Finite Group Databasebeta

← C3×#71114 #11780182

Subgroups — C3×#71114 #11780182

Order 1152.

522 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×Dic6C211yesmaximal, characteristic
2C32×#474C211yesmaximal, characteristic
3C3×#5090C211yesmaximal, characteristic, complemented
4C3×#5078C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic
6C3×#4486C211yesmaximal, characteristic, complemented
7C3×#4484C211yesmaximal, characteristic, complemented
8C3×#1649—31nomaximal
9#71114C311yesmaximal, characteristic, direct product factor
10C22×C3×Dic6—21no—
11C32×C4⋊Q8C2211yescharacteristic
12C32×C4×D4C2211yescharacteristic
13C2×C3×#216—21no—
14C3×D4×Dic3—21no—
15C3×#924—21no—
16C3×#888—21no—
17C3×#878—22no—
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20C32×#107—21no—
21C32×C4⋊C8C2211yescharacteristic
22C32×#102—21no—
23C3×#835—21no—
24C3×#807—22no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27C3×D4×Q8—31no—
28D4×Dic6C2×C311yescharacteristic
29C3×#500—31no—
30C3×#474—21no—
31C3×#474D311yescharacteristic
32C3×#474C2×C311yescharacteristic
33C3×#462—31no—
34#5090C2×C311yescharacteristic, complemented
35#5078C2×C311yescharacteristic, complemented
36C3×#332—31no—
37C3×Q8⋊C8—31no—
38C3×D4⋊C8—31no—
39D4⋊(C3⋊C8)C2×C311yescharacteristic
40#4486C2×C311yescharacteristic, complemented
41#4484C2×C311yescharacteristic, complemented
42C2×C32×Q8—21no—
43C2×C32×D4D411yescharacteristic
44C22×C32×C4—21no—
45C22×C3×Dic3—22no—
46C2×C3×Dic6—22no—
47C2×C3×Dic6—21no—
48C2×C3×Dic6—42no—
49C2×C3×Dic6—42no—
50C2×C3×Dic6D411yescharacteristic
51C2×C32×C8—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4D411yescharacteristic
55C32×C22⋊C4—21no—
56C32×C42C2311yescharacteristic
57C3×#217—22no—
58C3×#216—42no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3D412yes—
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—
69C22×Dic6—21no—
70C2×C3×Q16—61no—
71C3×C4⋊Q8—21no—
72C3×C4⋊Q8—31no—
73C3×C4⋊Q8—61no—
74C3×C4⋊Q8C2×D311yescharacteristic
75C3×C4⋊Q8C22×C311yescharacteristic
76C3×C22⋊Q8—62no—
77C3×C22⋊Q8—61no—
78C3×C4×Q8—31no—
79C3×C4×D4—21no—
80C3×C4×D4—61no—
81C3×C4×D4C2×D311yescharacteristic
82C3×C4×D4C22×C311yescharacteristic
83C2×#216—21no—
84D4×Dic3—21no—
85#924—21no—
86#888—21no—
87#878—22no—
88#869C22×C311yescharacteristic
89C4×Dic6C22×C311yescharacteristic
90C3×#107—22no—
91C3×#107—21no—
92C3×#107—21no—
93C3×#107—62no—
94C3×C4⋊C8—21no—
95C3×C4⋊C8—31no—
96C3×C4⋊C8C2×D311yescharacteristic
97C3×C4⋊C8C22×C311yescharacteristic
98C3×#103—61no—
99C3×#102—22no—
100C3×#102—21no—
101C3×#102—21no—
102C3×C4×C8—31no—
103#835—21no—
104#807—22no—
105C4⋊(C3⋊C8)C22×C311yescharacteristic
106C4×C3⋊C8C22×C311yescharacteristic
107C23×C32—21no—
108C32×Q8—41no—
109C32×Q8—41no—
110C32×D4—21no—
111C32×D4Q1612yescomplemented
112C2×C32×C4—21no—
113C2×C32×C4—41no—
114C2×C32×C4—41no—
115C2×C32×C4—41no—
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C3×Dic3—21no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—44no—
123C3×Dic6—21no—
124C3×Dic6—44no—
125C3×Dic6—41no—
126C3×Dic6—41no—
127C3×Dic6D812yes—
128C32×C8—41no—
129C3×C3⋊C8—22no—
130C3×C3⋊C8—41no—
131D4×Q8—31no—
132#500—31no—
133#474C3×D311yescharacteristic
134#462—31no—
