Finite Group Databasebeta

← #14739194

Subgroups — #14739194

Order 2816.

620 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078425C211yesmaximal, characteristic
2#13078398C211yesmaximal, characteristic
3#13077724C211yesmaximal, characteristic
4#13068071C212yesmaximal, complemented
5#13068064C212yesmaximal, complemented
6#13067983C212yesmaximal, complemented
7#13067978C212yesmaximal, complemented
8#13067391C211yesmaximal, characteristic, complemented
9#13067306C211yesmaximal, characteristic, complemented
10C2×#10622185C211yesmaximal, characteristic, complemented
11C11×#3209C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C4×#4339C2211yescharacteristic
15C11×#494C2212yes—
16C11×#487C2212yes—
17C11×#462—21no—
18C11×#462—21no—
19C11×#451—22no—
20C11×#431C2211yescharacteristic
21#10622707C2212yes—
22#10622707C2211yescharacteristic
23#10622704—21no—
24#10622704C2211yescharacteristic
25#10622700C2212yes—
26#10622700C2211yescharacteristic
27#10622697—21no—
28#10622697C2211yescharacteristic
29#10622679—21no—
30#10622676—21no—
31#10622615—21no—
32#10622611—21no—
33#10622579—21no—
34#10622577—21no—
35#10622537C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622446—21no—
39D11×C4⋊C8—21no—
40(C22⋊D11)⋊C8—22no—
41C8×D44C2212yes—
42C8×Dic22C2212yes—
43#10622185C2212yes—
44#10622185C2212yes—
45#10622185C2212yes—
46#10622184C2212yes—
47#10622096C2212yes—
48#10622096C2212yes—
49C22×Q8×C11—21no—
50C2×#4339D411yescharacteristic
51C2×C11×Q16—22no—
52C2×C11×Q16—22no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8C2311yescharacteristic
57C11×C4⋊Q8C2312yes—
58C11×C4⋊Q8C2311yescharacteristic
59C11×#125—21no—
60C11×C22⋊Q8—21no—
61C11×C22⋊Q8—21no—
62C4×Q8×C11—21no—
63C4×Q8×C11—21no—
64C11×#117—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C42×C11C2311yescharacteristic
68C4×C22⋊D11—21no—
69C4×C22⋊D11—21no—
70#66979D411yescharacteristic
71C2×#4318—21no—
72C22×C11⋊C8—21no—
73C22×C11⋊C8—21no—
74C2×C8×D11—22no—
75C4×D44D411yescharacteristic
76C4×D44C2311yescharacteristic
77#66925—21no—
78C42×D11—21no—
79C4×Dic22D411yescharacteristic
80C4×Dic22C2311yescharacteristic
81C11×C4⋊C8D411yescharacteristic
82C11×C4⋊C8D411yescharacteristic
83C11×#103—22no—
84C11×#103—22no—
85C11×C22⋊C8D412yes—
86C4×C8×C11C2312yes—
87(C2×D11)⋊C8—22no—
88Dic11⋊C8—22no—
89C8×Dic11—22no—
90#66874—22no—
91#66874—21no—
92#66874—21no—
93#66873—22no—
94#66873—21no—
95#66873—21no—
96#66872—22no—
97#66872—21no—
98#66872—21no—
99#66871—22no—
100#66871—21no—
101#66871—21no—
102C4⋊(C11⋊C8)—21no—
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)C2312yes—
106C4⋊(C11⋊C8)C2311yescharacteristic
107C4⋊(C11⋊C8)C2311yescharacteristic
108C4⋊(C11⋊C8)C2312yes—
109#19411—111nomaximal, Sylow
110C2×Q8×C11—22no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—41no—
114C2×Q8×C11—81no—
115C2×Q8×C11—81no—
116C22×C4×C11—41no—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11#4111yescharacteristic
120C2×C22⋊D11—21no—
121#4339—22no—
122#4339Q1614yescomplemented
123C2×D44C2×D411yescharacteristic
124C2×C4×D11—21no—
125C2×C4×D11—21no—
126C2×C4×D11—21no—
127C2×Dic22C2×D411yescharacteristic
128C11×Q16—82no—
129C11×Q16—82no—
130C2×C8×C11C2×D412yes—
131C2×C8×C11C2×D412yes—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—41no—
139C11×C4⋊C4—41no—
140C11×C4⋊C4—41no—
141C11×C4⋊C4—41no—
142C11×C22⋊C4—41no—
143C42×C11—41no—
