Finite Group Databasebeta

← C3×#69193 #11798163

Subgroups — C3×#69193 #11798163

Order 1152.

545 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 545 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C2×C3×D3×D8C211yesmaximal, characteristic
2C2×C3×#827C211yesmaximal, characteristic, complemented
3C2×C3×#800C211yesmaximal, characteristic, complemented
4C3×#4887C211yesmaximal, characteristic, complemented
5C32×#357C211yesmaximal, characteristic, complemented
6C3×(C2×D3)⋊C16C211yesmaximal, characteristic, complemented
7C3×#4491C211yesmaximal, characteristic, complemented
8C3×#2187—31nomaximal
9#69193C311yesmaximal, characteristic, direct product factor
10C2×C3×D3×D4—21no—
11C2×C32×D8C2211yescharacteristic
12C2×C3×#213—21no—
13C3×D3×D8—22no—
14C3×D3×D8—22no—
15C2×C3×Dic12C2211yescharacteristic, complemented
16C2×C3×D24C2211yescharacteristic
17C2×C3×D3×C8C2211yescharacteristic
18C3×#897—21no—
19C2×C32×C16C2211yescharacteristic, complemented
20C32×#107C2211yescharacteristic, complemented
21C3×#827—22no—
22C2×C3×C3⋊C16C2211yescharacteristic, complemented
23C3×#810—21no—
24C3×#800—22no—
25C22×C3×D8—31no—
26C2×D3×D8C2×C311yescharacteristic
27C2×C3×SD32—31no—
28C2×C3×SD32—31no—
29C3×#467—31no—
30C2×#827C2×C311yescharacteristic, complemented
31C2×#800C2×C311yescharacteristic, complemented
32#4887C2×C311yescharacteristic, complemented
33C3×#357—21no—
34C3×#357—31no—
35C3×#357D311yescharacteristic, complemented
36C3×#357C2×C311yescharacteristic, complemented
37C3×C22⋊C16—31no—
38(C2×D3)⋊C16C2×C311yescharacteristic, complemented
39#4491C2×C311yescharacteristic, complemented
40C23×C3×D3—41no—
41C2×C32×D4—21no—
42C2×C3×#67—41no—
43C3×D3×D4—24no—
44C3×D3×D4—42no—
45C2×C3×D12—21no—
46C2×C3×C4×D3D411yescharacteristic
47C2×C3×Dic6—21no—
48C32×D8—21no—
49C32×D8D412yes—
50C2×C32×C8C2311yescharacteristic
51C32×C4⋊C4—21no—
52C3×#213—24no—
53C3×(C2×D3)⋊C4—41no—
54C3×C4⋊Dic3—41no—
55C2×C3×C3⋊C8D411yescharacteristic
56C3×Dic12—21no—
57C3×Dic12—21no—
58C3×D24—21no—
59C3×D24D412yes—
60C3×D3×C8—21no—
61C3×D3×C8—21no—
62C32×C16—21no—
63C3×C3⋊C16—21no—
64#2187—31noSylow
65C22×C3×D4—61no—
66C2×D3×D4—21no—
67C2×C3×Q16—31no—
68C2×C3×D8—21no—
69C2×C3×D8—31no—
70C2×C3×D8—61no—
71C2×C3×D8—62no—
72C2×C3×D8—62no—
73C2×C3×D8C2×D311yescharacteristic
74C2×C3×D8C22×C311yescharacteristic
75C22×C3×C8—31no—
76C3×C22⋊Q8—61no—
77C2×#213—21no—
78D3×D8—22no—
79D3×D8—22no—
80C2×Dic12C22×C311yescharacteristic, complemented
81C2×D24C22×C311yescharacteristic
82C2×D3×C8C22×C311yescharacteristic
83#897—21no—
84C3×SD32—62no—
85C3×SD32—62no—
86C2×C3×C16—21no—
87C2×C3×C16—31no—
88C2×C3×C16C2×D311yescharacteristic, complemented
89C2×C3×C16C22×C311yescharacteristic, complemented
90C3×#107—21no—
91C3×#107C2×D311yescharacteristic, complemented
92C3×#107C22×C311yescharacteristic, complemented
93C3×#103—61no—
94#827—22no—
95C2×C3⋊C16C22×C311yescharacteristic, complemented
96#810—21no—
97#800—22no—
98C23×C32—41no—
99C22×C3×D3—44no—
100C22×C3×D3—41no—
101C22×C3×D3—82no—
102C22×C3×D3—82no—
103C22×C3×D3D811yescharacteristic
