Finite Group Databasebeta

← C3×#71048 #11780085

Subgroups — C3×#71048 #11780085

Order 1152.

540 conjugacy classes of subgroups.

The subgroup lattice has 437 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5555C211yesmaximal, characteristic
2C32×#461C211yesmaximal, characteristic, complemented
3C3×#5087C211yesmaximal, characteristic, complemented
4C3×#5078C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic, complemented
7C3×#4482C211yesmaximal, characteristic, complemented
8C3×#1647—31nomaximal
9#71048C311yesmaximal, characteristic, direct product factor
10C2×C3×#237—21no—
11C2×C32×SD16—21no—
12C32×C4⋊Q8C2211yescharacteristic
13C32×C4×D4C2211yescharacteristic
14C3×#930—21no—
15C2×C3×C4⋊Dic3—21no—
16C3×#897—21no—
17C3×#886—22no—
18C3×C4×D12C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C32×C4⋊C8C2211yescharacteristic
21C32×#103—21no—
22C3×#809—21no—
23C3×#807—22no—
24C3×#807—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27C3×#547—31no—
28#5555C2×C311yescharacteristic
29C3×#500—31no—
30C3×#474—31no—
31C3×#461—21no—
32C3×#461D311yescharacteristic, complemented
33C3×#461C2×C311yescharacteristic, complemented
34#5087C2×C311yescharacteristic, complemented
35#5078C2×C311yescharacteristic, complemented
36C3×#332—31no—
37C3×D4⋊C8—31no—
38C3×D4⋊C8—31no—
39D4⋊(C3⋊C8)C2×C311yescharacteristic, complemented
40#4483C2×C311yescharacteristic, complemented
41#4482C2×C311yescharacteristic, complemented
42C2×C32×Q8—21no—
43C2×C32×D4D411yescharacteristic
44C22×C32×C4—21no—
45C2×C3×#67—22no—
46C22×C3×Dic3—22no—
47C3×#237—42no—
48C3×#237—42no—
49C2×C3×D12D411yescharacteristic
50C2×C3×C4×D3—21no—
51C2×C3×Dic6—21no—
52C32×SD16—42no—
53C2×C32×C8—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4D411yescharacteristic
57C32×C22⋊C4—21no—
58C32×C42C2311yescharacteristic
59C3×(C2×D3)⋊C4—22no—
60C3×(C2×D3)⋊C4—21no—
61C3×C4⋊Dic3—22no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3D412yes—
64C3×C4⋊Dic3D411yescharacteristic
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#1647—31noSylow
68C2×C3×#41—61no—
69C2×#237—21no—
70C2×C3×SD16—22no—
71C2×C3×SD16—21no—
72C2×C3×SD16—21no—
73C3×C4⋊Q8—21no—
74C3×C4⋊Q8—31no—
75C3×C4⋊Q8C2×D311yescharacteristic
76C3×C4⋊Q8C22×C311yescharacteristic
77C3×#123—62no—
78C3×C22⋊Q8—61no—
79C3×#121—61no—
80C3×C4×D4—21no—
81C3×C4×D4—31no—
82C3×C4×D4C2×D311yescharacteristic
83C3×C4×D4C22×C311yescharacteristic
84C2×C3×C4⋊C4—61no—
85#930—21no—
86C2×C4⋊Dic3—21no—
87#897—21no—
88#886—22no—
89C4×D12C22×C311yescharacteristic
90#869C22×C311yescharacteristic
91C3×#107—61no—
92C3×#107—62no—
93C3×C4⋊C8—21no—
94C3×C4⋊C8—31no—
95C3×C4⋊C8C2×D311yescharacteristic
96C3×C4⋊C8C22×C311yescharacteristic
97C3×#103—22no—
98C3×#103—21no—
99C3×#103—21no—
100C3×#102—61no—
101C3×C4×C8—31no—
102#809—21no—
103#807—22no—
104#807—21no—
105C4⋊(C3⋊C8)C22×C311yescharacteristic
106C4×C3⋊C8C22×C311yescharacteristic
107C23×C32—21no—
108C22×C3×D3—21no—
109C32×Q8—41no—
110C32×Q8—41no—
111C32×D4—21no—
112C32×D4D812yes—
113C2×C32×C4—21no—
114C2×C32×C4—41no—
115C2×C32×C4—41no—
116C2×C32×C4—41no—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C3×#67—44no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—44no—
124C3×D12—21no—
125C3×D12—21no—
126C3×C4×D3—41no—
127C3×C4×D3—41no—
128C3×Dic6—41no—
129C3×Dic6—41no—
130C32×C8—41no—
131C3×C3⋊C8—22no—
132C3×C3⋊C8—41no—
133#547—31no—
134#500—31no—