144C42×C11C2×D411yescharacteristic
145C42×C11C2×D411yescharacteristic
146C42×C11#4111yescharacteristic
147C42×C11C2411yescharacteristic
148C22⋊Dic11—21no—
149(C2×D11)⋊C4—21no—
150(C2×D11)⋊C4—21no—
151C4⋊Dic11C2×D411yescharacteristic
152C4⋊Dic11C2×D411yescharacteristic
153Dic11⋊C4—21no—
154Dic11⋊C4—21no—
155C4×Dic11—21no—
156C4×Dic11—21no—
157C4×Dic11—21no—
158#4318—42no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—42no—
164C2×C11⋊C8—81no—
165C8×D11—82no—
166#3209D1111yescharacteristic, complemented
167#3079—111no—
168#3076—111no—
169#2988—111no—
170#1684—112no—
171#1683—112no—
172#1670—112no—
173#1669—112no—
174#1571—111no—
175#1550—111no—
176C2×#332—111no—
177C23×C11#12111yescharacteristic
178C22×D11—21no—
179Q8×C11—41no—
180Q8×C11—42no—
181Q8×C11—41no—
182Q8×C11—42no—
183Q8×C11—81no—
184Q8×C11—82no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—42no—
191C2×C4×C11—82no—
192C2×C4×C11#12111yescharacteristic
193C2×C4×C11#12111yescharacteristic
194C2×C4×C11#12111yescharacteristic
195C2×C4×C11C2×Q1612yes—
196C2×C4×C11#13512yes—
197C2×C4×C11C22×D411yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C22⋊D11—24no—
201C2×Dic11—21no—
202C2×Dic11—21no—
203C2×Dic11—21no—
204D44—21no—
205D44C2×Q1612yes—
206C4×D11—24no—
207C4×D11—41no—
208C4×D11—41no—
209C4×D11—81no—
210Dic22—21no—
211Dic22C2×Q1612yes—
212C8×C11—22no—
213C8×C11—22no—
214C11⋊C8—41no—
215C11⋊C8—41no—
216C11⋊C8—42no—
217C11⋊C8—42no—
218#533C2×D1111yescharacteristic
219C2×C4⋊Q8C2×D1111yescharacteristic
220C4×#41—111no—
221#494C2×D1112yes—
222#487C2×D1112yes—
223#479—221no—
224#478—221no—
225#477—111no—
226#477—221no—
227#476—111no—
228#476—221no—
229#475—111no—
230#475—112no—
231#474—111no—
232#474—112no—
233#462—21no—
234#462—21no—
235#451—22no—
236C8×Q8—112no—
237C8×D4—112no—
238C8×D4—222no—
239#431—221no—
240#431C2×D1111yescharacteristic
241#428—221no—
242#427—221no—
243#423—111no—
244C2×C4⋊C8—111no—
245C2×C4⋊C8—111no—
246C2×C4⋊C8—221no—
247#417—221no—
248#416—221no—
249#335—112no—
250#335—112no—
251#333—112no—
252#332—112no—
253#332—112no—
254#332—112no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11#46712yes—
258C22×C11C2×#12111yescharacteristic
259C2×D11—22no—
260C2×D11—41no—
261C2×D11—41no—
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—82no—
266C4×C11—81no—
267C4×C11—81no—
268C4×C11#46712yes—
269C4×C11C22×Q1611yescharacteristic
270C4×C11C2×#13511yescharacteristic
271C4×C11#57611yescharacteristic
272C4×C11#57711yescharacteristic
273Dic11—22no—
274Dic11—41no—
275Dic11—41no—
276C2×#41—111no—
277C22×Q8—21no—
278C2×Q16—22no—
279C2×Q16—22no—
280C2×M16—221no—
281C22×C8—221no—
282C22×C8—221no—
283C22×C8—222no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8—21no—
287C4⋊Q8C22×D1112yes—
288C4⋊Q8C22×D1111yescharacteristic
289C4⋊Q8C22×D1111yescharacteristic
290#125—21no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×Q8—111no—
296C4×Q8—111no—
297C4×D4—111no—
298C4×D4—111no—
299C4×D4—221no—
300C4×D4—221no—
301#117—21no—
302#117—111no—
303#117—221no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C42—221no—
307C2×C42C22×D1111yescharacteristic
308#107—221no—
309#107—221no—
310#107—222no—
311#106—221no—
312#106—221no—
313#106—222no—
314C4⋊C8—112no—
315C4⋊C8—111no—
316C4⋊C8—111no—
317C4⋊C8—112no—
318C4⋊C8—222no—
319C4⋊C8—221no—
320C4⋊C8—221no—
321C4⋊C8—221no—
322C4⋊C8C22⋊D1111yescharacteristic
323C4⋊C8C22⋊D1111yescharacteristic
