Finite Group Databasebeta

← #11796957

Subgroups — #11796957

Order 1152.

467 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#919C211yesmaximal, characteristic
2D3×#819C211yesmaximal, characteristic, complemented
3D3×#812C211yesmaximal, characteristic, complemented
4#10589431C211yesmaximal, characteristic, complemented
5C3×#4565C211yesmaximal, characteristic, complemented
6#10589127C211yesmaximal, characteristic, complemented
7#10589126C211yesmaximal, characteristic, complemented
8#72081—31nomaximal
9#69266—31nomaximal
10C2×C3×#239—21no—
11C2×C32×Q16C2211yescharacteristic
12C2×C3×#215—21no—
13C3×#919—21no—
14C3×#919—21no—
15C3×#919C412yes—
16C3×#919C412yes—
17C2×C3×D24C2211yescharacteristic
18C2×C3×D3×C8C2211yescharacteristic
19D3×#208—21no—
20#63646C2211yescharacteristic
21#63639C2211yescharacteristic
22C3×#819C2211yescharacteristic
23C3×#812C2211yescharacteristic
24#63577—21no—
25#63543—21no—
26D3×C3⋊C16—21no—
27C2×C3×#135—31no—
28C2×#919D311yescharacteristic
29C2×#819—31no—
30C2×#812—31no—
31D3×M32—31no—
32D3×#108—31no—
33C3×#362—31no—
34#4565—31no—
35#4565—31no—
36#4565—61no—
37#4565D311yescharacteristic, complemented
38#4563—31no—
39#4563—31no—
40#4516—31no—
41#4495—31no—
42C2×C32×Q8—21no—
43C3×#239—22no—
44C3×#239—22no—
45C3×#239—41no—
46C3×#239—41no—
47C2×C3×D12—21no—
48C2×C3×D12—41no—
49C2×C3×C4×D3—41no—
50C2×C3×C4×D3D411yescharacteristic
51C32×Q16—21no—
52C32×Q16C2×C412yes—
53C2×C32×C8C2311yescharacteristic
54#3748—21no—
55C3×#215—22no—
56C3×#215—22no—
57C3×#208—21no—
58C2×C3×C3⋊C8D411yescharacteristic
59C3×D24—21no—
60C3×D24C2×C412yes—
61C3×D3×C8C2×C411yescharacteristic
62C3×D3×C8C2×C411yescharacteristic
63C3×D3×C8D411yescharacteristic
64C3×D3×C8D411yescharacteristic
65#3711—41no—
66D3×C3⋊C8—41no—
67C3⋊(C3⋊C16)—21no—
68C3×C3⋊C16—21no—
69#2148—91noSylow
70C2×C3×#41—61no—
71C2×#239—21no—
72C3×#135—32no—
73C3×#135—32no—
74C3×#135—61no—
75C3×#135—61no—
76C2×C3×Q16—21no—
77C2×C3×Q16C2×D311yescharacteristic
78C2×C3×Q16C2×D311yescharacteristic
79C2×C3×SD16—61no—
80C2×C3×D8—31no—
81C22×C3×C8—31no—
82C2×#215—21no—
83C2×#208—61no—
84#919—21no—
85#919—21no—
86#919Dic312yes—
87#919Dic312yes—
88D3×M16—61no—
89C2×D24C2×D311yescharacteristic
90C2×D3×C8C2×D311yescharacteristic
91C3×M32—31no—
92C3×#108—31no—
93#822—61no—
94#819—31no—
95#819—31no—
96#819—61no—
97#819—61no—
98#819C2×D311yescharacteristic
99#812—31no—
100#812—31no—
101#812—61no—
102#812—61no—
103#812C2×D311yescharacteristic
104C2×C3⋊C16—61no—
105#798—61no—
106D3×C16—61no—
107C22×C3×D3—41no—
108C22×C3×D3SD1611yescharacteristic
109C32×Q8—22no—
110C32×Q8—41no—
111C2×C32×C4—41no—
112C2×C32×C4C2×D411yescharacteristic
113C2×C3×Dic3SD1611yescharacteristic
114C3×D12—22no—
115C3×D12—42no—
116C3×D12—42no—
117C3×D12—41no—
118C3×C4×D3—42no—
119C3×C4×D3—42no—
120C3×C4×D3C22⋊C411yescharacteristic
121C3×C4×D3C22⋊C411yescharacteristic
122C3×C4×D3D811yescharacteristic
123C3×C4×D3D811yescharacteristic
124C32×C8C22×C411yescharacteristic
