Finite Group Databasebeta

← #14908711

Subgroups — #14908711

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079184C211yesmaximal, characteristic, complemented
2C4×#66965C211yesmaximal, characteristic, complemented
3#13070826C211yesmaximal, characteristic, complemented
4#13070805C211yesmaximal, characteristic, complemented
5#13070779C211yesmaximal, characteristic, complemented
6#13070771C211yesmaximal, characteristic, complemented
7#13070677C211yesmaximal, characteristic, complemented
8#13070669C211yesmaximal, characteristic, complemented
9#13070557C211yesmaximal, characteristic, complemented
10#13070536C211yesmaximal, characteristic
11C4×Dic88C211yesmaximal, characteristic, complemented
12C4×#66891C211yesmaximal, characteristic, complemented
13C4×#66891C211yesmaximal, characteristic, complemented
14#13070413C211yesmaximal, characteristic, complemented
15C4×C11×D16C211yesmaximal, characteristic, complemented
16C2×#66965C2211yescharacteristic
17#10623088—21no—
18C4×#4341—21no—
19C2×C11×D16C2211yescharacteristic
20C4×C11×D8C2211yescharacteristic
21C4×C11×D8C2211yescharacteristic
22#10622770C2211yescharacteristic
23#10622768C2211yescharacteristic
24D8×Dic11C2211yescharacteristic
25C2×#66891C2211yescharacteristic
26C2×#66891C2211yescharacteristic
27C4×#4324—21no—
28C4×#4324—21no—
29C2×Dic88C2211yescharacteristic
30#10622500C2211yescharacteristic
31#10622493C2211yescharacteristic
32#10622491C2211yescharacteristic
33#10622486C2211yescharacteristic
34#10622391—21no—
35#10622385—21no—
36#10622381—21no—
37#10622371—21no—
38C4×Dic44C2211yescharacteristic
39C4×Dic44C2211yescharacteristic
40C4×C8×D11C2211yescharacteristic
41C11×#366C2211yescharacteristic
42C11×#357C2211yescharacteristic
43C11×#357C2211yescharacteristic
44C4×C11×C16C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47(C2×D11)⋊C16C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49#10622142C2211yescharacteristic
50#10622141C2211yescharacteristic
51#10622141C2211yescharacteristic
52Dic11⋊C16C2211yescharacteristic
53Dic11⋊C16C2211yescharacteristic
54#10622130C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622128C2211yescharacteristic
58C4×C11⋊C16C2211yescharacteristic
59C2×#4341—21no—
60C2×C11×D8C2311yescharacteristic
61C2×C11×D8C2311yescharacteristic
62C4×D4×C11—21no—
63C4×D4×C11—21no—
64#66991—21no—
65#66989—21no—
66D4×Dic11—21no—
67C2×#4324—21no—
68C2×#4324—21no—
69C4×C22⋊D11—41no—
70C4×C22⋊D11—41no—
71#66979—41no—
72C2×C4×Dic11—41no—
73#66965—22no—
74#66965—22no—
75C2×Dic44C2311yescharacteristic
76C2×Dic44C2311yescharacteristic
77C2×C8×D11D411yescharacteristic
78C2×C8×D11C2311yescharacteristic
79#66950—21no—
80#66945—21no—
81#66943—21no—
82#66940—21no—
83#66936—41no—
84(C22⋊D11)⋊C4—41no—
85#66932—41no—
86#66930—41no—
87C42×D11D411yescharacteristic
88C4×Dic22—21no—
89C4×Dic22—21no—
90C11×D16—22no—
91C2×C11×C16C2311yescharacteristic
92C2×C11×C16C2311yescharacteristic
93C11×#107C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#102—21no—
96C11×#102—21no—
97C4×C8×C11C2311yescharacteristic
98#66896—21no—
99#66896—21no—
100#66891—22no—
101#66891—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#66872—21no—
113#66872—21no—
114C4×C11⋊C8D411yescharacteristic
115Dic88—22no—
116#33662—111nomaximal, Sylow
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C22×C4×C11—41no—
120C22×C4×C11—41no—
121C2×C22⋊D11—41no—
122C2×C22⋊D11—41no—
123C22×Dic11—41no—
124C22×Dic11—41no—
125#4341—24no—
126#4341—42no—
127C2×C4×D11D811yescharacteristic
128C2×C4×D11D811yescharacteristic
129C2×C4×D11C2×D411yescharacteristic
130C2×Dic22—21no—
131C2×Dic22—21no—
132C11×D8—21no—
133C11×D8—21no—
