Finite Group Databasebeta

← #14911158

Subgroups — #14911158

Order 2816.

482 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#13081014C211yesmaximal, characteristic
2#13080980C211yesmaximal, characteristic, complemented
3#13070894C211yesmaximal, characteristic, complemented
4#13070827C211yesmaximal, characteristic, complemented
5#13070818C211yesmaximal, characteristic, complemented
6#13070809C211yesmaximal, characteristic, complemented
7#13070796C211yesmaximal, characteristic, complemented
8#13070783C211yesmaximal, characteristic, complemented
9#13070772C211yesmaximal, characteristic, complemented
10#13070713C211yesmaximal, characteristic, complemented
11#13070712C211yesmaximal, characteristic, complemented
12#13070467C211yesmaximal, characteristic, complemented
13C16×C22⋊D11C211yesmaximal, characteristic, complemented
14#13070399C211yesmaximal, characteristic, complemented
15C2×C11×#367C211yesmaximal, characteristic, complemented
16#10623045—21no—
17#10623044—21no—
18C22×C11×C16C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21#10622729C2211yescharacteristic
22#10622728C2211yescharacteristic
23C8×C22⋊D11C2211yescharacteristic
24#10622584—21no—
25#10622581—21no—
26C2×#66864C2211yescharacteristic
27C2×C16×D11C2211yescharacteristic
28#10622504—21no—
29#10622501—21no—
30#10622500C2211yescharacteristic
31#10622498—21no—
32#10622496C2211yescharacteristic
33#10622493C2211yescharacteristic
34#10622493C2211yescharacteristic
35#10622491C2211yescharacteristic
36#10622491C2211yescharacteristic
37#10622490—21no—
38#10622486C2211yescharacteristic
39#10622485C2211yescharacteristic
40C11×#367C2211yescharacteristic
41C11×#367C2211yescharacteristic
42C11×#367C2211yescharacteristic
43C11×#367C2211yescharacteristic
44C22⋊(C11⋊C16)C2211yescharacteristic
45#10622147C2211yescharacteristic
46(C2×D11)⋊C16C2211yescharacteristic
47#10622143C2211yescharacteristic
48#10622141C2211yescharacteristic
49Dic11⋊C16C2211yescharacteristic
50C16×Dic11C2211yescharacteristic
51#10622130C2211yescharacteristic
52#10622130C2211yescharacteristic
53#10622129C2211yescharacteristic
54#10622129C2211yescharacteristic
55#10622127C2211yescharacteristic
56#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622127C2211yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62#66983—21no—
63#66983—41no—
64#66982—41no—
65C4×C22⋊D11—41no—
66C4×C22⋊D11D411yescharacteristic
67#66979—41no—
68#66977—21no—
69C2×Dic44C2311yescharacteristic
70C2×D88C2311yescharacteristic
71C2×C8×D11C2311yescharacteristic
72#66951—41no—
73#66951—41no—
74#66950—21no—
75#66948—21no—
76#66947—41no—
77#66946—21no—
78#66945—21no—
79#66945—21no—
80#66943—21no—
81#66943—21no—
82#66942—41no—
83#66940—21no—
84C2×C11×C16—22no—
85C2×C11×C16C2311yescharacteristic
86C2×C11×C16C2311yescharacteristic
87C11×#107—21no—
88C11×#107—21no—
89C11×#107C2311yescharacteristic
90C11×#107C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#107C2311yescharacteristic
93C22⋊(C11⋊C8)D411yescharacteristic
94#66885—21no—
95(C2×D11)⋊C8D411yescharacteristic
96#66882C2311yescharacteristic
97#66882C2311yescharacteristic
98#66880—21no—
99Dic11⋊C8D411yescharacteristic
100C8×Dic11C2311yescharacteristic
101C2×C11⋊C16C2311yescharacteristic
102C2×C11⋊C16C2311yescharacteristic
103#66874—21no—
104#66874—21no—
105#66873—21no—
106#66873—21no—
107#66872—21no—
108#66872—21no—
109#66872—21no—
110#66872—21no—
111#66864—22no—
112C16×D11—22no—
113#33904—111nomaximal, Sylow
114C22×C4×C11—41no—
115C22×C4×C11—41no—
