Finite Group Databasebeta

← #14805351

Subgroups — #14805351

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
2#13073569C211yesmaximal, characteristic
3#13071676C211yesmaximal, characteristic, complemented
4#13070090C212yesmaximal, complemented
5#13070000C212yesmaximal
6#13069567C211yesmaximal, characteristic, complemented
7#13069371C212yesmaximal, complemented
8#13069332C211yesmaximal, characteristic, complemented
9#13069239C212yesmaximal
10C4×#66896C211yesmaximal, characteristic
11C2×C11×#474C211yesmaximal, characteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×Q8×Dic11—21no—
15C2×#66977—21no—
16C2×#66977—21no—
17C2×#66922C2211yescharacteristic
18C11×#474—24no—
19C2×C11×#107C2212yes—
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×#102C2212yes—
22#10622843—21no—
23#10622834C2212yes—
24C2×#66896C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26C2×Dic11⋊C8C2212yes—
27#10622691—24no—
28#10622598C2212yes—
29#10622594—22no—
30#10622589C2212yes—
31C4⋊C4×Dic11C2212yes—
32C2×#66871C2212yes—
33C2×#66871C2212yes—
34#10622562—22no—
35C4×C4⋊Dic11C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622189C2212yes—
39#10622189C2212yes—
40#10622188C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×Q8×C11—21no—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C22×Dic22—21no—
47C22×C8×C11C2312yes—
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8D414yes—
50C4×D4×C11—22no—
51C4×D4×C11—22no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C22⋊C4—21no—
56C2×C42×C11C2311yescharacteristic
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11—22no—
59Q8×Dic11—44no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11D411yescharacteristic
63C2×C4⋊Dic11D411yescharacteristic
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67#66977—44no—
68#66977—44no—
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—22no—
71C2×C4×Dic11—21no—
72C2×C4×Dic11—22no—
73C2×C4×Dic11C2312yes—
74C22×C11⋊C8C2311yescharacteristic
75C22×C11⋊C8C2311yescharacteristic
76#66922—22no—
77#66922—22no—
78C11×#107—24no—
79C11×C4⋊C8—22no—
80C11×#102—24no—
81#66896—22no—
82#66896Q814yescomplemented
83C11⋊#95—21no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86C11⋊#95D412yes—
87Dic11⋊C8—24no—
88#66871—24no—
89#66871—24no—
90C4×C11⋊C8—22no—
91#25449—111nomaximal, Sylow
92C24×C11—21no—
93C2×Q8×C11—24no—
94C2×Q8×C11—42no—
95C2×Q8×C11—42no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11C2×Q812yes—
102C22×C4×C11—22no—
103C22×C4×C11—21no—
104C22×C4×C11—42no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2411yescharacteristic
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—22no—
113C22×Dic11C2×D412yes—
114C22×Dic11C2×D412yes—
115C2×Dic22—42no—
116C2×Dic22—42no—
117C2×Dic22—42no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C11×C4⋊C4—24no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4C2×D414yes—
126C11×C22⋊C4—42no—
127C42×C11C2×D412yes—
128C42×C11#4112yes—
129C22⋊Dic11—44no—
130C22⋊Dic11—44no—
131C4⋊Dic11—22no—
132C4⋊Dic11—22no—
133C4⋊Dic11—21no—
134C4⋊Dic11—22no—
135C4⋊Dic11—21no—
136C4⋊Dic11—21no—
137C4⋊Dic11—44no—
138C4⋊Dic11—42no—
139C4⋊Dic11D814yes—
140C4⋊Dic11C2×Q812yes—
141Dic11⋊C4—44no—
142Dic11⋊C4—44no—
143C4×Dic11—22no—
144C4×Dic11—22no—
145C4×Dic11—44no—
146C4×Dic11—42no—
147C2×C11⋊C8—21no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8C2×Q812yes—
152C2×C11⋊C8#4112yes—
153C2×#500—111no—
