Finite Group Databasebeta

← #11790012

Subgroups — #11790012

Order 1152.

501 conjugacy classes of subgroups.

The subgroup lattice has 403 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592698C211yesmaximal, characteristic, complemented
2C3×#5002C211yesmaximal, characteristic
3C2×#63569C211yesmaximal, characteristic
4#10591071C211yesmaximal, characteristic
5C2×#63554C211yesmaximal, characteristic, complemented
6C3×#4532C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#70288—31nomaximal
9#68746—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C4⋊(C3⋊(C3⋊C8))—22no—
18C3×#810C412yescomplemented
19C3×#809C412yescomplemented
20#63569—22no—
21(C2×D3)⋊(C3⋊C8)—22no—
22#63554—22no—
23C3×#416—31no—
24C2×#837—31no—
25#5234—31no—
26#5129—31no—
27C2×#815—31no—
28#5002D311yescharacteristic
29#4999—31no—
30#4999—31no—
31#4999—61no—
32C2×#805—31no—
33C2×#803—31no—
34C3×#339—31no—
35#4558—31no—
36#4552—31no—
37#4532D311yescharacteristic, complemented
38C22×C32×C4C2311yescharacteristic
39C2×C3×#67—21no—
40C22×C3×Dic3—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×C4⋊C4C2×C412yes—
49C32×C22⋊C4—21no—
50C32×C42—21no—
51#3748—21no—
52#3748—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)D412yes—
57C3×C4×Dic3—21no—
58C3×C4×Dic3D412yes—
59C3×#208—21no—
60C3×#208—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8C2×C412yes—
65#1938—91noSylow
66C2×C3×#41—31no—
67C2×#235C2×D311yescharacteristic
68C2×C3×M16—31no—
69C22×C3×C8—31no—
70C3×#117—21no—
71C3×#117C2×D311yescharacteristic
72C3×#117C2×D311yescharacteristic
73C2×C3×C42—31no—
74C2×C4×Dic3C2×D311yescharacteristic
75C2×#208—31no—
76C2×#208—31no—
77C2×#208—61no—
78C2×#208C2×D311yescharacteristic
79C22×C3⋊C8—31no—
80C22×C3⋊C8—31no—
81C22×C3⋊C8—61no—
82C22×C3⋊C8C2×D311yescharacteristic
83C3×#103—32no—
84C3×#102—32no—
85#837—62no—
86#830—62no—
87(C2×D3)⋊C8—62no—
88#815—62no—
89#810Dic312yescomplemented
90#809Dic312yescomplemented
91#805—62no—
92C4⋊(C3⋊C8)—62no—
93C4⋊(C3⋊C8)—62no—
94C4⋊(C3⋊C8)—64no—
95#803—62no—
96C23×C32#4111yescharacteristic
97C22×C3×D3—21no—
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
105C3×#67—41no—
106C3×#67—41no—
107C2×C3×Dic3—21no—
108C2×C3×Dic3—22no—
109C2×C3×Dic3—42no—
110C3×D12—21no—
111C3×D12—21no—
112C3×C4×D3—41no—
113C3×C4×D3—41no—
114C3×Dic6—21no—
115C3×Dic6—21no—
116C3⋊(C3⋊C8)—22no—
117C3⋊(C3⋊C8)—41no—
118C3×C3⋊C8—22no—
119C3×C3⋊C8—41no—
120#424—91no—
121C2×#104—91no—
122#416—31no—
123#408—91no—
124C2×#97—91no—
125#341—91no—
126#339—31no—
127C3×#41—61no—
128C3×#41—61no—
129C3×#41—61no—
130C3×#41—61no—
131C2×C3×Q8—31no—
132C2×C3×D4—31no—
133C2×C3×D4—61no—
134C22×C3×C4—21no—
135C22×C3×C4—61no—
136C22×C3×C4—61no—
137C22×C3×C4C22×D311yescharacteristic
138C22×C3×C4C22×D311yescharacteristic
