Finite Group Databasebeta

← #14648949

Subgroups — #14648949

Order 2816.

492 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078647C211yesmaximal, characteristic
2#13077333C211yesmaximal, characteristic
3#13069557C211yesmaximal, characteristic, complemented
4#13067263C211yesmaximal, characteristic
5#13066511C211yesmaximal, characteristic, complemented
6#13066460C211yesmaximal, characteristic, complemented
7C11×#1487C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#66960—21no—
10#10623008C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13#10622840C412yes—
14#10622742—21no—
15#10622640—21no—
16C4×#4325—22no—
17#10622633—21no—
18#10622581C412yes—
19#10622538C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C2×#66867C2211yescharacteristic
22#10622449—22no—
23#10622449—22no—
24C11×Q8⋊C8—22no—
25#10622162—21no—
26#10622162—21no—
27#10622124—21no—
28#10622123—21no—
29C22×Q8×C11C2×C411yescharacteristic
30C2×#4339—21no—
31C2×C11×M16—21no—
32C4×Q8×C11—21no—
33C4×Q8×C11—21no—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C42×C11—21no—
39C2×C42×C11C2311yescharacteristic
40C2×#4325—22no—
41#66983—21no—
42#66983C2×C412yes—
43C22×C11⋊C8—21no—
44C22×C11⋊C8D411yescharacteristic
45C22×C11⋊C8D411yescharacteristic
46#66960—42no—
47#66960—42no—
48C2×#4313—22no—
49C2×C8×D11—22no—
50#66928—21no—
51#66927D411yescharacteristic
52C4×D44—21no—
53C4×D44D412yes—
54#66922D411yescharacteristic
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8D412yes—
58C11×C22⋊C8—21no—
59C4×C8×C11—21no—
60#66899—22no—
61C22⋊(C11⋊C8)C2×C412yes—
62(C2×D11)⋊C8—24no—
63#66873—22no—
64#66872—22no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68#66867—21no—
69#66867—21no—
70C4×C11⋊C8—21no—
71#9047—111nomaximal, Sylow
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11—42no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C2×C22⋊D11—22no—
81#4339—41no—
82#4339—41no—
83#4339—41no—
84#4339—41no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44C22⋊C412yes—
88C2×C4×D11—22no—
89C2×Dic22—21no—
90C11×M16—41no—
91C11×M16—41no—
92C2×C8×C11—22no—
93C2×C8×C11—41no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C42×C11—41no—
99C42×C11—41no—
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11#4111yescharacteristic
104#4325—44no—
105(C2×D11)⋊C4—22no—
106(C2×D11)⋊C4—22no—
107C4⋊Dic11—21no—
108C4⋊Dic11C22⋊C412yes—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—21no—
111C2×C11⋊C8—21no—
112C2×C11⋊C8—21no—
113C2×C11⋊C8—21no—
114C2×C11⋊C8—21no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—41no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8SD1612yescomplemented
119#4313—44no—
120C8×D11—44no—
121#3103—111no—
122#2932—111no—
123#1985—111no—
124#1540—111no—
125#1487D1111yescharacteristic, complemented
126#1301—111no—
127#1281—111no—
128C23×C11C4×D411yescharacteristic
129C22×D11—22no—
130Q8×C11—22no—
131Q8×C11—22no—
132Q8×C11—41no—
133Q8×C11—41no—
134C2×C4×C11—22no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—42no—
140C2×C4×C11—41no—
141C2×C4×C11C2×C22⋊C411yescharacteristic
142C2×C4×C11C4×D411yescharacteristic
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12311yescharacteristic
147C2×C4×C11C2×SD1611yescharacteristic
148C2×C4×C11#13511yescharacteristic
149C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C11#13711yescharacteristic
151C22⋊D11—42no—
152C22⋊D11—42no—
153C2×Dic11—22no—
154D44—42no—
155D44—41no—
156D44—41no—
157D44—81no—
158C4×D11—42no—
159C4×D11—42no—
160Dic22—41no—
161Dic22—41no—
162C8×C11—42no—
163C8×C11—81no—
164C11⋊C8—22no—
165C11⋊C8—42no—
166C11⋊C8—41no—
167C11⋊C8—81no—
168C2×#131—221no—
169#532—111no—
170C2×C4×Q8C2×D1111yescharacteristic
171#481—112no—
172#475—221no—
173#460—221no—
174#448—112no—
175C4×SD16—222no—
176#435—222no—
177#435—222no—
178#431—111no—
179#431C2×D1111yescharacteristic
180#423C2×D1111yescharacteristic
181C2×C4⋊C8—111no—
182#408—221no—
183C2×#97—111no—
184#336—221no—
185#336—221no—
186#332—221no—
187#331—221no—
188Q8⋊C8—22no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11#38611yescharacteristic
