Finite Group Databasebeta

← #14908848

Subgroups — #14908848

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
2#13070807C212yesmaximal, complemented
3#13070758C211yesmaximal, characteristic, complemented
4#13070753C211yesmaximal, characteristic, complemented
5#13070656C211yesmaximal, characteristic, complemented
6#13070651C211yesmaximal, characteristic, complemented
7#13070539C212yesmaximal, complemented
8#13070490C212yesmaximal, complemented
9#13070478C212yesmaximal, complemented
10#13070419C211yesmaximal, characteristic, complemented
11C4×C11×#135C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13C4×C11×#41—21no—
14#10623008—21no—
15C4×C11×Q16C2211yescharacteristic
16C4×C11×Q16C2211yescharacteristic
17C4×C11×SD16—21no—
18C4×C11×SD16—21no—
19C4×C11×D8C2211yescharacteristic
20C4×C11×D8C2211yescharacteristic
21C11×#427C2211yescharacteristic
22C11×#416—21no—
23C2×C4×C8×C11C2211yescharacteristic
24C2×#66892C2212yes—
25C2×#66890C2212yes—
26#10622728—21no—
27#10622728C2212yes—
28#10622308C2211yescharacteristic
29#10622307—21no—
30C4×D88—21no—
31C4×D88C2212yes—
32#10622295C2211yescharacteristic
33#10622202C2212yes—
34#10622200C2212yes—
35C22⋊(C11⋊C16)C2212yes—
36#10622129C2212yes—
37#10622129C2212yes—
38#10622128C2212yes—
39#10622127C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C4⋊(C11⋊C16)C2211yescharacteristic
42#10622099C2212yes—
43C2×C11×#41—21no—
44C2×#4339—41no—
45C11×#135—22no—
46C11×#135—22no—
47C2×C11×Q16C2311yescharacteristic
48C2×C11×SD16—21no—
49C2×C11×D8C2311yescharacteristic
50C22×C8×C11D411yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C4×Q8×C11—21no—
53C4×Q8×C11—21no—
54C4×D4×C11—21no—
55C4×D4×C11—21no—
56C4×D4×C11—41no—
57C4×D4×C11—41no—
58C11×#117—21no—
59C11×#117—41no—
60C2×C42×C11—41no—
61C2×C42×C11D411yescharacteristic
62#66983—22no—
63#66983—41no—
64C2×D88—21no—
65C2×D88C2312yes—
66#66928—41no—
67#66927—21no—
68C4×D44—22no—
69C4×D44—41no—
70#66922—21no—
71C11×#107C2311yescharacteristic
72C11×#107C2311yescharacteristic
73C11×#106—21no—
74C11×#103—21no—
75C11×#103—21no—
76C11×#102—21no—
77C11×#102—21no—
78C4×C8×C11D411yescharacteristic
79C4×C8×C11D411yescharacteristic
80C4×C8×C11C2311yescharacteristic
81C4×C8×C11C2311yescharacteristic
82#66892—24no—
83#66890—24no—
84#66885—22no—
85#66885—22no—
86#66882—21no—
87#66882C2312yes—
88C2×C11⋊C16C2312yes—
89C2×C11⋊C16C2312yes—
90#33675—111nomaximal, Sylow
91C11×#41—24no—
92C11×#41—42no—
93C2×Q8×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11D811yescharacteristic
100C22×C4×C11D811yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C2×C22⋊D11—42no—
103#4339—84no—
104C2×D44—22no—
105C2×D44—41no—
106C2×D44—41no—
107C2×C4×D11—42no—
108C2×Dic22—41no—
109C11×Q16—21no—
110C11×Q16#4112yescomplemented
111C11×SD16—24no—
112C11×D8—21no—
113C11×D8#4112yescomplemented
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11—41no—
117C2×C8×C11C2×D411yescharacteristic
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11C2411yescharacteristic
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4—41no—
125C11×C22⋊C4—41no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—41no—
128C42×C11—41no—
129C42×C11—41no—
130C42×C11—41no—
