Finite Group Databasebeta

← #14737321

Subgroups — #14737321

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#13079741C211yesmaximal, characteristic, complemented
3#13079010C211yesmaximal, characteristic, complemented
4#13068191C212yesmaximal, complemented
5#13068149C212yesmaximal, complemented
6#13068067C212yesmaximal, complemented
7#13068025C212yesmaximal, complemented
8#13067368C211yesmaximal, characteristic, complemented
9C2×#10622119C211yesmaximal, characteristic, complemented
10#13067266C211yesmaximal, characteristic, complemented
11C11×#2935C211yesmaximal, characteristic, complemented
12C2×C11×#131—21no—
13C11×#532C2211yescharacteristic
14#10623008C2211yescharacteristic
15C2×#66922C2211yescharacteristic
16C11×#436C2212yes—
17C11×#435—22no—
18C8×D4×C11C2212yes—
19C2×C11×C4⋊C8C2211yescharacteristic
20C11×#408—21no—
21C4×C11×M16C2211yescharacteristic
22#10622746—21no—
23#10622746—21no—
24#10622700—21no—
25#10622692—21no—
26#10622685—21no—
27#10622683—21no—
28#10622651—22no—
29#10622647—22no—
30#10622628C2212yes—
31#10622621C2212yes—
32#10622621C2212yes—
33#10622620C2212yes—
34#10622538C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622327—22no—
37#10622307C2212yes—
38#10622294C2212yes—
39#10622123C2211yescharacteristic
40#10622123C2211yescharacteristic
41#10622120C2211yescharacteristic
42#10622120C2211yescharacteristic
43#10622119C2212yes—
44#10622119C2212yes—
45#10622096C2212yes—
46#10622095C2212yes—
47C2×C11×#41—21no—
48C2×#4339—21no—
49C22×Dic22—21no—
50C11×#131—44no—
51C2×C11×M16—22no—
52C2×C11×M16D411yescharacteristic
53C2×C11×M16D411yescharacteristic
54C22×C8×C11—21no—
55C22×C8×C11—22no—
56C11×C4⋊Q8D411yescharacteristic
57C11×#127D411yescharacteristic
58C11×#124—21no—
59C11×#121—21no—
60C11×#121D412yes—
61C4×D4×C11—21no—
62C4×D4×C11C2312yes—
63C2×C42×C11C2311yescharacteristic
64C2×#4323—22no—
65#66983—21no—
66#66983—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C22×C11⋊C8—21no—
70#66928—21no—
71#66927C2311yescharacteristic
72C4×D44—21no—
73C4×D44—21no—
74#66922—21no—
75#66922—21no—
76#66922—21no—
77#66922C2312yes—
78#66922C2311yescharacteristic
79C11×C4⋊C8—21no—
80C11×C4⋊C8C2311yescharacteristic
81C11×C4⋊C8C2311yescharacteristic
82C11×C22⋊C8—22no—
83C11×C22⋊C8—22no—
84C11×#97D412yes—
85C4×C8×C11C2312yes—
86#66896—22no—
87#66896—22no—
88#66896—22no—
89C22⋊(C11⋊C8)—21no—
90#66885—22no—
91#66885—22no—
92#66880—22no—
93#66880—22no—
94#66873—22no—
95#66872—22no—
96#66872—22no—
97#66871—22no—
98C4⋊(C11⋊C8)—21no—
99C4⋊(C11⋊C8)C2312yes—
100C4⋊(C11⋊C8)C2311yescharacteristic
101C4⋊(C11⋊C8)C2311yescharacteristic
102C4×C11⋊C8—21no—
103#19236—111nomaximal, Sylow
104C11×#41—42no—
105C11×#41—42no—
106C2×Q8×C11—21no—
107C2×D4×C11—22no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11C2×D412yes—
111C22×C4×C11—22no—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11#4111yescharacteristic
115C2×C22⋊D11—41no—
116C22×Dic11—41no—
117#4339—42no—
118#4339—42no—
119C2×D44—21no—
120C2×D44—21no—
121C2×D44—21no—
122C2×C4×D11—41no—
