Finite Group Databasebeta

← #14909321

Subgroups — #14909321

Order 2816.

526 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079187C211yesmaximal, characteristic, complemented
2#13079181C211yesmaximal, characteristic, complemented
3#13070894C211yesmaximal, characteristic, complemented
4#13070876C211yesmaximal, characteristic, complemented
5#13070849C211yesmaximal, characteristic, complemented
6#13070846C211yesmaximal, characteristic, complemented
7#13070712C211yesmaximal, characteristic, complemented
8#13070705C211yesmaximal, characteristic, complemented
9#13070700C211yesmaximal, characteristic
10#13070472C211yesmaximal, characteristic, complemented
11SD32×Dic11C211yesmaximal, characteristic, complemented
12#13070467C211yesmaximal, characteristic, complemented
13#13070460C211yesmaximal, characteristic, complemented
14C2×C16×Dic11C211yesmaximal, characteristic, complemented
15C11×#2217C211yesmaximal, characteristic, complemented
16#10623155—21no—
17#10623131—21no—
18C2×C11×SD32C2211yescharacteristic
19C22×C11×C16C2211yescharacteristic
20C11×#467C2211yescharacteristic
21C11×#466C2211yescharacteristic
22#10622804C2211yescharacteristic
23Q16×Dic11C2211yescharacteristic
24C2×#66893C2211yescharacteristic
25#10622768C2211yescharacteristic
26D8×Dic11C2211yescharacteristic
27C2×#66890C2211yescharacteristic
28#10622729C2211yescharacteristic
29#10622728C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31C22×C11⋊C16C2211yescharacteristic
32#10622661—21no—
33#10622654—21no—
34C2×#66864C2211yescharacteristic
35#10622491C2211yescharacteristic
36#10622491C2211yescharacteristic
37#10622486C2211yescharacteristic
38#10622485C2211yescharacteristic
39#10622413—21no—
40#10622401—21no—
41#10622381—21no—
42#10622371—21no—
43C11×#367C2211yescharacteristic
44C11×#358C2211yescharacteristic
45C11×#357C2211yescharacteristic
46#10622202C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622143C2211yescharacteristic
50#10622141C2211yescharacteristic
51C16×Dic11C2211yescharacteristic
52C16×Dic11C2211yescharacteristic
53C16×Dic11C2211yescharacteristic
54C16×Dic11C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622129C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622127C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×D8C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C11×C22⋊Q8—21no—
63C11×#121—21no—
64#67000—21no—
65Q8×Dic11—21no—
66C2×#4325—21no—
67#66989—21no—
68#66988—41no—
69D4×Dic11—21no—
70D4×Dic11—41no—
71C2×#4324—21no—
72#66983—21no—
73#66977—21no—
74C2×C4×Dic11D411yescharacteristic
75C22×C11⋊C8D411yescharacteristic
76C2×Dic44C2311yescharacteristic
77C2×D88C2311yescharacteristic
78#66951—41no—
79#66946—21no—
80#66945—41no—
81#66943—21no—
82#66943—21no—
83#66940—21no—
84#66939—41no—
85(C22⋊D11)⋊C4—41no—
86#66932—41no—
87#66930—41no—
88C11×SD32—22no—
89C2×C11×C16—22no—
90C2×C11×C16C2311yescharacteristic
91C2×C11×C16C2311yescharacteristic
92C11×#107C2311yescharacteristic
93C11×#107C2311yescharacteristic
94C11×#103—21no—
95C11×#102—21no—
96#66899—21no—
97#66896—21no—
98#66893—22no—
99#66890—22no—
100#66885—21no—
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66880—21no—
104C8×Dic11D411yescharacteristic
105C8×Dic11D411yescharacteristic
106C8×Dic11C2311yescharacteristic
107C8×Dic11C2311yescharacteristic
108C2×C11⋊C16—22no—
109C2×C11⋊C16C2311yescharacteristic
110C2×C11⋊C16C2311yescharacteristic
111#66874—21no—
112#66873—21no—
113#66872—21no—
114#66872—21no—
115#66864—22no—
116#33735—111nomaximal, Sylow
117C2×Q8×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—41no—
120C22×C4×C11C2×D411yescharacteristic
121C2×C22⋊D11—41no—
122C22×Dic11—41no—
123C22×Dic11D811yescharacteristic
124C22×Dic11D811yescharacteristic
125C2×D44—21no—
126C2×C4×D11—41no—
