Finite Group Databasebeta

← C3×#71933 #11780232

Subgroups — C3×#71933 #11780232

Order 1152.

506 conjugacy classes of subgroups.

The subgroup lattice has 415 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#556C211yesmaximal, characteristic
2C3×#5078C211yesmaximal, characteristic, complemented
3C3×#5020C211yesmaximal, characteristic, complemented
4C3×#5019C211yesmaximal, characteristic
5C3×#4547C211yesmaximal, characteristic, complemented
6C3×#4535C211yesmaximal, characteristic, complemented
7C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic
8C3×#1650—31nomaximal
9#71933C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2211yescharacteristic
11C32×#126—22no—
12C32×#124—21no—
13C32×C22⋊Q8—21no—
14C32×C4×Q8—21no—
15C32×C4×Q8C2211yescharacteristic
16C32×C4×D4C2211yescharacteristic
17C32×#117—21no—
18C2×C3×#214—21no—
19C3×#869C2211yescharacteristic
20C3×#835—21no—
21C3×#810—21no—
22C3×#808—21no—
23C3×#807—22no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27C3×#556—21no—
28C3×#556D311yescharacteristic
29C3×#556C2×C311yescharacteristic
30C3×#500—31no—
31C3×#475—31no—
32C3×#461—31no—
33#5078C2×C311yescharacteristic, complemented
34#5020C2×C311yescharacteristic, complemented
35#5019C2×C311yescharacteristic
36C3×#332—31no—
37C3×Q8⋊C8—31no—
38C3×D4⋊C8—31no—
39#4547C2×C311yescharacteristic, complemented
40#4535C2×C311yescharacteristic, complemented
41D4⋊(C3⋊C8)C2×C311yescharacteristic
42C2×C32×Q8—21no—
43C2×C32×Q8D411yescharacteristic
44C2×C32×D4D411yescharacteristic
45C22×C32×C4—21no—
46C2×C3×Dic6—21no—
47C32×C4⋊C4—22no—
48C32×C4⋊C4—21no—
49C32×C4⋊C4—21no—
50C32×C4⋊C4D412yes—
51C32×C4⋊C4D411yescharacteristic
52C32×C4⋊C4D411yescharacteristic
53C32×C22⋊C4—22no—
54C32×C22⋊C4—22no—
55C32×C22⋊C4—21no—
56C32×C42—22no—
57C32×C42—21no—
58C32×C42C2311yescharacteristic
59C3×#214—42no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65#1650—31noSylow
66C2×C3×SD16—61no—
67C3×C4⋊Q8—21no—
68C3×C4⋊Q8—31no—
69C3×C4⋊Q8C2×D311yescharacteristic
70C3×C4⋊Q8C22×C311yescharacteristic
71C3×#126—24no—
72C3×#126—22no—
73C3×#126—22no—
74C3×#124—22no—
75C3×#124—21no—
76C3×#124—21no—
77C3×C22⋊Q8—22no—
78C3×C22⋊Q8—21no—
79C3×C22⋊Q8—21no—
80C3×C4×Q8—22no—
81C3×C4×Q8—21no—
82C3×C4×Q8—21no—
83C3×C4×Q8—21no—
84C3×C4×Q8C2×D311yescharacteristic
85C3×C4×Q8C22×C311yescharacteristic
86C3×C4×D4—21no—
87C3×C4×D4C2×D311yescharacteristic
88C3×C4×D4C22×C311yescharacteristic
89C3×#117—22no—
90C3×#117—21no—
91C3×#117—21no—
92C2×#214—21no—
93#869C22×C311yescharacteristic
94C3×#107—62no—
95C3×#106—61no—
96C3×C4⋊C8—31no—
97C3×C4⋊C8—31no—
98C3×#103—61no—
99C3×#103—61no—
100C3×C4×C8—31no—
101#835—21no—
102#810—21no—
103#808—21no—
104#807—22no—
105C4⋊(C3⋊C8)C22×C311yescharacteristic
106C4⋊(C3⋊C8)C22×C311yescharacteristic
107C4×C3⋊C8C22×C311yescharacteristic
108C23×C32—21no—
109C32×Q8—21no—
110C32×Q8—21no—
111C32×Q8—41no—
112C32×Q8—41no—
113C32×D4—21no—
114C32×D4—21no—
115C2×C32×C4—21no—
116C2×C32×C4—21no—
117C2×C32×C4—21no—
118C2×C32×C4—22no—
119C2×C32×C4—41no—
120C2×C32×C4—41no—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C3×Dic3—41no—
125C3×Dic6—41no—
126C3×Dic6—41no—
127C3×C3⋊C8—22no—
128C3×C3⋊C8—41no—
129C3×C3⋊C8—41no—
130#556C3×D311yescharacteristic
