Finite Group Databasebeta

← #14736932

Subgroups — #14736932

Order 2816.

726 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079543C211yesmaximal, characteristic, complemented
2#13079536C211yesmaximal, characteristic
3C2×#10622307C211yesmaximal, characteristic, complemented
4#13077329C211yesmaximal, characteristic, complemented
5#13068178C214yesmaximal, complemented
6#13068054C214yesmaximal, complemented
7#13067300C211yesmaximal, characteristic, complemented
8#13067283C211yesmaximal, characteristic, complemented
9C11×#1564C211yesmaximal, characteristic, complemented
10C2×#66954—21no—
11#10623008C2211yescharacteristic
12C2×#66927C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C11×#431C2211yescharacteristic
16C2×C4×C8×C11C2211yescharacteristic
17C2×#66885—21no—
18C2×#66885—21no—
19#10622723—21no—
20#10622537C2211yescharacteristic
21#10622456C2214yes—
22#10622454C2214yescomplemented
23#10622351—22no—
24#10622345—22no—
25#10622308—21no—
26#10622307—21no—
27#10622307—21no—
28#10622307—21no—
29#10622307C2212yes—
30#10622307C2212yes—
31#10622306—21no—
32#10622301—21no—
33#10622301C2212yescomplemented
34C8×D44—21no—
35C8×D44C2212yescomplemented
36#10622294—21no—
37C11×#335C2212yescomplemented
38C11×#334C2212yescomplemented
39#10622123C2214yes—
40#10622120C2214yescomplemented
41C2×#4339—21no—
42C22×D44—21no—
43C22×D44—21no—
44C22×D44—21no—
45C22×Dic22—21no—
46C22×C8×C11D411yescharacteristic
47C22×C8×C11D411yescharacteristic
48C2×C42×C11C2311yescharacteristic
49#66983—21no—
50#66983D412yes—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C2×#4318—21no—
54C2×D88—24no—
55C2×#4314—24no—
56#66954—44no—
57C2×#4313—22no—
58C2×C8×D11—22no—
59#66928—21no—
60#66927—21no—
61#66927—21no—
62#66927—21no—
63#66927D411yescharacteristic
64#66927C2312yes—
65C4×D44—21no—
66C4×D44C2312yes—
67#66922—21no—
68#66922—21no—
69#66922—21no—
70#66922D411yescharacteristic
71#66922C2312yes—
72C11×C4⋊C8C2312yes—
73C11×C4⋊C8C2312yes—
74C11×C22⋊C8—21no—
75C11×C22⋊C8—21no—
76C4×C8×C11—21no—
77C4×C8×C11—21no—
78C4×C8×C11D411yescharacteristic
79C4×C8×C11D411yescharacteristic
80C4×C8×C11C2311yescharacteristic
81C4×C8×C11C2311yescharacteristic
82#66885—22no—
83#66885—22no—
84#66885—22no—
85#66885—22no—
86#66885—24no—
87(C2×D11)⋊C8—22no—
88(C2×D11)⋊C8—22no—
89#66880—24no—
90C4⋊(C11⋊C8)—21no—
91C4⋊(C11⋊C8)C2312yes—
92#19198—111nomaximal, Sylow
93C23×D11—41no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11#4111yescharacteristic
97C2×C22⋊D11—22no—
98C22×Dic11—41no—
99#4339—42no—
100#4339—42no—
101C2×D44—21no—
102C2×D44—21no—
103C2×D44—22no—
104C2×D44—22no—
105C2×D44—22no—
106C2×D44—41no—
107C2×D44—41no—
108C2×D44—41no—
109C2×D44—42no—
110C2×D44—42no—
111C2×D44—82no—
112C2×D44—82no—
113C2×D44C2×D412yes—
114C2×C4×D11—22no—
115C2×Dic22—21no—
116C2×Dic22—22no—
117C2×Dic22—41no—
118C2×Dic22—82no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11C2×D411yescharacteristic
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128C42×C11C2×D411yescharacteristic
129C42×C11#4111yescharacteristic
130C42×C11C2411yescharacteristic
131(C2×D11)⋊C4—22no—
132(C2×D11)⋊C4—22no—
133C4⋊Dic11—21no—
134C4⋊Dic11—22no—
135C4⋊Dic11—22no—
136C4⋊Dic11—41no—
137C4⋊Dic11—41no—
138C4⋊Dic11C2×D412yes—
