Finite Group Databasebeta

← #14911465

Subgroups — #14911465

Order 2816.

472 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081601C211yesmaximal, characteristic
2#13081504C211yesmaximal, characteristic, complemented
3#13070846C211yesmaximal, characteristic
4#13070842C211yesmaximal, characteristic, complemented
5#13070782C211yesmaximal, characteristic, complemented
6#13070777C211yesmaximal, characteristic, complemented
7#13070751C211yesmaximal, characteristic
8#13070677C211yesmaximal, characteristic
9#13070675C211yesmaximal, characteristic
10#13070665C211yesmaximal, characteristic, complemented
11C16×Dic22C211yesmaximal, characteristic, complemented
12C4×Dic88C211yesmaximal, characteristic, complemented
13#13070472C211yesmaximal, characteristic, complemented
14#13070471C211yesmaximal, characteristic
15C11×#2242C211yesmaximal, characteristic
16#10623216—21no—
17#10623202—21no—
18C11×#499C2211yescharacteristic
19C11×#495C2211yescharacteristic
20Q16×Dic11C2211yescharacteristic
21#10622794C2211yescharacteristic
22C2×#66893C2211yescharacteristic
23#10622779—21no—
24#10622775—21no—
25#10622768C2211yescharacteristic
26D8×Dic11C2211yescharacteristic
27C2×#66891C2211yescharacteristic
28#10622676—21no—
29#10622667—21no—
30C2×Dic88C2211yescharacteristic
31#10622491C2211yescharacteristic
32#10622487C2211yescharacteristic
33#10622486C2211yescharacteristic
34#10622486C2211yescharacteristic
35#10622470—21no—
36#10622467—21no—
37C4×Dic44C2211yescharacteristic
38C4×Dic44C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40C11×#358C2211yescharacteristic
41C11×#358C2211yescharacteristic
42C11×#357C2211yescharacteristic
43C11×#357C2211yescharacteristic
44C4×C11×C16C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622142C2211yescharacteristic
48#10622141C2211yescharacteristic
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×Dic44C2311yescharacteristic
72#66943—21no—
73#66942—41no—
74#66942—41no—
75#66941—21no—
76#66941—41no—
77#66940—21no—
78#66940—21no—
79#66940—41no—
80#66932—41no—
81#66932—41no—
82#66931—41no—
83#66930—41no—
84C4×Dic22—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#66893—22no—
96#66891—22no—
97#66882C2311yescharacteristic
98#66882C2311yescharacteristic
99#66880—21no—
100#66880—21no—
101Dic11⋊C8D411yescharacteristic
102Dic11⋊C8D411yescharacteristic
103C8×Dic11C2311yescharacteristic
104C8×Dic11C2311yescharacteristic
105C2×C11⋊C16C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107#66874—21no—
108#66874—21no—
109#66872—21no—
110#66871—21no—
111C4⋊(C11⋊C8)D411yescharacteristic
112Dic88—22no—
113#33931—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×D4×C11—21no—
116C22×Dic11—41no—
117C2×Dic22—21no—
118C2×Dic22—21no—
119C2×Dic22—41no—
120C2×Dic22D811yescharacteristic
121C11×Q16—21no—
122C11×Q16—21no—
123C11×SD16—81no—
124C11×D8—21no—
125C11×D8—21no—
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11C2411yescharacteristic
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—41no—
131C11×C4⋊C4—41no—
132C11×C22⋊C4—41no—
133C11×C22⋊C4—41no—
134C42×C11C2×D411yescharacteristic
135C22⋊Dic11—41no—
136C22⋊Dic11—41no—
137C22⋊Dic11—41no—
138#4326—81no—
