Finite Group Databasebeta

← #14810394

Subgroups — #14810394

Order 2816.

1078 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623048C211yesmaximal, characteristic
2C2×#10622405C212yesmaximal, complemented
3#13076964C211yesmaximal, characteristic
4#13069766C212yesmaximal, complemented
5#13069765C212yesmaximal, complemented
6#13069575C212yesmaximal, complemented
7#13068929C211yesmaximal, characteristic
8#13068928C211yesmaximal, characteristic
9#13068926C211yesmaximal, characteristic
10C22⋊C8×Dic11C211yesmaximal, characteristic
11C11×#1873C211yesmaximal, characteristic
12C2×C11×C22⋊Q8C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×#66997C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C2×#66977C2211yescharacteristic
17C22×C4×Dic11C2211yescharacteristic
18#10623048—28no—
19C2×#66943C2212yes—
20C2×#66941C2212yes—
21C2×#66931—22no—
22C2×C4×Dic22—22no—
23C2×C11×#103C2212yes—
24C2×C11×C22⋊C8C2211yescharacteristic
25#10622843C2211yescharacteristic
26C2×#66899C2212yes—
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×#66880C2212yes—
29C2×C8×Dic11C2212yes—
30#10622589C2211yescharacteristic
31#10622587C2211yescharacteristic
32#10622585—22no—
33C2×#66874C2212yes—
34#10622555—22no—
35#10622405—28no—
36C11×#340C2212yes—
37#10622189C2212yes—
38#10622188C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41C22×Q8×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×Dic11D412yes—
44C22×Dic22—22no—
45C22×Dic22C2311yescharacteristic
46C22×C8×C11C2312yes—
47C11×C22⋊Q8—22no—
48C11×C22⋊Q8—22no—
49C11×#117—24no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C22⋊C4—21no—
54C2×C11×C22⋊C4—21no—
55C2×C42×C11—21no—
56C2×C22⋊Dic11—21no—
57C2×C22⋊Dic11—21no—
58#66997—24no—
59#66979—24no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11C2311yescharacteristic
62C2×C4⋊Dic11C2312yes—
63#66977—22no—
64#66977—22no—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—21no—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4—22no—
70C2×C4×Dic11—21no—
71C2×C4×Dic11—24no—
72C2×C4×Dic11D412yes—
73C2×C4×Dic11C2311yescharacteristic
74C2×C4×Dic11C2311yescharacteristic
75C22×C11⋊C8C2312yes—
76#66943—24no—
77#66943—24no—
78#66941—24no—
79#66941D418yes—
80#66931—216no—
81C4×Dic22—216no—
82C11×#103—24no—
83C11×C22⋊C8—22no—
84#66899—24no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C22⋊(C11⋊C8)—22no—
88#66880—24no—
89C8×Dic11—24no—
90#66874—24no—
91#25904—111nomaximal, Sylow
92C24×C11C2×D411yescharacteristic
93C2×Q8×C11—22no—
94C2×Q8×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11#4112yes—
104C22×C4×C11#4112yes—
105C22×C4×C11C2411yescharacteristic
106C22×Dic11—24no—
107C22×Dic11—24no—
108C22×Dic11—24no—
109C22×Dic11—22no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11C2×D412yes—
113C22×Dic11C2×D412yes—
114C2×Dic22—28no—
115C2×Dic22—22no—
116C2×Dic22—21no—
117C2×Dic22—21no—
118C2×Dic22—22no—
119C2×Dic22—44no—
120C2×Dic22—44no—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—42no—
128C11×C4⋊C4C2×D414yes—
129C11×C22⋊C4—24no—
130C11×C22⋊C4—42no—
131C42×C11—24no—
132C22⋊Dic11—24no—
133C22⋊Dic11—42no—
