Finite Group Databasebeta

← #14911427

Subgroups — #14911427

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#13081483C211yesmaximal, characteristic, complemented
3#13070847C211yesmaximal, characteristic, complemented
4#13070846C211yesmaximal, characteristic, complemented
5#13070842C211yesmaximal, characteristic, complemented
6#13070782C211yesmaximal, characteristic, complemented
7#13070781C211yesmaximal, characteristic, complemented
8#13070761C211yesmaximal, characteristic, complemented
9#13070669C211yesmaximal, characteristic
10#13070659C211yesmaximal, characteristic, complemented
11#13070518C211yesmaximal, characteristic, complemented
12SD32×Dic11C211yesmaximal, characteristic, complemented
13C4×#66891C211yesmaximal, characteristic, complemented
14D16×Dic11C211yesmaximal, characteristic
15C11×#2210C211yesmaximal, characteristic
16#10623202—21no—
17#10623070—21no—
18C2×C11×SD32C2211yescharacteristic
19C2×C11×D16C2211yescharacteristic
20C11×#495C2211yescharacteristic
21C4×C11×D8C2211yescharacteristic
22Q16×Dic11C2211yescharacteristic
23#10622794C2211yescharacteristic
24#10622779—21no—
25#10622775—21no—
26#10622768C2211yescharacteristic
27D8×Dic11C2211yescharacteristic
28D8×Dic11C2211yescharacteristic
29D8×Dic11C2211yescharacteristic
30C2×#66891C2211yescharacteristic
31#10622667—21no—
32#10622622—21no—
33#10622491C2211yescharacteristic
34#10622487C2211yescharacteristic
35#10622376—21no—
36#10622374—21no—
37C4×Dic44C2211yescharacteristic
38#10622296C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40C11×C4⋊C16C2211yescharacteristic
41C11×#358C2211yescharacteristic
42C11×#357C2211yescharacteristic
43#10622202C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622143C2211yescharacteristic
49#10622142C2211yescharacteristic
50#10622141C2211yescharacteristic
51#10622141C2211yescharacteristic
52Dic11⋊C16C2211yescharacteristic
53Dic11⋊C16C2211yescharacteristic
54C16×Dic11C2211yescharacteristic
55C16×Dic11C2211yescharacteristic
56#10622130C2211yescharacteristic
57#10622128C2211yescharacteristic
58C4×C11⋊C16C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×SD16—21no—
61C2×C11×D8C2311yescharacteristic
62C2×C11×D8C2311yescharacteristic
63C11×#124—21no—
64C4×D4×C11—21no—
65Q8×Dic11—21no—
66#66997—21no—
67C2×#4326—21no—
68#66989—21no—
69D4×Dic11—21no—
70D4×Dic11—21no—
71D4×Dic11—21no—
72C2×#4324—21no—
73#66977—41no—
74C2×Dic11⋊C4—41no—
75C2×Dic44C2311yescharacteristic
76#66943—21no—
77#66941—21no—
78#66932—41no—
79#66932—41no—
80#66931—41no—
81#66931—41no—
82#66931—41no—
83#66930—41no—
84#66923—21no—
85C4×Dic22—21no—
86C4×Dic22D411yescharacteristic
87C11×SD32—22no—
88C11×D16—22no—
89C2×C11×C16C2311yescharacteristic
90C2×C11×C16C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#102—21no—
93C4×C8×C11C2311yescharacteristic
94#66899—21no—
95#66896—21no—
96#66896—21no—
97#66896—21no—
98#66891—22no—
99#66882C2311yescharacteristic
100#66882C2311yescharacteristic
101#66882C2311yescharacteristic
102#66881—21no—
103#66880—21no—
104Dic11⋊C8D411yescharacteristic
105Dic11⋊C8D411yescharacteristic
106C8×Dic11C2311yescharacteristic
107C8×Dic11C2311yescharacteristic
108C2×C11⋊C16C2311yescharacteristic
