Finite Group Databasebeta

← #14911255

Subgroups — #14911255

Order 2816.

516 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081019C211yesmaximal, characteristic, complemented
2#13080964C211yesmaximal, characteristic, complemented
3#13070902C211yesmaximal, characteristic, complemented
4#13070808C211yesmaximal, characteristic, complemented
5#13070802C211yesmaximal, characteristic, complemented
6#13070802C211yesmaximal, characteristic, complemented
7#13070797C211yesmaximal, characteristic, complemented
8#13070774C211yesmaximal, characteristic, complemented
9#13070764C211yesmaximal, characteristic, complemented
10#13070719C211yesmaximal, characteristic, complemented
11#13070702C211yesmaximal, characteristic, complemented
12#13070493C211yesmaximal, characteristic, complemented
13#13070404C211yesmaximal, characteristic, complemented
14C2×#10622143C211yesmaximal, characteristic, complemented
15C11×#2168C211yesmaximal, characteristic, complemented
16#10623096—21no—
17#10623086—21no—
18C2×C11×M32C2211yescharacteristic
19C22×C11×C16C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21#10622728C2211yescharacteristic
22#10622728C2211yescharacteristic
23#10622728C2211yescharacteristic
24#10622728C2211yescharacteristic
25#10622719C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×D176C2211yescharacteristic
30#10622460—21no—
31#10622459—21no—
32#10622350—21no—
33#10622349—21no—
34#10622349—21no—
35#10622348—21no—
36C4×D88C2211yescharacteristic
37C4×D88C2211yescharacteristic
38#10622296C2211yescharacteristic
39#10622295C2211yescharacteristic
40C11×C4⋊C16C2211yescharacteristic
41C11×C22⋊C16C2211yescharacteristic
42C11×C22⋊C16C2211yescharacteristic
43C11×#346C2211yescharacteristic
44#10622147C2211yescharacteristic
45#10622147C2211yescharacteristic
46#10622147C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622143C2211yescharacteristic
51#10622143C2211yescharacteristic
52#10622143C2211yescharacteristic
53#10622143C2211yescharacteristic
54#10622143C2211yescharacteristic
55#10622143C2211yescharacteristic
56#10622142C2211yescharacteristic
57#10622142C2211yescharacteristic
58#10622142C2211yescharacteristic
59C2×#4341—41no—
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C4×D4×C11D411yescharacteristic
63#66992—41no—
64#66983—21no—
65#66983—21no—
66#66983—21no—
67#66983—21no—
68#66979—21no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—21no—
72C2×D88C2311yescharacteristic
73C2×D88C2311yescharacteristic
74#66951—41no—
75#66950—41no—
76#66939—41no—
77#66939—41no—
78#66936—41no—
79(C22⋊D11)⋊C4—41no—
80C4×D44—21no—
81C4×D44—21no—
82#66923—21no—
83#66922—21no—
84C11×M32—22no—
85C2×C11×C16—22no—
86C2×C11×C16C2311yescharacteristic
87C2×C11×C16C2311yescharacteristic
88C2×C11×C16C2311yescharacteristic
89C2×C11×C16C2311yescharacteristic
90C11×C4⋊C8D411yescharacteristic
91C11×C22⋊C8D411yescharacteristic
92C11×C22⋊C8D411yescharacteristic
93C4×C8×C11C2311yescharacteristic
94#66885—21no—
95#66885—21no—
96#66885—21no—
97#66885—21no—
98#66885—21no—
99#66885—21no—
100#66882—21no—
101#66882—21no—
102#66882—21no—
103#66882—21no—
104#66882C2311yescharacteristic
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66882C2311yescharacteristic
108#66882C2311yescharacteristic
109#66882C2311yescharacteristic
110#66881—21no—
111#66881—21no—
112D176—22no—
113#33912—111nomaximal, Sylow
114C2×D4×C11D811yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C2×C22⋊D11—41no—
118C2×C22⋊D11—41no—
119C2×C22⋊D11—41no—
120C2×C22⋊D11—41no—
121C22×Dic11—41no—
122C22×Dic11—41no—
123C22×Dic11—41no—
124#4341—84no—
125C2×D44—21no—
126C2×D44—21no—
127C2×C4×D11—41no—
128C2×C4×D11—41no—
129C2×Dic22—41no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11C2×D411yescharacteristic
