Finite Group Databasebeta

← #11792426

Subgroups — #11792426

Order 1152.

765 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C9×D8C211yesmaximal, characteristic, complemented
2C2×#63502C211yesmaximal, characteristic, complemented
3C22×#3673C211yesmaximal, characteristic, complemented
4#10588901C211yesmaximal, characteristic, complemented
5C2×#63392C211yesmaximal, characteristic, complemented
6C2×#63380C211yesmaximal, characteristic, complemented
7#10588228C211yesmaximal, characteristic, complemented
8#72044—31nomaximal
9C22×D4×C9C2211yescharacteristic
10C22×D4×C9C2211yescharacteristic
11C22×#611—22no—
12C22×D36C2211yescharacteristic
13C2×C9×D8—22no—
14C2×C9×D8—22no—
15C2×C9×D8—22no—
16C22×C8×C9C2211yescharacteristic
17C2×#3676—22no—
18#63502—22no—
19#63502—22no—
20C2×#3673—22no—
21C2×#3673—22no—
22C2×#3673—22no—
23C2×C4⋊Dic9C2211yescharacteristic
24C2×C4×Dic9C2211yescharacteristic
25C22×C9⋊C8C2211yescharacteristic
26#63392—22no—
27#63380—22no—
28C22×C3×D8D311yescharacteristic
29C2×#940—31no—
30C22×#213—31no—
31#5221—31no—
32C2×#832—31no—
33C2×#821—31no—
34#4550—31no—
35C24×C9—21no—
36C24×C9—21no—
37C23×D9—21no—
38C2×D4×C9—21no—
39C2×D4×C9—21no—
40C2×D4×C9—21no—
41C2×D4×C9—21no—
42C2×D4×C9—21no—
43C2×D4×C9—21no—
44C2×D4×C9—21no—
45C2×D4×C9—21no—
46C2×D4×C9—21no—
47C2×D4×C9—21no—
48C2×D4×C9D412yes—
49C2×D4×C9D412yescomplemented
50C22×C4×C9C2311yescharacteristic
51C2×#611—28no—
52C2×#611—44no—
53C2×#611—44no—
54C22×Dic9—21no—
55C22×Dic9D412yes—
56C2×D36—21no—
57C2×D36—21no—
58C2×D36—21no—
59C2×D36—21no—
60C2×D36—21no—
61C2×D36D412yes—
62C9×D8—28no—
63C2×C8×C9—21no—
64C2×C8×C9—21no—
65C2×C8×C9D412yescomplemented
66#3676—44no—
67#3673—28no—
68C4⋊Dic9—21no—
69C4⋊Dic9—21no—
70C4×Dic9—21no—
71C4×Dic9—21no—
72C2×C9⋊C8—21no—
73C2×C9⋊C8—21no—
74C2×C9⋊C8D412yescomplemented
75#2011—91noSylow
76C22×C3×D4C2×D311yescharacteristic
77C22×C3×D4C2×D311yescharacteristic
78C22×#67—62no—
79C22×D12—31no—
80C2×C3×D8—22no—
81C2×C3×D8—22no—
82C2×C3×D8—22no—
83C22×C3×C8C2×D311yescharacteristic
84C2×#217—62no—
85#940—62no—
86#940—62no—
87C2×#213—62no—
88C2×#213—62no—
89C2×#213—62no—
90C2×C4⋊Dic3—31no—
91C2×C4×Dic3—31no—
92C22×C3⋊C8—31no—
93#832—62no—
94#821—62no—
95C23×C9—22no—
96C23×C9—22no—
97C23×C9—41no—
98C23×C9—41no—
99C23×C9—41no—
100C23×C9—41no—
101C23×C9—42no—
102C23×C9—42no—
103C23×C9—42no—
104C23×C9—42no—
105C23×C9C2×D411yescharacteristic
106C22×D9—22no—
107C22×D9—41no—
108C22×D9—41no—
109C22×D9—42no—
110C22×D9—42no—
111D4×C9—22no—
112D4×C9—22no—
113D4×C9—22no—
114D4×C9—22no—
115D4×C9—41no—
116D4×C9—41no—
117D4×C9—41no—
118D4×C9—41no—
119C2×C4×C9C2×D411yescharacteristic
120C2×C4×C9C2×D411yescharacteristic
121C2×C4×C9C2×D411yescharacteristic
122C2×C4×C9C2×D411yescharacteristic
123C2×C4×C9C2×D411yescharacteristic
124C2×C4×C9#4111yescharacteristic
125#611—416no—
126C2×Dic9—22no—
127C2×Dic9—22no—
128C2×Dic9—41no—
129C2×Dic9—42no—
130C2×Dic9D814yescomplemented
131D36—22no—
132D36—22no—
133D36—41no—
134D36—41no—
135C8×C9—22no—
136C9⋊C8—22no—
137C22×D8—91no—
138C22×D8D911yescharacteristic, complemented
139C2×#127—91no—
