Finite Group Databasebeta

← C3×#70071 #11788771

Subgroups — C3×#70071 #11788771

Order 1152.

817 conjugacy classes of subgroups.

The subgroup lattice has 397 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5805C211yesmaximal, characteristic
2C3×#5798C211yesmaximal, characteristic, complemented
3C2×C32×#100C211yesmaximal, characteristic, complemented
4C3×#5139C212yesmaximal, complemented
5C3×#4557C212yesmaximal, complemented
6C3×#1911—31nomaximal
7#70071C311yesmaximal, characteristic, direct product factor
8C22×C32×D4C2211yescharacteristic
9C2×C3×#235C2211yescharacteristic
10C2×C32×M16C2212yes—
11C3×#953—22no—
12C2×C3×#217—22no—
13C3×#940C412yescomplemented
14C3×#938—22no—
15C3×#936C412yescomplemented
16C3×D4×Dic3—24no—
17C3×#926C2211yescharacteristic
18C3×#926C2212yes—
19C32×#100—22no—
20C3×#825—24no—
21C3×#535—31no—
22C3×#518—31no—
23#5805C2×C311yescharacteristic
24#5798C2×C311yescharacteristic, complemented
25C3×#421—32no—
26C2×C3×#100—21no—
27C2×C3×#100D311yescharacteristic, complemented
28C2×C3×#100C2×C311yescharacteristic, complemented
29#5139C2×C312yescomplemented
30C3×H(3,ℤ/4)—32no—
31#4557C2×C312yescomplemented
32C24×C32D412yes—
33C2×C32×D4—22no—
34C2×C32×D4—22no—
35C2×C32×D4C2×C412yes—
36C2×C32×D4D412yes—
37C22×C32×C4C2311yescharacteristic
38C2×C3×#67—21no—
39C2×C3×#67—24no—
40C22×C3×Dic3—24no—
41C3×#235—22no—
42C3×#235—22no—
43C2×C3×D12C2×C411yescharacteristic, complemented
44C2×C3×C4×D3—21no—
45C2×C3×Dic6C2×C411yescharacteristic, complemented
46C32×M16—22no—
47C32×M16—22no—
48C2×C32×C8—22no—
49C3×#217—24no—
50C3×#217—24no—
51C3×#217—22no—
52C3×#217—21no—
53C3×C4⋊Dic3—22no—
54C3×C4⋊Dic3—21no—
55C3×C4×Dic3C2×C412yescomplemented
56C3×C4×Dic3D414yescomplemented
57#1911—31noSylow
58C2×C3×#41—31no—
59C22×C3×D4—21no—
60C22×C3×D4C2×D311yescharacteristic
61C22×C3×D4C22×C311yescharacteristic
62C2×#235C22×C311yescharacteristic
63C2×C3×M16—22no—
64C2×C3×M16C2×D312yes—
65C2×C3×M16C22×C312yes—
66C3×#127—32no—
67C3×#124—32no—
68C3×#121—62no—
69C3×#120—62no—
70C3×C4×D4—64no—
71C3×#117—32no—
72C3×#117—31no—
73C2×C3×C22⋊C4—62no—
74#953—22no—
75C2×#217—22no—
76#940C3×C412yescomplemented
77#938—22no—
78#936C3×C412yescomplemented
79D4×Dic3—24no—
80#926C22×C311yescharacteristic
81#926C22×C312yes—
82C3×#104—64no—
83C3×#100—24no—
84C3×#100—22no—
85C3×#100—22no—
86#825—24no—
87C23×C32—22no—
88C23×C32—22no—
89C23×C32—82no—
90C23×C32C22⋊C414yes—
91C23×C32C2×D411yescharacteristic
92C22×C3×D3—21no—
93C32×D4—24no—
94C32×D4—24no—
95C2×C32×C4C22×C411yescharacteristic
96C2×C32×C4C2×D412yes—
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4#4112yes—
99C3×#67—41no—
100C3×#67—41no—
101C3×#67—84no—
102C2×C3×Dic3—22no—
103C2×C3×Dic3—21no—
104C2×C3×Dic3—24no—
105C2×C3×Dic3—84no—
106C3×D12—22no—
107C3×C4×D3—42no—
108C3×Dic6—22no—
109C32×C8—42no—
110#535—31no—
111#518—31no—
112#421—32no—
113C2×#100C3×D311yescharacteristic, complemented
114H(3,ℤ/4)—32no—
115C24×C3—22no—
116C24×C3D1212yes—
117C24×C3C3×D412yes—
118C3×#41—62no—
119C3×#41—62no—
120C2×C3×Q8—31no—
121C2×C3×D4—22no—
122C2×C3×D4—22no—
123C2×C3×D4—22no—
124C2×C3×D4—22no—
125C2×C3×D4—22no—
126C2×C3×D4—22no—
127C2×C3×D4—31no—
128C2×C3×D4—42no—
129C2×C3×D4—42no—
130C2×C3×D4—61no—
131C2×C3×D4—64no—
132C2×C3×D4C4×D312yes—
133C2×C3×D4#6712yes—
134C2×C3×D4C2×C3×C412yes—
135C2×C3×D4C3×D412yes—
136C22×C3×C4—21no—
137C22×C3×C4—64no—
138C22×C3×C4—61no—
139C22×C3×C4C22×D311yescharacteristic
140C22×C3×C4C23×C311yescharacteristic
141C2×#67—21no—
142C2×#67—24no—
143C22×Dic3—24no—
144#235—22no—
145#235—22no—
146C2×D12C2×C3×C411yescharacteristic, complemented
147C2×C4×D3—21no—
148C2×Dic6C2×C3×C411yescharacteristic, complemented
149C3×M16—24no—
150C3×M16—22no—
151C3×M16—22no—
152C3×M16—22no—
153C3×M16—22no—
154C3×M16—42no—
155C2×C3×C8—22no—
156C2×C3×C8—22no—
157C2×C3×C8—42no—
158C3×C4⋊C4—62no—
159C3×C4⋊C4—61no—
160C3×C22⋊C4—64no—
161C3×C22⋊C4—64no—
162C3×C22⋊C4—62no—
163C3×C22⋊C4—61no—
164C3×C42—32no—
165C3×C42—34no—
166#217—24no—
167#217—24no—
168#217—22no—
169#217—21no—
170C4⋊Dic3—22no—
171C4⋊Dic3—21no—
172C4×Dic3C2×C3×C412yescomplemented
173C4×Dic3C3×D414yescomplemented
174C22×C32—24no—
175C22×C32—41no—
176C22×C32—44no—
177C22×C32—44no—
178C22×C32—82no—
179C22×C32C2×C22⋊C411yescharacteristic
180C22×C32#12011yescharacteristic
181C22×C32#12311yescharacteristic
