Finite Group Databasebeta

← C3×#79626 #11896020

Subgroups — C3×#79626 #11896020

Order 1152.

737 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×Dic6C211yesmaximal, characteristic, complemented
2C3×#5542C211yesmaximal, characteristic
3C32×C4×SD16C211yesmaximal, characteristic
4C3×#5166C212yesmaximal
5C3×#5031C211yesmaximal, characteristic, complemented
6C3×#5008C211yesmaximal, characteristic
7C3×#4854C212yesmaximal, complemented
8C3×#4789C212yesmaximal, complemented
9C3×#4765C212yesmaximal
10C3×#4681C211yesmaximal, characteristic, complemented
11C3×#4679C211yesmaximal, characteristic, complemented
12C3×#3369—31nomaximal
13#79626C311yesmaximal, characteristic, direct product factor
14C2×C32×SD16C2211yescharacteristic
15C32×C4×Q8C2211yescharacteristic
16C32×C4×D4C2211yescharacteristic
17C3×Q8×Dic3C2212yes—
18C2×C3×#216C2212yes—
19C3×#936C2212yes—
20C3×#926—21no—
21C3×#924—21no—
22C3×#888—22no—
23C3×#888C2212yes—
24C3×#887C2212yes—
25C3×#879—22no—
26C3×#869—21no—
27C3×#869C2211yescharacteristic
28C3×#869C2211yescharacteristic
29C3×C4×Dic6—21no—
30C3×C4×Dic6C2211yescharacteristic
31C32×#106C2211yescharacteristic
32C32×#103C2211yescharacteristic
33C32×#102C2211yescharacteristic
34C32×C4×C8C2211yescharacteristic
35C3×#832C2212yes—
36C3×#816C2212yes—
37C3×#816C2212yes—
38C3×#815C2212yes—
39C3×Dic3⋊C8C2212yes—
40C3×#810C2212yes—
41C3×#808C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43C3×Q82—31no—
44C3×#556—31no—
45Q8×Dic6C2×C311yescharacteristic, complemented
46#5542C2×C311yescharacteristic
47C3×#489—32no—
48C3×#487—31no—
49C3×#476—31no—
50C3×#475—32no—
51C3×#464—32no—
52C3×#462—31no—
53C3×#446—31no—
54C3×#441—32no—
55C3×C4×SD16—21no—
56C3×C4×SD16D311yescharacteristic
57C3×C4×SD16C2×C311yescharacteristic
58#5166C2×C312yes—
59#5031C2×C311yescharacteristic, complemented
60#5008C2×C311yescharacteristic
61#4854C2×C312yescomplemented
62#4789C2×C312yescomplemented
63#4765C2×C312yes—
64#4681C2×C311yescharacteristic, complemented
65#4679C2×C311yescharacteristic, complemented
66C2×C32×Q8C2311yescharacteristic
67C2×C32×D4C2311yescharacteristic
68C22×C32×C4—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6—22no—
71C2×C3×Dic6D411yescharacteristic
72C2×C3×Dic6C2312yes—
73C32×SD16—22no—
74C2×C32×C8C2311yescharacteristic
75C2×C32×C8C2311yescharacteristic
76C32×C4⋊C4—21no—
77C32×C4⋊C4C2311yescharacteristic
78C32×C4⋊C4C2311yescharacteristic
79C32×C22⋊C4—21no—
80C32×C42—21no—
81C32×C42C2311yescharacteristic
82C3×#217—22no—
83C3×#217—22no—
84C3×#216—24no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3—22no—
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4D412yes—
94C3×C4×Dic3—22no—
95C3×C4×Dic3—22no—
96C3×C4×Dic3C2312yes—
97C2×C3×C3⋊C8C2312yes—
98#3369—31noSylow
99C2×C3×Q16—32no—
100C2×C3×SD16—21no—
101C2×C3×SD16C2×D311yescharacteristic
102C2×C3×SD16C22×C311yescharacteristic
103C3×C4⋊Q8—32no—
104C3×C4⋊Q8—31no—
105C3×C4⋊Q8—31no—
106C3×C4⋊Q8—61no—
107C3×C4⋊Q8—62no—
108C3×#126—62no—
109C3×#124—32no—
110C3×C22⋊Q8—61no—