134C11×D8—21no—
135C11×D8#4112yes—
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11C2411yescharacteristic
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C22⋊C4—41no—
141C11×C22⋊C4—41no—
142C42×C11C2×D411yescharacteristic
143C22⋊Dic11—41no—
144C22⋊Dic11—41no—
145C22⋊Dic11—41no—
146C22⋊Dic11—41no—
147#4324—24no—
148#4324—42no—
149(C2×D11)⋊C4—41no—
150(C2×D11)⋊C4—41no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—41no—
154C4⋊Dic11—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#3168—111no—
180C4×#135—111no—
181#2237—111no—
182#2234—111no—
183#2229—111no—
184#2228—111no—
185#2211—111no—
186#2210—111no—
187#2189—111no—
188#2186—111no—
189C4×Q32—111no—
190C4×SD32—111no—
191C4×SD32—111no—
192C4×D16D1111yescharacteristic, complemented
193#2162—111no—
194C23×C11—41no—
195C23×C11—41no—
196C22×D11C2×D811yescharacteristic
197D4×C11—22no—
198D4×C11—41no—
199D4×C11—41no—
200D4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—82no—
204C2×C4×C11—82no—
205C2×C4×C11C2×D811yescharacteristic
206C2×C4×C11C2×D811yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C22⋊D11—44no—
209C22⋊D11—82no—
210C2×Dic11—44no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—82no—
216C2×Dic11C2×D811yescharacteristic
217C2×Dic11C2×D811yescharacteristic
218C2×Dic11C2×D811yescharacteristic
219C4×D11—21no—
220C4×D11—21no—
221C4×D11—22no—
222C4×D11—41no—
223Dic22—22no—
224Dic22—41no—
225Dic22—41no—
226Dic22—41no—
227C8×C11—21no—
228C8×C11C2×#4111yescharacteristic
229C8×C11C2×#4111yescharacteristic
230C11⋊C8—21no—
231C11⋊C8—21no—
232C2×#135—111no—
233#529—221no—
234C4×#41—221no—
235C2×Q32—111no—
236C2×SD32—111no—
237C2×SD32—111no—
238C2×D16C2×D1111yescharacteristic
239#499—111no—
240#495—111no—
241#488—221no—
242#467—111no—
243#466—111no—
244#465—221no—
245C4×Q16—111no—
246C4×Q16—111no—
247C4×Q16—111no—
248C4×SD16—221no—
249C4×SD16—221no—
250C4×SD16—221no—
251C4×D8—111no—
252C4×D8C2×D1111yescharacteristic
253C4×D8C2×D1111yescharacteristic
254#427—111no—
255#416—221no—
256C2×C4×C8—111no—
257#367—111no—
258#367—111no—
259#366—111no—
260#366C2×D1111yescharacteristic
261C4⋊C16—111no—
262C4⋊C16—111no—
263#358—111no—
264#358—111no—
265#358—111no—
266#358—111no—
267#357—111no—
268#357—111no—
269#357C2×D1111yescharacteristic
270#357C2×D1111yescharacteristic
271C22⋊C16—111no—
272C22⋊C16—111no—
273C4×C16—111no—
274C4×C16C2×D1111yescharacteristic
275C22×C11—42no—
276C22×C11—81no—
277C22×C11—81no—
278C22×C11—81no—
279C22×C11—81no—
280C22×C11—81no—
281C22×C11C22×D811yescharacteristic
282C2×D11—21no—
283C2×D11—21no—
284C2×D11—21no—
285C4×C11—21no—
286C4×C11—81no—
287C4×C11—81no—
288C4×C11#50812yes—
289C4×C11#52511yescharacteristic
290C4×C11#57511yescharacteristic
291Dic11—21no—
292Dic11—21no—
293Dic11—21no—
294Dic11—42no—
295Dic11—81no—
296Dic11—81no—
297Dic11—81no—
298C2×#41—221no—
299#135—222no—
300#135—222no—
301C2×Q16—111no—
302C2×Q16—111no—
303C2×SD16—221no—
304C2×SD16—221no—
305C2×D8C22×D1111yescharacteristic
306C2×D8C22×D1111yescharacteristic
307C22×C8—111no—
308C22×C8—111no—
309#126—441no—
310#125—221no—
311#124—221no—
312#123—441no—
313C22⋊Q8—221no—
314#121—221no—
315C4×Q8—221no—
316C4×Q8—221no—
317C4×Q8—221no—
318C4×D4—21no—
319C4×D4—21no—
320C4×D4—221no—
321C4×D4—441no—
322C4×D4—441no—
323C4×D4—441no—
324#117—221no—
325#117—441no—
326#117—441no—
327C2×C42—111no—
328C2×C42—441no—
329Q32—222no—
330SD32—222no—
331SD32—222no—
332D16—22no—
333C2×C16—111no—
334C2×C16—111no—
335C2×C16C22×D1111yescharacteristic
336C2×C16C22×D1111yescharacteristic
337#107—111no—
338#107—111no—
339#107C22×D1111yescharacteristic
340#107C22×D1111yescharacteristic