123C2×Dic22—21no—
124C2×Dic22—22no—
125C2×Dic22—41no—
126C2×Dic22—82no—
127C11×M16—22no—
128C11×M16—22no—
129C11×M16—44no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—44no—
133C2×C8×C11—42no—
134C2×C8×C11C2×D412yes—
135C2×C8×C11C2×D412yes—
136C11×C4⋊C4—21no—
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—22no—
149C4⋊Dic11—22no—
150C4⋊Dic11—21no—
151C4⋊Dic11—41no—
152C4⋊Dic11—41no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—81no—
157#3245—111no—
158#3227—111no—
159#3141—111no—
160#2935D1111yescharacteristic, complemented
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—
172D4×C11—22no—
173D4×C11—22no—
174D4×C11—44no—
175D4×C11—42no—
176D4×C11—81no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—22no—
180C2×C4×C11—41no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#13512yes—
187C2×C4×C11AGL(1,ℤ/8)12yes—
188C2×C4×C11C22×D411yescharacteristic
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C2×#4111yescharacteristic
191C22⋊D11—82no—
192C2×Dic11—42no—
193C2×Dic11—41no—
194C2×Dic11—82no—
195D44—41no—
196D44—41no—
197D44—41no—
198D44—41no—
199D44—81no—
200C4×D11—82no—
201Dic22—41no—
202Dic22—41no—
203Dic22—82no—
204Dic22—82no—
205C8×C11—22no—
206C8×C11—22no—
207C8×C11—41no—
208C8×C11—41no—
209C11⋊C8—41no—
210C11⋊C8—42no—
211C11⋊C8—41no—
212C2×#131—21no—
213#532—111no—
214#532C2×D1111yescharacteristic
215C2×C4⋊Q8—111no—
216#498—221no—
217#489—222no—
218#487—112no—
219#486—112no—
220#486—221no—
221#481—222no—
222#476—112no—
223#476—112no—
224#474—112no—
225#474—221no—
226#466—222no—
227#459—112no—
228#459—221no—
229#436C2×D1112yes—
230#435—22no—
231C8×D4C2×D1112yes—
232#431—111no—
233C2×C4⋊C8—111no—
234C2×C4⋊C8C2×D1111yescharacteristic
235#417—221no—
236#417—221no—
237#408—21no—
238C4×M16C2×D1111yescharacteristic
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#46312yes—
262C4×C11C2×#13511yescharacteristic
263C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
264C4×C11#57711yescharacteristic
265C4×C11#57811yescharacteristic
266Dic11—81no—
267Dic11—82no—
268C2×#41—21no—
269C2×#41—221no—
270C22×Q8—221no—
271C2×D8—222no—
272#131—44no—
273C2×M16—22no—
274C2×M16C22⋊D1111yescharacteristic
275C2×M16C22⋊D1111yescharacteristic
276C22×C8—21no—
277C22×C8—22no—
278C22×C8—221no—
279C4⋊Q8—112no—
280C4⋊Q8—111no—
281C4⋊Q8—221no—
282C4⋊Q8—221no—
283C4⋊Q8—221no—
284C4⋊Q8D4411yescharacteristic
285#127—111no—
286#127D4411yescharacteristic
287#124—21no—
288#124—221no—
289#121—21no—
290#121—221no—
291#121—221no—
292#121D4412yes—
293C4×D4—21no—
294C4×D4—221no—
295C4×D4—221no—
296C4×D4C22×D1112yes—
297C2×C4⋊C4—221no—
298C2×C4⋊C4—221no—
299C2×C42C22×D1111yescharacteristic
300#107—222no—
301#106—222no—
302#106—222no—
303C4⋊C8—21no—
304C4⋊C8—111no—
305C4⋊C8—111no—
306C4⋊C8—112no—
307C4⋊C8—221no—
308C4⋊C8C22×D1111yescharacteristic
309C4⋊C8C22×D1111yescharacteristic
310#103—222no—
311#103—222no—
312#102—222no—
313#102—222no—
314#102—222no—
315#102—222no—
316#102—222no—
317#102—222no—
318C22⋊C8—22no—
319C22⋊C8—22no—
