Finite Group Databasebeta

← #14739092

Subgroups — #14739092

Order 2816.

632 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078734C211yesmaximal, characteristic, complemented
2#13078643C211yesmaximal, characteristic, complemented
3#13077696C211yesmaximal, characteristic, complemented
4#13068071C212yesmaximal, complemented
5#13068029C212yesmaximal, complemented
6#13067973C212yesmaximal, complemented
7#13067961C212yesmaximal, complemented
8#13067396C211yesmaximal, characteristic, complemented
9#13067321C211yesmaximal, characteristic, complemented
10#13067278C211yesmaximal, characteristic, complemented
11C11×#3207C211yesmaximal, characteristic
12C11×#532C2211yescharacteristic
13C11×#532C2211yescharacteristic
14C2×C4×Dic22C2211yescharacteristic
15C11×#493C2211yescharacteristic
16C11×#492C2211yescharacteristic
17C11×#487C2211yescharacteristic
18C11×#486C2211yescharacteristic
19C11×#463—22no—
20C11×#449—22no—
21C11×#431C2211yescharacteristic
22#10622707C2212yes—
23#10622704C2212yes—
24#10622688C2212yes—
25#10622688C2212yes—
26#10622653—21no—
27#10622653—21no—
28#10622647—21no—
29#10622646—21no—
30#10622631—22no—
31C4×#4324—22no—
32#10622539C2211yescharacteristic
33#10622538C2211yescharacteristic
34#10622538C2211yescharacteristic
35#10622443—22no—
36#10622331—22no—
37C8×Dic22C2212yes—
38C8×Dic22C2212yes—
39#10622185C2212yes—
40#10622184C2212yes—
41#10622182C2212yes—
42#10622182C2212yes—
43#10622096C2212yes—
44#10622095C2212yes—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C22×Dic22D411yescharacteristic
48C2×C11×SD16—22no—
49C2×C11×D8—22no—
50C11×C4⋊Q8C2311yescharacteristic
51C11×C4⋊Q8C2311yescharacteristic
52C11×#127C2311yescharacteristic
53C11×#127C2311yescharacteristic
54C11×#124—21no—
55C11×#124—21no—
56C11×#121—21no—
57C11×#121—21no—
58C11×#121—21no—
59C11×#121—21no—
60C4×D4×C11—21no—
61C4×D4×C11—21no—
62C4×D4×C11—21no—
63C4×D4×C11—21no—
64C2×C42×C11C2311yescharacteristic
65C2×#4324—22no—
66C2×#4324—22no—
67C2×C4⋊Dic11D411yescharacteristic
68C2×Dic11⋊C4—21no—
69C2×C4×Dic11—21no—
70C4×Dic22—21no—
71C4×Dic22—21no—
72C4×Dic22D412yes—
73C4×Dic22C2312yes—
74C11×C4⋊C8D412yes—
75C11×#103—22no—
76C11×#102—22no—
77C11×C22⋊C8D412yes—
78C4×C8×C11C2311yescharacteristic
79C4×C8×C11C2311yescharacteristic
80#66896—22no—
81#66896—22no—
82C22⋊(C11⋊C8)—21no—
83C22⋊(C11⋊C8)—21no—
84C22⋊(C11⋊C8)—21no—
85Dic11⋊C8—22no—
86Dic11⋊C8—22no—
87C8×Dic11—22no—
88C8×Dic11—22no—
89#66874—22no—
90#66874—22no—
91#66872—22no—
92#66871—22no—
93C4⋊(C11⋊C8)C2312yes—
94C4⋊(C11⋊C8)C2312yes—
95C4⋊(C11⋊C8)C2312yes—
96#66867—21no—
97C4×C11⋊C8—21no—
98C4×C11⋊C8—21no—
99#19401—111nomaximal, Sylow
100C11×#41—82no—
101C11×#41—82no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—41no—
111C2×D4×C11—41no—
112C22×C4×C11—41no—
113C22×C4×C11—41no—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11#4111yescharacteristic
117C22×Dic11—21no—
118C22×Dic11—21no—
119C2×Dic22—24no—
120C2×Dic22—21no—
121C2×Dic22C2×D412yes—
122C11×SD16—82no—
123C11×D8—82no—
124C2×C8×C11C2×D412yes—
