Finite Group Databasebeta

← #14911429

Subgroups — #14911429

Order 2816.

486 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081601C211yesmaximal, characteristic, complemented
2#13081480C211yesmaximal, characteristic, complemented
3#13070846C211yesmaximal, characteristic, complemented
4#13070842C211yesmaximal, characteristic, complemented
5#13070778C211yesmaximal, characteristic, complemented
6#13070777C211yesmaximal, characteristic, complemented
7#13070761C211yesmaximal, characteristic, complemented
8#13070670C211yesmaximal, characteristic
9#13070668C211yesmaximal, characteristic
10#13070660C211yesmaximal, characteristic, complemented
11C16×Dic22C211yesmaximal, characteristic, complemented
12C4×#66864C211yesmaximal, characteristic, complemented
13#13070465C211yesmaximal, characteristic, complemented
14#13070460C211yesmaximal, characteristic
15C11×#2242C211yesmaximal, characteristic, complemented
16#10623221—21no—
17#10623202—21no—
18C11×#499C2211yescharacteristic
19C11×#495C2211yescharacteristic
20Q16×Dic11C2211yescharacteristic
21#10622794C2211yescharacteristic
22C2×#66892C2211yescharacteristic
23#10622779—21no—
24#10622775—21no—
25#10622768C2211yescharacteristic
26D8×Dic11C2211yescharacteristic
27C2×#66890C2211yescharacteristic
28#10622679—21no—
29#10622667—21no—
30C2×#66864C2211yescharacteristic
31#10622491C2211yescharacteristic
32#10622487C2211yescharacteristic
33#10622485C2211yescharacteristic
34#10622485C2211yescharacteristic
35#10622484—21no—
36#10622483—21no—
37C4×Dic44C2211yescharacteristic
38C4×D88C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40C11×#358C2211yescharacteristic
41C11×#358C2211yescharacteristic
42C11×#357C2211yescharacteristic
43C11×#357C2211yescharacteristic
44C4×C11×C16C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622143C2211yescharacteristic
49#10622141C2211yescharacteristic
50Dic11⋊C16C2211yescharacteristic
51Dic11⋊C16C2211yescharacteristic
52C16×Dic11C2211yescharacteristic
53C16×Dic11C2211yescharacteristic
54#10622130C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4⋊(C11⋊C16)C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×SD16—21no—
61C2×C11×D8C2311yescharacteristic
62C11×#125—21no—
63C11×#124—21no—
64Q8×Dic11—21no—
65#66997—21no—
66C2×#4326—21no—
67#66989—21no—
68D4×Dic11—21no—
69C2×#4324—21no—
70C2×Dic44C2311yescharacteristic
71C2×D88C2311yescharacteristic
72#66950—41no—
73#66949—41no—
74#66949—41no—
75#66946—21no—
76#66946—21no—
77C4⋊C4×D11—41no—
78#66943—21no—
79#66941—21no—
80#66932—41no—
81#66932—41no—
82#66931—41no—
83#66930—41no—
84C4×D44—21no—
85C4×Dic22—21no—
86C4×Dic22D411yescharacteristic
87C2×C11×C16C2311yescharacteristic
88C2×C11×C16C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×#107C2311yescharacteristic
91C11×#106—21no—
92C4×C8×C11C2311yescharacteristic
93#66899—21no—
94#66896—21no—
95#66892—22no—
96#66890—22no—
97#66885—21no—
98#66882C2311yescharacteristic
99#66882C2311yescharacteristic
100#66880—21no—
101Dic11⋊C8D411yescharacteristic
102Dic11⋊C8D411yescharacteristic
103C8×Dic11C2311yescharacteristic
104C8×Dic11C2311yescharacteristic
105C2×C11⋊C16C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107#66873—21no—
108#66873—21no—
109#66872—21no—
110#66871—21no—
111C4⋊(C11⋊C8)D411yescharacteristic
112#66864—22no—
113#33927—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×D4×C11—21no—
116C22×Dic11—41no—
117C2×D44—21no—
118C2×C4×D11—41no—
119C2×C4×D11—41no—
120C2×C4×D11—41no—
121C2×Dic22—21no—
122C2×Dic22—41no—
123C2×Dic22D811yescharacteristic
