Finite Group Databasebeta

← #14664840

Subgroups — #14664840

Order 2816.

422 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 83 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#13078199C211yesmaximal, characteristic
2D11×C22⋊C16C211yesmaximal, characteristic, complemented
3#13068640C211yesmaximal, characteristic, complemented
4#13066628C211yesmaximal, characteristic, complemented
5#13066626C211yesmaximal, characteristic, complemented
6#13066624C211yesmaximal, characteristic, complemented
7C11×#1348C211yesmaximal, characteristic, complemented
8C2×#66972C411yescharacteristic, complemented
9C22×C8×D11C2211yescharacteristic
10#10623158—21no—
11C11×#467C2211yescharacteristic
12#10622801C411yescharacteristic, complemented
13#10622728C2211yescharacteristic
14#10622661—21no—
15#10622600—21no—
16C2×#66872—21no—
17C2×C16×D11—21no—
18#10622496C411yescharacteristic, complemented
19#10622493C411yescharacteristic, complemented
20#10622420—21no—
21#10622417—21no—
22C11×C22⋊C16C2211yescharacteristic
23C11×#340C2211yescharacteristic
24#10622189C2211yescharacteristic
25C22⋊(C11⋊C16)C2211yescharacteristic
26(C2×D11)⋊C16—21no—
27C2×#4343—21no—
28C22×C4×D11D411yescharacteristic
29C2×C11×Q16C2×C411yescharacteristic
30C22×C8×C11C2311yescharacteristic
31C11×C22⋊Q8—21no—
32C2×C11×C4⋊C4—21no—
33#66999—21no—
34C2×#4325—21no—
35#66983—21no—
36C2×(C2×D11)⋊C4—41no—
37C2×C4⋊Dic11—21no—
38C22×C11⋊C8D411yescharacteristic
39#66972—42no—
40C2×D88C2×C411yescharacteristic
41C2×C8×D11—42no—
42C2×C8×D11C2×C411yescharacteristic
43C2×C8×D11C2×C411yescharacteristic
44C2×C8×D11D411yescharacteristic
45C2×C8×D11D411yescharacteristic
46#66948—21no—
47#66947—41no—
48#66946—41no—
49#66945—21no—
50#66935—41no—
51(C22⋊D11)⋊C4—41no—
52C2×C11×C16—21no—
53C11×#107C2×C411yescharacteristic
54C11×#103—21no—
55#66899—21no—
56C11⋊#95—41no—
57#66885—21no—
58#66882C2×C411yescharacteristic
59C2×C11⋊C16—21no—
60#66873—21no—
61#66872—21no—
62#66872—42no—
63C16×D11—42no—
64#11885—111nomaximal, Sylow
65C23×D11D811yescharacteristic
66C2×Q8×C11—21no—
67C22×C4×C11—41no—
68C22×C4×C11C2×D411yescharacteristic
69C2×C22⋊D11—41no—
70C22×Dic11—41no—
71C22×Dic11D811yescharacteristic
72#4343—42no—
73#4343—42no—
74C2×D44—21no—
75C2×D44—41no—
76C2×D44—41no—
77C2×C4×D11—41no—
78C2×C4×D11—41no—
79C2×C4×D11—41no—
80C2×C4×D11C22⋊C411yescharacteristic
81C2×C4×D11C22⋊C411yescharacteristic
82C2×C4×D11SD1611yescharacteristic
83C2×C4×D11SD1611yescharacteristic
84C11×Q16—41no—
85C2×C8×C11—41no—
86C2×C8×C11C22×C411yescharacteristic
87C2×C8×C11C2×D411yescharacteristic
88C11×C4⋊C4—21no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C22⋊C4—41no—
93#4325—42no—
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4—41no—
96(C2×D11)⋊C4—41no—
97(C2×D11)⋊C4—41no—
98(C2×D11)⋊C4—82no—
99C4⋊Dic11—21no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102Dic11⋊C4—41no—
103C4×Dic11—41no—
104C2×C11⋊C8—22no—