140C2×#102—91no—
141C2×#102—91no—
142#390—91no—
143#336—91no—
144C24×C3—21no—
145C24×C3—21no—
146C23×D3—61no—
147C2×C3×D4—21no—
148C2×C3×D4—21no—
149C2×C3×D4—21no—
150C2×C3×D4—21no—
151C2×C3×D4—21no—
152C2×C3×D4—21no—
153C2×C3×D4—21no—
154C2×C3×D4—21no—
155C2×C3×D4—21no—
156C2×C3×D4—21no—
157C2×C3×D4#6712yes—
158C2×C3×D4#6712yes—
159C22×C3×C4C22×D311yescharacteristic
160C2×#67—68no—
161C2×#67—124no—
162C2×#67—124no—
163C22×Dic3—32no—
164C22×Dic3—61no—
165C2×D12—32no—
166C2×D12—61no—
167C2×D12—61no—
168C2×D12—61no—
169C2×D12—61no—
170C2×D12—61no—
171C3×D8—28no—
172C2×C3×C8—21no—
173C2×C3×C8—21no—
174C2×C3×C8#6712yes—
175#217—124no—
176#213—68no—
177C4⋊Dic3—61no—
178C4⋊Dic3—61no—
179C4×Dic3—61no—
180C4×Dic3—61no—
181C2×C3⋊C8—32no—
182C2×C3⋊C8—61no—
183C2×C3⋊C8—61no—
184C22×C9—42no—
185C22×C9—42no—
186C22×C9—44no—
187C22×C9—44no—
188C22×C9—82no—
189C22×C9—82no—
190C22×C9—81no—
191C22×C9—81no—
192C22×C9—81no—
193C22×C9—81no—
194C22×C9#12011yescharacteristic
195C22×C9#12111yescharacteristic
196C22×C9#12711yescharacteristic
197C22×C9C2×D812yes—
198C22×C9AGL(1,ℤ/8)12yes—
199C2×D9—42no—
200C2×D9—44no—
201C2×D9—82no—
202C2×D9—81no—
203C2×D9—81no—
204C4×C9#12011yescharacteristic
205C4×C9#12011yescharacteristic
206C4×C9#12111yescharacteristic
207C4×C9#12111yescharacteristic
208Dic9—24no—
209Dic9—81no—
210C22×D4—91no—
211C22×D4—182no—
212C22×D4C2×D911yescharacteristic
213C22×D4C2×D911yescharacteristic
214C2×D8—22no—
215C2×D8—22no—
216C2×D8—22no—
217C2×D8—182no—
218C2×D8—182no—
219C2×D8—182no—
220C22×C8—91no—
221C22×C8C2×D911yescharacteristic
222#127—182no—
223#127—182no—
224C2×C4⋊C4—91no—
225C2×C22⋊C4—182no—
226C2×C42—91no—
227#102—182no—
228#102—182no—
229C23×C3—22no—
230C23×C3—22no—
231C23×C3—42no—
232C23×C3—42no—
233C23×C3—42no—
234C23×C3—42no—
235C23×C3—41no—
236C23×C3—41no—
237C23×C3—41no—
238C23×C3—41no—
239C23×C3D3×D411yescharacteristic
240C22×D3—62no—
241C22×D3—122no—
242C22×D3—122no—
243C22×D3—121no—
244C22×D3—121no—
245C3×D4—22no—
246C3×D4—22no—
247C3×D4—22no—
248C3×D4—22no—
249C3×D4—41no—
250C3×D4—41no—
251C3×D4—41no—
252C3×D4—41no—
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4#23711yescharacteristic
256C2×C3×C4C2×#6711yescharacteristic
257C2×C3×C4C2×#6711yescharacteristic
258C2×C3×C4C2×#6711yescharacteristic
259#67—1216no—
260C2×Dic3—34no—
261C2×Dic3—62no—
262C2×Dic3—62no—
263C2×Dic3—122no—
264C2×Dic3—121no—
265D12—62no—
266D12—62no—
267D12—121no—
268D12—121no—
269C3×C8—22no—
270C3⋊C8—62no—
271C2×C9—82no—
272C2×C9—82no—
273C2×C9#39211yescharacteristic
274C2×C9#44712yes—
275C2×C9#45912yes—
276C2×C9#49311yescharacteristic
277C2×C9#49611yescharacteristic
278D9—82no—
279C24—21no—
280C24—21no—
281C24—181no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—92no—
293C2×D4—188no—
294C2×D4—181no—
295C2×D4—181no—
296C2×D4—181no—
297C2×D4—181no—
298C2×D4—181no—
299C2×D4—364no—
300C2×D4—364no—
301C2×D4#61112yes—
302C2×D4#61112yescomplemented
303C22×C4—92no—
304C22×C4—181no—
305C22×C4C22×D911yescharacteristic
306D8—28no—
307D8—188no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—92no—
