Finite Group Databasebeta

← #14908825

Subgroups — #14908825

Order 2816.

542 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079199C211yesmaximal, characteristic
2C4×Q16×D11C211yesmaximal, characteristic
3#13070815C211yesmaximal, characteristic
4#13070812C211yesmaximal, characteristic
5#13070757C211yesmaximal, characteristic, complemented
6#13070756C211yesmaximal, characteristic, complemented
7#13070665C211yesmaximal, characteristic, complemented
8#13070664C211yesmaximal, characteristic, complemented
9#13070551C211yesmaximal, characteristic
10#13070548C211yesmaximal, characteristic
11#13070488C211yesmaximal, characteristic, complemented
12#13070485C211yesmaximal, characteristic, complemented
13#13070485C211yesmaximal, characteristic, complemented
14#13070417C211yesmaximal, characteristic
15C11×#2176C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic
17#10623109—21no—
18C4×Q8×D11—21no—
19C2×C11×Q32C2211yescharacteristic
20C4×C11×Q16C2211yescharacteristic
21C4×C11×Q16C2211yescharacteristic
22#10622801C2211yescharacteristic
23Q16×Dic11C2211yescharacteristic
24#10622794C2211yescharacteristic
25C2×#66893C2211yescharacteristic
26C2×#66893C2211yescharacteristic
27C4×#4326—21no—
28C4×#4326—21no—
29C2×Dic88C2211yescharacteristic
30#10622500C2211yescharacteristic
31D11×#107C2211yescharacteristic
32#10622487C2211yescharacteristic
33#10622486C2211yescharacteristic
34#10622426—21no—
35D11×#103—21no—
36#10622405—21no—
37#10622403—21no—
38C4×Dic44C2211yescharacteristic
39C4×Dic44C2211yescharacteristic
40C4×C8×D11C2211yescharacteristic
41C11×#367C2211yescharacteristic
42C11×#358C2211yescharacteristic
43C11×#358C2211yescharacteristic
44C11×#346C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622202C2211yescharacteristic
47(C2×D11)⋊C16C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49#10622143C2211yescharacteristic
50#10622141C2211yescharacteristic
51#10622141C2211yescharacteristic
52Dic11⋊C16C2211yescharacteristic
53Dic11⋊C16C2211yescharacteristic
54#10622130C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622099C2211yescharacteristic
59C2×Q8×D11—21no—
60C2×C11×Q16C2311yescharacteristic
61C2×C11×Q16C2311yescharacteristic
62C4×Q8×C11—21no—
63C4×Q8×C11—21no—
64#66999—21no—
65Q8×Dic11—21no—
66#66997—21no—
67C2×#4326—21no—
68C2×#4326—21no—
69Q16×D11—22no—
70Q16×D11—22no—
71C2×Dic44C2311yescharacteristic
72C2×Dic44C2311yescharacteristic
73C2×C8×D11D411yescharacteristic
74C2×C8×D11C2311yescharacteristic
75#66950—21no—
76#66949—41no—
77C4⋊C4×D11—21no—
78C4⋊C4×D11—41no—
79#66942—41no—
80#66941—21no—
81#66940—21no—
82#66940—41no—
83#66925—41no—
84C42×D11—41no—
85C42×D11D411yescharacteristic
86C4×Dic22—21no—
87C4×Dic22—21no—
88C4×Dic22—41no—
89C4×Dic22—41no—
90C11×Q32—22no—
91C2×C11×C16C2311yescharacteristic
92C2×C11×C16C2311yescharacteristic
93C11×#107C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#103—21no—
96C11×#103—21no—
97C4×C8×C11C2311yescharacteristic
98#66899—21no—
99#66899—21no—
100#66893—22no—
101#66893—22no—
102#66882C2311yescharacteristic
103#66882C2311yescharacteristic
104#66880—21no—
105#66880—21no—
106C8×Dic11D411yescharacteristic
107C8×Dic11C2311yescharacteristic
108C2×C11⋊C16C2311yescharacteristic
109C2×C11⋊C16C2311yescharacteristic
110#66874—21no—
111#66874—21no—
112#66871—21no—
113#66871—21no—
114C4×C11⋊C8D411yescharacteristic
115Dic88—22no—
116#33673—111nomaximal, Sylow
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119Q8×D11—24no—
120Q8×D11—42no—
121C2×C4×D11—41no—
122C2×C4×D11—41no—
123C2×C4×D11D811yescharacteristic
124C2×C4×D11D811yescharacteristic
