Finite Group Databasebeta

← #14909583

Subgroups — #14909583

Order 2816.

588 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078197C211yesmaximal, characteristic
2C2×#10622729C211yesmaximal, characteristic, complemented
3#13070825C212yesmaximal, complemented
4#13070819C211yesmaximal, characteristic, complemented
5#13070802C211yesmaximal, characteristic, complemented
6#13070729C212yesmaximal, complemented
7#13070724C212yesmaximal, complemented
8#13070558C212yesmaximal, complemented
9#13070552C211yesmaximal, characteristic, complemented
10#13070535C211yesmaximal, characteristic, complemented
11C11×#2112C211yesmaximal, characteristic, complemented
12C23×C8×C11C2211yescharacteristic
13#10623322—21no—
14C2×#66977—21no—
15C22×Dic44C2211yescharacteristic
16C2×#66957C2211yescharacteristic
17C2×C11×M32C2212yes—
18#10622729—21no—
19#10622729—21no—
20#10622729C2211yescharacteristic
21#10622729C2212yes—
22#10622729C2212yes—
23#10622729C2211yescharacteristic
24#10622728C2211yescharacteristic
25#10622728C2211yescharacteristic
26#10622727—21no—
27#10622727—21no—
28#10622726—21no—
29#10622719C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66880—21no—
32C2×Dic88C2212yescomplemented
33C2×#66864C2212yescomplemented
34C11×C22⋊C16C2211yescharacteristic
35C11×C22⋊C16C2211yescharacteristic
36C11×C22⋊C16C2212yes—
37#10622147C2212yescomplemented
38#10622143C2212yescomplemented
39#10622142C2212yescomplemented
40#10622141C2212yescomplemented
41#10622141C2212yescomplemented
42#10622141C2212yescomplemented
43C23×C4×C11D411yescharacteristic
44C2×#4339—21no—
45C22×Dic22—21no—
46C22×C8×C11—42no—
47C22×C8×C11D411yescharacteristic
48C22×C8×C11D411yescharacteristic
49C22×C8×C11D411yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2311yescharacteristic
53#67006—41no—
54C2×C22⋊Dic11—41no—
55#66983—21no—
56#66983—21no—
57#66982—41no—
58C4×C22⋊D11—41no—
59C4×C22⋊D11—41no—
60#66979—21no—
61C2×C4⋊Dic11—21no—
62#66977—21no—
63#66977—21no—
64#66977—22no—
65#66977—22no—
66#66977—41no—
67#66977—41no—
68C2×Dic11⋊C4—41no—
69C2×Dic44—21no—
70C2×Dic44—42no—
71C2×Dic44C2311yescharacteristic
72C2×Dic44C2312yes—
73#66957—42no—
74C2×D88C2311yescharacteristic
75C2×#4314—21no—
76C11×M32—42no—
77C2×C11×C16C2312yes—
78C2×C11×C16C2312yes—
79#66885—21no—
80#66885—21no—
81#66882—21no—
82#66882C2311yescharacteristic
83#66882C2311yescharacteristic
84#66882C2312yes—
85#66881—21no—
86#66880—21no—
87#66880—21no—
88#66880—22no—
89#66880—22no—
90Dic88—42no—
91#66864—42no—
92#33762—111nomaximal, Sylow
93C24×C11D811yescharacteristic
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11D811yescharacteristic
97C22×C4×C11D811yescharacteristic
98C22×C4×C11D811yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C2×C22⋊D11—41no—
103C2×C22⋊D11—41no—
104C2×C22⋊D11—41no—
105C22×Dic11—41no—
106C22×Dic11—41no—
107#4339—42no—
108#4339—42no—
109C2×D44—21no—
110C2×C4×D11—41no—
111C2×Dic22—21no—
112C2×Dic22—22no—
113C2×Dic22—42no—
114C2×Dic22—42no—
115C2×Dic22—41no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—41no—
120C2×C8×C11—41no—
121C2×C8×C11—41no—
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11C2×D411yescharacteristic
125C2×C8×C11C2411yescharacteristic
126C22⋊Dic11—42no—
127C22⋊Dic11—42no—
128C22⋊Dic11—41no—
129C22⋊Dic11—41no—
130C22⋊Dic11—41no—