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11C2411yescharacteristic
138C11×C4⋊C4D811yescharacteristic
139C11×C22⋊C4D811yescharacteristic
140C11×C22⋊C4D811yescharacteristic
141C42×C11C2×D411yescharacteristic
142C22⋊Dic11—41no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4—41no—
145(C2×D11)⋊C4—41no—
146(C2×D11)⋊C4—41no—
147(C2×D11)⋊C4—41no—
148(C2×D11)⋊C4—41no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—41no—
156C4⋊Dic11—41no—
157C4⋊Dic11—41no—
158C4⋊Dic11—41no—
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161C4×Dic11—41no—
162D88—21no—
163D88—21no—
164D88—21no—
165D88—21no—
166C11×C16—21no—
167C11×C16—21no—
168C11×C16—21no—
169C11×C16#4112yescomplemented
170#3339—111no—
171#3334—111no—
172#2255—111no—
173#2234—111no—
174#2233—111no—
175#2233—111no—
176#2232—111no—
177#2228—111no—
178#2226—111no—
179#2218—111no—
180#2215—111no—
181#2177—111no—
182#2168D1111yescharacteristic, complemented
183#2159—111no—
184C2×#367—111no—
185C23×C11C2×D811yescharacteristic
186C23×C11C2×D811yescharacteristic
187C22×D11—41no—
188C22×D11—41no—
189D4×C11—22no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11C2×D811yescharacteristic
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11C2×D811yescharacteristic
197C2×C4×C11C2×D811yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C22⋊D11—82no—
200C22⋊D11—82no—
201C22⋊D11—82no—
202C22⋊D11—161no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—82no—
210C2×Dic11—82no—
211C2×Dic11—161no—
212D44—41no—
213D44—41no—
214D44—41no—
215D44—41no—
216C4×D11—82no—
217C4×D11—161no—
218Dic22—82no—
219C8×C11—21no—
220C8×C11—21no—
221C8×C11—21no—
222C8×C11C2×#4111yescharacteristic
223C8×C112−1+411yescharacteristic
224#553—221no—
225#547—221no—
226C2×D16—111no—
227C2×M32C2×D1111yescharacteristic
228C22×C16C2×D1111yescharacteristic
229#500—111no—
230#499—111no—
231#482—221no—
232#481—221no—
233#480—221no—
234#480—221no—
235#478—221no—
236#474—221no—
237#466—111no—
238#466—111no—
239#466—111no—
240#466—111no—
241C4×D8—111no—
242C4×D8—111no—
243C8×D4C2×D1111yescharacteristic
244#427—111no—
245C2×#107—111no—
246C2×#107—111no—
247C2×#107—111no—
248#367—111no—
249#367—111no—
250#367—111no—
251#367—111no—
252#367—111no—
253#367—111no—
254#366—111no—
255#366—111no—
256#366—111no—
257C4⋊C16C2×D1111yescharacteristic
258#357—111no—
259#357—111no—
260#357—111no—
261#357—111no—
262#357—111no—
263#357—111no—
264C22⋊C16C2×D1111yescharacteristic
265C22⋊C16C2×D1111yescharacteristic
266#346C2×D1111yescharacteristic
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—21no—
272C22×C11#50912yes—
273C22×C11C22×D811yescharacteristic
274C2×D11—81no—
275C2×D11—81no—
276C2×D11—81no—
277C2×D11—81no—
278C2×D11—81no—
279C2×D11—81no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—21no—
284C4×C11#54711yescharacteristic
285C4×C11#57811yescharacteristic
286Dic11—81no—
287Dic11—81no—
288Dic11—81no—
289Dic11—81no—
290Dic11—81no—
291Dic11—81no—
292C2×#41—441no—
293C2×D8—111no—
294C2×D8—111no—
295C22×C8C22×D1111yescharacteristic
296C22×C8C22×D1111yescharacteristic
297C4⋊Q8—221no—
298#126—441no—
299#125—221no—
300#123—441no—
301#123—441no—
302#123—441no—
303C22⋊Q8—441no—
304#121—221no—
305#121—221no—
306#121—221no—
307#121—221no—
308#121—441no—
309C4×D4—221no—
310C4×D4—221no—
311C4×D4—441no—
312C4×D4D4411yescharacteristic
313#117—221no—
314C2×C4⋊C4—221no—
315C2×C4⋊C4—221no—
316C2×C4⋊C4—221no—
317D16—222no—
318M32—22no—
319C2×C16—22no—
320C2×C16C22×D1111yescharacteristic
321C2×C16C22×D1111yescharacteristic
322C2×C16C22×D1111yescharacteristic
323C2×C16C22×D1111yescharacteristic
324#107—111no—
325#107—111no—
326#107—111no—
327#107—111no—
328#107—111no—
329#107—111no—
330#107—221no—
331#107—221no—
332#107—221no—
333#107—221no—
334#106—221no—
335#106—221no—