109C2×C11⋊C16C2311yescharacteristic
110#66872—21no—
111#66871—21no—
112C4⋊(C11⋊C8)D411yescharacteristic
113#33927—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C22×C4×C11—41no—
118C22×Dic11—41no—
119C22×Dic11—41no—
120C22×Dic11—41no—
121C2×Dic22—21no—
122C2×Dic22—41no—
123C2×Dic22D811yescharacteristic
124C11×Q16—21no—
125C11×Q16—21no—
126C11×SD16—81no—
127C11×D8—21no—
128C11×D8—21no—
129C11×D8—21no—
130C11×D8#4112yes—
131C2×C8×C11C2×D411yescharacteristic
132C2×C8×C11C2411yescharacteristic
133C11×C4⋊C4—21no—
134C11×C22⋊C4—41no—
135C11×C22⋊C4—41no—
136C11×C22⋊C4—41no—
137C42×C11C2×D411yescharacteristic
138C22⋊Dic11—41no—
139C22⋊Dic11—41no—
140C22⋊Dic11—41no—
141C22⋊Dic11—41no—
142C22⋊Dic11—41no—
143#4326—81no—
144#4324—81no—
145C4⋊Dic11—21no—
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⋊C4—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4D811yescharacteristic
159Dic11⋊C4D811yescharacteristic
160C4×Dic11—41no—
161C4×Dic11—41no—
162C4×Dic11C2×D411yescharacteristic
163C4×Dic11C2×D411yescharacteristic
164C2×C11⋊C8C2×D411yescharacteristic
165C2×C11⋊C8C2×D411yescharacteristic
166Dic44—21no—
167Dic44—21no—
168C11×C16—21no—
169C11×C16—21no—
170C11⋊C16—21no—
171C11⋊C16—21no—
172#3393—111no—
173#3380—111no—
174#2242—111no—
175#2242—111no—
176#2241—111no—
177#2229—111no—
178#2229—111no—
179#2226—111no—
180#2210—111no—
181#2210D1111yescharacteristic
182#2208—111no—
183Q8×C16—111no—
184C4×SD32—111no—
185C4×SD32—111no—
186C4×D16—111no—
187C23×C11—41no—
188C23×C11—41no—
189Q8×C11—41no—
190Q8×C11—41no—
191D4×C11—22no—
192D4×C11—41no—
193D4×C11—41no—
194D4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—161no—
198C2×C4×C11C2×D811yescharacteristic
199C2×C4×C11C2×D811yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—82no—
206C2×Dic11—82no—
207C2×Dic11—161no—
208C2×Dic11C2×D811yescharacteristic
209C2×Dic11C2×D811yescharacteristic
210C2×Dic11C2×D811yescharacteristic
211C2×Dic11C2×D811yescharacteristic
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×SD32C2×D1111yescharacteristic
225C2×D16C2×D1111yescharacteristic
226#500—111no—
227#499—111no—
228#499—111no—
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×D8C2×D1111yescharacteristic
245#367—111no—
246#367—111no—
247#366—111no—
248C4⋊C16—111no—
249C4⋊C16—111no—
250C4⋊C16C2×D1111yescharacteristic
251#358—111no—
252#358—111no—
253#358—111no—
254#358—111no—
255#358—111no—
256#358C2×D1111yescharacteristic
257#357—111no—
258#357—111no—
259#357—111no—
260#357C2×D1111yescharacteristic
261C4×C16—111no—
262C4×C16—111no—
263C4×C16—111no—
264C22×C11—42no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11—81no—
270C22×C11C22×D811yescharacteristic
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—81no—
274C4×C11—81no—
275C4×C11#54811yescharacteristic
276C4×C11#57711yescharacteristic
277Dic11—21no—
278Dic11—21no—
279Dic11—21no—
280Dic11—81no—
281Dic11—81no—
282Dic11—81no—
283Dic11—81no—
284Dic11#50812yes—
285C2×Q16—111no—
286C2×Q16—221no—
287C2×Q16C22×D1111yescharacteristic
288C2×SD16—21no—
289C2×SD16—221no—
290C2×D8C22×D1111yescharacteristic
291C2×D8C22×D1111yescharacteristic
292C4⋊Q8—221no—
293C4⋊Q8—221no—
294#126—441no—
295#126—441no—
