Finite Group Databasebeta

← #14805362

Subgroups — #14805362

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×#10622691C211yesmaximal, characteristic, complemented
2#13073789C211yesmaximal, characteristic
3#13071706C211yesmaximal, characteristic, complemented
4#13070101C212yesmaximal, complemented
5#13070000C212yesmaximal
6#13069563C211yesmaximal, characteristic, complemented
7#13069385C212yesmaximal, complemented
8#13069332C211yesmaximal, characteristic, complemented
9#13069239C212yesmaximal
10C4×#66896C211yesmaximal, characteristic
11C2×C11×#476C211yesmaximal, characteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66922C2211yescharacteristic
15C11×#476—24no—
16C2×C11×#106C2212yes—
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#102C2212yes—
19#10622843—22no—
20#10622834C2212yes—
21C2×#66896C2211yescharacteristic
22C2×#66896C2211yescharacteristic
23#10622825—21no—
24#10622825—21no—
25C2×Dic11⋊C8C2212yes—
26#10622691—24no—
27#10622598—21no—
28#10622598C2212yes—
29#10622590C2212yes—
30C4⋊C4×Dic11—21no—
31C4⋊C4×Dic11C2212yes—
32C2×#66871C2212yes—
33C2×#66871C2212yes—
34#10622560—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—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11D411yescharacteristic
62C2×C4⋊Dic11D411yescharacteristic
63C2×C4⋊Dic11C2312yes—
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4×Dic11—21no—
67C2×C4×Dic11—22no—
68C2×C4×Dic11C2312yes—
69C22×C11⋊C8C2311yescharacteristic
70C22×C11⋊C8C2311yescharacteristic
71#66922—22no—
72#66922—22no—
73C11×#106—24no—
74C11×C4⋊C8—22no—
75C11×#102—24no—
76#66896—22no—
77#66896Q814yescomplemented
78C11⋊#95—21no—
79C11⋊#95—22no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83C11⋊#95D412yes—
84Dic11⋊C8—24no—
85#66871—24no—
86#66871—24no—
87C4×C11⋊C8—22no—
88#25450—111nomaximal, Sylow
89C24×C11—21no—
90C2×Q8×C11—24no—
91C2×Q8×C11—81no—
92C2×Q8×C11—81no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11C2×Q812yes—
99C22×C4×C11—22no—
100C22×C4×C11—21no—
101C22×C4×C11—42no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2411yescharacteristic
107C22×Dic11—21no—
108C22×Dic11—21no—
109C22×Dic11—22no—
110C22×Dic11C2×D412yes—
111C22×Dic11C2×D412yes—
112C2×Dic22—42no—
113C2×Dic22—81no—
114C2×Dic22—81no—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4C2×D414yes—
123C11×C22⋊C4—42no—
124C42×C11C2×D412yes—
125C42×C11#4112yes—
126C22⋊Dic11—82no—
127C22⋊Dic11—82no—
128C4⋊Dic11—22no—
129C4⋊Dic11—22no—
130C4⋊Dic11—22no—
131C4⋊Dic11—21no—
132C4⋊Dic11—22no—
133C4⋊Dic11—21no—
134C4⋊Dic11—21no—
135C4⋊Dic11—42no—
136C4⋊Dic11—82no—
137C4⋊Dic11C2×Q812yes—
138C4×Dic11—22no—
139C4×Dic11—22no—
140C4×Dic11—42no—
141C4×Dic11—82no—
142C2×C11⋊C8—21no—
143C2×C11⋊C8—21no—
144C2×C11⋊C8—21no—
145C2×C11⋊C8—21no—
146C2×C11⋊C8C2×Q812yes—
147C2×C11⋊C8#4112yes—
148C2×#500—111no—
149C2×#476D1111yescharacteristic
150#2563—111no—
151#2369—111no—
152#2085—112no—
153#2067—112no—
154#1987—111no—
155#1949—112no—
156#1939—111no—
157#1925—112no—
158C4×#102—111no—
159C23×C11—22no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11C22×D411yescharacteristic
167Q8×C11—84no—
168D4×C11—22no—
169D4×C11—22no—
170D4×C11—41no—
