Finite Group Databasebeta

← D3×#1347 #10705404

Subgroups — D3×#1347 #10705404

Order 768.

558 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 101 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
1D3×#466C211yesmaximal, characteristic
2D3×C22⋊C16C211yesmaximal, characteristic, complemented
3D3×#340C211yesmaximal, characteristic, complemented
4C3×#1347C211yesmaximal, characteristic, complemented
5#67774C211yesmaximal, characteristic, complemented
6#67526C211yesmaximal, characteristic, complemented
7#67485C211yesmaximal, characteristic, complemented
8C2×#1347—31nomaximal, Sylow
9C2×D3×D8C411yescharacteristic, complemented
10C22×D3×C8C2211yescharacteristic
11D3×#121—21no—
12C2×D3×C4⋊C4—21no—
13C3×#466C2211yescharacteristic
14#5157C411yescharacteristic, complemented
15#5115C2211yescharacteristic
16#5038—21no—
17C2×D3×C16—21no—
18#4883C411yescharacteristic, complemented
19D3×#107C411yescharacteristic, complemented
20#4775—21no—
21D3×#102—21no—
22C3×C22⋊C16C2211yescharacteristic, complemented
23C3×#340C2211yescharacteristic, complemented
24#4551C2211yescharacteristic, complemented
25#4549C2211yescharacteristic, complemented
26#4529—21no—
27(C2×D3)⋊C16—21no—
28C2×#466—31no—
29C2×C22⋊C16—31no—
30C2×#340—31no—
31#1347—31no—
32#1347—31no—
33#1347—31no—
34#1347D311yescharacteristic, direct product factor
35C2×D3×D4—21no—
36C2×D3×D4—41no—
37C22×C4×D3—41no—
38C22×C4×D3D411yescharacteristic
39C2×C3×D8C2×C411yescharacteristic, complemented
40C22×C3×C8C2311yescharacteristic
41C3×#121—21no—
42C2×C3×C4⋊C4—21no—
43#939—41no—
44#938—21no—
45C2×#213—21no—
46#930—21no—
47C2×C4⋊Dic3—21no—
48C2×Dic3⋊C4—41no—
49C22×C3⋊C8D411yescharacteristic
50D3×D8—42no—
51C2×D24C2×C411yescharacteristic, complemented
52C2×D3×C8—42no—
53C2×D3×C8C2×C411yescharacteristic
54C2×D3×C8C2×C411yescharacteristic
55C2×D3×C8D411yescharacteristic
56C2×D3×C8D411yescharacteristic
57#895—21no—
58D3×C4⋊C4—24no—
59D3×C4⋊C4—21no—
60D3×C4⋊C4—42no—
61#884—41no—
62D3×C22⋊C4—41no—
63C2×C3×C16—21no—
64C3×#107C2×C411yescharacteristic, complemented
65C3×#102—21no—
66#832—21no—
67#821—21no—
68#818C2×C411yescharacteristic, complemented
69C2×C3⋊C16—21no—
70#809—21no—
71#807—21no—
72D3×C16—42no—
73C22×D8—31no—
74C23×C8—31no—
75C2×#121—61no—
76C22×C4⋊C4—61no—
77C22×C16—61no—
78#466—31no—
79#466—31no—
80#466—31no—
81#466—61no—
82#466—61no—
83#466C2×D311yescharacteristic
84C2×#107—31no—
85C2×#102—61no—
86C22⋊C16—31no—
87C22⋊C16—61no—
88C22⋊C16C2×D311yescharacteristic, complemented
89#340—31no—
90#340—61no—
91#340C2×D311yescharacteristic, complemented
92C23×D3—41no—
93C23×D3D811yescharacteristic
94C2×C3×D4—21no—
95C2×C3×D4—41no—
96C22×C3×C4—41no—
97C22×C3×C4C2×D411yescharacteristic
98C2×#67—41no—
99C2×#67—41no—
100C2×#67—41no—
101C22×Dic3—41no—
102C22×Dic3D811yescharacteristic
103D3×D4—42no—
104D3×D4—42no—
105D3×D4—82no—
106D3×D4—82no—
107C2×D12—21no—
108C2×D12—41no—
109C2×C4×D3—22no—
110C2×C4×D3—22no—
111C2×C4×D3—44no—
112C2×C4×D3—41no—
113C2×C4×D3—82no—
114C2×C4×D3—82no—
115C2×C4×D3C22⋊C411yescharacteristic
116C2×C4×D3C22⋊C411yescharacteristic
117C2×C4×D3SD1611yescharacteristic
118C2×C4×D3SD1611yescharacteristic
119C3×D8—41no—
120C2×C3×C8—41no—
121C2×C3×C8C22×C411yescharacteristic
