Finite Group Databasebeta

← #14722253

Subgroups — #14722253

Order 2816.

884 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082500C211yesmaximal, characteristic
2#13077725C211yesmaximal, characteristic
3#13077281C211yesmaximal, characteristic
4#13067323C212yesmaximal, complemented
5#13067313C212yesmaximal, complemented
6#13067304C211yesmaximal, characteristic, complemented
7#13067288C211yesmaximal, characteristic, complemented
8#13067279C212yesmaximal, complemented
9#13067274C211yesmaximal, characteristic, complemented
10#13067272C212yesmaximal, complemented
11C2×C11×#332C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13#10623347—21no—
14#10623343—21no—
15#10623263—21no—
16#10623263C412yes—
17#10623262—22no—
18#10623259C2212yes—
19#10623259C2212yes—
20#10623252—21no—
21#10623252C412yes—
22#10623044—22no—
23#10623044C414yes—
24C4×#4339C2211yescharacteristic
25#10623001C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28#10622723—21no—
29C8×C22⋊D11—22no—
30#10622714—21no—
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622453—22no—
34#10622448C2212yes—
35#10622447—21no—
36#10622446C2212yes—
37#10622446C2212yes—
38D11×C4⋊C8C2212yes—
39#10622443—21no—
40C11×#332C2212yes—
41C11×#332C2212yes—
42#10622185C2212yes—
43#10622185C2212yes—
44#10622124C2211yescharacteristic
45#10622124C2211yescharacteristic
46#10622120C2212yes—
47#10622119C2211yescharacteristic
48#10622119C2212yes—
49#10622119C2211yescharacteristic
50C22×Q8×C11—21no—
51C2×#4339D411yescharacteristic
52C22×C8×C11—21no—
53C22×C8×C11—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8C2×C412yes—
57C11×C4⋊Q8C2312yes—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4C2×C412yes—
60C2×C42×C11C2311yescharacteristic
61#67000—22no—
62#66999—22no—
63#66999—22no—
64Q8×Dic11—22no—
65Q8×Dic11—22no—
66Q8×Dic11—22no—
67Q8×Dic11—22no—
68#66997—22no—
69#66982—24no—
70C4×C22⋊D11C2×C412yes—
71C4×C22⋊D11D412yes—
72#66979—21no—
73#66979—24no—
74#66979D411yescharacteristic
75#66977—21no—
76#66977C2×C412yes—
77C2×#4318—21no—
78C2×C8×D11—22no—
79#66951—24no—
80#66951—24no—
81#66950—22no—
82#66950C2×C414yes—
83#66945—22no—
84#66945C2×C414yes—
85#66943—22no—
86#66943C2×C414yes—
87#66942—24no—
88#66942—24no—
89#66940—22no—
90#66940C2×C414yes—
91C4×D44C2×C411yescharacteristic
92C4×D44D411yescharacteristic
93#66925D412yes—
94C42×D11C2312yes—
95#66923—21no—
96#66922C2311yescharacteristic
97#66922C2311yescharacteristic
98C4×Dic22—21no—
99C4×Dic22C2×C412yes—
100C4×Dic22C2×C411yescharacteristic
101C4×Dic22D411yescharacteristic
102C11×C4⋊C8—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8C2312yes—
105C11×C4⋊C8C2311yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C22⋊(C11⋊C8)—21no—
108(C2×D11)⋊C8—22no—
109(C2×D11)⋊C8—22no—
110(C2×D11)⋊C8—22no—
