Finite Group Databasebeta

← #14805358

Subgroups — #14805358

Order 2816.

778 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622295C211yesmaximal, characteristic, complemented
2C2×#10622455C211yesmaximal, characteristic
3#13073785C211yesmaximal, characteristic
4#13071705C211yesmaximal, characteristic, complemented
5#13070099C212yesmaximal, complemented
6#13070003C212yesmaximal
7#13069563C211yesmaximal, characteristic, complemented
8#13069386C212yesmaximal, complemented
9#13069237C212yesmaximal
10C4×#66885C211yesmaximal, characteristic
11C11×#1939C211yesmaximal, characteristic, complemented
12C2×C4×D44C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C2×#66922C2211yescharacteristic
15C2×C11×C4⋊C8C2212yes—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C4×C8×C11C2211yescharacteristic
18C4×C11×C4⋊C4C2211yescharacteristic
19C2×#66885C2212yes—
20C2×#66885C2211yescharacteristic
21C2×#66885C2211yescharacteristic
22C2×#66882C2212yes—
23C2×#66882C2212yes—
24C2×#66881C2212yes—
25#10622600—21no—
26#10622600—21no—
27C4⋊C4×Dic11—21no—
28#10622586—21no—
29#10622552C2212yes—
30#10622549C2212yes—
31C4×C4⋊Dic11C2212yes—
32C4×C4⋊Dic11C2211yescharacteristic
33#10622541C2212yes—
34#10622455—24no—
35#10622295—24no—
36#10622286—22no—
37#10622259—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⋊Dic11C2311yescharacteristic
60C2×C4⋊Dic11C2312yes—
61C2×C4⋊Dic11C2311yescharacteristic
62C2×C4⋊Dic11C2312yes—
63C2×C4⋊Dic11C2311yescharacteristic
64C2×Dic11⋊C4—22no—
65C2×C4×Dic11—21no—
66C2×C4×Dic11—22no—
67C4×D44—22no—
68C4×D44—22no—
69#66922—22no—
70#66922—22no—
71#66922—22no—
72#66922D414yes—
73C11×C4⋊C8—24no—
74C11×C4⋊C8—22no—
75C4×C8×C11—22no—
76C11×#95D412yes—
77C11⋊#95—21no—
78C11⋊#95—22no—
79C11⋊#95—22no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82#66885—22no—
83#66885—24no—
84#66885Q814yescomplemented
85#66882—24no—
86#66882—24no—
87#66881—24no—
88#25450—111nomaximal, Sylow
89C23×D11—21no—
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2411yescharacteristic
95C22×Dic11—21no—
96C22×Dic11—22no—
97C22×Dic11—21no—
98C22×Dic11—21no—
99C22×Dic11—22no—
100C2×D44—21no—
101C2×D44—21no—
102C2×D44—21no—
103C2×D44—21no—
104C2×D44—21no—
105C2×D44C2×Q812yes—
106C2×C4×D11—42no—
107C2×C4×D11—42no—
108C2×C4×D11—42no—
109C2×Dic22—24no—
110C2×Dic22—42no—
111C2×Dic22—81no—
112C2×Dic22—81no—
113C2×Dic22—81no—
114C2×Dic22—81no—
115C2×C8×C11—21no—
116C2×C8×C11—21no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11—22no—
122C2×C8×C11C2×Q812yes—
123C2×C8×C11#4112yes—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C42×C11—22no—
127C42×C11—22no—
128C42×C11C2×D412yes—
129C42×C11#4112yes—
130(C2×D11)⋊C4—42no—
131(C2×D11)⋊C4—82no—
132(C2×D11)⋊C4—82no—
133C4⋊Dic11—24no—
134C4⋊Dic11—21no—
135C4⋊Dic11—22no—
136C4⋊Dic11—22no—
137C4⋊Dic11—21no—
138C4⋊Dic11—22no—
139C4⋊Dic11—21no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11—42no—
143C4⋊Dic11C2×D414yes—
144C4⋊Dic11C2×Q812yes—
145Dic11⋊C4—82no—
146C4×Dic11—42no—
147C4×Dic11—82no—
148C2×#500—111no—
149C2×#476—111no—
150#2563—111no—
151#2369—111no—
152#2085—112no—
153#2067—112no—
154#1987—111no—
155#1949—112no—
156#1939D1111yescharacteristic, complemented
157#1925—112no—
158C4×#102—111no—
159C23×C11C22×D411yescharacteristic
