Finite Group Databasebeta

← #14736697

Subgroups — #14736697

Order 2816.

618 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#13079012C211yesmaximal, characteristic
2#13078647C211yesmaximal, characteristic
3Q8×#4318C211yesmaximal, characteristic, complemented
4#13068200C212yesmaximal, complemented
5#13068158C212yesmaximal, complemented
6#13068076C212yesmaximal, complemented
7#13068034C212yesmaximal, complemented
8#13067366C211yesmaximal, characteristic, complemented
9#13067297C211yesmaximal, characteristic, complemented
10#13067291C211yesmaximal, characteristic
11C2×C11×#477C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14#10623008C2211yescharacteristic
15C11×#477—21no—
16C11×#477—21no—
17C11×#477C2212yes—
18C11×#477C2212yes—
19C2×C11×#107—21no—
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×#103—21no—
22#10622840—21no—
23#10622706C2212yes—
24#10622702—22no—
25#10622701C2212yes—
26#10622640C2211yescharacteristic
27#10622640C2211yescharacteristic
28C4×#4325—21no—
29C4×#4325—21no—
30#10622637—22no—
31#10622637C2212yes—
32Q8×C11⋊C8C2212yes—
33#10622633C2211yescharacteristic
34#10622633C2211yescharacteristic
35#10622581—21no—
36#10622579—21no—
37#10622579—21no—
38#10622538C2211yescharacteristic
39#10622537—21no—
40#10622537C2211yescharacteristic
41C4×#4318—21no—
42C4×#4318C2211yescharacteristic
43#10622184C2212yes—
44#10622184C2212yes—
45#10622124C2212yes—
46#10622123C2212yes—
47#10622118C2212yes—
48#10622117C2212yes—
49C22×Q8×C11—21no—
50C22×Q8×C11D411yescharacteristic
51C2×#4339—21no—
52C22×C8×C11—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8C2312yes—
57C4×Q8×C11—21no—
58C4×Q8×C11—21no—
59C4×Q8×C11D411yescharacteristic
60C4×Q8×C11D411yescharacteristic
61C4×Q8×C11C2311yescharacteristic
62C4×Q8×C11C2311yescharacteristic
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C42×C11—21no—
68C2×C42×C11C2311yescharacteristic
69C2×#4325—21no—
70C2×#4325—21no—
71#66983—21no—
72#66983—21no—
73C2×#4318—21no—
74C2×#4318D411yescharacteristic
75C2×#4318D411yescharacteristic
76#66928—21no—
77#66927C2311yescharacteristic
78C4×D44—21no—
79C4×D44—21no—
80#66922C2311yescharacteristic
81C11×#107—22no—
82C11×#107—22no—
83C11×C4⋊C8—21no—
84C11×C4⋊C8C2312yes—
85C11×#103—22no—
86C11×#103—22no—
87#66899—21no—
88#66899—21no—
89C22⋊(C11⋊C8)—21no—
90#66874—22no—
91#66874—22no—
92#66873—21no—
93#66873—21no—
94#66873—22no—
95#66873—22no—
96#66872—21no—
97#66872—21no—
98C4⋊(C11⋊C8)—21no—
99C4⋊(C11⋊C8)—22no—
100C4⋊(C11⋊C8)—22no—
101C4⋊(C11⋊C8)C2312yes—
102C4⋊(C11⋊C8)C2311yescharacteristic
103C4⋊(C11⋊C8)C2311yescharacteristic
104#66867—22no—
105#66867D412yes—
106C4×C11⋊C8—21no—
107C4×C11⋊C8—22no—
108C4×C11⋊C8C2312yes—
109#19176—111nomaximal, Sylow
110C2×Q8×C11—21no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—41no—
114C2×Q8×C11—41no—
115C2×Q8×C11—82no—
116C2×Q8×C11C2×D411yescharacteristic
117C2×Q8×C11C2×D411yescharacteristic
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—41no—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11#4111yescharacteristic
124C2×C22⋊D11—41no—
125#4339—42no—
126#4339—42no—
127C2×D44—21no—
128C2×D44—21no—
129C2×D44—21no—
130C2×C4×D11—41no—
131C2×Dic22—21no—
132C2×C8×C11—22no—
133C2×C8×C11—42no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—41no—
142C11×C4⋊C4—41no—
143C11×C4⋊C4C2×D411yescharacteristic
144C11×C4⋊C4C2×D411yescharacteristic
