Finite Group Databasebeta

← C3×#69585 #11794643

Subgroups — C3×#69585 #11794643

Order 1152.

641 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#384C211yesmaximal, characteristic, complemented
2C2×C3×#809C212yesmaximal
3C3×#4939C211yesmaximal, characteristic
4C3×#4529C212yesmaximal, complemented
5C3×#4524C211yesmaximal, characteristic, complemented
6C3×#2071—31nomaximal
7#69585C311yesmaximal, characteristic, direct product factor
8C22×C3×D12C2211yescharacteristic
9C2×C32×C4⋊C4—21no—
10C2×C32×C4⋊C4—21no—
11C2×C32×C4⋊C4C2212yes—
12C2×C32×C42C2211yescharacteristic
13C2×C3×(C2×D3)⋊C4—21no—
14C2×C3×(C2×D3)⋊C4—21no—
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2212yes—
17C3×#809—24no—
18C2×C3×#102—32no—
19C3×#390—31no—
20C3×#384—21no—
21C3×#384D311yescharacteristic, complemented
22C3×#384C2×C311yescharacteristic, complemented
23C2×#809C2×C312yes—
24#4939C2×C311yescharacteristic
25C3×#340—32no—
26C3×#336—31no—
27#4529C2×C312yescomplemented
28#4524C2×C311yescharacteristic, complemented
29C23×C3×D3—21no—
30C22×C32×C4—22no—
31C22×C32×C4D411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C22×C32×C4C2311yescharacteristic
34C22×C3×Dic3—21no—
35C2×C3×D12—22no—
36C2×C3×D12—22no—
37C2×C3×D12—21no—
38C2×C3×D12D412yes—
39C32×C4⋊C4—22no—
40C32×C4⋊C4—22no—
41C32×C4⋊C4—42no—
42C32×C4⋊C4—42no—
43C32×C42—22no—
44C3×(C2×D3)⋊C4—42no—
45C3×(C2×D3)⋊C4—42no—
46C3×C4⋊Dic3—22no—
47C2×C3×C3⋊C8—22no—
48C2×C3×C3⋊C8—22no—
49C2×C3×C3⋊C8—22no—
50#2071—31noSylow
51C22×C3×D4—31no—
52C22×D12C22×C311yescharacteristic
53C22×C3×C8—32no—
54C2×C3×C4⋊C4—22no—
55C2×C3×C4⋊C4—22no—
56C2×C3×C4⋊C4—21no—
57C2×C3×C4⋊C4—21no—
58C2×C3×C4⋊C4—21no—
59C2×C3×C4⋊C4—21no—
60C2×C3×C4⋊C4—22no—
61C2×C3×C4⋊C4—31no—
62C2×C3×C4⋊C4C2×D312yes—
63C2×C3×C4⋊C4C22×C312yes—
64C2×C3×C22⋊C4—61no—
65C2×C3×C22⋊C4—61no—
66C2×C3×C42—21no—
67C2×C3×C42C2×D311yescharacteristic
68C2×C3×C42C22×C311yescharacteristic
69C2×(C2×D3)⋊C4—21no—
70C2×(C2×D3)⋊C4—21no—
71C2×C4⋊Dic3C22×C311yescharacteristic
72C22×C3⋊C8C22×C312yes—
73C3×#102—64no—
74#809—24no—
75C23×C32C2×D411yescharacteristic
76C22×C3×D3—22no—
77C22×C3×D3—41no—
78C22×C3×D3—41no—
79C22×C3×D3—41no—
80C22×C3×D3—41no—
81C22×C3×D3—41no—
82C22×C3×D3—41no—
83C2×C32×C4—21no—
84C2×C32×C4—21no—
85C2×C32×C4—21no—
86C2×C32×C4—21no—
87C2×C32×C4—42no—
88C2×C32×C4—42no—
89C2×C32×C4—42no—
90C2×C32×C4D812yes—
91C2×C32×C4SD1612yes—
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4#4112yes—
94C2×C32×C4#4111yescharacteristic
95C2×C32×C4#4112yes—
96C2×C3×Dic3—41no—
97C2×C3×Dic3—41no—
98C2×C3×Dic3—41no—
99C3×D12—24no—
100C3×D12—42no—
101C3×C3⋊C8—42no—
102C2×#102—32no—
103#390—31no—
104#384C3×D311yescharacteristic, complemented
105#340—32no—
106#336—31no—
107C24×C3—61no—
108C23×D3—21no—
109C2×C3×D4—32no—
110C2×C3×D4—62no—
111C2×C3×D4—61no—
112C2×C3×D4—62no—
113C22×C3×C4—24no—
114C22×C3×C4—22no—
115C22×C3×C4—22no—
116C22×C3×C4—21no—
117C22×C3×C4—21no—
118C22×C3×C4—21no—
119C22×C3×C4—61no—
120C22×C3×C4#6711yescharacteristic
121C22×C3×C4#6711yescharacteristic
122C22×C3×C4C3×D411yescharacteristic
123C22×C3×C4C3×D411yescharacteristic
124C22×C3×C4C22×D311yescharacteristic
125C22×C3×C4C23×C311yescharacteristic
126C22×Dic3—21no—
127C2×D12—22no—
128C2×D12—22no—
129C2×D12—21no—
130C2×D12C3×D412yes—
131C2×C3×C8—62no—
132C2×C3×C8—62no—
133C2×C3×C8—62no—
134C3×C4⋊C4—22no—
135C3×C4⋊C4—22no—