296#125—221no—
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—21no—
308C4×D4—221no—
309C4×D4—221no—
310C4×D4—221no—
311#117—441no—
312C2×C4⋊C4—441no—
313SD32—22no—
314SD32—222no—
315D16—22no—
316C2×C16—111no—
317C2×C16—111no—
318C2×C16C22×D1111yescharacteristic
319C2×C16C22×D1111yescharacteristic
320#107—111no—
321#107—111no—
322#107—111no—
323#107—221no—
324#107C22×D1111yescharacteristic
325#106—221no—
326#106—221no—
327C4⋊C8—111no—
328C4⋊C8—111no—
329C4⋊C8—111no—
330#103—221no—
331#103—221no—
332#102—21no—
333#102—221no—
334#102—221no—
335#102—221no—
336C4×C8—111no—
337C4×C8—111no—
338C4×C8C22×D1111yescharacteristic
339C2×C11—82no—
340C2×C11—161no—
341C2×C11#335811yescharacteristic
342C2×C11C2×#50811yescharacteristic
343C2×C11#341611yescharacteristic
344C2×Q8—21no—
345C2×Q8—111no—
346C2×Q8—221no—
347C2×Q8—441no—
348C2×D4—21no—
349C2×D4—21no—
350C22×C4—41no—
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—21no—
364D8#434112yes—
365C2×C8—111no—
366C2×C8—111no—
367C2×C8D4×D1111yescharacteristic
368C2×C8C23×D1111yescharacteristic
369C4⋊C4—21no—
370C4⋊C4—111no—
371C4⋊C4—111no—
372C4⋊C4—111no—
373C4⋊C4—221no—
374C4⋊C4—221no—
375C4⋊C4—221no—
376C4⋊C4—441no—
377C4⋊C4—441no—
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—41no—
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—41no—
405Q8—41no—
406Q8—41no—
407Q8—222no—
408Q8—441no—
409Q8—441no—
410Q8—1761no—
411D4—22no—
412D4—41no—
413D4—41no—
414D4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—111no—
418C2×C4—111no—
419C2×C4—111no—
420C2×C4—111no—
421C2×C4—161no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—882no—
427C2×C4—882no—
428C2×C4—1761no—
429C2×C4D8×D1111yescharacteristic
430C2×C4D8×D1111yescharacteristic
431C2×C4C2×D4×D1111yescharacteristic
432C8—21no—
433C8—221no—
434C8—221no—
435C8C2×#434111yescharacteristic
436C8#6704311yescharacteristic
437C22—42no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22C2×D8×D1111yescharacteristic
444C4—21no—
445C4—21no—
446C4—81no—
447C4—81no—
448C4—112no—
449C4—221no—
450C4—221no—
451C4—221no—
452C4—881no—
453C4—881no—
454C4—881no—
455C4—881no—
456C4#1062312911yescharacteristic
457C4#1062330611yescharacteristic
458C2—82no—
459C2—161no—
460C2#1308124611yescharacteristic
461C2D11×#50811yescharacteristic
462C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2210C2
socleC22×C11C22×D8
prime radicalC2×C11×D16C22
hypercenter#2210D11
hypocenterC11#33927
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2210

Complements

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

NH ≅ G/Ntype
1. #13081601C2semidirect
2. #13081483C2semidirect
3. #13070847C2semidirect
4. #13070846C2semidirect
5. #13070842C2semidirect
6. #13070782C2semidirect
7. #13070781C2semidirect
8. #13070761C2semidirect
10. #13070659C2semidirect
11. #13070518C2semidirect
12. SD32×Dic11C2semidirect
13. C4×#66891C2semidirect
402. C11#33927semidirect

Maximal subgroups

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

subgroupindex
#130816012
#130814832
#130708472
#130708462
#130708422
#130707822
#130707812
#130707612
#130706692
#130706592
#130705182
SD32×Dic112
C4×#668912
D16×Dic112
C11×#22102
#3392711