Finite Group Databasebeta

← #14911565

Subgroups — #14911565

Order 2816.

476 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#13081621C211yesmaximal, characteristic, complemented
2#13081483C211yesmaximal, characteristic
3#13070862C211yesmaximal, characteristic, complemented
4#13070860C211yesmaximal, characteristic, complemented
5#13070842C211yesmaximal, characteristic, complemented
6#13070780C211yesmaximal, characteristic, complemented
7#13070779C211yesmaximal, characteristic, complemented
8#13070767C211yesmaximal, characteristic, complemented
9#13070661C211yesmaximal, characteristic
10#13070659C211yesmaximal, characteristic
11#13070659C211yesmaximal, characteristic
12#13070522C211yesmaximal, characteristic, complemented
13#13070477C211yesmaximal, characteristic
14#13070471C211yesmaximal, characteristic
15C11×#2175C211yesmaximal, characteristic
16#10623098—21no—
17#10623070—21no—
18C2×C11×SD32C2211yescharacteristic
19C4×C11×Q16C2211yescharacteristic
20C4×C11×D8C2211yescharacteristic
21#10622794C2211yescharacteristic
22#10622794C2211yescharacteristic
23D8×Dic11C2211yescharacteristic
24D8×Dic11C2211yescharacteristic
25C2×#66891C2211yescharacteristic
26C2×#66891C2211yescharacteristic
27#10622644—21no—
28#10622622—21no—
29#10622491C2211yescharacteristic
30#10622487C2211yescharacteristic
31#10622486C2211yescharacteristic
32#10622486C2211yescharacteristic
33#10622406—21no—
34#10622406—21no—
35#10622376—21no—
36#10622374—21no—
37#10622312C2211yescharacteristic
38#10622296C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40C11×#366C2211yescharacteristic
41C11×#358C2211yescharacteristic
42C11×#357C2211yescharacteristic
43C11×#346C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622141C2211yescharacteristic
47#10622141C2211yescharacteristic
48#10622141C2211yescharacteristic
49#10622141C2211yescharacteristic
50#10622140C2211yescharacteristic
51Dic11⋊C16C2211yescharacteristic
52Dic11⋊C16C2211yescharacteristic
53C16×Dic11C2211yescharacteristic
54#10622130C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4⋊(C11⋊C16)C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×D8C2311yescharacteristic
61C4×Q8×C11—21no—
62C4×D4×C11—21no—
63#66997—21no—
64#66997—21no—
65C2×#4326—21no—
66C2×#4326—21no—
67D4×Dic11—21no—
68D4×Dic11—21no—
69#66977—41no—
70C2×Dic11⋊C4—41no—
71C2×Dic44—21no—
72C2×Dic44C2311yescharacteristic
73C2×Dic44C2311yescharacteristic
74#66943—21no—
75#66942—41no—
76#66942—41no—
77#66941—21no—
78#66940—21no—
79#66940—21no—
80#66931—41no—
81#66931—41no—
82#66923—21no—
83#66923—41no—
84#66922—21no—
85C4×Dic22—41no—
86C4×Dic22D411yescharacteristic
87C11×SD32—22no—
88C2×C11×C16C2311yescharacteristic
89C2×C11×C16C2311yescharacteristic
90C11×#107C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#103—21no—
93C11×#102—21no—
94C4×C8×C11C2311yescharacteristic
95#66896—21no—
96#66896—21no—
97#66891—22no—
98#66891—22no—
99#66882C2311yescharacteristic
100#66882C2311yescharacteristic
101#66881—21no—
102Dic11⋊C8D411yescharacteristic
103Dic11⋊C8D411yescharacteristic
104C8×Dic11C2311yescharacteristic
105C8×Dic11C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108#66874—21no—
109#66874—21no—
110#66872—21no—
111#66871—21no—
112C4⋊(C11⋊C8)D411yescharacteristic
113#33939—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×D4×C11—21no—
