Finite Group Databasebeta

← #14648966

Subgroups — #14648966

Order 2816.

544 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078612C211yesmaximal, characteristic
2#13069414C211yesmaximal, characteristic, complemented
3#13067265C211yesmaximal, characteristic, complemented
4#13067040C211yesmaximal, characteristic, complemented
5#13066511C211yesmaximal, characteristic, complemented
6#13066461C211yesmaximal, characteristic, complemented
7C11×#2932C211yesmaximal, characteristic, complemented
8C2×C11×#131—21no—
9C11×#532C2211yescharacteristic
10C2×C4×D44C2211yescharacteristic
11C11×#435—22no—
12C11×#435—22no—
13C11×#423C2211yescharacteristic
14C11×#408—21no—
15C2×C11×#97C2211yescharacteristic
16C2×(C2×D11)⋊C8—21no—
17C2×(C2×D11)⋊C8—21no—
18#10622700—21no—
19#10622685—21no—
20#10622649C412yes—
21#10622646C412yes—
22C4×#4323—22no—
23#10622538C2211yescharacteristic
24#10622538C2211yescharacteristic
25C2×C4⋊(C11⋊C8)C2211yescharacteristic
26#10622185—21no—
27#10622182—21no—
28#10622121—22no—
29C2×C11×#41—21no—
30C22×D44C2×C411yescharacteristic
31C22×C4×D11—21no—
32C11×#131—42no—
33C11×#131—42no—
34C2×C11×M16—22no—
35C2×C11×M16—21no—
36C22×C8×C11—22no—
37C22×C8×C11D411yescharacteristic
38C22×C8×C11D411yescharacteristic
39C11×C4⋊Q8D411yescharacteristic
40C11×#127D411yescharacteristic
41C11×#124—21no—
42C11×#121—21no—
43C11×#121C2×C412yes—
44C4×D4×C11—21no—
45C4×D4×C11D412yes—
46C2×C42×C11C2311yescharacteristic
47C2×#4323—22no—
48C2×(C2×D11)⋊C4—21no—
49C2×C4⋊Dic11C2×C411yescharacteristic
50C22×C11⋊C8—21no—
51C4×D44—21no—
52C4×D44—21no—
53C4×D44—21no—
54C4×D44—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8D412yes—
57C11×C22⋊C8—24no—
58C11×#97—21no—
59C11×#97—21no—
60#66896—22no—
61C22⋊(C11⋊C8)—21no—
62C22⋊(C11⋊C8)C2×C412yes—
63(C2×D11)⋊C8—42no—
64(C2×D11)⋊C8—42no—
65#66873—22no—
66#66871—22no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71C4×C11⋊C8—21no—
72C4×C11⋊C8—21no—
73#9049—111nomaximal, Sylow
74C23×D11—21no—
75C11×#41—41no—
76C11×#41—41no—
77C11×#41—41no—
78C11×#41—41no—
79C2×Q8×C11—21no—
80C2×D4×C11—22no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11C22⋊C412yes—
84C22×C4×C11—22no—
85C22×C4×C11C22×C411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C22×Dic11—21no—
89C2×D44—21no—
90C2×D44—21no—
91C2×D44—42no—
92C2×C4×D11—41no—
93C2×C4×D11—41no—
94C2×C4×D11—41no—
95C2×C4×D11—41no—
96C2×C4×D11—41no—
97C2×C4×D11—41no—
98C11×M16—44no—
99C11×M16—41no—
100C11×M16—41no—
101C2×C8×C11—21no—
102C2×C8×C11—21no—
103C2×C8×C11—22no—
104C2×C8×C11—21no—
105C2×C8×C11—21no—
106C2×C8×C11—21no—
107C2×C8×C11—44no—
108C2×C8×C11D812yescomplemented
109C11×C4⋊C4—21no—
110C11×C4⋊C4C22⋊C412yes—
111C11×C22⋊C4—22no—
112C11×C22⋊C4—22no—
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11#4111yescharacteristic
117#4323—44no—
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—41no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—41no—
124C2×C11⋊C8—41no—
125C2×C11⋊C8—41no—
126C2×C11⋊C8—41no—
127#3100—111no—
128#2932D1111yescharacteristic, complemented
