Finite Group Databasebeta

← #11859453

Subgroups — #11859453

Order 1152.

750 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63464C212yesmaximal, complemented
2#10589650C211yesmaximal, characteristic
3C8×D4×C9C211yesmaximal, characteristic, complemented
4C8×#611C212yesmaximal, complemented
5#10588689C211yesmaximal, characteristic, complemented
6#10588522C211yesmaximal, characteristic, complemented
7#10588521C211yesmaximal, characteristic, complemented
8#10588411C212yesmaximal, complemented
9#10588409C212yesmaximal, complemented
10C8×D36C211yesmaximal, characteristic, complemented
11C4×C8×D9C211yesmaximal, characteristic, complemented
12#79422—31nomaximal
13C2×#3697C2212yes—
14C22×C8×C9C2212yes—
15C4×D4×C9C2211yescharacteristic
16#63502C411yescharacteristic
17#63500C411yescharacteristic
18C4×#611C2212yes—
19C2×#3667C2212yes—
20#63464—28no—
21C2×#3663C2212yes—
22C2×#3663C2212yes—
23C2×C8×D9C2212yes—
24C2×C8×D9C2211yescharacteristic
25C2×C8×D9C2211yescharacteristic
26#63457C411yescharacteristic
27#63450C411yescharacteristic
28#63447C412yes—
29#63446C412yes—
30C4×D36C2211yescharacteristic
31C42×D9C2211yescharacteristic
32C9×C4⋊C8C2211yescharacteristic
33C9×C22⋊C8C2212yes—
34C4×C8×C9C2211yescharacteristic
35#63389C2212yes—
36(C2×D9)⋊C8C2212yes—
37(C2×D9)⋊C8C2212yes—
38Dic9⋊C8C2212yes—
39C8×Dic9C2211yescharacteristic
40C8×Dic9C2211yescharacteristic
41C4⋊(C9⋊C8)C2211yescharacteristic
42C4×C9⋊C8C2211yescharacteristic
43C2×#901—32no—
44#5548—31no—
45C3×C8×D4D311yescharacteristic
46C8×#67—32no—
47#5012—31no—
48#4838—31no—
49#4837—31no—
50#4729—32no—
51#4727—32no—
52C8×D12—31no—
53C4×D3×C8—31no—
54C2×D4×C9C2×C411yescharacteristic
55C22×C4×C9C2312yes—
56C2×#611C2×C412yes—
57C2×#611C2×C412yes—
58C2×#611C2×C412yes—
59#3697—24no—
60#3697—24no—
61C2×D36C2×C411yescharacteristic
62C2×D36C2×C412yes—
63C2×C4×D9C2×C411yescharacteristic
64C2×C4×D9C2×C411yescharacteristic
65C2×C4×D9C2312yes—
66C2×C4×D9C2311yescharacteristic
67C2×Dic18C2×C412yes—
68C2×C8×C9—24no—
69C2×C8×C9C2312yes—
70C2×C8×C9C2311yescharacteristic
71C2×C8×C9C2311yescharacteristic
72C9×C4⋊C4C2×C411yescharacteristic
73C9×C22⋊C4C2×C412yes—
74C42×C9C2311yescharacteristic
75#3676C2×C412yes—
76(C2×D9)⋊C4C2×C412yes—
77(C2×D9)⋊C4C2×C412yes—
78C4⋊Dic9C2×C411yescharacteristic
79Dic9⋊C4C2×C412yes—
80C4×Dic9C2×C411yescharacteristic
81C4×Dic9C2×C411yescharacteristic
82C4×Dic9C2311yescharacteristic
83#3667—24no—
84C2×C9⋊C8C2311yescharacteristic
85C2×C9⋊C8C2312yes—
86C2×C9⋊C8C2311yescharacteristic
87#3663—24no—
88#3663—24no—
89C8×D9—22no—
90C8×D9—24no—
91C8×D9D414yescomplemented
92#2931—91noSylow
93C2×#235—32no—
94C22×C3×C8C2×D312yes—
95C3×C4×D4C2×D311yescharacteristic
96#940—31no—
97#938—31no—
98C4×#67—32no—
99C2×#208—32no—
100#901—68no—
101C2×ΓL(1,𝔽25)—32no—
102C2×ΓL(1,𝔽25)—32no—
103C2×D3×C8—31no—
104C2×D3×C8—31no—
105C2×D3×C8—32no—
106#895—31no—
107#888—31no—
108#885—32no—
109#884—32no—
110C4×D12—31no—
111C42×D3—31no—
112C3×C4⋊C8C2×D311yescharacteristic
113C3×C22⋊C8C2×D312yes—
114C3×C4×C8C2×D311yescharacteristic
115#830—32no—
116(C2×D3)⋊C8—32no—
117(C2×D3)⋊C8—32no—
118Dic3⋊C8—32no—
119C8×Dic3—31no—
120C8×Dic3—31no—
121C4⋊(C3⋊C8)—31no—
122C4×C3⋊C8—31no—
123C23×C9C22×C412yes—
124C22×D9C22×C412yes—
