Finite Group Databasebeta

← C3×#71912 #11780091

Subgroups — C3×#71912 #11780091

Order 1152.

626 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#547C211yesmaximal, characteristic
2C3×#5078C211yesmaximal, characteristic, complemented
3C3×#5019C211yesmaximal, characteristic, complemented
4C3×#5007C211yesmaximal, characteristic, complemented
5C3×#4547C211yesmaximal, characteristic, complemented
6C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
7C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C3×#1647—31nomaximal
9#71912C311yesmaximal, characteristic, direct product factor
10C2×C32×#41—21no—
11C32×C4⋊Q8C2211yescharacteristic
12C32×#123—22no—
13C32×C22⋊Q8—21no—
14C32×#121—21no—
15C32×C4×D4C2211yescharacteristic
16C32×C4×D4C2211yescharacteristic
17C2×C32×C4⋊C4—21no—
18C2×C3×#214—21no—
19C3×#869C2211yescharacteristic
20C3×#832—21no—
21C3×#810—21no—
22C3×#807—21no—
23C3×#807—22no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27C3×#547—21no—
28C3×#547D311yescharacteristic
29C3×#547C2×C311yescharacteristic
30C3×#500—31no—
31C3×#474—31no—
32C3×#461—31no—
33#5078C2×C311yescharacteristic, complemented
34#5019C2×C311yescharacteristic, complemented
35#5007C2×C311yescharacteristic, complemented
36C3×#332—31no—
37C3×D4⋊C8—31no—
38C3×D4⋊C8—31no—
39#4547C2×C311yescharacteristic, complemented
40D4⋊(C3⋊C8)C2×C311yescharacteristic, complemented
41D4⋊(C3⋊C8)C2×C311yescharacteristic, complemented
42C32×#41—42no—
43C32×#41—42no—
44C2×C32×Q8—21no—
45C2×C32×D4—22no—
46C2×C32×D4D411yescharacteristic
47C2×C32×D4D411yescharacteristic
48C22×C32×C4—22no—
49C22×C32×C4—21no—
50C22×C32×C4—21no—
51C2×C3×Dic6—21no—
52C32×C4⋊C4—22no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4D411yescharacteristic
55C32×C4⋊C4D412yes—
56C32×C4⋊C4D411yescharacteristic
57C32×C22⋊C4—22no—
58C32×C22⋊C4—21no—
59C32×C22⋊C4—21no—
60C32×C42C2311yescharacteristic
61C3×#214—42no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#1647—31noSylow
68C2×C3×#41—22no—
69C2×C3×#41—21no—
70C2×C3×#41—21no—
71C2×C3×SD16—61no—
72C3×C4⋊Q8—21no—
73C3×C4⋊Q8—31no—
74C3×C4⋊Q8C2×D311yescharacteristic
75C3×C4⋊Q8C22×C311yescharacteristic
76C3×#123—24no—
77C3×#123—22no—
78C3×#123—22no—
79C3×C22⋊Q8—22no—
80C3×C22⋊Q8—21no—
81C3×C22⋊Q8—21no—
82C3×#121—22no—
83C3×#121—21no—
84C3×#121—21no—
85C3×C4×D4—21no—
86C3×C4×D4—21no—
87C3×C4×D4C2×D311yescharacteristic
88C3×C4×D4C2×D311yescharacteristic
89C3×C4×D4C22×C311yescharacteristic
90C3×C4×D4C22×C311yescharacteristic
91C2×C3×C4⋊C4—22no—
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4—21no—
94C2×#214—21no—
95#869C22×C311yescharacteristic
96C3×#107—61no—
97C3×#107—62no—
98C3×C4⋊C8—31no—
99C3×C4⋊C8—31no—
100C3×#103—61no—
101C3×#102—61no—
102C3×C4×C8—31no—
103#832—21no—
104#810—21no—
105#807—21no—
106#807—22no—
107C4⋊(C3⋊C8)C22×C311yescharacteristic
108C4⋊(C3⋊C8)C22×C311yescharacteristic
109C4×C3⋊C8C22×C311yescharacteristic
110C23×C32—21no—
111C23×C32—21no—
112C32×Q8—41no—
113C32×Q8—41no—
114C32×D4—21no—
115C32×D4—21no—
116C32×D4—21no—
117C32×D4—44no—
118C32×D4D812yes—
119C2×C32×C4—21no—
120C2×C32×C4—21no—
121C2×C32×C4—22no—
122C2×C32×C4—44no—
123C2×C32×C4—41no—
124C2×C32×C4—41no—
125C2×C32×C4—41no—
126C2×C32×C4—41no—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C3×Dic3—41no—
131C3×Dic6—41no—
132C3×Dic6—41no—
133C3×C3⋊C8—22no—
134C3×C3⋊C8—41no—
135C3×C3⋊C8—41no—
136#547C3×D311yescharacteristic
137#500—31no—
138#474—31no—
139#461—31no—
140#332—31no—
141D4⋊C8—31no—
142D4⋊C8—31no—
143C3×#41—44no—
144C3×#41—42no—
