Finite Group Databasebeta

← #14805347

Subgroups — #14805347

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×#10622295C211yesmaximal, characteristic, complemented
2C2×#10622459C211yesmaximal, characteristic
3#13073565C211yesmaximal, characteristic
4#13071674C211yesmaximal, characteristic, complemented
5#13070089C212yesmaximal, complemented
6#13070003C212yesmaximal
7#13069567C211yesmaximal, characteristic, complemented
8#13069375C212yesmaximal, complemented
9#13069237C212yesmaximal
10C4×#66885C211yesmaximal, characteristic
11C11×#1939C211yesmaximal, characteristic, complemented
12C2×#66950—21no—
13C2×#66950—21no—
14C2×#66940—21no—
15C2×C4×D44C2211yescharacteristic
16C2×#66922C2211yescharacteristic
17C2×#66922C2211yescharacteristic
18C2×C11×C4⋊C8C2212yes—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C4×C8×C11C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C2×#66885C2212yes—
23C2×#66885C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66882C2212yes—
26C2×#66882C2212yes—
27C2×#66882C2212yes—
28#10622587—21no—
29#10622552C2212yes—
30#10622548C2212yes—
31C4×C4⋊Dic11C2212yes—
32C4×C4⋊Dic11C2211yescharacteristic
33#10622541C2212yes—
34#10622459—24no—
35#10622295—24no—
36#10622290—22no—
37#10622266—22no—
38C11×#336C2212yes—
39#10622189C2211yescharacteristic
40#10622189C2212yes—
41#10622189C2211yescharacteristic
42#10622189C2212yes—
43C22×D44C2311yescharacteristic
44C22×C4×D11—21no—
45C22×Dic22—21no—
46C22×Dic22—21no—
47C22×C8×C11C2312yes—
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C42×C11C2312yes—
53C2×C42×C11C2311yescharacteristic
54C2×(C2×D11)⋊C4—21no—
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11C2311yescharacteristic
62C2×C4⋊Dic11C2312yes—
63C2×C4⋊Dic11C2311yescharacteristic
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×Dic11⋊C4—22no—
67C2×C4×Dic11—22no—
68C2×C4×Dic11—21no—
69#66950—44no—
70#66950—44no—
71#66940—44no—
72C4×D44—22no—
73C4×D44—22no—
74#66922—22no—
75#66922—22no—
76#66922—22no—
77#66922D414yes—
78C11×C4⋊C8—24no—
79C11×C4⋊C8—22no—
80C4×C8×C11—22no—
81C11×#95D412yes—
82C11⋊#95—21no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85#66885—22no—
86#66885—24no—
87#66885Q814yescomplemented
88#66882—24no—
89#66882—24no—
90#66882—24no—
91#25449—111nomaximal, Sylow
92C23×D11—21no—
93C22×C4×C11C2×D412yes—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2411yescharacteristic
98C22×Dic11—21no—
99C22×Dic11—22no—
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—22no—
103C2×D44—21no—
104C2×D44—21no—
105C2×D44—21no—
106C2×D44—21no—
107C2×D44—21no—
108C2×D44C2×Q812yes—
109C2×C4×D11—42no—
110C2×C4×D11—42no—
111C2×C4×D11—42no—
112C2×Dic22—24no—
113C2×Dic22—42no—
114C2×Dic22—42no—
115C2×Dic22—42no—
116C2×Dic22—42no—
117C2×Dic22—42no—
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—22no—
125C2×C8×C11C2×Q812yes—
126C2×C8×C11#4112yes—
127C11×C4⋊C4—22no—
128C11×C4⋊C4D814yes—
129C42×C11—22no—
130C42×C11—22no—
131C42×C11C2×D412yes—
132C42×C11#4112yes—
133(C2×D11)⋊C4—44no—
134(C2×D11)⋊C4—42no—
135(C2×D11)⋊C4—44no—
136C4⋊Dic11—24no—
137C4⋊Dic11—22no—
138C4⋊Dic11—21no—
139C4⋊Dic11—22no—
140C4⋊Dic11—21no—
141C4⋊Dic11—22no—
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—44no—
146C4⋊Dic11—42no—
