Finite Group Databasebeta

← #11808761

Subgroups — #11808761

Order 1152.

852 conjugacy classes of subgroups.

The subgroup lattice has 417 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×Dic9C211yesmaximal, characteristic, complemented
2C2×#611⋊C4C211yesmaximal, characteristic
3C9×#393C211yesmaximal, characteristic, complemented
4#10588911C211yesmaximal, characteristic, complemented
5#10588641C212yesmaximal
6#10588633C211yesmaximal, characteristic, complemented
7C22⋊C4×Dic9C212yesmaximal, complemented
8#10588354C211yesmaximal, characteristic, complemented
9#10588346C212yesmaximal, complemented
10#10588340C212yesmaximal, complemented
11#10588328C211yesmaximal, characteristic, complemented
12#76779—31nomaximal
13C22×Q8×C9C2211yescharacteristic
14C22×#611C2211yescharacteristic
15C23×Dic9C2211yescharacteristic
16C22×C4×D9C2211yescharacteristic
17C2×C9×C22⋊C4C2211yescharacteristic
18C2×C9×C22⋊C4C2212yes—
19C2×#3676C2212yes—
20Q8×Dic9—24no—
21C2×(C2×D9)⋊C4C2211yescharacteristic
22C2×(C2×D9)⋊C4C2212yes—
23C2×(C2×D9)⋊C4C2212yes—
24C2×C4⋊Dic9C2212yes—
25C2×C4⋊Dic9C2211yescharacteristic
26C2×Dic9⋊C4C2211yescharacteristic
27C2×C4×Dic9C2212yes—
28C2×C4×Dic9C2212yes—
29C2×C4×Dic9C2211yescharacteristic
30#611⋊C4—24no—
31C9×#95C2211yescharacteristic
32C9×#95C2212yes—
33C9⋊#95C2212yes—
34C9⋊#95C2211yescharacteristic
35C9⋊#95C2212yes—
36C9⋊#95C2212yes—
37C9⋊#95C2212yes—
38C2×Q8×Dic3—31no—
39C2×#67⋊C4—31no—
40C3×#393D311yescharacteristic
41#5231—31no—
42#4961—32no—
43#4953—31no—
44Dic3×C22⋊C4—32no—
45#4674—31no—
46#4666—32no—
47#4660—32no—
48#4648—31no—
49C24×C9C2311yescharacteristic
50C23×D9C2311yescharacteristic
51C2×Q8×C9—22no—
52C2×Q8×C9—24no—
53C22×C4×C9C2312yes—
54C22×C4×C9C2311yescharacteristic
55C22×C4×C9C2311yescharacteristic
56C22×C4×C9C2312yes—
57C2×#611—22no—
58C2×#611—22no—
59C2×#611—22no—
60C22×Dic9—22no—
61C22×Dic9—24no—
62C22×Dic9C2312yes—
63C22×Dic9C2312yes—
64C22×Dic9C2311yescharacteristic
65C22×Dic9C2311yescharacteristic
66C22×Dic9C2311yescharacteristic
67C2×C4×D9—22no—
68C2×C4×D9—24no—
69C9×C22⋊C4—22no—
70C9×C22⋊C4—24no—
71#3676—24no—
72(C2×D9)⋊C4—24no—
73(C2×D9)⋊C4—22no—
74(C2×D9)⋊C4—24no—
75C4⋊Dic9—22no—
76C4⋊Dic9—24no—
77Dic9⋊C4—22no—
78C4×Dic9—24no—
79C4×Dic9—24no—
80C4×Dic9D414yes—
81#2398—91noSylow
82C22×C3×Q8C2×D311yescharacteristic
83C22×#67—31no—
84C23×Dic3—31no—
85C22×C4×D3—31no—
86C2×C3×C22⋊C4C2×D312yes—
87C2×C3×C22⋊C4C2×D311yescharacteristic
88C2×#217—32no—
89Q8×Dic3—64no—
90C2×(C2×D3)⋊C4—32no—
91C2×(C2×D3)⋊C4—32no—
92C2×(C2×D3)⋊C4—31no—
93C2×C4⋊Dic3—32no—
94C2×C4⋊Dic3—31no—
95C2×Dic3⋊C4—31no—
96C2×C4×Dic3—31no—
97C2×C4×Dic3—32no—
98C2×C4×Dic3—32no—
99#67⋊C4—64no—
100C3×#95C2×D311yescharacteristic
101C3×#95C2×D312yes—
102C3⋊#95—32no—
103C3⋊#95—31no—
104C3⋊#95—32no—
105C3⋊#95—32no—
106C3⋊#95—32no—
107C23×C9—21no—
108C23×C9—22no—
109C23×C9—22no—
110C23×C9—21no—
111C23×C9#4112yes—
112C23×C9C2411yescharacteristic
113C22×D9—21no—
114C22×D9—22no—
115C22×D9—22no—
116C22×D9—21no—
117C22×D9#4112yes—
118Q8×C9—28no—
119C2×C4×C9—22no—
120C2×C4×C9—22no—
