Finite Group Databasebeta

← #14908849

Subgroups — #14908849

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079195C211yesmaximal, characteristic, complemented
2C4×#66957C211yesmaximal, characteristic, complemented
3#13070808C212yesmaximal, complemented
4#13070759C211yesmaximal, characteristic, complemented
5#13070754C211yesmaximal, characteristic, complemented
6#13070657C211yesmaximal, characteristic, complemented
7#13070652C211yesmaximal, characteristic, complemented
8#13070541C212yesmaximal, complemented
9#13070493C212yesmaximal, complemented
10#13070482C212yesmaximal, complemented
11C11×#2163C211yesmaximal, characteristic, complemented
12C2×#66957C2211yescharacteristic
13#10623008—21no—
14C4×#4339—21no—
15C2×C4×C8×C11C2211yescharacteristic
16#10622728—21no—
17#10622728C2212yes—
18#10622726—21no—
19#10622719C2211yescharacteristic
20C2×#66864C2212yes—
21C2×D176C2212yes—
22C4×Dic44C2211yescharacteristic
23C4×Dic44C2211yescharacteristic
24#10622308C2211yescharacteristic
25#10622307—21no—
26C4×D88—21no—
27C4×D88C2211yescharacteristic
28C4×D88C2211yescharacteristic
29C4×D88C2212yes—
30C4×#4314—21no—
31C4×#4314—21no—
32#10622295C2211yescharacteristic
33C11×C4⋊C16C2211yescharacteristic
34C11×C4⋊C16C2211yescharacteristic
35C11×C22⋊C16C2212yes—
36C11×#346C2212yes—
37#10622147C2212yes—
38#10622147C2212yes—
39#10622147C2212yes—
40#10622143C2212yes—
41#10622142C2212yes—
42#10622141C2212yes—
43C2×#4339—21no—
44C2×#4339—41no—
45C22×C8×C11D411yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C2×C42×C11D411yescharacteristic
48#66983—22no—
49#66983—41no—
50C4×C22⋊D11—41no—
51C4×C22⋊D11—41no—
52#66979—21no—
53C2×Dic44C2311yescharacteristic
54#66957—22no—
55#66957—22no—
56C2×D88—21no—
57C2×D88C2312yes—
58C2×D88C2311yescharacteristic
59C2×#4314—21no—
60#66928—41no—
61#66927—21no—
62C4×D44—21no—
63C4×D44—21no—
64C4×D44—22no—
65C4×D44—41no—
66#66925—41no—
67C42×D11—41no—
68#66922—21no—
69C4×Dic22—21no—
70C4×Dic22—21no—
71C2×C11×C16C2312yes—
72C2×C11×C16C2312yes—
73C4×C8×C11D411yescharacteristic
74C4×C8×C11D411yescharacteristic
75C4×C8×C11C2311yescharacteristic
76C4×C8×C11C2311yescharacteristic
77#66885—21no—
78#66885—21no—
79#66885—22no—
80#66885—22no—
81#66882—21no—
82#66882C2312yes—
83#66882C2311yescharacteristic
84#66882C2311yescharacteristic
85#66881—21no—
86#66880—21no—
87#66880—21no—
88#66864—24no—
89D176—24no—
90#33675—111nomaximal, Sylow
91C22×C4×C11D811yescharacteristic
92C22×C4×C11D811yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C2×C22⋊D11—41no—
95C2×C22⋊D11—42no—
96#4339—24no—
97#4339—42no—
98#4339—84no—
99C2×D44—21no—
100C2×D44—22no—
101C2×D44—41no—
102C2×D44—41no—
103C2×C4×D11—41no—
104C2×C4×D11—41no—
105C2×C4×D11—41no—
106C2×C4×D11—42no—
107C2×Dic22—21no—
108C2×Dic22—41no—
109C2×C8×C11—21no—
110C2×C8×C11—21no—
111C2×C8×C11—41no—
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11C2×D411yescharacteristic
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11C2411yescharacteristic
116C42×C11D811yescharacteristic
117C42×C11D811yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C22⋊Dic11—41no—
121(C2×D11)⋊C4—41no—
122(C2×D11)⋊C4—41no—
123(C2×D11)⋊C4—42no—
124(C2×D11)⋊C4—42no—