131C42×C11D811yescharacteristic
132C42×C11D811yescharacteristic
133C42×C11C2×D411yescharacteristic
134C42×C11C2×D411yescharacteristic
135(C2×D11)⋊C4—42no—
136(C2×D11)⋊C4—42no—
137C4⋊Dic11—22no—
138C4⋊Dic11—41no—
139D88—22no—
140D88—22no—
141D88—42no—
142C11⋊C16—22no—
143C11⋊C16—22no—
144#3169—111no—
145C4×#135D1111yescharacteristic, complemented
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#2163—111no—
155C23×C11—41no—
156C23×C11C2×D811yescharacteristic
157C22×D11—42no—
158Q8×C11—22no—
159Q8×C11—41no—
160D4×C11—22no—
161D4×C11—44no—
162D4×C11—41no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—22no—
166C2×C4×C11—41no—
167C2×C4×C11—44no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—82no—
172C2×C4×C11—82no—
173C2×C4×C11C2×D811yescharacteristic
174C2×C4×C11C2×D811yescharacteristic
175C2×C4×C11C2×D811yescharacteristic
176C2×C4×C11C2×D811yescharacteristic
177C2×C4×C11C2×D811yescharacteristic
178C2×C4×C11C22×D411yescharacteristic
179C22⋊D11—84no—
180C2×Dic11—42no—
181D44—42no—
182D44—42no—
183D44—82no—
184D44—82no—
185C4×D11—84no—
186Dic22—82no—
187C8×C11—21no—
188C8×C11—21no—
189C8×C11—21no—
190C8×C11C2×#4111yescharacteristic
191C8×C11C2×#4111yescharacteristic
192C2×#135C2×D1111yescharacteristic
193#532—221no—
194C4×#41—21no—
195C2×SD32—112no—
196C2×D16—112no—
197#500—111no—
198#493—111no—
199#486—221no—
200#466—112no—
201#466—221no—
202C4×Q16C2×D1111yescharacteristic
203C4×Q16C2×D1111yescharacteristic
204C4×SD16—21no—
205C4×SD16—21no—
206C4×D8—112no—
207C4×D8—221no—
208C4×D8C2×D1111yescharacteristic
209C4×D8C2×D1111yescharacteristic
210#427C2×D1111yescharacteristic
211#416—21no—
212C2×C4×C8C2×D1111yescharacteristic
213#367—112no—
214#366—112no—
215C4⋊C16—111no—
216C4⋊C16—111no—
217#358—112no—
218#357—112no—
219#357—112no—
220#357—112no—
221C22⋊C16—112no—
222#346—112no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—42no—
227C22×C11—81no—
228C22×C11—81no—
229C22×C11C22×D811yescharacteristic
230C2×D11—82no—
231C2×D11—82no—
232C2×D11—82no—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—42no—
238C4×C11—81no—
239C4×C11—81no—
240C4×C11#50912yes—
241C4×C11#52511yescharacteristic
242C4×C11#57511yescharacteristic
243Dic11—82no—
244C2×#41—21no—
245C2×#41—441no—
246#135—22no—
247#135—22no—
248C2×Q16C22×D1111yescharacteristic
249C2×SD16—21no—
250C2×D8—112no—
251C2×D8—221no—
252C2×D8C22×D1111yescharacteristic
253C22×C8C22⋊D1111yescharacteristic
254C22×C8C22×D1111yescharacteristic
255C4⋊Q8—221no—
256#127—221no—
257#124—441no—
258#121—222no—
259#121—441no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×D4—21no—
263C4×D4—21no—
264C4×D4—41no—
265C4×D4—41no—
266C4×D4—222no—
267C4×D4—441no—
268#117—21no—
269#117—41no—
270C2×C42—41no—
271C2×C42C22⋊D1111yescharacteristic
272SD32—224no—
273D16—224no—
274C2×C16—112no—
275C2×C16—112no—
276#107—112no—
277#107—221no—
278#107C22×D1111yescharacteristic
279#107C22×D1111yescharacteristic
280#106—21no—
281#103—21no—
282#103—21no—
283#102—21no—
284#102—21no—
285#102—222no—
286#102—222no—
287C4×C8C22⋊D1111yescharacteristic
288C4×C8C22⋊D1111yescharacteristic
289C4×C8C22×D1111yescharacteristic
290C4×C8C22×D1111yescharacteristic
291C2×C11—41no—
292C2×C11—82no—
