Finite Group Databasebeta

← #14908854

Subgroups — #14908854

Order 2816.

548 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079197C211yesmaximal, characteristic, complemented
2#13077387C211yesmaximal, characteristic
3#13070824C211yesmaximal, characteristic, complemented
4#13070767C211yesmaximal, characteristic, complemented
5#13070762C211yesmaximal, characteristic, complemented
6#13070665C211yesmaximal, characteristic, complemented
7#13070660C211yesmaximal, characteristic, complemented
8#13070558C211yesmaximal, characteristic
9#13070554C211yesmaximal, characteristic
10#13070486C211yesmaximal, characteristic, complemented
11#13070484C211yesmaximal, characteristic, complemented
12#13070483C211yesmaximal, characteristic, complemented
13#13070479C211yesmaximal, characteristic, complemented
14#13070416C211yesmaximal, characteristic, complemented
15C11×#2237C211yesmaximal, characteristic, complemented
16C2×#66957C2211yescharacteristic
17#10623153—21no—
18#10623053—21no—
19C11×#467C2211yescharacteristic
20C11×#427C2211yescharacteristic
21Q16×Dic11C2211yescharacteristic
22#10622794C2211yescharacteristic
23C2×#66893C2211yescharacteristic
24C2×#66892C2211yescharacteristic
25#10622729C2211yescharacteristic
26C2×C8×Dic11C2211yescharacteristic
27#10622664—21no—
28#10622615—21no—
29C2×Dic88C2211yescharacteristic
30C2×#66864C2211yescharacteristic
31#10622487C2211yescharacteristic
32#10622486C2211yescharacteristic
33#10622486C2211yescharacteristic
34#10622486C2211yescharacteristic
35#10622485C2211yescharacteristic
36#10622485C2211yescharacteristic
37#10622465—21no—
38#10622465—21no—
39#10622405—21no—
40#10622403—21no—
41C11×#367C2211yescharacteristic
42C11×#366C2211yescharacteristic
43C11×#358C2211yescharacteristic
44C11×#358C2211yescharacteristic
45C11×C22⋊C16C2211yescharacteristic
46C22⋊(C11⋊C16)C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622141C2211yescharacteristic
49#10622140C2211yescharacteristic
50#10622140C2211yescharacteristic
51Dic11⋊C16C2211yescharacteristic
52Dic11⋊C16C2211yescharacteristic
53#10622130C2211yescharacteristic
54#10622130C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622129C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622127C2211yescharacteristic
59C2×#4339—21no—
60C2×C11×Q16C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C11×C22⋊Q8—21no—
63C11×#117—21no—
64Q8×Dic11—21no—
65#66997—21no—
66C2×#4326—21no—
67#66977—21no—
68C2×C4×Dic11D411yescharacteristic
69C22×C11⋊C8D411yescharacteristic
70C2×Dic44C2311yescharacteristic
71C2×Dic44C2311yescharacteristic
72#66957—22no—
73#66957—22no—
74C2×D88C2311yescharacteristic
75C2×#4314—21no—
76#66946—21no—
77#66946—21no—
78#66942—41no—
79#66941—21no—
80#66940—21no—
81#66940—21no—
82#66940—21no—
83#66940—41no—
84(C22⋊D11)⋊C4—41no—
85(C22⋊D11)⋊C4—41no—
86#66931—41no—
87#66930—41no—
88#66925—41no—
89C42×D11—41no—
90C2×C11×C16C2311yescharacteristic
91C2×C11×C16C2311yescharacteristic
92C11×#107C2311yescharacteristic
93C11×#107C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#106—21no—
96C11×#103—21no—
97#66899—21no—
98#66893—22no—
99#66892—22no—
100#66882C2311yescharacteristic
101#66880—21no—
102C8×Dic11D411yescharacteristic
103C8×Dic11D411yescharacteristic
104C8×Dic11C2311yescharacteristic
105C8×Dic11C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108#66874—21no—
109#66874—21no—
110#66874—21no—
111#66873—21no—
112#66873—21no—
113#66871—21no—
114Dic88—22no—
115#66864—22no—
116#33676—111nomaximal, Sylow
117C2×Q8×C11—21no—
118C22×C4×C11C2×D411yescharacteristic
119C2×C22⋊D11—41no—
120C22×Dic11D811yescharacteristic
121C22×Dic11D811yescharacteristic
122#4339—24no—
123#4339—42no—
124C2×D44—21no—
125C2×C4×D11—41no—
