Finite Group Databasebeta

← #14805352

Subgroups — #14805352

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×#10622700C211yesmaximal, characteristic
2#13073570C211yesmaximal, characteristic
3#13071676C211yesmaximal, characteristic, complemented
4#13070090C212yesmaximal, complemented
5#13069999C212yesmaximal
6#13069569C211yesmaximal, characteristic, complemented
7#13069371C212yesmaximal, complemented
8#13069334C211yesmaximal, characteristic, complemented
9#13069235C212yesmaximal
10C4×#66885C211yesmaximal, characteristic
11C2×C11×#500C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#66999—21no—
15C2×#66999—21no—
16C2×Q8×Dic11—21no—
17C2×C4×D44C2211yescharacteristic
18C11×#500—24no—
19C2×C11×#107C2212yes—
20C2×C11×#107C2212yes—
21C2×C4×C8×C11C2211yescharacteristic
22#10622843—21no—
23C2×#66885C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×Dic11⋊C8C2212yes—
26#10622700—24no—
27#10622605—22no—
28#10622601C2212yes—
29#10622598C2212yes—
30#10622594—22no—
31#10622589C2212yes—
32C4⋊C4×Dic11C2212yes—
33C2×#66873C2212yes—
34C2×#66871C2212yes—
35C4×C4⋊Dic11C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622189C2211yescharacteristic
39#10622189C2211yescharacteristic
40#10622188C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43C22×Q8×C11—21no—
44C22×Q8×C11—21no—
45C22×D44C2311yescharacteristic
46C22×C4×D11—21no—
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8D414yes—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C4⋊C4C2312yes—
57C2×C42×C11C2311yescharacteristic
58#66999—44no—
59#66999—44no—
60Q8×Dic11—44no—
61C2×(C2×D11)⋊C4—21no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11D411yescharacteristic
66C2×C4⋊Dic11D411yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2311yescharacteristic
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C2×C4×Dic11—21no—
73C2×C4×Dic11—22no—
74C2×C4×Dic11C2312yes—
75C22×C11⋊C8C2312yes—
76C4×D44—22no—
77C4×D44—22no—
78C11×#107—24no—
79C11×#107—24no—
80C4×C8×C11—22no—
81C11⋊#95—21no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84C11⋊#95D412yes—
85#66885—22no—
86#66885Q814yescomplemented
87Dic11⋊C8—24no—
88#66873—24no—
89#66871—24no—
90C4⋊(C11⋊C8)—22no—
91#25449—111nomaximal, Sylow
92C23×D11—21no—
93C2×Q8×C11—24no—
94C2×Q8×C11—42no—
95C2×Q8×C11—42no—
96C2×Q8×C11—42no—
97C2×Q8×C11—42no—
98C2×Q8×C11—42no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2411yescharacteristic
104C22×Dic11—21no—
105C22×Dic11—21no—
106C22×Dic11—21no—
107C22×Dic11C2×D412yes—
108C22×Dic11C2×D412yes—
109C2×D44—21no—
110C2×D44—21no—
111C2×D44—21no—
112C2×D44—21no—
113C2×D44—21no—
114C2×D44C2×Q812yes—
115C2×C4×D11—42no—
116C2×C4×D11—42no—
117C2×C4×D11—42no—
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11—21no—
122C2×C8×C11C2×Q812yes—
123C2×C8×C11#4112yes—
124C11×C4⋊C4—24no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—42no—
129C11×C4⋊C4C2×D414yes—
130C42×C11C2×D412yes—
131C42×C11#4112yes—
132(C2×D11)⋊C4—44no—
133(C2×D11)⋊C4—44no—
134(C2×D11)⋊C4—42no—
135C4⋊Dic11—22no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140C4⋊Dic11—21no—
