Finite Group Databasebeta

← #11858049

Subgroups — #11858049

Order 1152.

1089 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63716C211yesmaximal, characteristic
2C2×#63464C211yesmaximal, characteristic, complemented
3#10589625C211yesmaximal, characteristic, complemented
4C9×#416C211yesmaximal, characteristic, complemented
5#10588916C211yesmaximal, characteristic, complemented
6C2×#63376C211yesmaximal, characteristic, complemented
7#10588681C211yesmaximal, characteristic, complemented
8#10588482C212yesmaximal, complemented
9D9×#103C212yesmaximal, complemented
10#10588452C212yesmaximal, complemented
11#10588451C212yesmaximal, complemented
12#78832—31nomaximal
13C2×C9×#41C2211yescharacteristic
14#63716—24no—
15#63716C418yescomplemented
16C2×Q8×D9C2212yes—
17C2×#3699—22no—
18C2×#3699C2212yes—
19C2×#3697—21no—
20C2×#3697C2211yescharacteristic
21C22×Dic18—21no—
22C22×Dic18C2211yescharacteristic
23C22×C8×C9C2211yescharacteristic
24C9×#117C2211yescharacteristic
25C2×C4⋊Dic9C2211yescharacteristic
26C2×#3667C2211yescharacteristic
27#63464—24no—
28C2×#3663C2212yes—
29C2×C8×D9C2212yes—
30#63454C2212yes—
31C4⋊C4×D9C2212yes—
32#611⋊C4—22no—
33C4×D36—21no—
34C4×Dic18—21no—
35C9×#103C2211yescharacteristic
36C9×#103C2211yescharacteristic
37C9×#102C2211yescharacteristic
38C9×#102C2211yescharacteristic
39#63395C2212yes—
40#63392C2212yes—
41#63376C2212yes—
42#63376C2212yes—
43#63368C2212yes—
44#63368C2212yes—
45C2×#1010—31no—
46C2×#901—31no—
47#5523—31no—
48C3×#416D311yescharacteristic
49#5232—31no—
50C2×#816—31no—
51#5004—31no—
52#4802—32no—
53D3×#103—32no—
54#4772—32no—
55#4771—32no—
56C9×#41—22no—
57C9×#41C2×C414yescomplemented
58C2×Q8×C9C2311yescharacteristic
59C2×D4×C9—21no—
60C2×D4×C9C2311yescharacteristic
61C22×C4×C9—21no—
62C22×C4×C9C2311yescharacteristic
63C2×#611—22no—
64C2×#611D412yes—
65C22×Dic9—21no—
66C22×Dic9—22no—
67C22×Dic9—21no—
68Q8×D9—24no—
69Q8×D9C2×C418yescomplemented
70#3699—216no—
71#3699—24no—
72#3699C2×C418yescomplemented
73#3697—28no—
74#3697C2×C414yes—
75#3697D414yes—
76C2×D36D411yescharacteristic
77C2×C4×D9—22no—
78C2×C4×D9—22no—
79C2×C4×D9C2312yes—
80C2×Dic18—21no—
81C2×Dic18—22no—
82C2×Dic18—22no—
83C2×Dic18—28no—
84C2×Dic18C2×C414yescomplemented
85C2×Dic18D411yescharacteristic
86C2×Dic18C2312yes—
87C2×C8×C9—22no—
88C2×C8×C9C2311yescharacteristic
89C2×C8×C9C2311yescharacteristic
90C9×C4⋊C4C2311yescharacteristic
91C9×C4⋊C4C2311yescharacteristic
92C9×C22⋊C4—21no—
93C42×C9—21no—
94(C2×D9)⋊C4—22no—
95C4⋊Dic9—21no—
96C4⋊Dic9C2312yes—
97Dic9⋊C4—22no—
98C4×Dic9—22no—
99#3667—22no—
100C2×C9⋊C8C2312yes—
101#3663—24no—
102C8×D9—24no—
