Finite Group Databasebeta

← #14724438

Subgroups — #14724438

Order 2816.

600 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079171C211yesmaximal, characteristic
2#13077710C211yesmaximal, characteristic, complemented
3#13067518C212yesmaximal, complemented
4#13067504C212yesmaximal, complemented
5#13067428C212yesmaximal, complemented
6C8×#4324C212yesmaximal, complemented
7#13067377C211yesmaximal, characteristic, complemented
8#13067088C211yesmaximal, characteristic, complemented
9#13067085C211yesmaximal, characteristic
10#13066900C211yesmaximal, characteristic, complemented
11C11×#2981C211yesmaximal, characteristic
12C11×#532C2211yescharacteristic
13#10623001C2211yescharacteristic
14C11×#436C2212yes—
15C11×#435—22no—
16C8×D4×C11C2212yes—
17C11×#432C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C11×#408—22no—
20#10622706C411yescharacteristic
21#10622692C411yescharacteristic
22#10622689C411yescharacteristic
23#10622683C411yescharacteristic
24#10622654C412yes—
25#10622654C412yes—
26C4×#4324C2212yes—
27C4×#4324C2212yes—
28#10622539C2211yescharacteristic
29#10622538C2211yescharacteristic
30C2×C4×C11⋊C8C2211yescharacteristic
31#10622441—22no—
32#10622333—22no—
33#10622292C2212yes—
34C8×Dic22C2212yes—
35D4⋊(C11⋊C8)C2212yes—
36D4⋊(C11⋊C8)C2212yes—
37#10622122C2212yes—
38#10622122C2212yes—
39#10622118C2212yes—
40#10622117C2212yes—
41#10622092C2211yescharacteristic
42#10622092C2211yescharacteristic
43C8×C11⋊C8C2211yescharacteristic
44C8×C11⋊C8C2211yescharacteristic
45C2×C11×#41—21no—
46C2×C11×M16—22no—
47C22×C8×C11—22no—
48C11×C4⋊Q8C2×C411yescharacteristic
49C11×#127C2×C411yescharacteristic
50C11×#124—21no—
51C11×#121—21no—
52C11×#121C2×C412yes—
53C4×D4×C11—21no—
54C4×D4×C11C2312yes—
55C2×C42×C11C2311yescharacteristic
56C2×#4324C2×C412yes—
57C2×#4324C2×C412yes—
58#66979—21no—
59#66977—21no—
60#66977C2×C412yes—
61C22×C11⋊C8C2×C411yescharacteristic
62C22×C11⋊C8C2×C411yescharacteristic
63#66923—21no—
64#66922C2×C411yescharacteristic
65#66922C2×C411yescharacteristic
66C4×Dic22—21no—
67C4×Dic22C2312yes—
68C11×C4⋊C8D412yes—
69C11×C4⋊C8C2312yes—
70C11×C22⋊C8—21no—
71C11×C22⋊C8—22no—
72C11×C22⋊C8—22no—
73C11×C22⋊C8D412yes—
74C11×#97—21no—
75C4×C8×C11C2311yescharacteristic
76C4×C8×C11C2311yescharacteristic
77#66896C2×C412yes—
78#66896C2×C412yes—
79C22⋊(C11⋊C8)—21no—
80C22⋊(C11⋊C8)—21no—
81#66879—22no—
82Dic11⋊C8—22no—
83Dic11⋊C8—22no—
84C8×Dic11—22no—
85#66874C2×C412yes—
86#66874C2×C412yes—
87#66872C2×C412yes—
88#66872C2×C412yes—
89C4⋊(C11⋊C8)—21no—
90C4⋊(C11⋊C8)C2312yes—
91#66867—21no—
92C4×C11⋊C8C2×C411yescharacteristic
93C4×C11⋊C8C2×C411yescharacteristic
94C4×C11⋊C8C2311yescharacteristic
95C4×C11⋊C8C2311yescharacteristic
96C4×C11⋊C8C2311yescharacteristic
97C4×C11⋊C8C2311yescharacteristic
98#17971—111nomaximal, Sylow
99C11×#41—82no—
100C2×Q8×C11—21no—
101C2×D4×C11—22no—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11C22×C412yes—
105C22×C4×C11—22no—
106C22×C4×C11C22×C411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C2×Dic22—21no—
110C2×Dic22C22×C412yes—
111C11×M16—82no—
112C2×C8×C11—22no—
113C2×C8×C11—82no—
114C2×C8×C11C2×D412yes—
