Finite Group Databasebeta

← #11899513

Subgroups — #11899513

Order 1152.

785 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 785 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594684C212yesmaximal, complemented
2C2×C16×C3⋊D3C211yesmaximal, characteristic, complemented
3C3×#4904C212yesmaximal, complemented
4#10590629C212yesmaximal, complemented
5#10590245C212yesmaximal, complemented
6#10590244C212yesmaximal, complemented
7#10590240C211yesmaximal, characteristic, complemented
8#10590235C212yesmaximal, complemented
9#10590234C211yesmaximal, characteristic, complemented
10D3×#508—32nomaximal
11#64306—22no—
12C2×C8×C3⋊D3C2211yescharacteristic
13C3×#904C2214yescomplemented
14#63822—22no—
15#63810C2214yescomplemented
16#63809—22no—
17#63802C2212yes—
18#63797C2212yes—
19#63796—22no—
20C2×C32×C16C2211yescharacteristic, complemented
21C2×C3⋊(C3⋊C16)C2211yescharacteristic, complemented
22C16×C3⋊D3C2211yescharacteristic
23C16×C3⋊D3C2211yescharacteristic
24C16×C3⋊D3C2211yescharacteristic, complemented
25C16×C3⋊D3C2211yescharacteristic, complemented
26C3×Dic24C2212yescomplemented
27C3×#800C2214yescomplemented
28C3×D48C2212yescomplemented
29#63550C2212yescomplemented
30#63547C2214yescomplemented
31#63545C2212yescomplemented
32D3×#135—34no—
33C3×#508—32no—
34#5194—34no—
35#4919—32no—
36D3×Q32—32no—
37#4916—34no—
38D3×SD32—34no—
39#4912—32no—
40D3×D16—32no—
41#4904D312yescomplemented
42C2×D3×C16—32no—
43C2×D3×C16—61no—
44C2×C4×C3⋊D3D411yescharacteristic
45C3×#235—24no—
46#3811—42no—
47#3805—42no—
48#3802—22no—
49C4×D32—42no—
50#3798—42no—
51#3797—22no—
52#3796—24no—
53C2×C32×C8C2311yescharacteristic
54C2×C3⋊(C3⋊C8)D411yescharacteristic
55C8×C3⋊D3D411yescharacteristic
56C8×C3⋊D3D411yescharacteristic
57C8×C3⋊D3C2311yescharacteristic
58C8×C3⋊D3C2311yescharacteristic
59C3×Dic12C2314yes—
60C3×D24C2314yes—
61C3×#204—24no—
62#3718—22no—
63#3715—24no—
64#3713—22no—
65C32×C16C2311yescharacteristic
66C32×C16C2311yescharacteristic
67C3⋊(C3⋊C16)C2311yescharacteristic
68C3⋊(C3⋊C16)C2311yescharacteristic
69C2×#508—91noSylow
70D3×#41—64no—
71C3×#135—34no—
72#950—64no—
73#919—34no—
74D3×Q16—34no—
75#916—64no—
76D3×SD16—64no—
77#912—34no—
78D3×D8—34no—
79#904C2×D314yescomplemented
80C2×D3×C8—32no—
81C2×D3×C8—61no—
82C3×Q32—32no—
83C3×SD32—34no—
84C3×D16—32no—
85C2×C3×C16—21no—
86C2×C3×C16C2×D312yescomplemented
87#829—34no—
88#828—34no—
89#827—34no—
90#826—34no—
91C2×C3⋊C16—32no—
92C2×C3⋊C16—61no—
93Dic24C2×D312yescomplemented
94#800C2×D314yescomplemented
95D48C2×D312yescomplemented
96D3×C16—32no—
97D3×C16—32no—
98D3×C16—32no—
99D3×C16—32no—
100D3×C16—61no—
101D3×C16—61no—
102D3×C16—61no—
103D3×C16—61no—
104C22×C3⋊D3D811yescharacteristic
105C2×D32—42no—
106C2×C32×C4C2×D411yescharacteristic