104C32×D4—22no—
105C32×D4—41no—
106C2×C32×C4—41no—
107C2×C32×C4C2×D411yescharacteristic
108C3×#67—44no—
109C2×C3×Dic3—41no—
110C2×C3×Dic3D811yescharacteristic
111C3×D12—22no—
112C3×D12—41no—
113C3×C4×D3—21no—
114C3×C4×D3—21no—
115C3×Dic6—41no—
116C3×Dic6—41no—
117C32×C8C2×D411yescharacteristic
118C32×C8C2×D411yescharacteristic
119C3×C3⋊C8—21no—
120C22×D8—31no—
121C2×SD32—31no—
122C2×SD32—31no—
123#467—31no—
124#357—31no—
125#357C3×D311yescharacteristic, complemented
126C22⋊C16—31no—
127C24×C3—121no—
128C23×D3—41no—
129C2×C3×Q8—61no—
130C2×C3×D4—21no—
131C2×C3×D4—21no—
132C2×C3×D4—41no—
133C2×C3×D4—64no—
134C2×C3×D4—61no—
135C2×C3×D4—121no—
136C2×C3×D4—122no—
137C22×C3×C4—31no—
138C2×#67—41no—
139D3×D4—24no—
140D3×D4—42no—
141C2×D12—21no—
142C2×C4×D3C3×D411yescharacteristic
143C2×Dic6—21no—
144C3×Q16—61no—
145C3×Q16—61no—
146C3×D8—21no—
147C3×D8—21no—
148C3×D8—22no—
149C3×D8—32no—
150C3×D8—41no—
151C3×D8—64no—
152C3×D8—61no—
153C3×D8D1212yes—
154C3×D8C3×D412yes—
155C2×C3×C8—21no—
156C2×C3×C8—31no—
157C2×C3×C8—61no—
158C2×C3×C8—61no—
159C2×C3×C8C22×D311yescharacteristic
160C2×C3×C8C23×C311yescharacteristic
161C3×C4⋊C4—21no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4—41no—
164C3×C4⋊C4—121no—
165C3×C22⋊C4—121no—
166#213—24no—
167(C2×D3)⋊C4—41no—
168C4⋊Dic3—41no—
169C2×C3⋊C8C3×D411yescharacteristic
170Dic12—21no—
171Dic12—21no—
172D24—21no—
173D24C3×D412yes—
174D3×C8—21no—
175D3×C8—21no—
176C3×C16—21no—
177C3×C16—21no—
178C3×C16—41no—
179C3×C16—61no—
180C3⋊C16—21no—
181C22×C32—42no—
182C22×C32—81no—
183C22×C32—81no—
184C22×C32C2×D811yescharacteristic
185C2×C3×D3—21no—
186C2×C3×D3—21no—
187C2×C3×D3—42no—
188C2×C3×D3—88no—
189C2×C3×D3—81no—
190C2×C3×D3—81no—
191C2×C3×D3SD3212yescomplemented
192C32×C4—81no—
193C32×C4#12011yescharacteristic
194C32×C4AGL(1,ℤ/8)11yescharacteristic
195C3×Dic3—21no—
196C3×Dic3—81no—
197C22×D4—61no—
198C2×Q16—31no—
199C2×D8—31no—
200C2×D8—61no—
201C2×D8—62no—
202C2×D8—62no—
203C2×D8C2×C3×D311yescharacteristic
204C22×C8—31no—
205C22⋊Q8—61no—
206SD32—62no—
207SD32—62no—
208C2×C16—31no—
209C2×C16C2×C3×D311yescharacteristic, complemented
210#107C2×C3×D311yescharacteristic, complemented
211#103—61no—
212C23×C3—31no—
213C23×C3—41no—
214C23×C3—41no—
215C23×C3—81no—
216C23×C3—124no—
217C23×C3—121no—
218C23×C3—242no—
219C23×C3—242no—
220C22×D3—44no—
221C22×D3—41no—
222C22×D3—82no—
223C22×D3—82no—
224C22×D3C3×D811yescharacteristic
225C3×Q8—121no—
226C3×Q8—121no—
227C3×D4—22no—
228C3×D4—22no—
229C3×D4—42no—
230C3×D4—41no—
231C3×D4—41no—
232C3×D4—62no—
233C3×D4—81no—
234C3×D4—124no—
235C3×D4—121no—
236C2×C3×C4—21no—
237C2×C3×C4—31no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—61no—
241C2×C3×C4—61no—
242C2×C3×C4—81no—
243C2×C3×C4—121no—
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4C2×C3×D411yescharacteristic
246#67—44no—
247C2×Dic3—41no—
248C2×Dic3C3×D811yescharacteristic
249D12—22no—
250D12—41no—
251C4×D3—21no—
252C4×D3—21no—
253Dic6—41no—
254Dic6—41no—
255C3×C8—21no—
256C3×C8—21no—
257C3×C8—61no—
