Finite Group Databasebeta

← C3×#70371 #11789925

Subgroups — C3×#70371 #11789925

Order 1152.

545 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#104C211yesmaximal, characteristic
2C3×#5234C211yesmaximal, characteristic
3C3×#5233C211yesmaximal, characteristic
4C3×#5119C211yesmaximal, characteristic, complemented
5C2×C3×C4×C3⋊C8C211yesmaximal, characteristic, complemented
6C3×#4558C211yesmaximal, characteristic, complemented
7C3×#4523C211yesmaximal, characteristic, complemented
8C3×#1937—31nomaximal
9#70371C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C22×C3×C3⋊C8C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C32×#104—22no—
18C3×#835C412yescomplemented
19C3×#832C412yescomplemented
20C3×#830—22no—
21C3×Dic3⋊C8—22no—
22C3×C4×C3⋊C8—22no—
23C3×#424—31no—
24C2×C3×#104—21no—
25C2×C3×#104D311yescharacteristic
26C2×C3×#104C2×C311yescharacteristic
27C3×#416—31no—
28C3×#408—31no—
29C2×C3×C4×C8—31no—
30#5234C2×C311yescharacteristic
31#5233C2×C311yescharacteristic
32#5119C2×C311yescharacteristic, complemented
33C2×C4×C3⋊C8C2×C311yescharacteristic, complemented
34C3×#341—31no—
35C3×#339—31no—
36#4558C2×C311yescharacteristic, complemented
37#4523C2×C311yescharacteristic, complemented
38C32×#41—21no—
39C32×#41—21no—
40C32×#41—21no—
41C32×#41—21no—
42C2×C32×Q8C2×C411yescharacteristic
43C2×C32×D4—21no—
44C2×C32×D4C2×C411yescharacteristic
45C22×C32×C4—21no—
46C22×C32×C4—21no—
47C22×C32×C4C2311yescharacteristic
48C32×M16—21no—
49C32×M16—21no—
50C2×C32×C8—21no—
51C32×C42—21no—
52C32×C42D412yes—
53C3×#217—21no—
54C3×C4⋊Dic3C2×C412yes—
55C3×C4×Dic3—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—31noSylow
66C2×C3×#41—21no—
67C2×C3×#41C2×D311yescharacteristic
68C2×C3×#41C22×C311yescharacteristic
69C2×C3×M16—21no—
70C2×C3×M16—31no—
71C2×C3×M16C2×D311yescharacteristic
72C2×C3×M16C22×C311yescharacteristic
73C22×C3×C8—31no—
74C22×C3×C8—31no—
75C3×#117—31no—
76C2×C3×C42—21no—
77C2×C3×C42C2×D311yescharacteristic
78C2×C3×C42C22×C311yescharacteristic
79#926C22×C311yescharacteristic
80C2×#208C22×C311yescharacteristic
81C22×C3⋊C8C22×C311yescharacteristic
82C22×C3⋊C8C22×C311yescharacteristic
83C3×C4⋊C8—62no—
84C3×#104—24no—
85C3×#104—22no—
86C3×#104—22no—
87C3×#103—32no—
88C3×#102—32no—
89C3×C22⋊C8—62no—
90C3×C4×C8—62no—
91#835C3×C412yescomplemented
92#832C3×C412yescomplemented
93#830—22no—
94Dic3⋊C8—22no—
95C4×C3⋊C8—22no—
96C23×C32—21no—
97C23×C32#4111yescharacteristic
98C32×Q8—21no—
99C32×Q8—21no—
100C32×D4—21no—
101C32×D4—21no—
102C32×D4—41no—
103C32×D4—41no—
104C2×C32×C4—24no—
105C2×C32×C4—22no—
106C2×C32×C4—21no—
107C2×C32×C4—41no—
108C2×C32×C4—41no—
109C2×C32×C4C22×C411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C3×Dic3—22no—
116C32×C8—41no—
117C3×C3⋊C8—22no—
118C3×C3⋊C8—22no—
119C3×C3⋊C8—41no—
120#424—31no—
121C2×#104C3×D311yescharacteristic
122#416—31no—
123#408—31no—
124C2×C4×C8—31no—
125#341—31no—
126#339—31no—
127C3×#41—22no—
128C3×#41—22no—
129C3×#41—21no—
130C3×#41—21no—
131C3×#41—21no—
132C3×#41—21no—
133C3×#41—21no—
134C3×#41—21no—
135C3×#41—21no—
136C3×#41—21no—
137C3×#41—41no—
138C3×#41—41no—
139C2×C3×Q8—21no—
140C2×C3×Q8C4×D311yescharacteristic
141C2×C3×Q8C2×C3×C411yescharacteristic