154C2×#474D1111yescharacteristic
155#2542—111no—
156#2365—111no—
157#2083—112no—
158#2067—112no—
159#1988—111no—
160#1947—112no—
161#1939—111no—
162#1925—112no—
163C4×#102—111no—
164C23×C11—22no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11C22×D411yescharacteristic
172Q8×C11—48no—
173D4×C11—22no—
174D4×C11—22no—
175D4×C11—41no—
176D4×C11—41no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—24no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—84no—
186C2×C4×C11#12112yes—
187C2×C4×C11#12112yes—
188C2×C4×C11C2×D812yes—
189C2×C4×C11AGL(1,ℤ/8)12yes—
190C2×C4×C11C22×D411yescharacteristic
191C2×C4×C11C22×Q811yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C112−1+411yescharacteristic
195C2×C4×C112−1+411yescharacteristic
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—42no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—41no—
210C2×Dic11C2×D814yes—
211Dic22—84no—
212C8×C11—42no—
213C11⋊C8—22no—
214C11⋊C8—22no—
215C2×C4⋊Q8—111no—
216C2×C4⋊Q8C2×D1111yescharacteristic
217C2×C22⋊Q8—221no—
218C2×C22⋊Q8—221no—
219C2×C4×Q8—221no—
220C2×C4×D4C2×D1111yescharacteristic
221#500—224no—
222#474—24no—
223C2×#107—112no—
224C2×#107—112no—
225C2×#107C2×D1112yes—
226C2×C4⋊C8—112no—
227C2×C4⋊C8C2×D1111yescharacteristic
228C2×#102—111no—
229C2×#102—111no—
230C2×#102C2×D1112yes—
231C2×C4×C8—111no—
232#399—222no—
233#391—221no—
234#390—112no—
235#389—112no—
236#387—222no—
237#384—112no—
238C4×C4⋊C4—111no—
239C4×C4⋊C4—112no—
240C4×C4⋊C4—111no—
241#340—112no—
242#340—112no—
243#340—111no—
244#340—111no—
245#336—112no—
246C22×C11—42no—
247C22×C11—42no—
248C22×C11—42no—
249C22×C11—81no—
250C22×C11—81no—
251C22×C11—81no—
252C22×C11—81no—
253C22×C11C2×#12111yescharacteristic
254C22×C11#54711yescharacteristic
255C22×C11D4×Q811yescharacteristic
256C22×C11C22×D811yescharacteristic
257C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
258C22×C11#57811yescharacteristic
259C22×C11#57811yescharacteristic
260C4×C11—22no—
261C4×C11—44no—
262C4×C11—81no—
263C4×C11#45914yes—
264C4×C11#53311yescharacteristic
265C4×C11#54111yescharacteristic
266C4×C11#54811yescharacteristic
267C4×C11D4×Q811yescharacteristic
268Dic11—24no—
269Dic11—42no—
270Dic11—42no—
271Dic11—81no—
272Dic11—82no—
273C22×Q8—21no—
274C22×Q8—221no—
275C22×D4C22×D1111yescharacteristic
276C23×C4—21no—
277C22×C8—111no—
278C22×C8—111no—
279C22×C8C22×D1112yes—
280C4⋊Q8—22no—
281C4⋊Q8—222no—
282C4⋊Q8—222no—
283C4⋊Q8C22⋊D1114yes—
284C22⋊Q8—444no—
285C22⋊Q8—444no—
286C4×Q8—444no—
287C4×D4—22no—
288C4×D4—22no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—111no—
291C2×C4⋊C4—111no—
292C2×C4⋊C4—111no—
293C2×C4⋊C4—112no—
294C2×C4⋊C4—111no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4—222no—
297C2×C4⋊C4—222no—
298C2×C4⋊C4—221no—
299C2×C4⋊C4C22×D1111yescharacteristic
300C2×C4⋊C4C22×D1112yes—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—222no—
303C2×C22⋊C4—222no—
304C2×C42—112no—
305C2×C42—222no—
306C2×C42—221no—
307C2×C42C22×D1111yescharacteristic
308#107—24no—
309#107—224no—
310#107—224no—
311C4⋊C8—22no—
312C4⋊C8—224no—
313#102—24no—
314#102—114no—
315#102—222no—
316C4×C8—222no—
317#95—112no—
318#95—222no—
319#95—222no—
320#95—221no—
321C2×C11—82no—
322C2×C11#242911yescharacteristic
323C2×C11C2×#45911yescharacteristic
324C2×C11#304411yescharacteristic
325C2×C11#333411yescharacteristic
326C2×C11#335311yescharacteristic
327C2×C11Q8×D811yescharacteristic
