Finite Group Databasebeta

← #14737727

Subgroups — #14737727

Order 2816.

722 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622307C211yesmaximal, characteristic, complemented
2#13078431C211yesmaximal, characteristic, complemented
3#13078096C211yesmaximal, characteristic
4#13068032C214yesmaximal, complemented
5#13068025C214yesmaximal, complemented
6#13067372C211yesmaximal, characteristic, complemented
7#13067296C211yesmaximal, characteristic, complemented
8#13067283C211yesmaximal, characteristic, complemented
9C8×C11×#41C211yesmaximal, characteristic, complemented
10C4×C11×#41C2211yescharacteristic
11C2×#67002—21no—
12C2×#66927C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C8×Q8×C11C2212yescomplemented
15C8×D4×C11—22no—
16C8×D4×C11C2212yescomplemented
17C11×#431—21no—
18C11×#431C2211yescharacteristic
19C2×C4×C8×C11—21no—
20C2×C4×C8×C11C2211yescharacteristic
21#10622845—21no—
22C2×#66885—22no—
23#10622640—21no—
24#10622640C2212yes—
25#10622634C2212yescomplemented
26#10622633—21no—
27#10622628—21no—
28#10622628C2212yes—
29#10622621C2212yescomplemented
30#10622620—21no—
31#10622614—21no—
32#10622608—21no—
33#10622537C2211yescharacteristic
34#10622537C2211yescharacteristic
35#10622307—21no—
36#10622307—21no—
37#10622307C2214yes—
38#10622123C2214yes—
39#10622119C2214yescomplemented
40#10622095C2214yescomplemented
41C2×C11×#41D411yescharacteristic
42C22×D44—21no—
43C22×D44—21no—
44C22×D44—21no—
45C22×Dic22—21no—
46C22×C8×C11—22no—
47C22×C8×C11D412yes—
48C4×Q8×C11D411yescharacteristic
49C4×Q8×C11C2311yescharacteristic
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C4×D4×C11D411yescharacteristic
53C4×D4×C11C2311yescharacteristic
54C11×#117—21no—
55C11×#117D411yescharacteristic
56C2×C42×C11—21no—
57C2×C42×C11C2311yescharacteristic
58#67002—44no—
59C2×#4325—22no—
60C2×#4323—22no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C2×#4318—21no—
64C2×#4318—21no—
65#66927—21no—
66#66927—21no—
67#66927—21no—
68#66927C2312yes—
69#66922—21no—
70#66922—21no—
71#66922—21no—
72#66922C2312yes—
73C11×C4⋊C8—22no—
74C11×C4⋊C8C2312yes—
75C11×C22⋊C8—21no—
76C11×C22⋊C8—22no—
77C4×C8×C11—22no—
78C4×C8×C11—21no—
79C4×C8×C11D411yescharacteristic
80C4×C8×C11D411yescharacteristic
81C4×C8×C11C2312yes—
82#66899—22no—
83#66896—22no—
84#66885—24no—
85#66885—24no—
86#66873—22no—
87#66873—22no—
88#66872—22no—
89#66871—22no—
90C4⋊(C11⋊C8)—21no—
91C4⋊(C11⋊C8)—21no—
92C4⋊(C11⋊C8)C2312yes—
93C4⋊(C11⋊C8)C2312yes—
94#19274—111nomaximal, Sylow
95C23×D11—41no—
96C11×#41—22no—
97C11×#41SD1614yes—
98C2×Q8×C11C2×D411yescharacteristic
99C2×D4×C11—21no—
100C2×D4×C11C2×D411yescharacteristic
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11#4111yescharacteristic
107C22×Dic11—41no—
108C2×D44—22no—
109C2×D44—22no—
110C2×D44—22no—
111C2×D44—44no—
112C2×D44—41no—
113C2×D44—41no—
114C2×D44—41no—
115C2×D44—42no—
116C2×D44—42no—
117C2×D44—82no—
118C2×Dic22—22no—
119C2×Dic22—41no—
120C2×Dic22—82no—
121C2×C8×C11—22no—
122C2×C8×C11—42no—
123C2×C8×C11—44no—
124C2×C8×C11C2×D412yes—
125C2×C8×C11C2×D412yes—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4C2×D411yescharacteristic
129C11×C4⋊C4C2×D411yescharacteristic
130C11×C22⋊C4—21no—
131C11×C22⋊C4—21no—
132C11×C22⋊C4—21no—
133C42×C11—21no—
134C42×C11—21no—
135C42×C11—21no—
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11#4111yescharacteristic
