Finite Group Databasebeta

← C3×#70147 #11796296

Subgroups — C3×#70147 #11796296

Order 1152.

543 conjugacy classes of subgroups.

The subgroup lattice has 425 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5825C211yesmaximal, characteristic
2C32×#413C211yesmaximal, characteristic
3C3×#5240C211yesmaximal, characteristic
4C3×#4476C214yesmaximal, complemented
5C3×#2123—31nomaximal
6#70147C311yesmaximal, characteristic, direct product factor
7C2×C32×#41C2211yescharacteristic
8C22×C3×Dic6C411yescharacteristic, complemented
9C2×C32×M16—21no—
10C3×#944—21no—
11C3×#936—21no—
12C3×#935C412yescomplemented
13C3×#935C2212yes—
14C3×#926—21no—
15C3×#926C411yescharacteristic, complemented
16C3×#924—21no—
17C3×#924—21no—
18C32×#101—21no—
19C32×#100C2212yes—
20C3×#834—21no—
21C3×#834C2212yes—
22C3×#536—31no—
23#5825C2×C311yescharacteristic
24C3×#413—21no—
25C3×#413D311yescharacteristic
26C3×#413C2×C311yescharacteristic
27C3×#410—31no—
28#5240C2×C311yescharacteristic
29C3×#352—34no—
30#4476C2×C314yescomplemented
31C32×#41—41no—
32C32×#41—41no—
33C2×C32×Q8D411yescharacteristic
34C2×C32×D4C2×C411yescharacteristic
35C2×C32×D4D411yescharacteristic
36C2×C32×D4C2311yescharacteristic
37C22×C32×C4C2×C411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C22×C32×C4D411yescharacteristic
40C22×C3×Dic3C2×C412yes—
41C2×C3×Dic6—21no—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—41no—
44C2×C3×Dic6—41no—
45C32×M16—22no—
46C32×M16—41no—
47C2×C32×C8—41no—
48C3×#217—22no—
49C3×#217—22no—
50C3×#217—22no—
51C3×#217C2×C412yes—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—41no—
54C3×Dic3⋊C4—22no—
55C3×Dic3⋊C4—22no—
56C3×C4×Dic3—21no—
57C3×C4×Dic3—41no—
58#2123—31noSylow
59C2×C3×#41—21no—
60C2×C3×#41C2×D311yescharacteristic
61C2×C3×#41C22×C311yescharacteristic
62C22×C3×Q8—31no—
63C22×Dic6C3×C411yescharacteristic, complemented
64C2×C3×M16—22no—
65C2×C3×M16—21no—
66C2×C3×M16—21no—
67C3×C4⋊Q8—61no—
68C3×#124—61no—
69C3×#123—32no—
70C3×#123—32no—
71C3×C22⋊Q8—61no—
72C3×C22⋊Q8—61no—
73C3×#117—31no—
74C3×#117—61no—
75#944—21no—
76#936—21no—
77#935C3×C412yescomplemented
78#935C22×C312yes—
79#926—21no—
80#926C3×C411yescharacteristic, complemented
81#924—21no—
82#924—21no—
83C3×#101—22no—
84C3×#101—21no—
85C3×#101—21no—
86C3×#100—22no—
87C3×#100C2×D312yes—
88C3×#100C22×C312yes—
89C3×#99—32no—
90C3×#99—61no—
91#834—21no—
92#834C22×C312yes—
93C23×C32C22⋊C411yescharacteristic
94C23×C32C22×C411yescharacteristic
95C23×C32C2×D411yescharacteristic
96C32×Q8—41no—
97C32×D4—41no—
98C32×D4—41no—
99C32×D4—41no—
100C2×C32×C4—21no—
101C2×C32×C4—21no—
102C2×C32×C4—21no—
103C2×C32×C4—21no—
104C2×C32×C4—21no—
105C2×C32×C4—21no—
106C2×C32×C4C22⋊C411yescharacteristic
107C2×C32×C4C22⋊C411yescharacteristic
108C2×C32×C4C22⋊C411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C3×Dic3—22no—
111C2×C3×Dic3—22no—
112C2×C3×Dic3—42no—
113C2×C3×Dic3—42no—
114C3×Dic6—42no—
115C3×Dic6—41no—
116C3×Dic6—41no—
117C32×C8—42no—
118#536—31no—
119#413C3×D311yescharacteristic
120#410—31no—
121#352—34no—
122C3×#41—41no—
123C3×#41—41no—
124C3×#41—41no—
125C3×#41—41no—
126C3×#41—42no—
127C3×#41—42no—
128C2×C3×Q8—21no—
129C2×C3×Q8—61no—
130C2×C3×Q8—61no—
