Finite Group Databasebeta

← #14911244

Subgroups — #14911244

Order 2816.

472 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#13081005C211yesmaximal, characteristic
2#13080987C211yesmaximal, characteristic
3#13070900C211yesmaximal, characteristic, complemented
4#13070822C211yesmaximal, characteristic, complemented
5#13070816C211yesmaximal, characteristic, complemented
6#13070812C211yesmaximal, characteristic, complemented
7#13070811C211yesmaximal, characteristic, complemented
8#13070778C211yesmaximal, characteristic, complemented
9#13070756C211yesmaximal, characteristic, complemented
10#13070721C211yesmaximal, characteristic, complemented
11#13070487C211yesmaximal, characteristic, complemented
12#13070441C211yesmaximal, characteristic
13#13070401C211yesmaximal, characteristic, complemented
14C2×#10622143C211yesmaximal, characteristic, complemented
15C11×#2216C211yesmaximal, characteristic, complemented
16#10623173—21no—
17#10623166—21no—
18C2×C11×Q32C2211yescharacteristic
19C22×C11×C16C2211yescharacteristic
20C11×#467C2211yescharacteristic
21C11×#467C2211yescharacteristic
22#10622801C2211yescharacteristic
23#10622801C2211yescharacteristic
24Q16×Dic11C2211yescharacteristic
25Q16×Dic11C2211yescharacteristic
26C8×C22⋊D11C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29#10622657—21no—
30#10622656—21no—
31C2×#66862C2211yescharacteristic
32#10622493C2211yescharacteristic
33D11×#107C2211yescharacteristic
34#10622491C2211yescharacteristic
35#10622487C2211yescharacteristic
36#10622427—21no—
37#10622422—21no—
38#10622409—21no—
39#10622407—21no—
40C11×#366C2211yescharacteristic
41C11×#358C2211yescharacteristic
42C11×#358C2211yescharacteristic
43#10622202C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622202C2211yescharacteristic
47C22⋊(C11⋊C16)C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49#10622143C2211yescharacteristic
50#10622143C2211yescharacteristic
51#10622143C2211yescharacteristic
52#10622143C2211yescharacteristic
53#10622140C2211yescharacteristic
54Dic11⋊C16C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622127C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×Q16C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C11×C22⋊Q8—21no—
63C11×C22⋊Q8—21no—
64#66999—21no—
65#66999—21no—
66Q8×Dic11—21no—
67Q8×Dic11—21no—
68C4×C22⋊D11D411yescharacteristic
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—21no—
71C2×C8×D11C2311yescharacteristic
72#66951—41no—
73#66950—41no—
74#66945—21no—
75C4⋊C4×D11—21no—
76#66943—21no—
77#66943—41no—
78#66942—41no—
79#66941—21no—
80#66939—41no—
81(C22⋊D11)⋊C4—41no—
82#66931—41no—
83#66930—41no—
84C11×Q32—22no—
85C2×C11×C16—22no—
86C2×C11×C16C2311yescharacteristic
87C2×C11×C16C2311yescharacteristic
88C11×#107C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×#103—21no—
91C11×#103—21no—
92#66899—21no—
93#66899—21no—
94#66899—21no—
95#66899—21no—
96C22⋊(C11⋊C8)D411yescharacteristic
97(C2×D11)⋊C8D411yescharacteristic
98#66882—21no—
99#66882—21no—
100#66882C2311yescharacteristic
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66882C2311yescharacteristic
104Dic11⋊C8D411yescharacteristic
105C8×Dic11C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108#66872—21no—
109#66872—21no—
110#66871—21no—
111#66871—21no—
112#66862—22no—
113#33911—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C22×C4×C11C2×D411yescharacteristic
117C2×C22⋊D11D811yescharacteristic
118C22×Dic11—41no—
119C22×Dic11—41no—
120C2×C4×D11—41no—
121C2×C4×D11C2×D411yescharacteristic
