Finite Group Databasebeta

← #14910643

Subgroups — #14910643

Order 2816.

580 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080960C211yesmaximal, characteristic
2#13080365C211yesmaximal, characteristic, complemented
3#13070842C211yesmaximal, characteristic, complemented
4#13070815C211yesmaximal, characteristic, complemented
5#13070811C211yesmaximal, characteristic, complemented
6#13070757C211yesmaximal, characteristic, complemented
7#13070711C211yesmaximal, characteristic, complemented
8#13070659C211yesmaximal, characteristic, complemented
9#13070532C211yesmaximal, characteristic, complemented
10#13070531C211yesmaximal, characteristic, complemented
11#13070471C211yesmaximal, characteristic, complemented
12C16×C22⋊D11C211yesmaximal, characteristic, complemented
13C2×#10622141C211yesmaximal, characteristic, complemented
14D11×#358C211yesmaximal, characteristic, complemented
15C11×#2217C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic
17C22×Dic44C2211yescharacteristic
18#10623163—21no—
19#10623142—21no—
20C2×C11×SD32C2211yescharacteristic
21C22×C11×C16C2211yescharacteristic
22C11×#467C2211yescharacteristic
23C11×#466C2211yescharacteristic
24#10622794C2211yescharacteristic
25#10622770C2211yescharacteristic
26D8×Dic11C2211yescharacteristic
27C2×#66891C2211yescharacteristic
28C2×#66891C2211yescharacteristic
29C8×C22⋊D11C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31#10622663—21no—
32#10622646—21no—
33C2×C16×D11C2211yescharacteristic
34#10622500C2211yescharacteristic
35D11×#107C2211yescharacteristic
36#10622487C2211yescharacteristic
37#10622486C2211yescharacteristic
38#10622421—21no—
39#10622406—21no—
40#10622387—21no—
41#10622372—21no—
42C11×#367C2211yescharacteristic
43C11×#358C2211yescharacteristic
44C11×#357C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622202C2211yescharacteristic
47C22⋊(C11⋊C16)C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49#10622141C2211yescharacteristic
50#10622141C2211yescharacteristic
51#10622141C2211yescharacteristic
52#10622141C2211yescharacteristic
53Dic11⋊C16C2211yescharacteristic
54C16×Dic11C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622130C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622128C2211yescharacteristic
59C2×Q8×D11—21no—
60C2×#4341—41no—
61C22×Dic22—21no—
62C2×C11×Q16C2311yescharacteristic
63C2×C11×D8C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×C22⋊Q8—21no—
66C11×#121—21no—
67#66997—21no—
68C2×#4326—21no—
69C2×#4326—21no—
70#66991—21no—
71#66988—41no—
72D4×Dic11—21no—
73C4×C22⋊D11D411yescharacteristic
74C2×C4⋊Dic11—21no—
75Q16×D11—22no—
76Q16×D11—41no—
77C2×Dic44—22no—
78C2×Dic44—21no—
79C2×Dic44—41no—
80C2×Dic44C2311yescharacteristic
81C2×Dic44C2311yescharacteristic
82C2×C8×D11C2311yescharacteristic
83#66950—21no—
84#66949—41no—
85C4⋊C4×D11—21no—
86#66941—21no—
87#66941—41no—
88#66940—21no—
89#66936—41no—
90(C22⋊D11)⋊C4—41no—
91#66931—41no—
92#66931—41no—
93C11×SD32—41no—
94C2×C11×C16—41no—
95C2×C11×C16C2311yescharacteristic
