Finite Group Databasebeta

← #14805343

Subgroups — #14805343

Order 2816.

862 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622691C211yesmaximal, characteristic, complemented
2C2×#10622700C211yesmaximal, characteristic
3#13073565C211yesmaximal, characteristic
4#13070087C212yesmaximal, complemented
5#13070001C212yesmaximal
6#13069568C211yesmaximal, characteristic, complemented
7#13069374C212yesmaximal, complemented
8#13069335C211yesmaximal, characteristic, complemented
9#13069236C212yesmaximal
10C4×#66873C211yesmaximal, characteristic
11C11×#2365C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11—21no—
14C2×#66950—21no—
15C2×#66950—21no—
16C2×C4×D44C2211yescharacteristic
17C2×#66922C2211yescharacteristic
18C11×#391—21no—
19C11×#389C2212yes—
20C11×#387—22no—
21C4×C11×C4⋊C4C2211yescharacteristic
22C4×C11×C4⋊C4C2212yes—
23C4×C11×C4⋊C4C2211yescharacteristic
24#10622700—24no—
25#10622691—24no—
26C2×#66873C2212yes—
27C2×#66873C2211yescharacteristic
28C2×#66873C2211yescharacteristic
29C2×#66871C2212yes—
30C2×#66871C2212yes—
31C2×#66871C2212yes—
32#10622552C2212yes—
33#10622548C2212yes—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2212yes—
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622290—22no—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2211yescharacteristic
41#10622167C2211yescharacteristic
42#10622162C2212yes—
43C22×Q8×C11—21no—
44C22×D44C2311yescharacteristic
45C22×C4×D11—21no—
46C22×Dic22—21no—
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8D414yes—
49C4×Q8×C11—44no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C42×C11—22no—
58C2×C42×C11—21no—
59C2×C42×C11C2312yes—
60C2×C42×C11C2311yescharacteristic
61C2×(C2×D11)⋊C4—21no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11C2312yes—
68C2×C4⋊Dic11C2311yescharacteristic
69C22×C11⋊C8C2312yes—
70C22×C11⋊C8C2311yescharacteristic
71C22×C11⋊C8C2311yescharacteristic
72#66950—44no—
73#66950—44no—
74C4×D44—22no—
75C4×D44—22no—
76#66922—22no—
77#66922—22no—
78C11×#95—21no—
79C11×#95—22no—
80C11×#95—22no—
81C11×#95D412yes—
82#66873—24no—
83#66873—22no—
84#66873Q814yescomplemented
85#66871—24no—
86#66871—24no—
87#66871—24no—
88C4⋊(C11⋊C8)—22no—
89C4⋊(C11⋊C8)—24no—
90C4×C11⋊C8—22no—
91#25449—111nomaximal, Sylow
92C23×D11—21no—
93C2×Q8×C11—24no—
94C2×Q8×C11—42no—
95C2×Q8×C11—42no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2411yescharacteristic
104C22×Dic11—21no—
105C22×Dic11—22no—
106C2×D44—21no—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44—21no—
110C2×D44—21no—
111C2×D44C2×Q812yes—
112C2×C4×D11—42no—
113C2×C4×D11—42no—
114C2×C4×D11—42no—
115C2×Dic22—42no—
116C2×Dic22—42no—
117C2×Dic22—42no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—44no—
125C11×C4⋊C4D814yes—
126C11×C4⋊C4C2×D414yes—
127C11×C4⋊C4C2×Q812yes—
128C42×C11—22no—
129C42×C11—22no—
130C42×C11—44no—
131C42×C11—42no—
132C42×C11C2×D412yes—
133C42×C11#4112yes—
134(C2×D11)⋊C4—44no—
135(C2×D11)⋊C4—42no—
136(C2×D11)⋊C4—44no—
137C4⋊Dic11—22no—
138C4⋊Dic11—21no—
139C4⋊Dic11—22no—
140C4⋊Dic11—21no—
141C4⋊Dic11—44no—
142C4⋊Dic11—42no—
143C4⋊Dic11—44no—
144C2×C11⋊C8—21no—
145C2×C11⋊C8—21no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8C2×Q812yes—
152C2×C11⋊C8#4112yes—
153C2×#500—111no—
154C2×#474—111no—
155#2542—111no—
156#2365D1111yescharacteristic, complemented
157#2083—112no—
158#2067—112no—
159#1988—111no—
160#1947—112no—
