Finite Group Databasebeta

← #14775568

Subgroups — #14775568

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622700C211yesmaximal, characteristic
2C4⋊C4×D44C211yesmaximal, characteristic
3#13069578C211yesmaximal, characteristic, complemented
4#13069374C211yesmaximal, characteristic, complemented
5#13069346C212yesmaximal, complemented
6#13069187C212yesmaximal, complemented
7#13068862C212yesmaximal
8C4⋊C4×C11⋊C8C211yesmaximal, characteristic, complemented
9C4×#66873C212yesmaximal
10C4×#66873C211yesmaximal, characteristic
11C11×#2365C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11—21no—
14C2×C4⋊C4×D11—21no—
15C2×C4×D44C2212yes—
16C2×C4×D44C2211yescharacteristic
17C11×#391—21no—
18C11×#389C2212yes—
19C11×#387—22no—
20C4×C11×C4⋊C4C2211yescharacteristic
21C4×C11×C4⋊C4C2212yes—
22C4×C11×C4⋊C4C2211yescharacteristic
23#10622700C418yescomplemented
24#10622600—21no—
25C2×#66873C2211yescharacteristic
26C2×#66873C2212yes—
27C2×#66873C2211yescharacteristic
28C2×#66871C2212yes—
29C2×#66871C2212yes—
30#10622548C2211yescharacteristic
31#10622541C2212yes—
32C2×C4⋊(C11⋊C8)C2211yescharacteristic
33C2×C4×C11⋊C8C2211yescharacteristic
34C2×C4×C11⋊C8C2212yes—
35#10622281—22no—
36#10622167C2212yes—
37#10622167C2212yes—
38#10622167C2211yescharacteristic
39#10622167C2212yes—
40#10622167C2211yescharacteristic
41#10622162C2212yes—
42C22×Q8×C11—21no—
43C22×D44C2311yescharacteristic
44C22×C4×D11—21no—
45C22×C4×D11—22no—
46C11×C4⋊Q8—22no—
47C11×C4⋊Q8C2×C414yescomplemented
48C4×Q8×C11—44no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C42×C11—22no—
57C2×C42×C11—21no—
58C2×C42×C11C2312yes—
59C2×C42×C11C2311yescharacteristic
60C2×(C2×D11)⋊C4—21no—
61C2×(C2×D11)⋊C4—22no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×Dic11⋊C4—22no—
67C22×C11⋊C8C2311yescharacteristic
68C22×C11⋊C8C2312yes—
69C22×C11⋊C8C2311yescharacteristic
70C4⋊C4×D11—44no—
71C4×D44—22no—
72C4×D44—24no—
73C4×D44—42no—
74C4×D44C2×C414yes—
75C11×#95—21no—
76C11×#95—22no—
77C11×#95—22no—
78C11×#95D412yes—
79C11⋊#95—22no—
80#66873—22no—
81#66873C2×C418yes—
82#66873Q814yescomplemented
83#66871—42no—
84#66871C2×C418yescomplemented
85C4⋊(C11⋊C8)C2×C414yescomplemented
86C4×C11⋊C8—22no—
87C4×C11⋊C8—42no—
88#22962—111nomaximal, Sylow
89C23×D11—21no—
90C2×Q8×C11—24no—
91C2×Q8×C11—42no—
92C2×Q8×C11—42no—
93C22×C4×C11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—21no—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—21no—
102C22×Dic11—22no—
103C2×D44—21no—
104C2×D44—21no—
105C2×D44—21no—
106C2×D44C22×C412yes—
107C2×D44C2×Q812yes—
108C2×D44#4112yes—
109C2×C4×D11—24no—
110C2×C4×D11—44no—
111C2×C4×D11—42no—
112C2×C4×D11—44no—
113C2×C4×D11—42no—
114C2×C4×D11—82no—
115C11×C4⋊C4—24no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—44no—
122C11×C4⋊C4D814yes—
123C11×C4⋊C4C22×C414yes—
124C11×C4⋊C4C2×Q812yes—
125C42×C11—22no—
126C42×C11—22no—
127C42×C11—44no—
128C42×C11—42no—
129C42×C11C22×C412yes—
130C42×C11#4112yes—
131(C2×D11)⋊C4—24no—
132(C2×D11)⋊C4—44no—
133C4⋊Dic11—21no—
134C4⋊Dic11—22no—
135C4⋊Dic11—22no—
136C4⋊Dic11—42no—
137C4⋊Dic11—81no—
138C4⋊Dic11C22×C412yes—
139Dic11⋊C4—44no—
140C2×C11⋊C8—21no—
141C2×C11⋊C8—21no—
142C2×C11⋊C8—21no—
143C2×C11⋊C8—21no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—21no—
147C2×C11⋊C8C22×C414yes—
148C2×C11⋊C8C2×Q812yes—
149C2×#474—111no—
150#2365D1111yescharacteristic, complemented
151D4×C4⋊C4—111no—
152#1990—111no—
153#1947—111no—
154#1942—112no—
155#1918—112no—
156#1862—112no—
157C8×C4⋊C4—111no—
