Finite Group Databasebeta

← C3×#69993 #11792403

Subgroups — C3×#69993 #11792403

Order 1152.

883 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5791C212yesmaximal, complemented
2C3×#5748C211yesmaximal, characteristic, complemented
3C32×#407C211yesmaximal, characteristic, complemented
4C3×#5139C212yesmaximal, complemented
5C3×#4557C211yesmaximal, characteristic, complemented
6C3×#2010—31nomaximal
7#69993C311yesmaximal, characteristic, direct product factor
8C23×C32×C4C2211yescharacteristic
9C2×C3×#235C2212yes—
10C2×C32×M16C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C3×#953—22no—
13C3×#930—22no—
14C3×#929—22no—
15C3×C4×#67—24no—
16C3×#926C2212yes—
17C3×#924—22no—
18C3×#909—22no—
19C3×#908—22no—
20C3×#904—22no—
21C32×C22⋊C8—22no—
22C3×#825—24no—
23C3×#575—31no—
24C3×#525—32no—
25#5791C2×C312yescomplemented
26#5748C2×C311yescharacteristic, complemented
27C3×#421—32no—
28C3×#407—21no—
29C3×#407D311yescharacteristic, complemented
30C3×#407C2×C311yescharacteristic, complemented
31#5139C2×C312yescomplemented
32C3×H(3,ℤ/4)—31no—
33#4557C2×C311yescharacteristic, complemented
34C24×C32D411yescharacteristic
35C22×C32×C4—21no—
36C22×C32×C4—22no—
37C22×C32×C4—22no—
38C22×C32×C4—21no—
39C22×C32×C4D411yescharacteristic
40C22×C32×C4C2311yescharacteristic
41C2×C3×#67—24no—
42C2×C3×#67—22no—
43C3×#235—22no—
44C3×#235—22no—
45C3×#235—22no—
46C3×#235—22no—
47C2×C3×D12D412yescomplemented
48C2×C3×C4×D3—22no—
49C2×C3×Dic6D412yescomplemented
50C32×M16—22no—
51C32×M16—22no—
52C2×C32×C8—21no—
53C2×C32×C8D412yescomplemented
54C3×#217—24no—
55C3×#217—22no—
56C3×(C2×D3)⋊C4—24no—
57C3×C4⋊Dic3—22no—
58C3×Dic3⋊C4—24no—
59C3×C4×Dic3D414yescomplemented
60C3×Dic12—22no—
61C3×D24—22no—
62C3×#204—24no—
63#2010—31noSylow
64C2×C3×#41—32no—
65C23×C3×C4—21no—
66C23×C3×C4C2×D311yescharacteristic
67C23×C3×C4C22×C311yescharacteristic
68C2×#235C22×C312yes—
69C3×#137—62no—
70C3×AGL(1,ℤ/8)—62no—
71C3×#135—62no—
72C2×C3×M16—21no—
73C2×C3×M16—21no—
74C2×C3×M16C2×D311yescharacteristic
75C2×C3×M16C2×D311yescharacteristic
76C2×C3×M16C22×C311yescharacteristic
77C2×C3×M16C22×C311yescharacteristic
78C3×#123—62no—
79C3×C22⋊Q8—62no—
80C3×#121—62no—
81C3×#120—62no—
82C3×C4×D4—64no—
83C3×#117—32no—
84#953—22no—
85#930—22no—
86#929—22no—
87C4×#67—24no—
88#926C22×C312yes—
89#924—22no—
90#909—22no—
91#908—22no—
92#904—22no—
93C3×#104—64no—
94C3×C22⋊C8—24no—
95C3×C22⋊C8—22no—
96C3×C22⋊C8—22no—
97#825—24no—
98C23×C32—21no—
99C23×C32—22no—
100C23×C32—42no—
101C23×C32C2×D411yescharacteristic
102C22×C3×D3—22no—
103C2×C32×C4—21no—
104C2×C32×C4—22no—
105C2×C32×C4—41no—
106C2×C32×C4—42no—
107C2×C32×C4—41no—
108C2×C32×C4C2×D412yes—
109C2×C32×C4C2×D412yes—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4#4111yescharacteristic
112C3×#67—48no—
113C3×#67—42no—
114C3×#67—42no—
115C2×C3×Dic3—24no—
116C2×C3×Dic3—22no—
117C3×D12—22no—
118C3×D12—22no—
119C3×C4×D3—42no—
120C3×C4×D3—42no—
121C3×Dic6—22no—
122C3×Dic6—22no—
123C32×C8—22no—
124C32×C8—41no—
125#575—31no—
126#525—32no—
127#421—32no—
128#407C3×D311yescharacteristic, complemented
129H(3,ℤ/4)—31no—
130C24×C3—21no—
131C24×C3D1211yescharacteristic
132C24×C3C3×D411yescharacteristic
133C3×#41—62no—
134C3×#41—62no—
135C3×#41—62no—
136C3×#41—62no—
137C2×C3×Q8—32no—
138C2×C3×D4—32no—
139C2×C3×D4—64no—
140C2×C3×D4—62no—
141C22×C3×C4—22no—
142C22×C3×C4—22no—
143C22×C3×C4—21no—
144C22×C3×C4—22no—