145C3×#41—42no—
146C3×#41—44no—
147C3×#41—42no—
148C3×#41—42no—
149C2×C3×Q8—22no—
150C2×C3×Q8—21no—
151C2×C3×Q8—21no—
152C2×C3×Q8—61no—
153C2×C3×D4—24no—
154C2×C3×D4—22no—
155C2×C3×D4—22no—
156C2×C3×D4—21no—
157C2×C3×D4—21no—
158C2×C3×D4#6711yescharacteristic
159C2×C3×D4#6711yescharacteristic
160C2×C3×D4C3×D411yescharacteristic
161C2×C3×D4C3×D411yescharacteristic
162C22×C3×C4—22no—
163C22×C3×C4—24no—
164C22×C3×C4—22no—
165C22×C3×C4—22no—
166C22×C3×C4—22no—
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C2×Dic6—21no—
172C3×SD16—122no—
173C2×C3×C8—61no—
174C2×C3×C8—61no—
175C2×C3×C8—61no—
176C3×C4⋊C4—22no—
177C3×C4⋊C4—24no—
178C3×C4⋊C4—22no—
179C3×C4⋊C4—22no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—22no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4#6711yescharacteristic
188C3×C4⋊C4#6711yescharacteristic
189C3×C4⋊C4#6712yes—
190C3×C4⋊C4C3×D411yescharacteristic
191C3×C4⋊C4C3×D412yes—
192C3×C4⋊C4C3×D411yescharacteristic
193C3×C22⋊C4—22no—
194C3×C22⋊C4—22no—
195C3×C22⋊C4—24no—
196C3×C22⋊C4—22no—
197C3×C22⋊C4—22no—
198C3×C22⋊C4—21no—
199C3×C22⋊C4—21no—
200C3×C22⋊C4—21no—
201C3×C22⋊C4—21no—
202C3×C42—21no—
203C3×C42C22×D311yescharacteristic
204C3×C42C23×C311yescharacteristic
205#214—42no—
206C4⋊Dic3—21no—
207C4⋊Dic3—21no—
208C2×C3⋊C8—21no—
209C2×C3⋊C8—21no—
210C2×C3⋊C8—21no—
211C22×C32—22no—
212C22×C32—41no—
213C22×C32—41no—
214C22×C32—41no—
215C22×C32—41no—
216C22×C32—41no—
217C22×C32#12011yescharacteristic
218C32×C4—21no—
219C32×C4—41no—
220C32×C4—42no—
221C32×C4—41no—
222C32×C4C2×D811yescharacteristic
223C32×C4#13511yescharacteristic
224C32×C4AGL(1,ℤ/8)11yescharacteristic
225C32×C4#13711yescharacteristic
226C3×Dic3—81no—
227C2×#41—21no—
228C2×SD16—61no—
229C4⋊Q8—31no—
230C4⋊Q8C2×C3×D311yescharacteristic
231#123—22no—
232C22⋊Q8—21no—
233#121—21no—
234C4×D4C2×C3×D311yescharacteristic
235C4×D4C2×C3×D311yescharacteristic
236C2×C4⋊C4—21no—
237#107—61no—
238#107—62no—
239C4⋊C8—31no—
240C4⋊C8—31no—
241#103—61no—
242#102—61no—
243C4×C8—31no—
244C23×C3—22no—
245C23×C3—21no—
246C23×C3—21no—
247C23×C3—22no—
248C23×C3—21no—
249C23×C3—21no—
250C3×Q8—42no—
251C3×Q8—42no—
252C3×Q8—41no—
253C3×Q8—41no—
254C3×Q8—41no—
255C3×Q8—41no—
256C3×Q8—121no—
257C3×Q8—121no—
258C3×D4—22no—
259C3×D4—21no—
260C3×D4—21no—
261C3×D4—21no—
262C3×D4—21no—
263C3×D4—21no—
264C3×D4—21no—
265C3×D4—22no—
266C3×D4—41no—
267C3×D4—41no—
268C3×D4—48no—
269C3×D4—44no—
270C3×D4—44no—
271C3×D4#21312yes—
272C3×D4C3×D812yes—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—24no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—22no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—22no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—42no—
286C2×C3×C4—42no—
287C2×C3×C4—42no—
288C2×C3×C4—42no—
289C2×C3×C4—48no—
290C2×C3×C4—44no—
291C2×C3×C4—44no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—121no—
301C2×C3×C4C2×#6711yescharacteristic
302C2×C3×C4C2×#6711yescharacteristic
303C2×C3×C4C2×#6711yescharacteristic
304C2×C3×C4C2×C3×D411yescharacteristic
305C2×C3×C4C2×C3×D411yescharacteristic
306C2×C3×C4C2×C3×D411yescharacteristic
307C2×Dic3—41no—
308Dic6—41no—
309Dic6—41no—
310C3×C8—62no—
311C3×C8—121no—
312C3×C8—121no—
313C3⋊C8—22no—
314C3⋊C8—41no—
315C3⋊C8—41no—
316C2×C32—42no—
317C2×C32—81no—
318C2×C32#44711yescharacteristic
319C2×C32#45211yescharacteristic
320C2×C32#45611yescharacteristic
321#41—42no—
322#41—42no—
323C2×Q8—21no—
324C2×Q8—61no—
325C2×D4—22no—
326C2×D4C3×#6711yescharacteristic
327C2×D4C3×#6711yescharacteristic
