Finite Group Databasebeta

← #14790034

Subgroups — #14790034

Order 2816.

1078 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082419C211yesmaximal, characteristic, complemented
2#13078413C212yesmaximal, complemented
3#13069966C212yesmaximal, complemented
4#13069772C212yesmaximal, complemented
5#13069597C212yesmaximal, complemented
6#13069015C212yesmaximal
7#13068825C212yesmaximal, complemented
8#13068608C211yesmaximal, characteristic, complemented
9C11×#2328C211yesmaximal, characteristic
10C2×C11×#127C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C2×C4×D4×C11C2211yescharacteristic
13#10623329C2212yes—
14C2×#66977—22no—
15#10623074—22no—
16#10623070—24no—
17D4×Dic22—22no—
18#10623031C2212yes—
19#10623014—22no—
20#10623001C2212yes—
21C11×#390C2211yescharacteristic
22C11×#390C2211yescharacteristic
23C11×#386—22no—
24C11×#386—22no—
25C11×#382C2211yescharacteristic
26C11×#376C2211yescharacteristic
27C2×#66897C2212yes—
28#10622828C2214yes—
29#10622622—24no—
30#10622621—22no—
31#10622620—22no—
32#10622577C2214yes—
33#10622537C2212yes—
34#10622168C2212yes—
35#10622161C2214yes—
36#10622161C2214yes—
37C22×D4×C11—22no—
38C22×D4×C11C2311yescharacteristic
39C22×D4×C11C2311yescharacteristic
40C23×C4×C11—21no—
41C23×C4×C11D412yes—
42C22×Dic22—22no—
43C11×#127—22no—
44C11×#127Q814yescomplemented
45C4×D4×C11—22no—
46C4×D4×C11—22no—
47C4×D4×C11—22no—
48C4×D4×C11—22no—
49C2×C11×C4⋊C4C2311yescharacteristic
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4D412yes—
55C2×C42×C11C2311yescharacteristic
56C2×C42×C11C2311yescharacteristic
57C2×C42×C11C2311yescharacteristic
58C2×C22⋊Dic11—24no—
59D4×Dic11—24no—
60D4×Dic11—24no—
61#66979C2314yes—
62C2×C4⋊Dic11—22no—
63#66977—24no—
64#66977—24no—
65#66977—22no—
66#66977—22no—
67#66977—24no—
68C2×Dic11⋊C4—24no—
69C2×#4318C2314yes—
70#66943—24no—
71#66941—24no—
72#66931—28no—
73#66931—28no—
74#66923D414yescomplemented
75#66922D412yescomplemented
76#66922D412yescomplemented
77C4×Dic22—22no—
78C4×Dic22—22no—
79C11×#95—21no—
80C11×#95—21no—
81C11×#95—22no—
82#66897—24no—
83#66896—24no—
84#66896—24no—
85#66872—24no—
86#66871—24no—
87C4⋊(C11⋊C8)—22no—
88C4⋊(C11⋊C8)—22no—
89#24316—111nomaximal, Sylow
90C24×C11—21no—
91C24×C11C2×D412yes—
92C2×D4×C11—28no—
93C2×D4×C11—22no—
94C2×D4×C11—22no—
95C2×D4×C11—21no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—82no—
99C2×D4×C11—82no—
100C2×D4×C11C2×Q812yes—
101C2×D4×C11C2×Q812yescomplemented
102C2×D4×C11#4112yes—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—42no—
109C22×C4×C11—82no—
110C22×C4×C11—82no—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2411yescharacteristic
115C22×Dic11—24no—
116C22×Dic11—24no—
117C2×Dic22—24no—
118C2×Dic22—22no—
119C2×Dic22—22no—
120C2×Dic22—84no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C22⋊C4—24no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—41no—
126C11×C22⋊C4—82no—
127C11×C22⋊C4—82no—
128C42×C11—21no—
129C42×C11—22no—
130C42×C11C2×D412yes—
131C42×C11C2×D412yes—
132C42×C11C2×Q812yescomplemented
133C22⋊Dic11—28no—
134C22⋊Dic11—24no—
135C4⋊Dic11—24no—
136C4⋊Dic11—22no—
137C4⋊Dic11—22no—
138C4⋊Dic11C2×D414yes—
139C4⋊Dic11C2×D414yes—
140Dic11⋊C4—28no—
141Dic11⋊C4—24no—
142Dic11⋊C4—24no—
143C4×Dic11—24no—
