Finite Group Databasebeta

← C3×#69558 #11795393

Subgroups — C3×#69558 #11795393

Order 1152.

625 conjugacy classes of subgroups.

The subgroup lattice has 447 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#382C211yesmaximal, characteristic, complemented
2C2×C3×#809C211yesmaximal, characteristic
3C2×C3×#809C211yesmaximal, characteristic
4C2×C3×#808C211yesmaximal, characteristic, complemented
5C2×C3×#807C211yesmaximal, characteristic, complemented
6C3×#4939C211yesmaximal, characteristic
7C3×#4524C211yesmaximal, characteristic, complemented
8C3×#2092—31nomaximal
9#69558C311yesmaximal, characteristic, direct product factor
10C22×C3×D12C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4—22no—
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C32×#95—22no—
19C3×#809—22no—
20C3×#809—22no—
21C3×#808—22no—
22C3×#807—22no—
23C2×C3×#107—31no—
24C2×C3×#106—31no—
25C2×C3×#102—31no—
26C2×C3×#102—31no—
27C3×#390—31no—
28C3×#382—21no—
29C3×#382D311yescharacteristic, complemented
30C3×#382C2×C311yescharacteristic, complemented
31C2×#809C2×C311yescharacteristic
32C2×#809C2×C311yescharacteristic
33C2×#808C2×C311yescharacteristic, complemented
34C2×#807C2×C311yescharacteristic, complemented
35#4939C2×C311yescharacteristic
36C3×#336—31no—
37#4524C2×C311yescharacteristic, complemented
38C23×C3×D3—21no—
39C22×C32×C4—21no—
40C22×C32×C4—21no—
41C22×C32×C4D412yes—
42C22×C32×C4C2311yescharacteristic
43C22×C3×Dic3—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12Q812yes—
50C32×C4⋊C4—21no—
51C32×C4⋊C4—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4—21no—
54C32×C42—21no—
55C32×C42—21no—
56C3×(C2×D3)⋊C4—44no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C2×C3×C3⋊C8—21no—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8D412yes—
64C2×C3×C3⋊C8D412yes—
65#2092—31noSylow
66C22×C3×D4—31no—
67C22×D12C22×C311yescharacteristic
68C22×C3×C8—31no—
69C22×C3×C8—31no—
70C2×C3×C4⋊C4—21no—
71C2×C3×C4⋊C4—21no—
72C2×C3×C4⋊C4—31no—
73C2×C3×C4⋊C4C2×D311yescharacteristic
74C2×C3×C4⋊C4C2×D311yescharacteristic
75C2×C3×C4⋊C4C22×C311yescharacteristic
76C2×C3×C4⋊C4C22×C311yescharacteristic
77C2×C3×C22⋊C4—62no—
78C2×C3×C42—21no—
79C2×C3×C42C2×D311yescharacteristic
80C2×C3×C42C22×C311yescharacteristic
81C2×(C2×D3)⋊C4—22no—
82C2×C4⋊Dic3C22×C311yescharacteristic
83C22×C3⋊C8C22×C311yescharacteristic
84C22×C3⋊C8C22×C311yescharacteristic
85C3×#107—62no—
86C3×#106—62no—
87C3×#102—62no—
88C3×#102—62no—
89C3×#95—24no—
90C3×#95—22no—
91C3×#95—22no—
92#809—22no—
93#809—22no—
94#808—22no—
95#807—22no—
96C23×C32C2×D411yescharacteristic
97C22×C3×D3—22no—
98C22×C3×D3—41no—
99C22×C3×D3—41no—
100C22×C3×D3—42no—
101C22×C3×D3—42no—
102C2×C32×C4—22no—
103C2×C32×C4—22no—
104C2×C32×C4—22no—
105C2×C32×C4—41no—
106C2×C32×C4—41no—
107C2×C32×C4—42no—
108C2×C32×C4—42no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×Q811yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C3×Dic3—41no—
116C2×C3×Dic3—42no—
117C3×D12—22no—
118C3×D12—22no—
119C3×D12—41no—
120C3×D12—41no—
121C3×C3⋊C8—22no—
122C3×C3⋊C8—22no—
123C2×#107—31no—
124C2×#106—31no—
125C2×#102—31no—
126C2×#102—31no—
127#390—31no—
128#382C3×D311yescharacteristic, complemented
129#336—31no—
130C24×C3—61no—
131C23×D3—21no—
132C2×C3×D4—32no—
133C2×C3×D4—61no—
134C2×C3×D4—61no—
135C2×C3×D4—61no—
136C2×C3×D4—61no—
137C2×C3×D4—61no—
138C22×C3×C4—22no—
139C22×C3×C4—22no—
140C22×C3×C4—21no—
141C22×C3×C4—21no—
142C22×C3×C4—21no—
143C22×C3×C4—21no—
