Finite Group Databasebeta

← C3×#69852 #11774462

Subgroups — C3×#69852 #11774462

Order 1152.

539 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
1C3×#5479C211yesmaximal, characteristic
2C32×C4×M16C211yesmaximal, characteristic, complemented
3C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4C3×#4459C212yesmaximal, complemented
5C3×#4456C212yesmaximal, complemented
6C3×#1483—31nomaximal
7#69852C311yesmaximal, characteristic, direct product factor
8C2×C32×M16—21no—
9C2×C32×C42C2211yescharacteristic
10C3×#930C411yescharacteristic
11C3×#929—21no—
12C3×C4×#67—21no—
13C3×#924C411yescharacteristic
14C22×C3×C3⋊C8—21no—
15C3×#876—21no—
16C3×#875C411yescharacteristic
17C3×C4×D12C2211yescharacteristic
18C3×#872—21no—
19C3×#870C411yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21C32×#97—21no—
22C32×C4×C8C2212yes—
23C3×C4⋊(C3⋊C8)—21no—
24C3×C4⋊(C3⋊C8)C2212yes—
25C3×#529—31no—
26#5479C2×C311yescharacteristic
27C2×C3×C4⋊C8—31no—
28C3×C4×M16—21no—
29C3×C4×M16D311yescharacteristic, complemented
30C3×C4×M16C2×C311yescharacteristic, complemented
31C2×C4⋊(C3⋊C8)C2×C311yescharacteristic, complemented
32C3×Q8⋊C8—32no—
33C3×D4⋊C8—32no—
34#4459C2×C312yescomplemented
35#4456C2×C312yescomplemented
36C22×C32×C4C2×C411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C2×C3×#67—21no—
40C2×C3×D12C2×C411yescharacteristic
41C2×C3×C4×D3—21no—
42C2×C3×Dic6C2×C411yescharacteristic
43C32×M16—24no—
44C2×C32×C8—22no—
45C32×C42C2×C411yescharacteristic
46C32×C42D411yescharacteristic
47C32×C42D411yescharacteristic
48C32×C42C2311yescharacteristic
49C3×#217—21no—
50C3×(C2×D3)⋊C4—21no—
51C3×(C2×D3)⋊C4—21no—
52C3×(C2×D3)⋊C4—21no—
53C3×(C2×D3)⋊C4—21no—
54C3×C4⋊Dic3C2×C411yescharacteristic
55C3×C4⋊Dic3C2×C411yescharacteristic
56C3×Dic3⋊C4—21no—
57C3×Dic3⋊C4—21no—
58C3×Dic3⋊C4—21no—
59C3×Dic3⋊C4—21no—
60C3×C4×Dic3—21no—
61C2×C3×C3⋊C8—22no—
62C2×C3×C3⋊C8—42no—
63#1483—31noSylow
64C2×C3×M16—22no—
65C2×C3×M16—21no—
66C2×C3×M16—21no—
67C22×C3×C8—61no—
68C3×#126—61no—
69C3×#125—31no—
70C3×#124—31no—
71C3×#123—61no—
72C3×C22⋊Q8—31no—
73C3×#121—31no—
74C3×C4×Q8—31no—
75C3×C4×D4—31no—
76C3×C4×D4—61no—
77C3×#117—61no—
78C2×C3×C42—21no—
79C2×C3×C42C2×D311yescharacteristic
80C2×C3×C42C22×C311yescharacteristic
81#930C3×C411yescharacteristic
82#929—21no—
83C4×#67—21no—
84#924C3×C411yescharacteristic
85C22×C3⋊C8—21no—
86#876—21no—
87#875C3×C411yescharacteristic
88C4×D12C22×C311yescharacteristic
89#872—21no—
90#870C3×C411yescharacteristic
91C4×Dic6C22×C311yescharacteristic
92C3×C4⋊C8—32no—
93C3×C4⋊C8—61no—
94C3×#97—22no—
95C3×#97—21no—
96C3×#97—21no—