136C3×C4⋊C4—22no—
137C3×C4⋊C4—22no—
138C3×C4⋊C4—42no—
139C3×C4⋊C4—42no—
140C3×C4⋊C4—44no—
141C3×C4⋊C4—42no—
142C3×C4⋊C4—42no—
143C3×C4⋊C4—44no—
144C3×C4⋊C4—42no—
145C3×C4⋊C4—42no—
146C3×C4⋊C4—62no—
147C3×C22⋊C4—122no—
148C3×C22⋊C4—122no—
149C3×C42—24no—
150C3×C42—22no—
151C3×C42—22no—
152(C2×D3)⋊C4—42no—
153(C2×D3)⋊C4—42no—
154C4⋊Dic3—22no—
155C2×C3⋊C8—22no—
156C2×C3⋊C8—22no—
157C2×C3⋊C8—22no—
158C22×C32#12111yescharacteristic
159C22×C32#12311yescharacteristic
160C22×C32#12411yescharacteristic
161C22×C32C2×D811yescharacteristic
162C22×C32C2×SD1611yescharacteristic
163C22×C32AGL(1,ℤ/8)11yescharacteristic
164C22×C32#13711yescharacteristic
165C2×C3×D3—42no—
166C2×C3×D3—42no—
167C2×C3×D3—42no—
168C2×C3×D3—81no—
169C2×C3×D3—81no—
170C2×C3×D3—81no—
171C2×C3×D3—81no—
172C32×C4—22no—
173C32×C4—22no—
174C32×C4—82no—
175C32×C4#12312yes—
176C32×C4#12612yes—
177C3×Dic3—81no—
178C22×D4—31no—
179C22×C8—32no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—31no—
183C2×C4⋊C4C2×C3×D312yes—
184C2×C22⋊C4—61no—
185C2×C22⋊C4—61no—
186C2×C42C2×C3×D311yescharacteristic
187#102—64no—
188C23×C3—21no—
189C23×C3—62no—
190C23×C3—121no—
191C23×C3—121no—
192C23×C3—121no—
193C23×C3—121no—
194C23×C3—121no—
195C23×C3—121no—
196C23×C3C2×#6711yescharacteristic
197C23×C3C2×C3×D411yescharacteristic
198C22×D3—22no—
199C22×D3—41no—
200C22×D3—41no—
201C22×D3—41no—
202C22×D3—41no—
203C22×D3—41no—
204C22×D3—41no—
205C3×D4—64no—
206C3×D4—122no—
207C2×C3×C4—22no—
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—22no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—22no—
220C2×C3×C4—22no—
221C2×C3×C4—22no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—22no—
225C2×C3×C4—44no—
226C2×C3×C4—44no—
227C2×C3×C4—44no—
228C2×C3×C4—42no—
229C2×C3×C4—42no—
230C2×C3×C4—42no—
231C2×C3×C4—42no—
232C2×C3×C4—42no—
233C2×C3×C4—42no—
234C2×C3×C4—121no—
235C2×C3×C4—121no—
236C2×C3×C4—121no—
237C2×C3×C4#21312yes—
238C2×C3×C4#21512yes—
239C2×C3×C4C3×D812yes—
240C2×C3×C4C3×SD1612yes—
241C2×C3×C4#23512yes—
242C2×C3×C4D3×D411yescharacteristic
243C2×C3×C4#23711yescharacteristic
244C2×C3×C4#23912yes—
245C2×C3×C4C2×C3×D411yescharacteristic
246C2×C3×C4C3×#4112yes—
247C2×C3×C4C3×#4111yescharacteristic
248C2×C3×C4C3×#4112yes—
249C2×Dic3—41no—
250C2×Dic3—41no—
251C2×Dic3—41no—
252D12—24no—
253D12—42no—
254C3×C8—122no—
255C3⋊C8—42no—
256C2×C32#39711yescharacteristic
257C2×C32#45911yescharacteristic
258C2×C32#46111yescharacteristic
259C2×C32#48011yescharacteristic
260C2×C32#48111yescharacteristic
261C2×C32#48611yescharacteristic
262C2×C32#48911yescharacteristic
263C3×D3—82no—
264C24—61no—
265C2×D4—32no—
266C2×D4—62no—
267C2×D4—61no—
268C2×D4—62no—
269C22×C4—22no—
270C22×C4—61no—
271C22×C4C3×#6711yescharacteristic
272C22×C4C3×#6711yescharacteristic
273C22×C4C22×C3×D311yescharacteristic
274C2×C8—62no—
275C2×C8—62no—
276C2×C8—62no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4—62no—
282C22⋊C4—122no—
283C22⋊C4—122no—
284C42—22no—
285C22×C3—21no—
286C22×C3—21no—
287C22×C3—21no—
288C22×C3—21no—
289C22×C3—21no—
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—122no—
293C22×C3—122no—
294C22×C3—122no—
295C22×C3—241no—
296C22×C3—241no—
297C22×C3—241no—
298C22×C3—241no—
299C22×C3#92911yescharacteristic
300C22×C3C2×#21311yescharacteristic
301C22×C3#93211yescharacteristic
302C22×C3#93811yescharacteristic
303C22×C3C2×#21511yescharacteristic
