Finite Group Databasebeta

← C3×#79976 #11897627

Subgroups — C3×#79976 #11897627

Order 1152.

727 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5579C211yesmaximal, characteristic
2C3×Q8×Dic6C211yesmaximal, characteristic, complemented
3C32×#446C211yesmaximal, characteristic, complemented
4C3×#4850C211yesmaximal, characteristic, complemented
5C3×#4846C212yesmaximal
6C3×#4842C211yesmaximal, characteristic
7C3×#4829C212yesmaximal, complemented
8C3×#4710C212yesmaximal
9C3×#4702C212yesmaximal, complemented
10C3×C4×#204C211yesmaximal, characteristic
11C3×#4682C211yesmaximal, characteristic, complemented
12C3×#3385—31nomaximal
13#79976C311yesmaximal, characteristic, direct product factor
14C32×C4×Q8C2211yescharacteristic
15C3×#946—21no—
16C3×Q8×Dic3—21no—
17C2×C3×#204C2211yescharacteristic
18C3×#896—22no—
19C3×D3×C4⋊C4—21no—
20C3×#888—21no—
21C3×#888—22no—
22C3×C4×D12C2211yescharacteristic
23C3×C4×D12C2212yes—
24C3×#870C2212yes—
25C3×#869C2211yescharacteristic
26C3×#869C2211yescharacteristic
27C3×#869C2212yes—
28C3×C4×Dic6C2211yescharacteristic
29C3×C4×Dic6C2212yes—
30C32×C4⋊C8C2212yes—
31C32×C4⋊C8C2211yescharacteristic
32C32×#97C2212yes—
33C32×C4×C8C2211yescharacteristic
34C3×#821C2211yescharacteristic
35C3×#821C2212yes—
36C3×#818C2212yes—
37C3×#818C2212yes—
38C3×#818C2212yes—
39C3×#817C2211yescharacteristic
40C3×#817C2212yes—
41C3×#816C2211yescharacteristic
42C3×#816C2212yes—
43C3×Q82—31no—
44C3×#554—31no—
45#5579C2×C311yescharacteristic
46Q8×Dic6C2×C311yescharacteristic, complemented
47C3×#501—32no—
48C3×#500—31no—
49C3×#479—32no—
50C3×#477—31no—
51C3×#476—31no—
52C3×#474—32no—
53C3×#446—21no—
54C3×#446D311yescharacteristic, complemented
55C3×#446C2×C311yescharacteristic, complemented
56C3×#440—32no—
57C3×C4×SD16—31no—
58#4850C2×C311yescharacteristic, complemented
59#4846C2×C312yes—
60#4842C2×C311yescharacteristic
61#4829C2×C312yescomplemented
62#4710C2×C312yes—
63#4702C2×C312yescomplemented
64C4×#204C2×C311yescharacteristic
65#4682C2×C311yescharacteristic, complemented
66C2×C32×Q8D411yescharacteristic
67C2×C3×D12C2311yescharacteristic
68C2×C3×C4×D3—21no—
69C2×C3×C4×D3—22no—
70C2×C3×Dic6—22no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—21no—
73C2×C3×Dic6C2311yescharacteristic
74C2×C32×C8C2312yes—
75C2×C32×C8C2311yescharacteristic
76C2×C32×C8C2311yescharacteristic
77C32×C4⋊C4D411yescharacteristic
78C32×C4⋊C4D412yes—
79C32×C42C2311yescharacteristic
80C32×C42C2312yes—
81C3×(C2×D3)⋊C4—21no—
82C3×(C2×D3)⋊C4—22no—
83C3×C4⋊Dic3—22no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3C2311yescharacteristic
87C3×C4⋊Dic3C2312yes—
88C3×C4⋊Dic3C2311yescharacteristic
89C3×C4⋊Dic3C2312yes—
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4—21no—
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4—22no—
94C3×C4×Dic3—22no—
95C3×C4×Dic3—21no—
96C3×#204Q814yescomplemented
97#3385—31noSylow
98C2×C3×SD16—31no—
99C3×C4⋊Q8—32no—
100C3×C4⋊Q8—31no—
101C3×C4⋊Q8—31no—
102C3×C4⋊Q8—61no—
103C3×C4⋊Q8—62no—