144#4318—24no—
145#4318—24no—
146C2×C11⋊C8—24no—
147#3501—111no—
148#3077—112no—
149#2328D1111yescharacteristic
150#2061—112no—
151#2027—112no—
152#1995—112no—
153#1887—112no—
154#1856—112no—
155#1800—111no—
156C23×C11—22no—
157C23×C11—22no—
158C23×C11—22no—
159C23×C11—42no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11C22⋊Q814yes—
166C23×C11C22×D411yescharacteristic
167D4×C11—24no—
168D4×C11—24no—
169D4×C11—24no—
170D4×C11—42no—
171D4×C11—88no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—44no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—82no—
186C2×C4×C11—84no—
187C2×C4×C11#12011yescharacteristic
188C2×C4×C11#12012yes—
189C2×C4×C11#12011yescharacteristic
190C2×C4×C11C22×D412yes—
191C2×C4×C11C22×Q811yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C112−1+412yes—
194C2×Dic11—24no—
195C2×Dic11—24no—
196C2×Dic11—84no—
197C2×Dic11—84no—
198Dic22—44no—
199Dic22—82no—
200Dic22—84no—
201C11⋊C8—44no—
202#554—224no—
203#554—222no—
204D4×Q8—222no—
205#544—112no—
206#543—222no—
207#533—112no—
208C2×#127C2×D1111yescharacteristic
209C2×C22⋊Q8—222no—
210#518—112no—
211C2×C4×D4C2×D1111yescharacteristic
212C2×C4×D4C2×D1111yescharacteristic
213#478—224no—
214#476—222no—
215#474—222no—
216#428—114no—
217#423—112no—
218#418—114no—
219C2×#100—112no—
220#390C2×D1111yescharacteristic
221#390C2×D1111yescharacteristic
222#386—22no—
223#386—22no—
224#382C2×D1111yescharacteristic
225#376C2×D1111yescharacteristic
226#343—112no—
227#339—114no—
228#339—114no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—24no—
232C22×C11—44no—
233C22×C11—44no—
234C22×C11—42no—
235C22×C11—42no—
236C22×C11—42no—
237C22×C11—82no—
238C22×C11—82no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11C2×#12011yescharacteristic
242C22×C11C2×C22⋊Q811yescharacteristic
243C22×C11#53611yescharacteristic
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—22no—
247C4×C11—42no—
248C4×C11—42no—
249C4×C11—81no—
250C4×C11—81no—
251C4×C11#54812yes—
252C4×C11D4×Q812yes—
253Dic11—44no—
254Dic11—44no—
255C22×Q8—222no—
256C22×D4—22no—
257C22×D4C22×D1111yescharacteristic
258C22×D4C22×D1111yescharacteristic
259C23×C4—21no—
260C23×C4C22⋊D1112yes—
261C2×M16—114no—
262C4⋊Q8—112no—
263C4⋊Q8—112no—
264C4⋊Q8—224no—
265#127—22no—
266#127Dic2214yescomplemented
267#125—114no—
268#125—224no—
269C22⋊Q8—228no—
270C22⋊Q8—228no—
271C22⋊Q8—224no—
272C22⋊Q8—224no—
273C22⋊Q8—222no—
274C22⋊Q8—224no—
275C22⋊Q8—222no—
276C4×Q8—222no—
277C4×Q8—222no—
278C4×D4—22no—
279C4×D4—22no—
280C4×D4—22no—
281C4×D4—22no—
282C4×D4—224no—
283C4×D4—224no—
284#117—114no—
285C2×C4⋊C4—224no—
286C2×C4⋊C4—222no—
287C2×C4⋊C4C22×D1111yescharacteristic
288C2×C4⋊C4C22×D1111yescharacteristic
289C2×C22⋊C4—21no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—224no—
293C2×C22⋊C4C22⋊D1112yes—
294C2×C42C22×D1111yescharacteristic
295C2×C42C22×D1111yescharacteristic
296C2×C42C22×D1111yescharacteristic
297#107—224no—
298#106—224no—
299C4⋊C8—222no—
300C4⋊C8—222no—
301#102—224no—
302#102—224no—
303#100—224no—
304#95—21no—
305#95—21no—
306#95—22no—
307C2×C11—21no—
308C2×C11—21no—
309C2×C11—44no—
310C2×C11—82no—
311C2×C11#240911yescharacteristic
312C2×C11#301911yescharacteristic
313C2×C11#302111yescharacteristic
314C24—21no—