97C3×C4×C8—22no—
98C3×C4×C8C2×D312yes—
99C3×C4×C8C22×C312yes—
100C4⋊(C3⋊C8)—21no—
101C4⋊(C3⋊C8)C22×C312yes—
102C23×C32C22⋊C411yescharacteristic
103C22×C3×D3—21no—
104C2×C32×C4—22no—
105C2×C32×C4—22no—
106C2×C32×C4—21no—
107C2×C32×C4—21no—
108C2×C32×C4C22⋊C411yescharacteristic
109C2×C32×C4C22⋊C411yescharacteristic
110C2×C32×C4C22⋊C411yescharacteristic
111C2×C32×C4C22×C411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C3×#67—42no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—21no—
117C2×C3×Dic3—21no—
118C3×D12—22no—
119C3×C4×D3—41no—
120C3×C4×D3—41no—
121C3×Dic6—22no—
122C32×C8—24no—
123C3×C3⋊C8—42no—
124#529—31no—
125C2×C4⋊C8—31no—
126C4×M16C3×D311yescharacteristic, complemented
127Q8⋊C8—32no—
128D4⋊C8—32no—
129C2×C3×Q8—31no—
130C2×C3×D4—31no—
131C2×C3×D4—61no—
132C22×C3×C4—21no—
133C22×C3×C4—21no—
134C22×C3×C4—21no—
135C22×C3×C4—61no—
136C22×C3×C4C4×D311yescharacteristic
137C22×C3×C4D1211yescharacteristic
138C22×C3×C4#6711yescharacteristic
139C22×C3×C4C2×C3×C411yescharacteristic
140C22×C3×C4C3×D411yescharacteristic
141C22×C3×C4C3×D411yescharacteristic
142C2×#67—21no—
143C2×D12C2×C3×C411yescharacteristic
144C2×C4×D3—21no—
145C2×Dic6C2×C3×C411yescharacteristic
146C3×M16—28no—
147C3×M16—24no—
148C3×M16—24no—
149C2×C3×C8—24no—
150C2×C3×C8—22no—
151C2×C3×C8—22no—
152C2×C3×C8—62no—
153C2×C3×C8—122no—
154C3×C4⋊C4—31no—
155C3×C4⋊C4—31no—
156C3×C4⋊C4—61no—
157C3×C4⋊C4—61no—
158C3×C4⋊C4—61no—
159C3×C4⋊C4—61no—
160C3×C22⋊C4—61no—
161C3×C22⋊C4—61no—
162C3×C22⋊C4—61no—
163C3×C22⋊C4—61no—
164C3×C22⋊C4—61no—
165C3×C42—21no—
166C3×C42—21no—
167C3×C42—21no—
168C3×C42—21no—
169C3×C42—61no—
170C3×C42C4×D311yescharacteristic
171C3×C42D1211yescharacteristic
172C3×C42#6711yescharacteristic
173C3×C42C2×C3×C411yescharacteristic
174C3×C42C3×D411yescharacteristic
175C3×C42C3×D411yescharacteristic
176C3×C42C22×D311yescharacteristic
177C3×C42C23×C311yescharacteristic
178#217—21no—
179(C2×D3)⋊C4—21no—
180(C2×D3)⋊C4—21no—
181(C2×D3)⋊C4—21no—
182(C2×D3)⋊C4—21no—
183C4⋊Dic3C2×C3×C411yescharacteristic
184C4⋊Dic3C2×C3×C411yescharacteristic
185Dic3⋊C4—21no—
186Dic3⋊C4—21no—
187Dic3⋊C4—21no—
188Dic3⋊C4—21no—
189C4×Dic3—21no—
190C2×C3⋊C8—22no—
191C2×C3⋊C8—42no—
192C22×C32—21no—
193C22×C32—21no—
194C22×C32#10412yes—
195C22×C32C2×C22⋊C411yescharacteristic
196C2×C3×D3—41no—
197C2×C3×D3—41no—
198C2×C3×D3—41no—
199C32×C4—21no—
200C32×C4—21no—
201C32×C4—21no—
202C32×C4—21no—
203C32×C4#13112yes—
204C32×C4AGL(1,ℤ/8)11yescharacteristic
205C32×C4#13711yescharacteristic
206C3×Dic3—41no—
207C3×Dic3—41no—
208C3×Dic3—41no—
209C2×M16—21no—
