Finite Group Databasebeta

← #14911301

Subgroups — #14911301

Order 2816.

476 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#13081035C211yesmaximal, characteristic
2#13080980C211yesmaximal, characteristic, complemented
3#13070901C211yesmaximal, characteristic, complemented
4#13070827C211yesmaximal, characteristic, complemented
5#13070825C211yesmaximal, characteristic, complemented
6#13070805C211yesmaximal, characteristic, complemented
7#13070775C211yesmaximal, characteristic, complemented
8#13070757C211yesmaximal, characteristic, complemented
9#13070727C211yesmaximal, characteristic, complemented
10#13070711C211yesmaximal, characteristic, complemented
11#13070477C211yesmaximal, characteristic, complemented
12#13070444C211yesmaximal, characteristic, complemented
13#13070402C211yesmaximal, characteristic, complemented
14#13070399C211yesmaximal, characteristic, complemented
15C11×#2233C211yesmaximal, characteristic, complemented
16#10623147—21no—
17#10623044—21no—
18C11×#466C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20#10622770C2211yescharacteristic
21D8×Dic11C2211yescharacteristic
22C2×#66891C2211yescharacteristic
23#10622729C2211yescharacteristic
24C8×C22⋊D11C2211yescharacteristic
25#10622719C2211yescharacteristic
26C2×#66876C2211yescharacteristic
27#10622648—21no—
28#10622584—21no—
29C2×C16×D11C2211yescharacteristic
30#10622501—21no—
31#10622500C2211yescharacteristic
32#10622493C2211yescharacteristic
33#10622493C2211yescharacteristic
34#10622491C2211yescharacteristic
35#10622490—21no—
36#10622487C2211yescharacteristic
37#10622486C2211yescharacteristic
38#10622392—21no—
39#10622374—21no—
40C11×#367C2211yescharacteristic
41C11×#367C2211yescharacteristic
42C11×#357C2211yescharacteristic
43C11×#357C2211yescharacteristic
44C11×C22⋊C16C2211yescharacteristic
45#10622200C2211yescharacteristic
46(C2×D11)⋊C16C2211yescharacteristic
47#10622143C2211yescharacteristic
48#10622142C2211yescharacteristic
49#10622141C2211yescharacteristic
50#10622141C2211yescharacteristic
51#10622140C2211yescharacteristic
52Dic11⋊C16C2211yescharacteristic
53#10622130C2211yescharacteristic
54#10622128C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622127C2211yescharacteristic
59C2×C11×D8C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C11×#121—21no—
62C2×C11×C4⋊C4—21no—
63#66992—41no—
64#66991—21no—
65#66989—41no—
66D4×Dic11—21no—
67#66982—41no—
68C4×C22⋊D11D411yescharacteristic
69#66979—21no—
70#66979—41no—
71#66977—21no—
72C2×Dic44C2311yescharacteristic
73C2×C8×D11C2311yescharacteristic
74#66951—41no—
75#66950—21no—
76#66945—21no—
77#66945—21no—
78#66943—21no—
79#66942—41no—
80#66941—21no—
81#66940—21no—
82#66938—41no—
83#66930—41no—
84C2×C11×C16C2311yescharacteristic
85C2×C11×C16C2311yescharacteristic
86C11×#107—21no—
87C11×#107C2311yescharacteristic
88C11×#107C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×#102—21no—
91#66896—21no—
92#66896—21no—
93C22⋊(C11⋊C8)D411yescharacteristic
94#66891—22no—
95(C2×D11)⋊C8D411yescharacteristic
96#66882C2311yescharacteristic
97#66882C2311yescharacteristic
98#66882C2311yescharacteristic
99#66881—21no—
100#66880—21no—
101Dic11⋊C8D411yescharacteristic
102C8×Dic11C2311yescharacteristic
103#66876—22no—
104C2×C11⋊C16C2311yescharacteristic
105C2×C11⋊C16C2311yescharacteristic
106#66874—21no—
107#66874—21no—
108#66872—21no—
109#66872—21no—
110#66872—21no—
111#66871—21no—
112C16×D11—22no—
113#33915—111nomaximal, Sylow
114C2×D4×C11—21no—
115C2×D4×C11—41no—
116C22×C4×C11—41no—
117C22×C4×C11C2×D411yescharacteristic
118C2×C22⋊D11—41no—
119C2×C22⋊D11D811yescharacteristic
120C22×Dic11—41no—