160C22×D11—22no—
161C22×D11—41no—
162C22×D11—41no—
163C22×D11—41no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—41no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11#12112yes—
176C2×C4×C11#12112yes—
177C2×C4×C11#13512yes—
178C2×C4×C11#13712yes—
179C2×C4×C11C22×D411yescharacteristic
180C2×C4×C11C22×Q811yescharacteristic
181C2×C4×C11C2×#4111yescharacteristic
182C2×C4×C11C2×#4111yescharacteristic
183C2×C4×C112−1+411yescharacteristic
184C2×C4×C112−1+411yescharacteristic
185C2×Dic11—24no—
186C2×Dic11—22no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200D44—22no—
201D44—22no—
202D44—41no—
203D44—41no—
204C4×D11—84no—
205Dic22—84no—
206Dic22—84no—
207C8×C11—22no—
208C8×C11—22no—
209C8×C11—42no—
210C2×C4⋊Q8—111no—
211C2×C4⋊Q8—111no—
212C2×C4×D4—111no—
213#500—224no—
214#476—224no—
215C2×#107—112no—
216C2×#107—112no—
217C2×#106—112no—
218C2×C4⋊C8C2×D1112yes—
219C2×C4⋊C8C2×D1111yescharacteristic
220C2×#102—111no—
221C2×#102—111no—
222C2×#102—112no—
223C2×C4×C8C2×D1111yescharacteristic
224#393—222no—
225#391—222no—
226#390—112no—
227#389—112no—
228#389—221no—
229#382—112no—
230#380—221no—
231#380—221no—
232C4×C4⋊C4—112no—
233C4×C4⋊C4—111no—
234C4×C4⋊C4—221no—
235C4×C4⋊C4C2×D1111yescharacteristic
236#340—112no—
237#340—111no—
238#340—112no—
239#340—111no—
240#336C2×D1112yes—
241C22×C11C2×#12111yescharacteristic
242C22×C11#54711yescharacteristic
243C22×C11D4×Q811yescharacteristic
244C22×C11C2×#13511yescharacteristic
245C22×C11C2×#13711yescharacteristic
246C22×C11#57611yescharacteristic
247C22×C11#57611yescharacteristic
248C2×D11—42no—
249C2×D11—42no—
250C2×D11—42no—
251C2×D11—81no—
252C2×D11—81no—
253C2×D11—81no—
254C2×D11—81no—
255C4×C11—22no—
256C4×C11—42no—
257C4×C11—42no—
258C4×C11#46414yes—
259C4×C11#53311yescharacteristic
260C4×C11#54111yescharacteristic
261C4×C11#54811yescharacteristic
262C4×C11D4×Q811yescharacteristic
263Dic11—42no—
264Dic11—44no—
265Dic11—81no—
266Dic11—81no—
267Dic11—82no—
268C22×Q8—221no—
269C22×Q8—221no—
270C22×D4—111no—
271C23×C4—221no—
272C22×C8C22×D1112yes—
273C22×C8C22×D1111yescharacteristic
274C22×C8C22×D1111yescharacteristic
275C4⋊Q8—114no—
276C4⋊Q8—222no—
277C4⋊Q8—222no—
278C4⋊Q8—222no—
279C4×D4—222no—
280C4×D4—222no—
281C2×C4⋊C4—112no—
282C2×C4⋊C4—111no—
283C2×C4⋊C4—111no—
284C2×C4⋊C4—112no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—221no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4—222no—
289C2×C4⋊C4D4411yescharacteristic
290C2×C4⋊C4D4411yescharacteristic
291C2×C22⋊C4—221no—
292C2×C22⋊C4—222no—
293C2×C22⋊C4—222no—
294C2×C42—221no—
295C2×C42—222no—
296C2×C42C22×D1112yes—
297C2×C42C22×D1111yescharacteristic
298#107—224no—
299#107—224no—
300#106—224no—
301C4⋊C8—24no—
302C4⋊C8—22no—
303#102—114no—
304#102—224no—
305#102—222no—
306C4×C8—22no—
307#95—222no—
308#95—221no—
309#95—222no—
310#95—222no—
311#95—222no—
312#95D4412yes—
313C2×C11#242911yescharacteristic
314C2×C11C2×#46411yescharacteristic
315C2×C11#304111yescharacteristic
316C2×C11#334111yescharacteristic
317C2×C11#335711yescharacteristic
318C2×C11#338011yescharacteristic
319C2×C11#338511yescharacteristic
320D11—82no—
321C24—221no—
322C2×Q8—224no—
323C2×Q8—442no—
324C2×Q8—881no—
325C2×Q8—881no—
326C2×Q8—881no—
327C2×Q8—881no—
328C2×D4—112no—
329C2×D4—221no—
330C2×D4—221no—
