Finite Group Databasebeta

← #14737336

Subgroups — #14737336

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 464 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#13068179C212yesmaximal, complemented
5#13068165C212yesmaximal, complemented
6#13068055C212yesmaximal, complemented
7#13068041C212yesmaximal, complemented
8#13067369C211yesmaximal, characteristic, complemented
9#13067263C211yesmaximal, characteristic, complemented
10C2×#10622185C211yesmaximal, characteristic, complemented
11C11×#3206C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#67001—21no—
15#10623008C2211yescharacteristic
16C11×#492—21no—
17C11×#487—21no—
18C11×#461C2212yes—
19C11×#461C2212yes—
20C11×#448—22no—
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#10622185C2212yes—
40#10622185C2212yes—
41#10622124C2211yescharacteristic
42#10622124C2211yescharacteristic
43#10622123C2211yescharacteristic
44#10622123C2211yescharacteristic
45#10622118C2212yes—
46#10622117C2212yes—
47C2×C11×#41—21no—
48C22×Q8×C11—21no—
49C2×#4339—21no—
50C2×C11×SD16—22no—
51C2×C11×SD16—22no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8D411yescharacteristic
56C11×C4⋊Q8C2312yes—
57C11×#127D411yescharacteristic
58C11×#124—21no—
59C11×#121—21no—
60C11×#121D412yes—
61C4×D4×C11—21no—
62C4×D4×C11C2312yes—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C42×C11C2311yescharacteristic
66#67001—44no—
67C2×#4323—22no—
68#66983—21no—
69#66983—21no—
70C2×#4318—22no—
71C2×#4318D411yescharacteristic
72C2×#4318D411yescharacteristic
73C22×C11⋊C8—21no—
74C22×C11⋊C8—21no—
75C22×C11⋊C8—22no—
76#66928—21no—
77#66927C2311yescharacteristic
78C4×D44—21no—
79C4×D44—21no—
80#66922C2311yescharacteristic
81C11×C4⋊C8C2311yescharacteristic
82C11×C4⋊C8C2311yescharacteristic
83C11×#103—22no—
84C11×#103—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#19237—111nomaximal, Sylow
104C11×#41—42no—
105C11×#41—42no—
106C2×Q8×C11—21no—
107C2×Q8×C11—22no—
108C2×Q8×C11—41no—
109C2×Q8×C11—81no—
110C2×Q8×C11—81no—
111C2×D4×C11—22no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11C2×D412yes—
115C22×C4×C11—22no—
116C22×C4×C11—41no—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11#4111yescharacteristic
120C2×C22⋊D11—41no—
121#4339—42no—
122#4339—42no—
123C2×D44—21no—
124C2×D44—21no—
125C2×D44—21no—
126C2×C4×D11—41no—
127C2×Dic22—21no—
128C11×SD16—82no—
129C11×SD16—82no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—41no—
136C11×C4⋊C4—41no—
137C11×C4⋊C4C2×D412yes—
138C11×C22⋊C4—22no—
139C11×C22⋊C4—22no—
140C42×C11C2×D411yescharacteristic
141C42×C11C2×D411yescharacteristic
142C42×C11#4111yescharacteristic
143C42×C11C2411yescharacteristic
144#4323—82no—
145(C2×D11)⋊C4—41no—
146(C2×D11)⋊C4—41no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149#4318—22no—
150#4318—22no—
151#4318—44no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—44no—
156C2×C11⋊C8—42no—
157C2×C11⋊C8—81no—
158C2×C11⋊C8C2×D412yes—
159C2×C11⋊C8C2×D412yes—
160#3245—111no—
161#3206D1111yescharacteristic, complemented
162#3141—111no—
163#2935—111no—
164#1701—112no—
165#1699—112no—
166#1681—112no—
167#1679—112no—
168#1565—111no—