311C2×C8—181no—
312C2×C8—181no—
313C2×C8#61112yescomplemented
314C4⋊C4—181no—
315C4⋊C4—181no—
316C22⋊C4—364no—
317C42—181no—
318C42—181no—
319C22×C3—44no—
320C22×C3—44no—
321C22×C3—42no—
322C22×C3—42no—
323C22×C3—82no—
324C22×C3—81no—
325C22×C3—81no—
326C22×C3—81no—
327C22×C3—81no—
328C22×C3—82no—
329C22×C3D3×D812yes—
330C22×C3#91112yes—
331C22×C3#93711yescharacteristic
332C22×C3#93911yescharacteristic
333C22×C3#94011yescharacteristic
334C2×D3—124no—
335C2×D3—122no—
336C2×D3—242no—
337C2×D3—241no—
338C2×D3—241no—
339C3×C4#93711yescharacteristic
340C3×C4#93811yescharacteristic
341C3×C4#93911yescharacteristic
342C3×C4#95311yescharacteristic
343Dic3—64no—
344Dic3—241no—
345C9#201111yescharacteristic, complemented, Sylow
346C23—22no—
347C23—22no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—42no—
353C23—42no—
354C23—42no—
355C23—42no—
356C23—182no—
357C23—361no—
358C23—361no—
359C23—362no—
360C23—362no—
361C23D4×D911yescharacteristic
362D4—22no—
363D4—22no—
364D4—22no—
365D4—22no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—41no—
370D4—182no—
371D4—182no—
372D4—3616no—
373D4—361no—
374D4—361no—
375C2×C4—94no—
376C2×C4—182no—
377C2×C4—182no—
378C2×C4—361no—
379C2×C4—362no—
380C2×C4D4×D911yescharacteristic
381C2×C4D4×D911yescharacteristic
382C2×C4#369911yescharacteristic
383C2×C4C2×#61111yescharacteristic
384C2×C4C2×#61111yescharacteristic
385C2×C4C2×#61111yescharacteristic
386C8—22no—
387C8—182no—
388C2×C3—82no—
389C2×C3—82no—
390C2×C3#515012yes—
391C2×C3#515111yescharacteristic
392C2×C3#515411yescharacteristic
393C2×C3#515612yes—
394C2×C3#522311yescharacteristic
395D3—242no—
396C22—44no—
397C22—44no—
398C22—42no—
399C22—42no—
400C22—82no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—82no—
406C22—364no—
407C22—362no—
408C22—722no—
409C22—721no—
410C22—721no—
411C22D8×D912yes—
412C22#6347312yes—
413C22#6349911yescharacteristic
414C22#6350111yescharacteristic
415C22#6350211yescharacteristic
416C4—184no—
417C4—721no—
418C4#6349911yescharacteristic
419C4#6350011yescharacteristic
420C4#6350111yescharacteristic
421C4#6351511yescharacteristic
422C3#7204411yescharacteristic
423C2—82no—
424C2—82no—
425C2—722no—
426C2#1058883012yes—
427C2#1058883111yescharacteristic
428C2#1058883411yescharacteristic
429C2#1058883612yes—
430C2#1058890311yescharacteristic
subgroupG/H
centerC23D4×D9
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC22×C9×D8C2
socleC23×C3D3×D4
hypercenterC22×D8D9
hypocenterC9#2011
LCSG ▷ C22×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×C9×D8C2semidirect
2. C2×#63502C2semidirect
3. C22×#3673C2semidirect
4. #10588901C2semidirect
5. C2×#63392C2semidirect
6. C2×#63380C2semidirect
7. #10588228C2semidirect
49. C2×D4×C9D4semidirect
65. C2×C8×C9D4semidirect
74. C2×C9⋊C8D4semidirect
130. C2×Dic9D8semidirect
138. C22×D8D9semidirect
302. C2×D4#611semidirect
313. C2×C8#611semidirect
345. C9#2011semidirect

Maximal subgroups

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

subgroupindex
C22×C9×D82
C2×#635022
C22×#36732
#105889012
C2×#633922
C2×#633802
#105882282
#720443