Finite Group Databasebeta

← #14908316

Subgroups — #14908316

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622520C211yesmaximal, characteristic, complemented
2#13078282C211yesmaximal, characteristic
3#13078267C211yesmaximal, characteristic, complemented
4#13070726C212yesmaximal, complemented
5#13070721C212yesmaximal, complemented
6#13070709C212yesmaximal, complemented
7#13070704C212yesmaximal, complemented
8#13070404C211yesmaximal, characteristic, complemented
9#13070323C211yesmaximal, characteristic, complemented
10C2×#10622202C211yesmaximal, characteristic, complemented
11C2×C11×#510C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13C22×C11×Q16C2211yescharacteristic
14#10623364—21no—
15#10623347—21no—
16C2×#66954C2211yescharacteristic
17C11×#510—24no—
18C2×C11×Q32C2212yes—
19C2×C11×SD32C2212yes—
20C2×C11×M32C2211yescharacteristic
21#10622845—21no—
22#10622838—21no—
23#10622802—22no—
24#10622801C2212yes—
25#10622801C2212yes—
26#10622801C2212yes—
27#10622787—22no—
28#10622770C2212yes—
29#10622719C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C22×C11⋊C16C2211yescharacteristic
32#10622520—24no—
33C2×#66862C2212yes—
34C2×C16×D11C2212yes—
35#10622202C2211yescharacteristic
36#10622202C2212yes—
37#10622202C2211yescharacteristic
38#10622202C2212yes—
39#10622200C2211yescharacteristic
40#10622200C2211yescharacteristic
41#10622143C2212yes—
42#10622142C2212yes—
43C2×C11×#41—21no—
44C22×Q8×C11—21no—
45C2×#4339D411yescharacteristic
46C11×#135—22no—
47C11×#135—22no—
48C2×C11×Q16—22no—
49C2×C11×Q16—21no—
50C2×C11×Q16—22no—
51C2×C11×Q16C2312yes—
52C2×C11×Q16C2311yescharacteristic
53C2×C11×SD16—21no—
54C2×C11×D8C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56#67000—41no—
57#66999—22no—
58#66999—22no—
59#66999—22no—
60#66997—41no—
61#66992—42no—
62#66991—22no—
63#66983—41no—
64#66982—42no—
65#66979—21no—
66C2×C4⋊Dic11—21no—
67#66977—41no—
68C2×#4318D411yescharacteristic
69#66954—22no—
70#66954—22no—
71C2×#4313D412yes—
72C2×C8×D11C2312yes—
73C11×Q32—24no—
74C11×SD32—24no—
75C11×M32D414yescomplemented
76C2×C11×C16C2312yes—
77#66899—22no—
78#66899—22no—
79#66899—22no—
80#66896—22no—
81#66882—21no—
82#66882C2312yes—
83#66882C2311yescharacteristic
84#66882C2311yescharacteristic
85#66881—21no—
86C2×C11⋊C16—22no—
87C2×C11⋊C16C2311yescharacteristic
88C2×C11⋊C16C2311yescharacteristic
89#66862—24no—
90C16×D11—24no—
91#33613—111nomaximal, Sylow
92C11×#41—42no—
93C11×#41—42no—
94C2×Q8×C11—21no—
95C2×Q8×C11—22no—
96C2×Q8×C11—41no—
97C2×Q8×C11—42no—
98C2×Q8×C11—42no—
99C2×D4×C11—21no—
100C2×D4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11C2×D411yescharacteristic
104C2×C22⋊D11—42no—
105C2×C22⋊D11D812yes—
106C22×Dic11—41no—
107#4339—22no—
108#4339—22no—
109C2×D44D811yescharacteristic
110C2×C4×D11C2×D412yes—
111C2×Dic22D811yescharacteristic
112C11×Q16—22no—
113C11×Q16—21no—
114C11×Q16—22no—
115C11×Q16—21no—
116C11×Q16—42no—
117C11×SD16—42no—
118C11×D8—21no—
119C11×D8—21no—
120C2×C8×C11C2×D412yes—
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11#4112yes—
123C2×C8×C11C2411yescharacteristic