258C3×C8C2×D1211yescharacteristic
259C3×C8D3×D411yescharacteristic
260C3×C8C2×C3×D411yescharacteristic
261C3×C8C2×C3×D411yescharacteristic
262C3⋊C8—21no—
263C2×C32—82no—
264C2×C32#44711yescharacteristic
265C2×C32C2×SD3211yescharacteristic
266C2×C32#50911yescharacteristic
267C3×D3—22no—
268C3×D3—82no—
269C24—121no—
270C2×Q8—61no—
271C2×D4—21no—
272C2×D4—64no—
273C2×D4—61no—
274C2×D4—121no—
275C2×D4—122no—
276C22×C4—31no—
277Q16—61no—
278Q16—61no—
279D8—21no—
280D8—32no—
281D8—64no—
282D8—61no—
283D8C3×D1212yes—
284C2×C8—31no—
285C2×C8—61no—
286C2×C8—61no—
287C2×C8C22×C3×D311yescharacteristic
288C4⋊C4—21no—
289C4⋊C4—121no—
290C22⋊C4—121no—
291C16—21no—
292C16—61no—
293C22×C3—21no—
294C22×C3—32no—
295C22×C3—42no—
296C22×C3—42no—
297C22×C3—61no—
298C22×C3—61no—
299C22×C3—82no—
300C22×C3—81no—
301C22×C3—81no—
302C22×C3—81no—
303C22×C3—81no—
304C22×C3—122no—
305C22×C3—161no—
306C22×C3—161no—
307C22×C3—248no—
308C22×C3—241no—
309C22×C3—241no—
310C22×C3D3×D811yescharacteristic
311C22×C3C2×C3×D811yescharacteristic
312C2×D3—21no—
313C2×D3—21no—
314C2×D3—42no—
315C2×D3—88no—
316C2×D3—81no—
317C2×D3—81no—
318C2×D3C3×SD3212yescomplemented
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—61no—
322C3×C4—81no—
323C3×C4—81no—
324C3×C4—161no—
325C3×C4—241no—
326C3×C4#88211yescharacteristic
327C3×C4#91411yescharacteristic
328C3×C4C3×#12011yescharacteristic
329C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
330Dic3—21no—
331Dic3—81no—
332C32#218711yescharacteristic, complemented, Sylow
333C23—31no—
334C23—41no—
335C23—124no—
336C23—121no—
337C23—242no—
338C23—242no—
339Q8—121no—
340Q8—121no—
341D4—22no—
342D4—41no—
343D4—62no—
344D4—124no—
345D4—121no—
346C2×C4—31no—
347C2×C4—41no—
348C2×C4—61no—
349C2×C4—61no—
350C2×C4—121no—
351C2×C4C3×D3×D411yescharacteristic
352C8—61no—
353C8C2×C3×D1211yescharacteristic
354C8C3×D3×D411yescharacteristic
355C2×C3—21no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3—62no—
359C2×C3—82no—
360C2×C3—82no—
361C2×C3—162no—
362C2×C3—242no—
363C2×C3#477311yescharacteristic
364C2×C3#491111yescharacteristic
365C2×C3D3×SD3211yescharacteristic
366C2×C3C3×#44711yescharacteristic
367C2×C3C2×C3×SD3211yescharacteristic
368C2×C3C3×#50911yescharacteristic
369D3—22no—
370D3—82no—
371C22—32no—
372C22—42no—
373C22—61no—
374C22—61no—
375C22—81no—
376C22—81no—
377C22—122no—
378C22—248no—
379C22—241no—
380C22—241no—
381C22C3×D3×D811yescharacteristic
382C4—61no—
383C4—81no—
384C4—241no—
385C4C3×#88211yescharacteristic
386C4C3×#91411yescharacteristic
387C3—21no—
388C3#6919311yescharacteristic, direct product factor
389C3C3×#218711yescharacteristic, complemented
390C2—62no—
391C2—82no—
392C2—242no—
393C2C3×#477311yescharacteristic
394C2C3×#491111yescharacteristic
395C2C3×D3×SD3211yescharacteristic
subgroupG/H
centerC22×C3D3×D8
commutator, cosocleC2×C3×C8C23×C3
FrattiniC2×C8C22×C3×D3
FittingC32×#357C2
socleC22×C32C2×D8
prime radicalC2×C3×D3×D8C2
hypercenterC3×#357D3
hypocenterC3C3×#2187
LCSG ▷ C2×C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×C8 ◁ C3×#357

