Finite Group Databasebeta

← #14738626

Subgroups — #14738626

Order 2816.

596 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079846C211yesmaximal, characteristic
2#13079643C211yesmaximal, characteristic
3#13077591C211yesmaximal, characteristic
4#13068167C212yesmaximal, complemented
5#13068160C212yesmaximal, complemented
6#13068043C212yesmaximal, complemented
7#13068036C212yesmaximal, complemented
8#13067379C211yesmaximal, characteristic, complemented
9#13067333C211yesmaximal, characteristic, complemented
10#13067333C211yesmaximal, characteristic, complemented
11C2×C11×#487C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14#10623010C2211yescharacteristic
15C11×#487—21no—
16C11×#487—21no—
17C11×#487C2212yes—
18C11×#487C2212yes—
19C2×C11×#103—21no—
20C2×C11×#103—21no—
21C2×C4×C8×C11C2211yescharacteristic
22#10622841—21no—
23#10622840—21no—
24#10622724—21no—
25C8×C22⋊D11—21no—
26#10622707C2212yes—
27#10622703C2212yes—
28#10622702—21no—
29#10622700C2212yes—
30#10622699—21no—
31#10622696C2212yes—
32#10622695—21no—
33#10622693—21no—
34#10622583—21no—
35#10622581—21no—
36#10622539C2211yescharacteristic
37#10622539C2211yescharacteristic
38#10622539C2211yescharacteristic
39#10622303—21no—
40#10622302—21no—
41#10622301C2211yescharacteristic
42C8×D44C2211yescharacteristic
43#10622292C2211yescharacteristic
44C8×Dic22C2211yescharacteristic
45#10622185C2212yes—
46#10622185C2212yes—
47#10622185C2212yes—
48#10622185C2212yes—
49#10622096C2212yes—
50#10622095C2212yes—
51C22×Q8×C11—21no—
52C22×Q8×C11—21no—
53C22×C8×C11D411yescharacteristic
54C22×C8×C11D411yescharacteristic
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8—21no—
58C11×C4⋊Q8—21no—
59C11×C4⋊Q8—21no—
60C11×C4⋊Q8—21no—
61C11×C4⋊Q8C2312yes—
62C11×C4⋊Q8C2312yes—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C42×C11C2311yescharacteristic
68C2×#4326—22no—
69C2×#4325—22no—
70#66983D411yescharacteristic
71#66982—21no—
72C4×C22⋊D11—21no—
73#66977D411yescharacteristic
74C2×#4313—21no—
75C2×C8×D11—21no—
76#66929—21no—
77#66928D411yescharacteristic
78C4×D44C2311yescharacteristic
79#66925—21no—
80#66923D411yescharacteristic
81C4×Dic22C2311yescharacteristic
82C11×#103—22no—
83C11×#103—22no—
84C11×#103—22no—
85C11×#103—22no—
86C4×C8×C11D411yescharacteristic
87C4×C8×C11D411yescharacteristic
88C4×C8×C11C2311yescharacteristic
89C4×C8×C11C2311yescharacteristic
90#66899—22no—
91#66899—22no—
92C22⋊(C11⋊C8)—21no—
93C22⋊(C11⋊C8)—21no—
94C22⋊(C11⋊C8)—21no—
95(C2×D11)⋊C8—21no—
96(C2×D11)⋊C8—21no—
97#66879—21no—
98Dic11⋊C8—21no—
99Dic11⋊C8—21no—
100C8×Dic11—21no—
101#66874—22no—
102#66873—22no—
103#66872—22no—
104#66871—22no—
105C4⋊(C11⋊C8)C2311yescharacteristic
106C4⋊(C11⋊C8)C2311yescharacteristic
107C4⋊(C11⋊C8)C2312yes—
108C4⋊(C11⋊C8)C2312yes—
109#66867—21no—
110#66867—21no—
111#66867—21no—
112#19363—111nomaximal, Sylow
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—42no—
116C2×Q8×C11—42no—
117C2×Q8×C11—41no—
118C2×Q8×C11—41no—
119C2×Q8×C11—82no—
120C22×C4×C11—41no—
121C22×C4×C11—41no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11#4111yescharacteristic
125C2×C22⋊D11—21no—
126C2×D44C2×D411yescharacteristic
127C2×C4×D11—21no—
128C2×Dic22C2×D411yescharacteristic
129C2×C8×C11—41no—
130C2×C8×C11—41no—
131C2×C8×C11C2×D411yescharacteristic
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2×D411yescharacteristic
