Finite Group Databasebeta

← C3×#68714 #11793085

Subgroups — C3×#68714 #11793085

Order 1152.

535 conjugacy classes of subgroups.

The subgroup lattice has 451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5517C211yesmaximal, characteristic, complemented
2C2×C3×#825C211yesmaximal, characteristic
3C3×#5006C211yesmaximal, characteristic
4C3×#5005C211yesmaximal, characteristic
5C32×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
6C3×#4559C211yesmaximal, characteristic, complemented
7C3×#4532C211yesmaximal, characteristic, complemented
8C3×#2031—31nomaximal
9#68714C311yesmaximal, characteristic, direct product factor
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C32×#117C2211yescharacteristic
13C32×#117C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#890—21no—
18C3×#888—21no—
19C3×#878—22no—
20C3×C4×Dic6—22no—
21C3×#825—21no—
22C3×#825—21no—
23C3×#806—22no—
24C3×#805—22no—
25C3×#533—31no—
26#5517C2×C311yescharacteristic, complemented
27C3×#421—31no—
28C2×C3×#104—31no—
29C3×#410—31no—
30C2×#825C2×C311yescharacteristic
31#5006C2×C311yescharacteristic
32#5005C2×C311yescharacteristic
33C3×#344—31no—
34C3×#339—31no—
35C3×H(3,ℤ/4)—21no—
36C3×H(3,ℤ/4)D311yescharacteristic, complemented
37C3×H(3,ℤ/4)C2×C311yescharacteristic, complemented
38#4559C2×C311yescharacteristic, complemented
39#4532C2×C311yescharacteristic, complemented
40C22×C32×C4C2311yescharacteristic
41C2×C3×#67—21no—
42C22×C3×Dic3—21no—
43C3×#235—21no—
44C3×#235—21no—
45C3×#235—21no—
46C3×#235—21no—
47C2×C3×D12Q811yescharacteristic, complemented
48C2×C3×C4×D3—21no—
49C2×C3×Dic6—22no—
50C2×C3×Dic6Q811yescharacteristic, complemented
51C32×M16—21no—
52C32×M16—21no—
53C2×C32×C8—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4—21no—
56C32×C22⋊C4—21no—
57C32×C22⋊C4—21no—
58C32×C42—21no—
59C32×C42D412yes—
60C3×#217D412yes—
61C3×C4⋊Dic3—22no—
62C3×C4⋊Dic3—21no—
63C3×Dic3⋊C4—22no—
64C3×Dic3⋊C4—22no—
65C3×C4×Dic3—21no—
66C3×C4×Dic3—21no—
67C3×C4×Dic3D411yescharacteristic
68C3×C4×Dic3D411yescharacteristic
69C3×#208—21no—
70C3×#208—21no—
71C2×C3×C3⋊C8—21no—
72#2031—31noSylow
73C2×C3×#41—31no—
74C2×#235C22×C311yescharacteristic
75C2×C3×M16—21no—
76C2×C3×M16—31no—
77C2×C3×M16C2×D311yescharacteristic
78C2×C3×M16C22×C311yescharacteristic
79C3×C4⋊Q8—61no—
80C3×#125—61no—
81C3×C22⋊Q8—62no—
82C3×C4×Q8—62no—
83C3×#117—21no—
84C3×#117—21no—
85C3×#117—31no—
86C3×#117C2×D311yescharacteristic
87C3×#117C2×D311yescharacteristic
88C3×#117C22×C311yescharacteristic
89C3×#117C22×C311yescharacteristic
90C2×C3×C42—31no—
91#926C22×C311yescharacteristic
92C2×C4×Dic3C22×C311yescharacteristic
93C2×#208C22×C311yescharacteristic
94#890—21no—
95#888—21no—
96#878—22no—
97C4×Dic6—22no—
98C3×#104—61no—
99C3×#104—61no—
100C3×#104—62no—
101C3×#99—62no—
102#825—21no—
103#825—21no—
104#806—22no—
105#805—22no—
106C23×C32C2×D411yescharacteristic
107C22×C3×D3—21no—
108C2×C32×C4—22no—
109C2×C32×C4—41no—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×Q811yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C32×C4#4111yescharacteristic
116C3×#67—41no—
117C3×#67—41no—
118C2×C3×Dic3—21no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—42no—
123C3×D12—21no—
124C3×D12—21no—
125C3×C4×D3—41no—
126C3×C4×D3—41no—
127C3×Dic6—21no—
128C3×Dic6—21no—
129C3×Dic6—44no—
130C32×C8—41no—
131C3×C3⋊C8—41no—
132#533—31no—
133#421—31no—
134C2×#104—31no—
135#410—31no—
136#344—31no—
137#339—31no—
138H(3,ℤ/4)C3×D311yescharacteristic, complemented
139C3×#41—61no—
