Finite Group Databasebeta

← #14738579

Subgroups — #14738579

Order 2816.

608 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079645C211yesmaximal, characteristic
2#13079643C211yesmaximal, characteristic
3C2×#10622691C211yesmaximal, characteristic, complemented
4#13077585C211yesmaximal, characteristic
5#13068133C212yesmaximal, complemented
6#13068128C212yesmaximal, complemented
7#13068009C212yesmaximal, complemented
8#13068004C212yesmaximal, complemented
9#13067377C211yesmaximal, characteristic, complemented
10#13067332C211yesmaximal, characteristic, complemented
11C11×#1556C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13#10623010C2211yescharacteristic
14C2×#66922C2211yescharacteristic
15C11×#432C2211yescharacteristic
16C11×#432C2211yescharacteristic
17#10622841—21no—
18#10622840—21no—
19#10622703C2212yes—
20#10622699—21no—
21#10622696C2212yes—
22#10622695—21no—
23#10622691—21no—
24#10622691—21no—
25#10622691C2212yes—
26#10622691C2212yes—
27C2×#66871—21no—
28C2×#66871—21no—
29#10622539C2211yescharacteristic
30C2×C4×C11⋊C8C2211yescharacteristic
31#10622462C2212yes—
32#10622454C2212yes—
33#10622451C2211yescharacteristic
34#10622447C2211yescharacteristic
35#10622444C2211yescharacteristic
36#10622443C2211yescharacteristic
37#10622352—21no—
38#10622351—21no—
39#10622343—21no—
40(C22⋊D11)⋊C8—21no—
41#10622328—21no—
42#10622322—21no—
43#10622321—21no—
44#10622316—21no—
45C11×#332C2212yes—
46C11×#332C2212yes—
47#10622124C2212yes—
48#10622124C2212yes—
49#10622118C2212yes—
50#10622117C2212yes—
51C22×Q8×C11—21no—
52C22×Dic22—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8C2312yes—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C42×C11C2311yescharacteristic
60C2×#4326—22no—
61C2×#4325—22no—
62#66983D411yescharacteristic
63#66982—21no—
64C4×C22⋊D11—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—21no—
67#66977D411yescharacteristic
68C22×C11⋊C8D411yescharacteristic
69C22×C11⋊C8D411yescharacteristic
70C2×Dic44—22no—
71C2×#4314—22no—
72C2×#4313—21no—
73C2×C8×D11—21no—
74#66929—21no—
75#66928D411yescharacteristic
76C4×D44C2311yescharacteristic
77#66925—21no—
78#66923D411yescharacteristic
79#66922—21no—
80#66922—21no—
81#66922—21no—
82#66922C2312yes—
83C4×Dic22C2311yescharacteristic
84C11×C4⋊C8C2312yes—
85C11×C4⋊C8C2311yescharacteristic
86C11×C4⋊C8C2311yescharacteristic
87C11×C22⋊C8—21no—
88C11×C22⋊C8—21no—
89C11×#97—21no—
90C11×#97—21no—
91#66899—22no—
92#66899—22no—
93C22⋊(C11⋊C8)—21no—
94(C2×D11)⋊C8—21no—
95(C2×D11)⋊C8—21no—
96#66880—22no—
97#66880—22no—
98#66879—21no—
99Dic11⋊C8—21no—
100Dic11⋊C8—21no—
101C8×Dic11—21no—
102#66871—22no—
103#66871—22no—
104#66871—22no—
105#66871—22no—
106C4⋊(C11⋊C8)C2312yes—
107#66867—21no—
108C4×C11⋊C8D411yescharacteristic
109C4×C11⋊C8D411yescharacteristic
110C4×C11⋊C8C2311yescharacteristic
111C4×C11⋊C8C2311yescharacteristic
112#19358—111nomaximal, Sylow
113C2×Q8×C11—22no—
114C2×Q8×C11—41no—
115C2×Q8×C11—82no—
116C22×C4×C11—41no—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11#4111yescharacteristic
120C2×C22⋊D11—21no—
121C22×Dic11—41no—
122C2×D44C2×D411yescharacteristic
123C2×C4×D11—21no—
124C2×Dic22—22no—
125C2×Dic22—41no—
126C2×Dic22—82no—
127C2×Dic22C2×D411yescharacteristic
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—41no—
134C11×C4⋊C4—41no—
135C42×C11C2×D411yescharacteristic
136C42×C11C2×D411yescharacteristic