131(C2×D11)⋊C4—41no—
132(C2×D11)⋊C4—41no—
133C4⋊Dic11—22no—
134C4⋊Dic11—21no—
135C4⋊Dic11—21no—
136C4⋊Dic11—41no—
137Dic11⋊C4—42no—
138Dic11⋊C4—42no—
139Dic11⋊C4—41no—
140Dic11⋊C4—41no—
141C4×Dic11—41no—
142Dic44—22no—
143Dic44—22no—
144Dic44—22no—
145Dic44—42no—
146D88—22no—
147#4314—42no—
148C11×C16—22no—
149C11×C16—22no—
150#3050—111no—
151C2×#467—111no—
152#2237—112no—
153#2236—111no—
154#2233—111no—
155#2220—112no—
156#2219—112no—
157#2189—112no—
158#2188—111no—
159#2185—111no—
160#2112D1111yescharacteristic, complemented
161C23×C11—22no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11C2×D811yescharacteristic
165C23×C11C2×D811yescharacteristic
166C23×C11C2×D811yescharacteristic
167C22×D11—41no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11C2×D811yescharacteristic
178C2×C4×C11C2×D811yescharacteristic
179C2×C4×C11C2×D811yescharacteristic
180C2×C4×C11C22×D411yescharacteristic
181C22⋊D11—82no—
182C22⋊D11—82no—
183C22⋊D11—82no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11—41no—
189C2×Dic11—82no—
190C2×Dic11—82no—
191D44—41no—
192D44—41no—
193C4×D11—82no—
194Dic22—41no—
195Dic22—42no—
196Dic22—42no—
197Dic22—41no—
198Dic22—82no—
199C8×C11—21no—
200C8×C11—21no—
201C8×C11—21no—
202C8×C11H(5,𝔽2)12yes—
203C2×#135—111no—
204C22×Q16—111no—
205C23×C8C2×D1111yescharacteristic
206#525—221no—
207C2×C22⋊Q8—221no—
208C2×Q32—112no—
209C2×SD32—112no—
210C2×M32C2×D1112yes—
211#467—111no—
212#467—112no—
213#467—111no—
214#467—112no—
215#467—221no—
216#467—221no—
217#466—111no—
218#466—111no—
219#465—221no—
220#465—221no—
221#427—111no—
222C2×#107—111no—
223#416—221no—
224C2×#103—221no—
225#367—112no—
226#366—112no—
227#358—112no—
228#358—112no—
229#358—112no—
230#357—112no—
231C22⋊C16C2×D1111yescharacteristic
232C22⋊C16C2×D1111yescharacteristic
233C22⋊C16C2×D1112yes—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—44no—
243C22×C11#51012yes—
244C22×C11C22×D811yescharacteristic
245C2×D11—81no—
246C2×D11—81no—
247C2×D11—81no—
248C4×C11—21no—
249C4×C11—21no—
250C4×C11—21no—
251C4×C11#53411yescharacteristic
252C4×C11#57511yescharacteristic
253Dic11—81no—
254Dic11—82no—
255Dic11—81no—
256Dic11—82no—
257Dic11—81no—
258C2×#41—221no—
259C22×Q8—221no—
260C23×C4D4411yescharacteristic
261#135—442no—
262C2×Q16—112no—
263C2×Q16—111no—
264C2×Q16—221no—
265C2×Q16—442no—
266C2×SD16—221no—
267C2×D8—111no—
268C22×C8—42no—
269C22×C8D4411yescharacteristic
270C22×C8D4411yescharacteristic
271C22×C8D4411yescharacteristic
272C22×C8C22×D1111yescharacteristic
273C22×C8C22×D1111yescharacteristic
274C22×C8C22×D1111yescharacteristic
275#123—441no—
276C22⋊Q8—222no—
277C22⋊Q8—222no—
278C22⋊Q8—221no—
279C22⋊Q8—221no—
280C22⋊Q8—441no—
281C22⋊Q8—441no—
282#121—221no—
283#121—221no—
284#120—441no—
285C4×D4—441no—
286C4×D4—441no—
287#117—221no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4—441no—
290C2×C22⋊C4—441no—
291Q32—442no—
292SD32—442no—
293M32—42no—
294C2×C16C22×D1112yes—
295C2×C16C22×D1112yes—
296#107—112no—
297#107—111no—
298#107—111no—
299#107—221no—
300#106—221no—
301#103—222no—
302#103—222no—
303#103—221no—
304#103—221no—
305#102—221no—
306#102—221no—
307C2×C11—22no—
308C2×C11—41no—
309C2×C11—41no—
310C2×C11#318611yescharacteristic
311C2×C11C2×#51011yescharacteristic
312C2×C11#341411yescharacteristic