182C2×C3×D3—42no—
183C2×C3×D3—41no—
184C32×C4C4×D412yes—
185C32×C4#12112yes—
186C3×Dic3—44no—
187C3×Dic3—42no—
188C3×Dic3—41no—
189C2×#41—31no—
190C22×D4C2×C3×D311yescharacteristic
191C2×M16C2×C3×D312yes—
192#127—32no—
193#124—32no—
194#121—62no—
195#120—62no—
196C4×D4—64no—
197#117—32no—
198#117—31no—
199C2×C22⋊C4—62no—
200#104—64no—
201#100—22no—
202C23×C3—22no—
203C23×C3—22no—
204C23×C3—22no—
205C23×C3—22no—
206C23×C3—24no—
207C23×C3—21no—
208C23×C3—42no—
209C23×C3—42no—
210C23×C3—61no—
211C23×C3—82no—
212C23×C3—82no—
213C23×C3—84no—
214C23×C3(C2×D3)⋊C414yes—
215C23×C3C3×C22⋊C414yes—
216C23×C3C2×D1211yescharacteristic
217C23×C3C2×C3×D411yescharacteristic
218C22×D3—21no—
219C3×Q8—62no—
220C3×D4—24no—
221C3×D4—24no—
222C3×D4—24no—
223C3×D4—24no—
224C3×D4—44no—
225C3×D4—44no—
226C3×D4—62no—
227C3×D4—121no—
228C3×D4—121no—
229C3×D4—244no—
230C2×C3×C4—21no—
231C2×C3×C4—22no—
232C2×C3×C4—22no—
233C2×C3×C4—21no—
234C2×C3×C4—64no—
235C2×C3×C4—62no—
236C2×C3×C4—61no—
237C2×C3×C4—122no—
238C2×C3×C4—244no—
239C2×C3×C4C2×C4×D311yescharacteristic
240C2×C3×C4D3×D412yes—
241C2×C3×C4#23712yes—
242C2×C3×C4C2×#6711yescharacteristic
243C2×C3×C4C22×C3×C411yescharacteristic
244C2×C3×C4C2×C3×D412yes—
245C2×C3×C4C2×C3×D411yescharacteristic
246C2×C3×C4C3×#4112yes—
247#67—41no—
248#67—41no—
249#67—84no—
250C2×Dic3—22no—
251C2×Dic3—21no—
252C2×Dic3—24no—
253C2×Dic3—84no—
254D12—22no—
255C4×D3—42no—
256Dic6—22no—
257C3×C8—44no—
258C3×C8—42no—
259C3×C8—42no—
260C2×C32—21no—
261C2×C32—21no—
262C2×C32—21no—
263C2×C32—44no—
264C2×C32#38611yescharacteristic
265C3×D3—81no—
266C24C3×D1212yes—
267#41—62no—
268#41—62no—
269C2×Q8—31no—
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—31no—
273C2×D4—61no—
274C2×D4—64no—
275C2×D4C3×C4×D312yes—
276C2×D4C3×#6712yes—
277C22×C4—64no—
278C22×C4—61no—
279C22×C4C22×C3×D311yescharacteristic
280M16—22no—
281M16—22no—
282C2×C8—22no—
283C4⋊C4—62no—
284C4⋊C4—61no—
285C22⋊C4—64no—
286C22⋊C4—64no—
287C22⋊C4—62no—
288C22⋊C4—61no—
289C42—32no—
290C42—34no—
291C22×C3—24no—
292C22×C3—24no—
293C22×C3—21no—
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—44no—
297C22×C3—41no—
298C22×C3—41no—
299C22×C3—44no—
300C22×C3—44no—
301C22×C3—44no—
302C22×C3—44no—
303C22×C3—42no—
304C22×C3—84no—
305C22×C3—84no—
306C22×C3—82no—
307C22×C3—82no—
308C22×C3—84no—
309C22×C3—122no—
310C22×C3—121no—
311C22×C3#88211yescharacteristic
312C22×C3#88611yescharacteristic
313C22×C3C2×(C2×D3)⋊C411yescharacteristic
314C22×C3C2×C3×C22⋊C411yescharacteristic
315C22×C3C3×#12011yescharacteristic
316C22×C3C3×#12311yescharacteristic
317C2×D3—42no—
318C2×D3—41no—
319C3×C4—22no—
320C3×C4—22no—
321C3×C4—124no—
322C3×C4—122no—
323C3×C4—121no—
324C3×C4#67⋊C412yes—
325C3×C4#93912yes—
326C3×C4C3×C4×D412yes—
327C3×C4C3×#12112yes—
328Dic3—44no—
329Dic3—42no—
330Dic3—41no—
331C32#191111yescharacteristic, complemented, Sylow
332C23—22no—
333C23—22no—
334C23—61no—
335C23—82no—
336C23C3×(C2×D3)⋊C414yes—
337C23C2×C3×D1211yescharacteristic
338Q8—62no—
339D4—24no—
340D4—24no—
341D4—62no—
342D4—121no—
343D4—121no—
344D4—244no—
345C2×C4—64no—
346C2×C4—62no—
347C2×C4—61no—
348C2×C4—122no—
349C2×C4—244no—
350C2×C4C2×C3×C4×D311yescharacteristic
351C2×C4C3×D3×D412yes—
352C2×C4C3×#23712yes—
353C2×C4C2×C3×#6711yescharacteristic
354C8—42no—
355C2×C3—22no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—41no—
364C2×C3—41no—
365C2×C3—44no—
366C2×C3—44no—
367C2×C3—84no—
368C2×C3—241no—
369C2×C3#495811yescharacteristic
370C2×C3C3×#38611yescharacteristic
371D3—81no—
372C22—24no—
373C22—41no—
374C22—44no—
375C22—44no—
376C22—82no—
377C22—122no—
378C22—121no—
379C22C3×#88211yescharacteristic
380C22C3×#88611yescharacteristic
381C22C2×C3×(C2×D3)⋊C411yescharacteristic
382C4—124no—
383C4—122no—
384C4—121no—
385C4C3×#67⋊C412yes—
386C4C3×#93912yes—
387C3—21no—
388C3#7007111yescharacteristic, direct product factor
389C3C3×#191111yescharacteristic, complemented
390C2—21no—
391C2—21no—
392C2—21no—
393C2—44no—
394C2—241no—
395C2C3×#495811yescharacteristic
subgroupG/H
centerC2×C3#4958
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#100C2
socleC2×C32#386
prime radicalC3×#5805C2
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#100D3
hypocenterC3C3×#1911
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C2×C3×#100