105C2×C11⋊C8C22⋊C411yescharacteristic
106C2×C11⋊C8C22⋊C411yescharacteristic
107D88—41no—
108C8×D11—22no—
109C8×D11—22no—
110C8×D11—41no—
111C8×D11—41no—
112C11×C16—41no—
113C11⋊C16—41no—
114#3050—111no—
115C2×C22⋊C16—111no—
116#1807—111no—
117#1348—111no—
118#1348D1111yescharacteristic, complemented
119#1347—111no—
120#1347—111no—
121C23×C11C2×D811yescharacteristic
122C22×D11—21no—
123C22×D11—21no—
124C22×D11—22no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11#10211yescharacteristic
128C22×D11#10211yescharacteristic
129Q8×C11—41no—
130Q8×C11—41no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—81no—
136C2×C4×C11—81no—
137C2×C4×C11—81no—
138C2×C4×C11C2×C22⋊C411yescharacteristic
139C2×C4×C11C2×SD1611yescharacteristic
140C22⋊D11—81no—
141C22⋊D11—81no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—81no—
145C2×Dic11—81no—
146C2×Dic11—81no—
147C2×Dic11#10211yescharacteristic
148C2×Dic11#10211yescharacteristic
149D44—41no—
150D44—41no—
151D44—82no—
152D44—82no—
153C4×D11—21no—
154C4×D11—21no—
155C4×D11—21no—
156C4×D11—21no—
157C4×D11—41no—
158C4×D11—41no—
159C4×D11—82no—
160C8×C11—21no—
161C8×C11—21no—
162C11⋊C8—21no—
163C11⋊C8#9912yes—
164C2×#135—111no—
165C23×C8—111no—
166#525—221no—
167C22×C16—221no—
168#467—111no—
169#467C2×D1111yescharacteristic
170#466—111no—
171#466—111no—
172#465—221no—
173#465—221no—
174#427—111no—
175C2×#106—221no—
176#416—221no—
177#380—221no—
178C22⋊C16—111no—
179C22⋊C16—221no—
180C22⋊C16C2×D1111yescharacteristic
181#340—111no—
182#340C2×D1111yescharacteristic
183C22×C11—21no—
184C22×C11—21no—
185C22×C11C2×#10211yescharacteristic
186C22×C11#50811yescharacteristic
187C22×C11#50811yescharacteristic
188C2×D11—21no—
189C2×D11—21no—
190C2×D11—21no—
191C2×D11—21no—
192C2×D11—21no—
193C2×D11—42no—
194C2×D11—42no—
195C2×D11—81no—
196C2×D11—81no—
197C2×D11—81no—
198C2×D11#36012yes—
199C4×C11—21no—
200C4×C11—81no—
201C4×C11—81no—
202C4×C11—161no—
203C4×C11C2×#9911yescharacteristic
204C4×C11#42111yescharacteristic
205Dic11—21no—
206Dic11—21no—
207Dic11—81no—
208Dic11—161no—
209C2×#41—221no—
210C23×C4—111no—
211#135—442no—
212C2×Q16C4×D1111yescharacteristic
213C2×SD16—221no—
214C2×D8—111no—
215C22×C8—111no—
216C22×C8—111no—
217C22×C8—111no—
218C22×C8—111no—
219C22×C8—111no—
220C22×C8—442no—
221C22×C8C22×D1111yescharacteristic
222#123—441no—
223C22⋊Q8—21no—
224C22⋊Q8—221no—
225#121—221no—
226#121—221no—
227#120—441no—
228C4×D4—441no—
229C4×D4—441no—
230#117—221no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—221no—
233C2×C22⋊C4—441no—
234C2×C16—21no—
235C2×C16—221no—
236C2×C16—442no—
237#107—111no—
238#107C4×D1111yescharacteristic
239#106—221no—
240#106—442no—
241#103—21no—
242#103—221no—
243#102—221no—
244#102—221no—
245#95—441no—
246C2×C11—21no—
247C2×C11—21no—
248C2×C11#151911yescharacteristic
249C2×C11#213811yescharacteristic
250C2×C11C2×#36011yescharacteristic
251D11—22no—
252D11—41no—
253D11—161no—
254C24—111no—