313D11—161no—
314C24D8811yescharacteristic
315#41—442no—
316#41—442no—
317C2×Q8—221no—
318C2×Q8—222no—
319C2×Q8—442no—
320C2×Q8—442no—
321C2×Q8—441no—
322C2×D4—221no—
323C2×D4—441no—
324C2×D4—441no—
325C2×D4—441no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—441no—
329C22×C4—441no—
330C22×C4—441no—
331C22×C4D8811yescharacteristic
332C22×C4D8811yescharacteristic
333C22×C4D8811yescharacteristic
334C22×C4C2×D4411yescharacteristic
335C22×C4C2×D4411yescharacteristic
336C22×C4C2×D4411yescharacteristic
337Q16—222no—
338Q16—222no—
339Q16—222no—
340Q16—442no—
341SD16—442no—
342D8—222no—
343C2×C8—22no—
344C2×C8—22no—
345C2×C8—22no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8C2×D4411yescharacteristic
350C2×C8C2×D4411yescharacteristic
351C2×C8C2×D4411yescharacteristic
352C2×C8C23×D1111yescharacteristic
353C4⋊C4—221no—
354C4⋊C4—221no—
355C4⋊C4—222no—
356C4⋊C4—441no—
357C4⋊C4—442no—
358C4⋊C4—442no—
359C4⋊C4—441no—
360C4⋊C4—441no—
361C22⋊C4—442no—
362C22⋊C4—442no—
363C22⋊C4—441no—
364C22⋊C4—441no—
365C22⋊C4—441no—
366C22⋊C4—441no—
367C22⋊C4—441no—
368C42—441no—
369C16—22no—
370C16—22no—
371C11#3376211yescharacteristic, complemented, Sylow
372C23—22no—
373C23—41no—
374C23—41no—
375C23—441no—
376C23C2×D8811yescharacteristic
377C23C2×D8811yescharacteristic
378C23C2×D8811yescharacteristic
379Q8—442no—
380Q8—441no—
381Q8—441no—
382Q8—442no—
383Q8—882no—
384D4—441no—
385D4—441no—
386D4—882no—
387D4—882no—
388D4—882no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—442no—
401C2×C4—441no—
402C2×C4—442no—
403C2×C4—882no—
404C2×C4—882no—
405C2×C4—882no—
406C2×C4C2×D8811yescharacteristic
407C2×C4C2×D8811yescharacteristic
408C2×C4C2×D8811yescharacteristic
409C2×C4C22×D4411yescharacteristic
410C8—21no—
411C8—21no—
412C8—21no—
413C8#6703712yes—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—44no—
423C22—881no—
424C22—881no—
425C22—881no—
426C22#1062252212yes—
427C22C22×D8811yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—881no—
432C4—882no—
433C4—881no—
434C4—882no—
435C4—881no—
436C4#1062302411yescharacteristic
437C4#1062327911yescharacteristic
438C2—22no—
439C2—41no—
440C2—41no—
441C2—1761no—
442C2#1307936711yescharacteristic
443C2C2×#1062252211yescharacteristic
444C2#1308175211yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2112C2
socleC22×C11C22×D8
prime radical#13078197C2
hypercenter#2112D11
hypocenterC11#33762
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #2112

Complements

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

NH ≅ G/Ntype
2. C2×#10622729C2semidirect
3. #13070825C2semidirect
4. #13070819C2semidirect
5. #13070802C2semidirect
6. #13070729C2semidirect
7. #13070724C2semidirect
8. #13070558C2semidirect
9. #13070552C2semidirect
10. #13070535C2semidirect
11. C11×#2112C2semidirect
32. C2×Dic88C22semidirect
33. C2×#66864C22semidirect
37. #10622147C22semidirect
38. #10622143C22semidirect
39. #10622142C22semidirect
40. #10622141C22semidirect
41. #10622141C22semidirect
42. #10622141C22semidirect
160. #2112D11semidirect
371. C11#33762semidirect

Maximal subgroups

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

subgroupindex
#130781972
C2×#106227292
#130708252
#130708192
#130708022
#130707292
#130707242
#130705582
#130705522
#130705352
C11×#21122
#3376211