161#1939—111no—
162#1925—112no—
163C4×#102—111no—
164C23×C11C22×D411yescharacteristic
165C22×D11—22no—
166C22×D11—41no—
167C22×D11—41no—
168C22×D11—41no—
169C22×D11—41no—
170C22×D11—41no—
171C22×D11—41no—
172Q8×C11—48no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—24no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11#12112yes—
190C2×C4×C11#12112yes—
191C2×C4×C11C2×D814yes—
192C2×C4×C11C2×D812yes—
193C2×C4×C11AGL(1,ℤ/8)12yes—
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C22×Q811yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C112−1+411yescharacteristic
199C2×C4×C112−1+411yescharacteristic
200C2×Dic11—42no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—42no—
204C2×Dic11—41no—
205C2×Dic11—42no—
206D44—22no—
207D44—22no—
208D44—41no—
209D44—41no—
210C4×D11—84no—
211Dic22—84no—
212C11⋊C8—22no—
213C11⋊C8—22no—
214C11⋊C8—42no—
215C2×C4⋊Q8—111no—
216C2×C4⋊Q8C2×D1111yescharacteristic
217C2×C22⋊Q8—221no—
218C2×C22⋊Q8—221no—
219C2×C4×Q8—21no—
220C2×C4×D4—111no—
221#500—224no—
222#474—224no—
223C2×#107—112no—
224C2×#107—112no—
225C2×#107—112no—
226C2×C4⋊C8—112no—
227C2×C4⋊C8—111no—
228C2×#102—111no—
229C2×#102—111no—
230C2×#102—112no—
231C2×C4×C8—111no—
232#399—222no—
233#391—21no—
234#390—112no—
235#389C2×D1112yes—
236#387—22no—
237#384—112no—
238C4×C4⋊C4C2×D1112yes—
239C4×C4⋊C4C2×D1111yescharacteristic
240C4×C4⋊C4C2×D1111yescharacteristic
241#340—112no—
242#340—111no—
243#340—112no—
244#340—111no—
245#336—112no—
246C22×C11C2×#12111yescharacteristic
247C22×C11#54711yescharacteristic
248C22×C11D4×Q811yescharacteristic
249C22×C11C22×D811yescharacteristic
250C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
251C22×C11#57811yescharacteristic
252C22×C11#57811yescharacteristic
253C2×D11—42no—
254C2×D11—42no—
255C2×D11—42no—
256C2×D11—81no—
257C2×D11—81no—
258C2×D11—81no—
259C2×D11—81no—
260C4×C11—24no—
261C4×C11—22no—
262C4×C11—42no—
263C4×C11—42no—
264C4×C11—44no—
265C4×C11—81no—
266C4×C11#45914yes—
267C4×C11#53311yescharacteristic
268C4×C11#54111yescharacteristic
269C4×C11#54811yescharacteristic
270C4×C11D4×Q811yescharacteristic
271Dic11—82no—
272Dic11—81no—
273C22×Q8—21no—
274C22×Q8—221no—
275C22×D4—111no—
276C23×C4—221no—
277C22×C8—111no—
278C22×C8—111no—
279C22×C8—112no—
280C4⋊Q8—22no—
281C4⋊Q8—222no—
282C4⋊Q8—222no—
283C4⋊Q8D4414yes—
284C22⋊Q8—444no—
285C22⋊Q8—444no—
286C4×Q8—44no—
287C4×D4—222no—
288C4×D4—222no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—111no—
292C2×C4⋊C4—112no—
293C2×C4⋊C4—222no—
294C2×C4⋊C4—222no—
295C2×C4⋊C4—221no—
296C2×C4⋊C4C22⋊D1111yescharacteristic
297C2×C4⋊C4C22⋊D1111yescharacteristic
298C2×C4⋊C4C22×D1111yescharacteristic
299C2×C4⋊C4C22×D1112yes—
300C2×C4⋊C4C22×D1111yescharacteristic
301C2×C22⋊C4—221no—
302C2×C22⋊C4—222no—
303C2×C22⋊C4—222no—
304C2×C42—22no—
305C2×C42—21no—
306C2×C42C22×D1112yes—
307C2×C42C22×D1111yescharacteristic
308#107—224no—
309#107—224no—
310#107—224no—
311C4⋊C8—224no—
312C4⋊C8—222no—
313#102—114no—
314#102—222no—
315#102—224no—
316C4×C8—222no—
317#95—21no—
318#95—22no—
319#95—22no—
320#95C22⋊D1112yes—
321C2×C11#242911yescharacteristic
322C2×C11C2×#45911yescharacteristic
323C2×C11#304411yescharacteristic
324C2×C11#333411yescharacteristic
325C2×C11#335311yescharacteristic
326C2×C11Q8×D811yescharacteristic
327C2×C11#338611yescharacteristic
328D11—82no—
329C24—221no—
330C2×Q8—24no—
331C2×Q8—42no—
332C2×Q8—42no—
333C2×Q8—442no—