139C2×#67—21no—
140C22×Dic3—21no—
141#235—21no—
142#235—21no—
143#235—21no—
144#235—21no—
145C2×D12C2×Dic311yescharacteristic
146C2×C4×D3—21no—
147C2×Dic6C2×Dic311yescharacteristic
148C3×M16—61no—
149C3×M16—61no—
150C2×C3×C8—32no—
151C2×C3×C8—61no—
152C2×C3×C8—61no—
153C2×C3×C8—61no—
154C3×C4⋊C4—22no—
155C3×C4⋊C4C4×D312yes—
156C3×C4⋊C4C2×Dic312yes—
157C3×C22⋊C4—22no—
158C3×C22⋊C4—21no—
159C3×C22⋊C4—21no—
160C3×C42—22no—
161C3×C42—21no—
162C3×C42—21no—
163C3×C42—32no—
164C3×C42—61no—
165C4×Dic3—21no—
166C4×Dic3D1212yes—
167#208—21no—
168#208—21no—
169#208—61no—
170#208—61no—
171#208—61no—
172#208—61no—
173#208—121no—
174#208—121no—
175C2×C3⋊C8—21no—
176C2×C3⋊C8—21no—
177C2×C3⋊C8—21no—
178C2×C3⋊C8—32no—
179C2×C3⋊C8—32no—
180C2×C3⋊C8—62no—
181C2×C3⋊C8—61no—
182C2×C3⋊C8—61no—
183C2×C3⋊C8—61no—
184C2×C3⋊C8—61no—
185C2×C3⋊C8—62no—
186C2×C3⋊C8—61no—
187C2×C3⋊C8—61no—
188C2×C3⋊C8—121no—
189C2×C3⋊C8—121no—
190C2×C3⋊C8C2×Dic312yes—
191C22×C32—22no—
192C22×C32C4×D411yescharacteristic
193C22×C32#12311yescharacteristic
194C22×C32#12611yescharacteristic
195C2×C3×D3—41no—
196C2×C3×D3—42no—
197C32×C4—42no—
198C32×C4#11711yescharacteristic
199C32×C4C4×D411yescharacteristic
200C32×C4#12111yescharacteristic
201C32×C4#12411yescharacteristic
202C3×Dic3—42no—
203C3×Dic3—41no—
204C2×#41—31no—
205C2×M16—31no—
206C2×M16—91no—
207C22×C8—31no—
208C22×C8—91no—
209#117D3211yescharacteristic
210C2×C42—31no—
211C4⋊C8—182no—
212#104—182no—
213#103—32no—
214#102—32no—
215C22⋊C8—182no—
216#97—182no—
217C23×C3—21no—
218C23×C3—61no—
219C23×C3#23711yescharacteristic
220C23×C3#23711yescharacteristic
221C22×D3—21no—
222C3×Q8—61no—
223C3×Q8—61no—
224C3×D4—61no—
225C3×D4—61no—
226C3×D4—121no—
227C3×D4—121no—
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—61no—
238C2×C3×C4—62no—
239C2×C3×C4—122no—
240C2×C3×C4—121no—
241C2×C3×C4—121no—
242C2×C3×C4C2×C4×D311yescharacteristic
243C2×C3×C4C2×D1211yescharacteristic
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×C4#23711yescharacteristic
251C2×C3×C4#23711yescharacteristic
252C2×C3×C4#23911yescharacteristic
253C2×C3×C4C22×Dic311yescharacteristic
254#67—41no—
255#67—41no—
256C2×Dic3—22no—
257C2×Dic3—21no—
258C2×Dic3—42no—
259D12—21no—
260D12—21no—
261C4×D3—41no—
262C4×D3—41no—
263Dic6—21no—
264Dic6—21no—
265C3×C8—62no—
266C3×C8—121no—
267C3⋊C8—22no—
268C3⋊C8—41no—
269C3⋊C8—62no—
270C3⋊C8—62no—
271C3⋊C8—122no—
272C3⋊C8—122no—
273C3⋊C8—121no—
274C3⋊C8—121no—
275C2×C32—21no—
276C2×C32—21no—
277C2×C32#38811yescharacteristic
278C2×C32#44412yes—
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—61no—
288C22×C4—61no—
289C22×C4C2×D3211yescharacteristic
290M16—61no—
291M16—61no—
292M16—181no—
293M16—181no—
294C2×C8—32no—
295C2×C8—61no—
296C2×C8—61no—
