Finite Group Databasebeta

← #14911285

Subgroups — #14911285

Order 2816.

488 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081039C211yesmaximal, characteristic, complemented
2#13081019C211yesmaximal, characteristic, complemented
3#13070902C211yesmaximal, characteristic, complemented
4#13070808C211yesmaximal, characteristic, complemented
5#13070808C211yesmaximal, characteristic, complemented
6#13070808C211yesmaximal, characteristic, complemented
7#13070797C211yesmaximal, characteristic, complemented
8#13070774C211yesmaximal, characteristic, complemented
9#13070754C211yesmaximal, characteristic, complemented
10#13070719C211yesmaximal, characteristic, complemented
11#13070702C211yesmaximal, characteristic, complemented
12#13070493C211yesmaximal, characteristic, complemented
13#13070404C211yesmaximal, characteristic, complemented
14#13070400C211yesmaximal, characteristic, complemented
15C11×#2168C211yesmaximal, characteristic, complemented
16#10623096—21no—
17#10623094—21no—
18C2×C11×M32C2211yescharacteristic
19C22×C11×C16C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21#10622728C2211yescharacteristic
22#10622728C2211yescharacteristic
23#10622728C2211yescharacteristic
24#10622728C2211yescharacteristic
25#10622719C2211yescharacteristic
26#10622719C2211yescharacteristic
27#10622719C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×D176C2211yescharacteristic
30#10622460—21no—
31#10622455—21no—
32#10622350—21no—
33#10622350—21no—
34#10622350—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#10622142C2211yescharacteristic
55#10622142C2211yescharacteristic
56#10622142C2211yescharacteristic
57#10622142C2211yescharacteristic
58#10622142C2211yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C4×D4×C11D411yescharacteristic
62#66992—41no—
63#66991—41no—
64#66983—21no—
65#66983—21no—
66#66983—21no—
67#66983—21no—
68#66979—21no—
69#66979—21no—
70#66979—21no—
71C2×C4⋊Dic11—21no—
72C2×D88C2311yescharacteristic
73C2×D88C2311yescharacteristic
74#66951—41no—
75#66945—41no—
76#66938—41no—
77#66938—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#66882C2311yescharacteristic
103#66882C2311yescharacteristic
104#66882C2311yescharacteristic
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66882C2311yescharacteristic
108#66881—21no—
109#66881—21no—
110#66881—21no—
111#66881—21no—
112D176—22no—
113#33914—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—
122C2×D44—21no—
123C2×D44—21no—
124C2×C4×D11—41no—
125C2×C4×D11—41no—
126C2×Dic22—41no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11C2×D411yescharacteristic
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2411yescharacteristic
135C11×C4⋊C4D811yescharacteristic
136C11×C22⋊C4D811yescharacteristic
137C11×C22⋊C4D811yescharacteristic
138C42×C11C2×D411yescharacteristic
139C22⋊Dic11—41no—
140C22⋊Dic11—41no—
141C22⋊Dic11—41no—
142(C2×D11)⋊C4—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—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—41no—
155C4⋊Dic11—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158C4×Dic11—41no—
159C4×Dic11—41no—
160C4×Dic11—41no—
161D88—21no—
162D88—21no—
163D88—21no—
164D88—21no—
165C11×C16—21no—
166C11×C16—21no—
167C11×C16—21no—
