Finite Group Databasebeta

← #14738487

Subgroups — #14738487

Order 2816.

612 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079999C211yesmaximal, characteristic, complemented
2#13079191C211yesmaximal, characteristic
3#13077551C211yesmaximal, characteristic, complemented
4#13068142C212yesmaximal, complemented
5#13068098C212yesmaximal, complemented
6#13068034C212yesmaximal, complemented
7#13068030C212yesmaximal, complemented
8#13067371C211yesmaximal, characteristic, complemented
9#13067351C211yesmaximal, characteristic, complemented
10#13067349C211yesmaximal, characteristic, complemented
11C11×#3254C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C11×#532C2211yescharacteristic
14#10623008C2211yescharacteristic
15C11×#477C2212yes—
16C11×#474—21no—
17C11×#468—22no—
18C11×#461—21no—
19C11×#460C2212yes—
20C11×#423C2211yescharacteristic
21#10622701C2211yescharacteristic
22#10622700—21no—
23#10622696—21no—
24#10622691C2211yescharacteristic
25#10622686C2211yescharacteristic
26#10622683C2211yescharacteristic
27#10622662—22no—
28#10622651—21no—
29#10622651—21no—
30#10622640C2212yes—
31#10622637—21no—
32#10622637C2212yes—
33Q8×C11⋊C8—21no—
34Q8×C11⋊C8C2212yes—
35#10622634C2212yes—
36C4×#4323—21no—
37C4×#4323—21no—
38#10622612—21no—
39#10622610—21no—
40#10622537C2211yescharacteristic
41#10622537C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622184C2212yes—
44#10622182C2212yes—
45#10622123C2212yes—
46#10622119C2212yes—
47#10622118C2212yes—
48#10622118C2212yes—
49C2×C11×#41—21no—
50C2×#4339—21no—
51C2×C11×SD16—22no—
52C2×C11×M16—21no—
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8D411yescharacteristic
55C11×C4⋊Q8C2311yescharacteristic
56C11×#127C2311yescharacteristic
57C11×#125—21no—
58C11×#124—21no—
59C11×C22⋊Q8—21no—
60C11×C22⋊Q8D412yes—
61C11×#121—21no—
62C11×#121—21no—
63C4×Q8×C11—21no—
64C4×Q8×C11C2312yes—
65C4×D4×C11—21no—
66C4×D4×C11—21no—
67C11×#117—21no—
68C2×C42×C11C2311yescharacteristic
69C2×#4325—22no—
70C2×#4323—21no—
71C2×#4323—21no—
72#66983—21no—
73#66983—21no—
74C2×#4318—21no—
75C2×#4318—21no—
76C22×C11⋊C8D411yescharacteristic
77C22×C11⋊C8D411yescharacteristic
78#66928—21no—
79#66927C2311yescharacteristic
80C4×D44—21no—
81C4×D44—21no—
82#66922C2311yescharacteristic
83C11×#107—22no—
84C11×C4⋊C8—21no—
85C11×C4⋊C8C2312yes—
86C11×#103—22no—
87C11×#102—22no—
88#66899—22no—
89#66896—21no—
90#66896—21no—
91#66873—22no—
92#66873—21no—
93#66873—21no—
94#66871—22no—
95#66871—21no—
96#66871—21no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)—21no—
99C4⋊(C11⋊C8)—22no—
100C4⋊(C11⋊C8)—22no—
101C4⋊(C11⋊C8)C2312yes—
102C4⋊(C11⋊C8)C2312yes—
103#66867—22no—
104C4×C11⋊C8—22no—
105C4×C11⋊C8D411yescharacteristic
106C4×C11⋊C8D411yescharacteristic
107C4×C11⋊C8C2311yescharacteristic
108C4×C11⋊C8C2311yescharacteristic
109#19349—111nomaximal, Sylow
110C11×#41—82no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11C2×D412yes—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—41no—
118C22×C4×C11—41no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11#4111yescharacteristic
122C2×C22⋊D11—41no—
123#4339—82no—
124C2×D44—21no—
125C2×D44—21no—
126C2×D44—21no—
127C2×C4×D11—41no—
128C2×Dic22—21no—
129C11×SD16—82no—
130C11×M16—81no—
131C2×C8×C11—22no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4C2×D412yes—
140C11×C22⋊C4—22no—
141C11×C22⋊C4—41no—
142C11×C22⋊C4—41no—
143C42×C11—22no—