115C2×C8×C11C2×D412yes—
116C11×C4⋊C4—21no—
117C11×C4⋊C4C22×C412yes—
118C11×C22⋊C4—22no—
119C11×C22⋊C4—22no—
120C42×C11C22×C411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11#4111yescharacteristic
123C42×C11C2411yescharacteristic
124C22⋊Dic11—22no—
125#4324—24no—
126#4324—24no—
127C4⋊Dic11—21no—
128C4⋊Dic11—21no—
129C4⋊Dic11—21no—
130C4⋊Dic11C22×C412yes—
131Dic11⋊C4—22no—
132Dic11⋊C4—22no—
133C4×Dic11—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—21no—
138C2×C11⋊C8—21no—
139C2×C11⋊C8C22×C411yescharacteristic
140C2×C11⋊C8C22×C411yescharacteristic
141C2×C11⋊C8C22×C411yescharacteristic
142C2×C11⋊C8C22×C411yescharacteristic
143#3167—111no—
144#2985—111no—
145#2981D1111yescharacteristic
146#1592—112no—
147#1590—112no—
148SD16⋊C8—112no—
149C8×SD16—112no—
150#1568—111no—
151#1497—111no—
152#1496—111no—
153#1450—111no—
154C23×C11—22no—
155C23×C11C4×D411yescharacteristic
156Q8×C11—81no—
157D4×C11—22no—
158D4×C11—22no—
159D4×C11—81no—
160D4×C11—81no—
161D4×C11—82no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—41no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11C4×D411yescharacteristic
170C2×C4×C11C4×D411yescharacteristic
171C2×C4×C11C4×D411yescharacteristic
172C2×C4×C11C23×C411yescharacteristic
173C2×C4×C11C22×D411yescharacteristic
174C2×C4×C11C2×#4111yescharacteristic
175C2×Dic11—22no—
176C2×Dic11—22no—
177Dic22—22no—
178Dic22—22no—
179Dic22—81no—
180C8×C11—22no—
181C8×C11—22no—
182C8×C11—42no—
183C11⋊C8—21no—
184C11⋊C8—21no—
185C11⋊C8—41no—
186C11⋊C8—41no—
187C11⋊C8—42no—
188C11⋊C8#13112yes—
189C11⋊C8#13112yes—
190#533—111no—
191#532C2×D1111yescharacteristic
192#498—111no—
193#492—111no—
194#487—111no—
195#486—111no—
196#465—112no—
197#465—112no—
198#446—112no—
199#446—222no—
200C8×Q8—112no—
201C4×SD16—112no—
202C4×SD16—112no—
203#436C2×D1112yes—
204#435—22no—
205C8×D4C2×D1112yes—
206#433—222no—
207#432—111no—
208#432C2×D1111yescharacteristic
209#431—111no—
210#431C2×D1111yescharacteristic
211#408—22no—
212C2×C4×C8—111no—
213#335—112no—
214#334—112no—
215Q8⋊C8—112no—
216Q8⋊C8—112no—
217D4⋊C8—112no—
218D4⋊C8—112no—
219#322—111no—
220#322—111no—
221C82—111no—
222C82—111no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—42no—
227C22×C11—42no—
228C22×C11—42no—
229C22×C11C2×C4×D411yescharacteristic
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—42no—
235C4×C11C2×#13111yescharacteristic
236C4×C11C2×#13111yescharacteristic
237C4×C11#57712yes—
238Dic11—42no—
239Dic11—42no—
240C2×#41—21no—
241C2×SD16—112no—
242C2×SD16—112no—
243C2×M16—22no—
244C22×C8—22no—
245C22×C8—111no—
246C22×C8—111no—
247C4⋊Q8—111no—
248C4⋊Q8—111no—
249C4⋊Q8C4×D1111yescharacteristic
250#127C4×D1111yescharacteristic
251#125—221no—
252#124—21no—
253C22⋊Q8—112no—
254C22⋊Q8—221no—
255#121—21no—
256#121C4×D1112yes—
257C4×Q8—112no—
258C4×Q8—221no—
259C4×D4—21no—
260C4×D4C22×D1112yes—
261#117—221no—
262C2×C42C22×D1111yescharacteristic
263#106—112no—
264#106—112no—
265C4⋊C8—112no—
266C4⋊C8—222no—
267C4⋊C8—222no—
268C4⋊C8—221no—
269C4⋊C8C22⋊D1112yes—
270C4⋊C8C22×D1112yes—
271#103—112no—
272#103—112no—
273#102—112no—
274#102—112no—
275C22⋊C8—21no—