145C42×C11—21no—
146C42×C11—21no—
147C42×C11—21no—
148C42×C11—21no—
149C42×C11C2×D411yescharacteristic
150C42×C11C2×D411yescharacteristic
151C42×C11#4111yescharacteristic
152C42×C11C2411yescharacteristic
153#4325—42no—
154#4325—42no—
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4—41no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159#4318—22no—
160#4318—22no—
161#4318—42no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8C2×D412yes—
166C2×C11⋊C8C2×D412yes—
167#3141—111no—
168#3103—111no—
169C2×#477D1111yescharacteristic, complemented
170Q8×M16—111no—
171#1704—112no—
172#1698—112no—
173#1684—112no—
174#1678—112no—
175#1565—111no—
176#1548—111no—
177#1547—111no—
178C23×C11#12111yescharacteristic
179C22×D11—41no—
180Q8×C11—21no—
181Q8×C11—21no—
182Q8×C11—21no—
183Q8×C11—42no—
184Q8×C11—82no—
185Q8×C11—82no—
186Q8×C11#13712yes—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—41no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—81no—
197C2×C4×C11—82no—
198C2×C4×C11#12111yescharacteristic
199C2×C4×C11#12111yescharacteristic
200C2×C4×C11#12111yescharacteristic
201C2×C4×C11#13512yes—
202C2×C4×C11#13712yes—
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C22⋊D11—82no—
207C2×Dic11—41no—
208D44—41no—
209D44—41no—
210D44—41no—
211D44—41no—
212D44—81no—
213C4×D11—82no—
214Dic22—41no—
215Dic22—41no—
216C8×C11—42no—
217C11⋊C8—22no—
218C11⋊C8—22no—
219C11⋊C8—42no—
220C11⋊C8—41no—
221C11⋊C8—41no—
222#532—111no—
223C2×C4⋊Q8C2×D1111yescharacteristic
224C2×C4×Q8C2×D1111yescharacteristic
225#489—222no—
226#487—112no—
227#486—112no—
228#481—221no—
229#477—21no—
230#477—21no—
231#477C2×D1112yes—
232#477C2×D1112yes—
233#475—111no—
234#475—111no—
235#460—111no—
236#460—111no—
237#448—221no—
238#446—112no—
239#446—222no—
240C8×Q8—112no—
241C4×SD16—221no—
242C4×SD16—221no—
243#431—111no—
244C2×#107—21no—
245#423—111no—
246#423—221no—
247C2×C4⋊C8C2×D1111yescharacteristic
248#417—221no—
249#417—221no—
250C2×#103—21no—
251C4×M16—111no—
252C4×M16—221no—
253#335—112no—
254#334—112no—
255#333—112no—
256#333—112no—
257#332—112no—
258#331—112no—
259C22×C11—21no—
260C22×C11—21no—
261C22×C11#46412yes—
262C22×C11C2×#12111yescharacteristic
263C2×D11—81no—
264C2×D11—81no—
265C2×D11—81no—
266C4×C11—21no—
267C4×C11—22no—
268C4×C11—21no—
269C4×C11—21no—
270C4×C11—41no—
271C4×C11—41no—
272C4×C11—41no—
273C4×C11—82no—
274C4×C11#46412yes—
275C4×C11C2×#13511yescharacteristic
276C4×C11C2×#13711yescharacteristic
277C4×C11C2×#13711yescharacteristic
278C4×C11#57511yescharacteristic
279Dic11—81no—
280C2×#41—221no—
281C22×Q8—21no—
282C22×Q8C22⋊D1111yescharacteristic
283C2×SD16—221no—
284C2×SD16—221no—
285C2×M16—111no—
286C2×M16—111no—
287C2×M16—221no—
288C22×C8—21no—
289C4⋊Q8—21no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—111no—
293C4⋊Q8C22×D1112yes—
294#127—111no—
295#124—221no—
296#121—221no—
297#121—221no—
298C4×Q8—21no—
299C4×Q8—21no—
300C4×Q8C22⋊D1111yescharacteristic
301C4×Q8C22⋊D1111yescharacteristic
302C4×Q8C22×D1111yescharacteristic
303C4×Q8C22×D1111yescharacteristic
304C4×D4—221no—
305C4×D4—221no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4C22⋊D1111yescharacteristic
310C2×C42—21no—
311C2×C42C22×D1111yescharacteristic
312#107—22no—
313#107—22no—
314#106—221no—
315#106—221no—
316C4⋊C8—21no—
317C4⋊C8—112no—
318C4⋊C8—111no—
319C4⋊C8—111no—
320C4⋊C8—222no—
321C4⋊C8—222no—
