Finite Group Databasebeta

← #11868724

Subgroups — #11868724

Order 1152.

1128 conjugacy classes of subgroups.

The subgroup lattice has 393 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596199C211yesmaximal, characteristic
2C4×Q8×C3⋊D3C211yesmaximal, characteristic
3C32×#477C211yesmaximal, characteristic, complemented
4#10592790C211yesmaximal, characteristic, complemented
5#10592719C211yesmaximal, characteristic, complemented
6#10592580C212yesmaximal
7#10592576C212yesmaximal, complemented
8#10592550C211yesmaximal, characteristic, complemented
9#10592536C211yesmaximal, characteristic
10#10592501C212yesmaximal
11#10592498C212yesmaximal, complemented
12#81108—34nomaximal
13C2×Q8×C3⋊D3C2211yescharacteristic
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4×Q8C2211yescharacteristic
16#64155—21no—
17Q8×C3⋊Dic3—21no—
18Q8×C3⋊Dic3C2211yescharacteristic
19C2×#3743C2212yes—
20#64106—21no—
21#64101C2212yes—
22C4⋊C4×C3⋊D3—21no—
23C4⋊C4×C3⋊D3C2211yescharacteristic
24#64099C2212yes—
25#64096—21no—
26#64096—21no—
27#64096C2211yescharacteristic
28C42×C3⋊D3—21no—
29C42×C3⋊D3C2211yescharacteristic
30#64078C2211yescharacteristic
31C4×#634—21no—
32C4×#634C2211yescharacteristic
33C32×#107C2212yes—
34C32×C4⋊C8C2211yescharacteristic
35C32×#103C2212yes—
36#63662C2212yes—
37#63644C2212yes—
38#63643C2212yes—
39#63641C2212yes—
40#63637C2212yes—
41#63635C2212yes—
42#63634C2212yes—
43C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
44#5728—34no—
45C4×D3×Q8—34no—
46C3×#477D314yescomplemented
47#5091—34no—
48#5020—34no—
49#4881—38no—
50#4877—38no—
51#4851—34no—
52#4837—34no—
53#4802—38no—
54#4799—38no—
55C2×C32×Q8—21no—
56C2×C32×Q8C2311yescharacteristic
57Q8×C3⋊D3—22no—
58Q8×C3⋊D3Q814yescomplemented
59C2×C4×C3⋊D3—21no—
60C2×C4×C3⋊D3—21no—
61C2×C4×C3⋊D3D411yescharacteristic
62C2×C4×C3⋊D3D411yescharacteristic
63C2×C4×C3⋊D3C2311yescharacteristic
64C2×#634—21no—
65C2×#634—21no—
66C2×#634C2311yescharacteristic
67C2×C32×C8C2312yes—
68C32×C4⋊C4—21no—
69C32×C4⋊C4—21no—
70C32×C4⋊C4C2311yescharacteristic
71C32×C4⋊C4C2312yes—
72C32×C42—21no—
73C32×C42C2311yescharacteristic
74#3752—22no—
75C4⋊(C3⋊Dic3)—21no—
76C4⋊(C3⋊Dic3)—21no—
77C4⋊(C3⋊Dic3)—22no—
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79C4⋊(C3⋊Dic3)C2312yes—
80#3750—21no—
81#3750—21no—
82#3750—21no—
83#3750—22no—
84C4×C3⋊Dic3—21no—
85C4×C3⋊Dic3—21no—
86C4×C3⋊Dic3—21no—
87C4×C3⋊Dic3—22no—
88C4×C3⋊Dic3D411yescharacteristic
89C4×C3⋊Dic3D411yescharacteristic
90C4×C3⋊Dic3C2311yescharacteristic
91C2×C3⋊(C3⋊C8)C2312yes—
92#3743—24no—
93#3078—91noSylow
94C2×D3×Q8—34no—
95C3×C4⋊Q8C2×D314yes—
96C3×C4×Q8C2×D314yes—
97#946—64no—
98Q8×Dic3—34no—
99Q8×Dic3—64no—
100C2×ΓL(1,𝔽25)—38no—
101#897—64no—
102#892—38no—
103D3×C4⋊C4—34no—
104D3×C4⋊C4—64no—
105#890—38no—
106#887—34no—
107#887—64no—
108#887—64no—
109C42×D3—34no—
110C42×D3—64no—
111#869—34no—
112C4×Dic6—34no—
113C4×Dic6—64no—
114C3×#107C2×D318yes—