125C2×C8×C11C2×D412yes—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—41no—
133C11×C22⋊C4—41no—
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11#4111yescharacteristic
137C42×C11C2411yescharacteristic
138#4324—44no—
139#4324—44no—
140C4⋊Dic11—21no—
141C4⋊Dic11C2×D412yes—
142Dic11⋊C4—22no—
143Dic11⋊C4—22no—
144C4×Dic11—22no—
145C4×Dic11—22no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149#3207D1111yescharacteristic
150#3112—111no—
151#3103—111no—
152#2982—111no—
153#1684—112no—
154#1678—112no—
155#1668—112no—
156#1666—112no—
157#1572—111no—
158#1553—111no—
159#1543—111no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11#12111yescharacteristic
163Q8×C11—42no—
164Q8×C11—81no—
165D4×C11—42no—
166D4×C11—42no—
167D4×C11—42no—
168D4×C11—42no—
169D4×C11—81no—
170D4×C11—81no—
171D4×C11—82no—
172D4×C11—82no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—82no—
179C2×C4×C11—82no—
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11C22×D411yescharacteristic
184C2×C4×C11C22×D411yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C2×Dic11—24no—
187C2×Dic11—22no—
188C2×Dic11—22no—
189C2×Dic11—81no—
190Dic22—24no—
191Dic22—22no—
192Dic22#13514yes—
193C8×C11—22no—
194C8×C11—22no—
195C11⋊C8—42no—
196C11⋊C8—42no—
197C11⋊C8—42no—
198#532C2×D1111yescharacteristic
199#532C2×D1111yescharacteristic
200C2×C4×Q8—111no—
201#493C2×D1111yescharacteristic
202#492C2×D1111yescharacteristic
203#487C2×D1111yescharacteristic
204#486C2×D1111yescharacteristic
205#481—221no—
206#480—221no—
207#477—112no—
208#475—112no—
209#463—22no—
210#460—112no—
211#460—112no—
212#449—22no—
213#448—221no—
214#448—221no—
215C8×Q8—112no—
216C8×Q8—112no—
217C8×Q8—222no—
218#440—222no—
219C4×SD16—222no—
220#432—111no—
221#431—111no—
222#431—111no—
223#431—222no—
224#431C2×D1111yescharacteristic
225#335—112no—
226#334—112no—
227#333—112no—
228#332—112no—
229#331—112no—
230#331—112no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—81no—
235C22×C11—81no—
236C22×C11—81no—
237C22×C11—81no—
238C22×C11—81no—
239C22×C11—81no—
240C22×C11C2×#12111yescharacteristic
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—21no—
244C4×C11—21no—
245C4×C11—81no—
246C4×C11—81no—
247C4×C11C2×#13512yes—
248C4×C11#57712yes—
249Dic11—24no—
250Dic11—42no—
251C2×#41—21no—
252C2×#41—21no—
253C22×Q8—111no—
254C2×SD16—22no—
255C2×SD16—222no—
256C2×SD16—222no—
257C2×D8—22no—
258C4⋊Q8C22×D1111yescharacteristic
259C4⋊Q8C22×D1111yescharacteristic
260#127C22×D1111yescharacteristic
261#127C22×D1111yescharacteristic
262#124—21no—
263#124—21no—
264#121—21no—
265#121—21no—
266#121—21no—
267#121—21no—
268C4×Q8—112no—
269C4×Q8—112no—
270C4×Q8—221no—
271C4×Q8—221no—
272C4×D4—21no—
273C4×D4—21no—
274C4×D4—21no—
275C4×D4—21no—
276C2×C4⋊C4—111no—
277C2×C4⋊C4—221no—
278C2×C42—221no—
279C2×C42C22×D1111yescharacteristic
280#107—222no—
281#106—222no—
282C4⋊C8—112no—
283C4⋊C8—112no—
284C4⋊C8—112no—
285C4⋊C8—222no—
286C4⋊C8—222no—
287C4⋊C8C22⋊D1112yes—
288#103—22no—
289#103—222no—
290#103—222no—
291#102—22no—