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—41no—
140C11×C4⋊C4—41no—
141C11×C4⋊C4—41no—
142C11×C4⋊C4—41no—
143C42×C11C2×D411yescharacteristic
144C42×C11C2×D411yescharacteristic
145C42×C11#4111yescharacteristic
146C42×C11C2411yescharacteristic
147C22⋊Dic11—21no—
148#4326—82no—
149#4325—82no—
150(C2×D11)⋊C4—21no—
151(C2×D11)⋊C4—21no—
152(C2×D11)⋊C4—21no—
153(C2×D11)⋊C4—21no—
154C4⋊Dic11C2×D411yescharacteristic
155C4⋊Dic11C2×D411yescharacteristic
156Dic11⋊C4—21no—
157Dic11⋊C4—21no—
158Dic11⋊C4—21no—
159Dic11⋊C4—21no—
160C4×Dic11—21no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—22no—
165#4313—42no—
166C8×D11—42no—
167#3239—111no—
168#3218—111no—
169C2×#487D1111yescharacteristic, complemented
170#2966—111no—
171#1700—112no—
172#1699—112no—
173#1680—112no—
174#1679—112no—
175#1568—111no—
176#1556—111no—
177#1556—111no—
178C23×C11#12111yescharacteristic
179C22×D11—21no—
180Q8×C11—42no—
181Q8×C11—42no—
182Q8×C11—42no—
183Q8×C11—42no—
184Q8×C11—82no—
185Q8×C11—82no—
186C2×C4×C11—22no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—22no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—82no—
193C2×C4×C11—82no—
194C2×C4×C11#12111yescharacteristic
195C2×C4×C11#12111yescharacteristic
196C2×C4×C11#12111yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C22⋊D11—42no—
201C2×Dic11—21no—
202C2×Dic11—21no—
203C2×Dic11—21no—
204D44—22no—
205C4×D11—41no—
206C4×D11—41no—
207Dic22—22no—
208C8×C11—21no—
209C8×C11—21no—
210C8×C11—21no—
211C8×C11—21no—
212C11⋊C8—41no—
213C11⋊C8—41no—
214C11⋊C8—42no—
215C11⋊C8—42no—
216C2×C4⋊Q8C2×D1111yescharacteristic
217C2×C4⋊Q8C2×D1111yescharacteristic
218#529—111no—
219#501—221no—
220#497—221no—
221#491—221no—
222#489—221no—
223#487—21no—
224#487—21no—
225#487C2×D1112yes—
226#487C2×D1112yes—
227#484—221no—
228#481—221no—
229#475—112no—
230#474—112no—
231#462—112no—
232#461—112no—
233#451—221no—
234#448—221no—
235#446—111no—
236C8×Q8—111no—
237#436—111no—
238#435—221no—
239C8×D4—111no—
240C8×D4—221no—
241#433—221no—
242#432—111no—
243#432—111no—
244#432—111no—
245C2×#103—21no—
246C2×#103—21no—
247#405—221no—
248C2×C4×C8C2×D1111yescharacteristic
249#335—112no—
250#334—112no—
251#332—112no—
252#332—112no—
253#332—112no—
254#332—112no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11#47312yes—
258C22×C11C2×#12111yescharacteristic
259C2×D11—41no—
260C2×D11—41no—
261C2×D11—41no—
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—82no—
267C4×C11—82no—
268C4×C11#57511yescharacteristic
269C4×C11#57511yescharacteristic
270C4×C11#57712yes—
271Dic11—41no—
272Dic11—41no—
273Dic11—41no—
274C22×Q8—21no—
275C22×Q8—21no—
276C2×Q16—222no—
277C2×SD16—222no—
278C2×M16—221no—
279C22×C8—221no—
280C22×C8C22⋊D1111yescharacteristic
281C22×C8C22⋊D1111yescharacteristic
282C4⋊Q8—21no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8—21no—
287C4⋊Q8—21no—
288C4⋊Q8C22×D1112yes—
289C4⋊Q8C22×D1112yes—
290#126—221no—
291#125—111no—
292#124—111no—
293#123—221no—
294C22⋊Q8—111no—
295#121—111no—
296C4×Q8—111no—
297C4×D4—111no—
298C4×D4—221no—
299#117—221no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C42C22×D1111yescharacteristic
305#107—222no—
306#106—222no—
307C4⋊C8—111no—
308C4⋊C8—111no—
309C4⋊C8—112no—
310C4⋊C8—112no—
311C4⋊C8—221no—
312C4⋊C8—221no—
313#103—22no—
314#103—22no—
315#103—22no—