328C2×C11#338611yescharacteristic
329C24—21no—
330C2×Q8—24no—
331C2×Q8—42no—
332C2×Q8—42no—
333C2×Q8—442no—
334C2×Q8—442no—
335C2×Q8—442no—
336C2×D4—21no—
337C2×D4—21no—
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4Q8×D1112yes—
342C22×C4—22no—
343C22×C4—21no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—112no—
348C22×C4—112no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4—222no—
352C22×C4D4×D1111yescharacteristic
353C22×C4D4×D1111yescharacteristic
354C22×C4C23×D1111yescharacteristic
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—112no—
359C2×C8—112no—
360C2×C8—221no—
361C2×C8—221no—
362C2×C8—221no—
363C2×C8—221no—
364C4⋊C4—24no—
365C4⋊C4—22no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—114no—
369C4⋊C4—112no—
370C4⋊C4—222no—
371C4⋊C4—221no—
372C4⋊C4—222no—
373C4⋊C4—221no—
374C4⋊C4—221no—
375C4⋊C4—222no—
376C4⋊C4—444no—
377C4⋊C4—444no—
378C4⋊C4—444no—
379C4⋊C4—442no—
380C4⋊C4C2×C22⋊D1114yes—
381C22⋊C4—42no—
382C22⋊C4—444no—
383C22⋊C4—444no—
384C42—222no—
385C42—222no—
386C42—444no—
387C42—442no—
388C42#434112yes—
389C42C2×C22⋊D1112yes—
390C11#2544911yescharacteristic, complemented, Sylow
391C23—22no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23C2×D4×D1111yescharacteristic
399Q8—48no—
400Q8—884no—
401D4—22no—
402D4—22no—
403D4—41no—
404D4—41no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—24no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—84no—
414C2×C4—114no—
415C2×C4—222no—
416C2×C4—222no—
417C2×C4—222no—
418C2×C4—222no—
419C2×C4—222no—
420C2×C4—222no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—442no—
425C2×C4—442no—
426C2×C4—441no—
427C2×C4—442no—
428C2×C4—441no—
429C2×C4D8×D1112yes—
430C2×C4#6696412yes—
431C2×C4#6699212yes—
432C2×C4#6699212yes—
433C2×C4C2×#434111yescharacteristic
434C2×C4C2×Q8×D1111yescharacteristic
435C2×C4#6704011yescharacteristic
436C2×C4#41×D1111yescharacteristic
437C2×C4#6704311yescharacteristic
438C2×C4C22×C22⋊D1111yescharacteristic
439C8—42no—
440C8—222no—
441C8—222no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22—81no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22#1062316211yescharacteristic
450C22#1062316311yescharacteristic
451C22C2×D8×D1111yescharacteristic
452C22C2×#6696411yescharacteristic
453C22#1062331011yescharacteristic
454C22#1062331011yescharacteristic
455C22C2×#6699211yescharacteristic
456C4—22no—
457C4—44no—
458C4—81no—
459C4—224no—
460C4—442no—
461C4—442no—
462C4—882no—
463C4—881no—
464C4#1062276314yes—
465C4#1062315311yescharacteristic
466C4#1062315611yescharacteristic
467C4Q8×C22⋊D1111yescharacteristic
468C4#1062336211yescharacteristic
469C2—82no—
470C2#1307221711yescharacteristic
471C2C2×#1062276311yescharacteristic
472C2#1307814811yescharacteristic
473C2#1308096211yescharacteristic
474C2#1308119711yescharacteristic
475C2#1308146611yescharacteristic
476C2#1308154111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#474C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#474D11
hypocenterC11#25449
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#10622691C2semidirect
3. #13071676C2semidirect
4. #13070090C2semidirect
6. #13069567C2semidirect
7. #13069371C2semidirect
8. #13069332C2semidirect
82. #66896Q8semidirect
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
#130735692
#130716762
#130700902
#130700002
#130695672
#130693712
#130693322
#130692392
C4×#668962
C2×C11×#4742
#2544911