Finite Group Databasebeta

← #14910680

Subgroups — #14910680

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081013C211yesmaximal, characteristic, complemented
2#13080360C211yesmaximal, characteristic, complemented
3#13070849C211yesmaximal, characteristic, complemented
4#13070821C211yesmaximal, characteristic, complemented
5#13070803C211yesmaximal, characteristic, complemented
6#13070783C211yesmaximal, characteristic, complemented
7#13070701C211yesmaximal, characteristic, complemented
8#13070673C211yesmaximal, characteristic, complemented
9#13070537C211yesmaximal, characteristic, complemented
10#13070531C211yesmaximal, characteristic, complemented
11#13070471C211yesmaximal, characteristic, complemented
12C16×C22⋊D11C211yesmaximal, characteristic, complemented
13#13070324C211yesmaximal, characteristic, complemented
14D11×#358C211yesmaximal, characteristic, complemented
15C11×#2217C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic
17C2×#66957C2211yescharacteristic
18#10623164—21no—
19#10623145—21no—
20C2×C11×SD32C2211yescharacteristic
21C22×C11×C16C2211yescharacteristic
22C11×#467C2211yescharacteristic
23C11×#466C2211yescharacteristic
24#10622804C2211yescharacteristic
25#10622770C2211yescharacteristic
26D8×Dic11C2211yescharacteristic
27C2×#66891C2211yescharacteristic
28C2×#66890C2211yescharacteristic
29C8×C22⋊D11C2211yescharacteristic
30#10622719C2211yescharacteristic
31#10622660—21no—
32#10622648—21no—
33C2×C16×D11C2211yescharacteristic
34#10622496C2211yescharacteristic
35D11×#107C2211yescharacteristic
36#10622491C2211yescharacteristic
37#10622486C2211yescharacteristic
38#10622419—21no—
39#10622411—21no—
40#10622390—21no—
41#10622376—21no—
42C11×#367C2211yescharacteristic
43C11×#358C2211yescharacteristic
44C11×#357C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622202C2211yescharacteristic
47C22⋊(C11⋊C16)C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50(C2×D11)⋊C16C2211yescharacteristic
51#10622141C2211yescharacteristic
52#10622141C2211yescharacteristic
53Dic11⋊C16C2211yescharacteristic
54C16×Dic11C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622129C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622127C2211yescharacteristic
59C2×Q8×D11—21no—
60C2×#4339—21no—
61C2×C11×Q16C2311yescharacteristic
62C2×C11×D8C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×C22⋊Q8—21no—
65C11×#121—21no—
66#67000—21no—
67C2×#4326—21no—
68C2×#4325—21no—
69#66991—21no—
70#66991—41no—
71#66988—41no—
72D4×Dic11—21no—
73C4×C22⋊D11D411yescharacteristic
74#66979—21no—
75Q16×D11—22no—
76Q16×D11—41no—
77C2×Dic44C2311yescharacteristic
78#66957—22no—
79#66957—41no—
80C2×D88C2311yescharacteristic
81C2×#4314—21no—
82C2×C8×D11C2311yescharacteristic
83#66949—41no—
84#66948—21no—
85#66946—41no—
86C4⋊C4×D11—21no—
87#66943—21no—
88#66940—21no—
89#66938—41no—
90#66937—41no—
91(C22⋊D11)⋊C4—41no—
92#66932—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#66890—41no—
106(C2×D11)⋊C8D411yescharacteristic
107#66882C2311yescharacteristic
108#66882C2311yescharacteristic
109#66881—21no—
110Dic11⋊C8D411yescharacteristic
111C8×Dic11C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113C2×C11⋊C16C2311yescharacteristic
114#66874—21no—
115#66873—21no—
116#66872—21no—
117#66871—21no—
118C16×D11—41no—
119#33868—111nomaximal, Sylow
120C2×Q8×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—41no—
123C22×C4×C11C2×D411yescharacteristic
124C2×C22⋊D11—41no—
125C2×C22⋊D11—41no—
126C2×C22⋊D11D811yescharacteristic
127C22×Dic11—41no—
128Q8×D11—42no—
129Q8×D11—81no—
130#4339—42no—
131#4339—81no—
132C2×D44—21no—
133C2×D44—41no—
134C2×C4×D11—41no—
135C2×C4×D11—41no—
136C2×C4×D11—41no—
137C2×C4×D11C2×D411yescharacteristic
138C2×Dic22—21no—
139C2×Dic22—41no—
140C11×Q16—21no—
141C11×Q16—21no—
142C11×D8—21no—
