Finite Group Databasebeta

← #14729929

Subgroups — #14729929

Order 2816.

908 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079012C211yesmaximal, characteristic
2#13078738C211yesmaximal, characteristic
3#13078738C211yesmaximal, characteristic
4#13067774C214yesmaximal, complemented
5#13067712C214yesmaximal, complemented
6#13067333C211yesmaximal, characteristic, complemented
7#13067063C211yesmaximal, characteristic, complemented
8#13067063C211yesmaximal, characteristic, complemented
9C2×C11×#557C211yesmaximal, characteristic, complemented
10C11×#557—22no—
11C11×#557—22no—
12C11×#557—22no—
13C11×#557C2214yes—
14C2×C11×C4⋊Q8—21no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125—22no—
17C2×C11×#125—21no—
18C2×C4×Q8×C11—21no—
19C2×C4×Q8×C11—21no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22#10623008C2211yescharacteristic
23#10622840—21no—
24#10622840—21no—
25#10622706C2212yes—
26#10622702—22no—
27#10622701C2212yes—
28#10622640C2212yes—
29#10622640C2212yes—
30#10622639—22no—
31#10622639—22no—
32#10622634C2212yes—
33#10622634C2212yes—
34#10622580—21no—
35#10622580—21no—
36#10622579—22no—
37#10622539C2211yescharacteristic
38#10622539C2211yescharacteristic
39C4×#4318C2211yescharacteristic
40#10622185C2214yes—
41Q8⋊(C11⋊C8)C2214yes—
42Q8⋊(C11⋊C8)C2214yes—
43C22×Q8×C11—21no—
44C22×Q8×C11D411yescharacteristic
45C22×Q8×C11D411yescharacteristic
46C2×#4339—21no—
47C11×C4⋊Q8—24no—
48C11×C4⋊Q8—24no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8D412yes—
52C11×C4⋊Q8C2312yes—
53C11×#125—28no—
54C11×#125—24no—
55C11×#125—28no—
56C11×#125—24no—
57C4×Q8×C11—24no—
58C4×Q8×C11—24no—
59C4×Q8×C11—24no—
60C4×Q8×C11—24no—
61C4×Q8×C11—21no—
62C4×Q8×C11—21no—
63C4×Q8×C11—21no—
64C4×Q8×C11—21no—
65C4×Q8×C11D412yes—
66C4×Q8×C11D412yes—
67C4×Q8×C11C2312yes—
68C4×Q8×C11C2312yes—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4D412yes—
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C42×C11—22no—
79C2×C42×C11—21no—
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×#4325—22no—
83C2×#4325—22no—
84#66983—21no—
85#66983—21no—
86C2×#4318—21no—
87#66928—21no—
88#66927C2311yescharacteristic
89C4×D44—21no—
90C4×D44—21no—
91#66922C2311yescharacteristic
92#66899—22no—
93#66899—22no—
94C22⋊(C11⋊C8)—21no—
95C22⋊(C11⋊C8)—21no—
96#66874—24no—
97#66873—24no—
98#66873—22no—
99#66873—22no—
100#66871—22no—
101#66871—22no—
102C4⋊(C11⋊C8)C2312yes—
103C4⋊(C11⋊C8)C2312yes—
104#66867—21no—
105#66867—21no—
106#66867—21no—
107C4×C11⋊C8C2312yes—
108#18535—111nomaximal, Sylow
109C2×Q8×C11—24no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—42no—
115C2×Q8×C11—44no—
116C2×Q8×C11C2×D412yes—
117C2×Q8×C11C2×D412yes—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C2×C22⋊D11—41no—
127#4339—44no—
128C2×D44—21no—
129C2×D44—21no—
130C2×D44—21no—
131C2×C4×D11—41no—
132C2×Dic22—21no—
133C11×C4⋊C4—28no—
134C11×C4⋊C4—28no—
135C11×C4⋊C4—28no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4C2×D412yes—
146C11×C4⋊C4C2×D412yes—
147C11×C4⋊C4C2×D414yes—
148C42×C11—28no—
149C42×C11—22no—
