Finite Group Databasebeta

← #14772077

Subgroups — #14772077

Order 2816.

974 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622631C212yesmaximal
2C2×C4×#4324C211yesmaximal, characteristic
3#13071536C211yesmaximal, characteristic, complemented
4#13069356C212yesmaximal, complemented
5#13068883C212yesmaximal, complemented
6#13068877C212yesmaximal
7#13068778C211yesmaximal, characteristic, complemented
8#13068628C211yesmaximal, characteristic, complemented
9#13068626C211yesmaximal, characteristic
10#13068485C211yesmaximal, characteristic, complemented
11C11×#2349C211yesmaximal, characteristic
12C2×C4×D4×C11C2212yes—
13C2×C4×D4×C11C2211yescharacteristic
14C22×#4324C2211yescharacteristic
15C2×C4×Dic22C2212yes—
16C2×C4×Dic22C2211yescharacteristic
17C11×#389C2212yes—
18C11×#385—22no—
19C11×#382C2211yescharacteristic
20C11×#380—21no—
21C4×C11×C4⋊C4C2211yescharacteristic
22C2×C11×#95—21no—
23C2×#66896C2212yes—
24C2×#66896C2211yescharacteristic
25#10622631—28no—
26C4×#4324C418yescomplemented
27#10622585—22no—
28C2×#66874C2212yes—
29C2×#66874C2211yescharacteristic
30C2×#66872C2212yes—
31C2×#66872C2211yescharacteristic
32C2×#66871C2212yes—
33#10622549C2211yescharacteristic
34#10622541C2212yes—
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C2×#66867C2212yes—
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622263—21no—
39#10622262—21no—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622162C2212yes—
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C23×C4×C11—22no—
46C22×Dic22C2311yescharacteristic
47C4×D4×C11—24no—
48C4×D4×C11—22no—
49C4×D4×C11—42no—
50C4×D4×C11C2×C414yes—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4D412yes—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C22⋊C4—21no—
56C2×C11×C22⋊C4—22no—
57C2×C42×C11C2312yes—
58C2×C42×C11C2311yescharacteristic
59C2×#4324C2×C414yes—
60C2×#4324D414yes—
61C2×#4324Q814yes—
62C2×C4⋊Dic11C2312yes—
63C2×C4⋊Dic11C2311yescharacteristic
64C2×Dic11⋊C4—21no—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—22no—
67C2×C4×Dic11—21no—
68C2×C4×Dic11—22no—
69C22×C11⋊C8C2312yes—
70C22×C11⋊C8C2311yescharacteristic
71C22×C11⋊C8C2311yescharacteristic
72C4×Dic22—22no—
73C4×Dic22—24no—
74C4×Dic22—42no—
75C4×Dic22C2×C414yescomplemented
76C11×#95—21no—
77C11×#95—22no—
78C11×#95—21no—
79C11×#95D411yescharacteristic
80C11×#95D411yescharacteristic
81#66896—24no—
82#66896C2×C414yes—
83C11⋊#95—21no—
84C11⋊#95—22no—
85C11⋊#95—21no—
86#66874—24no—
87#66874C2×C414yescomplemented
88#66872—42no—
89#66872C2×C414yescomplemented
90#66871—24no—
91C4⋊(C11⋊C8)—22no—
92#66867—24no—
93C4×C11⋊C8C2×C414yescomplemented
94#22673—111nomaximal, Sylow
95C24×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11C22×C412yes—
100C2×D4×C11C2×D412yes—
101C2×D4×C11C2×Q812yes—
102C22×C4×C11—21no—
103C22×C4×C11—24no—
104C22×C4×C11—22no—
105C22×C4×C11—44no—
106C22×C4×C11—44no—
107C22×C4×C11—82no—
108C22×C4×C11—82no—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2411yescharacteristic
114C22×Dic11—21no—
115C22×Dic11—21no—
116C22×Dic11—22no—
117C2×Dic22—21no—
118C2×Dic22—21no—
119C2×Dic22—21no—
120C2×Dic22C22×C412yes—
121C2×Dic22C2×D412yes—
122C2×Dic22C2×Q812yes—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—42no—
127C11×C4⋊C4—82no—
128C11×C4⋊C4C22×C412yes—
129C11×C22⋊C4—24no—
130C11×C22⋊C4—44no—
131C42×C11—22no—
132C42×C11—22no—
133C42×C11C22×C412yes—
134C42×C11#4112yes—
135#4324C4⋊C4116yescomplemented