210C22×C8—61no—
211#126—61no—
212#125—31no—
213#124—31no—
214#123—61no—
215C22⋊Q8—31no—
216#121—31no—
217C4×Q8—31no—
218C4×D4—31no—
219C4×D4—61no—
220#117—61no—
221C2×C42C2×C3×D311yescharacteristic
222C4⋊C8—32no—
223C4⋊C8—61no—
224#97—21no—
225C4×C8C2×C3×D312yes—
226C23×C3—21no—
227C23×C3—61no—
228C23×C3(C2×D3)⋊C411yescharacteristic
229C23×C3C3×C22⋊C411yescharacteristic
230C22×D3—21no—
231C3×Q8—62no—
232C3×D4—62no—
233C3×D4—122no—
234C2×C3×C4—24no—
235C2×C3×C4—22no—
236C2×C3×C4—22no—
237C2×C3×C4—22no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—22no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—42no—
250C2×C3×C4—41no—
251C2×C3×C4—41no—
252C2×C3×C4—61no—
253C2×C3×C4—61no—
254C2×C3×C4—61no—
255C2×C3×C4—121no—
256C2×C3×C4—121no—
257C2×C3×C4(C2×D3)⋊C411yescharacteristic
258C2×C3×C4(C2×D3)⋊C411yescharacteristic
259C2×C3×C4(C2×D3)⋊C411yescharacteristic
260C2×C3×C4C3×C22⋊C411yescharacteristic
261C2×C3×C4C3×C22⋊C411yescharacteristic
262C2×C3×C4C3×C22⋊C411yescharacteristic
263C2×C3×C4C2×C4×D311yescharacteristic
264C2×C3×C4C2×D1211yescharacteristic
265C2×C3×C4C2×#6711yescharacteristic
266C2×C3×C4C22×C3×C411yescharacteristic
267C2×C3×C4C2×C3×D411yescharacteristic
268C2×C3×C4C2×C3×D411yescharacteristic
269#67—42no—
270C2×Dic3—21no—
271C2×Dic3—21no—
272C2×Dic3—21no—
273D12—22no—
274C4×D3—41no—
275C4×D3—41no—
276Dic6—22no—
277C3×C8—28no—
278C3×C8—24no—
279C3×C8—24no—
280C3×C8—122no—
281C3⋊C8—42no—
282C2×C32—22no—
283C2×C32#40811yescharacteristic
284C2×C32#41711yescharacteristic
285C2×C32C2×#10411yescharacteristic
286C3×D3—81no—
287C2×Q8—31no—
288C2×D4—31no—
289C2×D4—61no—
290C22×C4—61no—
291C22×C4C3×C4×D311yescharacteristic
292C22×C4C3×D1211yescharacteristic
293C22×C4C3×#6711yescharacteristic
294M16—24no—
295C2×C8—22no—
296C2×C8—62no—
297C2×C8—122no—
298C4⋊C4—31no—
299C4⋊C4—31no—
300C4⋊C4—61no—
301C4⋊C4—61no—
302C4⋊C4—61no—
303C4⋊C4—61no—
304C22⋊C4—61no—
305C22⋊C4—61no—
306C22⋊C4—61no—
307C22⋊C4—61no—
308C22⋊C4—61no—
309C42—61no—
310C42C3×C4×D311yescharacteristic
311C42C3×D1211yescharacteristic
312C42C3×#6711yescharacteristic
313C42C22×C3×D311yescharacteristic
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—22no—
320C22×C3—41no—
321C22×C3—41no—
322C22×C3—121no—
323C22×C3—121no—
324C22×C3—121no—
325C22×C3#80512yes—
326C22×C3C3×#10412yes—
327C22×C3C2×(C2×D3)⋊C411yescharacteristic
328C22×C3C2×C3×C22⋊C411yescharacteristic
329C2×D3—41no—
330C2×D3—41no—
331C2×D3—41no—
332C3×C4—22no—
333C3×C4—22no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—22no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—41no—