168C11×C16#4112yes—
169#3341—111no—
170#3339—111no—
171#2255—111no—
172#2234—111no—
173#2234—111no—
174#2234—111no—
175#2232—111no—
176#2228—111no—
177#2224—111no—
178#2218—111no—
179#2215—111no—
180#2177—111no—
181#2168D1111yescharacteristic, complemented
182#2159—111no—
183#2158—111no—
184C23×C11C2×D811yescharacteristic
185C23×C11C2×D811yescharacteristic
186C22×D11—41no—
187C22×D11—41no—
188D4×C11—41no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11C2×D811yescharacteristic
194C2×C4×C11C2×D811yescharacteristic
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11C2×D811yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C22⋊D11—82no—
199C22⋊D11—161no—
200C22⋊D11—161no—
201C22⋊D11—161no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—161no—
209D44—41no—
210D44—41no—
211D44—41no—
212D44—41no—
213C4×D11—82no—
214C4×D11—161no—
215Dic22—161no—
216C8×C11—21no—
217C8×C11—21no—
218C8×C11—21no—
219C8×C11C2×#4111yescharacteristic
220C8×C112−1+411yescharacteristic
221#555—221no—
222#553—221no—
223C2×D16—111no—
224C2×M32C2×D1111yescharacteristic
225C22×C16C2×D1111yescharacteristic
226#500—111no—
227#499—111no—
228#482—221no—
229#482—221no—
230#482—221no—
231#481—221no—
232#478—221no—
233#476—221no—
234#466—111no—
235#466—111no—
236#466—111no—
237#466—111no—
238C4×D8—111no—
239C4×D8—111no—
240C8×D4C2×D1111yescharacteristic
241#427—111no—
242#427—111no—
243#427—111no—
244C2×#107—111no—
245#367—111no—
246#367—111no—
247#367—111no—
248#367—111no—
249#366—111no—
250#366—111no—
251#366—111no—
252#366—111no—
253#366—111no—
254C4⋊C16C2×D1111yescharacteristic
255#357—111no—
256#357—111no—
257#357—111no—
258#357—111no—
259#357—111no—
260#357—111no—
261C22⋊C16C2×D1111yescharacteristic
262C22⋊C16C2×D1111yescharacteristic
263#346C2×D1111yescharacteristic
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11C22×D811yescharacteristic
271C2×D11—81no—
272C2×D11—81no—
273C2×D11—81no—
274C2×D11—81no—
275C2×D11—81no—
276C2×D11—81no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11#54711yescharacteristic
282C4×C11#57811yescharacteristic
283Dic11—81no—
284Dic11—81no—
285Dic11—81no—
286Dic11—81no—
287Dic11—81no—
288Dic11—81no—
289C2×D8—111no—
290C2×D8—111no—
291C22×C8C22×D1111yescharacteristic
292C22×C8C22×D1111yescharacteristic
293C4⋊Q8—221no—
294#126—441no—
295#125—221no—
296#124—441no—
297#124—441no—
298#123—441no—
299#121—221no—
300#121—221no—
301#121—221no—
302#121—221no—
303#121—441no—
304#121—441no—
305C4×D4—221no—
306C4×D4—221no—
307C4×D4—441no—
308C4×D4D4411yescharacteristic
309#117—221no—
310#117—221no—
311#117—221no—
312#117—441no—
313C2×C4⋊C4—221no—
314D16—222no—
315M32—22no—
316C2×C16—22no—
317C2×C16C22×D1111yescharacteristic
318C2×C16C22×D1111yescharacteristic
319C2×C16C22×D1111yescharacteristic
320C2×C16C22×D1111yescharacteristic
321#107—111no—
322#107—111no—
323#107—111no—
324#107—111no—
325#107—111no—
326#107—111no—
327#107—221no—
328#107—221no—
329#106—221no—
330#106—221no—
331#106—221no—
332#106—221no—
333C4⋊C8D4411yescharacteristic
334#102—221no—
335#102—221no—
336#102—221no—
337#102—221no—
338#102—221no—
339#102—221no—
340C22⋊C8D4411yescharacteristic
341C22⋊C8D4411yescharacteristic
342C4×C8C22×D1111yescharacteristic
