Finite Group Databasebeta

← C3×#71376 #11780176

Subgroups — C3×#71376 #11780176

Order 1152.

517 conjugacy classes of subgroups.

The subgroup lattice has 407 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5727C211yesmaximal, characteristic
2C32×#500C211yesmaximal, characteristic, complemented
3C3×#5090C211yesmaximal, characteristic, complemented
4C3×#5087C211yesmaximal, characteristic
5C3×#4547C211yesmaximal, characteristic, complemented
6C3×#4459C211yesmaximal, characteristic
7C3×#4456C211yesmaximal, characteristic, complemented
8C3×#1649—31nomaximal
9#71376C311yesmaximal, characteristic, direct product factor
10C2×C3×D3×Q8—21no—
11C32×C4⋊Q8C2211yescharacteristic
12C32×C4⋊Q8C2211yescharacteristic
13C3×#946—21no—
14C2×C3×#216—21no—
15C3×#896—22no—
16C3×#893—21no—
17C3×#888—21no—
18C3×C4×D12C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20C32×#107—22no—
21C32×C4×C8C2211yescharacteristic
22C3×#835—21no—
23C3×#809—21no—
24C3×#807—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27C3×D4×Q8—31no—
28#5727C2×C311yescharacteristic
29C3×#500—21no—
30C3×#500D311yescharacteristic, complemented
31C3×#500C2×C311yescharacteristic, complemented
32C3×#474—31no—
33C3×#462—31no—
34#5090C2×C311yescharacteristic, complemented
35#5087C2×C311yescharacteristic
36C3×#332—31no—
37C3×Q8⋊C8—31no—
38C3×D4⋊C8—31no—
39#4547C2×C311yescharacteristic, complemented
40#4459C2×C311yescharacteristic
41#4456C2×C311yescharacteristic, complemented
42C2×C32×Q8—21no—
43C2×C32×Q8—21no—
44C3×D3×Q8—42no—
45C3×D3×Q8—42no—
46C2×C3×D12D411yescharacteristic
47C2×C3×C4×D3—22no—
48C2×C3×C4×D3—21no—
49C2×C3×Dic6—22no—
50C2×C3×Dic6D411yescharacteristic
51C2×C32×C8—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4D412yes—
56C32×C42C2311yescharacteristic
57C3×#216—42no—
58C3×(C2×D3)⋊C4—22no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3D411yescharacteristic
61C3×C4⋊Dic3D411yescharacteristic
62C3×Dic3⋊C4—22no—
63C3×Dic3⋊C4—21no—
64C3×C4×Dic3—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#1649—31noSylow
68C22×C3×Q8—61no—
69C2×D3×Q8—21no—
70C2×C3×Q16—61no—
71C3×C4⋊Q8—21no—
72C3×C4⋊Q8—21no—
73C3×C4⋊Q8—61no—
74C3×C4⋊Q8C2×D311yescharacteristic
75C3×C4⋊Q8C2×D311yescharacteristic
76C3×C4⋊Q8C22×C311yescharacteristic
77C3×C4⋊Q8C22×C311yescharacteristic
78C3×C22⋊Q8—61no—
79C3×C22⋊Q8—62no—
80C3×C4×Q8—31no—
81C3×C4×D4—31no—
82C3×C4×D4—61no—
83#946—21no—
84C2×#216—21no—
85#896—22no—
86#893—21no—
87#888—21no—
88C4×D12C22×C311yescharacteristic
89C4×Dic6C22×C311yescharacteristic
90C3×#107—24no—
91C3×#107—22no—
92C3×#107—22no—
93C3×#107—61no—
94C3×C4⋊C8—31no—
95C3×C4⋊C8—31no—
96C3×#103—61no—
97C3×#102—61no—
98C3×C4×C8—21no—
99C3×C4×C8C2×D311yescharacteristic
100C3×C4×C8C22×C311yescharacteristic
101#835—21no—
102#809—21no—
103#807—21no—
104C4⋊(C3⋊C8)C22×C311yescharacteristic
105C4⋊(C3⋊C8)C22×C311yescharacteristic
106C22×C3×D3—21no—
107C32×Q8—41no—
108C32×Q8—41no—
109C32×Q8—41no—
110C32×Q8—41no—
111C2×C32×C4—22no—
112C2×C32×C4—41no—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C3×Dic3—21no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—21no—
119C3×D12—21no—
120C3×D12Q1612yescomplemented
121C3×C4×D3—44no—
122C3×C4×D3—41no—
123C3×C4×D3—41no—
124C3×Dic6—21no—
