Finite Group Databasebeta

← #14670942

Subgroups — #14670942

Order 2816.

476 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622808C211yesmaximal, characteristic
2C2×#10622134C211yesmaximal, characteristic, complemented
3#13070328C211yesmaximal, characteristic
4#13069477C211yesmaximal, characteristic, complemented
5#13066726C211yesmaximal, characteristic, complemented
6#13066698C211yesmaximal, characteristic, complemented
7C2×C11×#443C211yesmaximal, characteristic
8C2×C11×#135C2211yescharacteristic
9C2×C11×#131—21no—
10C22×Dic44C2211yescharacteristic
11C11×#443—22no—
12C11×#443—22no—
13C2×C11×#108C2211yescharacteristic
14C2×C11×#104—21no—
15C2×C4×C8×C11C2211yescharacteristic
16#10622808—22no—
17#10622808C414yescomplemented
18C2×#66893—21no—
19C2×#66891—21no—
20C2×#66882C2211yescharacteristic
21C2×#66880—21no—
22C2×#66876C2211yescharacteristic
23C2×#66876C2211yescharacteristic
24#10622542—21no—
25#10622202—21no—
26#10622200—21no—
27#10622134—22no—
28C2×C11×#41—21no—
29C22×Dic22—21no—
30C11×#135—21no—
31C11×#135—21no—
32C11×#135C2×C412yes—
33C11×#135D412yes—
34C2×C11×Q16D411yescharacteristic
35C2×C11×SD16—21no—
36C2×C11×D8D411yescharacteristic
37C11×#131—24no—
38C11×#131—42no—
39C2×C11×M16—21no—
40C2×C11×M16—41no—
41C22×C8×C11—41no—
42C22×C8×C11D411yescharacteristic
43C22×C8×C11C2311yescharacteristic
44C2×C42×C11D411yescharacteristic
45C2×C4⋊Dic11—21no—
46C2×Dic44—21no—
47C2×Dic44—21no—
48C2×Dic44—21no—
49C2×Dic44—21no—
50C2×Dic44—21no—
51C2×Dic44C2×C412yes—
52C11×#108—21no—
53C11×#108D412yes—
54C11×#104—24no—
55C4×C8×C11—21no—
56C4×C8×C11—21no—
57C11⋊#95—42no—
58#66893—24no—
59#66891—24no—
60#66882—21no—
61#66882—21no—
62#66880—41no—
63#66880—41no—
64#66876—21no—
65#66876—21no—
66#66876—21no—
67#66876C2×C412yes—
68C2×C11⋊C16—21no—
69C2×C11⋊C16—21no—
70#13028—111nomaximal, Sylow
71C11×#41—22no—
72C11×#41—22no—
73C11×#41—41no—
74C11×#41—41no—
75C2×Q8×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—41no—
78C22×C4×C11—21no—
79C22×C4×C11—41no—
80C22×C4×C11C2×D411yescharacteristic
81C22×Dic11—41no—
82C22×Dic11—41no—
83C2×Dic22—22no—
84C2×Dic22—41no—
85C2×Dic22—41no—
86C2×Dic22—41no—
87C2×Dic22—41no—
88C2×Dic22—41no—
89C11×Q16—21no—
90C11×Q16C22⋊C412yes—
91C11×SD16—22no—
92C11×SD16—22no—
93C11×D8—21no—
94C11×D8C22⋊C412yes—
95C11×M16—22no—
96C11×M16—44no—
97C11×M16—41no—
98C2×C8×C11—21no—
99C2×C8×C11—21no—
100C2×C8×C11—44no—
101C2×C8×C11—41no—
102C2×C8×C11D811yescharacteristic
103C2×C8×C11D811yescharacteristic
104C2×C8×C11C22×C411yescharacteristic
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11C2×D411yescharacteristic
108C2×C8×C11#4111yescharacteristic
109C2×C8×C11#4111yescharacteristic
110C42×C11—21no—
111C42×C11—21no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114Dic44—22no—
115Dic44—22no—
116Dic44—41no—
117Dic44—41no—
118C11⋊C16—22no—
119C11⋊C16—41no—
120C2×#510—111no—
121C2×#443D1111yescharacteristic
122C2×#362—111no—
123#2139—111no—
124#1969—111no—
125#1387—111no—
126#1376—111no—
127C23×C11—41no—
128C23×C11AGL(1,ℤ/8)11yescharacteristic
129Q8×C11—22no—
130Q8×C11—41no—
131D4×C11—22no—
132D4×C11—42no—
133D4×C11—42no—
134D4×C11—41no—
135C2×C4×C11—22no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11C4×D411yescharacteristic
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11C2×D811yescharacteristic
145C2×C4×C11#13511yescharacteristic
146C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
147C2×Dic11—42no—
148C2×Dic11—81no—
149C2×Dic11—81no—
150C2×Dic11—82no—
151C2×Dic11—81no—
152Dic22—42no—
153Dic22—42no—
154Dic22—81no—
155Dic22—81no—
156C8×C11—21no—
157C8×C11—21no—
158C8×C11—42no—
159C8×C11C2×C22⋊C411yescharacteristic
160C8×C11C4×D411yescharacteristic
161C8×C11#12111yescharacteristic
162C8×C11#12311yescharacteristic
163C2×#135C2×D1111yescharacteristic
164C22×Q16—111no—
165C2×#131—21no—
166#510—114no—
167#510—222no—
168C2×Q32—221no—
169C2×SD32—221no—
170C2×M32—111no—
171C2×M32—111no—
172#443—22no—
173#443—22no—
174C2×#108C2×D1111yescharacteristic
175C2×#107—111no—
176C2×#104—21no—
177C2×#103—221no—
178C2×C4×C8C2×D1111yescharacteristic
179#391—221no—
180#362—222no—
181#358—221no—
