Finite Group Databasebeta

← #14909532

Subgroups — #14909532

Order 2816.

594 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
2#13070821C212yesmaximal, complemented
3#13070813C211yesmaximal, characteristic, complemented
4#13070796C211yesmaximal, characteristic, complemented
5#13070714C212yesmaximal, complemented
6#13070705C212yesmaximal, complemented
7#13070554C212yesmaximal, complemented
8#13070550C211yesmaximal, characteristic, complemented
9#13070533C211yesmaximal, characteristic, complemented
10C2×C22⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
11C2×C11×#467C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×C22⋊Q8—21no—
15#10623322—21no—
16C2×#66957C2211yescharacteristic
17C11×#467—21no—
18C11×#467—21no—
19C11×#467C2212yes—
20C11×#467C2212yes—
21C2×C11×#107C2211yescharacteristic
22C2×C11×#103—21no—
23C2×#66893C2212yescomplemented
24C2×#66892C2212yescomplemented
25#10622729C2211yescharacteristic
26#10622729C2211yescharacteristic
27#10622728C2211yescharacteristic
28#10622728C2211yescharacteristic
29#10622727—21no—
30#10622727—21no—
31#10622726—21no—
32#10622719C2211yescharacteristic
33C22×C11⋊C16C2212yes—
34#10622202C2212yescomplemented
35#10622202C2212yescomplemented
36C22⋊(C11⋊C16)C2211yescharacteristic
37C22⋊(C11⋊C16)C2211yescharacteristic
38C22⋊(C11⋊C16)C2212yes—
39#10622130C2212yescomplemented
40#10622129C2212yescomplemented
41#10622128C2212yescomplemented
42#10622127C2212yescomplemented
43C22×Q8×C11—21no—
44C23×C4×C11D411yescharacteristic
45C2×#4339—21no—
46C2×C11×Q16—21no—
47C2×C11×Q16—42no—
48C2×C11×Q16C2312yes—
49C22×C8×C11—42no—
50C22×C8×C11D411yescharacteristic
51C22×C8×C11D411yescharacteristic
52C22×C8×C11D411yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C11×C22⋊Q8—22no—
57C11×C22⋊Q8—22no—
58C11×C22⋊Q8—41no—
59C11×C22⋊Q8—41no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—41no—
62C2×C11×C22⋊C4—41no—
63#67006—41no—
64#66983—21no—
65#66983—21no—
66#66982—41no—
67C4×C22⋊D11—41no—
68C4×C22⋊D11—41no—
69#66979—21no—
70#66977—21no—
71#66977—21no—
72C2×Dic44C2311yescharacteristic
73#66957—42no—
74C2×D88C2311yescharacteristic
75C2×#4314—21no—
76C11×#107—21no—
77C11×#107C2312yes—
78C11×#103—22no—
79C11×#103—22no—
80#66893—42no—
81#66892—42no—
82#66885—21no—
83#66885—21no—
84#66882C2311yescharacteristic
85#66882C2311yescharacteristic
86#66881—21no—
87#66880—21no—
88#66880—21no—
89C2×C11⋊C16—42no—
90C2×C11⋊C16C2312yes—
91C2×C11⋊C16C2312yes—
92#33756—111nomaximal, Sylow
93C24×C11D811yescharacteristic
94C2×Q8×C11—22no—
95C2×Q8×C11—42no—
96C2×Q8×C11—42no—
97C2×Q8×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11D811yescharacteristic
103C22×C4×C11D811yescharacteristic
104C22×C4×C11D811yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C2×C22⋊D11—41no—
109C2×C22⋊D11—41no—
110C2×C22⋊D11—41no—
111#4339—42no—
112#4339—42no—
113C2×D44—21no—
114C2×C4×D11—41no—
115C2×Dic22—21no—
116C11×Q16—22no—
117C11×Q16—22no—
118C11×Q16—42no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C2×C8×C11—41no—
123C2×C8×C11—41no—
124C2×C8×C11—41no—
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2411yescharacteristic
129C11×C4⋊C4—22no—
130C11×C4⋊C4—41no—
131C11×C4⋊C4—42no—
132C11×C4⋊C4—42no—
