Finite Group Databasebeta

← #11795367

Subgroups — #11795367

Order 1152.

495 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
1#10592823C211yesmaximal, characteristic, complemented
2C3×#5126C211yesmaximal, characteristic
3C3×#5124C211yesmaximal, characteristic, complemented
4#10591141C211yesmaximal, characteristic, complemented
5#10591069C211yesmaximal, characteristic
6#10591069C211yesmaximal, characteristic
7#10589159C211yesmaximal, characteristic, complemented
8#70729—31nomaximal
9#69987—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63649—22no—
18C3×#822—22no—
19C3×(C2×D3)⋊C8—22no—
20#63577—22no—
21(C2×D3)⋊(C3⋊C8)—22no—
22(C2×D3)⋊(C3⋊C8)—22no—
23C3×#430—31no—
24C3×#407—31no—
25#5207—31no—
26#5207—31no—
27#5126—31no—
28#5126—31no—
29#5126D311yescharacteristic
30#5125—31no—
31#5124—31no—
32#5124—31no—
33#5124—31no—
34#5124—61no—
35#5124D311yescharacteristic, complemented
36C3⋊#338—31no—
37C3⋊#338—31no—
38C23×C3×D3Q811yescharacteristic
39C22×C32×C4C2311yescharacteristic
40C22×C3×Dic3Q811yescharacteristic
41C2×C3×C4×D3—21no—
42C2×C3×C4×D3—21no—
43C2×C3×C4×D3—21no—
44C2×C3×C4×D3—21no—
45C2×C3×C4×D3—21no—
46C2×C3×C4×D3—21no—
47C32×M16—21no—
48C32×M16—21no—
49C2×C32×C8—21no—
50#3748—21no—
51#3748—21no—
52#3748—21no—
53#3748—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)D412yes—
56C3×#208—21no—
57C3×#208—21no—
58C3×#208—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8D412yes—
64C2×C3×C3⋊C8D412yes—
65#2091—91noSylow
66C23×C3×C4—31no—
67C22×C4×D3C2×D311yescharacteristic
68C2×C3×M16—21no—
69C2×C3×M16—31no—
70C2×C3×M16—31no—
71C2×C3×M16—31no—
72C2×C3×M16C2×D311yescharacteristic
73C2×C3×M16C2×D311yescharacteristic
74C2×#208—31no—
75C2×#208—31no—
76C2×#208—31no—
77C2×#208—31no—
78C2×#208—61no—
79C2×#208—61no—
80C2×#208C2×D311yescharacteristic
81C2×#208C2×D311yescharacteristic
82C2×#208C2×D311yescharacteristic
83C3×#108—62no—
84C3×C22⋊C8—62no—
85#830—62no—
86#830—62no—
87#822—22no—
88#822—62no—
89#822—62no—
90#822—64no—
91#822—62no—
92(C2×D3)⋊C8—22no—
93(C2×D3)⋊C8—62no—
94(C2×D3)⋊C8—62no—
95#819—62no—
96C23×C32C2×Q811yescharacteristic
97C22×C3×D3—21no—
98C22×C3×D3—21no—
99C22×C3×D3—21no—
100C22×C3×D3—42no—
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4#4111yescharacteristic
105C2×C32×C4#4111yescharacteristic
106C2×C32×C4#4111yescharacteristic
107C2×C3×Dic3—21no—
108C2×C3×Dic3—21no—
109C2×C3×Dic3—21no—
110C3×C4×D3—41no—
111C3×C4×D3—41no—
112C3×C4×D3—41no—
113C3×C4×D3—41no—
114C32×C8—41no—
115C3⋊(C3⋊C8)—22no—
116C3⋊(C3⋊C8)—41no—
117C3×C3⋊C8—22no—
118C3×C3⋊C8—22no—
119C3×C3⋊C8—41no—
120#430—31no—
121#430—91no—
122#430—91no—
123#407—31no—
124#407—91no—
125#407—91no—
126#338—91no—
127C24×C3—31no—
128C23×D3Dic611yescharacteristic
129C22×C3×C4—21no—
130C22×C3×C4—31no—
131C22×C3×C4—61no—
132C22×C3×C4—61no—
133C22×C3×C4—61no—
134C22×C3×C4—61no—
135C22×C3×C4—61no—
136C22×C3×C4—61no—
137C22×C3×C4C22×D311yescharacteristic
