Finite Group Databasebeta

← D3×#4542 #11796461

Subgroups — D3×#4542 #11796461

Order 1152.

552 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 100 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×D3×#124C211yesmaximal, characteristic
2D3×#836C212yesmaximal, complemented
3#10589408C211yesmaximal, characteristic, complemented
4C3×#4542C211yesmaximal, characteristic, complemented
5#10589182C212yesmaximal, complemented
6C2×#4542—31nomaximal
7D3×#355—31nomaximal
8C2×C3×D3×Q8C2211yescharacteristic
9C2×C3×D3×D4C411yescharacteristic
10C32×#124C2211yescharacteristic
11C3×#947C2211yescharacteristic
12C3×#936C411yescharacteristic
13C3×#885—22no—
14C3×D3×C22⋊C4—22no—
15C3×#875C411yescharacteristic
16C3×C42×D3C411yescharacteristic
17D3×#208—22no—
18#63663C2212yescomplemented
19C3×#836C2212yescomplemented
20#63560—22no—
21C2×C3×#124—31no—
22D3×#124D311yescharacteristic
23C2×#836—32no—
24D3×#101—32no—
25C3×#355—31no—
26#4542—31no—
27#4542—31no—
28#4542—32no—
29#4542—61no—
30#4542D311yescharacteristic, direct product factor
31#4477—32no—
32C23×C3×D3—21no—
33C2×C32×Q8C2311yescharacteristic
34C2×C32×D4C2×C411yescharacteristic
35C2×C3×#67—21no—
36C3×D3×Q8—41no—
37C3×D3×Q8—41no—
38C3×D3×D4—41no—
39C3×D3×D4—41no—
40C2×C3×D12C2×C411yescharacteristic
41C2×C3×C4×D3—21no—
42C2×C3×C4×D3C2×C411yescharacteristic
43C2×C3×C4×D3D412yes—
44C2×C3×Dic6C2×C411yescharacteristic
45C2×C3×Dic6D412yes—
46C32×C22⋊C4—22no—
47C32×C42C2×C411yescharacteristic
48#3748—22no—
49C3×#217—22no—
50C3×(C2×D3)⋊C4—22no—
51C3×(C2×D3)⋊C4—22no—
52C3×C4×Dic3—21no—
53C3×C4×Dic3C2×C411yescharacteristic
54C3×#208—22no—
55#3711—42no—
56D3×C3⋊C8—42no—
57C2×#355—91noSylow
58C22×C3×Q8—31no—
59C22×C3×D4—31no—
60C2×D3×Q8C2×D311yescharacteristic
61C2×D3×D4Dic311yescharacteristic
62C3×#124—21no—
63C3×#124—31no—
64C3×#124—31no—
65C3×#124—31no—
66C3×#124—62no—
67C3×#124C2×D311yescharacteristic
68C3×#124C2×D311yescharacteristic
69C2×C3×C22⋊C4—62no—
70C2×C3×C42—31no—
71#947C2×D311yescharacteristic
72#936Dic311yescharacteristic
73C2×#208—62no—
74D3×M16—62no—
75#885—22no—
76D3×C22⋊C4—22no—
77#875Dic311yescharacteristic
78C42×D3Dic311yescharacteristic
79C3×#101—32no—
80#836—32no—
81#836—32no—
82#836—62no—
83#836—62no—
84#836C2×D312yescomplemented
85#824—62no—
86C23×C32—21no—
87C22×C3×D3—21no—
88C22×C3×D3—44no—
89C22×C3×D3—41no—
90C22×C3×D3—41no—
91C22×C3×D3C22⋊C411yescharacteristic
92C32×Q8—41no—
93C32×D4—41no—
94C2×C32×C4—21no—
95C2×C32×C4C22×C411yescharacteristic
96C2×C32×C4C2×D412yes—
97C3×#67—42no—
98C2×C3×Dic3—21no—
99C2×C3×Dic3C22⋊C411yescharacteristic
100C2×C3×Dic3C22⋊C412yes—
101C3×D12—41no—
102C3×C4×D3—22no—
103C3×C4×D3—22no—
104C3×C4×D3—21no—
105C3×C4×D3—21no—
106C3×C4×D3—42no—
107C3×Dic6—41no—
108C3×Dic6—42no—
109C3⋊(C3⋊C8)—42no—
110C3×C3⋊C8—42no—
111C2×#124—31no—
112C2×#101—92no—
113#355—31no—
114#355—92no—
115#355—91no—
116C24×C3—61no—
117C23×D3—21no—
118C2×C3×Q8—21no—
119C2×C3×Q8—31no—
