Finite Group Databasebeta

← #14655535

Subgroups — #14655535

Order 2816.

614 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 109 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#13079069C211yesmaximal, characteristic
2C2×#10622701C211yesmaximal, characteristic, complemented
3#13069606C211yesmaximal, characteristic, complemented
4#13067283C211yesmaximal, characteristic, complemented
5#13067067C211yesmaximal, characteristic, complemented
6#13066452C211yesmaximal, characteristic, complemented
7C11×#3227C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#67002—22no—
11C2×#66927C2211yescharacteristic
12C11×#498—21no—
13C11×#486—21no—
14C11×#481—22no—
15C11×#476—22no—
16C11×#431C2211yescharacteristic
17#10622701—22no—
18#10622701—22no—
19#10622698—21no—
20#10622686—21no—
21#10622671—22no—
22C2×#66873—22no—
23#10622537C2211yescharacteristic
24C4×#4318C2211yescharacteristic
25C2×C4×C11⋊C8C2211yescharacteristic
26D4⋊(C11⋊C8)—22no—
27#10622168—22no—
28#10622123—22no—
29C2×C11×#41—21no—
30C22×Q8×C11—21no—
31C22×D44—21no—
32C22×D44—21no—
33C22×D44—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8D411yescharacteristic
39C11×#127D411yescharacteristic
40C11×#124—21no—
41C11×#121—21no—
42C11×#121—21no—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D412yes—
47C2×C42×C11C2311yescharacteristic
48#67002—44no—
49#67002—44no—
50C2×#4325—24no—
51C2×#4323—24no—
52C2×#4318—21no—
53C2×#4318D412yes—
54C22×C11⋊C8—21no—
55#66927—21no—
56#66927—21no—
57#66927—21no—
58#66927D412yes—
59C11×#106—24no—
60C11×C4⋊C8D412yes—
61C11×#102—24no—
62C11×C22⋊C8—21no—
63C4×C8×C11—21no—
64#66873—28no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67#66867—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8—21no—
70C4×C11⋊C8D412yes—
71#10148—111nomaximal, Sylow
72C23×D11—41no—
73C11×#41—42no—
74C11×#41—42no—
75C2×Q8×C11—21no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—82no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—41no—
83C22×C4×C11—22no—
84C22×C4×C11—41no—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C2×D44—22no—
89C2×D44—22no—
90C2×D44—22no—
91C2×D44—44no—
92C2×D44—41no—
93C2×D44—41no—
94C2×D44—41no—
95C2×D44—42no—
96C2×D44—42no—
97C2×D44—82no—
98C2×C8×C11—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111#4325—48no—
112#4323—48no—
113#4318—22no—
114#4318—42no—
115#4318SD1614yes—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—42no—
119C2×C11⋊C8—41no—
120#3227D1111yescharacteristic, complemented
121#3151—111no—
122C2×#486—111no—
123#1997—111no—
124#1545—111no—
125#1492—111no—
126#1278—111no—
127C23×C11—41no—
128C23×C11#12111yescharacteristic
129C22×D11—42no—
130C22×D11—82no—
131C22×D11—82no—
132C22×D11—82no—
133Q8×C11—42no—
134Q8×C11—82no—
135Q8×C11—82no—
136D4×C11—42no—
137D4×C11—42no—
138D4×C11—42no—
139D4×C11—82no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11—82no—
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12711yescharacteristic
153C2×C4×C11C2×SD1612yes—
154C2×C4×C11AGL(1,ℤ/8)12yes—
155D44—44no—
156D44—44no—
157D44—82no—
158D44—82no—
159D44—82no—
160D44—81no—
161D44—81no—
162C8×C11—42no—
163C11⋊C8—24no—
164C11⋊C8—42no—
165C11⋊C8—81no—
166C2×AGL(1,ℤ/8)—222no—
167#532C2×D1111yescharacteristic
168C2×C4⋊Q8C2×D1111yescharacteristic
169C2×#127—111no—
170#498—21no—
171#496—222no—
172#493—221no—
173#492—221no—
174#486—21no—
175#486—222no—
176#486—222no—
177#481—22no—
178#476—22no—
179#431C2×D1111yescharacteristic
180#423—111no—
181C2×#102—222no—
182C4×M16—111no—
183C2×C4×C8—111no—
184#343—222no—
185#331—222no—
186D4⋊C8—222no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11#39211yescharacteristic
193C22×C11#46012yes—
194C2×D11—82no—
195C2×D11—82no—
196C2×D11—82no—
197C2×D11—164no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—81no—
