Finite Group Databasebeta

← C3×#71597 #11774304

Subgroups — C3×#71597 #11774304

Order 1152.

837 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic
2C3×#4925C211yesmaximal, characteristic, complemented
3C3×#4925C211yesmaximal, characteristic, complemented
4C3×D4⋊(C3⋊C8)C214yesmaximal, complemented
5C3×#1478—31nomaximal
6#71597C311yesmaximal, characteristic, direct product factor
7C22×C32×D4C411yescharacteristic
8C23×C32×C4—21no—
9C32×C4×D4—21no—
10C32×C4×D4—21no—
11C32×C4×D4C412yes—
12C32×C4×D4C2212yes—
13C2×C32×C4⋊C4C411yescharacteristic
14C2×C32×C22⋊C4—21no—
15C2×C32×C42C2211yescharacteristic
16C3×#830—21no—
17C3×#830—21no—
18C3×C4⋊(C3⋊C8)—21no—
19C3×C4⋊(C3⋊C8)C2212yescomplemented
20C3×C4×C3⋊C8—21no—
21C3×C4×C3⋊C8C2212yescomplemented
22C2×C3×C4×D4—21no—
23C2×C3×C4×D4D311yescharacteristic
24C2×C3×C4×D4C2×C311yescharacteristic
25C3×#431—31no—
26C3×#431—31no—
27#4925C2×C311yescharacteristic, complemented
28#4925C2×C311yescharacteristic, complemented
29C3×D4⋊C8—34no—
30D4⋊(C3⋊C8)C2×C314yescomplemented
31C24×C32—21no—
32C2×C32×D4—21no—
33C2×C32×D4—22no—
34C2×C32×D4C814yescomplemented
35C2×C32×D4C2×C412yes—
36C22×C32×C4—21no—
37C22×C32×C4—22no—
38C22×C32×C4—22no—
39C22×C32×C4—44no—
40C22×C32×C4C2×C411yescharacteristic
41C22×C32×C4D411yescharacteristic
42C22×C32×C4D411yescharacteristic
43C32×C4⋊C4—21no—
44C32×C4⋊C4C2×C412yes—
45C32×C22⋊C4—22no—
46C32×C22⋊C4—22no—
47C32×C42C2×C411yescharacteristic
48C32×C42D411yescharacteristic
49C32×C42D411yescharacteristic
50C32×C42C2311yescharacteristic
51C2×C3×C3⋊C8—22no—
52C2×C3×C3⋊C8—22no—
53#1478—31noSylow
54C22×C3×D4—21no—
55C22×C3×D4Dic311yescharacteristic
56C22×C3×D4C3×C411yescharacteristic
57C23×C3×C4—22no—
58C23×C3×C4—21no—
59C23×C3×C4—21no—
60C3×C4×D4—22no—
61C3×C4×D4—22no—
62C3×C4×D4—21no—
63C3×C4×D4—21no—
64C3×C4×D4—21no—
65C3×C4×D4—21no—
66C3×C4×D4—22no—
67C3×C4×D4—22no—
68C3×C4×D4Dic312yes—
69C3×C4×D4C3×C412yes—
70C3×C4×D4C2×D312yes—
71C3×C4×D4C22×C312yes—
72C2×C3×C4⋊C4—21no—
73C2×C3×C4⋊C4Dic311yescharacteristic
74C2×C3×C4⋊C4C3×C411yescharacteristic
75C2×C3×C22⋊C4—22no—
76C2×C3×C22⋊C4—21no—
77C2×C3×C22⋊C4—21no—
78C2×C3×C42—21no—
79C2×C3×C42C2×D311yescharacteristic
80C2×C3×C42C22×C311yescharacteristic
81C3×C4⋊C8—32no—
82C3×C4⋊C8—61no—
83C3×C22⋊C8—61no—
84C3×C22⋊C8—61no—
85C3×C4×C8—32no—
86C3×C4×C8—61no—
87#830—21no—
88#830—21no—
89C4⋊(C3⋊C8)—21no—
90C4⋊(C3⋊C8)C22×C312yescomplemented
91C4×C3⋊C8—21no—
92C4×C3⋊C8C22×C312yescomplemented
93C23×C32—24no—
94C23×C32—22no—
95C23×C32—42no—
96C23×C32—42no—
97C23×C32C22⋊C411yescharacteristic
98C32×D4—24no—
99C32×D4—22no—
100C32×D4C2×C814yes—
