Finite Group Databasebeta

← C3×#19417 #10638024

Subgroups — C3×#19417 #10638024

Order 768.

608 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3230C211yesmaximal, characteristic, complemented
2C3×#3079C211yesmaximal, characteristic
3C3×#3076C211yesmaximal, characteristic
4C3×#2988C211yesmaximal, characteristic
5C3×#1684C212yesmaximal, complemented
6C3×#1683C212yesmaximal, complemented
7C3×#1676C212yesmaximal, complemented
8C3×#1675C212yesmaximal, complemented
9C3×#1571C211yesmaximal, characteristic, complemented
10C3×#1550C211yesmaximal, characteristic, complemented
11C2×C3×#333C211yesmaximal, characteristic, complemented
12#19417C311yesmaximal, characteristic, direct product factor, Sylow
13C3×#533C2211yescharacteristic
14C2×C3×C4⋊Q8C2211yescharacteristic
15C3×C4×#41C2211yescharacteristic
16C3×#500C2212yes—
17C3×#487C2212yes—
18C3×#484—22no—
19C3×#479—21no—
20C3×#478—21no—
21C3×#477—21no—
22C3×#477—21no—
23C3×#477C2211yescharacteristic
24C3×#477C2212yes—
25C3×#476C2211yescharacteristic
26C3×#476C2212yes—
27C3×#475—21no—
28C3×#475C2211yescharacteristic
29C3×#474—21no—
30C3×#474C2211yescharacteristic
31C3×C8×Q8C2212yes—
32C3×C8×D4—22no—
33C3×C8×D4C2212yes—
34C3×#431—21no—
35C3×#431C2211yescharacteristic
36C3×#428—21no—
37C3×#427—21no—
38C3×#423C2211yescharacteristic
39C2×C3×C4⋊C8—21no—
40C2×C3×C4⋊C8C2211yescharacteristic
41C2×C3×C4⋊C8C2211yescharacteristic
42C3×#417—21no—
43C3×#416—21no—
44C3×#335C2212yes—
45C3×#335C2212yes—
46C3×#333C2212yes—
47C3×#333C2212yes—
48C3×#333C2212yes—
49C3×#332C2212yes—
50#3230C2×C311yescharacteristic, complemented
51#3079C2×C311yescharacteristic
52#3076C2×C311yescharacteristic
53#2988C2×C311yescharacteristic
54#1684C2×C312yescomplemented
55#1683C2×C312yescomplemented
56#1676C2×C312yescomplemented
57#1675C2×C312yescomplemented
58#1571C2×C311yescharacteristic, complemented
59#1550C2×C311yescharacteristic, complemented
60C2×#333C2×C311yescharacteristic, complemented
61C2×C3×#41D411yescharacteristic
62C22×C3×Q8—21no—
63C2×C3×M16—21no—
64C22×C3×C8—21no—
65C22×C3×C8—21no—
66C22×C3×C8—22no—
67C3×C4⋊Q8—21no—
68C3×C4⋊Q8—21no—
69C3×C4⋊Q8—21no—
70C3×C4⋊Q8C2311yescharacteristic
71C3×C4⋊Q8C2312yes—
72C3×C4⋊Q8C2311yescharacteristic
73C3×#125—21no—
74C3×C22⋊Q8—21no—
75C3×C22⋊Q8—21no—
76C3×C4×Q8—21no—
77C3×C4×Q8—21no—
78C3×C4×Q8D411yescharacteristic
79C3×C4×Q8C2311yescharacteristic
80C3×C4×D4—21no—
81C3×C4×D4—21no—
82C3×C4×D4D411yescharacteristic
83C3×C4×D4C2311yescharacteristic
84C3×#117—21no—
85C3×#117—21no—
86C3×#117D411yescharacteristic
87C2×C3×C4⋊C4—21no—
88C2×C3×C4⋊C4—21no—
89C2×C3×C42—21no—
90C2×C3×C42C2311yescharacteristic
91C3×#107—22no—
92C3×#107—22no—
93C3×#107—21no—
94C3×#107—21no—
95C3×#107—22no—
96C3×#106—21no—
97C3×#106—21no—
98C3×#106—22no—
99C3×C4⋊C8—22no—
100C3×C4⋊C8—21no—
101C3×C4⋊C8—21no—
102C3×C4⋊C8—21no—
103C3×C4⋊C8D411yescharacteristic
104C3×C4⋊C8D411yescharacteristic
105C3×C4⋊C8C2312yes—
106C3×C4⋊C8C2311yescharacteristic
107C3×C4⋊C8C2311yescharacteristic
108C3×C4⋊C8C2312yes—
109C3×#103—21no—
110C3×#103—21no—
111C3×#103—22no—
112C3×#103—22no—
113C3×#103—22no—
114C3×#102—21no—
115C3×#102—21no—
116C3×#102—22no—
117C3×C22⋊C8—22no—
118C3×C22⋊C8D412yes—
119C3×C4×C8—22no—
120C3×C4×C8C2312yes—
121#533C22×C311yescharacteristic
122C2×C4⋊Q8C22×C311yescharacteristic
123C4×#41C22×C311yescharacteristic
124#500C22×C312yes—
125#487C22×C312yes—
126#484—22no—
127#479—21no—
128#478—21no—
129#477—21no—
130#477—21no—
131#477C22×C311yescharacteristic
132#477C22×C312yes—
133#476C22×C311yescharacteristic
134#476C22×C312yes—
135#475—21no—
136#475C22×C311yescharacteristic