104C3×#125—32no—
105C3×C22⋊Q8—61no—
106C3×C22⋊Q8—62no—
107C3×C4×Q8—21no—
108C3×C4×Q8—31no—
109C3×C4×Q8—32no—
110C3×C4×Q8—61no—
111C3×C4×Q8C2×D311yescharacteristic
112C3×C4×Q8C22×C311yescharacteristic
113C3×C4×D4—31no—
114C3×C4×D4—32no—
115C2×C3×C4⋊C4—61no—
116#946—21no—
117Q8×Dic3—21no—
118C2×#204C22×C311yescharacteristic
119#896—22no—
120D3×C4⋊C4—21no—
121#888—21no—
122#888—22no—
123C4×D12C22×C311yescharacteristic
124C4×D12C22×C312yes—
125#870C22×C312yes—
126#869C22×C311yescharacteristic
127#869C22×C311yescharacteristic
128#869C22×C312yes—
129C4×Dic6C22×C311yescharacteristic
130C4×Dic6C22×C312yes—
131C3×#107—32no—
132C3×#107—32no—
133C3×#107—32no—
134C3×#106—31no—
135C3×#106—32no—
136C3×C4⋊C8—22no—
137C3×C4⋊C8—21no—
138C3×C4⋊C8C2×D312yes—
139C3×C4⋊C8C2×D311yescharacteristic
140C3×C4⋊C8C22×C312yes—
141C3×C4⋊C8C22×C311yescharacteristic
142C3×#103—31no—
143C3×#103—32no—
144C3×#102—31no—
145C3×#102—32no—
146C3×#97—22no—
147C3×#97C2×D312yes—
148C3×#97C22×C312yes—
149C3×C4×C8—21no—
150C3×C4×C8C2×D311yescharacteristic
151C3×C4×C8C22×C311yescharacteristic
152#821C22×C311yescharacteristic
153#821C22×C312yes—
154#818C22×C312yes—
155#818C22×C312yes—
156#818C22×C312yes—
157#817C22×C311yescharacteristic
158#817C22×C312yes—
159#816C22×C311yescharacteristic
160#816C22×C312yes—
161C22×C3×D3—21no—
162C32×Q8—22no—
163C2×C32×C4C2×D412yes—
164C2×C32×C4C2×D412yes—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2411yescharacteristic
168C2×C3×Dic3—21no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—22no—
173C3×D12—21no—
174C3×D12C2×Q812yes—
175C3×C4×D3—42no—
176C3×C4×D3—82no—
177C3×Dic6—21no—
178C3×Dic6—81no—
179C3×Dic6—82no—
180C3×Dic6—81no—
181C3×Dic6C2×Q812yes—
182C32×C8—22no—
183C32×C8—21no—
184C32×C8C2×Q812yes—
185Q82—31no—
186#554—31no—
187#501—32no—
188#500—31no—
189#479—32no—
190#477—31no—
191#476—31no—
192#474—32no—
193#446C3×D311yescharacteristic, complemented
194#440—32no—
195C4×SD16—31no—
196C2×C3×Q8—21no—
197C2×C3×Q8—31no—
198C2×C3×Q8—61no—
199C2×C3×Q8—61no—
200C2×C3×Q8—62no—
201C2×C3×Q8D1211yescharacteristic
202C2×C3×Q8C3×D411yescharacteristic
203C2×C3×D4—31no—
204C22×C3×C4—61no—
205C22×C3×C4—62no—
206C2×D12C23×C311yescharacteristic
207C2×C4×D3—21no—
208C2×C4×D3—22no—
209C2×Dic6—22no—
210C2×Dic6—21no—
211C2×Dic6—21no—
212C2×Dic6C23×C311yescharacteristic
213C3×SD16—34no—
214C2×C3×C8—21no—
215C2×C3×C8—21no—
216C2×C3×C8—22no—
217C2×C3×C8C22×D311yescharacteristic
218C2×C3×C8C22×D312yes—
219C2×C3×C8C22×D311yescharacteristic
220C2×C3×C8C23×C312yes—
221C2×C3×C8C23×C311yescharacteristic
222C2×C3×C8C23×C311yescharacteristic
223C3×C4⋊C4—21no—
224C3×C4⋊C4—22no—
225C3×C4⋊C4—31no—
226C3×C4⋊C4—32no—
227C3×C4⋊C4—31no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—62no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4—62no—
232C3×C4⋊C4—62no—
233C3×C4⋊C4—61no—
234C3×C4⋊C4—62no—
235C3×C4⋊C4—61no—
236C3×C4⋊C4D1211yescharacteristic
237C3×C4⋊C4D1212yes—
238C3×C4⋊C4C3×D411yescharacteristic
