Finite Group Databasebeta

← #14656331

Subgroups — #14656331

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622701C211yesmaximal, characteristic
2C2×#10622640C211yesmaximal, characteristic
3#13069553C211yesmaximal, characteristic, complemented
4C2×#10622184C211yesmaximal, characteristic, complemented
5C2×#10622123C211yesmaximal, characteristic
6#13066450C211yesmaximal, characteristic, complemented
7C2×C11×#477C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C22×#4325—21no—
11C2×#66927C2211yescharacteristic
12C11×#477—22no—
13C11×#477—22no—
14C2×C11×#107—21no—
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×#103—21no—
17#10622701—22no—
18#10622701—22no—
19#10622640—22no—
20#10622640—22no—
21C2×#66873—21no—
22C2×#66873—22no—
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24C2×C4⋊(C11⋊C8)C2211yescharacteristic
25C2×C4×C11⋊C8C2211yescharacteristic
26#10622184—22no—
27#10622162—22no—
28#10622123—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11D411yescharacteristic
31C22×D44—21no—
32C22×D44—21no—
33C22×D44—21no—
34C22×C8×C11—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8D412yes—
39C4×Q8×C11—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C42×C11—21no—
48C2×C42×C11C2311yescharacteristic
49C2×#4325—24no—
50C2×#4325—42no—
51C2×#4325—42no—
52C22×C11⋊C8—21no—
53C22×C11⋊C8—21no—
54C22×C11⋊C8D412yes—
55#66927—21no—
56#66927—21no—
57#66927—21no—
58#66927D412yes—
59C11×#107—24no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8D412yes—
62C11×#103—24no—
63#66873—24no—
64#66873—28no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)D412yes—
69C4×C11⋊C8—21no—
70C4×C11⋊C8—21no—
71#10269—111nomaximal, Sylow
72C23×D11—41no—
73C2×Q8×C11—21no—
74C2×Q8×C11—21no—
75C2×Q8×C11—21no—
76C2×Q8×C11—22no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—41no—
80C2×Q8×C11—82no—
81C2×Q8×C11SD1612yes—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—41no—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C2×D44—22no—
89C2×D44—22no—
90C2×D44—22no—
91C2×D44—41no—
92C2×D44—41no—
93C2×D44—41no—
94C2×D44—41no—
95C2×D44—42no—
96C2×D44—41no—
97C2×D44—41no—
98C2×D44—42no—
99C2×D44—41no—
100C2×D44—82no—
101C2×C8×C11—22no—
102C2×C8×C11—41no—
103C2×C8×C11—41no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C42×C11—41no—
113C42×C11—41no—
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118#4325—48no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—41no—
124C2×C11⋊C8—41no—
125C2×C11⋊C8—42no—
126C2×C11⋊C8—41no—
127C2×#486—111no—
128C2×#477D1111yescharacteristic, complemented
129C2×#460—111no—
130#1984—111no—
131C2×#333—111no—
132C2×#331—111no—
133#1277—111no—
134C23×C11#12111yescharacteristic
135C22×D11—42no—
136C22×D11—82no—
137C22×D11—81no—
138C22×D11—81no—
139C22×D11—82no—
140Q8×C11—22no—
141Q8×C11—22no—
142Q8×C11—41no—
143Q8×C11—41no—
144Q8×C11—82no—
145Q8×C11—82no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—82no—
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12711yescharacteristic
160C2×C4×C11C2×SD1611yescharacteristic
161C2×C4×C11#13512yes—
162C2×C4×C11#13511yescharacteristic
163C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C11#13712yes—
165C2×C4×C11#13711yescharacteristic
166D44—42no—
167D44—44no—
168D44—42no—
169D44—82no—
170D44—82no—
171D44—81no—
172D44—81no—
173D44—81no—
174D44—81no—
175C8×C11—42no—
176C11⋊C8—42no—
177C11⋊C8—42no—
178C11⋊C8—81no—
179C22×SD16—221no—
180C2×C4⋊Q8C2×D1111yescharacteristic
181C2×#127—111no—
182C2×C4×Q8C2×D1111yescharacteristic
183#486—222no—
184#486—222no—
185#477—22no—
186#477—22no—
187#460—222no—
188#460—222no—
189C2×#107—21no—
190C2×C4⋊C8—111no—
191C2×C4⋊C8—111no—
192C2×C4⋊C8C2×D1111yescharacteristic
193C2×#103—21no—
194C2×#102—222no—
195C2×#102—221no—
196C2×C4×C8—111no—
197#336—222no—
198#333—222no—
199#331—222no—
200C22×C11#39211yescharacteristic
201C22×C11#46412yes—
202C22×C11#46511yescharacteristic
203C22×C11#46811yescharacteristic
204C22×C11#47212yes—
205C2×D11—82no—
206C2×D11—82no—
207C2×D11—82no—
208C2×D11—162no—
209C2×D11—162no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—42no—
213C4×C11—81no—
214C4×C11—82no—
215C4×C11#44811yescharacteristic
216C4×C11#44911yescharacteristic
