Finite Group Databasebeta

← #14656182

Subgroups — #14656182

Order 2816.

558 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079744C211yesmaximal, characteristic
2#13078088C211yesmaximal, characteristic
3#13067301C211yesmaximal, characteristic, complemented
4#13067110C211yesmaximal, characteristic
5#13067011C211yesmaximal, characteristic, complemented
6#13066519C211yesmaximal, characteristic, complemented
7C11×#2567C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×#66995—21no—
11#10623008C2211yescharacteristic
12C11×#395—22no—
13C11×#391—21no—
14C11×#389—22no—
15C11×#384—21no—
16C4×C11×C4⋊C4C2211yescharacteristic
17#10622701—21no—
18#10622697—22no—
19#10622692—21no—
20#10622644—21no—
21#10622641—22no—
22#10622640—21no—
23#10622581—22no—
24#10622579—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622185—22no—
29Q8⋊(C11⋊C8)—22no—
30#10622089—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11D411yescharacteristic
33C2×#4339—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C4×Q8×C11—21no—
39C4×Q8×C11—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—24no—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C4⋊C4D412yes—
48C2×C42×C11—21no—
49C2×C42×C11—21no—
50C2×C42×C11C2311yescharacteristic
51C2×#4326—22no—
52#66995—42no—
53#66995—42no—
54C2×#4325—22no—
55#66983—21no—
56#66983—21no—
57C2×#4318—21no—
58#66928—21no—
59#66927D411yescharacteristic
60C4×D44—21no—
61C4×D44—21no—
62#66922D411yescharacteristic
63C11×#95—24no—
64C11×#95D412yes—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—21no—
67#66874—22no—
68#66873—22no—
69#66873—24no—
70#66872—24no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)D412yes—
74C4⋊(C11⋊C8)D412yes—
75C4×C11⋊C8—21no—
76C4×C11⋊C8—21no—
77#10245—111nomaximal, Sylow
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C2×Q8×C11—82no—
86C2×Q8×C11SD1612yes—
87C22×C4×C11—21no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C2×C22⋊D11—41no—
95#4339—41no—
96#4339—41no—
97#4339—41no—
98#4339—41no—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44—21no—
102C2×C4×D11—41no—
103C2×Dic22—21no—
104C11×C4⋊C4—24no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—84no—
114C42×C11—41no—
115C42×C11—41no—
116C42×C11—41no—
117C42×C11—41no—
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11#4111yescharacteristic
122#4326—44no—
123#4325—44no—
124(C2×D11)⋊C4—41no—
125(C2×D11)⋊C4—41no—
126C4⋊Dic11—21no—
127C4⋊Dic11—21no—
128#4318—41no—
129#4318—41no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—41no—
133#3227—111no—
134#3037—111no—
135#2567D1111yescharacteristic, complemented
136#1549—111no—
137#1502—111no—
138#1479—111no—
139#1303—111no—
140C23×C11#12011yescharacteristic
141C22×D11—41no—
142Q8×C11—22no—
143Q8×C11—22no—
144Q8×C11—41no—
145Q8×C11—41no—
146Q8×C11—82no—
147Q8×C11—82no—
148C2×C4×C11—22no—
149C2×C4×C11—24no—
150C2×C4×C11—22no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—44no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11#12011yescharacteristic
161C2×C4×C11#12011yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12711yescharacteristic
166C2×C4×C11C2×SD1611yescharacteristic
167C2×C4×C11#13511yescharacteristic
168C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C11#13711yescharacteristic
170C22⋊D11—81no—
171C22⋊D11—81no—
172C2×Dic11—41no—
173D44—41no—
174D44—41no—
175D44—42no—
176D44—81no—
177C4×D11—81no—
178C4×D11—81no—
179Dic22—41no—
180Dic22—41no—
181C11⋊C8—42no—
182C11⋊C8—42no—
183C11⋊C8—81no—
184C2×#137—221no—
185#532—111no—
186C2×C4⋊Q8C2×D1111yescharacteristic
187C2×C4×Q8C2×D1111yescharacteristic
188#498—221no—
189#486—221no—
190#481—222no—
191#476—222no—
192#464—222no—
193#462—221no—
194#460—221no—
195#431—111no—
196#431—111no—
197#423—111no—
198#417—221no—
199#395—22no—
200#391—21no—
201#389—22no—
202#384—21no—
203C4×C4⋊C4C2×D1111yescharacteristic
204#332—222no—
205#327—222no—
206Q8⋊C8—222no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11#39211yescharacteristic
210C22×C11#44811yescharacteristic
211C22×C11#44911yescharacteristic
212C2×D11—81no—
213C2×D11—81no—