125C4⋊Dic11—21no—
126C4⋊Dic11—21no—
127C4⋊Dic11—22no—
128C4⋊Dic11—41no—
129Dic11⋊C4—41no—
130Dic11⋊C4—41no—
131C4×Dic11—41no—
132C4×Dic11—41no—
133C4×Dic11—41no—
134Dic44—21no—
135Dic44#4112yescomplemented
136D88—21no—
137D88—22no—
138D88—22no—
139D88—42no—
140D88#4112yescomplemented
141#4314—24no—
142C11×C16—22no—
143C11×C16—22no—
144#3169—111no—
145C4×#135—111no—
146#2234—112no—
147#2225—111no—
148#2224—111no—
149#2207—111no—
150#2206—111no—
151#2186—112no—
152#2177—112no—
153#2175—112no—
154#2163D1111yescharacteristic, complemented
155C23×C11C2×D811yescharacteristic
156C22×D11—41no—
157C22×D11—42no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—22no—
161C2×C4×C11—41no—
162C2×C4×C11C2×D811yescharacteristic
163C2×C4×C11C2×D811yescharacteristic
164C2×C4×C11C2×D811yescharacteristic
165C2×C4×C11C2×D811yescharacteristic
166C2×C4×C11C2×D811yescharacteristic
167C2×C4×C11C22×D411yescharacteristic
168C22⋊D11—44no—
169C22⋊D11—84no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—42no—
174D44—22no—
175D44—42no—
176D44—41no—
177D44—42no—
178D44—82no—
179D44—82no—
180C4×D11—44no—
181C4×D11—82no—
182C4×D11—84no—
183C4×D11—82no—
184Dic22—22no—
185Dic22—41no—
186Dic22—82no—
187C8×C11—21no—
188C8×C11—21no—
189C8×C11—21no—
190C8×C11C2×#4111yescharacteristic
191C8×C11C2×#4111yescharacteristic
192C2×#135—111no—
193#532—221no—
194C4×#41—221no—
195C2×SD32—112no—
196C2×D16—112no—
197#500—111no—
198#493—111no—
199#486—221no—
200#466—112no—
201#466—221no—
202C4×Q16—111no—
203C4×Q16—111no—
204C4×SD16—221no—
205C4×SD16—221no—
206C4×D8—112no—
207C4×D8—111no—
208C4×D8—111no—
209C4×D8—221no—
210#427—111no—
211#416—221no—
212C2×C4×C8C2×D1111yescharacteristic
213#367—112no—
214#366—112no—
215C4⋊C16C2×D1111yescharacteristic
216C4⋊C16C2×D1111yescharacteristic
217#358—112no—
218#357—112no—
219#357—112no—
220#357—112no—
221C22⋊C16C2×D1112yes—
222#346C2×D1112yes—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11C22×D811yescharacteristic
227C2×D11—42no—
228C2×D11—81no—
229C2×D11—81no—
230C2×D11—82no—
231C2×D11—82no—
232C2×D11—82no—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11#50912yes—
238C4×C11#52511yescharacteristic
239C4×C11#57511yescharacteristic
240Dic11—42no—
241Dic11—82no—
242Dic11—81no—
243Dic11—81no—
244C2×#41—221no—
245C2×#41—441no—
246#135—222no—
247#135—222no—
248C2×Q16—111no—
249C2×SD16—221no—
250C2×D8—111no—
251C2×D8—112no—
252C2×D8—221no—
253C22×C8D4411yescharacteristic
254C22×C8C22×D1111yescharacteristic
255C4⋊Q8—221no—
256#127—221no—
257#124—441no—
258#121—222no—
259#121—441no—
260C4×Q8—221no—
261C4×Q8—221no—
262C4×D4—221no—
263C4×D4—221no—
264C4×D4—222no—
265C4×D4—441no—
266C4×D4—441no—
267C4×D4—441no—
268#117—221no—
269#117—441no—
270C2×C42—441no—
271C2×C42D4411yescharacteristic
272SD32—224no—
273D16—224no—
274C2×C16C22×D1112yes—
275C2×C16C22×D1112yes—
276#107—111no—
277#107—111no—
278#107—112no—
279#107—221no—
280#106—221no—
281#103—221no—
282#103—221no—
283#102—221no—
284#102—221no—
285#102—222no—
286#102—222no—
287C4×C8D4411yescharacteristic
288C4×C8D4411yescharacteristic
289C4×C8C22×D1111yescharacteristic
290C4×C8C22×D1111yescharacteristic
291C2×C11—41no—
292C2×C11#310011yescharacteristic
