Finite Group Databasebeta

← C3×#70535 #11789931

Subgroups — C3×#70535 #11789931

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
1C32×#424C211yesmaximal, characteristic, complemented
2C2×C3×#825C211yesmaximal, characteristic
3C3×#5110C211yesmaximal, characteristic
4C2×C3×C8×Dic3C211yesmaximal, characteristic, complemented
5C3×#5002C211yesmaximal, characteristic
6C3×#4558C211yesmaximal, characteristic, complemented
7C3×#4532C211yesmaximal, characteristic, complemented
8C3×#1937—31nomaximal
9#70535C311yesmaximal, characteristic, direct product factor
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C32×#117C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C32×C4⋊C8—22no—
18C3×#825—22no—
19C3×(C2×D3)⋊C8—22no—
20C3×C8×Dic3—22no—
21C3×#810C412yescomplemented
22C3×#809C412yescomplemented
23C3×#424—21no—
24C3×#424D311yescharacteristic, complemented
25C3×#424C2×C311yescharacteristic, complemented
26C2×C3×#104—31no—
27C3×#416—31no—
28C3×#408—31no—
29C2×C3×C4×C8—31no—
30C2×#825C2×C311yescharacteristic
31#5110C2×C311yescharacteristic
32C2×C8×Dic3C2×C311yescharacteristic, complemented
33#5002C2×C311yescharacteristic
34C3×#341—31no—
35C3×#339—31no—
36#4558C2×C311yescharacteristic, complemented
37#4532C2×C311yescharacteristic, 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×M16—21no—
49C32×M16—21no—
50C2×C32×C8—21no—
51C2×C32×C8—21no—
52C2×C32×C8—21no—
53C2×C32×C8D412yes—
54C32×C4⋊C4C2×C412yes—
55C32×C22⋊C4—21no—
56C32×C42—21no—
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—31noSylow
66C2×C3×#41—31no—
67C2×#235C22×C311yescharacteristic
68C2×C3×M16—21no—
69C2×C3×M16—31no—
70C2×C3×M16C2×D311yescharacteristic
71C2×C3×M16C22×C311yescharacteristic
72C22×C3×C8—21no—
73C22×C3×C8—31no—
74C22×C3×C8C2×D311yescharacteristic
75C22×C3×C8C22×C311yescharacteristic
76C3×#117—21no—
77C3×#117C2×D311yescharacteristic
78C3×#117C22×C311yescharacteristic
79C2×C3×C42—31no—
80C2×C4×Dic3C22×C311yescharacteristic
81C2×#208C22×C311yescharacteristic
82C22×C3⋊C8C22×C311yescharacteristic
83C3×C4⋊C8—24no—
84C3×C4⋊C8—22no—
85C3×C4⋊C8—22no—
86C3×#104—62no—
87C3×#103—32no—
88C3×#102—32no—
89C3×C22⋊C8—62no—
90C3×C4×C8—62no—
91#825—22no—
92(C2×D3)⋊C8—22no—
93C8×Dic3—22no—
94#810C3×C412yescomplemented
95#809C3×C412yescomplemented
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—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—22no—
117C32×C8—41no—
118C3×C3⋊C8—22no—
119C3×C3⋊C8—41no—
120#424C3×D311yescharacteristic, complemented
121C2×#104—31no—
122#416—31no—
123#408—31no—
124C2×C4×C8—31no—
125#341—31no—
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×C4C23×C311yescharacteristic
139C2×#67—21no—
140C22×Dic3—21no—
141#235—21no—
142#235—21no—
143#235—21no—
144#235—21no—
145C2×D12C2×C3×C411yescharacteristic
146C2×C4×D3—21no—
147C2×Dic6C2×C3×C411yescharacteristic
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—21no—
157C2×C3×C8—21no—
158C2×C3×C8—21no—
159C2×C3×C8—21no—
160C2×C3×C8—22no—
161C2×C3×C8—21no—
162C2×C3×C8—21no—
163C2×C3×C8—22no—
164C2×C3×C8—32no—
165C2×C3×C8—41no—
166C2×C3×C8—41no—
167C2×C3×C8—61no—
168C2×C3×C8—61no—
169C2×C3×C8—61no—
170C2×C3×C8#6712yes—
171C2×C3×C8C3×D412yes—
172C3×C4⋊C4—22no—
173C3×C4⋊C4C4×D312yes—
174C3×C4⋊C4C2×C3×C412yes—
175C3×C22⋊C4—22no—
176C3×C22⋊C4—21no—
177C3×C22⋊C4—21no—
178C3×C42—22no—
179C3×C42—21no—
180C3×C42—21no—
181C3×C42—32no—
182C3×C42—61no—
183C4×Dic3—21no—
184C4×Dic3C3×D412yes—
185#208—21no—
186#208—21no—
187C2×C3⋊C8—21no—
188C2×C3⋊C8—21no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8C2×C3×C412yes—
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—24no—
203C3×Dic3—41no—
204C2×#41—31no—
205C2×M16—31no—
206C2×M16C2×C3×D311yescharacteristic
207C22×C8—31no—
208C22×C8C2×C3×D311yescharacteristic
209#117C2×C3×D311yescharacteristic
210C2×C42—31no—
211C4⋊C8—22no—
212#104—62no—
213#103—32no—
214#102—32no—
215C22⋊C8—62no—
216C4×C8—62no—
217C23×C3—21no—
218C23×C3—61no—
219C23×C3#23511yescharacteristic
220C23×C3C3×#4111yescharacteristic
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—64no—
238C2×C3×C4—62no—
