Finite Group Databasebeta

← #11868775

Subgroups — #11868775

Order 1152.

624 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
1D9×C4⋊Q8C211yesmaximal, characteristic, complemented
2C4×#3699C211yesmaximal, characteristic
3C9×#474C211yesmaximal, characteristic, complemented
4#10588767C211yesmaximal, characteristic, complemented
5#10588690C211yesmaximal, characteristic, complemented
6#10588561C212yesmaximal, complemented
7#10588555C212yesmaximal, complemented
8#10588521C211yesmaximal, characteristic, complemented
9#10588515C211yesmaximal, characteristic, complemented
10#10588451C212yesmaximal
11#10588441C212yesmaximal, complemented
12#80966—31nomaximal
13C2×Q8×D9—21no—
14C2×#3699C2211yescharacteristic
15C9×C4⋊Q8C2211yescharacteristic
16C4×D4×C9C2211yescharacteristic
17#63506—21no—
18D4×Dic9C2211yescharacteristic
19C4×#611—21no—
20C2×C4×Dic9—21no—
21C2×#3663C2212yes—
22#63454C2211yescharacteristic
23C4⋊C4×D9—21no—
24C4⋊C4×D9C2212yes—
25#63450—21no—
26#63450C2212yes—
27#63449C2211yescharacteristic
28#611⋊C4—21no—
29#63439—21no—
30C42×D9C2211yescharacteristic
31#63431C2211yescharacteristic
32C4×Dic18C2211yescharacteristic
33C9×#107C2212yes—
34C9×C4⋊C8C2211yescharacteristic
35C9×#102C2212yes—
36#63392C2212yes—
37#63377C2212yes—
38#63376C2212yes—
39Dic9⋊C8C2212yes—
40#63368C2212yes—
41#63367C2212yes—
42#63366C2212yes—
43C4⋊(C9⋊C8)C2211yescharacteristic
44D3×C4⋊Q8—31no—
45C4×#237—31no—
46C3×#474D311yescharacteristic
47#5094—31no—
48#5007—31no—
49#4881—32no—
50#4875—32no—
51#4851—31no—
52#4837—31no—
53#4771—32no—
54#4761—32no—
55C2×Q8×C9—21no—
56C2×D4×C9C2311yescharacteristic
57C22×C4×C9—21no—
58C2×#611—21no—
59C22×Dic9—21no—
60C22×Dic9—21no—
61Q8×D9—44no—
62#3699—22no—
63#3699Q814yescomplemented
64C2×C4×D9—22no—
65C2×C4×D9D411yescharacteristic
66C2×C4×D9D411yescharacteristic
67C2×C4×D9C2311yescharacteristic
68C2×Dic18—21no—
69C2×Dic18—22no—
70C2×Dic18C2311yescharacteristic
71C2×C8×C9C2312yes—
72C9×C4⋊C4—21no—
73C9×C4⋊C4C2311yescharacteristic
74C9×C4⋊C4C2312yes—
75C9×C22⋊C4—21no—
76C42×C9C2311yescharacteristic
77#3676—21no—
78(C2×D9)⋊C4—21no—
79C4⋊Dic9—21no—
80C4⋊Dic9C2311yescharacteristic
81C4⋊Dic9C2312yes—
82Dic9⋊C4—21no—
83Dic9⋊C4—21no—
84Dic9⋊C4—22no—
85Dic9⋊C4—22no—
86C4×Dic9—21no—
87C4×Dic9—21no—
88C4×Dic9—21no—
89C4×Dic9D411yescharacteristic
90C4×Dic9D411yescharacteristic
91C4×Dic9C2311yescharacteristic
92C2×C9⋊C8C2312yes—
93#3663—24no—
94#3079—91noSylow
95C2×D3×Q8—61no—
96C2×#237—31no—
97C3×C4⋊Q8C2×D311yescharacteristic
98C3×C4×D4C2×D311yescharacteristic
99#944—61no—
100D4×Dic3—31no—
101C4×#67—61no—
102C2×C4×Dic3—61no—
103C2×ΓL(1,𝔽25)—32no—
104#892—31no—
105D3×C4⋊C4—32no—
106D3×C4⋊C4—61no—
107#888—32no—
108#888—61no—
109#887—31no—
110#67⋊C4—61no—
111#877—61no—
112C42×D3—31no—
113#869—31no—
114C4×Dic6—31no—
115C3×#107C2×D312yes—
116C3×C4⋊C8C2×D311yescharacteristic
117C3×#102C2×D312yes—
118#832—32no—
119#817—32no—
120#816—32no—
121Dic3⋊C8—32no—
122#810—32no—
123#808—32no—
124#807—32no—
125C4⋊(C3⋊C8)—31no—
126C23×C9—21no—
127C22×D9C2×D411yescharacteristic