121C2×C4×D11C2×D411yescharacteristic
122C2×Dic22—21no—
123C2×Dic22—41no—
124C11×D8—21no—
125C11×D8—21no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2411yescharacteristic
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—41no—
134C11×C22⋊C4—41no—
135C22⋊Dic11—41no—
136C22⋊Dic11—41no—
137C22⋊Dic11—41no—
138C22⋊Dic11—41no—
139C22⋊Dic11D811yescharacteristic
140(C2×D11)⋊C4—41no—
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4D811yescharacteristic
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—41no—
148C4⋊Dic11—41no—
149Dic11⋊C4—41no—
150Dic11⋊C4—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4D811yescharacteristic
154C4×Dic11—41no—
155C4×Dic11—41no—
156C4×Dic11—41no—
157C4×Dic11—41no—
158C4×Dic11C2×D411yescharacteristic
159C2×C11⋊C8C2×D411yescharacteristic
160C2×C11⋊C8C2×D411yescharacteristic
161Dic44—21no—
162Dic44—21no—
163C8×D11—21no—
164C8×D11—21no—
165C11×C16—21no—
166C11×C16—21no—
167C11⋊C16—21no—
168C11⋊C16#4112yes—
169#3341—111no—
170#3336—111no—
171#2255—111no—
172#2237—111no—
173#2237—111no—
174#2234—111no—
175#2233D1111yescharacteristic, complemented
176#2228—111no—
177#2225—111no—
178#2220—111no—
179#2217—111no—
180#2175—111no—
181#2168—111no—
182#2159—111no—
183#2158—111no—
184C23×C11—41no—
185C23×C11C2×D811yescharacteristic
186C22×D11C2×D811yescharacteristic
187D4×C11—41no—
188D4×C11—41no—
189D4×C11—161no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—82no—
196C2×C4×C11C2×D811yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C22⋊D11—41no—
199C22⋊D11—161no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—82no—
205C2×Dic11C2×D811yescharacteristic
206C2×Dic11C2×D811yescharacteristic
207C2×Dic11C2×D811yescharacteristic
208C4×D11—21no—
209C4×D11—21no—
210Dic22—41no—
211Dic22—41no—
212Dic22—161no—
213C8×C11—21no—
214C8×C11C2×#4111yescharacteristic
215C8×C112−1+411yescharacteristic
216C11⋊C8—21no—
217C11⋊C8—21no—
218#555—221no—
219#552—221no—
220C2×SD32—111no—
221C2×M32—111no—
222C22×C16—111no—
223#500—111no—
224#499—111no—
225#485—221no—
226#483—221no—
227#482—221no—
228#482—221no—
229#479—221no—
230#476—221no—
231#467—111no—
232#467—111no—
233#466—111no—
234#466C2×D1111yescharacteristic
235C4×Q16—111no—
236C4×D8—111no—
237C8×D4—111no—
238#427—111no—
239#427—111no—
240#427—111no—
241C2×#107C2×D1111yescharacteristic
242#367—111no—
243#367—111no—
244#367—111no—
245#367C2×D1111yescharacteristic
246#367C2×D1111yescharacteristic
247#366—111no—
248#366—111no—
249#366—111no—
250#366—111no—
251C4⋊C16—111no—
252#358—111no—
253#358—111no—
254#358—111no—
255#357—111no—
256#357C2×D1111yescharacteristic
257#357C2×D1111yescharacteristic
258C22⋊C16—111no—
259C22⋊C16C2×D1111yescharacteristic
260#346—111no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—81no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11C22×D811yescharacteristic
268C2×D11—21no—
269C2×D11—21no—
270C2×D11—21no—
271C4×C11—21no—
272C4×C11—81no—
273C4×C11—81no—
274C4×C11—81no—
275C4×C11#54711yescharacteristic
276C4×C11#57811yescharacteristic
277Dic11—21no—
278Dic11—21no—
279Dic11—21no—
280Dic11—81no—
281Dic11—81no—
282Dic11—81no—
283Dic11—81no—
284C2×Q16—111no—
285C2×D8C22×D1111yescharacteristic
286C22×C8—111no—
287C22×C8C22×D1111yescharacteristic
288C4⋊Q8—221no—
289#126—441no—
290#125—221no—
291#125—441no—
292#124—441no—
293#124—441no—
294#123—441no—
295C22⋊Q8—221no—
296C22⋊Q8—221no—
297#121—21no—
298#121—221no—
299#121—441no—
300C4×Q8—221no—
301C4×D4—111no—
302C4×D4—221no—
303#117—221no—
304#117—221no—
305#117—221no—
306#117—441no—
307#117—441no—
308C2×C4⋊C4—21no—
309SD32—222no—
310M32—222no—
311C2×C16—111no—
