacteristic
214C22×C11#46312yes—
215C22×C11#46511yescharacteristic
216C22×C11#46811yescharacteristic
217C22×C11#47212yes—
218C2×D11—82no—
219C2×D11—82no—
220C2×D11—82no—
221C2×D11—162no—
222C2×D11—162no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—81no—
226C4×C11—82no—
227C4×C11#44811yescharacteristic
228C4×C11#44912yes—
229C4×C11#44911yescharacteristic
230C4×C11#45011yescharacteristic
231C4×C11#45211yescharacteristic
232C4×C11#49511yescharacteristic
233C4×C11#49611yescharacteristic
234C22×Q8—21no—
235C22×D4—221no—
236C22×D4—221no—
237C22×D4—221no—
238C22×D4C22⋊D1111yescharacteristic
239C23×C4—21no—
240C2×D8—224no—
241C2×D8—442no—
242C2×D8—442no—
243C22×C8—21no—
244C22×C8—112no—
245C22×C8—221no—
246C22×C8—221no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8C22⋊D1112yes—
251#127—112no—
252#127—221no—
253#127—221no—
254#127—221no—
255C4×D4—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4C22⋊D1111yescharacteristic
262C2×C22⋊C4—21no—
263C2×C42C22×D1111yescharacteristic
264#106—24no—
265C4⋊C8—21no—
266C4⋊C8—112no—
267C4⋊C8—221no—
268C4⋊C8—221no—
269C4⋊C8—221no—
270C4⋊C8C22⋊D1112yes—
271#102—24no—
272#102—224no—
273#102—228no—
274C22⋊C8—444no—
275C4×C8—221no—
276C4×C8—221no—
277C2×C11—82no—
278C2×C11#167712yes—
279C2×C11#169712yes—
280C2×C11#200011yescharacteristic
281C2×C11#201211yescharacteristic
282C2×C11#201811yescharacteristic
283D11—162no—
284C24—21no—
285C24—441no—
286C2×Q8—22no—
287C2×Q8—41no—
288C2×Q8—82no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—222no—
295C2×D4—222no—
296C2×D4—222no—
297C2×D4—442no—
298C2×D4—442no—
299C2×D4—441no—
300C2×D4—441no—
301C2×D4—441no—
302C2×D4—441no—
303C2×D4—441no—
304C2×D4—441no—
305C2×D4—441no—
306C2×D4—882no—
307C2×D4#432512yes—
308C22×C4—21no—
309C22×C4—41no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4D4×D1111yescharacteristic
315C22×C4#434111yescharacteristic
316C22×C4C2×C22⋊D1111yescharacteristic
317D8—448no—
318C2×C8—22no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—222no—
322C2×C8—222no—
323C2×C8—222no—
324C2×C8—222no—
325C2×C8—441no—
326C2×C8—441no—
327C2×C8—442no—
328C2×C8—441no—
329C4⋊C4—22no—
330C4⋊C4—21no—
331C4⋊C4—22no—
332C4⋊C4—21no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C42D4×D1111yescharacteristic
338C42D4×D1111yescharacteristic
339C42C2×C22⋊D1111yescharacteristic
340C42C2×C22⋊D1111yescharacteristic
341C11#1026711yescharacteristic, complemented, Sylow
342C23—22no—
343C23—42no—
344C23—42no—
345C23—41no—
346C23—41no—
347C23—442no—
348C23—882no—
349C23—882no—
350C23—881no—
351C23—881no—
352C23#6699211yescharacteristic
353Q8—82no—
354Q8—82no—
355D4—22no—
356D4—22no—
357D4—41no—
358D4—41no—
359D4—444no—
360D4—442no—
361D4—442no—
362D4—882no—
363D4—882no—
364D4—881no—
365D4—881no—
366D4—881no—
367D4—881no—
368C2×C4—22no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—82no—
373C2×C4—81no—
374C2×C4—82no—
375C2×C4—81no—
376C2×C4#6696712yes—
377C2×C4#6696912yes—
378C2×C4#6699011yescharacteristic
379C2×C4#6699011yescharacteristic
380C2×C4#6699111yescharacteristic
381C2×C4#6699211yescharacteristic
382C2×C4#6699311yescharacteristic
383C2×C4C2×#432511yescharacteristic
384C2×C4#6699511yescharacteristic
385C2×C4#6700211yescharacteristic
386C2×C4#6700311yescharacteristic
387C2×C4#6700611yescharacteristic
388C8—42no—
389C8—442no—
390C8—442no—
391C8—881no—
392C22—42no—
393C22—44no—
394C22—82no—
395C22—81no—
396C22—81no—
397C22—882no—
398C22—882no—
399C22—882no—
400C22—1762no—
401C22—1762no—
402C22#1062266111yescharacteristic
403C22#1062266211yescharacteristic
404C22#1062277812yes—
405C22#1062281212yes—
406C22#1062283611yescharacteristic
407C4—21no—
408C4—21no—
409C4—81no—
410C4—82no—
411C4#1062265911yescharacteristic
412C4#1062266011yescharacteristic
413C4#1062278111yescharacteristic
414C4#1062278512yes—
415C4#1062278911yescharacteristic
416C4#1062284011yescharacteristic
417C4#1062285111yescharacteristic
418C2—82no—
419C2—1762no—
420C2#1306802712yes—
421C2#1306815112yes—
422C2#1306961711yescharacteristic
423C2#1306969011yescharacteristic
424C2#1306972211yescharacteristic
subgroupG/H
centerC23#66992
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#476C2
socleC23×C11#121
prime radicalC2×#10622628C2
hypercenterC2×#476D11
hypocenterC11#10267
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#10622701C2semidirect
3. #13069411C2semidirect
4. C2×#10622184C2semidirect
5. C2×#10622123C2semidirect
6. #13066450C2semidirect
7. C2×C11×#476C2semidirect
131. C2×#476D11semidirect
341. C11#10267semidirect

Maximal subgroups

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

subgroupindex
C2×#106227012
C2×#106226282
#130694112
C2×#106221842
C2×#106221232
#130664502
C2×C11×#4762
#1026711