Finite Group Databasebeta

← #14908574

Subgroups — #14908574

Order 2816.

590 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078197C211yesmaximal, characteristic
2C2×#10622719C211yesmaximal, characteristic, complemented
3#13070825C212yesmaximal, complemented
4#13070819C211yesmaximal, characteristic, complemented
5#13070814C211yesmaximal, characteristic, complemented
6#13070808C212yesmaximal, complemented
7#13070802C211yesmaximal, characteristic, complemented
8#13070797C211yesmaximal, characteristic, complemented
9#13070400C212yesmaximal, complemented
10#13070324C212yesmaximal, complemented
11C2×C11×C22⋊C16C211yesmaximal, characteristic, complemented
12C23×C8×C11C2211yescharacteristic
13#10623322—21no—
14C2×#66979—21no—
15C2×#66957C2211yescharacteristic
16C22×C11×C16C2212yes—
17#10622729C2211yescharacteristic
18#10622729C2211yescharacteristic
19#10622728C2211yescharacteristic
20#10622728C2211yescharacteristic
21#10622727—21no—
22#10622727—21no—
23#10622726—21no—
24#10622719—21no—
25#10622719—21no—
26#10622719C2211yescharacteristic
27#10622719C2212yes—
28#10622719C2212yes—
29C2×#66882C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66881—21no—
32C11×C22⋊C16C2211yescharacteristic
33C11×C22⋊C16C2211yescharacteristic
34C11×C22⋊C16C2212yes—
35#10622147C2212yescomplemented
36#10622147C2212yescomplemented
37#10622143C2212yescomplemented
38#10622143C2212yescomplemented
39#10622142C2212yescomplemented
40#10622142C2212yescomplemented
41#10622141C2212yescomplemented
42#10622141C2212yescomplemented
43C23×C4×C11D411yescharacteristic
44C2×#4339—21no—
45C22×C8×C11—24no—
46C22×C8×C11D411yescharacteristic
47C22×C8×C11D411yescharacteristic
48C22×C8×C11D411yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52#67006—41no—
53C2×C22⋊Dic11—41no—
54#66983—21no—
55#66983—21no—
56#66982—41no—
57C4×C22⋊D11—41no—
58C4×C22⋊D11—41no—
59#66979—21no—
60#66979—22no—
61#66979—22no—
62#66979—41no—
63#66979—41no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66#66977—21no—
67#66977—21no—
68C2×C4×Dic11—41no—
69C2×Dic44C2311yescharacteristic
70#66957—24no—
71C2×D88C2311yescharacteristic
72C2×#4314—21no—
73C2×C11×C16—24no—
74C2×C11×C16C2312yes—
75C2×C11×C16C2312yes—
76#66885—21no—
77#66885—21no—
78#66882—21no—
79#66882—21no—
80#66882C2311yescharacteristic
81#66882C2311yescharacteristic
82#66882C2312yes—
83#66882C2312yes—
84#66881—21no—
85#66881—22no—
86#66881—22no—
87#66880—21no—
88#66880—21no—
89#33645—111nomaximal, Sylow
90C24×C11D811yescharacteristic
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11D811yescharacteristic
94C22×C4×C11D811yescharacteristic
95C22×C4×C11D811yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C2×C22⋊D11—41no—
100C2×C22⋊D11—41no—
101C2×C22⋊D11—41no—
102C22×Dic11—41no—
103C22×Dic11—41no—
104#4339—42no—
105#4339—42no—
106C2×D44—21no—
107C2×C4×D11—41no—
108C2×Dic22—21no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11C2×D411yescharacteristic
116C2×C8×C11C2×D411yescharacteristic
117C2×C8×C11#4114yes—
118C2×C8×C11C2411yescharacteristic
119C22⋊Dic11—41no—
120C22⋊Dic11—41no—
121C22⋊Dic11—42no—
122C22⋊Dic11—42no—
123C22⋊Dic11—41no—
124(C2×D11)⋊C4—41no—
125(C2×D11)⋊C4—41no—
126C4⋊Dic11—21no—
127C4⋊Dic11—21no—
128C4⋊Dic11—22no—
129C4⋊Dic11—22no—