139#4318—42no—
140C2×C11⋊C8—22no—
141D88—84no—
142#4314—84no—
143#4313—44no—
144C8×D11—44no—
145#3206—111no—
146#3205—111no—
147C2×#486—111no—
148#2931—111no—
149#1701—114no—
150#1681—114no—
151#1564D1111yescharacteristic, complemented
152#1549—111no—
153#1545—111no—
154C23×C11#12111yescharacteristic
155C22×D11—22no—
156C22×D11—42no—
157C22×D11—82no—
158C22×D11—82no—
159C22×D11—82no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#13512yes—
166C2×C4×C11AGL(1,ℤ/8)12yes—
167C2×C4×C11C22×D411yescharacteristic
168C2×C4×C11C22×D411yescharacteristic
169C2×C4×C11C2×#4111yescharacteristic
170C22⋊D11—44no—
171C2×Dic11—22no—
172C2×Dic11—42no—
173C2×Dic11—82no—
174D44—24no—
175D44—42no—
176D44—42no—
177D44—44no—
178D44—42no—
179D44—42no—
180D44—82no—
181D44—82no—
182D44—82no—
183D44—82no—
184C4×D11—42no—
185C4×D11—42no—
186Dic22—42no—
187Dic22—44no—
188Dic22—82no—
189C8×C11—21no—
190C8×C11—21no—
191C8×C11—21no—
192C8×C11—21no—
193C8×C11—42no—
194C8×C11—42no—
195C11⋊C8—42no—
196C2×#131—221no—
197#532—111no—
198C2×C4⋊Q8—111no—
199C2×#127—111no—
200#493—221no—
201#492—221no—
202#487—221no—
203#486—112no—
204#486—112no—
205#486—221no—
206#486—221no—
207#486—221no—
208#461—114no—
209#459—114no—
210#448—222no—
211#447—222no—
212#436—112no—
213#436—221no—
214C8×D4—112no—
215C8×D4—221no—
216#431C2×D1111yescharacteristic
217#431C2×D1111yescharacteristic
218#423—111no—
219C2×#102—221no—
220C2×#102—221no—
221#408—221no—
222C2×C4×C8C2×D1111yescharacteristic
223#335C2×D1112yescomplemented
224#334C2×D1112yescomplemented
225#332—114no—
226#331—114no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11#46312yes—
230C22×C11C2×#12111yescharacteristic
231C2×D11—42no—
232C2×D11—42no—
233C2×D11—42no—
234C2×D11—82no—
235C2×D11—82no—
236C2×D11—82no—
237C2×D11—164no—
238C4×C11—21no—
239C4×C11—21no—
240C4×C11#46312yes—
241C4×C11#47112yes—
242C4×C11C2×#13511yescharacteristic
243C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
244C4×C11#57612yes—
245Dic11—42no—
246Dic11—82no—
247C2×#41—221no—
248C22×Q8—221no—
249C22×D4—221no—
250C22×D4—221no—
251C22×D4—221no—
252C2×SD16—224no—
253C2×D8—224no—
254#131—444no—
255C2×M16—221no—
256C2×M16—222no—
257C22×C8—222no—
258C22×C8D4411yescharacteristic
259C22×C8D4411yescharacteristic
260C4⋊Q8—111no—
261C4⋊Q8—112no—
262C4⋊Q8—221no—
263C4⋊Q8—221no—
264C4⋊Q8—221no—
265#127—111no—
266#127—112no—
267#127—221no—
268#127—221no—
269#127—221no—
270#124—221no—
271#121—112no—
272#121—221no—
273C4×D4—112no—
274C4×D4—221no—
275C2×C4⋊C4—221no—
276C2×C4⋊C4—221no—
277C2×C42C22×D1111yescharacteristic
278C4⋊C8—112no—
279C4⋊C8—221no—
280C4⋊C8C22×D1112yes—
281C4⋊C8C22×D1112yes—
282#103—224no—
283#102—224no—
284#102—222no—
285#102—222no—
286#102—222no—
287#102—222no—
288C22⋊C8—21no—
289C22⋊C8—21no—
290C22⋊C8—222no—
291C22⋊C8—222no—
292C4×C8—21no—
293C4×C8—21no—
294C4×C8D4411yescharacteristic
295C4×C8D4411yescharacteristic
296C4×C8C22×D1111yescharacteristic
297C4×C8C22×D1111yescharacteristic
298C2×C11—22no—
299C2×C11C2×#46311yescharacteristic
300C2×C11#305811yescharacteristic
301C2×C11C2×#47111yescharacteristic
302D11—82no—
303D11—162no—
304C24—441no—
305#41—442no—
306#41—442no—
307C2×Q8—221no—
308C2×Q8—222no—
309C2×Q8—441no—
310C2×Q8—882no—
