Finite Group Databasebeta

← #14670909

Subgroups — #14670909

Order 2816.

474 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077492C211yesmaximal, characteristic
2C2×#10622205C211yesmaximal, characteristic
3C2×#10622202C211yesmaximal, characteristic, complemented
4#13069532C211yesmaximal, characteristic, complemented
5#13066725C211yesmaximal, characteristic, complemented
6#13066706C211yesmaximal, characteristic, complemented
7C2×C11×#510C211yesmaximal, characteristic
8C2×C11×#135C2211yescharacteristic
9C22×C11×Q16C2211yescharacteristic
10#10623358—21no—
11C11×#510—22no—
12C11×#510C414yescomplemented
13C2×C11×Q32—21no—
14C2×C11×SD32—21no—
15C2×C11×M32C2211yescharacteristic
16#10622845—21no—
17C2×#66900—21no—
18#10622838—21no—
19Q16×Dic11—21no—
20#10622777—22no—
21D8×Dic11—21no—
22C2×#66883C2211yescharacteristic
23C2×#66882C2211yescharacteristic
24#10622714C2211yescharacteristic
25C22×C11⋊C16C2211yescharacteristic
26#10622205—22no—
27#10622202—22no—
28C2×C11×#41—21no—
29C22×Q8×C11—21no—
30C11×#135—21no—
31C11×#135—21no—
32C11×#135C2×C412yes—
33C11×#135D412yes—
34C2×C11×Q16—21no—
35C2×C11×Q16—21no—
36C2×C11×Q16—21no—
37C2×C11×Q16—21no—
38C2×C11×Q16—21no—
39C2×C11×Q16C2×C412yescomplemented
40C2×C11×Q16D411yescharacteristic
41C2×C11×SD16—21no—
42C2×C11×D8D411yescharacteristic
43C22×C8×C11C2311yescharacteristic
44Q8×Dic11—22no—
45D4×Dic11—22no—
46D4×Dic11—42no—
47#66979—41no—
48#66979D411yescharacteristic
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—41no—
51C2×#4318—21no—
52C2×#4318D411yescharacteristic
53C11×Q32—24no—
54C11×SD32—24no—
55C11×M32—21no—
56C11×M32C2×C412yescomplemented
57C2×C11×C16—21no—
58#66900—42no—
59#66899—22no—
60#66899—41no—
61#66899—41no—
62#66896—22no—
63#66883—21no—
64#66883—21no—
65#66882—21no—
66#66882D412yes—
67#66879—21no—
68C8×Dic11—21no—
69C2×C11⋊C16—21no—
70C2×C11⋊C16—21no—
71C2×C11⋊C16—21no—
72#13023—111nomaximal, Sylow
73C11×#41—22no—
74C11×#41—22no—
75C11×#41—41no—
76C11×#41—41no—
77C2×Q8×C11—22no—
78C2×Q8×C11—21no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C2×D4×C11—21no—
85C2×D4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11C2×D411yescharacteristic
89C22×Dic11—42no—
90C22×Dic11—41no—
91C11×Q16—21no—
92C11×Q16—22no—
93C11×Q16—22no—
94C11×Q16—41no—
95C11×Q16—41no—
96C11×Q16C22⋊C412yes—
97C11×SD16—22no—
98C11×SD16—22no—
99C11×D8—21no—
100C11×D8C22⋊C412yes—
101C2×C8×C11C22×C411yescharacteristic
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11C2×D411yescharacteristic
104C2×C8×C11C2×D411yescharacteristic
105C2×C8×C11#4111yescharacteristic
106C2×C8×C11#4111yescharacteristic
107C22⋊Dic11—21no—
108C22⋊Dic11—42no—
109C4⋊Dic11—22no—
110C4⋊Dic11—42no—
111C4⋊Dic11—41no—
112C4⋊Dic11D811yescharacteristic
113C4⋊Dic11D811yescharacteristic
114C4×Dic11—21no—
115C4×Dic11—42no—
116#4318—21no—
117#4318—21no—
118#4318—41no—
119#4318—41no—
120C2×C11⋊C8—21no—
121C2×C11⋊C8—41no—
122C11×C16—22no—
123C11⋊C16—41no—
124C2×#510D1111yescharacteristic
125#2951—111no—
126C2×#359—111no—
127C2×#358—111no—
128#1979—111no—
129#1387—111no—
130#1379—111no—
131C23×C11—41no—
132C23×C11AGL(1,ℤ/8)11yescharacteristic
133Q8×C11—22no—
134Q8×C11—41no—
135Q8×C11—42no—
136Q8×C11—42no—
137Q8×C11—81no—
138Q8×C11—81no—
139D4×C11—22no—
140D4×C11—42no—
141D4×C11—42no—
142D4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—81no—
148C2×C4×C11—81no—
149C2×C4×C11C4×D411yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11C2×D811yescharacteristic
153C2×C4×C11#13511yescharacteristic
154C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—42no—
158C2×Dic11—162no—
159C2×Dic11—161no—
160C8×C11C2×C22⋊C411yescharacteristic
161C8×C11C4×D411yescharacteristic
162C8×C11#12111yescharacteristic
163C8×C11#12311yescharacteristic
164C11⋊C8—41no—
165C11⋊C8—81no—
166C2×#135C2×D1111yescharacteristic
167C22×Q16C2×D1111yescharacteristic
168#520—221no—
169#510—22no—
170#510Dic1114yescomplemented
171C2×Q32—21no—
172C2×SD32—21no—
173C2×M32C2×D1111yescharacteristic
174C22×C16—111no—
175#440—222no—
176C4×Q16—221no—
177C4×D8—221no—
178C2×#108—111no—
179C2×#107—111no—
180#419—221no—
181#417—221no—
182C2×#101—221no—
183#405—111no—
184#359—222no—
185#358—222no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—42no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11#44211yescharacteristic