126C2×C4×D11—41no—
127C2×C4×D11—41no—
128C2×Dic22—21no—
129C2×Dic22—21no—
130C2×Dic22—41no—
131C11×Q16—21no—
132C11×Q16—21no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11C2×D411yescharacteristic
136C2×C8×C11C2411yescharacteristic
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—41no—
141C11×C22⋊C4—41no—
142C11×C22⋊C4—41no—
143C42×C11—41no—
144C22⋊Dic11—41no—
145#4326—42no—
146(C2×D11)⋊C4—41no—
147(C2×D11)⋊C4—41no—
148C4⋊Dic11—21no—
149C4⋊Dic11—41no—
150Dic11⋊C4—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157C4×Dic11—41no—
158C4×Dic11—41no—
159C4×Dic11—41no—
160C4×Dic11—41no—
161C4×Dic11D811yescharacteristic
162C4×Dic11D811yescharacteristic
163C4×Dic11C2×D411yescharacteristic
164C4×Dic11C2×D411yescharacteristic
165C2×C11⋊C8—41no—
166C2×C11⋊C8C2×D411yescharacteristic
167C2×C11⋊C8C2×D411yescharacteristic
168Dic44—21no—
169Dic44—21no—
170Dic44—21no—
171Dic44#4112yes—
172D88—21no—
173D88#4112yes—
174#4314—24no—
175C11×C16—21no—
176C11×C16—21no—
177C11⋊C16—21no—
178C11⋊C16—21no—
179#3170—111no—
180C4×#135—111no—
181#2237—111no—
182#2237D1111yescharacteristic, complemented
183#2227—111no—
184#2226—111no—
185#2209—111no—
186#2208—111no—
187#2189—111no—
188#2189—111no—
189#2176—111no—
190#2176—111no—
191#2175—111no—
192#2175—111no—
193#2163—111no—
194C23×C11C2×D811yescharacteristic
195C22×D11—41no—
196Q8×C11—41no—
197Q8×C11—41no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11C2×D811yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C22⋊D11—44no—
207C2×Dic11—22no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11C2×D811yescharacteristic
213C2×Dic11C2×D811yescharacteristic
214C2×Dic11C2×D811yescharacteristic
215C2×Dic11C2×D811yescharacteristic
216D44—22no—
217D44—41no—
218C4×D11—44no—
219C4×D11—82no—
220C4×D11—82no—
221Dic22—22no—
222Dic22—41no—
223Dic22—41no—
224Dic22—41no—
225Dic22—82no—
226C8×C11—21no—
227C8×C11C2×#4111yescharacteristic
228C8×C11C2×#4111yescharacteristic
229C11⋊C8—21no—
230C11⋊C8—21no—
231C2×#135—111no—
232#533—221no—
233C4×#41—221no—
234C2×Q32—111no—
235C2×Q32—111no—
236C2×SD32—111no—
237C2×SD32—111no—
238#500—111no—
239#494—111no—
240#487—221no—
241#467—111no—
242#467—221no—
243#467C2×D1111yescharacteristic
244C4×Q16—111no—
245C4×Q16—111no—
246C4×Q16—111no—
247C4×Q16—111no—
248C4×Q16—221no—
249C4×SD16—221no—
250C4×SD16—221no—
251C4×D8—111no—
252C4×D8—111no—
253#427C2×D1111yescharacteristic
254#416—221no—
255C2×C4×C8—111no—
256#367—111no—
257#367C2×D1111yescharacteristic
258#366—111no—
259#366C2×D1111yescharacteristic
260C4⋊C16—111no—
261C4⋊C16—111no—
262#358—111no—
263#358—111no—
264#358—111no—
265#358—111no—
266#358C2×D1111yescharacteristic
267#358C2×D1111yescharacteristic
268#357—111no—
269#357—111no—
270C22⋊C16—111no—
271C22⋊C16C2×D1111yescharacteristic
272#346—111no—
273#346—111no—
274C22×C11—21no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11C22×D811yescharacteristic
278C2×D11—42no—
279C2×D11—81no—
280C2×D11—81no—
281C4×C11—21no—
282C4×C11—81no—
283C4×C11—81no—
284C4×C11—81no—
285C4×C11—81no—
286C4×C11#52511yescharacteristic
287C4×C11#57511yescharacteristic
288Dic11—21no—
289Dic11—21no—
290Dic11—21no—
291Dic11—42no—
292Dic11—81no—
293Dic11—81no—
294Dic11#51012yes—
295C2×#41—221no—
296#135—222no—
297#135—222no—
298C2×Q16—111no—
299C2×Q16—111no—
300C2×Q16—221no—
301C2×Q16C22×D1111yescharacteristic
302C2×SD16—221no—
303C2×D8—111no—
304C22×C8—111no—
305C22×C8C22×D1111yescharacteristic
306C4⋊Q8—221no—
307C4⋊Q8—221no—
308#125—441no—
309C22⋊Q8—21no—
310C22⋊Q8—221no—
311C22⋊Q8—441no—
312C4×Q8—221no—
313C4×Q8—221no—
314C4×Q8—221no—
315C4×Q8—221no—
316C4×Q8—441no—
317C4×D4—221no—
318C4×D4—221no—
319C4×D4—441no—
320C4×D4—441no—
321#117—21no—
