Finite Group Databasebeta

← #14650499

Subgroups — #14650499

Order 2816.

632 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 109 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#13079536C211yesmaximal, characteristic
2#13071341C211yesmaximal, characteristic, complemented
3#13069448C211yesmaximal, characteristic, complemented
4#13067283C211yesmaximal, characteristic, complemented
5#13067177C211yesmaximal, characteristic, complemented
6#13066475C211yesmaximal, characteristic, complemented
7C11×#1274C211yesmaximal, characteristic, complemented
8#10623008C2211yescharacteristic
9C2×#66927C2211yescharacteristic
10C2×C4×D44—21no—
11C11×#431C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#376C2211yescharacteristic
14#10622552—21no—
15#10622549C2211yescharacteristic
16C2×#66869—21no—
17C2×#66869—21no—
18#10622537C2211yescharacteristic
19#10622456—22no—
20#10622345—22no—
21#10622308C412yescomplemented
22#10622307C412yescomplemented
23#10622278—22no—
24#10622278—22no—
25#10622123—22no—
26#10622108—22no—
27C2×#4339—21no—
28C22×D44—21no—
29C22×D44—21no—
30C22×D44D412yes—
31C22×C4×D11—22no—
32C2×C42×C11D411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C42×C11C2311yescharacteristic
35#66983—21no—
36#66983—21no—
37C2×(C2×D11)⋊C4—22no—
38C2×(C2×D11)⋊C4—22no—
39C2×(C2×D11)⋊C4—22no—
40C2×C4⋊Dic11—21no—
41C2×#4318—21no—
42C2×D88—24no—
43#66928—21no—
44#66927—21no—
45#66927—21no—
46#66927C2×C412yes—
47#66927C2×C411yescharacteristic, complemented
48#66927D412yes—
49C4×D44—21no—
50C4×D44—21no—
51C4×D44—42no—
52C4×D44—42no—
53#66922C2×C411yescharacteristic, complemented
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C22⋊C8—21no—
57C11×C22⋊C8—21no—
58C4×C8×C11—21no—
59C4×C8×C11C2×C412yescomplemented
60C11×#95—21no—
61C11×#95—21no—
62C11⋊#95—21no—
63C11⋊#95D412yes—
64#66885—24no—
65#66869—42no—
66#66869—42no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69#9299—111nomaximal, Sylow
70C23×D11—22no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C2×C22⋊D11—41no—
77C22×Dic11—22no—
78#4339—41no—
79#4339—41no—
80#4339—41no—
81#4339—41no—
82C2×D44—21no—
83C2×D44—22no—
84C2×D44—22no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44—22no—
88C2×D44—22no—
89C2×D44—22no—
90C2×D44—41no—
91C2×D44—41no—
92C2×D44—41no—
93C2×D44—41no—
94C2×D44—82no—
95C2×D44—82no—
96C2×D44C22⋊C414yes—
97C2×C4×D11—44no—
98C2×C4×D11—41no—
99C2×C4×D11—82no—
100C2×C4×D11—82no—
101C2×Dic22—21no—
102C2×C8×C11—22no—
103C2×C8×C11—41no—
104C42×C11—21no—
105C42×C11—21no—
106C42×C11—21no—
107C42×C11D812yescomplemented
108C42×C11C22×C411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11#4111yescharacteristic
111C42×C11#4111yescharacteristic
112(C2×D11)⋊C4—44no—
113(C2×D11)⋊C4—41no—
114(C2×D11)⋊C4—41no—
115(C2×D11)⋊C4—82no—
116(C2×D11)⋊C4—82no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—41no—
120C4⋊Dic11—41no—
121#4318—41no—
122#4318—41no—
123C2×C11⋊C8—41no—
124D88—84no—
125#3205—111no—
126#2328—111no—
127#1963—111no—
128#1545—111no—
129#1517—111no—
130#1286—111no—
131#1274D1111yescharacteristic, complemented
