Finite Group Databasebeta

← C3×#83631 #11897621

Subgroups — C3×#83631 #11897621

Order 1152.

794 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#554C211yesmaximal, characteristic
2C3×Q8×Dic6C211yesmaximal, characteristic, complemented
3C3×#5091C211yesmaximal, characteristic, complemented
4C3×#5078C211yesmaximal, characteristic, complemented
5C3×#5064C212yesmaximal, complemented
6C3×#5063C212yesmaximal, complemented
7C3×#5024C211yesmaximal, characteristic, complemented
8C3×#5018C212yesmaximal
9C3×C4×#214C211yesmaximal, characteristic
10C3×#5008C211yesmaximal, characteristic
11C3×#5007C212yesmaximal
12C3×#3385—31nomaximal
13#83631C311yesmaximal, characteristic, direct product factor
14C32×C4⋊Q8C2211yescharacteristic
15C32×#125C2212yes—
16C32×C22⋊Q8—21no—
17C32×C22⋊Q8—22no—
18C32×C4×Q8C2211yescharacteristic
19C32×C4×D4C2212yes—
20C32×C4×D4C2211yescharacteristic
21C2×C32×C4⋊C4—21no—
22C3×Q8×Dic3—21no—
23C2×C3×#214C2211yescharacteristic
24C3×#888—21no—
25C3×#888—22no—
26C3×#869C2212yes—
27C3×#869C2211yescharacteristic
28C3×C4×Dic6C2211yescharacteristic
29C3×C4×Dic6C2212yes—
30C3×#832C2211yescharacteristic
31C3×#832C2212yes—
32C3×#810C2211yescharacteristic
33C3×#810C2212yes—
34C3×#808C2212yes—
35C3×#808C2211yescharacteristic
36C3×#807C2212yes—
37C3×#807C2212yes—
38C3×#807C2212yes—
39C3×C4⋊(C3⋊C8)C2212yes—
40C3×C4⋊(C3⋊C8)C2211yescharacteristic
41C3×#803C2212yes—
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×Q82—31no—
44C3×#554—21no—
45C3×#554D311yescharacteristic
46C3×#554C2×C311yescharacteristic
47Q8×Dic6C2×C311yescharacteristic, complemented
48C3×#501—32no—
49C3×#500—31no—
50C3×#479—32no—
51C3×#477—31no—
52C3×#476—31no—
53C3×#474—32no—
54C3×#446—31no—
55C3×#440—32no—
56C3×C4×SD16—31no—
57#5091C2×C311yescharacteristic, complemented
58#5078C2×C311yescharacteristic, complemented
59#5064C2×C312yescomplemented
60#5063C2×C312yescomplemented
61#5024C2×C311yescharacteristic, complemented
62#5018C2×C312yes—
63C4×#214C2×C311yescharacteristic
64#5008C2×C311yescharacteristic
65#5007C2×C312yes—
66C2×C32×Q8—21no—
67C2×C32×Q8D411yescharacteristic
68C2×C32×D4C2311yescharacteristic
69C22×C32×C4—21no—
70C22×C32×C4—22no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—22no—
73C2×C3×Dic6C2311yescharacteristic
74C32×C4⋊C4—22no—
75C32×C4⋊C4—21no—
76C32×C4⋊C4—22no—
77C32×C4⋊C4D411yescharacteristic
78C32×C4⋊C4D412yes—
79C32×C4⋊C4C2312yes—
80C32×C4⋊C4C2311yescharacteristic
81C32×C22⋊C4—21no—
82C32×C22⋊C4—22no—
83C32×C42C2311yescharacteristic
84C32×C42C2312yes—