122C2×C3×C8C2×D411yescharacteristic
123C3×C4⋊C4—22no—
124C3×C4⋊C4—21no—
125C3×C4⋊C4—41no—
126C3×C22⋊C4—41no—
127#217—41no—
128#213—42no—
129(C2×D3)⋊C4—41no—
130(C2×D3)⋊C4—41no—
131C4⋊Dic3—22no—
132C4⋊Dic3—21no—
133C4⋊Dic3—41no—
134Dic3⋊C4—44no—
135Dic3⋊C4—41no—
136C2×C3⋊C8—41no—
137C2×C3⋊C8C22⋊C411yescharacteristic
138C2×C3⋊C8C22⋊C411yescharacteristic
139D24—41no—
140D3×C8—22no—
141D3×C8—22no—
142D3×C8—41no—
143D3×C8—41no—
144C3×C16—41no—
145C3⋊C16—41no—
146C22×D4—61no—
147C22×D4—121no—
148C23×C4—31no—
149C23×C4—121no—
150C2×D8—31no—
151C2×D8—61no—
152C2×D8—122no—
153C2×D8C4×D311yescharacteristic, complemented
154C22×C8—31no—
155C22×C8—31no—
156C22×C8—31no—
157C22×C8—31no—
158C22×C8—31no—
159C22×C8—122no—
160C22×C8C22×D311yescharacteristic
161#121—21no—
162#121—61no—
163#121—61no—
164#121—61no—
165#121—121no—
166#121—121no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—61no—
169C2×C4⋊C4—64no—
170C2×C4⋊C4—61no—
171C2×C4⋊C4—122no—
172C2×C4⋊C4—121no—
173C2×C22⋊C4—121no—
174C2×C16—21no—
175C2×C16—61no—
176C2×C16—122no—
177#107—31no—
178#107—61no—
179#107C4×D311yescharacteristic, complemented
180#102—21no—
181#102—61no—
182#102—61no—
183#102—61no—
184C23×C3—41no—
185C23×C3C2×D811yescharacteristic
186C22×D3—22no—
187C22×D3—22no—
188C22×D3—41no—
189C22×D3—82no—
190C22×D3—82no—
191C22×D3—82no—
192C22×D3#10211yescharacteristic
193C22×D3#10211yescharacteristic
194C22×D3D1612yes—
195C22×D3SD3212yes—
196C3×D4—41no—
197C3×D4—41no—
198C3×D4—81no—
199C3×D4—81no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—42no—
203C2×C3×C4—41no—
204C2×C3×C4—81no—
205C2×C3×C4—81no—
206C2×C3×C4C2×C22⋊C411yescharacteristic
207C2×C3×C4C2×SD1611yescharacteristic
208#67—81no—
209#67—81no—
210#67—82no—
211#67—82no—
212C2×Dic3—22no—
213C2×Dic3—42no—
214C2×Dic3—41no—
215C2×Dic3—81no—
216C2×Dic3—81no—
217C2×Dic3#10211yescharacteristic
218C2×Dic3#10211yescharacteristic
219D12—41no—
220D12—41no—
221D12—82no—
222C4×D3—22no—
223C4×D3—21no—
224C4×D3—21no—
225C4×D3—22no—
226C4×D3—88no—
227C4×D3—82no—
228C4×D3#9912yes—
229C4×D3#10412yes—
230C3×C8—21no—
231C3×C8—21no—
232C3⋊C8—21no—
233C3⋊C8—21no—
234C24—31no—
235C24—121no—
236C2×D4—21no—
237C2×D4—41no—
238C2×D4—61no—
239C2×D4—122no—
240C2×D4—122no—
241C2×D4—121no—
242C2×D4—121no—
243C2×D4—121no—
244C2×D4—121no—
245C2×D4—242no—
246C2×D4—242no—
247C22×C4—31no—
248C22×C4—31no—
249C22×C4—31no—
250C22×C4—31no—
251C22×C4—31no—
252C22×C4—41no—
253C22×C4—62no—
254C22×C4—62no—
255C22×C4—121no—
256C22×C4—124no—
257C22×C4—121no—
258C22×C4—242no—
259C22×C4—242no—
260C22×C4D3×D411yescharacteristic
261D8—41no—
262D8—121no—
263D8—122no—
264C2×C8—31no—
265C2×C8—31no—
266C2×C8—41no—
267C2×C8—62no—
268C2×C8—62no—
269C2×C8—121no—
270C2×C8—121no—
271C2×C8—121no—
272C2×C8C2×C4×D311yescharacteristic
273C2×C8D3×D411yescharacteristic
274C4⋊C4—22no—
275C4⋊C4—21no—
276C4⋊C4—41no—
277C4⋊C4—62no—
278C4⋊C4—61no—
279C4⋊C4—121no—
280C4⋊C4—121no—
281C4⋊C4—124no—
282C22⋊C4—41no—
283C22⋊C4—121no—
284C22⋊C4—121no—
285C22⋊C4—121no—
286C16—41no—
287C16—121no—
288C22×C3—21no—
289C22×C3—21no—
290C22×C3—81no—
291C22×C3—81no—
292C22×C3—81no—
293C22×C3C2×#10211yescharacteristic
294C22×C3C2×D1611yescharacteristic
295C22×C3C2×SD3211yescharacteristic
296C2×D3—21no—
297C2×D3—21no—