131C2×C3×Q8—121no—
132C2×C3×Q8—121no—
133C2×C3×Q8#6711yescharacteristic
134C2×C3×Q8C3×D411yescharacteristic
135C2×C3×D4—21no—
136C2×C3×D4—21no—
137C2×C3×D4—21no—
138C2×C3×D4C4×D311yescharacteristic
139C2×C3×D4D1211yescharacteristic
140C2×C3×D4C2×C3×C411yescharacteristic
141C2×C3×D4C3×D411yescharacteristic
142C2×C3×D4C22×D311yescharacteristic
143C2×C3×D4C23×C311yescharacteristic
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—32no—
148C22×C3×C4C4×D311yescharacteristic
149C22×C3×C4D1211yescharacteristic
150C22×C3×C4#6711yescharacteristic
151C22×C3×C4C2×C3×C411yescharacteristic
152C22×C3×C4C3×D411yescharacteristic
153C22×C3×C4C3×D411yescharacteristic
154C22×Dic3C2×C3×C412yes—
155C2×Dic6—21no—
156C2×Dic6—21no—
157C2×Dic6—41no—
158C2×Dic6—41no—
159C3×M16—24no—
160C3×M16—22no—
161C3×M16—22no—
162C3×M16—42no—
163C3×M16—41no—
164C3×M16—41no—
165C2×C3×C8—42no—
166C2×C3×C8—41no—
167C2×C3×C8—41no—
168C3×C4⋊C4—62no—
169C3×C4⋊C4—61no—
170C3×C4⋊C4—62no—
171C3×C4⋊C4—121no—
172C3×C22⋊C4—32no—
173C3×C22⋊C4—62no—
174C3×C22⋊C4—62no—
175C3×C22⋊C4—62no—
176C3×C42—61no—
177C3×C42—121no—
178#217—22no—
179#217—22no—
180#217—22no—
181#217C2×C3×C412yes—
182C4⋊Dic3—21no—
183C4⋊Dic3—41no—
184Dic3⋊C4—22no—
185Dic3⋊C4—22no—
186C4×Dic3—21no—
187C4×Dic3—41no—
188C22×C32—21no—
189C22×C32—21no—
190C22×C32—21no—
191C22×C32—41no—
192C22×C32—41no—
193C22×C32—41no—
194C22×C32C2×C22⋊C411yescharacteristic
195C32×C4—21no—
196C32×C4—21no—
197C32×C4—21no—
198C32×C4#9911yescharacteristic
199C32×C4#9911yescharacteristic
200C3×Dic3—42no—
201C3×Dic3—42no—
202C3×Dic3—82no—
203C2×#41C2×C3×D311yescharacteristic
204C22×Q8—31no—
205C2×M16—21no—
206C4⋊Q8—61no—
207#124—61no—
208#123—32no—
209#123—32no—
210C22⋊Q8—61no—
211C22⋊Q8—61no—
212#117—31no—
213#117—61no—
214#101—21no—
215#100C2×C3×D312yes—
216#99—32no—
217#99—61no—
218C23×C3—21no—
219C23×C3—21no—
220C23×C3—21no—
221C23×C3(C2×D3)⋊C411yescharacteristic
222C23×C3C3×C22⋊C411yescharacteristic
223C23×C3C2×C4×D311yescharacteristic
224C23×C3C2×D1211yescharacteristic
225C23×C3C22×C3×C411yescharacteristic
226C23×C3C2×C3×D411yescharacteristic
227C3×Q8—41no—
228C3×Q8—41no—
229C3×Q8—42no—
230C3×Q8—122no—
231C3×Q8—121no—
232C3×Q8—121no—
233C3×D4—41no—
234C3×D4—41no—
235C3×D4—41no—
236C3×D4—41no—
237C3×D4—41no—
238C3×D4—41no—
239C3×D4—42no—
240C3×D4—42no—
241C3×D4—42no—
242C2×C3×C4—22no—
243C2×C3×C4—22no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—62no—
265C2×C3×C4—62no—
266C2×C3×C4—122no—
267C2×C3×C4—122no—
268C2×C3×C4(C2×D3)⋊C411yescharacteristic
269C2×C3×C4(C2×D3)⋊C411yescharacteristic
270C2×C3×C4(C2×D3)⋊C411yescharacteristic
271C2×C3×C4C3×C22⋊C411yescharacteristic
272C2×C3×C4C3×C22⋊C411yescharacteristic
273C2×C3×C4C3×C22⋊C411yescharacteristic
274C2×C3×C4C2×#6711yescharacteristic
275C2×C3×C4C2×C3×D411yescharacteristic
276C2×Dic3—22no—
277C2×Dic3—22no—
278C2×Dic3—42no—
279C2×Dic3—42no—
280Dic6—42no—
281Dic6—41no—
282Dic6—41no—
283C3×C8—44no—
284C3×C8—42no—
285C3×C8—42no—
286C2×C32—21no—
287C2×C32—41no—
288C2×C32—41no—
289C2×C32—41no—
290C2×C32C2×#9911yescharacteristic
291#41—41no—
292#41—41no—
293C2×Q8—61no—
294C2×Q8—61no—
295C2×Q8—121no—
296C2×Q8—121no—
297C2×Q8C3×#6711yescharacteristic
