Finite Group Databasebeta

← #11792395

Subgroups — #11792395

Order 1152.

591 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 591 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#525C211yesmaximal, characteristic, complemented
2#10589925C211yesmaximal, characteristic, complemented
3#10589893C211yesmaximal, characteristic, complemented
4#10588914C211yesmaximal, characteristic, complemented
5#10588887C211yesmaximal, characteristic, complemented
6#10588685C211yesmaximal, characteristic, complemented
7#10588210C211yesmaximal, characteristic, complemented
8#71715—31nomaximal
9C2×C9×#41C2211yescharacteristic
10C23×C4×C9C2211yescharacteristic
11C2×#3697C2211yescharacteristic
12C9×#123—21no—
13C9×C22⋊Q8—21no—
14C9×#121—21no—
15C9×#120—21no—
16C4×D4×C9—22no—
17C9×#117C2211yescharacteristic
18#63515—21no—
19#63513—22no—
20#63512—21no—
21#63511—21no—
22#63505—21no—
23#63495—21no—
24#63492—21no—
25#63491—21no—
26C4×#611—22no—
27#63488C2211yescharacteristic
28#63486—21no—
29C2×#3667C2211yescharacteristic
30C2×#3667C2211yescharacteristic
31#63396—22no—
32#63389—22no—
33#63364—22no—
34C3×#525D311yescharacteristic
35#5822—31no—
36#5791—31no—
37#5236—31no—
38#5207—31no—
39#5005—31no—
40#4531—31no—
41C24×C9D411yescharacteristic
42C9×#41—21no—
43C9×#41—21no—
44C9×#41—21no—
45C9×#41—21no—
46C2×Q8×C9D411yescharacteristic, complemented
47C2×D4×C9—22no—
48C2×D4×C9—21no—
49C2×D4×C9D411yescharacteristic, complemented
50C22×C4×C9—21no—
51C22×C4×C9—21no—
52C22×C4×C9—21no—
53C22×C4×C9—21no—
54C22×C4×C9—21no—
55C22×C4×C9—21no—
56C22×C4×C9—21no—
57C22×C4×C9D411yescharacteristic
58C22×C4×C9C2311yescharacteristic
59C2×#611—22no—
60C2×#611—21no—
61#3697—21no—
62#3697—21no—
63#3697—21no—
64#3697—21no—
65C2×D36D411yescharacteristic, complemented
66C2×C4×D9—21no—
67C2×Dic18D411yescharacteristic, complemented
68C9×C4⋊C4—22no—
69C9×C4⋊C4—21no—
70C9×C22⋊C4—22no—
71C9×C22⋊C4—22no—
72C9×C22⋊C4—21no—
73C42×C9D412yescomplemented
74#3676—22no—
75#3676—21no—
76#3675—22no—
77#3674—22no—
78#3673—22no—
79#3672—22no—
80(C2×D9)⋊C4—22no—
81C4⋊Dic9—21no—
82Dic9⋊C4—22no—
83C4×Dic9D412yescomplemented
84#3667—21no—
85#3667—21no—
86#3667—21no—
87#3667—21no—
88C2×C9⋊C8—21no—
89C2×C9⋊C8D412yescomplemented
90#2010—91noSylow
91C2×C3×#41C2×D311yescharacteristic
92C23×C3×C4C2×D311yescharacteristic
93C2×#235—31no—
94C3×#123—21no—
95C3×C22⋊Q8—21no—
96C3×#121—21no—
97C3×#120—21no—
98C3×C4×D4—22no—
99C3×#117C2×D311yescharacteristic
100#953—61no—
101#951—61no—
102#950—62no—
103#949—61no—
104#942—61no—
105#932—61no—
106#930—61no—
107#929—61no—
108C4×#67—62no—
109#926—31no—
110#924—61no—
111C2×#208—31no—
112C2×#208—31no—
113#837—62no—
114#830—62no—
115#805—62no—
116C23×C9—21no—
117C23×C9—21no—
118C23×C9—21no—
119C23×C9—21no—
120C23×C9—42no—
121C23×C9C2×D411yescharacteristic
122C22×D9—21no—
123Q8×C9—21no—
124Q8×C9—21no—
125D4×C9—21no—
126D4×C9—21no—
127D4×C9—44no—
128D4×C9—41no—
129D4×C9—41no—
130C2×C4×C9—21no—
131C2×C4×C9—22no—
132C2×C4×C9—21no—
133C2×C4×C9—21no—
134C2×C4×C9—21no—
135C2×C4×C9—41no—
136C2×C4×C9—41no—
137C2×C4×C9—41no—
138C2×C4×C9—41no—
139C2×C4×C9—41no—
140C2×C4×C9—41no—
141C2×C4×C9C2×D411yescharacteristic
142C2×C4×C9C2×D411yescharacteristic
143C2×C4×C9C2×D411yescharacteristic
144C2×C4×C9C2×D411yescharacteristic
145C2×C4×C9C2×D411yescharacteristic