111#66879—22no—
112Dic11⋊C8—22no—
113C8×Dic11—22no—
114C8×Dic11—22no—
115C4⋊(C11⋊C8)—21no—
116C4⋊(C11⋊C8)C2312yes—
117C4⋊(C11⋊C8)C2311yescharacteristic
118C4⋊(C11⋊C8)C2311yescharacteristic
119C4×C11⋊C8—21no—
120#17725—111nomaximal, Sylow
121C2×Q8×C11—22no—
122C2×Q8×C11—22no—
123C2×Q8×C11—42no—
124C2×Q8×C11—42no—
125C22×C4×C11—22no—
126C22×C4×C11C22×C411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C2×C22⋊D11C22⋊C412yes—
130#4339—22no—
131#4339—22no—
132C2×D44C22⋊C411yescharacteristic
133C2×C4×D11C22×C412yes—
134C2×C4×D11C2×D412yes—
135C2×C4×D11C2×D412yes—
136C2×Dic22—21no—
137C2×Dic22C22⋊C411yescharacteristic
138C2×Dic22C22×C412yes—
139C2×C8×C11—21no—
140C2×C8×C11—22no—
141C2×C8×C11—21no—
142C2×C8×C11—42no—
143C2×C8×C11—81no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4C22×C414yes—
148C42×C11C22×C411yescharacteristic
149C42×C11C2×D411yescharacteristic
150C42×C11C2×D411yescharacteristic
151C42×C11C2411yescharacteristic
152C22⋊Dic11—22no—
153C22⋊Dic11C22⋊C412yes—
154(C2×D11)⋊C4—24no—
155(C2×D11)⋊C4—24no—
156(C2×D11)⋊C4C22⋊C412yes—
157(C2×D11)⋊C4C22⋊C412yes—
158C4⋊Dic11—24no—
159C4⋊Dic11—24no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163C4⋊Dic11C22⋊C411yescharacteristic
164C4⋊Dic11C22⋊C411yescharacteristic
165C4⋊Dic11C22×C412yes—
166Dic11⋊C4—24no—
167Dic11⋊C4—24no—
168Dic11⋊C4—22no—
169Dic11⋊C4—22no—
170Dic11⋊C4C22⋊C412yes—
171Dic11⋊C4C22⋊C412yes—
172C4×Dic11—24no—
173C4×Dic11—24no—
174C4×Dic11—22no—
175C4×Dic11C22×C412yes—
176C4×Dic11C2×D412yes—
177C4×Dic11C2×D412yes—
178#4318—42no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—22no—
182C8×D11—82no—
183#3509—111no—
184#2988—111no—
185#2925—111no—
186#1554—112no—
187#1552—112no—
188#1550—111no—
189#1546—111no—
190#1544—112no—
191#1542—111no—
192#1542—112no—
193C2×#332D1111yescharacteristic, complemented
194C23×C11C2×C22⋊C411yescharacteristic
195C22×D11C2×C22⋊C412yes—
196Q8×C11—42no—
197Q8×C11—42no—
198Q8×C11—44no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—24no—
202C2×C4×C11—41no—
203C2×C4×C11—44no—
204C2×C4×C11C2×C22⋊C411yescharacteristic
205C2×C4×C11C2×C22⋊C411yescharacteristic
206C2×C4×C11C2×C22⋊C411yescharacteristic
207C2×C4×C11#13512yes—
208C2×C4×C11#13512yes—
209C2×C4×C11C23×C411yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C22⋊D11—24no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11C2×C22⋊C412yes—
216C2×Dic11C2×C22⋊C412yes—
217C2×Dic11C2×C22⋊C412yes—
218D44—22no—
219C4×D11—22no—
220C4×D11—22no—
221C4×D11—22no—
222C4×D11—22no—
223C4×D11—42no—
224Dic22—22no—
225Dic22—41no—
226Dic22—41no—
227Dic22—42no—
228C8×C11—41no—
229C8×C11—41no—
230C8×C11—42no—
231C11⋊C8—42no—
232C11⋊C8—41no—
233C11⋊C8—41no—
234#557—112no—
235#557—221no—
236#556—112no—
237#556—221no—
238#552—114no—
239#552—222no—
240#541—222no—
