Finite Group Databasebeta

← #11789951

Subgroups — #11789951

Order 1152.

515 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#805C211yesmaximal, characteristic
2C2×C3×C4×C3⋊C8C211yesmaximal, characteristic, complemented
3#10591119C211yesmaximal, characteristic, complemented
4#10591084C211yesmaximal, characteristic
5#10591070C211yesmaximal, characteristic
6#10589389C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#70371—31nomaximal
9#69793—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C22×C3×C3⋊C8C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C3×#805—22no—
18C3×C4×C3⋊C8—22no—
19#63572—22no—
20#63566C412yescomplemented
21#63563C412yescomplemented
22(C2×D3)⋊(C3⋊C8)—22no—
23C2×C3×#104—31no—
24C2×C3×C4×C8—31no—
25#5234—31no—
26#5233—31no—
27#5119—31no—
28#5113—31no—
29#5110—31no—
30#5102—31no—
31C2×#805D311yescharacteristic
32C2×C4×C3⋊C8D311yescharacteristic, complemented
33#4558—31no—
34#4552—31no—
35#4523—31no—
36#4523—31no—
37#4523—61no—
38C22×C32×C4—21no—
39C22×C32×C4C2311yescharacteristic
40C2×C3×#67—21no—
41C3×#235—21no—
42C3×#235—21no—
43C3×#235—21no—
44C3×#235—21no—
45C2×C3×D12C2×C411yescharacteristic
46C2×C3×C4×D3—21no—
47C2×C3×Dic6C2×C411yescharacteristic
48C32×C42—21no—
49C32×C42D412yes—
50#3757—21no—
51C4⋊(C3⋊Dic3)C2×C412yes—
52C4×C3⋊Dic3—21no—
53#3748—21no—
54#3748—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×#208—21no—
57C3×#208—21no—
58C2×C3×C3⋊C8—21no—
59C2×C3×C3⋊C8—21no—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8C2×C412yes—
64C2×C3×C3⋊C8D412yes—
65#1937—91noSylow
66C2×C3×#41—31no—
67C2×#235C2×D311yescharacteristic
68C2×C3×M16—31no—
69C22×C3×C8—31no—
70C22×C3×C8—31no—
71C2×C3×C42—21no—
72C2×C3×C42C2×D311yescharacteristic
73C2×C3×C42C2×D311yescharacteristic
74#926—31no—
75#926—31no—
76#926—61no—
77C2×#208—31no—
78C2×#208—31no—
79C2×#208—61no—
80C2×#208C2×D311yescharacteristic
81C22×C3⋊C8C2×D311yescharacteristic
82C22×C3⋊C8C2×D311yescharacteristic
83C3×#104—62no—
84C3×C4×C8—62no—
85#835—32no—
86#832—32no—
87#830—62no—
88#821—32no—
89(C2×D3)⋊C8—62no—
90#816—32no—
91Dic3⋊C8—62no—
92Dic3⋊C8—62no—
93#805—22no—
94C4×C3⋊C8—22no—
95C23×C32#4111yescharacteristic
96C22×C3×D3—21no—
97C2×C32×C4—24no—
98C2×C32×C4—22no—
99C2×C32×C4C22×C411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C2×C32×C4#4111yescharacteristic
105C2×C3⋊Dic3—22no—
106C3×#67—41no—
107C3×#67—41no—
108C2×C3×Dic3—21no—
109C3×D12—21no—
110C3×D12—21no—
111C3×C4×D3—41no—
112C3×C4×D3—41no—
113C3×Dic6—21no—
114C3×Dic6—21no—
115C3⋊(C3⋊C8)—41no—
116C3×C3⋊C8—22no—
117C3×C3⋊C8—22no—
118C3×C3⋊C8—41no—
119#424—91no—
120C2×#104—31no—
121#416—91no—
122#408—91no—
123C2×C4×C8—31no—
124#341—91no—
125#339—91no—
126C3×#41—61no—
127C3×#41—61no—
128C3×#41—61no—
129C3×#41—61no—
130C2×C3×Q8—31no—
131C2×C3×D4—31no—
132C2×C3×D4—61no—
133C22×C3×C4—21no—
134C22×C3×C4—21no—
135C22×C3×C4—21no—
136C22×C3×C4—41no—
137C22×C3×C4—61no—