125C32×C8C2×D411yescharacteristic
126C3⋊(C3⋊C8)—41no—
127C3×C3⋊C8—41no—
128C3×C3⋊C8C22⋊C411yescharacteristic
129C3×C3⋊C8C22⋊C411yescharacteristic
130C2×#135—31no—
131C2×M32—91no—
132C2×#108—91no—
133#362—31no—
134#362—91no—
135#361—91no—
136#361—91no—
137C3×#41—62no—
138C3×#41—62no—
139C3×#41—121no—
140C3×#41—121no—
141C2×C3×Q8—21no—
142C2×C3×Q8—21no—
143C2×C3×Q8—41no—
144C2×C3×D4—61no—
145C2×C3×D4—121no—
146C22×C3×C4—31no—
147C22×C3×C4—121no—
148#239—22no—
149#239—22no—
150#239—41no—
151#239—41no—
152C2×D12—21no—
153C2×D12—41no—
154C2×C4×D3—41no—
155C2×C4×D3#6711yescharacteristic
156C3×Q16—21no—
157C3×Q16—21no—
158C3×Q16—22no—
159C3×Q16—41no—
160C3×Q16C4×D312yes—
161C3×Q16C2×Dic312yes—
162C3×SD16—62no—
163C3×SD16—62no—
164C3×D8—32no—
165C3×D8—61no—
166C3×M16—61no—
167C2×C3×C8—21no—
168C2×C3×C8—31no—
169C2×C3×C8—31no—
170C2×C3×C8—31no—
171C2×C3×C8—31no—
172C2×C3×C8—31no—
173C2×C3×C8C22×D311yescharacteristic
174C2×C3×C8C22×D311yescharacteristic
175#215—22no—
176#215—22no—
177#208—21no—
178#208—61no—
179#208—61no—
180#208—121no—
181#208—121no—
182C2×C3⋊C8—121no—
183C2×C3⋊C8#6711yescharacteristic
184D24—21no—
185D24C2×Dic312yes—
186ΓL(1,𝔽25)—121no—
187D3×C8—121no—
188D3×C8C2×Dic311yescharacteristic
189D3×C8C2×Dic311yescharacteristic
190D3×C8#6711yescharacteristic
191D3×C8#6711yescharacteristic
192C3×C16—61no—
193C3⋊C16—21no—
194C3⋊C16—61no—
195C3⋊C16—61no—
196C3⋊C16—121no—
197C22×C32C2×SD1611yescharacteristic
198C2×C3×D3—41no—
199C2×C3×D3—42no—
200C2×C3×D3—82no—
201C2×C3×D3#10211yescharacteristic
202C2×C3×D3#10211yescharacteristic
203C32×C4—42no—
204C32×C4C2×C22⋊C411yescharacteristic
205C32×C4C2×D811yescharacteristic
206C3×Dic3#10211yescharacteristic
207C3×Dic3#10211yescharacteristic
208C2×#41—61no—
209#135—32no—
210#135—32no—
211#135—61no—
212#135—61no—
213C2×Q16D3211yescharacteristic
214C2×SD16—61no—
215C2×D8—31no—
216C2×M16—181no—
217C22×C8—31no—
218M32—31no—
219M32—91no—
220M32—181no—
221C2×C16—181no—
222#108—31no—
223#108—91no—
224#108—181no—
225C23×C3—31no—
226C23×C3—121no—
227C22×D3—41no—
228C22×D3#21411yescharacteristic
229C3×Q8—22no—
230C3×Q8—22no—
231C3×Q8—42no—
232C3×Q8—41no—
233C3×Q8—41no—
234C3×Q8—81no—
235C3×D4—62no—
236C3×D4—122no—
237C3×D4—122no—
238C3×D4—121no—
239C2×C3×C4—21no—
240C2×C3×C4—31no—
241C2×C3×C4—31no—
242C2×C3×C4—31no—
243C2×C3×C4—31no—
244C2×C3×C4—31no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—81no—
248C2×C3×C4—122no—
249C2×C3×C4—122no—
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4C2×#6711yescharacteristic
252C2×Dic3#21411yescharacteristic
253D12—22no—
254D12—42no—
255D12—42no—
256D12—41no—
257C4×D3—42no—
258C4×D3—42no—
259C4×D3#21311yescharacteristic
260C4×D3#21311yescharacteristic
261C4×D3#21711yescharacteristic
262C4×D3#21711yescharacteristic
263C3×C8—21no—
264C3×C8—21no—
265C3×C8—31no—
266C3×C8—31no—
267C3×C8—121no—
268C3×C8C2×C4×D311yescharacteristic
269C3×C8D3×D411yescharacteristic
270C3×C8C22×Dic311yescharacteristic