192C22×C11#44711yescharacteristic
193C22×C11#46311yescharacteristic
194C4×C11—42no—
195C4×C11—82no—
196C4×C11#38611yescharacteristic
197C4×C11C4×D811yescharacteristic
198C4×C11#44911yescharacteristic
199C4×C11#45911yescharacteristic
200Dic11—41no—
201Dic11—41no—
202Dic11—82no—
203C2×#41—21no—
204C22×Q8—21no—
205#135—21no—
206#135—21no—
207#135C2×Dic1112yes—
208#135C22⋊D1112yes—
209C2×Q16—21no—
210C2×Q16—21no—
211C2×Q16—21no—
212C2×Q16—21no—
213C2×Q16—21no—
214C2×Q16C2×Dic1112yescomplemented
215C2×Q16C22⋊D1111yescharacteristic
216C2×SD16—21no—
217C2×D8C22⋊D1111yescharacteristic
218C2×M16—111no—
219C2×M16—221no—
220C22×C8C22×D1111yescharacteristic
221C4×Q8—222no—
222C4×D4—222no—
223C4×D4—442no—
224#117—111no—
225#117—441no—
226C2×C4⋊C4—221no—
227C2×C4⋊C4—441no—
228Q32—24no—
229SD32—24no—
230M32—21no—
231M32C2×Dic1112yescomplemented
232C2×C16—21no—
233C2×C16—221no—
234C2×C16—221no—
235C2×C16—221no—
236#108—221no—
237#108—221no—
238#107—112no—
239#107—221no—
240#103—222no—
241#103—441no—
242#103—441no—
243#102—222no—
244#101—442no—
245#97—221no—
246C4×C8—221no—
247C2×C11—21no—
248C2×C11—21no—
249C2×C11—82no—
250C2×C11#187911yescharacteristic
251C2×C11#219411yescharacteristic
252C2×C11#219511yescharacteristic
253#41—22no—
254#41—22no—
255#41—41no—
256#41—41no—
257C2×Q8—22no—
258C2×Q8—21no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×Q8—41no—
264C2×D4—21no—
265C2×D4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—442no—
269C22×C4—441no—
270C22×C4D4×D1111yescharacteristic
271Q16—22no—
272Q16—21no—
273Q16—22no—
274Q16—41no—
275Q16—41no—
276Q16C22⋊Dic1112yes—
277SD16—22no—
278SD16—22no—
279D8—21no—
280D8C22⋊Dic1112yes—
281M16—221no—
282M16—221no—
283M16—441no—
284M16—441no—
285C2×C8—221no—
286C2×C8—441no—
287C2×C8D4×D1111yescharacteristic
288C2×C8#434111yescharacteristic
289C2×C8#434111yescharacteristic
290C2×C8C22×Dic1111yescharacteristic
291C2×C8C2×C22⋊D1111yescharacteristic
292C2×C8C2×C22⋊D1111yescharacteristic
293C4⋊C4—111no—
294C4⋊C4—111no—
295C4⋊C4—222no—
296C4⋊C4—442no—
297C4⋊C4—441no—
298C22⋊C4—221no—
299C22⋊C4—442no—
300C42—221no—
301C42—442no—
302C16—22no—
303C16—441no—
304C11#1302311yescharacteristic, complemented, Sylow
305C23—41no—
306C23#6696411yescharacteristic
307Q8—22no—
308Q8—41no—
309Q8—42no—
310Q8—42no—
311Q8—81no—
312Q8—81no—
313D4—22no—
314D4—42no—
315D4—42no—
316D4—41no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—442no—
326C2×C4—1762no—
327C2×C4—1761no—
328C2×C4D8×D1111yescharacteristic
329C2×C4#6696411yescharacteristic
330C2×C4#6696511yescharacteristic
331C2×C4D4×Dic1111yescharacteristic
332C2×C4#6699011yescharacteristic
333C2×C4#6699211yescharacteristic
334C8—441no—
335C8—881no—
336C8D4×Dic1111yescharacteristic
337C8#6698811yescharacteristic
338C8#6699211yescharacteristic
339C8C2×C22⋊Dic1111yescharacteristic
340C22—21no—
341C22—21no—
342C22—42no—
343C22—81no—
344C22—81no—
345C22#1062276511yescharacteristic
346C22#1062276611yescharacteristic
347C22#1062276911yescharacteristic
348C4—42no—
349C4—82no—
350C4—441no—
351C4—441no—
352C4—882no—
353C4D8×Dic1111yescharacteristic
354C4#1062276311yescharacteristic
355C4#1062277111yescharacteristic
356C4#1062283311yescharacteristic
357C2—21no—
358C2—21no—
359C2—82no—
360C2#1306896611yescharacteristic
361C2#1307058411yescharacteristic
362C2#1307059111yescharacteristic
subgroupG/H
centerC22#10622769
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#510C2
socleC22×C11#447
prime radicalC2×C11×#135C22
cosocleC22×C8×C11C23
hypercenterC2×#510D11
hypocenterC11#13023
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#510

Complements

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

NH ≅ G/Ntype
3. C2×#10622202C2semidirect
4. #13069532C2semidirect
5. #13066725C2semidirect
6. #13066706C2semidirect
12. C11×#510C4semidirect
39. C2×C11×Q16C2×C4semidirect
56. C11×M32C2×C4semidirect
170. #510Dic11semidirect
214. C2×Q16C2×Dic11semidirect
231. M32C2×Dic11semidirect
304. C11#13023semidirect

Maximal subgroups

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

subgroupindex
#130774922
C2×#106222052
C2×#106222022
#130695322
#130667252
#130667062
C2×C11×#5102
#1302311