116C22×C4×C11—41no—
117C22×Dic11—41no—
118C22×Dic11—41no—
119C2×Dic22—21no—
120C2×Dic22—21no—
121C2×Dic22—41no—
122C2×Dic22D811yescharacteristic
123C11×Q16—21no—
124C11×Q16—21no—
125C11×D8—21no—
126C11×D8#4112yes—
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2411yescharacteristic
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—41no—
132C11×C22⋊C4—41no—
133C42×C11—41no—
134C42×C11C2×D411yescharacteristic
135C22⋊Dic11—41no—
136C22⋊Dic11—41no—
137#4326—81no—
138#4326—81no—
139C4⋊Dic11—21no—
140C4⋊Dic11—21no—
141C4⋊Dic11—41no—
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⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4D811yescharacteristic
156Dic11⋊C4D811yescharacteristic
157C4×Dic11—41no—
158C4×Dic11—41no—
159C4×Dic11C2×D411yescharacteristic
160C4×Dic11C2×D411yescharacteristic
161C2×C11⋊C8C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163Dic44—21no—
164Dic44—21no—
165Dic44—21no—
166Dic44—21no—
167Dic44—81no—
168C11×C16—21no—
169C11×C16—21no—
170C11⋊C16—21no—
171C11⋊C16—21no—
172#3395—111no—
173#3380—111no—
174#2245—111no—
175#2245—111no—
176#2241—111no—
177#2229—111no—
178#2229—111no—
179#2227—111no—
180#2208—111no—
181#2208—111no—
182#2208—111no—
183#2183—111no—
184#2175—111no—
185#2175D1111yescharacteristic
186C4×SD32—111no—
187C23×C11—41no—
188Q8×C11—41no—
189Q8×C11—41no—
190D4×C11—22no—
191D4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—161no—
196C2×C4×C11C2×D811yescharacteristic
197C2×C4×C11C2×D811yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—82no—
204C2×Dic11—161no—
205C2×Dic11C2×D811yescharacteristic
206C2×Dic11C2×D811yescharacteristic
207C2×Dic11C2×D811yescharacteristic
208C2×Dic11C2×D811yescharacteristic
209Dic22—22no—
210Dic22—41no—
211Dic22—41no—
212Dic22—41no—
213Dic22—41no—
214Dic22—161no—
215C8×C11—21no—
216C8×C11C2×#4111yescharacteristic
217C8×C112−1+411yescharacteristic
218C11⋊C8—21no—
219C11⋊C8—21no—
220#557—221no—
221#554—221no—
222C2×SD32—111no—
223C2×SD32—111no—
224C2×SD32C2×D1111yescharacteristic
225#500—111no—
226#499—111no—
227#499—111no—
228#494—111no—
229#494—111no—
230#494—111no—
231#478—221no—
232#478—221no—
233#476—221no—
234#462—221no—
235#462—221no—
236#462—221no—
237C8×Q8—111no—
238C4×Q16—111no—
239C4×Q16—111no—
240C4×Q16C2×D1111yescharacteristic
241C4×D8—111no—
242C4×D8—111no—
243C4×D8C2×D1111yescharacteristic
244#367—111no—
245#366—111no—
246#366C2×D1111yescharacteristic
247C4⋊C16—111no—
248C4⋊C16—111no—
249C4⋊C16—111no—
250#358—111no—
251#358—111no—
252#358—111no—
253#358—111no—
254#358—111no—
255#358—111no—
256#358—111no—
257#358—111no—
258#358C2×D1111yescharacteristic
259#357C2×D1111yescharacteristic
260#346—111no—
261#346C2×D1111yescharacteristic
262C4×C16—111no—
263C22×C11—42no—
264C22×C11—81no—
265C22×C11—81no—
266C22×C11C22×D811yescharacteristic
267C4×C11—21no—
268C4×C11—21no—
269C4×C11—81no—
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—111no—
284C2×Q16—221no—
285C2×Q16—221no—
286C2×Q16—221no—
287C2×Q16C22×D1111yescharacteristic
288C2×D8C22×D1111yescharacteristic
289C4⋊Q8—221no—
290C4⋊Q8—221no—
291C4⋊Q8—221no—
292C4⋊Q8—221no—
293#125—221no—
294#125—221no—
295#125—441no—
296#125—441no—
297#125—441no—
298C22⋊Q8—441no—
299C22⋊Q8—441no—
300C22⋊Q8—441no—
301C4×Q8—21no—
302C4×Q8—111no—
303C4×Q8—221no—
304C4×Q8—221no—
