Finite Group Databasebeta

← C3×#70038 #11793094

Subgroups — C3×#70038 #11793094

Order 1152.

567 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5517C211yesmaximal, characteristic, complemented
2C32×#410C211yesmaximal, characteristic
3C3×#5236C211yesmaximal, characteristic
4C2×C3×#837C211yesmaximal, characteristic
5C3×#4533C211yesmaximal, characteristic, complemented
6C3×#4532C211yesmaximal, characteristic, complemented
7C3×#4531C211yesmaximal, characteristic, complemented
8C3×#2031—31nomaximal
9#70038C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C32×#117C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#890—21no—
18C3×#888—21no—
19C3×#878—22no—
20C3×C4×Dic6—22no—
21C32×#99—22no—
22C3×#837—21no—
23C3×#837—21no—
24C3×#837—22no—
25C3×#533—31no—
26#5517C2×C311yescharacteristic, complemented
27C3×#421—31no—
28C2×C3×#104—31no—
29C3×#410—21no—
30C3×#410D311yescharacteristic
31C3×#410C2×C311yescharacteristic
32#5236C2×C311yescharacteristic
33C2×#837C2×C311yescharacteristic
34C3×#344—31no—
35C3×#339—31no—
36C3×H(3,ℤ/4)—31no—
37#4533C2×C311yescharacteristic, complemented
38#4532C2×C311yescharacteristic, complemented
39#4531C2×C311yescharacteristic, complemented
40C32×#41—21no—
41C32×#41—21no—
42C32×#41—21no—
43C32×#41—21no—
44C2×C32×Q8Q811yescharacteristic, complemented
45C2×C32×D4—21no—
46C2×C32×D4Q811yescharacteristic, complemented
47C22×C32×C4—21no—
48C22×C32×C4C2311yescharacteristic
49C22×C3×Dic3—21no—
50C2×C3×Dic6—22no—
51C32×C4⋊C4—21no—
52C32×C4⋊C4—21no—
53C32×C22⋊C4—21no—
54C32×C22⋊C4D412yes—
55C32×C42—21no—
56C32×C42—21no—
57C3×#217—21no—
58C3×C4⋊Dic3—22no—
59C3×C4⋊Dic3—21no—
60C3×Dic3⋊C4—22no—
61C3×Dic3⋊C4—22no—
62C3×C4×Dic3—21no—
63C3×C4×Dic3D411yescharacteristic
64C3×C4×Dic3D411yescharacteristic
65C3×C4×Dic3D412yes—
66C3×#208—21no—
67C3×#208—21no—
68C3×#208—21no—
69C3×#208—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72#2031—31noSylow
73C2×C3×#41—21no—
74C2×C3×#41C2×D311yescharacteristic
75C2×C3×#41C22×C311yescharacteristic
76C2×C3×M16—31no—
77C2×C3×M16—31no—
78C3×C4⋊Q8—61no—
79C3×#125—61no—
80C3×C22⋊Q8—62no—
81C3×C4×Q8—62no—
82C3×#117—21no—
83C3×#117—21no—
84C3×#117—31no—
85C3×#117C2×D311yescharacteristic
86C3×#117C2×D311yescharacteristic
87C3×#117C22×C311yescharacteristic
88C3×#117C22×C311yescharacteristic
89C2×C3×C42—31no—
90#926C22×C311yescharacteristic
91C2×C4×Dic3C22×C311yescharacteristic
92C2×#208C22×C311yescharacteristic
93C2×#208C22×C311yescharacteristic
94#890—21no—
95#888—21no—
96#878—22no—
97C4×Dic6—22no—
98C3×#104—61no—
99C3×#104—61no—
100C3×#104—62no—
101C3×#99—24no—
102C3×#99—22no—
103C3×#99—22no—
104#837—21no—
105#837—21no—
106#837—22no—
107C23×C32—21no—
108C23×C32C2×D411yescharacteristic
109C32×Q8—21no—
110C32×Q8—21no—
111C32×D4—21no—
112C32×D4—21no—
113C32×D4—41no—
114C32×D4—41no—
115C2×C32×C4—21no—
116C2×C32×C4—22no—
117C2×C32×C4—41no—
118C2×C32×C4—41no—
119C2×C32×C4—41no—
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×Q811yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C32×C4#4111yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—42no—
130C3×Dic6—44no—
131C3×C3⋊C8—41no—
132C3×C3⋊C8—41no—
133#533—31no—
134#421—31no—
135C2×#104—31no—
136#410C3×D311yescharacteristic
137#344—31no—
138#339—31no—
139H(3,ℤ/4)—31no—
140C3×#41—21no—
141C3×#41—21no—
142C3×#41—21no—
143C3×#41—21no—
144C3×#41—21no—
145C3×#41—21no—
146C3×#41—21no—
147C3×#41—21no—
148C3×#41—41no—
149C3×#41—41no—
150C3×#41—41no—
151C3×#41—41no—
152C2×C3×Q8—21no—
153C2×C3×Q8—62no—
154C2×C3×Q8Dic611yescharacteristic, complemented
155C2×C3×Q8C3×Q811yescharacteristic, complemented