136C4⋊Dic11—22no—
137C4⋊Dic11—21no—
138C4⋊Dic11—22no—
139C4⋊Dic11C22×C412yes—
140Dic11⋊C4—24no—
141Dic11⋊C4—44no—
142Dic11⋊C4—44no—
143C4×Dic11—24no—
144C4×Dic11—44no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—21no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8C22×C412yes—
151C2×C11⋊C8C22×C412yes—
152C2×C11⋊C8C2×D412yes—
153C2×C11⋊C8C2×Q812yes—
154C2×#440—112no—
155C2×C4×SD16—111no—
156#2351—111no—
157#2349D1111yescharacteristic
158#1944—112no—
159#1865—112no—
160#1864—112no—
161#1846—111no—
162#1805—111no—
163#1804—111no—
164#1770—111no—
165C23×C11—22no—
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—42no—
169C23×C11—42no—
170C23×C11C22×D411yescharacteristic
171D4×C11—22no—
172D4×C11—22no—
173D4×C11—22no—
174D4×C11C2×C4⋊C414yes—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—84no—
189C2×C4×C11—88no—
190C2×C4×C11C4×D412yes—
191C2×C4×C11C4×D412yes—
192C2×C4×C11C23×C411yescharacteristic
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C22×Q811yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×C4×C11H(5,𝔽2)11yescharacteristic
197C2×C4×C112−1+411yescharacteristic
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206Dic22—22no—
207Dic22—22no—
208Dic22—22no—
209Dic22C2×C4⋊C414yes—
210C11⋊C8—22no—
211C11⋊C8—42no—
212C11⋊C8C2×C4⋊C414yes—
213C22×SD16—111no—
214C2×C4×Q8—111no—
215C2×C4×Q8—112no—
216C2×C4×D4C2×D1112yes—
217C2×C4×D4C2×D1111yescharacteristic
218#440—228no—
219C4×SD16—118no—
220C2×#107—112no—
221C2×#106—111no—
222C2×#106—112no—
223C2×C4⋊C8—111no—
224C2×#103—111no—
225C2×#103—112no—
226C2×#102—111no—
227C2×#102—112no—
228C2×#97—112no—
229C2×C4×C8—111no—
230#389—112no—
231#389—222no—
232#389C2×D1112yes—
233#385—22no—
234#382—111no—
235#382—221no—
236#382C2×D1111yescharacteristic
237#380—21no—
238C4×C4⋊C4—221no—
239C4×C4⋊C4C2×D1111yescharacteristic
240C2×#95—21no—
241#340—112no—
242#340—112no—
243#336—112no—
244C22×C11—24no—
245C22×C11—44no—
246C22×C11—42no—
247C22×C11—42no—
248C22×C11—44no—
249C22×C11C2×C4×D411yescharacteristic
250C22×C11D4211yescharacteristic
251C22×C11D4×Q811yescharacteristic
252C22×C11#57512yes—
253C22×C11#57712yes—
254C4×C11—22no—
255C4×C11—22no—
256C4×C11—42no—
257C4×C11—42no—
258C4×C11—42no—
259C4×C11—82no—
260C4×C11C22×C4⋊C411yescharacteristic
261C4×C11#52011yescharacteristic
262C4×C11#54711yescharacteristic
263C4×C11#55411yescharacteristic
264Dic11—24no—
265Dic11—42no—
266Dic11—82no—
267C22×Q8—111no—
268C22×D4C22×D1111yescharacteristic
269C23×C4—21no—
270C23×C4—22no—
271C2×SD16—114no—
272C2×SD16—114no—
273C2×SD16—114no—
274C22×C8—111no—
275C22×C8—111no—
276C22×C8—112no—
277C4×Q8—114no—
278C4×Q8—224no—
279C4×Q8—222no—
280C4×Q8—442no—
281C4×D4—24no—
282C4×D4—22no—
283C4×D4—42no—
284C4×D4C4×D1114yes—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—112no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4—222no—
290C2×C4⋊C4—222no—
291C2×C4⋊C4C22⋊D1112yes—
292C2×C4⋊C4C22×D1112yes—
293C2×C4⋊C4C22×D1111yescharacteristic
294C2×C22⋊C4—21no—
295C2×C22⋊C4—22no—
296C2×C42—221no—
297C2×C42—222no—
298C2×C42C22×D1112yes—
299C2×C42C22×D1111yescharacteristic
300#107—224no—
301#106—114no—
302#106—442no—
303C4⋊C8—222no—
304#103—114no—
305#103—224no—
306#102—114no—
307#102—224no—
308#97—224no—
309C4×C8—114no—
310#95—21no—
311#95—22no—
312#95—21no—
313#95—221no—
314#95—221no—
315#95—222no—
316#95C22⋊D1111yescharacteristic
317#95C22⋊D1111yescharacteristic
318C2×C11—44no—
319C2×C11D4×C4⋊C411yescharacteristic
