Finite Group Databasebeta

← #14911232

Subgroups — #14911232

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#13080985C211yesmaximal, characteristic
2#13070899C211yesmaximal, characteristic, complemented
3#13070821C211yesmaximal, characteristic, complemented
4#13070818C211yesmaximal, characteristic, complemented
5#13070813C211yesmaximal, characteristic, complemented
6#13070811C211yesmaximal, characteristic, complemented
7#13070780C211yesmaximal, characteristic, complemented
8#13070755C211yesmaximal, characteristic, complemented
9#13070722C211yesmaximal, characteristic, complemented
10#13070705C211yesmaximal, characteristic, complemented
11#13070485C211yesmaximal, characteristic, complemented
12#13070442C211yesmaximal, characteristic
13#13070402C211yesmaximal, characteristic, complemented
14C2×#10622128C211yesmaximal, characteristic, complemented
15C11×#3338C211yesmaximal, characteristic
16C11×#554—21no—
17#10623072—21no—
18C11×#500C2211yescharacteristic
19C11×#484—21no—
20C11×#484—21no—
21C11×#477—21no—
22C11×#467C2211yescharacteristic
23C11×#467C2211yescharacteristic
24C4×C11×Q16C2211yescharacteristic
25C8×D4×C11C2211yescharacteristic
26C2×C11×#107C2211yescharacteristic
27C2×C11×#107C2211yescharacteristic
28C2×#66893C2211yescharacteristic
29#10622729C2211yescharacteristic
30#10622729C2211yescharacteristic
31#10622719C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66876C2211yescharacteristic
34C22×C11⋊C16C2211yescharacteristic
35#10622442—21no—
36#10622336—21no—
37#10622334—21no—
38C4×Dic44C2211yescharacteristic
39#10622296C2211yescharacteristic
40#10622202C2211yescharacteristic
41#10622202C2211yescharacteristic
42#10622202C2211yescharacteristic
43C22⋊(C11⋊C16)C2211yescharacteristic
44C22⋊(C11⋊C16)C2211yescharacteristic
45#10622130C2211yescharacteristic
46#10622130C2211yescharacteristic
47#10622130C2211yescharacteristic
48#10622128C2211yescharacteristic
49#10622128C2211yescharacteristic
50#10622128C2211yescharacteristic
51#10622128C2211yescharacteristic
52#10622128C2211yescharacteristic
53#10622128C2211yescharacteristic
54#10622127C2211yescharacteristic
55#10622127C2211yescharacteristic
56#10622127C2211yescharacteristic
57C4⋊(C11⋊C16)C2211yescharacteristic
58#10622099C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C11×C4⋊Q8—21no—
63C11×#125—41no—
64C11×C22⋊Q8—21no—
65C11×C22⋊Q8—21no—
66C11×C22⋊Q8—41no—
67C11×C22⋊Q8—41no—
68C4×Q8×C11—21no—
69C4×D4×C11—41no—
70C4×D4×C11D411yescharacteristic
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73#66988—41no—
74#66979—21no—
75C2×C4⋊Dic11—21no—
76#66977—21no—
77#66977—21no—
78C2×Dic44C2311yescharacteristic
79#66942—41no—
80#66932—41no—
81#66930—41no—
82#66923—21no—
83C4×Dic22—21no—
84C11×#107—21no—
85C11×#107—21no—
86C11×#107—21no—
87C11×#107C2311yescharacteristic
88C11×#107C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×C4⋊C8D411yescharacteristic
91C11×#103—21no—
92C11×#103—21no—
93C11×#103—21no—
94C11×C22⋊C8D411yescharacteristic
95C11×C22⋊C8D411yescharacteristic
96C4×C8×C11C2311yescharacteristic
97#66893—22no—
98#66882—21no—
99#66882C2311yescharacteristic
100#66882C2311yescharacteristic
101#66882C2311yescharacteristic
102#66881—21no—
103#66881—21no—
104#66880—21no—
105#66880—21no—
106#66880—21no—
107#66876—22no—
108C2×C11⋊C16—22no—
109C2×C11⋊C16C2311yescharacteristic
110C2×C11⋊C16C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113#33911—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×Q8×C11—41no—
116C2×D4×C11D811yescharacteristic