158C4×#102—111no—
159C4×#102—112no—
160C23×C11C22×D411yescharacteristic
161C22×D11—22no—
162C22×D11—22no—
163C22×D11—22no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—41no—
167C22×D11—41no—
168Q8×C11—48no—
169C2×C4×C11—22no—
170C2×C4×C11—21no—
171C2×C4×C11—22no—
172C2×C4×C11—21no—
173C2×C4×C11—24no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11C4×D412yes—
186C2×C4×C11C4×D412yes—
187C2×C4×C11C2×D814yes—
188C2×C4×C11C2×D812yes—
189C2×C4×C11#13512yes—
190C2×C4×C11C23×C411yescharacteristic
191C2×C4×C11C22×Q811yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C11H(5,𝔽2)11yescharacteristic
195C2×C4×C112−1+411yescharacteristic
196C2×Dic11—22no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202D44—22no—
203D44—22no—
204D44—22no—
205D44C4×Q814yescomplemented
206C4×D11—48no—
207C4×D11—88no—
208C11⋊C8—24no—
209C11⋊C8—22no—
210C11⋊C8—41no—
211C2×C4⋊Q8C2×D1111yescharacteristic
212C2×C4×Q8—21no—
213C2×C4×D4—111no—
214C2×C4×D4—112no—
215C22×C4⋊C4—221no—
216#474—118no—
217C2×#107—112no—
218C2×#107—112no—
219C2×C4⋊C8—111no—
220C2×#102—112no—
221C2×#102—111no—
222C2×#102—111no—
223C2×C4×C8—111no—
224C2×C4×C8—112no—
225#391—21no—
226#389—112no—
227#389C2×D1112yes—
228#387—22no—
229#385—222no—
230#384—111no—
231#380—221no—
232C4×C4⋊C4C2×D1112yes—
233C4×C4⋊C4C2×D1111yescharacteristic
234C4×C4⋊C4C2×D1111yescharacteristic
235#340—112no—
236#340—111no—
237#340—112no—
238#340—111no—
239#340—112no—
240#336—112no—
241C22×C11C2×C4×D411yescharacteristic
242C22×C11#54611yescharacteristic
243C22×C11D4×Q811yescharacteristic
244C22×C11C22×D811yescharacteristic
245C22×C11C2×#13511yescharacteristic
246C22×C11#57711yescharacteristic
247C22×C11#57811yescharacteristic
248C2×D11—24no—
249C2×D11—42no—
250C2×D11—42no—
251C2×D11—42no—
252C2×D11—42no—
253C2×D11—42no—
254C2×D11—42no—
255C4×C11—22no—
256C4×C11—24no—
257C4×C11—42no—
258C4×C11—44no—
259C4×C11—42no—
260C4×C11—81no—
261C4×C11C4×D814yes—
262C4×C11C2×C4×Q811yescharacteristic
263C4×C11#52011yescharacteristic
264C4×C11#55211yescharacteristic
265C4×C11#55411yescharacteristic
266Dic11—42no—
267Dic11—82no—
268C22×Q8—21no—
269C22×D4—111no—
270C23×C4—221no—
271C23×C4—222no—
272C22×C8—112no—
273C22×C8—111no—
274C22×C8—111no—
275C4⋊Q8—22no—
276C4⋊Q8C4×D1114yescomplemented
277C4×Q8—44no—
278C4×D4—114no—
279C4×D4—224no—
280C4×D4—222no—
281C4×D4—442no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—111no—
285C2×C4⋊C4—112no—
286C2×C4⋊C4—221no—
287C2×C4⋊C4—222no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4—444no—
290C2×C4⋊C4C22⋊D1111yescharacteristic
291C2×C4⋊C4C22⋊D1111yescharacteristic
292C2×C4⋊C4C22×D1111yescharacteristic
293C2×C4⋊C4C22×D1112yes—
294C2×C4⋊C4C22×D1111yescharacteristic
295C2×C22⋊C4—221no—
296C2×C22⋊C4—222no—
297C2×C42—22no—
298C2×C42—21no—
299C2×C42C22×D1112yes—
300C2×C42C22×D1111yescharacteristic
301#107—118no—
302#107—442no—
303C4⋊C8—114no—
304#102—118no—
305#102—114no—
306#102—222no—
307C4×C8—222no—
308C4×C8—442no—
309#95—21no—
310#95—22no—
311#95—22no—
312#95—222no—
313#95C22⋊D1112yes—
314C2×C11#236011yescharacteristic
315C2×C11C2×C4×D811yescharacteristic
316C2×C11#294711yescharacteristic
317C2×C11#329411yescharacteristic
318C2×C11#330211yescharacteristic
319C2×C11Q8×D811yescharacteristic
320C2×C11#338111yescharacteristic
321D11—44no—
322C24—221no—
323C2×Q8—24no—
324C2×Q8—42no—
325C2×Q8—42no—
326C2×D4—112no—
327C2×D4—112no—
328C2×D4—112no—
329C2×D4—221no—
330C2×D4—221no—
331C2×D4—221no—
