Finite Group Databasebeta

← #11796946

Subgroups — #11796946

Order 1152.

471 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63808C211yesmaximal, characteristic
2C3×D3×#108C211yesmaximal, characteristic, complemented
3D3×#812C211yesmaximal, characteristic, complemented
4#10589361C211yesmaximal, characteristic, complemented
5C3×#4496C211yesmaximal, characteristic, complemented
6#10589129C211yesmaximal, characteristic, complemented
7#10589128C211yesmaximal, characteristic, complemented
8#70687—31nomaximal
9#69266—31nomaximal
10C2×#3799—21no—
11C2×#3745C2211yescharacteristic
12C3×D3×M16—21no—
13C2×C3×Dic12C2211yescharacteristic
14C2×C3×D3×C8C2211yescharacteristic
15C2×#3717—21no—
16#63808—21no—
17#63808—21no—
18#63808C412yes—
19#63808C412yes—
20C32×#108C2211yescharacteristic
21#63639C2211yescharacteristic
22C3×#822—21no—
23C3×#819C2211yescharacteristic
24C3×#812C2211yescharacteristic
25#63543—21no—
26D3×C3⋊C16—21no—
27C2×#919—31no—
28C2×#904—31no—
29C2×C3×#108—31no—
30C2×#812—31no—
31D3×M32—31no—
32D3×#108D311yescharacteristic, complemented
33C3×#362—31no—
34#4565—31no—
35#4516—31no—
36#4496—31no—
37#4496D311yescharacteristic, complemented
38#4495—31no—
39#4495—31no—
40#4495—31no—
41#4495—61no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C3×C4×D3D411yescharacteristic
44C2×C3×Dic6—21no—
45C2×#626—41no—
46C2×#624—41no—
47#3799—22no—
48#3799—22no—
49#3799—41no—
50#3799—41no—
51C32×M16—21no—
52C2×C32×C8C2311yescharacteristic
53#3745—21no—
54#3745C2×C412yes—
55C3×#208—21no—
56C2×C3×C3⋊C8D411yescharacteristic
57C3×Dic12—21no—
58C3×Dic12C2×C412yes—
59C3×ΓL(1,𝔽25)—41no—
60C3×D3×C8—41no—
61C3×D3×C8C2×C411yescharacteristic
62C3×D3×C8C2×C411yescharacteristic
63C3×D3×C8D411yescharacteristic
64C3×D3×C8D411yescharacteristic
65#3717—22no—
66#3717—22no—
67C3⋊(C3⋊C16)—21no—
68C3×C3⋊C16—21no—
69#2148—91noSylow
70C2×#239—61no—
71C2×#235—61no—
72C2×C3×Q16—31no—
73C2×C3×M16—61no—
74C22×C3×C8—31no—
75C2×#215—61no—
76#919—32no—
77#919—32no—
78#919—61no—
79#919—61no—
80D3×M16—21no—
81C2×Dic12C2×D311yescharacteristic
82#904—32no—
83#904—32no—
84#904—61no—
85#904—61no—
86C2×D24—31no—
87C2×D24—31no—
88C2×D24—61no—
89C2×#204—61no—
90C2×D3×C8C2×D311yescharacteristic
91C3×M32—31no—
92C3×#108—21no—
93C3×#108—31no—
94C3×#108—61no—
95C3×#108C2×D311yescharacteristic
96C3×#108C2×D311yescharacteristic
97#822—21no—
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
109C2×C32×C4C2×D411yescharacteristic
110C4⋊(C3⋊D3)—22no—
111C4⋊(C3⋊D3)—41no—
112C2×C3×Dic3—41no—
113C2×C3×Dic3SD1611yescharacteristic
114C3×C4×D3C22⋊C411yescharacteristic
115C3×C4×D3C22⋊C411yescharacteristic
116C3×C4×D3D811yescharacteristic
117C3×C4×D3D811yescharacteristic
118C3×Dic6—22no—
119C3×Dic6—41no—
120#626—42no—
121#626—42no—
122#624—42no—
123#624—42no—
124C32×C8—41no—
125C32×C8C22×C411yescharacteristic
126C32×C8C2×D411yescharacteristic
127C3×C3⋊C8—41no—
128C3×C3⋊C8C22⋊C411yescharacteristic
129C3×C3⋊C8C22⋊C411yescharacteristic