145C22×C3×C4—22no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4—22no—
149C22×C3×C4—22no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—42no—
154C22×C3×C4—42no—
155C22×C3×C4—62no—
156C22×C3×C4D1211yescharacteristic
157C22×C3×C4C3×D411yescharacteristic
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C23×C311yescharacteristic
160C2×#67—24no—
161C2×#67—22no—
162#235—22no—
163#235—22no—
164#235—22no—
165#235—22no—
166C2×D12C3×D412yescomplemented
167C2×C4×D3—22no—
168C2×Dic6C3×D412yescomplemented
169C3×Q16—62no—
170C3×SD16—64no—
171C3×D8—62no—
172C3×M16—22no—
173C3×M16—22no—
174C3×M16—22no—
175C3×M16—22no—
176C3×M16—42no—
177C3×M16—42no—
178C2×C3×C8—22no—
179C2×C3×C8—21no—
180C2×C3×C8—21no—
181C2×C3×C8—22no—
182C2×C3×C8#6712yescomplemented
183C2×C3×C8C3×D412yescomplemented
184C3×C4⋊C4—64no—
185C3×C4⋊C4—62no—
186C3×C22⋊C4—64no—
187C3×C22⋊C4—64no—
188C3×C22⋊C4—62no—
189C3×C42—34no—
190#217—24no—
191#217—22no—
192(C2×D3)⋊C4—24no—
193C4⋊Dic3—22no—
194Dic3⋊C4—24no—
195C4×Dic3C3×D414yescomplemented
196Dic12—22no—
197D24—22no—
198#204—24no—
199C22×C32—22no—
200C22×C32—24no—
201C22×C32—41no—
202C22×C32—41no—
203C22×C32—42no—
204C22×C32—41no—
205C22×C32#12012yes—
206C22×C32#12111yescharacteristic
207C2×C3×D3—44no—
208C2×C3×D3—42no—
209C32×C4—41no—
210C32×C4#12011yescharacteristic
211C32×C4#12112yes—
212C32×C4#12711yescharacteristic
213C3×Dic3—44no—
214C3×Dic3—42no—
215C2×#41—32no—
216C23×C4C2×C3×D311yescharacteristic
217#137—62no—
218AGL(1,ℤ/8)—62no—
219#135—62no—
220C2×M16C2×C3×D311yescharacteristic
221C2×M16C2×C3×D311yescharacteristic
222#123—62no—
223C22⋊Q8—62no—
224#121—62no—
225#120—62no—
226C4×D4—64no—
227#117—32no—
228#104—64no—
229C22⋊C8—22no—
230C23×C3—22no—
231C23×C3—22no—
232C23×C3—21no—
233C23×C3—22no—
234C23×C3—21no—
235C23×C3—21no—
236C23×C3—42no—
237C23×C3—42no—
238C23×C3—42no—
239C23×C3—44no—
240C23×C3—62no—
241C23×C3C2×D1211yescharacteristic
242C23×C3C2×C3×D411yescharacteristic
243C22×D3—22no—
244C3×Q8—62no—
245C3×Q8—62no—
246C3×D4—62no—
247C3×D4—62no—
248C3×D4—128no—
249C3×D4—122no—
250C3×D4—122no—
251C2×C3×C4—22no—
252C2×C3×C4—22no—
253C2×C3×C4—21no—
254C2×C3×C4—22no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—21no—
260C2×C3×C4—42no—
261C2×C3×C4—44no—
262C2×C3×C4—42no—
263C2×C3×C4—42no—
264C2×C3×C4—42no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4—42no—
269C2×C3×C4—41no—
270C2×C3×C4—64no—
271C2×C3×C4—62no—
272C2×C3×C4—122no—
273C2×C3×C4—122no—
274C2×C3×C4#23511yescharacteristic
275C2×C3×C4D3×D412yes—
276C2×C3×C4D3×D412yes—
277C2×C3×C4C2×#6711yescharacteristic
278C2×C3×C4C2×C3×D412yes—
279C2×C3×C4C2×C3×D412yes—
280C2×C3×C4C2×C3×D411yescharacteristic
281C2×C3×C4C3×#4111yescharacteristic
282#67—48no—
283#67—42no—
284#67—42no—
285C2×Dic3—24no—
286C2×Dic3—22no—
287D12—22no—
288D12—22no—
289C4×D3—42no—
290C4×D3—42no—
291Dic6—22no—
292Dic6—22no—
293C3×C8—22no—
294C3×C8—22no—
295C3×C8—42no—
296C3×C8—42no—
297C3×C8—41no—
298C3×C8—41no—
299C2×C32—21no—
300C2×C32—22no—
301C2×C32—42no—
302C2×C32#39211yescharacteristic
303C3×D3—82no—
304C24C3×D1211yescharacteristic
305#41—62no—
306#41—62no—
307#41—62no—
308#41—62no—
309C2×Q8—32no—
310C2×D4—32no—
311C2×D4—64no—
312C2×D4—62no—
313C22×C4—21no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—21no—
317C22×C4—62no—
318C22×C4C3×D1211yescharacteristic
319C22×C4C22×C3×D311yescharacteristic
320Q16—62no—
321SD16—64no—
322D8—62no—
323M16—22no—