320C2×C11#294311yescharacteristic
321C2×C11#294911yescharacteristic
322C2×C11#327512yes—
323C2×C11#338812yes—
324C24—21no—
325C2×Q8—112no—
326C2×Q8—112no—
327C2×Q8—112no—
328C2×Q8—221no—
329C2×Q8—221no—
330C2×Q8—221no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4C2×C4×D1112yes—
335C2×D4D4×D1112yes—
336C2×D4Q8×D1112yes—
337C22×C4—21no—
338C22×C4—24no—
339C22×C4—22no—
340C22×C4—44no—
341C22×C4—44no—
342C22×C4—82no—
343C22×C4—82no—
344C22×C4—221no—
345C22×C4—221no—
346C22×C4—222no—
347C22×C4C2×C22⋊D1112yes—
348C22×C4C2×C22⋊D1112yes—
349C22×C4C2×C22⋊D1111yescharacteristic
350C22×C4C2×C22⋊D1111yescharacteristic
351C22×C4C23×D1111yescharacteristic
352SD16—1116no—
353C2×C8—112no—
354C2×C8—112no—
355C2×C8—112no—
356C2×C8—112no—
357C2×C8—221no—
358C2×C8—221no—
359C2×C8—222no—
360C2×C8—222no—
361C2×C8—222no—
362C4⋊C4—21no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—42no—
366C4⋊C4—82no—
367C4⋊C4—112no—
368C4⋊C4—224no—
369C4⋊C4—221no—
370C4⋊C4—222no—
371C4⋊C4—222no—
372C4⋊C4—444no—
373C4⋊C4—444no—
374C4⋊C4C2×C4×D1112yes—
375C22⋊C4—24no—
376C22⋊C4—44no—
377C42—22no—
378C42—22no—
379C42—224no—
380C42—444no—
381C42C2×C4×D1112yes—
382C42#433912yes—
383C11#2267311yescharacteristic, complemented, Sylow
384C23—22no—
385C23—22no—
386C23—22no—
387C23—42no—
388C23—42no—
389C23C22×C22⋊D1111yescharacteristic
390Q8—114no—
391Q8—222no—
392Q8—222no—
393Q8—222no—
394D4—22no—
395D4—22no—
396D4—22no—
397D4C4⋊C4×D1114yes—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—84no—
412C2×C4—88no—
413C2×C4—222no—
414C2×C4—222no—
415C2×C4—222no—
416C2×C4—222no—
417C2×C4—442no—
418C2×C4—442no—
419C2×C4—442no—
420C2×C4—442no—
421C2×C4C4×C22⋊D1112yes—
422C2×C4C4×C22⋊D1112yes—
423C2×C4C22×C4×D1111yescharacteristic
424C2×C4C2×#433911yescharacteristic
425C2×C4C2×D4×D1111yescharacteristic
426C2×C4#6703711yescharacteristic
427C2×C4C2×Q8×D1111yescharacteristic
428C2×C4#6704011yescharacteristic
429C8—114no—
430C8—222no—
431C8—442no—
432C22—24no—
433C22—42no—
434C22—44no—
435C22—44no—
436C22—42no—
437C22C2×C4×C22⋊D1111yescharacteristic
438C22D4×C22⋊D1111yescharacteristic
439C22Q8×C22⋊D1111yescharacteristic
440C22#1062335312yes—
441C22#1062336712yes—
442C4—22no—
443C4—22no—
444C4—42no—
445C4—42no—
446C4—42no—
447C4—82no—
448C4—224no—
449C4—442no—
450C4—882no—
451C4C2×C4⋊C4×D1111yescharacteristic
452C4#1062303511yescharacteristic
453C4#1062303811yescharacteristic
454C4#1062304211yescharacteristic
455C2—44no—
456C2C4⋊C4×C22⋊D1111yescharacteristic
457C2#1307741411yescharacteristic
458C2#1307747311yescharacteristic
459C2#1308024312yes—
460C2#1308156112yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2349C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#2349D11
hypocenterC11#22673
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2349

Complements

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

NH ≅ G/Ntype
3. #13071536C2semidirect
4. #13069356C2semidirect
5. #13068883C2semidirect
7. #13068778C2semidirect
8. #13068628C2semidirect
10. #13068485C2semidirect
26. C4×#4324C4semidirect
75. C4×Dic22C2×C4semidirect
87. #66874C2×C4semidirect
89. #66872C2×C4semidirect
93. C4×C11⋊C8C2×C4semidirect
135. #4324C4⋊C4semidirect
383. C11#22673semidirect

Maximal subgroups

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

subgroupindex
C2×#106226312
C2×C4×#43242
#130715362
#130693562
#130688832
#130688772
#130687782
#130686282
#130686262
#130684852
C11×#23492
#2267311