128Q8×C9—42no—
129D4×C9—21no—
130D4×C9C2×Q812yescomplemented
131C2×C4×C9—21no—
132C2×C4×C9—22no—
133C2×C4×C9—42no—
134C2×C4×C9C2×D411yescharacteristic
135C2×C4×C9C2×D411yescharacteristic
136C2×C4×C9C2411yescharacteristic
137#611—24no—
138C2×Dic9—21no—
139C2×Dic9—24no—
140C2×Dic9—21no—
141C2×Dic9—22no—
142C2×Dic9—42no—
143C2×Dic9C2×D411yescharacteristic
144C2×Dic9C2×D411yescharacteristic
145C2×Dic9C2×D411yescharacteristic
146C4×D9—22no—
147C4×D9—22no—
148C4×D9—44no—
149C4×D9C2×Q812yes—
150C4×D9#4112yes—
151Dic18—21no—
152Dic18—44no—
153Dic18—42no—
154Dic18C2×Q812yescomplemented
155C8×C9—22no—
156C9⋊C8—22no—
157C2×C4⋊Q8—91no—
158C4×#41—91no—
159#477—92no—
160#476—92no—
161#475—91no—
162#475—91no—
163#474—91no—
164#474D911yescharacteristic, complemented
165#428—92no—
166#423—91no—
167#417—92no—
168C2×C3×Q8—21no—
169C2×C3×D4C22×D311yescharacteristic
170C22×C3×C4—21no—
171C2×#67—61no—
172C22×Dic3—61no—
173C22×Dic3—61no—
174D3×Q8—124no—
175#237—34no—
176#237—62no—
177C2×C4×D3—31no—
178C2×C4×D3—31no—
179C2×C4×D3—31no—
180C2×C4×D3—62no—
181C2×Dic6—31no—
182C2×Dic6—62no—
183C2×Dic6—61no—
184C2×C3×C8C22×D312yes—
185C3×C4⋊C4—21no—
186C3×C4⋊C4C22×D311yescharacteristic
187C3×C4⋊C4C22×D312yes—
188C3×C22⋊C4—21no—
189C3×C42C22×D311yescharacteristic
190#217—61no—
191(C2×D3)⋊C4—61no—
192C4⋊Dic3—32no—
193C4⋊Dic3—31no—
194C4⋊Dic3—61no—
195Dic3⋊C4—61no—
196Dic3⋊C4—62no—
197Dic3⋊C4—62no—
198Dic3⋊C4—61no—
199C4×Dic3—31no—
200C4×Dic3—31no—
201C4×Dic3—31no—
202C4×Dic3—61no—
203C4×Dic3—61no—
204C4×Dic3—61no—
205C2×C3⋊C8—32no—
206ΓL(1,𝔽25)—64no—
207C22×C9—22no—
208C22×C9—41no—
209C22×C9—41no—
210C22×C9C22×D411yescharacteristic
211C2×D9—21no—
212C2×D9—21no—
213C2×D9C22⋊Q812yes—
214C4×C9—21no—
215C4×C9—42no—
216C4×C9—41no—
217C4×C9AGL(1,ℤ/8)12yes—
218C4×C9C22×Q811yescharacteristic
219C4×C9C2×#4111yescharacteristic
220Dic9—22no—
221Dic9—21no—
222Dic9—42no—
223Dic9—41no—
224Dic9C22⋊Q812yes—
225Dic9#13712yes—
226C2×#41—91no—
227C22×Q8—181no—
228C2×M16—92no—
229C4⋊Q8—92no—
230C4⋊Q8—91no—
231C4⋊Q8—181no—
232C4⋊Q8—181no—
233C4⋊Q8C2×D911yescharacteristic
234C4×Q8—91no—
235C4×Q8—91no—
236C4×D4—91no—
237C4×D4—181no—
238C4×D4—181no—
239C4×D4C2×D911yescharacteristic
240#117—91no—
241#117—181no—
242C2×C4⋊C4—92no—
243C2×C4⋊C4—181no—
244C2×C42—91no—
245C2×C42—181no—
246#107—92no—
247#107C2×D912yes—
248#106—92no—
249#106—92no—
250C4⋊C8—92no—
251C4⋊C8—91no—
252C4⋊C8C2×D911yescharacteristic
253#103—92no—
254#103—92no—
255#102—92no—
256#102C2×D912yes—
257C23×C3—21no—
258C22×D3—31no—
259C3×Q8—42no—
260C3×D4—21no—
261C3×D4D3×Q812yes—
262C2×C3×C4—21no—
263C2×C3×C4—22no—
264C2×C3×C4—42no—
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4C23×D311yescharacteristic
268#67—64no—
269C2×Dic3—31no—
270C2×Dic3—31no—
271C2×Dic3—31no—
272C2×Dic3—64no—
273C2×Dic3—61no—
274C2×Dic3—61no—
275C2×Dic3—62no—
276C2×Dic3—122no—
277C4×D3—32no—
278C4×D3—32no—
279C4×D3—62no—
280C4×D3—62no—
281C4×D3—124no—
282Dic6—32no—
283Dic6—61no—
284Dic6—124no—
285Dic6—122no—
286C3×C8—22no—
287C3⋊C8—62no—
288C2×C9—42no—
289C2×C9C2×C22⋊Q811yescharacteristic