133C11×C22⋊C4—42no—
134C11×C22⋊C4—42no—
135C22⋊Dic11—41no—
136C22⋊Dic11—41no—
137C22⋊Dic11—41no—
138(C2×D11)⋊C4—41no—
139(C2×D11)⋊C4—41no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142Dic11⋊C4—41no—
143Dic11⋊C4—41no—
144C4×Dic11—41no—
145Dic44—22no—
146D88—22no—
147#4314—42no—
148C11⋊C16—22no—
149C11⋊C16—22no—
150#3050—111no—
151C2×#467D1111yescharacteristic, complemented
152#2237—112no—
153#2235—111no—
154#2232—111no—
155#2217—112no—
156#2216—112no—
157#2189—112no—
158#2188—111no—
159#2185—111no—
160C2×C22⋊C16—111no—
161C23×C11—22no—
162C23×C11—22no—
163C23×C11—41no—
164C23×C11C2×D811yescharacteristic
165C23×C11C2×D811yescharacteristic
166C23×C11C2×D811yescharacteristic
167C22×D11—41no—
168Q8×C11—42no—
169Q8×C11—42no—
170Q8×C11—82no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—82no—
183C2×C4×C11—82no—
184C2×C4×C11C2×D811yescharacteristic
185C2×C4×C11C2×D811yescharacteristic
186C2×C4×C11C2×D811yescharacteristic
187C2×C4×C11C22×D411yescharacteristic
188C22⋊D11—82no—
189C22⋊D11—82no—
190C22⋊D11—82no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194D44—41no—
195D44—41no—
196C4×D11—82no—
197Dic22—41no—
198Dic22—41no—
199C8×C11—21no—
200C8×C11—21no—
201C8×C11—21no—
202C8×C11H(5,𝔽2)12yes—
203C2×#135—111no—
204C22×Q16C2×D1111yescharacteristic
205C23×C8C2×D1111yescharacteristic
206#525—221no—
207C2×C22⋊Q8—21no—
208C2×Q32—112no—
209C2×SD32—112no—
210C22×C16—112no—
211#467—21no—
212#467—21no—
213#467—111no—
214#467—111no—
215#467C2×D1112yes—
216#467C2×D1112yes—
217#466—111no—
218#466—111no—
219#465—221no—
220#465—221no—
221#427—111no—
222C2×#107C2×D1111yescharacteristic
223#416—221no—
224C2×#103—21no—
225#367—112no—
226#366—112no—
227#358—112no—
228#358—112no—
229#358—112no—
230#357—112no—
231C22⋊C16—111no—
232C22⋊C16—111no—
233C22⋊C16—112no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—44no—
242C22×C11#50812yes—
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—82no—
252C4×C11—82no—
253C4×C11#53411yescharacteristic
254C4×C11#57511yescharacteristic
255Dic11—81no—
256Dic11—81no—
257Dic11—81no—
258C2×#41—221no—
259C22×Q8—21no—
260C23×C4C22⋊D1111yescharacteristic
261#135—442no—
262C2×Q16—21no—
263C2×Q16—42no—
264C2×Q16—111no—
265C2×Q16C22×D1112yes—
266C2×SD16—221no—
267C2×D8—111no—
268C22×C8—42no—
269C22×C8C22⋊D1111yescharacteristic
270C22×C8C22⋊D1111yescharacteristic
271C22×C8C22⋊D1111yescharacteristic
272C22×C8C22×D1111yescharacteristic
273C22×C8C22×D1111yescharacteristic
274C22×C8C22×D1111yescharacteristic
275#123—441no—
276C22⋊Q8—22no—
277C22⋊Q8—22no—
278C22⋊Q8—41no—
279C22⋊Q8—41no—
280C22⋊Q8—221no—
281C22⋊Q8—221no—
282#121—221no—
283#121—221no—
284#120—441no—
285C4×D4—441no—
286C4×D4—441no—
287#117—221no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—41no—
290C2×C22⋊C4—41no—
291Q32—442no—
292SD32—442no—
293C2×C16—112no—
294C2×C16—112no—
295C2×C16—442no—
296#107—21no—
297#107—111no—
298#107—111no—
299#107C22×D1112yes—
300#106—221no—
301#103—22no—
302#103—22no—
303#103—221no—
304#103—221no—
305#102—221no—
306#102—221no—
307C2×C11—22no—
308C2×C11—22no—
309C2×C11—41no—
310C2×C11#318611yescharacteristic
311C2×C11C2×#50811yescharacteristic
312C2×C11C2×#51011yescharacteristic
313D11—161no—