101C2×C32×C4—22no—
102C2×C32×C4—22no—
103C2×C32×C4—41no—
104C2×C32×C4—44no—
105C2×C32×C4—42no—
106C2×C32×C4—44no—
107C2×C32×C4C22⋊C411yescharacteristic
108C2×C32×C4C22⋊C411yescharacteristic
109C2×C32×C4C22⋊C411yescharacteristic
110C2×C32×C4C2×C812yes—
111C2×C32×C4M1612yes—
112C2×C32×C4C22×C411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C3×C3⋊C8—42no—
116C3×C3⋊C8—42no—
117C2×C4×D4C3×D311yescharacteristic
118#431—31no—
119#431—31no—
120D4⋊C8—34no—
121C24×C3—22no—
122C24×C3—21no—
123C24×C3—21no—
124C2×C3×D4—22no—
125C2×C3×D4—24no—
126C2×C3×D4—22no—
127C2×C3×D4—21no—
128C2×C3×D4—21no—
129C2×C3×D4—22no—
130C2×C3×D4—24no—
131C2×C3×D4—22no—
132C2×C3×D4C3⋊C814yescomplemented
133C2×C3×D4C3×C814yescomplemented
134C2×C3×D4C2×Dic312yes—
135C2×C3×D4C2×C3×C412yes—
136C22×C3×C4—22no—
137C22×C3×C4—24no—
138C22×C3×C4—24no—
139C22×C3×C4—21no—
140C22×C3×C4—21no—
141C22×C3×C4—22no—
142C22×C3×C4—22no—
143C22×C3×C4—22no—
144C22×C3×C4—22no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4—48no—
149C22×C3×C4—44no—
150C22×C3×C4—44no—
151C22×C3×C4C2×Dic311yescharacteristic
152C22×C3×C4#6711yescharacteristic
153C22×C3×C4#6711yescharacteristic
154C22×C3×C4C2×C3×C411yescharacteristic
155C22×C3×C4C3×D411yescharacteristic
156C22×C3×C4C3×D411yescharacteristic
157C2×C3×C8—62no—
158C2×C3×C8—62no—
159C3×C4⋊C4—22no—
160C3×C4⋊C4—21no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—22no—
163C3×C4⋊C4C2×Dic312yes—
164C3×C4⋊C4C2×C3×C412yes—
165C3×C22⋊C4—24no—
166C3×C22⋊C4—24no—
167C3×C22⋊C4—22no—
168C3×C22⋊C4—22no—
169C3×C22⋊C4—22no—
170C3×C22⋊C4—22no—
171C3×C42—21no—
172C3×C42—21no—
173C3×C42—21no—
174C3×C42—21no—
175C3×C42C2×Dic311yescharacteristic
176C3×C42#6711yescharacteristic
177C3×C42#6711yescharacteristic
178C3×C42C2×C3×C411yescharacteristic
179C3×C42C3×D411yescharacteristic
180C3×C42C3×D411yescharacteristic
181C3×C42C22×D311yescharacteristic
182C3×C42C23×C311yescharacteristic
183C2×C3⋊C8—22no—
184C2×C3⋊C8—22no—
185C22×C32—21no—
186C22×C32—21no—
187C22×C32—24no—
188C22×C32—48no—
189C22×C32—42no—
190C22×C32—42no—
191C22×C32C22⋊C812yes—
192C22×C32C2×C22⋊C411yescharacteristic
193C32×C4—21no—
194C32×C4—21no—
195C32×C4—21no—
196C32×C4—42no—
197C32×C4C22⋊C812yes—
198C32×C4C22×C811yescharacteristic
199C32×C4C2×M1611yescharacteristic
200C32×C4AGL(1,ℤ/8)12yes—
201C22×D4C3×Dic311yescharacteristic
202C23×C4—21no—
203C4×D4—21no—
204C4×D4—21no—
205C4×D4C3×Dic312yes—
206C4×D4C2×C3×D312yes—
207C2×C4⋊C4C3×Dic311yescharacteristic
208C2×C22⋊C4—21no—
209C2×C42C2×C3×D311yescharacteristic
210C4⋊C8—32no—
211C4⋊C8—61no—
212C22⋊C8—61no—
213C22⋊C8—61no—
214C4×C8—32no—