298C2×D4C3×C4×D311yescharacteristic
299C2×D4C3×D1211yescharacteristic
300C2×D4C22×C3×D311yescharacteristic
301C22×C4—32no—
302C22×C4C3×C4×D311yescharacteristic
303C22×C4C3×D1211yescharacteristic
304C22×C4C3×#6711yescharacteristic
305M16—22no—
306M16—41no—
307C2×C8—41no—
308C4⋊C4—61no—
309C4⋊C4—62no—
310C4⋊C4—62no—
311C4⋊C4—121no—
312C22⋊C4—32no—
313C22⋊C4—62no—
314C22⋊C4—62no—
315C22⋊C4—62no—
316C42—61no—
317C42—121no—
318C22×C3—22no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—41no—
327C22×C3—41no—
328C22×C3—41no—
329C22×C3—41no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—41no—
333C22×C3—41no—
334C22×C3—81no—
335C22×C3—81no—
336C22×C3—81no—
337C22×C3C2×(C2×D3)⋊C411yescharacteristic
338C22×C3C2×C3×C22⋊C411yescharacteristic
339C3×C4—22no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—41no—
349C3×C4—41no—
350C3×C4—122no—
351C3×C4—122no—
352C3×C4—242no—
353C3×C4#80611yescharacteristic
354C3×C4#80611yescharacteristic
355C3×C4C3×#9911yescharacteristic
356C3×C4C3×#9911yescharacteristic
357Dic3—42no—
358Dic3—42no—
359Dic3—82no—
360C32#212311yescharacteristic, complemented, Sylow
361C23C3×(C2×D3)⋊C411yescharacteristic
362C23C2×C3×C4×D311yescharacteristic
363C23C2×C3×D1211yescharacteristic
364Q8—41no—
365Q8—122no—
366Q8—121no—
367Q8—121no—
368D4—41no—
369D4—41no—
370D4—41no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—62no—
378C2×C4—62no—
379C2×C4—122no—
380C2×C4—122no—
381C2×C4C3×(C2×D3)⋊C411yescharacteristic
382C2×C4C3×(C2×D3)⋊C411yescharacteristic
383C2×C4C3×(C2×D3)⋊C411yescharacteristic
384C2×C4C2×C3×#6711yescharacteristic
385C8—42no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—41no—
390C2×C3—42no—
391C2×C3—41no—
392C2×C3—41no—
393C2×C3—41no—
394C2×C3—41no—
395C2×C3—41no—
396C2×C3—41no—
397C2×C3—81no—
398C2×C3—81no—
399C2×C3C2×#80611yescharacteristic
400C2×C3C2×C3×#9911yescharacteristic
401C22—21no—
402C22—21no—
403C22—21no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22C2×C3×(C2×D3)⋊C411yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—122no—
412C4—122no—
413C4—242no—
414C4C3×#80611yescharacteristic
415C4C3×#80611yescharacteristic
416C3—21no—
417C3#7014711yescharacteristic, direct product factor
418C3C3×#212311yescharacteristic, complemented
419C2—21no—
420C2—41no—
421C2—41no—
422C2—41no—
423C2C2×C3×#80611yescharacteristic
subgroupG/H
centerC2×C3C2×#806
commutatorC23×C3C22×C3×C4
FrattiniC2×D4C22×C3×D3
FittingC32×#413C2
socleC2×C32C2×#99
prime radicalC2×C32×#41C22
cosocleC2×C3×D4C23×C3
hypercenterC3×#413D3
hypocenterC3C3×#2123
LCSG ▷ C23×C3 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×#41 ◁ C3×#413

Complements

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

NH ≅ G/Ntype
4. C3×#4476C2semidirect
6. #70147C3direct (N × H)
8. C22×C3×Dic6C4semidirect
12. C3×#935C4semidirect
15. C3×#926C4semidirect
30. #4476C2×C3semidirect
63. C22×Dic6C3×C4semidirect
77. #935C3×C4semidirect
80. #926C3×C4semidirect
360. C32#2123semidirect
417. C3#70147direct (N × H)
418. C3C3×#2123semidirect

Maximal subgroups

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

subgroupindex
C3×#58252
C32×#4132
C3×#52402
C3×#44762
C3×#21233
#701473