Complements

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

NH ≅ G/Ntype
2. C3×#5798C2semidirect
3. C2×C32×#100C2semidirect
4. C3×#5139C2semidirect
5. C3×#4557C2semidirect
7. #70071C3direct (N × H)
13. C3×#940C4semidirect
15. C3×#936C4semidirect
24. #5798C2×C3semidirect
27. C2×C3×#100D3semidirect
28. C2×C3×#100C2×C3semidirect
29. #5139C2×C3semidirect
31. #4557C2×C3semidirect
43. C2×C3×D12C2×C4semidirect
45. C2×C3×Dic6C2×C4semidirect
55. C3×C4×Dic3C2×C4semidirect
56. C3×C4×Dic3D4semidirect
76. #940C3×C4semidirect
78. #936C3×C4semidirect
113. C2×#100C3×D3semidirect
146. C2×D12C2×C3×C4semidirect
148. C2×Dic6C2×C3×C4semidirect
172. C4×Dic3C2×C3×C4semidirect
173. C4×Dic3C3×D4semidirect
331. C32#1911semidirect
388. C3#70071direct (N × H)
389. C3C3×#1911semidirect

Maximal subgroups

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

subgroupindex
C3×#58052
C3×#57982
C2×C32×#1002
C3×#51392
C3×#45572
C3×#19113
#700713