138C22×C3×C4C22×D311yescharacteristic
139C22×Dic3Dic611yescharacteristic
140C2×C4×D3—21no—
141C2×C4×D3—21no—
142C2×C4×D3—21no—
143C2×C4×D3—21no—
144C2×C4×D3—21no—
145C2×C4×D3—21no—
146C3×M16—22no—
147C3×M16—21no—
148C3×M16—21no—
149C3×M16—21no—
150C3×M16—21no—
151C3×M16—41no—
152C3×M16—61no—
153C3×M16—61no—
154C3×M16—61no—
155C3×M16—61no—
156C3×M16—61no—
157C3×M16—61no—
158C2×C3×C8—21no—
159C2×C3×C8—21no—
160C2×C3×C8—32no—
161C2×C3×C8—32no—
162C2×C3×C8—41no—
163C2×C3×C8—61no—
164#208—21no—
165#208—21no—
166#208—21no—
167#208—21no—
168#208—21no—
169#208—21no—
170#208—62no—
171#208—62no—
172#208—61no—
173#208—61no—
174#208—61no—
175#208—61no—
176#208—62no—
177#208—61no—
178#208—61no—
179#208—61no—
180#208—61no—
181#208—121no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—32no—
184C2×C3⋊C8—32no—
185C2×C3⋊C8—62no—
186C2×C3⋊C8—61no—
187C2×C3⋊C8—61no—
188C2×C3⋊C8—121no—
189C2×C3⋊C8#6712yes—
190C2×C3⋊C8#6712yes—
191C22×C32—41no—
192C22×C32C22⋊Q811yescharacteristic
193C22×C32C22⋊Q811yescharacteristic
194C22×C32C22⋊Q811yescharacteristic
195C2×C3×D3—22no—
196C2×C3×D3—22no—
197C2×C3×D3—22no—
198C2×C3×D3—41no—
199C2×C3×D3—41no—
200C2×C3×D3—41no—
201C2×C3×D3—41no—
202C32×C4#12311yescharacteristic
203C32×C4#12311yescharacteristic
204C32×C4#12311yescharacteristic
205C32×C4#12711yescharacteristic
206C3×Dic3—41no—
207C23×C4—31no—
208C2×M16—31no—
209C2×M16—31no—
210C2×M16—31no—
211C2×M16—91no—
212C2×M16—91no—
213C2×M16D3211yescharacteristic
214#108—62no—
215#108—182no—
216#108—182no—
217C22⋊C8—62no—
218C22⋊C8—182no—
219C22⋊C8—182no—
220C23×C3—21no—
221C23×C3—61no—
222C23×C3—61no—
223C23×C3—61no—
224C23×C3—122no—
225C23×C3C2×Dic611yescharacteristic
226C23×C3D3×Q811yescharacteristic
227C22×D3—21no—
228C22×D3—21no—
229C22×D3—21no—
230C22×D3—42no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—61no—
238C2×C3×C4—61no—
239C2×C3×C4—61no—
240C2×C3×C4—121no—
241C2×C3×C4—121no—
242C2×C3×C4—121no—
243C2×C3×C4—121no—
244C2×C3×C4#23511yescharacteristic
245C2×C3×C4#23511yescharacteristic
246C2×C3×C4#23511yescharacteristic
247C2×C3×C4D3×D411yescharacteristic
248C2×C3×C4D3×D411yescharacteristic
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4#23711yescharacteristic
252C2×C3×C4#23711yescharacteristic
253C2×C3×C4#23911yescharacteristic
254C2×C3×C4C2×#6711yescharacteristic
255C2×C3×C4C2×#6711yescharacteristic
256C2×Dic3—21no—
257C2×Dic3—21no—
258C2×Dic3—21no—
259C4×D3—41no—
260C4×D3—41no—
261C4×D3—41no—
262C4×D3—41no—
263C3×C8—42no—
264C3×C8—41no—
265C3×C8—41no—
266C3×C8—62no—
267C3×C8—62no—
268C3×C8—121no—
269C3⋊C8—22no—
270C3⋊C8—22no—
271C3⋊C8—41no—
272C3⋊C8—64no—
273C3⋊C8—62no—
274C3⋊C8—62no—
275C3⋊C8—122no—
276C3⋊C8—121no—
277C3⋊C8—121no—
278C2×C32—21no—
279C2×C32—21no—
280C2×C32—21no—
281C2×C32#39911yescharacteristic
282C3×D3—42no—
283C24—31no—
284C22×C4—31no—
285C22×C4—61no—
286C22×C4—61no—
287C22×C4—61no—
288C22×C4—61no—
289C22×C4—61no—
290C22×C4—61no—