135#474—31no—
136#461C3×D311yescharacteristic, complemented
137#332—31no—
138D4⋊C8—31no—
139D4⋊C8—31no—
140C3×#41—122no—
141C3×#41—122no—
142C2×C3×Q8—22no—
143C2×C3×Q8—21no—
144C2×C3×Q8—21no—
145C2×C3×Q8—61no—
146C2×C3×D4—21no—
147C2×C3×D4—31no—
148C2×C3×D4—62no—
149C2×C3×D4#6711yescharacteristic
150C2×C3×D4C3×D411yescharacteristic
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—41no—
154C22×C3×C4—62no—
155C22×C3×C4—61no—
156C2×#67—22no—
157C22×Dic3—22no—
158#237—42no—
159#237—42no—
160C2×D12C3×D411yescharacteristic
161C2×C4×D3—21no—
162C2×Dic6—21no—
163C3×SD16—44no—
164C3×SD16—42no—
165C3×SD16—42no—
166C2×C3×C8—22no—
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C2×C3×C8—61no—
170C2×C3×C8—61no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—31no—
177C3×C4⋊C4—32no—
178C3×C4⋊C4—41no—
179C3×C4⋊C4—41no—
180C3×C4⋊C4—62no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4#6711yescharacteristic
183C3×C4⋊C4C3×D411yescharacteristic
184C3×C22⋊C4—21no—
185C3×C22⋊C4—21no—
186C3×C22⋊C4—41no—
187C3×C22⋊C4—62no—
188C3×C22⋊C4—61no—
189C3×C42—21no—
190C3×C42C22×D311yescharacteristic
191C3×C42C23×C311yescharacteristic
192(C2×D3)⋊C4—22no—
193(C2×D3)⋊C4—21no—
194C4⋊Dic3—22no—
195C4⋊Dic3—21no—
196C4⋊Dic3C3×D412yes—
197C4⋊Dic3C3×D411yescharacteristic
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C22×C32—22no—
201C22×C32—41no—
202C22×C32—41no—
203C22×C32#12011yescharacteristic
204C2×C3×D3—41no—
205C2×C3×D3—41no—
206C2×C3×D3—41no—
207C32×C4—21no—
208C32×C4—41no—
209C32×C4—81no—
210C32×C4C2×D811yescharacteristic
211C32×C4#13511yescharacteristic
212C32×C4AGL(1,ℤ/8)11yescharacteristic
213C32×C4#13711yescharacteristic
214C3×Dic3—42no—
215C3×Dic3—41no—
216C2×#41—61no—
217C2×SD16—21no—
218C4⋊Q8—31no—
219C4⋊Q8C2×C3×D311yescharacteristic
220#123—62no—
221C22⋊Q8—61no—
222#121—61no—
223C4×D4—31no—
224C4×D4C2×C3×D311yescharacteristic
225C2×C4⋊C4—61no—
226#107—61no—
227#107—62no—
228C4⋊C8—31no—
229C4⋊C8C2×C3×D311yescharacteristic
230#103—21no—
231#102—61no—
232C4×C8—31no—
233C23×C3—21no—
234C23×C3—21no—
235C23×C3—41no—
236C23×C3—61no—
237C22×D3—21no—
238C3×Q8—42no—
239C3×Q8—42no—
240C3×Q8—41no—
241C3×Q8—41no—
242C3×Q8—41no—
243C3×Q8—41no—
244C3×Q8—121no—
245C3×Q8—121no—
246C3×D4—21no—
247C3×D4—21no—
248C3×D4—22no—
249C3×D4—41no—
250C3×D4—61no—
251C3×D4—61no—
252C3×D4—124no—
253C3×D4#21312yes—
254C3×D4C3×D812yes—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—42no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4—61no—
269C2×C3×C4—62no—
270C2×C3×C4—81no—
271C2×C3×C4—81no—
272C2×C3×C4—124no—
273C2×C3×C4—121no—
274C2×C3×C4—121no—
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4C2×#6711yescharacteristic
278C2×C3×C4C2×C3×D411yescharacteristic
279C2×C3×C4C2×C3×D411yescharacteristic
280C2×C3×C4C2×C3×D411yescharacteristic
281#67—44no—
282C2×Dic3—22no—
283C2×Dic3—21no—
284C2×Dic3—44no—
285D12—21no—
286D12—21no—
287C4×D3—41no—
288C4×D3—41no—
289Dic6—41no—
290Dic6—41no—
291C3×C8—42no—
292C3×C8—41no—
293C3×C8—41no—
294C3×C8—62no—
295C3×C8—121no—
296C3⋊C8—22no—
297C3⋊C8—41no—
298C2×C32—42no—
299C2×C32#44711yescharacteristic
300C2×C32#45211yescharacteristic
301C2×C32#45611yescharacteristic
302C3×D3—81no—
303#41—122no—
304#41—122no—
305C2×Q8—21no—
306C2×Q8—61no—
307C2×D4—31no—
308C2×D4—62no—
309C2×D4C3×#6711yescharacteristic
310C22×C4—21no—
311C22×C4—62no—
312C22×C4—61no—
313SD16—42no—