320C22⋊C8—221no—
321#97C22⋊D1112yes—
322C4×C8—221no—
323C4×C8C22×D1112yes—
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—222no—
336C2×Q8—221no—
337C2×Q8—441no—
338C2×Q8—882no—
339C2×D4—22no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—221no—
343C2×D4—221no—
344C2×D4—221no—
345C2×D4—441no—
346C2×D4C2×D4412yes—
347C22×C4—22no—
348C22×C4—441no—
349C22×C4—441no—
350C22×C4C2×D4411yescharacteristic
351C22×C4#433911yescharacteristic
352C22×C4C2×C22⋊D1111yescharacteristic
353D8—882no—
354M16—22no—
355M16—22no—
356M16—44no—
357C2×C8—21no—
358C2×C8—21no—
359C2×C8—44no—
360C2×C8—42no—
361C2×C8—221no—
362C2×C8—221no—
363C2×C8—222no—
364C2×C8—881no—
365C2×C8C2×C22⋊D1112yes—
366C2×C8C2×C22⋊D1112yes—
367C4⋊C4—21no—
368C4⋊C4—222no—
369C4⋊C4—221no—
370C4⋊C4—221no—
371C4⋊C4—222no—
372C4⋊C4—441no—
373C4⋊C4—441no—
374C4⋊C4C2×D4412yes—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—441no—
378C22⋊C4—441no—
379C42C2×D4411yescharacteristic
380C42#433911yescharacteristic
381C42C2×C22⋊D1111yescharacteristic
382C42C23×D1111yescharacteristic
383C11#1923611yescharacteristic, complemented, Sylow
384C23—22no—
385C23—441no—
386C23#6698311yescharacteristic
387Q8—42no—
388Q8—441no—
389Q8—441no—
390Q8—882no—
391Q8—882no—
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—441no—
410C2×C4—442no—
411C2×C4—882no—
412C2×C4—882no—
413C2×C4#6698311yescharacteristic
414C2×C4#6698311yescharacteristic
415C2×C4#6698311yescharacteristic
416C2×C4#6698512yes—
417C2×C4#6700312yes—
418C2×C4C22×D4411yescharacteristic
419C2×C4C2×#433911yescharacteristic
420C2×C4C22×C22⋊D1111yescharacteristic
421C8—22no—
422C8—22no—
423C8—41no—
424C8—41no—
425C8—442no—
426C8—441no—
427C8—441no—
428C22—21no—
429C22—21no—
430C22—42no—
431C22—42no—
432C22—42no—
433C22—881no—
434C22—881no—
435C22—881no—
436C22#1062262912yes—
437C22C2×#6698311yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—42no—
442C4—881no—
443C4—882no—
444C4#1062262912yes—
445C4#1062328211yescharacteristic
446C4#1062328411yescharacteristic
447C4C2×#6698511yescharacteristic
448C4C2×#6700311yescharacteristic
449C2—22no—
450C2—82no—
451C2—1761no—
452C2C2×#1062262911yescharacteristic
453C2#1307830711yescharacteristic
454C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2935C2
socleC22×C11C2×#121
prime radical#13079923C2
hypercenter#2935D11
hypocenterC11#19236
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2935

Complements

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

NH ≅ G/Ntype
2. #13079741C2semidirect
3. #13079010C2semidirect
4. #13068191C2semidirect
5. #13068149C2semidirect
6. #13068067C2semidirect
7. #13068025C2semidirect
8. #13067368C2semidirect
9. C2×#10622119C2semidirect
10. #13067266C2semidirect
11. C11×#2935C2semidirect
160. #2935D11semidirect
383. C11#19236semidirect

Maximal subgroups

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

subgroupindex
#130799232
#130797412
#130790102
#130681912
#130681492
#130680672
#130680252
#130673682
C2×#106221192
#130672662
C11×#29352
#1923611