116C22×C4×C11C2×D411yescharacteristic
117C2×C22⋊D11—41no—
118C2×C22⋊D11D811yescharacteristic
119C2×D44—21no—
120C2×D44—41no—
121C2×C4×D11—41no—
122C2×C4×D11C2×D411yescharacteristic
123C2×Dic22—21no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11C2411yescharacteristic
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—41no—
133C11×C4⋊C4—41no—
134C22⋊Dic11—41no—
135C22⋊Dic11D811yescharacteristic
136(C2×D11)⋊C4—41no—
137(C2×D11)⋊C4—41no—
138(C2×D11)⋊C4—41no—
139(C2×D11)⋊C4—41no—
140(C2×D11)⋊C4—41no—
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4D811yescharacteristic
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—41no—
146C4⋊Dic11—41no—
147C4⋊Dic11—41no—
148Dic11⋊C4—41no—
149Dic11⋊C4—41no—
150Dic11⋊C4—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4D811yescharacteristic
153C4×Dic11—41no—
154C4×Dic11—41no—
155C4×Dic11—41no—
156C4×Dic11C2×D411yescharacteristic
157C2×C11⋊C8C2×D411yescharacteristic
158C2×C11⋊C8C2×D411yescharacteristic
159Dic44—21no—
160Dic44—21no—
161D88—21no—
162D88—21no—
163C8×D11—21no—
164C8×D11—21no—
165C11×C16—21no—
166C11×C16#4112yes—
167C11⋊C16—21no—
168C11⋊C16—21no—
169#3339—111no—
170#3336—111no—
171#2253—111no—
172#2237—111no—
173#2236—111no—
174#2234—111no—
175#2232—111no—
176#2229—111no—
177#2228—111no—
178#2217—111no—
179#2217—111no—
180C4×SD32—111no—
181D4×C16—111no—
182#2158—111no—
183C2×#367D1111yescharacteristic, complemented
184C23×C11C2×D811yescharacteristic
185C22×D11—41no—
186C22×D11C2×D811yescharacteristic
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—82no—
194C2×C4×C11—161no—
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C22⋊D11—22no—
198C22⋊D11—82no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11C2×D811yescharacteristic
203C2×Dic11C2×D811yescharacteristic
204C2×Dic11C2×D811yescharacteristic
205D44—41no—
206D44—41no—
207D44—161no—
208C4×D11—21no—
209C4×D11—21no—
210C4×D11—161no—
211Dic22—41no—
212Dic22—41no—
213C8×C11—21no—
214C8×C11C2×#4111yescharacteristic
215C8×C112−1+411yescharacteristic
216C11⋊C8—21no—
217C11⋊C8—21no—
218#553—221no—
219#552—221no—
220C2×SD32—111no—
221C22×C16—111no—
222C22×C16C2×D1111yescharacteristic
223#499—111no—
224#499—111no—
225#485—221no—
226#483—221no—
227#482—221no—
228#481—221no—
229#479—221no—
230#478—221no—
231#467—111no—
232#467—111no—
233#466—111no—
234#466—111no—
235C4×Q16—111no—
236C4×D8—111no—
237C8×D4—111no—
238#427—111no—
239#427—111no—
240C2×#107C2×D1111yescharacteristic
241C2×#107C2×D1111yescharacteristic
242#367—111no—
243#367C2×D1111yescharacteristic
244#367C2×D1111yescharacteristic
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#357—111no—
257#357—111no—
258C22⋊C16—111no—
259C22⋊C16—111no—
260C4×C16—111no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11#50812yes—
264C22×C11C22×D811yescharacteristic
265C2×D11—21no—
266C2×D11—21no—
267C2×D11—21no—
268C2×D11—81no—
269C2×D11—81no—
270C2×D11—81no—
271C4×C11—21no—
272C4×C11—81no—
273C4×C11—81no—
274C4×C11—81no—
275C4×C11—81no—
276C4×C11#54711yescharacteristic
277C4×C11#57811yescharacteristic
278Dic11—21no—
279Dic11—21no—
280Dic11—21no—
281Dic11—81no—
282Dic11—81no—
283Dic11—81no—
284C2×Q16—111no—
285C2×D8—111no—
286C22×C8—111no—
287C22×C8C22×D1111yescharacteristic
288#126—441no—
289#126—441no—
290#125—221no—
291#125—221no—
292#125—441no—
293#123—441no—
294#123—441no—
295C22⋊Q8—221no—
296C22⋊Q8—221no—
297#121—221no—
298#121—221no—
299#121—441no—
300C4×Q8—221no—
301C4×D4—111no—
302C4×D4—221no—
303C4×D4—441no—
304#117—221no—