324#103—22no—
325#103—22no—
326#103—221no—
327#103—221no—
328#103—222no—
329#102—221no—
330#102—221no—
331#102—222no—
332C22⋊C8—222no—
333C22⋊C8C22⋊D1112yes—
334C4×C8—222no—
335C4×C8C22×D1112yes—
336C2×C11—22no—
337C2×C11#304511yescharacteristic
338C2×C11C2×#46711yescharacteristic
339C2×C11#306911yescharacteristic
340D11—42no—
341#41—114no—
342#41—222no—
343C2×Q8—21no—
344C2×Q8—22no—
345C2×Q8—21no—
346C2×Q8—41no—
347C2×Q8—81no—
348C2×Q8—81no—
349C2×Q8—111no—
350C2×D4—111no—
351C2×D4—221no—
352C22×C4—41no—
353C22×C4—221no—
354C22×C4—221no—
355C22×C4—221no—
356C22×C4D4×D1111yescharacteristic
357C22×C4#434111yescharacteristic
358C22×C4C2×C22⋊D1111yescharacteristic
359Q16—82no—
360Q16—82no—
361M16—442no—
362C2×C8—221no—
363C2×C8—222no—
364C2×C8—221no—
365C2×C8—222no—
366C2×C8—442no—
367C2×C8—882no—
368C2×C8—881no—
369C2×C8C2×C22⋊D1112yes—
370C2×C8C2×C22⋊D1112yes—
371C4⋊C4—22no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—22no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—111no—
382C4⋊C4—111no—
383C4⋊C4—221no—
384C4⋊C4—221no—
385C22⋊C4—41no—
386C22⋊C4—221no—
387C22⋊C4—221no—
388C22⋊C4—221no—
389C42—41no—
390C42—221no—
391C42—221no—
392C42—221no—
393C42D4×D1111yescharacteristic
394C42#434111yescharacteristic
395C42C2×C22⋊D1111yescharacteristic
396C42C23×D1111yescharacteristic
397C11#1941111yescharacteristic, complemented, Sylow
398C23—221no—
399C23#6699111yescharacteristic
400Q8—41no—
401Q8—42no—
402Q8—41no—
403Q8—42no—
404Q8—81no—
405Q8—82no—
406Q8—112no—
407Q8—221no—
408D4—112no—
409D4—224no—
410D4—221no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—82no—
418C2×C4—221no—
419C2×C4—224no—
420C2×C4—221no—
421C2×C4—221no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—881no—
425C2×C4Q16×D1112yes—
426C2×C4#6697212yes—
427C2×C4#6699111yescharacteristic
428C2×C4#6699111yescharacteristic
429C2×C4#6699111yescharacteristic
430C2×C4C2×D4×D1111yescharacteristic
431C2×C4C2×#434111yescharacteristic
432C2×C4C22×C22⋊D1111yescharacteristic
433C8—22no—
434C8—22no—
435C8—441no—
436C8—441no—
437C8—442no—
438C8—442no—
439C22—21no—
440C22—21no—
441C22—222no—
442C22—441no—
443C22—441no—
444C22#1062280112yes—
445C22C2×#6699111yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—81no—
450C4—82no—
451C4—81no—
452C4—222no—
453C4—441no—
454C4—441no—
455C4#1062280112yes—
456C4C2×Q16×D1111yescharacteristic
457C4C2×#6697211yescharacteristic
458C4#1062336611yescharacteristic
459C4#1062336711yescharacteristic
460C2—22no—
461C2—442no—
462C2#1307815111yescharacteristic
463C2C2×#1062280111yescharacteristic
464C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3209C2
socleC22×C11C2×#121
prime radicalC2×#4339D4
hypercenter#3209D11
hypocenterC11#19411
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3209

Complements

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

NH ≅ G/Ntype
4. #13068071C2semidirect
5. #13068064C2semidirect
6. #13067983C2semidirect
7. #13067978C2semidirect
8. #13067391C2semidirect
9. #13067306C2semidirect
10. C2×#10622185C2semidirect
11. C11×#3209C2semidirect
122. #4339Q16semidirect
166. #3209D11semidirect
397. C11#19411semidirect

Maximal subgroups

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

subgroupindex
#130784252
#130783982
#130777242
#130680712
#130680642
#130679832
#130679782
#130673912
#130673062
C2×#106221852
C11×#32092
#1941111