Finite Group Databasebeta

← C3×#79981 #11896032

Subgroups — C3×#79981 #11896032

Order 1152.

723 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5584C211yesmaximal, characteristic
2C3×Q8×Dic6C211yesmaximal, characteristic, complemented
3C32×#446C211yesmaximal, characteristic, complemented
4C3×#4851C212yesmaximal, complemented
5C3×#4849C211yesmaximal, characteristic, complemented
6C3×#4845C212yesmaximal
7C3×#4842C211yesmaximal, characteristic
8C3×#4716C212yesmaximal, complemented
9C3×#4714C212yesmaximal
10C3×C4×#204C211yesmaximal, characteristic
11C3×#4681C211yesmaximal, characteristic, complemented
12C3×#3369—31nomaximal
13#79981C311yesmaximal, characteristic, direct product factor
14C32×C4×Q8C2211yescharacteristic
15C3×#946—21no—
16C3×Q8×Dic3—21no—
17C2×C3×Dic12C2212yes—
18C2×C3×#204C2211yescharacteristic
19C3×#898—22no—
20C3×#892—21no—
21C3×#888—21no—
22C3×#888—22no—
23C3×#875C2212yes—
24C3×C4×D12C2211yescharacteristic
25C3×#869C2211yescharacteristic
26C3×#869C2211yescharacteristic
27C3×#869C2212yes—
28C3×C4×Dic6C2211yescharacteristic
29C3×C4×Dic6C2212yes—
30C3×C4×Dic6C2212yes—
31C32×C4⋊C8C2211yescharacteristic
32C32×C4⋊C8C2212yes—
33C32×#97C2212yes—
34C32×C4×C8C2211yescharacteristic
35C3×#821C2211yescharacteristic
36C3×#821C2212yes—
37C3×#817C2211yescharacteristic
38C3×#817C2212yes—
39C3×#816C2212yes—
40C3×#816C2212yes—
41C3×#816C2211yescharacteristic
42C3×#816C2212yes—
43C3×Q82—31no—
44C3×#556—31no—
45#5584C2×C311yescharacteristic
46Q8×Dic6C2×C311yescharacteristic, complemented
47C3×#489—32no—
48C3×#487—31no—
49C3×#476—31no—
50C3×#475—32no—
51C3×#464—32no—
52C3×#462—31no—
53C3×#446—21no—
54C3×#446D311yescharacteristic, complemented
55C3×#446C2×C311yescharacteristic, complemented
56C3×#441—32no—
57C3×C4×SD16—31no—
58#4851C2×C312yescomplemented
59#4849C2×C311yescharacteristic, complemented
60#4845C2×C312yes—
61#4842C2×C311yescharacteristic
62#4716C2×C312yescomplemented
63#4714C2×C312yes—
64C4×#204C2×C311yescharacteristic
65#4681C2×C311yescharacteristic, complemented
66C2×C32×Q8D411yescharacteristic
67C2×C3×D12C2311yescharacteristic
68C2×C3×C4×D3—21no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6C2312yes—
72C2×C3×Dic6C2311yescharacteristic
73C2×C32×C8C2311yescharacteristic
74C2×C32×C8C2312yes—
75C2×C32×C8C2311yescharacteristic
76C32×C4⋊C4D411yescharacteristic
77C32×C4⋊C4D412yes—
78C32×C42C2311yescharacteristic
79C32×C42C2312yes—
80C3×(C2×D3)⋊C4—22no—
81C3×(C2×D3)⋊C4—21no—
82C3×(C2×D3)⋊C4—22no—
83C3×C4⋊Dic3—22no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3C2312yes—
88C3×C4⋊Dic3C2311yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4—21no—
92C3×Dic3⋊C4—22no—
93C3×C4×Dic3—22no—
94C3×C4×Dic3—21no—
95C3×C4×Dic3—22no—
96C3×Dic12—24no—
97C3×#204—22no—
98#3369—31noSylow
99C2×C3×Q16—32no—
100C2×C3×SD16—31no—
101C3×C4⋊Q8—32no—
102C3×C4⋊Q8—31no—
103C3×C4⋊Q8—31no—
104C3×C4⋊Q8—61no—
105C3×C4⋊Q8—62no—
106C3×#126—62no—
107C3×#124—32no—
108C3×C22⋊Q8—61no—
109C3×C4×Q8—21no—
110C3×C4×Q8—31no—
111C3×C4×Q8—32no—