142C2×C3×D4—21no—
143C2×C3×D4—21no—
144C2×C3×D4—21no—
145C2×C3×D4—41no—
146C2×C3×D4C4×D311yescharacteristic
147C2×C3×D4C2×C3×C411yescharacteristic
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—41no—
154C22×C3×C4—41no—
155C22×C3×C4C22×D311yescharacteristic
156C22×C3×C4C23×C311yescharacteristic
157C3×M16—22no—
158C3×M16—21no—
159C3×M16—21no—
160C3×M16—21no—
161C3×M16—21no—
162C3×M16—41no—
163C3×M16—61no—
164C3×M16—61no—
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C2×C3×C8—32no—
168C2×C3×C8—32no—
169C2×C3×C8—41no—
170C2×C3×C8—61no—
171C2×C3×C8—61no—
172C2×C3×C8—61no—
173C2×C3×C8—61no—
174C2×C3×C8—61no—
175C3×C4⋊C4—32no—
176C3×C22⋊C4—61no—
177C3×C42—21no—
178C3×C42—21no—
179C3×C42—22no—
180C3×C42—41no—
181C3×C42—61no—
182C3×C42#6712yes—
183C3×C42C3×D412yes—
184#217—21no—
185C4⋊Dic3C2×C3×C412yes—
186C4×Dic3—21no—
187#208—21no—
188#208—21no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8C2×C3×C412yes—
195C2×C3⋊C8C3×D412yes—
196C22×C32—22no—
197C22×C32—41no—
198C22×C32—42no—
199C22×C32C4×D411yescharacteristic
200C22×C32#12311yescharacteristic
201C22×C32#12611yescharacteristic
202C32×C4—24no—
203C32×C4—41no—
204C32×C4#11711yescharacteristic
205C32×C4C4×D411yescharacteristic
206C32×C4#12111yescharacteristic
207C32×C4#12411yescharacteristic
208C3×Dic3—42no—
209C2×#41C2×C3×D311yescharacteristic
210C2×M16—31no—
211C2×M16C2×C3×D311yescharacteristic
212C22×C8—31no—
213C22×C8—31no—
214#117—31no—
215C2×C42C2×C3×D311yescharacteristic
216C4⋊C8—62no—
217#104—22no—
218#103—32no—
219#102—32no—
220C22⋊C8—62no—
221C4×C8—62no—
222C23×C3—21no—
223C23×C3—21no—
224C23×C3—21no—
225C23×C3—41no—
226C23×C3#23711yescharacteristic
227C23×C3C3×#4111yescharacteristic
228C3×Q8—22no—
229C3×Q8—21no—
230C3×Q8—21no—
231C3×Q8—21no—
232C3×Q8—21no—
233C3×Q8—41no—
234C3×D4—22no—
235C3×D4—21no—
236C3×D4—21no—
237C3×D4—21no—
238C3×D4—21no—
239C3×D4—41no—
240C3×D4—42no—
241C3×D4—42no—
242C3×D4—41no—
243C3×D4—41no—
244C3×D4—41no—
245C3×D4—41no—
246C2×C3×C4—24no—
247C2×C3×C4—24no—
248C2×C3×C4—22no—
249C2×C3×C4—22no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—42no—
259C2×C3×C4—41no—
260C2×C3×C4—44no—
261C2×C3×C4—42no—
262C2×C3×C4—42no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—62no—
268C2×C3×C4C2×C4×D311yescharacteristic
269C2×C3×C4#23511yescharacteristic
270C2×C3×C4D3×D411yescharacteristic
271C2×C3×C4#23711yescharacteristic
272C2×C3×C4#23711yescharacteristic
273C2×C3×C4C2×#6711yescharacteristic
274C2×C3×C4C22×C3×C411yescharacteristic
275C2×C3×C4C2×C3×D411yescharacteristic
276C2×C3×C4C2×C3×D411yescharacteristic
277C2×C3×C4C3×#4111yescharacteristic
278C2×C3×C4C3×#4111yescharacteristic
279C2×C3×C4C3×#4111yescharacteristic
280C2×Dic3—22no—
281C3×C8—42no—
282C3×C8—41no—
283C3×C8—41no—
284C3×C8—62no—
285C3×C8—62no—
286C3×C8—121no—
287C3⋊C8—22no—
288C3⋊C8—22no—
289C3⋊C8—41no—
290C2×C32—21no—
291C2×C32—21no—
292C2×C32—81no—
293C2×C32#38811yescharacteristic
294C2×C32#44312yes—
295#41—21no—
296#41—21no—
297#41—21no—
298#41—21no—
299C2×Q8C3×C4×D311yescharacteristic
300C2×D4—21no—
301C2×D4C3×C4×D311yescharacteristic
302C22×C4—21no—
303C22×C4—21no—
304C22×C4C22×C3×D311yescharacteristic
305M16—21no—
306M16—21no—
307M16—61no—
308M16—61no—