150C42×C11—22no—
151C42×C11—22no—
152C42×C11—22no—
153C42×C11C2×D411yescharacteristic
154C42×C11C2×D411yescharacteristic
155C42×C11C2×D411yescharacteristic
156C42×C11C2411yescharacteristic
157#4325—44no—
158#4325—44no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4—41no—
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163#4318—42no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×#557D1111yescharacteristic, complemented
168#3141—111no—
169#3112—111no—
170#3112—111no—
171#1636—114no—
172#1626—114no—
173#1556—111no—
174#1491—111no—
175#1491—111no—
176C23×C11#12011yescharacteristic
177C22×D11—41no—
178Q8×C11—24no—
179Q8×C11—22no—
180Q8×C11—22no—
181Q8×C11—22no—
182Q8×C11—42no—
183Q8×C11—44no—
184Q8×C11—44no—
185Q8×C11#13714yes—
186C2×C4×C11—24no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—24no—
195C2×C4×C11—42no—
196C2×C4×C11—44no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11#12011yescharacteristic
200C2×C4×C11#12011yescharacteristic
201C2×C4×C11#12011yescharacteristic
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C22×D411yescharacteristic
205C22⋊D11—82no—
206C2×Dic11—41no—
207D44—42no—
208D44—42no—
209D44—42no—
210C4×D11—82no—
211Dic22—42no—
212C11⋊C8—42no—
213C11⋊C8—42no—
214C11⋊C8—42no—
215#557—22no—
216#557—22no—
217#557—22no—
218#557C2×D1114yes—
219#532—111no—
220C2×C4⋊Q8—21no—
221C2×C4⋊Q8C2×D1111yescharacteristic
222C2×#125—22no—
223C2×#125—21no—
224C2×C4×Q8—21no—
225C2×C4×Q8—21no—
226C2×C4×Q8C2×D1111yescharacteristic
227C2×C4×Q8C2×D1111yescharacteristic
228#489—222no—
229#487—112no—
230#486—112no—
231#480—221no—
232#480—221no—
233#477—112no—
234#477—112no—
235#460—112no—
236#460—112no—
237#448—221no—
238#448—221no—
239#440—222no—
240#440—222no—
241#432—111no—
242#432—111no—
243#417—222no—
244C4×M16—111no—
245#332—114no—
246Q8⋊C8—114no—
247Q8⋊C8—114no—
248C22×C11—21no—
249C22×C11—21no—
250C22×C11#45412yes—
251C22×C11C2×#12011yescharacteristic
252C2×D11—81no—
253C2×D11—81no—
254C2×D11—81no—
255C4×C11—24no—
256C4×C11—21no—
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—42no—
261C4×C11—44no—
262C4×C11—42no—
263C4×C11—42no—
264C4×C11C2×#13712yes—
265C4×C11#57512yes—
266Dic11—81no—
267C2×#41—221no—
268C22×Q8—21no—
269C22×Q8C22⋊D1111yescharacteristic
270C22×Q8C22⋊D1111yescharacteristic
271C2×SD16—222no—
272C2×SD16—222no—
273C2×M16—221no—
274C4⋊Q8—24no—
275C4⋊Q8—24no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8—111no—
279C4⋊Q8C22⋊D1112yes—
280C4⋊Q8C22×D1112yes—
281#127—111no—
282#125—28no—
283#125—24no—
284#125—28no—
285#125—24no—
286#124—221no—
287#121—221no—
288#121—221no—
289C4×Q8—24no—
290C4×Q8—24no—
291C4×Q8—24no—
292C4×Q8—24no—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8C22⋊D1112yes—
298C4×Q8C22⋊D1112yes—
299C4×Q8C22×D1112yes—
300C4×Q8C22×D1112yes—
301C4×D4—221no—
302C4×D4—221no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4C22⋊D1111yescharacteristic
310C2×C4⋊C4C22⋊D1111yescharacteristic
311C2×C4⋊C4C22⋊D1112yes—
312C2×C42—22no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42C22×D1111yescharacteristic