324M16—22no—
325C2×C8—21no—
326C2×C8C3×#6712yescomplemented
327C4⋊C4—64no—
328C4⋊C4—62no—
329C22⋊C4—64no—
330C22⋊C4—64no—
331C22⋊C4—62no—
332C42—34no—
333C22×C3—24no—
334C22×C3—24no—
335C22×C3—24no—
336C22×C3—22no—
337C22×C3—22no—
338C22×C3—22no—
339C22×C3—21no—
340C22×C3—44no—
341C22×C3—41no—
342C22×C3—41no—
343C22×C3—42no—
344C22×C3—42no—
345C22×C3—42no—
346C22×C3—42no—
347C22×C3—41no—
348C22×C3—42no—
349C22×C3—41no—
350C22×C3—44no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—124no—
354C22×C3—122no—
355C22×C3#88212yes—
356C22×C3#93011yescharacteristic
357C22×C3C3×#12012yes—
358C22×C3C3×#12111yescharacteristic
359C2×D3—44no—
360C2×D3—42no—
361C3×C4—22no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—42no—
365C3×C4—41no—
366C3×C4—41no—
367C3×C4—124no—
368C3×C4—122no—
369C3×C4#88412yes—
370C3×C4#93711yescharacteristic
371C3×C4#94011yescharacteristic
372C3×C4C3×#12011yescharacteristic
373C3×C4C3×#12112yes—
374C3×C4C3×#12711yescharacteristic
375Dic3—44no—
376Dic3—42no—
377C32#201011yescharacteristic, complemented, Sylow
378C23—22no—
379C23—21no—
380C23—42no—
381C23—62no—
382C23C2×C3×D1211yescharacteristic
383Q8—62no—
384Q8—62no—
385D4—62no—
386D4—62no—
387D4—128no—
388D4—122no—
389D4—122no—
390C2×C4—22no—
391C2×C4—21no—
392C2×C4—42no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—64no—
396C2×C4—62no—
397C2×C4—122no—
398C2×C4—122no—
399C2×C4C3×#23511yescharacteristic
400C2×C4C3×D3×D412yes—
401C2×C4C3×D3×D412yes—
402C2×C4C2×C3×#6711yescharacteristic
403C8—22no—
404C8—41no—
405C2×C3—22no—
406C2×C3—22no—
407C2×C3—21no—
408C2×C3—22no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—42no—
412C2×C3—44no—
413C2×C3—42no—
414C2×C3—42no—
415C2×C3—242no—
416C2×C3#496011yescharacteristic
417C2×C3C3×#39211yescharacteristic
418D3—82no—
419C22—24no—
420C22—22no—
421C22—41no—
422C22—42no—
423C22—41no—
424C22—41no—
425C22—124no—
426C22—122no—
427C22C3×#88212yes—
428C22C3×#93011yescharacteristic
429C4—41no—
430C4—124no—
431C4—122no—
432C4C3×#88412yes—
433C4C3×#93711yescharacteristic
434C4C3×#94011yescharacteristic
435C3—21no—
436C3#6999311yescharacteristic, direct product factor
437C3C3×#201011yescharacteristic, complemented
438C2—22no—
439C2—21no—
440C2—42no—
441C2—242no—
442C2C3×#496011yescharacteristic
subgroupG/H
centerC3×C4#940
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#407C2
socleC2×C32#392
hypercenterC3×#407D3
hypocenterC3C3×#2010
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#407

Complements

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

NH ≅ G/Ntype
1. C3×#5791C2semidirect
2. C3×#5748C2semidirect
3. C32×#407C2semidirect
4. C3×#5139C2semidirect
5. C3×#4557C2semidirect
7. #69993C3direct (N × H)
25. #5791C2×C3semidirect
26. #5748C2×C3semidirect
29. C3×#407D3semidirect
30. C3×#407C2×C3semidirect
31. #5139C2×C3semidirect
33. #4557C2×C3semidirect
47. C2×C3×D12D4semidirect
49. C2×C3×Dic6D4semidirect
53. C2×C32×C8D4semidirect
59. C3×C4×Dic3D4semidirect
128. #407C3×D3semidirect
166. C2×D12C3×D4semidirect
168. C2×Dic6C3×D4semidirect
182. C2×C3×C8#67semidirect
183. C2×C3×C8C3×D4semidirect
195. C4×Dic3C3×D4semidirect
326. C2×C8C3×#67semidirect
377. C32#2010semidirect
436. C3#69993direct (N × H)
437. C3C3×#2010semidirect

Maximal subgroups

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

subgroupindex
C3×#57912
C3×#57482
C32×#4072
C3×#51392
C3×#45572
C3×#20103
#699933