Finite Group Databasebeta

← C3×#71874 #11778549

Subgroups — C3×#71874 #11778549

Order 1152.

655 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 655 conjugacy classes of subgroups — too many to draw. Only its 114 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
1C32×#537C211yesmaximal, characteristic
2C3×#5033C212yesmaximal, complemented
3C3×#4981C211yesmaximal, characteristic, complemented
4C3×#4537C212yesmaximal, complemented
5C3×#4528C211yesmaximal, characteristic, complemented
6C3×#1610—31nomaximal
7#71874C311yesmaximal, characteristic, direct product factor
8C2×C32×#41—21no—
9C32×C22⋊Q8—22no—
10C32×#121—22no—
11C32×#121—21no—
12C32×#121C2212yes—
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×Dic3⋊C4—21no—
16C3×#832—22no—
17C3×C3⋊#95—21no—
18C3×C3⋊#95C2211yescharacteristic
19C3×#830C2212yes—
20C3×#807—22no—
21C3×#537—21no—
22C3×#537D311yescharacteristic
23C3×#537C2×C311yescharacteristic
24C3×#480—32no—
25C3×#398—31no—
26#5033C2×C312yescomplemented
27#4981C2×C311yescharacteristic, complemented
28C3×#327—32no—
29C3×#324—31no—
30#4537C2×C312yescomplemented
31#4528C2×C311yescharacteristic, complemented
32C32×#41—42no—
33C32×#41—42no—
34C2×C32×Q8—21no—
35C2×C32×D4—21no—
36C2×C32×D4—22no—
37C2×C32×D4—21no—
38C2×C32×D4D412yes—
39C22×C32×C4—22no—
40C22×C32×C4D411yescharacteristic
41C22×C32×C4D411yescharacteristic
42C22×C32×C4C2311yescharacteristic
43C22×C3×Dic3—21no—
44C22×C3×Dic3—21no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4—22no—
47C32×C4⋊C4D412yes—
48C32×C22⋊C4—22no—
49C32×C22⋊C4—22no—
50C3×C4⋊Dic3—22no—
51C3×Dic3⋊C4—42no—
52C2×C3×C3⋊C8—22no—
53#1610—31noSylow
54C2×C3×#41—22no—
55C2×C3×#41—21no—
56C2×C3×#41—21no—
57C3×C22⋊Q8—24no—
58C3×C22⋊Q8—22no—
59C3×C22⋊Q8—22no—
60C3×#121—24no—
61C3×#121—22no—
62C3×#121—22no—
63C3×#121—22no—
64C3×#121—21no—
65C3×#121—21no—
66C3×#121—22no—
67C3×#121C2×D312yes—
68C3×#121C22×C312yes—
69C2×C3×C4⋊C4—21no—
70C2×C3×C4⋊C4—31no—
71C2×C3×C4⋊C4—61no—
72C2×C3×C4⋊C4C2×D311yescharacteristic
73C2×C3×C4⋊C4C22×C311yescharacteristic
74C2×C4⋊Dic3C22×C311yescharacteristic
75C2×Dic3⋊C4—21no—
76C3×#107—62no—
77C3×#102—62no—
78C3×C22⋊C8—32no—
79C3×#95—31no—
80C3×#95—61no—
81#832—22no—
82C3⋊#95—21no—
83C3⋊#95C22×C311yescharacteristic
84#830C22×C312yes—
85#807—22no—
86C23×C32—22no—
87C23×C32C2×D411yescharacteristic
88C32×Q8—42no—
89C32×D4—42no—
90C32×D4—42no—
91C32×D4—42no—
92C32×D4—42no—
93C32×D4—81no—
94C2×C32×C4—21no—
95C2×C32×C4—21no—
96C2×C32×C4—21no—
97C2×C32×C4—22no—
98C2×C32×C4—44no—
99C2×C32×C4—41no—
100C2×C32×C4—41no—
101C2×C32×C4D812yes—
102C2×C32×C4C2×D412yes—
103C2×C3×Dic3—22no—
104C2×C3×Dic3—41no—
105C2×C3×Dic3—41no—
106C2×C3×Dic3—41no—
107C2×C3×Dic3—41no—
108C2×C3×Dic3—41no—
109C3×C3⋊C8—42no—
110#537C3×D311yescharacteristic
111#480—32no—
112#398—31no—
113#327—32no—
114#324—31no—
115C3×#41—44no—
116C3×#41—42no—
117C3×#41—42no—
118C3×#41—44no—
119C3×#41—42no—
120C3×#41—42no—
121C2×C3×Q8—22no—
122C2×C3×Q8—21no—
123C2×C3×Q8—21no—
124C2×C3×D4—22no—
125C2×C3×D4—21no—