138C22×C3×C4C22×D311yescharacteristic
139C22×C3×C4C22×D311yescharacteristic
140C2×#67—21no—
141#235—21no—
142#235—21no—
143#235—21no—
144#235—21no—
145C2×D12C4×D311yescharacteristic
146C2×C4×D3—21no—
147C2×Dic6C4×D311yescharacteristic
148C3×M16—61no—
149C3×M16—61no—
150C2×C3×C8—32no—
151C2×C3×C8—32no—
152C2×C3×C8—61no—
153C2×C3×C8—61no—
154C2×C3×C8—61no—
155C2×C3×C8—61no—
156C2×C3×C8—61no—
157C3×C42—21no—
158C3×C42—21no—
159C3×C42—22no—
160C3×C42—41no—
161C3×C42#6712yes—
162C3×C42#6712yes—
163#217—61no—
164#217—61no—
165#217—121no—
166C4⋊Dic3—32no—
167C4⋊Dic3—32no—
168C4⋊Dic3—62no—
169C4×Dic3—61no—
170C4×Dic3—61no—
171C4×Dic3—121no—
172#208—21no—
173#208—21no—
174#208—62no—
175#208—61no—
176#208—61no—
177#208—61no—
178#208—61no—
179#208—121no—
180C2×C3⋊C8—21no—
181C2×C3⋊C8—21no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—21no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—61no—
186C2×C3⋊C8—61no—
187C2×C3⋊C8—121no—
188C2×C3⋊C8C4×D312yes—
189C2×C3⋊C8D1212yes—
190C22×C32—22no—
191C22×C32C4×D411yescharacteristic
192C22×C32#12311yescharacteristic
193C22×C32#12611yescharacteristic
194C2×C3×D3—41no—
195C2×C3×D3—42no—
196C32×C4—24no—
197C32×C4#11711yescharacteristic
198C32×C4C4×D411yescharacteristic
199C32×C4#12111yescharacteristic
200C32×C4#12411yescharacteristic
201C3⋊Dic3—42no—
202C3×Dic3—41no—
203C2×#41—31no—
204C2×M16—31no—
205C2×M16—91no—
206C22×C8—31no—
207C22×C8—31no—
208#117—91no—
209C2×C42D3211yescharacteristic
210C4⋊C8—182no—
211#104—62no—
212#103—92no—
213#102—92no—
214C22⋊C8—182no—
215C4×C8—62no—
216C23×C3—21no—
217C23×C3—61no—
218C23×C3#23511yescharacteristic
219C23×C3#23711yescharacteristic
220C22×D3—21no—
221C3×Q8—61no—
222C3×Q8—61no—
223C3×D4—61no—
224C3×D4—61no—
225C3×D4—121no—
226C3×D4—121no—
227C2×C3×C4—24no—
228C2×C3×C4—24no—
229C2×C3×C4—22no—
230C2×C3×C4—22no—
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—42no—
238C2×C3×C4—44no—
239C2×C3×C4—61no—
240C2×C3×C4—121no—
241C2×C3×C4—121no—
242C2×C3×C4C2×C4×D311yescharacteristic
243C2×C3×C4C2×C4×D311yescharacteristic
244C2×C3×C4C2×D1211yescharacteristic
245C2×C3×C4#23511yescharacteristic
246C2×C3×C4#23511yescharacteristic
247C2×C3×C4#23511yescharacteristic
248C2×C3×C4#23511yescharacteristic
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4#23711yescharacteristic
251C2×C3×C4#23711yescharacteristic
252C2×C3×C4C2×#6711yescharacteristic
253C2×C3×C4C2×#6711yescharacteristic
254#67—41no—
255#67—41no—
256C2×Dic3—21no—
257C2×Dic3—62no—
258C2×Dic3—62no—
259C2×Dic3—122no—
260D12—21no—
261D12—21no—
262C4×D3—41no—
263C4×D3—41no—
264Dic6—21no—
265Dic6—21no—
266C3×C8—62no—
267C3×C8—62no—
268C3×C8—121no—
269C3⋊C8—22no—
270C3⋊C8—22no—
271C3⋊C8—41no—
272C3⋊C8—122no—
273C3⋊C8—121no—
274C3⋊C8—121no—
275C2×C32—21no—
276C2×C32—21no—
277C2×C32#38811yescharacteristic
278C2×C32#44312yes—
279C3×D3—81no—
280#41—61no—
281#41—61no—
282#41—61no—
283#41—61no—
284C2×Q8—31no—