341#106—221no—
342#106—221no—
343#103—221no—
344#103—221no—
345#103—221no—
346#103—221no—
347#102—21no—
348#102—21no—
349#102—221no—
350#102—221no—
351C4×C8—111no—
352C4×C8—111no—
353C4×C8—111no—
354C4×C8C22×D1111yescharacteristic
355C2×C11—82no—
356C2×C11—161no—
357C2×C11#310011yescharacteristic
358C2×C11C2×#50811yescharacteristic
359C2×C11#341411yescharacteristic
360D11—41no—
361#41—224no—
362#41—442no—
363C2×Q8—221no—
364C2×Q8—221no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—441no—
368C2×D4—441no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—111no—
372C22×C4—111no—
373C22×C4—111no—
374C22×C4—441no—
375C22×C4—441no—
376Q16—112no—
377Q16—221no—
378Q16—221no—
379Q16—221no—
380SD16—224no—
381SD16—442no—
382D8—21no—
383D8—21no—
384D8—21no—
385D8#433912yes—
386C2×C8—111no—
387C2×C8—111no—
388C2×C8—221no—
389C2×C8—221no—
390C2×C8—441no—
391C2×C8D4×D1111yescharacteristic
392C2×C8C23×D1111yescharacteristic
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—221no—
396C4⋊C4—221no—
397C4⋊C4—441no—
398C4⋊C4—441no—
399C4⋊C4—441no—
400C4⋊C4—441no—
401C4⋊C4—441no—
402C4⋊C4—441no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C22⋊C4—441no—
406C22⋊C4—441no—
407C22⋊C4—441no—
408C22⋊C4—441no—
409C22⋊C4—441no—
410C22⋊C4—441no—
411C42—111no—
412C42—111no—
413C42—111no—
414C42—441no—
415C42—441no—
416C42—441no—
417C42—441no—
418C42D4×D1111yescharacteristic
419C16—21no—
420C16—21no—
421C16—221no—
422C16—221no—
423C11#3366211yescharacteristic, complemented, Sylow
424C23—41no—
425C23—41no—
426C23—111no—
427Q8—222no—
428Q8—441no—
429Q8—441no—
430Q8—441no—
431D4—22no—
432D4—41no—
433D4—41no—
434D4—41no—
435D4—444no—
436D4—882no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—82no—
440C2×C4—82no—
441C2×C4—111no—
442C2×C4—111no—
443C2×C4—111no—
444C2×C4—222no—
445C2×C4—221no—
446C2×C4—221no—
447C2×C4—441no—
448C2×C4—444no—
449C2×C4—441no—
450C2×C4—441no—
451C2×C4—441no—
452C2×C4—441no—
453C2×C4—882no—
454C2×C4D8×D1111yescharacteristic
455C2×C4D8×D1111yescharacteristic
456C2×C4C2×D4×D1111yescharacteristic
457C8—21no—
458C8—221no—
459C8—221no—
460C8C2×#433911yescharacteristic
461C8#41×D1111yescharacteristic
462C22—42no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22—221no—
469C22—221no—
470C22—221no—
471C22C2×D8×D1111yescharacteristic
472C4—21no—
473C4—81no—
474C4—81no—
475C4—221no—
476C4—221no—
477C4—221no—
478C4—442no—
479C4—881no—
480C4—881no—
481C4—881no—
482C4#1062252512yes—
483C4#1062307811yescharacteristic
484C4#1062329911yescharacteristic
485C2—82no—
486C2—161no—
487C2—441no—
488C2#1307861411yescharacteristic
489C2C2×#1062252511yescharacteristic
490C2#1308174911yescharacteristic
subgroupG/H
centerC2×C4D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×D16C2
socleC22×C11C22×D8
prime radical#13070536C2
hypercenterC4×D16D11
hypocenterC11#33662
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×D16

Complements

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

NH ≅ G/Ntype
1. #13079184C2semidirect
2. C4×#66965C2semidirect
3. #13070826C2semidirect
4. #13070805C2semidirect
5. #13070779C2semidirect
6. #13070771C2semidirect
7. #13070677C2semidirect
8. #13070669C2semidirect
9. #13070557C2semidirect
11. C4×Dic88C2semidirect
12. C4×#66891C2semidirect
13. C4×#66891C2semidirect
14. #13070413C2semidirect
15. C4×C11×D16C2semidirect
192. C4×D16D11semidirect
423. C11#33662semidirect

Maximal subgroups

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

subgroupindex
#130791842
C4×#669652
#130708262
#130708052
#130707792
#130707712
#130706772
#130706692
#130705572
#130705362
C4×Dic882
C4×#668912
#130704132
C4×C11×D162
#3366211