130C4⋊Dic11—41no—
131C4⋊Dic11—41no—
132Dic11⋊C4—41no—
133Dic11⋊C4—41no—
134C4×Dic11—42no—
135C4×Dic11—42no—
136C4×Dic11—41no—
137Dic44—22no—
138D88—22no—
139#4314—42no—
140C11×C16—22no—
141C11×C16—22no—
142#3050—111no—
143C2×#427—111no—
144#2237—112no—
145#2236—111no—
146#2235—111no—
147#2234—112no—
148#2233—111no—
149#2232—111no—
150#2158—112no—
151#2138—112no—
152C2×C22⋊C16D1111yescharacteristic, complemented
153C23×C11—22no—
154C23×C11—22no—
155C23×C11—41no—
156C23×C11C2×D811yescharacteristic
157C23×C11C2×D811yescharacteristic
158C23×C11C2×D811yescharacteristic
159C22×D11—41no—
160C2×C4×C11—22no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11#12312yes—
168C2×C4×C11C2×D811yescharacteristic
169C2×C4×C11C2×D811yescharacteristic
170C2×C4×C11C2×D811yescharacteristic
171C2×C4×C11#13712yes—
172C2×C4×C11C22×D411yescharacteristic
173C22⋊D11—82no—
174C22⋊D11—82no—
175C22⋊D11—82no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—82no—
182C2×Dic11—82no—
183D44—41no—
184D44—41no—
185C4×D11—82no—
186Dic22—41no—
187Dic22—41no—
188C8×C11—21no—
189C8×C11—21no—
190C8×C11#12312yes—
191C8×C11C2×#4112yes—
192C2×#135—111no—
193C23×C8C2×D1111yescharacteristic
194#525—221no—
195C2×#117—221no—
196C22×C16C2×D1112yes—
197#467—111no—
198#467—111no—
199#466—111no—
200#466—111no—
201#465—221no—
202#465—221no—
203#427—112no—
204#427—112no—
205#427—111no—
206#427—221no—
207#427—221no—
208C2×#107—111no—
209C2×#107—111no—
210C2×#106—221no—
211#416—221no—
212#367—112no—
213#367—112no—
214#366—112no—
215#366—112no—
216#358—112no—
217#358—112no—
218#357—112no—
219#357—112no—
220C22⋊C16C2×D1111yescharacteristic
221C22⋊C16C2×D1111yescharacteristic
222C22⋊C16C2×D1112yes—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—44no—
231C22×C11#48012yes—
232C22×C11#50812yes—
233C22×C11C22×D811yescharacteristic
234C2×D11—81no—
235C2×D11—81no—
236C2×D11—81no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11#48012yes—
240C4×C11C2×#12311yescharacteristic
241C4×C11C2×#13711yescharacteristic
242Dic11—81no—
243Dic11—82no—
244Dic11—81no—
245Dic11—82no—
246Dic11—81no—
247C2×#41—221no—
248C23×C4D4411yescharacteristic
249#135—224no—
250C2×Q16—111no—
251C2×SD16—221no—
252C2×D8—111no—
253C22×C8—24no—
254C22×C8D4411yescharacteristic
255C22×C8D4411yescharacteristic
256C22×C8D4411yescharacteristic
257C22×C8C22×D1111yescharacteristic
258C22×C8C22×D1111yescharacteristic
259C22×C8C22×D1111yescharacteristic
260#123—441no—
261C22⋊Q8—221no—
262C22⋊Q8—221no—
263#121—221no—
264#121—221no—
265#120—441no—
266C4×D4—441no—
267C4×D4—441no—
268#117—222no—
269#117—222no—
270#117—221no—
271#117—441no—
272#117—441no—
273C2×C4⋊C4—221no—
274C2×C4⋊C4—221no—
275C2×C22⋊C4—441no—
276C2×C42—441no—
277C2×C16—24no—
278C2×C16C22×D1112yes—
279C2×C16C22×D1112yes—
280#107—112no—
281#107—112no—
282#107—111no—
283#107—111no—
284#107—221no—
285#107—221no—
286#106—222no—
287#106—222no—
288#106—221no—
289#103—221no—
290#103—221no—
291#102—221no—
292#102—221no—
293C2×C11—22no—
294C2×C11—22no—
295C2×C11—41no—
296C2×C11C2×#48011yescharacteristic
297C2×C11C2×#50811yescharacteristic
298C2×C11#341411yescharacteristic
299D11—161no—
300C24D8811yescharacteristic
301#41—442no—
302#41—442no—
303C2×Q8—221no—
304C2×D4—221no—
305C2×D4—441no—
306C2×D4—441no—