290C2×C9C2×AGL(1,ℤ/8)11yescharacteristic
291C2×C9C2×#13711yescharacteristic
292D9—22no—
293#41—94no—
294#41—182no—
295C2×Q8—21no—
296C2×Q8—91no—
297C2×Q8—182no—
298C2×Q8—181no—
299C2×Q8—364no—
300C2×D4—181no—
301C2×D4C22×D911yescharacteristic
302C22×C4—21no—
303C22×C4—91no—
304C22×C4—91no—
305C22×C4—91no—
306C22×C4—182no—
307C22×C4—181no—
308C22×C4—181no—
309M16—184no—
310C2×C8—92no—
311C2×C8C22×D912yes—
312C4⋊C4—21no—
313C4⋊C4—92no—
314C4⋊C4—91no—
315C4⋊C4—182no—
316C4⋊C4—182no—
317C4⋊C4—181no—
318C4⋊C4—181no—
319C4⋊C4—181no—
320C4⋊C4C22×D912yes—
321C4⋊C4C22×D911yescharacteristic
322C22⋊C4—21no—
323C22⋊C4—181no—
324C22⋊C4—181no—
325C42—91no—
326C42—91no—
327C42—91no—
328C42—181no—
329C42—181no—
330C42—181no—
331C42C22×D911yescharacteristic
332C22×C3—22no—
333C22×C3—41no—
334C22×C3—41no—
335C22×C3C2×D3×D411yescharacteristic
336C2×D3—32no—
337C2×D3—61no—
338C2×D3—61no—
339C3×C4—21no—
340C3×C4—42no—
341C3×C4—41no—
342C3×C4#91112yes—
343C3×C4C2×D3×Q811yescharacteristic
344C3×C4D3×#4111yescharacteristic
345Dic3—32no—
346Dic3—32no—
347Dic3—61no—
348Dic3—62no—
349Dic3—122no—
350Dic3—121no—
351C9#307911yescharacteristic, complemented, Sylow
352C23—21no—
353C23—91no—
354Q8—42no—
355Q8—92no—
356Q8—181no—
357Q8—364no—
358Q8—362no—
359D4—21no—
360D4—184no—
361D4Q8×D912yescomplemented
362C2×C4—21no—
363C2×C4—22no—
364C2×C4—42no—
365C2×C4—91no—
366C2×C4—91no—
367C2×C4—92no—
368C2×C4—92no—
369C2×C4—91no—
370C2×C4—182no—
371C2×C4—184no—
372C2×C4—181no—
373C2×C4—182no—
374C2×C4—181no—
375C2×C4—182no—
376C2×C4—364no—
377C2×C4—362no—
378C2×C4D4×D911yescharacteristic
379C2×C4D4×D911yescharacteristic
380C2×C4C23×D911yescharacteristic
381C8—22no—
382C8—182no—
383C2×C3—42no—
384C2×C3D3×C22⋊Q811yescharacteristic
385C2×C3C2×#91111yescharacteristic
386C2×C3D3×#13711yescharacteristic
387D3—62no—
388C22—22no—
389C22—41no—
390C22—41no—
391C22—92no—
392C22—181no—
393C22—181no—
394C22C2×D4×D911yescharacteristic
395C4—21no—
396C4—41no—
397C4—42no—
398C4—92no—
399C4—92no—
400C4—182no—
401C4—181no—
402C4—362no—
403C4—361no—
404C4#6347312yes—
405C4C2×Q8×D911yescharacteristic
406C4#41×D911yescharacteristic
407C3#8096611yescharacteristic
408C2—42no—
409C2—182no—
410C2D9×C22⋊Q811yescharacteristic
411C2C2×#6347311yescharacteristic
412C2D9×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#474C2
socleC22×C3C2×D3×D4
prime radicalC2×#3699C22
hypercenter#474D9
hypocenterC9#3079
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. D9×C4⋊Q8C2semidirect
3. C9×#474C2semidirect
4. #10588767C2semidirect
5. #10588690C2semidirect
6. #10588561C2semidirect
7. #10588555C2semidirect
8. #10588521C2semidirect
9. #10588515C2semidirect
11. #10588441C2semidirect
63. #3699Q8semidirect
130. D4×C9C2×Q8semidirect
154. Dic18C2×Q8semidirect
164. #474D9semidirect
351. C9#3079semidirect
361. D4Q8×D9semidirect

Maximal subgroups

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

subgroupindex
D9×C4⋊Q82
C4×#36992
C9×#4742
#105887672
#105886902
#105885612
#105885552
#105885212
#105885152
#105884512
#105884412
#809663