135#332—31no—
136Q8⋊C8—31no—
137D4⋊C8—31no—
138C2×C3×Q8—21no—
139C2×C3×Q8—21no—
140C2×C3×Q8—31no—
141C2×C3×Q8—41no—
142C2×C3×Q8—62no—
143C2×C3×Q8—61no—
144C2×C3×Q8—122no—
145C2×C3×Q8—122no—
146C2×C3×D4—21no—
147C2×C3×D4#6711yescharacteristic
148C2×C3×D4C3×D411yescharacteristic
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—41no—
152C22×C3×C4—62no—
153C22×Dic3—22no—
154C2×Dic6—22no—
155C2×Dic6—21no—
156C2×Dic6—42no—
157C2×Dic6—42no—
158C2×Dic6C3×D411yescharacteristic
159C3×Q16—122no—
160C2×C3×C8—22no—
161C2×C3×C8—21no—
162C2×C3×C8—21no—
163C2×C3×C8—61no—
164C2×C3×C8—61no—
165C3×C4⋊C4—22no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—31no—
172C3×C4⋊C4—32no—
173C3×C4⋊C4—41no—
174C3×C4⋊C4—62no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4#6711yescharacteristic
178C3×C4⋊C4C3×D411yescharacteristic
179C3×C22⋊C4—21no—
180C3×C22⋊C4—21no—
181C3×C22⋊C4—41no—
182C3×C22⋊C4—62no—
183C3×C42—21no—
184C3×C42—61no—
185C3×C42C22×D311yescharacteristic
186C3×C42C23×C311yescharacteristic
187#217—22no—
188#216—42no—
189C4⋊Dic3—21no—
190C4⋊Dic3C3×D412yes—
191C4⋊Dic3C3×D411yescharacteristic
192Dic3⋊C4—22no—
193Dic3⋊C4—21no—
194C4×Dic3—21no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—21no—
197C22×C32—22no—
198C22×C32—41no—
199C22×C32—41no—
200C22×C32#12011yescharacteristic
201C32×C4—21no—
202C32×C4—41no—
203C32×C4—81no—
204C32×C4C2×D811yescharacteristic
205C32×C4C2×Q1611yescharacteristic
206C32×C4AGL(1,ℤ/8)11yescharacteristic
207C32×C4#13711yescharacteristic
208C3×Dic3—22no—
209C3×Dic3—42no—
210C3×Dic3—41no—
211C22×Q8—61no—
212C2×Q16—61no—
213C4⋊Q8—31no—
214C4⋊Q8—61no—
215C4⋊Q8C2×C3×D311yescharacteristic
216C22⋊Q8—62no—
217C22⋊Q8—61no—
218C4×Q8—31no—
219C4×D4—61no—
220C4×D4C2×C3×D311yescharacteristic
221#107—21no—
222#107—62no—
223C4⋊C8—31no—
224C4⋊C8C2×C3×D311yescharacteristic
225#103—61no—
226#102—21no—
227C4×C8—31no—
228C23×C3—21no—
229C23×C3—21no—
230C23×C3—41no—
231C3×Q8—32no—
232C3×Q8—41no—
233C3×Q8—41no—
234C3×Q8—41no—
235C3×Q8—41no—
236C3×Q8—61no—
237C3×Q8—81no—
238C3×Q8—81no—
239C3×Q8—124no—
240C3×Q8—121no—
241C3×Q8—121no—
242C3×D4—21no—
243C3×D4—21no—
244C3×D4—22no—
245C3×D4—41no—
246C3×D4#21612yescomplemented
247C3×D4C3×Q1612yescomplemented
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—41no—
258C2×C3×C4—42no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—61no—
262C2×C3×C4—61no—
263C2×C3×C4—62no—
264C2×C3×C4—81no—
265C2×C3×C4—81no—
266C2×C3×C4—124no—
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4C2×#6711yescharacteristic
270C2×C3×C4C2×C3×D411yescharacteristic
271C2×C3×C4C2×C3×D411yescharacteristic
272C2×C3×C4C2×C3×D411yescharacteristic
273C2×Dic3—21no—
274C2×Dic3—21no—
275C2×Dic3—22no—
276C2×Dic3—44no—
277Dic6—21no—
278Dic6—44no—
279Dic6—41no—
280Dic6—41no—
281Dic6C3×D812yes—
282C3×C8—42no—
283C3×C8—41no—
284C3×C8—41no—
285C3×C8—62no—
286C3×C8—121no—
287C3⋊C8—22no—
288C3⋊C8—41no—
289C2×C32—42no—
290C2×C32#44711yescharacteristic
291C2×C32#45111yescharacteristic
292C2×C32#45611yescharacteristic
293C2×Q8—21no—
294C2×Q8—31no—
295C2×Q8—62no—
296C2×Q8—61no—
297C2×Q8—122no—
298C2×Q8—122no—
299C2×D4C3×#6711yescharacteristic
300C22×C4—21no—
301C22×C4—62no—
302Q16—122no—
