Finite Group Databasebeta

← #11796949

Subgroups — #11796949

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×C3×#912C211yesmaximal, characteristic
2D3×#819C211yesmaximal, characteristic, complemented
3D3×#812C211yesmaximal, characteristic, complemented
4#10589429C211yesmaximal, characteristic, complemented
5C3×#4563C211yesmaximal, characteristic, complemented
6#10589130C211yesmaximal, characteristic, complemented
7#10589129C211yesmaximal, characteristic, complemented
8#72081—31nomaximal
9#69256—31nomaximal
10C2×C3×#237—21no—
11C2×C32×D8C2211yescharacteristic
12C2×C3×#214—21no—
13C3×#912—21no—
14C3×#912—21no—
15C3×#912C412yes—
16C3×#912C412yes—
17C2×C3×Dic12C2211yescharacteristic
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×#912D311yescharacteristic
29C2×#819—31no—
30C2×#812—31no—
31D3×M32—31no—
32D3×#108—31no—
33C3×#361—31no—
34#4565—31no—
35#4565—31no—
36#4563—31no—
37#4563—31no—
38#4563—61no—
39#4563D311yescharacteristic, complemented
40#4517—31no—
41#4496—31no—
42C2×C32×D4—21no—
43C2×C3×#67—41no—
44C22×C3×Dic3—41no—
45C3×#237—22no—
46C3×#237—22no—
47C3×#237—41no—
48C3×#237—41no—
49C2×C3×C4×D3D411yescharacteristic
50C2×C3×Dic6—21no—
51C32×D8—21no—
52C32×D8C2×C412yes—
53C2×C32×C8C2311yescharacteristic
54#3748—21no—
55C3×#214—22no—
56C3×#214—22no—
57C3×#208—21no—
58C2×C3×C3⋊C8D411yescharacteristic
59C3×Dic12—21no—
60C3×Dic12C2×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×#237—21no—
72C3×#135—32no—
73C3×#135—32no—
74C3×#135—61no—
75C3×#135—61no—
76C2×C3×Q16—31no—
77C2×C3×SD16—61no—
78C2×C3×D8—21no—
79C2×C3×D8C2×D311yescharacteristic
80C2×C3×D8C2×D311yescharacteristic
81C22×C3×C8—31no—
82C2×#214—21no—
83C2×#208—61no—
84#912—21no—
85#912—21no—
86#912Dic312yes—
87#912Dic312yes—
88D3×M16—61no—
89C2×Dic12C2×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—
107C23×C32—41no—
108C22×C3×D3SD1611yescharacteristic
109C32×D4—22no—
110C32×D4—41no—
111C2×C32×C4C2×D411yescharacteristic
112C3×#67—42no—
113C3×#67—42no—
114C2×C3×Dic3—41no—
115C2×C3×Dic3—42no—
116C2×C3×Dic3—42no—
117C2×C3×Dic3SD1611yescharacteristic
118C3×C4×D3C22⋊C411yescharacteristic
119C3×C4×D3C22⋊C411yescharacteristic
120C3×C4×D3D811yescharacteristic
121C3×C4×D3D811yescharacteristic
122C3×Dic6—22no—
123C3×Dic6—41no—
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—91no—
134#362—91no—
135#361—31no—
136#361—91no—
137C3×#41—62no—
138C3×#41—62no—
139C3×#41—121no—
140C3×#41—121no—
141C2×C3×Q8—61no—
142C2×C3×D4—21no—
143C2×C3×D4—21no—
144C2×C3×D4—41no—
145C2×C3×D4—121no—
146C22×C3×C4—31no—
147C22×C3×C4—121no—
148C2×#67—41no—
149C22×Dic3—41no—
150#237—22no—
151#237—22no—
152#237—41no—
153#237—41no—
154C2×C4×D3#6711yescharacteristic
155C2×Dic6—21no—
156C3×Q16—32no—
157C3×Q16—61no—
158C3×SD16—62no—
159C3×SD16—62no—
160C3×D8—21no—
161C3×D8—21no—
162C3×D8—22no—
163C3×D8—41no—
164C3×D8C4×D312yes—
165C3×D8C2×Dic312yes—
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#214—22no—
176#214—22no—
177#208—21no—
178#208—61no—
179#208—61no—
180#208—121no—
181#208—121no—
182C2×C3⋊C8—121no—
183C2×C3⋊C8#6711yescharacteristic
184Dic12—21no—
185Dic12C2×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×C32—42no—
198C22×C32—82no—
199C22×C32C2×SD1611yescharacteristic
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—61no—
209#135—32no—
210#135—32no—
211#135—61no—
212#135—61no—
213C2×Q16—31no—
214C2×SD16—61no—
215C2×D8D3211yescharacteristic
