Finite Group Databasebeta

← #14655266

Subgroups — #14655266

Order 2816.

498 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 89 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#13079994C211yesmaximal, characteristic
2#13079737C211yesmaximal, characteristic, complemented
3#13069606C211yesmaximal, characteristic, complemented
4#13067207C211yesmaximal, characteristic, complemented
5#13067033C211yesmaximal, characteristic, complemented
6#13066506C211yesmaximal, characteristic, complemented
7C11×#3141C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10#10623008C2211yescharacteristic
11C11×#489—22no—
12C11×#487—21no—
13C11×#486—21no—
14C11×#417—22no—
15C4×C11×M16C2211yescharacteristic
16#10622701—21no—
17#10622700—22no—
18#10622697—21no—
19#10622691—21no—
20#10622685—21no—
21#10622652—22no—
22#10622628—21no—
23#10622621—21no—
24#10622580—22no—
25#10622538C2211yescharacteristic
26#10622537C2211yescharacteristic
27C4×#4318C2211yescharacteristic
28D4⋊(C11⋊C8)—22no—
29#10622168—22no—
30#10622102—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C2×#4339—21no—
34C2×C11×M16—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8D411yescharacteristic
40C11×#127D411yescharacteristic
41C11×#124—21no—
42C11×#121—21no—
43C11×#121—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4D412yes—
48C2×C42×C11C2311yescharacteristic
49C2×#4323—22no—
50#66983—21no—
51#66983—21no—
52C2×#4318—21no—
53C2×#4318D412yes—
54#66928—21no—
55#66927D411yescharacteristic
56C4×D44—21no—
57C4×D44—21no—
58#66922D411yescharacteristic
59C11×#103—24no—
60C11×#102—24no—
61C11×#97D412yes—
62C4×C8×C11—21no—
63#66896—22no—
64C22⋊(C11⋊C8)—21no—
65#66873—24no—
66#66873—22no—
67#66872—22no—
68#66871—24no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)D412yes—
72#66867—21no—
73C4×C11⋊C8—21no—
74C4×C11⋊C8—21no—
75#10110—111nomaximal, Sylow
76C11×#41—44no—
77C2×Q8×C11—21no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11—82no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—41no—
85C22×C4×C11—22no—
86C22×C4×C11—41no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C2×C22⋊D11—41no—
91#4339—82no—
92C2×D44—21no—
93C2×D44—21no—
94C2×D44—21no—
95C2×C4×D11—41no—
96C2×Dic22—21no—
97C11×M16—42no—
98C2×C8×C11—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—22no—
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#4323—82no—
112(C2×D11)⋊C4—41no—
113(C2×D11)⋊C4—41no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116#4318—22no—
117#4318—42no—
118#4318—41no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—41no—
122#3253—111no—
123#3226—111no—
124#3141D1111yescharacteristic, complemented
125#1997—111no—
126#1525—111no—
127#1484—111no—
128#1299—111no—
129C23×C11—41no—
130C23×C11#12111yescharacteristic
131C22×D11—41no—
132Q8×C11—42no—
133Q8×C11—82no—
134Q8×C11—82no—
135D4×C11—42no—
136D4×C11—41no—
137D4×C11—41no—
138D4×C11—42no—
139D4×C11—82no—
140C2×C4×C11—22no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—22no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—82no—
147C2×C4×C11—82no—
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12711yescharacteristic
154C22⋊D11—82no—
155C2×Dic11—41no—
156D44—42no—
157D44—41no—
158D44—41no—
159D44—81no—
160C4×D11—82no—
161Dic22—81no—
162C8×C11—42no—
163C11⋊C8—42no—
164C11⋊C8—42no—
165C11⋊C8—42no—
166#532—111no—
167#532C2×D1111yescharacteristic
168C2×C4⋊Q8C2×D1111yescharacteristic
169#500—221no—
170#489—22no—
171#487—21no—
172#486—21no—
173#486—221no—
174#480—222no—
175#476—221no—
176#476—221no—
177#474—222no—
178#469—222no—
179#459—221no—
180#459—221no—
181#431—111no—
182#423—111no—
183#417—22no—
184C4×M16—111no—
185C4×M16C2×D1111yescharacteristic
186#343—222no—
187#329—222no—