107C2×C3⋊Dic3D811yescharacteristic
108C4×C3⋊D3D811yescharacteristic
109C4×C3⋊D3D811yescharacteristic
110C4×C3⋊D3C2×D411yescharacteristic
111C4×C3⋊D3C2×D411yescharacteristic
112C3×#67—44no—
113C3×D12—24no—
114C3×C4×D3—44no—
115C3×Dic6—24no—
116#627—42no—
117#626—44no—
118#625—42no—
119#624—42no—
120D3×Dic3—44no—
121C32×C8C2×D411yescharacteristic
122C32×C8C2411yescharacteristic
123C3⋊(C3⋊C8)C2×D411yescharacteristic
124C3⋊(C3⋊C8)C2×D411yescharacteristic
125C2×#135—92no—
126#508—32no—
127#508—92no—
128#508—92no—
129#508—92no—
130C2×Q32—91no—
131C2×SD32—92no—
132C2×D16—91no—
133C22×C16—91no—
134C3×#41—64no—
135#239—64no—
136D3×Q8—64no—
137#237—64no—
138#237—124no—
139D3×D4—64no—
140D3×D4—124no—
141#235—24no—
142#235—124no—
143C2×C4×D3—32no—
144C2×C4×D3—61no—
145C2×C4×D3—124no—
146C3×Q16—34no—
147C3×SD16—64no—
148C3×D8—34no—
149C2×C3×C8—21no—
150C2×C3×C8C22×D312yes—
151#216—64no—
152#215—64no—
153#214—64no—
154#213—64no—
155C2×C3⋊C8—32no—
156C2×C3⋊C8—61no—
157Dic12C22×D314yes—
158D24C22×D314yes—
159#204—24no—
160D3×C8—32no—
161D3×C8—32no—
162D3×C8—32no—
163D3×C8—32no—
164D3×C8—61no—
165D3×C8—61no—
166D3×C8—61no—
167D3×C8—61no—
168C3×C16—21no—
169C3×C16—21no—
170C3×C16C22×D312yes—
171C3×C16C22×D312yes—
172C3⋊C16—32no—
173C3⋊C16—32no—
174C3⋊C16—61no—
175C3⋊C16—61no—
176C22×C32C2×D811yescharacteristic
177C2×C3⋊D3—22no—
178C2×C3⋊D3C2×D811yescharacteristic
179C2×C3⋊D3C2×D811yescharacteristic
180C2×C3×D3—44no—
181D32—84no—
182C32×C4C2×D811yescharacteristic
183C32×C4C22×D411yescharacteristic
184C3⋊Dic3C2×D811yescharacteristic
185C3⋊Dic3C2×D811yescharacteristic
186C3×Dic3—44no—
187C2×#41—182no—
188#135—34no—
189#135—94no—
190#135—182no—
191#135—182no—
192C2×Q16—92no—
193C2×SD16—182no—
194C2×D8—92no—
195C22×C8—91no—
196Q32—32no—
197Q32—92no—
198SD32—34no—
199SD32—94no—
200D16—32no—
201D16—92no—
202C2×C16—91no—
203C2×C16—91no—
204C2×C16—91no—
205C2×C16—91no—
206C2×C16—91no—
207C2×C16D3211yescharacteristic, complemented
208C22×D3—32no—
209C22×D3—61no—
210C22×D3—124no—
211C3×Q8—64no—
212C3×D4—64no—
213C3×D4—124no—
214C2×C3×C4—21no—
215C2×C3×C4—124no—
216C2×C3×C4D3×D412yes—
217#67—44no—
218#67—124no—
219#67—124no—
220C2×Dic3—32no—
221C2×Dic3—61no—
222C2×Dic3—124no—
223D12—24no—
224D12—124no—
225C4×D3—32no—
226C4×D3—32no—
227C4×D3—32no—
228C4×D3—32no—
229C4×D3—44no—
230C4×D3—61no—
231C4×D3—61no—
232C4×D3—61no—
233C4×D3—61no—
234C4×D3—124no—
235C4×D3—124no—
236Dic6—24no—
237Dic6—124no—
238C3×C8—21no—
239C3×C8—21no—
240C3×C8D3×D412yes—
241C3×C8C23×D312yes—
242C3⋊C8—32no—
243C3⋊C8—32no—
244C3⋊C8—61no—
245C3⋊C8—61no—
246C2×C32—21no—
247C2×C32C22×D811yescharacteristic
248C3⋊D3—21no—
249C3⋊D3#50812yescomplemented
250C3×D3—84no—
251#41—64no—
252#41—184no—
253#41—362no—
254#41—362no—
255C2×Q8—182no—
256C2×D4—182no—