132C23×C11#12011yescharacteristic
133C22×D11—24no—
134C22×D11—42no—
135C22×D11—42no—
136C22×D11—42no—
137C22×D11—42no—
138C22×D11—42no—
139C22×D11—42no—
140C22×D11—41no—
141C2×C4×C11—22no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11C2×C22⋊C411yescharacteristic
150C2×C4×C11C4×D411yescharacteristic
151C2×C4×C11C4×D411yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12311yescharacteristic
155C2×C4×C11C2×D811yescharacteristic
156C2×C4×C11#13511yescharacteristic
157C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
159C22⋊D11—81no—
160C22⋊D11—81no—
161C2×Dic11—42no—
162C2×Dic11—42no—
163C2×Dic11—41no—
164C2×Dic11—42no—
165D44—44no—
166D44—42no—
167D44—42no—
168D44—41no—
169D44—42no—
170D44—41no—
171D44—42no—
172D44—42no—
173D44—82no—
174D44—82no—
175D44—82no—
176D44—81no—
177C4×D11—88no—
178C4×D11—81no—
179C4×D11—81no—
180Dic22—41no—
181Dic22—41no—
182C8×C11—42no—
183C8×C11—81no—
184C11⋊C8—81no—
185#532—111no—
186C2×#127—111no—
187C2×C4×D4—221no—
188#493—112no—
189#486—112no—
190#459—222no—
191#447—222no—
192#431C2×D1111yescharacteristic
193#431C2×D1111yescharacteristic
194#423—111no—
195C2×#104—221no—
196C2×#104—221no—
197#390—221no—
198#386—222no—
199#386—222no—
200#382—111no—
201#376C2×D1111yescharacteristic
202#331—222no—
203#327—222no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11#38611yescharacteristic
207C22×C11#44711yescharacteristic
208C22×C11#44911yescharacteristic
209C2×D11—44no—
210C2×D11—44no—
211C2×D11—44no—
212C2×D11—82no—
213C2×D11—82no—
214C2×D11—82no—
215C2×D11—82no—
216C2×D11—81no—
217C2×D11—81no—
218C2×D11—81no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—42no—
224C4×C11—81no—
225C4×C11C4×D811yescharacteristic
226C4×C11#44211yescharacteristic
227C4×C11#45911yescharacteristic
228C4×C11#46311yescharacteristic
229Dic11—82no—
230Dic11—81no—
231C2×#41—221no—
232C22×D4—112no—
233C22×D4—221no—
234C22×D4—221no—
235C23×C4—222no—
236C2×D8—224no—
237C2×M16—221no—
238C4⋊Q8—111no—
239#127—112no—
240#127—111no—
241#127—112no—
242#127—221no—
243#127—221no—
244#124—221no—
245#121—221no—
246#121—221no—
247C4×D4—221no—
248C4×D4—221no—
249C4×D4—442no—
250C4×D4—442no—
251C2×C4⋊C4—221no—
252C2×C22⋊C4—222no—
253C2×C22⋊C4—222no—
254C2×C22⋊C4—222no—
255C2×C42D4411yescharacteristic
256C2×C42D4411yescharacteristic
257C2×C42C22×D1111yescharacteristic
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8—221no—
261C4⋊C8—221no—
262#104—442no—
263#104—442no—
264#102—224no—
265C22⋊C8—21no—
266C22⋊C8—21no—
267C4×C8—21no—
268C4×C8C4×D1112yescomplemented
269#95—21no—
270#95—21no—
271#95—112no—
272#95—221no—
273C2×C11—21no—
274C2×C11—21no—
275C2×C11#187911yescharacteristic
276C2×C11#190411yescharacteristic
277C2×C11#191111yescharacteristic
278D11—84no—
279D11—161no—
280C24—222no—
281#41—441no—
282#41—441no—
283#41—441no—
284#41—441no—
285C2×Q8—221no—
286C2×D4—114no—
287C2×D4—222no—
288C2×D4—221no—
289C2×D4—221no—
290C2×D4—222no—
291C2×D4—222no—
292C2×D4—221no—
293C2×D4—222no—
294C2×D4—222no—
295C2×D4—441no—
296C2×D4—441no—
297C2×D4—441no—
298C2×D4—441no—
299C2×D4—441no—
