Finite Group Databasebeta

← #14908318

Subgroups — #14908318

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×#10622792C211yesmaximal, characteristic, complemented
2C2×#10622753C211yesmaximal, characteristic, complemented
3#13078286C211yesmaximal, characteristic
4#13070731C212yesmaximal, complemented
5#13070722C212yesmaximal, complemented
6#13070714C212yesmaximal, complemented
7#13070705C212yesmaximal, complemented
8#13070405C211yesmaximal, characteristic, complemented
9#13070321C211yesmaximal, characteristic, complemented
10C2×#10622202C211yesmaximal, characteristic, complemented
11C11×#3059C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C2×C11×#131C2211yescharacteristic
14C11×#536—21no—
15#10623364—21no—
16C2×#66957C2211yescharacteristic
17C11×#470—22no—
18C11×#467C2212yes—
19C11×#467C2212yes—
20C11×#427C2211yescharacteristic
21C11×#419—21no—
22C2×#66893C2212yes—
23#10622792—24no—
24C2×#66892C2212yes—
25#10622753—24no—
26#10622747—22no—
27#10622746—21no—
28#10622729C2212yes—
29#10622728C2212yes—
30C2×#66882C2211yescharacteristic
31C2×#66876C2212yes—
32C2×#66876C2211yescharacteristic
33C22×C11⋊C16C2212yes—
34C22×C11⋊C16C2211yescharacteristic
35#10622202C2212yes—
36#10622202C2212yes—
37#10622130C2211yescharacteristic
38#10622130C2211yescharacteristic
39#10622129C2211yescharacteristic
40#10622129C2211yescharacteristic
41#10622128C2212yes—
42#10622127C2212yes—
43C2×C11×#41D411yescharacteristic
44C22×Q8×C11—21no—
45C2×#4339—21no—
46C2×C11×Q16—22no—
47C2×C11×Q16—21no—
48C2×C11×Q16—22no—
49C2×C11×Q16C2312yes—
50C11×#131—22no—
51C11×#131—22no—
52C2×C11×M16D411yescharacteristic
53C2×C11×M16D412yes—
54C22×C8×C11C2312yes—
55C22×C8×C11C2311yescharacteristic
56C11×C4⋊Q8—41no—
57C11×#124—41no—
58C11×#123—42no—
59C11×C22⋊Q8—22no—
60C11×C22⋊Q8—22no—
61C11×#117—21no—
62#66999—41no—
63#66992—42no—
64#66991—41no—
65#66983—22no—
66C2×C4⋊Dic11—21no—
67#66977—22no—
68C2×Dic44C2311yescharacteristic
69#66957—22no—
70#66957—22no—
71C2×D88C2311yescharacteristic
72C2×#4314—21no—
73C11×#107C2311yescharacteristic
74C11×#107C2311yescharacteristic
75C11×#106—21no—
76C11×#103—22no—
77C11×#103—22no—
78#66893—24no—
79#66892—24no—
80#66885—22no—
81#66882—21no—
82#66882C2312yes—
83#66880—22no—
84#66876—24no—
85#66876D414yescomplemented
86C2×C11⋊C16—22no—
87C2×C11⋊C16—24no—
88C2×C11⋊C16C2311yescharacteristic
89C2×C11⋊C16C2311yescharacteristic
90C2×C11⋊C16C2312yes—
91#33613—111nomaximal, Sylow
92C11×#41—22no—
93C11×#41—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11—41no—
96C2×Q8×C11—42no—
97C2×Q8×C11—42no—
98C2×Q8×C11D811yescharacteristic
99C2×D4×C11D811yescharacteristic
100C2×D4×C11D812yes—
101C22×C4×C11—41no—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D411yescharacteristic
104C2×C22⋊D11—41no—
105C2×C22⋊D11—42no—
106C22×Dic11—41no—
107#4339—42no—
108#4339—42no—
109C2×D44—21no—
110C2×C4×D11—41no—
111C2×Dic22—21no—
112C11×Q16—22no—
113C11×Q16—22no—
114C11×Q16—42no—
115C11×M16—24no—
116C11×M16—22no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11C2×D412yes—
120C2×C8×C11C2×D412yes—