307C2×D4—441no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—441no—
311C22×C4—441no—
312C22×C4—441no—
313C22×C4D8811yescharacteristic
314C22×C4D8811yescharacteristic
315C22×C4D8811yescharacteristic
316C22×C4C2×D4411yescharacteristic
317C22×C4C2×D4411yescharacteristic
318C22×C4C2×D4411yescharacteristic
319Q16—222no—
320SD16—442no—
321D8—222no—
322C2×C8—22no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8C2×D4411yescharacteristic
328C2×C8C2×D4411yescharacteristic
329C2×C8C2×D4411yescharacteristic
330C2×C8#434114yes—
331C2×C8C23×D1111yescharacteristic
332C4⋊C4—221no—
333C4⋊C4—221no—
334C4⋊C4—222no—
335C4⋊C4—222no—
336C4⋊C4—441no—
337C4⋊C4—441no—
338C4⋊C4—441no—
339C4⋊C4—441no—
340C22⋊C4—442no—
341C22⋊C4—442no—
342C22⋊C4—441no—
343C22⋊C4—441no—
344C22⋊C4—441no—
345C22⋊C4—441no—
346C22⋊C4—441no—
347C42—442no—
348C42—442no—
349C42—441no—
350C16—22no—
351C16—22no—
352C11#3364511yescharacteristic, complemented, Sylow
353C23—22no—
354C23—22no—
355C23—41no—
356C23—441no—
357C23C2×D8811yescharacteristic
358C23C2×D8811yescharacteristic
359C23C2×D8811yescharacteristic
360Q8—441no—
361Q8—441no—
362D4—441no—
363D4—441no—
364D4—882no—
365D4—882no—
366D4—882no—
367C2×C4—22no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—442no—
375C2×C4—442no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4—441no—
379C2×C4—882no—
380C2×C4—882no—
381C2×C4—882no—
382C2×C4#6693912yes—
383C2×C4C2×D8811yescharacteristic
384C2×C4C2×D8811yescharacteristic
385C2×C4C2×D8811yescharacteristic
386C2×C4#6696212yes—
387C2×C4C22×D4411yescharacteristic
388C8—21no—
389C8—21no—
390C8#6693912yes—
391C8C2×#434112yes—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—44no—
400C22—881no—
401C22—881no—
402C22—881no—
403C22#1062234912yes—
404C22#1062251712yes—
405C22C22×D8811yescharacteristic
406C4—21no—
407C4—21no—
408C4—882no—
409C4—881no—
410C4—882no—
411C4—881no—
412C4—881no—
413C4#1062234912yes—
414C4C2×#6693911yescharacteristic
415C4C2×#6696211yescharacteristic
416C2—22no—
417C2—22no—
418C2—41no—
419C2—1761no—
420C2C2×#1062234911yescharacteristic
421C2C2×#1062251711yescharacteristic
422C2#1308175211yescharacteristic
subgroupG/H
centerC2×C4C2×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×C22⋊C16C2
socleC22×C11C22×D8
prime radical#13078197C2
hypercenterC2×C22⋊C16D11
hypocenterC11#33645
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8 ◁ C2×C22⋊C16

Complements

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

NH ≅ G/Ntype
2. C2×#10622719C2semidirect
3. #13070825C2semidirect
4. #13070819C2semidirect
5. #13070814C2semidirect
6. #13070808C2semidirect
7. #13070802C2semidirect
8. #13070797C2semidirect
9. #13070400C2semidirect
10. #13070324C2semidirect
11. C2×C11×C22⋊C16C2semidirect
35. #10622147C22semidirect
36. #10622147C22semidirect
37. #10622143C22semidirect
38. #10622143C22semidirect
39. #10622142C22semidirect
40. #10622142C22semidirect
41. #10622141C22semidirect
42. #10622141C22semidirect
152. C2×C22⋊C16D11semidirect
352. C11#33645semidirect

Maximal subgroups

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

subgroupindex
#130781972
C2×#106227192
#130708252
#130708192
#130708142
#130708082
#130708022
#130707972
#130704002
#130703242
C2×C11×C22⋊C162
#3364511