Finite Group Databasebeta

← C3×#69907 #11783604

Subgroups — C3×#69907 #11783604

Order 1152.

773 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#926C211yesmaximal, characteristic
2C2×C32×C22⋊C8C211yesmaximal, characteristic
3C2×C3×#830C211yesmaximal, characteristic
4C2×C3×#815C211yesmaximal, characteristic, complemented
5C2×C3×C8×Dic3C211yesmaximal, characteristic, complemented
6C3×#4550C211yesmaximal, characteristic, complemented
7C3×#4550C211yesmaximal, characteristic, complemented
8C3×#1750—31nomaximal
9#69907C311yesmaximal, characteristic, direct product factor
10C23×C32×C4C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C3×#217C412yes—
14C3×#926—22no—
15C3×#926—22no—
16C2×C3×C4⋊Dic3C412yes—
17C2×C3×C4×Dic3C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C32×C22⋊C8C414yescomplemented
22C3×#830C414yescomplemented
23C3×#815—22no—
24C3×C8×Dic3—22no—
25C2×C3×#117—31no—
26C2×#926C2×C311yescharacteristic
27C2×C3×C22⋊C8—21no—
28C2×C3×C22⋊C8—31no—
29C2×C3×C22⋊C8D311yescharacteristic
30C2×C3×C22⋊C8C2×C311yescharacteristic
31C2×C3×#97—31no—
32C2×C3×C4×C8—31no—
33C2×#830C2×C311yescharacteristic
34C2×#815C2×C311yescharacteristic, complemented
35C2×C8×Dic3C2×C311yescharacteristic, complemented
36C3×#336—31no—
37C3×#336—31no—
38#4550C2×C311yescharacteristic, complemented
39#4550C2×C311yescharacteristic, complemented
40C24×C32C2×C411yescharacteristic
41C22×C32×C4—21no—
42C22×C32×C4—21no—
43C22×C32×C4—21no—
44C22×C32×C4—21no—
45C22×C32×C4C2×C411yescharacteristic
46C22×C32×C4C2×C412yes—
47C22×C32×C4C2×C412yes—
48C22×C32×C4C2311yescharacteristic
49C22×C3×Dic3C2×C412yes—
50C22×C3×Dic3C2×C412yes—
51C2×C32×C8—21no—
52C2×C32×C8—21no—
53C2×C32×C8—21no—
54C2×C32×C8—21no—
55C2×C32×C8C2×C412yes—
56C2×C32×C8C2×C412yes—
57C3×#217—24no—
58C3×C4⋊Dic3—24no—
59C3×C4×Dic3—21no—
60C3×C4×Dic3—21no—
61C3×C4×Dic3D412yes—
62C3×C4×Dic3D412yes—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8C2×C412yes—
68C2×C3×C3⋊C8C2×C412yes—
69#1750—31noSylow
70C23×C3×C4—21no—
71C23×C3×C4C2×D311yescharacteristic
72C23×C3×C4C22×C311yescharacteristic
73C22×C3×C8—21no—
74C22×C3×C8—21no—
75C22×C3×C8—31no—
76C22×C3×C8—31no—
77C22×C3×C8C2×D311yescharacteristic
78C22×C3×C8C2×D311yescharacteristic
79C22×C3×C8C22×C311yescharacteristic
80C22×C3×C8C22×C311yescharacteristic
81C3×#117—62no—
82C3×#117—62no—
83C2×C3×C4⋊C4—32no—
84C2×C3×C22⋊C4—32no—
85C2×C3×C42—31no—
86C2×C3×C42—31no—
87C2×#217C3×C412yes—
88#926—22no—
89#926—22no—
90C2×C4⋊Dic3C3×C412yes—
91C2×C4×Dic3C22×C311yescharacteristic
92C2×C4×Dic3C22×C311yescharacteristic
93C22×C3⋊C8C22×C311yescharacteristic
94C22×C3⋊C8C22×C311yescharacteristic
95C3×C22⋊C8—24no—
96C3×C22⋊C8—34no—
97C3×C22⋊C8Dic314yescomplemented
98C3×C22⋊C8C3×C414yescomplemented
99C3×#97—62no—
100C3×C4×C8—62no—
101#830C3×C414yescomplemented
102#815—22no—
103C8×Dic3—22no—
104C23×C32—22no—
105C23×C32—21no—