147C4⋊Dic11—44no—
148C4⋊Dic11C2×D414yes—
149C4⋊Dic11C2×Q812yes—
150Dic11⋊C4—44no—
151C4×Dic11—44no—
152C4×Dic11—42no—
153C2×#500—111no—
154C2×#474—111no—
155#2542—111no—
156#2365—111no—
157#2083—112no—
158#2067—112no—
159#1988—111no—
160#1947—112no—
161#1939D1111yescharacteristic, complemented
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—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11#12112yes—
180C2×C4×C11#12112yes—
181C2×C4×C11C2×D814yes—
182C2×C4×C11C2×D812yes—
183C2×C4×C11AGL(1,ℤ/8)12yes—
184C2×C4×C11C22×D411yescharacteristic
185C2×C4×C11C22×Q811yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C2×C4×C11C2×#4111yescharacteristic
188C2×C4×C112−1+411yescharacteristic
189C2×C4×C112−1+411yescharacteristic
190C2×Dic11—24no—
191C2×Dic11—22no—
192C2×Dic11—41no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—41no—
196C2×Dic11—42no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—42no—
202C2×Dic11—41no—
203C2×Dic11—42no—
204C2×Dic11—41no—
205D44—22no—
206D44—22no—
207D44—41no—
208D44—41no—
209C4×D11—84no—
210Dic22—48no—
211Dic22—84no—
212C8×C11—22no—
213C8×C11—22no—
214C8×C11—42no—
215C2×C4⋊Q8—111no—
216C2×C4⋊Q8—111no—
217C2×C22⋊Q8—221no—
218C2×C22⋊Q8—221no—
219C2×C4×Q8—221no—
220C2×C4×D4—111no—
221#500—224no—
222#474—224no—
223C2×#107—112no—
224C2×#107—112no—
225C2×#107—112no—
226C2×C4⋊C8C2×D1112yes—
227C2×C4⋊C8C2×D1111yescharacteristic
228C2×#102—111no—
229C2×#102—111no—
230C2×#102—112no—
231C2×C4×C8C2×D1111yescharacteristic
232#399—222no—
233#391—221no—
234#390—112no—
235#389—112no—
236#387—222no—
237#384—112no—
238C4×C4⋊C4—112no—
239C4×C4⋊C4—111no—
240C4×C4⋊C4C2×D1111yescharacteristic
241#340—112no—
242#340—111no—
243#340—112no—
244#340—111no—
245#336C2×D1112yes—
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#45914yes—
264C4×C11#53311yescharacteristic
265C4×C11#54111yescharacteristic
266C4×C11#54811yescharacteristic
267C4×C11D4×Q811yescharacteristic
268Dic11—42no—
269Dic11—44no—
270Dic11—81no—
271Dic11—82no—
272Dic11—81no—
273C22×Q8—221no—
274C22×Q8—221no—
275C22×D4—111no—
276C23×C4—221no—
277C22×C8C22×D1112yes—
278C22×C8C22×D1111yescharacteristic
279C22×C8C22×D1111yescharacteristic
280C4⋊Q8—114no—
281C4⋊Q8—222no—
282C4⋊Q8—222no—
283C4⋊Q8—222no—
284C22⋊Q8—444no—
285C22⋊Q8—444no—
286C4×Q8—444no—
287C4×D4—222no—
288C4×D4—222no—
289C2×C4⋊C4—112no—
290C2×C4⋊C4—111no—
291C2×C4⋊C4—111no—
292C2×C4⋊C4—112no—
293C2×C4⋊C4—111no—
294C2×C4⋊C4—221no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4—222no—
297C2×C4⋊C4—222no—
298C2×C4⋊C4—221no—
299C2×C4⋊C4D4411yescharacteristic
300C2×C4⋊C4D4411yescharacteristic
301C2×C22⋊C4—221no—
302C2×C22⋊C4—222no—
303C2×C22⋊C4—222no—
304C2×C42—222no—
305C2×C42—221no—
306C2×C42C22×D1112yes—
307C2×C42C22×D1111yescharacteristic
308#107—224no—
309#107—224no—
310#107—224no—
311C4⋊C8—24no—
312C4⋊C8—22no—
313#102—114no—
314#102—224no—
315#102—222no—
316C4×C8—22no—
317#95—221no—
318#95—222no—
319#95—222no—
320#95D4412yes—
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—224no—
331C2×Q8—442no—
332C2×Q8—442no—
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—221no—
343C22×C4—222no—
344C22×C4—221no—
345C22×C4—222no—
346C22×C4—221no—
347C22×C4—442no—
348C22×C4—442no—
349C22×C4—442no—