314C24#432311yescharacteristic
315#41—442no—
316#41—442no—
317C2×Q8—22no—
318C2×Q8—42no—
319C2×Q8—42no—
320C2×Q8—41no—
321C2×Q8—221no—
322C2×D4—221no—
323C2×D4—441no—
324C2×D4—441no—
325C2×D4—441no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—441no—
331C22×C4#432311yescharacteristic
332C22×C4#432311yescharacteristic
333C22×C4#432311yescharacteristic
334C22×C4C2×C22⋊D1111yescharacteristic
335C22×C4C2×C22⋊D1111yescharacteristic
336C22×C4C2×C22⋊D1111yescharacteristic
337Q16—22no—
338Q16—22no—
339Q16—42no—
340Q16—222no—
341SD16—442no—
342D8—222no—
343C2×C8—22no—
344C2×C8—22no—
345C2×C8—22no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8C2×C22⋊D1111yescharacteristic
350C2×C8C2×C22⋊D1111yescharacteristic
351C2×C8C2×C22⋊D1111yescharacteristic
352C2×C8C23×D1111yescharacteristic
353C4⋊C4—22no—
354C4⋊C4—41no—
355C4⋊C4—42no—
356C4⋊C4—42no—
357C4⋊C4—221no—
358C4⋊C4—221no—
359C4⋊C4—441no—
360C4⋊C4—441no—
361C22⋊C4—42no—
362C22⋊C4—42no—
363C22⋊C4—441no—
364C22⋊C4—441no—
365C22⋊C4—441no—
366C22⋊C4—441no—
367C22⋊C4—441no—
368C42—441no—
369C16—222no—
370C16—222no—
371C11#3375611yescharacteristic, complemented, Sylow
372C23—22no—
373C23—22no—
374C23—41no—
375C23—441no—
376C23C2×#432311yescharacteristic
377C23C2×#432311yescharacteristic
378C23C2×#432311yescharacteristic
379Q8—42no—
380Q8—42no—
381Q8—82no—
382Q8—441no—
383Q8—441no—
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—42no—
399C2×C4—42no—
400C2×C4—82no—
401C2×C4—82no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—441no—
405C2×C4—882no—
406C2×C4C2×#432311yescharacteristic
407C2×C4C2×#432311yescharacteristic
408C2×C4C2×#432311yescharacteristic
409C2×C4C22×C22⋊D1111yescharacteristic
410C8—21no—
411C8—21no—
412C8—21no—
413C8#6703712yes—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—44no—
422C22—881no—
423C22—881no—
424C22—881no—
425C22#1062279212yes—
426C22#1062280712yes—
427C22C22×#432311yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—82no—
432C4—82no—
433C4—881no—
434C4—881no—
435C4—881no—
436C4#1062333511yescharacteristic
437C4#1062335311yescharacteristic
438C2—22no—
439C2—22no—
440C2—41no—
441C2—1761no—
442C2#1307936411yescharacteristic
443C2C2×#1062280711yescharacteristic
444C2C2×#1062279211yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#467C2
socleC22×C11C22×D8
prime radical#13078197C2
hypercenterC2×#467D11
hypocenterC11#33756
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
2. #13070821C2semidirect
3. #13070813C2semidirect
4. #13070796C2semidirect
5. #13070714C2semidirect
6. #13070705C2semidirect
7. #13070554C2semidirect
8. #13070550C2semidirect
9. #13070533C2semidirect
10. C2×C22⋊(C11⋊C16)C2semidirect
11. C2×C11×#467C2semidirect
23. C2×#66893C22semidirect
24. C2×#66892C22semidirect
34. #10622202C22semidirect
35. #10622202C22semidirect
39. #10622130C22semidirect
40. #10622129C22semidirect
41. #10622128C22semidirect
42. #10622127C22semidirect
151. C2×#467D11semidirect
371. C11#33756semidirect

Maximal subgroups

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

subgroupindex
#130781972
#130708212
#130708132
#130707962
#130707142
#130707052
#130705542
#130705502
#130705332
C2×C22⋊(C11⋊C16)2
C2×C11×#4672
#3375611