131#500—31no—
132#475—31no—
133#461—31no—
134#332—31no—
135Q8⋊C8—31no—
136D4⋊C8—31no—
137C2×C3×Q8—22no—
138C2×C3×Q8—21no—
139C2×C3×Q8—21no—
140C2×C3×Q8—21no—
141C2×C3×Q8—61no—
142C2×C3×Q8#6711yescharacteristic
143C2×C3×Q8C3×D411yescharacteristic
144C2×C3×D4—21no—
145C2×C3×D4#6711yescharacteristic
146C2×C3×D4C3×D411yescharacteristic
147C22×C3×C4—22no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C2×Dic6—21no—
151C3×SD16—122no—
152C2×C3×C8—61no—
153C2×C3×C8—61no—
154C2×C3×C8—61no—
155C3×C4⋊C4—22no—
156C3×C4⋊C4—24no—
157C3×C4⋊C4—22no—
158C3×C4⋊C4—22no—
159C3×C4⋊C4—22no—
160C3×C4⋊C4—21no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—22no—
167C3×C4⋊C4—61no—
168C3×C4⋊C4—61no—
169C3×C4⋊C4#6711yescharacteristic
170C3×C4⋊C4#6711yescharacteristic
171C3×C4⋊C4#6712yes—
172C3×C4⋊C4C3×D412yes—
173C3×C4⋊C4C3×D411yescharacteristic
174C3×C4⋊C4C3×D411yescharacteristic
175C3×C22⋊C4—24no—
176C3×C22⋊C4—22no—
177C3×C22⋊C4—22no—
178C3×C22⋊C4—22no—
179C3×C22⋊C4—24no—
180C3×C22⋊C4—22no—
181C3×C22⋊C4—22no—
182C3×C22⋊C4—21no—
183C3×C22⋊C4—21no—
184C3×C42—24no—
185C3×C42—22no—
186C3×C42—22no—
187C3×C42—22no—
188C3×C42—21no—
189C3×C42—21no—
190C3×C42—21no—
191C3×C42C22×D311yescharacteristic
192C3×C42C23×C311yescharacteristic
193#214—42no—
194C4⋊Dic3—21no—
195C4⋊Dic3—21no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—21no—
199C22×C32—41no—
200C22×C32—41no—
201C22×C32—41no—
202C22×C32#12011yescharacteristic
203C32×C4—21no—
204C32×C4—42no—
205C32×C4—41no—
206C32×C4—41no—
207C32×C4—41no—
208C32×C4#13511yescharacteristic
209C32×C4#13511yescharacteristic
210C32×C4AGL(1,ℤ/8)11yescharacteristic
211C32×C4#13711yescharacteristic
212C3×Dic3—81no—
213C2×SD16—61no—
214C4⋊Q8—31no—
215C4⋊Q8C2×C3×D311yescharacteristic
216#126—22no—
217#124—21no—
218C22⋊Q8—21no—
219C4×Q8—21no—
220C4×Q8C2×C3×D311yescharacteristic
221C4×D4C2×C3×D311yescharacteristic
222#117—21no—
223#107—62no—
224#106—61no—
225C4⋊C8—31no—
226C4⋊C8—31no—
227#103—61no—
228#103—61no—
229C4×C8—31no—
230C23×C3—22no—
231C23×C3—21no—
232C23×C3—21no—
233C3×Q8—21no—
234C3×Q8—21no—
235C3×Q8—21no—
236C3×Q8—21no—
237C3×Q8—41no—
238C3×Q8—41no—
239C3×Q8—42no—
240C3×Q8—42no—
241C3×Q8—41no—
242C3×Q8—41no—
243C3×Q8—41no—
244C3×Q8—41no—
245C3×Q8—121no—
246C3×Q8—121no—
247C3×D4—21no—
248C3×D4—21no—
249C3×D4—21no—
250C3×D4—21no—
251C3×D4—41no—
252C3×D4—41no—
253C2×C3×C4—22no—
254C2×C3×C4—22no—
255C2×C3×C4—22no—
256C2×C3×C4—24no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—22no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—22no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—42no—
269C2×C3×C4—42no—
270C2×C3×C4—41no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—121no—
275C2×C3×C4C2×#6711yescharacteristic
276C2×C3×C4C2×#6711yescharacteristic
277C2×C3×C4C2×#6711yescharacteristic
278C2×C3×C4C2×C3×D411yescharacteristic
279C2×C3×C4C2×C3×D411yescharacteristic
280C2×C3×C4C2×C3×D411yescharacteristic
281C2×Dic3—41no—
282Dic6—41no—
283Dic6—41no—
284C3×C8—62no—
285C3×C8—121no—
286C3×C8—121no—
287C3⋊C8—22no—
288C3⋊C8—41no—
289C3⋊C8—41no—
290C2×C32—81no—
291C2×C32#44911yescharacteristic
292C2×C32#45211yescharacteristic
293C2×C32#45611yescharacteristic
294C2×Q8—21no—
295C2×Q8—61no—