125C3×Dic6—44no—
126C3×Dic6D812yes—
127C32×C8—22no—
128C3×C3⋊C8—41no—
129C3×C3⋊C8—41no—
130D4×Q8—31no—
131#500C3×D311yescharacteristic, complemented
132#474—31no—
133#462—31no—
134#332—31no—
135Q8⋊C8—31no—
136D4⋊C8—31no—
137C2×C3×Q8—21no—
138C2×C3×Q8—21no—
139C2×C3×Q8—21no—
140C2×C3×Q8—21no—
141C2×C3×Q8—31no—
142C2×C3×Q8—41no—
143C2×C3×Q8—41no—
144C2×C3×Q8—62no—
145C2×C3×Q8—122no—
146C2×C3×Q8—122no—
147C2×C3×D4—31no—
148C22×C3×C4—62no—
149C22×C3×C4—61no—
150D3×Q8—42no—
151D3×Q8—42no—
152C2×D12C3×D411yescharacteristic
153C2×C4×D3—22no—
154C2×C4×D3—21no—
155C2×Dic6—22no—
156C2×Dic6C3×D411yescharacteristic
157C3×Q16—122no—
158C2×C3×C8—22no—
159C2×C3×C8—21no—
160C2×C3×C8—21no—
161C2×C3×C8—61no—
162C2×C3×C8—61no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—22no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—22no—
171C3×C4⋊C4—31no—
172C3×C4⋊C4—31no—
173C3×C4⋊C4—41no—
174C3×C4⋊C4—41no—
175C3×C4⋊C4—62no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4#6712yes—
178C3×C4⋊C4C3×D412yes—
179C3×C22⋊C4—62no—
180C3×C22⋊C4—61no—
181C3×C42—21no—
182C3×C42—61no—
183C3×C42C22×D311yescharacteristic
184C3×C42C23×C311yescharacteristic
185#216—42no—
186(C2×D3)⋊C4—22no—
187(C2×D3)⋊C4—21no—
188C4⋊Dic3C3×D411yescharacteristic
189C4⋊Dic3C3×D411yescharacteristic
190Dic3⋊C4—22no—
191Dic3⋊C4—21no—
192C4×Dic3—21no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—21no—
195C22×C32#12011yescharacteristic
196C2×C3×D3—22no—
197C2×C3×D3—41no—
198C2×C3×D3—41no—
199C32×C4—21no—
200C32×C4—42no—
201C32×C4—81no—
202C32×C4C2×D811yescharacteristic
203C32×C4C2×Q1611yescharacteristic
204C32×C4AGL(1,ℤ/8)11yescharacteristic
205C32×C4#13711yescharacteristic
206C3×Dic3—22no—
207C3×Dic3—41no—
208C3×Dic3—41no—
209C22×Q8—61no—
210C2×Q16—61no—
211C4⋊Q8—61no—
212C4⋊Q8C2×C3×D311yescharacteristic
213C4⋊Q8C2×C3×D311yescharacteristic
214C22⋊Q8—61no—
215C22⋊Q8—62no—
216C4×Q8—31no—
217C4×D4—31no—
218C4×D4—61no—
219#107—22no—
220#107—61no—
221C4⋊C8—31no—
222C4⋊C8—31no—
223#103—61no—
224#102—61no—
225C4×C8C2×C3×D311yescharacteristic
226C23×C3—61no—
227C22×D3—21no—
228C3×Q8—32no—
229C3×Q8—41no—
230C3×Q8—41no—
231C3×Q8—41no—
232C3×Q8—41no—
233C3×Q8—41no—
234C3×Q8—41no—
235C3×Q8—41no—
236C3×Q8—41no—
237C3×Q8—61no—
238C3×Q8—81no—
239C3×Q8—81no—
240C3×Q8—81no—
241C3×Q8—81no—
242C3×Q8—124no—
243C3×D4—32no—
244C3×D4—61no—
245C2×C3×C4—22no—
246C2×C3×C4—22no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—42no—
251C2×C3×C4—42no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—61no—
255C2×C3×C4—61no—
256C2×C3×C4—61no—
257C2×C3×C4—124no—
258C2×C3×C4—121no—
259C2×C3×C4—121no—
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4C2×#6711yescharacteristic
263C2×C3×C4C2×C3×D411yescharacteristic
264C2×C3×C4C2×C3×D411yescharacteristic
265C2×C3×C4C2×C3×D411yescharacteristic
266C2×Dic3—21no—
267C2×Dic3—21no—
268C2×Dic3—21no—
269D12—21no—
270D12C3×Q1612yescomplemented
271C4×D3—44no—
272C4×D3—41no—
273C4×D3—41no—
274Dic6—21no—
275Dic6—44no—
276Dic6C3×D812yes—
277C3×C8—24no—
278C3×C8—22no—
279C3×C8—22no—
280C3×C8—121no—
281C3×C8—121no—
282C3⋊C8—41no—
283C3⋊C8—41no—
284C2×C32#44711yescharacteristic
285C2×C32#45111yescharacteristic
286C2×C32#45611yescharacteristic