328C22×C4—22no—
329C22×C4—21no—
330C22×C4—21no—
331SD16—122no—
332C2×C8—61no—
333C2×C8—61no—
334C2×C8—61no—
335C4⋊C4—22no—
336C4⋊C4—21no—
337C4⋊C4—61no—
338C4⋊C4—61no—
339C4⋊C4C3×#6711yescharacteristic
340C4⋊C4C3×#6711yescharacteristic
341C4⋊C4C3×#6712yes—
342C22⋊C4—22no—
343C22⋊C4—21no—
344C22⋊C4—21no—
345C42C22×C3×D311yescharacteristic
346C22×C3—24no—
347C22×C3—22no—
348C22×C3—22no—
349C22×C3—21no—
350C22×C3—42no—
351C22×C3—42no—
352C22×C3—42no—
353C22×C3—42no—
354C22×C3—42no—
355C22×C3—41no—
356C22×C3—41no—
357C22×C3—41no—
358C22×C3—41no—
359C22×C3—41no—
360C22×C3—41no—
361C22×C3—41no—
362C22×C3—41no—
363C22×C3—41no—
364C22×C3—41no—
365C22×C3#95311yescharacteristic
366C22×C3C3×#12011yescharacteristic
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—41no—
374C3×C4—42no—
375C3×C4—44no—
376C3×C4—42no—
377C3×C4—41no—
378C3×C4—42no—
379C3×C4—41no—
380C3×C4—41no—
381C3×C4—42no—
382C3×C4—41no—
383C3×C4—241no—
384C3×C4C2×#21311yescharacteristic
385C3×C4#93211yescharacteristic
386C3×C4#95011yescharacteristic
387C3×C4#95111yescharacteristic
388C3×C4C2×C3×D811yescharacteristic
389C3×C4C3×#13511yescharacteristic
390C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
391C3×C4C3×#13711yescharacteristic
392Dic3—81no—
393C32#164711yescharacteristic, complemented, Sylow
394C23—21no—
395C23—21no—
396Q8—41no—
397Q8—41no—
398Q8—121no—
399Q8—121no—
400D4—21no—
401D4—21no—
402D4—21no—
403D4—44no—
404D4C3×#21312yes—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—22no—
408C2×C4—44no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—121no—
414C2×C4C2×C3×#6711yescharacteristic
415C2×C4C2×C3×#6711yescharacteristic
416C2×C4C2×C3×#6711yescharacteristic
417C8—62no—
418C8—121no—
419C8—121no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—44no—
424C2×C3—42no—
425C2×C3—42no—
426C2×C3—82no—
427C2×C3—81no—
428C2×C3—81no—
429C2×C3#521711yescharacteristic
430C2×C3#523911yescharacteristic
431C2×C3#524611yescharacteristic
432C2×C3C3×#44711yescharacteristic
433C2×C3C3×#45211yescharacteristic
434C2×C3C3×#45611yescharacteristic
435C22—22no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22C3×#95311yescharacteristic
442C4—21no—
443C4—41no—
444C4—42no—
445C4—41no—
446C4—241no—
447C4C2×C3×#21311yescharacteristic
448C4C3×#93211yescharacteristic
449C4C3×#95011yescharacteristic
450C4C3×#95111yescharacteristic
451C3—21no—
452C3#7191211yescharacteristic, direct product factor
453C3C3×#164711yescharacteristic, complemented
454C2—42no—
455C2—81no—
456C2C3×#521711yescharacteristic
457C2C3×#523911yescharacteristic
458C2C3×#524611yescharacteristic
subgroupG/H
centerC22×C3#953
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
Fitting, prime radicalC32×#547C2
socleC22×C32#120
hypercenterC3×#547D3
hypocenterC3C3×#1647
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#547

Complements

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

NH ≅ G/Ntype
2. C3×#5078C2semidirect
3. C3×#5019C2semidirect
4. C3×#5007C2semidirect
5. C3×#4547C2semidirect
6. C3×D4⋊(C3⋊C8)C2semidirect
7. C3×D4⋊(C3⋊C8)C2semidirect
9. #71912C3direct (N × H)
33. #5078C2×C3semidirect
34. #5019C2×C3semidirect
35. #5007C2×C3semidirect
39. #4547C2×C3semidirect
40. D4⋊(C3⋊C8)C2×C3semidirect
41. D4⋊(C3⋊C8)C2×C3semidirect
393. C32#1647semidirect
452. C3#71912direct (N × H)
453. C3C3×#1647semidirect

Maximal subgroups

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

subgroupindex
C32×#5472
C3×#50782
C3×#50192
C3×#50072
C3×#45472
C3×D4⋊(C3⋊C8)2
C3×#16473
#719123