314C2×C8—21no—
315C2×C8—61no—
316C2×C8—61no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—31no—
320C4⋊C4—32no—
321C4⋊C4—62no—
322C4⋊C4—61no—
323C4⋊C4C3×#6711yescharacteristic
324C22⋊C4—21no—
325C22⋊C4—62no—
326C22⋊C4—61no—
327C42C22×C3×D311yescharacteristic
328C22×C3—22no—
329C22×C3—22no—
330C22×C3—21no—
331C22×C3—42no—
332C22×C3—41no—
333C22×C3—41no—
334C22×C3—41no—
335C22×C3—41no—
336C22×C3—81no—
337C22×C3—81no—
338C22×C3—121no—
339C22×C3—121no—
340C22×C3—121no—
341C22×C3#93711yescharacteristic
342C22×C3C3×#12011yescharacteristic
343C2×D3—41no—
344C2×D3—41no—
345C2×D3—41no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—41no—
353C3×C4—41no—
354C3×C4—41no—
355C3×C4—81no—
356C3×C4—82no—
357C3×C4—81no—
358C3×C4—81no—
359C3×C4—121no—
360C3×C4—122no—
361C3×C4#91511yescharacteristic
362C3×C4#91611yescharacteristic
363C3×C4C2×#21311yescharacteristic
364C3×C4#94911yescharacteristic
365C3×C4C2×C3×D811yescharacteristic
366C3×C4C3×#13511yescharacteristic
367C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
368C3×C4C3×#13711yescharacteristic
369Dic3—42no—
370Dic3—41no—
371C32#164711yescharacteristic, complemented, Sylow
372C23—21no—
373C23—61no—
374Q8—41no—
375Q8—41no—
376Q8—121no—
377Q8—121no—
378D4—21no—
379D4—61no—
380D4—61no—
381D4—124no—
382D4C3×#21312yes—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—61no—
388C2×C4—62no—
389C2×C4—124no—
390C2×C4—121no—
391C2×C4—121no—
392C2×C4C3×D3×D411yescharacteristic
393C2×C4C3×D3×D411yescharacteristic
394C2×C4C2×C3×#6711yescharacteristic
395C8—41no—
396C8—62no—
397C8—121no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—42no—
402C2×C3—42no—
403C2×C3—82no—
404C2×C3—241no—
405C2×C3#503611yescharacteristic
406C2×C3#517311yescharacteristic
407C2×C3#520511yescharacteristic
408C2×C3C3×#44711yescharacteristic
409C2×C3C3×#45211yescharacteristic
410C2×C3C3×#45611yescharacteristic
411D3—81no—
412C22—22no—
413C22—41no—
414C22—41no—
415C22—121no—
416C22—121no—
417C22—121no—
418C22C3×#93711yescharacteristic
419C4—21no—
420C4—41no—
421C4—81no—
422C4—121no—
423C4—122no—
424C4C3×#91511yescharacteristic
425C4C3×#91611yescharacteristic
426C4C2×C3×#21311yescharacteristic
427C4C3×#94911yescharacteristic
428C3—21no—
429C3#7104811yescharacteristic, direct product factor
430C3C3×#164711yescharacteristic, complemented
431C2—42no—
432C2—241no—
433C2C3×#503611yescharacteristic
434C2C3×#517311yescharacteristic
435C2C3×#520511yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#461C2
socleC22×C32#120
prime radicalC3×#5555C2
hypercenterC3×#461D3
hypocenterC3C3×#1647
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#461

Complements

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

NH ≅ G/Ntype
2. C32×#461C2semidirect
3. C3×#5087C2semidirect
4. C3×#5078C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
6. C3×#4483C2semidirect
7. C3×#4482C2semidirect
9. #71048C3direct (N × H)
32. C3×#461D3semidirect
33. C3×#461C2×C3semidirect
34. #5087C2×C3semidirect
35. #5078C2×C3semidirect
39. D4⋊(C3⋊C8)C2×C3semidirect
40. #4483C2×C3semidirect
41. #4482C2×C3semidirect
136. #461C3×D3semidirect
371. C32#1647semidirect
429. C3#71048direct (N × H)
430. C3C3×#1647semidirect

Maximal subgroups

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

subgroupindex
C3×#55552
C32×#4612
C3×#50872
C3×#50782
C3×D4⋊(C3⋊C8)2
C3×#44832
C3×#44822
C3×#16473
#710483