Finite Group Databasebeta

← #14772196

Subgroups — #14772196

Order 2816.

986 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×C4×#4325C212yesmaximal
2C2×C4×#4325C211yesmaximal, characteristic
3#13071527C211yesmaximal, characteristic
4#13069341C212yesmaximal, complemented
5#13068870C212yesmaximal, complemented
6#13068862C212yesmaximal
7#13068778C211yesmaximal, characteristic, complemented
8#13068631C211yesmaximal, characteristic, complemented
9#13068623C211yesmaximal, characteristic
10C4⋊C4×C11⋊C8C211yesmaximal, characteristic, complemented
11C11×#2351C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2212yes—
13C2×C4×Q8×C11C2211yescharacteristic
14C22×#4325C2211yescharacteristic
15C2×C4×D44C2212yes—
16C2×C4×D44C2211yescharacteristic
17C11×#389—22no—
18C11×#389C2212yes—
19C11×#382—21no—
20C11×#382C2211yescharacteristic
21C4×C11×C4⋊C4—21no—
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×#66899C2212yes—
24C2×#66899C2211yescharacteristic
25C4×#4325—28no—
26C4×#4325C418yescomplemented
27#10622602—22no—
28C2×#66873C2212yes—
29C2×#66873C2211yescharacteristic
30C2×#66872C2212yes—
31C2×#66872C2211yescharacteristic
32C2×#66871C2212yes—
33#10622549C2211yescharacteristic
34#10622541C2212yes—
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C2×C4×C11⋊C8C2212yes—
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622280—21no—
39D11×#95—21no—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622162C2212yes—
43C22×Q8×C11C2311yescharacteristic
44C22×D44C2311yescharacteristic
45C22×C4×D11—21no—
46C22×C4×D11—22no—
47C4×Q8×C11—22no—
48C4×Q8×C11—24no—
49C4×Q8×C11—42no—
50C4×Q8×C11C2×C414yescomplemented
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4D412yes—
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C42×C11—21no—
58C2×C42×C11—22no—
59C2×C42×C11C2312yes—
60C2×C42×C11C2311yescharacteristic
61C2×#4325C2×C414yes—
62C2×#4325D414yes—
63C2×#4325Q814yes—
64C2×(C2×D11)⋊C4—21no—
65C2×(C2×D11)⋊C4—22no—
66C2×C4⋊Dic11C2312yes—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×Dic11⋊C4—22no—
69C22×C11⋊C8C2312yes—
70C22×C11⋊C8C2311yescharacteristic
71C22×C11⋊C8C2311yescharacteristic
72C4×D44—22no—
73C4×D44—24no—
74C4×D44—42no—
75C4×D44C2×C414yes—
76C11×#95—21no—
77C11×#95—22no—
78C11×#95—21no—
79C11×#95D411yescharacteristic
80C11×#95D411yescharacteristic
81#66899—24no—
82#66899C2×C414yescomplemented
83C11⋊#95—21no—
84C11⋊#95—22no—
85C11⋊#95—21no—
86#66873—24no—
87#66873C2×C414yes—
88#66872—24no—
89#66872C2×C414yescomplemented
90#66871—42no—
91C4⋊(C11⋊C8)—22no—
92C4×C11⋊C8—24no—
93C4×C11⋊C8C2×C414yescomplemented
94#22683—111nomaximal, Sylow
95C23×D11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11C22×C412yes—
100C2×Q8×C11C2×D412yes—
101C2×Q8×C11C2×Q812yes—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2411yescharacteristic
110C22×Dic11—21no—
111C22×Dic11—22no—
112C2×D44—21no—
113C2×D44—21no—
114C2×D44—21no—
115C2×D44C22×C412yes—
116C2×D44C2×D412yes—
117C2×D44C2×Q812yes—
118C2×C4×D11—24no—
119C2×C4×D11—44no—
120C2×C4×D11—44no—
121C2×C4×D11—82no—
122C2×C4×D11—82no—
123C11×C4⋊C4—24no—
124C11×C4⋊C4—24no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—44no—
129C11×C4⋊C4—44no—
130C11×C4⋊C4C22×C412yes—
131C42×C11—24no—
132C42×C11—22no—