137#474—21no—
138#474C22×C311yescharacteristic
139C8×Q8C22×C312yes—
140C8×D4—22no—
141C8×D4C22×C312yes—
142#431—21no—
143#431C22×C311yescharacteristic
144#428—21no—
145#427—21no—
146#423C22×C311yescharacteristic
147C2×C4⋊C8—21no—
148C2×C4⋊C8C22×C311yescharacteristic
149C2×C4⋊C8C22×C311yescharacteristic
150#417—21no—
151#416—21no—
152#335C22×C312yes—
153#335C22×C312yes—
154#333C22×C312yes—
155#333C22×C312yes—
156#333C22×C312yes—
157#332C22×C312yes—
158C3×#41—22no—
159C3×#41Q1614yes—
160C2×C3×Q8—21no—
161C2×C3×Q8—21no—
162C2×C3×Q8—22no—
163C2×C3×Q8—41no—
164C2×C3×Q8—82no—
165C2×C3×Q8C2×D411yescharacteristic
166C2×C3×D4—21no—
167C2×C3×D4C2×D411yescharacteristic
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—41no—
172C22×C3×C4C2×D411yescharacteristic
173C22×C3×C4C2×D411yescharacteristic
174C22×C3×C4#4111yescharacteristic
175C3×M16—42no—
176C2×C3×C8—22no—
177C2×C3×C8—21no—
178C2×C3×C8—22no—
179C2×C3×C8—21no—
180C2×C3×C8—42no—
181C2×C3×C8—82no—
182C2×C3×C8—81no—
183C2×C3×C8C2×D412yes—
184C2×C3×C8C2×D412yes—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—22no—
188C3×C4⋊C4—21no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—22no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4—21no—
193C3×C4⋊C4—41no—
194C3×C4⋊C4—41no—
195C3×C4⋊C4—41no—
196C3×C4⋊C4—41no—
197C3×C4⋊C4C2×D411yescharacteristic
198C3×C4⋊C4C2×D411yescharacteristic
199C3×C22⋊C4—21no—
200C3×C22⋊C4—21no—
201C3×C22⋊C4—21no—
202C3×C22⋊C4—41no—
203C3×C42—21no—
204C3×C42—21no—
205C3×C42—21no—
206C3×C42—41no—
207C3×C42C2×D411yescharacteristic
208C3×C42C2×D411yescharacteristic
209C3×C42#4111yescharacteristic
210C3×C42C2411yescharacteristic
211C2×#41C3×D411yescharacteristic
212C22×Q8—21no—
213C2×M16—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—22no—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8C23×C312yes—
221C4⋊Q8C23×C311yescharacteristic
222C4⋊Q8C23×C311yescharacteristic
223#125—21no—
224C22⋊Q8—21no—
225C22⋊Q8—21no—
226C4×Q8—21no—
227C4×Q8—21no—
228C4×Q8C3×D411yescharacteristic
229C4×Q8C23×C311yescharacteristic
230C4×D4—21no—
231C4×D4—21no—
232C4×D4C3×D411yescharacteristic
233C4×D4C23×C311yescharacteristic
234#117—21no—
235#117—21no—
236#117C3×D411yescharacteristic
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C42—21no—
240C2×C42C23×C311yescharacteristic
241#107—22no—
242#107—22no—
243#107—21no—
244#107—21no—
245#107—22no—
246#106—21no—
247#106—21no—
248#106—22no—
249C4⋊C8—22no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8C3×D411yescharacteristic
254C4⋊C8C3×D411yescharacteristic
255C4⋊C8C23×C312yes—
256C4⋊C8C23×C312yes—
257C4⋊C8C23×C311yescharacteristic
258C4⋊C8C23×C311yescharacteristic
259#103—21no—
260#103—21no—
261#103—22no—
262#103—22no—
263#103—22no—
264#102—21no—
265#102—21no—
266#102—22no—
267C22⋊C8—22no—
268C22⋊C8C3×D412yes—
269C4×C8—22no—
270C4×C8C23×C312yes—
271C23×C3—21no—
272C23×C3#12111yescharacteristic
273C3×Q8—21no—
274C3×Q8—41no—
275C3×Q8—41no—
276C3×Q8—81no—
277C3×Q8—82no—
278C3×Q8—82no—
279C3×Q8C2×Q1612yes—
280C3×D4—24no—
281C3×D4—21no—
282C3×D4C2×Q1612yes—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—24no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—42no—
295C2×C3×C4—81no—
296C2×C3×C4—82no—
297C2×C3×C4#12111yescharacteristic
298C2×C3×C4#12111yescharacteristic
299C2×C3×C4#12111yescharacteristic
300C2×C3×C4C2×Q1612yes—
301C2×C3×C4#13512yes—
302C2×C3×C4C22×D411yescharacteristic
303C2×C3×C4C22×D411yescharacteristic
304C2×C3×C4C2×#4111yescharacteristic
305C3×C8—22no—
306C3×C8—22no—
307C3×C8—41no—
308C3×C8—41no—
309C3×C8—42no—
310C3×C8—42no—
311#41—22no—