122C2×Dic22—41no—
123C11×Q16—21no—
124C11×Q16—21no—
125C11×Q16—21no—
126C11×Q16—21no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11C2411yescharacteristic
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—41no—
134C11×C4⋊C4—41no—
135C11×C22⋊C4—41no—
136C11×C22⋊C4—41no—
137C22⋊Dic11D811yescharacteristic
138(C2×D11)⋊C4—41no—
139(C2×D11)⋊C4—41no—
140(C2×D11)⋊C4—41no—
141(C2×D11)⋊C4D811yescharacteristic
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—41no—
147C4⋊Dic11—41no—
148C4⋊Dic11—41no—
149C4⋊Dic11—41no—
150C4⋊Dic11—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4D811yescharacteristic
157C4×Dic11—41no—
158C4×Dic11—41no—
159C4×Dic11—41no—
160C4×Dic11C2×D411yescharacteristic
161C2×C11⋊C8C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163C8×D11—21no—
164C8×D11—21no—
165C11×C16—21no—
166C11×C16#4112yes—
167C11⋊C16—21no—
168C11⋊C16—21no—
169#3338—111no—
170#3336—111no—
171#2255—111no—
172#2237—111no—
173#2236—111no—
174#2235—111no—
175#2235—111no—
176#2229—111no—
177#2225—111no—
178#2219—111no—
179#2216D1111yescharacteristic, complemented
180#2176—111no—
181#2168—111no—
182#2159—111no—
183C2×#367—111no—
184C23×C11C2×D811yescharacteristic
185C22×D11C2×D811yescharacteristic
186Q8×C11—41no—
187Q8×C11—41no—
188Q8×C11—41no—
189Q8×C11—41no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11C2×D811yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C22⋊D11—22no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—82no—
204C2×Dic11—161no—
205C2×Dic11C2×D811yescharacteristic
206C2×Dic11C2×D811yescharacteristic
207C2×Dic11C2×D811yescharacteristic
208C4×D11—21no—
209C4×D11—21no—
210C4×D11—161no—
211Dic22—161no—
212C8×C11—21no—
213C8×C11C2×#4111yescharacteristic
214C8×C112−1+411yescharacteristic
215C11⋊C8—21no—
216C11⋊C8—21no—
217#554—221no—
218#552—221no—
219C2×Q32C2×D1111yescharacteristic
220C2×M32—111no—
221C22×C16C2×D1111yescharacteristic
222#500—111no—
223#499—111no—
224#485—221no—
225#484—221no—
226#484—221no—
227#483—221no—
228#479—221no—
229#477—221no—
230#467—111no—
231#467—111no—
232#467C2×D1111yescharacteristic
233#467C2×D1111yescharacteristic
234C4×Q16—111no—
235C4×Q16—111no—
236C8×D4—111no—
237#427—111no—
238C2×#107—111no—
239C2×#107—111no—
240C2×#107—111no—
241#367—111no—
242#367—111no—
243#367—111no—
244#367—111no—
245#367—111no—
246#367—111no—
247#366—111no—
248#366—111no—
249#366C2×D1111yescharacteristic
250C4⋊C16—111no—
251#358—111no—
252#358—111no—
253#358—111no—
254#358—111no—
255#358C2×D1111yescharacteristic
256#358C2×D1111yescharacteristic
257C22⋊C16—111no—
258C22⋊C16—111no—
259#346—111no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11#51012yes—
263C22×C11C22×D811yescharacteristic
264C2×D11—21no—
265C2×D11—21no—
266C2×D11—21no—
267C4×C11—21no—
268C4×C11—81no—
269C4×C11—81no—
270C4×C11—81no—
271C4×C11—81no—
272C4×C11#54711yescharacteristic
273C4×C11#57811yescharacteristic
274Dic11—21no—
275Dic11—21no—
276Dic11—21no—
277Dic11—81no—
278Dic11—81no—
279Dic11—81no—
280Dic11—81no—
281C2×Q16C22×D1111yescharacteristic
282C2×Q16C22×D1111yescharacteristic
283C22×C8—111no—
284C22×C8C22×D1111yescharacteristic
285C4⋊Q8—221no—
286#126—441no—
287#125—221no—
288#125—441no—
289#125—441no—
290#123—441no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8—221no—
294C22⋊Q8—221no—
295C22⋊Q8—441no—
296C22⋊Q8—441no—
297C4×Q8—221no—
298C4×Q8—221no—
299C4×D4—111no—
300C4×D4—441no—
301#117—221no—
302#117—441no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4—221no—
305C2×C4⋊C4—221no—