103#2898—91noSylow
104C2×C3×#41C2×D311yescharacteristic
105#1010—38no—
106#1010—64no—
107C2×D3×Q8—32no—
108C2×#237—32no—
109C2×#237—62no—
110C2×#235—31no—
111C2×#235—61no—
112C22×Dic6—31no—
113C22×Dic6—61no—
114C22×C3×C8C2×D311yescharacteristic
115C3×#117C2×D311yescharacteristic
116C2×C4⋊Dic3—31no—
117C2×#208—31no—
118#901—64no—
119C2×ΓL(1,𝔽25)—32no—
120C2×D3×C8—32no—
121#892—32no—
122D3×C4⋊C4—32no—
123#67⋊C4—62no—
124C4×D12—61no—
125C4×Dic6—61no—
126C3×#103C2×D311yescharacteristic
127C3×#103C2×D311yescharacteristic
128C3×#102C2×D311yescharacteristic
129C3×#102C2×D311yescharacteristic
130#835—32no—
131#832—32no—
132#816—32no—
133#816—32no—
134#810—32no—
135#810—32no—
136C23×C9—21no—
137C23×C9C2×D411yescharacteristic
138C22×D9C2×D412yes—
139Q8×C9—21no—
140Q8×C9C22×C412yes—
141D4×C9—24no—
142D4×C9—21no—
143D4×C9C22×C412yes—
144C2×C4×C9—21no—
145C2×C4×C9—24no—
146C2×C4×C9—21no—
147C2×C4×C9—21no—
148C2×C4×C9C22×C412yes—
149C2×C4×C9C2×D411yescharacteristic
150C2×C4×C9C2×D412yes—
151C2×C4×C9C2411yescharacteristic
152#611—28no—
153#611C22⋊C418yes—
154C2×Dic9—24no—
155C2×Dic9—22no—
156C2×Dic9—28no—
157C2×Dic9—22no—
158C2×Dic9—81no—
159C2×Dic9C2×D412yes—
160D36C22⋊C414yes—
161C4×D9—28no—
162C4×D9—82no—
163C4×D9C22×C414yes—
164C4×D9C2×D414yes—
165Dic18—24no—
166Dic18—22no—
167Dic18—28no—
168Dic18C22⋊C414yes—
169Dic18C22×C414yes—
170C8×C9—21no—
171C8×C9—21no—
172C9⋊C8—22no—
173C2×2−1+4—91no—
174C2×#131—91no—
175#520—91no—
176#419—91no—
177#419—92no—
178#417—91no—
179#417—92no—
180#416—92no—
181#416D911yescharacteristic, complemented
182C2×#103—91no—
183C2×#103—92no—
184C3×#41—22no—
185C3×#41C4×D314yes—
186C2×C3×Q8C22×D311yescharacteristic
187C2×C3×D4—21no—
188C2×C3×D4C22×D311yescharacteristic
189C22×C3×C4—21no—
190C22×C3×C4C22×D311yescharacteristic
191C2×#67—32no—
192C2×#67—62no—
193C22×Dic3—62no—
194C22×Dic3—61no—
195C22×Dic3—61no—
196D3×Q8—38no—
197D3×Q8—64no—
198#237—38no—
199#237—64no—
200#237—616no—
201#235—34no—
202#235—34no—
203#235—68no—
204C2×D12—31no—
205C2×C4×D3—32no—
206C2×C4×D3—62no—
207C2×C4×D3—62no—
208C2×Dic6—31no—
209C2×Dic6—34no—
210C2×Dic6—32no—
211C2×Dic6—68no—
212C2×Dic6—62no—
213C2×Dic6—61no—
214C2×Dic6—62no—
215C2×C3×C8—22no—
216C2×C3×C8C22×D311yescharacteristic
217C2×C3×C8C22×D311yescharacteristic
218C3×C4⋊C4C22×D311yescharacteristic
219C3×C4⋊C4C22×D311yescharacteristic
220C3×C22⋊C4—21no—
221C3×C42—21no—
222(C2×D3)⋊C4—62no—
223C4⋊Dic3—32no—
224C4⋊Dic3—61no—
225Dic3⋊C4—62no—
226C4×Dic3—62no—
227#208—62no—
228C2×C3⋊C8—32no—
229ΓL(1,𝔽25)—64no—
230D3×C8—64no—
231C22×C9—21no—
232C22×C9—21no—
233C22×C9—22no—
234C22×C9—41no—
235C22×C9—41no—
