Finite Group Databasebeta

← C3×#71804 #11776128

Subgroups — C3×#71804 #11776128

Order 1152.

667 conjugacy classes of subgroups.

The subgroup lattice has 419 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#532C211yesmaximal, characteristic
2C3×#4925C211yesmaximal, characteristic, complemented
3C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4C3×#4547C212yesmaximal, complemented
5C3×#4544C212yesmaximal, complemented
6C3×#1540—31nomaximal
7#71804C311yesmaximal, characteristic, direct product factor
8C2×C32×#41—21no—
9C32×C4⋊Q8C2211yescharacteristic
10C32×#127C2211yescharacteristic
11C32×#124—21no—
12C32×#121—21no—
13C32×#121C412yes—
14C32×C4×D4—21no—
15C32×C4×D4C412yes—
16C2×C32×C42C2211yescharacteristic
17C22×C3×C3⋊C8—21no—
18C3×#830—21no—
19C3×C4⋊(C3⋊C8)—21no—
20C3×C4⋊(C3⋊C8)C2212yes—
21C3×C4⋊(C3⋊C8)C2212yes—
22C3×C4×C3⋊C8—21no—
23C3×#532—21no—
24C3×#532D311yescharacteristic
25C3×#532C2×C311yescharacteristic
26C3×#431—31no—
27C2×C3×C4⋊C8—31no—
28#4925C2×C311yescharacteristic, complemented
29C2×C4⋊(C3⋊C8)C2×C311yescharacteristic, complemented
30C3×#332—32no—
31C3×#331—32no—
32#4547C2×C312yescomplemented
33#4544C2×C312yescomplemented
34C32×#41—42no—
35C32×#41—42no—
36C2×C32×Q8—21no—
37C2×C32×D4—22no—
38C2×C32×D4—21no—
39C2×C32×D4—21no—
40C2×C32×D4C2×C412yes—
41C22×C32×C4—22no—
42C22×C32×C4C2×C411yescharacteristic
43C22×C32×C4D411yescharacteristic
44C22×C32×C4D411yescharacteristic
45C32×C4⋊C4—21no—
46C32×C4⋊C4C2×C412yes—
47C32×C22⋊C4—22no—
48C32×C22⋊C4—22no—
49C32×C42C2×C411yescharacteristic
50C32×C42D411yescharacteristic
51C32×C42D411yescharacteristic
52C32×C42C2311yescharacteristic
53C2×C3×C3⋊C8—22no—
54C2×C3×C3⋊C8—22no—
55C2×C3×C3⋊C8—42no—
56#1540—31noSylow
57C2×C3×#41—22no—
58C2×C3×#41—21no—
59C2×C3×#41—21no—
60C22×C3×C8—61no—
61C3×C4⋊Q8—21no—
62C3×C4⋊Q8C2×D311yescharacteristic
63C3×C4⋊Q8C22×C311yescharacteristic
64C3×#127—21no—
65C3×#127C2×D311yescharacteristic
66C3×#127C22×C311yescharacteristic
67C3×#124—22no—
68C3×#124—21no—
69C3×#124—21no—
70C3×#121—22no—
71C3×#121—21no—
72C3×#121—21no—
73C3×#121—22no—
74C3×#121Dic312yes—
75C3×#121C3×C412yes—
76C3×C4×D4—22no—
77C3×C4×D4—21no—
78C3×C4×D4—21no—
79C3×C4×D4—22no—
80C3×C4×D4Dic312yes—
81C3×C4×D4C3×C412yes—
82C2×C3×C42—21no—
83C2×C3×C42C2×D311yescharacteristic
84C2×C3×C42C22×C311yescharacteristic
85C22×C3⋊C8—21no—
86C3×C4⋊C8—32no—
87C3×C4⋊C8—32no—
88C3×C4⋊C8—61no—
89C3×C22⋊C8—61no—
90C3×C4×C8—61no—
91#830—21no—
92C4⋊(C3⋊C8)—21no—
93C4⋊(C3⋊C8)C22×C312yes—
94C4⋊(C3⋊C8)C22×C312yes—
95C4×C3⋊C8—21no—
96C23×C32—22no—
97C23×C32C22⋊C411yescharacteristic
98C32×Q8—41no—
99C32×Q8—41no—
100C32×D4—42no—
101C32×D4—44no—
102C32×D4—41no—
103C32×D4—41no—
104C32×D4—42no—
105C2×C32×C4—22no—
106C2×C32×C4—22no—
107C2×C32×C4—41no—
108C2×C32×C4—44no—
109C2×C32×C4C22⋊C411yescharacteristic
110C2×C32×C4C22⋊C411yescharacteristic
111C2×C32×C4C22⋊C411yescharacteristic
112C2×C32×C4D812yes—
113C2×C32×C4SD1612yes—
114C2×C32×C4C22×C411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C3×C3⋊C8—42no—
118C3×C3⋊C8—42no—
119#532C3×D311yescharacteristic
120#431—31no—
121C2×C4⋊C8—31no—
122#332—32no—
123#331—32no—
124C3×#41—44no—
125C3×#41—44no—
126C3×#41—42no—
127C3×#41—42no—
128C3×#41—42no—
129C3×#41—42no—
130C2×C3×Q8—22no—
131C2×C3×Q8—21no—
132C2×C3×Q8—21no—
133C2×C3×D4—22no—
134C2×C3×D4—24no—
135C2×C3×D4—22no—
136C2×C3×D4—22no—
