Finite Group Databasebeta

← #14908853

Subgroups — #14908853

Order 2816.

548 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66957C211yesmaximal, characteristic
2#13070821C212yesmaximal, complemented
3#13070765C211yesmaximal, characteristic, complemented
4#13070760C211yesmaximal, characteristic, complemented
5#13070663C211yesmaximal, characteristic, complemented
6#13070658C211yesmaximal, characteristic, complemented
7#13070554C212yesmaximal
8#13070485C212yesmaximal, complemented
9#13070478C212yesmaximal, complemented
10#13070419C211yesmaximal, characteristic, complemented
11C11×#3170C211yesmaximal, characteristic, complemented
12C11×#533—21no—
13C2×#66957C2211yescharacteristic
14C4×#4339—21no—
15C11×#500C2211yescharacteristic
16C11×#494C2211yescharacteristic
17C11×#487—21no—
18C11×#467—21no—
19C11×#467C2212yes—
20C4×C11×Q16—21no—
21C4×C11×Q16C2212yes—
22C2×C4×C8×C11C2211yescharacteristic
23C2×#66893C2212yes—
24C2×#66892C2212yes—
25#10622726—21no—
26#10622719C2211yescharacteristic
27C4×Dic44C2211yescharacteristic
28C4×Dic44C2211yescharacteristic
29C4×D88C2211yescharacteristic
30C4×D88C2211yescharacteristic
31C4×#4314—21no—
32C4×#4314—21no—
33#10622202C2212yes—
34#10622202C2212yes—
35C22⋊(C11⋊C16)C2212yes—
36#10622130C2212yes—
37#10622129C2212yes—
38#10622128C2212yes—
39#10622127C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C4⋊(C11⋊C16)C2211yescharacteristic
42#10622099C2212yes—
43C2×#4339—21no—
44C2×C11×Q16—21no—
45C2×C11×Q16C2312yes—
46C22×C8×C11D411yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×#125—41no—
51C11×C22⋊Q8—22no—
52C11×C22⋊Q8—41no—
53C4×Q8×C11—22no—
54C4×Q8×C11—41no—
55C11×#117—41no—
56C2×C42×C11D411yescharacteristic
57C4×C22⋊D11—41no—
58C4×C22⋊D11—41no—
59#66979—21no—
60C2×Dic44C2311yescharacteristic
61#66957—22no—
62#66957—22no—
63C2×D88C2311yescharacteristic
64C2×#4314—21no—
65C4×D44—21no—
66C4×D44—21no—
67#66925—41no—
68C42×D11—41no—
69C4×Dic22—21no—
70C4×Dic22—21no—
71C11×#107—21no—
72C11×#107C2312yes—
73C11×#103—22no—
74C11×#103—22no—
75C4×C8×C11D411yescharacteristic
76C4×C8×C11D411yescharacteristic
77C4×C8×C11C2311yescharacteristic
78C4×C8×C11C2311yescharacteristic
79#66893—24no—
80#66892—24no—
81#66885—21no—
82#66885—21no—
83#66882C2311yescharacteristic
84#66882C2311yescharacteristic
85#66881—21no—
86#66880—21no—
87#66880—21no—
88C2×C11⋊C16C2312yes—
89C2×C11⋊C16C2312yes—
90#33676—111nomaximal, Sylow
91C2×Q8×C11—22no—
92C2×Q8×C11—41no—
93C22×C4×C11D811yescharacteristic
94C22×C4×C11D811yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C2×C22⋊D11—41no—
97#4339—24no—
98#4339—42no—
99C2×D44—21no—
100C2×C4×D11—41no—
101C2×C4×D11—41no—
102C2×C4×D11—41no—
103C2×Dic22—21no—
104C11×Q16—22no—
105C11×Q16—22no—
106C11×Q16—42no—
107C2×C8×C11—21no—
108C2×C8×C11—21no—
109C2×C8×C11—41no—
110C2×C8×C11C2×D411yescharacteristic
111C2×C8×C11C2×D411yescharacteristic
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11C2411yescharacteristic
114C11×C4⋊C4—22no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—42no—
118C11×C4⋊C4—42no—
119C11×C4⋊C4—41no—
120C11×C22⋊C4—42no—
121C42×C11—42no—