236C22×C9C2×C22⋊C412yes—
237C22×C9C22×D411yescharacteristic
238C2×D9—22no—
239C2×D9—22no—
240C2×D9C2×C22⋊C414yes—
241C4×C9—22no—
242C4×C9—41no—
243C4×C9—41no—
244C4×C9C2×C22⋊C412yes—
245C4×C9C23×C411yescharacteristic
246C4×C9C22×D411yescharacteristic
247Dic9—24no—
248Dic9—42no—
249Dic9C2×C22⋊C414yes—
2502−1+4—98no—
2512−1+4—184no—
252C2×#41—91no—
253C2×#41—92no—
254C2×#41—181no—
255C2×#41—182no—
256C2×#41C2×D911yescharacteristic
257C22×Q8—92no—
258C22×Q8—91no—
259C22×Q8—181no—
260#131—184no—
261C2×M16—91no—
262C2×M16—92no—
263C22×C8—92no—
264C22×C8C2×D911yescharacteristic
265C4×Q8—181no—
266C4×D4—181no—
267C4×D4—182no—
268#117—92no—
269#117C2×D911yescharacteristic
270C2×C4⋊C4—91no—
271C2×C4⋊C4—92no—
272#103—92no—
273#103—92no—
274#103—92no—
275#103—92no—
276#103—92no—
277#103C2×D911yescharacteristic
278#103C2×D911yescharacteristic
279#102—92no—
280#102C2×D911yescharacteristic
281#102C2×D911yescharacteristic
282C23×C3—21no—
283C23×C3D3×D411yescharacteristic
284C22×D3—32no—
285C3×Q8—21no—
286C3×Q8C2×C4×D312yes—
287C3×D4—24no—
288C3×D4—21no—
289C3×D4C2×C4×D312yes—
290C2×C3×C4—21no—
291C2×C3×C4—24no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4C2×C4×D312yes—
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4D3×D412yes—
297C2×C3×C4C23×D311yescharacteristic
298#67—38no—
299#67—68no—
300C2×Dic3—32no—
301C2×Dic3—68no—
302C2×Dic3—64no—
303C2×Dic3—62no—
304C2×Dic3—62no—
305C2×Dic3—241no—
306D12—34no—
307C4×D3—34no—
308C4×D3—34no—
309C4×D3—68no—
310C4×D3—242no—
311Dic6—34no—
312Dic6—34no—
313Dic6—68no—
314Dic6—64no—
315Dic6—62no—
316C3×C8—21no—
317C3×C8—21no—
318C3⋊C8—62no—
319C2×C9—22no—
320C2×C9—42no—
321C2×C9C22×C22⋊C411yescharacteristic
322C2×C9#57711yescharacteristic
323C2×C9#57811yescharacteristic
324D9—24no—
325#41—22no—
326#41—94no—
327#41—94no—
328#41—98no—
329#41—188no—
330#41—184no—
331#41—1816no—
332#41C4×D914yescomplemented
333C2×Q8—91no—
334C2×Q8—98no—
335C2×Q8—94no—
336C2×Q8—92no—
337C2×Q8—182no—
338C2×Q8—188no—
339C2×Q8—184no—
340C2×Q8—181no—
341C2×Q8—182no—
342C2×Q8C22×D911yescharacteristic
343C2×D4—21no—
344C2×D4—92no—
345C2×D4—91no—
346C2×D4—182no—
347C2×D4C22×D911yescharacteristic
348C22×C4—21no—
349C22×C4—92no—
350C22×C4—182no—
351C22×C4—182no—
352C22×C4—182no—
353C22×C4—181no—
354C22×C4—181no—
355C22×C4C22×D911yescharacteristic
356M16—184no—
357M16—182no—
358C2×C8—22no—
359C2×C8—92no—
360C2×C8—184no—
361C2×C8C22×D911yescharacteristic
362C2×C8C22×D911yescharacteristic
363C4⋊C4—92no—
364C4⋊C4—182no—
365C4⋊C4—181no—
366C4⋊C4C22×D911yescharacteristic
367C4⋊C4C22×D911yescharacteristic
368C22⋊C4—21no—
369C22⋊C4—182no—
370C42—21no—