129#1955—111no—
130#1540—111no—
131#1486—111no—
132#1301—111no—
133#1281—111no—
134C23×C11—22no—
135C23×C11C4×D411yescharacteristic
136C22×D11—22no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—41no—
143Q8×C11—41no—
144Q8×C11—41no—
145D4×C11—42no—
146D4×C11—42no—
147D4×C11—42no—
148D4×C11—41no—
149D4×C11—41no—
150D4×C11—81no—
151C2×C4×C11—22no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11C2×C22⋊C411yescharacteristic
157C2×C4×C11C4×D411yescharacteristic
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12311yescharacteristic
162C2×C4×C11C2×D811yescharacteristic
163C2×C4×C11#13511yescharacteristic
164C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169D44—22no—
170D44—22no—
171D44—41no—
172D44—41no—
173C4×D11—81no—
174C4×D11—81no—
175C4×D11—81no—
176C4×D11—81no—
177C8×C11—22no—
178C8×C11—42no—
179C8×C11—41no—
180C11⋊C8—42no—
181C11⋊C8—81no—
182C11⋊C8—81no—
183C2×#131—21no—
184#532C2×D1111yescharacteristic
185C2×C4×D4—111no—
186#480—112no—
187#474—221no—
188#459—221no—
189#447—112no—
190C4×D8—222no—
191#435—22no—
192#435—22no—
193#431—111no—
194#431—111no—
195#423C2×D1111yescharacteristic
196C2×C4⋊C8—111no—
197#408—21no—
198C2×C22⋊C8—221no—
199C2×C22⋊C8—221no—
200C2×#97C2×D1111yescharacteristic
201#332—221no—
202#331—221no—
203D4⋊C8—222no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—42no—
207C22×C11—42no—
208C22×C11—42no—
209C22×C11#38611yescharacteristic
210C22×C11C4×D811yescharacteristic
211C22×C11#44211yescharacteristic
212C2×D11—42no—
213C2×D11—42no—
214C2×D11—42no—
215C2×D11—81no—
216C2×D11—81no—
217C2×D11—81no—
218C2×D11—81no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—42no—
224C4×C11#44711yescharacteristic
225C4×C11#44911yescharacteristic
226C4×C11#45911yescharacteristic
227C4×C11#46311yescharacteristic
228Dic11—81no—
229C2×#41—21no—
230C22×D4—111no—
231C23×C4—221no—
232C2×D8—222no—
233#131—42no—
234#131—42no—
235C2×M16—22no—
236C2×M16—21no—
237C22×C8—22no—
238C22×C8—221no—
239C22×C8C22⋊D1111yescharacteristic
240C22×C8C22⋊D1111yescharacteristic
241C4⋊Q8D4411yescharacteristic
242#127D4411yescharacteristic
243#124—21no—
244#121—21no—
245#121C4×D1112yes—
246C4×D4—21no—
247C4×D4—221no—
248C4×D4—221no—
249C4×D4—221no—
250C4×D4—221no—
251C4×D4C22⋊D1112yes—
252C2×C4⋊C4—111no—
253C2×C22⋊C4—221no—
254C2×C42C22×D1111yescharacteristic
255#107—222no—
256C4⋊C8—21no—
257C4⋊C8—221no—
258C4⋊C8—221no—
259C4⋊C8—221no—
260C4⋊C8—221no—
261C4⋊C8C22⋊D1112yes—
262#102—222no—
263#102—222no—
264C22⋊C8—24no—
265C22⋊C8—112no—
266C22⋊C8—221no—
267C22⋊C8—442no—
268C22⋊C8—442no—
269#97—21no—
270#97—21no—
271C4×C8—221no—
272C4×C8—221no—
273C2×C11—21no—
274C2×C11—21no—
275C2×C11—82no—
276C2×C11#187911yescharacteristic
277C2×C11#188111yescharacteristic
278C2×C11#189111yescharacteristic
279D11—82no—
280C24—221no—
281#41—41no—
282#41—41no—
283#41—41no—
284#41—41no—
285C2×Q8—21no—
286C2×D4—22no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—221no—
290C2×D4—221no—
291C2×D4—442no—
292C2×D4(C2×D11)⋊C412yes—
293C22×C4—22no—