241#536—221no—
242#533—112no—
243#533—112no—
244#533—111no—
245C2×C4⋊Q8C2×D1111yescharacteristic
246#519—221no—
247C4×#41—111no—
248C8×Q8—221no—
249C8×D4—221no—
250C8×D4—222no—
251#433—222no—
252#432—112no—
253#431—111no—
254#431—112no—
255#431—112no—
256#423—111no—
257C2×C4⋊C8—112no—
258C2×C4⋊C8C2×D1111yescharacteristic
259C2×C4⋊C8C2×D1111yescharacteristic
260#408—221no—
261#405—221no—
262#333—111no—
263#333—112no—
264#333—111no—
265#332—112no—
266#332—112no—
267#332—111no—
268#332—111no—
269#332—112no—
270#332C2×D1112yes—
271#332C2×D1112yes—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11#41612yes—
275C22×C11C22×C22⋊C411yescharacteristic
276C2×D11—22no—
277C2×D11—22no—
278C2×D11—22no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—44no—
283C4×C11#41612yes—
284C4×C11C2×#13511yescharacteristic
285C4×C11C2×#13511yescharacteristic
286C4×C11#57711yescharacteristic
287C4×C11#57811yescharacteristic
288Dic11—22no—
289Dic11—22no—
290Dic11—22no—
291Dic11—42no—
292Dic11—42no—
293C2×#41—111no—
294C22×Q8—21no—
295C2×M16—221no—
296C22×C8—21no—
297C22×C8—21no—
298C22×C8—222no—
299C4⋊Q8—21no—
300C4⋊Q8—21no—
301C4⋊Q8—111no—
302C4⋊Q8—111no—
303C4⋊Q8—222no—
304C4⋊Q8C4×D1112yes—
305C4⋊Q8C22×D1112yes—
306#126—224no—
307#126—224no—
308#125—114no—
309#125—222no—
310#125—224no—
311#125—224no—
312#125—221no—
313#124—222no—
314#123—224no—
315C22⋊Q8—112no—
316C22⋊Q8—114no—
317C22⋊Q8—222no—
318C22⋊Q8—222no—
319C22⋊Q8—222no—
320C22⋊Q8—221no—
321C4×Q8—111no—
322C4×Q8—111no—
323C4×Q8—114no—
324C4×Q8—112no—
325C4×Q8—222no—
326C4×Q8—222no—
327C4×Q8—222no—
328C4×Q8—222no—
329C4×Q8—222no—
330C4×Q8—221no—
331C4×D4—112no—
332C4×D4—112no—
333C4×D4—111no—
334C4×D4—111no—
335#117—111no—
336#117—112no—
337#117—114no—
338#117—224no—
339#117—222no—
340#117—221no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4C4×D1112yes—
343C2×C42—112no—
344C2×C42C22×D1111yescharacteristic
345C4⋊C8—21no—
346C4⋊C8—21no—
347C4⋊C8—111no—
348C4⋊C8—112no—
349C4⋊C8—111no—
350C4⋊C8—222no—
351C4⋊C8—221no—
352C4⋊C8C22×D1112yes—
353C4⋊C8C22×D1111yescharacteristic
354C4⋊C8C22×D1111yescharacteristic
355C22⋊C8—222no—
356C22⋊C8—222no—
357C22⋊C8—222no—
358C22⋊C8—221no—
359#97—222no—
360C4×C8—222no—
361C4×C8—222no—
362C4×C8—221no—
363C2×C11—22no—
364C2×C11#288911yescharacteristic
365C2×C11C2×#41611yescharacteristic
366C2×C11#289811yescharacteristic
367D11—42no—
368#41—222no—
369#41—222no—
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8—42no—
373C2×Q8—42no—
374C2×Q8—111no—
375C2×Q8—112no—
376C2×Q8—221no—
377C2×D4—112no—
378C2×D4—111no—
379C22×C4—22no—
380C22×C4—112no—
381C22×C4—112no—
382C22×C4—112no—
383C22×C4C2×C4×D1111yescharacteristic
384C22×C4D4×D1111yescharacteristic
385C22×C4D4×D1111yescharacteristic
386M16—442no—
387C2×C8—21no—
388C2×C8—22no—