140C3×#41—61no—
141C3×#41—61no—
142C3×#41—61no—
143C2×C3×Q8—31no—
144C2×C3×Q8—62no—
145C2×C3×D4—31no—
146C2×C3×D4—61no—
147C22×C3×C4—21no—
148C22×C3×C4—61no—
149C22×C3×C4—61no—
150C22×C3×C4C22×D311yescharacteristic
151C22×C3×C4C23×C311yescharacteristic
152C2×#67—21no—
153C22×Dic3—21no—
154#235—21no—
155#235—21no—
156#235—21no—
157#235—21no—
158C2×D12C3×Q811yescharacteristic, complemented
159C2×C4×D3—21no—
160C2×Dic6—22no—
161C2×Dic6C3×Q811yescharacteristic, complemented
162C3×M16—21no—
163C3×M16—21no—
164C3×M16—21no—
165C3×M16—21no—
166C3×M16—41no—
167C3×M16—41no—
168C3×M16—61no—
169C3×M16—61no—
170C2×C3×C8—22no—
171C2×C3×C8—21no—
172C2×C3×C8—21no—
173C2×C3×C8—61no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—41no—
179C3×C4⋊C4—41no—
180C3×C4⋊C4—62no—
181C3×C4⋊C4—62no—
182C3×C4⋊C4—62no—
183C3×C4⋊C4—61no—
184C3×C22⋊C4—21no—
185C3×C22⋊C4—21no—
186C3×C22⋊C4—21no—
187C3×C22⋊C4—21no—
188C3×C22⋊C4—32no—
189C3×C22⋊C4—41no—
190C3×C22⋊C4—41no—
191C3×C42—22no—
192C3×C42—21no—
193C3×C42—21no—
194C3×C42—22no—
195C3×C42—31no—
196C3×C42—31no—
197C3×C42—61no—
198C3×C42—61no—
199C3×C42D1212yes—
200C3×C42C3×D412yes—
201#217C3×D412yes—
202C4⋊Dic3—22no—
203C4⋊Dic3—21no—
204Dic3⋊C4—22no—
205Dic3⋊C4—22no—
206C4×Dic3—21no—
207C4×Dic3—21no—
208C4×Dic3C3×D411yescharacteristic
209C4×Dic3C3×D411yescharacteristic
210#208—21no—
211#208—21no—
212C2×C3⋊C8—21no—
213C22×C32—41no—
214C22×C32#12011yescharacteristic
215C22×C32C22⋊Q811yescharacteristic
216C22×C32#12411yescharacteristic
217C2×C3×D3—41no—
218C2×C3×D3—81no—
219C32×C4—42no—
220C32×C4—81no—
221C32×C4C22⋊Q811yescharacteristic
222C32×C4C22⋊Q811yescharacteristic
223C32×C4#12411yescharacteristic
224C32×C4#12411yescharacteristic
225C3×Dic3—22no—
226C3×Dic3—42no—
227C3×Dic3—41no—
228C3×Dic3—41no—
229C2×#41—31no—
230C2×M16—31no—
231C2×M16C2×C3×D311yescharacteristic
232C4⋊Q8—61no—
233#125—61no—
234C22⋊Q8—62no—
235C4×Q8—62no—
236#117—31no—
237#117C2×C3×D311yescharacteristic
238#117C2×C3×D311yescharacteristic
239C2×C42—31no—
240#104—61no—
241#104—61no—
242#104—62no—
243#99—62no—
244C23×C3—21no—
245C23×C3—61no—
246C23×C3D3×D411yescharacteristic
247C23×C3C2×C3×D411yescharacteristic
248C22×D3—21no—
249C3×Q8—61no—
250C3×Q8—61no—
251C3×Q8—124no—
252C3×D4—61no—
253C3×D4—61no—
254C3×D4—121no—
255C3×D4—121no—
256C2×C3×C4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—42no—
265C2×C3×C4—42no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4—61no—
269C2×C3×C4—61no—
270C2×C3×C4—62no—
271C2×C3×C4—61no—
272C2×C3×C4—122no—
273C2×C3×C4—121no—
274C2×C3×C4—121no—
275C2×C3×C4C2×D1211yescharacteristic
276C2×C3×C4#23511yescharacteristic
277C2×C3×C4#23511yescharacteristic
278C2×C3×C4D3×D411yescharacteristic
279C2×C3×C4#23711yescharacteristic
280C2×C3×C4D3×Q811yescharacteristic
281C2×C3×C4C2×C3×D411yescharacteristic
282C2×C3×C4C2×C3×D411yescharacteristic
283C2×C3×C4C2×C3×Q811yescharacteristic
284C2×C3×C4C3×#4111yescharacteristic
285C2×C3×C4C3×#4111yescharacteristic
286C2×C3×C4C3×#4111yescharacteristic
287#67—41no—
288#67—41no—
289C2×Dic3—21no—
290C2×Dic3—21no—
291C2×Dic3—22no—
292C2×Dic3—21no—
293C2×Dic3—42no—
294D12—21no—
295D12—21no—
296C4×D3—41no—
297C4×D3—41no—
298Dic6—21no—
299Dic6—21no—
300Dic6—44no—
301C3×C8—42no—
302C3×C8—41no—
303C3×C8—41no—
304C3×C8—121no—
305C3⋊C8—41no—
306C2×C32—21no—
307C2×C32—21no—
308C2×C32—21no—
309C2×C32#39311yescharacteristic
310C3×D3—81no—
311#41—61no—
312#41—61no—
313#41—61no—
314#41—61no—
315C2×Q8—31no—
316C2×Q8—62no—
317C2×D4—31no—
318C2×D4—61no—