297C2×C8—61no—
298C2×C8—92no—
299C2×C8—181no—
300C2×C8—181no—
301C2×C8—181no—
302C4⋊C4D3×Dic312yes—
303C22⋊C4—21no—
304C42—21no—
305C42—32no—
306C42—61no—
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×C3#87911yescharacteristic
316C22×C3#67⋊C411yescharacteristic
317C22×C3#88311yescharacteristic
318C22×C3#88611yescharacteristic
319C22×C3#89811yescharacteristic
320C22×C3D4×Dic311yescharacteristic
321C2×D3—42no—
322C2×D3—41no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—44no—
328C3×C4—42no—
329C3×C4—42no—
330C3×C4—122no—
331C3×C4—121no—
332C3×C4C4×D1211yescharacteristic
333C3×C4#88411yescharacteristic
334C3×C4#88511yescharacteristic
335C3×C4#88511yescharacteristic
336C3×C4#89211yescharacteristic
337C3×C4#89511yescharacteristic
338C3×C4#92611yescharacteristic
339C3×C4D4×Dic311yescharacteristic
340Dic3—42no—
341Dic3—41no—
342C32#193811yescharacteristic, complemented, Sylow
343C23—61no—
344C23#380511yescharacteristic
345Q8—61no—
346Q8—61no—
347D4—61no—
348D4—61no—
349D4—121no—
350D4—121no—
351C2×C4—22no—
352C2×C4—62no—
353C2×C4—61no—
354C2×C4—122no—
355C2×C4—121no—
356C2×C4—121no—
357C2×C4#379511yescharacteristic
358C2×C4#379511yescharacteristic
359C2×C4#379911yescharacteristic
360C2×C4D3×D1211yescharacteristic
361C2×C4C2×D3×Dic311yescharacteristic
362C2×C4#381111yescharacteristic
363C8—62no—
364C8—121no—
365C8—182no—
366C8—361no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—22no—
373C2×C3—41no—
374C2×C3—41no—
375C2×C3—241no—
376C2×C3#467011yescharacteristic
377C2×C3#482312yes—
378C2×C3#495111yescharacteristic
379C2×C3#519712yes—
380D3—81no—
381C22—22no—
382C22—121no—
383C22—122no—
384C22#6386111yescharacteristic
385C22#6389111yescharacteristic
386C22#67⋊Dic311yescharacteristic
387C4—42no—
388C4—122no—
389C4—121no—
390C4#6384111yescharacteristic
391C4Dic3×D1211yescharacteristic
392C4#6391011yescharacteristic
393C4#6391311yescharacteristic
394C3—21no—
395C3#6874611yescharacteristic, complemented
396C3#7028811yescharacteristic, complemented
397C2—21no—
398C2—21no—
399C2—241no—
400C2#1059131611yescharacteristic
401C2#1059167612yes—
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32C4×D4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1938
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10592698C2semidirect
5. C2×#63554C2semidirect
6. C3×#4532C2semidirect
7. #10589166C2semidirect
18. C3×#810C4semidirect
19. C3×#809C4semidirect
37. #4532D3semidirect
89. #810Dic3semidirect
90. #809Dic3semidirect
342. C32#1938semidirect
395. C3#68746semidirect
396. C3#70288semidirect

Maximal subgroups

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

subgroupindex
#105926982
C3×#50022
C2×#635692
#105910712
C2×#635542
C3×#45322
#105891662
#702883
#687463