124C22⋊Dic11—42no—
125C22⋊Dic11—41no—
126(C2×D11)⋊C4—42no—
127(C2×D11)⋊C4—42no—
128(C2×D11)⋊C4—42no—
129C4⋊Dic11—21no—
130C4⋊Dic11—21no—
131C4⋊Dic11—22no—
132C4⋊Dic11—41no—
133Dic11⋊C4—42no—
134Dic11⋊C4—42no—
135Dic11⋊C4—42no—
136C4×Dic11—41no—
137#4318—22no—
138C2×C11⋊C8C2×D412yes—
139#4313—24no—
140C8×D11—22no—
141C8×D11—22no—
142C11×C16C2×D414yes—
143C11⋊C16—21no—
144C11⋊C16—21no—
145C2×#510D1111yescharacteristic, complemented
146C2×#504—111no—
147#3061—111no—
148#3059—111no—
149#2220—112no—
150#2219—112no—
151#2217—112no—
152#2216—112no—
153#2159—111no—
154#2138—111no—
155C2×#358—111no—
156C23×C11—41no—
157C23×C11C2×D811yescharacteristic
158C22×D11C2×D812yes—
159Q8×C11—41no—
160Q8×C11—42no—
161Q8×C11—42no—
162Q8×C11—41no—
163Q8×C11—82no—
164D4×C11—41no—
165D4×C11—41no—
166D4×C11—82no—
167C2×C4×C11—41no—
168C2×C4×C11—42no—
169C2×C4×C11—82no—
170C2×C4×C11—82no—
171C2×C4×C11#12112yes—
172C2×C4×C11C2×D811yescharacteristic
173C2×C4×C11#13512yes—
174C2×C4×C11C22×D411yescharacteristic
175C22⋊D11—24no—
176C22⋊D11—162no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—42no—
180C2×Dic11—161no—
181C2×Dic11C2×D812yes—
182D44—22no—
183C4×D11—22no—
184C4×D11—22no—
185Dic22—22no—
186C8×C11#12112yes—
187C8×C11C22×D411yescharacteristic
188C8×C11C2×#4111yescharacteristic
189C11⋊C8—22no—
190C2×#135C2×D1111yescharacteristic
191C22×Q16C2×D1111yescharacteristic
192C2×#131—111no—
193#537—221no—
194#536—221no—
195#510—24no—
196C2×Q32C2×D1112yes—
197C2×SD32C2×D1112yes—
198#504—224no—
199C2×M32—112no—
200C2×M32C2×D1111yescharacteristic
201C22×C16—111no—
202C22×C16—112no—
203#470—222no—
204#468—222no—
205#467—112no—
206#467—112no—
207#467—112no—
208#466—112no—
209#427—111no—
210C2×#107—111no—
211#419—221no—
212#417—221no—
213#367—112no—
214#366—112no—
215#358—112no—
216#358—112no—
217#358—111no—
218#358—111no—
219#357—111no—
220#357—111no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11—81no—
226C22×C11#46612yes—
227C22×C11C22×D811yescharacteristic
228C2×D11—22no—
229C2×D11—22no—
230C2×D11—22no—
231C4×C11—81no—
232C4×C11—82no—
233C4×C11#46612yes—
234C4×C11C2×#12111yescharacteristic
235C4×C11C2×#13511yescharacteristic
236Dic11—22no—
237Dic11—81no—
238Dic11—82no—
239Dic11—81no—
240C2×#41—21no—
241C2×#41—111no—
242C22×Q8—21no—
243#135—22no—
244#135—22no—
245C2×Q16—21no—
246C2×Q16—22no—
247C2×Q16—22no—
248C2×Q16C22×D1112yes—
249C2×Q16C22×D1111yescharacteristic
250C2×SD16—21no—
251C2×D8C22×D1111yescharacteristic
252#131—222no—
253#131—222no—
254C2×M16—111no—
255C2×M16—112no—
256C22×C8—112no—
257C22×C8C22×D1111yescharacteristic
258C4⋊Q8—441no—
259#124—441no—
260#123—442no—
261C22⋊Q8—222no—
262C22⋊Q8—222no—
263C22⋊Q8—222no—
264C22⋊Q8—441no—
265#121—222no—
266#121—441no—
267#121—442no—
268#117—221no—
269C2×C4⋊C4—221no—
270Q32—24no—
271SD32—24no—
272M32—224no—
273M32C22⋊D1114yescomplemented
274C2×C16—111no—
275C2×C16—111no—
276C2×C16—222no—
277C2×C16—224no—
278C2×C16C22×D1112yes—
279#107—111no—
280#107—111no—
281#107—112no—
282#107—221no—
283#106—221no—
284#103—222no—
285#103—222no—
286#103—222no—