85C3×#214Q814yescomplemented
86C3×C4⋊Dic3—22no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3C2312yes—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4—21no—
91C3×Dic3⋊C4—22no—
92C3×C4×Dic3—22no—
93C3×C4×Dic3—21no—
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97#3385—31noSylow
98C2×C3×SD16—31no—
99C3×C4⋊Q8—21no—
100C3×C4⋊Q8—32no—
101C3×C4⋊Q8—31no—
102C3×C4⋊Q8—61no—
103C3×C4⋊Q8—62no—
104C3×C4⋊Q8C2×D311yescharacteristic
105C3×C4⋊Q8C22×C311yescharacteristic
106C3×#125—22no—
107C3×#125C2×D312yes—
108C3×#125C22×C312yes—
109C3×C22⋊Q8—22no—
110C3×C22⋊Q8—24no—
111C3×C22⋊Q8—21no—
112C3×C22⋊Q8—21no—
113C3×C22⋊Q8—22no—
114C3×C22⋊Q8—22no—
115C3×C4×Q8—21no—
116C3×C4×Q8—31no—
117C3×C4×Q8—32no—
118C3×C4×Q8—61no—
119C3×C4×Q8C2×D311yescharacteristic
120C3×C4×Q8C22×C311yescharacteristic
121C3×C4×D4—21no—
122C3×C4×D4—22no—
123C3×C4×D4C2×D311yescharacteristic
124C3×C4×D4C2×D312yes—
125C3×C4×D4C22×C312yes—
126C3×C4×D4C22×C311yescharacteristic
127C2×C3×C4⋊C4—22no—
128C2×C3×C4⋊C4—21no—
129C2×C3×C4⋊C4—21no—
130Q8×Dic3—21no—
131C2×#214C22×C311yescharacteristic
132#888—21no—
133#888—22no—
134#869C22×C312yes—
135#869C22×C311yescharacteristic
136C4×Dic6C22×C311yescharacteristic
137C4×Dic6C22×C312yes—
138C3×#107—32no—
139C3×#107—32no—
140C3×#107—32no—
141C3×#106—31no—
142C3×#106—32no—
143C3×C4⋊C8—32no—
144C3×C4⋊C8—31no—
145C3×#103—31no—
146C3×#103—32no—
147C3×#102—31no—
148C3×#102—32no—
149C3×#97—32no—
150C3×C4×C8—31no—
151#832C22×C311yescharacteristic
152#832C22×C312yes—
153#810C22×C311yescharacteristic
154#810C22×C312yes—
155#808C22×C312yes—
156#808C22×C311yescharacteristic
157#807C22×C312yes—
158#807C22×C312yes—
159#807C22×C312yes—
160C4⋊(C3⋊C8)C22×C312yes—
161C4⋊(C3⋊C8)C22×C311yescharacteristic
162#803C22×C312yes—
163C4×C3⋊C8C22×C311yescharacteristic
164C23×C32—21no—
165C32×Q8—22no—
166C32×Q8—81no—
167C32×D4—21no—
168C32×D4C2×Q812yes—
169C2×C32×C4—21no—
170C2×C32×C4—22no—
171C2×C32×C4—42no—
172C2×C32×C4—82no—
173C2×C32×C4C2×D412yes—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D412yes—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2411yescharacteristic
178C2×C3×Dic3—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—21no—
181C3×Dic6—21no—
182C3×Dic6—82no—
183C3×Dic6—81no—
184C3×Dic6C2×Q812yes—
185C3×C3⋊C8—21no—
186C3×C3⋊C8—22no—
187C3×C3⋊C8C2×Q812yes—
188Q82—31no—
189#554C3×D311yescharacteristic
190#501—32no—
191#500—31no—
192#479—32no—
193#477—31no—
194#476—31no—
195#474—32no—
196#446—31no—
197#440—32no—
198C4×SD16—31no—
199C2×C3×Q8—22no—