239C2×C3×C4—61no—
240C2×C3×C4—121no—
241C2×C3×C4—121no—
242C2×C3×C4C2×C4×D311yescharacteristic
243C2×C3×C4D3×D411yescharacteristic
244C2×C3×C4#23711yescharacteristic
245C2×C3×C4#23911yescharacteristic
246C2×C3×C4#23911yescharacteristic
247C2×C3×C4C2×#6711yescharacteristic
248C2×C3×C4C22×C3×C411yescharacteristic
249C2×C3×C4C2×C3×D411yescharacteristic
250C2×C3×C4C2×C3×D411yescharacteristic
251C2×C3×C4C3×#4111yescharacteristic
252C2×C3×C4C3×#4111yescharacteristic
253C2×C3×C4C3×#4111yescharacteristic
254#67—41no—
255#67—41no—
256C2×Dic3—24no—
257C2×Dic3—22no—
258C2×Dic3—21no—
259D12—21no—
260D12—21no—
261C4×D3—41no—
262C4×D3—41no—
263Dic6—21no—
264Dic6—21no—
265C3×C8—22no—
266C3×C8—22no—
267C3×C8—42no—
268C3×C8—42no—
269C3×C8—41no—
270C3×C8—41no—
271C3×C8—62no—
272C3×C8—121no—
273C3⋊C8—22no—
274C3⋊C8—41no—
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×C4C22×C3×D311yescharacteristic
290M16—21no—
291M16—21no—
292M16—61no—
293M16—61no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—32no—
298C2×C8—61no—
299C2×C8—61no—
300C2×C8—61no—
301C2×C8C3×#6712yes—
302C4⋊C4C3×C4×D312yes—
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—122no—
314C22×C3—121no—
315C22×C3#89411yescharacteristic
316C22×C3#89811yescharacteristic
317C22×C3C4×#6711yescharacteristic
318C22×C3C3×C4×D411yescharacteristic
319C22×C3C3×#12311yescharacteristic
320C22×C3C3×#12611yescharacteristic
321C2×D3—41no—
322C2×D3—42no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—44no—
328C3×C4—42no—
329C3×C4—42no—
330C3×C4—64no—
331C3×C4—121no—
332C3×C4#89211yescharacteristic
333C3×C4#89311yescharacteristic
334C3×C4#93911yescharacteristic
335C3×C4#94711yescharacteristic
336C3×C4C3×#11711yescharacteristic
337C3×C4C3×C4×D411yescharacteristic
338C3×C4C3×#12111yescharacteristic
339C3×C4C3×#12411yescharacteristic
340Dic3—24no—
341Dic3—41no—
342C32#193711yescharacteristic, complemented, Sylow
343C23—61no—
344C23C3×#23511yescharacteristic
345Q8—61no—
346Q8—61no—
347D4—61no—
348D4—61no—
349D4—121no—
350D4—121no—
351C2×C4—22no—
352C2×C4—64no—
353C2×C4—62no—
354C2×C4—61no—
355C2×C4—121no—
356C2×C4—121no—
357C2×C4C2×C3×C4×D311yescharacteristic
358C2×C4C3×D3×D411yescharacteristic
359C2×C4C3×#23711yescharacteristic
360C2×C4C3×#23911yescharacteristic
361C2×C4C3×#23911yescharacteristic
362C2×C4C2×C3×#6711yescharacteristic
363C8—22no—
364C8—41no—
365C8—62no—
366C8—121no—
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#499011yescharacteristic
377C2×C3#514412yes—
378C2×C3C3×#38811yescharacteristic
379C2×C3C3×#44312yes—
380D3—81no—
381C22—22no—
382C22—121no—
383C22—122no—
384C22C3×#89411yescharacteristic
385C22C3×#89811yescharacteristic
386C22C3×C4×#6711yescharacteristic
387C4—42no—
388C4—64no—
389C4—121no—
390C4C3×#89211yescharacteristic
391C4C3×#89311yescharacteristic
392C4C3×#93911yescharacteristic
393C4C3×#94711yescharacteristic
394C3—21no—
395C3#7053511yescharacteristic, direct product factor
396C3C3×#193711yescharacteristic, complemented
397C2—21no—
398C2—21no—
399C2—241no—
400C2C3×#499011yescharacteristic
401C2C3×#514412yes—
subgroupG/H
centerC2×C3×C4C2×#67
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#424C2
socleC22×C32C4×D4
prime radicalC2×C3×#235C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#424D3
hypocenterC3C3×#1937
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C8 ◁ C3×#424

Complements

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

NH ≅ G/Ntype
1. C32×#424C2semidirect
4. C2×C3×C8×Dic3C2semidirect
6. C3×#4558C2semidirect
7. C3×#4532C2semidirect
9. #70535C3direct (N × H)
21. C3×#810C4semidirect
22. C3×#809C4semidirect
24. C3×#424D3semidirect
25. C3×#424C2×C3semidirect
32. C2×C8×Dic3C2×C3semidirect
36. #4558C2×C3semidirect
37. #4532C2×C3semidirect
94. #810C3×C4semidirect
95. #809C3×C4semidirect
120. #424C3×D3semidirect
342. C32#1937semidirect
395. C3#70535direct (N × H)
396. C3C3×#1937semidirect

Maximal subgroups

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

subgroupindex
C32×#4242
C2×C3×#8252
C3×#51102
C2×C3×C8×Dic32
C3×#50022
C3×#45582
C3×#45322
C3×#19373
#705353