Finite Group Databasebeta

← C3×#70020 #11785897

Subgroups — C3×#70020 #11785897

Order 1152.

697 conjugacy classes of subgroups.

The subgroup lattice has 419 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5798C211yesmaximal, characteristic
2C2×C32×#99C211yesmaximal, characteristic
3C2×C3×#834C211yesmaximal, characteristic
4C3×#4527C212yesmaximal, complemented
5C3×#4526C212yesmaximal, complemented
6C3×#1828—31nomaximal
7#70020C311yesmaximal, characteristic, direct product factor
8C22×C32×D4C2211yescharacteristic
9C2×C32×C22⋊C4C2212yes—
10C2×C3×#217C412yescomplemented
11C2×C3×#217C2212yes—
12C2×C3×#217C2211yescharacteristic
13C2×C3×#217C2211yescharacteristic
14C3×D4×Dic3—22no—
15C3×D4×Dic3—22no—
16C3×#926C412yescomplemented
17C32×#99—22no—
18C3×#834—22no—
19C3×#518—31no—
20#5798C2×C311yescharacteristic
21C2×C3×#99—21no—
22C2×C3×#99—31no—
23C2×C3×#99D311yescharacteristic
24C2×C3×#99C2×C311yescharacteristic
25C2×#834C2×C311yescharacteristic
26C3×#342—32no—
27C3×#342—32no—
28#4527C2×C312yescomplemented
29#4526C2×C312yescomplemented
30C24×C32C2×C411yescharacteristic
31C24×C32C2311yescharacteristic
32C2×C32×D4—22no—
33C2×C32×D4—22no—
34C2×C32×D4D412yes—
35C2×C32×D4D412yes—
36C22×C32×C4—22no—
37C22×C32×C4C2×C411yescharacteristic
38C22×C3×Dic3—22no—
39C22×C3×Dic3—21no—
40C22×C3×Dic3—21no—
41C22×C3×Dic3—22no—
42C32×C22⋊C4—22no—
43C32×C22⋊C4—22no—
44C3×#217—22no—
45C3×#217—21no—
46C3×#217—21no—
47C3×#217—22no—
48C3×#217—22no—
49C3×#217C2×C412yes—
50C3×#217C2×C412yes—
51C3×C4⋊Dic3—22no—
52C3×C4×Dic3—22no—
53#1828—31noSylow
54C22×C3×D4—21no—
55C22×C3×D4C2×D311yescharacteristic
56C22×C3×D4C22×C311yescharacteristic
57C3×C4×D4—62no—
58C3×C4×D4—62no—
59C3×#117—32no—
60C2×C3×C22⋊C4—22no—
61C2×C3×C22⋊C4—32no—
62C2×C3×C22⋊C4—31no—
63C2×C3×C22⋊C4—31no—
64C2×C3×C22⋊C4—32no—
65C2×C3×C22⋊C4C2×D312yes—
66C2×C3×C22⋊C4C22×C312yes—
67C2×#217C3×C412yescomplemented
68C2×#217C22×C312yes—
69C2×#217C22×C311yescharacteristic
70C2×#217C22×C311yescharacteristic
71D4×Dic3—22no—
72D4×Dic3—22no—
73#926C3×C412yescomplemented
74C3×#99—24no—
75C3×#99—22no—
76C3×#99—22no—
77C3×#99—62no—
78#834—22no—
79C23×C32—21no—
80C23×C32—21no—
81C23×C32—81no—
82C23×C32—81no—
83C23×C32C22⋊C412yes—
84C23×C32C22×C411yescharacteristic
85C23×C32C2×D411yescharacteristic
86C23×C32C2×D411yescharacteristic
87C23×C32#4112yes—
88C23×C32#4112yes—
89C32×D4—24no—
90C32×D4—24no—
91C2×C32×C4—21no—
92C2×C32×C4—21no—
93C2×C32×C4—42no—
94C2×C32×C4—82no—
95C2×C32×C4C22⋊C412yes—
96C2×C3×Dic3—22no—
97C2×C3×Dic3—22no—
98C2×C3×Dic3—42no—
99C2×C3×Dic3—81no—
100C2×C3×Dic3—81no—
101C2×C3×Dic3—82no—
102C2×C3×Dic3—82no—
103#518—31no—
104C2×#99—31no—
105C2×#99C3×D311yescharacteristic
106#342—32no—
107#342—32no—
108C24×C3—21no—
109C24×C3—21no—
110C24×C3C4×D311yescharacteristic
111C24×C3C2×C3×C411yescharacteristic
112C24×C3C22×D311yescharacteristic
113C24×C3C23×C311yescharacteristic
114C2×C3×D4—22no—
115C2×C3×D4—22no—
116C2×C3×D4—22no—
117C2×C3×D4—22no—
118C2×C3×D4—22no—
119C2×C3×D4—22no—
120C2×C3×D4—42no—
121C2×C3×D4—42no—
122C2×C3×D4D1212yes—
123C2×C3×D4#6712yes—
124C2×C3×D4C3×D412yes—
125C2×C3×D4C3×D412yes—
126C22×C3×C4—22no—
127C22×C3×C4—22no—
128C22×C3×C4—21no—
