Finite Group Databasebeta

← C3×#67489 #11771781

Subgroups — C3×#67489 #11771781

Order 1152.

515 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 515 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#4960C211yesmaximal, characteristic
2C32×#342C211yesmaximal, characteristic, complemented
3C3×#4525C211yesmaximal, characteristic, complemented
4C3×#1343—31nomaximal
5#67489C311yesmaximal, characteristic, direct product factor
6C22×C3×#67—21no—
7C22×C3×D12C411yescharacteristic, complemented
8C2×C32×C22⋊C4—21no—
9C2×C32×C22⋊C4C2211yescharacteristic
10C2×C3×(C2×D3)⋊C4—21no—
11C3×C3⋊#95C411yescharacteristic, complemented
12C3×#830—21no—
13C3×#392—31no—
14#4960C2×C311yescharacteristic
15C3×#342—21no—
16C3×#342D311yescharacteristic, complemented
17C3×#342C2×C311yescharacteristic, complemented
18C3×#323—31no—
19#4525C2×C311yescharacteristic, complemented
20C24×C32D411yescharacteristic
21C23×C3×D3—21no—
22C22×C32×C4—41no—
23C22×C32×C4C2×C411yescharacteristic
24C22×C32×C4D411yescharacteristic
25C2×C3×#67—42no—
26C2×C3×#67—42no—
27C2×C3×#67—41no—
28C2×C3×#67—41no—
29C22×C3×Dic3—21no—
30C2×C3×D12—41no—
31C2×C3×D12—42no—
32C32×C22⋊C4—22no—
33C32×C22⋊C4—41no—
34C32×C22⋊C4—41no—
35C3×(C2×D3)⋊C4—42no—
36C2×C3×C3⋊C8—41no—
37#1343—31noSylow
38C22×C3×D4—31no—
39C22×C3×D4—61no—
40C22×#67—21no—
41C22×D12C3×C411yescharacteristic, complemented
42C2×C3×C22⋊C4—22no—
43C2×C3×C22⋊C4—21no—
44C2×C3×C22⋊C4—21no—
45C2×C3×C22⋊C4—21no—
46C2×C3×C22⋊C4—61no—
47C2×C3×C22⋊C4C2×D311yescharacteristic
48C2×C3×C22⋊C4C22×C311yescharacteristic
49C2×(C2×D3)⋊C4—21no—
50C3×C22⋊C8—61no—
51C3×#95—31no—
52C3⋊#95C3×C411yescharacteristic, complemented
53#830—21no—
54C23×C32—21no—
55C23×C32—21no—
56C23×C32—41no—
57C23×C32—41no—
58C23×C32C22⋊C411yescharacteristic
59C23×C32D811yescharacteristic
60C23×C32SD1611yescharacteristic
61C22×C3×D3—22no—
62C22×C3×D3—41no—
63C22×C3×D3—41no—
64C22×C3×D3—41no—
65C22×C3×D3—41no—
66C22×C3×D3—41no—
67C22×C3×D3—41no—
68C2×C32×C4—21no—
69C2×C32×C4—21no—
70C2×C32×C4—42no—
71C2×C32×C4—41no—
72C2×C32×C4—41no—
73C2×C32×C4—81no—
74C2×C32×C4—81no—
75C3×#67—44no—
76C3×#67—44no—
77C2×C3×Dic3—22no—
78C2×C3×Dic3—41no—
79C2×C3×Dic3—41no—
80C3×D12—42no—
81C3×D12—42no—
82C3×C3⋊C8—81no—
83#392—31no—
84#342C3×D311yescharacteristic, complemented
85#323—31no—
86C24×C3—21no—
87C24×C3—61no—
88C24×C3#6711yescharacteristic
89C24×C3C3×D411yescharacteristic
90C23×D3—21no—
91C2×C3×D4—121no—
92C2×C3×D4—122no—
93C2×C3×D4—122no—
94C2×C3×D4—122no—
95C2×C3×D4—121no—
96C2×C3×D4—121no—
97C22×C3×C4—21no—
98C22×C3×C4—21no—
99C22×C3×C4—42no—
100C22×C3×C4—41no—
101C22×C3×C4—41no—
102C22×C3×C4—61no—
103C22×C3×C4C4×D311yescharacteristic
104C22×C3×C4D1211yescharacteristic
105C22×C3×C4C2×C3×C411yescharacteristic
106C22×C3×C4C3×D411yescharacteristic
107C2×#67—42no—
108C2×#67—42no—
109C2×#67—41no—
110C2×#67—41no—
111C22×Dic3—21no—
112C2×D12—41no—
113C2×D12—42no—
114C2×C3×C8—121no—
115C3×C22⋊C4—24no—
116C3×C22⋊C4—22no—
117C3×C22⋊C4—22no—