144C42×C11C2×D411yescharacteristic
145C42×C11C2×D411yescharacteristic
146C42×C11#4111yescharacteristic
147C42×C11C2411yescharacteristic
148#4325—82no—
149#4323—42no—
150#4323—42no—
151(C2×D11)⋊C4—41no—
152(C2×D11)⋊C4—41no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155#4318—42no—
156#4318—81no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—41no—
161C2×C11⋊C8C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163C2×C11⋊C8C2×D411yescharacteristic
164C2×C11⋊C8C2×D411yescharacteristic
165#3254—111no—
166#3254D1111yescharacteristic, complemented
167#3169—111no—
168#2960—111no—
169#1696—112no—
170#1688—112no—
171#1678—112no—
172#1678—112no—
173#1566—111no—
174#1560—111no—
175#1560—111no—
176C23×C11—41no—
177C23×C11#12111yescharacteristic
178C22×D11—41no—
179Q8×C11—22no—
180Q8×C11—22no—
181Q8×C11—42no—
182Q8×C11—81no—
183D4×C11—41no—
184D4×C11—41no—
185D4×C11—41no—
186D4×C11—41no—
187D4×C11—81no—
188D4×C11—82no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—41no—
197C2×C4×C11—82no—
198C2×C4×C11#12111yescharacteristic
199C2×C4×C11#12111yescharacteristic
200C2×C4×C11#12111yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C22⋊D11—82no—
205C2×Dic11—41no—
206D44—41no—
207D44—41no—
208D44—41no—
209D44—41no—
210D44—81no—
211C4×D11—82no—
212Dic22—81no—
213C8×C11—42no—
214C11⋊C8—21no—
215C11⋊C8—21no—
216C11⋊C8—21no—
217C11⋊C8—42no—
218C11⋊C8—42no—
219C11⋊C8#13712yes—
220#533C2×D1111yescharacteristic
221#532—111no—
222#532C2×D1111yescharacteristic
223#500—111no—
224#493—111no—
225#486—111no—
226#486—111no—
227#477—112no—
228#477C2×D1112yes—
229#474—21no—
230#474—221no—
231#468—22no—
232#468—222no—
233#466—221no—
234#466—221no—
235#461—21no—
236#461—221no—
237#460—112no—
238#460C2×D1112yes—
239#446—112no—
240#446—221no—
241C8×Q8—112no—
242C8×Q8—221no—
243C4×D8—221no—
244C4×D8—221no—
245#424—221no—
246#423—111no—
247#423—111no—
248#423C2×D1111yescharacteristic
249#405—221no—
250C2×C4×C8—111no—
251#334—112no—
252#334—112no—
253#333—112no—
254#333—112no—
255#331—112no—
256#331—112no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11—81no—
261C22×C11—81no—
262C22×C11—81no—
263C22×C11C2×#12111yescharacteristic
264C2×D11—81no—
265C2×D11—81no—
266C2×D11—81no—
267C4×C11—21no—
268C4×C11—21no—
269C4×C11—21no—
270C4×C11—42no—
271C4×C11—42no—
272C4×C11—81no—
273C4×C11#47212yes—
274C4×C11C2×#13711yescharacteristic
275C4×C11#57511yescharacteristic
276C4×C11#57711yescharacteristic
277C4×C11#57711yescharacteristic
278Dic11—81no—
279C2×#41—21no—
280C2×#41—221no—
281C2×SD16—22no—
282C2×SD16—222no—
283C2×D8—221no—
284C2×D8—221no—
285C2×M16—21no—
286C2×M16—221no—
287C2×M16—221no—
288C22×C8—111no—
289C22×C8—111no—
290C4⋊Q8—111no—
291C4⋊Q8C22⋊D1111yescharacteristic
292C4⋊Q8C22⋊D1111yescharacteristic
293C4⋊Q8C22×D1111yescharacteristic
294#127—111no—
295#127C22×D1111yescharacteristic
296#125—21no—
297#124—21no—
298#124—221no—
299C22⋊Q8—21no—
300C22⋊Q8C22⋊D1112yes—
301#121—21no—
302#121—21no—
303#121—221no—
304#121—221no—
305C4×Q8—21no—
306C4×Q8C22×D1112yes—
307C4×D4—21no—
308C4×D4—21no—
309C4×D4—221no—
310C4×D4—221no—
311#117—21no—
312C2×C42C22×D1111yescharacteristic
313#107—22no—
314#107—221no—
315#107—221no—
316#107—222no—
317C4⋊C8—21no—
318C4⋊C8—112no—
319C4⋊C8—112no—
320C4⋊C8—222no—
321C4⋊C8—222no—
322C4⋊C8—221no—
323C4⋊C8—221no—
324C4⋊C8C22×D1112yes—
325#103—22no—
326#103—222no—
327#102—22no—
