Finite Group Databasebeta

← #14651639

Subgroups — #14651639

Order 2816.

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

normal subgroups only

This group has 602 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#13077656C211yesmaximal, characteristic, complemented
2#13073517C211yesmaximal, characteristic
3#13068605C211yesmaximal, characteristic, complemented
4#13067041C211yesmaximal, characteristic, complemented
5#13066476C211yesmaximal, characteristic, complemented
6#13066475C211yesmaximal, characteristic, complemented
7C11×#1486C211yesmaximal, characteristic, complemented
8C2×C4×D4×C11C2211yescharacteristic
9C2×#66983—21no—
10C2×C4×D44C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13#10622836C412yes—
14#10622825—21no—
15C2×#66887—21no—
16#10622606C412yes—
17#10622569—22no—
18#10622549C2211yescharacteristic
19#10622538C2211yescharacteristic
20#10622537C2211yescharacteristic
21#10622451—22no—
22#10622339—22no—
23#10622301—22no—
24C11×D4⋊C8—22no—
25#10622192—21no—
26D4⋊(C11⋊C8)—22no—
27C22×D4×C11C2×C411yescharacteristic
28C23×C4×C11—21no—
29C22×C22⋊D11—22no—
30C22×D44D411yescharacteristic
31C22×C4×D11D412yes—
32C2×C11×M16—21no—
33C4×D4×C11—21no—
34C4×D4×C11—21no—
35C4×D4×C11—21no—
36C4×D4×C11—21no—
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C22⋊C4—21no—
39C2×C42×C11C2311yescharacteristic
40C2×C22⋊Dic11—22no—
41#66983—42no—
42#66983—42no—
43C2×(C2×D11)⋊C4—22no—
44C2×(C2×D11)⋊C4C2×C412yes—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11D411yescharacteristic
47C2×#4318—21no—
48C2×#4313—24no—
49C4×D44—21no—
50C4×D44—21no—
51C4×D44—21no—
52C4×D44—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C22⋊C8—21no—
57C4×C8×C11D412yescomplemented
58C11⋊#95—21no—
59C11⋊#95—22no—
60C11⋊#95C2×C412yes—
61C22⋊(C11⋊C8)—21no—
62#66887—42no—
63(C2×D11)⋊C8—24no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4×C11⋊C8D412yescomplemented
68#9489—111nomaximal, Sylow
69C24×C11—21no—
70C23×D11C22⋊C412yes—
71C2×D4×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—42no—
74C22×C4×C11—21no—
75C22×C4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C2×C22⋊D11—44no—
85C2×C22⋊D11—44no—
86C2×C22⋊D11—82no—
87C22×Dic11—22no—
88C22×Dic11C22⋊C412yes—
89C2×D44—21no—
90C2×D44—21no—
91C2×D44—21no—
92C2×D44—21no—
93C2×D44—21no—
94C2×D44—21no—
95C2×C4×D11—22no—
96C2×C4×D11—22no—
97C2×C4×D11—82no—
98C11×M16—41no—
99C11×M16—41no—
100C2×C8×C11—22no—
101C2×C8×C11—41no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11#4111yescharacteristic
109C42×C11#4111yescharacteristic
110C22⋊Dic11—82no—
111(C2×D11)⋊C4—22no—
112(C2×D11)⋊C4—22no—
113(C2×D11)⋊C4—44no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118#4318—41no—
119#4318—41no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—41no—
122#4313—84no—
123#2975—111no—
124#2535—111no—
125#1800—111no—
126#1486—111no—
127#1486D1111yescharacteristic, complemented
128#1286—111no—
129#1286—111no—
130C23×C11—22no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11C2×C22⋊C411yescharacteristic
138C22×D11—22no—
139C22×D11—22no—
140C22×D11—22no—
141C22×D11—42no—
142C22×D11—42no—
143D4×C11—22no—
144D4×C11—22no—
145D4×C11—41no—
146D4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—81no—
153C2×C4×C11—81no—
154C2×C4×C11—81no—
155C2×C4×C11—81no—
156C2×C4×C11C4×D411yescharacteristic
157C2×C4×C11C4×D411yescharacteristic
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12311yescharacteristic
162C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C11#13711yescharacteristic
166C22⋊D11—88no—
167C2×Dic11—22no—
168C2×Dic11—42no—
169C2×Dic11—42no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172D44—41no—
173D44—41no—
174D44—41no—
175D44—41no—
176C4×D11—44no—
177C4×D11—82no—
178C8×C11—42no—
179C8×C11—81no—
180C11⋊C8—42no—
181C11⋊C8—81no—
182C2×#121—221no—
183C2×C4×D4—111no—
184C2×C4×D4C2×D1111yescharacteristic
185#436—222no—
186#436—222no—
187#431—111no—
188#431C2×D1111yescharacteristic
189#423—111no—
190#423C2×D1111yescharacteristic
191C2×#100—221no—
192#407—222no—
193#397—112no—
194#392—112no—
195#386—222no—
196#382—111no—
197#380—221no—
198#343—221no—
199D4⋊C8—22no—
200D4⋊C8—222no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—42no—
204C22×C11—42no—
205C22×C11—42no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11—81no—
209C22×C11—81no—
210C22×C11#38611yescharacteristic
211C22×C11#41711yescharacteristic
212C22×C11#41811yescharacteristic