96C2×C11×C16C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#107C2311yescharacteristic
99C11×#103—21no—
100C11×#102—21no—
101#66896—21no—
102#66896—21no—
103C22⋊(C11⋊C8)D411yescharacteristic
104#66891—22no—
105#66891—41no—
106(C2×D11)⋊C8D411yescharacteristic
107#66882—21no—
108#66882C2311yescharacteristic
109#66882C2311yescharacteristic
110Dic11⋊C8D411yescharacteristic
111C8×Dic11C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113C2×C11⋊C16C2311yescharacteristic
114#66874—21no—
115#66874—21no—
116#66871—21no—
117#66871—21no—
118C16×D11—41no—
119#33865—111nomaximal, Sylow
120C2×Q8×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—41no—
123C22×C4×C11C2×D411yescharacteristic
124C2×C22⋊D11—41no—
125C2×C22⋊D11D811yescharacteristic
126C22×Dic11—41no—
127C22×Dic11—41no—
128C22×Dic11—41no—
129Q8×D11—42no—
130Q8×D11—81no—
131#4341—84no—
132C2×C4×D11—41no—
133C2×C4×D11—41no—
134C2×C4×D11C2×D411yescharacteristic
135C2×Dic22—21no—
136C2×Dic22—21no—
137C2×Dic22—42no—
138C2×Dic22—41no—
139C2×Dic22—41no—
140C2×Dic22—41no—
141C2×Dic22—81no—
142C11×Q16—21no—
143C11×Q16—21no—
144C11×D8—21no—
145C11×D8—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11C2×D411yescharacteristic
149C2×C8×C11C2411yescharacteristic
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—41no—
153C11×C22⋊C4—41no—
154C11×C22⋊C4—41no—
155C22⋊Dic11—41no—
156C22⋊Dic11—41no—
157C22⋊Dic11D811yescharacteristic
158#4326—42no—
159#4326—81no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4D811yescharacteristic
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11—41no—
165C4⋊Dic11—41no—
166Dic11⋊C4—41no—
167Dic11⋊C4—41no—
168Dic11⋊C4—41no—
169Dic11⋊C4—41no—
170Dic11⋊C4—41no—
171Dic11⋊C4D811yescharacteristic
172C4×Dic11—41no—
173C4×Dic11C2×D411yescharacteristic
174C2×C11⋊C8C2×D411yescharacteristic
175C2×C11⋊C8C2×D411yescharacteristic
176Dic44—21no—
177Dic44—21no—
178Dic44—21no—
179Dic44—42no—
180Dic44#4112yescomplemented
181C8×D11—21no—
182C8×D11—21no—
183C11×C16—21no—
184C11×C16—21no—
185C11⋊C16—21no—
186C11⋊C16—21no—
187#3334—111no—
188D4×Q16—111no—
189#2241—111no—
190#2235—111no—
191#2235—111no—
192#2225—111no—
193#2217—111no—
194#2217D1111yescharacteristic, complemented
195#2208—111no—
196#2185—111no—
197#2185—111no—
198C4×SD32—111no—
199D4×C16—111no—
200C2×#358—111no—
201C2×#358—111no—
202C23×C11—41no—
203C23×C11C2×D811yescharacteristic
204C22×D11C2×D811yescharacteristic
205Q8×C11—41no—
206Q8×C11—41no—
207D4×C11—41no—
208D4×C11—41no—
209D4×C11—82no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11C2×D811yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C22⋊D11—82no—
218C22⋊D11SD3214yescomplemented
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—82no—
224C2×Dic11—82no—
225C2×Dic11—82no—
226C2×Dic11C2×D811yescharacteristic
227C2×Dic11C2×D811yescharacteristic
228C2×Dic11C2×D811yescharacteristic
229C4×D11—21no—
230C4×D11—21no—
231C4×D11—82no—
232C4×D11—82no—
233Dic22—22no—
234Dic22—41no—
235Dic22—41no—
236Dic22—41no—
237Dic22—82no—
238Dic22—82no—
239Dic22—82no—