143C11×D8—21no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11C2×D411yescharacteristic
147C2×C8×C11C2411yescharacteristic
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—41no—
151C11×C22⋊C4—41no—
152C11×C22⋊C4—41no—
153C22⋊Dic11—41no—
154C22⋊Dic11—41no—
155C22⋊Dic11—41no—
156C22⋊Dic11D811yescharacteristic
157#4326—42no—
158#4325—81no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4—41no—
162(C2×D11)⋊C4D811yescharacteristic
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11—41no—
166Dic11⋊C4—41no—
167Dic11⋊C4—41no—
168Dic11⋊C4—41no—
169Dic11⋊C4D811yescharacteristic
170C4×Dic11—41no—
171C4×Dic11—41no—
172C4×Dic11C2×D411yescharacteristic
173C2×C11⋊C8C2×D411yescharacteristic
174C2×C11⋊C8C2×D411yescharacteristic
175Dic44—21no—
176Dic44#4112yes—
177D88—21no—
178D88—21no—
179#4314—42no—
180C8×D11—21no—
181C8×D11—21no—
182C11×C16—21no—
183C11×C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186#3339—111no—
187#3285—111no—
188#2242—111no—
189#2237—111no—
190#2233—111no—
191#2229—111no—
192#2217D1111yescharacteristic, complemented
193#2215—111no—
194#2210—111no—
195#2186—111no—
196#2185—111no—
197C4×SD32—111no—
198D4×C16—111no—
199#2138—111no—
200C2×#358—111no—
201C23×C11—41no—
202C23×C11C2×D811yescharacteristic
203C22×D11—41no—
204C22×D11C2×D811yescharacteristic
205Q8×C11—41no—
206Q8×C11—41no—
207D4×C11—41no—
208D4×C11—41no—
209D4×C11—161no—
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—22no—
218C22⋊D11—82no—
219C22⋊D11—82no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—161no—
224C2×Dic11C2×D811yescharacteristic
225C2×Dic11C2×D811yescharacteristic
226C2×Dic11C2×D811yescharacteristic
227D44—41no—
228D44—41no—
229D44—82no—
230C4×D11—21no—
231C4×D11—21no—
232C4×D11—82no—
233C4×D11—82no—
234C4×D11—161no—
235Dic22—22no—
236Dic22—41no—
237Dic22—82no—
238C8×C11—21no—
239C8×C11C2×#4111yescharacteristic
240C8×C11H(5,𝔽2)11yescharacteristic
241C11⋊C8—21no—
242C11⋊C8—21no—
243C2×#135—111no—
244C22×Q16—111no—
245#553—221no—
246#548—221no—
247C2×SD32—111no—
248C2×SD32C2×D1111yescharacteristic
249C2×D16—111no—
250C22×C16—111no—
251C22×C16C2×D1111yescharacteristic
252#499—111no—
253#495—111no—
254#482—221no—
255#481—221no—
256#478—221no—
257#467C2×D1111yescharacteristic
258#466—111no—
259#466—111no—
260#466C2×D1111yescharacteristic
261#464—221no—
262#452—221no—
263#448—221no—
264C4×Q16—111no—
265C4×D8—111no—
266C8×D4—111no—
267#427—111no—
268C2×#107—111no—
269#367—111no—
270#367C2×D1111yescharacteristic
271#366—111no—
272C4⋊C16—111no—
273#358—111no—
274#358—111no—
275#358—111no—
276#358—111no—
277#358—111no—
278#358C2×D1111yescharacteristic
279#357—111no—
280#357—111no—
281#357—111no—
282#357C2×D1111yescharacteristic
283C22⋊C16—111no—
284C22⋊C16—111no—
285C4×C16—111no—
286C22×C11—21no—
287C22×C11—21no—
288C22×C11—21no—
289C22×C11—81no—
290C22×C11—81no—
291C22×C11—81no—
292C22×C11C22×D811yescharacteristic
293C2×D11—21no—
294C2×D11—21no—
295C2×D11—81no—
296C2×D11—81no—
297C2×D11—81no—
298C2×D11#50812yes—
299C4×C11—21no—
300C4×C11—81no—
301C4×C11—81no—
302C4×C11—81no—
303C4×C11#54611yescharacteristic
304C4×C11#57711yescharacteristic
305Dic11—21no—
306Dic11—21no—
307Dic11—21no—
308Dic11—42no—
309Dic11—81no—
310Dic11—81no—
311C2×#41—221no—
312C22×Q8—221no—
313#135—222no—
314#135—441no—
315C2×Q16—111no—
316C2×Q16—221no—
317C2×Q16—222no—
318C2×Q16—441no—
319C2×Q16C22×D1111yescharacteristic
320C2×SD16—221no—
321C2×SD16—221no—
322C2×D8—111no—
323C2×D8C22×D1111yescharacteristic
324C22×C8—111no—
325C22×C8C22×D1111yescharacteristic
326#126—441no—
327#125—221no—
328#124—221no—
329#124—441no—
330#123—441no—
331C22⋊Q8—21no—
332C22⋊Q8—441no—
333#121—21no—
334#121—221no—
335#121—221no—
336#121—441no—
337#121—441no—
338C4×Q8—221no—
339C4×D4—111no—
340C4×D4—221no—
341C4×D4—441no—