293C2×C11C2×#50911yescharacteristic
294C2×C11#341411yescharacteristic
295D11—82no—
296D11—162no—
297#41—224no—
298#41—442no—
299#41—884no—
300C2×Q8—221no—
301C2×Q8—441no—
302C2×D4—221no—
303C2×D4—222no—
304C2×D4—441no—
305C2×D4—442no—
306C2×D4—441no—
307C2×D4—441no—
308C22×C4—441no—
309C22×C4—441no—
310C22×C4—441no—
311C22×C4—442no—
312C22×C4D8811yescharacteristic
313C22×C4D8811yescharacteristic
314C22×C4C2×D4411yescharacteristic
315Q16—112no—
316Q16—221no—
317SD16—224no—
318D8—112no—
319D8—221no—
320D8—222no—
321D8—222no—
322D8—442no—
323C2×C8—21no—
324C2×C8—21no—
325C2×C8—41no—
326C2×C8C2×D4411yescharacteristic
327C2×C8C2×D4411yescharacteristic
328C2×C8C2×D4411yescharacteristic
329C2×C8C23×D1111yescharacteristic
330C4⋊C4—222no—
331C4⋊C4—221no—
332C4⋊C4—221no—
333C4⋊C4—441no—
334C4⋊C4—441no—
335C4⋊C4—441no—
336C22⋊C4—441no—
337C22⋊C4—441no—
338C22⋊C4—441no—
339C22⋊C4—442no—
340C22⋊C4—442no—
341C42—441no—
342C42—441no—
343C42—441no—
344C42D8811yescharacteristic
345C42D8811yescharacteristic
346C42C2×D4411yescharacteristic
347C42C2×D4411yescharacteristic
348C16—22no—
349C16—22no—
350C11#3367511yescharacteristic, complemented, Sylow
351C23—441no—
352C23—442no—
353C23C2×D8811yescharacteristic
354Q8—222no—
355Q8—441no—
356Q8—882no—
357D4—222no—
358D4—444no—
359D4—441no—
360D4—442no—
361D4—442no—
362D4—882no—
363D4—884no—
364D4—882no—
365C2×C4—21no—
366C2×C4—22no—
367C2×C4—21no—
368C2×C4—41no—
369C2×C4—444no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—442no—
374C2×C4—884no—
375C2×C4—882no—
376C2×C4—882no—
377C2×C4C2×D8811yescharacteristic
378C2×C4C2×D8811yescharacteristic
379C2×C4C2×D8811yescharacteristic
380C2×C4C2×D8811yescharacteristic
381C2×C4C2×D8811yescharacteristic
382C2×C4C22×D4411yescharacteristic
383C8—21no—
384C8—21no—
385C8—21no—
386C8#41×D1111yescharacteristic
387C8#41×D1111yescharacteristic
388C22—21no—
389C22—21no—
390C22—21no—
391C22—442no—
392C22—881no—
393C22—881no—
394C22—882no—
395C22—882no—
396C22—882no—
397C22C22×D8811yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—442no—
403C4—882no—
404C4—881no—
405C4—881no—
406C4#1062252112yes—
407C4#1062305511yescharacteristic
408C4#1062327911yescharacteristic
409C2—41no—
410C2—882no—
411C2—1762no—
412C2#1307861711yescharacteristic
413C2C2×#1062252111yescharacteristic
414C2#1308175211yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2163C2
socleC22×C11C22×D8
hypercenter#2163D11
hypocenterC11#33675
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #2163

Complements

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

NH ≅ G/Ntype
1. #13079195C2semidirect
2. C4×#66957C2semidirect
3. #13070808C2semidirect
4. #13070759C2semidirect
5. #13070754C2semidirect
6. #13070657C2semidirect
7. #13070652C2semidirect
8. #13070541C2semidirect
9. #13070493C2semidirect
10. #13070482C2semidirect
11. C11×#2163C2semidirect
135. Dic44#41semidirect
140. D88#41semidirect
154. #2163D11semidirect
350. C11#33675semidirect

Maximal subgroups

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

subgroupindex
#130791952
C4×#669572
#130708082
#130707592
#130707542
#130706572
#130706522
#130705412
#130704932
#130704822
C11×#21632
#3367511