303C2×C8—21no—
304C2×C8—61no—
305C2×C8—61no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—31no—
309C4⋊C4—32no—
310C4⋊C4—62no—
311C4⋊C4—61no—
312C4⋊C4—61no—
313C4⋊C4C3×#6711yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—62no—
316C42—61no—
317C42C22×C3×D311yescharacteristic
318C22×C3—22no—
319C22×C3—22no—
320C22×C3—21no—
321C22×C3—42no—
322C22×C3—41no—
323C22×C3—41no—
324C22×C3—41no—
325C22×C3—41no—
326C22×C3—81no—
327C22×C3—81no—
328C22×C3#93711yescharacteristic
329C22×C3C3×#12011yescharacteristic
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—41no—
337C3×C4—41no—
338C3×C4—41no—
339C3×C4—62no—
340C3×C4—81no—
341C3×C4—82no—
342C3×C4—81no—
343C3×C4—81no—
344C3×C4—122no—
345C3×C4—121no—
346C3×C4D3×D811yescharacteristic
347C3×C4#91111yescharacteristic
348C3×C4C2×#21611yescharacteristic
349C3×C4#95111yescharacteristic
350C3×C4C2×C3×D811yescharacteristic
351C3×C4C2×C3×Q1611yescharacteristic
352C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
353C3×C4C3×#13711yescharacteristic
354Dic3—22no—
355Dic3—42no—
356Dic3—41no—
357C32#164911yescharacteristic, complemented, Sylow
358C23—21no—
359Q8—32no—
360Q8—41no—
361Q8—41no—
362Q8—61no—
363Q8—124no—
364Q8—121no—
365Q8—121no—
366D4—21no—
367D4C3×#21612yescomplemented
368C2×C4—21no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—61no—
373C2×C4—61no—
374C2×C4—62no—
375C2×C4—124no—
376C2×C4C3×D3×D411yescharacteristic
377C2×C4C3×D3×D411yescharacteristic
378C2×C4C2×C3×#6711yescharacteristic
379C8—41no—
380C8—62no—
381C8—121no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—42no—
386C2×C3—42no—
387C2×C3—82no—
388C2×C3#505011yescharacteristic
389C2×C3#515611yescharacteristic
390C2×C3#520511yescharacteristic
391C2×C3C3×#44711yescharacteristic
392C2×C3C3×#45111yescharacteristic
393C2×C3C3×#45611yescharacteristic
394C22—22no—
395C22—41no—
396C22—41no—
397C22C3×#93711yescharacteristic
398C4—21no—
399C4—41no—
400C4—62no—
401C4—81no—
402C4—121no—
403C4—122no—
404C4C3×D3×D811yescharacteristic
405C4C3×#91111yescharacteristic
406C4C2×C3×#21611yescharacteristic
407C4C3×#95111yescharacteristic
408C3—21no—
409C3#7111411yescharacteristic, direct product factor
410C3C3×#164911yescharacteristic, complemented
411C2—42no—
412C2C3×#505011yescharacteristic
413C2C3×#515611yescharacteristic
414C2C3×#520511yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#474C2
socleC22×C32#120
prime radicalC2×C32×D4D4
hypercenterC3×#474D3
hypocenterC3C3×#1649
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#474

Complements

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

NH ≅ G/Ntype
3. C3×#5090C2semidirect
4. C3×#5078C2semidirect
6. C3×#4486C2semidirect
7. C3×#4484C2semidirect
9. #71114C3direct (N × H)
34. #5090C2×C3semidirect
35. #5078C2×C3semidirect
40. #4486C2×C3semidirect
41. #4484C2×C3semidirect
111. C32×D4Q16semidirect
246. C3×D4#216semidirect
247. C3×D4C3×Q16semidirect
357. C32#1649semidirect
367. D4C3×#216semidirect
409. C3#71114direct (N × H)
410. C3C3×#1649semidirect

Maximal subgroups

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

subgroupindex
C3×D4×Dic62
C32×#4742
C3×#50902
C3×#50782
C3×D4⋊(C3⋊C8)2
C3×#44862
C3×#44842
C3×#16493
#711143