117C22×C4×C11—41no—
118C22×C4×C11—41no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×Dic11—41no—
122C2×Dic22—21no—
123C11×Q16—21no—
124C11×Q16—21no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11C2×D411yescharacteristic
131C2×C8×C11C2×D411yescharacteristic
132C2×C8×C11C2411yescharacteristic
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—41no—
137C11×C4⋊C4—41no—
138C11×C4⋊C4—41no—
139C11×C4⋊C4—41no—
140C11×C4⋊C4—41no—
141C11×C4⋊C4—41no—
142C11×C4⋊C4D811yescharacteristic
143C11×C22⋊C4—41no—
144C11×C22⋊C4—41no—
145C11×C22⋊C4D811yescharacteristic
146C11×C22⋊C4D811yescharacteristic
147C42×C11—41no—
148C42×C11C2×D411yescharacteristic
149C22⋊Dic11—41no—
150C22⋊Dic11—41no—
151C22⋊Dic11—41no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4—41no—
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161C4×Dic11—41no—
162C4×Dic11—41no—
163Dic44—21no—
164Dic44—21no—
165C11⋊C16—21no—
166C11⋊C16—21no—
167C11⋊C16—21no—
168C11⋊C16#4112yes—
169#3338D1111yescharacteristic
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#2216—111no—
180#2176—111no—
181#2168—111no—
182#2159—111no—
183C2×#367—111no—
184C23×C11C2×D811yescharacteristic
185C23×C11C2×D811yescharacteristic
186Q8×C11—41no—
187Q8×C11—41no—
188Q8×C11—161no—
189D4×C11—22no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—161no—
199C2×C4×C11—161no—
200C2×C4×C11C2×D811yescharacteristic
201C2×C4×C11C2×D811yescharacteristic
202C2×C4×C11C2×D811yescharacteristic
203C2×C4×C11C2×D811yescharacteristic
204C2×C4×C11C22×D411yescharacteristic
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—82no—
210Dic22—41no—
211Dic22—41no—
212C8×C11—21no—
213C8×C11—21no—
214C8×C11—21no—
215C8×C11C2×#4111yescharacteristic
216C8×C112−1+411yescharacteristic
217#554—21no—
218#552—221no—
219C2×Q32—111no—
220C2×M32—111no—
221C22×C16—111no—
222#500C2×D1111yescharacteristic
223#499—111no—
224#485—221no—
225#484—21no—
226#484—21no—
227#483—221no—
228#479—221no—
229#477—21no—
230#467—111no—
231#467—111no—
232#467C2×D1111yescharacteristic
233#467C2×D1111yescharacteristic
234C4×Q16—111no—
235C4×Q16C2×D1111yescharacteristic
236C8×D4C2×D1111yescharacteristic
237#427—111no—
238C2×#107—111no—
239C2×#107C2×D1111yescharacteristic
240C2×#107C2×D1111yescharacteristic
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#366—111no—
250C4⋊C16—111no—
251#358—111no—
252#358—111no—
253#358—111no—
254#358—111no—
255#358—111no—
256#358—111no—
257C22⋊C16—111no—
258C22⋊C16—111no—
259#346—111no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11#51012yes—
266C22×C11C22×D811yescharacteristic
267C4×C11—21no—
268C4×C11—21no—
269C4×C11—21no—
270C4×C11—21no—
271C4×C11—81no—
272C4×C11—81no—
273C4×C11—81no—
274C4×C11—81no—
275C4×C11#54711yescharacteristic
276C4×C11#57811yescharacteristic
277Dic11—81no—
278Dic11—81no—
279Dic11—81no—
280Dic11—81no—
281C2×Q16—111no—
282C2×Q16C22×D1111yescharacteristic
283C22×C8C22×D1111yescharacteristic
284C22×C8C22×D1111yescharacteristic
285C4⋊Q8—21no—
286#126—441no—
287#125—41no—
288#125—221no—
289#125—441no—
290#123—441no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8—41no—
294C22⋊Q8—41no—
295C22⋊Q8—221no—
296C22⋊Q8—221no—
297C4×Q8—21no—
298C4×Q8—221no—
299C4×D4—41no—
300C4×D4C22⋊D1111yescharacteristic
301#117—221no—
302#117—441no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—221no—
306Q32—222no—
307M32—222no—
308C2×C16—111no—
309C2×C16—111no—
310C2×C16—111no—
311C2×C16—111no—
312C2×C16—222no—
313#107—21no—
314#107—21no—
315#107—21no—
316#107—111no—