200C2×C3×Q8—21no—
201C2×C3×Q8—21no—
202C2×C3×Q8—21no—
203C2×C3×Q8—31no—
204C2×C3×Q8—61no—
205C2×C3×Q8—62no—
206C2×C3×Q8#6711yescharacteristic
207C2×C3×Q8C3×D411yescharacteristic
208C2×C3×D4—21no—
209C2×C3×D4C22×D311yescharacteristic
210C2×C3×D4C23×C311yescharacteristic
211C22×C3×C4—22no—
212C22×C3×C4—24no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C2×Dic6—21no—
218C2×Dic6—22no—
219C2×Dic6C23×C311yescharacteristic
220C3×SD16—34no—
221C2×C3×C8—31no—
222C2×C3×C8—31no—
223C2×C3×C8—32no—
224C3×C4⋊C4—24no—
225C3×C4⋊C4—22no—
226C3×C4⋊C4—24no—
227C3×C4⋊C4—22no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—22no—
230C3×C4⋊C4—22no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—22no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—22no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—22no—
237C3×C4⋊C4—31no—
238C3×C4⋊C4—32no—
239C3×C4⋊C4—61no—
240C3×C4⋊C4—62no—
241C3×C4⋊C4—62no—
242C3×C4⋊C4—61no—
243C3×C4⋊C4#6711yescharacteristic
244C3×C4⋊C4#6712yes—
245C3×C4⋊C4C3×D411yescharacteristic
246C3×C4⋊C4C3×D412yes—
247C3×C4⋊C4C22×D311yescharacteristic
248C3×C4⋊C4C22×D312yes—
249C3×C4⋊C4C23×C312yes—
250C3×C4⋊C4C23×C311yescharacteristic
251C3×C22⋊C4—22no—
252C3×C22⋊C4—24no—
253C3×C22⋊C4—21no—
254C3×C22⋊C4—22no—
255C3×C22⋊C4—21no—
256C3×C22⋊C4—22no—
257C3×C42—22no—
258C3×C42—21no—
259C3×C42—62no—
260C3×C42—61no—
261C3×C42C22×D311yescharacteristic
262C3×C42C22×D312yes—
263C3×C42C23×C311yescharacteristic
264C3×C42C23×C312yes—
265#214C3×Q814yescomplemented
266C4⋊Dic3—22no—
267C4⋊Dic3—21no—
268C4⋊Dic3C23×C312yes—
269C4⋊Dic3C23×C311yescharacteristic
270Dic3⋊C4—21no—
271Dic3⋊C4—22no—
272C4×Dic3—22no—
273C4×Dic3—21no—
274C2×C3⋊C8C23×C311yescharacteristic
275C2×C3⋊C8C23×C312yes—
276C2×C3⋊C8C23×C311yescharacteristic
277C22×C32—22no—
278C22×C32—41no—
279C22×C32—41no—
280C22×C32C22×D411yescharacteristic
281C32×C4—22no—
282C32×C4—22no—
283C32×C4—21no—
284C32×C4—41no—
285C32×C4—42no—
286C32×C4#13712yes—
287C32×C4C22×Q811yescharacteristic
288C32×C42−1+411yescharacteristic
289C3×Dic3—22no—
290C3×Dic3—41no—
291C3×Dic3—42no—
292C2×SD16—31no—
293C4⋊Q8—32no—
294C4⋊Q8—31no—
295C4⋊Q8—61no—
296C4⋊Q8—62no—
297C4⋊Q8C2×C3×D311yescharacteristic
298#125C2×C3×D312yes—
299C22⋊Q8—21no—
300C22⋊Q8—22no—
301C4×Q8—31no—
302C4×Q8—32no—
303C4×Q8—61no—
304C4×Q8C2×C3×D311yescharacteristic
305C4×D4C2×C3×D311yescharacteristic
306C4×D4C2×C3×D312yes—
307C2×C4⋊C4—21no—
308#107—32no—
309#107—32no—
310#107—32no—
311#106—31no—
312#106—32no—
313C4⋊C8—32no—
314C4⋊C8—31no—
315#103—31no—