106C23×C32—21no—
107C23×C32—22no—
108C23×C32C4212yes—
109C23×C32C22×C411yescharacteristic
110C2×C32×C4—21no—
111C2×C32×C4—21no—
112C2×C32×C4—22no—
113C2×C32×C4—22no—
114C2×C32×C4—22no—
115C2×C32×C4—22no—
116C2×C32×C4C4212yes—
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C3×Dic3—22no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3C22⋊C414yes—
129C32×C8—22no—
130C32×C8—22no—
131C3×C3⋊C8—22no—
132C3×C3⋊C8—22no—
133C2×#117—31no—
134C2×C22⋊C8—31no—
135C2×C22⋊C8C3×D311yescharacteristic
136C2×#97—31no—
137C2×C4×C8—31no—
138#336—31no—
139#336—31no—
140C24×C3—21no—
141C24×C3C4×D311yescharacteristic
142C24×C3C2×C3×C411yescharacteristic
143C22×C3×C4—21no—
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—22no—
153C22×C3×C4—22no—
154C22×C3×C4—21no—
155C22×C3×C4—32no—
156C22×C3×C4—32no—
157C22×C3×C4—41no—
158C22×C3×C4—41no—
159C22×C3×C4—41no—
160C22×C3×C4—41no—
161C22×C3×C4C4×D311yescharacteristic
162C22×C3×C4C4×D312yes—
163C22×C3×C4C2×Dic312yes—
164C22×C3×C4C2×C3×C411yescharacteristic
165C22×C3×C4C2×C3×C412yes—
166C22×C3×C4C2×C3×C412yes—
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C23×C311yescharacteristic
169C22×Dic3C2×C3×C412yes—
170C22×Dic3C2×C3×C412yes—
171C2×C3×C8—21no—
172C2×C3×C8—21no—
173C2×C3×C8—21no—
174C2×C3×C8—21no—
175C2×C3×C8—21no—
176C2×C3×C8—21no—
177C2×C3×C8—21no—
178C2×C3×C8—21no—
179C2×C3×C8—22no—
180C2×C3×C8—22no—
181C2×C3×C8—32no—
182C2×C3×C8—32no—
183C2×C3×C8—41no—
184C2×C3×C8—41no—
185C2×C3×C8—41no—
186C2×C3×C8—41no—
187C2×C3×C8—61no—
188C2×C3×C8—61no—
189C2×C3×C8—61no—
190C2×C3×C8—61no—
191C2×C3×C8C2×Dic312yes—
192C2×C3×C8C2×Dic312yes—
193C2×C3×C8C2×C3×C412yes—
194C2×C3×C8C2×C3×C412yes—
195C3×C4⋊C4—64no—
196C3×C22⋊C4—64no—
197C3×C42—32no—
198C3×C42—32no—
199C3×C42—61no—
200C3×C42—61no—
201#217—24no—
202C4⋊Dic3—24no—
203C4×Dic3—21no—
204C4×Dic3—21no—
205C4×Dic3C3×D412yes—
206C4×Dic3C3×D412yes—
207C2×C3⋊C8—21no—
208C2×C3⋊C8—21no—
209C2×C3⋊C8—21no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8C2×C3×C412yes—
212C2×C3⋊C8C2×C3×C412yes—
213C22×C32—22no—
214C22×C32—22no—
215C22×C32—22no—
216C22×C32—42no—
217C22×C32—42no—
218C22×C32C2×C4211yescharacteristic
219C22×C32C2×C22⋊C411yescharacteristic
220C22×C32#11711yescharacteristic
221C22×C32#13112yes—
222C22×C32#13112yes—
223C32×C4—22no—
224C32×C4C4×D411yescharacteristic
225C32×C4C4×D411yescharacteristic
226C32×C4C4×D411yescharacteristic
227C32×C4C4×D411yescharacteristic
228C3×Dic3—24no—
229C3×Dic3—42no—
230C23×C4C2×C3×D311yescharacteristic
231C22×C8—31no—
232C22×C8—31no—
233C22×C8C2×C3×D311yescharacteristic
234C22×C8C2×C3×D311yescharacteristic
235#117—62no—
236#117—62no—
237C2×C4⋊C4—32no—
238C2×C22⋊C4—32no—
239C2×C42—31no—
240C2×C42—31no—
241C22⋊C8—34no—
242C22⋊C8C3×Dic314yescomplemented
243#97—62no—
244C4×C8—62no—
245C23×C3—24no—
246C23×C3—21no—
247C23×C3—21no—
248C23×C3—22no—
249C23×C3—22no—