111C3×C4×Q8—21no—
112C3×C4×Q8—31no—
113C3×C4×Q8—32no—
114C3×C4×Q8—32no—
115C3×C4×Q8—61no—
116C3×C4×Q8C2×D311yescharacteristic
117C3×C4×Q8C22×C311yescharacteristic
118C3×C4×D4—21no—
119C3×C4×D4C2×D311yescharacteristic
120C3×C4×D4C22×C311yescharacteristic
121C3×#117—61no—
122Q8×Dic3C22×C312yes—
123C2×#216C22×C312yes—
124#936C22×C312yes—
125#926—21no—
126#924—21no—
127#888—22no—
128#888C22×C312yes—
129#887C22×C312yes—
130#879—22no—
131#869—21no—
132#869C22×C311yescharacteristic
133#869C22×C311yescharacteristic
134C4×Dic6—21no—
135C4×Dic6C22×C311yescharacteristic
136C3×#106—21no—
137C3×#106—32no—
138C3×#106C2×D311yescharacteristic
139C3×#106C22×C311yescharacteristic
140C3×C4⋊C8—32no—
141C3×C4⋊C8—31no—
142C3×#103—21no—
143C3×#103—32no—
144C3×#103—32no—
145C3×#103—32no—
146C3×#103C2×D311yescharacteristic
147C3×#103C22×C311yescharacteristic
148C3×#102—21no—
149C3×#102—32no—
150C3×#102C2×D311yescharacteristic
151C3×#102C22×C311yescharacteristic
152C3×#97—32no—
153C3×C4×C8—21no—
154C3×C4×C8C2×D311yescharacteristic
155C3×C4×C8C22×C311yescharacteristic
156#832C22×C312yes—
157#816C22×C312yes—
158#816C22×C312yes—
159#815C22×C312yes—
160Dic3⋊C8C22×C312yes—
161#810C22×C312yes—
162#808C22×C312yes—
163C4⋊(C3⋊C8)C22×C311yescharacteristic
164C23×C32—21no—
165C32×Q8—21no—
166C32×Q8#4112yes—
167C32×D4—21no—
168C32×D4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—42no—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2411yescharacteristic
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×D412yes—
180C3×Dic6—22no—
181C3×Dic6—22no—
182C3×Dic6—22no—
183C3×Dic6—82no—
184C3×Dic6—81no—
185C32×C8—21no—
186C32×C8—21no—
187C3×C3⋊C8—22no—
188Q82—31no—
189#556—31no—
190#489—32no—
191#487—31no—
192#476—31no—
193#475—32no—
194#464—32no—
195#462—31no—
196#446—31no—
197#441—32no—
198C4×SD16C3×D311yescharacteristic
199C2×C3×Q8—21no—
200C2×C3×Q8—31no—
201C2×C3×Q8—32no—
202C2×C3×Q8—62no—
203C2×C3×Q8—61no—
204C2×C3×Q8C22×D311yescharacteristic
205C2×C3×Q8C23×C311yescharacteristic
206C2×C3×D4—21no—
207C2×C3×D4C22×D311yescharacteristic
208C2×C3×D4C23×C311yescharacteristic
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—41no—
212C2×Dic6—21no—
213C2×Dic6—22no—
214C2×Dic6C3×D411yescharacteristic
215C2×Dic6C23×C312yes—
216C3×Q16—64no—
217C3×SD16—24no—
218C3×SD16—22no—
219C3×SD16—22no—
220C2×C3×C8—21no—
221C2×C3×C8—21no—
222C2×C3×C8—32no—
223C2×C3×C8C22×D311yescharacteristic
224C2×C3×C8C22×D311yescharacteristic
225C2×C3×C8C23×C311yescharacteristic
226C2×C3×C8C23×C311yescharacteristic
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—32no—
232C3×C4⋊C4—31no—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—41no—
235C3×C4⋊C4—62no—
236C3×C4⋊C4—62no—
237C3×C4⋊C4—62no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4—61no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4C22×D311yescharacteristic
242C3×C4⋊C4C22×D311yescharacteristic
243C3×C4⋊C4C23×C311yescharacteristic
244C3×C4⋊C4C23×C311yescharacteristic
245C3×C22⋊C4—21no—
246C3×C22⋊C4—21no—