276C22⋊C8—22no—
277C22⋊C8—22no—
278C22⋊C8—221no—
279C22⋊C8—221no—
280C22⋊C8C22⋊D1112yes—
281#97—21no—
282#97—222no—
283#97—221no—
284C4×C8—111no—
285C4×C8—111no—
286C4×C8—111no—
287C4×C8—111no—
288C4×C8—111no—
289C4×C8—111no—
290C4×C8—222no—
291C4×C8C22×D1111yescharacteristic
292C4×C8C22×D1111yescharacteristic
293C2×C11—41no—
294C2×C11—82no—
295C2×C11#293111yescharacteristic
296C2×C11#294911yescharacteristic
297C2×C11#295711yescharacteristic
298#41—82no—
299C2×Q8—21no—
300C2×Q8—112no—
301C2×Q8—221no—
302C2×D4—22no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4C2×C4×D1112yes—
306C22×C4—22no—
307C22×C4C2×C4×D1111yescharacteristic
308C22×C4#433911yescharacteristic
309C22×C4C2×C22⋊D1111yescharacteristic
310SD16—224no—
311SD16—224no—
312M16—82no—
313C2×C8—22no—
314C2×C8—82no—
315C2×C8—111no—
316C2×C8—111no—
317C2×C8—111no—
318C2×C8—111no—
319C2×C8—222no—
320C2×C8—222no—
321C2×C8—221no—
322C2×C8—221no—
323C2×C8—222no—
324C2×C8C2×C22⋊D1112yes—
325C2×C8C2×C22⋊D1112yes—
326C4⋊C4—21no—
327C4⋊C4—112no—
328C4⋊C4—221no—
329C4⋊C4—221no—
330C4⋊C4—222no—
331C4⋊C4—221no—
332C4⋊C4—222no—
333C4⋊C4C2×C4×D1112yes—
334C22⋊C4—22no—
335C22⋊C4—22no—
336C22⋊C4—222no—
337C42—222no—
338C42C2×C4×D1111yescharacteristic
339C42#433911yescharacteristic
340C42C2×C22⋊D1111yescharacteristic
341C42C23×D1111yescharacteristic
342C11#1797111yescharacteristic, complemented, Sylow
343C23—22no—
344C23C4×C22⋊D1111yescharacteristic
345Q8—81no—
346Q8—222no—
347Q8—222no—
348Q8—881no—
349D4—22no—
350D4—22no—
351D4—81no—
352D4—81no—
353D4—82no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—222no—
362C2×C4—222no—
363C2×C4C4×C22⋊D1111yescharacteristic
364C2×C4C4×C22⋊D1111yescharacteristic
365C2×C4C4×C22⋊D1111yescharacteristic
366C2×C4C22×C4×D1111yescharacteristic
367C2×C4C2×#433911yescharacteristic
368C2×C4C22×C22⋊D1111yescharacteristic
369C8—22no—
370C8—22no—
371C8—42no—
372C8—112no—
373C8—112no—
374C8—221no—
375C8—221no—
376C8—441no—
377C8—441no—
378C8—442no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—42no—
383C22—42no—
384C22—42no—
385C22C2×C4×C22⋊D1111yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—42no—
391C4—442no—
392C4—442no—
393C4D11×#13111yescharacteristic
394C4D11×#13111yescharacteristic
395C4#1062336712yes—
396C2—41no—
397C2—82no—
398C2#1307732611yescharacteristic
399C2#1307747311yescharacteristic
400C2#1307753111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2981C2
socleC22×C11C2×C4×D4
prime radicalC11×#532C22
cosocleC42×C11C24
hypercenter#2981D11
hypocenterC11#17971
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2981

Complements

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

NH ≅ G/Ntype
2. #13077710C2semidirect
3. #13067518C2semidirect
4. #13067504C2semidirect
5. #13067428C2semidirect
6. C8×#4324C2semidirect
7. #13067377C2semidirect
8. #13067088C2semidirect
10. #13066900C2semidirect
342. C11#17971semidirect

Maximal subgroups

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

subgroupindex
#130791712
#130777102
#130675182
#130675042
#130674282
C8×#43242
#130673772
#130670882
#130670852
#130669002
C11×#29812
#1797111