300C2×D4—882no—
301C2×D4—882no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—222no—
305C22×C4—444no—
306C22×C4—441no—
307C22×C4—882no—
308C22×C4—882no—
309C22×C4C2×D4411yescharacteristic
310C22×C4D4×D1111yescharacteristic
311C22×C4D4×D1111yescharacteristic
312D8—884no—
313M16—441no—
314M16—441no—
315C2×C8—22no—
316C2×C8—41no—
317C2×C8—441no—
318C4⋊C4—221no—
319C4⋊C4—221no—
320C4⋊C4—441no—
321C4⋊C4—441no—
322C22⋊C4—444no—
323C22⋊C4—441no—
324C22⋊C4—441no—
325C22⋊C4—882no—
326C22⋊C4—882no—
327C42—21no—
328C42—21no—
329C42—21no—
330C42D8812yescomplemented
331C42C2×C4×D1111yescharacteristic
332C42#433911yescharacteristic
333C42D4×D1111yescharacteristic
334C42#434311yescharacteristic
335C11#929911yescharacteristic, complemented, Sylow
336C23—224no—
337C23—442no—
338C23—442no—
339C23—442no—
340C23—442no—
341C23—442no—
342C23—442no—
343C23—441no—
344C23#6693511yescharacteristic
345Q8—441no—
346Q8—441no—
347D4—444no—
348D4—442no—
349D4—442no—
350D4—441no—
351D4—442no—
352D4—441no—
353D4—442no—
354D4—442no—
355D4—882no—
356D4—882no—
357D4—882no—
358D4—881no—
359D4—881no—
360D4—881no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—442no—
370C2×C4—442no—
371C2×C4—441no—
372C2×C4—442no—
373C2×C4—888no—
374C2×C4—881no—
375C2×C4—881no—
376C2×C4C4×D4411yescharacteristic
377C2×C4C22⋊C4×D1111yescharacteristic
378C2×C4#6693711yescharacteristic
379C2×C4#6694611yescharacteristic
380C2×C4#6694711yescharacteristic
381C2×C4#6694811yescharacteristic
382C2×C4C2×D8811yescharacteristic
383C2×C4#6695711yescharacteristic
384C2×C4#6696111yescharacteristic
385C2×C4#6696111yescharacteristic
386C8—42no—
387C8—81no—
388C8—881no—
389C22—21no—
390C22—21no—
391C22—444no—
392C22—444no—
393C22—444no—
394C22—882no—
395C22—882no—
396C22—882no—
397C22—882no—
398C22—881no—
399C22—881no—
400C22—881no—
401C22#1062227811yescharacteristic
402C22#1062234511yescharacteristic
403C22#1062234711yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—42no—
409C4—81no—
410C4—882no—
411C4—881no—
412C4C4×D8811yescharacteristic
413C4#1062232411yescharacteristic
414C4#1062245611yescharacteristic
415C4#1062245711yescharacteristic
416C2—21no—
417C2—21no—
418C2—884no—
419C2—1761no—
420C2#1306896311yescharacteristic
421C2#1306910411yescharacteristic
422C2#1306914711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1274C2
socleC22×C11#386
prime radical#13079536C2
cosocleC2×C42×C11C23
hypercenter#1274D11
hypocenterC11#9299
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
2. #13071341C2semidirect
3. #13069448C2semidirect
4. #13067283C2semidirect
5. #13067177C2semidirect
6. #13066475C2semidirect
7. C11×#1274C2semidirect
21. #10622308C4semidirect
22. #10622307C4semidirect
47. #66927C2×C4semidirect
53. #66922C2×C4semidirect
59. C4×C8×C11C2×C4semidirect
107. C42×C11D8semidirect
131. #1274D11semidirect
268. C4×C8C4×D11semidirect
330. C42D88semidirect
335. C11#9299semidirect

Maximal subgroups

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

subgroupindex
#130795362
#130713412
#130694482
#130672832
#130671772
#130664752
C11×#12742
#929911