Finite Group Databasebeta

← #14911518

Subgroups — #14911518

Order 2816.

474 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#13081601C211yesmaximal, characteristic
2Q16×Dic22C211yesmaximal, characteristic, complemented
3#13070852C211yesmaximal, characteristic
4#13070851C211yesmaximal, characteristic
5#13070842C211yesmaximal, characteristic, complemented
6#13070761C211yesmaximal, characteristic
7#13070759C211yesmaximal, characteristic, complemented
8#13070756C211yesmaximal, characteristic, complemented
9#13070676C211yesmaximal, characteristic
10#13070664C211yesmaximal, characteristic, complemented
11#13070523C211yesmaximal, characteristic, complemented
12#13070487C211yesmaximal, characteristic, complemented
13#13070485C211yesmaximal, characteristic, complemented
14SD32×Dic11C211yesmaximal, characteristic
15C11×#2211C211yesmaximal, characteristic
16#10623202—21no—
17Q8×Dic22—21no—
18C2×C11×Q32C2211yescharacteristic
19C2×C11×SD32C2211yescharacteristic
20C11×#495C2211yescharacteristic
21C4×C11×Q16C2211yescharacteristic
22Q16×Dic11C2211yescharacteristic
23Q16×Dic11C2211yescharacteristic
24Q16×Dic11C2211yescharacteristic
25#10622794C2211yescharacteristic
26C2×#66893C2211yescharacteristic
27#10622779—21no—
28#10622775—21no—
29#10622768C2211yescharacteristic
30D8×Dic11C2211yescharacteristic
31#10622667—21no—
32#10622634—21no—
33#10622487C2211yescharacteristic
34#10622487C2211yescharacteristic
35#10622407—21no—
36#10622407—21no—
37C4×Dic44C2211yescharacteristic
38#10622295C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40C11×C4⋊C16C2211yescharacteristic
41C11×#358C2211yescharacteristic
42C11×#357C2211yescharacteristic
43#10622202C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622143C2211yescharacteristic
49#10622143C2211yescharacteristic
50#10622141C2211yescharacteristic
51#10622141C2211yescharacteristic
52#10622140C2211yescharacteristic
53Dic11⋊C16C2211yescharacteristic
54Dic11⋊C16C2211yescharacteristic
55C16×Dic11C2211yescharacteristic
56#10622130C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622099C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×Q16C2311yescharacteristic
61C2×C11×SD16—21no—
62C2×C11×D8C2311yescharacteristic
63C11×#124—21no—
64C4×Q8×C11—21no—
65Q8×Dic11—21no—
66Q8×Dic11—21no—
67Q8×Dic11—21no—
68#66997—21no—
69C2×#4326—21no—
70#66989—21no—
71D4×Dic11—21no—
72C2×#4324—21no—
73C2×Dic44C2311yescharacteristic
74#66941—21no—
75#66941—21no—
76#66941—41no—
77#66941—41no—
78#66932—41no—
79#66932—41no—
80#66931—41no—
81#66930—41no—
82#66922—21no—
83#66922—41no—
84C4×Dic22—21no—
85C4×Dic22—41no—
86C4×Dic22D411yescharacteristic
87C11×Q32—22no—
88C11×SD32—22no—
89C2×C11×C16C2311yescharacteristic
90C2×C11×C16C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#103—21no—
93C4×C8×C11C2311yescharacteristic
94#66899—21no—
95#66899—21no—
96#66899—21no—
97#66896—21no—
98#66893—22no—
99#66882—21no—
100#66882C2311yescharacteristic
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66880—21no—
104Dic11⋊C8D411yescharacteristic
105Dic11⋊C8D411yescharacteristic
106C8×Dic11C2311yescharacteristic
107C8×Dic11C2311yescharacteristic
108C2×C11⋊C16C2311yescharacteristic
109C2×C11⋊C16C2311yescharacteristic
110#66871—21no—
111#66871—21no—
112C4⋊(C11⋊C8)D411yescharacteristic