125C2×C4×D11C2×D411yescharacteristic
126C2×Dic22—21no—
127C2×Dic22—21no—
128C2×Dic22—41no—
129C2×Dic22—41no—
130C11×Q16—21no—
131C11×Q16—21no—
132C11×Q16—21no—
133C11×Q16#4112yes—
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11C2411yescharacteristic
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—41no—
139C11×C4⋊C4—41no—
140C42×C11—41no—
141C42×C11—41no—
142C42×C11C2×D411yescharacteristic
143#4326—24no—
144#4326—42no—
145(C2×D11)⋊C4—41no—
146(C2×D11)⋊C4—41no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—41no—
150C4⋊Dic11—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4—41no—
159C4×Dic11—41no—
160C4×Dic11—41no—
161C4×Dic11—41no—
162C4×Dic11—41no—
163C4×Dic11D811yescharacteristic
164C4×Dic11D811yescharacteristic
165C4×Dic11C2×D411yescharacteristic
166C2×C11⋊C8C2×D411yescharacteristic
167C2×C11⋊C8C2×D411yescharacteristic
168Dic44—21no—
169Dic44—21no—
170Dic44—21no—
171Dic44#4112yes—
172C8×D11—21no—
173C8×D11—21no—
174C8×D11—41no—
175C11×C16—21no—
176C11×C16—21no—
177C11⋊C16—21no—
178C11⋊C16—21no—
179#3170—111no—
180C2×C4×Q16—111no—
181#2235—111no—
182#2235—111no—
183#2225—111no—
184#2225—111no—
185#2209—111no—
186#2209—111no—
187#2188—111no—
188#2188—111no—
189#2176—111no—
190#2176—111no—
191#2176—111no—
192#2176D1111yescharacteristic, complemented
193#2163—111no—
194C22×D11C2×D811yescharacteristic
195Q8×C11—22no—
196Q8×C11—41no—
197Q8×C11—41no—
198Q8×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11C2×D811yescharacteristic
204C2×C4×C11C2×D811yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11C2×D811yescharacteristic
211C2×Dic11C2×D811yescharacteristic
212C2×Dic11C2×D811yescharacteristic
213C4×D11—22no—
214C4×D11—21no—
215C4×D11—21no—
216C4×D11—22no—
217C4×D11—44no—
218C4×D11—82no—
219Dic22—22no—
220Dic22—44no—
221Dic22—41no—
222Dic22—41no—
223Dic22—41no—
224Dic22—82no—
225C8×C11—21no—
226C8×C11C2×#4111yescharacteristic
227C8×C11C2×#4111yescharacteristic
228C11⋊C8—21no—
229C11⋊C8—21no—
230C22×Q16—111no—
231#533—221no—
232C2×C4×Q8—221no—
233C2×Q32—111no—
234C2×Q32—111no—
235C2×Q32—111no—
236C2×Q32C2×D1111yescharacteristic
237#500—111no—
238#494—111no—
239#487—221no—
240#467—111no—
241#467—111no—
242#467—221no—
243C4×Q16—111no—
244C4×Q16—111no—
245C4×Q16—111no—
246C4×Q16—111no—
247C4×Q16—221no—
248C4×Q16—221no—
249C4×Q16—221no—
250C4×Q16C2×D1111yescharacteristic
251C4×Q16C2×D1111yescharacteristic
252C2×#107—111no—
253C2×#103—221no—
254C2×C4×C8—111no—
255#367—111no—
256#367—111no—
257#367—111no—
258#367C2×D1111yescharacteristic
259C4⋊C16—111no—
260C4⋊C16—111no—
261#358—111no—
262#358—111no—
263#358—111no—
264#358—111no—
265#358—111no—
266#358—111no—
267#358C2×D1111yescharacteristic
268#358C2×D1111yescharacteristic
269C22⋊C16—111no—
270C22⋊C16—111no—
271#346—111no—
272#346C2×D1111yescharacteristic
273C22×C11C22×D811yescharacteristic
274C2×D11—21no—
275C2×D11—21no—
276C2×D11#51012yes—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—42no—
280C4×C11—81no—
281C4×C11—81no—
282C4×C11—81no—
283C4×C11#52511yescharacteristic
284C4×C11#57511yescharacteristic
285Dic11—21no—
286Dic11—21no—
287Dic11—42no—
288Dic11—81no—
289Dic11—81no—
290Dic11—81no—
291Dic11#51012yes—
292C22×Q8—221no—
293C2×Q16—111no—
294C2×Q16—111no—
295C2×Q16—221no—
296C2×Q16—221no—
297C2×Q16—222no—
298C2×Q16—222no—
299C2×Q16C22×D1111yescharacteristic
300C2×Q16C22×D1111yescharacteristic
301C22×C8—111no—
302C22×C8—111no—
303C4⋊Q8—221no—
304C4⋊Q8—221no—
305#125—441no—
306C22⋊Q8—221no—
307C22⋊Q8—221no—
308C22⋊Q8—441no—
309C4×Q8—21no—
310C4×Q8—21no—
311C4×Q8—221no—
312C4×Q8—221no—
313C4×Q8—221no—
314C4×Q8—221no—