129C22×C3×C4—42no—
130C22×C3×C4—62no—
131C22×C3×C4—61no—
132C22×C3×C4—61no—
133C22×C3×C4—62no—
134C22×C3×C4C4×D311yescharacteristic
135C22×C3×C4C2×C3×C411yescharacteristic
136C22×Dic3—22no—
137C22×Dic3—21no—
138C22×Dic3—21no—
139C22×Dic3—22no—
140C3×C4⋊C4—62no—
141C3×C22⋊C4—24no—
142C3×C22⋊C4—22no—
143C3×C22⋊C4—22no—
144C3×C22⋊C4—22no—
145C3×C22⋊C4—22no—
146C3×C22⋊C4—32no—
147C3×C22⋊C4—32no—
148C3×C22⋊C4—42no—
149C3×C22⋊C4—62no—
150C3×C22⋊C4—61no—
151C3×C22⋊C4—61no—
152C3×C22⋊C4—62no—
153C3×C22⋊C4—62no—
154C3×C42—62no—
155#217—22no—
156#217—21no—
157#217—21no—
158#217—22no—
159#217—22no—
160#217C2×C3×C412yes—
161#217C2×C3×C412yes—
162C4⋊Dic3—22no—
163C4×Dic3—22no—
164C22×C32—22no—
165C22×C32—42no—
166C22×C32—41no—
167C22×C32—41no—
168C22×C32—41no—
169C22×C32—42no—
170C22×C32—42no—
171C22×C32—81no—
172C22×C32—81no—
173C22×C32C2×C22⋊C411yescharacteristic
174C22×C32#11711yescharacteristic
175C22×C32#11711yescharacteristic
176C22×C32#12312yes—
177C22×C32#12312yes—
178C32×C4—22no—
179C32×C4—82no—
180C3×Dic3—42no—
181C3×Dic3—42no—
182C3×Dic3—82no—
183C22×D4C2×C3×D311yescharacteristic
184C4×D4—62no—
185C4×D4—62no—
186#117—32no—
187C2×C22⋊C4—32no—
188C2×C22⋊C4—31no—
189C2×C22⋊C4—31no—
190C2×C22⋊C4—32no—
191C2×C22⋊C4C2×C3×D312yes—
192#99—22no—
193#99—62no—
194C23×C3—21no—
195C23×C3—21no—
196C23×C3—21no—
197C23×C3—21no—
198C23×C3—22no—
199C23×C3—21no—
200C23×C3—21no—
201C23×C3—22no—
202C23×C3—22no—
203C23×C3—21no—
204C23×C3—41no—
205C23×C3—41no—
206C23×C3—81no—
207C23×C3—81no—
208C23×C3—81no—
209C23×C3—81no—
210C23×C3—82no—
211C23×C3—82no—
212C23×C3(C2×D3)⋊C412yes—
213C23×C3C3×C22⋊C412yes—
214C23×C3C2×C4×D311yescharacteristic
215C23×C3C2×D1211yescharacteristic
216C23×C3#23712yes—
217C23×C3#23712yes—
218C23×C3C2×#6711yescharacteristic
219C23×C3C22×C3×C411yescharacteristic
220C23×C3C2×C3×D411yescharacteristic
221C23×C3C2×C3×D411yescharacteristic
222C23×C3C3×#4112yes—
223C23×C3C3×#4112yes—
224C3×D4—24no—
225C3×D4—24no—
226C3×D4—24no—
227C3×D4—24no—
228C3×D4—44no—
229C3×D4—44no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—22no—
235C2×C3×C4—41no—
236C2×C3×C4—41no—
237C2×C3×C4—44no—
238C2×C3×C4—42no—
239C2×C3×C4—42no—
240C2×C3×C4—62no—
241C2×C3×C4—62no—
242C2×C3×C4—84no—
243C2×C3×C4—82no—
244C2×C3×C4—82no—
245C2×C3×C4—122no—
246C2×C3×C4—241no—
247C2×C3×C4—241no—
248C2×C3×C4—242no—
249C2×C3×C4—242no—
250C2×C3×C4(C2×D3)⋊C412yes—
251C2×C3×C4C3×C22⋊C412yes—
252C2×Dic3—22no—
253C2×Dic3—22no—
254C2×Dic3—42no—
255C2×Dic3—81no—
256C2×Dic3—81no—
257C2×Dic3—82no—
258C2×Dic3—82no—
259C2×C32—21no—
260C2×C32—21no—
261C2×C32—22no—
262C2×C32—22no—
263C2×C32—21no—
264C2×C32—42no—
265C2×C32#38111yescharacteristic
266C24C3×C4×D311yescharacteristic
267C24C22×C3×D311yescharacteristic
268C2×D4—22no—
269C2×D4—22no—
270C2×D4C3×D1212yes—
271C2×D4C3×#6712yes—
272C22×C4—22no—
273C22×C4—62no—
274C22×C4—61no—
275C22×C4—61no—
276C22×C4—62no—
277C22×C4C3×C4×D311yescharacteristic
278C4⋊C4—62no—
279C22⋊C4—22no—
280C22⋊C4—22no—
281C22⋊C4—32no—
282C22⋊C4—32no—
283C22⋊C4—62no—
284C22⋊C4—61no—
285C22⋊C4—61no—
286C22⋊C4—62no—
287C22⋊C4—62no—
288C42—62no—
289C22×C3—22no—
290C22×C3—22no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3—22no—