294C22×C4—221no—
295C22×C4—441no—
296C22×C4—441no—
297C22×C4—441no—
298C22×C4—441no—
299C22×C4—441no—
300C22×C4—441no—
301C22×C4C2×C4×D1111yescharacteristic
302C22×C4#433911yescharacteristic
303C22×C4C2×C22⋊D1111yescharacteristic
304D8—444no—
305M16—44no—
306M16—41no—
307M16—41no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—22no—
314C2×C8—44no—
315C2×C8—222no—
316C2×C8—441no—
317C2×C8—441no—
318C2×C8—441no—
319C2×C8—441no—
320C2×C8#432312yescomplemented
321C4⋊C4—21no—
322C4⋊C4—221no—
323C4⋊C4—221no—
324C4⋊C4(C2×D11)⋊C412yes—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C22⋊C4—441no—
328C22⋊C4—441no—
329C42C2×D4411yescharacteristic
330C42#433911yescharacteristic
331C42C2×C22⋊D1111yescharacteristic
332C42C2×C22⋊D1111yescharacteristic
333C11#904911yescharacteristic, complemented, Sylow
334C23—22no—
335C23—222no—
336C23—441no—
337C23—441no—
338C23—441no—
339C23—441no—
340C23—441no—
341C23—441no—
342C23C4×C22⋊D1111yescharacteristic
343Q8—41no—
344Q8—41no—
345D4—42no—
346D4—42no—
347D4—42no—
348D4—41no—
349D4—41no—
350D4—81no—
351D4—222no—
352D4—222no—
353D4—441no—
354D4—441no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—881no—
364C2×C4—881no—
365C2×C4—881no—
366C2×C4—881no—
367C2×C4C2×(C2×D11)⋊C411yescharacteristic
368C2×C4C4×C22⋊D1111yescharacteristic
369C2×C4#6698211yescharacteristic
370C2×C4#6698311yescharacteristic
371C2×C4#6698311yescharacteristic
372C2×C4C2×#432311yescharacteristic
373C2×C4#6698511yescharacteristic
374C2×C4#6700211yescharacteristic
375C2×C4#6700311yescharacteristic
376C2×C4#6700611yescharacteristic
377C8—22no—
378C8—42no—
379C8—41no—
380C8—442no—
381C8—881no—
382C8—881no—
383C22—21no—
384C22—21no—
385C22—42no—
386C22—42no—
387C22—42no—
388C22—442no—
389C22—442no—
390C22—442no—
391C22—881no—
392C22—881no—
393C22—881no—
394C22—881no—
395C22C4×#432311yescharacteristic
396C22#1062262711yescharacteristic
397C22#1062282611yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—42no—
403C4—881no—
404C4#1062262811yescharacteristic
405C4#1062262911yescharacteristic
406C4#1062283011yescharacteristic
407C4#1062285111yescharacteristic
408C2—21no—
409C2—21no—
410C2—82no—
411C2—882no—
412C2#1306896411yescharacteristic
413C2#1306897811yescharacteristic
414C2#1306903411yescharacteristic
subgroupG/H
centerC2×C4#67006
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2932C2
socleC22×C11#386
prime radical#13078612C2
cosocleC2×C42×C11C23
hypercenter#2932D11
hypocenterC11#9049
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2932

Complements

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

NH ≅ G/Ntype
2. #13069414C2semidirect
3. #13067265C2semidirect
4. #13067040C2semidirect
5. #13066511C2semidirect
6. #13066461C2semidirect
7. C11×#2932C2semidirect
108. C2×C8×C11D8semidirect
128. #2932D11semidirect
320. C2×C8#4323semidirect
333. C11#9049semidirect

Maximal subgroups

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

subgroupindex
#130786122
#130694142
#130672652
#130670402
#130665112
#130664612
C11×#29322
#904911