319C22×C4—61no—
320C22×C4—61no—
321C22×C4C22×C3×D311yescharacteristic
322M16—21no—
323M16—21no—
324M16—61no—
325M16—61no—
326C2×C8—21no—
327C2×C8—61no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—62no—
331C4⋊C4—62no—
332C4⋊C4—62no—
333C4⋊C4—61no—
334C22⋊C4—21no—
335C22⋊C4—21no—
336C22⋊C4—32no—
337C42—21no—
338C42—31no—
339C42—31no—
340C42—61no—
341C42—61no—
342C42C3×D1212yes—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—41no—
347C22×C3—41no—
348C22×C3—81no—
349C22×C3—121no—
350C22×C3—241no—
351C22×C3#88211yescharacteristic
352C22×C3#88511yescharacteristic
353C22×C3#89611yescharacteristic
354C22×C3C3×#12011yescharacteristic
355C22×C3C3×C22⋊Q811yescharacteristic
356C22×C3C3×#12411yescharacteristic
357C2×D3—41no—
358C2×D3—81no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—42no—
364C3×C4—42no—
365C3×C4—62no—
366C3×C4—82no—
367C3×C4—81no—
368C3×C4—81no—
369C3×C4—82no—
370C3×C4—121no—
371C3×C4—122no—
372C3×C4—121no—
373C3×C4#87511yescharacteristic
374C3×C4#88511yescharacteristic
375C3×C4#89611yescharacteristic
376C3×C4#89711yescharacteristic
377C3×C4C3×C22⋊Q811yescharacteristic
378C3×C4C3×C22⋊Q811yescharacteristic
379C3×C4C3×#12411yescharacteristic
380C3×C4C3×#12411yescharacteristic
381Dic3—22no—
382Dic3—42no—
383Dic3—41no—
384Dic3—41no—
385C32#203111yescharacteristic, complemented, Sylow
386C23—61no—
387C23C3×D3×D411yescharacteristic
388Q8—61no—
389Q8—61no—
390Q8—124no—
391D4—61no—
392D4—61no—
393D4—121no—
394D4—121no—
395C2×C4—22no—
396C2×C4—41no—
397C2×C4—61no—
398C2×C4—61no—
399C2×C4—62no—
400C2×C4—61no—
401C2×C4—122no—
402C2×C4—121no—
403C2×C4—121no—
404C2×C4C2×C3×D1211yescharacteristic
405C2×C4C3×#23511yescharacteristic
406C2×C4C3×#23511yescharacteristic
407C2×C4C3×D3×D411yescharacteristic
408C2×C4C3×#23711yescharacteristic
409C2×C4C3×D3×Q811yescharacteristic
410C8—41no—
411C8—121no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—41no—
420C2×C3—41no—
421C2×C3—41no—
422C2×C3—241no—
423C2×C3#467311yescharacteristic
424C2×C3C3×#39311yescharacteristic
425D3—81no—
426C22—41no—
427C22—121no—
428C22—241no—
429C22C3×#88211yescharacteristic
430C22C3×#88511yescharacteristic
431C22C3×#89611yescharacteristic
432C4—42no—
433C4—62no—
434C4—81no—
435C4—121no—
436C4—122no—
437C4—121no—
438C4C3×#87511yescharacteristic
439C4C3×#88511yescharacteristic
440C4C3×#89611yescharacteristic
441C4C3×#89711yescharacteristic
442C3—21no—
443C3#6871411yescharacteristic, direct product factor
444C3C3×#203111yescharacteristic, complemented
445C2—21no—
446C2—21no—
447C2—21no—
448C2—241no—
449C2C3×#467311yescharacteristic
subgroupG/H
centerC3×C4#875
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×H(3,ℤ/4)C2
socleC2×C32#393
prime radicalC2×C3×#235C22
hypercenterC3×H(3,ℤ/4)D3
hypocenterC3C3×#2031
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. C3×#5517C2semidirect
5. C32×H(3,ℤ/4)C2semidirect
6. C3×#4559C2semidirect
7. C3×#4532C2semidirect
9. #68714C3direct (N × H)
26. #5517C2×C3semidirect
36. C3×H(3,ℤ/4)D3semidirect
37. C3×H(3,ℤ/4)C2×C3semidirect
38. #4559C2×C3semidirect
39. #4532C2×C3semidirect
47. C2×C3×D12Q8semidirect
50. C2×C3×Dic6Q8semidirect
138. H(3,ℤ/4)C3×D3semidirect
158. C2×D12C3×Q8semidirect
161. C2×Dic6C3×Q8semidirect
385. C32#2031semidirect
443. C3#68714direct (N × H)
444. C3C3×#2031semidirect

Maximal subgroups

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

subgroupindex
C3×#55172
C2×C3×#8252
C3×#50062
C3×#50052
C32×H(3,ℤ/4)2
C3×#45592
C3×#45322
C3×#20313
#687143