213C2×D11—44no—
214C2×D11—42no—
215C2×D11—42no—
216C2×D11—42no—
217C2×D11—82no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—81no—
223C4×C11#46811yescharacteristic
224C4×C11#46811yescharacteristic
225C4×C11#46911yescharacteristic
226C4×C11#46911yescharacteristic
227Dic11—42no—
228Dic11—82no—
229C22×D4—111no—
230C22×D4—222no—
231C22×D4C4×D1111yescharacteristic
232C23×C4—21no—
233C23×C4—112no—
234C2×M16—21no—
235C2×M16—224no—
236C2×M16—221no—
237#121—442no—
238#121—442no—
239C4×D4—21no—
240C4×D4—21no—
241C4×D4—21no—
242C4×D4—21no—
243C4×D4—221no—
244C4×D4—221no—
245C4×D4—221no—
246C4×D4—221no—
247C2×C4⋊C4—111no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4C4×D1111yescharacteristic
250C2×C22⋊C4—21no—
251C2×C22⋊C4—112no—
252C2×C22⋊C4—222no—
253C2×C22⋊C4—222no—
254C2×C42C22×D1111yescharacteristic
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—221no—
259C4⋊C8—221no—
260C4⋊C8—221no—
261#100—442no—
262C22⋊C8—21no—
263C22⋊C8—224no—
264C22⋊C8—221no—
265C4×C8—112no—
266C4×C8C22⋊D1112yescomplemented
267#95—112no—
268#95—222no—
269#95—221no—
270C2×C11—21no—
271C2×C11—21no—
272C2×C11—82no—
273C2×C11#189111yescharacteristic
274C2×C11#189511yescharacteristic
275C2×C11#191111yescharacteristic
276D11—82no—
277C24—21no—
278C24—112no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—42no—
282C2×D4—221no—
283C2×D4—221no—
284C2×D4—221no—
285C2×D4—221no—
286C2×D4—221no—
287C2×D4—221no—
288C2×D4—444no—
289C2×D4—444no—
290C2×D4—882no—
291C22×C4—21no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—112no—
299C22×C4—222no—
300C22×C4—222no—
301C22×C4—222no—
302C22×C4—882no—
303C22×C4C2×C4×D1111yescharacteristic
304C22×C4D4×D1111yescharacteristic
305C22×C4D4×D1111yescharacteristic
306M16—41no—
307M16—41no—
308M16—441no—
309M16—441no—
310M16—884no—
311C2×C8—22no—
312C2×C8—41no—
313C2×C8—222no—
314C2×C8—441no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—221no—
318C4⋊C4—221no—
319C4⋊C4—441no—
320C4⋊C4—441no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—222no—
324C22⋊C4—222no—
325C22⋊C4—444no—
326C22⋊C4—882no—
327C42#433911yescharacteristic
328C42D4×D1111yescharacteristic
329C42#434111yescharacteristic
330C42C2×C22⋊D1111yescharacteristic
331C11#948911yescharacteristic, complemented, Sylow
332C23—22no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—222no—
340C23—222no—
341C23—222no—
342C23—442no—
343C23—442no—
344C23C22⋊C4×D1111yescharacteristic
345D4—22no—
346D4—22no—
347D4—41no—
348D4—41no—
349D4—441no—
350D4—441no—
351D4—441no—
352D4—441no—
353D4—888no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—222no—
364C2×C4—444no—
365C2×C4—442no—
366C2×C4—442no—
367C2×C4—442no—
368C2×C4—442no—
369C2×C4—882no—
370C2×C4(C22⋊D11)⋊C411yescharacteristic
371C2×C4#6693611yescharacteristic
372C2×C4#6693711yescharacteristic
373C2×C4#6696411yescharacteristic
374C2×C4#6696411yescharacteristic
375C2×C4#6696711yescharacteristic
376C2×C4#6696811yescharacteristic
377C2×C4C4×C22⋊D1111yescharacteristic
378C2×C4#6699011yescharacteristic
379C2×C4#6699111yescharacteristic
380C8—42no—
381C8—81no—
382C8—442no—
383C8—881no—
384C22—21no—
385C22—21no—
386C22—42no—
387C22—42no—
388C22—42no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22—444no—
394C22—442no—
395C22—442no—
396C22—442no—
397C22—882no—
398C22#1062238311yescharacteristic
399C22#1062238411yescharacteristic
400C22#1062256911yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—81no—
406C4—442no—
407C4—882no—
408C4#1062239311yescharacteristic
409C4#1062239511yescharacteristic
410C4#1062277211yescharacteristic
411C4#1062278711yescharacteristic
412C2—21no—
413C2—21no—
414C2—82no—
415C2—882no—
416C2#1306903111yescharacteristic
417C2#1306905111yescharacteristic
418C2#1306914511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1486C2
socleC22×C11#386
prime radical#13073517C2
cosocleC2×C42×C11C23
hypercenter#1486D11
hypocenterC11#9489
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
1. #13077656C2semidirect
3. #13068605C2semidirect
4. #13067041C2semidirect
5. #13066476C2semidirect
6. #13066475C2semidirect
7. C11×#1486C2semidirect
57. C4×C8×C11D4semidirect
67. C4×C11⋊C8D4semidirect
127. #1486D11semidirect
266. C4×C8C22⋊D11semidirect
331. C11#9489semidirect

Maximal subgroups

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

subgroupindex
#130776562
#130735172
#130686052
#130670412
#130664762
#130664752
C11×#14862
#948911