287#102—222no—
288C2×C11—22no—
289C2×C11—161no—
290C2×C11C2×#46611yescharacteristic
291C2×C11#341611yescharacteristic
292C2×C11#341711yescharacteristic
293D11—42no—
294#41—42no—
295#41—42no—
296#41—222no—
297#41—222no—
298C2×Q8—21no—
299C2×Q8—22no—
300C2×Q8—41no—
301C2×Q8—42no—
302C2×Q8—42no—
303C2×Q8—111no—
304C2×D4—21no—
305C2×D4—41no—
306C2×D4—112no—
307C2×D4—111no—
308C2×D4—442no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—112no—
312C22×C4—441no—
313C22×C4D4×D1111yescharacteristic
314Q16—22no—
315Q16—21no—
316Q16—22no—
317Q16—21no—
318Q16—42no—
319SD16—42no—
320D8—21no—
321D8—21no—
322M16—222no—
323M16—224no—
324C2×C8—112no—
325C2×C8—222no—
326C2×C8—222no—
327C2×C8D4×D1111yescharacteristic
328C2×C8#434112yes—
329C2×C8C2×C22⋊D1112yes—
330C2×C8C23×D1111yescharacteristic
331C4⋊C4—222no—
332C4⋊C4—221no—
333C4⋊C4—221no—
334C4⋊C4—442no—
335C4⋊C4—442no—
336C4⋊C4—442no—
337C4⋊C4—441no—
338C22⋊C4—442no—
339C22⋊C4—442no—
340C22⋊C4—442no—
341C22⋊C4—442no—
342C22⋊C4—441no—
343C42—441no—
344C16—221no—
345C16—221no—
346C16C2×C22⋊D1114yes—
347C11#3361311yescharacteristic, complemented, Sylow
348C23—41no—
349C23—112no—
350C23D8×D1111yescharacteristic
351Q8—42no—
352Q8—41no—
353Q8—41no—
354Q8—42no—
355Q8—82no—
356Q8—222no—
357D4—41no—
358D4—41no—
359D4—82no—
360D4—224no—
361D4—222no—
362D4—1762no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—82no—
366C2×C4—82no—
367C2×C4—112no—
368C2×C4—222no—
369C2×C4—222no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—442no—
373C2×C4—1761no—
374C2×C4D8×D1111yescharacteristic
375C2×C4#6696512yes—
376C2×C4#6699112yes—
377C2×C4C2×D4×D1111yescharacteristic
378C8—222no—
379C8#6699112yes—
380C8C2×#434111yescharacteristic
381C8C22×C22⋊D1111yescharacteristic
382C22—21no—
383C22—21no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—222no—
388C22—222no—
389C22—222no—
390C22#1062277012yes—
391C22C2×D8×D1111yescharacteristic
392C4—81no—
393C4—82no—
394C4—222no—
395C4—882no—
396C4—881no—
397C4—881no—
398C4#1062277012yes—
399C4C2×#6696511yescharacteristic
400C4C2×#6699111yescharacteristic
401C2—22no—
402C2—161no—
403C2—442no—
404C2C2×#1062277011yescharacteristic
405C2#1308176111yescharacteristic
406C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#510C2
socleC22×C11C22×D8
prime radical#13078282C2
hypercenterC2×#510D11
hypocenterC11#33613
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#510

Complements

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

NH ≅ G/Ntype
1. C2×#10622520C2semidirect
3. #13078267C2semidirect
4. #13070726C2semidirect
5. #13070721C2semidirect
6. #13070709C2semidirect
7. #13070704C2semidirect
8. #13070404C2semidirect
9. #13070323C2semidirect
10. C2×#10622202C2semidirect
11. C2×C11×#510C2semidirect
75. C11×M32D4semidirect
145. C2×#510D11semidirect
273. M32C22⋊D11semidirect
347. C11#33613semidirect

Maximal subgroups

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

subgroupindex
C2×#106225202
#130782822
#130782672
#130707262
#130707212
#130707092
#130707042
#130704042
#130703232
C2×#106222022
C2×C11×#5102
#3361311