188D4⋊C8—222no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11#39211yescharacteristic
196C2×D11—81no—
197C2×D11—81no—
198C2×D11—81no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—81no—
203C4×C11—82no—
204C4×C11#45412yes—
205C4×C11#45511yescharacteristic
206C4×C11#45611yescharacteristic
207C4×C11#47212yes—
208Dic11—81no—
209C2×#41—21no—
210C2×#41—221no—
211C22×Q8—21no—
212C2×D8—222no—
213C2×M16—21no—
214C2×M16—112no—
215C2×M16—221no—
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—111no—
221C4⋊Q8C22⋊D1111yescharacteristic
222#127—111no—
223#127C22⋊D1111yescharacteristic
224#124—21no—
225#124—221no—
226#121—21no—
227#121—21no—
228#121—221no—
229#121—221no—
230C4×D4—21no—
231C4×D4—21no—
232C4×D4—221no—
233C4×D4—221no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4C22⋊D1112yes—
236C2×C42C22×D1111yescharacteristic
237#107—224no—
238#106—222no—
239C4⋊C8—112no—
240C4⋊C8—221no—
241C4⋊C8—221no—
242#103—24no—
243#102—24no—
244#102—222no—
245#102—224no—
246#102—222no—
247C22⋊C8—221no—
248#97—221no—
249#97C22⋊D1112yes—
250C4×C8—21no—
251C4×C8—221no—
252C4×C8—221no—
253C2×C11—41no—
254C2×C11—161no—
255C2×C11#200311yescharacteristic
256C2×C11#200711yescharacteristic
257C2×C11#201811yescharacteristic
258D11—161no—
259#41—44no—
260#41—882no—
261C2×Q8—21no—
262C2×Q8—41no—
263C2×Q8—41no—
264C2×Q8—82no—
265C2×Q8—221no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—41no—
270C2×D4—221no—
271C2×D4—221no—
272C2×D4—221no—
273C2×D4—441no—
274C22×C4—22no—
275C22×C4—41no—
276C22×C4—441no—
277C22×C4D4×D1111yescharacteristic
278C22×C4#434111yescharacteristic
279C22×C4C2×C22⋊D1111yescharacteristic
280D8—882no—
281M16—42no—
282M16—222no—
283M16—441no—
284M16—442no—
285C2×C8—22no—
286C2×C8—222no—
287C2×C8—222no—
288C2×C8—441no—
289C4⋊C4—21no—
290C4⋊C4—22no—
291C4⋊C4—21no—
292C4⋊C4—22no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—441no—
300C22⋊C4—441no—
301C42D4×D1111yescharacteristic
302C42D4×D1111yescharacteristic
303C42C2×C22⋊D1111yescharacteristic
304C42C2×C22⋊D1111yescharacteristic
305C11#1011011yescharacteristic, complemented, Sylow
306C23—41no—
307C23—441no—
308C23#6699211yescharacteristic
309Q8—42no—
310Q8—82no—
311Q8—82no—
312Q8—881no—
313D4—42no—
314D4—42no—
315D4—41no—
316D4—41no—
317D4—82no—
318D4—441no—
319D4—441no—
320D4—442no—
321D4—881no—
322D4—882no—
323C2×C4—22no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4—441no—
332C2×C4—882no—
333C2×C4#6699011yescharacteristic
334C2×C4#6699011yescharacteristic
335C2×C4#6699111yescharacteristic
336C2×C4#6699211yescharacteristic
337C2×C4#6699311yescharacteristic
338C2×C4#6700611yescharacteristic
339C8—42no—
340C8—442no—
341C8—442no—
342C8—442no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22—881no—
350C22—881no—
351C22—881no—
352C22#1062283611yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—81no—
357C4—82no—
358C4—881no—
359C4#1062267512yes—
360C4#1062281212yes—
361C4#1062281511yescharacteristic
362C4#1062281811yescharacteristic
363C2—41no—
364C2—161no—
365C2—1761no—
366C2#1306963811yescharacteristic
367C2#1306966111yescharacteristic
368C2#1306972211yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3141C2
socleC22×C11#392
prime radical#13079994C2
hypercenter#3141D11
hypocenterC11#10110
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3141

Complements

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

NH ≅ G/Ntype
2. #13079737C2semidirect
3. #13069606C2semidirect
4. #13067207C2semidirect
5. #13067033C2semidirect
6. #13066506C2semidirect
7. C11×#3141C2semidirect
124. #3141D11semidirect
305. C11#10110semidirect

Maximal subgroups

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

subgroupindex
#130799942
#130797372
#130696062
#130672072
#130670332
#130665062
C11×#31412
#1011011