Finite Group Databasebeta

← #14908920

Subgroups — #14908920

Order 2816.

532 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077485C211yesmaximal, characteristic, complemented
2#13070821C211yesmaximal, characteristic, complemented
3#13070804C211yesmaximal, characteristic
4#13070765C211yesmaximal, characteristic, complemented
5#13070755C211yesmaximal, characteristic, complemented
6#13070675C211yesmaximal, characteristic, complemented
7#13070675C211yesmaximal, characteristic, complemented
8#13070549C211yesmaximal, characteristic, complemented
9#13070532C211yesmaximal, characteristic
10#13070485C211yesmaximal, characteristic, complemented
11#13070480C211yesmaximal, characteristic, complemented
12C4×#66893C211yesmaximal, characteristic, complemented
13C4×#66891C211yesmaximal, characteristic, complemented
14#13070423C211yesmaximal, characteristic, complemented
15C11×#3175C211yesmaximal, characteristic
16C11×#542—21no—
17C22×Dic44C2211yescharacteristic
18#10623047—21no—
19C11×#500C2211yescharacteristic
20C11×#495C2211yescharacteristic
21C11×#489—21no—
22C11×#468—21no—
23C11×#467C2211yescharacteristic
24C11×#466C2211yescharacteristic
25C11×#440—21no—
26C4×C11×Q16C2211yescharacteristic
27C4×C11×D8C2211yescharacteristic
28C11×#405C2211yescharacteristic
29C2×#66893C2211yescharacteristic
30C2×#66893C2211yescharacteristic
31C2×#66891C2211yescharacteristic
32C2×#66891C2211yescharacteristic
33#10622733—21no—
34#10622719C2211yescharacteristic
35#10622329—21no—
36#10622329—21no—
37C4×Dic44C2211yescharacteristic
38C4×Dic44C2211yescharacteristic
39C4×Dic44C2211yescharacteristic
40C4×Dic44C2211yescharacteristic
41#10622202C2211yescharacteristic
42#10622202C2211yescharacteristic
43#10622200C2211yescharacteristic
44#10622200C2211yescharacteristic
45C22⋊(C11⋊C16)C2211yescharacteristic
46C22⋊(C11⋊C16)C2211yescharacteristic
47#10622130C2211yescharacteristic
48#10622130C2211yescharacteristic
49#10622130C2211yescharacteristic
50#10622130C2211yescharacteristic
51#10622128C2211yescharacteristic
52#10622128C2211yescharacteristic
53#10622127C2211yescharacteristic
54#10622127C2211yescharacteristic
55C4⋊(C11⋊C16)C2211yescharacteristic
56C4⋊(C11⋊C16)C2211yescharacteristic
57#10622099C2211yescharacteristic
58C4×C11⋊C16C2211yescharacteristic
59C22×Dic22—21no—
60C2×C11×Q16C2311yescharacteristic
61C2×C11×SD16—21no—
62C2×C11×D8C2311yescharacteristic
63C2×C11×M16D411yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×C4⋊Q8—21no—
66C11×#126—41no—
67C11×#124—21no—
68C11×#124—41no—
69C11×#123—41no—
70C11×C22⋊Q8—21no—
71C11×C22⋊Q8—41no—
72C11×#121—21no—
73C4×Q8×C11—21no—
74C4×D4×C11—21no—
75C11×#117D411yescharacteristic
76#66979—21no—
77C2×Dic44—21no—
78C2×Dic44—22no—
79C2×Dic44—22no—
80C2×Dic44C2311yescharacteristic
81C2×Dic44C2311yescharacteristic
82#66940—41no—
83#66940—41no—
84#66930—41no—
85#66930—41no—
86C4×Dic22—21no—
87C4×Dic22—21no—
88C4×Dic22—21no—
89C4×Dic22—21no—
90C11×#107—21no—
91C11×#107C2311yescharacteristic
92C11×#107C2311yescharacteristic
93C11×#103—21no—
94C11×#103—21no—
95C11×#102—21no—
96C11×#102—21no—
97C11×#97D411yescharacteristic
98C11×#97D411yescharacteristic
99C4×C8×C11C2311yescharacteristic
100C4×C8×C11C2311yescharacteristic
101#66893—22no—
102#66893—22no—
103#66891—22no—
104#66891—22no—
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66881—21no—
108#66880—21no—
109#66880—21no—
110#66880—21no—
111#66880—21no—
112C2×C11⋊C16C2311yescharacteristic
113C2×C11⋊C16C2311yescharacteristic
114C2×C11⋊C16C2311yescharacteristic
115C2×C11⋊C16C2311yescharacteristic
116#33681—111nomaximal, Sylow
117C2×Q8×C11—21no—
118C2×Q8×C11—41no—
119C2×D4×C11—21no—
120C2×D4×C11—41no—
121C22×C4×C11—41no—
122C22×C4×C11C2×D411yescharacteristic
123C22×Dic11—41no—
124C2×Dic22—24no—
125C2×Dic22—21no—
126C2×Dic22—21no—
