Finite Group Databasebeta

← C3×#69793 #11789934

Subgroups — C3×#69793 #11789934

Order 1152.

541 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×C32×C4×C8C211yesmaximal, characteristic, complemented
2C3×#5113C211yesmaximal, characteristic
3C3×#5110C211yesmaximal, characteristic
4C3×#5102C211yesmaximal, characteristic, complemented
5C2×C3×#805C211yesmaximal, characteristic
6C3×#4552C211yesmaximal, characteristic, complemented
7C3×#4523C211yesmaximal, characteristic, complemented
8C3×#1937—31nomaximal
9#69793C311yesmaximal, characteristic, direct product factor
10C2×C3×#235C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C32×C4×C8—22no—
18C3×#821C412yescomplemented
19C3×(C2×D3)⋊C8—22no—
20C3×#816C412yescomplemented
21C3×Dic3⋊C8—22no—
22C3×#805—22no—
23C3×#424—31no—
24C2×C3×#104—31no—
25C3×#416—31no—
26C3×#408—31no—
27C2×C3×C4×C8—21no—
28C2×C3×C4×C8D311yescharacteristic, complemented
29C2×C3×C4×C8C2×C311yescharacteristic, complemented
30#5113C2×C311yescharacteristic
31#5110C2×C311yescharacteristic
32#5102C2×C311yescharacteristic, complemented
33C2×#805C2×C311yescharacteristic
34C3×#341—31no—
35C3×#339—31no—
36#4552C2×C311yescharacteristic, complemented
37#4523C2×C311yescharacteristic, complemented
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
48C2×C32×C8—21no—
49C2×C32×C8—21no—
50C2×C32×C8—21no—
51C2×C32×C8—21no—
52C2×C32×C8C2×C412yes—
53C2×C32×C8D412yes—
54C32×C42—21no—
55C32×C42D412yes—
56C3×#217—21no—
57C3×C4⋊Dic3C2×C412yes—
58C3×C4×Dic3—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208—21no—
62C3×#208—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65#1937—31noSylow
66C2×C3×#41—31no—
67C2×#235C22×C311yescharacteristic
68C2×C3×M16—31no—
69C2×C3×M16—31no—
70C22×C3×C8—21no—
71C22×C3×C8—21no—
72C22×C3×C8C2×D311yescharacteristic
73C22×C3×C8C2×D311yescharacteristic
74C22×C3×C8C22×C311yescharacteristic
75C22×C3×C8C22×C311yescharacteristic
76C3×#117—31no—
77C2×C3×C42—21no—
78C2×C3×C42C2×D311yescharacteristic
79C2×C3×C42C22×C311yescharacteristic
80#926C22×C311yescharacteristic
81C2×#208C22×C311yescharacteristic
82C2×#208C22×C311yescharacteristic
83C3×C4⋊C8—62no—
84C3×#104—62no—
85C3×#103—32no—
86C3×#102—32no—
87C3×C22⋊C8—62no—
88C3×C4×C8—24no—
89C3×C4×C8—22no—
90C3×C4×C8—22no—
91#821C3×C412yescomplemented
92(C2×D3)⋊C8—22no—
93#816C3×C412yescomplemented
94Dic3⋊C8—22no—
95#805—22no—
96C23×C32#4111yescharacteristic
97C22×C3×D3—21no—
98C2×C32×C4—24no—
99C2×C32×C4—22no—
100C2×C32×C4C22×C411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C2×C32×C4#4111yescharacteristic
105C2×C32×C4#4111yescharacteristic
106C3×#67—41no—
107C3×#67—41no—
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—22no—
118C3×C3⋊C8—41no—
119C3×C3⋊C8—41no—
120#424—31no—
121C2×#104—31no—
122#416—31no—
123#408—31no—
124C2×C4×C8C3×D311yescharacteristic, complemented
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—22no—
135C22×C3×C4—21no—
136C22×C3×C4—21no—
137C22×C3×C4—21no—
138C22×C3×C4—61no—
139C22×C3×C4C22×D311yescharacteristic
140C22×C3×C4C23×C311yescharacteristic