285C2×D4—31no—
286C2×D4—61no—
287C22×C4—21no—
288C22×C4—61no—
289C22×C4C2×D3211yescharacteristic
290M16—61no—
291M16—61no—
292M16—181no—
293M16—181no—
294C2×C8—32no—
295C2×C8—32no—
296C2×C8—61no—
297C2×C8—61no—
298C2×C8—61no—
299C2×C8—61no—
300C2×C8—61no—
301C2×C8—181no—
302C4⋊C4—92no—
303C22⋊C4—181no—
304C42—21no—
305C42—181no—
306C42#62512yes—
307C22×C3—22no—
308C22×C3—22no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3—42no—
313C22×C3—121no—
314C22×C3—122no—
315C22×C3C4×D1211yescharacteristic
316C22×C3#87611yescharacteristic
317C22×C3#87911yescharacteristic
318C22×C3#67⋊C411yescharacteristic
319C22×C3#92911yescharacteristic
320C22×C3#93511yescharacteristic
321C2×D3—41no—
322C2×D3—42no—
323C3×C4—24no—
324C3×C4—24no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—44no—
330C3×C4—121no—
331C3×C4#87211yescharacteristic
332C3×C4#87511yescharacteristic
333C3×C4#87711yescharacteristic
334C3×C4#88511yescharacteristic
335C3×C4C4×#6711yescharacteristic
336C3×C4C4×#6711yescharacteristic
337C3×C4#93011yescharacteristic
338C3×C4#93811yescharacteristic
339Dic3—41no—
340Dic3—122no—
341Dic3—122no—
342Dic3—242no—
343C32#193711yescharacteristic, complemented, Sylow
344C23—61no—
345C23#380411yescharacteristic
346Q8—61no—
347Q8—61no—
348D4—61no—
349D4—61no—
350D4—121no—
351D4—121no—
352C2×C4—24no—
353C2×C4—22no—
354C2×C4—61no—
355C2×C4—121no—
356C2×C4—121no—
357C2×C4—182no—
358C2×C4#379511yescharacteristic
359C2×C4#379811yescharacteristic
360C2×C4C4×D3211yescharacteristic
361C2×C4D3×D1211yescharacteristic
362C2×C4#380411yescharacteristic
363C2×C4C2×#62511yescharacteristic
364C8—62no—
365C8—62no—
366C8—121no—
367C8—361no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—22no—
374C2×C3—41no—
375C2×C3—41no—
376C2×C3—241no—
377C2×C3#470012yes—
378C2×C3#482412yes—
379C2×C3#494011yescharacteristic
380C2×C3#494411yescharacteristic
381D3—81no—
382C22—22no—
383C22—121no—
384C22—122no—
385C22#6385911yescharacteristic
386C22#6388011yescharacteristic
387C22#6396111yescharacteristic
388C4—24no—
389C4—121no—
390C4—362no—
391C4#6385211yescharacteristic
392C4#6387711yescharacteristic
393C4C4×#62511yescharacteristic
394C4#6390811yescharacteristic
395C3—21no—
396C3#6979311yescharacteristic, complemented
397C3#7037111yescharacteristic, complemented
398C2—21no—
399C2—21no—
400C2—241no—
401C2#1059034112yes—
402C2#1059127911yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C4×D4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1937
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×C3⋊C8C2semidirect
3. #10591119C2semidirect
6. #10589389C2semidirect
7. #10589166C2semidirect
20. #63566C4semidirect
21. #63563C4semidirect
32. C2×C4×C3⋊C8D3semidirect
343. C32#1937semidirect
396. C3#69793semidirect
397. C3#70371semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8052
C2×C3×C4×C3⋊C82
#105911192
#105910842
#105910702
#105893892
#105891662
#703713
#697933