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11#4112yes—
123C2×C8×C11C2411yescharacteristic
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—42no—
127C11×C4⋊C4—42no—
128C11×C22⋊C4—41no—
129C11×C22⋊C4—42no—
130C11×C22⋊C4—42no—
131C42×C11—41no—
132C22⋊Dic11—42no—
133(C2×D11)⋊C4—42no—
134C4⋊Dic11—22no—
135C4⋊Dic11—41no—
136Dic11⋊C4—42no—
137Dic44—21no—
138Dic44—21no—
139D88—21no—
140D88—21no—
141#4314—42no—
142C11⋊C16—21no—
143C11⋊C16—21no—
144C11⋊C16C2×D414yes—
145C2×#510—111no—
146C2×#504—111no—
147#3061—111no—
148#3059D1111yescharacteristic, complemented
149#2220—112no—
150#2219—112no—
151#2217—112no—
152#2216—112no—
153#2159—111no—
154#2138—111no—
155C2×#358—111no—
156C23×C11C2×D812yes—
157C23×C11C2×D811yescharacteristic
158C22×D11—41no—
159Q8×C11—22no—
160Q8×C11—42no—
161Q8×C11—42no—
162Q8×C11—82no—
163D4×C11—24no—
164D4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—42no—
170C2×C4×C11—82no—
171C2×C4×C11#12112yes—
172C2×C4×C11C2×D812yes—
173C2×C4×C11C2×D811yescharacteristic
174C2×C4×C11#13512yes—
175C2×C4×C11C22×D411yescharacteristic
176C22⋊D11—82no—
177C22⋊D11—162no—
178C2×Dic11—41no—
179C2×Dic11—42no—
180C2×Dic11—161no—
181D44—41no—
182D44—41no—
183C4×D11—82no—
184Dic22—41no—
185Dic22—41no—
186C8×C11—22no—
187C8×C11#12112yes—
188C8×C11C22×D411yescharacteristic
189C8×C11C2×#4111yescharacteristic
190C2×#135—111no—
191C22×Q16C2×D1111yescharacteristic
192C2×#131C2×D1111yescharacteristic
193#537—221no—
194#536—21no—
195#510—224no—
196C2×Q32—112no—
197C2×SD32—112no—
198#504—224no—
199C2×M32—111no—
200C2×M32—112no—
201C22×C16—111no—
202C22×C16—112no—
203#470—22no—
204#468—222no—
205#467—112no—
206#467C2×D1112yes—
207#467C2×D1112yes—
208#466—112no—
209#427C2×D1111yescharacteristic
210C2×#107—111no—
211#419—21no—
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—22no—
224C22×C11—22no—
225C22×C11—22no—
226C22×C11#46612yes—
227C22×C11C22×D811yescharacteristic
228C2×D11—81no—
229C2×D11—81no—
230C2×D11—81no—
231C4×C11—22no—
232C4×C11—81no—
233C4×C11—81no—
234C4×C11—82no—
235C4×C11#46612yes—
236C4×C11C2×#12111yescharacteristic
237C4×C11C2×#13511yescharacteristic
238Dic11—82no—
239Dic11—81no—
240C2×#41—221no—
241C2×#41C22⋊D1111yescharacteristic
242C22×Q8—21no—
243#135—222no—
244#135—222no—
245C2×Q16—22no—
246C2×Q16—22no—
247C2×Q16—21no—
248C2×Q16—111no—
249C2×Q16C22×D1112yes—
250C2×SD16—221no—
251C2×D8—111no—
252#131—22no—
253#131—22no—
254C2×M16C22⋊D1111yescharacteristic
255C2×M16C22⋊D1112yes—
256C22×C8C22×D1112yes—
257C22×C8C22×D1111yescharacteristic
258C4⋊Q8—41no—
259#124—41no—
260#123—42no—
261C22⋊Q8—22no—
262C22⋊Q8—22no—
263C22⋊Q8—222no—
264C22⋊Q8—441no—
265#121—222no—
266#121—441no—
267#121—442no—
268#117—21no—
269C2×C4⋊C4—221no—
270Q32—224no—
271SD32—224no—
272M32—114no—
273M32—224no—
274C2×C16—112no—
275C2×C16—111no—
276C2×C16—111no—
277C2×C16—224no—
278C2×C16—222no—
279#107—112no—
280#107—221no—
281#107C22×D1111yescharacteristic
282#107C22×D1111yescharacteristic
283#106—21no—
284#103—22no—
285#103—22no—
286#103—222no—
287#102—222no—