137C42×C11#4111yescharacteristic
138C42×C11C2411yescharacteristic
139C22⋊Dic11—21no—
140#4326—82no—
141#4325—82no—
142(C2×D11)⋊C4—21no—
143(C2×D11)⋊C4—21no—
144(C2×D11)⋊C4—21no—
145(C2×D11)⋊C4—21no—
146C4⋊Dic11—22no—
147C4⋊Dic11—22no—
148C4⋊Dic11—41no—
149C4⋊Dic11—41no—
150C4⋊Dic11C2×D411yescharacteristic
151C4⋊Dic11C2×D411yescharacteristic
152Dic11⋊C4—21no—
153Dic11⋊C4—21no—
154Dic11⋊C4—21no—
155Dic11⋊C4—21no—
156C4×Dic11—21no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8C2×D411yescharacteristic
161C2×C11⋊C8C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163C2×C11⋊C8C2×D411yescharacteristic
164Dic44—82no—
165#4314—82no—
166#4313—42no—
167C8×D11—42no—
168#3218—111no—
169#3218—111no—
170C2×#500—111no—
171#2966—111no—
172#1694—112no—
173#1693—112no—
174#1674—112no—
175#1673—112no—
176#1568—111no—
177#1556—111no—
178#1556D1111yescharacteristic, complemented
179C23×C11#12111yescharacteristic
180C22×D11—21no—
181Q8×C11—42no—
182Q8×C11—42no—
183Q8×C11—82no—
184C2×C4×C11—22no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—22no—
188C2×C4×C11—42no—
189C2×C4×C11—82no—
190C2×C4×C11#12111yescharacteristic
191C2×C4×C11#12111yescharacteristic
192C2×C4×C11#12111yescharacteristic
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C22⋊D11—42no—
197C2×Dic11—21no—
198C2×Dic11—21no—
199C2×Dic11—21no—
200C2×Dic11—42no—
201C2×Dic11—82no—
202D44—22no—
203C4×D11—41no—
204C4×D11—41no—
205Dic22—22no—
206Dic22—42no—
207Dic22—42no—
208Dic22—82no—
209C8×C11—41no—
210C8×C11—41no—
211C8×C11—42no—
212C11⋊C8—21no—
213C11⋊C8—21no—
214C11⋊C8—42no—
215C11⋊C8#13712yes—
216C11⋊C8#13712yes—
217C2×C4⋊Q8—111no—
218C2×C4⋊Q8C2×D1111yescharacteristic
219#529—111no—
220#500—112no—
221#500—112no—
222#500—221no—
223#500—221no—
224#497—221no—
225#497—221no—
226#491—221no—
227#491—221no—
228#462—112no—
229#462—112no—
230#461—112no—
231#461—112no—
232#451—221no—
233#451—221no—
234#448—221no—
235#448—221no—
236#446—111no—
237C8×Q8—111no—
238#436—111no—
239#435—221no—
240C8×D4—111no—
241C8×D4—221no—
242#433—221no—
243#432—111no—
244#432C2×D1111yescharacteristic
245#432C2×D1111yescharacteristic
246C2×#107—221no—
247C2×#107—221no—
248#405—221no—
249C2×C4×C8—111no—
250#335—112no—
251#334—112no—
252#332—112no—
253#332—112no—
254#332C2×D1112yes—
255#332C2×D1112yes—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11#47312yes—
259C22×C11C2×#12111yescharacteristic
260C2×D11—41no—
261C2×D11—41no—
262C2×D11—41no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—82no—
268C4×C11C2×#13711yescharacteristic
269C4×C11C2×#13711yescharacteristic
270C4×C11#57612yes—
271Dic11—41no—
272Dic11—41no—
273Dic11—41no—
274Dic11—82no—
275C22×Q8—21no—
276C22×Q8—221no—
277C2×Q16—222no—
278C2×Q16—222no—
279C2×SD16—222no—
280C2×SD16—222no—
281C2×M16—221no—
282C22×C8—111no—
283C22×C8—111no—
284C22×C8—221no—
285C4⋊Q8—21no—
286C4⋊Q8—21no—
287C4⋊Q8—21no—
288C4⋊Q8—112no—
289C4⋊Q8—221no—
290C4⋊Q8—221no—
291C4⋊Q8—221no—
292C4⋊Q8C22×D1112yes—
293#126—221no—
294#125—111no—
295#124—111no—
296#123—221no—
297C22⋊Q8—111no—
298#121—111no—
299C4×Q8—111no—
300C4×D4—111no—
301C4×D4—221no—
302#117—221no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4—221no—
307C2×C42C22×D1111yescharacteristic
308#107—222no—
309#107—222no—
310#107—222no—
311#107—222no—
312C4⋊C8—112no—
313C4⋊C8—221no—
314C4⋊C8—221no—
315C4⋊C8C22×D1111yescharacteristic
316C4⋊C8C22×D1111yescharacteristic