141C4⋊Dic11—44no—
142C4⋊Dic11D814yes—
143C4⋊Dic11C2×Q812yes—
144Dic11⋊C4—44no—
145Dic11⋊C4—44no—
146C4×Dic11—22no—
147C4×Dic11—22no—
148C4×Dic11—44no—
149C4×Dic11—42no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—22no—
153C2×#500D1111yescharacteristic, complemented
154C2×#474—111no—
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×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—
173Q8×C11—84no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—24no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11#12112yes—
183C2×C4×C11#12112yes—
184C2×C4×C11C2×D812yes—
185C2×C4×C11AGL(1,ℤ/8)12yes—
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11C22×Q811yescharacteristic
188C2×C4×C11C2×#4111yescharacteristic
189C2×C4×C11C2×#4111yescharacteristic
190C2×C4×C112−1+411yescharacteristic
191C2×C4×C112−1+411yescharacteristic
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11C2×D814yes—
207D44—22no—
208D44—22no—
209D44—41no—
210D44—41no—
211C4×D11—84no—
212C8×C11—22no—
213C8×C11—22no—
214C11⋊C8—42no—
215C2×C4⋊Q8C2×D1111yescharacteristic
216C2×C4⋊Q8C2×D1111yescharacteristic
217C2×C22⋊Q8—221no—
218C2×C22⋊Q8—221no—
219C2×C4×Q8—221no—
220C2×C4×D4—111no—
221#500—24no—
222#474—224no—
223C2×#107—112no—
224C2×#107C2×D1112yes—
225C2×#107C2×D1112yes—
226C2×C4⋊C8—112no—
227C2×C4⋊C8—111no—
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—111no—
239C4×C4⋊C4—112no—
240C4×C4⋊C4—111no—
241#340—111no—
242#340—111no—
243#340—112no—
244#340—112no—
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—22no—
261C4×C11—44no—
262C4×C11—82no—
263C4×C11#45914yes—
264C4×C11#53311yescharacteristic
265C4×C11#54111yescharacteristic
266C4×C11#54811yescharacteristic
267C4×C11D4×Q811yescharacteristic
268Dic11—24no—
269Dic11—42no—
270Dic11—42no—
271Dic11—81no—
272Dic11—81no—
273C22×Q8—21no—
274C22×Q8—21no—
275C22×D4—111no—
276C23×C4—221no—
277C22×C8—112no—
278C22×C8C22×D1111yescharacteristic
279C22×C8C22×D1111yescharacteristic
280C4⋊Q8—22no—
281C4⋊Q8—22no—
282C4⋊Q8—22no—
283C4⋊Q8C22⋊D1114yes—
284C22⋊Q8—444no—
285C22⋊Q8—444no—
286C4×Q8—444no—
287C4×D4—222no—
288C4×D4—222no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—111no—
292C2×C4⋊C4—111no—
293C2×C4⋊C4—111no—
294C2×C4⋊C4—111no—
295C2×C4⋊C4—111no—
296C2×C4⋊C4—222no—
297C2×C4⋊C4—222no—
298C2×C4⋊C4—222no—
299C2×C4⋊C4C22×D1112yes—
300C2×C4⋊C4C22×D1112yes—
301C2×C22⋊C4—222no—
302C2×C22⋊C4—222no—
303C2×C22⋊C4—221no—
304C2×C42—112no—
305C2×C42—222no—
306C2×C42—221no—
307C2×C42C22×D1111yescharacteristic
308#107—24no—
309#107—24no—
310#107—224no—
311C4⋊C8—224no—
312C4⋊C8—222no—
313#102—114no—
314#102—222no—
315#102—224no—
316C4×C8—22no—
317#95—112no—
318#95—222no—
319#95—222no—
320#95—221no—
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—42no—
334C2×Q8—42no—
335C2×Q8—42no—
336C2×D4—112no—
337C2×D4—221no—
338C2×D4—221no—
339C2×D4—221no—
340C2×D4—221no—
341C2×D4—221no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—112no—
345C22×C4—112no—
346C22×C4—221no—
347C22×C4—221no—
348C22×C4—221no—
349C22×C4—442no—
350C22×C4—442no—
351C22×C4—442no—