328#102—221no—
329#102—221no—
330#102—221no—
331#102—221no—
332#102—222no—
333#97—222no—
334C4×C8—111no—
335C4×C8—111no—
336C4×C8—111no—
337C4×C8—111no—
338C4×C8—222no—
339C2×C11—41no—
340C2×C11—161no—
341C2×C11#303711yescharacteristic
342C2×C11#306011yescharacteristic
343C2×C11C2×#47211yescharacteristic
344D11—161no—
345#41—82no—
346#41—882no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—221no—
350C2×Q8C2×C22⋊D1112yes—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—41no—
355C2×D4—221no—
356C2×D4—221no—
357C2×D4—221no—
358C2×D4—441no—
359C22×C4—41no—
360C22×C4—441no—
361C22×C4D4×D1111yescharacteristic
362C22×C4#434111yescharacteristic
363C22×C4C2×C22⋊D1111yescharacteristic
364SD16—82no—
365SD16—882no—
366D8—442no—
367D8—442no—
368M16—81no—
369M16—442no—
370M16—881no—
371C2×C8—22no—
372C2×C8—111no—
373C2×C8—111no—
374C2×C8—111no—
375C2×C8—111no—
376C2×C8—222no—
377C2×C8—222no—
378C2×C8—222no—
379C2×C8—441no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—221no—
388C4⋊C4—221no—
389C4⋊C4C2×C22⋊D1112yes—
390C22⋊C4—22no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—441no—
394C22⋊C4—441no—
395C42—22no—
396C42D4×D1111yescharacteristic
397C42#434111yescharacteristic
398C42C2×C22⋊D1111yescharacteristic
399C42C23×D1111yescharacteristic
400C11#1934911yescharacteristic, complemented, Sylow
401C23—41no—
402C23—441no—
403C23#6699211yescharacteristic
404Q8—22no—
405Q8—22no—
406Q8—42no—
407Q8—81no—
408Q8—881no—
409D4—41no—
410D4—41no—
411D4—41no—
412D4—41no—
413D4—81no—
414D4—82no—
415D4—441no—
416D4—441no—
417D4—441no—
418D4—441no—
419D4—881no—
420D4—882no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—22no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—41no—
429C2×C4—82no—
430C2×C4—441no—
431C2×C4—882no—
432C2×C4#6699211yescharacteristic
433C2×C4#6699211yescharacteristic
434C2×C4#6699211yescharacteristic
435C2×C4C2×D4×D1111yescharacteristic
436C2×C4C2×#434111yescharacteristic
437C2×C4C22×C22⋊D1111yescharacteristic
438C8—42no—
439C8—112no—
440C8—221no—
441C8—221no—
442C8—221no—
443C8—442no—
444C8—442no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—881no—
452C22—881no—
453C22—881no—
454C22C2×#6699211yescharacteristic
455C4—21no—
456C4—21no—
457C4—21no—
458C4—42no—
459C4—42no—
460C4—81no—
461C4—881no—
462C4#1062281212yes—
463C4D11×#13711yescharacteristic
464C4#1062330811yescharacteristic
465C4#1062336711yescharacteristic
466C4#1062336811yescharacteristic
467C2—41no—
468C2—161no—
469C2—1761no—
470C2#1307808511yescharacteristic
471C2#1307827511yescharacteristic
472C2C2×#1062281211yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3254C2
socleC22×C11C2×#121
prime radical#13079191C2
hypercenter#3254D11
hypocenterC11#19349
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3254

Complements

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

NH ≅ G/Ntype
1. #13079999C2semidirect
3. #13077551C2semidirect
4. #13068142C2semidirect
5. #13068098C2semidirect
6. #13068034C2semidirect
7. #13068030C2semidirect
8. #13067371C2semidirect
9. #13067351C2semidirect
10. #13067349C2semidirect
11. C11×#3254C2semidirect
166. #3254D11semidirect
400. C11#19349semidirect

Maximal subgroups

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

subgroupindex
#130799992
#130791912
#130775512
#130681422
#130680982
#130680342
#130680302
#130673712
#130673512
#130673492
C11×#32542
#1934911