317#107—111no—
318#107—111no—
319#107—221no—
320#107C22×D1111yescharacteristic
321#107C22×D1111yescharacteristic
322#107C22×D1111yescharacteristic
323#106—221no—
324#106—221no—
325C4⋊C8C22⋊D1111yescharacteristic
326#103—21no—
327#103—21no—
328#103—21no—
329#103—221no—
330#103—221no—
331#103—221no—
332C22⋊C8C22⋊D1111yescharacteristic
333C22⋊C8C22⋊D1111yescharacteristic
334C4×C8C22×D1111yescharacteristic
335C2×C11—22no—
336C2×C11—41no—
337C2×C11#333411yescharacteristic
338C2×C11C2×#51011yescharacteristic
339C2×C11#341611yescharacteristic
340C2×Q8—21no—
341C2×Q8—41no—
342C2×Q8—221no—
343C2×D4#432311yescharacteristic
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—441no—
347C22×C4C2×C22⋊D1111yescharacteristic
348C22×C4C2×C22⋊D1111yescharacteristic
349Q16—21no—
350Q16—21no—
351Q16—221no—
352Q16—221no—
353C2×C8—21no—
354C2×C8—21no—
355C2×C8—21no—
356C2×C8—21no—
357C2×C8C2×C22⋊D1111yescharacteristic
358C2×C8C2×C22⋊D1111yescharacteristic
359C2×C8C2×C22⋊D1111yescharacteristic
360C2×C8C23×D1111yescharacteristic
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—221no—
371C4⋊C4—221no—
372C4⋊C4—221no—
373C4⋊C4—441no—
374C4⋊C4—441no—
375C4⋊C4—441no—
376C4⋊C4—441no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C4⋊C4#432311yescharacteristic
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—441no—
383C22⋊C4—441no—
384C22⋊C4—441no—
385C22⋊C4#432311yescharacteristic
386C22⋊C4#432311yescharacteristic
387C42—41no—
388C42—441no—
389C42—441no—
390C42C2×C22⋊D1111yescharacteristic
391C16—112no—
392C16—221no—
393C16—221no—
394C16—221no—
395C11#3391111yescharacteristic, complemented, Sylow
396C23C2×#432311yescharacteristic
397C23C2×#432311yescharacteristic
398Q8—41no—
399Q8—41no—
400Q8—161no—
401Q8—441no—
402Q8—441no—
403D4—22no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—161no—
413C2×C4—161no—
414C2×C4—441no—
415C2×C4—441no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—882no—
419C2×C4C2×#432311yescharacteristic
420C2×C4C2×#432311yescharacteristic
421C2×C4C2×#432311yescharacteristic
422C2×C4C2×#432311yescharacteristic
423C2×C4C22×C22⋊D1111yescharacteristic
424C8—21no—
425C8—21no—
426C8—21no—
427C8#41×D1111yescharacteristic
428C8#6704311yescharacteristic
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22#1062279212yes—
435C22C22×#432311yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—81no—
441C4—81no—
442C4—81no—
443C4—81no—
444C4—881no—
445C4—881no—
446C4—881no—
447C4—881no—
448C4#1062335511yescharacteristic
449C4#1062336911yescharacteristic
450C2—22no—
451C2—41no—
452C2#1308095911yescharacteristic
453C2C2×#1062279211yescharacteristic
454C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3338C2
socleC22×C11C22×D8
prime radicalC2×D4×C11D8
hypercenter#3338D11
hypocenterC11#33911
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3338

Complements

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

NH ≅ G/Ntype
2. #13070899C2semidirect
3. #13070821C2semidirect
4. #13070818C2semidirect
5. #13070813C2semidirect
6. #13070811C2semidirect
7. #13070780C2semidirect
8. #13070755C2semidirect
9. #13070722C2semidirect
10. #13070705C2semidirect
11. #13070485C2semidirect
13. #13070402C2semidirect
14. C2×#10622128C2semidirect
395. C11#33911semidirect

Maximal subgroups

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

subgroupindex
#130809852
#130708992
#130708212
#130708182
#130708132
#130708112
#130707802
#130707552
#130707222
#130707052
#130704852
#130704422
#130704022
C2×#106221282
C11×#33382
#3391111