113#33936—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×D4×C11—21no—
117C22×Dic11—41no—
118C2×Dic22—21no—
119C2×Dic22—41no—
120C2×Dic22—41no—
121C2×Dic22—41no—
122C2×Dic22D811yescharacteristic
123C11×Q16—21no—
124C11×Q16—21no—
125C11×Q16—21no—
126C11×Q16#4112yes—
127C11×SD16—81no—
128C11×D8—21no—
129C11×D8—21no—
130C2×C8×C11C2×D411yescharacteristic
131C2×C8×C11C2411yescharacteristic
132C11×C4⋊C4—21no—
133C11×C4⋊C4—41no—
134C11×C22⋊C4—41no—
135C11×C22⋊C4—41no—
136C42×C11—41no—
137C42×C11C2×D411yescharacteristic
138C22⋊Dic11—41no—
139C22⋊Dic11—41no—
140C22⋊Dic11—41no—
141#4326—81no—
142#4324—81no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—41no—
147C4⋊Dic11—41no—
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×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—
173Q8×Q16—111no—
174#2243—111no—
175#2243—111no—
176#2241—111no—
177#2226—111no—
178#2225—111no—
179#2225—111no—
180#2211—111no—
181#2211D1111yescharacteristic
182#2209—111no—
183#2183—111no—
184#2176—111no—
185#2176—111no—
186C4×SD32—111no—
187C23×C11—41no—
188Q8×C11—22no—
189Q8×C11—41no—
190Q8×C11—41no—
191Q8×C11—41no—
192D4×C11—41no—
193D4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11C2×D811yescharacteristic
198C2×C4×C11C2×D811yescharacteristic
199C2×C4×C11C22×D411yescharacteristic
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—82no—
205C2×Dic11C2×D811yescharacteristic
206C2×Dic11C2×D811yescharacteristic
207C2×Dic11C2×D811yescharacteristic
208C2×Dic11C2×D811yescharacteristic
209Dic22—22no—
210Dic22—41no—
211Dic22—41no—
212Dic22—161no—
213Dic22—161no—
214Dic22—161no—
215C8×C11—21no—
216C8×C11C2×#4111yescharacteristic
217C8×C112−1+411yescharacteristic
218C11⋊C8—21no—
219C11⋊C8—21no—
220Q82—221no—
221#556—221no—
222C2×Q32—111no—
223C2×Q32C2×D1111yescharacteristic
224C2×SD32C2×D1111yescharacteristic
225#500—111no—
226#500—111no—
227#500—111no—
228#495—111no—
229#495C2×D1111yescharacteristic
230#494—111no—
231#477—221no—
232#477—221no—
233#477—221no—
234#464—221no—
235#464—221no—
236#461—221no—
237C8×Q8—111no—
238C4×Q16—111no—
239C4×Q16—111no—
240C4×Q16—111no—
241C4×Q16—111no—
242C4×Q16C2×D1111yescharacteristic
243C4×D8—111no—
244#367—111no—
245#367—111no—
246#367—111no—
247C4⋊C16—111no—
248C4⋊C16—111no—
249C4⋊C16C2×D1111yescharacteristic
250#358—111no—
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#357C2×D1111yescharacteristic
260#346—111no—
261#346—111no—
262C4×C16—111no—
263C22×C11—81no—
264C22×C11—81no—
265C22×C11—81no—
266C22×C11C22×D811yescharacteristic
267C4×C11—21no—
268C4×C11—21no—
269C4×C11—42no—
270C4×C11—81no—
271C4×C11—81no—
272C4×C11#54811yescharacteristic
273C4×C11#57711yescharacteristic
274Dic11—21no—
275Dic11—21no—
276Dic11—21no—
277Dic11—81no—
278Dic11—81no—
279Dic11—81no—
280Dic11—81no—
281Dic11#51012yes—
282C2×Q16—111no—
283C2×Q16—221no—
284C2×Q16C22×D1111yescharacteristic
285C2×Q16C22×D1111yescharacteristic
286C2×SD16—21no—
287C2×SD16—221no—
288C2×D8C22×D1111yescharacteristic
289C4⋊Q8—221no—
290C4⋊Q8—221no—
291C4⋊Q8—221no—
292C4⋊Q8—221no—
293C4⋊Q8—441no—
294C4⋊Q8—441no—
295C4⋊Q8—441no—
296#126—441no—
297#126—441no—
298#124—21no—
299#124—221no—
300C22⋊Q8—441no—
301C4×Q8—21no—
302C4×Q8—111no—
303C4×Q8—221no—
304C4×Q8—221no—
305C4×Q8—221no—
306C4×Q8—221no—
307C4×Q8—441no—
308C4×D4—221no—
309#117—441no—
310Q32—22no—
311Q32—222no—