122C42×C11D811yescharacteristic
123C42×C11D811yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C22⋊Dic11—41no—
127(C2×D11)⋊C4—41no—
128(C2×D11)⋊C4—41no—
129C4⋊Dic11—21no—
130C4⋊Dic11—21no—
131Dic11⋊C4—41no—
132Dic11⋊C4—41no—
133C4×Dic11—41no—
134C4×Dic11—41no—
135C4×Dic11—41no—
136Dic44—21no—
137Dic44#4112yes—
138D88—21no—
139D88#4112yes—
140#4314—24no—
141C11⋊C16—22no—
142C11⋊C16—22no—
143#3170D1111yescharacteristic, complemented
144C4×#135—111no—
145#2237—112no—
146#2227—111no—
147#2226—111no—
148#2209—111no—
149#2208—111no—
150#2189—112no—
151#2176—112no—
152#2175—112no—
153#2163—111no—
154C23×C11C2×D811yescharacteristic
155C22×D11—41no—
156Q8×C11—42no—
157Q8×C11—42no—
158Q8×C11—82no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—22no—
162C2×C4×C11—41no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11C2×D811yescharacteristic
166C2×C4×C11C2×D811yescharacteristic
167C2×C4×C11C2×D811yescharacteristic
168C2×C4×C11C2×D811yescharacteristic
169C2×C4×C11C2×D811yescharacteristic
170C2×C4×C11C22×D411yescharacteristic
171C22⋊D11—44no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175D44—22no—
176D44—41no—
177C4×D11—44no—
178C4×D11—82no—
179C4×D11—82no—
180Dic22—22no—
181Dic22—41no—
182C8×C11—21no—
183C8×C11—21no—
184C8×C11—21no—
185C8×C11C2×#4111yescharacteristic
186C8×C11C2×#4111yescharacteristic
187C2×#135—111no—
188#533—21no—
189C4×#41—221no—
190C2×Q32—112no—
191C2×SD32—112no—
192#500C2×D1111yescharacteristic
193#494C2×D1111yescharacteristic
194#487—21no—
195#467—21no—
196#467C2×D1112yes—
197C4×Q16—21no—
198C4×Q16—111no—
199C4×Q16—111no—
200C4×Q16C2×D1112yes—
201C4×SD16—221no—
202C4×SD16—221no—
203C4×D8—111no—
204C4×D8—111no—
205#427—111no—
206#416—221no—
207C2×C4×C8C2×D1111yescharacteristic
208#367—112no—
209#366—112no—
210C4⋊C16—111no—
211C4⋊C16—111no—
212#358—112no—
213#358—112no—
214#358—112no—
215#357—112no—
216C22⋊C16—112no—
217#346—112no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11C22×D811yescharacteristic
222C2×D11—42no—
223C2×D11—81no—
224C2×D11—81no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—82no—
230C4×C11—82no—
231C4×C11#51012yes—
232C4×C11#52511yescharacteristic
233C4×C11#57511yescharacteristic
234Dic11—42no—
235Dic11—81no—
236Dic11—81no—
237C2×#41—221no—
238#135—222no—
239#135—222no—
240C2×Q16—21no—
241C2×Q16—111no—
242C2×Q16C22×D1112yes—
243C2×SD16—221no—
244C2×D8—111no—
245C22×C8C22⋊D1111yescharacteristic
246C22×C8C22×D1111yescharacteristic
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249#125—41no—
250C22⋊Q8—22no—
251C22⋊Q8—41no—
252C4×Q8—22no—
253C4×Q8—41no—
254C4×Q8—221no—
255C4×Q8—221no—
256C4×D4—221no—
257C4×D4—221no—
258C4×D4—441no—
259C4×D4—441no—
260#117—41no—
261#117—221no—
262#117—441no—
263C2×C42—441no—
264C2×C42C22⋊D1111yescharacteristic
265Q32—224no—
266SD32—224no—
267C2×C16—112no—
268C2×C16—112no—
269#107—21no—
270#107—111no—
271#107—111no—
272#107C22×D1112yes—
273#106—221no—
274#103—22no—
275#103—22no—
276#103—221no—
277#103—221no—
278#102—221no—
279#102—221no—
280C4×C8C22⋊D1111yescharacteristic
281C4×C8C22⋊D1111yescharacteristic
282C4×C8C22×D1111yescharacteristic
