Finite Group Databasebeta

← #14656176

Subgroups — #14656176

Order 2816.

554 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 103 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#13079543C211yesmaximal, characteristic
2#13078088C211yesmaximal, characteristic
3#13073828C211yesmaximal, characteristic, complemented
4#13067296C211yesmaximal, characteristic, complemented
5#13067112C211yesmaximal, characteristic
6#13066518C211yesmaximal, characteristic, complemented
7C11×#1479C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#66995—21no—
10#10623008C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#431C2211yescharacteristic
14#10622843—21no—
15#10622644—21no—
16#10622641—22no—
17#10622640—21no—
18#10622599—22no—
19#10622590—21no—
20#10622579—21no—
21C4×C4⋊Dic11C2211yescharacteristic
22#10622542—22no—
23#10622537C2211yescharacteristic
24#10622454—22no—
25#10622351—22no—
26#10622306—21no—
27#10622294—21no—
28C11×Q8⋊C8—22no—
29#10622119—22no—
30#10622108—22no—
31C22×Q8×C11D411yescharacteristic
32C2×#4339—21no—
33C22×Dic22D412yes—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C42×C11—21no—
41C2×C42×C11C2311yescharacteristic
42C2×#4326—22no—
43#66995—42no—
44#66995—42no—
45C2×#4325—22no—
46#66983—21no—
47#66983—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×C4×Dic11—21no—
52C2×#4318—21no—
53C2×#4314—24no—
54#66928—21no—
55#66927D411yescharacteristic
56C4×D44—21no—
57C4×D44—21no—
58#66922—21no—
59#66922—21no—
60#66922—21no—
61#66922—21no—
62#66922D411yescharacteristic
63C11×C4⋊C8—21no—
64C11×C4⋊C8D412yes—
65C11×C22⋊C8—21no—
66C11×C22⋊C8—21no—
67C4×C8×C11—21no—
68C4×C8×C11—21no—
69C11⋊#95—24no—
70C11⋊#95—24no—
71C11⋊#95D412yes—
72#66880—24no—
73#66874—22no—
74#66873—22no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)D412yes—
77#10244—111nomaximal, Sylow
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11SD1612yescomplemented
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C2×C22⋊D11—41no—
90C22×Dic11—22no—
91C22×Dic11—22no—
92#4339—41no—
93#4339—41no—
94#4339—41no—
95#4339—41no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44—21no—
99C2×C4×D11—41no—
100C2×Dic22—21no—
101C2×Dic22—22no—
102C2×Dic22—22no—
103C2×Dic22—44no—
104C2×C8×C11—22no—
105C2×C8×C11—41no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C42×C11—41no—
111C42×C11—41no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11#4111yescharacteristic
116#4326—44no—
117#4325—44no—
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—41no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122C4⋊Dic11—42no—
123C4⋊Dic11—41no—
124C4⋊Dic11—41no—
125C4⋊Dic11—41no—
126C4⋊Dic11—41no—
127C4×Dic11—41no—
128C4×Dic11—41no—
129#4318—41no—
130#4318—41no—
131C2×C11⋊C8—22no—
132#4314—84no—
133#3206—111no—
134#3037—111no—
135#2568—111no—
136#1548—111no—
137#1502—111no—
138#1479D1111yescharacteristic, complemented
139#1303—111no—
140C23×C11#12011yescharacteristic
141C22×D11—41no—
142Q8×C11—22no—
143Q8×C11—22no—
144Q8×C11—41no—
145Q8×C11—41no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—41no—
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12711yescharacteristic
159C2×C4×C11C2×SD1611yescharacteristic
160C2×C4×C11#13511yescharacteristic
161C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C11#13711yescharacteristic
163C22⋊D11—81no—
164C22⋊D11—81no—
165C2×Dic11—42no—
166C2×Dic11—44no—
167C2×Dic11—42no—
168C2×Dic11—41no—
169C2×Dic11—42no—
170C2×Dic11—42no—
171D44—41no—
172D44—41no—
173D44—42no—
174D44—81no—
175C4×D11—81no—
176C4×D11—81no—
177Dic22—41no—
178Dic22—41no—
179Dic22—44no—
180Dic22—82no—
181C8×C11—42no—
182C8×C11—81no—
183C11⋊C8—42no—
184C2×#137—221no—
185#532—111no—
186C2×C4⋊Q8—111no—
187C2×C4×Q8C2×D1111yescharacteristic
188#492—221no—
189#487—221no—
190#464—222no—
191#462—221no—
192#461—222no—
193#460—221no—
194#448—222no—
195#431C2×D1111yescharacteristic
196#431C2×D1111yescharacteristic
197#423—111no—
198#417—221no—
199#400—222no—
200#391—222no—
201#391—221no—
202#382—221no—
203C4×C4⋊C4—111no—
204#333—222no—
205#327—222no—
206Q8⋊C8—22no—