137C2×C3×D4—22no—
138C2×C3×D4—21no—
139C2×C3×D4—21no—
140C2×C3×D4—21no—
141C2×C3×D4—21no—
142C2×C3×D4—22no—
143C2×C3×D4C2×Dic312yes—
144C2×C3×D4C2×C3×C412yes—
145C22×C3×C4—24no—
146C22×C3×C4—22no—
147C22×C3×C4—22no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
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—
159C2×C3×C8—122no—
160C3×C4⋊C4—22no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4—22no—
164C3×C4⋊C4C2×Dic312yes—
165C3×C4⋊C4C2×C3×C412yes—
166C3×C22⋊C4—24no—
167C3×C22⋊C4—24no—
168C3×C22⋊C4—22no—
169C3×C22⋊C4—22no—
170C3×C22⋊C4—22no—
171C3×C22⋊C4—22no—
172C3×C42—21no—
173C3×C42—21no—
174C3×C42—21no—
175C3×C42—21no—
176C3×C42C2×Dic311yescharacteristic
177C3×C42#6711yescharacteristic
178C3×C42#6711yescharacteristic
179C3×C42C2×C3×C411yescharacteristic
180C3×C42C3×D411yescharacteristic
181C3×C42C3×D411yescharacteristic
182C3×C42C22×D311yescharacteristic
183C3×C42C23×C311yescharacteristic
184C2×C3⋊C8—22no—
185C2×C3⋊C8—22no—
186C2×C3⋊C8—42no—
187C22×C32—21no—
188C22×C32—21no—
189C22×C32—42no—
190C22×C32—42no—
191C22×C32—42no—
192C22×C32#10212yes—
193C22×C32C2×C22⋊C411yescharacteristic
194C32×C4—21no—
195C32×C4—21no—
196C32×C4—21no—
197C32×C4—42no—
198C32×C4#10212yes—
199C32×C4C2×D811yescharacteristic
200C32×C4C2×SD1611yescharacteristic
201C32×C4#13512yes—
202C2×#41—21no—
203C22×C8—61no—
204C4⋊Q8C2×C3×D311yescharacteristic
205#127C2×C3×D311yescharacteristic
206#124—21no—
207#121—21no—
208#121C3×Dic312yes—
209C4×D4—21no—
210C4×D4C3×Dic312yes—
211C2×C42C2×C3×D311yescharacteristic
212C4⋊C8—32no—
213C4⋊C8—32no—
214C4⋊C8—61no—
215C22⋊C8—61no—
216C4×C8—61no—
217C23×C3—24no—
218C23×C3—22no—
219C23×C3—22no—
220C23×C3—21no—
221C23×C3#21711yescharacteristic
222C23×C3C3×C22⋊C411yescharacteristic
223C3×Q8—42no—
224C3×Q8—42no—
225C3×Q8—41no—
226C3×Q8—41no—
227C3×Q8—41no—
228C3×Q8—41no—
229C3×D4—42no—
230C3×D4—42no—
231C3×D4—44no—
232C3×D4—44no—
233C3×D4—42no—
234C3×D4—42no—
235C3×D4—48no—
236C3×D4—44no—
237C3×D4—44no—
238C3×D4—41no—
239C3×D4—41no—
240C3×D4—42no—
241C3×D4—41no—
242C3×D4—41no—
243C3×D4—42no—
244C2×C3×C4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—24no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4—22no—
250C2×C3×C4—22no—
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—42no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—42no—
261C2×C3×C4—48no—
262C2×C3×C4—44no—
263C2×C3×C4—44no—
264C2×C3×C4#21312yes—
265C2×C3×C4#21412yes—
266C2×C3×C4#21711yescharacteristic
267C2×C3×C4#21711yescharacteristic
268C2×C3×C4#21711yescharacteristic
269C2×C3×C4C3×C22⋊C411yescharacteristic
270C2×C3×C4C3×C22⋊C411yescharacteristic
271C2×C3×C4C3×C22⋊C411yescharacteristic
272C2×C3×C4C3×D812yes—
273C2×C3×C4C3×SD1612yes—
274C2×C3×C4C22×Dic311yescharacteristic
275C2×C3×C4C2×#6711yescharacteristic
276C2×C3×C4C2×#6711yescharacteristic
277C2×C3×C4C22×C3×C411yescharacteristic
278C2×C3×C4C2×C3×D411yescharacteristic
279C2×C3×C4C2×C3×D411yescharacteristic
280C3×C8—122no—
281C3×C8—122no—
282C3⋊C8—42no—
283C3⋊C8—42no—
284C2×C32—22no—
285C2×C32—82no—
286C2×C32#41311yescharacteristic
287C2×C32C2×#10211yescharacteristic
288C2×C32#41611yescharacteristic
289#41—42no—
290#41—42no—
291C2×Q8—21no—
292C2×D4—22no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4C2×C3×Dic312yes—
296C22×C4—22no—
297C22×C4C2×C3×Dic311yescharacteristic
298C22×C4C3×#6711yescharacteristic