292#102—222no—
293#102—222no—
294C22⋊C8—221no—
295C22⋊C8—221no—
296C22⋊C8—221no—
297C22⋊C8C22⋊D1112yes—
298#97—221no—
299C4×C8—222no—
300C4×C8—222no—
301C4×C8—221no—
302C4×C8—221no—
303C4×C8C22×D1111yescharacteristic
304C4×C8C22×D1111yescharacteristic
305C2×C11—41no—
306C2×C11—161no—
307C2×C11—161no—
308C2×C11#304311yescharacteristic
309C2×C11#305011yescharacteristic
310C2×C11#306811yescharacteristic
311#41—82no—
312#41—82no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—112no—
316C2×Q8—224no—
317C2×Q8—221no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—41no—
325C2×D4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—221no—
329C22×C4—221no—
330C22×C4D4×D1111yescharacteristic
331C22×C4#434111yescharacteristic
332C22×C4C2×C22⋊D1111yescharacteristic
333SD16—82no—
334SD16—444no—
335SD16—444no—
336D8—82no—
337C2×C8—222no—
338C2×C8—222no—
339C2×C8—222no—
340C2×C8C2×C22⋊D1112yes—
341C2×C8C2×C22⋊D1112yes—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—112no—
347C4⋊C4—221no—
348C4⋊C4—222no—
349C4⋊C4—222no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C42—222no—
355C42—222no—
356C42D4×D1111yescharacteristic
357C42#434111yescharacteristic
358C42C2×C22⋊D1111yescharacteristic
359C42C23×D1111yescharacteristic
360C11#1940111yescharacteristic, complemented, Sylow
361C23—41no—
362C23—41no—
363C23#6699111yescharacteristic
364Q8—42no—
365Q8—81no—
366Q8—114no—
367Q8—224no—
368Q8—222no—
369D4—42no—
370D4—42no—
371D4—42no—
372D4—42no—
373D4—81no—
374D4—81no—
375D4—82no—
376D4—82no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—82no—
383C2×C4—82no—
384C2×C4—224no—
385C2×C4—222no—
386C2×C4—222no—
387C2×C4—881no—
388C2×C4#6699111yescharacteristic
389C2×C4#6699111yescharacteristic
390C2×C4#6699111yescharacteristic
391C2×C4C2×D4×D1111yescharacteristic
392C2×C4C2×#434111yescharacteristic
393C2×C4C22×C22⋊D1111yescharacteristic
394C8—22no—
395C8—22no—
396C8—442no—
397C8—442no—
398C8—442no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22C2×#6699111yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—81no—
414C4—81no—
415C4—224no—
416C4—442no—
417C4D11×#13512yes—
418C4#1062336712yes—
419C2—41no—
420C2—161no—
421C2—161no—
422C2#1307813311yescharacteristic
423C2#1307819311yescharacteristic
424C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3207C2
socleC22×C11C2×#121
hypercenter#3207D11
hypocenterC11#19401
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3207

Complements

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

NH ≅ G/Ntype
1. #13078734C2semidirect
2. #13078643C2semidirect
3. #13077696C2semidirect
4. #13068071C2semidirect
5. #13068029C2semidirect
6. #13067973C2semidirect
7. #13067961C2semidirect
8. #13067396C2semidirect
9. #13067321C2semidirect
10. #13067278C2semidirect
360. C11#19401semidirect

Maximal subgroups

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

subgroupindex
#130787342
#130786432
#130776962
#130680712
#130680292
#130679732
#130679612
#130673962
#130673212
#130672782
C11×#32072
#1940111