115C3×C4⋊C8C2×D314yes—
116C3×#103C2×D318yes—
117#835—38no—
118#817—38no—
119#816—38no—
120Dic3⋊C8—38no—
121#810—38no—
122#808—38no—
123#807—38no—
124C4⋊(C3⋊C8)—34no—
125C22×C3⋊D3C2×D411yescharacteristic
126C32×Q8—21no—
127C32×Q8—42no—
128C32×Q8C2×Q812yes—
129C2×C32×C4—21no—
130C2×C32×C4—21no—
131C2×C32×C4—22no—
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2411yescharacteristic
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3C2×D411yescharacteristic
139C2×C3⋊Dic3C2×D411yescharacteristic
140C2×C3⋊Dic3C2×D411yescharacteristic
141C4×C3⋊D3—24no—
142C4×C3⋊D3—22no—
143C4×C3⋊D3—41no—
144C4×C3⋊D3—42no—
145C4×C3⋊D3C2×Q812yes—
146C4×C3⋊D3#4112yes—
147#634—21no—
148#634—24no—
149#634—42no—
150#634C2×Q812yes—
151C32×C8—22no—
152C3⋊(C3⋊C8)—22no—
153#533—91no—
154C2×C4×Q8—91no—
155#479—92no—
156#479—92no—
157#477—91no—
158#477C3⋊D311yescharacteristic, complemented
159#475—91no—
160#475—91no—
161#428—92no—
162#423—91no—
163#419—92no—
164C2×C3×Q8—24no—
165C2×C3×Q8C22×D314yes—
166D3×Q8—316no—
167D3×Q8—68no—
168C2×C4×D3—34no—
169C2×C4×D3—34no—
170C2×C4×D3—34no—
171C2×C4×D3—64no—
172C2×C4×D3—64no—
173C2×Dic6—34no—
174C2×Dic6—64no—
175C2×Dic6—64no—
176C2×C3×C8C22×D318yes—
177C3×C4⋊C4—24no—
178C3×C4⋊C4—24no—
179C3×C4⋊C4C22×D318yes—
180C3×C4⋊C4C22×D314yes—
181C3×C42—24no—
182C3×C42C22×D314yes—
183(C2×D3)⋊C4—68no—
184C4⋊Dic3—34no—
185C4⋊Dic3—38no—
186C4⋊Dic3—64no—
187C4⋊Dic3—68no—
188C4⋊Dic3—64no—
189Dic3⋊C4—64no—
190Dic3⋊C4—64no—
191Dic3⋊C4—68no—
192Dic3⋊C4—64no—
193C4×Dic3—34no—
194C4×Dic3—34no—
195C4×Dic3—34no—
196C4×Dic3—64no—
197C4×Dic3—64no—
198C4×Dic3—68no—
199C4×Dic3—64no—
200C2×C3⋊C8—38no—
201ΓL(1,𝔽25)—616no—
202C22×C32C22×D411yescharacteristic
203C2×C3⋊D3—21no—
204C2×C3⋊D3—21no—
205C2×C3⋊D3C22⋊Q812yes—
206C32×C4—22no—
207C32×C4—21no—
208C32×C4—41no—
209C32×C4—42no—
210C32×C4#13712yes—
211C32×C4C22×Q811yescharacteristic
212C32×C4C2×#4111yescharacteristic
213C3⋊Dic3—22no—
214C3⋊Dic3—21no—
215C3⋊Dic3—21no—
216C3⋊Dic3—42no—
217C3⋊Dic3—41no—
218C3⋊Dic3C22⋊Q812yes—
219C22×Q8—91no—
220C2×M16—92no—
221C4⋊Q8—91no—
222C4⋊Q8C2×C3⋊D311yescharacteristic
223#125—92no—
224C22⋊Q8—181no—
225C22⋊Q8—181no—
226C4×Q8—91no—
227C4×Q8—91no—
228C4×Q8—91no—
229C4×Q8—181no—
230C4×Q8—181no—
231C4×Q8—181no—
232C4×Q8—181no—
233C4×Q8C2×C3⋊D311yescharacteristic
234#117—92no—
235C2×C4⋊C4—91no—
236C2×C4⋊C4—181no—
237C2×C42—91no—
238C2×C42—181no—
239#107—92no—
240#107C2×C3⋊D312yes—
241#106—92no—
242#106—92no—
243C4⋊C8—92no—
244C4⋊C8—91no—
245C4⋊C8C2×C3⋊D311yescharacteristic
246#103—92no—
247#103—92no—
248#103—92no—
249#103C2×C3⋊D312yes—
250C22×D3—34no—
251C3×Q8—24no—
252C3×Q8—48no—
253C3×Q8D3×Q818yes—
254C2×C3×C4—24no—
255C2×C3×C4—24no—
256C2×C3×C4—28no—
257C2×C3×C4D3×D414yes—
258C2×C3×C4D3×D414yes—
259C2×C3×C4C23×D314yes—
260C2×Dic3—34no—
261C2×Dic3—34no—
262C2×Dic3—34no—
263C2×Dic3—64no—
264C2×Dic3—64no—
265C2×Dic3—68no—
266C4×D3—38no—
267C4×D3—38no—
268C4×D3—616no—
269C4×D3—68no—