171D4×C11—41no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—24no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—84no—
181C2×C4×C11#12112yes—
182C2×C4×C11#12112yes—
183C2×C4×C11#13512yes—
184C2×C4×C11#13712yes—
185C2×C4×C11C22×D411yescharacteristic
186C2×C4×C11C22×Q811yescharacteristic
187C2×C4×C11C2×#4111yescharacteristic
188C2×C4×C11C2×#4111yescharacteristic
189C2×C4×C112−1+411yescharacteristic
190C2×C4×C112−1+411yescharacteristic
191C2×Dic11—22no—
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—42no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206Dic22—84no—
207C8×C11—42no—
208C11⋊C8—22no—
209C11⋊C8—22no—
210C2×C4⋊Q8—111no—
211C2×C4⋊Q8C2×D1111yescharacteristic
212C2×C4×D4C2×D1111yescharacteristic
213#500—224no—
214#476—24no—
215C2×#107—112no—
216C2×#107—112no—
217C2×#106C2×D1112yes—
218C2×C4⋊C8—112no—
219C2×C4⋊C8C2×D1111yescharacteristic
220C2×#102—111no—
221C2×#102—111no—
222C2×#102C2×D1112yes—
223C2×C4×C8—111no—
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—111no—
233C4×C4⋊C4—112no—
234C4×C4⋊C4—111no—
235C4×C4⋊C4—221no—
236#340—112no—
237#340—112no—
238#340—111no—
239#340—111no—
240#336—112no—
241C22×C11—42no—
242C22×C11—42no—
243C22×C11—42no—
244C22×C11—81no—
245C22×C11—81no—
246C22×C11—81no—
247C22×C11—81no—
248C22×C11C2×#12111yescharacteristic
249C22×C11#54711yescharacteristic
250C22×C11D4×Q811yescharacteristic
251C22×C11C2×#13511yescharacteristic
252C22×C11C2×#13711yescharacteristic
253C22×C11#57611yescharacteristic
254C22×C11#57611yescharacteristic
255C4×C11—22no—
256C4×C11—44no—
257C4×C11—81no—
258C4×C11#46414yes—
259C4×C11#53311yescharacteristic
260C4×C11#54111yescharacteristic
261C4×C11#54811yescharacteristic
262C4×C11D4×Q811yescharacteristic
263Dic11—42no—
264Dic11—42no—
265Dic11—42no—
266Dic11—81no—
267Dic11—82no—
268C22×Q8—21no—
269C22×Q8—221no—
270C22×D4C22×D1111yescharacteristic
271C23×C4—21no—
272C22×C8—111no—
273C22×C8—111no—
274C22×C8C22×D1112yes—
275C4⋊Q8—22no—
276C4⋊Q8—222no—
277C4⋊Q8—222no—
278C4⋊Q8C22⋊D1114yes—
279C4×D4—22no—
280C4×D4—22no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—111no—
283C2×C4⋊C4—111no—
284C2×C4⋊C4—111no—
285C2×C4⋊C4—112no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4—222no—
289C2×C4⋊C4C22×D1111yescharacteristic
290C2×C4⋊C4C22×D1112yes—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—222no—
293C2×C22⋊C4—222no—
294C2×C42—112no—
295C2×C42—221no—
296C2×C42—222no—
297C2×C42C22×D1111yescharacteristic
298#107—224no—
299#107—224no—
300#106—24no—
301C4⋊C8—22no—
302C4⋊C8—224no—
303#102—24no—
304#102—114no—
305#102—222no—
306C4×C8—222no—
307#95—112no—
308#95—222no—
309#95—222no—
310#95—222no—
311#95—222no—
312#95—221no—
313C2×C11—82no—
314C2×C11#242911yescharacteristic
315C2×C11C2×#46411yescharacteristic
316C2×C11#304111yescharacteristic
317C2×C11#334111yescharacteristic
318C2×C11#335711yescharacteristic
319C2×C11#338011yescharacteristic
320C2×C11#338511yescharacteristic
321C24—21no—
322C2×Q8—24no—
323C2×Q8—81no—
324C2×Q8—81no—
325C2×Q8—442no—
326C2×Q8—881no—
327C2×Q8—881no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4Q8×D1112yes—
334C22×C4—22no—
335C22×C4—21no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—112no—