112C3×C4×Q8—32no—
113C3×C4×Q8—61no—
114C3×C4×Q8C2×D311yescharacteristic
115C3×C4×Q8C22×C311yescharacteristic
116C3×C4×D4—31no—
117C3×#117—61no—
118#946—21no—
119Q8×Dic3—21no—
120C2×Dic12C22×C312yes—
121C2×#204C22×C311yescharacteristic
122#898—22no—
123#892—21no—
124#888—21no—
125#888—22no—
126#875C22×C312yes—
127C4×D12C22×C311yescharacteristic
128#869C22×C311yescharacteristic
129#869C22×C311yescharacteristic
130#869C22×C312yes—
131C4×Dic6C22×C311yescharacteristic
132C4×Dic6C22×C312yes—
133C4×Dic6C22×C312yes—
134C3×#106—31no—
135C3×#106—32no—
136C3×C4⋊C8—21no—
137C3×C4⋊C8—22no—
138C3×C4⋊C8C2×D311yescharacteristic
139C3×C4⋊C8C2×D312yes—
140C3×C4⋊C8C22×C311yescharacteristic
141C3×C4⋊C8C22×C312yes—
142C3×#103—31no—
143C3×#103—32no—
144C3×#103—32no—
145C3×#103—32no—
146C3×#102—31no—
147C3×#102—32no—
148C3×#97—22no—
149C3×#97C2×D312yes—
150C3×#97C22×C312yes—
151C3×C4×C8—21no—
152C3×C4×C8C2×D311yescharacteristic
153C3×C4×C8C22×C311yescharacteristic
154#821C22×C311yescharacteristic
155#821C22×C312yes—
156#817C22×C311yescharacteristic
157#817C22×C312yes—
158#816C22×C312yes—
159#816C22×C312yes—
160#816C22×C311yescharacteristic
161#816C22×C312yes—
162C22×C3×D3—21no—
163C32×Q8—22no—
164C2×C32×C4C2×D412yes—
165C2×C32×C4C2×D412yes—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2411yescharacteristic
169C2×C3×Dic3—21no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—22no—
174C3×D12—21no—
175C3×D12—21no—
176C3×C4×D3—42no—
177C3×Dic6—21no—
178C3×Dic6—22no—
179C3×Dic6—22no—
180C3×Dic6—82no—
181C3×Dic6—81no—
182C3×Dic6#4112yes—
183C32×C8—21no—
184C32×C8—21no—
185C32×C8—22no—
186Q82—31no—
187#556—31no—
188#489—32no—
189#487—31no—
190#476—31no—
191#475—32no—
192#464—32no—
193#462—31no—
194#446C3×D311yescharacteristic, complemented
195#441—32no—
196C4×SD16—31no—
197C2×C3×Q8—21no—
198C2×C3×Q8—31no—
199C2×C3×Q8—32no—
200C2×C3×Q8—62no—
201C2×C3×Q8—61no—
202C2×C3×Q8D1211yescharacteristic
203C2×C3×Q8C3×D411yescharacteristic
204C2×C3×D4—31no—
205C22×C3×C4—61no—
206C2×D12C23×C311yescharacteristic
207C2×C4×D3—21no—
208C2×Dic6—22no—
209C2×Dic6—21no—
210C2×Dic6C23×C312yes—
211C2×Dic6C23×C311yescharacteristic
212C3×Q16—64no—
213C3×SD16—62no—
214C2×C3×C8—21no—
215C2×C3×C8—21no—
216C2×C3×C8—22no—
217C2×C3×C8C22×D311yescharacteristic
218C2×C3×C8C22×D311yescharacteristic
219C2×C3×C8C22×D312yes—
220C2×C3×C8C23×C311yescharacteristic
221C2×C3×C8C23×C311yescharacteristic
222C2×C3×C8C23×C312yes—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—22no—
225C3×C4⋊C4—31no—
226C3×C4⋊C4—32no—
227C3×C4⋊C4—31no—
228C3×C4⋊C4—62no—
229C3×C4⋊C4—62no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4—61no—
232C3×C4⋊C4—62no—
233C3×C4⋊C4—61no—
234C3×C4⋊C4—61no—
235C3×C4⋊C4D1211yescharacteristic
236C3×C4⋊C4D1212yes—
237C3×C4⋊C4C3×D411yescharacteristic
238C3×C4⋊C4C3×D412yes—
239C3×C22⋊C4—62no—
240C3×C22⋊C4—61no—
241C3×C22⋊C4—62no—
242C3×C42—21no—
243C3×C42—22no—
244C3×C42—62no—
245C3×C42—62no—
246C3×C42—61no—
247C3×C42C22×D311yescharacteristic