139C42×C11C2411yescharacteristic
140#4325—44no—
141#4323—44no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—41no—
145C4⋊Dic11—41no—
146#4318—42no—
147#4318—42no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×#486—111no—
151#3079—111no—
152#3038—111no—
153C8×#41D1111yescharacteristic, complemented
154#1678—114no—
155#1677—114no—
156#1566—111no—
157#1548—111no—
158#1545—111no—
159C23×C11—21no—
160C23×C11#12111yescharacteristic
161C22×D11—42no—
162C22×D11—82no—
163C22×D11—82no—
164C22×D11—82no—
165Q8×C11—21no—
166Q8×C11C2×SD1612yes—
167D4×C11—24no—
168D4×C11—21no—
169D4×C11C2×SD1612yes—
170C2×C4×C11—21no—
171C2×C4×C11—22no—
172C2×C4×C11—24no—
173C2×C4×C11—22no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11C2×SD1612yes—
182C2×C4×C11#13512yes—
183C2×C4×C11C22×D411yescharacteristic
184C2×C4×C11C22×D411yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C2×Dic11—42no—
187C2×Dic11—82no—
188D44—42no—
189D44—42no—
190D44—44no—
191D44—82no—
192D44—82no—
193D44—82no—
194D44—82no—
195Dic22—82no—
196Dic22—82no—
197C8×C11—22no—
198C8×C11—22no—
199C8×C11—42no—
200C11⋊C8—42no—
201C11⋊C8—42no—
202C2×AGL(1,ℤ/8)—221no—
203C2×C4⋊Q8—111no—
204C2×#127—111no—
205C4×#41C2×D1111yescharacteristic
206#486—114no—
207#486—221no—
208#486—221no—
209#477—112no—
210#476—112no—
211#475—221no—
212#474—221no—
213#460—112no—
214#460—221no—
215#459—112no—
216#459—221no—
217C8×Q8C2×D1112yescomplemented
218C8×D4—22no—
219C8×D4C2×D1112yescomplemented
220#431—21no—
221#431C2×D1111yescharacteristic
222#428—221no—
223#423—111no—
224#423—111no—
225#418—221no—
226#417—221no—
227C2×#102—222no—
228C2×C4×C8—21no—
229C2×C4×C8C2×D1111yescharacteristic
230#334—114no—
231#333—114no—
232#331—114no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—22no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11#46512yes—
239C22×C11C2×#12111yescharacteristic
240C2×D11—82no—
241C2×D11—82no—
242C2×D11—82no—
243C2×D11—164no—
244C4×C11—21no—
245C4×C11—22no—
246C4×C11—21no—
247C4×C11—41no—
248C4×C11—41no—
249C4×C11#46512yes—
250C4×C11#47212yes—
251C4×C11C22×SD1611yescharacteristic
252C4×C11C2×#13511yescharacteristic
253C4×C11#57512yes—
254Dic11—82no—
255C2×#41D4411yescharacteristic
256C22×Q8—221no—
257C22×D4—221no—
258C22×D4—221no—
259C22×D4—221no—
260AGL(1,ℤ/8)—444no—
261C2×SD16—222no—
262C2×D8—222no—
263C2×M16—221no—
264C2×M16—221no—
265C22×C8—22no—
266C22×C8C22⋊D1112yes—
267C4⋊Q8—112no—
268C4⋊Q8—221no—
269C4⋊Q8—221no—
270C4⋊Q8—221no—
271#127—112no—
272#127—221no—
273#127—221no—
274#127—221no—
275C4×Q8D4411yescharacteristic
276C4×Q8C22×D1111yescharacteristic
277C4×D4—21no—
278C4×D4—21no—
279C4×D4D4411yescharacteristic
280C4×D4C22×D1111yescharacteristic
281#117—21no—
282#117D4411yescharacteristic
283C2×C4⋊C4—221no—
284C2×C4⋊C4—221no—
285C2×C42—21no—
286C2×C42C22×D1111yescharacteristic
287#107—222no—
288#106—222no—
289C4⋊C8—22no—
290C4⋊C8—112no—
291C4⋊C8—112no—
292C4⋊C8—221no—
293C4⋊C8—221no—
294C4⋊C8C22×D1112yes—
295#103—222no—
296#102—222no—
297#102—224no—
298#102—224no—
299#102—222no—
300#102—222no—
301C22⋊C8—21no—
302C22⋊C8—22no—
303C4×C8—22no—
304C4×C8—21no—
305C4×C8C22⋊D1111yescharacteristic
306C4×C8C22⋊D1111yescharacteristic
307C4×C8C22×D1112yes—
308C2×C11—22no—
309C2×C11—42no—
310C2×C11#304011yescharacteristic
311C2×C11C2×#46511yescharacteristic