127C2×Dic22—42no—
128C2×Dic22—41no—
129C11×Q16—21no—
130C11×Q16—21no—
131C11×SD16—42no—
132C11×D8—21no—
133C11×D8—21no—
134C11×M16—41no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11C2×D411yescharacteristic
138C2×C8×C11C2×D411yescharacteristic
139C2×C8×C11C2×D411yescharacteristic
140C2×C8×C11C2411yescharacteristic
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—41no—
144C11×C4⋊C4—41no—
145C11×C4⋊C4—41no—
146C11×C4⋊C4D811yescharacteristic
147C11×C4⋊C4D811yescharacteristic
148C11×C22⋊C4—41no—
149C11×C22⋊C4—41no—
150C11×C22⋊C4—41no—
151C11×C22⋊C4—41no—
152C11×C22⋊C4—41no—
153C11×C22⋊C4D811yescharacteristic
154C11×C22⋊C4D811yescharacteristic
155C42×C11—41no—
156C42×C11C2×D411yescharacteristic
157C42×C11C2×D411yescharacteristic
158C22⋊Dic11—41no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161Dic11⋊C4—41no—
162Dic11⋊C4—41no—
163Dic11⋊C4—41no—
164Dic11⋊C4—41no—
165C4×Dic11—41no—
166C4×Dic11—41no—
167C4×Dic11—41no—
168C4×Dic11—41no—
169C4×Dic11—41no—
170Dic44—24no—
171Dic44—21no—
172Dic44—21no—
173Dic44#4112yes—
174Dic44#4112yes—
175C11⋊C16—21no—
176C11⋊C16—21no—
177C11⋊C16—21no—
178C11⋊C16—21no—
179#3175D1111yescharacteristic
180#2950—111no—
181#2237—111no—
182#2234—111no—
183#2227—111no—
184#2225—111no—
185#2211—111no—
186#2211—111no—
187#2188—111no—
188#2185—111no—
189#2176—111no—
190#2175—111no—
191C4×Q32—111no—
192C4×SD32—111no—
193#2164—111no—
194C23×C11—41no—
195C23×C11C2×D811yescharacteristic
196Q8×C11—41no—
197Q8×C11—41no—
198Q8×C11—161no—
199D4×C11—41no—
200D4×C11—41no—
201D4×C11—161no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—161no—
208C2×C4×C11C2×D811yescharacteristic
209C2×C4×C11C2×D811yescharacteristic
210C2×C4×C11C2×D811yescharacteristic
211C2×C4×C11C2×D811yescharacteristic
212C2×C4×C11C2×D811yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×Dic11—44no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219Dic22—22no—
220Dic22—22no—
221Dic22—44no—
222Dic22—41no—
223Dic22—41no—
224C8×C11—21no—
225C8×C11—21no—
226C8×C11—21no—
227C8×C11C2×#4111yescharacteristic
228C8×C11C2×#4111yescharacteristic
229C22×Q16—111no—
230#542—21no—
231#519—221no—
232C2×Q32—111no—
233C2×Q32—111no—
234C2×SD32—111no—
235C2×SD32—111no—
236#500C2×D1111yescharacteristic
237#495C2×D1111yescharacteristic
238#489—21no—
239#468—21no—
240#467C2×D1111yescharacteristic
241#466C2×D1111yescharacteristic
242#441—221no—
243#441—221no—
244#440—21no—
245C4×Q16—111no—
246C4×Q16—111no—
247C4×Q16—111no—
248C4×Q16—111no—
249C4×Q16C2×D1111yescharacteristic
250C4×D8C2×D1111yescharacteristic
251#427—111no—
252#419—221no—
253#405C2×D1111yescharacteristic
254#367—111no—
255#367—111no—
256#366—111no—
257#366—111no—
258C4⋊C16—111no—
259C4⋊C16—111no—
260#358—111no—
261#358—111no—
262#358—111no—
263#358—111no—
264#358—111no—
265#358—111no—
266#357—111no—
267#357—111no—
268C22⋊C16—111no—
269C22⋊C16—111no—
270#346—111no—
271C4×C16—111no—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11—81no—
276C22×C11—81no—
277C22×C11—81no—
278C22×C11C22×D811yescharacteristic
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—81no—
285C4×C11—81no—
286C4×C11—81no—
287C4×C11#52511yescharacteristic
288C4×C11#57511yescharacteristic
289Dic11—42no—
290Dic11—42no—
291Dic11—81no—
292Dic11—81no—
293C22×Q8—221no—
294C2×Q16—111no—
295C2×Q16—111no—
296C2×Q16—222no—
297C2×Q16—222no—
298C2×Q16—221no—
299C2×Q16C22×D1111yescharacteristic
300C2×SD16—21no—
301C2×D8C22×D1111yescharacteristic
302C2×M16C22⋊D1111yescharacteristic
303C22×C8C22×D1111yescharacteristic
304C4⋊Q8—21no—
305#126—41no—
306#124—21no—
307#124—41no—
308#123—41no—
309C22⋊Q8—21no—
310C22⋊Q8—41no—
311#121—21no—
312C4×Q8—21no—
313C4×Q8—221no—
314C4×Q8—221no—
315C4×Q8—221no—
316C4×Q8—221no—
317C4×Q8—441no—
318C4×Q8—441no—
319C4×D4—21no—
