Finite Group Databasebeta

← #14737220

Subgroups — #14737220

Order 2816.

628 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079942C212yesmaximal, complemented
2#13079195C211yesmaximal, characteristic, complemented
3#13068144C211yesmaximal, characteristic, complemented
4#13068139C211yesmaximal, characteristic, complemented
5#13068100C211yesmaximal, characteristic, complemented
6#13068095C211yesmaximal, characteristic, complemented
7#13068032C212yesmaximal, complemented
8#13068025C212yesmaximal, complemented
9C2×#10622095C211yesmaximal, characteristic, complemented
10#13067312C212yesmaximal, complemented
11C11×#2966C211yesmaximal, characteristic, complemented
12C11×#529C2211yescharacteristic
13#10623008C2212yes—
14C11×#446C2211yescharacteristic
15C8×Q8×C11C2211yescharacteristic
16C11×#436C2211yescharacteristic
17C11×#435—21no—
18C8×D4×C11—21no—
19C8×D4×C11C2211yescharacteristic
20C11×#433—21no—
21C11×#432C2211yescharacteristic
22C11×#405—21no—
23C2×C4×C8×C11C2211yescharacteristic
24#10622728—21no—
25#10622728—21no—
26#10622679—22no—
27#10622670—22no—
28#10622661—22no—
29#10622651—22no—
30#10622640C2212yes—
31#10622634C2212yes—
32#10622628C2212yes—
33#10622621C2212yes—
34C2×C4⋊(C11⋊C8)C2212yes—
35#10622308C2211yescharacteristic
36#10622307C2212yes—
37C4×D88—21no—
38C4×D88—21no—
39#10622295C2211yescharacteristic
40#10622123C2212yes—
41#10622123C2212yes—
42#10622119C2212yes—
43#10622119C2212yes—
44#10622095C2212yes—
45#10622095C2211yescharacteristic
46#10622095C2211yescharacteristic
47C2×#4339—22no—
48C2×C11×M16—21no—
49C22×C8×C11—21no—
50C22×C8×C11D411yescharacteristic
51C22×C8×C11D411yescharacteristic
52C11×#126—21no—
53C11×#125D411yescharacteristic
54C11×#124D411yescharacteristic
55C11×#123—21no—
56C11×C22⋊Q8D411yescharacteristic
57C11×#121D411yescharacteristic
58C4×Q8×C11C2311yescharacteristic
59C4×D4×C11—21no—
60C4×D4×C11C2311yescharacteristic
61C11×#117—21no—
62C2×C42×C11C2311yescharacteristic
63C2×#4325—22no—
64C2×#4323—22no—
65#66983—22no—
66#66983—22no—
67C22×C11⋊C8—22no—
68C2×D88—21no—
69C2×D88—21no—
70#66928—22no—
71#66927C2312yes—
72C4×D44—22no—
73C4×D44—22no—
74#66922C2312yes—
75C11×C4⋊C8—21no—
76C11×C4⋊C8—21no—
77C11×C4⋊C8C2311yescharacteristic
78C11×C4⋊C8C2311yescharacteristic
79C11×C22⋊C8—21no—
80C11×C22⋊C8—21no—
81C11×C22⋊C8—21no—
82C11×#97—21no—
83C11×#97—21no—
84C4×C8×C11—21no—
85C4×C8×C11D411yescharacteristic
86C4×C8×C11D411yescharacteristic
87C4×C8×C11C2311yescharacteristic
88C4×C8×C11C2311yescharacteristic
89#66899—22no—
90#66896—22no—
91#66885—22no—
92#66885—22no—
93#66882—21no—
94#66882—21no—
95#66873—22no—
96#66873—22no—
97#66872—22no—
98#66871—22no—
99C4⋊(C11⋊C8)—22no—
100C4⋊(C11⋊C8)C2312yes—
101C4⋊(C11⋊C8)C2312yes—
102#19227—111nomaximal, Sylow
103C2×Q8×C11C2×D411yescharacteristic
104C2×D4×C11—21no—
105C2×D4×C11C2×D411yescharacteristic
106C22×C4×C11—21no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11#4111yescharacteristic
110C2×C22⋊D11—42no—
111#4339—84no—
112C2×D44—22no—
113C2×D44—22no—
114C2×D44—22no—
115C2×C4×D11—42no—
116C2×Dic22—22no—
117C11×M16—42no—
118C2×C8×C11—22no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11—41no—
122C2×C8×C11—42no—
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11C2×D411yescharacteristic
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11C2×D411yescharacteristic