317C4⋊C8C22×D1112yes—
318#103—222no—
319#103—222no—
320#103—222no—
321#103—222no—
322C22⋊C8—21no—
323C22⋊C8—21no—
324C22⋊C8—221no—
325C22⋊C8—221no—
326C22⋊C8—221no—
327#97—21no—
328#97—21no—
329#97—221no—
330#97—221no—
331C4×C8—111no—
332C4×C8—111no—
333C4×C8—111no—
334C4×C8—111no—
335C4×C8—221no—
336C2×C11—22no—
337C2×C11#303911yescharacteristic
338C2×C11#305811yescharacteristic
339C2×C11C2×#47311yescharacteristic
340D11—81no—
341C2×Q8—22no—
342C2×Q8—41no—
343C2×Q8—82no—
344C2×Q8—111no—
345C2×Q8—222no—
346C2×Q8—441no—
347C2×Q8—882no—
348C2×D4—111no—
349C2×D4—221no—
350C22×C4—41no—
351C22×C4—221no—
352C22×C4—441no—
353C22×C4#433911yescharacteristic
354C22×C4D4×D1111yescharacteristic
355C22×C4D4×D1111yescharacteristic
356Q16—882no—
357Q16—882no—
358SD16—882no—
359SD16—882no—
360M16—442no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8—22no—
364C2×C8—111no—
365C2×C8—111no—
366C2×C8—111no—
367C2×C8—111no—
368C2×C8—222no—
369C2×C8—222no—
370C2×C8—222no—
371C2×C8—442no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—111no—
377C4⋊C4—111no—
378C4⋊C4—221no—
379C4⋊C4—221no—
380C4⋊C4—221no—
381C4⋊C4—221no—
382C4⋊C4—222no—
383C4⋊C4—222no—
384C4⋊C4—441no—
385C4⋊C4—441no—
386C22⋊C4—221no—
387C22⋊C4—221no—
388C22⋊C4—221no—
389C22⋊C4—221no—
390C22⋊C4—221no—
391C42—221no—
392C42#433911yescharacteristic
393C42D4×D1111yescharacteristic
394C42D4×D1111yescharacteristic
395C42C23×D1111yescharacteristic
396C11#1935811yescharacteristic, complemented, Sylow
397C23—221no—
398C23#6693711yescharacteristic
399Q8—42no—
400Q8—42no—
401Q8—82no—
402Q8—222no—
403Q8—442no—
404Q8—442no—
405Q8—882no—
406D4—222no—
407D4—442no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—42no—
413C2×C4—82no—
414C2×C4—221no—
415C2×C4—221no—
416C2×C4—221no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—442no—
420C2×C4—882no—
421C2×C4#6693711yescharacteristic
422C2×C4#6693711yescharacteristic
423C2×C4#6693711yescharacteristic
424C2×C4C2×#433911yescharacteristic
425C2×C4C2×D4×D1111yescharacteristic
426C2×C4C2×D4×D1111yescharacteristic
427C8—42no—
428C8—41no—
429C8—41no—
430C8—112no—
431C8—112no—
432C8—221no—
433C8—221no—
434C8—442no—
435C22—21no—
436C22—21no—
437C22—441no—
438C22—441no—
439C22—441no—
440C22#1062236812yes—
441C22C2×#6693711yescharacteristic
442C4—21no—
443C4—21no—
444C4—21no—
445C4—21no—
446C4—82no—
447C4—441no—
448C4—441no—
449C4—441no—
450C4—882no—
451C4#1062330512yes—
452C4D11×#13711yescharacteristic
453C4D11×#13711yescharacteristic
454C2—22no—
455C2—881no—
456C2#1307810211yescharacteristic
457C2#1307826311yescharacteristic
458C2C2×#1062236811yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1556C2
socleC22×C11C2×#121
prime radical#66983D4
hypercenter#1556D11
hypocenterC11#19358
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1556

Complements

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

NH ≅ G/Ntype
3. C2×#10622691C2semidirect
5. #13068133C2semidirect
6. #13068128C2semidirect
7. #13068009C2semidirect
8. #13068004C2semidirect
9. #13067377C2semidirect
10. #13067332C2semidirect
11. C11×#1556C2semidirect
178. #1556D11semidirect
396. C11#19358semidirect

Maximal subgroups

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

subgroupindex
#130796452
#130796432
C2×#106226912
#130775852
#130681332
#130681282
#130680092
#130680042
#130673772
#130673322
C11×#15562
#1935811