214C2×D11—81no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—44no—
219C4×C11—42no—
220C4×C11—81no—
221C4×C11—82no—
222C4×C11#45011yescharacteristic
223C4×C11#45211yescharacteristic
224C4×C11#45612yes—
225C4×C11#46511yescharacteristic
226C4×C11#46811yescharacteristic
227Dic11—81no—
228C2×#41—221no—
229C22×Q8—21no—
230C22×Q8C22⋊D1111yescharacteristic
231#137—442no—
232#137—442no—
233C2×Q16—222no—
234C2×SD16—222no—
235C2×M16—221no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—111no—
241#127—111no—
242#124—221no—
243#121—221no—
244#121—221no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×Q8—21no—
248C4×Q8—21no—
249C4×D4—221no—
250C4×D4—221no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4C22⋊D1111yescharacteristic
256C2×C4⋊C4C22⋊D1112yes—
257C2×C42—21no—
258C2×C42—21no—
259C2×C42C22×D1111yescharacteristic
260#106—224no—
261C4⋊C8—112no—
262C4⋊C8—112no—
263C4⋊C8—221no—
264C4⋊C8—221no—
265#103—222no—
266#102—222no—
267#102—224no—
268C22⋊C8—221no—
269C22⋊C8—221no—
270C4×C8—221no—
271C4×C8—221no—
272#95—24no—
273#95C22⋊D1112yes—
274C2×C11—21no—
275C2×C11—21no—
276C2×C11#200011yescharacteristic
277C2×C11#200511yescharacteristic
278C2×C11#200811yescharacteristic
279D11—161no—
280#41—441no—
281#41—441no—
282#41—441no—
283#41—441no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—82no—
292C2×Q8—221no—
293C2×Q8#432512yes—
294C2×D4—221no—
295C2×D4—221no—
296C2×D4—221no—
297C2×D4—441no—
298C22×C4—21no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—21no—
302C22×C4—441no—
303C22×C4C2×C22⋊D1111yescharacteristic
304C22×C4C2×C22⋊D1111yescharacteristic
305C22×C4C2×C22⋊D1111yescharacteristic
306Q16—444no—
307SD16—444no—
308M16—441no—
309M16—441no—
310C2×C8—222no—
311C2×C8—222no—
312C2×C8—441no—
313C4⋊C4—24no—
314C4⋊C4—21no—
315C4⋊C4—22no—
316C4⋊C4—21no—
317C4⋊C4—22no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—84no—
323C4⋊C4—221no—
324C4⋊C4—221no—
325C22⋊C4—441no—
326C22⋊C4—441no—
327C42—41no—
328C42—41no—
329C42—41no—
330C42—41no—
331C42D4×D1111yescharacteristic
332C42D4×D1111yescharacteristic
333C42D4×D1111yescharacteristic
334C42#434111yescharacteristic
335C11#1024511yescharacteristic, complemented, Sylow
336C23—441no—
337C23#6700611yescharacteristic
338Q8—22no—
339Q8—22no—
340Q8—41no—
341Q8—41no—
342Q8—82no—
343Q8—82no—
344Q8—441no—
345Q8—441no—
346D4—441no—
347D4—441no—
348D4—442no—
349D4—881no—
350D4—881no—
351D4—881no—
352C2×C4—22no—
353C2×C4—24no—
354C2×C4—22no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—44no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—441no—
365C2×C4—881no—
366C2×C4—881no—
367C2×C4#6699011yescharacteristic
368C2×C4#6699011yescharacteristic
369C2×C4#6699111yescharacteristic
370C2×C4#6699211yescharacteristic
371C2×C4#6699211yescharacteristic
372C2×C4#6699311yescharacteristic
373C2×C4C2×#432511yescharacteristic
374C2×C4#6699511yescharacteristic
375C2×C4#6700211yescharacteristic
376C2×C4#6700311yescharacteristic
377C8—442no—
378C8—442no—
379C8—881no—
380C22—21no—
381C22—21no—
382C22—881no—
383C22—881no—
384C22—881no—
385C22#1062283611yescharacteristic
386C22#1062284011yescharacteristic
387C22#1062285111yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—44no—
392C4—42no—
393C4—82no—
394C4—81no—
395C4—881no—
396C4#1062265911yescharacteristic
397C4#1062266011yescharacteristic
398C4#1062266111yescharacteristic
399C4#1062266211yescharacteristic
400C4#1062270812yes—
401C2—21no—
402C2—21no—
403C2—1761no—
404C2#1306961711yescharacteristic
405C2#1306965211yescharacteristic
406C2#1306966911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2567C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#2567D11
hypocenterC11#10245
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2567

Complements

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

NH ≅ G/Ntype
3. #13067301C2semidirect
5. #13067011C2semidirect
6. #13066519C2semidirect
7. C11×#2567C2semidirect
135. #2567D11semidirect
335. C11#10245semidirect

Maximal subgroups

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

subgroupindex
#130797442
#130780882
#130673012
#130671102
#130670112
#130665192
C11×#25672
#1024511