315C4×Q8—441no—
316C4×Q8—441no—
317C4×Q8—441no—
318#117—441no—
319C2×C4⋊C4—221no—
320C2×C4⋊C4—441no—
321C2×C42—111no—
322C2×C42—441no—
323Q32—22no—
324Q32—222no—
325Q32—222no—
326Q32—222no—
327C2×C16—111no—
328C2×C16—111no—
329C2×C16C22×D1111yescharacteristic
330C2×C16C22×D1111yescharacteristic
331#107—111no—
332#107—111no—
333#107—221no—
334#107—221no—
335#107C22×D1111yescharacteristic
336#107C22×D1111yescharacteristic
337#103—21no—
338#103—21no—
339#103—221no—
340#103—221no—
341#103—221no—
342#103—221no—
343#103—221no—
344#103—221no—
345C4×C8—111no—
346C4×C8—111no—
347C4×C8—111no—
348C4×C8C22×D1111yescharacteristic
349C2×C11#310011yescharacteristic
350C2×C11C2×#51011yescharacteristic
351C2×C11C2×#51011yescharacteristic
352D11—22no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—224no—
356C2×Q8—221no—
357C2×Q8—221no—
358C2×Q8—441no—
359C2×Q8—441no—
360C2×Q8—442no—
361C22×C4—111no—
362C22×C4—111no—
363C22×C4—111no—
364C22×C4—441no—
365C22×C4—441no—
366Q16—21no—
367Q16—21no—
368Q16—21no—
369Q16—112no—
370Q16—224no—
371Q16—221no—
372Q16—221no—
373Q16—221no—
374Q16—442no—
375Q16#433912yes—
376C2×C8—111no—
377C2×C8—111no—
378C2×C8—221no—
379C2×C8—221no—
380C2×C8—441no—
381C2×C8D4×D1111yescharacteristic
382C2×C8C23×D1111yescharacteristic
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—221no—
388C4⋊C4—221no—
389C4⋊C4—441no—
390C4⋊C4—441no—
391C4⋊C4—441no—
392C4⋊C4—441no—
393C4⋊C4—441no—
394C4⋊C4—441no—
395C4⋊C4—441no—
396C4⋊C4—441no—
397C4⋊C4—441no—
398C4⋊C4—441no—
399C22⋊C4—441no—
400C22⋊C4—441no—
401C42—41no—
402C42—41no—
403C42—111no—
404C42—111no—
405C42—111no—
406C42—441no—
407C42—441no—
408C42—441no—
409C42—441no—
410C42D4×D1111yescharacteristic
411C16—21no—
412C16—21no—
413C16—221no—
414C16—221no—
415C11#3367311yescharacteristic, complemented, Sylow
416C23—111no—
417Q8—22no—
418Q8—41no—
419Q8—41no—
420Q8—41no—
421Q8—222no—
422Q8—444no—
423Q8—441no—
424Q8—441no—
425Q8—441no—
426Q8—882no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—111no—
432C2×C4—111no—
433C2×C4—111no—
434C2×C4—222no—
435C2×C4—222no—
436C2×C4—221no—
437C2×C4—221no—
438C2×C4—444no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—882no—
444C2×C4D8×D1111yescharacteristic
445C2×C4D8×D1111yescharacteristic
446C2×C4C2×D4×D1111yescharacteristic
447C8—21no—
448C8—221no—
449C8—221no—
450C8C2×#433911yescharacteristic
451C8#41×D1111yescharacteristic
452C22—112no—
453C22—221no—
454C22—221no—
455C22C2×D8×D1111yescharacteristic
456C4—21no—
457C4—21no—
458C4—42no—
459C4—81no—
460C4—81no—
461C4—81no—
462C4—112no—
463C4—221no—
464C4—221no—
465C4—442no—
466C4—881no—
467C4—881no—
468C4—881no—
469C4#1062307811yescharacteristic
470C4#1062329911yescharacteristic
471C2—222no—
472C2#1307861411yescharacteristic
473C2D11×#51011yescharacteristic
474C2D11×#51011yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2176C2
socleC22×C11C22×D8
prime radicalC22×D11C2×D8
hypercenter#2176D11
hypocenterC11#33673
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2176

Complements

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

NH ≅ G/Ntype
5. #13070757C2semidirect
6. #13070756C2semidirect
7. #13070665C2semidirect
8. #13070664C2semidirect
11. #13070488C2semidirect
12. #13070485C2semidirect
13. #13070485C2semidirect
15. C11×#2176C2semidirect
192. #2176D11semidirect
415. C11#33673semidirect

Maximal subgroups

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

subgroupindex
#130791992
C4×Q16×D112
#130708152
#130708122
#130707572
#130707562
#130706652
#130706642
#130705512
#130705482
#130704882
#130704852
#130704172
C11×#21762
#3367311