Finite Group Databasebeta

← #14908681

Subgroups — #14908681

Order 2816.

534 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078267C211yesmaximal, characteristic
2#13077224C211yesmaximal, characteristic
3#13070834C218yesmaximal, complemented
4#13070390C211yesmaximal, characteristic, complemented
5#13070389C211yesmaximal, characteristic, complemented
6C2×#10622203C211yesmaximal, characteristic, complemented
7#13070236C211yesmaximal, characteristic
8C2×C11×#362C211yesmaximal, characteristic, complemented
9C22×C11×Q16C2211yescharacteristic
10#10623347—21no—
11#10623276—21no—
12C2×#66954C2211yescharacteristic
13C2×C11×M32C2211yescharacteristic
14C2×C11×#108C2211yescharacteristic
15#10622838—21no—
16#10622802C2214yes—
17#10622801—22no—
18#10622737—21no—
19C2×#66883C2211yescharacteristic
20#10622719C2211yescharacteristic
21C2×#66876C2211yescharacteristic
22#10622506C2214yes—
23D11×#108—22no—
24C11×#362C2214yes—
25#10622203C2214yes—
26#10622152C2214yes—
27#10622151C2214yes—
28#10622132C2214yes—
29C22×Q8×C11—21no—
30C2×#4339D411yescharacteristic
31C2×C11×Q16—21no—
32C2×C11×Q16—21no—
33C2×C11×Q16—21no—
34C2×C11×Q16—21no—
35C2×C11×Q16—21no—
36C2×C11×Q16C2312yes—
37C2×C11×M16—21no—
38C22×C8×C11C2311yescharacteristic
39#67000—41no—
40#66999—24no—
41#66997—41no—
42#66982—42no—
43#66979—21no—
44C2×#4318—21no—
45C2×#4318D411yescharacteristic
46#66960—42no—
47M16×D11—24no—
48#66954—21no—
49#66954—21no—
50#66954—21no—
51#66954—21no—
52#66954—42no—
53C2×#4313C2312yes—
54C2×C8×D11D412yes—
55C11×M32—21no—
56C11×M32C2312yes—
57C2×C11×C16—21no—
58C11×#108—21no—
59C11×#108C2312yes—
60#66899—24no—
61#66886—24no—
62#66883—21no—
63#66883C2312yes—
64#66882—21no—
65#66881C2312yes—
66#66876—21no—
67#66876C2312yes—
68C2×C11⋊C16—21no—
69#33658—111nomaximal, Sylow
70C2×Q8×C11—22no—
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C2×Q8×C11—41no—
74C2×Q8×C11—41no—
75C2×Q8×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11C2×D411yescharacteristic
78C2×C22⋊D11SD1612yes—
79#4339—21no—
80#4339—21no—
81#4339—21no—
82#4339—21no—
83C2×D44SD1611yescharacteristic
84C2×C4×D11C2×D412yes—
85C2×Dic22SD1611yescharacteristic
86C11×Q16—22no—
87C11×Q16—22no—
88C11×Q16—41no—
89C11×Q16—41no—
90C11×M16—22no—
91C11×M16—41no—
92C2×C8×C11—41no—
93C2×C8×C11C2×D411yescharacteristic
94C2×C8×C11#4111yescharacteristic
95C2×C8×C11#4111yescharacteristic
96C2×C8×C11#4111yescharacteristic
97C2×C8×C11#4111yescharacteristic
98C2×C8×C11C2411yescharacteristic
99C22⋊Dic11—41no—
100(C2×D11)⋊C4—44no—
101C4⋊Dic11—22no—
102Dic11⋊C4—44no—
103C4×Dic11—41no—
104#4318—21no—
105#4318—21no—
106#4318—22no—
107#4318—41no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8C2×D412yes—
110#4313—22no—
111#4313—22no—
112#4313—44no—
113C8×D11—22no—
114C8×D11—22no—
115C8×D11—44no—
116C11×C16—22no—
117C11⋊C16—22no—
118#3059—111no—
119#2916—111no—
120#2239—118no—
121#2155—111no—
122#2155—111no—
123C2×#362—111no—
124C2×#362D1111yescharacteristic, complemented
125#2115—111no—
126C23×C11C2×SD1611yescharacteristic
127C22×D11C2×SD1612yes—
128Q8×C11—42no—
129Q8×C11—42no—
130Q8×C11—81no—
131Q8×C11—81no—
132C2×C4×C11—42no—
133C2×C4×C11—81no—
134C2×C4×C11—81no—
135C2×C4×C11#12311yescharacteristic
136C2×C4×C11#12311yescharacteristic
137C2×C4×C11C2×SD1611yescharacteristic
138C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C11C22×D411yescharacteristic
141C22⋊D11—22no—
142C22⋊D11—22no—
143C2×Dic11—42no—
144C2×Dic11C2×SD1612yes—
145D44—21no—
146D44—21no—
147C4×D11—22no—
148C4×D11—22no—
149Dic22—21no—
150Dic22—21no—
151C8×C11—42no—
152C8×C11#12311yescharacteristic
153C8×C11#12311yescharacteristic
154C8×C11C2×#4111yescharacteristic
155C8×C11C2×#4111yescharacteristic
156C11⋊C8—22no—
157C11⋊C8—42no—
158C22×Q16C2×D1111yescharacteristic
159#568—221no—
160C2×#131—111no—
161#536—221no—
162C2×M32—111no—
163C2×M32C2×D1111yescharacteristic
164#470—114no—
165#467—222no—
166#430—114no—
167#430—221no—
168C2×#108—111no—