309C2×C8—21no—
310C2×C8—32no—
311C2×C8—32no—
312C2×C8—61no—
313C2×C8—61no—
314C2×C8—61no—
315C2×C8—61no—
316C2×C8—61no—
317C4⋊C4—32no—
318C22⋊C4—61no—
319C42—21no—
320C42—61no—
321C42C3×#6712yes—
322C22×C3—22no—
323C22×C3—22no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—42no—
328C22×C3—42no—
329C22×C3—41no—
330C22×C3—41no—
331C22×C3—42no—
332C22×C3—42no—
333C22×C3—82no—
334C22×C3#87911yescharacteristic
335C22×C3#67⋊C411yescharacteristic
336C22×C3#93511yescharacteristic
337C22×C3C3×C4×D411yescharacteristic
338C22×C3C3×#12311yescharacteristic
339C22×C3C3×#12611yescharacteristic
340C3×C4—24no—
341C3×C4—24no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—44no—
347C3×C4—42no—
348C3×C4—41no—
349C3×C4—41no—
350C3×C4—122no—
351C3×C4#87711yescharacteristic
352C3×C4#88511yescharacteristic
353C3×C4C4×#6711yescharacteristic
354C3×C4#93811yescharacteristic
355C3×C4C3×#11711yescharacteristic
356C3×C4C3×C4×D411yescharacteristic
357C3×C4C3×#12111yescharacteristic
358C3×C4C3×#12411yescharacteristic
359Dic3—42no—
360C32#193711yescharacteristic, complemented, Sylow
361C23—21no—
362C23C3×#23711yescharacteristic
363Q8—21no—
364Q8—21no—
365D4—21no—
366D4—21no—
367D4—41no—
368D4—41no—
369C2×C4—24no—
370C2×C4—22no—
371C2×C4—21no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—62no—
375C2×C4C2×C3×C4×D311yescharacteristic
376C2×C4C3×#23511yescharacteristic
377C2×C4C3×D3×D411yescharacteristic
378C2×C4C3×#23711yescharacteristic
379C2×C4C3×#23711yescharacteristic
380C2×C4C2×C3×#6711yescharacteristic
381C8—41no—
382C8—62no—
383C8—62no—
384C8—121no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—22no—
391C2×C3—41no—
392C2×C3—41no—
393C2×C3—82no—
394C2×C3—81no—
395C2×C3—81no—
396C2×C3#482412yes—
397C2×C3#494411yescharacteristic
398C2×C3C3×#38811yescharacteristic
399C2×C3C3×#44312yes—
400C22—22no—
401C22—41no—
402C22—42no—
403C22C3×#87911yescharacteristic
404C22C3×#67⋊C411yescharacteristic
405C22C3×#93511yescharacteristic
406C4—24no—
407C4—41no—
408C4—122no—
409C4C3×#87711yescharacteristic
410C4C3×#88511yescharacteristic
411C4C3×C4×#6711yescharacteristic
412C4C3×#93811yescharacteristic
413C3—21no—
414C3#7037111yescharacteristic, direct product factor
415C3C3×#193711yescharacteristic, complemented
416C2—21no—
417C2—21no—
418C2—81no—
419C2C3×#482412yes—
420C2C3×#494411yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#104C2
socleC22×C32C4×D4
prime radicalC2×C32×#41C22
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#104D3
hypocenterC3C3×#1937
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C2×C3×#104

Complements

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

NH ≅ G/Ntype
4. C3×#5119C2semidirect
5. C2×C3×C4×C3⋊C8C2semidirect
6. C3×#4558C2semidirect
7. C3×#4523C2semidirect
9. #70371C3direct (N × H)
18. C3×#835C4semidirect
19. C3×#832C4semidirect
32. #5119C2×C3semidirect
33. C2×C4×C3⋊C8C2×C3semidirect
36. #4558C2×C3semidirect
37. #4523C2×C3semidirect
91. #835C3×C4semidirect
92. #832C3×C4semidirect
360. C32#1937semidirect
414. C3#70371direct (N × H)
415. C3C3×#1937semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1042
C3×#52342
C3×#52332
C3×#51192
C2×C3×C4×C3⋊C82
C3×#45582
C3×#45232
C3×#19373
#703713