125C22×D9C22×C411yescharacteristic
126D4×C9—22no—
127C2×C4×C9—22no—
128C2×C4×C9—22no—
129C2×C4×C9C22×C411yescharacteristic
130C2×C4×C9C22×C412yes—
131C2×C4×C9C22×C411yescharacteristic
132C2×C4×C9C2411yescharacteristic
133#611—24no—
134#611—24no—
135#611—24no—
136C2×Dic9C22×C411yescharacteristic
137C2×Dic9C22×C412yes—
138C2×Dic9C22×C411yescharacteristic
139C2×Dic9C22×C411yescharacteristic
140D36—24no—
141D36—22no—
142C4×D9—22no—
143C4×D9—22no—
144C4×D9—22no—
145C4×D9—22no—
146C4×D9C2×D412yes—
147C4×D9#4112yes—
148Dic18—24no—
149C8×C9—22no—
150C8×C9—21no—
151C8×C9C2×D412yes—
152C9⋊C8—22no—
153C9⋊C8—21no—
154C9⋊C8C2×D412yes—
155C2×#131—92no—
156#532—91no—
157#436—91no—
158#436—91no—
159#436—92no—
160C8×D4—92no—
161C8×D4—91no—
162C8×D4D911yescharacteristic, complemented
163#423—91no—
164#408—92no—
165C2×C4×C8—91no—
166C2×C3×D4C4×D311yescharacteristic
167C22×C3×C4C22×D312yes—
168C2×#67—32no—
169C2×#67—32no—
170C2×#67—32no—
171#235—64no—
172#235—64no—
173C2×D12—31no—
174C2×D12—32no—
175C2×C4×D3—31no—
176C2×C4×D3—31no—
177C2×C4×D3—31no—
178C2×C4×D3—32no—
179C2×Dic6—32no—
180C2×C3×C8—24no—
181C2×C3×C8C22×D311yescharacteristic
182C2×C3×C8C22×D312yes—
183C2×C3×C8C22×D311yescharacteristic
184C3×C4⋊C4C4×D311yescharacteristic
185C3×C22⋊C4C4×D312yes—
186C3×C42C22×D311yescharacteristic
187#217—32no—
188(C2×D3)⋊C4—32no—
189(C2×D3)⋊C4—32no—
190C4⋊Dic3—31no—
191Dic3⋊C4—32no—
192C4×Dic3—31no—
193C4×Dic3—31no—
194C4×Dic3—31no—
195#208—64no—
196C2×C3⋊C8—31no—
197C2×C3⋊C8—31no—
198C2×C3⋊C8—32no—
199ΓL(1,𝔽25)—64no—
200ΓL(1,𝔽25)—64no—
201D3×C8—34no—
202D3×C8—62no—
203D3×C8—64no—
204C22×C9—22no—
205C22×C9—22no—
206C22×C9—22no—
207C22×C9C23×C411yescharacteristic
208C2×D9—21no—
209C2×D9—21no—
210C2×D9—22no—
211C2×D9—22no—
212C2×D9—22no—
213C2×D9C4×D412yes—
214C4×C9—22no—
215C4×C9—21no—
216C4×C9#13112yescomplemented
217C4×C9C22×D411yescharacteristic
218C4×C9C2×#4111yescharacteristic
219Dic9—22no—
220Dic9—21no—
221Dic9C4×D412yes—
222Dic9#13112yescomplemented
223C2×#41—92no—
224#131—188no—
225C2×M16—92no—
226C2×M16—92no—
227C2×M16—92no—
228C22×C8—91no—
229C22×C8—91no—
230C22×C8—92no—
231C22×C8C2×D912yes—
232C4⋊Q8—91no—
233#127—91no—
234#124—92no—
235#121—91no—
236#121—91no—
237#121—92no—
238C4×D4—92no—
239C4×D4—91no—
240C4×D4C2×D911yescharacteristic
241C2×C42—91no—
242C4⋊C8—92no—
243C4⋊C8—91no—
244C4⋊C8C2×D911yescharacteristic
245C22⋊C8—92no—
246C22⋊C8—92no—
247C22⋊C8—92no—
248C22⋊C8C2×D912yes—
249C4×C8—91no—
250C4×C8—91no—
251C4×C8—91no—
252C4×C8C2×D911yescharacteristic
253C23×C3C2×C4×D312yes—
254C22×D3—31no—
255C22×D3—32no—
256C3×D4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4C2×C4×D311yescharacteristic
260C2×C3×C4C2×C4×D312yes—
261C2×C3×C4C2×C4×D311yescharacteristic
262C2×C3×C4C23×D311yescharacteristic
263#67—64no—
264#67—64no—
265#67—64no—
266C2×Dic3—31no—
267C2×Dic3—31no—
268C2×Dic3—31no—
269C2×Dic3—32no—
270D12—64no—
271D12—62no—
272C4×D3—32no—
273C4×D3—32no—
274C4×D3—62no—
275C4×D3—62no—
276C4×D3—62no—
277C4×D3—62no—
278Dic6—64no—
279C3×C8—22no—
280C3×C8—21no—
281C3×C8D3×D412yes—
282C3⋊C8—32no—
283C3⋊C8—62no—
284C3⋊C8—61no—
285C2×C9—42no—
286C2×C9C2×C4×D411yescharacteristic
287C2×C9C2×#13111yescharacteristic
288C2×C9C2×#13111yescharacteristic