139#4324—81no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11—41no—
143C4⋊Dic11—41no—
144C4⋊Dic11D811yescharacteristic
145Dic11⋊C4—41no—
146Dic11⋊C4—41no—
147Dic11⋊C4—41no—
148Dic11⋊C4—41no—
149Dic11⋊C4—41no—
150Dic11⋊C4—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4D811yescharacteristic
154Dic11⋊C4D811yescharacteristic
155C4×Dic11—41no—
156C4×Dic11—41no—
157C4×Dic11—41no—
158C4×Dic11—41no—
159C4×Dic11—41no—
160C4×Dic11C2×D411yescharacteristic
161C4×Dic11C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163C2×C11⋊C8C2×D411yescharacteristic
164Dic44—21no—
165Dic44—21no—
166Dic44—21no—
167Dic44#4112yes—
168C11×C16—21no—
169C11×C16—21no—
170C11⋊C16—21no—
171C11⋊C16—21no—
172#3393—111no—
173#3383—111no—
174#2242—111no—
175#2242D1111yescharacteristic
176#2241—111no—
177#2229—111no—
178#2229—111no—
179#2224—111no—
180#2211—111no—
181#2211—111no—
182#2209—111no—
183Q8×C16—111no—
184C4×Q32—111no—
185C4×Q32—111no—
186C4×SD32—111no—
187C23×C11—41no—
188Q8×C11—41no—
189Q8×C11—41no—
190D4×C11—41no—
191D4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11C2×D811yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—82no—
203C2×Dic11C2×D811yescharacteristic
204C2×Dic11C2×D811yescharacteristic
205C2×Dic11C2×D811yescharacteristic
206C2×Dic11C2×D811yescharacteristic
207Dic22—22no—
208Dic22—22no—
209Dic22—41no—
210Dic22—41no—
211Dic22—41no—
212Dic22—82no—
213C8×C11—21no—
214C8×C11C2×#4111yescharacteristic
215C8×C112−1+411yescharacteristic
216C11⋊C8—21no—
217C11⋊C8—21no—
218#557—221no—
219#556—221no—
220C2×Q32—111no—
221C2×Q32—111no—
222C2×SD32—111no—
223#500—111no—
224#499—111no—
225#499C2×D1111yescharacteristic
226#495—111no—
227#495C2×D1111yescharacteristic
228#494—111no—
229#479—221no—
230#479—221no—
231#475—221no—
232#464—221no—
233#464—221no—
234#461—221no—
235C8×Q8—111no—
236C4×Q16—111no—
237C4×Q16—111no—
238C4×Q16—111no—
239C4×Q16—111no—
240C4×Q16—111no—
241C4×D8—111no—
242#367—111no—
243#366—111no—
244#366—111no—
245C4⋊C16—111no—
246C4⋊C16—111no—
247C4⋊C16—111no—
248#358—111no—
249#358—111no—
250#358—111no—
251#358—111no—
252#358—111no—
253#358C2×D1111yescharacteristic
254#358C2×D1111yescharacteristic
255#357—111no—
256#357C2×D1111yescharacteristic
257#357C2×D1111yescharacteristic
258C4×C16—111no—
259C4×C16—111no—
260C4×C16C2×D1111yescharacteristic
261C22×C11—81no—
262C22×C11—81no—
263C22×C11—81no—
264C22×C11C22×D811yescharacteristic
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—81no—
268C4×C11—81no—
269C4×C11—81no—
270C4×C11#54811yescharacteristic
271C4×C11#57711yescharacteristic
272Dic11—21no—
273Dic11—21no—
274Dic11—21no—
275Dic11—42no—
276Dic11—81no—
277Dic11—81no—
278Dic11—81no—
279Dic11#50812yes—
280C2×Q16—111no—
281C2×Q16—111no—
282C2×Q16—221no—
283C2×Q16C22×D1111yescharacteristic
284C2×SD16—21no—
285C2×SD16—221no—
286C2×D8C22×D1111yescharacteristic
287C4⋊Q8—221no—
288C4⋊Q8—221no—
289C4⋊Q8—441no—
290#126—441no—
291#126—441no—
292#125—21no—
293#125—221no—
294#125—441no—
295#125—441no—
296#124—21no—
297#124—221no—
298C22⋊Q8—441no—
299C4×Q8—111no—
300C4×Q8—221no—
301C4×Q8—221no—
302C4×Q8—221no—
303C4×Q8—221no—
304C4×Q8—221no—
305C4×Q8—441no—
306C4×D4—221no—
307#117—441no—
308Q32—222no—