316#103—32no—
317#102—31no—
318#102—32no—
319#97—32no—
320C4×C8—31no—
321C23×C3—22no—
322C23×C3—21no—
323C23×C3—21no—
324C3×Q8—22no—
325C3×Q8—22no—
326C3×Q8—32no—
327C3×Q8—42no—
328C3×Q8—61no—
329C3×Q8—81no—
330C3×Q8—81no—
331C3×Q8—82no—
332C3×Q8—242no—
333C3×Q8—241no—
334C3×D4—22no—
335C3×D4—21no—
336C3×D4—21no—
337C3×D4—22no—
338C3×D4D3×Q812yes—
339C3×D4C2×C3×Q812yes—
340C2×C3×C4—22no—
341C2×C3×C4—24no—
342C2×C3×C4—21no—
343C2×C3×C4—22no—
344C2×C3×C4—21no—
345C2×C3×C4—22no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—22no—
349C2×C3×C4—21no—
350C2×C3×C4—22no—
351C2×C3×C4—44no—
352C2×C3×C4—42no—
353C2×C3×C4—42no—
354C2×C3×C4—61no—
355C2×C3×C4—62no—
356C2×C3×C4—61no—
357C2×C3×C4—82no—
358C2×C3×C4—82no—
359C2×C3×C4—84no—
360C2×C3×C4C2×#6712yes—
361C2×C3×C4C2×#6711yescharacteristic
362C2×C3×C4C2×#6712yes—
363C2×C3×C4C2×#6711yescharacteristic
364C2×C3×C4C2×C3×D412yes—
365C2×C3×C4C2×C3×D411yescharacteristic
366C2×C3×C4C2×C3×D412yes—
367C2×C3×C4C2×C3×D411yescharacteristic
368C2×C3×C4C23×D311yescharacteristic
369C2×C3×C4C24×C311yescharacteristic
370C2×Dic3—21no—
371C2×Dic3—22no—
372C2×Dic3—21no—
373Dic6—21no—
374Dic6—82no—
375Dic6—81no—
376Dic6C2×C3×Q812yes—
377C3×C8—32no—
378C3×C8—61no—
379C3×C8—62no—
380C3⋊C8—21no—
381C3⋊C8—22no—
382C3⋊C8C2×C3×Q812yes—
383C2×C32—42no—
384C2×C32D4×Q811yescharacteristic
385C2×C32C2×#13711yescharacteristic
386C2×C32#57611yescharacteristic
387C2×Q8—21no—
388C2×Q8—31no—
389C2×Q8—61no—
390C2×Q8—62no—
391C2×Q8C3×#6711yescharacteristic
392C2×D4C22×C3×D311yescharacteristic
393C22×C4—21no—
394C22×C4—22no—
395SD16—34no—
396C2×C8—31no—
397C2×C8—31no—
398C2×C8—32no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—22no—
402C4⋊C4—31no—
403C4⋊C4—32no—
404C4⋊C4—61no—
405C4⋊C4—62no—
406C4⋊C4—62no—
407C4⋊C4—61no—
408C4⋊C4C3×#6711yescharacteristic
409C4⋊C4C3×#6712yes—
410C4⋊C4C22×C3×D311yescharacteristic
411C4⋊C4C22×C3×D312yes—
412C22⋊C4—21no—
413C22⋊C4—22no—
414C42—62no—
415C42—61no—
416C42C22×C3×D311yescharacteristic
417C42C22×C3×D312yes—
418C22×C3—24no—
419C22×C3—22no—
420C22×C3—22no—
421C22×C3—21no—
422C22×C3—42no—
423C22×C3—42no—
424C22×C3—41no—
425C22×C3—41no—
426C22×C3—41no—
427C22×C3—41no—
428C22×C3C22×#6711yescharacteristic
429C22×C3C22×C3×D411yescharacteristic
430C3×C4—22no—
431C3×C4—22no—
432C3×C4—21no—
433C3×C4—22no—
434C3×C4—22no—
435C3×C4—21no—
436C3×C4—22no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—42no—
440C3×C4—42no—
441C3×C4—41no—
442C3×C4—42no—
443C3×C4—44no—
444C3×C4—41no—
445C3×C4—42no—
446C3×C4—41no—