156C2×C3×D4—22no—
157C2×C3×D4—21no—
158C2×C3×D4—21no—
159C2×C3×D4—21no—
160C2×C3×D4Dic611yescharacteristic, complemented
161C2×C3×D4C3×Q811yescharacteristic, complemented
162C22×C3×C4—22no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—61no—
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C23×C311yescharacteristic
169C22×Dic3—21no—
170C2×Dic6—22no—
171C3×M16—61no—
172C3×M16—61no—
173C3×M16—61no—
174C3×M16—61no—
175C2×C3×C8—61no—
176C2×C3×C8—61no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—41no—
182C3×C4⋊C4—41no—
183C3×C4⋊C4—62no—
184C3×C4⋊C4—62no—
185C3×C4⋊C4—62no—
186C3×C4⋊C4—61no—
187C3×C22⋊C4—22no—
188C3×C22⋊C4—21no—
189C3×C22⋊C4—21no—
190C3×C22⋊C4—22no—
191C3×C22⋊C4—61no—
192C3×C22⋊C4#6712yes—
193C3×C22⋊C4C3×D412yes—
194C3×C42—21no—
195C3×C42—21no—
196C3×C42—21no—
197C3×C42—21no—
198C3×C42—31no—
199C3×C42—31no—
200C3×C42—32no—
201C3×C42—41no—
202C3×C42—41no—
203C3×C42—61no—
204#217—21no—
205C4⋊Dic3—22no—
206C4⋊Dic3—21no—
207Dic3⋊C4—22no—
208Dic3⋊C4—22no—
209C4×Dic3—21no—
210C4×Dic3C3×D412yes—
211C4×Dic3C3×D411yescharacteristic
212C4×Dic3C3×D411yescharacteristic
213#208—21no—
214#208—21no—
215#208—21no—
216#208—21no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—21no—
219C22×C32—41no—
220C22×C32—41no—
221C22×C32—81no—
222C22×C32#12011yescharacteristic
223C22×C32C22⋊Q811yescharacteristic
224C22×C32#12411yescharacteristic
225C32×C4—41no—
226C32×C4—42no—
227C32×C4—81no—
228C32×C4C22⋊Q811yescharacteristic
229C32×C4C22⋊Q811yescharacteristic
230C32×C4#12411yescharacteristic
231C32×C4#12411yescharacteristic
232C3×Dic3—22no—
233C3×Dic3—42no—
234C3×Dic3—41no—
235C2×#41C2×C3×D311yescharacteristic
236C2×M16—31no—
237C2×M16—31no—
238C4⋊Q8—61no—
239#125—61no—
240C22⋊Q8—62no—
241C4×Q8—62no—
242#117—31no—
243#117C2×C3×D311yescharacteristic
244#117C2×C3×D311yescharacteristic
245C2×C42—31no—
246#104—61no—
247#104—61no—
248#104—62no—
249#99—22no—
250C23×C3—22no—
251C23×C3—21no—
252C23×C3—21no—
253C23×C3—21no—
254C23×C3C2×#6711yescharacteristic
255C23×C3C2×C3×D411yescharacteristic
256C3×Q8—21no—
257C3×Q8—21no—
258C3×Q8—21no—
259C3×Q8—21no—
260C3×Q8—41no—
261C3×Q8—41no—
262C3×Q8—124no—
263C3×D4—21no—
264C3×D4—21no—
265C3×D4—21no—
266C3×D4—21no—
267C3×D4—41no—
268C3×D4—41no—
269C3×D4—42no—
270C3×D4—42no—
271C3×D4—41no—
272C3×D4—41no—
273C3×D4—41no—
274C3×D4—41no—
275C2×C3×C4—22no—
276C2×C3×C4—21no—
277C2×C3×C4—22no—
278C2×C3×C4—22no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—42no—
287C2×C3×C4—42no—
288C2×C3×C4—42no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—42no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—61no—
297C2×C3×C4—61no—
298C2×C3×C4—62no—
299C2×C3×C4—122no—
300C2×C3×C4C2×Dic611yescharacteristic
301C2×C3×C4#23511yescharacteristic
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4#23711yescharacteristic
305C2×C3×C4#23711yescharacteristic
306C2×C3×C4C2×C3×D411yescharacteristic
307C2×C3×C4C2×C3×D411yescharacteristic
308C2×C3×C4C2×C3×Q811yescharacteristic
309C2×C3×C4C3×#4111yescharacteristic
310C2×C3×C4C3×#4111yescharacteristic
311C2×C3×C4C3×#4111yescharacteristic
312C2×Dic3—21no—
313C2×Dic3—21no—
314C2×Dic3—22no—
315C2×Dic3—42no—
316Dic6—44no—
317C3×C8—121no—
318C3×C8—121no—
319C3⋊C8—41no—
320C3⋊C8—41no—
321C2×C32—21no—
322C2×C32—21no—
323C2×C32—21no—
324C2×C32—81no—
325C2×C32#39311yescharacteristic
326#41—21no—
327#41—21no—
328#41—21no—
329#41—21no—
330C2×Q8—62no—
331C2×Q8C3×Dic611yescharacteristic, complemented
332C2×D4—21no—
333C2×D4C3×Dic611yescharacteristic, complemented
334C22×C4—21no—
335C22×C4—61no—
336C22×C4C22×C3×D311yescharacteristic