312#41C3×Q1614yes—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—22no—
316C2×Q8—41no—
317C2×Q8—82no—
318C2×Q8C2×C3×D411yescharacteristic
319C2×D4—21no—
320C2×D4C2×C3×D411yescharacteristic
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—41no—
325C22×C4C2×C3×D411yescharacteristic
326C22×C4C2×C3×D411yescharacteristic
327C22×C4C3×#4111yescharacteristic
328M16—42no—
329C2×C8—22no—
330C2×C8—21no—
331C2×C8—22no—
332C2×C8—21no—
333C2×C8—42no—
334C2×C8—82no—
335C2×C8—81no—
336C2×C8C2×C3×D412yes—
337C2×C8C2×C3×D412yes—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—22no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—22no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4C2×C3×D411yescharacteristic
351C4⋊C4C2×C3×D411yescharacteristic
352C22⋊C4—21no—
353C22⋊C4—21no—
354C22⋊C4—21no—
355C22⋊C4—41no—
356C42—21no—
357C42—21no—
358C42—21no—
359C42—41no—
360C42C2×C3×D411yescharacteristic
361C42C2×C3×D411yescharacteristic
362C42C3×#4111yescharacteristic
363C42C24×C311yescharacteristic
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—22no—
367C22×C3—41no—
368C22×C3—41no—
369C22×C3#46712yes—
370C22×C3C2×#12111yescharacteristic
371C3×C4—21no—
372C3×C4—22no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—41no—
376C3×C4—41no—
377C3×C4—81no—
378C3×C4—82no—
379C3×C4—81no—
380C3×C4#46712yes—
381C3×C4C22×Q1611yescharacteristic
382C3×C4C2×#13511yescharacteristic
383C3×C4#57711yescharacteristic
384C3×C4#57811yescharacteristic
385C23—21no—
386C23C3×#12111yescharacteristic
387Q8—21no—
388Q8—41no—
389Q8—41no—
390Q8—82no—
391Q8—81no—
392Q8—82no—
393Q8C2×C3×Q1612yes—
394D4—24no—
395D4—21no—
396D4C2×C3×Q1612yes—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—24no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—81no—
410C2×C4—82no—
411C2×C4C3×#12111yescharacteristic
412C2×C4C3×#12111yescharacteristic
413C2×C4C3×#12111yescharacteristic
414C2×C4C2×C3×Q1612yes—
415C2×C4C3×#13512yes—
416C2×C4C22×C3×D411yescharacteristic
417C2×C4C22×C3×D411yescharacteristic
418C2×C4C2×C3×#4111yescharacteristic
419C8—22no—
420C8—22no—
421C8—41no—
422C8—41no—
423C8—42no—
424C8—42no—
425C2×C3—22no—
426C2×C3—42no—
427C2×C3#304611yescharacteristic
428C2×C3C2×#46711yescharacteristic
429C2×C3#306811yescharacteristic
430C22—21no—
431C22—21no—
432C22—22no—
433C22—41no—
434C22—41no—
435C22C3×#46712yes—
436C22C2×C3×#12111yescharacteristic
437C4—21no—
438C4—22no—
439C4—21no—
440C4—21no—
441C4—41no—
442C4—41no—
443C4—81no—
444C4—82no—
445C4—81no—
446C4C3×#46712yes—
447C4C22×C3×Q1611yescharacteristic
448C4C2×C3×#13511yescharacteristic
449C4C3×#57711yescharacteristic
450C4C3×#57811yescharacteristic
451C3#1941711yescharacteristic, direct product factor, Sylow
452C2—22no—
453C2—42no—
454C2C3×#304611yescharacteristic
455C2C2×C3×#46711yescharacteristic
456C2C3×#306811yescharacteristic
subgroupG/H
center, socleC22×C3C2×#121
commutator, Frattini, cosocleC42C24×C3
prime radicalC2×C3×#41D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#3230C2semidirect
5. C3×#1684C2semidirect
6. C3×#1683C2semidirect
7. C3×#1676C2semidirect
8. C3×#1675C2semidirect
9. C3×#1571C2semidirect
10. C3×#1550C2semidirect
11. C2×C3×#333C2semidirect
12. #19417C3direct (N × H)
50. #3230C2×C3semidirect
54. #1684C2×C3semidirect
55. #1683C2×C3semidirect
56. #1676C2×C3semidirect
57. #1675C2×C3semidirect
58. #1571C2×C3semidirect
59. #1550C2×C3semidirect
60. C2×#333C2×C3semidirect
451. C3#19417direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#32302
C3×#30792
C3×#30762
C3×#29882
C3×#16842
C3×#16832
C3×#16762
C3×#16752
C3×#15712
C3×#15502
C2×C3×#3332
#194173