239C3×C4⋊C4C3×D412yes—
240C3×C22⋊C4—61no—
241C3×C22⋊C4—62no—
242C3×C42—21no—
243C3×C42—22no—
244C3×C42—62no—
245C3×C42—61no—
246C3×C42C22×D311yescharacteristic
247C3×C42C22×D312yes—
248C3×C42C23×C311yescharacteristic
249C3×C42C23×C312yes—
250(C2×D3)⋊C4—21no—
251(C2×D3)⋊C4—22no—
252C4⋊Dic3—22no—
253C4⋊Dic3—21no—
254C4⋊Dic3—21no—
255C4⋊Dic3C23×C311yescharacteristic
256C4⋊Dic3C23×C312yes—
257C4⋊Dic3C23×C311yescharacteristic
258C4⋊Dic3C23×C312yes—
259Dic3⋊C4—22no—
260Dic3⋊C4—21no—
261Dic3⋊C4—22no—
262Dic3⋊C4—22no—
263C4×Dic3—22no—
264C4×Dic3—21no—
265#204C3×Q814yescomplemented
266C22×C32C22×D411yescharacteristic
267C2×C3×D3—22no—
268C2×C3×D3—41no—
269C2×C3×D3—41no—
270C32×C4—22no—
271C32×C4—21no—
272C32×C4—22no—
273C32×C4#13712yes—
274C32×C4C22×Q811yescharacteristic
275C32×C42−1+411yescharacteristic
276C3×Dic3—22no—
277C3×Dic3—41no—
278C3×Dic3—42no—
279C3×Dic3—41no—
280C3×Dic3—42no—
281C2×SD16—31no—
282C4⋊Q8—31no—
283C4⋊Q8—32no—
284C4⋊Q8—31no—
285C4⋊Q8—61no—
286C4⋊Q8—62no—
287#125—32no—
288C22⋊Q8—61no—
289C22⋊Q8—62no—
290C4×Q8—31no—
291C4×Q8—32no—
292C4×Q8—61no—
293C4×Q8C2×C3×D311yescharacteristic
294C4×D4—31no—
295C4×D4—32no—
296C2×C4⋊C4—61no—
297#107—32no—
298#107—32no—
299#107—32no—
300#106—31no—
301#106—32no—
302C4⋊C8C2×C3×D312yes—
303C4⋊C8C2×C3×D311yescharacteristic
304#103—31no—
305#103—32no—
306#102—31no—
307#102—32no—
308#97C2×C3×D312yes—
309C4×C8C2×C3×D311yescharacteristic
310C23×C3—61no—
311C22×D3—21no—
312C3×Q8—22no—
313C3×Q8—22no—
314C3×Q8—32no—
315C3×Q8—42no—
316C3×Q8—61no—
317C3×Q8—242no—
318C3×Q8—241no—
319C3×Q8—241no—
320C3×D4—32no—
321C3×D4—61no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—61no—
328C2×C3×C4—62no—
329C2×C3×C4—61no—
330C2×C3×C4—61no—
331C2×C3×C4—62no—
332C2×C3×C4—122no—
333C2×C3×C4—242no—
334C2×C3×C4C2×D1212yes—
335C2×C3×C4C2×D1211yescharacteristic
336C2×C3×C4C2×D1212yes—
337C2×C3×C4C2×D1211yescharacteristic
338C2×C3×C4C2×C3×D412yes—
339C2×C3×C4C2×C3×D412yes—
340C2×C3×C4C2×C3×D411yescharacteristic
341C2×C3×C4C2×C3×D411yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343C2×C3×C4C24×C311yescharacteristic
344C2×Dic3—21no—
345C2×Dic3—22no—
346C2×Dic3—21no—
347C2×Dic3—21no—
348C2×Dic3—22no—
349D12—21no—
350D12C2×C3×Q812yes—
351C4×D3—42no—
352C4×D3—82no—
353Dic6—21no—
354Dic6—81no—
355Dic6—82no—
356Dic6—81no—
357Dic6C2×C3×Q812yes—
358C3×C8—21no—
359C3×C8—22no—
360C3×C8—22no—
361C3×C8—21no—
362C3×C8—22no—
363C3×C8—41no—
364C3×C8—42no—
365C3×C8D3×Q812yes—
366C3×C8C2×C3×Q812yes—
367C2×C32D4×Q811yescharacteristic
368C2×C32C2×#13711yescharacteristic
369C2×C32#57611yescharacteristic
370C3×D3—42no—
371C2×Q8—31no—
372C2×Q8—61no—
373C2×Q8—61no—
374C2×Q8—62no—
375C2×Q8C3×D1211yescharacteristic
376C2×D4—31no—
377C22×C4—61no—
378C22×C4—62no—
379SD16—34no—
380C2×C8C22×C3×D311yescharacteristic
381C2×C8C22×C3×D312yes—
382C2×C8C22×C3×D311yescharacteristic
383C4⋊C4—31no—
384C4⋊C4—32no—
385C4⋊C4—31no—
386C4⋊C4—32no—
387C4⋊C4—62no—
388C4⋊C4—61no—
389C4⋊C4—61no—
390C4⋊C4—62no—
391C4⋊C4—62no—