120C2×C3×Q8—32no—
121C2×C3×Q8—121no—
122C2×C3×Q8—121no—
123C2×C3×Q8C22×D311yescharacteristic
124C2×C3×Q8C22×D311yescharacteristic
125C2×C3×D4—21no—
126C2×C3×D4—31no—
127C2×C3×D4—61no—
128C2×C3×D4—121no—
129C2×C3×D4—121no—
130C2×C3×D4C4×D311yescharacteristic
131C2×C3×D4C2×Dic311yescharacteristic
132C22×C3×C4—31no—
133C22×C3×C4—32no—
134C22×C3×C4—61no—
135C2×#67—21no—
136D3×Q8—41no—
137D3×Q8—41no—
138D3×D4—41no—
139D3×D4—41no—
140C2×D12C2×Dic311yescharacteristic
141C2×C4×D3—21no—
142C2×C4×D3C2×Dic311yescharacteristic
143C2×C4×D3#6712yes—
144C2×Dic6C2×Dic311yescharacteristic
145C2×Dic6#6712yes—
146C3×M16—62no—
147C3×C22⋊C4—22no—
148C3×C22⋊C4—22no—
149C3×C22⋊C4—42no—
150C3×C22⋊C4—62no—
151C3×C22⋊C4—62no—
152C3×C22⋊C4—62no—
153C3×C42—21no—
154C3×C42—31no—
155C3×C42—61no—
156C3×C42C4×D311yescharacteristic
157C3×C42C2×Dic311yescharacteristic
158#217—22no—
159(C2×D3)⋊C4—22no—
160(C2×D3)⋊C4—22no—
161C4×Dic3—21no—
162C4×Dic3C2×Dic311yescharacteristic
163#208—22no—
164#208—62no—
165#208—62no—
166#208—122no—
167#208—122no—
168C2×C3⋊C8—122no—
169ΓL(1,𝔽25)—122no—
170D3×C8—122no—
171C22×C32—42no—
172C22×C32—41no—
173C22×C32C2×C22⋊C411yescharacteristic
174C2×C3×D3—22no—
175C2×C3×D3—42no—
176C2×C3×D3—41no—
177C2×C3×D3—82no—
178C2×C3×D3—82no—
179C2×C3×D3#9911yescharacteristic
180C2×C3×D3#9911yescharacteristic
181C32×C4—22no—
182C32×C4—21no—
183C32×C4—41no—
184C3×Dic3—22no—
185C3×Dic3—21no—
186C3×Dic3—41no—
187C22×Q8—31no—
188C22×D4—31no—
189C2×M16—182no—
190#124—31no—
191#124—31no—
192#124—31no—
193#124—62no—
194#124D3211yescharacteristic
195C2×C22⋊C4—62no—
196C2×C42—31no—
197#101—32no—
198#101—92no—
199#101—182no—
200C23×C3—21no—
201C23×C3—21no—
202C23×C3—31no—
203C23×C3—41no—
204C23×C3—61no—
205C23×C3—121no—
206C23×C3—121no—
207C23×C3—124no—
208C22×D3—21no—
209C22×D3—44no—
210C22×D3—41no—
211C22×D3—41no—
212C22×D3#21711yescharacteristic
213C3×Q8—41no—
214C3×Q8—41no—
215C3×Q8—81no—
216C3×Q8—122no—
217C3×Q8—121no—
218C3×D4—41no—
219C3×D4—41no—
220C3×D4—81no—
221C3×D4—121no—
222C3×D4—122no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—22no—
227C2×C3×C4—31no—
228C2×C3×C4—32no—
229C2×C3×C4—41no—
230C2×C3×C4—62no—
231C2×C3×C4—62no—
232C2×C3×C4—61no—
233C2×C3×C4—61no—
234C2×C3×C4—61no—
235C2×C3×C4—122no—
236C2×C3×C4C2×C4×D311yescharacteristic
237C2×C3×C4D3×D412yes—
238C2×C3×C4C22×Dic311yescharacteristic
239C2×C3×C4C2×#6712yes—
240#67—42no—
241C2×Dic3—21no—
242C2×Dic3#21711yescharacteristic
243C2×Dic3#21712yes—
244D12—41no—
245C4×D3—22no—
246C4×D3—22no—
247C4×D3—21no—
248C4×D3—21no—
249C4×D3—42no—
250Dic6—41no—
251Dic6—42no—
252C3×C8—122no—
253C3⋊C8—42no—
254C3⋊C8—122no—
255C3⋊C8—122no—
256C3⋊C8—242no—
257C2×C32—21no—
258C2×C32—81no—
259C2×C32C2×#9911yescharacteristic
260C3×D3—21no—
261C3×D3—81no—
262C3×D3#35512yescomplemented
263C24—61no—
264C2×Q8—31no—
265C2×Q8—32no—
266C2×Q8—121no—
267C2×Q8—121no—
268C2×Q8C2×D3211yescharacteristic
269C2×D4—31no—