309Q32—222no—
310SD32—222no—
311C2×C16—111no—
312C2×C16—111no—
313C2×C16C22×D1111yescharacteristic
314C2×C16C22×D1111yescharacteristic
315#107—111no—
316#107—111no—
317#107—221no—
318#107C22×D1111yescharacteristic
319#107C22×D1111yescharacteristic
320#106—21no—
321#106—221no—
322C4⋊C8—111no—
323C4⋊C8—111no—
324C4⋊C8—111no—
325#103—221no—
326#103—221no—
327#103—221no—
328#103—221no—
329#103—221no—
330#102—221no—
331C4×C8—111no—
332C4×C8—111no—
333C4×C8C22×D1111yescharacteristic
334C2×C11—161no—
335C2×C11#335811yescharacteristic
336C2×C11C2×#50811yescharacteristic
337C2×C11#341711yescharacteristic
338C2×Q8—21no—
339C2×Q8—111no—
340C2×Q8—221no—
341C2×Q8—221no—
342C2×Q8—441no—
343C2×D4—21no—
344C22×C4—441no—
345Q16—21no—
346Q16—21no—
347Q16—112no—
348Q16—221no—
349Q16—221no—
350Q16—221no—
351Q16—881no—
352SD16—81no—
353SD16—881no—
354D8—21no—
355D8—21no—
356C2×C8—111no—
357C2×C8—111no—
358C2×C8D4×D1111yescharacteristic
359C2×C8C23×D1111yescharacteristic
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—111no—
365C4⋊C4—111no—
366C4⋊C4—111no—
367C4⋊C4—221no—
368C4⋊C4—221no—
369C4⋊C4—441no—
370C4⋊C4—441no—
371C4⋊C4—441no—
372C4⋊C4—441no—
373C4⋊C4—441no—
374C4⋊C4—441no—
375C4⋊C4—441no—
376C4⋊C4—441no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—441no—
382C22⋊C4—441no—
383C22⋊C4—441no—
384C42—111no—
385C42—111no—
386C42—441no—
387C42—441no—
388C42—441no—
389C42—441no—
390C42—441no—
391C42D4×D1111yescharacteristic
392C16—21no—
393C16—21no—
394C16—221no—
395C16—221no—
396C11#3393111yescharacteristic, complemented, Sylow
397C23—41no—
398Q8—41no—
399Q8—41no—
400Q8—222no—
401Q8—222no—
402Q8—441no—
403Q8—441no—
404Q8—441no—
405Q8—882no—
406D4—41no—
407D4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—111no—
412C2×C4—111no—
413C2×C4—111no—
414C2×C4—111no—
415C2×C4—441no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—882no—
420C2×C4D8×D1111yescharacteristic
421C2×C4D8×D1111yescharacteristic
422C2×C4C2×D4×D1111yescharacteristic
423C8—21no—
424C8—221no—
425C8—221no—
426C8#41×D1111yescharacteristic
427C8#6704311yescharacteristic
428C22—81no—
429C22—81no—
430C22—81no—
431C22C2×D8×D1111yescharacteristic
432C4—21no—
433C4—21no—
434C4—81no—
435C4—81no—
436C4—81no—
437C4—112no—
438C4—221no—
439C4—221no—
440C4—221no—
441C4—442no—
442C4—881no—
443C4—881no—
444C4—881no—
445C4#1062320811yescharacteristic
446C4#1062329311yescharacteristic
447C2—161no—
448C2#1308124811yescharacteristic
449C2D11×#50811yescharacteristic
450C2#1308176611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2242C2
socleC22×C11C22×D8
prime radicalC2×C11×D8C23
hypercenter#2242D11
hypocenterC11#33931
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
2. #13081504C2semidirect
4. #13070842C2semidirect
5. #13070782C2semidirect
6. #13070777C2semidirect
10. #13070665C2semidirect
11. C16×Dic22C2semidirect
12. C4×Dic88C2semidirect
13. #13070472C2semidirect
396. C11#33931semidirect

Maximal subgroups

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

subgroupindex
#130816012
#130815042
#130708462
#130708422
#130707822
#130707772
#130707512
#130706772
#130706752
#130706652
C16×Dic222
C4×Dic882
#130704722
#130704712
C11×#22422
#3393111