271C3×C8C2×#6711yescharacteristic
272C3⋊C8—41no—
273C3⋊C8—121no—
274C3⋊C8—121no—
275C3⋊C8—241no—
276C3⋊C8#21711yescharacteristic
277C3⋊C8#21711yescharacteristic
278C2×C32—21no—
279C2×C32C2×#10211yescharacteristic
280C3×D3—21no—
281C3×D3—21no—
282C3×D3—82no—
283#41—62no—
284#41—62no—
285#41—121no—
286#41—121no—
287C2×Q8—21no—
288C2×D4—61no—
289C2×D4—121no—
290C22×C4—31no—
291C22×C4—121no—
292Q16—21no—
293Q16D3×Dic312yes—
294SD16—62no—
295SD16—62no—
296D8—32no—
297D8—61no—
298M16—61no—
299M16—181no—
300M16—361no—
301C2×C8—31no—
302C2×C8—31no—
303C2×C8—31no—
304C2×C8—31no—
305C2×C8—31no—
306C2×C8—361no—
307C2×C8C2×D3211yescharacteristic
308C16—61no—
309C16—181no—
310C22×C3—21no—
311C22×C3—31no—
312C22×C3—31no—
313C22×C3—121no—
314C22×C3—122no—
315C22×C3—242no—
316C22×C3D3×SD1611yescharacteristic
317C22×C3C2×#21411yescharacteristic
318C2×D3—41no—
319C2×D3—42no—
320C2×D3—82no—
321C2×D3#83211yescharacteristic
322C2×D3#83211yescharacteristic
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—31no—
326C3×C4—31no—
327C3×C4—42no—
328C3×C4—42no—
329C3×C4—82no—
330C3×C4D3×C22⋊C411yescharacteristic
331C3×C4D3×D811yescharacteristic
332C3×C4C2×#21311yescharacteristic
333C3×C4C2×#21711yescharacteristic
334Dic3#83211yescharacteristic
335Dic3#83211yescharacteristic
336C32#214811yescharacteristic, complemented, Sylow
337C23—31no—
338C23—121no—
339Q8—22no—
340Q8—41no—
341D4—62no—
342D4—122no—
343D4—122no—
344D4—121no—
345C2×C4—31no—
346C2×C4—31no—
347C2×C4—31no—
348C2×C4—31no—
349C2×C4—31no—
350C2×C4—41no—
351C2×C4—122no—
352C2×C4—122no—
353C2×C4D3×#6711yescharacteristic
354C8—31no—
355C8—31no—
356C8—121no—
357C8—361no—
358C8C2×D3×Dic311yescharacteristic
359C8D3×#6711yescharacteristic
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—41no—
364C2×C3—61no—
365C2×C3—61no—
366C2×C3—242no—
367C2×C3D3×#10211yescharacteristic
368C2×C3C2×#83211yescharacteristic
369D3—21no—
370D3—21no—
371D3—82no—
372C22—31no—
373C22—31no—
374C22—121no—
375C22—122no—
376C22—242no—
377C22D3×#21411yescharacteristic
378C4—31no—
379C4—31no—
380C4—42no—
381C4D3×#21311yescharacteristic
382C4D3×#21711yescharacteristic
383C3—21no—
384C3#6926611yescharacteristic, complemented
385C3#7208111yescharacteristic, complemented
386C2—21no—
387C2—61no—
388C2—61no—
389C2—242no—
390C2D3×#83211yescharacteristic
subgroupG/H
centerC2D3×#832
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC2×C32×Q16C22
socleC2×C32C2×#102
prime radicalC2×C3×#919C2
cosocleC2×C32×C8C23
hypercenterC2×Q16D32
hypocenterC32#2148
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. D3×#819C2semidirect
3. D3×#812C2semidirect
4. #10589431C2semidirect
5. C3×#4565C2semidirect
6. #10589127C2semidirect
7. #10589126C2semidirect
37. #4565D3semidirect
336. C32#2148semidirect
384. C3#69266semidirect
385. C3#72081semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9192
D3×#8192
D3×#8122
#105894312
C3×#45652
#105891272
#105891262
#720813
#692663