215C4×C8—61no—
216C23×C3—24no—
217C23×C3—28no—
218C23×C3—24no—
219C23×C3—24no—
220C23×C3—22no—
221C23×C3—22no—
222C23×C3—21no—
223C23×C3—44no—
224C23×C3—42no—
225C23×C3—42no—
226C23×C3—44no—
227C23×C3—42no—
228C23×C3—42no—
229C23×C3#21711yescharacteristic
230C23×C3C3×C22⋊C411yescharacteristic
231C3×D4—24no—
232C3×D4—28no—
233C3×D4—24no—
234C3×D4—24no—
235C3×D4—22no—
236C3×D4—22no—
237C3×D4—24no—
238C3×D4C2×C3⋊C814yes—
239C3×D4C2×C3×C814yes—
240C2×C3×C4—24no—
241C2×C3×C4—22no—
242C2×C3×C4—22no—
243C2×C3×C4—24no—
244C2×C3×C4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4—48no—
257C2×C3×C4—44no—
258C2×C3×C4—44no—
259C2×C3×C4—48no—
260C2×C3×C4—42no—
261C2×C3×C4—44no—
262C2×C3×C4—42no—
263C2×C3×C4—42no—
264C2×C3×C4—44no—
265C2×C3×C4—44no—
266C2×C3×C4C2×C3⋊C812yes—
267C2×C3×C4#20812yes—
268C2×C3×C4#21711yescharacteristic
269C2×C3×C4#21711yescharacteristic
270C2×C3×C4#21711yescharacteristic
271C2×C3×C4C3×C22⋊C411yescharacteristic
272C2×C3×C4C3×C22⋊C411yescharacteristic
273C2×C3×C4C3×C22⋊C411yescharacteristic
274C2×C3×C4C2×C3×C812yes—
275C2×C3×C4C3×M1612yes—
276C2×C3×C4C22×Dic311yescharacteristic
277C2×C3×C4C2×#6711yescharacteristic
278C2×C3×C4C2×#6711yescharacteristic
279C2×C3×C4C22×C3×C411yescharacteristic
280C2×C3×C4C2×C3×D411yescharacteristic
281C2×C3×C4C2×C3×D411yescharacteristic
282C3×C8—122no—
283C3×C8—122no—
284C3⋊C8—42no—
285C3⋊C8—42no—
286C2×C32—22no—
287C2×C32—44no—
288C2×C32C2×C22⋊C811yescharacteristic
289C2×C32#41811yescharacteristic
290C2×C32#42111yescharacteristic
291C24—21no—
292C2×D4—22no—
293C2×D4—21no—
294C2×D4C3×C3⋊C814yescomplemented
295C2×D4C2×C3×Dic312yes—
296C22×C4—21no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—44no—
300C22×C4C2×C3×Dic311yescharacteristic
301C22×C4C3×#6711yescharacteristic
302C22×C4C3×#6711yescharacteristic
303C2×C8—62no—
304C2×C8—62no—
305C4⋊C4—21no—
306C4⋊C4C2×C3×Dic312yes—
307C22⋊C4—22no—
308C22⋊C4—22no—
309C42C2×C3×Dic311yescharacteristic
310C42C3×#6711yescharacteristic
311C42C3×#6711yescharacteristic
312C42C22×C3×D311yescharacteristic
313C22×C3—22no—
314C22×C3—22no—
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—28no—
320C22×C3—24no—
321C22×C3—24no—
322C22×C3—21no—
323C22×C3—22no—
324C22×C3—44no—
325C22×C3—416no—
326C22×C3—48no—
327C22×C3—48no—
328C22×C3—44no—
329C22×C3—42no—
330C22×C3—42no—
331C22×C3—42no—
332C22×C3—42no—
333C22×C3#83012yes—
334C22×C3C3×C22⋊C812yes—
335C22×C3C2×#21711yescharacteristic
336C22×C3C2×C3×C22⋊C411yescharacteristic
337C3×C4—22no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—22no—
347C3×C4—22no—
348C3×C4—41no—
349C3×C4—41no—
350C3×C4—44no—
