Finite Group Databasebeta

← #14737325

Subgroups — #14737325

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079923C211yesmaximal, characteristic
2#13079012C211yesmaximal, characteristic, complemented
3#13077360C211yesmaximal, characteristic, complemented
4#13068193C212yesmaximal, complemented
5#13068151C212yesmaximal, complemented
6#13068069C212yesmaximal, complemented
7#13068027C212yesmaximal, complemented
8#13067369C211yesmaximal, characteristic, complemented
9C2×#10622184C211yesmaximal, characteristic, complemented
10#13067263C211yesmaximal, characteristic, complemented
11C11×#3227C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#67001—21no—
15#10623008C2211yescharacteristic
16C11×#498—21no—
17C11×#486—21no—
18C11×#481—22no—
19C11×#476C2212yes—
20C11×#476C2212yes—
21C11×#431C2211yescharacteristic
22#10622847—21no—
23#10622706C2212yes—
24#10622702—22no—
25#10622701C2212yes—
26#10622700—21no—
27#10622685—21no—
28#10622651—22no—
29#10622628C2212yes—
30#10622625C2212yes—
31#10622624—22no—
32D4×C11⋊C8C2212yes—
33#10622620C2212yes—
34#10622579—21no—
35#10622579—21no—
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C4×#4318C2211yescharacteristic
39#10622184C2212yes—
40#10622184C2212yes—
41#10622124C2211yescharacteristic
42#10622124C2211yescharacteristic
43#10622123C2211yescharacteristic
44#10622123C2211yescharacteristic
45#10622118C2212yes—
46#10622117C2212yes—
47C2×C11×#41—21no—
48C22×Q8×C11—21no—
49C2×#4339—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8C2312yes—
55C11×#127D411yescharacteristic
56C11×#124—21no—
57C11×#121—21no—
58C11×#121D412yes—
59C4×D4×C11—21no—
60C4×D4×C11C2312yes—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C42×C11C2311yescharacteristic
64#67001—44no—
65C2×#4323—22no—
66#66983—21no—
67#66983—21no—
68C2×#4318—22no—
69C2×#4318D411yescharacteristic
70C2×#4318D411yescharacteristic
71C22×C11⋊C8—21no—
72C22×C11⋊C8—21no—
73C22×C11⋊C8—22no—
74#66928—21no—
75#66927C2311yescharacteristic
76C4×D44—21no—
77C4×D44—21no—
78#66922C2311yescharacteristic
79C11×#106—22no—
80C11×#106—22no—
81C11×C4⋊C8C2311yescharacteristic
82C11×C4⋊C8C2311yescharacteristic
83C11×#102—22no—
84C11×#102—22no—
85C11×C22⋊C8—21no—
86C4×C8×C11—21no—
87#66896—22no—
88C22⋊(C11⋊C8)—22no—
89C22⋊(C11⋊C8)—22no—
90#66874—22no—
91#66874—22no—
92#66873—22no—
93#66873—22no—
94#66873—22no—
95#66871—22no—
96C4⋊(C11⋊C8)—21no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)C2312yes—
99C4⋊(C11⋊C8)C2311yescharacteristic
100C4⋊(C11⋊C8)C2311yescharacteristic
101#66867D412yes—
102C4×C11⋊C8C2312yes—
103#19236—111nomaximal, Sylow
104C11×#41—42no—
105C11×#41—42no—
106C2×Q8×C11—21no—
107C2×Q8×C11—22no—
108C2×Q8×C11—41no—
109C2×Q8×C11—82no—
110C2×D4×C11—22no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11C2×D412yes—
114C22×C4×C11—22no—
115C22×C4×C11—41no—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11#4111yescharacteristic
119C2×C22⋊D11—41no—
120#4339—42no—
121#4339—42no—
122C2×D44—21no—
123C2×D44—21no—
124C2×D44—21no—
125C2×C4×D11—41no—
126C2×Dic22—21no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—41no—
133C11×C4⋊C4—41no—
134C11×C4⋊C4C2×D412yes—
135C11×C22⋊C4—22no—
136C11×C22⋊C4—22no—
137C42×C11C2×D411yescharacteristic
138C42×C11C2×D411yescharacteristic
139C42×C11#4111yescharacteristic
140C42×C11C2411yescharacteristic
141#4323—82no—