134C4⋊Dic11—28no—
135C4⋊Dic11—22no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138C4⋊Dic11C2×D414yes—
139Dic11⋊C4—28no—
140Dic11⋊C4—28no—
141Dic11⋊C4—44no—
142Dic11⋊C4—44no—
143Dic11⋊C4—42no—
144C4×Dic11—24no—
145C4×Dic11—24no—
146C4×Dic11—22no—
147C4×Dic11C2×D414yes—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151C2×#533—111no—
152C2×#487—112no—
153#2857—111no—
154#2026—112no—
155#2026—112no—
156#1990—112no—
157#1873—111no—
158#1873—111no—
159#1873—111no—
160#1873D1111yescharacteristic
161C4×C22⋊C8—111no—
162C23×C11—21no—
163C23×C11—21no—
164C23×C11—22no—
165C23×C11—22no—
166C23×C11#12412yes—
167C23×C11C22×D411yescharacteristic
168Q8×C11—42no—
169Q8×C11—42no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—24no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—42no—
182C2×C4×C11#12412yes—
183C2×C4×C11C22×D412yes—
184C2×C4×C11C2×#4111yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C2×C4×C112−1+412yes—
187C2×Dic11—22no—
188C2×Dic11—24no—
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—48no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—42no—
199C2×Dic11#12014yes—
200C2×Dic11#13514yes—
201C2×Dic11#13714yes—
202Dic22—416no—
203Dic22—42no—
204Dic22—42no—
205C8×C11—42no—
206C11⋊C8—42no—
207#533—228no—
208C2×C4⋊Q8—112no—
209C2×C4⋊Q8—111no—
210C2×#125—112no—
211C2×C22⋊Q8—111no—
212C2×C22⋊Q8—222no—
213C2×C22⋊Q8C2×D1111yescharacteristic
214C2×C4×Q8—222no—
215C2×#117—111no—
216C2×#117C2×D1111yescharacteristic
217C22×C42—111no—
218#487—228no—
219C2×#103—112no—
220C2×#103—112no—
221C2×#103—112no—
222C2×#103C2×D1112yes—
223C2×C22⋊C8—111no—
224C2×C22⋊C8C2×D1111yescharacteristic
225C2×C4×C8—112no—
226#391—111no—
227#391—111no—
228#389—222no—
229#384—111no—
230#380—222no—
231#340—112no—
232#340—112no—
233#340—112no—
234#340C2×D1112yes—
235#336—112no—
236C22×C11—22no—
237C22×C11—22no—
238C22×C11—22no—
239C22×C11—42no—
240C22×C11—42no—
241C22×C11C2×#12011yescharacteristic
242C22×C11C2×#12411yescharacteristic
243C22×C11#53611yescharacteristic
244C22×C11C2×#13512yes—
245C22×C11C2×#13712yes—
246C4×C11—22no—
247C4×C11—44no—
248C4×C11—81no—
249C4×C11—81no—
250C4×C11#54812yes—
251C4×C11#54812yes—
252Dic11—44no—
253Dic11—42no—
254Dic11—81no—
255Dic11—81no—
256Dic11#45218yes—
257C22×Q8—111no—
258C22×Q8—222no—
259C22×Q8C22×D1111yescharacteristic
260C23×C4—112no—
261C23×C4C22×D1111yescharacteristic
262C22×C8—112no—
263C22×C8C22×D1112yes—
264C4⋊Q8—118no—
265C4⋊Q8—224no—
266C4⋊Q8—224no—
267#125—224no—
268#125—224no—
269C22⋊Q8—22no—
270C22⋊Q8—22no—
271C22⋊Q8—2216no—
272C22⋊Q8—222no—
273C22⋊Q8—222no—
274C4×Q8—2216no—
275#117—24no—
276#117—224no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—112no—
279C2×C4⋊C4—111no—
280C2×C4⋊C4—222no—
281C2×C4⋊C4—222no—
282C2×C4⋊C4—222no—
283C2×C4⋊C4—222no—
284C2×C4⋊C4—222no—
285C2×C4⋊C4—221no—
286C2×C4⋊C4C22×D1111yescharacteristic
287C2×C4⋊C4C22×D1112yes—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—221no—
291C2×C22⋊C4—221no—
292C2×C42—21no—
293C2×C42—111no—
294C2×C42—112no—
295C2×C42—111no—
296C2×C42—224no—
297C2×C42—221no—
298#103—24no—
299#103—224no—
300#103—224no—