126C2×C3×D4—21no—
127C2×C3×D4—24no—
128C2×C3×D4—22no—
129C2×C3×D4—22no—
130C2×C3×D4—22no—
131C2×C3×D4—21no—
132C2×C3×D4—21no—
133C2×C3×D4—22no—
134C2×C3×D4#6712yes—
135C2×C3×D4C3×D412yes—
136C22×C3×C4—24no—
137C22×C3×C4—22no—
138C22×C3×C4—22no—
139C22×C3×C4—21no—
140C22×C3×C4—21no—
141C22×C3×C4—21no—
142C22×C3×C4—61no—
143C22×C3×C4—61no—
144C22×C3×C4#6711yescharacteristic
145C22×C3×C4#6711yescharacteristic
146C22×C3×C4C3×D411yescharacteristic
147C22×C3×C4C3×D411yescharacteristic
148C22×C3×C4C22×D311yescharacteristic
149C22×C3×C4C23×C311yescharacteristic
150C22×Dic3—21no—
151C22×Dic3—21no—
152C2×C3×C8—62no—
153C3×C4⋊C4—24no—
154C3×C4⋊C4—22no—
155C3×C4⋊C4—21no—
156C3×C4⋊C4—21no—
157C3×C4⋊C4—22no—
158C3×C4⋊C4—22no—
159C3×C4⋊C4—22no—
160C3×C4⋊C4—62no—
161C3×C4⋊C4—122no—
162C3×C4⋊C4#6712yes—
163C3×C4⋊C4C3×D412yes—
164C3×C22⋊C4—24no—
165C3×C22⋊C4—22no—
166C3×C22⋊C4—22no—
167C3×C22⋊C4—24no—
168C3×C22⋊C4—22no—
169C3×C22⋊C4—22no—
170C4⋊Dic3—22no—
171Dic3⋊C4—42no—
172C2×C3⋊C8—22no—
173C22×C32—21no—
174C22×C32—21no—
175C22×C32—42no—
176C22×C32—42no—
177C22×C32—42no—
178C22×C32#12011yescharacteristic
179C22×C32C2×D811yescharacteristic
180C22×C32AGL(1,ℤ/8)11yescharacteristic
181C32×C4—22no—
182C32×C4—22no—
183C32×C4—42no—
184C32×C4—41no—
185C3×Dic3—42no—
186C3×Dic3—81no—
187C2×#41—21no—
188C22⋊Q8—22no—
189#121—22no—
190#121—21no—
191#121C2×C3×D312yes—
192C2×C4⋊C4—31no—
193C2×C4⋊C4—61no—
194C2×C4⋊C4C2×C3×D311yescharacteristic
195#107—62no—
196#102—62no—
197C22⋊C8—32no—
198#95—31no—
199#95—61no—
200C23×C3—24no—
201C23×C3—22no—
202C23×C3—22no—
203C23×C3—21no—
204C23×C3C2×#6711yescharacteristic
205C23×C3C2×C3×D411yescharacteristic
206C3×Q8—44no—
207C3×Q8—42no—
208C3×Q8—42no—
209C3×D4—42no—
210C3×D4—42no—
211C3×D4—44no—
212C3×D4—42no—
213C3×D4—42no—
214C3×D4—44no—
215C3×D4—44no—
216C3×D4—42no—
217C3×D4—42no—
218C3×D4—42no—
219C3×D4—42no—
220C3×D4—82no—
221C3×D4—82no—
222C3×D4—81no—
223C3×D4—81no—
224C2×C3×C4—22no—
225C2×C3×C4—22no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—22no—
231C2×C3×C4—24no—
232C2×C3×C4—21no—
233C2×C3×C4—22no—
234C2×C3×C4—21no—
235C2×C3×C4—22no—
236C2×C3×C4—22no—
237C2×C3×C4—22no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—48no—
241C2×C3×C4—44no—
242C2×C3×C4—44no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4—62no—
246C2×C3×C4—81no—
247C2×C3×C4—81no—
248C2×C3×C4—121no—
249C2×C3×C4—121no—
250C2×C3×C4—121no—
251C2×C3×C4—121no—
252C2×C3×C4—121no—
253C2×C3×C4#21312yes—
254C2×C3×C4C3×D812yes—
255C2×C3×C4C2×#6712yes—
256C2×C3×C4C2×C3×D412yes—
257C2×Dic3—22no—
258C2×Dic3—41no—
259C2×Dic3—41no—
260C2×Dic3—41no—
261C2×Dic3—41no—
262C2×Dic3—41no—
263C3×C8—122no—
264C3⋊C8—42no—
265C2×C32—21no—
266C2×C32—21no—
267C2×C32—82no—
268C2×C32#44711yescharacteristic
269C2×C32#45611yescharacteristic
270C2×C32#45811yescharacteristic
271#41—42no—
272#41—42no—
273C2×Q8—21no—
274C2×D4—21no—
275C2×D4—22no—
276C2×D4—21no—
277C2×D4C3×#6712yes—
278C22×C4—22no—
279C22×C4—61no—
280C22×C4—61no—
281C22×C4C3×#6711yescharacteristic