283C4×C8C22×D1111yescharacteristic
284C2×C11—41no—
285C2×C11#310011yescharacteristic
286C2×C11C2×#51011yescharacteristic
287C2×C11#341411yescharacteristic
288D11—82no—
289#41—224no—
290#41—442no—
291C2×Q8—22no—
292C2×Q8—41no—
293C2×Q8—221no—
294C2×D4—221no—
295C2×D4—441no—
296C22×C4—441no—
297C22×C4—441no—
298C22×C4—441no—
299C22×C4#432311yescharacteristic
300C22×C4#432311yescharacteristic
301C22×C4C2×C22⋊D1111yescharacteristic
302Q16—22no—
303Q16—22no—
304Q16—42no—
305Q16—112no—
306Q16—221no—
307SD16—224no—
308D8—112no—
309D8—221no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—41no—
313C2×C8C2×C22⋊D1111yescharacteristic
314C2×C8C2×C22⋊D1111yescharacteristic
315C2×C8C2×C22⋊D1111yescharacteristic
316C2×C8C23×D1111yescharacteristic
317C4⋊C4—22no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—42no—
321C4⋊C4—42no—
322C4⋊C4—41no—
323C4⋊C4—221no—
324C4⋊C4—221no—
325C4⋊C4—441no—
326C4⋊C4—441no—
327C22⋊C4—42no—
328C22⋊C4—441no—
329C22⋊C4—441no—
330C22⋊C4—441no—
331C42—42no—
332C42—441no—
333C42—441no—
334C42—441no—
335C42#432311yescharacteristic
336C42#432311yescharacteristic
337C42C2×C22⋊D1111yescharacteristic
338C42C2×C22⋊D1111yescharacteristic
339C16—222no—
340C16—222no—
341C11#3367611yescharacteristic, complemented, Sylow
342C23—441no—
343C23C2×#432311yescharacteristic
344Q8—42no—
345Q8—42no—
346Q8—82no—
347Q8—222no—
348Q8—441no—
349D4—222no—
350D4—444no—
351D4—441no—
352C2×C4—22no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—444no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—882no—
363C2×C4—882no—
364C2×C4C2×#432311yescharacteristic
365C2×C4C2×#432311yescharacteristic
366C2×C4C2×#432311yescharacteristic
367C2×C4C2×#432311yescharacteristic
368C2×C4C2×#432311yescharacteristic
369C2×C4C22×C22⋊D1111yescharacteristic
370C8—21no—
371C8—21no—
372C8—21no—
373C8#41×D1111yescharacteristic
374C8#41×D1111yescharacteristic
375C22—21no—
376C22—21no—
377C22—21no—
378C22—442no—
379C22—881no—
380C22—881no—
381C22C22×#432311yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—82no—
387C4—82no—
388C4—442no—
389C4—881no—
390C4—881no—
391C4#1062279212yes—
392C4#1062335311yescharacteristic
393C4#1062335911yescharacteristic
394C2—41no—
395C2—882no—
396C2#1307861211yescharacteristic
397C2C2×#1062279211yescharacteristic
398C2#1308175011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3170C2
socleC22×C11C22×D8
prime radicalC2×#66957C22
hypercenter#3170D11
hypocenterC11#33676
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3170

Complements

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

NH ≅ G/Ntype
2. #13070821C2semidirect
3. #13070765C2semidirect
4. #13070760C2semidirect
5. #13070663C2semidirect
6. #13070658C2semidirect
8. #13070485C2semidirect
9. #13070478C2semidirect
10. #13070419C2semidirect
11. C11×#3170C2semidirect
143. #3170D11semidirect
341. C11#33676semidirect

Maximal subgroups

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

subgroupindex
C4×#669572
#130708212
#130707652
#130707602
#130706632
#130706582
#130705542
#130704852
#130704782
#130704192
C11×#31702
#3367611