346C3×C4—41no—
347C3×C4—121no—
348C3×C4—121no—
349C3×C4—121no—
350C3×C4#90712yes—
351C3×C4#90811yescharacteristic
352C3×C4#90911yescharacteristic
353C3×C4C3×#13112yes—
354C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
355C3×C4C3×#13711yescharacteristic
356Dic3—41no—
357Dic3—41no—
358Dic3—41no—
359C32#148311yescharacteristic, complemented, Sylow
360C23—61no—
361C23C3×(C2×D3)⋊C411yescharacteristic
362Q8—62no—
363D4—62no—
364D4—122no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—61no—
370C2×C4—61no—
371C2×C4—61no—
372C2×C4—121no—
373C2×C4—121no—
374C2×C4C3×(C2×D3)⋊C411yescharacteristic
375C2×C4C3×(C2×D3)⋊C411yescharacteristic
376C2×C4C3×(C2×D3)⋊C411yescharacteristic
377C2×C4C2×C3×C4×D311yescharacteristic
378C2×C4C2×C3×D1211yescharacteristic
379C2×C4C2×C3×#6711yescharacteristic
380C8—24no—
381C8—122no—
382C2×C3—22no—
383C2×C3—22no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—42no—
388C2×C3—241no—
389C2×C3C2×#80511yescharacteristic
390C2×C3#512911yescharacteristic
391C2×C3#513311yescharacteristic
392C2×C3C3×#40811yescharacteristic
393C2×C3C3×#41711yescharacteristic
394C2×C3C2×C3×#10411yescharacteristic
395D3—81no—
396C22—21no—
397C22—21no—
398C22—121no—
399C22—121no—
400C22—121no—
401C22C3×#80512yes—
402C22C2×C3×(C2×D3)⋊C411yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—121no—
408C4—121no—
409C4—121no—
410C4C3×#90712yes—
411C4C3×#90811yescharacteristic
412C4C3×#90911yescharacteristic
413C3—21no—
414C3#6985211yescharacteristic, direct product factor
415C3C3×#148311yescharacteristic, complemented
416C2—22no—
417C2—241no—
418C2C2×C3×#80511yescharacteristic
419C2C3×#512911yescharacteristic
420C2C3×#513311yescharacteristic
subgroupG/H
centerC2×C3×C4C2×D12
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×C4×M16C2
socleC22×C32C2×C22⋊C4
prime radicalC3×#930C4
cosocleC3×C42C23×C3
hypercenterC3×C4×M16D3
hypocenterC3C3×#1483
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×C4×M16

Complements

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

NH ≅ G/Ntype
2. C32×C4×M16C2semidirect
3. C2×C3×C4⋊(C3⋊C8)C2semidirect
4. C3×#4459C2semidirect
5. C3×#4456C2semidirect
7. #69852C3direct (N × H)
29. C3×C4×M16D3semidirect
30. C3×C4×M16C2×C3semidirect
31. C2×C4⋊(C3⋊C8)C2×C3semidirect
34. #4459C2×C3semidirect
35. #4456C2×C3semidirect
126. C4×M16C3×D3semidirect
359. C32#1483semidirect
414. C3#69852direct (N × H)
415. C3C3×#1483semidirect

Maximal subgroups

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

subgroupindex
C3×#54792
C32×C4×M162
C2×C3×C4⋊(C3⋊C8)2
C3×#44592
C3×#44562
C3×#14833
#698523