389C2×C8—21no—
390C2×C8—42no—
391C2×C8—81no—
392C2×C8—221no—
393C2×C8—222no—
394C2×C8—221no—
395C2×C8—882no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—111no—
400C4⋊C4—111no—
401C4⋊C4—112no—
402C4⋊C4—112no—
403C4⋊C4—112no—
404C4⋊C4—224no—
405C4⋊C4—224no—
406C4⋊C4—224no—
407C4⋊C4—224no—
408C4⋊C4—222no—
409C4⋊C4—222no—
410C4⋊C4—221no—
411C4⋊C4—221no—
412C4⋊C4—221no—
413C4⋊C4C2×C4×D1114yes—
414C22⋊C4—112no—
415C22⋊C4—112no—
416C22⋊C4—112no—
417C22⋊C4—224no—
418C22⋊C4—224no—
419C22⋊C4—222no—
420C42—112no—
421C42—112no—
422C42—112no—
423C42—224no—
424C42—224no—
425C42—222no—
426C42C2×C4×D1111yescharacteristic
427C42D4×D1111yescharacteristic
428C42D4×D1111yescharacteristic
429C42C23×D1111yescharacteristic
430C11#1772511yescharacteristic, complemented, Sylow
431C23—112no—
432C23C22⋊C4×D1111yescharacteristic
433Q8—42no—
434Q8—42no—
435Q8—44no—
436Q8—222no—
437Q8—442no—
438Q8—441no—
439Q8—441no—
440D4—224no—
441D4—222no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—24no—
445C2×C4—41no—
446C2×C4—44no—
447C2×C4—112no—
448C2×C4—112no—
449C2×C4—112no—
450C2×C4—222no—
451C2×C4—222no—
452C2×C4—222no—
453C2×C4—222no—
454C2×C4—222no—
455C2×C4—222no—
456C2×C4—442no—
457C2×C4C22⋊C4×D1111yescharacteristic
458C2×C4C22⋊C4×D1111yescharacteristic
459C2×C4C22⋊C4×D1111yescharacteristic
460C2×C4#6696512yes—
461C2×C4#6696912yes—
462C2×C4C22×C4×D1111yescharacteristic
463C2×C4C2×D4×D1111yescharacteristic
464C2×C4C2×D4×D1111yescharacteristic
465C8—41no—
466C8—41no—
467C8—42no—
468C8—442no—
469C8—441no—
470C8—441no—
471C22—21no—
472C22—21no—
473C22—222no—
474C22—222no—
475C22—222no—
476C22#1062238512yes—
477C22C2×C22⋊C4×D1111yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—44no—
482C4—222no—
483C4—222no—
484C4—222no—
485C4—442no—
486C4—442no—
487C4#1062238512yes—
488C4C2×#6696511yescharacteristic
489C4C2×#6696911yescharacteristic
490C4#1062329311yescharacteristic
491C4#1062329711yescharacteristic
492C2—22no—
493C2—442no—
494C2#1307709611yescharacteristic
495C2C2×#1062238511yescharacteristic
496C2#1307714411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC2×C11×#332C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#4339D4
cosocleC42×C11C24
hypercenterC2×#332D11
hypocenterC11#17725
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
4. #13067323C2semidirect
5. #13067313C2semidirect
6. #13067304C2semidirect
7. #13067288C2semidirect
8. #13067279C2semidirect
9. #13067274C2semidirect
10. #13067272C2semidirect
11. C2×C11×#332C2semidirect
193. C2×#332D11semidirect
430. C11#17725semidirect

Maximal subgroups

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

subgroupindex
#130825002
#130777252
#130772812
#130673232
#130673132
#130673042
#130672882
#130672792
#130672742
#130672722
C2×C11×#3322
#1772511