288C2×C11—22no—
289C2×C11—42no—
290C2×C11C2×#46611yescharacteristic
291C2×C11#341611yescharacteristic
292C2×C11#341711yescharacteristic
293D11—161no—
294#41—22no—
295#41—22no—
296#41—442no—
297#41—442no—
298C2×Q8—22no—
299C2×Q8—41no—
300C2×Q8—42no—
301C2×Q8—42no—
302C2×Q8—221no—
303C2×Q8#432311yescharacteristic
304C2×D4—221no—
305C2×D4—441no—
306C2×D4—442no—
307C2×D4#432312yes—
308C2×D4#432311yescharacteristic
309C22×C4—41no—
310C22×C4—441no—
311C22×C4—441no—
312C22×C4C2×C22⋊D1112yes—
313C22×C4C2×C22⋊D1111yescharacteristic
314Q16—22no—
315Q16—22no—
316Q16—42no—
317Q16—221no—
318Q16—221no—
319SD16—442no—
320D8—221no—
321D8—221no—
322M16—22no—
323M16—24no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8D4×D1112yes—
327C2×C8#434112yes—
328C2×C8C2×C22⋊D1112yes—
329C2×C8C2×C22⋊D1111yescharacteristic
330C2×C8C23×D1111yescharacteristic
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—42no—
334C4⋊C4—42no—
335C4⋊C4—222no—
336C4⋊C4—441no—
337C4⋊C4—442no—
338C22⋊C4—41no—
339C22⋊C4—42no—
340C22⋊C4—42no—
341C22⋊C4—442no—
342C22⋊C4—442no—
343C42—41no—
344C16—114no—
345C16—221no—
346C16—221no—
347C11#3361311yescharacteristic, complemented, Sylow
348C23—441no—
349C23C2×#432312yes—
350C23C2×#432311yescharacteristic
351Q8—22no—
352Q8—42no—
353Q8—42no—
354Q8—82no—
355Q8—441no—
356Q8—441no—
357D4—24no—
358D4—22no—
359D4—441no—
360D4—441no—
361D4—882no—
362D4—1762no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—82no—
369C2×C4—442no—
370C2×C4—441no—
371C2×C4—882no—
372C2×C4—1761no—
373C2×C4C2×#432312yes—
374C2×C4C2×#432311yescharacteristic
375C2×C4#6699212yes—
376C2×C4#6700312yes—
377C2×C4C22×C22⋊D1111yescharacteristic
378C8—22no—
379C8#6699212yes—
380C8C2×D4×D1111yescharacteristic
381C8C2×#434111yescharacteristic
382C22—21no—
383C22—21no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—881no—
388C22—881no—
389C22—881no—
390C22#1062265112yes—
391C22C22×#432311yescharacteristic
392C4—22no—
393C4—81no—
394C4—82no—
395C4—81no—
396C4—882no—
397C4—881no—
398C4#1062265112yes—
399C4C2×#6699211yescharacteristic
400C4C2×#6700311yescharacteristic
401C2—22no—
402C2—42no—
403C2—1761no—
404C2C2×#1062265111yescharacteristic
405C2#1308176011yescharacteristic
406C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3059C2
socleC22×C11C22×D8
prime radical#13078286C2
hypercenter#3059D11
hypocenterC11#33613
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ #3059

Complements

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

NH ≅ G/Ntype
1. C2×#10622792C2semidirect
2. C2×#10622753C2semidirect
4. #13070731C2semidirect
5. #13070722C2semidirect
6. #13070714C2semidirect
7. #13070705C2semidirect
8. #13070405C2semidirect
9. #13070321C2semidirect
10. C2×#10622202C2semidirect
11. C11×#3059C2semidirect
85. #66876D4semidirect
148. #3059D11semidirect
347. C11#33613semidirect

Maximal subgroups

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

subgroupindex
C2×#106227922
C2×#106227532
#130782862
#130707312
#130707222
#130707142
#130707052
#130704052
#130703212
C2×#106222022
C11×#30592
#3361311