270C4×D3—124no—
271C4×D3—128no—
272Dic6—38no—
273Dic6—616no—
274Dic6—64no—
275Dic6—128no—
276C3×C8—28no—
277C3⋊C8—68no—
278C2×C32C2×C22⋊Q811yescharacteristic
279C2×C32C2×#13711yescharacteristic
280C2×C32#57511yescharacteristic
281C3⋊D3—22no—
282C2×Q8—21no—
283C2×Q8—94no—
284C2×Q8—91no—
285C2×Q8—181no—
286C2×Q8—182no—
287C2×Q8—181no—
288C2×Q8C22×C3⋊D311yescharacteristic
289C22×C4—91no—
290C22×C4—91no—
291C22×C4—91no—
292C22×C4—181no—
293C22×C4—181no—
294M16—184no—
295C2×C8—92no—
296C2×C8C22×C3⋊D312yes—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—92no—
300C4⋊C4—91no—
301C4⋊C4—181no—
302C4⋊C4—181no—
303C4⋊C4—181no—
304C4⋊C4—182no—
305C4⋊C4—182no—
306C4⋊C4—181no—
307C4⋊C4—181no—
308C4⋊C4C22×C3⋊D312yes—
309C4⋊C4C22×C3⋊D311yescharacteristic
310C22⋊C4—182no—
311C42—21no—
312C42—91no—
313C42—91no—
314C42—91no—
315C42—181no—
316C42—181no—
317C42—182no—
318C42—181no—
319C42C22×C3⋊D311yescharacteristic
320C22×C3C2×D3×D414yes—
321C2×D3—38no—
322C2×D3—64no—
323C2×D3—64no—
324C3×C4—24no—
325C3×C4—28no—
326C3×C4—44no—
327C3×C4—48no—
328C3×C4#91818yes—
329C3×C4C2×D3×Q814yes—
330C3×C4D3×#4114yes—
331Dic3—38no—
332Dic3—64no—
333Dic3—64no—
334Dic3—68no—
335Dic3—128no—
336Dic3—124no—
337C32#307811yescharacteristic, complemented, Sylow
338C23—91no—
339Q8—21no—
340Q8—42no—
341Q8—92no—
342Q8—184no—
343Q8—181no—
344Q8—362no—
345Q8Q8×C3⋊D312yes—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—91no—
350C2×C4—92no—
351C2×C4—92no—
352C2×C4—91no—
353C2×C4—91no—
354C2×C4—184no—
355C2×C4—181no—
356C2×C4—182no—
357C2×C4—181no—
358C2×C4—182no—
359C2×C4—361no—
360C2×C4—362no—
361C2×C4D4×C3⋊D311yescharacteristic
362C2×C4D4×C3⋊D311yescharacteristic
363C2×C4C23×C3⋊D311yescharacteristic
364C8—22no—
365C8—182no—
366C2×C3D3×C22⋊Q814yes—
367C2×C3C2×#91814yes—
368C2×C3#577314yes—
369D3—68no—
370C22—92no—
371C22—181no—
372C22—181no—
373C22C2×D4×C3⋊D311yescharacteristic
374C4—22no—
375C4—21no—
376C4—41no—
377C4—42no—
378C4—92no—
379C4—182no—
380C4—181no—
381C4—181no—
382C4—362no—
383C4—361no—
384C4#6412712yes—
385C4C2×Q8×C3⋊D311yescharacteristic
386C4#41×C3⋊D311yescharacteristic
387C3#8110814yescomplemented
388C2—182no—
389C2C3⋊D3×C22⋊Q811yescharacteristic
390C2C2×#6412711yescharacteristic
391C2#1059624411yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#477C2
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#477C3⋊D3
hypocenterC32#3078
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
3. C32×#477C2semidirect
4. #10592790C2semidirect
5. #10592719C2semidirect
7. #10592576C2semidirect
8. #10592550C2semidirect
11. #10592498C2semidirect
46. C3×#477D3semidirect
58. Q8×C3⋊D3Q8semidirect
158. #477C3⋊D3semidirect
337. C32#3078semidirect
387. C3#81108semidirect

Maximal subgroups

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

subgroupindex
#105961992
C4×Q8×C3⋊D32
C32×#4772
#105927902
#105927192
#105925802
#105925762
#105925502
#105925362
#105925012
#105924982
#811083