141C2×#67—21no—
142#235—21no—
143#235—21no—
144#235—21no—
145#235—21no—
146C2×D12C2×C3×C411yescharacteristic
147C2×C4×D3—21no—
148C2×Dic6C2×C3×C411yescharacteristic
149C3×M16—61no—
150C3×M16—61no—
151C3×M16—61no—
152C3×M16—61no—
153C2×C3×C8—22no—
154C2×C3×C8—22no—
155C2×C3×C8—22no—
156C2×C3×C8—22no—
157C2×C3×C8—21no—
158C2×C3×C8—21no—
159C2×C3×C8—21no—
160C2×C3×C8—21no—
161C2×C3×C8—21no—
162C2×C3×C8—21no—
163C2×C3×C8—21no—
164C2×C3×C8—21no—
165C2×C3×C8—22no—
166C2×C3×C8—22no—
167C2×C3×C8—61no—
168C2×C3×C8—61no—
169C2×C3×C8C4×D312yes—
170C2×C3×C8D1212yes—
171C2×C3×C8C2×C3×C412yes—
172C2×C3×C8C3×D412yes—
173C3×C4⋊C4—32no—
174C3×C22⋊C4—61no—
175C3×C42—22no—
176C3×C42—21no—
177C3×C42—21no—
178C3×C42—22no—
179C3×C42—61no—
180C3×C42#6712yes—
181C3×C42C3×D412yes—
182#217—21no—
183C4⋊Dic3C2×C3×C412yes—
184C4×Dic3—21no—
185#208—21no—
186#208—21no—
187#208—21no—
188#208—21no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—21no—
191C22×C32—22no—
192C22×C32C4×D411yescharacteristic
193C22×C32#12311yescharacteristic
194C22×C32#12611yescharacteristic
195C2×C3×D3—41no—
196C2×C3×D3—42no—
197C32×C4—24no—
198C32×C4#11711yescharacteristic
199C32×C4C4×D411yescharacteristic
200C32×C4#12111yescharacteristic
201C32×C4#12411yescharacteristic
202C3×Dic3—41no—
203C3×Dic3—42no—
204C2×#41—31no—
205C2×M16—31no—
206C2×M16—31no—
207C22×C8C2×C3×D311yescharacteristic
208C22×C8C2×C3×D311yescharacteristic
209#117—31no—
210C2×C42C2×C3×D311yescharacteristic
211C4⋊C8—62no—
212#104—62no—
213#103—32no—
214#102—32no—
215C22⋊C8—62no—
216C4×C8—22no—
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—28no—
230C2×C3×C4—24no—
231C2×C3×C4—24no—
232C2×C3×C4—22no—
233C2×C3×C4—22no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—62no—
241C2×C3×C4—61no—
242C2×C3×C4—121no—
243C2×C3×C4—121no—
244C2×C3×C4C2×C4×D311yescharacteristic
245C2×C3×C4C2×D1211yescharacteristic
246C2×C3×C4#23511yescharacteristic
247C2×C3×C4#23511yescharacteristic
248C2×C3×C4#23511yescharacteristic
249C2×C3×C4C2×#6711yescharacteristic
250C2×C3×C4C22×C3×C411yescharacteristic
251C2×C3×C4C2×C3×D411yescharacteristic
252C2×C3×C4C2×C3×D411yescharacteristic
253C2×C3×C4C3×#4111yescharacteristic
254C2×C3×C4C3×#4111yescharacteristic
255C2×C3×C4C3×#4111yescharacteristic
256#67—41no—
257#67—41no—
258C2×Dic3—22no—
259C2×Dic3—21no—
260D12—21no—
261D12—21no—
262C4×D3—41no—
263C4×D3—41no—
264Dic6—21no—
265Dic6—21no—
266C3×C8—24no—
267C3×C8—24no—
268C3×C8—22no—
269C3×C8—22no—
270C3×C8—22no—
271C3×C8—22no—
272C3×C8—121no—
273C3×C8—121no—
274C3⋊C8—41no—
275C3⋊C8—41no—
276C2×C32—21no—
277C2×C32—21no—
278C2×C32#38811yescharacteristic
279C2×C32#44312yes—
280C3×D3—81no—
281#41—61no—
282#41—61no—
283#41—61no—
284#41—61no—
285C2×Q8—31no—
286C2×D4—31no—
287C2×D4—61no—
288C22×C4—21no—
289C22×C4—61no—
290C22×C4C22×C3×D311yescharacteristic
291M16—61no—
292M16—61no—
293M16—61no—
294M16—61no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—61no—
300C2×C8—61no—
301C2×C8C3×C4×D312yes—
302C2×C8C3×D1212yes—
303C4⋊C4—32no—
304C22⋊C4—61no—
305C42—21no—
306C42—61no—