332C22×C4—21no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—221no—
336C22×C4—224no—
337C22×C4—222no—
338C22×C4—444no—
339C22×C4—442no—
340C22×C4—442no—
341C22×C4—444no—
342C22×C4—882no—
343C22×C4C2×C22⋊D1112yes—
344C22×C4C2×C22⋊D1111yescharacteristic
345C22×C4C2×C22⋊D1112yes—
346C22×C4C2×C22⋊D1111yescharacteristic
347C22×C4C23×D1111yescharacteristic
348C2×C8—114no—
349C2×C8—112no—
350C2×C8—221no—
351C2×C8—222no—
352C2×C8—221no—
353C2×C8—222no—
354C2×C8—221no—
355C2×C8—221no—
356C2×C8—221no—
357C4⋊C4—24no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—44no—
364C4⋊C4—112no—
365C4⋊C4—221no—
366C4⋊C4—222no—
367C4⋊C4—222no—
368C4⋊C4—444no—
369C4⋊C4—442no—
370C4⋊C4—881no—
371C4⋊C4#432314yes—
372C4⋊C4C2×C4×D1114yes—
373C4⋊C4Q8×D1112yes—
374C22⋊C4—224no—
375C22⋊C4—444no—
376C42—22no—
377C42—22no—
378C42—44no—
379C42—42no—
380C42C2×C4×D1112yes—
381C42#433912yes—
382C11#2296211yescharacteristic, complemented, Sylow
383C23—222no—
384C23—222no—
385C23—222no—
386C23—441no—
387C23—441no—
388C23—441no—
389C23—441no—
390C23C22×C22⋊D1111yescharacteristic
391Q8—48no—
392D4—114no—
393D4—222no—
394D4—222no—
395D4—222no—
396C2×C4—22no—
397C2×C4—21no—
398C2×C4—22no—
399C2×C4—21no—
400C2×C4—24no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—222no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4—448no—
416C2×C4—442no—
417C2×C4—442no—
418C2×C4—442no—
419C2×C4—888no—
420C2×C4C4×C22⋊D1112yes—
421C2×C4C4×C22⋊D1112yes—
422C2×C4C2×#432314yes—
423C2×C4C2×#432312yes—
424C2×C4#6700312yes—
425C2×C4C22×C4×D1111yescharacteristic
426C2×C4C2×#433911yescharacteristic
427C2×C4C2×Q8×D1111yescharacteristic
428C2×C4#6704011yescharacteristic
429C2×C4#41×D1111yescharacteristic
430C2×C4#6704211yescharacteristic
431C8—224no—
432C8—222no—
433C8—441no—
434C22—224no—
435C22—442no—
436C22—442no—
437C22—442no—
438C22—442no—
439C22—442no—
440C22—442no—
441C22C2×C4×C22⋊D1111yescharacteristic
442C22C22×#432311yescharacteristic
443C22Q8×C22⋊D1111yescharacteristic
444C22C2×#6700311yescharacteristic
445C22#1062336011yescharacteristic
446C22#1062336811yescharacteristic
447C22#1062336911yescharacteristic
448C4—24no—
449C4—22no—
450C4—44no—
451C4—42no—
452C4—42no—
453C4—81no—
454C4—442no—
455C4—882no—
456C4C4×#432314yes—
457C4C4×Q8×D1111yescharacteristic
458C4#1062310511yescharacteristic
459C4#1062311011yescharacteristic
460C4#1062311211yescharacteristic
461C2—444no—
462C2#1307161711yescharacteristic
463C2C2×C4×#432311yescharacteristic
464C2#1307745911yescharacteristic
465C2#1308042311yescharacteristic
466C2#1308052711yescharacteristic
467C2Q8×#432311yescharacteristic
468C2#1308148711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2365C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#2365D11
hypocenterC11#22962
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2365

Complements

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

NH ≅ G/Ntype
3. #13069578C2semidirect
4. #13069374C2semidirect
5. #13069346C2semidirect
6. #13069187C2semidirect
8. C4⋊C4×C11⋊C8C2semidirect
11. C11×#2365C2semidirect
23. #10622700C4semidirect
47. C11×C4⋊Q8C2×C4semidirect
82. #66873Q8semidirect
84. #66871C2×C4semidirect
85. C4⋊(C11⋊C8)C2×C4semidirect
150. #2365D11semidirect
205. D44C4×Q8semidirect
276. C4⋊Q8C4×D11semidirect
382. C11#22962semidirect

Maximal subgroups

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

subgroupindex
C2×#106227002
C4⋊C4×D442
#130695782
#130693742
#130693462
#130691872
#130688622
C4⋊C4×C11⋊C82
C4×#668732
C11×#23652
#2296211