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4C2×D411yescharacteristic
132C11×C4⋊C4C2×D411yescharacteristic
133C11×C22⋊C4—21no—
134C11×C22⋊C4—21no—
135C11×C22⋊C4—21no—
136C11×C22⋊C4—21no—
137C11×C22⋊C4—21no—
138C42×C11—21no—
139C42×C11C2×D411yescharacteristic
140C42×C11C2×D411yescharacteristic
141C42×C11#4111yescharacteristic
142C42×C11C2411yescharacteristic
143#4325—82no—
144#4323—82no—
145(C2×D11)⋊C4—42no—
146(C2×D11)⋊C4—42no—
147C4⋊Dic11—22no—
148C4⋊Dic11—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—82no—
152D88—42no—
153D88—42no—
154#3247—112no—
155#3169—111no—
156#2966D1111yescharacteristic, complemented
157#1696—111no—
158#1695—111no—
159#1688—111no—
160#1687—111no—
161#1678—112no—
162#1677—112no—
163C2×#334—111no—
164#1551—112no—
165C23×C11—21no—
166C23×C11#12111yescharacteristic
167C22×D11—42no—
168Q8×C11—22no—
169D4×C11—22no—
170D4×C11—42no—
171C2×C4×C11—22no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—22no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11C22×D411yescharacteristic
184C2×C4×C11C22×D411yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C22⋊D11—84no—
187C2×Dic11—42no—
188D44—42no—
189D44—42no—
190D44—42no—
191D44—42no—
192D44—82no—
193C4×D11—84no—
194Dic22—82no—
195C8×C11—21no—
196C8×C11—21no—
197C8×C11—21no—
198C8×C11—41no—
199C8×C11—41no—
200C8×C11#13512yes—
201C11⋊C8—42no—
202C11⋊C8—42no—
203#532—112no—
204#529C2×D1111yescharacteristic
205#500—111no—
206#493—111no—
207#486—112no—
208#478—222no—
209#477—112no—
210#476—112no—
211#466—221no—
212#466—221no—
213#466—222no—
214#465—222no—
215#463—222no—
216#460—112no—
217#459—112no—
218#446C2×D1111yescharacteristic
219C8×Q8C2×D1111yescharacteristic
220C4×D8—221no—
221C4×D8—221no—
222#436C2×D1111yescharacteristic
223#435—21no—
224C8×D4—21no—
225C8×D4C2×D1111yescharacteristic
226#433—21no—
227#432C2×D1111yescharacteristic
228C2×C4⋊C8—112no—
229#405—21no—
230C2×C4×C8C2×D1111yescharacteristic
231#334—112no—
232#334—111no—
233#334—111no—
234#333—112no—
235#333—112no—
236#331—112no—
237#331—112no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—41no—
241C22×C11—41no—
242C22×C11—41no—
243C22×C11#47212yes—
244C22×C11C2×#12111yescharacteristic
245C2×D11—82no—
246C2×D11—82no—
247C2×D11—82no—
248C4×C11—21no—
249C4×C11—21no—
250C4×C11—21no—
251C4×C11—21no—
252C4×C11—41no—
253C4×C11—41no—
254C4×C11—41no—
255C4×C11C2×#13511yescharacteristic
256C4×C11#57511yescharacteristic
257C4×C11#57712yes—
258Dic11—82no—
259C2×#41—222no—
260C2×SD16—222no—
261C2×D8—222no—
262C2×D8—221no—
263C2×D8—221no—
264C2×M16—21no—
265C22×C8—21no—
266C22×C8—222no—
267C22×C8C22⋊D1111yescharacteristic
268C22×C8C22⋊D1111yescharacteristic
269C4⋊Q8—112no—
270#127—112no—
271#126—21no—
272#125D4411yescharacteristic
273#124—222no—
274#124D4411yescharacteristic
275#123—21no—
276C22⋊Q8D4411yescharacteristic
277#121—222no—
278#121—222no—
279#121D4411yescharacteristic
280C4×Q8C22×D1111yescharacteristic
281C4×D4—21no—
282C4×D4—222no—
283C4×D4—222no—
284C4×D4C22×D1111yescharacteristic
285#117—21no—
286C2×C42C22×D1111yescharacteristic
287#107—221no—
288#107—221no—
289#107—222no—
290#106—222no—
291C4⋊C8—21no—
292C4⋊C8—21no—
293C4⋊C8—112no—
294C4⋊C8—112no—
295C4⋊C8—222no—
296C4⋊C8C22×D1111yescharacteristic
297C4⋊C8C22×D1111yescharacteristic
298#103—222no—
299#102—222no—
300#102—222no—
301#102—222no—
302#102—222no—
303#102—222no—
304C22⋊C8—21no—
305C22⋊C8—21no—