182#357—221no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—42no—
186C22×C11—81no—
187C22×C11—81no—
188C22×C11#44211yescharacteristic
189C22×C11#44911yescharacteristic
190C22×C11#45911yescharacteristic
191C4×C11—42no—
192C4×C11—42no—
193C4×C11#38611yescharacteristic
194C4×C11C4×D811yescharacteristic
195C4×C11#44711yescharacteristic
196C4×C11#46311yescharacteristic
197Dic11—82no—
198Dic11—161no—
199C2×#41—21no—
200C22×Q8—221no—
201#135—21no—
202#135—21no—
203#135C4×D1112yes—
204#135C22⋊D1112yes—
205C2×Q16—112no—
206C2×Q16—221no—
207C2×Q16—221no—
208C2×Q16—221no—
209C2×Q16—221no—
210C2×Q16—221no—
211C2×Q16D4411yescharacteristic
212C2×SD16—21no—
213C2×D8D4411yescharacteristic
214#131—24no—
215#131—42no—
216C2×M16—21no—
217C2×M16—41no—
218C22×C8—41no—
219C22×C8C22⋊D1111yescharacteristic
220C22×C8C22×D1111yescharacteristic
221C2×C4⋊C4—221no—
222C2×C42C22⋊D1111yescharacteristic
223Q32—224no—
224SD32—224no—
225M32—112no—
226M32—221no—
227M32—221no—
228M32—221no—
229C2×C16—221no—
230C2×C16—221no—
231#108—21no—
232#108C22⋊D1112yes—
233#107—221no—
234#107—221no—
235#104—24no—
236#103—441no—
237#103—441no—
238C4×C8—21no—
239C4×C8—21no—
240#95—442no—
241C2×C11—21no—
242C2×C11—21no—
243C2×C11—82no—
244C2×C11#187911yescharacteristic
245C2×C11#221211yescharacteristic
246C2×C11#221411yescharacteristic
247#41—22no—
248#41—22no—
249#41—41no—
250#41—41no—
251C2×Q8—21no—
252C2×Q8—222no—
253C2×Q8—441no—
254C2×Q8—441no—
255C2×Q8—441no—
256C2×Q8—441no—
257C2×Q8—441no—
258C2×D4—21no—
259C2×D4—41no—
260C22×C4—21no—
261C22×C4—41no—
262C22×C4—441no—
263C22×C4—441no—
264C22×C4C2×C22⋊D1111yescharacteristic
265Q16—21no—
266Q16—222no—
267Q16—222no—
268Q16—441no—
269Q16—441no—
270Q16(C2×D11)⋊C412yes—
271SD16—22no—
272SD16—22no—
273D8—21no—
274D8(C2×D11)⋊C412yes—
275M16—22no—
276M16—44no—
277M16—41no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—44no—
281C2×C8—41no—
282C2×C8#432311yescharacteristic
283C2×C8#432311yescharacteristic
284C2×C8C2×C4×D1111yescharacteristic
285C2×C8C2×D4411yescharacteristic
286C2×C8#433911yescharacteristic
287C2×C8#433911yescharacteristic
288C2×C8C2×C22⋊D1111yescharacteristic
289C2×C8C2×C22⋊D1111yescharacteristic
290C4⋊C4—441no—
291C4⋊C4—441no—
292C42—21no—
293C42—21no—
294C16—222no—
295C16—441no—
296C11#1302811yescharacteristic, complemented, Sylow
297C23—41no—
298C23#6700211yescharacteristic
299Q8—22no—
300Q8—41no—
301Q8—442no—
302Q8—442no—
303Q8—881no—
304Q8—881no—
305D4—22no—
306D4—42no—
307D4—42no—
308D4—41no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—442no—
316C2×C4—881no—
317C2×C4—881no—
318C2×C4—882no—
319C2×C4—881no—
320C2×C4C4×C22⋊D1111yescharacteristic
321C2×C4#6698311yescharacteristic
322C2×C4C2×#432311yescharacteristic
323C2×C4#6698511yescharacteristic
324C2×C4#6700311yescharacteristic
325C2×C4#6700611yescharacteristic
326C8—21no—
327C8—21no—
328C8—42no—
329C8C2×(C2×D11)⋊C411yescharacteristic
330C8C4×C22⋊D1111yescharacteristic
331C8#6698211yescharacteristic
332C8#6698311yescharacteristic
333C22—21no—
334C22—21no—
335C22—42no—
336C22—81no—
337C22—81no—
338C22#1062262711yescharacteristic
339C22#1062262811yescharacteristic
340C22#1062285111yescharacteristic
341C4—42no—
342C4—42no—
343C4—882no—
344C4—1761no—
345C4C4×#432311yescharacteristic
346C4#1062262911yescharacteristic
347C4#1062282611yescharacteristic
348C4#1062283011yescharacteristic
349C2—21no—
350C2—21no—
351C2—82no—
352C2#1306896411yescharacteristic
353C2#1307068511yescharacteristic
354C2#1307069711yescharacteristic
subgroupG/H
centerC22#10622628
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#443C2
socleC22×C11#459
prime radicalC2×C11×#135C22
cosocleC22×C8×C11C23
hypercenterC2×#443D11
hypocenterC11#13028
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#443

Complements

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

NH ≅ G/Ntype
2. C2×#10622134C2semidirect
4. #13069477C2semidirect
5. #13066726C2semidirect
6. #13066698C2semidirect
17. #10622808C4semidirect
296. C11#13028semidirect

Maximal subgroups

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

subgroupindex
C2×#106228082
C2×#106221342
#130703282
#130694772
#130667262
#130666982
C2×C11×#4432
#1302811