118C3×C22⋊C4—41no—
119C3×C22⋊C4—41no—
120C3×C22⋊C4—42no—
121C3×C22⋊C4—42no—
122C3×C22⋊C4—41no—
123C3×C22⋊C4—41no—
124C3×C22⋊C4—122no—
125(C2×D3)⋊C4—42no—
126C2×C3⋊C8—41no—
127C22×C32—21no—
128C22×C32—21no—
129C22×C32—21no—
130C22×C32—21no—
131C22×C32—41no—
132C22×C32—41no—
133C22×C32—41no—
134C22×C32—41no—
135C22×C32—81no—
136C22×C32#9911yescharacteristic
137C22×C32#10211yescharacteristic
138C22×C32#10411yescharacteristic
139C2×C3×D3—42no—
140C2×C3×D3—42no—
141C2×C3×D3—42no—
142C2×C3×D3—81no—
143C2×C3×D3—81no—
144C2×C3×D3—81no—
145C2×C3×D3—81no—
146C32×C4—41no—
147C32×C4—41no—
148C32×C4—82no—
149C3×Dic3—42no—
150C22×D4—31no—
151C22×D4—61no—
152C2×C22⋊C4—21no—
153C2×C22⋊C4—61no—
154C2×C22⋊C4C2×C3×D311yescharacteristic
155C22⋊C8—61no—
156#95—31no—
157C23×C3—22no—
158C23×C3—22no—
159C23×C3—21no—
160C23×C3—21no—
161C23×C3—21no—
162C23×C3—21no—
163C23×C3—21no—
164C23×C3—21no—
165C23×C3—21no—
166C23×C3—41no—
167C23×C3—41no—
168C23×C3—41no—
169C23×C3—41no—
170C23×C3—62no—
171C23×C3—81no—
172C23×C3—81no—
173C23×C3—121no—
174C23×C3—121no—
175C23×C3—121no—
176C23×C3—121no—
177C23×C3—121no—
178C23×C3—121no—
179C23×C3(C2×D3)⋊C411yescharacteristic
180C23×C3#21311yescharacteristic
181C23×C3#21511yescharacteristic
182C23×C3C3×C22⋊C411yescharacteristic
183C23×C3C3×D811yescharacteristic
184C23×C3C3×SD1611yescharacteristic
185C22×D3—22no—
186C22×D3—41no—
187C22×D3—41no—
188C22×D3—41no—
189C22×D3—41no—
190C22×D3—41no—
191C22×D3—41no—
192C3×D4—122no—
193C3×D4—122no—
194C3×D4—124no—
195C3×D4—124no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—41no—
201C2×C3×C4—41no—
202C2×C3×C4—41no—
203C2×C3×C4—41no—
204C2×C3×C4—41no—
205C2×C3×C4—41no—
206C2×C3×C4—44no—
207C2×C3×C4—42no—
208C2×C3×C4—42no—
209C2×C3×C4—62no—
210C2×C3×C4—81no—
211C2×C3×C4—81no—
212C2×C3×C4—82no—
213C2×C3×C4—82no—
214C2×C3×C4—81no—
215C2×C3×C4—81no—
216C2×C3×C4—81no—
217C2×C3×C4—81no—
218C2×C3×C4—121no—
219C2×C3×C4—121no—
220#67—44no—
221#67—44no—
222C2×Dic3—22no—
223C2×Dic3—41no—
224C2×Dic3—41no—
225D12—42no—
226D12—42no—
227C3×C8—241no—
228C3⋊C8—81no—
229C2×C32—21no—
230C2×C32—21no—
231C2×C32—41no—
232C2×C32—41no—
233C2×C32#32711yescharacteristic
234C2×C32AΣL(1,𝔽16)11yescharacteristic
235C2×C32#35311yescharacteristic
236C3×D3—82no—
237C24—61no—
238C24C3×#6711yescharacteristic
239C2×D4—121no—
240C2×D4—122no—
241C2×D4—122no—
242C2×D4—122no—
243C2×D4—121no—
244C2×D4—121no—
245C22×C4—41no—
246C22×C4—61no—
247C22×C4C3×C4×D311yescharacteristic
248C22×C4C3×D1211yescharacteristic
249C2×C8—121no—
250C22⋊C4—22no—
251C22⋊C4—41no—
252C22⋊C4—41no—
253C22⋊C4—122no—
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—22no—
259C22×C3—22no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—21no—
267C22×C3—41no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3—41no—
271C22×C3—41no—
272C22×C3—41no—
273C22×C3—42no—
274C22×C3—42no—
275C22×C3—41no—
276C22×C3—41no—
277C22×C3—41no—
278C22×C3—41no—
279C22×C3—81no—
280C22×C3—81no—
281C22×C3—81no—
282C22×C3—81no—