392C4⋊C4—61no—
393C4⋊C4—62no—
394C4⋊C4C3×D1211yescharacteristic
395C4⋊C4C3×D1212yes—
396C22⋊C4—61no—
397C22⋊C4—62no—
398C42—62no—
399C42—61no—
400C42C22×C3×D311yescharacteristic
401C42C22×C3×D312yes—
402C22×C3—21no—
403C22×C3—62no—
404C22×C3—121no—
405C22×C3—121no—
406C22×C3C22×D1211yescharacteristic
407C22×C3C22×C3×D411yescharacteristic
408C2×D3—22no—
409C2×D3—41no—
410C2×D3—41no—
411C3×C4—22no—
412C3×C4—21no—
413C3×C4—22no—
414C3×C4—22no—
415C3×C4—22no—
416C3×C4—21no—
417C3×C4—22no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—42no—
421C3×C4—42no—
422C3×C4—41no—
423C3×C4—62no—
424C3×C4—121no—
425C3×C4—122no—
426C3×C4—121no—
427C3×C4—122no—
428C3×C4#90912yes—
429C3×C4C3×#13712yes—
430C3×C4C2×D3×Q811yescharacteristic
431C3×C4#101011yescharacteristic
432C3×C4C22×C3×Q811yescharacteristic
433C3×C4C3×2−1+411yescharacteristic
434Dic3—22no—
435Dic3—41no—
436Dic3—42no—
437Dic3—41no—
438Dic3—42no—
439C32#338511yescharacteristic, complemented, Sylow
440C23—61no—
441Q8—22no—
442Q8—32no—
443Q8—61no—
444Q8—242no—
445Q8—241no—
446Q8—241no—
447D4—32no—
448D4—61no—
449C2×C4—61no—
450C2×C4—62no—
451C2×C4—61no—
452C2×C4—61no—
453C2×C4—62no—
454C2×C4—122no—
455C2×C4—242no—
456C2×C4C2×C3×D1212yes—
457C2×C4C2×C3×D1211yescharacteristic
458C2×C4C2×C3×D1212yes—
459C2×C4C2×C3×D1211yescharacteristic
460C2×C4C23×C3×D311yescharacteristic
461C8—21no—
462C8—22no—
463C8C3×D3×Q812yes—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—122no—
468C2×C3Q8×D1211yescharacteristic
469C2×C3C2×#90911yescharacteristic
470C2×C3#575211yescharacteristic
471C2×C3C3×D4×Q811yescharacteristic
472C2×C3C2×C3×#13711yescharacteristic
473C2×C3C3×#57611yescharacteristic
474D3—42no—
475C22—62no—
476C22—121no—
477C22—121no—
478C22C22×C3×D1211yescharacteristic
479C4—22no—
480C4—22no—
481C4—21no—
482C4—62no—
483C4—121no—
484C4—122no—
485C4—121no—
486C4—122no—
487C4C3×#90912yes—
488C4C2×C3×D3×Q811yescharacteristic
489C4C3×#101011yescharacteristic
490C3—21no—
491C3#7997611yescharacteristic, direct product factor
492C3C3×#338511yescharacteristic, complemented
493C2—122no—
494C2C3×Q8×D1211yescharacteristic
495C2C2×C3×#90911yescharacteristic
496C2C3×#575211yescharacteristic
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×#3385
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×#4850C2semidirect
7. C3×#4829C2semidirect
9. C3×#4702C2semidirect
11. C3×#4682C2semidirect
13. #79976C3direct (N × H)
46. Q8×Dic6C2×C3semidirect
54. C3×#446D3semidirect
55. C3×#446C2×C3semidirect
58. #4850C2×C3semidirect
61. #4829C2×C3semidirect
63. #4702C2×C3semidirect
65. #4682C2×C3semidirect
96. C3×#204Q8semidirect
193. #446C3×D3semidirect
265. #204C3×Q8semidirect
439. C32#3385semidirect
491. C3#79976direct (N × H)
492. C3C3×#3385semidirect

Maximal subgroups

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

subgroupindex
C3×#55792
C3×Q8×Dic62
C32×#4462
C3×#48502
C3×#48462
C3×#48422
C3×#48292
C3×#47102
C3×#47022
C3×C4×#2042
C3×#46822
C3×#33853
#799763