130C2×#135—91no—
131C2×M32—91no—
132C2×#108—31no—
133#362—31no—
134#362—91no—
135#361—91no—
136#361—91no—
137C2×C3×Q8—61no—
138C22×C3×C4—31no—
139C2×#67—121no—
140#239—62no—
141#239—62no—
142#239—121no—
143#239—121no—
144#235—62no—
145#235—62no—
146#235—121no—
147#235—121no—
148C2×D12—61no—
149C2×D12—61no—
150C2×D12—121no—
151C2×D12—121no—
152C2×C4×D3—121no—
153C2×C4×D3—121no—
154C2×C4×D3#6711yescharacteristic
155C2×Dic6—21no—
156C3×Q16—32no—
157C3×Q16—61no—
158C3×M16—21no—
159C3×M16—21no—
160C3×M16—41no—
161C3×M16—61no—
162C3×M16—121no—
163C2×C3×C8—21no—
164C2×C3×C8—31no—
165C2×C3×C8—31no—
166C2×C3×C8—31no—
167C2×C3×C8—31no—
168C2×C3×C8—31no—
169C2×C3×C8—121no—
170C2×C3×C8C22×D311yescharacteristic
171C2×C3×C8C22×D311yescharacteristic
172#215—62no—
173#215—62no—
174#208—21no—
175C2×C3⋊C8#6711yescharacteristic
176Dic12—21no—
177Dic12C4×D312yes—
178D24—32no—
179D24—32no—
180D24—62no—
181D24—61no—
182D24—61no—
183D24—121no—
184#204—62no—
185#204—62no—
186ΓL(1,𝔽25)—41no—
187D3×C8—41no—
188D3×C8C4×D311yescharacteristic
189D3×C8C4×D311yescharacteristic
190D3×C8D1211yescharacteristic
191D3×C8D1211yescharacteristic
192C3×C16—61no—
193C3⋊C16—21no—
194C3⋊C16—61no—
195C3⋊C16—61no—
196C3⋊C16—121no—
197C22×C32C2×SD1611yescharacteristic
198C2×C3⋊D3—42no—
199C2×C3⋊D3—82no—
200C2×C3×D3—41no—
201C2×C3×D3#10211yescharacteristic
202C2×C3×D3#10211yescharacteristic
203C32×C4C2×C22⋊C411yescharacteristic
204C32×C4C2×D811yescharacteristic
205C3×Dic3—42no—
206C3×Dic3#10211yescharacteristic
207C3×Dic3#10211yescharacteristic
208C2×#41—181no—
209#135—92no—
210#135—92no—
211#135—181no—
212#135—181no—
213C2×Q16—31no—
214C2×SD16—181no—
215C2×D8—91no—
216C2×M16—61no—
217C22×C8—31no—
218M32—31no—
219M32—91no—
220M32—181no—
221C2×C16—181no—
222#108—31no—
223#108—61no—
224#108D3211yescharacteristic
225C23×C3—31no—
226C22×D3—121no—
227C22×D3—121no—
228C22×D3—241no—
229C22×D3#21511yescharacteristic
230C3×Q8—62no—
231C3×Q8—121no—
232C2×C3×C4—21no—
233C2×C3×C4—31no—
234C2×C3×C4—31no—
235C2×C3×C4—31no—
236C2×C3×C4—31no—
237C2×C3×C4—31no—
238C2×C3×C4—121no—
239C2×C3×C4D3×D411yescharacteristic
240C2×C3×C4C2×#6711yescharacteristic
241#67—122no—
242#67—122no—
243C2×Dic3—41no—
244C2×Dic3#21511yescharacteristic
245D12—62no—
246D12—62no—
247D12—122no—
248D12—122no—
249D12—122no—
250D12—121no—
251D12—121no—
252D12—241no—
253C4×D3—122no—
254C4×D3—122no—
255C4×D3—122no—
256C4×D3—122no—
257C4×D3(C2×D3)⋊C411yescharacteristic
258C4×D3(C2×D3)⋊C411yescharacteristic
259C4×D3#21311yescharacteristic
260C4×D3#21311yescharacteristic
261Dic6—22no—
262Dic6—41no—
263C3×C8—21no—
264C3×C8—21no—
265C3×C8—31no—
266C3×C8—31no—
267C3×C8—41no—
268C3×C8—41no—
269C3×C8—81no—
270C3×C8—121no—
271C3×C8C2×C4×D311yescharacteristic
272C3×C8C2×C4×D311yescharacteristic
273C3×C8C2×D1211yescharacteristic
274C3×C8D3×D411yescharacteristic
275C3⋊C8—41no—
276C3⋊C8(C2×D3)⋊C411yescharacteristic
277C3⋊C8(C2×D3)⋊C411yescharacteristic
278C2×C32—21no—
