Finite Group Databasebeta

← #11860844

Subgroups — #11860844

Order 1152.

1452 conjugacy classes of subgroups.

The subgroup lattice has 369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64121C211yesmaximal, characteristic
2#10596017C212yesmaximal, complemented
3C32×C4×D8C211yesmaximal, characteristic, complemented
4D8×C3⋊Dic3C211yesmaximal, characteristic, complemented
5#10592717C212yesmaximal, complemented
6C3⋊D3×#107C211yesmaximal, characteristic, complemented
7#10592572C211yesmaximal, characteristic, complemented
8#10592470C212yesmaximal, complemented
9#10592456C212yesmaximal, complemented
10C4×#3746C211yesmaximal, characteristic, complemented
11#10592388C211yesmaximal, characteristic, complemented
12#79589—34nomaximal
13C2×#3830C2212yes—
14C2×C32×D8C2211yescharacteristic
15C32×C4×D4C2212yes—
16D4×C3⋊Dic3C2212yes—
17C2×#3754C2212yes—
18C4×#638—22no—
19C2×#3750—22no—
20#64121C418yescomplemented
21C2×#3746C2211yescharacteristic
22C2×#3743C2211yescharacteristic
23C2×C8×C3⋊D3C2211yescharacteristic
24C4⋊C4×C3⋊D3C2212yes—
25#64096C2212yes—
26#64090—22no—
27#64086—22no—
28#64081C2211yescharacteristic
29C4×#634C2212yes—
30C32×#107C2211yescharacteristic
31C32×#102C2212yes—
32C32×C4×C8C2211yescharacteristic
33#63659C2212yes—
34#63645C2211yescharacteristic
35#63643C2212yes—
36#63642C2211yescharacteristic
37C8×C3⋊Dic3C2211yescharacteristic
38#63637C2212yes—
39#63634C2212yes—
40#63630C2211yescharacteristic
41C2×#912—34no—
42#5546—38no—
43C3×C4×D8D314yescomplemented
44Dic3×D8—34no—
45#5018—38no—
46D3×#107—34no—
47#4873—34no—
48#4771—38no—
49#4757—38no—
50C4×Dic12—34no—
51#4689—34no—
52C2×C32×D4C2312yes—
53C22×C32×C4—22no—
54C2×#638—22no—
55C22×C3⋊Dic3—22no—
56C22×C3⋊Dic3—22no—
57#3830—24no—
58#3830C2×C418yescomplemented
59C2×C4×C3⋊D3—22no—
60C2×C4×C3⋊D3C2311yescharacteristic
61C2×#634C2312yes—
62C32×D8C2×C414yescomplemented
63C2×C32×C8C2311yescharacteristic
64C2×C32×C8C2311yescharacteristic
65C32×C4⋊C4C2312yes—
66C32×C22⋊C4—22no—
67C32×C42C2311yescharacteristic
68#3757—22no—
69#3754C2×C418yescomplemented
70#3752D411yescharacteristic
71#3752D411yescharacteristic
72C4⋊(C3⋊Dic3)C2312yes—
73#3750—22no—
74#3750—22no—
75#3750—22no—
76#3750D411yescharacteristic
77#3750D411yescharacteristic
78C4×C3⋊Dic3—22no—
79C4×C3⋊Dic3—22no—
80C4×C3⋊Dic3C2311yescharacteristic
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83#3746C2×C414yescomplemented
84#3743—22no—
85C8×C3⋊D3C2×C414yescomplemented
86#2951—91noSylow
87C2×#237—38no—
88C2×C3×D8C2×D314yes—
89C3×C4×D4C2×D318yes—
90D4×Dic3—38no—
91C2×#214—38no—
92C4×#67—68no—
93C2×Dic3⋊C4—68no—
94#912—332no—
95C2×Dic12—34no—
96C2×ΓL(1,𝔽25)—34no—
97C2×D3×C8—34no—
98D3×C4⋊C4—38no—
99#887—38no—
100#67⋊C4—68no—
101#877—68no—
102#872—34no—
103C4×Dic6—38no—
104C3×#107C2×D314yes—
105C3×#102C2×D318yes—
106C3×C4×C8C2×D314yes—
107#832—38no—
108#818—34no—
109#816—38no—
110#815—34no—
111C8×Dic3—34no—
112#810—38no—
113#807—38no—
114#803—34no—