320#117—221no—
321#117—441no—
322#117—441no—
323#117C22⋊D1111yescharacteristic
324Q32—222no—
325Q32—222no—
326SD32—222no—
327SD32—222no—
328C2×C16—111no—
329C2×C16—111no—
330C2×C16—111no—
331C2×C16—111no—
332#107—21no—
333#107—111no—
334#107—111no—
335#107C22×D1111yescharacteristic
336#107C22×D1111yescharacteristic
337#106—221no—
338#103—21no—
339#103—21no—
340#103—221no—
341#103—221no—
342#103—221no—
343#103—221no—
344#102—21no—
345#102—21no—
346#97C22⋊D1111yescharacteristic
347#97C22⋊D1111yescharacteristic
348C4×C8C22×D1111yescharacteristic
349C4×C8C22×D1111yescharacteristic
350C2×C11—41no—
351C2×C11—161no—
352C2×C11#310011yescharacteristic
353C2×C11#341611yescharacteristic
354C2×C11#341711yescharacteristic
355C2×Q8—21no—
356C2×Q8—41no—
357C2×Q8—224no—
358C2×Q8—221no—
359C2×Q8—221no—
360C2×Q8—442no—
361C2×Q8—441no—
362C2×D4—21no—
363C2×D4—41no—
364C22×C4—41no—
365C22×C4—441no—
366C22×C4C2×C22⋊D1111yescharacteristic
367Q16—21no—
368Q16—21no—
369Q16—112no—
370Q16—112no—
371Q16—224no—
372Q16—221no—
373Q16—221no—
374SD16—42no—
375D8—21no—
376D8—21no—
377M16—41no—
378C2×C8—21no—
379C2×C8—21no—
380C2×C8C2×C22⋊D1111yescharacteristic
381C2×C8C2×C22⋊D1111yescharacteristic
382C2×C8C2×C22⋊D1111yescharacteristic
383C2×C8C23×D1111yescharacteristic
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—221no—
390C4⋊C4—221no—
391C4⋊C4—441no—
392C4⋊C4—441no—
393C4⋊C4—441no—
394C4⋊C4—441no—
395C4⋊C4#432311yescharacteristic
396C4⋊C4#432311yescharacteristic
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4—441no—
403C22⋊C4#432311yescharacteristic
404C22⋊C4#432311yescharacteristic
405C42—41no—
406C42—441no—
407C42—441no—
408C42—441no—
409C42—441no—
410C42—441no—
411C42C2×C22⋊D1111yescharacteristic
412C42C2×C22⋊D1111yescharacteristic
413C16—221no—
414C16—221no—
415C16—221no—
416C16—221no—
417C11#3368111yescharacteristic, complemented, Sylow
418C23—41no—
419C23C2×#432311yescharacteristic
420Q8—41no—
421Q8—41no—
422Q8—161no—
423Q8—222no—
424Q8—222no—
425Q8—444no—
426Q8—441no—
427Q8—441no—
428D4—41no—
429D4—41no—
430D4—161no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—161no—
437C2×C4—444no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4C2×#432311yescharacteristic
443C2×C4C2×#432311yescharacteristic
444C2×C4C2×#432311yescharacteristic
445C2×C4C2×#432311yescharacteristic
446C2×C4C2×#432311yescharacteristic
447C2×C4C22×C22⋊D1111yescharacteristic
448C8—21no—
449C8—21no—
450C8—21no—
451C8#41×D1111yescharacteristic
452C8#41×D1111yescharacteristic
453C22—21no—
454C22—21no—
455C22—21no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22C22×#432311yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—81no—
466C4—81no—
467C4—81no—
468C4—442no—
469C4—442no—
470C4—881no—
471C4—881no—
472C4#1062335311yescharacteristic
473C4#1062335911yescharacteristic
474C2—41no—
475C2—161no—
476C2#1307861211yescharacteristic
477C2#1308176311yescharacteristic
478C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3175C2
socleC22×C11C22×D8
prime radicalC11×#466C22
hypercenter#3175D11
hypocenterC11#33681
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3175

Complements

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

NH ≅ G/Ntype
1. #13077485C2semidirect
2. #13070821C2semidirect
4. #13070765C2semidirect
5. #13070755C2semidirect
6. #13070675C2semidirect
7. #13070675C2semidirect
8. #13070549C2semidirect
10. #13070485C2semidirect
11. #13070480C2semidirect
12. C4×#66893C2semidirect
13. C4×#66891C2semidirect
14. #13070423C2semidirect
417. C11#33681semidirect

Maximal subgroups

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

subgroupindex
#130774852
#130708212
#130708042
#130707652
#130707552
#130706752
#130705492
#130705322
#130704852
#130704802
C4×#668932
C4×#668912
#130704232
C11×#31752
#3368111