305#117—221no—
306#117—441no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309SD32—222no—
310C2×C16—22no—
311C2×C16—111no—
312C2×C16—111no—
313C2×C16—222no—
314C2×C16C22×D1111yescharacteristic
315C2×C16C22×D1111yescharacteristic
316#107—21no—
317#107—21no—
318#107—111no—
319#107—111no—
320#107C22×D1111yescharacteristic
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—221no—
333#102—221no—
334#102—221no—
335C22⋊C8—111no—
336C22⋊C8—111no—
337C4×C8—111no—
338C2×C11—22no—
339C2×C11#333411yescharacteristic
340C2×C11C2×#50811yescharacteristic
341C2×C11#341611yescharacteristic
342D11—41no—
343D11—161no—
344C2×Q8—221no—
345C2×D4—111no—
346C2×D4—221no—
347C2×D4—441no—
348C2×D4—441no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—111no—
352C22×C4—441no—
353C22×C4D4×D1111yescharacteristic
354Q16—221no—
355Q16—221no—
356D8—221no—
357D8—221no—
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—21no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—111no—
373C4⋊C4—221no—
374C4⋊C4—221no—
375C4⋊C4—441no—
376C4⋊C4—441no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C4⋊C4—441no—
381C4⋊C4—441no—
382C22⋊C4—111no—
383C22⋊C4—111no—
384C22⋊C4—441no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C22⋊C4—441no—
388C22⋊C4—441no—
389C22⋊C4—441no—
390C22⋊C4—441no—
391C42—111no—
392C42—441no—
393C42—441no—
394C42—441no—
395C16—21no—
396C16—221no—
397C16—221no—
398C16#433912yes—
399C11#3390411yescharacteristic, complemented, Sylow
400C23—111no—
401C23—441no—
402C23D8×D1111yescharacteristic
403Q8—441no—
404Q8—441no—
405D4—222no—
406D4—441no—
407D4—441no—
408D4—882no—
409D4—1761no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—82no—
417C2×C4—111no—
418C2×C4—111no—
419C2×C4—111no—
420C2×C4—161no—
421C2×C4—221no—
422C2×C4—221no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—1761no—
427C2×C4D8×D1111yescharacteristic
428C2×C4C2×D4×D1111yescharacteristic
429C8—21no—
430C8—221no—
431C8—221no—
432C8C2×#433911yescharacteristic
433C8#6704011yescharacteristic
434C22—21no—
435C22—21no—
436C22—221no—
437C22—221no—
438C22—221no—
439C22—881no—
440C22—881no—
441C22—881no—
442C22#1062252912yes—
443C22C2×D8×D1111yescharacteristic
444C4—21no—
445C4—81no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—221no—
450C4—221no—
451C4—221no—
452C4—881no—
453C4—881no—
454C4—881no—
455C4#1062303811yescharacteristic
456C4#1062329711yescharacteristic
457C2—22no—
458C2—441no—
459C2—1761no—
460C2#1308096111yescharacteristic
461C2C2×#1062252911yescharacteristic
462C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#367C2
socleC22×C11C22×D8
prime radical#13081014C2
hypercenterC2×#367D11
hypocenterC11#33904
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#367

Complements

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

NH ≅ G/Ntype
2. #13080980C2semidirect
3. #13070894C2semidirect
4. #13070827C2semidirect
5. #13070818C2semidirect
6. #13070809C2semidirect
7. #13070796C2semidirect
8. #13070783C2semidirect
9. #13070772C2semidirect
10. #13070713C2semidirect
11. #13070712C2semidirect
12. #13070467C2semidirect
13. C16×C22⋊D11C2semidirect
14. #13070399C2semidirect
15. C2×C11×#367C2semidirect
183. C2×#367D11semidirect
399. C11#33904semidirect

Maximal subgroups

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

subgroupindex
#130810142
#130809802
#130708942
#130708272
#130708182
#130708092
#130707962
#130707832
#130707722
#130707132
#130707122
#130704672
C16×C22⋊D112
#130703992
C2×C11×#3672
#3390411