250C23×C3—21no—
251C23×C3—21no—
252C23×C3—22no—
253C23×C3—22no—
254C23×C3—22no—
255C23×C3—21no—
256C23×C3—41no—
257C23×C3—41no—
258C23×C3—42no—
259C23×C3C4×Dic312yes—
260C23×C3C3×C4212yes—
261C23×C3C2×C4×D311yescharacteristic
262C23×C3C22×C3×C411yescharacteristic
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—22no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—34no—
283C2×C3×C4—42no—
284C2×C3×C4—42no—
285C2×C3×C4—42no—
286C2×C3×C4—42no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—62no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4C4×Dic312yes—
295C2×C3×C4C3×C4212yes—
296C2×C3×C4C2×C4×D311yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4#23711yescharacteristic
300C2×C3×C4#23711yescharacteristic
301C2×C3×C4C22×Dic311yescharacteristic
302C2×C3×C4C22×C3×C411yescharacteristic
303C2×C3×C4C22×C3×C411yescharacteristic
304C2×C3×C4C2×C3×D411yescharacteristic
305C2×C3×C4C2×C3×D411yescharacteristic
306C2×C3×C4C3×#4111yescharacteristic
307C2×C3×C4C3×#4111yescharacteristic
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—22no—
311C2×Dic3—22no—
312C2×Dic3—22no—
313C2×Dic3C3×C22⋊C414yes—
314C3×C8—22no—
315C3×C8—22no—
316C3×C8—22no—
317C3×C8—22no—
318C3×C8—42no—
319C3×C8—42no—
320C3×C8—62no—
321C3×C8—62no—
322C3⋊C8—22no—
323C3⋊C8—22no—
324C2×C32—42no—
325C2×C32C4×C22⋊C411yescharacteristic
326C2×C32#40511yescharacteristic
327C2×C32#40511yescharacteristic
328C2×C32#40812yes—
329C2×C32#43312yes—
330C24C3×C4×D311yescharacteristic
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—32no—
336C22×C4—32no—
337C22×C4C3×C4×D311yescharacteristic
338C22×C4C3×C4×D312yes—
339C22×C4C2×C3×Dic312yes—
340C22×C4C22×C3×D311yescharacteristic
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—32no—
346C2×C8—32no—
347C2×C8—61no—
348C2×C8—61no—
349C2×C8—61no—
350C2×C8—61no—
351C2×C8C2×C3×Dic312yes—
352C2×C8C2×C3×Dic312yes—
353C4⋊C4—64no—
354C22⋊C4—64no—
355C42—32no—
356C42—32no—
357C42—61no—
358C42—61no—
359C22×C3—24no—
360C22×C3—22no—
361C22×C3—22no—
362C22×C3—22no—
363C22×C3—22no—
364C22×C3—22no—
365C22×C3—22no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—22no—
369C22×C3—22no—
370C22×C3—21no—
371C22×C3—42no—
372C22×C3—42no—
373C22×C3—44no—
374C22×C3—44no—
375C22×C3—42no—
376C22×C3—42no—
377C22×C3—42no—
378C22×C3—42no—
379C22×C3#87711yescharacteristic
380C22×C3D3×C22⋊C411yescharacteristic
381C22×C3#90112yes—
382C22×C3#90712yes—
383C22×C3C2×C4×Dic311yescharacteristic
384C22×C3C2×C3×C4211yescharacteristic
385C22×C3C2×C3×C22⋊C411yescharacteristic
386C22×C3C3×#11711yescharacteristic
387C22×C3C3×#13112yes—
388C22×C3C3×#13112yes—
389C3×C4—22no—
390C3×C4—22no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—42no—
396C3×C4—64no—
397C3×C4—122no—
398C3×C4#67⋊C411yescharacteristic
399C3×C4#67⋊C411yescharacteristic
400C3×C4D4×Dic311yescharacteristic
401C3×C4D4×Dic311yescharacteristic