301#103—224no—
302C22⋊C8—22no—
303C22⋊C8—222no—
304C4×C8—224no—
305#95—222no—
306#95—222no—
307C2×C11—42no—
308C2×C11#243611yescharacteristic
309C2×C11C2×#45212yes—
310C2×C11#313111yescharacteristic
311C2×C11#313911yescharacteristic
312C2×C11#323112yes—
313C24D4×D1111yescharacteristic
314C2×Q8—21no—
315C2×Q8—22no—
316C2×Q8—21no—
317C2×Q8—22no—
318C2×Q8—228no—
319C2×Q8—221no—
320C2×Q8—222no—
321C2×Q8—221no—
322C2×Q8—222no—
323C2×Q8—444no—
324C2×Q8—444no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—112no—
331C22×C4—112no—
332C22×C4—224no—
333C22×C4—224no—
334C22×C4—224no—
335C22×C4—222no—
336C22×C4—221no—
337C22×C4—221no—
338C22×C4#433912yes—
339C22×C4D4×D1111yescharacteristic
340C22×C4#434112yes—
341C22×C4C23×D1111yescharacteristic
342C2×C8—22no—
343C2×C8—22no—
344C2×C8—22no—
345C2×C8—222no—
346C2×C8—222no—
347C2×C8—222no—
348C4⋊C4—22no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—42no—
352C4⋊C4—114no—
353C4⋊C4—228no—
354C4⋊C4—228no—
355C4⋊C4—228no—
356C4⋊C4—222no—
357C4⋊C4—221no—
358C4⋊C4—221no—
359C4⋊C4—444no—
360C4⋊C4—444no—
361C4⋊C4—442no—
362C4⋊C4D4×D1114yes—
363C22⋊C4—24no—
364C22⋊C4—42no—
365C22⋊C4—224no—
366C22⋊C4—442no—
367C42—24no—
368C42—114no—
369C42—224no—
370C42—224no—
371C42—222no—
372C11#2590411yescharacteristic, complemented, Sylow
373C23—22no—
374C23—22no—
375C23—21no—
376C23—21no—
377C23#6693812yes—
378C23C2×D4×D1111yescharacteristic
379Q8—42no—
380Q8—42no—
381Q8—4416no—
382Q8—442no—
383Q8—442no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—24no—
387C2×C4—24no—
388C2×C4—24no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—114no—
397C2×C4—114no—
398C2×C4—114no—
399C2×C4—222no—
400C2×C4—222no—
401C2×C4—222no—
402C2×C4—224no—
403C2×C4—448no—
404C2×C4—442no—
405C2×C4—442no—
406C2×C4—441no—
407C2×C4—441no—
408C2×C4—442no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4#6693812yes—
412C2×C4C2×#433911yescharacteristic
413C2×C4C2×D4×D1112yes—
414C2×C4C2×#434111yescharacteristic
415C2×C4#6704312yes—
416C8—42no—
417C8—442no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—42no—
422C22—42no—
423C22C2×#6693811yescharacteristic
424C22D11×#12011yescharacteristic
425C22#1062317911yescharacteristic
426C22D11×#13512yes—
427C22D11×#13712yes—
428C4—22no—
429C4—44no—
430C4—81no—
431C4—81no—
432C4—118no—
433C4—442no—
434C4—444no—
435C4—881no—
436C4—881no—
437C4#1062308312yes—
438C4#1062312912yes—
439C2—42no—
440C2#1307227211yescharacteristic
441C2D11×#45212yes—
442C2#1307893611yescharacteristic
443C2#1307899411yescharacteristic
444C2#1307977312yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1873C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1873D11
hypocenterC11#25904
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
2. C2×#10622405C2semidirect
4. #13069766C2semidirect
5. #13069765C2semidirect
6. #13069575C2semidirect
372. C11#25904semidirect

Maximal subgroups

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

subgroupindex
C2×#106230482
C2×#106224052
#130769642
#130697662
#130697652
#130695752
#130689292
#130689282
#130689262
C22⋊C8×Dic112
C11×#18732
#2590411