322#117—441no—
323#117—441no—
324C2×C42—111no—
325C2×C42—441no—
326Q32—222no—
327Q32—222no—
328SD32—222no—
329SD32—222no—
330C2×C16—111no—
331C2×C16—111no—
332C2×C16C22×D1111yescharacteristic
333C2×C16C22×D1111yescharacteristic
334#107—111no—
335#107—221no—
336#107C22×D1111yescharacteristic
337#107C22×D1111yescharacteristic
338#107C22×D1111yescharacteristic
339#106—21no—
340#103—21no—
341#103—221no—
342#103—221no—
343#103—221no—
344#103—221no—
345#103—221no—
346#102—221no—
347#102—221no—
348C4×C8—111no—
349C4×C8—111no—
350C4×C8—111no—
351C4×C8—111no—
352C2×C11—41no—
353C2×C11#310011yescharacteristic
354C2×C11C2×#51011yescharacteristic
355C2×C11#341411yescharacteristic
356D11—82no—
357#41—224no—
358#41—442no—
359C2×Q8—21no—
360C2×Q8—221no—
361C2×Q8—221no—
362C2×Q8—441no—
363C2×D4—221no—
364C2×D4—441no—
365C22×C4—111no—
366C22×C4—111no—
367C22×C4—441no—
368C22×C4—441no—
369C22×C4—441no—
370C22×C4D4×D1111yescharacteristic
371Q16—21no—
372Q16—21no—
373Q16—112no—
374Q16—221no—
375Q16—221no—
376Q16—221no—
377Q16—442no—
378SD16—224no—
379D8—112no—
380D8—221no—
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—111no—
384C2×C8—111no—
385C2×C8—441no—
386C2×C8D4×D1111yescharacteristic
387C2×C8C23×D1111yescharacteristic
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—41no—
392C4⋊C4—221no—
393C4⋊C4—441no—
394C4⋊C4—441no—
395C4⋊C4—441no—
396C4⋊C4—441no—
397C4⋊C4—441no—
398C4⋊C4—441no—
399C4⋊C4—441no—
400C4⋊C4—441no—
401C22⋊C4—41no—
402C22⋊C4—41no—
403C22⋊C4—441no—
404C22⋊C4—441no—
405C22⋊C4—441no—
406C42—41no—
407C42—111no—
408C42—111no—
409C42—111no—
410C42—111no—
411C42—441no—
412C42—441no—
413C42—441no—
414C42—441no—
415C16—21no—
416C16—21no—
417C16—221no—
418C16—221no—
419C11#3367611yescharacteristic, complemented, Sylow
420C23—441no—
421C23D8×D1111yescharacteristic
422Q8—41no—
423Q8—41no—
424Q8—222no—
425Q8—441no—
426Q8—441no—
427Q8—441no—
428Q8—882no—
429D4—222no—
430D4—444no—
431D4—441no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—111no—
439C2×C4—111no—
440C2×C4—111no—
441C2×C4—111no—
442C2×C4—222no—
443C2×C4—444no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4—882no—
449C2×C4—882no—
450C2×C4D8×D1111yescharacteristic
451C2×C4C2×D4×D1111yescharacteristic
452C8—21no—
453C8—221no—
454C8—221no—
455C8#41×D1111yescharacteristic
456C8#41×D1111yescharacteristic
457C22—21no—
458C22—21no—
459C22—21no—
460C22—442no—
461C22—881no—
462C22—881no—
463C22C2×D8×D1111yescharacteristic
464C4—21no—
465C4—81no—
466C4—81no—
467C4—81no—
468C4—81no—
469C4—112no—
470C4—221no—
471C4—221no—
472C4—221no—
473C4—442no—
474C4—881no—
475C4—881no—
476C4#1062318711yescharacteristic
477C4#1062330811yescharacteristic
478C2—41no—
479C2—882no—
480C2#1307861311yescharacteristic
481C2D11×#51011yescharacteristic
482C2#1308174911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2237C2
socleC22×C11C22×D8
prime radicalC2×#66957C22
hypercenter#2237D11
hypocenterC11#33676
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2237

Complements

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

NH ≅ G/Ntype
1. #13079197C2semidirect
3. #13070824C2semidirect
4. #13070767C2semidirect
5. #13070762C2semidirect
6. #13070665C2semidirect
7. #13070660C2semidirect
10. #13070486C2semidirect
11. #13070484C2semidirect
12. #13070483C2semidirect
13. #13070479C2semidirect
14. #13070416C2semidirect
15. C11×#2237C2semidirect
182. #2237D11semidirect
419. C11#33676semidirect

Maximal subgroups

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

subgroupindex
#130791972
#130773872
#130708242
#130707672
#130707622
#130706652
#130706602
#130705582
#130705542
#130704862
#130704842
#130704832
#130704792
#130704162
C11×#22372
#3367611