115C23×C32—22no—
116C22×C3⋊D3C2×D411yescharacteristic
117C32×D4—22no—
118C32×D4C22×C414yes—
119C2×C32×C4—22no—
120C2×C32×C4—82no—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2411yescharacteristic
124#638—28no—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—28no—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—82no—
129C2×C3⋊Dic3C2×D411yescharacteristic
130C2×C3⋊Dic3C2×D411yescharacteristic
131C2×C3⋊Dic3C2×D411yescharacteristic
132C4×C3⋊D3—82no—
133C4×C3⋊D3C22×C412yes—
134C4×C3⋊D3#4112yes—
135#634—22no—
136#634C22×C414yes—
137C32×C8—21no—
138C32×C8C22×C412yes—
139C3⋊(C3⋊C8)—21no—
140C3⋊(C3⋊C8)C22×C412yes—
141C2×#135—91no—
142#520—92no—
143#440—92no—
144#440—92no—
145C4×Q16—91no—
146C4×Q16—91no—
147C4×D8—91no—
148C4×D8C3⋊D311yescharacteristic, complemented
149C2×#107—91no—
150#417—92no—
151#405—91no—
152C2×C3×D4C22×D318yes—
153C22×C3×C4—28no—
154C2×#67—68no—
155C22×Dic3—68no—
156C22×Dic3—68no—
157#237—332no—
158#237—616no—
159C2×C4×D3—34no—
160C2×C4×D3—68no—
161C2×Dic6—38no—
162C3×D8C4×D3116yescomplemented
163C2×C3×C8C22×D314yes—
164C2×C3×C8C22×D314yes—
165C3×C4⋊C4C22×D318yes—
166C3×C22⋊C4—28no—
167C3×C42C22×D314yes—
168#217—68no—
169#214—332no—
170(C2×D3)⋊C4—34no—
171(C2×D3)⋊C4—34no—
172C4⋊Dic3—38no—
173Dic3⋊C4—34no—
174Dic3⋊C4—34no—
175Dic3⋊C4—68no—
176Dic3⋊C4—68no—
177Dic3⋊C4—68no—
178C4×Dic3—34no—
179C4×Dic3—68no—
180C4×Dic3—68no—
181C2×C3⋊C8—34no—
182C2×C3⋊C8—34no—
183Dic12—316no—
184ΓL(1,𝔽25)—68no—
185D3×C8—316no—
186C22×C32—24no—
187C22×C32—42no—
188C22×C32—42no—
189C22×C32C22×D411yescharacteristic
190C2×C3⋊D3—21no—
191C2×C3⋊D3—21no—
192C2×C3⋊D3C4×D412yes—
193C32×C4—21no—
194C32×C4—21no—
195C32×C4—42no—
196C32×C4C23×C411yescharacteristic
197C32×C4C2×#4111yescharacteristic
198C3⋊Dic3—24no—
199C3⋊Dic3—21no—
200C3⋊Dic3—21no—
201C3⋊Dic3—42no—
202C3⋊Dic3C4×D412yes—
203C2×#41—92no—
204#135—98no—
205C2×Q16—91no—
206C2×SD16—92no—
207C2×D8C2×C3⋊D311yescharacteristic
208C2×M16—91no—
209C22×C8—91no—
210C4×Q8—92no—
211C4×Q8—92no—
212C4×D4—92no—
213C4×D4—182no—
214C4×D4—182no—
215C4×D4C2×C3⋊D312yes—
216#117—91no—
217#117—182no—
218C2×C4⋊C4—92no—
219C2×C4⋊C4—182no—
220#107—91no—
221#107—92no—
222#107C2×C3⋊D311yescharacteristic
223#103—92no—
224#103—92no—
225#102—92no—
226#102C2×C3⋊D312yes—
227#97—91no—
228#97—91no—
229C4×C8—91no—
230C4×C8C2×C3⋊D311yescharacteristic
231C23×C3—28no—
232C22×D3—34no—
233C3×D4—28no—
234C3×D4C2×C4×D3116yes—
235C2×C3×C4—28no—
236C2×C3×C4—88no—
237C2×C3×C4D3×D414yes—
238C2×C3×C4D3×D414yes—
239C2×C3×C4C23×D314yes—
240#67—632no—
241C2×Dic3—34no—
242C2×Dic3—34no—
243C2×Dic3—34no—
244C2×Dic3—632no—
245C2×Dic3—68no—
246C2×Dic3—68no—
247C2×Dic3—248no—
248C4×D3—38no—
249C4×D3—38no—
250C4×D3—248no—
251Dic6—316no—
252Dic6—68no—
253C3×C8—24no—
254C3×C8C2×C4×D318yes—
255C3⋊C8—38no—
256C3⋊C8—64no—
257C2×C32—44no—
258C2×C32C2×C4×D411yescharacteristic
259C2×C32#57611yescharacteristic
260C2×C32#57811yescharacteristic
261C3⋊D3—22no—