307C42C3×#6712yes—
308C22×C3—24no—
309C22×C3—22no—
310C22×C3—22no—
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—21no—
314C22×C3—121no—
315C22×C3—122no—
316C22×C3C4×D1211yescharacteristic
317C22×C3#87611yescharacteristic
318C22×C3#92911yescharacteristic
319C22×C3C3×C4×D411yescharacteristic
320C22×C3C3×#12311yescharacteristic
321C22×C3C3×#12611yescharacteristic
322C2×D3—41no—
323C2×D3—42no—
324C3×C4—28no—
325C3×C4—24no—
326C3×C4—24no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—121no—
332C3×C4—122no—
333C3×C4#87211yescharacteristic
334C3×C4#87511yescharacteristic
335C3×C4C4×#6711yescharacteristic
336C3×C4#93011yescharacteristic
337C3×C4C3×#11711yescharacteristic
338C3×C4C3×C4×D411yescharacteristic
339C3×C4C3×#12111yescharacteristic
340C3×C4C3×#12411yescharacteristic
341Dic3—41no—
342Dic3—42no—
343C32#193711yescharacteristic, complemented, Sylow
344C23—61no—
345C23C3×#23511yescharacteristic
346Q8—61no—
347Q8—61no—
348D4—61no—
349D4—61no—
350D4—121no—
351D4—121no—
352C2×C4—24no—
353C2×C4—22no—
354C2×C4—62no—
355C2×C4—61no—
356C2×C4—121no—
357C2×C4—121no—
358C2×C4C2×C3×C4×D311yescharacteristic
359C2×C4C2×C3×D1211yescharacteristic
360C2×C4C3×#23511yescharacteristic
361C2×C4C3×#23511yescharacteristic
362C2×C4C3×#23511yescharacteristic
363C2×C4C2×C3×#6711yescharacteristic
364C8—22no—
365C8—22no—
366C8—121no—
367C8—121no—
368C2×C3—22no—
369C2×C3—22no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—22no—
376C2×C3—241no—
377C2×C3#470012yes—
378C2×C3#494011yescharacteristic
379C2×C3C3×#38811yescharacteristic
380C2×C3C3×#44312yes—
381D3—81no—
382C22—22no—
383C22—121no—
384C22—122no—
385C22C3×C4×D1211yescharacteristic
386C22C3×#87611yescharacteristic
387C22C3×#92911yescharacteristic
388C4—24no—
389C4—121no—
390C4—122no—
391C4C3×#87211yescharacteristic
392C4C3×#87511yescharacteristic
393C4C3×C4×#6711yescharacteristic
394C4C3×#93011yescharacteristic
395C3—21no—
396C3#6979311yescharacteristic, direct product factor
397C3C3×#193711yescharacteristic, complemented
398C2—21no—
399C2—21no—
400C2—241no—
401C2C3×#470012yes—
402C2C3×#494011yescharacteristic
subgroupG/H
centerC2×C3×C4C2×D12
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C4×C8C2
socleC22×C32C4×D4
prime radicalC2×C3×#235C22
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×C4×C8D3
hypocenterC3C3×#1937
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C8 ◁ C2×C3×C4×C8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×C8C2semidirect
4. C3×#5102C2semidirect
6. C3×#4552C2semidirect
7. C3×#4523C2semidirect
9. #69793C3direct (N × H)
18. C3×#821C4semidirect
20. C3×#816C4semidirect
28. C2×C3×C4×C8D3semidirect
29. C2×C3×C4×C8C2×C3semidirect
32. #5102C2×C3semidirect
36. #4552C2×C3semidirect
37. #4523C2×C3semidirect
91. #821C3×C4semidirect
93. #816C3×C4semidirect
124. C2×C4×C8C3×D3semidirect
343. C32#1937semidirect
396. C3#69793direct (N × H)
397. C3C3×#1937semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×C82
C3×#51132
C3×#51102
C3×#51022
C2×C3×#8052
C3×#45522
C3×#45232
C3×#19373
#697933