304C22×C3#94211yescharacteristic
305C22×C3#94711yescharacteristic
306C22×C3C3×#12111yescharacteristic
307C22×C3C3×#12311yescharacteristic
308C22×C3C3×#12411yescharacteristic
309C22×C3C2×C3×D811yescharacteristic
310C22×C3C2×C3×SD1611yescharacteristic
311C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
312C22×C3C3×#13711yescharacteristic
313C2×D3—42no—
314C2×D3—42no—
315C2×D3—42no—
316C2×D3—81no—
317C2×D3—81no—
318C2×D3—81no—
319C2×D3—81no—
320C3×C4—24no—
321C3×C4—24no—
322C3×C4—22no—
323C3×C4—22no—
324C3×C4—22no—
325C3×C4—22no—
326C3×C4—22no—
327C3×C4—22no—
328C3×C4—84no—
329C3×C4—82no—
330C3×C4—82no—
331C3×C4—241no—
332C3×C4#89412yes—
333C3×C4#89812yes—
334C3×C4C3×#12312yes—
335C3×C4C3×#12612yes—
336Dic3—81no—
337C32#207111yescharacteristic, complemented, Sylow
338C23—62no—
339C23—121no—
340C23—121no—
341C23—121no—
342C23—121no—
343C23—121no—
344C23—121no—
345C23C2×C3×#6711yescharacteristic
346D4—64no—
347D4—122no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—121no—
356C2×C4—121no—
357C2×C4—121no—
358C2×C4C3×#21312yes—
359C2×C4C3×#21512yes—
360C2×C4C3×#23512yes—
361C2×C4C3×D3×D411yescharacteristic
362C2×C4C3×#23711yescharacteristic
363C2×C4C3×#23912yes—
364C8—122no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—242no—
373C2×C3#496711yescharacteristic
374C2×C3#496811yescharacteristic
375C2×C3#499211yescharacteristic
376C2×C3#507211yescharacteristic
377C2×C3#508311yescharacteristic
378C2×C3#508811yescharacteristic
379C2×C3#508911yescharacteristic
380C2×C3C3×#39711yescharacteristic
381C2×C3C3×#45911yescharacteristic
382C2×C3C3×#46111yescharacteristic
383C2×C3C3×#48011yescharacteristic
384C2×C3C3×#48111yescharacteristic
385C2×C3C3×#48611yescharacteristic
386C2×C3C3×#48911yescharacteristic
387D3—82no—
388C22—122no—
389C22—122no—
390C22—122no—
391C22—241no—
392C22—241no—
393C22—241no—
394C22—241no—
395C22C3×#92911yescharacteristic
396C22C2×C3×#21311yescharacteristic
397C22C3×#93211yescharacteristic
398C22C3×#93811yescharacteristic
399C22C2×C3×#21511yescharacteristic
400C22C3×#94211yescharacteristic
401C22C3×#94711yescharacteristic
402C4—22no—
403C4—22no—
404C4—82no—
405C4—241no—
406C4C3×#89412yes—
407C4C3×#89812yes—
408C3—21no—
409C3#6958511yescharacteristic, direct product factor
410C3C3×#207111yescharacteristic, complemented
411C2—242no—
412C2C3×#496711yescharacteristic
413C2C3×#496811yescharacteristic
414C2C3×#499211yescharacteristic
415C2C3×#507211yescharacteristic
416C2C3×#508311yescharacteristic
417C2C3×#508811yescharacteristic
418C2C3×#508911yescharacteristic
subgroupG/H
centerC23×C3C2×#67
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#384C2
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC3×#384D3
hypocenterC3C3×#2071
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C3×#384

Complements

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

NH ≅ G/Ntype
1. C32×#384C2semidirect
4. C3×#4529C2semidirect
5. C3×#4524C2semidirect
7. #69585C3direct (N × H)
21. C3×#384D3semidirect
22. C3×#384C2×C3semidirect
27. #4529C2×C3semidirect
28. #4524C2×C3semidirect
104. #384C3×D3semidirect
337. C32#2071semidirect
409. C3#69585direct (N × H)
410. C3C3×#2071semidirect

Maximal subgroups

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

subgroupindex
C32×#3842
C2×C3×#8092
C3×#49392
C3×#45292
C3×#45242
C3×#20713
#695853