240C8×C11—21no—
241C8×C11C2×#4111yescharacteristic
242C8×C11H(5,𝔽2)11yescharacteristic
243C11⋊C8—21no—
244C11⋊C8—21no—
245C22×Q16—111no—
246C22×Q16—111no—
247D4×Q8—221no—
248#547—221no—
249C2×SD32—111no—
250C2×SD32—111no—
251C2×SD32C2×D1111yescharacteristic
252C22×C16—111no—
253C22×C16C2×D1111yescharacteristic
254#500—111no—
255#494—111no—
256#480—221no—
257#480—221no—
258#474—221no—
259#467—111no—
260#467C2×D1111yescharacteristic
261#466—111no—
262#466C2×D1111yescharacteristic
263#462—221no—
264#451—221no—
265#451—221no—
266C4×Q16—111no—
267C4×D8—111no—
268C8×D4—111no—
269C2×#107—111no—
270C2×#107—111no—
271#367—111no—
272#367—111no—
273#367C2×D1111yescharacteristic
274C4⋊C16—111no—
275#358—111no—
276#358—111no—
277#358—111no—
278#358—111no—
279#358—111no—
280#358—111no—
281#358—111no—
282#358—111no—
283#358C2×D1111yescharacteristic
284#357C2×D1111yescharacteristic
285C22⋊C16—111no—
286C22⋊C16—111no—
287C4×C16—111no—
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—81no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11C2×SD3212yes—
294C22×C11C22×D811yescharacteristic
295C2×D11—21no—
296C2×D11—21no—
297C2×D11C2×SD3212yes—
298C4×C11—21no—
299C4×C11—81no—
300C4×C11—81no—
301C4×C11—81no—
302C4×C11#54611yescharacteristic
303C4×C11#57711yescharacteristic
304Dic11—21no—
305Dic11—21no—
306Dic11—42no—
307Dic11—81no—
308Dic11—81no—
309Dic11—81no—
310Dic11C2×SD3212yes—
311C2×#41—441no—
312C22×Q8—221no—
313C22×Q8—221no—
314C2×Q16—111no—
315C2×Q16—111no—
316C2×Q16—222no—
317C2×Q16—221no—
318C2×Q16—221no—
319C2×Q16—222no—
320C2×Q16—221no—
321C2×Q16—441no—
322C2×Q16—441no—
323C2×Q16C22×D1111yescharacteristic
324C2×D8C22×D1111yescharacteristic
325C22×C8—111no—
326C22×C8C22×D1111yescharacteristic
327C4⋊Q8—221no—
328C4⋊Q8—221no—
329C4⋊Q8—441no—
330#123—441no—
331#123—441no—
332C22⋊Q8—21no—
333C22⋊Q8—221no—
334C22⋊Q8—441no—
335C22⋊Q8—441no—
336C22⋊Q8—441no—
337#121—21no—
338#121—221no—
339C4×Q8—221no—
340C4×D4—111no—
341C4×D4—221no—
342C4×D4—441no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4—221no—
345SD32—41no—
346SD32—222no—
347SD32—441no—
348C2×C16—41no—
349C2×C16—111no—
350C2×C16—111no—
351C2×C16—441no—
352C2×C16C22×D1111yescharacteristic
353C2×C16C22×D1111yescharacteristic
354#107—111no—
355#107—111no—
356#107—221no—
357#107—221no—
358#107—221no—
359#107C22×D1111yescharacteristic
360#107C22×D1111yescharacteristic
361C4⋊C8—111no—
362#103—21no—
363#103—221no—
364#103—221no—
365#102—21no—
366#102—221no—
367#102—221no—
368C22⋊C8—111no—
369C22⋊C8—111no—
370C4×C8—111no—
371C2×C11—22no—
372C2×C11—161no—
373C2×C11#329411yescharacteristic
374C2×C11C22×SD3211yescharacteristic
375C2×C11#341711yescharacteristic
376D11—22no—
377#41—884no—
378C2×Q8—21no—
379C2×Q8—221no—
380C2×Q8—221no—
381C2×Q8—442no—
382C2×Q8—441no—
383C2×Q8—441no—
384C2×Q8—442no—
385C2×Q8—441no—
386C2×Q8—881no—
387C2×Q8—881no—
388C2×D4—21no—
389C2×D4—41no—
390C2×D4—111no—
391C2×D4—441no—
392C22×C4—111no—
393C22×C4—441no—
394C22×C4—441no—
395C22×C4—441no—
396C22×C4—441no—
397C22×C4—441no—