247C3×C22⋊C4—41no—
248C3×C22⋊C4—62no—
249C3×C22⋊C4—62no—
250C3×C42—21no—
251C3×C42—21no—
252C3×C42—21no—
253C3×C42—32no—
254C3×C42—41no—
255C3×C42—62no—
256C3×C42—62no—
257C3×C42C22×D311yescharacteristic
258C3×C42C23×C311yescharacteristic
259#217—22no—
260#217—22no—
261#216—24no—
262C4⋊Dic3—21no—
263C4⋊Dic3—21no—
264C4⋊Dic3—21no—
265C4⋊Dic3—22no—
266C4⋊Dic3C3×D411yescharacteristic
267C4⋊Dic3C23×C312yes—
268Dic3⋊C4—22no—
269Dic3⋊C4—22no—
270Dic3⋊C4C3×D412yes—
271C4×Dic3—22no—
272C4×Dic3—22no—
273C4×Dic3C23×C312yes—
274C2×C3⋊C8C23×C312yes—
275C22×C32—41no—
276C22×C32—41no—
277C22×C32—41no—
278C22×C32C22×D411yescharacteristic
279C32×C4—22no—
280C32×C4—21no—
281C32×C4—41no—
282C32×C4—41no—
283C32×C4#13712yes—
284C32×C4C2×#4111yescharacteristic
285C32×C42−1+411yescharacteristic
286C3×Dic3—22no—
287C3×Dic3—22no—
288C3×Dic3—42no—
289C3×Dic3—42no—
290C2×Q16—32no—
291C2×SD16C2×C3×D311yescharacteristic
292C4⋊Q8—32no—
293C4⋊Q8—31no—
294C4⋊Q8—31no—
295C4⋊Q8—61no—
296C4⋊Q8—62no—
297#126—62no—
298#124—32no—
299C22⋊Q8—61no—
300C4×Q8—31no—
301C4×Q8—32no—
302C4×Q8—32no—
303C4×Q8—61no—
304C4×Q8C2×C3×D311yescharacteristic
305C4×D4C2×C3×D311yescharacteristic
306#117—61no—
307#106—32no—
308#106C2×C3×D311yescharacteristic
309C4⋊C8—32no—
310C4⋊C8—31no—
311#103—32no—
312#103—32no—
313#103—32no—
314#103C2×C3×D311yescharacteristic
315#102—32no—
316#102C2×C3×D311yescharacteristic
317#97—32no—
318C4×C8C2×C3×D311yescharacteristic
319C23×C3—21no—
320C23×C3—21no—
321C23×C3—41no—
322C3×Q8—21no—
323C3×Q8—21no—
324C3×Q8—22no—
325C3×Q8—41no—
326C3×Q8—62no—
327C3×Q8—62no—
328C3×Q8—62no—
329C3×Q8—241no—
330C3×Q8—242no—
331C3×Q8#23512yes—
332C3×Q8C3×#4112yes—
333C3×D4—22no—
334C3×D4—21no—
335C3×D4—21no—
336C3×D4—21no—
337C3×D4—21no—
338C3×D4—41no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—41no—
351C2×C3×C4—41no—
352C2×C3×C4—41no—
353C2×C3×C4—42no—
354C2×C3×C4—42no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—82no—
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4C2×C3×D411yescharacteristic
361C2×C3×C4C2×C3×D411yescharacteristic
362C2×C3×C4C23×D311yescharacteristic
363C2×C3×C4C24×C311yescharacteristic
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3C2×C3×D412yes—
367C2×Dic3C2×C3×D412yes—
368Dic6—22no—
369Dic6—22no—
370Dic6—22no—
371Dic6—82no—
372Dic6—81no—
373C3×C8—22no—
374C3×C8—21no—
375C3×C8—21no—
376C3×C8—21no—
377C3×C8—21no—
378C3×C8—41no—
379C3×C8—62no—
380C3⋊C8—22no—
381C2×C32—81no—
382C2×C32#54811yescharacteristic
383C2×C32C2×#13711yescharacteristic
384C2×C32#57711yescharacteristic
385C2×Q8—31no—
386C2×Q8—32no—
387C2×Q8—62no—
388C2×Q8—61no—
389C2×Q8C22×C3×D311yescharacteristic
390C2×D4C22×C3×D311yescharacteristic
391C22×C4—21no—
392Q16—64no—
393SD16—22no—
394C2×C8—32no—
395C2×C8C22×C3×D311yescharacteristic
396C2×C8C22×C3×D311yescharacteristic
397C4⋊C4—21no—
398C4⋊C4—31no—
399C4⋊C4—32no—
400C4⋊C4—32no—
401C4⋊C4—62no—
402C4⋊C4—62no—
403C4⋊C4—62no—
404C4⋊C4—61no—
405C4⋊C4—61no—
406C4⋊C4—61no—
407C4⋊C4C22×C3×D311yescharacteristic