402C3×C4C3×C4×D411yescharacteristic
403C3×C4C3×C4×D411yescharacteristic
404C3×C4C3×C4×D411yescharacteristic
405C3×C4C3×C4×D411yescharacteristic
406Dic3—24no—
407Dic3—42no—
408C32#175011yescharacteristic, complemented, Sylow
409C23—21no—
410C23—21no—
411C23—22no—
412C23—22no—
413C23C3×C4×Dic312yes—
414C23C2×C3×C4×D311yescharacteristic
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—34no—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4C3×C4×Dic312yes—
428C2×C4C2×C3×C4×D311yescharacteristic
429C2×C4C3×D3×D411yescharacteristic
430C2×C4C3×D3×D411yescharacteristic
431C2×C4C3×#23711yescharacteristic
432C2×C4C3×#23711yescharacteristic
433C2×C4C22×C3×Dic311yescharacteristic
434C8—22no—
435C8—22no—
436C8—62no—
437C8—62no—
438C2×C3—21no—
439C2×C3—22no—
440C2×C3—22no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—44no—
444C2×C3—42no—
445C2×C3—42no—
446C2×C3#472012yes—
447C2×C3#472712yes—
448C2×C3Dic3×C22⋊C411yescharacteristic
449C2×C3#510111yescharacteristic
450C2×C3#512211yescharacteristic
451C2×C3C3×C4×C22⋊C411yescharacteristic
452C2×C3C3×#40511yescharacteristic
453C2×C3C3×#40511yescharacteristic
454C2×C3C3×#40812yes—
455C2×C3C3×#43312yes—
456C22—22no—
457C22—22no—
458C22—22no—
459C22—42no—
460C22—42no—
461C22C3×#87711yescharacteristic
462C22C3×D3×C22⋊C411yescharacteristic
463C22C3×#90112yes—
464C22C3×#90712yes—
465C22C2×C3×C4×Dic311yescharacteristic
466C4—22no—
467C4—64no—
468C4—122no—
469C4C3×#67⋊C411yescharacteristic
470C4C3×#67⋊C411yescharacteristic
471C4C3×D4×Dic311yescharacteristic
472C4C3×D4×Dic311yescharacteristic
473C3—21no—
474C3#6990711yescharacteristic, direct product factor
475C3C3×#175011yescharacteristic, complemented
476C2—42no—
477C2C3×#472012yes—
478C2C3×#472712yes—
479C2C3×Dic3×C22⋊C411yescharacteristic
480C2C3×#510111yescharacteristic
481C2C3×#512211yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D3
commutatorC22×C3C2×C3×C42
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C22⋊C8C2
socleC23×C32C22×C4
prime radicalC24×C32C2×C4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×C22⋊C8D3
hypocenterC3C3×#1750
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C22⋊C8

Complements

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

NH ≅ G/Ntype
4. C2×C3×#815C2semidirect
5. C2×C3×C8×Dic3C2semidirect
6. C3×#4550C2semidirect
7. C3×#4550C2semidirect
9. #69907C3direct (N × H)
21. C32×C22⋊C8C4semidirect
22. C3×#830C4semidirect
34. C2×#815C2×C3semidirect
35. C2×C8×Dic3C2×C3semidirect
38. #4550C2×C3semidirect
39. #4550C2×C3semidirect
97. C3×C22⋊C8Dic3semidirect
98. C3×C22⋊C8C3×C4semidirect
101. #830C3×C4semidirect
242. C22⋊C8C3×Dic3semidirect
408. C32#1750semidirect
474. C3#69907direct (N × H)
475. C3C3×#1750semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9262
C2×C32×C22⋊C82
C2×C3×#8302
C2×C3×#8152
C2×C3×C8×Dic32
C3×#45502
C3×#17503
#699073