398C22×C4D4×D1111yescharacteristic
399Q16—21no—
400Q16—21no—
401Q16—112no—
402Q16—221no—
403Q16—221no—
404Q16—221no—
405Q16—442no—
406Q16—442no—
407Q16—881no—
408D8—21no—
409D8—21no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—111no—
413C2×C8—111no—
414C2×C8—221no—
415C2×C8—221no—
416C2×C8D4×D1111yescharacteristic
417C2×C8C23×D1111yescharacteristic
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—41no—
421C4⋊C4—111no—
422C4⋊C4—221no—
423C4⋊C4—221no—
424C4⋊C4—441no—
425C4⋊C4—441no—
426C4⋊C4—441no—
427C4⋊C4—441no—
428C4⋊C4—441no—
429C4⋊C4—441no—
430C4⋊C4—441no—
431C22⋊C4—41no—
432C22⋊C4—41no—
433C22⋊C4—111no—
434C22⋊C4—111no—
435C22⋊C4—441no—
436C22⋊C4—441no—
437C22⋊C4—441no—
438C42—111no—
439C42—441no—
440C16—21no—
441C16—21no—
442C16—221no—
443C16—221no—
444C11#3386511yescharacteristic, complemented, Sylow
445C23—41no—
446C23—111no—
447C23D8×D1111yescharacteristic
448Q8—41no—
449Q8—41no—
450Q8—222no—
451Q8—441no—
452Q8—441no—
453Q8—441no—
454Q8—882no—
455Q8—882no—
456Q8—882no—
457D4—41no—
458D4—41no—
459D4—82no—
460D4—114no—
461D4—882no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—111no—
468C2×C4—111no—
469C2×C4—111no—
470C2×C4—221no—
471C2×C4—221no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—882no—
477C2×C4—882no—
478C2×C4—882no—
479C2×C4—882no—
480C2×C4—882no—
481C2×C4D8×D1111yescharacteristic
482C2×C4C2×D4×D1111yescharacteristic
483C8—21no—
484C8—221no—
485C8—221no—
486C8#6703711yescharacteristic
487C8#41×D1111yescharacteristic
488C22—21no—
489C22—21no—
490C22—81no—
491C22—81no—
492C22—81no—
493C22—112no—
494C22—221no—
495C22—221no—
496C22D11×SD3212yes—
497C22C2×D8×D1111yescharacteristic
498C4—21no—
499C4—81no—
500C4—81no—
501C4—81no—
502C4—112no—
503C4—221no—
504C4—221no—
505C4—442no—
506C4—881no—
507C4—881no—
508C4—881no—
509C4#1062314111yescharacteristic
510C4#1062330111yescharacteristic
511C2—22no—
512C2—161no—
513C2—222no—
514C2#1308042411yescharacteristic
515C2C2×D11×SD3211yescharacteristic
516C2#1308176611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2217C2
socleC22×C11C22×D8
prime radical#13080960C2
hypercenter#2217D11
hypocenterC11#33865
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2217

Complements

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

NH ≅ G/Ntype
2. #13080365C2semidirect
3. #13070842C2semidirect
4. #13070815C2semidirect
5. #13070811C2semidirect
6. #13070757C2semidirect
7. #13070711C2semidirect
8. #13070659C2semidirect
9. #13070532C2semidirect
10. #13070531C2semidirect
11. #13070471C2semidirect
12. C16×C22⋊D11C2semidirect
13. C2×#10622141C2semidirect
14. D11×#358C2semidirect
15. C11×#2217C2semidirect
180. Dic44#41semidirect
194. #2217D11semidirect
218. C22⋊D11SD32semidirect
444. C11#33865semidirect

Maximal subgroups

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

subgroupindex
#130809602
#130803652
#130708422
#130708152
#130708112
#130707572
#130707112
#130706592
#130705322
#130705312
#130704712
C16×C22⋊D112
C2×#106221412
D11×#3582
C11×#22172
#3386511