331C2×D4—221no—
332C2×D4—221no—
333C2×D4—221no—
334C22×C4—221no—
335C22×C4—222no—
336C22×C4—221no—
337C22×C4—221no—
338C22×C4—222no—
339C22×C4—442no—
340C22×C4—442no—
341C22×C4—442no—
342C22×C4C2×D4412yes—
343C22×C4C2×D4412yes—
344C22×C4C2×D4411yescharacteristic
345C22×C4C2×D4411yescharacteristic
346C22×C4C23×D1111yescharacteristic
347C2×C8—21no—
348C2×C8—21no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8—22no—
352C2×C8—22no—
353C2×C8—22no—
354C2×C8#434112yes—
355C2×C8Q8×D1112yes—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—114no—
359C4⋊C4—112no—
360C4⋊C4—224no—
361C4⋊C4—222no—
362C4⋊C4—221no—
363C4⋊C4—221no—
364C4⋊C4—222no—
365C4⋊C4—221no—
366C4⋊C4—221no—
367C4⋊C4—222no—
368C4⋊C4—221no—
369C4⋊C4—442no—
370C4⋊C4—882no—
371C22⋊C4—442no—
372C22⋊C4—882no—
373C22⋊C4—882no—
374C42—22no—
375C42—22no—
376C42—442no—
377C42—882no—
378C42D4×D1112yes—
379C42#434312yes—
380C11#2545011yescharacteristic, complemented, Sylow
381C23—222no—
382C23—441no—
383C23—441no—
384C23—441no—
385C23—441no—
386C23—441no—
387C23—441no—
388C23C22×D4411yescharacteristic
389Q8—884no—
390Q8—884no—
391D4—222no—
392D4—222no—
393D4—441no—
394D4—441no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—224no—
404C2×C4—222no—
405C2×C4—441no—
406C2×C4—441no—
407C2×C4—442no—
408C2×C4—442no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4—442no—
413C2×C4—442no—
414C2×C4—441no—
415C2×C4—441no—
416C2×C4—442no—
417C2×C4—441no—
418C2×C4—884no—
419C2×C4#6694812yes—
420C2×C4#6694812yes—
421C2×C4#6695712yes—
422C2×C4#6696212yes—
423C2×C4C2×D4×D1111yescharacteristic
424C2×C4C2×#434111yescharacteristic
425C2×C4C2×Q8×D1111yescharacteristic
426C2×C4C2×#434311yescharacteristic
427C2×C4#6704311yescharacteristic
428C2×C4#6704311yescharacteristic
429C8—22no—
430C8—22no—
431C8—42no—
432C22—442no—
433C22—442no—
434C22—442no—
435C22—881no—
436C22—881no—
437C22—881no—
438C22—881no—
439C22C2×#6694811yescharacteristic
440C22#1062308611yescharacteristic
441C22Q8×D4411yescharacteristic
442C22C2×#6695711yescharacteristic
443C22C2×#6696211yescharacteristic
444C22#1062328311yescharacteristic
445C22#1062328311yescharacteristic
446C4—22no—
447C4—42no—
448C4—42no—
449C4—444no—
450C4—442no—
451C4—881no—
452C4—882no—
453C4—881no—
454C4#1062245814yes—
455C4#1062312911yescharacteristic
456C4#1062316311yescharacteristic
457C4#1062322811yescharacteristic
458C4#1062325911yescharacteristic
459C2—882no—
460C2#1307221311yescharacteristic
461C2C2×#1062245811yescharacteristic
462C2#1307812011yescharacteristic
463C2#1308103911yescharacteristic
464C2#1308124311yescharacteristic
465C2#1308148411yescharacteristic
466C2#1308152811yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1939C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1939D11
hypocenterC11#25450
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. #13071705C2semidirect
5. #13070099C2semidirect
7. #13069563C2semidirect
8. #13069386C2semidirect
11. C11×#1939C2semidirect
84. #66885Q8semidirect
156. #1939D11semidirect
380. C11#25450semidirect

Maximal subgroups

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

subgroupindex
C2×#106222952
C2×#106224552
#130737852
#130717052
#130700992
#130700032
#130695632
#130693862
#130692372
C4×#668852
C11×#19392
#2545011