312C2×C11C2×#47211yescharacteristic
313D11—162no—
314C24—441no—
315#41—22no—
316#41#431414yes—
317C2×Q8—222no—
318C2×Q8—441no—
319C2×Q8—882no—
320C2×Q8C2×D4411yescharacteristic
321C2×D4—21no—
322C2×D4—222no—
323C2×D4—222no—
324C2×D4—222no—
325C2×D4—444no—
326C2×D4—442no—
327C2×D4—442no—
328C2×D4—441no—
329C2×D4—441no—
330C2×D4—441no—
331C2×D4—882no—
332C2×D4C2×D4411yescharacteristic
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—441no—
337C22×C4C2×D4411yescharacteristic
338C22×C4#433911yescharacteristic
339C22×C4C2×C22⋊D1111yescharacteristic
340SD16—444no—
341D8—444no—
342M16—442no—
343M16—442no—
344C2×C8—22no—
345C2×C8—42no—
346C2×C8—44no—
347C2×C8—222no—
348C2×C8—222no—
349C2×C8C2×C22⋊D1112yes—
350C2×C8C2×C22⋊D1112yes—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—222no—
354C4⋊C4—222no—
355C4⋊C4—441no—
356C4⋊C4—441no—
357C4⋊C4C2×D4411yescharacteristic
358C4⋊C4C2×D4411yescharacteristic
359C22⋊C4—21no—
360C22⋊C4—21no—
361C22⋊C4—21no—
362C42—21no—
363C42—21no—
364C42—21no—
365C42C2×D4411yescharacteristic
366C42#433911yescharacteristic
367C42C2×C22⋊D1111yescharacteristic
368C42C23×D1111yescharacteristic
369C11#1927411yescharacteristic, complemented, Sylow
370C23—21no—
371C23—442no—
372C23—882no—
373C23—882no—
374C23—882no—
375C23#6698311yescharacteristic
376Q8—21no—
377Q8—882no—
378Q8—882no—
379Q8C2×#431412yes—
380D4—24no—
381D4—21no—
382D4—442no—
383D4—442no—
384D4—444no—
385D4—882no—
386D4—882no—
387D4—882no—
388D4—882no—
389D4C2×#431412yes—
390C2×C4—21no—
391C2×C4—24no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—442no—
399C2×C4—882no—
400C2×C4C2×#431412yes—
401C2×C4#6695712yes—
402C2×C4#6698311yescharacteristic
403C2×C4#6698311yescharacteristic
404C2×C4#6698311yescharacteristic
405C2×C4C22×D4411yescharacteristic
406C2×C4C2×#433911yescharacteristic
407C2×C4C22×C22⋊D1111yescharacteristic
408C8—22no—
409C8—22no—
410C8—42no—
411C8—442no—
412C8—442no—
413C22—21no—
414C22—21no—
415C22—22no—
416C22—41no—
417C22—41no—
418C22—882no—
419C22—882no—
420C22—882no—
421C22—1764no—
422C22#1062272712yes—
423C22C2×#6698311yescharacteristic
424C4—21no—
425C4—21no—
426C4—22no—
427C4—41no—
428C4—41no—
429C4—882no—
430C4#1062272712yes—
431C4#1062275512yes—
432C4C22×#431411yescharacteristic
433C4C2×#6695711yescharacteristic
434C4#1062335312yes—
435C2—22no—
436C2—42no—
437C2—1762no—
438C2#1307811011yescharacteristic
439C2C2×#1062272711yescharacteristic
440C2C2×#1062275511yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC8×C11×#41C2
socleC22×C11C2×#121
prime radical#13078096C2
hypercenterC8×#41D11
hypocenterC11#19274
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
1. C2×#10622307C2semidirect
2. #13078431C2semidirect
4. #13068032C2semidirect
5. #13068025C2semidirect
6. #13067372C2semidirect
7. #13067296C2semidirect
8. #13067283C2semidirect
9. C8×C11×#41C2semidirect
14. C8×Q8×C11C22semidirect
16. C8×D4×C11C22semidirect
25. #10622634C22semidirect
29. #10622621C22semidirect
39. #10622119C22semidirect
40. #10622095C22semidirect
153. C8×#41D11semidirect
217. C8×Q8C2×D11semidirect
219. C8×D4C2×D11semidirect
369. C11#19274semidirect

Maximal subgroups

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

subgroupindex
C2×#106223072
#130784312
#130780962
#130680322
#130680252
#130673722
#130672962
#130672832
C8×C11×#412
#1927411