334C2×Q8—442no—
335C2×Q8—442no—
336C2×D4—112no—
337C2×D4—221no—
338C2×D4—221no—
339C2×D4—221no—
340C2×D4—221no—
341C2×D4—221no—
342C22×C4—21no—
343C22×C4—22no—
344C22×C4—21no—
345C22×C4—222no—
346C22×C4—221no—
347C22×C4—442no—
348C22×C4—442no—
349C22×C4—442no—
350C22×C4C2×C22⋊D1112yes—
351C22×C4C2×C22⋊D1111yescharacteristic
352C22×C4C2×C22⋊D1112yes—
353C22×C4C2×C22⋊D1111yescharacteristic
354C22×C4C23×D1111yescharacteristic
355C2×C8—112no—
356C2×C8—112no—
357C2×C8—221no—
358C2×C8—221no—
359C2×C8—221no—
360C2×C8—221no—
361C2×C8—222no—
362C2×C8—222no—
363C2×C8—222no—
364C4⋊C4—24no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—44no—
371C4⋊C4—221no—
372C4⋊C4—222no—
373C4⋊C4—221no—
374C4⋊C4—222no—
375C4⋊C4—444no—
376C4⋊C4—442no—
377C4⋊C4—444no—
378C4⋊C4#432314yes—
379C4⋊C4C2×D4414yes—
380C4⋊C4Q8×D1112yes—
381C22⋊C4—444no—
382C22⋊C4—442no—
383C22⋊C4—444no—
384C42—22no—
385C42—22no—
386C42—44no—
387C42—42no—
388C42C2×D4412yes—
389C42#433912yes—
390C11#2544911yescharacteristic, complemented, Sylow
391C23—222no—
392C23—441no—
393C23—441no—
394C23—441no—
395C23—441no—
396C23—441no—
397C23—441no—
398C23C22×C22⋊D1111yescharacteristic
399Q8—48no—
400Q8—884no—
401D4—222no—
402D4—222no—
403D4—441no—
404D4—441no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—24no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—441no—
422C2×C4—442no—
423C2×C4—442no—
424C2×C4—441no—
425C2×C4—442no—
426C2×C4—441no—
427C2×C4—884no—
428C2×C4#6698312yes—
429C2×C4#6698312yes—
430C2×C4C2×#432314yes—
431C2×C4C2×#432312yes—
432C2×C4#6700212yes—
433C2×C4C22×D4411yescharacteristic
434C2×C4C2×#433911yescharacteristic
435C2×C4C2×Q8×D1111yescharacteristic
436C2×C4#6704011yescharacteristic
437C2×C4#41×D1111yescharacteristic
438C2×C4#6704311yescharacteristic
439C8—222no—
440C8—222no—
441C8—442no—
442C22—442no—
443C22—442no—
444C22—442no—
445C22—881no—
446C22—881no—
447C22—881no—
448C22—881no—
449C22C2×#6698311yescharacteristic
450C22C22×#432311yescharacteristic
451C22Q8×C22⋊D1111yescharacteristic
452C22C2×#6700211yescharacteristic
453C22#1062335511yescharacteristic
454C22#1062336911yescharacteristic
455C22#1062336911yescharacteristic
456C4—24no—
457C4—22no—
458C4—44no—
459C4—42no—
460C4—42no—
461C4—81no—
462C4—881no—
463C4—882no—
464C4#1062262814yes—
465C4Q8×D4411yescharacteristic
466C4#1062310711yescharacteristic
467C4#1062310911yescharacteristic
468C4#1062311411yescharacteristic
469C2—882no—
470C2#1307220911yescharacteristic
471C2C2×#1062262811yescharacteristic
472C2#1307814611yescharacteristic
473C2#1308095911yescharacteristic
474C2#1308119411yescharacteristic
475C2Q8×#432311yescharacteristic
476C2#1308153311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2365C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2365D11
hypocenterC11#25449
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2365

Complements

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

NH ≅ G/Ntype
1. C2×#10622691C2semidirect
4. #13070087C2semidirect
6. #13069568C2semidirect
7. #13069374C2semidirect
8. #13069335C2semidirect
11. C11×#2365C2semidirect
84. #66873Q8semidirect
156. #2365D11semidirect
390. C11#25449semidirect

Maximal subgroups

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

subgroupindex
C2×#106226912
C2×#106227002
#130735652
#130700872
#130700012
#130695682
#130693742
#130693352
#130692362
C4×#668732
C11×#23652
#2544911