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4—41no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146#4318—22no—
147#4318—22no—
148#4318—44no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—44no—
153C2×C11⋊C8—42no—
154C2×C11⋊C8—81no—
155C2×C11⋊C8C2×D412yes—
156C2×C11⋊C8C2×D412yes—
157#3245—111no—
158#3227D1111yescharacteristic, complemented
159#3141—111no—
160#2935—111no—
161#1703—112no—
162#1697—112no—
163#1683—112no—
164#1677—112no—
165#1565—111no—
166C2×#333—111no—
167#1540—111no—
168C23×C11—22no—
169C23×C11#12111yescharacteristic
170C22×D11—41no—
171Q8×C11—42no—
172Q8×C11—82no—
173Q8×C11—82no—
174D4×C11—22no—
175D4×C11—22no—
176D4×C11—44no—
177D4×C11—42no—
178D4×C11—81no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—22no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—82no—
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11#12111yescharacteristic
189C2×C4×C11#12111yescharacteristic
190C2×C4×C11#13512yes—
191C2×C4×C11AGL(1,ℤ/8)12yes—
192C2×C4×C11C22×D411yescharacteristic
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C2×#4111yescharacteristic
195C22⋊D11—82no—
196C2×Dic11—41no—
197D44—41no—
198D44—41no—
199D44—41no—
200D44—41no—
201D44—81no—
202C4×D11—82no—
203Dic22—41no—
204Dic22—41no—
205C8×C11—41no—
206C8×C11—41no—
207C11⋊C8—22no—
208C11⋊C8—22no—
209C11⋊C8—41no—
210C11⋊C8—41no—
211C11⋊C8—42no—
212C2×#131—221no—
213#532—111no—
214#532C2×D1111yescharacteristic
215C2×C4⋊Q8C2×D1111yescharacteristic
216#498—21no—
217#489—222no—
218#487—112no—
219#486—21no—
220#486—112no—
221#481—22no—
222#476C2×D1112yes—
223#476C2×D1112yes—
224#474—112no—
225#474—221no—
226#466—222no—
227#459—112no—
228#459—221no—
229#436—112no—
230#435—222no—
231C8×D4—112no—
232#431C2×D1111yescharacteristic
233C2×C4⋊C8—111no—
234C2×C4⋊C8—111no—
235#417—221no—
236#417—221no—
237#408—221no—
238C4×M16—111no—
239#335—112no—
240#334—112no—
241#333—112no—
242#333—112no—
243#332—111no—
244#332—111no—
245#331—111no—
246#331—111no—
247C22×C11—21no—
248C22×C11—21no—
249C22×C11—42no—
250C22×C11—42no—
251C22×C11—42no—
252C22×C11#46312yes—
253C22×C11C2×#12111yescharacteristic
254C2×D11—81no—
255C2×D11—81no—
256C2×D11—81no—
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—42no—
261C4×C11—82no—
262C4×C11#46312yes—
263C4×C11C2×#13511yescharacteristic
264C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
265C4×C11#57711yescharacteristic
266C4×C11#57811yescharacteristic
267Dic11—81no—
268C2×#41—21no—
269C2×#41—221no—
270C22×Q8—21no—
271C2×D8—222no—
272#131—444no—
273C2×M16—111no—
274C2×M16—111no—
275C2×M16—222no—
276C22×C8—222no—
277C22×C8—221no—
278C22×C8—221no—
279C4⋊Q8—21no—
280C4⋊Q8—21no—
281C4⋊Q8—21no—
282C4⋊Q8—111no—
283C4⋊Q8C22⋊D1111yescharacteristic
284C4⋊Q8C22×D1112yes—
285#127—111no—
286#127C22⋊D1111yescharacteristic
287#124—21no—
288#124—221no—
289#121—21no—
290#121—221no—
291#121—221no—
292#121C22⋊D1112yes—
293C4×D4—21no—
294C4×D4—221no—
295C4×D4—221no—
296C4×D4C22×D1112yes—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C42C22×D1111yescharacteristic
300#107—222no—
301#106—22no—
302#106—22no—
303C4⋊C8—111no—
304C4⋊C8—111no—
305C4⋊C8—112no—
306C4⋊C8—221no—
307C4⋊C8—221no—
308C4⋊C8C22×D1111yescharacteristic
309C4⋊C8C22×D1111yescharacteristic
310#103—222no—
311#103—222no—
312#102—22no—
313#102—22no—
314#102—222no—
315#102—222no—
316#102—222no—