352C22×C4D4×D1111yescharacteristic
353C22×C4D4×D1111yescharacteristic
354C22×C4C23×D1111yescharacteristic
355C2×C8—21no—
356C2×C8—21no—
357C2×C8—21no—
358C2×C8—21no—
359C2×C8—222no—
360C2×C8—222no—
361C2×C8—222no—
362C2×C8Q8×D1112yes—
363C2×C8#434312yes—
364C4⋊C4—24no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—42no—
369C4⋊C4—114no—
370C4⋊C4—112no—
371C4⋊C4—222no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C4⋊C4—221no—
375C4⋊C4—221no—
376C4⋊C4—221no—
377C4⋊C4—444no—
378C4⋊C4—444no—
379C4⋊C4—444no—
380C4⋊C4C2×C22⋊D1114yes—
381C22⋊C4—444no—
382C22⋊C4—444no—
383C22⋊C4—442no—
384C42—222no—
385C42—222no—
386C42—444no—
387C42—442no—
388C42#434112yes—
389C42C2×C22⋊D1112yes—
390C11#2544911yescharacteristic, complemented, Sylow
391C23—222no—
392C23—441no—
393C23—441no—
394C23—441no—
395C23—441no—
396C23—441no—
397C23—441no—
398C23C2×D4×D1111yescharacteristic
399Q8—48no—
400Q8—84no—
401D4—222no—
402D4—222no—
403D4—441no—
404D4—441no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—24no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—114no—
414C2×C4—222no—
415C2×C4—222no—
416C2×C4—222no—
417C2×C4—222no—
418C2×C4—222no—
419C2×C4—222no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4—884no—
429C2×C4D8×D1112yes—
430C2×C4#6696412yes—
431C2×C4#6699212yes—
432C2×C4#6699212yes—
433C2×C4C2×#434111yescharacteristic
434C2×C4C2×Q8×D1111yescharacteristic
435C2×C4C2×#434311yescharacteristic
436C2×C4#6704011yescharacteristic
437C2×C4#6704011yescharacteristic
438C2×C4C22×C22⋊D1111yescharacteristic
439C8—22no—
440C8—22no—
441C8—442no—
442C22—442no—
443C22—442no—
444C22—442no—
445C22—881no—
446C22—881no—
447C22—881no—
448C22—881no—
449C22#1062325711yescharacteristic
450C22#1062325811yescharacteristic
451C22C2×D8×D1111yescharacteristic
452C22C2×#6696411yescharacteristic
453C22#1062329711yescharacteristic
454C22#1062329711yescharacteristic
455C22C2×#6699211yescharacteristic
456C4—22no—
457C4—44no—
458C4—82no—
459C4—224no—
460C4—442no—
461C4—442no—
462C4—881no—
463C4—881no—
464C4#1062276314yes—
465C4#1062325911yescharacteristic
466C4#1062326211yescharacteristic
467C4Q8×C22⋊D1111yescharacteristic
468C4#1062334811yescharacteristic
469C2—882no—
470C2#1307221811yescharacteristic
471C2C2×#1062276311yescharacteristic
472C2#1307814311yescharacteristic
473C2#1308096311yescharacteristic
474C2#1308119911yescharacteristic
475C2#1308146811yescharacteristic
476C2#1308154211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#500C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×#500D11
hypocenterC11#25449
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
3. #13071676C2semidirect
4. #13070090C2semidirect
6. #13069569C2semidirect
7. #13069371C2semidirect
8. #13069334C2semidirect
11. C2×C11×#500C2semidirect
86. #66885Q8semidirect
153. C2×#500D11semidirect
390. C11#25449semidirect

Maximal subgroups

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

subgroupindex
C2×#106227002
#130735702
#130716762
#130700902
#130699992
#130695692
#130693712
#130693342
#130692352
C4×#668852
C2×C11×#5002
#2544911