371C42—182no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—22no—
375C22×C3—41no—
376C22×C3—41no—
377C22×C3D3×C22⋊C412yes—
378C22×C3C2×D3×D411yescharacteristic
379C2×D3—34no—
380C2×D3—62no—
381C2×D3—62no—
382C3×C4—22no—
383C3×C4—41no—
384C3×C4—41no—
385C3×C4D3×C22⋊C412yes—
386C3×C4C22×C4×D311yescharacteristic
387C3×C4C2×D3×D411yescharacteristic
388Dic3—34no—
389Dic3—64no—
390Dic3—122no—
391C9#289811yescharacteristic, complemented, Sylow
392C23—21no—
393C23—92no—
394C23D4×D911yescharacteristic
395Q8—21no—
396Q8—94no—
397Q8—94no—
398Q8—188no—
399Q8—184no—
400Q8—182no—
401Q8C2×C4×D912yes—
402D4—24no—
403D4—21no—
404D4—98no—
405D4—94no—
406D4—188no—
407D4C2×C4×D912yes—
408C2×C4—21no—
409C2×C4—24no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—92no—
413C2×C4—94no—
414C2×C4—94no—
415C2×C4—188no—
416C2×C4—188no—
417C2×C4—184no—
418C2×C4—182no—
419C2×C4—182no—
420C2×C4—722no—
421C2×C4—721no—
422C2×C4C2×C4×D912yes—
423C2×C4D4×D911yescharacteristic
424C2×C4D4×D912yes—
425C2×C4C23×D911yescharacteristic
426C8—21no—
427C8—21no—
428C8—182no—
429C2×C3—22no—
430C2×C3—42no—
431C2×C3C2×D3×C22⋊C411yescharacteristic
432C2×C3#577011yescharacteristic
433C2×C3#577111yescharacteristic
434D3—64no—
435C22—21no—
436C22—21no—
437C22—22no—
438C22—41no—
439C22—41no—
440C22—94no—
441C22—182no—
442C22—182no—
443C22C22⋊C4×D912yes—
444C22C2×D4×D911yescharacteristic
445C4—22no—
446C4—41no—
447C4—41no—
448C4—94no—
449C4—184no—
450C4—362no—
451C4C22⋊C4×D912yes—
452C4C22×C4×D911yescharacteristic
453C4C2×D4×D911yescharacteristic
454C3#7883211yescharacteristic
455C2—22no—
456C2—42no—
457C2—184no—
458C2C2×C22⋊C4×D911yescharacteristic
459C2#1058987211yescharacteristic
460C2#1058987311yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutatorC4×C9C23×C4
FrattiniC2×C3×C4C23×D3
FittingC9×#416C2
socleC22×C3C2×D3×D4
prime radicalC2×#63716C2
cosocleC2×C4×C9C24
hypercenter#416D9
hypocenterC9#2898
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. C2×#63464C2semidirect
3. #10589625C2semidirect
4. C9×#416C2semidirect
5. #10588916C2semidirect
6. C2×#63376C2semidirect
7. #10588681C2semidirect
8. #10588482C2semidirect
9. D9×#103C2semidirect
10. #10588452C2semidirect
11. #10588451C2semidirect
15. #63716C4semidirect
57. C9×#41C2×C4semidirect
69. Q8×D9C2×C4semidirect
72. #3699C2×C4semidirect
84. C2×Dic18C2×C4semidirect
181. #416D9semidirect
332. #41C4×D9semidirect
391. C9#2898semidirect

Maximal subgroups

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

subgroupindex
C2×#637162
C2×#634642
#105896252
C9×#4162
#105889162
C2×#633762
#105886812
#105884822
D9×#1032
#105884522
#105884512
#788323