340C22×C4—112no—
341C22×C4—221no—
342C22×C4—221no—
343C22×C4—222no—
344C22×C4D4×D1111yescharacteristic
345C22×C4D4×D1111yescharacteristic
346C22×C4C23×D1111yescharacteristic
347C2×C8—22no—
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—112no—
351C2×C8—112no—
352C2×C8—221no—
353C2×C8—221no—
354C2×C8—221no—
355C2×C8—221no—
356C4⋊C4—24no—
357C4⋊C4—22no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—112no—
361C4⋊C4—222no—
362C4⋊C4—222no—
363C4⋊C4—221no—
364C4⋊C4—222no—
365C4⋊C4—221no—
366C4⋊C4—221no—
367C4⋊C4—222no—
368C4⋊C4—442no—
369C4⋊C4—882no—
370C4⋊C4C2×C22⋊D1114yes—
371C22⋊C4—42no—
372C22⋊C4—882no—
373C22⋊C4—882no—
374C42—222no—
375C42—222no—
376C42—442no—
377C42—882no—
378C42#434112yes—
379C42C2×C22⋊D1112yes—
380C11#2545011yescharacteristic, complemented, Sylow
381C23—22no—
382C23—41no—
383C23—41no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23C2×D4×D1111yescharacteristic
389Q8—84no—
390Q8—884no—
391D4—22no—
392D4—22no—
393D4—41no—
394D4—41no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—24no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—84no—
404C2×C4—222no—
405C2×C4—222no—
406C2×C4—222no—
407C2×C4—222no—
408C2×C4—222no—
409C2×C4—222no—
410C2×C4—222no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—442no—
415C2×C4—442no—
416C2×C4—441no—
417C2×C4—442no—
418C2×C4—441no—
419C2×C4#6696812yes—
420C2×C4#6696912yes—
421C2×C4#6699212yes—
422C2×C4#6699212yes—
423C2×C4C2×#434111yescharacteristic
424C2×C4C2×Q8×D1111yescharacteristic
425C2×C4#6704011yescharacteristic
426C2×C4#41×D1111yescharacteristic
427C2×C4#6704311yescharacteristic
428C2×C4C22×C22⋊D1111yescharacteristic
429C8—42no—
430C8—222no—
431C8—222no—
432C22—42no—
433C22—42no—
434C22—42no—
435C22—81no—
436C22—81no—
437C22—81no—
438C22—81no—
439C22#1062316211yescharacteristic
440C22#1062316311yescharacteristic
441C22C2×#6696811yescharacteristic
442C22C2×#6696911yescharacteristic
443C22#1062330511yescharacteristic
444C22#1062330511yescharacteristic
445C22C2×#6699211yescharacteristic
446C4—22no—
447C4—44no—
448C4—81no—
449C4—442no—
450C4—442no—
451C4—442no—
452C4—882no—
453C4—881no—
454C4#1062277914yes—
455C4#1062315311yescharacteristic
456C4#1062315611yescharacteristic
457C4Q8×C22⋊D1111yescharacteristic
458C4#1062336211yescharacteristic
459C2—82no—
460C2#1307221711yescharacteristic
461C2C2×#1062277911yescharacteristic
462C2#1307812111yescharacteristic
463C2#1308103711yescharacteristic
464C2#1308124511yescharacteristic
465C2#1308148211yescharacteristic
466C2#1308153011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#476C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#476D11
hypocenterC11#25450
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#10622691C2semidirect
3. #13071706C2semidirect
4. #13070101C2semidirect
6. #13069563C2semidirect
7. #13069385C2semidirect
8. #13069332C2semidirect
77. #66896Q8semidirect
380. C11#25450semidirect

Maximal subgroups

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

subgroupindex
C2×#106226912
#130737892
#130717062
#130701012
#130700002
#130695632
#130693852
#130693322
#130692392
C4×#668962
C2×C11×#4762
#2545011