311C2×D4—112no—
312C2×D4—222no—
313C2×D4—221no—
314C2×D4—221no—
315C2×D4—222no—
316C2×D4—222no—
317C2×D4—222no—
318C2×D4—441no—
319C2×D4—441no—
320C2×D4—441no—
321C2×D4—442no—
322C2×D4—442no—
323C2×D4—882no—
324C2×D4—882no—
325C22×C4—222no—
326C22×C4—441no—
327C22×C4C2×D4411yescharacteristic
328C22×C4D4×D1111yescharacteristic
329C22×C4#434311yescharacteristic
330SD16—884no—
331D8—884no—
332M16—444no—
333M16—442no—
334C2×C8—22no—
335C2×C8—22no—
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—222no—
339C2×C8—444no—
340C2×C8C2×D4411yescharacteristic
341C2×C8C2×D4411yescharacteristic
342C2×C8C2×D4411yescharacteristic
343C2×C8C2×D4411yescharacteristic
344C4⋊C4—112no—
345C4⋊C4—221no—
346C4⋊C4—222no—
347C4⋊C4—222no—
348C4⋊C4—441no—
349C4⋊C4—441no—
350C22⋊C4—222no—
351C22⋊C4—222no—
352C42C2×D4411yescharacteristic
353C42D4×D1111yescharacteristic
354C42#434311yescharacteristic
355C42C23×D1111yescharacteristic
356C11#1919811yescharacteristic, complemented, Sylow
357C23—222no—
358C23—442no—
359C23—882no—
360C23—882no—
361C23—882no—
362C23#6694811yescharacteristic
363Q8—442no—
364Q8—444no—
365Q8—882no—
366D4—224no—
367D4—444no—
368D4—442no—
369D4—442no—
370D4—442no—
371D4—444no—
372D4—442no—
373D4—882no—
374D4—882no—
375D4—882no—
376D4—882no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—222no—
380C2×C4—442no—
381C2×C4—442no—
382C2×C4—442no—
383C2×C4—882no—
384C2×C4#6694811yescharacteristic
385C2×C4#6694811yescharacteristic
386C2×C4#6694811yescharacteristic
387C2×C4#6695712yes—
388C2×C4#6696112yes—
389C2×C4C22×D4411yescharacteristic
390C2×C4C2×D4×D1111yescharacteristic
391C2×C4C2×#434311yescharacteristic
392C8—21no—
393C8—21no—
394C8—21no—
395C8—21no—
396C8—42no—
397C8—42no—
398C8—442no—
399C22—21no—
400C22—21no—
401C22—442no—
402C22—442no—
403C22—442no—
404C22—882no—
405C22—882no—
406C22—882no—
407C22—1764no—
408C22#1062245712yes—
409C22C2×#6694811yescharacteristic
410C4—21no—
411C4—21no—
412C4—442no—
413C4—882no—
414C4#1062245712yes—
415C4#1062251112yes—
416C4C2×#6695711yescharacteristic
417C4C2×#6696111yescharacteristic
418C4#1062330012yes—
419C2—22no—
420C2—882no—
421C2—1762no—
422C2C2×#1062245711yescharacteristic
423C2#1307826511yescharacteristic
424C2C2×#1062251111yescharacteristic
subgroupG/H
centerC22C2×#66948
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1564C2
socleC22×C11C2×#121
prime radical#13079536C2
hypercenter#1564D11
hypocenterC11#19198
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1564

Complements

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

NH ≅ G/Ntype
1. #13079543C2semidirect
3. C2×#10622307C2semidirect
4. #13077329C2semidirect
5. #13068178C2semidirect
6. #13068054C2semidirect
7. #13067300C2semidirect
8. #13067283C2semidirect
9. C11×#1564C2semidirect
22. #10622454C22semidirect
33. #10622301C22semidirect
35. C8×D44C22semidirect
37. C11×#335C22semidirect
38. C11×#334C22semidirect
40. #10622120C22semidirect
151. #1564D11semidirect
223. #335C2×D11semidirect
224. #334C2×D11semidirect
356. C11#19198semidirect

Maximal subgroups

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

subgroupindex
#130795432
#130795362
C2×#106223072
#130773292
#130681782
#130680542
#130673002
#130672832
C11×#15642
#1919811