255#41—442no—
256#41—442no—
257C2×Q8—21no—
258C2×D4—221no—
259C2×D4—441no—
260C2×D4—441no—
261C2×D4—441no—
262C22×C4—41no—
263C22×C4—111no—
264C22×C4—111no—
265C22×C4—111no—
266C22×C4—111no—
267C22×C4—111no—
268C22×C4—441no—
269C22×C4—441no—
270C22×C4—441no—
271C22×C4—441no—
272C22×C4D4×D1111yescharacteristic
273Q16—41no—
274SD16—442no—
275D8—441no—
276C2×C8—41no—
277C2×C8—111no—
278C2×C8—111no—
279C2×C8—222no—
280C2×C8—222no—
281C2×C8—222no—
282C2×C8—441no—
283C2×C8—441no—
284C2×C8C2×C4×D1111yescharacteristic
285C2×C8D4×D1111yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—221no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C4⋊C4—441no—
294C22⋊C4—41no—
295C22⋊C4—441no—
296C22⋊C4—441no—
297C22⋊C4—441no—
298C22⋊C4—441no—
299C22⋊C4—882no—
300C42—441no—
301C16—41no—
302C16—441no—
303C11#1188511yescharacteristic, complemented, Sylow
304C23—111no—
305C23—111no—
306C23—222no—
307C23—221no—
308C23—221no—
309C23—441no—
310C23—441no—
311C23D8×D1111yescharacteristic
312Q8—41no—
313Q8—41no—
314D4—441no—
315D4—441no—
316D4—882no—
317D4—882no—
318D4—881no—
319D4—881no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—111no—
328C2×C4—111no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—221no—
332C2×C4—221no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—882no—
338C2×C4—881no—
339C2×C4—881no—
340C2×C4—881no—
341C2×C4C22⋊C4×D1111yescharacteristic
342C2×C4SD16×D1111yescharacteristic
343C8—21no—
344C8—21no—
345C8—112no—
346C8—221no—
347C22—21no—
348C22—21no—
349C22—112no—
350C22—221no—
351C22—221no—
352C22—221no—
353C22—221no—
354C22—221no—
355C22—442no—
356C22—442no—
357C22—881no—
358C22—881no—
359C22—881no—
360C22D11×#10211yescharacteristic
361C22#1062252911yescharacteristic
362C22#1062253211yescharacteristic
363C4—21no—
364C4—81no—
365C4—81no—
366C4—161no—
367C4—221no—
368C4—221no—
369C4—881no—
370C4—1761no—
371C4D11×#9911yescharacteristic
372C4#1062243411yescharacteristic
373C2—21no—
374C2—21no—
375C2—222no—
376C2—441no—
377C2—1761no—
378C2#1306718211yescharacteristic
379C2#1307032211yescharacteristic
380C2D11×#36011yescharacteristic
subgroupG/H
centerC22D11×#102
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1348C2
socleC22×C11C2×#102
prime radical#13078199C2
cosocleC22×C8×C11C23
hypercenter#1348D11
hypocenterC11#11885
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1348

Complements

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

NH ≅ G/Ntype
2. D11×C22⋊C16C2semidirect
3. #13068640C2semidirect
4. #13066628C2semidirect
5. #13066626C2semidirect
6. #13066624C2semidirect
7. C11×#1348C2semidirect
8. C2×#66972C4semidirect
12. #10622801C4semidirect
18. #10622496C4semidirect
19. #10622493C4semidirect
118. #1348D11semidirect
303. C11#11885semidirect

Maximal subgroups

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

subgroupindex
#130781992
D11×C22⋊C162
#130686402
#130666282
#130666262
#130666242
C11×#13482
#1188511