287C3×D3—42no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—31no—
291C2×Q8—62no—
292C2×Q8—122no—
293C2×Q8—122no—
294C2×D4—31no—
295C22×C4—62no—
296C22×C4—61no—
297Q16—122no—
298C2×C8—21no—
299C2×C8—61no—
300C2×C8—61no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—31no—
305C4⋊C4—31no—
306C4⋊C4—62no—
307C4⋊C4—61no—
308C4⋊C4C3×#6712yes—
309C22⋊C4—62no—
310C22⋊C4—61no—
311C42—61no—
312C42C22×C3×D311yescharacteristic
313C22×C3—21no—
314C22×C3—62no—
315C22×C3—121no—
316C22×C3—121no—
317C22×C3#93711yescharacteristic
318C22×C3C3×#12011yescharacteristic
319C2×D3—22no—
320C2×D3—41no—
321C2×D3—41no—
322C3×C4—22no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—42no—
330C3×C4—42no—
331C3×C4—62no—
332C3×C4—82no—
333C3×C4—82no—
334C3×C4—81no—
335C3×C4—81no—
336C3×C4—121no—
337C3×C4—121no—
338C3×C4D3×D811yescharacteristic
339C3×C4#91111yescharacteristic
340C3×C4D3×Q1611yescharacteristic
341C3×C4#91811yescharacteristic
342C3×C4C2×C3×D811yescharacteristic
343C3×C4C2×C3×Q1611yescharacteristic
344C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
345C3×C4C3×#13711yescharacteristic
346Dic3—22no—
347Dic3—41no—
348Dic3—41no—
349C32#164911yescharacteristic, complemented, Sylow
350C23—61no—
351Q8—32no—
352Q8—41no—
353Q8—41no—
354Q8—41no—
355Q8—41no—
356Q8—61no—
357Q8—124no—
358D4—32no—
359D4—61no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—61no—
363C2×C4—61no—
364C2×C4—61no—
365C2×C4—124no—
366C2×C4—121no—
367C2×C4—121no—
368C2×C4C3×D3×D411yescharacteristic
369C2×C4C3×D3×D411yescharacteristic
370C2×C4C2×C3×#6711yescharacteristic
371C8—22no—
372C8—121no—
373C8—121no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—122no—
378C2×C3#509511yescharacteristic
379C2×C3#515611yescharacteristic
380C2×C3#518611yescharacteristic
381C2×C3C3×#44711yescharacteristic
382C2×C3C3×#45111yescharacteristic
383C2×C3C3×#45611yescharacteristic
384D3—42no—
385C22—62no—
386C22—121no—
387C22—121no—
388C22C3×#93711yescharacteristic
389C4—21no—
390C4—42no—
391C4—62no—
392C4—81no—
393C4—121no—
394C4—121no—
395C4C3×D3×D811yescharacteristic
396C4C3×#91111yescharacteristic
397C4C3×D3×Q1611yescharacteristic
398C4C3×#91811yescharacteristic
399C3—21no—
400C3#7137611yescharacteristic, direct product factor
401C3C3×#164911yescharacteristic, complemented
402C2—122no—
403C2C3×#509511yescharacteristic
404C2C3×#515611yescharacteristic
405C2C3×#518611yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#500C2
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC3×#500D3
hypocenterC3C3×#1649
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#500

Complements

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

NH ≅ G/Ntype
2. C32×#500C2semidirect
3. C3×#5090C2semidirect
5. C3×#4547C2semidirect
7. C3×#4456C2semidirect
9. #71376C3direct (N × H)
30. C3×#500D3semidirect
31. C3×#500C2×C3semidirect
34. #5090C2×C3semidirect
39. #4547C2×C3semidirect
41. #4456C2×C3semidirect
120. C3×D12Q16semidirect
131. #500C3×D3semidirect
270. D12C3×Q16semidirect
349. C32#1649semidirect
400. C3#71376direct (N × H)
401. C3C3×#1649semidirect

Maximal subgroups

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

subgroupindex
C3×#57272
C32×#5002
C3×#50902
C3×#50872
C3×#45472
C3×#44592
C3×#44562
C3×#16493
#713763