144C22×C3×C4—22no—
145C22×C3×C4—21no—
146C22×C3×C4—61no—
147C22×C3×C4#6712yes—
148C22×C3×C4C3×D412yes—
149C22×C3×C4C22×D311yescharacteristic
150C22×C3×C4C23×C311yescharacteristic
151C22×Dic3—21no—
152C2×D12—21no—
153C2×D12—21no—
154C2×D12—21no—
155C2×D12—21no—
156C2×D12—21no—
157C2×D12C3×Q812yes—
158C2×C3×C8—32no—
159C2×C3×C8—32no—
160C2×C3×C8—61no—
161C2×C3×C8—61no—
162C2×C3×C8—61no—
163C2×C3×C8—61no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—41no—
173C3×C4⋊C4—41no—
174C3×C4⋊C4—41no—
175C3×C4⋊C4—41no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C22⋊C4—124no—
179C3×C42—22no—
180C3×C42—22no—
181C3×C42—21no—
182C3×C42—21no—
183C3×C42—21no—
184C3×C42—21no—
185(C2×D3)⋊C4—44no—
186C4⋊Dic3—21no—
187C4⋊Dic3—21no—
188C2×C3⋊C8—21no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8C3×D412yes—
193C2×C3⋊C8C3×D412yes—
194C22×C32C22⋊Q811yescharacteristic
195C22×C32#12311yescharacteristic
196C22×C32#12711yescharacteristic
197C22×C32#13512yes—
198C22×C32AGL(1,ℤ/8)12yes—
199C2×C3×D3—42no—
200C2×C3×D3—44no—
201C2×C3×D3—82no—
202C2×C3×D3—81no—
203C2×C3×D3—81no—
204C32×C4—42no—
205C32×C4—81no—
206C32×C4—81no—
207C32×C4C22⋊Q811yescharacteristic
208C32×C4C22⋊Q811yescharacteristic
209C32×C4#12311yescharacteristic
210C32×C4#12311yescharacteristic
211C3×Dic3—81no—
212C22×D4—31no—
213C22×C8—31no—
214C22×C8—31no—
215C2×C4⋊C4—31no—
216C2×C4⋊C4C2×C3×D311yescharacteristic
217C2×C4⋊C4C2×C3×D311yescharacteristic
218C2×C22⋊C4—62no—
219C2×C42C2×C3×D311yescharacteristic
220#107—62no—
221#106—62no—
222#102—62no—
223#102—62no—
224#95—22no—
225C23×C3—21no—
226C23×C3—62no—
227C23×C3—121no—
228C23×C3—121no—
229C23×C3—122no—
230C23×C3—122no—
231C23×C3C2×#6711yescharacteristic
232C23×C3C2×C3×D411yescharacteristic
233C22×D3—22no—
234C22×D3—41no—
235C22×D3—41no—
236C22×D3—42no—
237C22×D3—42no—
238C3×D4—62no—
239C3×D4—62no—
240C3×D4—121no—
241C3×D4—121no—
242C2×C3×C4—24no—
243C2×C3×C4—22no—
244C2×C3×C4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—42no—
256C2×C3×C4—42no—
257C2×C3×C4—42no—
258C2×C3×C4—42no—
259C2×C3×C4—44no—
260C2×C3×C4—44no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—42no—
264C2×C3×C4—42no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—42no—
268C2×C3×C4—42no—
269C2×C3×C4—121no—
270C2×C3×C4—122no—
271C2×C3×C4#23511yescharacteristic
272C2×C3×C4#23511yescharacteristic
273C2×C3×C4D3×D411yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4D3×Q811yescharacteristic
276C2×C3×C4#23911yescharacteristic
277C2×C3×C4C2×C3×D411yescharacteristic
278C2×C3×C4C2×C3×D411yescharacteristic
279C2×C3×C4C2×C3×Q811yescharacteristic
280C2×C3×C4C3×#4111yescharacteristic
281C2×C3×C4C3×#4111yescharacteristic
282C2×C3×C4C3×#4111yescharacteristic
283C2×Dic3—41no—
284C2×Dic3—42no—
285D12—22no—
286D12—22no—
287D12—41no—
288D12—41no—
289C3×C8—62no—
290C3×C8—62no—
291C3⋊C8—22no—
292C3⋊C8—22no—
293C2×C32#39911yescharacteristic
294C2×C32#47812yes—
295C2×C32#48212yes—
296C2×C32#49511yescharacteristic
297C2×C32#49611yescharacteristic
298C3×D3—82no—
299C24—61no—
300C2×D4—32no—
301C2×D4—61no—
302C2×D4—61no—
303C2×D4—61no—
304C2×D4—61no—
305C2×D4—61no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—61no—
309C22×C4C3×#6712yes—
310C22×C4C22×C3×D311yescharacteristic
311C2×C8—32no—
312C2×C8—32no—
313C2×C8—61no—
314C2×C8—61no—
315C2×C8—61no—
316C2×C8—61no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—61no—
322C4⋊C4—61no—
323C22⋊C4—124no—
324C42—21no—