127C2×Dic22—21no—
128C11×Q16—21no—
129C11×Q16—21no—
130C11×D8—21no—
131C11×D8—21no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11C2411yescharacteristic
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—41no—
139C11×C22⋊C4—41no—
140C11×C22⋊C4—41no—
141C22⋊Dic11—41no—
142C22⋊Dic11—41no—
143C22⋊Dic11—41no—
144C22⋊Dic11—41no—
145#4325—42no—
146#4324—42no—
147(C2×D11)⋊C4—41no—
148(C2×D11)⋊C4—41no—
149(C2×D11)⋊C4—41no—
150(C2×D11)⋊C4—41no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—41no—
154C4⋊Dic11—41no—
155C4⋊Dic11—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4—41no—
159Dic11⋊C4—41no—
160C4×Dic11—41no—
161C4×Dic11—41no—
162C4×Dic11D811yescharacteristic
163C4×Dic11D811yescharacteristic
164C4×Dic11C2×D411yescharacteristic
165C4×Dic11C2×D411yescharacteristic
166C2×C11⋊C8—22no—
167C2×C11⋊C8C2×D411yescharacteristic
168C2×C11⋊C8C2×D411yescharacteristic
169Dic44—21no—
170Dic44—21no—
171D88—21no—
172D88—21no—
173C11×C16—21no—
174C11×C16#4112yes—
175C11⋊C16—21no—
176C11⋊C16#4112yes—
177#3168—111no—
178#3168—111no—
179#2253—111no—
180#2249—111no—
181#2242—111no—
182#2242—111no—
183#2217—111no—
184#2217D1111yescharacteristic, complemented
185#2216—111no—
186#2215—111no—
187C4×Q32—111no—
188C4×SD32—111no—
189C4×SD32—111no—
190C4×D16—111no—
191C2×C4×C16—111no—
192C23×C11—41no—
193C23×C11C2×D811yescharacteristic
194C22×D11—41no—
195Q8×C11—41no—
196Q8×C11—41no—
197D4×C11—41no—
198D4×C11—41no—
199D4×C11—82no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11C2×D811yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C22⋊D11—82no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—82no—
214C2×Dic11C2×D811yescharacteristic
215C2×Dic11C2×D811yescharacteristic
216C2×Dic11C2×D811yescharacteristic
217C2×Dic11C2×D811yescharacteristic
218D44—41no—
219D44—41no—
220C4×D11—82no—
221Dic22—41no—
222Dic22—41no—
223C8×C11—21no—
224C8×C11C2×#4111yescharacteristic
225C8×C11C2×#4111yescharacteristic
226C11⋊C8—21no—
227C11⋊C8#13512yes—
228#529—221no—
229#529—221no—
230C2×Q32—111no—
231C2×SD32—111no—
232C2×SD32C2×D1111yescharacteristic
233C2×D16—111no—
234C22×C16—111no—
235C22×C16C2×D1111yescharacteristic
236#499—111no—
237#499—111no—
238#495—111no—
239#495—111no—
240#488—221no—
241#488—221no—
242#467—111no—
243#467C2×D1111yescharacteristic
244#466—111no—
245#466C2×D1111yescharacteristic
246#465—221no—
247#465—221no—
248C4×Q16—111no—
249C4×Q16—111no—
250C4×SD16—221no—
251C4×SD16—221no—
252C4×D8—111no—
253C4×D8—111no—
254C2×C4×C8—111no—
255#367—111no—
256#367C2×D1111yescharacteristic
257#366—111no—
258#366—111no—
259#358—111no—
260#358—111no—
261#358—111no—
262#358C2×D1111yescharacteristic
263#357—111no—
264#357—111no—
265#357—111no—
266#357C2×D1111yescharacteristic
267C4×C16—111no—
268C4×C16—111no—
269C4×C16—111no—
270C4×C16—111no—
271C22×C11—21no—
272C22×C11—21no—
273C22×C11—81no—
274C22×C11—81no—
275C22×C11—81no—
276C22×C11#50812yes—
277C22×C11C22×D811yescharacteristic
278C2×D11—81no—
279C2×D11—81no—
280C2×D11—81no—
281C4×C11—21no—
282C4×C11—81no—
283C4×C11—81no—
284C4×C11—81no—
285C4×C11#53211yescharacteristic
286C4×C11C2×#13511yescharacteristic
287Dic11—21no—
288Dic11—21no—
289Dic11—21no—
290Dic11—81no—
291Dic11—81no—
292Dic11—81no—
293Dic11#50812yes—
294C2×Q16—111no—
295C2×Q16C22×D1111yescharacteristic
296C2×SD16—221no—
297C2×SD16—221no—
298C2×D8—111no—
299C2×D8C22×D1111yescharacteristic
300C22×C8—111no—
301C22×C8C22×D1111yescharacteristic
302#126—441no—
303#126—441no—
304#125—221no—
305#125—221no—
306#124—221no—
307#124—221no—
308#123—441no—
309#123—441no—
310C22⋊Q8—21no—
311C22⋊Q8—221no—
312#121—21no—
313#121—221no—
314C4×Q8—221no—
315C4×Q8—221no—
316C4×D4—221no—
317C4×D4—221no—
318C4×D4—441no—
319C4×D4—441no—
320#117—441no—
321#117—441no—
322C2×C42—111no—