124C11×Q16—21no—
125C11×Q16—21no—
126C11×SD16—81no—
127C11×D8—21no—
128C11×D8—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—
137C42×C11C2×D411yescharacteristic
138C22⋊Dic11—41no—
139C22⋊Dic11—41no—
140C22⋊Dic11—41no—
141#4326—81no—
142#4324—81no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4—41no—
145(C2×D11)⋊C4—41no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—41no—
149C4⋊Dic11—41no—
150C4⋊Dic11D811yescharacteristic
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4D811yescharacteristic
157Dic11⋊C4D811yescharacteristic
158C4×Dic11—41no—
159C4×Dic11—41no—
160C4×Dic11C2×D411yescharacteristic
161C4×Dic11C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163C2×C11⋊C8C2×D411yescharacteristic
164Dic44—21no—
165Dic44—21no—
166D88—21no—
167D88#4112yes—
168C11×C16—21no—
169C11×C16—21no—
170C11⋊C16—21no—
171C11⋊C16—21no—
172#3393—111no—
173#3380—111no—
174#2242—111no—
175#2242D1111yescharacteristic, complemented
176#2241—111no—
177#2229—111no—
178#2229—111no—
179#2226—111no—
180#2210—111no—
181#2210—111no—
182#2208—111no—
183Q8×C16—111no—
184C4×SD32—111no—
185C4×SD32—111no—
186C4×D16—111no—
187C23×C11—41no—
188C22×D11—41no—
189Q8×C11—41no—
190Q8×C11—41no—
191D4×C11—41no—
192D4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11C2×D811yescharacteristic
197C2×C4×C11C2×D811yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—82no—
203C2×Dic11C2×D811yescharacteristic
204C2×Dic11C2×D811yescharacteristic
205C2×Dic11C2×D811yescharacteristic
206C2×Dic11C2×D811yescharacteristic
207D44—22no—
208D44—41no—
209C4×D11—82no—
210C4×D11—161no—
211C4×D11—161no—
212Dic22—22no—
213Dic22—41no—
214Dic22—41no—
215Dic22—161no—
216C8×C11—21no—
217C8×C11C2×#4111yescharacteristic
218C8×C112−1+411yescharacteristic
219C11⋊C8—21no—
220C11⋊C8—21no—
221#556—221no—
222#554—221no—
223C2×SD32—111no—
224C2×SD32—111no—
225C2×D16—111no—
226#500—111no—
227#499—111no—
228#499C2×D1111yescharacteristic
229#495—111no—
230#495C2×D1111yescharacteristic
231#494—111no—
232#478—221no—
233#478—221no—
234#476—221no—
235#464—221no—
236#464—221no—
237#461—221no—
238C8×Q8—111no—
239C4×Q16—111no—
240C4×Q16—111no—
241C4×D8—111no—
242C4×D8—111no—
243C4×D8—111no—
244C4×D8—111no—
245#367—111no—
246#367—111no—
247#366—111no—
248C4⋊C16—111no—
249C4⋊C16—111no—
250C4⋊C16—111no—
251#358—111no—
252#358—111no—
253#358—111no—
254#358—111no—
255#358C2×D1111yescharacteristic
256#358C2×D1111yescharacteristic
257#357—111no—
258#357—111no—
259#357C2×D1111yescharacteristic
260#357C2×D1111yescharacteristic
261C4×C16—111no—
262C4×C16—111no—
263C4×C16C2×D1111yescharacteristic
264C22×C11—81no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11C22×D811yescharacteristic
268C2×D11—42no—
269C2×D11—81no—
270C2×D11—81no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—81no—
274C4×C11—81no—
275C4×C11—81no—
276C4×C11#54811yescharacteristic
277C4×C11#57711yescharacteristic
278Dic11—21no—
279Dic11—21no—
280Dic11—21no—
281Dic11—81no—
282Dic11—81no—
283Dic11—81no—
284Dic11#50812yes—
285C2×Q16—111no—
286C2×Q16—221no—
287C2×Q16C22×D1111yescharacteristic
288C2×SD16—21no—
289C2×SD16—221no—
290C2×D8—111no—
291C2×D8C22×D1111yescharacteristic
292C4⋊Q8—221no—
293C4⋊Q8—221no—
294#126—441no—
295#126—441no—
296#125—21no—
297#125—221no—
298#124—21no—
299#124—221no—
300C22⋊Q8—441no—
301C22⋊Q8—441no—
302C22⋊Q8—441no—
303C22⋊Q8—441no—
304C4×Q8—111no—
305C4×Q8—221no—
306C4×Q8—221no—
307C4×D4—221no—
308C4×D4—221no—
309C4×D4—221no—
310C4×D4—221no—
311#117—441no—
312C2×C4⋊C4—441no—
313SD32—222no—
314SD32—222no—
315D16—222no—