294C22×C3—21no—
295C22×C3—22no—
296C22×C3—42no—
297C22×C3—41no—
298C22×C3—41no—
299C22×C3—42no—
300C22×C3—42no—
301C22×C3—42no—
302C22×C3—41no—
303C22×C3—42no—
304C22×C3—41no—
305C22×C3—41no—
306C22×C3—41no—
307C22×C3—42no—
308C22×C3—42no—
309C22×C3—44no—
310C22×C3—42no—
311C22×C3—81no—
312C22×C3—82no—
313C22×C3—81no—
314C22×C3—82no—
315C22×C3—81no—
316C22×C3—81no—
317C22×C3—81no—
318C22×C3—81no—
319C22×C3—82no—
320C22×C3—82no—
321C22×C3#87711yescharacteristic
322C22×C3#87711yescharacteristic
323C22×C3#88612yes—
324C22×C3C2×(C2×D3)⋊C411yescharacteristic
325C22×C3#93512yes—
326C22×C3C2×C3×C22⋊C411yescharacteristic
327C22×C3C3×#11711yescharacteristic
328C22×C3C3×#11711yescharacteristic
329C22×C3C3×#12312yes—
330C22×C3C3×#12312yes—
331C3×C4—22no—
332C3×C4—22no—
333C3×C4—42no—
334C3×C4—82no—
335C3×C4—82no—
336C3×C4—84no—
337C3×C4—122no—
338C3×C4—122no—
339C3×C4—242no—
340Dic3—42no—
341Dic3—42no—
342Dic3—82no—
343C32#182811yescharacteristic, complemented, Sylow
344C23—21no—
345C23—21no—
346C23—81no—
347C23—81no—
348C23C3×(C2×D3)⋊C412yes—
349C23C2×C3×C4×D311yescharacteristic
350C23C2×C3×D1211yescharacteristic
351C23C3×#23712yes—
352C23C3×#23712yes—
353C23C2×C3×#6711yescharacteristic
354D4—24no—
355D4—24no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—62no—
360C2×C4—62no—
361C2×C4—82no—
362C2×C4—122no—
363C2×C4—241no—
364C2×C4—241no—
365C2×C4—242no—
366C2×C4—242no—
367C2×C4C3×(C2×D3)⋊C412yes—
368C2×C3—22no—
369C2×C3—21no—
370C2×C3—22no—
371C2×C3—22no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—22no—
375C2×C3—21no—
376C2×C3—22no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—42no—
381C2×C3—41no—
382C2×C3—41no—
383C2×C3—42no—
384C2×C3—42no—
385C2×C3—42no—
386C2×C3—82no—
387C2×C3#494311yescharacteristic
388C2×C3C3×#38111yescharacteristic
389C22—22no—
390C22—42no—
391C22—41no—
392C22—42no—
393C22—41no—
394C22—41no—
395C22—42no—
396C22—81no—
397C22—81no—
398C22C3×#87711yescharacteristic
399C22C3×#87711yescharacteristic
400C22C3×#88612yes—
401C22C2×C3×(C2×D3)⋊C411yescharacteristic
402C22C3×#93512yes—
403C4—22no—
404C4—82no—
405C4—122no—
406C4—122no—
407C4—242no—
408C3—21no—
409C3#7002011yescharacteristic, direct product factor
410C3C3×#182811yescharacteristic, complemented
411C2—22no—
412C2—21no—
413C2—22no—
414C2—21no—
415C2—21no—
416C2—42no—
417C2C3×#494311yescharacteristic
subgroupG/H
centerC2×C3#4943
commutatorC23×C3C22×C3×C4
FrattiniC24C22×C3×D3
FittingC2×C32×#99C2
socleC2×C32#381
prime radicalC22×C32×D4C22
cosocleC24×C3C23×C3
hypercenterC2×C3×#99D3
hypocenterC3C3×#1828
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C24×C3 ◁ C2×C3×#99

Complements

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

NH ≅ G/Ntype
4. C3×#4527C2semidirect
5. C3×#4526C2semidirect
7. #70020C3direct (N × H)
10. C2×C3×#217C4semidirect
16. C3×#926C4semidirect
28. #4527C2×C3semidirect
29. #4526C2×C3semidirect
67. C2×#217C3×C4semidirect
73. #926C3×C4semidirect
343. C32#1828semidirect
409. C3#70020direct (N × H)
410. C3C3×#1828semidirect

Maximal subgroups

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

subgroupindex
C3×#57982
C2×C32×#992
C2×C3×#8342
C3×#45272
C3×#45262
C3×#18283
#700203