306C22⋊C8—21no—
307#97—21no—
308#97—21no—
309C4×C8—21no—
310C4×C8C22⋊D1111yescharacteristic
311C4×C8C22⋊D1111yescharacteristic
312C4×C8C22×D1111yescharacteristic
313C4×C8C22×D1111yescharacteristic
314C2×C11—22no—
315C2×C11—81no—
316C2×C11#303511yescharacteristic
317C2×C11#306011yescharacteristic
318C2×C11C2×#47211yescharacteristic
319D11—162no—
320#41—884no—
321C2×Q8—222no—
322C2×Q8C2×D4411yescharacteristic
323C2×D4—21no—
324C2×D4—222no—
325C2×D4—222no—
326C2×D4—222no—
327C2×D4—442no—
328C2×D4C2×D4411yescharacteristic
329C22×C4—21no—
330C22×C4—442no—
331C22×C4C2×D4411yescharacteristic
332C22×C4#433911yescharacteristic
333C22×C4C2×C22⋊D1111yescharacteristic
334SD16—882no—
335D8—442no—
336D8—442no—
337D8—882no—
338M16—42no—
339C2×C8—22no—
340C2×C8—21no—
341C2×C8—21no—
342C2×C8—41no—
343C2×C8—42no—
344C2×C8—222no—
345C2×C8—222no—
346C2×C8—882no—
347C2×C8C2×C22⋊D1111yescharacteristic
348C2×C8C2×C22⋊D1111yescharacteristic
349C2×C8C2×C22⋊D1111yescharacteristic
350C2×C8C2×C22⋊D1111yescharacteristic
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—222no—
356C4⋊C4—222no—
357C4⋊C4C2×D4411yescharacteristic
358C4⋊C4C2×D4411yescharacteristic
359C22⋊C4—21no—
360C22⋊C4—21no—
361C22⋊C4—21no—
362C22⋊C4—21no—
363C22⋊C4—21no—
364C22⋊C4—442no—
365C22⋊C4—442no—
366C42—21no—
367C42C2×D4411yescharacteristic
368C42#433911yescharacteristic
369C42C2×C22⋊D1111yescharacteristic
370C42C23×D1111yescharacteristic
371C11#1922711yescharacteristic, complemented, Sylow
372C23—21no—
373C23—442no—
374C23#6698311yescharacteristic
375Q8—22no—
376Q8—882no—
377D4—22no—
378D4—42no—
379D4—442no—
380D4—442no—
381D4—442no—
382D4—442no—
383D4—882no—
384D4—884no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—442no—
395C2×C4—884no—
396C2×C4#6698311yescharacteristic
397C2×C4#6698311yescharacteristic
398C2×C4#6698311yescharacteristic
399C2×C4C22×D4411yescharacteristic
400C2×C4C2×#433911yescharacteristic
401C2×C4C22×C22⋊D1111yescharacteristic
402C8—21no—
403C8—21no—
404C8—21no—
405C8—41no—
406C8—41no—
407C8—442no—
408C8—442no—
409C8#6700312yes—
410C22—21no—
411C22—21no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—882no—
416C22—882no—
417C22—882no—
418C22#1062275512yes—
419C22C2×#6698311yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—21no—
424C4—41no—
425C4—41no—
426C4—41no—
427C4—882no—
428C4#1062328212yes—
429C4C2×#6700311yescharacteristic
430C4#1062335311yescharacteristic
431C2—22no—
432C2—81no—
433C2—1762no—
434C2#1307807111yescharacteristic
435C2#1307827811yescharacteristic
436C2C2×#1062275511yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2966C2
socleC22×C11C2×#121
hypercenter#2966D11
hypocenterC11#19227
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2966

Complements

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

NH ≅ G/Ntype
1. #13079942C2semidirect
2. #13079195C2semidirect
3. #13068144C2semidirect
4. #13068139C2semidirect
5. #13068100C2semidirect
6. #13068095C2semidirect
7. #13068032C2semidirect
8. #13068025C2semidirect
9. C2×#10622095C2semidirect
10. #13067312C2semidirect
11. C11×#2966C2semidirect
156. #2966D11semidirect
371. C11#19227semidirect

Maximal subgroups

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

subgroupindex
#130799422
#130791952
#130681442
#130681392
#130681002
#130680952
#130680322
#130680252
C2×#106220952
#130673122
C11×#29662
#1922711