312SD32—22no—
313C2×C16—111no—
314C2×C16—111no—
315C2×C16C22×D1111yescharacteristic
316C2×C16C22×D1111yescharacteristic
317#107—111no—
318#107—111no—
319#107—111no—
320#107—221no—
321#107—221no—
322#107—221no—
323#107C22×D1111yescharacteristic
324C4⋊C8—111no—
325C4⋊C8—111no—
326C4⋊C8—111no—
327#103—21no—
328#103—221no—
329#103—221no—
330#103—221no—
331#103—221no—
332#102—221no—
333C4×C8—111no—
334C4×C8—111no—
335C4×C8C22×D1111yescharacteristic
336C2×C11—161no—
337C2×C11#335811yescharacteristic
338C2×C11C2×#51011yescharacteristic
339C2×C11#341611yescharacteristic
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—111no—
343C2×Q8—221no—
344C2×Q8—441no—
345C2×Q8—441no—
346C2×Q8—441no—
347C2×D4—21no—
348C22×C4—441no—
349Q16—21no—
350Q16—21no—
351Q16—21no—
352Q16—221no—
353Q16—221no—
354Q16—881no—
355Q16#434112yes—
356SD16—81no—
357SD16—881no—
358D8—21no—
359D8—21no—
360C2×C8—111no—
361C2×C8—111no—
362C2×C8D4×D1111yescharacteristic
363C2×C8C23×D1111yescharacteristic
364C4⋊C4—21no—
365C4⋊C4—41no—
366C4⋊C4—111no—
367C4⋊C4—111no—
368C4⋊C4—111no—
369C4⋊C4—221no—
370C4⋊C4—221no—
371C4⋊C4—221no—
372C4⋊C4—441no—
373C4⋊C4—441no—
374C4⋊C4—441no—
375C4⋊C4—441no—
376C4⋊C4—441no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C4⋊C4—441no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—441no—
384C22⋊C4—441no—
385C22⋊C4—441no—
386C42—41no—
387C42—111no—
388C42—111no—
389C42—441no—
390C42—441no—
391C42—441no—
392C42—441no—
393C42D4×D1111yescharacteristic
394C16—21no—
395C16—21no—
396C16—221no—
397C16—221no—
398C11#3393611yescharacteristic, complemented, Sylow
399C23—41no—
400Q8—22no—
401Q8—41no—
402Q8—41no—
403Q8—41no—
404Q8—222no—
405Q8—441no—
406Q8—441no—
407Q8—1761no—
408Q8—1761no—
409Q8—1761no—
410D4—41no—
411D4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—111no—
416C2×C4—111no—
417C2×C4—111no—
418C2×C4—111no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—882no—
424C2×C4D8×D1111yescharacteristic
425C2×C4D8×D1111yescharacteristic
426C2×C4C2×D4×D1111yescharacteristic
427C8—21no—
428C8—221no—
429C8—221no—
430C8C2×#434111yescharacteristic
431C8#6704311yescharacteristic
432C22—81no—
433C22—81no—
434C22—81no—
435C22C2×D8×D1111yescharacteristic
436C4—21no—
437C4—21no—
438C4—42no—
439C4—81no—
440C4—81no—
441C4—112no—
442C4—221no—
443C4—221no—
444C4—221no—
445C4—881no—
446C4—881no—
447C4—881no—
448C4—881no—
449C4#1062312911yescharacteristic
450C4#1062330611yescharacteristic
451C2—161no—
452C2#1308124611yescharacteristic
453C2D11×#51011yescharacteristic
454C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2211C2
socleC22×C11C22×D8
prime radicalC2×C11×D8C23
hypercenter#2211D11
hypocenterC11#33936
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2211

Complements

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

NH ≅ G/Ntype
2. Q16×Dic22C2semidirect
5. #13070842C2semidirect
7. #13070759C2semidirect
8. #13070756C2semidirect
10. #13070664C2semidirect
11. #13070523C2semidirect
12. #13070487C2semidirect
13. #13070485C2semidirect
398. C11#33936semidirect

Maximal subgroups

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

subgroupindex
#130816012
Q16×Dic222
#130708522
#130708512
#130708422
#130707612
#130707592
#130707562
#130706762
#130706642
#130705232
#130704872
#130704852
SD32×Dic112
C11×#22112
#3393611