169#1540—111no—
170C2×#332—111no—
171C23×C11—22no—
172C23×C11#12111yescharacteristic
173C22×D11—41no—
174Q8×C11—42no—
175Q8×C11—42no—
176Q8×C11—42no—
177Q8×C11—82no—
178D4×C11—22no—
179D4×C11—22no—
180D4×C11—44no—
181D4×C11—42no—
182D4×C11—81no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—22no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—82no—
191C2×C4×C11#12111yescharacteristic
192C2×C4×C11#12111yescharacteristic
193C2×C4×C11#12111yescharacteristic
194C2×C4×C11#13512yes—
195C2×C4×C11AGL(1,ℤ/8)12yes—
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C22⋊D11—82no—
200C2×Dic11—41no—
201D44—41no—
202D44—41no—
203D44—41no—
204D44—41no—
205D44—81no—
206C4×D11—82no—
207Dic22—41no—
208Dic22—41no—
209C8×C11—41no—
210C8×C11—41no—
211C11⋊C8—22no—
212C11⋊C8—22no—
213C11⋊C8—41no—
214C11⋊C8—41no—
215C11⋊C8—42no—
216C2×#131—221no—
217#532—111no—
218#532C2×D1111yescharacteristic
219C2×C4⋊Q8C2×D1111yescharacteristic
220#492—21no—
221#489—222no—
222#487—21no—
223#487—112no—
224#486—112no—
225#474—112no—
226#474—221no—
227#466—222no—
228#461C2×D1112yes—
229#461C2×D1112yes—
230#459—112no—
231#459—221no—
232#448—22no—
233#436—112no—
234#435—222no—
235C8×D4—112no—
236#431C2×D1111yescharacteristic
237C2×C4⋊C8—111no—
238C2×C4⋊C8—111no—
239#417—221no—
240#417—221no—
241#408—221no—
242C4×M16—111no—
243#335—112no—
244#334—112no—
245#332—112no—
246#332—112no—
247#332—111no—
248#332—111no—
249#331—111no—
250#331—111no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—42no—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11#46312yes—
257C22×C11C2×#12111yescharacteristic
258C2×D11—81no—
259C2×D11—81no—
260C2×D11—81no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—42no—
265C4×C11—82no—
266C4×C11#46312yes—
267C4×C11C2×#13511yescharacteristic
268C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
269C4×C11#57611yescharacteristic
270C4×C11#57711yescharacteristic
271Dic11—81no—
272C2×#41—21no—
273C2×#41—221no—
274C22×Q8—21no—
275C2×SD16—22no—
276C2×SD16—22no—
277C2×D8—222no—
278#131—444no—
279C2×M16—111no—
280C2×M16—111no—
281C2×M16—222no—
282C22×C8—222no—
283C22×C8—221no—
284C22×C8—221no—
285C4⋊Q8—21no—
286C4⋊Q8—21no—
287C4⋊Q8—21no—
288C4⋊Q8—111no—
289C4⋊Q8C22⋊D1111yescharacteristic
290C4⋊Q8C22×D1112yes—
291#127—111no—
292#127C22⋊D1111yescharacteristic
293#124—21no—
294#124—221no—
295#121—21no—
296#121—221no—
297#121—221no—
298#121C22⋊D1112yes—
299C4×D4—21no—
300C4×D4—221no—
301C4×D4—221no—
302C4×D4C22×D1112yes—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C42C22×D1111yescharacteristic
306#107—222no—
307C4⋊C8—111no—
308C4⋊C8—111no—
309C4⋊C8—112no—
310C4⋊C8—221no—
311C4⋊C8—221no—
312C4⋊C8C22×D1111yescharacteristic
313C4⋊C8C22×D1111yescharacteristic
314#103—22no—
315#103—22no—
316#103—222no—
317#103—222no—
318#102—222no—
319#102—222no—
320#102—222no—
321#102—222no—
322C22⋊C8—21no—
323C22⋊C8—222no—
324C22⋊C8—222no—
325#97—112no—
326C4×C8—21no—
327C4×C8—112no—
328C2×C11—22no—
329C2×C11—82no—
330C2×C11C2×#46311yescharacteristic
331C2×C11#306211yescharacteristic
332C2×C11#306911yescharacteristic
333D11—161no—
334#41—42no—
335#41—42no—
336#41—442no—