336C4⋊C8D4411yescharacteristic
337#102—221no—
338#102—221no—
339#102—221no—
340#102—221no—
341#102—221no—
342#102—221no—
343C22⋊C8D4411yescharacteristic
344C22⋊C8D4411yescharacteristic
345C4×C8C22×D1111yescharacteristic
346C2×C11—22no—
347C2×C11—41no—
348C2×C11#333411yescharacteristic
349C2×C11C2×#50911yescharacteristic
350C2×C11#341611yescharacteristic
351D11—161no—
352D11—161no—
353#41—884no—
354C2×Q8—441no—
355C2×D4—221no—
356C2×D4—221no—
357C2×D4—441no—
358C2×D4—441no—
359C2×D4—441no—
360C2×D4—441no—
361C2×D4D8811yescharacteristic
362C22×C4—441no—
363C22×C4—441no—
364C22×C4—441no—
365C22×C4—441no—
366C22×C4—441no—
367C22×C4C2×D4411yescharacteristic
368C22×C4C2×D4411yescharacteristic
369D8—221no—
370D8—221no—
371D8—221no—
372D8—221no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8C2×D4411yescharacteristic
378C2×C8C2×D4411yescharacteristic
379C2×C8C2×D4411yescharacteristic
380C2×C8C23×D1111yescharacteristic
381C4⋊C4—221no—
382C4⋊C4—221no—
383C4⋊C4—221no—
384C4⋊C4—221no—
385C4⋊C4—221no—
386C4⋊C4—221no—
387C4⋊C4—441no—
388C4⋊C4—441no—
389C4⋊C4—441no—
390C4⋊C4—441no—
391C4⋊C4—441no—
392C4⋊C4—441no—
393C4⋊C4D8811yescharacteristic
394C22⋊C4—441no—
395C22⋊C4—441no—
396C22⋊C4—441no—
397C22⋊C4—441no—
398C22⋊C4—441no—
399C22⋊C4—441no—
400C22⋊C4—441no—
401C22⋊C4D8811yescharacteristic
402C22⋊C4D8811yescharacteristic
403C42—441no—
404C42C2×D4411yescharacteristic
405C16—21no—
406C16—21no—
407C16—21no—
408C16#434112yescomplemented
409C11#3391211yescharacteristic, complemented, Sylow
410C23—441no—
411C23—441no—
412C23C2×D8811yescharacteristic
413C23C2×D8811yescharacteristic
414Q8—882no—
415D4—22no—
416D4—441no—
417D4—441no—
418D4—441no—
419D4—441no—
420D4—882no—
421D4—882no—
422D4—882no—
423D4—1761no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—441no—
429C2×C4—441no—
430C2×C4—441no—
431C2×C4—441no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4—882no—
435C2×C4—882no—
436C2×C4—882no—
437C2×C4—1761no—
438C2×C4—1761no—
439C2×C4C2×D8811yescharacteristic
440C2×C4C2×D8811yescharacteristic
441C2×C4C2×D8811yescharacteristic
442C2×C4C2×D8811yescharacteristic
443C2×C4C22×D4411yescharacteristic
444C8—21no—
445C8—21no—
446C8—21no—
447C8C2×#434111yescharacteristic
448C8#6704311yescharacteristic
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—881no—
455C22—881no—
456C22—881no—
457C22—881no—
458C22—881no—
459C22—881no—
460C22#1062252112yes—
461C22C22×D8811yescharacteristic
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—881no—
467C4—881no—
468C4—881no—
469C4—881no—
470C4—881no—
471C4—881no—
472C4#1062308611yescharacteristic
473C4#1062328411yescharacteristic
474C2—22no—
475C2—41no—
476C2—1761no—
477C2—1761no—
478C2#1308096411yescharacteristic
479C2C2×#1062252111yescharacteristic
480C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2168C2
socleC22×C11C22×D8
hypercenter#2168D11
hypocenterC11#33912
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #2168

Complements

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

NH ≅ G/Ntype
1. #13081019C2semidirect
2. #13080964C2semidirect
3. #13070902C2semidirect
4. #13070808C2semidirect
5. #13070802C2semidirect
6. #13070802C2semidirect
7. #13070797C2semidirect
8. #13070774C2semidirect
9. #13070764C2semidirect
10. #13070719C2semidirect
11. #13070702C2semidirect
12. #13070493C2semidirect
13. #13070404C2semidirect
14. C2×#10622143C2semidirect
15. C11×#2168C2semidirect
169. C11×C16#41semidirect
182. #2168D11semidirect
408. C16#4341semidirect
409. C11#33912semidirect

Maximal subgroups

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

subgroupindex
#130810192
#130809642
#130709022
#130708082
#130708022
#130707972
#130707742
#130707642
#130707192
#130707022
#130704932
#130704042
C2×#106221432
C11×#21682
#3391211