121C2×C4×C9—22no—
122C2×C4×C9—21no—
123C2×C4×C9—22no—
124C2×C4×C9—22no—
125C2×C4×C9—22no—
126C2×C4×C9—22no—
127C2×C4×C9C2×D412yes—
128C2×C4×C9#4114yes—
129#611—28no—
130C2×Dic9—21no—
131C2×Dic9—21no—
132C2×Dic9—22no—
133C2×Dic9—21no—
134C2×Dic9—22no—
135C2×Dic9—22no—
136C2×Dic9—22no—
137C2×Dic9—22no—
138C2×Dic9—22no—
139C2×Dic9—22no—
140C2×Dic9—44no—
141C2×Dic9C2×D412yes—
142C2×Dic9C2×D412yes—
143C2×Dic9#4114yes—
144C4×D9—44no—
145C2×C4×Q8—91no—
146C2×C4×D4—91no—
147#400—92no—
148#397—91no—
149#397—91no—
150#394—92no—
151#393—91no—
152#393D911yescharacteristic, complemented
153C4×C22⋊C4—92no—
154C4×C22⋊C4—92no—
155#376—91no—
156C24×C3C22×D311yescharacteristic
157C23×D3—31no—
158C2×C3×Q8—22no—
159C2×C3×Q8—24no—
160C22×C3×C4C22×D312yes—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C22×C3×C4C22×D312yes—
164C2×#67—62no—
165C2×#67—62no—
166C2×#67—62no—
167C22×Dic3—31no—
168C22×Dic3—31no—
169C22×Dic3—32no—
170C22×Dic3—31no—
171C22×Dic3—32no—
172C22×Dic3—62no—
173C22×Dic3—64no—
174C2×C4×D3—62no—
175C2×C4×D3—64no—
176C3×C22⋊C4—22no—
177C3×C22⋊C4—24no—
178#217—64no—
179(C2×D3)⋊C4—64no—
180(C2×D3)⋊C4—62no—
181(C2×D3)⋊C4—64no—
182C4⋊Dic3—64no—
183C4⋊Dic3—62no—
184Dic3⋊C4—62no—
185C4×Dic3—34no—
186C4×Dic3—64no—
187C4×Dic3—64no—
188C22×C9—22no—
189C22×C9—24no—
190C22×C9—41no—
191C22×C9—41no—
192C22×C9—42no—
193C22×C9C22×D411yescharacteristic
194C22×C9C2×#4112yes—
195C22×C9C2×#4111yescharacteristic
196C22×C9C2×#4111yescharacteristic
197C22×C9C2×#4112yes—
198C2×D9—22no—
199C2×D9—24no—
200C2×D9—41no—
201C2×D9—41no—
202C2×D9—42no—
203C4×C9—22no—
204C4×C9—24no—
205C4×C9—41no—
206C4×C9—42no—
207Dic9—22no—
208Dic9—42no—
209Dic9—41no—
210Dic9—42no—
211Dic9#12414yes—
212C22×Q8C2×D911yescharacteristic
213C22×D4—91no—
214C23×C4—91no—
215C23×C4—91no—
216C4×Q8—184no—
217C4×D4—184no—
218C2×C4⋊C4—91no—
219C2×C4⋊C4—92no—
220C2×C4⋊C4—91no—
221C2×C22⋊C4—92no—
222C2×C22⋊C4—91no—
223C2×C22⋊C4—92no—
224C2×C22⋊C4—92no—
225C2×C22⋊C4C2×D911yescharacteristic
226C2×C22⋊C4C2×D912yes—
227C2×C42—91no—
228C2×C42—92no—
229C2×C42—92no—
230#95—91no—
231#95—92no—
232#95—92no—
233#95—92no—
234#95—92no—
235#95C2×D911yescharacteristic
236#95C2×D912yes—
237C23×C3—21no—
238C23×C3—22no—
239C23×C3—22no—
240C23×C3—21no—
241C23×C3#23912yes—
242C23×C3C23×D311yescharacteristic
243C22×D3—32no—
244C22×D3—61no—
245C22×D3—62no—
246C22×D3—61no—
247C22×D3—62no—
248C3×Q8—28no—
249C2×C3×C4—22no—
250C2×C3×C4—22no—
251C2×C3×C4—22no—
252C2×C3×C4—21no—
253C2×C3×C4—22no—
254C2×C3×C4—22no—
255C2×C3×C4—22no—
256C2×C3×C4—22no—
257C2×C3×C4D3×D412yes—
258C2×C3×C4#23714yes—
259#67—68no—
260C2×Dic3—32no—
261C2×Dic3—34no—
262C2×Dic3—32no—
263C2×Dic3—61no—
264C2×Dic3—61no—
265C2×Dic3—62no—
266C2×Dic3—61no—
267C2×Dic3—62no—
268C2×Dic3—62no—
269C2×Dic3—62no—
270C2×Dic3—62no—
271C2×Dic3—62no—
272C2×Dic3—62no—
273C2×Dic3—124no—
274C4×D3—124no—
275C2×C9—42no—
276C2×C9#52511yescharacteristic
277C2×C9#52511yescharacteristic
278C2×C9C2×#12411yescharacteristic
279C2×C9#52912yes—
280C2×C9#52912yes—
281D9—42no—
282C24—91no—