312C2×C16—111no—
313C2×C16—222no—
314C2×C16C22×D1111yescharacteristic
315C2×C16C22×D1111yescharacteristic
316#107—21no—
317#107—111no—
318#107—111no—
319#107—111no—
320#107—221no—
321#107C22×D1111yescharacteristic
322#107C22×D1111yescharacteristic
323#107C22×D1111yescharacteristic
324#106—221no—
325#106—221no—
326#106—221no—
327#106—221no—
328C4⋊C8—111no—
329#103—221no—
330#103—221no—
331#103—221no—
332#102—21no—
333#102—221no—
334#102—221no—
335C22⋊C8—111no—
336C22⋊C8—111no—
337C4×C8—111no—
338C2×C11—41no—
339C2×C11—161no—
340C2×C11#333411yescharacteristic
341C2×C11#341411yescharacteristic
342C2×C11#341611yescharacteristic
343D11—41no—
344C2×Q8—221no—
345C2×Q8—441no—
346C2×D4—21no—
347C2×D4—41no—
348C2×D4—111no—
349C2×D4—441no—
350C22×C4—41no—
351C22×C4—111no—
352C22×C4—441no—
353C22×C4D4×D1111yescharacteristic
354Q16—221no—
355Q16—221no—
356D8—21no—
357D8—21no—
358C2×C8—21no—
359C2×C8—21no—
360C2×C8—111no—
361C2×C8—111no—
362C2×C8—221no—
363C2×C8—221no—
364C2×C8D4×D1111yescharacteristic
365C2×C8C23×D1111yescharacteristic
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—41no—
370C4⋊C4—111no—
371C4⋊C4—221no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C4⋊C4—441no—
375C4⋊C4—441no—
376C4⋊C4—441no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C22⋊C4—41no—
381C22⋊C4—111no—
382C22⋊C4—111no—
383C22⋊C4—441no—
384C22⋊C4—441no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C22⋊C4—441no—
388C22⋊C4—441no—
389C22⋊C4—441no—
390C42—111no—
391C42—441no—
392C42—441no—
393C42—441no—
394C42—441no—
395C16—21no—
396C16—21no—
397C16—112no—
398C16—221no—
399C11#3391511yescharacteristic, complemented, Sylow
400C23—41no—
401C23—111no—
402C23D8×D1111yescharacteristic
403Q8—441no—
404Q8—441no—
405Q8—1761no—
406D4—41no—
407D4—41no—
408D4—161no—
409D4—441no—
410D4—1761no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—82no—
417C2×C4—111no—
418C2×C4—111no—
419C2×C4—111no—
420C2×C4—221no—
421C2×C4—221no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—882no—
427C2×C4D8×D1111yescharacteristic
428C2×C4C2×D4×D1111yescharacteristic
429C8—21no—
430C8—221no—
431C8—221no—
432C8#41×D1111yescharacteristic
433C8#6704311yescharacteristic
434C22—21no—
435C22—21no—
436C22—21no—
437C22—81no—
438C22—81no—
439C22—81no—
440C22—221no—
441C22—221no—
442C22—221no—
443C22C2×D8×D1111yescharacteristic
444C4—21no—
445C4—81no—
446C4—81no—
447C4—81no—
448C4—221no—
449C4—221no—
450C4—221no—
451C4—881no—
452C4—881no—
453C4—881no—
454C4—881no—
455C4#1062318611yescharacteristic
456C4#1062331011yescharacteristic
457C2—41no—
458C2—161no—
459C2—441no—
460C2#1308095811yescharacteristic
461C2#1308174811yescharacteristic
462C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2233C2
socleC22×C11C22×D8
prime radical#13081035C2
hypercenter#2233D11
hypocenterC11#33915
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2233

Complements

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

NH ≅ G/Ntype
2. #13080980C2semidirect
3. #13070901C2semidirect
4. #13070827C2semidirect
5. #13070825C2semidirect
6. #13070805C2semidirect
7. #13070775C2semidirect
8. #13070757C2semidirect
9. #13070727C2semidirect
10. #13070711C2semidirect
11. #13070477C2semidirect
12. #13070444C2semidirect
13. #13070402C2semidirect
14. #13070399C2semidirect
15. C11×#2233C2semidirect
175. #2233D11semidirect
399. C11#33915semidirect

Maximal subgroups

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

subgroupindex
#130810352
#130809802
#130709012
#130708272
#130708252
#130708052
#130707752
#130707572
#130707272
#130707112
#130704772
#130704442
#130704022
#130703992
C11×#22332
#3391511