169C2×#108—222no—
170C2×#108C2×D1111yescharacteristic
171#427—111no—
172#419—221no—
173#365—114no—
174#365—114no—
175#362—114no—
176#362C2×D1114yes—
177#349—114no—
178C22×C11—41no—
179C22×C11#48111yescharacteristic
180C22×C11#48111yescharacteristic
181C22×C11C22×SD1611yescharacteristic
182C2×D11—22no—
183C2×D11—42no—
184C4×C11—82no—
185C4×C11#48111yescharacteristic
186C4×C11#48111yescharacteristic
187C4×C11C2×#12311yescharacteristic
188C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
189Dic11—22no—
190Dic11—82no—
191C2×#41—111no—
192C22×Q8—21no—
193C2×Q16—21no—
194C2×Q16—21no—
195C2×Q16—21no—
196C2×Q16—21no—
197C2×Q16—21no—
198C2×Q16C22×D1112yes—
199#131—221no—
200#131—221no—
201#131—221no—
202#131—221no—
203#131—442no—
204#131—442no—
205C2×M16—21no—
206C2×M16—111no—
207C2×M16—112no—
208C2×M16—224no—
209C2×M16—221no—
210C22×C8—112no—
211C22×C8C22×D1111yescharacteristic
212C4⋊Q8—441no—
213#124—441no—
214#123—442no—
215C22⋊Q8—224no—
216#117—221no—
217M32—21no—
218M32—112no—
219M32—221no—
220M32C22×D1112yes—
221C2×C16—21no—
222C2×C16—221no—
223#108—21no—
224#108—112no—
225#108—224no—
226#108—221no—
227#108C22×D1112yes—
228#107—221no—
229#106—112no—
230#103—224no—
231C2×C11—21no—
232C2×C11—21no—
233C2×C11—21no—
234C2×C11C2×#48111yescharacteristic
235D11—42no—
236#41—221no—
237#41—221no—
238#41—221no—
239#41—221no—
240C2×Q8—22no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—111no—
247C2×D4—112no—
248C2×D4—111no—
249C22×C4—41no—
250C22×C4—112no—
251C22×C4D4×D1111yescharacteristic
252Q16—22no—
253Q16—22no—
254Q16—41no—
255Q16—41no—
256M16—22no—
257M16—41no—
258M16—221no—
259M16—221no—
260M16—222no—
261M16—222no—
262M16—222no—
263M16—444no—
264M16—441no—
265C2×C8—41no—
266C2×C8—112no—
267C2×C8—222no—
268C2×C8—222no—
269C2×C8—444no—
270C2×C8—441no—
271C2×C8#433911yescharacteristic
272C2×C8#433911yescharacteristic
273C2×C8D4×D1111yescharacteristic
274C2×C8#434111yescharacteristic
275C2×C8#434111yescharacteristic
276C2×C8C23×D1111yescharacteristic
277C4⋊C4—222no—
278C4⋊C4—444no—
279C22⋊C4—444no—
280C22⋊C4—441no—
281C42—441no—
282C16—22no—
283C16—222no—
284C11#3365811yescharacteristic, complemented, Sylow
285C23—112no—
286C23SD16×D1111yescharacteristic
287Q8—42no—
288Q8—42no—
289Q8—81no—
290Q8—81no—
291Q8—221no—
292Q8—221no—
293D4—222no—
294D4—222no—
295D4—221no—
296D4—221no—
297C2×C4—42no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—112no—
301C2×C4—222no—
302C2×C4—222no—
303C2×C4—442no—
304C2×C4#6693611yescharacteristic
305C2×C4#6693611yescharacteristic
306C2×C4#6696411yescharacteristic
307C2×C4#6696411yescharacteristic
308C2×C4SD16×D1111yescharacteristic
309C2×C4C2×D4×D1111yescharacteristic
310C8—42no—
311C8—222no—
312C8—442no—
313C8#6693611yescharacteristic
314C8#6693611yescharacteristic
315C8C2×#433911yescharacteristic
316C8C2×#434111yescharacteristic
317C22—41no—
318C22—222no—
319C22—442no—
320C22#1062239011yescharacteristic
321C22#1062239011yescharacteristic
322C22C2×SD16×D1111yescharacteristic
323C4—82no—
324C4—222no—
325C4—882no—
326C4#1062239011yescharacteristic
327C4#1062239011yescharacteristic
328C4C2×#6693611yescharacteristic
329C4C2×#6696411yescharacteristic
330C2—21no—
331C2—21no—
332C2—21no—
333C2—442no—
334C2C2×#1062239011yescharacteristic
subgroupG/H
centerC2C2×#10622390
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#362C2
socleC2×C11C2×#481
prime radicalC2×#4339D4
hypercenterC2×#362D11
hypocenterC11#33658
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ C2×#362

Complements

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

NH ≅ G/Ntype
3. #13070834C2semidirect
4. #13070390C2semidirect
5. #13070389C2semidirect
6. C2×#10622203C2semidirect
8. C2×C11×#362C2semidirect
124. C2×#362D11semidirect
284. C11#33658semidirect

Maximal subgroups

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

subgroupindex
#130782672
#130772242
#130708342
#130703902
#130703892
C2×#106222032
#130702362
C2×C11×#3622
#3365811