317#102—222no—
318C22⋊C8—21no—
319C22⋊C8—222no—
320C22⋊C8—222no—
321#97—112no—
322C4×C8—21no—
323C4×C8—112no—
324C2×C11—22no—
325C2×C11—82no—
326C2×C11C2×#46311yescharacteristic
327C2×C11#306311yescharacteristic
328C2×C11#306811yescharacteristic
329D11—161no—
330#41—42no—
331#41—42no—
332#41—442no—
333#41—442no—
334C2×Q8—21no—
335C2×Q8—22no—
336C2×Q8—41no—
337C2×Q8—82no—
338C2×Q8—221no—
339C2×D4—22no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—221no—
343C2×D4—221no—
344C2×D4—221no—
345C2×D4—441no—
346C2×D4C2×C22⋊D1112yes—
347C22×C4—22no—
348C22×C4—41no—
349C22×C4—441no—
350C22×C4D4×D1111yescharacteristic
351C22×C4#434111yescharacteristic
352C22×C4C2×C22⋊D1111yescharacteristic
353D8—882no—
354M16—222no—
355M16—222no—
356M16—444no—
357C2×C8—21no—
358C2×C8—21no—
359C2×C8—112no—
360C2×C8—112no—
361C2×C8—221no—
362C2×C8—221no—
363C2×C8—222no—
364C2×C8—444no—
365C2×C8—442no—
366C2×C8—881no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C4⋊C4C2×C22⋊D1112yes—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—441no—
378C22⋊C4—441no—
379C42D4×D1111yescharacteristic
380C42#434111yescharacteristic
381C42C2×C22⋊D1111yescharacteristic
382C42C23×D1111yescharacteristic
383C11#1923611yescharacteristic, complemented, Sylow
384C23—22no—
385C23—441no—
386C23#6699211yescharacteristic
387Q8—42no—
388Q8—82no—
389Q8—82no—
390Q8—441no—
391Q8—441no—
392D4—22no—
393D4—22no—
394D4—44no—
395D4—42no—
396D4—81no—
397D4—441no—
398D4—441no—
399D4—441no—
400D4—441no—
401D4—881no—
402D4—882no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—22no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—82no—
411C2×C4—441no—
412C2×C4—882no—
413C2×C4#6696712yes—
414C2×C4#6696912yes—
415C2×C4#6699211yescharacteristic
416C2×C4#6699211yescharacteristic
417C2×C4#6699211yescharacteristic
418C2×C4C2×D4×D1111yescharacteristic
419C2×C4C2×#434111yescharacteristic
420C2×C4C22×C22⋊D1111yescharacteristic
421C8—41no—
422C8—41no—
423C8—222no—
424C8—222no—
425C8—441no—
426C8—441no—
427C8—442no—
428C22—21no—
429C22—21no—
430C22—42no—
431C22—42no—
432C22—42no—
433C22—881no—
434C22—881no—
435C22—881no—
436C22#1062277812yes—
437C22C2×#6699211yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—42no—
442C4—82no—
443C4—881no—
444C4#1062277812yes—
445C4C2×#6696711yescharacteristic
446C4C2×#6696911yescharacteristic
447C4#1062336811yescharacteristic
448C4#1062336911yescharacteristic
449C2—22no—
450C2—82no—
451C2—1761no—
452C2C2×#1062277811yescharacteristic
453C2#1307830311yescharacteristic
454C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3227C2
socleC22×C11C2×#121
prime radical#13079923C2
hypercenter#3227D11
hypocenterC11#19236
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3227

Complements

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

NH ≅ G/Ntype
2. #13079012C2semidirect
3. #13077360C2semidirect
4. #13068193C2semidirect
5. #13068151C2semidirect
6. #13068069C2semidirect
7. #13068027C2semidirect
8. #13067369C2semidirect
9. C2×#10622184C2semidirect
10. #13067263C2semidirect
11. C11×#3227C2semidirect
158. #3227D11semidirect
383. C11#19236semidirect

Maximal subgroups

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

subgroupindex
#130799232
#130790122
#130773602
#130681932
#130681512
#130680692
#130680272
#130673692
C2×#106221842
#130672632
C11×#32272
#1923611