322C4⋊C8—221no—
323C4⋊C8C22×D1112yes—
324#103—22no—
325#103—22no—
326#103—222no—
327#103—222no—
328#103—221no—
329#103—221no—
330#102—222no—
331#102—222no—
332#102—221no—
333#102—221no—
334C22⋊C8—221no—
335#97—112no—
336#97—222no—
337C4×C8—112no—
338C4×C8—222no—
339C4×C8—221no—
340C2×C11—22no—
341C2×C11C2×#46411yescharacteristic
342C2×C11#305611yescharacteristic
343C2×C11#306811yescharacteristic
344D11—161no—
345#41—442no—
346#41—442no—
347C2×Q8—21no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8—41no—
351C2×Q8—41no—
352C2×Q8—82no—
353C2×Q8—221no—
354C2×Q8C2×C22⋊D1111yescharacteristic
355C2×Q8C2×C22⋊D1111yescharacteristic
356C2×D4—221no—
357C2×D4—221no—
358C2×D4—221no—
359C2×D4—441no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—41no—
363C22×C4—441no—
364C22×C4D4×D1111yescharacteristic
365C22×C4#434111yescharacteristic
366C22×C4C2×C22⋊D1111yescharacteristic
367SD16—442no—
368SD16—442no—
369M16—222no—
370M16—222no—
371M16—442no—
372C2×C8—22no—
373C2×C8—42no—
374C2×C8—112no—
375C2×C8—112no—
376C2×C8—222no—
377C2×C8—221no—
378C2×C8—221no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4—221no—
389C4⋊C4—221no—
390C4⋊C4C2×C22⋊D1111yescharacteristic
391C4⋊C4C2×C22⋊D1111yescharacteristic
392C22⋊C4—441no—
393C22⋊C4—441no—
394C42—21no—
395C42—21no—
396C42—21no—
397C42—21no—
398C42D4×D1111yescharacteristic
399C42#434111yescharacteristic
400C42C2×C22⋊D1111yescharacteristic
401C42C23×D1111yescharacteristic
402C11#1917611yescharacteristic, complemented, Sylow
403C23—441no—
404C23#6699211yescharacteristic
405Q8—21no—
406Q8—21no—
407Q8—21no—
408Q8—42no—
409Q8—82no—
410Q8—82no—
411Q8—441no—
412Q8—441no—
413Q8#6699512yes—
414D4—441no—
415D4—441no—
416D4—441no—
417D4—441no—
418D4—881no—
419D4—882no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—81no—
430C2×C4—82no—
431C2×C4—441no—
432C2×C4—882no—
433C2×C4#6697112yes—
434C2×C4#6697212yes—
435C2×C4#6699211yescharacteristic
436C2×C4#6699211yescharacteristic
437C2×C4#6699211yescharacteristic
438C2×C4C2×D4×D1111yescharacteristic
439C2×C4C2×#434111yescharacteristic
440C2×C4C22×C22⋊D1111yescharacteristic
441C8—42no—
442C8—222no—
443C8—222no—
444C8—442no—
445C8—441no—
446C8—441no—
447C22—21no—
448C22—21no—
449C22—881no—
450C22—881no—
451C22—881no—
452C22#1062279812yes—
453C22C2×#6699211yescharacteristic
454C4—21no—
455C4—21no—
456C4—21no—
457C4—22no—
458C4—41no—
459C4—41no—
460C4—41no—
461C4—82no—
462C4—881no—
463C4#1062279812yes—
464C4C2×#6697111yescharacteristic
465C4C2×#6697211yescharacteristic
466C4C2×#6699511yescharacteristic
467C4#1062335311yescharacteristic
468C2—22no—
469C2—1761no—
470C2C2×#1062279811yescharacteristic
471C2#1307824211yescharacteristic
472C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#477C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenterC2×#477D11
hypocenterC11#19176
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
3. Q8×#4318C2semidirect
4. #13068200C2semidirect
5. #13068158C2semidirect
6. #13068076C2semidirect
7. #13068034C2semidirect
8. #13067366C2semidirect
9. #13067297C2semidirect
11. C2×C11×#477C2semidirect
169. C2×#477D11semidirect
402. C11#19176semidirect

Maximal subgroups

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

subgroupindex
#130790122
#130786472
Q8×#43182
#130682002
#130681582
#130680762
#130680342
#130673662
#130672972
#130672912
C2×C11×#4772
#1917611