282C22×C4C3×#6711yescharacteristic
283C22×C4C22×C3×D311yescharacteristic
284C2×C8—62no—
285C4⋊C4—21no—
286C4⋊C4—22no—
287C4⋊C4—62no—
288C4⋊C4—122no—
289C4⋊C4C3×#6712yes—
290C22⋊C4—22no—
291C22⋊C4—22no—
292C22×C3—21no—
293C22×C3—21no—
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—21no—
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—41no—
300C22×C3—41no—
301C22×C3—44no—
302C22×C3—44no—
303C22×C3—44no—
304C22×C3—42no—
305C22×C3—42no—
306C22×C3—42no—
307C22×C3—42no—
308C22×C3—42no—
309C22×C3—42no—
310C22×C3C2×#21311yescharacteristic
311C22×C3#93211yescharacteristic
312C22×C3#95311yescharacteristic
313C22×C3C3×#12011yescharacteristic
314C22×C3C2×C3×D811yescharacteristic
315C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
316C3×C4—24no—
317C3×C4—22no—
318C3×C4—22no—
319C3×C4—22no—
320C3×C4—22no—
321C3×C4—42no—
322C3×C4—44no—
323C3×C4—42no—
324C3×C4—42no—
325C3×C4—41no—
326C3×C4—42no—
327C3×C4—41no—
328C3×C4—122no—
329C3×C4—241no—
330Dic3—42no—
331Dic3—81no—
332C32#161011yescharacteristic, complemented, Sylow
333C23—22no—
334C23C2×C3×#6711yescharacteristic
335Q8—42no—
336D4—42no—
337D4—42no—
338D4—42no—
339D4—42no—
340D4—81no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—44no—
347C2×C4—41no—
348C2×C4—62no—
349C2×C4—121no—
350C2×C4—121no—
351C2×C4—121no—
352C2×C4—121no—
353C2×C4—121no—
354C2×C4C3×#21312yes—
355C2×C4C2×C3×#6712yes—
356C8—122no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—21no—
364C2×C3—41no—
365C2×C3—41no—
366C2×C3—84no—
367C2×C3—82no—
368C2×C3—82no—
369C2×C3#521711yescharacteristic
370C2×C3#524311yescharacteristic
371C2×C3#524611yescharacteristic
372C2×C3C3×#44711yescharacteristic
373C2×C3C3×#45611yescharacteristic
374C2×C3C3×#45811yescharacteristic
375C22—21no—
376C22—21no—
377C22—42no—
378C22—42no—
379C22—42no—
380C22C2×C3×#21311yescharacteristic
381C22C3×#93211yescharacteristic
382C22C3×#95311yescharacteristic
383C4—22no—
384C4—22no—
385C4—42no—
386C4—41no—
387C4—122no—
388C4—241no—
389C3—21no—
390C3#7187411yescharacteristic, direct product factor
391C3C3×#161011yescharacteristic, complemented
392C2—21no—
393C2—21no—
394C2—82no—
395C2C3×#521711yescharacteristic
396C2C3×#524311yescharacteristic
397C2C3×#524611yescharacteristic
subgroupG/H
centerC22×C3#953
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
Fitting, prime radicalC32×#537C2
socleC22×C32#120
hypercenterC3×#537D3
hypocenterC3C3×#1610
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#537

Complements

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

NH ≅ G/Ntype
2. C3×#5033C2semidirect
3. C3×#4981C2semidirect
4. C3×#4537C2semidirect
5. C3×#4528C2semidirect
7. #71874C3direct (N × H)
26. #5033C2×C3semidirect
27. #4981C2×C3semidirect
30. #4537C2×C3semidirect
31. #4528C2×C3semidirect
332. C32#1610semidirect
390. C3#71874direct (N × H)
391. C3C3×#1610semidirect

Maximal subgroups

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

subgroupindex
C32×#5372
C3×#50332
C3×#49812
C3×#45372
C3×#45282
C3×#16103
#718743