Finite Group Databasebeta

← #11789948

Subgroups — #11789948

Order 1152.

517 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#10592818C211yesmaximal, characteristic, complemented
2C2×C3×#825C211yesmaximal, characteristic
3#10591084C211yesmaximal, characteristic
4#10591071C211yesmaximal, characteristic
5C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
6C3×#4558C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8#70371—31nomaximal
9#68918—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12#64135C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63641—22no—
18C3×#825—22no—
19#63566C412yescomplemented
20#63563C412yescomplemented
21(C2×D3)⋊(C3⋊C8)—22no—
22Dic3×C3⋊C8—22no—
23C2×C3×#104—31no—
24#5234—31no—
25#5233—31no—
26C2×#825D311yescharacteristic
27#5129—31no—
28#5119—31no—
29#5119—31no—
30#5119—61no—
31#5113—31no—
32C2×C8×Dic3—31no—
33C2×C4×C3⋊C8—31no—
34C3×#341—31no—
35#4558D311yescharacteristic, complemented
36#4555—31no—
37#4523—31no—
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×M16—21no—
49C32×M16—21no—
50C2×C32×C8—21no—
51#3757—21no—
52C4⋊(C3⋊Dic3)C2×C412yes—
53C4×C3⋊Dic3—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#1937—91noSylow
66C2×C3×#41—31no—
67C2×#235C2×D311yescharacteristic
68C2×C3×M16—21no—
69C2×C3×M16—31no—
70C2×C3×M16C2×D311yescharacteristic
71C2×C3×M16C2×D311yescharacteristic
72C22×C3×C8—31no—
73C2×C3×C42—31no—
74#926—31no—
75#926—31no—
76#926—61no—
77C2×C4×Dic3C2×D311yescharacteristic
78C2×#208C2×D311yescharacteristic
79C22×C3⋊C8—31no—
80C22×C3⋊C8—31no—
81C22×C3⋊C8—61no—
82C22×C3⋊C8C2×D311yescharacteristic
83C3×#104—62no—
84#835—32no—
85#832—32no—
86#830—62no—
87#825—22no—
88#821—32no—
89(C2×D3)⋊C8—62no—
90#816—32no—
91Dic3⋊C8—62no—
92Dic3⋊C8—62no—
93Dic3⋊C8—64no—
94C8×Dic3—62no—
95C4×C3⋊C8—62no—
96C23×C32#4111yescharacteristic
97C22×C3×D3—21no—
98C2×C32×C4C22×C411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C2×C3⋊Dic3—22no—
105C3×#67—41no—
106C3×#67—41no—
107C2×C3×Dic3—24no—
108C2×C3×Dic3—22no—
109C2×C3×Dic3—21no—
110C3×D12—21no—
111C3×D12—21no—
112C3×C4×D3—41no—
113C3×C4×D3—41no—
114C3×Dic6—21no—
115C3×Dic6—21no—
116C32×C8—41no—
117C3⋊(C3⋊C8)—22no—
118C3×C3⋊C8—22no—
119C3×C3⋊C8—41no—
120#424—91no—
121C2×#104—31no—
122#416—91no—
123#408—91no—
124C2×C4×C8—91no—
125#341—31no—
126#339—91no—
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×D12C4×D311yescharacteristic
146C2×C4×D3—21no—
147C2×Dic6C4×D311yescharacteristic
148C3×M16—21no—
149C3×M16—21no—
150C3×M16—21no—
151C3×M16—21no—
152C3×M16—41no—
153C3×M16—41no—
154C3×M16—61no—
155C3×M16—61no—
156C2×C3×C8—22no—
157C2×C3×C8—21no—
158C2×C3×C8—21no—
159C2×C3×C8—32no—
160C2×C3×C8—61no—
161C2×C3×C8—61no—
162C2×C3×C8—61no—
163C3×C42—32no—
164C3×C42—61no—
165#217—62no—
166#217—61no—
167#217—61no—
168C4⋊Dic3—32no—
169C4⋊Dic3—32no—
170C4⋊Dic3—62no—
171C4×Dic3—21no—
172C4×Dic3—62no—
173C4×Dic3—61no—
174C4×Dic3—61no—
175C4×Dic3#6712yes—
176#208—21no—
177#208—21no—
178C2×C3⋊C8—21no—
179C2×C3⋊C8—21no—
180C2×C3⋊C8—21no—
181C2×C3⋊C8—32no—
182C2×C3⋊C8—32no—
183C2×C3⋊C8—62no—
184C2×C3⋊C8—61no—
185C2×C3⋊C8—61no—
186C2×C3⋊C8—61no—
187C2×C3⋊C8—61no—
188C2×C3⋊C8—121no—
189C2×C3⋊C8—121no—
190C2×C3⋊C8C4×D312yes—
191C22×C32—22no—
192C22×C32C4×D411yescharacteristic
193C22×C32#12311yescharacteristic
194C22×C32#12611yescharacteristic
195C2×C3×D3—41no—
196C2×C3×D3—42no—
197C32×C4#11711yescharacteristic
198C32×C4C4×D411yescharacteristic
199C32×C4#12111yescharacteristic
200C32×C4#12411yescharacteristic
201C3⋊Dic3—42no—
202C3×Dic3—24no—
203C3×Dic3—41no—
204C2×#41—31no—
205C2×M16—31no—
206C2×M16D3211yescharacteristic
207C22×C8—31no—
208C22×C8—91no—
209#117—91no—
210C2×C42—31no—
211C4⋊C8—182no—
212#104—62no—
213#103—92no—
214#102—92no—
215C22⋊C8—182no—
216C4×C8—182no—
217C23×C3—21no—
218C23×C3—61no—
219C23×C3#23711yescharacteristic
220C23×C3#23911yescharacteristic
221C22×D3—21no—
222C3×Q8—61no—
223C3×Q8—61no—
224C3×D4—61no—