291C22×C4C2×D3211yescharacteristic
292M16—21no—
293M16—21no—
294M16—61no—
295M16—61no—
296M16—61no—
297M16—61no—
298M16—61no—
299M16—61no—
300M16—181no—
301M16—181no—
302M16—181no—
303M16—181no—
304C2×C8—21no—
305C2×C8—32no—
306C2×C8—32no—
307C2×C8—61no—
308C2×C8—92no—
309C2×C8—181no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—41no—
314C22×C3—41no—
315C22×C3—62no—
316C22×C3—62no—
317C22×C3—62no—
318C22×C3—81no—
319C22×C3—121no—
320C22×C3—121no—
321C22×C3—121no—
322C22×C3—121no—
323C22×C3#87811yescharacteristic
324C22×C3#87811yescharacteristic
325C22×C3#89611yescharacteristic
326C22×C3#89611yescharacteristic
327C22×C3#92411yescharacteristic
328C22×C3#94611yescharacteristic
329C2×D3—22no—
330C2×D3—22no—
331C2×D3—22no—
332C2×D3—41no—
333C2×D3—41no—
334C2×D3—41no—
335C2×D3—41no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—121no—
341C3×C4#88311yescharacteristic
342C3×C4#88311yescharacteristic
343C3×C4#89411yescharacteristic
344C3×C4#89411yescharacteristic
345C3×C4#92911yescharacteristic
346C3×C4#93511yescharacteristic
347C3×C4#94011yescharacteristic
348C3×C4#94011yescharacteristic
349Dic3—41no—
350C32#209111yescharacteristic, complemented, Sylow
351C23—61no—
352C23—61no—
353C23—61no—
354C23—122no—
355C23D3×Dic611yescharacteristic
356C2×C4—61no—
357C2×C4—61no—
358C2×C4—61no—
359C2×C4—121no—
360C2×C4—121no—
361C2×C4—121no—
362C2×C4—121no—
363C2×C4#379511yescharacteristic
364C2×C4#379611yescharacteristic
365C2×C4#379811yescharacteristic
366C2×C4D3×#6711yescharacteristic
367C2×C4D3×#6711yescharacteristic
368C2×C4#381111yescharacteristic
369C8—41no—
370C8—62no—
371C8—62no—
372C8—121no—
373C8—182no—
374C8—361no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—41no—
383C2×C3—41no—
384C2×C3—41no—
385C2×C3—122no—
386C2×C3#494911yescharacteristic
387C2×C3#499311yescharacteristic
388D3—42no—
389C22—41no—
390C22—62no—
391C22—62no—
392C22—62no—
393C22—121no—
394C22—121no—
395C22—121no—
396C22—121no—
397C22#6385111yescharacteristic
398C22#6388711yescharacteristic
399C22#6389611yescharacteristic
400C4—121no—
401C4#6385311yescharacteristic
402C4#6388411yescharacteristic
403C4#6390511yescharacteristic
404C4#6397911yescharacteristic
405C3—21no—
406C3#6998711yescharacteristic, complemented
407C3#7072911yescharacteristic, complemented
408C2—21no—
409C2—21no—
410C2—21no—
411C2—122no—
412C2#1059130311yescharacteristic
subgroupG/H
centerC4#63979
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#399
prime radicalC23×C3×D3Q8
hypercenterC2×M16D32
hypocenterC32#2091
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #10592823C2semidirect
3. C3×#5124C2semidirect
4. #10591141C2semidirect
7. #10589159C2semidirect
35. #5124D3semidirect
350. C32#2091semidirect
406. C3#69987semidirect
407. C3#70729semidirect

Maximal subgroups

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

subgroupindex
#105928232
C3×#51262
C3×#51242
#105911412
#105910692
#105891592
#707293
#699873