316C2×C16—111no—
317C2×C16—111no—
318C2×C16C22×D1111yescharacteristic
319C2×C16C22×D1111yescharacteristic
320#107—111no—
321#107—111no—
322#107—221no—
323#107C22×D1111yescharacteristic
324#107C22×D1111yescharacteristic
325#106—21no—
326#106—221no—
327C4⋊C8—111no—
328C4⋊C8—111no—
329C4⋊C8—111no—
330#103—221no—
331#103—221no—
332#102—221no—
333#102—221no—
334#102—221no—
335#102—221no—
336C4×C8—111no—
337C4×C8—111no—
338C4×C8C22×D1111yescharacteristic
339C2×C11—161no—
340C2×C11#335811yescharacteristic
341C2×C11C2×#50811yescharacteristic
342C2×C11#341611yescharacteristic
343D11—82no—
344C2×Q8—21no—
345C2×Q8—111no—
346C2×Q8—221no—
347C2×Q8—441no—
348C2×D4—21no—
349C2×D4—221no—
350C22×C4—441no—
351C22×C4—441no—
352C22×C4—441no—
353C22×C4—441no—
354Q16—21no—
355Q16—21no—
356Q16—221no—
357Q16—221no—
358Q16—881no—
359SD16—81no—
360SD16—881no—
361D8—21no—
362D8—21no—
363D8—112no—
364D8—221no—
365C2×C8—111no—
366C2×C8—111no—
367C2×C8D4×D1111yescharacteristic
368C2×C8C23×D1111yescharacteristic
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—111no—
374C4⋊C4—111no—
375C4⋊C4—111no—
376C4⋊C4—221no—
377C4⋊C4—221no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C4⋊C4—441no—
381C4⋊C4—441no—
382C4⋊C4—441no—
383C4⋊C4—441no—
384C4⋊C4—441no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—441no—
388C22⋊C4—441no—
389C22⋊C4—441no—
390C22⋊C4—441no—
391C22⋊C4—441no—
392C22⋊C4—441no—
393C42—111no—
394C42—111no—
395C42—441no—
396C42—441no—
397C42D4×D1111yescharacteristic
398C16—21no—
399C16—21no—
400C16—221no—
401C16—221no—
402C11#3392711yescharacteristic, complemented, Sylow
403C23—41no—
404C23—441no—
405Q8—41no—
406Q8—41no—
407Q8—222no—
408Q8—441no—
409Q8—441no—
410Q8—1761no—
411D4—41no—
412D4—41no—
413D4—222no—
414D4—441no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—111no—
419C2×C4—111no—
420C2×C4—111no—
421C2×C4—111no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—882no—
426C2×C4—882no—
427C2×C4—1761no—
428C2×C4—1761no—
429C2×C4D8×D1111yescharacteristic
430C2×C4D8×D1111yescharacteristic
431C2×C4C2×D4×D1111yescharacteristic
432C8—21no—
433C8—221no—
434C8—221no—
435C8#41×D1111yescharacteristic
436C8#6704311yescharacteristic
437C22—81no—
438C22—81no—
439C22—81no—
440C22—442no—
441C22—881no—
442C22—881no—
443C22C2×D8×D1111yescharacteristic
444C4—21no—
445C4—21no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—112no—
450C4—221no—
451C4—221no—
452C4—221no—
453C4—881no—
454C4—881no—
455C4—881no—
456C4#1062320811yescharacteristic
457C4#1062329311yescharacteristic
458C2—161no—
459C2—882no—
460C2#1308124811yescharacteristic
461C2D11×#50811yescharacteristic
462C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2242C2
socleC22×C11C22×D8
prime radicalC2×#66890C22
hypercenter#2242D11
hypocenterC11#33927
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2242

Complements

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

NH ≅ G/Ntype
1. #13081601C2semidirect
2. #13081480C2semidirect
3. #13070846C2semidirect
4. #13070842C2semidirect
5. #13070778C2semidirect
6. #13070777C2semidirect
7. #13070761C2semidirect
10. #13070660C2semidirect
11. C16×Dic22C2semidirect
12. C4×#66864C2semidirect
13. #13070465C2semidirect
15. C11×#2242C2semidirect
175. #2242D11semidirect
402. C11#33927semidirect

Maximal subgroups

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

subgroupindex
#130816012
#130814802
#130708462
#130708422
#130707782
#130707772
#130707612
#130706702
#130706682
#130706602
C16×Dic222
C4×#668642
#130704652
#130704602
C11×#22422
#3392711