262#41—98no—
263#41—184no—
264C2×Q8—92no—
265C2×D4—182no—
266C2×D4C22×C3⋊D312yes—
267C22×C4—22no—
268C22×C4—91no—
269C22×C4—182no—
270C22×C4—182no—
271C22×C4—182no—
272Q16—94no—
273SD16—98no—
274D8C4×C3⋊D314yescomplemented
275M16—182no—
276C2×C8—91no—
277C2×C8—94no—
278C2×C8—91no—
279C2×C8C22×C3⋊D311yescharacteristic
280C2×C8C22×C3⋊D311yescharacteristic
281C4⋊C4—91no—
282C4⋊C4—91no—
283C4⋊C4—92no—
284C4⋊C4—182no—
285C4⋊C4—182no—
286C4⋊C4—182no—
287C4⋊C4C22×C3⋊D312yes—
288C22⋊C4—22no—
289C22⋊C4—91no—
290C22⋊C4—91no—
291C22⋊C4—182no—
292C42—91no—
293C42—182no—
294C42—182no—
295C42C22×C3⋊D311yescharacteristic
296C22×C3—216no—
297C22×C3—48no—
298C22×C3—48no—
299C22×C3C2×D3×D414yes—
300C2×D3—38no—
301C2×D3—64no—
302C2×D3—64no—
303C3×C4—24no—
304C3×C4—24no—
305C3×C4—48no—
306C3×C4C22×C4×D314yes—
307C3×C4D3×#4114yes—
308Dic3—38no—
309Dic3—64no—
310Dic3—64no—
311Dic3—616no—
312Dic3—128no—
313C32#295111yescharacteristic, complemented, Sylow
314C23—22no—
315C23—91no—
316Q8—94no—
317Q8—182no—
318D4—22no—
319D4—188no—
320D4C2×C4×C3⋊D314yes—
321C2×C4—22no—
322C2×C4—82no—
323C2×C4—91no—
324C2×C4—92no—
325C2×C4—92no—
326C2×C4—91no—
327C2×C4—91no—
328C2×C4—188no—
329C2×C4—182no—
330C2×C4—182no—
331C2×C4—722no—
332C2×C4—722no—
333C2×C4D4×C3⋊D311yescharacteristic
334C2×C4D4×C3⋊D311yescharacteristic
335C2×C4C23×C3⋊D311yescharacteristic
336C8—21no—
337C8—92no—
338C8—181no—
339C8C2×C4×C3⋊D312yes—
340C2×C3—416no—
341C2×C3C4×D3×D414yes—
342C2×C3#575714yes—
343C2×C3#577114yes—
344D3—68no—
345C22—24no—
346C22—42no—
347C22—42no—
348C22—92no—
349C22—181no—
350C22—181no—
351C22C2×D4×C3⋊D311yescharacteristic
352C4—21no—
353C4—21no—
354C4—42no—
355C4—92no—
356C4—181no—
357C4—181no—
358C4—184no—
359C4—362no—
360C4C22×C4×C3⋊D311yescharacteristic
361C4#41×C3⋊D311yescharacteristic
362C3#7958914yescomplemented
363C2—44no—
364C2—182no—
365C2C4×D4×C3⋊D311yescharacteristic
366C2#1059622811yescharacteristic
367C2#1059624211yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×D8C2
socleC22×C32C22×D4
prime radicalC2×#64121C2
cosocleC2×C32×C4C24
hypercenterC4×D8C3⋊D3
hypocenterC32#2951
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
2. #10596017C2semidirect
3. C32×C4×D8C2semidirect
4. D8×C3⋊Dic3C2semidirect
5. #10592717C2semidirect
6. C3⋊D3×#107C2semidirect
7. #10592572C2semidirect
8. #10592470C2semidirect
9. #10592456C2semidirect
10. C4×#3746C2semidirect
11. #10592388C2semidirect
20. #64121C4semidirect
43. C3×C4×D8D3semidirect
58. #3830C2×C4semidirect
62. C32×D8C2×C4semidirect
69. #3754C2×C4semidirect
83. #3746C2×C4semidirect
85. C8×C3⋊D3C2×C4semidirect
148. C4×D8C3⋊D3semidirect
162. C3×D8C4×D3semidirect
274. D8C4×C3⋊D3semidirect
313. C32#2951semidirect
362. C3#79589semidirect

Maximal subgroups

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

subgroupindex
C2×#641212
#105960172
C32×C4×D82
D8×C3⋊Dic32
#105927172
C3⋊D3×#1072
#105925722
#105924702
#105924562
C4×#37462
#105923882
#795893