325C42—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—22no—
330C22×C3—22no—
331C22×C3—122no—
332C22×C3—124no—
333C22×C3—242no—
334C22×C3—241no—
335C22×C3—241no—
336C22×C3#92911yescharacteristic
337C22×C3#94011yescharacteristic
338C22×C3#94611yescharacteristic
339C22×C3#94912yes—
340C22×C3#95012yes—
341C22×C3C3×C22⋊Q811yescharacteristic
342C22×C3C3×#12311yescharacteristic
343C22×C3C3×#12711yescharacteristic
344C22×C3C3×#13512yes—
345C22×C3C3×AGL(1,ℤ/8)12yes—
346C2×D3—42no—
347C2×D3—44no—
348C2×D3—82no—
349C2×D3—81no—
350C2×D3—81no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—44no—
356C3×C4—42no—
357C3×C4—42no—
358C3×C4—82no—
359C3×C4—82no—
360C3×C4—81no—
361C3×C4—81no—
362C3×C4—81no—
363C3×C4—81no—
364C3×C4—241no—
365C3×C4#89411yescharacteristic
366C3×C4#89411yescharacteristic
367C3×C4#89611yescharacteristic
368C3×C4#89611yescharacteristic
369C3×C4C3×C22⋊Q811yescharacteristic
370C3×C4C3×C22⋊Q811yescharacteristic
371C3×C4C3×#12311yescharacteristic
372C3×C4C3×#12311yescharacteristic
373Dic3—81no—
374C32#209211yescharacteristic, complemented, Sylow
375C23—62no—
376C23—121no—
377C23—121no—
378C23—122no—
379C23—122no—
380C23C2×C3×#6711yescharacteristic
381D4—62no—
382D4—62no—
383D4—121no—
384D4—121no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—121no—
393C2×C4—122no—
394C2×C4C3×#23511yescharacteristic
395C2×C4C3×#23511yescharacteristic
396C2×C4C3×D3×D411yescharacteristic
397C2×C4C3×D3×D411yescharacteristic
398C2×C4C3×D3×Q811yescharacteristic
399C2×C4C3×#23911yescharacteristic
400C8—62no—
401C8—62no—
402C2×C3—21no—
403C2×C3—22no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—22no—
407C2×C3—242no—
408C2×C3#499311yescharacteristic
409C2×C3#500312yes—
410C2×C3#505811yescharacteristic
411C2×C3#505911yescharacteristic
412C2×C3#506612yes—
413C2×C3C3×#39911yescharacteristic
414C2×C3C3×#47812yes—
415C2×C3C3×#48212yes—
416C2×C3C3×#49511yescharacteristic
417C2×C3C3×#49611yescharacteristic
418D3—82no—
419C22—122no—
420C22—124no—
421C22—242no—
422C22—241no—
423C22—241no—
424C22C3×#92911yescharacteristic
425C22C3×#94011yescharacteristic
426C22C3×#94611yescharacteristic
427C22C3×#94912yes—
428C22C3×#95012yes—
429C4—42no—
430C4—81no—
431C4—81no—
432C4—241no—
433C4C3×#89411yescharacteristic
434C4C3×#89411yescharacteristic
435C4C3×#89611yescharacteristic
436C4C3×#89611yescharacteristic
437C3—21no—
438C3#6955811yescharacteristic, direct product factor
439C3C3×#209211yescharacteristic, complemented
440C2—242no—
441C2C3×#499311yescharacteristic
442C2C3×#500312yes—
443C2C3×#505811yescharacteristic
444C2C3×#505911yescharacteristic
445C2C3×#506612yes—
subgroupG/H
centerC23×C3C2×#67
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#382C2
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC3×#382D3
hypocenterC3C3×#2092
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C3×#382

Complements

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

NH ≅ G/Ntype
1. C32×#382C2semidirect
4. C2×C3×#808C2semidirect
5. C2×C3×#807C2semidirect
7. C3×#4524C2semidirect
9. #69558C3direct (N × H)
29. C3×#382D3semidirect
30. C3×#382C2×C3semidirect
33. C2×#808C2×C3semidirect
34. C2×#807C2×C3semidirect
37. #4524C2×C3semidirect
128. #382C3×D3semidirect
374. C32#2092semidirect
438. C3#69558direct (N × H)
439. C3C3×#2092semidirect

Maximal subgroups

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

subgroupindex
C32×#3822
C2×C3×#8092
C2×C3×#8082
C2×C3×#8072
C3×#49392
C3×#45242
C3×#20923
#695583