323Q32—222no—
324SD32—22no—
325SD32—222no—
326D16—222no—
327C2×C16—22no—
328C2×C16—111no—
329C2×C16—111no—
330C2×C16—222no—
331C2×C16C22×D1111yescharacteristic
332C2×C16C22×D1111yescharacteristic
333#107—111no—
334#107—111no—
335#107C22×D1111yescharacteristic
336#107C22×D1111yescharacteristic
337#106—221no—
338#106—221no—
339#103—21no—
340#103—221no—
341#103—221no—
342#103—221no—
343#102—21no—
344#102—221no—
345#102—221no—
346#102—221no—
347C4×C8—111no—
348C4×C8—111no—
349C4×C8—111no—
350C4×C8—111no—
351C2×C11—22no—
352C2×C11—161no—
353C2×C11#316911yescharacteristic
354C2×C11C2×#50811yescharacteristic
355C2×C11C2×#50811yescharacteristic
356D11—161no—
357C2×Q8—21no—
358C2×Q8—221no—
359C2×D4—21no—
360C2×D4—41no—
361C2×D4—221no—
362C2×D4—441no—
363C22×C4—111no—
364C22×C4—111no—
365C22×C4—441no—
366C22×C4—441no—
367C22×C4D4×D1111yescharacteristic
368Q16—21no—
369Q16—21no—
370Q16—221no—
371Q16—221no—
372SD16—442no—
373SD16—442no—
374D8—21no—
375D8—21no—
376D8—221no—
377D8—221no—
378C2×C8—21no—
379C2×C8—21no—
380C2×C8—111no—
381C2×C8—111no—
382C2×C8—222no—
383C2×C8D4×D1111yescharacteristic
384C2×C8C23×D1111yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—41no—
388C4⋊C4—221no—
389C4⋊C4—221no—
390C4⋊C4—441no—
391C4⋊C4—441no—
392C4⋊C4—441no—
393C4⋊C4—441no—
394C4⋊C4—441no—
395C4⋊C4—441no—
396C4⋊C4—441no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—441no—
400C22⋊C4—441no—
401C22⋊C4—441no—
402C22⋊C4—441no—
403C22⋊C4—441no—
404C22⋊C4—441no—
405C22⋊C4—441no—
406C22⋊C4—441no—
407C42—111no—
408C42—111no—
409C42—111no—
410C42—111no—
411C42—441no—
412C42—441no—
413C16—21no—
414C16—112no—
415C16—221no—
416C16#434112yes—
417C11#3373511yescharacteristic, complemented, Sylow
418C23—41no—
419C23—441no—
420C23D8×D1111yescharacteristic
421Q8—41no—
422Q8—41no—
423Q8—441no—
424Q8—441no—
425D4—41no—
426D4—41no—
427D4—82no—
428D4—441no—
429D4—441no—
430D4—882no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—111no—
437C2×C4—111no—
438C2×C4—111no—
439C2×C4—111no—
440C2×C4—222no—
441C2×C4—222no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—882no—
446C2×C4—882no—
447C2×C4D8×D1111yescharacteristic
448C2×C4C2×D4×D1111yescharacteristic
449C8—21no—
450C8—112no—
451C8—221no—
452C8C2×#434111yescharacteristic
453C8#41×D1111yescharacteristic
454C22—21no—
455C22—21no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—881no—
460C22—881no—
461C22—881no—
462C22#1062252912yes—
463C22C2×D8×D1111yescharacteristic
464C4—21no—
465C4—81no—
466C4—81no—
467C4—81no—
468C4—112no—
469C4—221no—
470C4—221no—
471C4—221no—
472C4—881no—
473C4—881no—
474C4—881no—
475C4#1062312711yescharacteristic
476C4D11×#13511yescharacteristic
477C2—22no—
478C2—161no—
479C2—1761no—
480C2#1307919011yescharacteristic
481C2D11×#50811yescharacteristic
482C2C2×#1062252911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2217C2
socleC22×C11C22×D8
prime radical#13070700C2
hypercenter#2217D11
hypocenterC11#33735
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2217

Complements

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

NH ≅ G/Ntype
1. #13079187C2semidirect
2. #13079181C2semidirect
3. #13070894C2semidirect
4. #13070876C2semidirect
5. #13070849C2semidirect
6. #13070846C2semidirect
7. #13070712C2semidirect
8. #13070705C2semidirect
10. #13070472C2semidirect
11. SD32×Dic11C2semidirect
12. #13070467C2semidirect
13. #13070460C2semidirect
14. C2×C16×Dic11C2semidirect
15. C11×#2217C2semidirect
184. #2217D11semidirect
417. C11#33735semidirect

Maximal subgroups

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

subgroupindex
#130791872
#130791812
#130708942
#130708762
#130708492
#130708462
#130707122
#130707052
#130707002
#130704722
SD32×Dic112
#130704672
#130704602
C2×C16×Dic112
C11×#22172
#3373511