306Q32—22no—
307M32—222no—
308C2×C16—22no—
309C2×C16—111no—
310C2×C16—111no—
311C2×C16C22×D1111yescharacteristic
312C2×C16C22×D1111yescharacteristic
313#107—111no—
314#107—111no—
315#107—111no—
316#107—111no—
317#107—221no—
318#107—221no—
319#107—221no—
320#107—221no—
321#107C22×D1111yescharacteristic
322#107C22×D1111yescharacteristic
323#106—221no—
324#106—221no—
325C4⋊C8—111no—
326#103—21no—
327#103—21no—
328#103—221no—
329#103—221no—
330#103—221no—
331#103—221no—
332C22⋊C8—111no—
333C22⋊C8—111no—
334C4×C8—111no—
335C2×C11—22no—
336C2×C11#333411yescharacteristic
337C2×C11C2×#51011yescharacteristic
338C2×C11#341611yescharacteristic
339D11—41no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—441no—
343C2×D4—111no—
344C22×C4—111no—
345C22×C4—441no—
346C22×C4—441no—
347C22×C4—441no—
348C22×C4D4×D1111yescharacteristic
349Q16—21no—
350Q16—21no—
351Q16—21no—
352Q16—21no—
353C2×C8—21no—
354C2×C8—21no—
355C2×C8—111no—
356C2×C8—111no—
357C2×C8—221no—
358C2×C8—221no—
359C2×C8D4×D1111yescharacteristic
360C2×C8C23×D1111yescharacteristic
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—111no—
366C4⋊C4—221no—
367C4⋊C4—221no—
368C4⋊C4—221no—
369C4⋊C4—221no—
370C4⋊C4—441no—
371C4⋊C4—441no—
372C4⋊C4—441no—
373C4⋊C4—441no—
374C4⋊C4—441no—
375C4⋊C4—441no—
376C4⋊C4—441no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—111no—
383C22⋊C4—111no—
384C22⋊C4—441no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C42—111no—
388C42—441no—
389C42—441no—
390C42—441no—
391C16—21no—
392C16—221no—
393C16—221no—
394C16#434112yes—
395C11#3391111yescharacteristic, complemented, Sylow
396C23—111no—
397C23D8×D1111yescharacteristic
398Q8—41no—
399Q8—41no—
400Q8—41no—
401Q8—41no—
402Q8—1761no—
403D4—222no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—111no—
411C2×C4—111no—
412C2×C4—111no—
413C2×C4—221no—
414C2×C4—221no—
415C2×C4—441no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—882no—
420C2×C4—1761no—
421C2×C4—1761no—
422C2×C4D8×D1111yescharacteristic
423C2×C4C2×D4×D1111yescharacteristic
424C8—21no—
425C8—221no—
426C8—221no—
427C8C2×#434111yescharacteristic
428C8#6704311yescharacteristic
429C22—21no—
430C22—21no—
431C22—221no—
432C22—221no—
433C22—221no—
434C22#1062253112yes—
435C22C2×D8×D1111yescharacteristic
436C4—21no—
437C4—81no—
438C4—81no—
439C4—81no—
440C4—81no—
441C4—221no—
442C4—221no—
443C4—221no—
444C4—881no—
445C4—881no—
446C4—881no—
447C4—881no—
448C4#1062314211yescharacteristic
449C4#1062330211yescharacteristic
450C2—22no—
451C2—441no—
452C2#1308096011yescharacteristic
453C2C2×#1062253111yescharacteristic
454C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2216C2
socleC22×C11C22×D8
prime radicalC2×C22⋊D11D8
hypercenter#2216D11
hypocenterC11#33911
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2216

Complements

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

NH ≅ G/Ntype
3. #13070900C2semidirect
4. #13070822C2semidirect
5. #13070816C2semidirect
6. #13070812C2semidirect
7. #13070811C2semidirect
8. #13070778C2semidirect
9. #13070756C2semidirect
10. #13070721C2semidirect
11. #13070487C2semidirect
13. #13070401C2semidirect
14. C2×#10622143C2semidirect
15. C11×#2216C2semidirect
179. #2216D11semidirect
395. C11#33911semidirect

Maximal subgroups

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

subgroupindex
#130810052
#130809872
#130709002
#130708222
#130708162
#130708122
#130708112
#130707782
#130707562
#130707212
#130704872
#130704412
#130704012
C2×#106221432
C11×#22162
#3391111