337M16—61no—
338M16—61no—
339M16—61no—
340M16—61no—
341C2×C8—61no—
342C2×C8—61no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—62no—
346C4⋊C4—62no—
347C4⋊C4—62no—
348C4⋊C4—61no—
349C22⋊C4—21no—
350C22⋊C4—61no—
351C22⋊C4C3×#6712yes—
352C42—21no—
353C42—21no—
354C42—31no—
355C42—31no—
356C42—32no—
357C42—61no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—41no—
362C22×C3—41no—
363C22×C3—42no—
364C22×C3—41no—
365C22×C3—41no—
366C22×C3—81no—
367C22×C3—81no—
368C22×C3—81no—
369C22×C3—82no—
370C22×C3#92411yescharacteristic
371C22×C3#93611yescharacteristic
372C22×C3#93711yescharacteristic
373C22×C3C3×#12011yescharacteristic
374C22×C3C3×C22⋊Q811yescharacteristic
375C22×C3C3×#12411yescharacteristic
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—42no—
381C3×C4—42no—
382C3×C4—42no—
383C3×C4—41no—
384C3×C4—41no—
385C3×C4—62no—
386C3×C4—82no—
387C3×C4—81no—
388C3×C4—81no—
389C3×C4—82no—
390C3×C4—121no—
391C3×C4—122no—
392C3×C4#87811yescharacteristic
393C3×C4#87811yescharacteristic
394C3×C4#88511yescharacteristic
395C3×C4#88511yescharacteristic
396C3×C4C3×C22⋊Q811yescharacteristic
397C3×C4C3×C22⋊Q811yescharacteristic
398C3×C4C3×#12411yescharacteristic
399C3×C4C3×#12411yescharacteristic
400Dic3—22no—
401Dic3—42no—
402Dic3—41no—
403C32#203111yescharacteristic, complemented, Sylow
404C23—21no—
405C23C2×C3×#6711yescharacteristic
406Q8—21no—
407Q8—21no—
408Q8—124no—
409D4—21no—
410D4—21no—
411D4—41no—
412D4—41no—
413C2×C4—21no—
414C2×C4—22no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—61no—
419C2×C4—61no—
420C2×C4—62no—
421C2×C4—122no—
422C2×C4C2×C3×Dic611yescharacteristic
423C2×C4C3×#23511yescharacteristic
424C2×C4C3×D3×D411yescharacteristic
425C2×C4C3×D3×D411yescharacteristic
426C2×C4C3×#23711yescharacteristic
427C2×C4C3×#23711yescharacteristic
428C8—121no—
429C8—121no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—41no—
438C2×C3—41no—
439C2×C3—41no—
440C2×C3—82no—
441C2×C3—81no—
442C2×C3—81no—
443C2×C3#494711yescharacteristic
444C2×C3C3×#39311yescharacteristic
445C22—41no—
446C22—41no—
447C22—81no—
448C22C3×#92411yescharacteristic
449C22C3×#93611yescharacteristic
450C22C3×#93711yescharacteristic
451C4—42no—
452C4—41no—
453C4—62no—
454C4—81no—
455C4—121no—
456C4—122no—
457C4C3×#87811yescharacteristic
458C4C3×#87811yescharacteristic
459C4C3×#88511yescharacteristic
460C4C3×#88511yescharacteristic
461C3—21no—
462C3#7003811yescharacteristic, direct product factor
463C3C3×#203111yescharacteristic, complemented
464C2—21no—
465C2—21no—
466C2—21no—
467C2—81no—
468C2C3×#494711yescharacteristic
subgroupG/H
centerC3×C4#885
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#410C2
socleC2×C32#393
prime radicalC2×C32×#41C22
hypercenterC3×#410D3
hypocenterC3C3×#2031
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#410

Complements

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

NH ≅ G/Ntype
1. C3×#5517C2semidirect
5. C3×#4533C2semidirect
6. C3×#4532C2semidirect
7. C3×#4531C2semidirect
9. #70038C3direct (N × H)
26. #5517C2×C3semidirect
37. #4533C2×C3semidirect
38. #4532C2×C3semidirect
39. #4531C2×C3semidirect
44. C2×C32×Q8Q8semidirect
46. C2×C32×D4Q8semidirect
154. C2×C3×Q8Dic6semidirect
155. C2×C3×Q8C3×Q8semidirect
160. C2×C3×D4Dic6semidirect
161. C2×C3×D4C3×Q8semidirect
331. C2×Q8C3×Dic6semidirect
333. C2×D4C3×Dic6semidirect
403. C32#2031semidirect
462. C3#70038direct (N × H)
463. C3C3×#2031semidirect

Maximal subgroups

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

subgroupindex
C3×#55172
C32×#4102
C3×#52362
C2×C3×#8372
C3×#45332
C3×#45322
C3×#45312
C3×#20313
#700383