305C4×Q8—441no—
306C4×D4—21no—
307C4×D4—221no—
308C4×D4—221no—
309C2×C4⋊C4—441no—
310SD32—22no—
311SD32—222no—
312SD32—222no—
313C2×C16—111no—
314C2×C16—111no—
315C2×C16C22×D1111yescharacteristic
316C2×C16C22×D1111yescharacteristic
317#107—111no—
318#107—111no—
319#107—221no—
320#107C22×D1111yescharacteristic
321#107C22×D1111yescharacteristic
322#106—221no—
323#106—221no—
324C4⋊C8—111no—
325C4⋊C8—111no—
326C4⋊C8—111no—
327#103—21no—
328#103—221no—
329#103—221no—
330#102—21no—
331#102—221no—
332#102—221no—
333C4×C8—111no—
334C4×C8—111no—
335C4×C8C22×D1111yescharacteristic
336C2×C11—82no—
337C2×C11#335811yescharacteristic
338C2×C11C2×#51011yescharacteristic
339C2×C11#341611yescharacteristic
340C2×Q8—21no—
341C2×Q8—111no—
342C2×Q8—221no—
343C2×Q8—221no—
344C2×Q8—441no—
345C2×D4—21no—
346C22×C4—41no—
347C22×C4—441no—
348C22×C4—441no—
349Q16—21no—
350Q16—21no—
351Q16—221no—
352Q16—221no—
353Q16—221no—
354Q16—221no—
355Q16—881no—
356Q16—881no—
357Q16—881no—
358D8—21no—
359D8#433912yes—
360C2×C8—111no—
361C2×C8—111no—
362C2×C8D4×D1111yescharacteristic
363C2×C8C23×D1111yescharacteristic
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—41no—
367C4⋊C4—111no—
368C4⋊C4—111no—
369C4⋊C4—111no—
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—
381C4⋊C4—441no—
382C4⋊C4—441no—
383C4⋊C4—441no—
384C4⋊C4—441no—
385C22⋊C4—41no—
386C22⋊C4—441no—
387C22⋊C4—441no—
388C42—41no—
389C42—111no—
390C42—111no—
391C42—441no—
392C42—441no—
393C42D4×D1111yescharacteristic
394C16—21no—
395C16—21no—
396C16—221no—
397C16—221no—
398C11#3393911yescharacteristic, complemented, Sylow
399C23—41no—
400Q8—41no—
401Q8—41no—
402Q8—222no—
403Q8—441no—
404Q8—441no—
405Q8—441no—
406Q8—441no—
407Q8—1761no—
408D4—22no—
409D4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—111no—
414C2×C4—111no—
415C2×C4—111no—
416C2×C4—111no—
417C2×C4—161no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—882no—
423C2×C4—1761no—
424C2×C4D8×D1111yescharacteristic
425C2×C4D8×D1111yescharacteristic
426C2×C4C2×D4×D1111yescharacteristic
427C8—21no—
428C8—221no—
429C8—221no—
430C8C2×#433911yescharacteristic
431C8#6704311yescharacteristic
432C22—42no—
433C22—81no—
434C22—81no—
435C22C2×D8×D1111yescharacteristic
436C4—21no—
437C4—21no—
438C4—81no—
439C4—81no—
440C4—81no—
441C4—112no—
442C4—221no—
443C4—221no—
444C4—221no—
445C4—881no—
446C4—881no—
447C4—881no—
448C4—881no—
449C4#1062308311yescharacteristic
450C4#1062330111yescharacteristic
451C2—82no—
452C2#1308124911yescharacteristic
453C2D11×#51011yescharacteristic
454C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2175C2
socleC22×C11C22×D8
prime radicalC2×C11×D8C23
hypercenter#2175D11
hypocenterC11#33939
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2175

Complements

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

NH ≅ G/Ntype
1. #13081621C2semidirect
3. #13070862C2semidirect
4. #13070860C2semidirect
5. #13070842C2semidirect
6. #13070780C2semidirect
7. #13070779C2semidirect
8. #13070767C2semidirect
12. #13070522C2semidirect
398. C11#33939semidirect

Maximal subgroups

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

subgroupindex
#130816212
#130814832
#130708622
#130708602
#130708422
#130707802
#130707792
#130707672
#130706612
#130706592
#130705222
#130704772
#130704712
C11×#21752
#3393911