296C2×Q8C3×#6711yescharacteristic
297C2×D4C3×#6711yescharacteristic
298C22×C4—21no—
299SD16—122no—
300C2×C8—61no—
301C2×C8—61no—
302C2×C8—61no—
303C4⋊C4—22no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—61no—
307C4⋊C4—61no—
308C4⋊C4C3×#6711yescharacteristic
309C4⋊C4C3×#6711yescharacteristic
310C4⋊C4C3×#6712yes—
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—21no—
314C42—22no—
315C42—21no—
316C42C22×C3×D311yescharacteristic
317C22×C3—21no—
318C22×C3—42no—
319C22×C3—42no—
320C22×C3—42no—
321C22×C3—41no—
322C22×C3—41no—
323C22×C3—41no—
324C22×C3—41no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3#95311yescharacteristic
328C22×C3C3×#12011yescharacteristic
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—41no—
336C3×C4—42no—
337C3×C4—44no—
338C3×C4—42no—
339C3×C4—42no—
340C3×C4—42no—
341C3×C4—41no—
342C3×C4—41no—
343C3×C4—41no—
344C3×C4—42no—
345C3×C4—41no—
346C3×C4—41no—
347C3×C4—41no—
348C3×C4—241no—
349C3×C4#94911yescharacteristic
350C3×C4#95011yescharacteristic
351C3×C4#95011yescharacteristic
352C3×C4#95111yescharacteristic
353C3×C4C3×#13511yescharacteristic
354C3×C4C3×#13511yescharacteristic
355C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
356C3×C4C3×#13711yescharacteristic
357Dic3—81no—
358C32#165011yescharacteristic, complemented, Sylow
359C23—21no—
360Q8—21no—
361Q8—21no—
362Q8—41no—
363Q8—41no—
364Q8—121no—
365Q8—121no—
366D4—21no—
367D4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—121no—
375C2×C4C2×C3×#6711yescharacteristic
376C2×C4C2×C3×#6711yescharacteristic
377C2×C4C2×C3×#6711yescharacteristic
378C8—62no—
379C8—121no—
380C8—121no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—82no—
385C2×C3—81no—
386C2×C3—81no—
387C2×C3#523811yescharacteristic
388C2×C3#523911yescharacteristic
389C2×C3#524611yescharacteristic
390C2×C3C3×#44911yescharacteristic
391C2×C3C3×#45211yescharacteristic
392C2×C3C3×#45611yescharacteristic
393C22—41no—
394C22—41no—
395C22—41no—
396C22C3×#95311yescharacteristic
397C4—21no—
398C4—42no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—241no—
403C4C3×#94911yescharacteristic
404C4C3×#95011yescharacteristic
405C4C3×#95011yescharacteristic
406C4C3×#95111yescharacteristic
407C3—21no—
408C3#7193311yescharacteristic, direct product factor
409C3C3×#165011yescharacteristic, complemented
410C2—81no—
411C2C3×#523811yescharacteristic
412C2C3×#523911yescharacteristic
413C2C3×#524611yescharacteristic
subgroupG/H
centerC22×C3#953
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#556C2
socleC22×C32#120
prime radicalC2×C32×D4D4
hypercenterC3×#556D3
hypocenterC3C3×#1650
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#556

Complements

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

NH ≅ G/Ntype
2. C3×#5078C2semidirect
3. C3×#5020C2semidirect
5. C3×#4547C2semidirect
6. C3×#4535C2semidirect
9. #71933C3direct (N × H)
33. #5078C2×C3semidirect
34. #5020C2×C3semidirect
39. #4547C2×C3semidirect
40. #4535C2×C3semidirect
358. C32#1650semidirect
408. C3#71933direct (N × H)
409. C3C3×#1650semidirect

Maximal subgroups

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

subgroupindex
C32×#5562
C3×#50782
C3×#50202
C3×#50192
C3×#45472
C3×#45352
C3×D4⋊(C3⋊C8)2
C3×#16503
#719333