283C22×C3—82no—
284C22×C3—122no—
285C22×C3—122no—
286C22×C3—122no—
287C22×C3—241no—
288C22×C3—241no—
289C22×C3—241no—
290C22×C3—241no—
291C22×C3#80511yescharacteristic
292C22×C3#80611yescharacteristic
293C22×C3#80911yescharacteristic
294C22×C3C3×#9911yescharacteristic
295C22×C3C3×#10211yescharacteristic
296C22×C3C3×#10411yescharacteristic
297C2×D3—42no—
298C2×D3—42no—
299C2×D3—42no—
300C2×D3—81no—
301C2×D3—81no—
302C2×D3—81no—
303C2×D3—81no—
304C3×C4—41no—
305C3×C4—41no—
306C3×C4—41no—
307C3×C4—41no—
308C3×C4—81no—
309C3×C4—81no—
310C3×C4—84no—
311C3×C4—82no—
312C3×C4—82no—
313C3×C4—122no—
314Dic3—42no—
315C32#134311yescharacteristic, complemented, Sylow
316C23—21no—
317C23—21no—
318C23—41no—
319C23—41no—
320C23—62no—
321C23—121no—
322C23—121no—
323C23—121no—
324C23—121no—
325C23—121no—
326C23—121no—
327C23C3×(C2×D3)⋊C411yescharacteristic
328C23C3×#21311yescharacteristic
329C23C3×#21511yescharacteristic
330D4—122no—
331D4—122no—
332D4—124no—
333D4—124no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—62no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—121no—
343C2×C4—121no—
344C8—241no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—41no—
353C2×C3—41no—
354C2×C3—42no—
355C2×C3—42no—
356C2×C3—41no—
357C2×C3—41no—
358C2×C3—41no—
359C2×C3—41no—
360C2×C3—242no—
361C2×C3#445111yescharacteristic
362C2×C3#447111yescharacteristic
363C2×C3#447411yescharacteristic
364C2×C3C3×#32711yescharacteristic
365C2×C3C3×AΣL(1,𝔽16)11yescharacteristic
366C2×C3C3×#35311yescharacteristic
367D3—82no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—81no—
377C22—122no—
378C22—122no—
379C22—122no—
380C22—241no—
381C22—241no—
382C22—241no—
383C22—241no—
384C22C3×#80511yescharacteristic
385C22C3×#80611yescharacteristic
386C22C3×#80911yescharacteristic
387C4—41no—
388C4—41no—
389C4—82no—
390C4—122no—
391C3—21no—
392C3#6748911yescharacteristic, direct product factor
393C3C3×#134311yescharacteristic, complemented
394C2—21no—
395C2—21no—
396C2—41no—
397C2—41no—
398C2—242no—
399C2C3×#445111yescharacteristic
400C2C3×#447111yescharacteristic
401C2C3×#447411yescharacteristic
subgroupG/H
centerC22×C3#806
commutatorC22×C3×C4C2×C3×C4
FrattiniC2×C22⋊C4C2×C3×D3
FittingC32×#342C2
socleC22×C32#99
prime radicalC3×#4960C2
cosocleC2×C3×C22⋊C4C22×C3
hypercenterC3×#342D3
hypocenterC3C3×#1343
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C2×C3×C22⋊C4 ◁ C3×#342

Complements

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

NH ≅ G/Ntype
2. C32×#342C2semidirect
3. C3×#4525C2semidirect
5. #67489C3direct (N × H)
7. C22×C3×D12C4semidirect
11. C3×C3⋊#95C4semidirect
16. C3×#342D3semidirect
17. C3×#342C2×C3semidirect
19. #4525C2×C3semidirect
41. C22×D12C3×C4semidirect
52. C3⋊#95C3×C4semidirect
84. #342C3×D3semidirect
315. C32#1343semidirect
392. C3#67489direct (N × H)
393. C3C3×#1343semidirect

Maximal subgroups

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

subgroupindex
C3×#49602
C32×#3422
C3×#45252
C3×#13433
#674893