Complements

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

NH ≅ G/Ntype
2. C2×C3×#827C2semidirect
3. C2×C3×#800C2semidirect
4. C3×#4887C2semidirect
5. C32×#357C2semidirect
6. C3×(C2×D3)⋊C16C2semidirect
7. C3×#4491C2semidirect
9. #69193C3direct (N × H)
15. C2×C3×Dic12C22semidirect
19. C2×C32×C16C22semidirect
20. C32×#107C22semidirect
22. C2×C3×C3⋊C16C22semidirect
30. C2×#827C2×C3semidirect
31. C2×#800C2×C3semidirect
32. #4887C2×C3semidirect
35. C3×#357D3semidirect
36. C3×#357C2×C3semidirect
38. (C2×D3)⋊C16C2×C3semidirect
39. #4491C2×C3semidirect
80. C2×Dic12C22×C3semidirect
88. C2×C3×C16C2×D3semidirect
89. C2×C3×C16C22×C3semidirect
91. C3×#107C2×D3semidirect
92. C3×#107C22×C3semidirect
95. C2×C3⋊C16C22×C3semidirect
125. #357C3×D3semidirect
191. C2×C3×D3SD32semidirect
209. C2×C16C2×C3×D3semidirect
210. #107C2×C3×D3semidirect
318. C2×D3C3×SD32semidirect
332. C32#2187semidirect
388. C3#69193direct (N × H)
389. C3C3×#2187semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×D82
C2×C3×#8272
C2×C3×#8002
C3×#48872
C32×#3572
C3×(C2×D3)⋊C162
C3×#44912
C3×#21873
#691933