192C22×C11C4×SD1611yescharacteristic
193C22×C11#44011yescharacteristic
194C2×D11—42no—
195C2×D11—42no—
196C2×D11—42no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—42no—
202C4×C11—81no—
203C4×C11#45011yescharacteristic
204C4×C11#45211yescharacteristic
205C4×C11#46111yescharacteristic
206C4×C11#46311yescharacteristic
207Dic11—42no—
208C2×#41—221no—
209C22×Q8C4×D1111yescharacteristic
210C2×SD16—222no—
211#131—442no—
212#131—442no—
213C2×M16—21no—
214C2×M16—222no—
215C22×C8—111no—
216C22×C8—111no—
217C22×C8—222no—
218C22×C8—221no—
219C4⋊Q8—111no—
220#127—111no—
221#124—221no—
222#121—112no—
223#121—221no—
224C4×Q8—21no—
225C4×Q8—21no—
226C4×Q8—21no—
227C4×Q8—21no—
228C4×D4—112no—
229C4×D4—221no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4C4×D1111yescharacteristic
232C2×C42—21no—
233C2×C42C22×D1111yescharacteristic
234#106—222no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—221no—
238C4⋊C8—221no—
239C4⋊C8—221no—
240C4⋊C8C22⋊D1112yes—
241#103—222no—
242#102—222no—
243C22⋊C8—21no—
244C22⋊C8—112no—
245C22⋊C8—224no—
246#97—221no—
247#97—221no—
248C4×C8—21no—
249C4×C8—221no—
250C2×C11—21no—
251C2×C11—21no—
252C2×C11#187711yescharacteristic
253C2×C11#188111yescharacteristic
254C2×C11#189111yescharacteristic
255D11—82no—
256#41—441no—
257#41—441no—
258#41—441no—
259#41—441no—
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8—42no—
263C2×Q8—221no—
264C2×D4—112no—
265C2×D4—222no—
266C2×D4—221no—
267C2×D4—221no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—222no—
271C22×C4C2×C4×D1111yescharacteristic
272C22×C4D4×D1111yescharacteristic
273C22×C4#434111yescharacteristic
274SD16—444no—
275M16—41no—
276M16—41no—
277M16—444no—
278C2×C8—22no—
279C2×C8—41no—
280C2×C8—112no—
281C2×C8—221no—
282C2×C8—221no—
283C2×C8—222no—
284C2×C8—221no—
285C2×C8—221no—
286C2×C8—221no—
287C2×C8—444no—
288C2×C8—441no—
289C2×C8—441no—
290C2×C8—441no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—112no—
296C4⋊C4—221no—
297C22⋊C4—222no—
298C22⋊C4—222no—
299C42—41no—
300C42—41no—
301C42#433911yescharacteristic
302C42D4×D1111yescharacteristic
303C42D4×D1111yescharacteristic
304C42C2×C22⋊D1111yescharacteristic
305C11#904711yescharacteristic, complemented, Sylow
306C23—222no—
307C23(C22⋊D11)⋊C411yescharacteristic
308Q8—22no—
309Q8—22no—
310Q8—41no—
311Q8—41no—
312Q8—441no—
313Q8—441no—
314D4—442no—
315D4—442no—
316D4—442no—
317D4—441no—
318D4—441no—
319D4—881no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—222no—
328C2×C4—442no—
329C2×C4—442no—
330C2×C4C22⋊C4×D1111yescharacteristic
331C2×C4#6693611yescharacteristic
332C2×C4#6693711yescharacteristic
333C2×C4SD16×D1111yescharacteristic
334C2×C4#6696711yescharacteristic
335C2×C4#6697111yescharacteristic
336C2×C4#6697211yescharacteristic
337C2×C4C4×C22⋊D1111yescharacteristic
338C2×C4#6699011yescharacteristic
339C2×C4#6699111yescharacteristic
340C8—42no—
341C8—81no—
342C8—222no—
343C8—442no—
344C8—441no—
345C8—881no—
346C22—21no—
347C22—21no—
348C22—442no—
349C22—442no—
350C22—442no—
351C22#1062240111yescharacteristic
352C22#1062243011yescharacteristic
353C22#1062256911yescharacteristic
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—42no—
359C4—81no—
360C4—442no—
361C4#1062243111yescharacteristic
362C4#1062243211yescharacteristic
363C4#1062278211yescharacteristic
364C4#1062280011yescharacteristic
365C2—21no—
366C2—21no—
367C2—882no—
368C2#1306894711yescharacteristic
369C2#1306897511yescharacteristic
370C2#1306903111yescharacteristic
subgroupG/H
centerC2×C4#66990
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1487C2
socleC22×C11#386
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1487D11
hypocenterC11#9047
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
3. #13069557C2semidirect
5. #13066511C2semidirect
6. #13066460C2semidirect
7. C11×#1487C2semidirect
118. C2×C11⋊C8SD16semidirect
125. #1487D11semidirect
305. C11#9047semidirect

Maximal subgroups

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

subgroupindex
#130786472
#130773332
#130695572
#130672632
#130665112
#130664602
C11×#14872
#904711