225C3×D4—61no—
226C3×D4—121no—
227C3×D4—121no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—64no—
235C2×C3×C4—62no—
236C2×C3×C4—61no—
237C2×C3×C4—121no—
238C2×C3×C4—121no—
239C2×C3×C4C2×C4×D311yescharacteristic
240C2×C3×C4C2×C4×D311yescharacteristic
241C2×C3×C4#23511yescharacteristic
242C2×C3×C4#23511yescharacteristic
243C2×C3×C4#23511yescharacteristic
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4D3×D411yescharacteristic
247C2×C3×C4#23711yescharacteristic
248C2×C3×C4#23711yescharacteristic
249C2×C3×C4#23711yescharacteristic
250C2×C3×C4C2×#6711yescharacteristic
251#67—41no—
252#67—41no—
253C2×Dic3—24no—
254C2×Dic3—22no—
255C2×Dic3—21no—
256C2×Dic3—64no—
257C2×Dic3—62no—
258C2×Dic3—62no—
259D12—21no—
260D12—21no—
261C4×D3—41no—
262C4×D3—41no—
263Dic6—21no—
264Dic6—21no—
265C3×C8—42no—
266C3×C8—41no—
267C3×C8—41no—
268C3×C8—62no—
269C3×C8—121no—
270C3⋊C8—22no—
271C3⋊C8—41no—
272C3⋊C8—62no—
273C3⋊C8—62no—
274C3⋊C8—122no—
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—61no—
288C22×C4—61no—
289C22×C4C2×D3211yescharacteristic
290M16—21no—
291M16—21no—
292M16—61no—
293M16—61no—
294C2×C8—21no—
295C2×C8—32no—
296C2×C8—61no—
297C2×C8—61no—
298C2×C8—61no—
299C2×C8—92no—
300C2×C8—181no—
301C2×C8—181no—
302C4⋊C4—92no—
303C22⋊C4—181no—
304C42—32no—
305C42—61no—
306C42—181no—
307C22×C3—22no—
308C22×C3—22no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3—42no—
313C22×C3—122no—
314C22×C3—121no—
315C22×C3#87911yescharacteristic
316C22×C3#67⋊C411yescharacteristic
317C22×C3#89311yescharacteristic
318C22×C3#89411yescharacteristic
319C22×C3#89811yescharacteristic
320C22×C3#93511yescharacteristic
321C2×D3—41no—
322C2×D3—42no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—64no—
328C3×C4—121no—
329C3×C4#87211yescharacteristic
330C3×C4#87711yescharacteristic
331C3×C4#67⋊C411yescharacteristic
332C3×C4#88411yescharacteristic
333C3×C4#88511yescharacteristic
334C3×C4#88511yescharacteristic
335C3×C4C4×#6711yescharacteristic
336C3×C4#93811yescharacteristic
337Dic3—24no—
338Dic3—41no—
339Dic3—124no—
340Dic3—122no—
341Dic3—122no—
342C32#193711yescharacteristic, complemented, Sylow
343C23—61no—
344C23#379611yescharacteristic
345Q8—61no—
346Q8—61no—
347D4—61no—
348D4—61no—
349D4—121no—
350D4—121no—
351C2×C4—64no—
352C2×C4—62no—
353C2×C4—61no—
354C2×C4—121no—
355C2×C4—121no—
356C2×C4—182no—
357C2×C4#379511yescharacteristic
358C2×C4#379511yescharacteristic
359C2×C4C4×D3211yescharacteristic
360C2×C4#380411yescharacteristic
361C2×C4D3×#6711yescharacteristic
362C2×C4#381111yescharacteristic
363C8—41no—
364C8—62no—
365C8—121no—
366C8—182no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—22no—
372C2×C3—21no—
373C2×C3—41no—
374C2×C3—41no—
375C2×C3—241no—
376C2×C3#466911yescharacteristic
377C2×C3#482412yes—
378C2×C3#489512yes—
379C2×C3#494411yescharacteristic
380D3—81no—
381C22—22no—
382C22—122no—
383C22—121no—
384C22#6385811yescharacteristic
385C22#6388111yescharacteristic
386C22#6388411yescharacteristic
387C4—64no—
388C4—121no—
389C4—362no—
390C4#6387711yescharacteristic
391C4#6387911yescharacteristic
392C4#6391311yescharacteristic
393C4#6395811yescharacteristic
394C3—21no—
395C3#6891811yescharacteristic, complemented
396C3#7037111yescharacteristic, complemented
397C2—21no—
398C2—21no—
399C2—241no—
400C2#1059097712yes—
401C2#1059128111yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C4×D4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1937
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #10592818C2semidirect
5. C2×Dic3×C3⋊C8C2semidirect
6. C3×#4558C2semidirect
7. #10589162C2semidirect
19. #63566C4semidirect
20. #63563C4semidirect
35. #4558D3semidirect
342. C32#1937semidirect
395. C3#68918semidirect
396. C3#70371semidirect

Maximal subgroups

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

subgroupindex
#105928182
C2×C3×#8252
#105910842
#105910712
C2×Dic3×C3⋊C82
C3×#45582
#105891622
#703713
#689183