299C22×C4C3×#6711yescharacteristic
300C2×C8—62no—
301C2×C8—62no—
302C2×C8—122no—
303C4⋊C4—21no—
304C4⋊C4C2×C3×Dic312yes—
305C22⋊C4—22no—
306C22⋊C4—22no—
307C42C2×C3×Dic311yescharacteristic
308C42C3×#6711yescharacteristic
309C42C3×#6711yescharacteristic
310C42C22×C3×D311yescharacteristic
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—21no—
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—22no—
317C22×C3—41no—
318C22×C3—41no—
319C22×C3—44no—
320C22×C3—44no—
321C22×C3—44no—
322C22×C3—42no—
323C22×C3—42no—
324C22×C3—42no—
325C22×C3—42no—
326C22×C3—42no—
327C22×C3—42no—
328C22×C3#83212yes—
329C22×C3C3×#10212yes—
330C22×C3C2×#21711yescharacteristic
331C22×C3C2×C3×C22⋊C411yescharacteristic
332C3×C4—22no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—22no—
342C3×C4—22no—
343C3×C4—41no—
344C3×C4—41no—
345C3×C4—44no—
346C3×C4—42no—
347C3×C4—42no—
348C3×C4#83212yes—
349C3×C4C3×#10212yes—
350C3×C4C2×#21311yescharacteristic
351C3×C4C2×#21411yescharacteristic
352C3×C4#95012yes—
353C3×C4C2×C3×D811yescharacteristic
354C3×C4C2×C3×SD1611yescharacteristic
355C3×C4C3×#13512yes—
356C32#154011yescharacteristic, complemented, Sylow
357C23—22no—
358C23C3×#21711yescharacteristic
359Q8—41no—
360Q8—41no—
361D4—42no—
362D4—44no—
363D4—41no—
364D4—41no—
365D4—42no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—44no—
370C2×C4C3×#21312yes—
371C2×C4C3×#21412yes—
372C2×C4C3×#21711yescharacteristic
373C2×C4C3×#21711yescharacteristic
374C2×C4C3×#21711yescharacteristic
375C2×C4C22×C3×Dic311yescharacteristic
376C2×C4C2×C3×#6711yescharacteristic
377C2×C4C2×C3×#6711yescharacteristic
378C8—122no—
379C8—122no—
380C2×C3—22no—
381C2×C3—22no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—42no—
386C2×C3—84no—
387C2×C3—82no—
388C2×C3—82no—
389C2×C3C2×#83211yescharacteristic
390C2×C3#523311yescharacteristic
391C2×C3#523711yescharacteristic
392C2×C3C3×#41311yescharacteristic
393C2×C3C2×C3×#10211yescharacteristic
394C2×C3C3×#41611yescharacteristic
395C22—21no—
396C22—21no—
397C22—42no—
398C22—42no—
399C22—42no—
400C22C3×#83212yes—
401C22C2×C3×#21711yescharacteristic
402C4—21no—
403C4—21no—
404C4—21no—
405C4—42no—
406C4C3×#83212yes—
407C4C2×C3×#21311yescharacteristic
408C4C2×C3×#21411yescharacteristic
409C4C3×#95012yes—
410C3—21no—
411C3#7180411yescharacteristic, direct product factor
412C3C3×#154011yescharacteristic, complemented
413C2—22no—
414C2—82no—
415C2C2×C3×#83211yescharacteristic
416C2C3×#523311yescharacteristic
417C2C3×#523711yescharacteristic
subgroupG/H
centerC2×C3×C4#217
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
Fitting, prime radicalC32×#532C2
socleC22×C32C2×C22⋊C4
cosocleC3×C42C23×C3
hypercenterC3×#532D3
hypocenterC3C3×#1540
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×#532

Complements

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

NH ≅ G/Ntype
2. C3×#4925C2semidirect
3. C2×C3×C4⋊(C3⋊C8)C2semidirect
4. C3×#4547C2semidirect
5. C3×#4544C2semidirect
7. #71804C3direct (N × H)
28. #4925C2×C3semidirect
29. C2×C4⋊(C3⋊C8)C2×C3semidirect
32. #4547C2×C3semidirect
33. #4544C2×C3semidirect
356. C32#1540semidirect
411. C3#71804direct (N × H)
412. C3C3×#1540semidirect

Maximal subgroups

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

subgroupindex
C32×#5322
C3×#49252
C2×C3×C4⋊(C3⋊C8)2
C3×#45472
C3×#45442
C3×#15403
#718043