133C42×C11—22no—
134C42×C11—44no—
135C42×C11C22×C412yes—
136C42×C11#4112yes—
137#4325C4⋊C4116yescomplemented
138(C2×D11)⋊C4—24no—
139(C2×D11)⋊C4—44no—
140C4⋊Dic11—22no—
141C4⋊Dic11—21no—
142C4⋊Dic11—22no—
143C4⋊Dic11C22×C412yes—
144Dic11⋊C4—82no—
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×C4×SD16—111no—
155C2×C4×SD16—112no—
156#2351D1111yescharacteristic, complemented
157#2349—111no—
158#1941—112no—
159#1863—112no—
160#1862—112no—
161#1846—111no—
162#1805—111no—
163#1804—111no—
164C8×C4⋊C4—111no—
165C23×C11C22×D411yescharacteristic
166C22×D11—22no—
167C22×D11—22no—
168C22×D11—22no—
169C22×D11—42no—
170C22×D11—42no—
171Q8×C11—22no—
172Q8×C11—22no—
173Q8×C11—22no—
174Q8×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—22no—
185C2×C4×C11—22no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11C4×D412yes—
191C2×C4×C11C4×D412yes—
192C2×C4×C11#13514yes—
193C2×C4×C11C23×C411yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C22×Q811yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C11H(5,𝔽2)11yescharacteristic
198C2×C4×C112−1+411yescharacteristic
199C2×Dic11—22no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204D44—22no—
205D44—22no—
206D44—22no—
207D44C2×C4⋊C414yes—
208C4×D11—84no—
209C4×D11—88no—
210C11⋊C8—22no—
211C11⋊C8—42no—
212C11⋊C8C2×C4⋊C414yes—
213C22×SD16—111no—
214C2×C4×Q8C2×D1112yes—
215C2×C4×Q8C2×D1111yescharacteristic
216C2×C4×D4—111no—
217C2×C4×D4—112no—
218C4×SD16—118no—
219C4×SD16—228no—
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×C4×C8—111no—
229C2×C4×C8—112no—
230#389—22no—
231#389—112no—
232#389C2×D1112yes—
233#385—222no—
234#382—21no—
235#382—111no—
236#382C2×D1111yescharacteristic
237#380—221no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4C2×D1111yescharacteristic
240C2×#95—221no—
241#340—112no—
242#340—112no—
243#336—112no—
244C22×C11C2×C4×D411yescharacteristic
245C22×C11D4211yescharacteristic
246C22×C11D4×Q811yescharacteristic
247C22×C11C2×#13512yes—
248C22×C11#57712yes—
249C2×D11—24no—
250C2×D11—44no—
251C2×D11—42no—
252C2×D11—42no—
253C2×D11—44no—
254C4×C11—24no—
255C4×C11—22no—
256C4×C11—22no—
257C4×C11—24no—
258C4×C11—42no—
259C4×C11—42no—
260C4×C11—82no—
261C4×C11C22×C4⋊C411yescharacteristic
262C4×C11#52011yescharacteristic
263C4×C11#54711yescharacteristic
264C4×C11#55411yescharacteristic
265Dic11—42no—
266Dic11—82no—
267C22×Q8C22×D1111yescharacteristic
268C22×D4—111no—
269C23×C4—221no—
270C23×C4—222no—
271C2×SD16—114no—
272C2×SD16—114no—
273C2×SD16—114no—
274C22×C8—111no—
275C22×C8—111no—
276C22×C8—112no—
277C4×Q8—22no—
278C4×Q8—24no—
279C4×Q8—42no—
280C4×Q8C4×D1114yescomplemented
281C4×D4—114no—
282C4×D4—224no—
283C4×D4—222no—
284C4×D4—442no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—111no—
289C2×C4⋊C4—112no—
290C2×C4⋊C4—222no—
291C2×C4⋊C4C22⋊D1112yes—
292C2×C4⋊C4C22×D1112yes—
293C2×C4⋊C4C22×D1111yescharacteristic
294C2×C22⋊C4—221no—
295C2×C22⋊C4—222no—
296C2×C42—21no—
297C2×C42—22no—
298C2×C42C22×D1112yes—
299C2×C42C22×D1111yescharacteristic
300#107—442no—
301#106—114no—
302#106—224no—
303C4⋊C8—222no—
304#103—114no—
305#103—224no—
306#102—114no—
307#102—224no—
308C4×C8—114no—
309C4×C8—224no—
310#95—21no—
311#95—22no—
312#95—21no—
313#95—221no—
314#95—222no—
315#95—221no—