447C3×C4—42no—
448C3×C4—62no—
449C3×C4—121no—
450C3×C4—122no—
451C3×C4#95112yes—
452C3×C4C3×#13712yes—
453C3×C4C2×D3×Q811yescharacteristic
454C3×C4#100711yescharacteristic
455C3×C4C22×C3×Q811yescharacteristic
456C3×C4C3×2−1+411yescharacteristic
457Dic3—22no—
458Dic3—41no—
459Dic3—42no—
460C32#338511yescharacteristic, complemented, Sylow
461C23—21no—
462Q8—22no—
463Q8—32no—
464Q8—61no—
465Q8—81no—
466Q8—242no—
467Q8—241no—
468D4—21no—
469D4C3×D3×Q812yes—
470C2×C4—21no—
471C2×C4—22no—
472C2×C4—42no—
473C2×C4—61no—
474C2×C4—62no—
475C2×C4—61no—
476C2×C4—82no—
477C2×C4C2×C3×#6712yes—
478C2×C4C2×C3×#6711yescharacteristic
479C2×C4C2×C3×#6712yes—
480C2×C4C2×C3×#6711yescharacteristic
481C2×C4C23×C3×D311yescharacteristic
482C8—32no—
483C8—61no—
484C8—62no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—44no—
489C2×C3—42no—
490C2×C3—42no—
491C2×C3Q8×#6711yescharacteristic
492C2×C3C2×#95111yescharacteristic
493C2×C3#583511yescharacteristic
494C2×C3C3×D4×Q811yescharacteristic
495C2×C3C2×C3×#13711yescharacteristic
496C2×C3C3×#57611yescharacteristic
497C22—22no—
498C22—41no—
499C22—41no—
500C22C22×C3×#6711yescharacteristic
501C4—22no—
502C4—22no—
503C4—21no—
504C4—41no—
505C4—42no—
506C4—62no—
507C4—121no—
508C4—122no—
509C4C3×#95112yes—
510C4C2×C3×D3×Q811yescharacteristic
511C4C3×#100711yescharacteristic
512C3—21no—
513C3#8363111yescharacteristic, direct product factor
514C3C3×#338511yescharacteristic, complemented
515C2—42no—
516C2C3×Q8×#6711yescharacteristic
517C2C2×C3×#95111yescharacteristic
518C2C3×#583511yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#554C2
socleC22×C32C22×D4
prime radicalC2×C32×D4C23
hypercenterC3×#554D3
hypocenterC3C3×#3385
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×Q8 ◁ C3×#554

Complements

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

NH ≅ G/Ntype
2. C3×Q8×Dic6C2semidirect
3. C3×#5091C2semidirect
4. C3×#5078C2semidirect
5. C3×#5064C2semidirect
6. C3×#5063C2semidirect
7. C3×#5024C2semidirect
13. #83631C3direct (N × H)
47. Q8×Dic6C2×C3semidirect
57. #5091C2×C3semidirect
58. #5078C2×C3semidirect
59. #5064C2×C3semidirect
60. #5063C2×C3semidirect
61. #5024C2×C3semidirect
85. C3×#214Q8semidirect
265. #214C3×Q8semidirect
460. C32#3385semidirect
513. C3#83631direct (N × H)
514. C3C3×#3385semidirect

Maximal subgroups

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

subgroupindex
C32×#5542
C3×Q8×Dic62
C3×#50912
C3×#50782
C3×#50642
C3×#50632
C3×#50242
C3×#50182
C3×C4×#2142
C3×#50082
C3×#50072
C3×#33853
#836313