315C24C2×C22⋊D1112yes—
316C2×Q8—224no—
317C2×Q8—222no—
318C2×Q8—222no—
319C2×Q8—884no—
320C2×D4—28no—
321C2×D4—21no—
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—82no—
327C2×D4—82no—
328C2×D4C2×Dic2212yes—
329C2×D4C2×Dic2212yescomplemented
330C2×D4#433912yes—
331C22×C4—21no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—42no—
337C22×C4—82no—
338C22×C4—82no—
339C22×C4—224no—
340C22×C4—224no—
341C22×C4C2×C22⋊D1112yes—
342C22×C4C2×C22⋊D1111yescharacteristic
343C22×C4C2×C22⋊D1111yescharacteristic
344C22×C4C23×D1111yescharacteristic
345M16—224no—
346M16—224no—
347C2×C8—224no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—114no—
351C4⋊C4—114no—
352C4⋊C4—224no—
353C4⋊C4—228no—
354C4⋊C4—224no—
355C4⋊C4—222no—
356C4⋊C4—224no—
357C4⋊C4—222no—
358C22⋊C4—24no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C22⋊C4—82no—
362C22⋊C4—82no—
363C22⋊C4—228no—
364C22⋊C4—224no—
365C42—21no—
366C42—22no—
367C42—224no—
368C42C2×Dic2212yescomplemented
369C42D4×D1112yes—
370C42D4×D1112yes—
371C11#2431611yescharacteristic, complemented, Sylow
372C23—22no—
373C23—22no—
374C23—22no—
375C23—42no—
376C23—42no—
377C23—42no—
378C23—42no—
379C23—41no—
380C23—41no—
381C23#6697714yes—
382C23C22×C22⋊D1111yescharacteristic
383Q8—444no—
384Q8—882no—
385Q8—884no—
386D4—24no—
387D4—24no—
388D4—24no—
389D4—42no—
390D4—88no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—44no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—82no—
405C2×C4—84no—
406C2×C4—224no—
407C2×C4—224no—
408C2×C4—884no—
409C2×C4—884no—
410C2×C4#6699012yes—
411C2×C4#6699011yescharacteristic
412C2×C4#6699011yescharacteristic
413C2×C4C22×Dic2211yescharacteristic
414C2×C4C2×#433911yescharacteristic
415C2×C4C2×D4×D1112yes—
416C2×C4#6704312yes—
417C8—444no—
418C22—21no—
419C22—21no—
420C22—24no—
421C22—44no—
422C22—44no—
423C22—42no—
424C22—42no—
425C22—42no—
426C22—82no—
427C22—82no—
428C22—81no—
429C22—81no—
430C22C2×#6697711yescharacteristic
431C22C2×#6699011yescharacteristic
432C22#1062335611yescharacteristic
433C4—21no—
434C4—21no—
435C4—22no—
436C4—42no—
437C4—42no—
438C4—81no—
439C4—81no—
440C4—444no—
441C4—444no—
442C4D4×Dic2212yes—
443C4#1062308312yes—
444C2—21no—
445C2—21no—
446C2—44no—
447C2—82no—
448C2#1307198111yescharacteristic
449C2#1307797211yescharacteristic
450C2#1307798711yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2328C2
socleC22×C11C2×#120
prime radicalC2×C11×#127C22
hypercenter#2328D11
hypocenterC11#24316
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2328

Complements

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

NH ≅ G/Ntype
1. #13082419C2semidirect
2. #13078413C2semidirect
3. #13069966C2semidirect
4. #13069772C2semidirect
5. #13069597C2semidirect
7. #13068825C2semidirect
8. #13068608C2semidirect
44. C11×#127Q8semidirect
74. #66923D4semidirect
75. #66922D4semidirect
76. #66922D4semidirect
101. C2×D4×C11C2×Q8semidirect
132. C42×C11C2×Q8semidirect
266. #127Dic22semidirect
329. C2×D4C2×Dic22semidirect
368. C42C2×Dic22semidirect
371. C11#24316semidirect

Maximal subgroups

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

subgroupindex
#130824192
#130784132
#130699662
#130697722
#130695972
#130690152
#130688252
#130686082
C11×#23282
#2431611