316#95C22⋊D1111yescharacteristic
317#95C22⋊D1111yescharacteristic
318C2×C11D4×C4⋊C411yescharacteristic
319C2×C11C4×#13511yescharacteristic
320C2×C11#294911yescharacteristic
321C2×C11#328212yes—
322C2×C11#338112yes—
323D11—44no—
324C24—221no—
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8C2×C4×D1112yes—
329C2×Q8D4×D1112yes—
330C2×Q8Q8×D1112yes—
331C2×D4—112no—
332C2×D4—112no—
333C2×D4—112no—
334C2×D4—221no—
335C2×D4—221no—
336C2×D4—221no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—22no—
340C22×C4—221no—
341C22×C4—224no—
342C22×C4—222no—
343C22×C4—444no—
344C22×C4—444no—
345C22×C4—882no—
346C22×C4—882no—
347C22×C4C2×C22⋊D1112yes—
348C22×C4C2×C22⋊D1111yescharacteristic
349C22×C4C2×C22⋊D1111yescharacteristic
350C22×C4C2×C22⋊D1112yes—
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—24no—
363C4⋊C4—24no—
364C4⋊C4—21no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—44no—
368C4⋊C4—44no—
369C4⋊C4—112no—
370C4⋊C4—221no—
371C4⋊C4—222no—
372C4⋊C4—222no—
373C4⋊C4—882no—
374C4⋊C4C2×C4×D1112yes—
375C22⋊C4—224no—
376C22⋊C4—444no—
377C42—24no—
378C42—22no—
379C42—22no—
380C42—44no—
381C42C2×C4×D1112yes—
382C42#433912yes—
383C11#2268311yescharacteristic, complemented, Sylow
384C23—222no—
385C23—222no—
386C23—222no—
387C23—442no—
388C23—442no—
389C23C22×C22⋊D1111yescharacteristic
390Q8—22no—
391Q8—22no—
392Q8—22no—
393Q8C4⋊C4×D1114yes—
394D4—114no—
395D4—222no—
396D4—222no—
397D4—222no—
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—22no—
408C2×C4—22no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—222no—
414C2×C4—442no—
415C2×C4—442no—
416C2×C4—442no—
417C2×C4—442no—
418C2×C4—884no—
419C2×C4—888no—
420C2×C4C4×C22⋊D1112yes—
421C2×C4C4×C22⋊D1112yes—
422C2×C4#6700314yes—
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—224no—
433C22—444no—
434C22—442no—
435C22—444no—
436C22—442no—
437C22C2×C4×C22⋊D1111yescharacteristic
438C22D4×C22⋊D1111yescharacteristic
439C22Q8×C22⋊D1111yescharacteristic
440C22C2×#6700312yes—
441C22#1062336812yes—
442C4—24no—
443C4—22no—
444C4—24no—
445C4—22no—
446C4—42no—
447C4—42no—
448C4—82no—
449C4—442no—
450C4—882no—
451C4C2×C4⋊C4×D1111yescharacteristic
452C4#1062303511yescharacteristic
453C4#1062303811yescharacteristic
454C4#1062304211yescharacteristic
455C2—444no—
456C2C4⋊C4×C22⋊D1111yescharacteristic
457C2C4×#6700311yescharacteristic
458C2#1307747511yescharacteristic
459C2#1308032412yes—
460C2#1308148712yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2351C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#2351D11
hypocenterC11#22683
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2351

Complements

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

NH ≅ G/Ntype
4. #13069341C2semidirect
5. #13068870C2semidirect
7. #13068778C2semidirect
8. #13068631C2semidirect
10. C4⋊C4×C11⋊C8C2semidirect
11. C11×#2351C2semidirect
26. C4×#4325C4semidirect
50. C4×Q8×C11C2×C4semidirect
82. #66899C2×C4semidirect
89. #66872C2×C4semidirect
93. C4×C11⋊C8C2×C4semidirect
137. #4325C4⋊C4semidirect
156. #2351D11semidirect
280. C4×Q8C4×D11semidirect
383. C11#22683semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43252
#130715272
#130693412
#130688702
#130688622
#130687782
#130686312
#130686232
C4⋊C4×C11⋊C82
C11×#23512
#2268311