201C4×C11—82no—
202C4×C11#45012yes—
203C4×C11#45412yes—
204C4×C11#47212yes—
205C4×C11#49211yescharacteristic
206C4×C11#49611yescharacteristic
207C2×#41—21no—
208C22×Q8—21no—
209C22×D4—221no—
210C22×D4—221no—
211C22×D4—221no—
212AGL(1,ℤ/8)—444no—
213AGL(1,ℤ/8)—444no—
214C2×SD16—224no—
215C2×D8—224no—
216C2×M16—112no—
217C2×M16—221no—
218C22×C8—221no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8C22⋊D1111yescharacteristic
224#127—112no—
225#127—221no—
226#127—221no—
227#127—221no—
228#127C22⋊D1111yescharacteristic
229#124—21no—
230#121—21no—
231#121—21no—
232C4×D4—21no—
233C4×D4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4C22⋊D1112yes—
236C2×C42C22×D1111yescharacteristic
237#106—24no—
238C4⋊C8—221no—
239C4⋊C8—221no—
240C4⋊C8C22⋊D1112yes—
241#102—24no—
242#102—228no—
243C22⋊C8—21no—
244#97—221no—
245C4×C8—21no—
246C4×C8—112no—
247C4×C8—221no—
248C4×C8—221no—
249C2×C11—22no—
250C2×C11—161no—
251C2×C11#200311yescharacteristic
252C2×C11#201411yescharacteristic
253C2×C11#201811yescharacteristic
254D11—162no—
255C24—441no—
256#41—42no—
257#41—42no—
258C2×Q8—21no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×Q8—82no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—41no—
266C2×D4—222no—
267C2×D4—222no—
268C2×D4—222no—
269C2×D4—444no—
270C2×D4—442no—
271C2×D4—442no—
272C2×D4—441no—
273C2×D4—441no—
274C2×D4—441no—
275C2×D4—882no—
276C22×C4—22no—
277C22×C4—41no—
278C22×C4D4×D1111yescharacteristic
279C22×C4#434111yescharacteristic
280C22×C4C2×C22⋊D1111yescharacteristic
281SD16—448no—
282D8—448no—
283M16—114no—
284M16—222no—
285M16—442no—
286C2×C8—22no—
287C2×C8—222no—
288C2×C8—222no—
289C2×C8—442no—
290C2×C8—441no—
291C4⋊C4—22no—
292C4⋊C4—21no—
293C4⋊C4—22no—
294C4⋊C4—21no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C42D4×D1111yescharacteristic
300C42D4×D1111yescharacteristic
301C42C2×C22⋊D1111yescharacteristic
302C42C2×C22⋊D1111yescharacteristic
303C11#1014811yescharacteristic, complemented, Sylow
304C23—41no—
305C23—442no—
306C23—882no—
307C23—882no—
308C23—882no—
309C23#6699211yescharacteristic
310Q8—42no—
311Q8—82no—
312Q8—82no—
313D4—42no—
314D4—42no—
315D4—42no—
316D4—82no—
317D4—444no—
318D4—444no—
319D4—882no—
320D4—881no—
321D4—881no—
322D4—882no—
323D4—882no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—82no—
331C2×C4SD16×D1112yes—
332C2×C4#6696712yes—
333C2×C4#6699011yescharacteristic
334C2×C4#6699011yescharacteristic
335C2×C4#6699111yescharacteristic
336C2×C4#6699211yescharacteristic
337C2×C4#6699311yescharacteristic
338C2×C4#6700611yescharacteristic
339C8—42no—
340C8—224no—
341C8—442no—
342C8—881no—
343C22—21no—
344C22—21no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22—882no—
349C22—882no—
350C22—882no—
351C22—1764no—
352C22#1062277612yes—
353C22#1062283611yescharacteristic
354C4—21no—
355C4—21no—
356C4—81no—
357C4—82no—
358C4#1062278212yes—
359C4#1062278811yescharacteristic
360C4#1062278911yescharacteristic
361C4#1062281212yes—
362C4#1062285812yes—
363C2—22no—
364C2—161no—
365C2—1762no—
366C2#1306963611yescharacteristic
367C2#1306970211yescharacteristic
368C2#1306972211yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3227C2
socleC22×C11#392
prime radical#13079069C2
hypercenter#3227D11
hypocenterC11#10148
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3227

Complements

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

NH ≅ G/Ntype
2. C2×#10622701C2semidirect
3. #13069606C2semidirect
4. #13067283C2semidirect
5. #13067067C2semidirect
6. #13066452C2semidirect
7. C11×#3227C2semidirect
120. #3227D11semidirect
303. C11#10148semidirect

Maximal subgroups

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

subgroupindex
#130790692
C2×#106227012
#130696062
#130672832
#130670672
#130664522
C11×#32272
#1014811