248C3×C42C22×D312yes—
249C3×C42C23×C311yescharacteristic
250C3×C42C23×C312yes—
251(C2×D3)⋊C4—21no—
252(C2×D3)⋊C4—22no—
253(C2×D3)⋊C4—22no—
254C4⋊Dic3—22no—
255C4⋊Dic3—21no—
256C4⋊Dic3—21no—
257C4⋊Dic3—21no—
258C4⋊Dic3C23×C312yes—
259C4⋊Dic3C23×C311yescharacteristic
260C4⋊Dic3C23×C311yescharacteristic
261Dic3⋊C4—22no—
262Dic3⋊C4—21no—
263Dic3⋊C4—22no—
264C4×Dic3—22no—
265C4×Dic3—21no—
266C4×Dic3—22no—
267Dic12—24no—
268#204—22no—
269C22×C32C22×D411yescharacteristic
270C2×C3×D3—41no—
271C2×C3×D3—41no—
272C2×C3×D3—41no—
273C32×C4—22no—
274C32×C4—22no—
275C32×C4—21no—
276C32×C4#13712yes—
277C32×C4C2×#4111yescharacteristic
278C32×C42−1+411yescharacteristic
279C3×Dic3—22no—
280C3×Dic3—42no—
281C3×Dic3—41no—
282C3×Dic3—41no—
283C3×Dic3—42no—
284C2×Q16—32no—
285C2×SD16—31no—
286C4⋊Q8—32no—
287C4⋊Q8—31no—
288C4⋊Q8—31no—
289C4⋊Q8—61no—
290C4⋊Q8—62no—
291#126—62no—
292#124—32no—
293C22⋊Q8—61no—
294C4×Q8—32no—
295C4×Q8—31no—
296C4×Q8—32no—
297C4×Q8—61no—
298C4×Q8C2×C3×D311yescharacteristic
299C4×D4—31no—
300#117—61no—
301#106—31no—
302#106—32no—
303C4⋊C8C2×C3×D311yescharacteristic
304C4⋊C8C2×C3×D312yes—
305#103—31no—
306#103—32no—
307#103—32no—
308#103—32no—
309#102—31no—
310#102—32no—
311#97C2×C3×D312yes—
312C4×C8C2×C3×D311yescharacteristic
313C23×C3—61no—
314C22×D3—21no—
315C3×Q8—22no—
316C3×Q8—22no—
317C3×Q8—32no—
318C3×Q8—42no—
319C3×Q8—61no—
320C3×Q8—62no—
321C3×Q8—62no—
322C3×Q8—242no—
323C3×Q8—241no—
324C3×D4—61no—
325C3×D4—61no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—22no—
331C2×C3×C4—61no—
332C2×C3×C4—61no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—61no—
336C2×C3×C4—122no—
337C2×C3×C4C2×D1212yes—
338C2×C3×C4C2×D1212yes—
339C2×C3×C4C2×D1211yescharacteristic
340C2×C3×C4C2×D1211yescharacteristic
341C2×C3×C4C2×C3×D412yes—
342C2×C3×C4C2×C3×D412yes—
343C2×C3×C4C2×C3×D411yescharacteristic
344C2×C3×C4C2×C3×D411yescharacteristic
345C2×C3×C4C23×D311yescharacteristic
346C2×C3×C4C24×C311yescharacteristic
347C2×Dic3—21no—
348C2×Dic3—21no—
349C2×Dic3—22no—
350C2×Dic3—21no—
351C2×Dic3—22no—
352D12—21no—
353D12—21no—
354C4×D3—42no—
355Dic6—21no—
356Dic6—22no—
357Dic6—22no—
358Dic6—82no—
359Dic6—81no—
360Dic6C3×#4112yes—
361C3×C8—22no—
362C3×C8—21no—
363C3×C8—21no—
364C3×C8—22no—
365C3×C8—21no—
366C3×C8—22no—
367C3×C8—21no—
368C3×C8—41no—
369C3×C8—42no—
370C2×C32#54811yescharacteristic
371C2×C32C2×#13711yescharacteristic
372C2×C32#57711yescharacteristic
373C3×D3—81no—
374C2×Q8—31no—
375C2×Q8—32no—
376C2×Q8—62no—
377C2×Q8—61no—
378C2×Q8C3×D1211yescharacteristic
379C2×D4—31no—
380C22×C4—61no—
381Q16—64no—
382SD16—62no—
383C2×C8C22×C3×D311yescharacteristic
384C2×C8C22×C3×D311yescharacteristic
385C2×C8C22×C3×D312yes—
386C4⋊C4—31no—
387C4⋊C4—32no—
388C4⋊C4—31no—
389C4⋊C4—61no—
390C4⋊C4—62no—
391C4⋊C4—62no—
392C4⋊C4—61no—
393C4⋊C4—62no—
394C4⋊C4—61no—
395C4⋊C4—61no—
396C4⋊C4C3×D1211yescharacteristic
397C4⋊C4C3×D1212yes—
398C22⋊C4—62no—
399C22⋊C4—61no—
400C22⋊C4—62no—
401C42—62no—
402C42—62no—
403C42—61no—
404C42C22×C3×D311yescharacteristic