217C4×C11#45011yescharacteristic
218C4×C11#45212yes—
219C4×C11#45211yescharacteristic
220C4×C11#49511yescharacteristic
221C4×C11#49711yescharacteristic
222C22×Q8—21no—
223C22×Q8C22⋊D1111yescharacteristic
224C22×D4—221no—
225C22×D4—221no—
226C22×D4—221no—
227C2×SD16—224no—
228C2×SD16—442no—
229C2×SD16—442no—
230C22×C8—21no—
231C22×C8—112no—
232C22×C8—221no—
233C22×C8—221no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8C22⋊D1112yes—
238#127—112no—
239#127—221no—
240#127—221no—
241#127—221no—
242C4×Q8—21no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×Q8—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4C22⋊D1111yescharacteristic
250C2×C42—21no—
251C2×C42C22×D1111yescharacteristic
252#107—24no—
253C4⋊C8—21no—
254C4⋊C8—112no—
255C4⋊C8—221no—
256C4⋊C8—221no—
257C4⋊C8—221no—
258C4⋊C8C22⋊D1112yes—
259#103—24no—
260#102—224no—
261#102—228no—
262C4×C8—221no—
263C4×C8—221no—
264C2×C11#167812yes—
265C2×C11#169812yes—
266C2×C11#200011yescharacteristic
267C2×C11#201511yescharacteristic
268C2×C11#201811yescharacteristic
269D11—162no—
270C24—441no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—22no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—21no—
277C2×Q8—41no—
278C2×Q8—82no—
279C2×Q8#432512yes—
280C2×D4—222no—
281C2×D4—222no—
282C2×D4—222no—
283C2×D4—442no—
284C2×D4—442no—
285C2×D4—441no—
286C2×D4—441no—
287C2×D4—441no—
288C2×D4—441no—
289C2×D4—441no—
290C2×D4—441no—
291C2×D4—441no—
292C2×D4—882no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—41no—
296C22×C4D4×D1111yescharacteristic
297C22×C4#434111yescharacteristic
298C22×C4C2×C22⋊D1111yescharacteristic
299SD16—448no—
300C2×C8—22no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—222no—
304C2×C8—222no—
305C2×C8—222no—
306C2×C8—222no—
307C2×C8—441no—
308C2×C8—441no—
309C2×C8—442no—
310C2×C8—441no—
311C4⋊C4—22no—
312C4⋊C4—21no—
313C4⋊C4—22no—
314C4⋊C4—21no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C42—41no—
320C42—41no—
321C42D4×D1111yescharacteristic
322C42D4×D1111yescharacteristic
323C42C2×C22⋊D1111yescharacteristic
324C42C2×C22⋊D1111yescharacteristic
325C11#1026911yescharacteristic, complemented, Sylow
326C23—442no—
327C23—882no—
328C23—882no—
329C23—881no—
330C23—881no—
331C23#6699211yescharacteristic
332Q8—22no—
333Q8—22no—
334Q8—41no—
335Q8—41no—
336Q8—82no—
337Q8—82no—
338D4—444no—
339D4—442no—
340D4—442no—
341D4—882no—
342D4—882no—
343D4—881no—
344D4—881no—
345D4—881no—
346D4—881no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—82no—
355C2×C4#6697112yes—
356C2×C4#6697212yes—
357C2×C4#6699011yescharacteristic
358C2×C4#6699011yescharacteristic
359C2×C4#6699111yescharacteristic
360C2×C4#6699211yescharacteristic
361C2×C4#6699311yescharacteristic
362C2×C4C2×#432511yescharacteristic
363C2×C4#6699511yescharacteristic
364C2×C4#6700211yescharacteristic
365C2×C4#6700311yescharacteristic
366C2×C4#6700611yescharacteristic
367C8—42no—
368C8—442no—
369C8—442no—
370C8—881no—
371C22—882no—
372C22—882no—
373C22—882no—
374C22—1762no—
375C22—1762no—
376C22#1062266111yescharacteristic
377C22#1062266211yescharacteristic
378C22#1062279812yes—
379C22#1062281212yes—
380C22#1062283611yescharacteristic
381C4—21no—
382C4—21no—
383C4—42no—
384C4—81no—
385C4—82no—
386C4#1062265911yescharacteristic
387C4#1062266011yescharacteristic
388C4#1062280012yes—
389C4#1062280311yescharacteristic
390C4#1062280411yescharacteristic
391C4#1062284011yescharacteristic
392C4#1062285111yescharacteristic
393C2—1762no—
394C2#1306803412yes—
395C2#1306815812yes—
396C2#1306961711yescharacteristic
397C2#1306970711yescharacteristic
398C2#1306972211yescharacteristic
subgroupG/H
centerC23#66992
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#477C2
socleC23×C11#121
prime radicalC2×#66927C22
hypercenterC2×#477D11
hypocenterC11#10269
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
3. #13069553C2semidirect
4. C2×#10622184C2semidirect
6. #13066450C2semidirect
7. C2×C11×#477C2semidirect
128. C2×#477D11semidirect
325. C11#10269semidirect

Maximal subgroups

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

subgroupindex
C2×#106227012
C2×#106226402
#130695532
C2×#106221842
C2×#106221232
#130664502
C2×C11×#4772
#1026911