146C2×C4×C9#4111yescharacteristic
147#611—44no—
148#611—41no—
149#611—41no—
150C2×Dic9—22no—
151C2×Dic9—21no—
152D36—21no—
153D36—21no—
154C4×D9—41no—
155C4×D9—41no—
156Dic18—21no—
157Dic18—21no—
158C9⋊C8—22no—
159C9⋊C8—41no—
160#575—91no—
161#525—91no—
162#525D911yescharacteristic, complemented
163#421—91no—
164#421—91no—
165#407—91no—
166H(3,ℤ/4)—91no—
167C24×C3#6711yescharacteristic
168C3×#41—21no—
169C3×#41—21no—
170C3×#41—21no—
171C3×#41—21no—
172C2×C3×Q8#6711yescharacteristic
173C2×C3×D4—22no—
174C2×C3×D4—21no—
175C2×C3×D4#6711yescharacteristic
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4#6711yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C2×#67—62no—
186C2×#67—61no—
187#235—61no—
188#235—61no—
189#235—61no—
190#235—61no—
191C2×D12—31no—
192C2×C4×D3—61no—
193C2×Dic6—31no—
194C3×C4⋊C4—22no—
195C3×C4⋊C4—21no—
196C3×C22⋊C4—22no—
197C3×C22⋊C4—22no—
198C3×C22⋊C4—21no—
199C3×C42#6712yes—
200#217—62no—
201#217—61no—
202#216—62no—
203#215—62no—
204#214—62no—
205#213—62no—
206(C2×D3)⋊C4—62no—
207C4⋊Dic3—61no—
208Dic3⋊C4—62no—
209C4×Dic3—32no—
210#208—61no—
211#208—61no—
212#208—61no—
213#208—61no—
214C2×C3⋊C8—32no—
215C2×C3⋊C8—61no—
216C22×C9—22no—
217C22×C9—22no—
218C22×C9—22no—
219C22×C9—41no—
220C22×C9—41no—
221C22×C9—41no—
222C22×C9—41no—
223C22×C9—42no—
224C22×C9—41no—
225C22×C9—41no—
226C22×C9#12011yescharacteristic
227C22×C9#12011yescharacteristic
228C22×C9#12111yescharacteristic
229C2×D9—42no—
230C2×D9—41no—
231C4×C9—42no—
232C4×C9—41no—
233C4×C9—41no—
234C4×C9#12011yescharacteristic
235C4×C9#12111yescharacteristic
236C4×C9#12111yescharacteristic
237C4×C9#12711yescharacteristic
238Dic9—42no—
239Dic9—41no—
240C2×#41—91no—
241C2×#41C2×D911yescharacteristic
242C23×C4C2×D911yescharacteristic
243#137—181no—
244#137—181no—
245AGL(1,ℤ/8)—181no—
246AGL(1,ℤ/8)—181no—
247#135—182no—
248C2×M16—91no—
249C2×M16—91no—
250#123—21no—
251#123—181no—
252C22⋊Q8—21no—
253C22⋊Q8—181no—
254#121—21no—
255#121—181no—
256#120—21no—
257#120—181no—
258C4×D4—22no—
259C4×D4—182no—
260#117—91no—
261#117C2×D911yescharacteristic
262#104—182no—
263#104—182no—
264C22⋊C8—182no—
265C23×C3—21no—
266C23×C3—21no—
267C23×C3—21no—
268C23×C3—21no—
269C23×C3—42no—
270C23×C3C2×#6711yescharacteristic
271C22×D3—61no—
272C3×Q8—21no—
273C3×Q8—21no—
274C3×D4—21no—
275C3×D4—21no—
276C3×D4—44no—
277C3×D4—41no—
278C3×D4—41no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—22no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4D3×D411yescharacteristic
291C2×C3×C4D3×D411yescharacteristic
292C2×C3×C4D3×D411yescharacteristic
293C2×C3×C4#23711yescharacteristic
294C2×C3×C4C2×#6711yescharacteristic
295C2×C3×C4C2×#6711yescharacteristic
296#67—124no—
297#67—121no—
298#67—121no—
299C2×Dic3—62no—
300C2×Dic3—61no—
301D12—61no—
302D12—61no—
303C4×D3—121no—
304C4×D3—121no—
305Dic6—61no—
306Dic6—61no—
307C3⋊C8—62no—
308C3⋊C8—121no—
309C2×C9—21no—
310C2×C9—21no—
311C2×C9—21no—
312C2×C9—42no—
313C2×C9—81no—
314C2×C9#39211yescharacteristic
315D9—81no—
316C24#61111yescharacteristic
317#41—21no—
318#41—21no—
319#41—21no—
320#41—21no—
321#41—181no—
322#41—181no—
323#41—181no—
324#41—181no—
325C2×Q8—91no—
326C2×Q8#61111yescharacteristic, complemented
327C2×D4—22no—
328C2×D4—21no—
329C2×D4—91no—
330C2×D4—182no—
331C2×D4—181no—