343C2×C11—41no—
344C2×C11—41no—
345C2×C11#333411yescharacteristic
346C2×C11#341411yescharacteristic
347C2×C11#341511yescharacteristic
348D11—161no—
349D11—161no—
350C2×Q8—441no—
351C2×D4—221no—
352C2×D4—221no—
353C2×D4—441no—
354C2×D4—441no—
355C2×D4—441no—
356C2×D4—441no—
357C2×D4D8811yescharacteristic
358C22×C4—441no—
359C22×C4—441no—
360C22×C4—441no—
361C22×C4C2×D4411yescharacteristic
362C22×C4C2×D4411yescharacteristic
363D8—221no—
364D8—221no—
365D8—221no—
366D8—221no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8C2×D4411yescharacteristic
372C2×C8C2×D4411yescharacteristic
373C2×C8C2×D4411yescharacteristic
374C2×C8C23×D1111yescharacteristic
375C4⋊C4—221no—
376C4⋊C4—221no—
377C4⋊C4—221no—
378C4⋊C4—221no—
379C4⋊C4—221no—
380C4⋊C4—221no—
381C4⋊C4—441no—
382C4⋊C4—441no—
383C4⋊C4—441no—
384C4⋊C4—441no—
385C4⋊C4D8811yescharacteristic
386C22⋊C4—441no—
387C22⋊C4—441no—
388C22⋊C4—441no—
389C22⋊C4—441no—
390C22⋊C4—441no—
391C22⋊C4—441no—
392C22⋊C4—441no—
393C22⋊C4—441no—
394C22⋊C4—441no—
395C22⋊C4D8811yescharacteristic
396C22⋊C4D8811yescharacteristic
397C42—441no—
398C42—441no—
399C42—441no—
400C42C2×D4411yescharacteristic
401C16—21no—
402C16—21no—
403C16—21no—
404C16#434112yes—
405C11#3391411yescharacteristic, complemented, Sylow
406C23—441no—
407C23—441no—
408C23C2×D8811yescharacteristic
409C23C2×D8811yescharacteristic
410Q8—1761no—
411D4—41no—
412D4—441no—
413D4—441no—
414D4—441no—
415D4—441no—
416D4—882no—
417D4—1761no—
418D4—1761no—
419D4—1761no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4—441no—
429C2×C4—441no—
430C2×C4—882no—
431C2×C4—1761no—
432C2×C4—1761no—
433C2×C4C2×D8811yescharacteristic
434C2×C4C2×D8811yescharacteristic
435C2×C4C2×D8811yescharacteristic
436C2×C4C2×D8811yescharacteristic
437C2×C4C22×D4411yescharacteristic
438C8—21no—
439C8—21no—
440C8—21no—
441C8C2×#434111yescharacteristic
442C8#6704311yescharacteristic
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—881no—
450C22—881no—
451C22—881no—
452C22—881no—
453C22—881no—
454C22—881no—
455C22C22×D8811yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—881no—
461C4—881no—
462C4—881no—
463C4—881no—
464C4—881no—
465C4—881no—
466C4#1062308611yescharacteristic
467C4#1062328411yescharacteristic
468C2—41no—
469C2—41no—
470C2—1761no—
471C2—1761no—
472C2#1308096411yescharacteristic
473C2#1308175211yescharacteristic
474C2#1308175711yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2168C2
socleC22×C11C22×D8
hypercenter#2168D11
hypocenterC11#33914
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. #13081039C2semidirect
2. #13081019C2semidirect
3. #13070902C2semidirect
4. #13070808C2semidirect
5. #13070808C2semidirect
6. #13070808C2semidirect
7. #13070797C2semidirect
8. #13070774C2semidirect
9. #13070754C2semidirect
10. #13070719C2semidirect
11. #13070702C2semidirect
12. #13070493C2semidirect
13. #13070404C2semidirect
14. #13070400C2semidirect
15. C11×#2168C2semidirect
181. #2168D11semidirect
405. C11#33914semidirect

Maximal subgroups

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

subgroupindex
#130810392
#130810192
#130709022
#130708082
#130707972
#130707742
#130707542
#130707192
#130707022
#130704932
#130704042
#130704002
C11×#21682
#3391411