257C2×D4—362no—
258C22×C4—91no—
259C22×C4—362no—
260Q16—34no—
261Q16—182no—
262SD16—64no—
263SD16—184no—
264D8—34no—
265D8—182no—
266C2×C8—91no—
267C2×C8—91no—
268C2×C8—91no—
269C2×C8—91no—
270C2×C8—91no—
271C2×C8C2×D3211yescharacteristic
272C16—91no—
273C16—91no—
274C16C2×D3211yescharacteristic
275C16C2×D3211yescharacteristic
276C22×C3—21no—
277C22×C3—124no—
278C22×C3D3×D812yes—
279C2×D3—32no—
280C2×D3—32no—
281C2×D3—44no—
282C2×D3—61no—
283C2×D3—61no—
284C2×D3—64no—
285C2×D3—64no—
286C2×D3—248no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—124no—
290C3×C4D3×D812yes—
291C3×C4C2×D3×D412yes—
292Dic3—32no—
293Dic3—32no—
294Dic3—44no—
295Dic3—61no—
296Dic3—61no—
297C32C2×#50811yescharacteristic, complemented, Sylow
298C23—91no—
299C23—362no—
300Q8—64no—
301Q8—362no—
302D4—64no—
303D4—124no—
304D4—362no—
305D4—364no—
306C2×C4—91no—
307C2×C4—91no—
308C2×C4—91no—
309C2×C4—91no—
310C2×C4—91no—
311C2×C4—124no—
312C2×C4—364no—
313C2×C4—362no—
314C2×C4#380211yescharacteristic
315C8—91no—
316C8—91no—
317C8#380211yescharacteristic
318C8C22×D3211yescharacteristic
319C2×C3—22no—
320C2×C3—22no—
321C2×C3—21no—
322C2×C3—244no—
323C2×C3C2×D3×D812yes—
324D3—34no—
325D3—62no—
326D3—62no—
327D3—62no—
328D3—84no—
329C22—91no—
330C22—91no—
331C22—124no—
332C22—182no—
333C22—724no—
334C22#6379711yescharacteristic
335C4—91no—
336C4—91no—
337C4—124no—
338C4#6379711yescharacteristic
339C4C2×#380211yescharacteristic
340C3—21no—
341C3D3×#50812yescomplemented
342C2—21no—
343C2—92no—
344C2—181no—
345C2—244no—
346C2C2×#6379711yescharacteristic
subgroupG/H
centerC4#63797
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC2×C32×C16C22
socleC2×C32C22×D8
hypercenterC2×C16D32
hypocenterC32C2×#508
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
1. #10594684C2semidirect
2. C2×C16×C3⋊D3C2semidirect
3. C3×#4904C2semidirect
4. #10590629C2semidirect
5. #10590245C2semidirect
6. #10590244C2semidirect
7. #10590240C2semidirect
8. #10590235C2semidirect
9. #10590234C2semidirect
13. C3×#904C22semidirect
15. #63810C22semidirect
20. C2×C32×C16C22semidirect
21. C2×C3⋊(C3⋊C16)C22semidirect
24. C16×C3⋊D3C22semidirect
25. C16×C3⋊D3C22semidirect
26. C3×Dic24C22semidirect
27. C3×#800C22semidirect
28. C3×D48C22semidirect
29. #63550C22semidirect
30. #63547C22semidirect
31. #63545C22semidirect
41. #4904D3semidirect
79. #904C2×D3semidirect
86. C2×C3×C16C2×D3semidirect
93. Dic24C2×D3semidirect
94. #800C2×D3semidirect
95. D48C2×D3semidirect
207. C2×C16D32semidirect
249. C3⋊D3#508semidirect
297. C32C2×#508semidirect
341. C3D3×#508semidirect

Maximal subgroups

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

subgroupindex
#105946842
C2×C16×C3⋊D32
C3×#49042
#105906292
#105902452
#105902442
#105902402
#105902352
#105902342
D3×#5083