270C2×D4—61no—
271C2×D4—121no—
272C2×D4—121no—
273C2×D4D3×Dic311yescharacteristic
274C22×C4—31no—
275C22×C4—32no—
276C22×C4—61no—
277M16—62no—
278M16—182no—
279M16—362no—
280C2×C8—362no—
281C22⋊C4—22no—
282C22⋊C4—62no—
283C22⋊C4—62no—
284C22⋊C4—62no—
285C42—31no—
286C42—61no—
287C42D3×Dic311yescharacteristic
288C22×C3—21no—
289C22×C3—31no—
290C22×C3—31no—
291C22×C3—42no—
292C22×C3—42no—
293C22×C3—41no—
294C22×C3—41no—
295C22×C3—62no—
296C22×C3—81no—
297C22×C3—82no—
298C22×C3—122no—
299C22×C3—121no—
300C22×C3—242no—
301C22×C3—242no—
302C22×C3D3×C22⋊C411yescharacteristic
303C22×C3C2×#21711yescharacteristic
304C2×D3—22no—
305C2×D3—42no—
306C2×D3—41no—
307C2×D3—82no—
308C2×D3—82no—
309C2×D3#83411yescharacteristic
310C2×D3#83411yescharacteristic
311C3×C4—22no—
312C3×C4—21no—
313C3×C4—22no—
314C3×C4—21no—
315C3×C4—42no—
316C3×C4—41no—
317C3×C4—41no—
318C3×C4—41no—
319C3×C4—61no—
320C3×C4—62no—
321C3×C4—81no—
322C3×C4—121no—
323Dic3—21no—
324Dic3—22no—
325Dic3—41no—
326C32C2×#35511yescharacteristic, complemented, Sylow
327C23—21no—
328C23—31no—
329C23—61no—
330C23—121no—
331C23—121no—
332C23—124no—
333Q8—41no—
334Q8—122no—
335Q8—121no—
336D4—41no—
337D4—121no—
338D4—122no—
339C2×C4—21no—
340C2×C4—31no—
341C2×C4—32no—
342C2×C4—62no—
343C2×C4—62no—
344C2×C4—61no—
345C2×C4—61no—
346C2×C4—61no—
347C2×C4—122no—
348C2×C4C2×D3×Dic311yescharacteristic
349C2×C4D3×#6712yes—
350C8—122no—
351C8—362no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—32no—
356C2×C3—41no—
357C2×C3—61no—
358C2×C3—81no—
359C2×C3—81no—
360C2×C3—161no—
361C2×C3—241no—
362C2×C3D3×#9911yescharacteristic
363C2×C3C2×#83411yescharacteristic
364D3—21no—
365D3—81no—
366D3#454212yesdirect product factor
367C22—31no—
368C22—31no—
369C22—42no—
370C22—41no—
371C22—62no—
372C22—122no—
373C22—121no—
374C22—242no—
375C22—242no—
376C22D3×#21711yescharacteristic
377C4—22no—
378C4—21no—
379C4—41no—
380C4—61no—
381C4—62no—
382C4—121no—
383C3—21no—
384C3D3×#35511yescharacteristic, complemented
385C3C2×#454211yescharacteristic, complemented
386C2—21no—
387C2—32no—
388C2—61no—
389C2—81no—
390C2—241no—
391C2D3×#83411yescharacteristic
subgroupG/H
centerC2D3×#834
commutatorC2×C32×C4C22×C4
FrattiniC2×Q8C2×D32
FittingC32×#124C22
socleC2×C32C2×#99
prime radicalC2×C3×D3×D4C4
cosocleC2×C32×Q8C23
hypercenter#124D32
hypocenterC32C2×#355
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #124

Complements

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

NH ≅ G/Ntype
2. D3×#836C2semidirect
3. #10589408C2semidirect
4. C3×#4542C2semidirect
5. #10589182C2semidirect
18. #63663C22semidirect
19. C3×#836C22semidirect
30. #4542D3direct (N × H)
84. #836C2×D3semidirect
262. C3×D3#355semidirect
326. C32C2×#355semidirect
366. D3#4542direct (N × H)
384. C3D3×#355semidirect
385. C3C2×#4542semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1242
D3×#8362
#105894082
C3×#45422
#105891822
C2×#45423
D3×#3553