408C4⋊C4C22×C3×D311yescharacteristic
409C22⋊C4—21no—
410C22⋊C4—62no—
411C22⋊C4—62no—
412C42—21no—
413C42—32no—
414C42—62no—
415C42—62no—
416C42C22×C3×D311yescharacteristic
417C22×C3—21no—
418C22×C3—42no—
419C22×C3—41no—
420C22×C3—41no—
421C22×C3—41no—
422C22×C3—41no—
423C22×C3—41no—
424C22×C3—41no—
425C22×C3—81no—
426C22×C3—81no—
427C22×C3C2×D3×D411yescharacteristic
428C22×C3C22×C3×D411yescharacteristic
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—22no—
432C3×C4—22no—
433C3×C4—22no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—41no—
437C3×C4—42no—
438C3×C4—41no—
439C3×C4—41no—
440C3×C4—41no—
441C3×C4—41no—
442C3×C4—62no—
443C3×C4—62no—
444C3×C4—81no—
445C3×C4—81no—
446C3×C4—122no—
447C3×C4—122no—
448C3×C4#91512yes—
449C3×C4C3×#13712yes—
450C3×C4C2×#23511yescharacteristic
451C3×C4#101011yescharacteristic
452C3×C4C2×C3×#4111yescharacteristic
453C3×C4C3×2−1+411yescharacteristic
454Dic3—22no—
455Dic3—22no—
456Dic3—42no—
457Dic3—42no—
458C32#336911yescharacteristic, complemented, Sylow
459C23—21no—
460Q8—21no—
461Q8—62no—
462Q8—62no—
463Q8—62no—
464Q8—241no—
465Q8—242no—
466Q8C3×#23512yes—
467D4—21no—
468D4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—32no—
473C2×C4—32no—
474C2×C4—42no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4C3×D3×D411yescharacteristic
478C2×C4C3×D3×D411yescharacteristic
479C2×C4C23×C3×D311yescharacteristic
480C8—21no—
481C8—21no—
482C8—62no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—82no—
487C2×C3—81no—
488C2×C3—81no—
489C2×C3#555211yescharacteristic
490C2×C3C2×#91511yescharacteristic
491C2×C3#577011yescharacteristic
492C2×C3C3×#54811yescharacteristic
493C2×C3C2×C3×#13711yescharacteristic
494C2×C3C3×#57711yescharacteristic
495C22—41no—
496C22—41no—
497C22—41no—
498C22C2×C3×D3×D411yescharacteristic
499C4—21no—
500C4—22no—
501C4—41no—
502C4—41no—
503C4—62no—
504C4—62no—
505C4—122no—
506C4—122no—
507C4C3×#91512yes—
508C4C2×C3×#23511yescharacteristic
509C4C3×#101011yescharacteristic
510C3—21no—
511C3#7962611yescharacteristic, direct product factor
512C3C3×#336911yescharacteristic, complemented
513C2—81no—
514C2C3×#555211yescharacteristic
515C2C2×C3×#91511yescharacteristic
516C2C3×#577011yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C4×SD16C2
socleC22×C32C22×D4
prime radicalC2×C32×D4C23
hypercenterC3×C4×SD16D3
hypocenterC3C3×#3369
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C3×Q8×Dic6C2semidirect
5. C3×#5031C2semidirect
7. C3×#4854C2semidirect
8. C3×#4789C2semidirect
10. C3×#4681C2semidirect
11. C3×#4679C2semidirect
13. #79626C3direct (N × H)
45. Q8×Dic6C2×C3semidirect
59. #5031C2×C3semidirect
61. #4854C2×C3semidirect
62. #4789C2×C3semidirect
64. #4681C2×C3semidirect
65. #4679C2×C3semidirect
458. C32#3369semidirect
511. C3#79626direct (N × H)
512. C3C3×#3369semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×Dic62
C3×#55422
C32×C4×SD162
C3×#51662
C3×#50312
C3×#50082
C3×#48542
C3×#47892
C3×#47652
C3×#46812
C3×#46792
C3×#33693
#796263