316#103—22no—
317#103—222no—
318#103—222no—
319#103—222no—
320#102—222no—
321C22⋊C8—221no—
322C22⋊C8—221no—
323C22⋊C8—221no—
324C22⋊C8—221no—
325C22⋊C8—221no—
326#97—221no—
327#97—221no—
328#97—221no—
329#97—221no—
330C4×C8—221no—
331C4×C8C22⋊D1111yescharacteristic
332C4×C8C22⋊D1111yescharacteristic
333C4×C8C22×D1111yescharacteristic
334C4×C8C22×D1111yescharacteristic
335C2×C11—22no—
336C2×C11#304011yescharacteristic
337C2×C11#305711yescharacteristic
338C2×C11C2×#47311yescharacteristic
339D11—81no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8—42no—
343C2×Q8—42no—
344C2×Q8—41no—
345C2×Q8—41no—
346C2×Q8—82no—
347C2×Q8—111no—
348C2×D4—111no—
349C2×D4—221no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—221no—
353C22×C4D4×D1111yescharacteristic
354C22×C4#434111yescharacteristic
355C22×C4C2×C22⋊D1111yescharacteristic
356Q16—882no—
357SD16—882no—
358M16—442no—
359C2×C8—41no—
360C2×C8—41no—
361C2×C8—222no—
362C2×C8—222no—
363C2×C8—221no—
364C2×C8—221no—
365C2×C8—442no—
366C2×C8C2×C22⋊D1111yescharacteristic
367C2×C8C2×C22⋊D1111yescharacteristic
368C2×C8C2×C22⋊D1111yescharacteristic
369C2×C8C2×C22⋊D1111yescharacteristic
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—111no—
379C4⋊C4—111no—
380C4⋊C4—221no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C4⋊C4—221no—
384C22⋊C4—221no—
385C22⋊C4—221no—
386C22⋊C4—221no—
387C22⋊C4—221no—
388C22⋊C4—221no—
389C42—221no—
390C42D4×D1111yescharacteristic
391C42#434111yescharacteristic
392C42C2×C22⋊D1111yescharacteristic
393C42C23×D1111yescharacteristic
394C11#1936311yescharacteristic, complemented, Sylow
395C23—221no—
396C23#6699111yescharacteristic
397Q8—42no—
398Q8—42no—
399Q8—42no—
400Q8—42no—
401Q8—82no—
402Q8—82no—
403Q8—222no—
404D4—222no—
405D4—442no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—82no—
413C2×C4—82no—
414C2×C4—221no—
415C2×C4—221no—
416C2×C4—221no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4#6699111yescharacteristic
420C2×C4#6699111yescharacteristic
421C2×C4#6699111yescharacteristic
422C2×C4C2×D4×D1111yescharacteristic
423C2×C4C2×#434111yescharacteristic
424C2×C4C22×C22⋊D1111yescharacteristic
425C8—21no—
426C8—21no—
427C8—21no—
428C8—21no—
429C8—442no—
430C8—442no—
431C8—441no—
432C8—441no—
433C22—21no—
434C22—21no—
435C22—441no—
436C22—441no—
437C22—441no—
438C22#1062280512yes—
439C22C2×#6699111yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—82no—
445C4—82no—
446C4—441no—
447C4—441no—
448C4—441no—
449C4#1062329312yes—
450C4#1062335311yescharacteristic
451C4#1062335311yescharacteristic
452C2—22no—
453C2—881no—
454C2#1307810611yescharacteristic
455C2#1307825111yescharacteristic
456C2C2×#1062280511yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#487C2
socleC22×C11C2×#121
prime radical#66983D4
hypercenterC2×#487D11
hypocenterC11#19363
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
4. #13068167C2semidirect
5. #13068160C2semidirect
6. #13068043C2semidirect
7. #13068036C2semidirect
8. #13067379C2semidirect
9. #13067333C2semidirect
10. #13067333C2semidirect
11. C2×C11×#487C2semidirect
169. C2×#487D11semidirect
394. C11#19363semidirect

Maximal subgroups

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

subgroupindex
#130798462
#130796432
#130775912
#130681672
#130681602
#130680432
#130680362
#130673792
#130673332
C2×C11×#4872
#1936311