289D9—22no—
290D9—42no—
291#41—184no—
292#41—184no—
293C2×Q8—92no—
294C2×D4—92no—
295C2×D4—92no—
296C2×D4—92no—
297C2×D4—91no—
298C2×D4—92no—
299C2×D4C4×D911yescharacteristic
300C22×C4—91no—
301C22×C4—91no—
302C22×C4—91no—
303C22×C4—92no—
304C22×C4C22×D912yes—
305M16—184no—
306M16—184no—
307M16—184no—
308C2×C8—24no—
309C2×C8—91no—
310C2×C8—94no—
311C2×C8—91no—
312C2×C8—92no—
313C2×C8—182no—
314C2×C8—184no—
315C2×C8C22×D911yescharacteristic
316C2×C8C22×D912yes—
317C2×C8C22×D911yescharacteristic
318C4⋊C4—92no—
319C4⋊C4—91no—
320C4⋊C4C4×D911yescharacteristic
321C22⋊C4—92no—
322C22⋊C4—92no—
323C22⋊C4—92no—
324C22⋊C4C4×D912yes—
325C42—91no—
326C42—91no—
327C42—91no—
328C42C22×D911yescharacteristic
329C22×C3—22no—
330C22×C3—22no—
331C22×C3—22no—
332C22×C3C22×C4×D311yescharacteristic
333C2×D3—32no—
334C2×D3—61no—
335C2×D3—61no—
336C2×D3—62no—
337C2×D3—62no—
338C2×D3—62no—
339C3×C4—21no—
340C3×C4—22no—
341C3×C4#90112yes—
342C3×C4C2×D3×D411yescharacteristic
343C3×C4D3×#4111yescharacteristic
344Dic3—32no—
345Dic3—32no—
346Dic3—61no—
347Dic3—62no—
348C9#293111yescharacteristic, complemented, Sylow
349C23—91no—
350C23—92no—
351C23C2×C4×D912yes—
352Q8—184no—
353D4—22no—
354D4—184no—
355D4—184no—
356D4—184no—
357D4—184no—
358D4—182no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—91no—
362C2×C4—91no—
363C2×C4—92no—
364C2×C4—92no—
365C2×C4—91no—
366C2×C4—92no—
367C2×C4—182no—
368C2×C4—182no—
369C2×C4—182no—
370C2×C4—182no—
371C2×C4C2×C4×D911yescharacteristic
372C2×C4C2×C4×D912yes—
373C2×C4C2×C4×D911yescharacteristic
374C2×C4C23×D911yescharacteristic
375C8—22no—
376C8—21no—
377C8—92no—
378C8—182no—
379C8—181no—
380C8D4×D912yes—
381C2×C3—42no—
382C2×C3C4×D3×D411yescharacteristic
383C2×C3C2×#90111yescharacteristic
384C2×C3D3×#13111yescharacteristic
385D3—62no—
386D3—122no—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—92no—
391C22—181no—
392C22—181no—
393C22—182no—
394C22—182no—
395C22—182no—
396C22C22×C4×D911yescharacteristic
397C4—21no—
398C4—22no—
399C4—92no—
400C4—92no—
401C4—181no—
402C4—182no—
403C4#6346412yescomplemented
404C4C2×D4×D911yescharacteristic
405C4#41×D911yescharacteristic
406C3#7942211yescharacteristic
407C2—42no—
408C2—182no—
409C2—362no—
410C2C4×D4×D911yescharacteristic
411C2C2×#6346411yescharacteristic
412C2D9×#13111yescharacteristic
subgroupG/H
centerC2×C8C22×D9
commutatorC22×C9C23×C4
FrattiniC2×C3×C4C23×D3
FittingC8×D4×C9C2
socleC22×C3C22×C4×D3
prime radical#10589650C2
cosocleC2×C4×C9C24
hypercenterC8×D4D9
hypocenterC9#2931
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C2×C8 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. C2×#63464C2semidirect
3. C8×D4×C9C2semidirect
4. C8×#611C2semidirect
5. #10588689C2semidirect
6. #10588522C2semidirect
7. #10588521C2semidirect
8. #10588411C2semidirect
9. #10588409C2semidirect
10. C8×D36C2semidirect
11. C4×C8×D9C2semidirect
91. C8×D9D4semidirect
162. C8×D4D9semidirect
216. C4×C9#131semidirect
222. Dic9#131semidirect
348. C9#2931semidirect
403. C4#63464semidirect

Maximal subgroups

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

subgroupindex
C2×#634642
#105896502
C8×D4×C92
C8×#6112
#105886892
#105885222
#105885212
#105884112
#105884092
C8×D362
C4×C8×D92
#794223