332C2×D4#61111yescharacteristic, complemented
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—181no—
341C22×C4#61111yescharacteristic
342C22×C4C22×D911yescharacteristic
343Q16—182no—
344SD16—182no—
345SD16—182no—
346D8—182no—
347M16—181no—
348M16—181no—
349M16—181no—
350M16—181no—
351C2×C8—92no—
352C2×C8—181no—
353C4⋊C4—22no—
354C4⋊C4—21no—
355C4⋊C4—182no—
356C4⋊C4—181no—
357C22⋊C4—22no—
358C22⋊C4—22no—
359C22⋊C4—21no—
360C22⋊C4—182no—
361C22⋊C4—182no—
362C22⋊C4—181no—
363C42—92no—
364C42#61112yescomplemented
365C22×C3—22no—
366C22×C3—22no—
367C22×C3—22no—
368C22×C3—41no—
369C22×C3—41no—
370C22×C3—41no—
371C22×C3—41no—
372C22×C3—42no—
373C22×C3—41no—
374C22×C3—41no—
375C22×C3#93711yescharacteristic
376C22×C3#93911yescharacteristic
377C22×C3#95311yescharacteristic
378C2×D3—122no—
379C2×D3—121no—
380C3×C4—42no—
381C3×C4—41no—
382C3×C4—41no—
383C3×C4#93711yescharacteristic
384C3×C4#93811yescharacteristic
385C3×C4#93911yescharacteristic
386C3×C4#94011yescharacteristic
387Dic3—122no—
388Dic3—121no—
389C9#201011yescharacteristic, complemented, Sylow
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—42no—
395C23—181no—
396C23C2×#61111yescharacteristic
397Q8—21no—
398Q8—21no—
399Q8—181no—
400Q8—181no—
401D4—21no—
402D4—21no—
403D4—44no—
404D4—41no—
405D4—41no—
406D4—181no—
407D4—181no—
408D4—364no—
409D4—361no—
410D4—361no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—22no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—182no—
423C2×C4—181no—
424C2×C4—361no—
425C2×C4—361no—
426C2×C4D4×D911yescharacteristic
427C2×C4D4×D911yescharacteristic
428C2×C4D4×D911yescharacteristic
429C2×C4#369911yescharacteristic
430C2×C4C2×#61111yescharacteristic
431C2×C4C2×#61111yescharacteristic
432C8—182no—
433C8—361no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—42no—
438C2×C3—81no—
439C2×C3#522311yescharacteristic
440D3—241no—
441C22—22no—
442C22—22no—
443C22—22no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—42no—
449C22—41no—
450C22—41no—
451C22—362no—
452C22—361no—
453C22#6349911yescharacteristic
454C22#6350111yescharacteristic
455C22#6351511yescharacteristic
456C4—42no—
457C4—41no—
458C4—41no—
459C4—362no—
460C4—361no—
461C4#6349911yescharacteristic
462C4#6350011yescharacteristic
463C4#6350111yescharacteristic
464C4#6350211yescharacteristic
465C3#7171511yescharacteristic
466C2—21no—
467C2—21no—
468C2—21no—
469C2—42no—
470C2—81no—
471C2—721no—
472C2#1058890311yescharacteristic
subgroupG/H
centerC4#63502
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC9×#525C2
socleC2×C3#5223
hypercenter#525D9
hypocenterC9#2010
LCSG ▷ C22×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C9×#525C2semidirect
2. #10589925C2semidirect
3. #10589893C2semidirect
4. #10588914C2semidirect
5. #10588887C2semidirect
6. #10588685C2semidirect
7. #10588210C2semidirect
46. C2×Q8×C9D4semidirect
49. C2×D4×C9D4semidirect
65. C2×D36D4semidirect
67. C2×Dic18D4semidirect
73. C42×C9D4semidirect
83. C4×Dic9D4semidirect
89. C2×C9⋊C8D4semidirect
162. #525D9semidirect
326. C2×Q8#611semidirect
332. C2×D4#611semidirect
364. C42#611semidirect
389. C9#2010semidirect

Maximal subgroups

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

subgroupindex
C9×#5252
#105899252
#105898932
#105889142
#105888872
#105886852
#105882102
#717153