350C22×C4C2×D4412yes—
351C22×C4C2×D4411yescharacteristic
352C22×C4C2×D4412yes—
353C22×C4C2×D4411yescharacteristic
354C22×C4C23×D1111yescharacteristic
355C2×C8—21no—
356C2×C8—21no—
357C2×C8—21no—
358C2×C8—21no—
359C2×C8—22no—
360C2×C8—22no—
361C2×C8—22no—
362C2×C8#434112yes—
363C2×C8Q8×D1112yes—
364C4⋊C4—22no—
365C4⋊C4—114no—
366C4⋊C4—112no—
367C4⋊C4—224no—
368C4⋊C4—222no—
369C4⋊C4—221no—
370C4⋊C4—221no—
371C4⋊C4—222no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C4⋊C4—222no—
375C4⋊C4—221no—
376C4⋊C4—444no—
377C4⋊C4—442no—
378C4⋊C4—444no—
379C4⋊C4—444no—
380C4⋊C4D8814yes—
381C22⋊C4—444no—
382C22⋊C4—442no—
383C22⋊C4—444no—
384C42—22no—
385C42—22no—
386C42—444no—
387C42—442no—
388C42D4×D1112yes—
389C42#434312yes—
390C11#2544911yescharacteristic, complemented, Sylow
391C23—222no—
392C23—441no—
393C23—441no—
394C23—441no—
395C23—441no—
396C23—441no—
397C23—441no—
398C23C22×D4411yescharacteristic
399Q8—448no—
400Q8—884no—
401D4—222no—
402D4—222no—
403D4—441no—
404D4—441no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—224no—
413C2×C4—222no—
414C2×C4—441no—
415C2×C4—442no—
416C2×C4—442no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—442no—
420C2×C4—441no—
421C2×C4—442no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—442no—
426C2×C4—441no—
427C2×C4—884no—
428C2×C4#6694812yes—
429C2×C4#6694812yes—
430C2×C4C2×D8814yes—
431C2×C4C2×D8812yes—
432C2×C4#6696112yes—
433C2×C4C2×D4×D1111yescharacteristic
434C2×C4C2×#434111yescharacteristic
435C2×C4C2×Q8×D1111yescharacteristic
436C2×C4C2×#434311yescharacteristic
437C2×C4#6704311yescharacteristic
438C2×C4#6704311yescharacteristic
439C8—22no—
440C8—22no—
441C8—42no—
442C22—442no—
443C22—442no—
444C22—442no—
445C22—881no—
446C22—881no—
447C22—881no—
448C22—881no—
449C22C2×#6694811yescharacteristic
450C22#1062308611yescharacteristic
451C22Q8×D4411yescharacteristic
452C22C22×D8811yescharacteristic
453C22C2×#6696111yescharacteristic
454C22#1062328411yescharacteristic
455C22#1062328411yescharacteristic
456C4—22no—
457C4—24no—
458C4—42no—
459C4—444no—
460C4—442no—
461C4—881no—
462C4—882no—
463C4—881no—
464C4#1062245614yes—
465C4#1062312911yescharacteristic
466C4#1062316311yescharacteristic
467C4#1062322811yescharacteristic
468C4#1062325911yescharacteristic
469C2—882no—
470C2#1307221311yescharacteristic
471C2C2×#1062245611yescharacteristic
472C2#1307814711yescharacteristic
473C2#1308096411yescharacteristic
474C2#1308120111yescharacteristic
475C2Q8×D8811yescharacteristic
476C2#1308153911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1939C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1939D11
hypocenterC11#25449
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1939

Complements

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

NH ≅ G/Ntype
1. C2×#10622295C2semidirect
4. #13071674C2semidirect
5. #13070089C2semidirect
7. #13069567C2semidirect
8. #13069375C2semidirect
11. C11×#1939C2semidirect
87. #66885Q8semidirect
161. #1939D11semidirect
390. C11#25449semidirect

Maximal subgroups

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

subgroupindex
C2×#106222952
C2×#106224592
#130735652
#130716742
#130700892
#130700032
#130695672
#130693752
#130692372
C4×#668852
C11×#19392
#2544911