293C2×C11#310011yescharacteristic
294C2×C11C2×#50911yescharacteristic
295C2×C11#341411yescharacteristic
296D11—162no—
297#41—24no—
298#41—42no—
299#41—884no—
300C2×Q8—21no—
301C2×Q8—441no—
302C2×D4—21no—
303C2×D4—41no—
304C2×D4—222no—
305C2×D4—442no—
306C2×D4—441no—
307C2×D4—441no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—442no—
312C22×C4#432311yescharacteristic
313C22×C4#432311yescharacteristic
314C22×C4C2×C22⋊D1111yescharacteristic
315Q16—21no—
316Q16#433912yescomplemented
317SD16—24no—
318D8—21no—
319D8—222no—
320D8—222no—
321D8—442no—
322D8#433912yescomplemented
323C2×C8—21no—
324C2×C8—21no—
325C2×C8—41no—
326C2×C8C2×C22⋊D1111yescharacteristic
327C2×C8C2×C22⋊D1111yescharacteristic
328C2×C8C2×C22⋊D1111yescharacteristic
329C2×C8C23×D1111yescharacteristic
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—222no—
335C4⋊C4—441no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—442no—
340C22⋊C4—442no—
341C42—41no—
342C42—41no—
343C42—41no—
344C42#432311yescharacteristic
345C42#432311yescharacteristic
346C42C2×C22⋊D1111yescharacteristic
347C42C2×C22⋊D1111yescharacteristic
348C16—222no—
349C16—222no—
350C11#3367511yescharacteristic, complemented, Sylow
351C23—41no—
352C23—442no—
353C23C2×#432311yescharacteristic
354Q8—22no—
355Q8—41no—
356Q8—882no—
357D4—22no—
358D4—44no—
359D4—41no—
360D4—442no—
361D4—442no—
362D4—882no—
363D4—884no—
364D4—882no—
365C2×C4—22no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—41no—
369C2×C4—44no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—82no—
374C2×C4—82no—
375C2×C4—442no—
376C2×C4—884no—
377C2×C4C2×#432311yescharacteristic
378C2×C4C2×#432311yescharacteristic
379C2×C4C2×#432311yescharacteristic
380C2×C4C2×#432311yescharacteristic
381C2×C4C2×#432311yescharacteristic
382C2×C4C22×C22⋊D1111yescharacteristic
383C8—21no—
384C8—21no—
385C8—21no—
386C8C2×#433911yescharacteristic
387C8C2×#433911yescharacteristic
388C22—21no—
389C22—21no—
390C22—21no—
391C22—42no—
392C22—81no—
393C22—81no—
394C22—882no—
395C22—882no—
396C22—882no—
397C22C22×#432311yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—42no—
403C4—81no—
404C4—81no—
405C4—882no—
406C4#1062280612yes—
407C4#1062332211yescharacteristic
408C4#1062335311yescharacteristic
409C2—41no—
410C2—82no—
411C2—1762no—
412C2#1307861611yescharacteristic
413C2C2×#1062280611yescharacteristic
414C2#1308175011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×#135C2
socleC22×C11C22×D8
hypercenterC4×#135D11
hypocenterC11#33675
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
1. #13079195C2semidirect
2. #13070807C2semidirect
3. #13070758C2semidirect
4. #13070753C2semidirect
5. #13070656C2semidirect
6. #13070651C2semidirect
7. #13070539C2semidirect
8. #13070490C2semidirect
9. #13070478C2semidirect
10. #13070419C2semidirect
11. C4×C11×#135C2semidirect
110. C11×Q16#41semidirect
113. C11×D8#41semidirect
145. C4×#135D11semidirect
316. Q16#4339semidirect
322. D8#4339semidirect
350. C11#33675semidirect

Maximal subgroups

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

subgroupindex
#130791952
#130708072
#130707582
#130707532
#130706562
#130706512
#130705392
#130704902
#130704782
#130704192
C4×C11×#1352
#3367511