351C3×C4—42no—
352C3×C4—42no—
353C3×C4#83012yes—
354C3×C4C3×C22⋊C812yes—
355C3×C4C22×C3⋊C811yescharacteristic
356C3×C4C2×#20811yescharacteristic
357C3×C4#93212yes—
358C3×C4C22×C3×C811yescharacteristic
359C3×C4C2×C3×M1611yescharacteristic
360C3×C4C3×AGL(1,ℤ/8)12yes—
361C32#147811yescharacteristic, complemented, Sylow
362C23—22no—
363C23—24no—
364C23—42no—
365C23—42no—
366C23C3×#21711yescharacteristic
367D4—22no—
368D4—24no—
369D4C2×C3×C3⋊C814yes—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—41no—
373C2×C4—44no—
374C2×C4—42no—
375C2×C4—44no—
376C2×C4C2×C3×C3⋊C812yes—
377C2×C4C3×#20812yes—
378C2×C4C3×#21711yescharacteristic
379C2×C4C3×#21711yescharacteristic
380C2×C4C3×#21711yescharacteristic
381C2×C4C22×C3×Dic311yescharacteristic
382C2×C4C2×C3×#6711yescharacteristic
383C2×C4C2×C3×#6711yescharacteristic
384C8—122no—
385C8—122no—
386C2×C3—24no—
387C2×C3—22no—
388C2×C3—22no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—48no—
393C2×C3—44no—
394C2×C3—44no—
395C2×C3C2×#83011yescharacteristic
396C2×C3#521511yescharacteristic
397C2×C3#523611yescharacteristic
398C2×C3C2×C3×C22⋊C811yescharacteristic
399C2×C3C3×#41811yescharacteristic
400C2×C3C3×#42111yescharacteristic
401C22—21no—
402C22—21no—
403C22—24no—
404C22—48no—
405C22—42no—
406C22—42no—
407C22C3×#83012yes—
408C22C2×C3×#21711yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—42no—
413C4C3×#83012yes—
414C4C22×C3×C3⋊C811yescharacteristic
415C4C2×C3×#20811yescharacteristic
416C4C3×#93212yes—
417C3—21no—
418C3#7159711yescharacteristic, direct product factor
419C3C3×#147811yescharacteristic, complemented
420C2—22no—
421C2—44no—
422C2C2×C3×#83011yescharacteristic
423C2C3×#521511yescharacteristic
424C2C3×#523611yescharacteristic
subgroupG/H
centerC2×C3×C4C2×#67
commutatorC3×C4C22×C3×C8
FrattiniC42C22×C3×D3
FittingC2×C32×C4×D4C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C32×D4C4
cosocleC3×C42C23×C3
hypercenterC2×C3×C4×D4D3
hypocenterC3C3×#1478
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×#4925C2semidirect
3. C3×#4925C2semidirect
4. C3×D4⋊(C3⋊C8)C2semidirect
6. #71597C3direct (N × H)
19. C3×C4⋊(C3⋊C8)C22semidirect
21. C3×C4×C3⋊C8C22semidirect
27. #4925C2×C3semidirect
28. #4925C2×C3semidirect
30. D4⋊(C3⋊C8)C2×C3semidirect
34. C2×C32×D4C8semidirect
90. C4⋊(C3⋊C8)C22×C3semidirect
92. C4×C3⋊C8C22×C3semidirect
132. C2×C3×D4C3⋊C8semidirect
133. C2×C3×D4C3×C8semidirect
294. C2×D4C3×C3⋊C8semidirect
361. C32#1478semidirect
418. C3#71597direct (N × H)
419. C3C3×#1478semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C3×#49252
C3×D4⋊(C3⋊C8)2
C3×#14783
#715973