283C24C22×D911yescharacteristic
284C2×Q8—22no—
285C2×Q8—24no—
286C2×D4—182no—
287C2×D4—182no—
288C2×D4—182no—
289C22×C4—91no—
290C22×C4—91no—
291C22×C4—92no—
292C22×C4—91no—
293C22×C4—92no—
294C22×C4—182no—
295C22×C4—184no—
296C22×C4—182no—
297C22×C4—184no—
298C22×C4C22×D912yes—
299C22×C4C22×D911yescharacteristic
300C22×C4C22×D911yescharacteristic
301C22×C4C22×D912yes—
302C4⋊C4—182no—
303C4⋊C4—184no—
304C4⋊C4—182no—
305C22⋊C4—22no—
306C22⋊C4—24no—
307C22⋊C4—184no—
308C22⋊C4—184no—
309C22⋊C4—182no—
310C22⋊C4—184no—
311C42—94no—
312C42—184no—
313C42—184no—
314C22×C3—24no—
315C22×C3—22no—
316C22×C3—41no—
317C22×C3—42no—
318C22×C3—41no—
319C22×C3C2×D3×D411yescharacteristic
320C22×C3C2×#23712yes—
321C22×C3C2×#23911yescharacteristic
322C22×C3D3×#4112yes—
323C22×C3D3×#4111yescharacteristic
324C2×D3—64no—
325C2×D3—62no—
326C2×D3—121no—
327C2×D3—121no—
328C2×D3—122no—
329C3×C4—22no—
330C3×C4—24no—
331C3×C4—41no—
332C3×C4—42no—
333Dic3—34no—
334Dic3—62no—
335Dic3—121no—
336Dic3—122no—
337Dic3—122no—
338C9#239811yescharacteristic, complemented, Sylow
339C23—21no—
340C23—22no—
341C23—22no—
342C23—21no—
343C23—92no—
344C23—181no—
345C23—182no—
346C23—181no—
347C23—182no—
348C23#370112yes—
349C23C23×D911yescharacteristic
350Q8—28no—
351D4—188no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—21no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—92no—
361C2×C4—94no—
362C2×C4—92no—
363C2×C4—181no—
364C2×C4—181no—
365C2×C4—182no—
366C2×C4—181no—
367C2×C4—182no—
368C2×C4—182no—
369C2×C4—182no—
370C2×C4—182no—
371C2×C4—182no—
372C2×C4—182no—
373C2×C4—364no—
374C2×C4—364no—
375C2×C4D4×D912yes—
376C2×C4#369914yes—
377C2×C3—42no—
378C2×C3#558611yescharacteristic
379C2×C3#562412yes—
380C2×C3#562711yescharacteristic
381C2×C3D3×#12411yescharacteristic
382C2×C3#568012yes—
383D3—122no—
384C22—24no—
385C22—22no—
386C22—41no—
387C22—42no—
388C22—41no—
389C22—182no—
390C22—184no—
391C22—362no—
392C22—361no—
393C22—361no—
394C22C2×D4×D911yescharacteristic
395C22C2×#369912yes—
396C22C2×#370111yescharacteristic
397C22#41×D912yes—
398C22#41×D911yescharacteristic
399C4—22no—
400C4—24no—
401C4—41no—
402C4—42no—
403C4—94no—
404C4—182no—
405C4—362no—
406C4—362no—
407C4—361no—
408C3#7677911yescharacteristic
409C2—42no—
410C2—362no—
411C2#1058968811yescharacteristic
412C2#1058972612yes—
413C2#1058972911yescharacteristic
414C2D9×#12411yescharacteristic
415C2#1058978212yes—
subgroupG/H
centerC23C23×D9
commutator, cosocleC23×C9C24
Frattini, socleC23×C3C23×D3
FittingC9×#393C2
prime radicalC22×#611C22
hypercenter#393D9
hypocenterC9#2398
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic9C2semidirect
3. C9×#393C2semidirect
4. #10588911C2semidirect
6. #10588633C2semidirect
7. C22⋊C4×Dic9C2semidirect
8. #10588354C2semidirect
9. #10588346C2semidirect
10. #10588340C2semidirect
11. #10588328C2semidirect
152. #393D9semidirect
338. C9#2398semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic92
C2×#611⋊C42
C9×#3932
#105889112
#105886412
#105886332
C22⋊C4×Dic92
#105883542
#105883462
#105883402
#105883282
#767793