405C42C22×C3×D312yes—
406C22×C3—21no—
407C22×C3—121no—
408C22×C3—121no—
409C22×C3—121no—
410C22×C3C22×D1211yescharacteristic
411C22×C3C22×C3×D411yescharacteristic
412C2×D3—41no—
413C2×D3—41no—
414C2×D3—41no—
415C3×C4—22no—
416C3×C4—22no—
417C3×C4—21no—
418C3×C4—22no—
419C3×C4—22no—
420C3×C4—21no—
421C3×C4—22no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—42no—
425C3×C4—42no—
426C3×C4—41no—
427C3×C4—62no—
428C3×C4—121no—
429C3×C4—122no—
430C3×C4—121no—
431C3×C4—122no—
432C3×C4#90912yes—
433C3×C4C3×#13712yes—
434C3×C4#100711yescharacteristic
435C3×C4D3×#4111yescharacteristic
436C3×C4C2×C3×#4111yescharacteristic
437C3×C4C3×2−1+411yescharacteristic
438Dic3—22no—
439Dic3—41no—
440Dic3—41no—
441Dic3—42no—
442Dic3—42no—
443C32#336911yescharacteristic, complemented, Sylow
444C23—61no—
445Q8—22no—
446Q8—32no—
447Q8—61no—
448Q8—62no—
449Q8—62no—
450Q8—242no—
451Q8—241no—
452D4—61no—
453D4—61no—
454C2×C4—61no—
455C2×C4—61no—
456C2×C4—62no—
457C2×C4—62no—
458C2×C4—61no—
459C2×C4—122no—
460C2×C4C2×C3×D1212yes—
461C2×C4C2×C3×D1212yes—
462C2×C4C2×C3×D1211yescharacteristic
463C2×C4C2×C3×D1211yescharacteristic
464C2×C4C23×C3×D311yescharacteristic
465C8—21no—
466C8—21no—
467C8—22no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—241no—
472C2×C3#557611yescharacteristic
473C2×C3C2×#90911yescharacteristic
474C2×C3#575111yescharacteristic
475C2×C3C3×#54811yescharacteristic
476C2×C3C2×C3×#13711yescharacteristic
477C2×C3C3×#57711yescharacteristic
478D3—81no—
479C22—121no—
480C22—121no—
481C22—121no—
482C22C22×C3×D1211yescharacteristic
483C4—22no—
484C4—22no—
485C4—21no—
486C4—62no—
487C4—121no—
488C4—122no—
489C4—121no—
490C4—122no—
491C4C3×#90912yes—
492C4C3×#100711yescharacteristic
493C4C3×D3×#4111yescharacteristic
494C3—21no—
495C3#7998111yescharacteristic, direct product factor
496C3C3×#336911yescharacteristic, complemented
497C2—241no—
498C2C3×#557611yescharacteristic
499C2C2×C3×#90911yescharacteristic
500C2C3×#575111yescharacteristic
subgroupG/H
centerC22×C3C22×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#446C2
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC3×#446D3
hypocenterC3C3×#3369
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×Q8 ◁ C3×#446

Complements

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

NH ≅ G/Ntype
2. C3×Q8×Dic6C2semidirect
3. C32×#446C2semidirect
4. C3×#4851C2semidirect
5. C3×#4849C2semidirect
8. C3×#4716C2semidirect
11. C3×#4681C2semidirect
13. #79981C3direct (N × H)
46. Q8×Dic6C2×C3semidirect
54. C3×#446D3semidirect
55. C3×#446C2×C3semidirect
58. #4851C2×C3semidirect
59. #4849C2×C3semidirect
62. #4716C2×C3semidirect
65. #4681C2×C3semidirect
194. #446C3×D3semidirect
443. C32#3369semidirect
495. C3#79981direct (N × H)
496. C3C3×#3369semidirect

Maximal subgroups

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

subgroupindex
C3×#55842
C3×Q8×Dic62
C32×#4462
C3×#48512
C3×#48492
C3×#48452
C3×#48422
C3×#47162
C3×#47142
C3×C4×#2042
C3×#46812
C3×#33693
#799813