337#41—442no—
338C2×Q8—21no—
339C2×Q8—22no—
340C2×Q8—41no—
341C2×Q8—81no—
342C2×Q8—81no—
343C2×Q8—221no—
344C2×D4—22no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—221no—
348C2×D4—221no—
349C2×D4—221no—
350C2×D4—441no—
351C2×D4C2×C22⋊D1112yes—
352C22×C4—22no—
353C22×C4—41no—
354C22×C4—441no—
355C22×C4D4×D1111yescharacteristic
356C22×C4#434111yescharacteristic
357C22×C4C2×C22⋊D1111yescharacteristic
358SD16—82no—
359SD16—82no—
360D8—882no—
361M16—222no—
362M16—222no—
363M16—444no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8—112no—
367C2×C8—112no—
368C2×C8—221no—
369C2×C8—221no—
370C2×C8—222no—
371C2×C8—444no—
372C2×C8—442no—
373C2×C8—881no—
374C4⋊C4—21no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—221no—
380C4⋊C4—221no—
381C4⋊C4C2×C22⋊D1112yes—
382C22⋊C4—22no—
383C22⋊C4—22no—
384C22⋊C4—441no—
385C22⋊C4—441no—
386C42D4×D1111yescharacteristic
387C42#434111yescharacteristic
388C42C2×C22⋊D1111yescharacteristic
389C42C23×D1111yescharacteristic
390C11#1923711yescharacteristic, complemented, Sylow
391C23—22no—
392C23—441no—
393C23#6699211yescharacteristic
394Q8—42no—
395Q8—42no—
396Q8—42no—
397Q8—82no—
398Q8—441no—
399Q8—441no—
400D4—22no—
401D4—22no—
402D4—44no—
403D4—42no—
404D4—81no—
405D4—441no—
406D4—441no—
407D4—441no—
408D4—441no—
409D4—881no—
410D4—882no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—22no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—82no—
419C2×C4—441no—
420C2×C4—882no—
421C2×C4#6696712yes—
422C2×C4#6696912yes—
423C2×C4#6699211yescharacteristic
424C2×C4#6699211yescharacteristic
425C2×C4#6699211yescharacteristic
426C2×C4C2×D4×D1111yescharacteristic
427C2×C4C2×#434111yescharacteristic
428C2×C4C22×C22⋊D1111yescharacteristic
429C8—41no—
430C8—41no—
431C8—222no—
432C8—222no—
433C8—441no—
434C8—441no—
435C8—442no—
436C22—21no—
437C22—21no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—881no—
442C22—881no—
443C22—881no—
444C22#1062277812yes—
445C22C2×#6699211yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—42no—
450C4—82no—
451C4—881no—
452C4#1062277812yes—
453C4C2×#6696711yescharacteristic
454C4C2×#6696911yescharacteristic
455C4#1062336611yescharacteristic
456C4#1062336711yescharacteristic
457C2—22no—
458C2—82no—
459C2—1761no—
460C2C2×#1062277811yescharacteristic
461C2#1307829211yescharacteristic
462C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3206C2
socleC22×C11C2×#121
prime radical#13079923C2
hypercenter#3206D11
hypocenterC11#19237
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3206

Complements

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

NH ≅ G/Ntype
2. #13079012C2semidirect
3. #13077360C2semidirect
4. #13068179C2semidirect
5. #13068165C2semidirect
6. #13068055C2semidirect
7. #13068041C2semidirect
8. #13067369C2semidirect
9. #13067263C2semidirect
10. C2×#10622185C2semidirect
11. C11×#3206C2semidirect
161. #3206D11semidirect
390. C11#19237semidirect

Maximal subgroups

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

subgroupindex
#130799232
#130790122
#130773602
#130681792
#130681652
#130680552
#130680412
#130673692
#130672632
C2×#106221852
C11×#32062
#1923711