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—42no—
219C4×C11—81no—
220C4×C11#45011yescharacteristic
221C4×C11#45211yescharacteristic
222C4×C11#45512yes—
223C4×C11#46511yescharacteristic
224C4×C11#46811yescharacteristic
225Dic11—82no—
226Dic11—81no—
227Dic11—82no—
228C2×#41—221no—
229C22×Q8—112no—
230C22×Q8D4411yescharacteristic
231#137—442no—
232#137—442no—
233C2×Q16—222no—
234C2×SD16—224no—
235C2×SD16—222no—
236C2×M16—221no—
237C4⋊Q8—111no—
238C4⋊Q8—221no—
239C4⋊Q8—221no—
240C4⋊Q8—221no—
241C4⋊Q8—221no—
242#127—111no—
243#124—221no—
244#121—221no—
245#121—221no—
246C4×Q8—21no—
247C4×Q8—21no—
248C4×Q8—21no—
249C4×Q8—21no—
250C4×D4—221no—
251C4×D4—221no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—221no—
254C2×C4⋊C4—221no—
255C2×C4⋊C4—221no—
256C2×C4⋊C4D4411yescharacteristic
257C2×C42—21no—
258C2×C42—221no—
259C2×C42C22×D1111yescharacteristic
260C4⋊C8—21no—
261C4⋊C8—112no—
262C4⋊C8—221no—
263C4⋊C8C22⋊D1112yes—
264#103—222no—
265#103—224no—
266#102—222no—
267C22⋊C8—21no—
268C22⋊C8—21no—
269C4×C8—21no—
270C4×C8—21no—
271#95—112no—
272#95—224no—
273#95—224no—
274C2×C11—21no—
275C2×C11—21no—
276C2×C11#200011yescharacteristic
277C2×C11#200411yescharacteristic
278C2×C11#200911yescharacteristic
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—221no—
290C2×Q8—222no—
291C2×Q8—222no—
292C2×Q8—444no—
293C2×Q8#431412yescomplemented
294C2×D4—221no—
295C2×D4—221no—
296C2×D4—221no—
297C2×D4—441no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—222no—
301C22×C4—222no—
302C22×C4—441no—
303C22×C4C2×D4411yescharacteristic
304C22×C4D4×D1111yescharacteristic
305C22×C4D4×D1111yescharacteristic
306Q16—444no—
307SD16—444no—
308SD16—884no—
309M16—441no—
310M16—441no—
311C2×C8—22no—
312C2×C8—41no—
313C2×C8—222no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—221no—
319C4⋊C4—221no—
320C4⋊C4—442no—
321C4⋊C4—441no—
322C4⋊C4—441no—
323C4⋊C4—441no—
324C4⋊C4—441no—
325C22⋊C4—441no—
326C22⋊C4—441no—
327C42—41no—
328C42—41no—
329C42—441no—
330C42—441no—
331C42#433911yescharacteristic
332C42D4×D1111yescharacteristic
333C42D4×D1111yescharacteristic
334C42C2×C22⋊D1111yescharacteristic
335C11#1024411yescharacteristic, complemented, Sylow
336C23—441no—
337C23#6693511yescharacteristic
338Q8—22no—
339Q8—22no—
340Q8—41no—
341Q8—41no—
342Q8—444no—
343Q8—441no—
344Q8—441no—
345Q8—882no—
346D4—442no—
347D4—441no—
348D4—441no—
349D4—881no—
350D4—881no—
351D4—881no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—442no—
360C2×C4—444no—
361C2×C4—442no—
362C2×C4—441no—
363C2×C4—442no—
364C2×C4—442no—
365C2×C4—881no—
366C2×C4—881no—
367C2×C4#6693511yescharacteristic
368C2×C4#6693711yescharacteristic
369C2×C4#6693711yescharacteristic
370C2×C4C2×#431411yescharacteristic
371C2×C4#6695711yescharacteristic
372C2×C4#6696111yescharacteristic
373C2×C4#6696211yescharacteristic
374C2×C4#6698311yescharacteristic
375C2×C4#6699011yescharacteristic
376C2×C4#6699311yescharacteristic
377C8—42no—
378C8—81no—
379C8—442no—
380C22—21no—
381C22—21no—
382C22—881no—
383C22—881no—
384C22—881no—
385C22#1062234711yescharacteristic
386C22#1062235111yescharacteristic
387C22#1062257311yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—42no—
392C4—81no—
393C4—882no—
394C4—881no—
395C4—882no—
396C4#1062234411yescharacteristic
397C4#1062234611yescharacteristic
398C4#1062272711yescharacteristic
399C4#1062274711yescharacteristic
400C4#1062281512yes—
401C2—21no—
402C2—21no—
403C2—1761no—
404C2#1306962111yescharacteristic
405C2#1306964611yescharacteristic
406C2#1306967711yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1479C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#1479D11
hypocenterC11#10244
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
3. #13073828C2semidirect
4. #13067296C2semidirect
6. #13066518C2semidirect
7. C11×#1479C2semidirect
83. C2×Q8×C11SD16semidirect
138. #1479D11semidirect
293. C2×Q8#4314semidirect
335. C11#10244semidirect

Maximal subgroups

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

subgroupindex
#130795432
#130780882
#130738282
#130672962
#130671122
#130665182
C11×#14792
#1024411