279C2×C32C2×#10211yescharacteristic
280C3⋊D3—82no—
281C3×D3—21no—
282C3×D3—21no—
283#41—182no—
284#41—182no—
285#41—361no—
286#41—361no—
287C2×Q8—61no—
288C2×D4—181no—
289C2×D4—361no—
290C22×C4—31no—
291C22×C4—361no—
292Q16—32no—
293Q16—61no—
294SD16—182no—
295SD16—182no—
296D8—92no—
297D8—181no—
298M16—21no—
299M16—61no—
300M16—121no—
301C2×C8—31no—
302C2×C8—31no—
303C2×C8—31no—
304C2×C8—31no—
305C2×C8—31no—
306C2×C8—121no—
307C2×C8C2×D3211yescharacteristic
308C16—61no—
309C16—181no—
310C22×C3—21no—
311C22×C3—31no—
312C22×C3—31no—
313C22×C3—121no—
314C22×C3D3×SD1611yescharacteristic
315C22×C3C2×#21511yescharacteristic
316C2×D3—41no—
317C2×D3—122no—
318C2×D3—122no—
319C2×D3—242no—
320C2×D3—242no—
321C2×D3—242no—
322C2×D3—482no—
323C2×D3#80911yescharacteristic
324C2×D3#80911yescharacteristic
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—31no—
328C3×C4—31no—
329C3×C4—122no—
330C3×C4D3×C22⋊C411yescharacteristic
331C3×C4D3×D811yescharacteristic
332C3×C4C2×(C2×D3)⋊C411yescharacteristic
333C3×C4C2×#21311yescharacteristic
334Dic3—42no—
335Dic3#80911yescharacteristic
336Dic3#80911yescharacteristic
337C32#214811yescharacteristic, complemented, Sylow
338C23—31no—
339C23—361no—
340Q8—62no—
341Q8—121no—
342D4—182no—
343D4—362no—
344D4—362no—
345D4—361no—
346C2×C4—31no—
347C2×C4—31no—
348C2×C4—31no—
349C2×C4—31no—
350C2×C4—31no—
351C2×C4—121no—
352C2×C4—362no—
353C2×C4—362no—
354C2×C4D3×#6711yescharacteristic
355C8—31no—
356C8—31no—
357C8—41no—
358C8—121no—
359C8C4×D3211yescharacteristic
360C8D3×D1211yescharacteristic
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—21no—
364C2×C3—41no—
365C2×C3—61no—
366C2×C3—61no—
367C2×C3D3×#10211yescharacteristic
368C2×C3C2×#80911yescharacteristic
369D3—21no—
370D3—21no—
371D3—242no—
372D3—242no—
373D3—482no—
374C22—31no—
375C22—31no—
376C22—121no—
377C22—362no—
378C22—722no—
379C22D3×#21511yescharacteristic
380C4—31no—
381C4—31no—
382C4—122no—
383C4D3×(C2×D3)⋊C411yescharacteristic
384C4D3×#21311yescharacteristic
385C3—21no—
386C3#6926611yescharacteristic, complemented
387C3#7068711yescharacteristic, complemented
388C2—21no—
389C2—61no—
390C2—61no—
391C2—722no—
392C2D3×#80911yescharacteristic
subgroupG/H
centerC2D3×#809
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×#108C22
socleC2×C32C2×#102
prime radicalC2×#63808C2
cosocleC2×C32×C8C23
hypercenter#108D32
hypocenterC32#2148
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #108

Complements

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

NH ≅ G/Ntype
2. C3×D3×#108C2semidirect
3. D3×#812C2semidirect
4. #10589361C2semidirect
5. C3×#4496C2semidirect
6. #10589129C2semidirect
7. #10589128C2semidirect
32. D3×#108D3semidirect
37. #4496D3semidirect
337. C32#2148semidirect
386. C3#69266semidirect
387. C3#70687semidirect

Maximal subgroups

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

subgroupindex
C2×#638082
C3×D3×#1082
D3×#8122
#105893612
C3×#44962
#105891292
#105891282
#706873
#692663