342C4×D4—441no—
343#117—221no—
344C2×C4⋊C4—221no—
345SD32—41no—
346SD32—222no—
347D16—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#107C22×D1111yescharacteristic
358#107C22×D1111yescharacteristic
359#106—221no—
360#106—221no—
361C4⋊C8—111no—
362#103—21no—
363#103—221no—
364#102—21no—
365#102—221no—
366#102—221no—
367#102—221no—
368C22⋊C8—111no—
369C22⋊C8—111no—
370C4×C8—111no—
371C2×C11—41no—
372C2×C11—161no—
373C2×C11#329411yescharacteristic
374C2×C11C2×#50811yescharacteristic
375C2×C11#341611yescharacteristic
376D11—22no—
377D11—161no—
378#41—442no—
379#41—881no—
380C2×Q8—21no—
381C2×Q8—221no—
382C2×Q8—441no—
383C2×Q8—442no—
384C2×Q8—881no—
385C2×D4—21no—
386C2×D4—41no—
387C2×D4—111no—
388C2×D4—221no—
389C2×D4—441no—
390C2×D4—441no—
391C2×D4—441no—
392C22×C4—111no—
393C22×C4—441no—
394C22×C4—441no—
395C22×C4—441no—
396C22×C4—441no—
397C22×C4D4×D1111yescharacteristic
398Q16—21no—
399Q16—21no—
400Q16—112no—
401Q16—221no—
402Q16—442no—
403SD16—442no—
404SD16—881no—
405D8—21no—
406D8—21no—
407D8—221no—
408D8—221no—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—111no—
412C2×C8—111no—
413C2×C8—221no—
414C2×C8—221no—
415C2×C8D4×D1111yescharacteristic
416C2×C8C23×D1111yescharacteristic
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—41no—
420C4⋊C4—111no—
421C4⋊C4—221no—
422C4⋊C4—221no—
423C4⋊C4—441no—
424C4⋊C4—441no—
425C4⋊C4—441no—
426C4⋊C4—441no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—111no—
430C22⋊C4—111no—
431C22⋊C4—441no—
432C22⋊C4—441no—
433C22⋊C4—441no—
434C22⋊C4—441no—
435C22⋊C4—441no—
436C22⋊C4—441no—
437C42—111no—
438C42—441no—
439C42—441no—
440C16—21no—
441C16—21no—
442C16—221no—
443C16—221no—
444C11#3386811yescharacteristic, complemented, Sylow
445C23—41no—
446C23—111no—
447C23—441no—
448C23D8×D1111yescharacteristic
449Q8—41no—
450Q8—41no—
451Q8—222no—
452Q8—441no—
453Q8—882no—
454D4—41no—
455D4—41no—
456D4—161no—
457D4—222no—
458D4—441no—
459D4—441no—
460D4—882no—
461D4—882no—
462D4—882no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—111no—
469C2×C4—111no—
470C2×C4—111no—
471C2×C4—221no—
472C2×C4—221no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—882no—
477C2×C4—882no—
478C2×C4—1761no—
479C2×C4—1761no—
480C2×C4D8×D1111yescharacteristic
481C2×C4C2×D4×D1111yescharacteristic
482C8—21no—
483C8—221no—
484C8—221no—
485C8#6703711yescharacteristic
486C8#41×D1111yescharacteristic
487C22—21no—
488C22—21no—
489C22—21no—
490C22—81no—
491C22—81no—
492C22—81no—
493C22—112no—
494C22—221no—
495C22—221no—
496C22—881no—
497C22—881no—
498C22—881no—
499C22C2×D8×D1111yescharacteristic
500C4—21no—
501C4—81no—
502C4—81no—
503C4—81no—
504C4—221no—
505C4—221no—
506C4—221no—
507C4—442no—
508C4—881no—
509C4—881no—
510C4#1062314111yescharacteristic
511C4#1062330111yescharacteristic
512C2—41no—
513C2—161no—
514C2—222no—
515C2—1761no—
516C2#1308042411yescharacteristic
517C2D11×#50811yescharacteristic
518C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2217C2
socleC22×C11C22×D8
hypercenter#2217D11
hypocenterC11#33868
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
1. #13081013C2semidirect
2. #13080360C2semidirect
3. #13070849C2semidirect
4. #13070821C2semidirect
5. #13070803C2semidirect
6. #13070783C2semidirect
7. #13070701C2semidirect
8. #13070673C2semidirect
9. #13070537C2semidirect
10. #13070531C2semidirect
11. #13070471C2semidirect
12. C16×C22⋊D11C2semidirect
13. #13070324C2semidirect
14. D11×#358C2semidirect
15. C11×#2217C2semidirect
192. #2217D11semidirect
444. C11#33868semidirect

Maximal subgroups

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

subgroupindex
#130810132
#130803602
#130708492
#130708212
#130708032
#130707832
#130707012
#130706732
#130705372
#130705312
#130704712
C16×C22⋊D112
#130703242
D11×#3582
C11×#22172
#3386811