316#107—222no—
317#107—222no—
318C4⋊C8—112no—
319C4⋊C8—112no—
320#103—222no—
321#103—222no—
322#103—224no—
323#102—224no—
324#102—222no—
325#102—222no—
326C22⋊C8—221no—
327C22⋊C8—221no—
328#97—221no—
329#97—221no—
330#97—221no—
331C4×C8—112no—
332C2×C11—22no—
333C2×C11#300411yescharacteristic
334C2×C11#300511yescharacteristic
335C2×C11C2×#45411yescharacteristic
336D11—161no—
337#41—444no—
338C2×Q8—24no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—22no—
342C2×Q8—22no—
343C2×Q8—42no—
344C2×Q8—44no—
345C2×Q8—221no—
346C2×Q8C2×C22⋊D1112yes—
347C2×Q8C2×C22⋊D1112yes—
348C2×D4—221no—
349C2×D4—221no—
350C2×D4—221no—
351C2×D4—441no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—441no—
358C22×C4C2×C22⋊D1111yescharacteristic
359C22×C4C2×C22⋊D1111yescharacteristic
360C22×C4C2×C22⋊D1111yescharacteristic
361SD16—444no—
362SD16—444no—
363M16—442no—
364C2×C8—222no—
365C2×C8—222no—
366C2×C8—222no—
367C4⋊C4—28no—
368C4⋊C4—28no—
369C4⋊C4—28no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—221no—
380C4⋊C4—221no—
381C4⋊C4C2×C22⋊D1114yes—
382C4⋊C4C2×C22⋊D1112yes—
383C4⋊C4C2×C22⋊D1112yes—
384C22⋊C4—441no—
385C22⋊C4—441no—
386C42—28no—
387C42—22no—
388C42—22no—
389C42—22no—
390C42—22no—
391C42C2×C22⋊D1111yescharacteristic
392C42C2×C22⋊D1111yescharacteristic
393C42C2×C22⋊D1111yescharacteristic
394C42C23×D1111yescharacteristic
395C11#1853511yescharacteristic, complemented, Sylow
396C23—441no—
397C23#6700611yescharacteristic
398Q8—24no—
399Q8—22no—
400Q8—22no—
401Q8—22no—
402Q8—42no—
403Q8—44no—
404Q8—44no—
405Q8—442no—
406Q8#6699514yes—
407D4—442no—
408D4—442no—
409D4—442no—
410D4—882no—
411C2×C4—24no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—24no—
420C2×C4—42no—
421C2×C4—44no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—441no—
425C2×C4—882no—
426C2×C4#6700611yescharacteristic
427C2×C4#6700611yescharacteristic
428C2×C4#6700611yescharacteristic
429C2×C4C22×C22⋊D1111yescharacteristic
430C2×C4C22×C22⋊D1111yescharacteristic
431C2×C4C22×C22⋊D1111yescharacteristic
432C8—442no—
433C8—442no—
434C8—442no—
435C22—21no—
436C22—21no—
437C22—881no—
438C22—881no—
439C22—881no—
440C22#1062285812yes—
441C22C2×#6700611yescharacteristic
442C4—24no—
443C4—21no—
444C4—21no—
445C4—21no—
446C4—21no—
447C4—42no—
448C4—44no—
449C4—42no—
450C4—42no—
451C4—881no—
452C4C2×#6699512yes—
453C4#1062335312yes—
454C2—22no—
455C2—1761no—
456C2#1307785011yescharacteristic
457C2#1307785811yescharacteristic
458C2C2×#1062285811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#557C2
socleC22×C11C2×#120
prime radical#10623008C22
hypercenterC2×#557D11
hypocenterC11#18535
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
4. #13067774C2semidirect
5. #13067712C2semidirect
6. #13067333C2semidirect
7. #13067063C2semidirect
8. #13067063C2semidirect
9. C2×C11×#557C2semidirect
167. C2×#557D11semidirect
395. C11#18535semidirect

Maximal subgroups

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

subgroupindex
#130790122
#130787382
#130677742
#130677122
#130673332
#130670632
C2×C11×#5572
#1853511