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—41no—
227C23×C3—41no—
228C23×C3—81no—
229C22×D3#21411yescharacteristic
230C3×Q8—62no—
231C3×Q8—121no—
232C3×D4—22no—
233C3×D4—22no—
234C3×D4—42no—
235C3×D4—41no—
236C3×D4—41no—
237C3×D4—81no—
238C3×D4—122no—
239C3×D4—122no—
240C2×C3×C4—21no—
241C2×C3×C4—31no—
242C2×C3×C4—31no—
243C2×C3×C4—31no—
244C2×C3×C4—31no—
245C2×C3×C4—31no—
246C2×C3×C4—122no—
247C2×C3×C4—122no—
248C2×C3×C4—121no—
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4C2×#6711yescharacteristic
251#67—42no—
252#67—42no—
253C2×Dic3—41no—
254C2×Dic3—42no—
255C2×Dic3—42no—
256C2×Dic3#21411yescharacteristic
257C4×D3#21311yescharacteristic
258C4×D3#21311yescharacteristic
259C4×D3#21711yescharacteristic
260C4×D3#21711yescharacteristic
261Dic6—22no—
262Dic6—41no—
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×C32—82no—
280C2×C32C2×#10211yescharacteristic
281C3×D3—21no—
282C3×D3—21no—
283#41—62no—
284#41—62no—
285#41—121no—
286#41—121no—
287C2×Q8—61no—
288C2×D4—21no—
289C2×D4—121no—
290C22×C4—31no—
291C22×C4—121no—
292Q16—32no—
293Q16—61no—
294SD16—62no—
295SD16—62no—
296D8—21no—
297D8D3×Dic312yes—
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—42no—
314C22×C3—42no—
315C22×C3—82no—
316C22×C3—82no—
317C22×C3—82no—
318C22×C3—121no—
319C22×C3—162no—
320C22×C3D3×SD1611yescharacteristic
321C22×C3C2×#21411yescharacteristic
322C2×D3—41no—
323C2×D3#83211yescharacteristic
324C2×D3#83211yescharacteristic
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—31no—
328C3×C4—31no—
329C3×C4—122no—
330C3×C4D3×C22⋊C411yescharacteristic
331C3×C4D3×D811yescharacteristic
332C3×C4C2×#21311yescharacteristic
333C3×C4C2×#21711yescharacteristic
334Dic3—42no—
335Dic3#83211yescharacteristic
336Dic3#83211yescharacteristic
337C32#214811yescharacteristic, complemented, Sylow
338C23—31no—
339C23—41no—
340Q8—62no—
341Q8—121no—
342D4—22no—
343D4—41no—
344D4—122no—
345D4—122no—
346C2×C4—31no—
347C2×C4—31no—
348C2×C4—31no—
349C2×C4—31no—
350C2×C4—31no—
351C2×C4—122no—
352C2×C4—122no—
353C2×C4—121no—
354C2×C4D3×#6711yescharacteristic
355C8—31no—
356C8—31no—
357C8—121no—
358C8—361no—
359C8C2×D3×Dic311yescharacteristic
360C8D3×#6711yescharacteristic
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—21no—
364C2×C3—41no—
365C2×C3—61no—
366C2×C3—61no—
367C2×C3—82no—
368C2×C3—82no—
369C2×C3—162no—
370C2×C3D3×#10211yescharacteristic
371C2×C3C2×#83211yescharacteristic
372D3—21no—
373D3—21no—
374C22—31no—
375C22—31no—
376C22—42no—
377C22—82no—
378C22—121no—
379C22D3×#21411yescharacteristic
380C4—31no—
381C4—31no—
382C4—122no—
383C4D3×#21311yescharacteristic
384C4D3×#21711yescharacteristic
385C3—21no—
386C3#6925611yescharacteristic, complemented
387C3#7208111yescharacteristic, complemented
388C2—21no—
389C2—61no—
390C2—61no—
391C2—82no—
392C2D3×#83211yescharacteristic
subgroupG/H
centerC2D3×#832
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC2×C32×D8C22
socleC2×C32C2×#102
prime radicalC2×C3×#912C2
cosocleC2×C32×C8C23
hypercenterC2×D8D32
hypocenterC32#2148
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. D3×#819C2semidirect
3. D3×#812C2semidirect
4. #10589429C2semidirect
5. C3×#4563C2semidirect
6. #10589130C2semidirect
7. #10589129C2semidirect
39. #4563D3semidirect
337. C32#2148semidirect
386. C3#69256semidirect
387. C3#72081semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9122
D3×#8192
D3×#8122
#105894292
C3×#45632
#105891302
#105891292
#720813
#692563