298C2×D3—24no—
299C2×D3—24no—
300C2×D3—81no—
301C2×D3—81no—
302C2×D3—81no—
303C2×D3—164no—
304C2×D3#32712yes—
305C2×D3#35712yes—
306C2×D3#35712yes—
307C2×D3#36012yes—
308C3×C4—21no—
309C3×C4—82no—
310C3×C4—81no—
311C3×C4C2×#9911yescharacteristic
312C3×C4C2×#10411yescharacteristic
313Dic3—21no—
314Dic3—82no—
315Dic3—81no—
316Dic3#32712yes—
317C23—31no—
318C23—32no—
319C23—32no—
320C23—31no—
321C23—41no—
322C23—62no—
323C23—62no—
324C23—121no—
325C23—242no—
326C23—242no—
327C23—242no—
328C23D3×D811yescharacteristic
329D4—41no—
330D4—41no—
331D4—81no—
332D4—81no—
333D4—121no—
334D4—121no—
335D4—242no—
336D4—242no—
337D4—242no—
338D4—241no—
339D4—241no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—31no—
343C2×C4—32no—
344C2×C4—32no—
345C2×C4—31no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—62no—
349C2×C4—62no—
350C2×C4—62no—
351C2×C4—61no—
352C2×C4—61no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—122no—
356C2×C4—121no—
357C2×C4—242no—
358C2×C4—248no—
359C2×C4—241no—
360C2×C4—241no—
361C2×C4D3×C22⋊C411yescharacteristic
362C2×C4D3×SD1611yescharacteristic
363C8—21no—
364C8—21no—
365C8—61no—
366C8—61no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—161no—
370C2×C3C2×#32711yescharacteristic
371C2×C3C2×#35711yescharacteristic
372C2×C3C2×#36011yescharacteristic
373D3—22no—
374D3—161no—
375D3#134714yesdirect product factor
376C22—21no—
377C22—21no—
378C22—32no—
379C22—32no—
380C22—32no—
381C22—32no—
382C22—64no—
383C22—64no—
384C22—61no—
385C22—61no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22—241no—
390C22—241no—
391C22—241no—
392C22—484no—
393C22D3×#10211yescharacteristic
394C22D3×D1611yescharacteristic
395C22D3×SD3211yescharacteristic
396C4—21no—
397C4—32no—
398C4—61no—
399C4—82no—
400C4—81no—
401C4—242no—
402C4—241no—
403C4D3×#9911yescharacteristic
404C4D3×#10411yescharacteristic
405C3C2×#134711yescharacteristic, complemented, Sylow
406C2—21no—
407C2—21no—
408C2—34no—
409C2—62no—
410C2—161no—
411C2—481no—
412C2D3×#32711yescharacteristic
413C2D3×#35711yescharacteristic
414C2D3×#36011yescharacteristic
subgroupG/H
centerC22D3×#102
commutatorC2×C3×C8C22×C4
FrattiniC22×C8C22×D3
FittingC3×#1347C2
socleC22×C3C2×#102
prime radicalD3×#466C2
cosocleC22×C3×C8C23
hypercenter#1347D3
hypocenterC3C2×#1347
LCSG ▷ C2×C3×C8 ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1347

Complements

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

NH ≅ G/Ntype
2. D3×C22⋊C16C2semidirect
3. D3×#340C2semidirect
4. C3×#1347C2semidirect
5. #67774C2semidirect
6. #67526C2semidirect
7. #67485C2semidirect
9. C2×D3×D8C4semidirect
14. #5157C4semidirect
18. #4883C4semidirect
19. D3×#107C4semidirect
22. C3×C22⋊C16C22semidirect
23. C3×#340C22semidirect
24. #4551C22semidirect
25. #4549C22semidirect
34. #1347D3direct (N × H)
39. C2×C3×D8C2×C4semidirect
51. C2×D24C2×C4semidirect
64. C3×#107C2×C4semidirect
68. #818C2×C4semidirect
88. C22⋊C16C2×D3semidirect
91. #340C2×D3semidirect
153. C2×D8C4×D3semidirect
179. #107C4×D3semidirect
375. D3#1347direct (N × H)
405. C3C2×#1347semidirect

Maximal subgroups

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

subgroupindex
D3×#4662
D3×C22⋊C162
D3×#3402
C3×#13472
#677742
#675262
#674852
C2×#13473