Finite Group Databasebeta

← #10691367

Subgroups — #10691367

Order 768.

678 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4843C211yesmaximal, characteristic
2C2×C8×D12C211yesmaximal, characteristic, complemented
3#70479C211yesmaximal, characteristic, complemented
4C2×#4485C211yesmaximal, characteristic, complemented
5#69772C211yesmaximal, characteristic, complemented
6C3×#1277C211yesmaximal, characteristic, complemented
7#67702C211yesmaximal, characteristic, complemented
8#9221—31nomaximal, Sylow
9C22×D24—21no—
10C22×D3×C8—21no—
11C2×#874C2211yescharacteristic
12C2×C4×D12C2211yescharacteristic
13C2×C3×C4⋊C8C2211yescharacteristic
14C2×C3×C4⋊C8C2211yescharacteristic
15C2×C3×C4×C8C2211yescharacteristic
16C2×#821—21no—
17C2×#821—21no—
18C2×#821—21no—
19C2×#821—21no—
20C2×(C2×D3)⋊C8—21no—
21#4935C2211yescharacteristic
22C2×C4⋊(C3⋊C8)C2211yescharacteristic
23#4843—22no—
24#4843C414yescomplemented
25C8×D12—22no—
26C8×D12—22no—
27#4551—21no—
28#4485—22no—
29C2×#459—31no—
30C2×C8×D4—31no—
31#1957—31no—
32#1802—31no—
33C2×#331—31no—
34#1296—31no—
35#1277D311yescharacteristic, complemented
36C22×D12—21no—
37C22×D12—21no—
38C22×D12—21no—
39C22×D12D411yescharacteristic
40C22×C4×D3—21no—
41C22×C3×C8—21no—
42C22×C3×C8—21no—
43C22×C3×C8D411yescharacteristic
44C22×C3×C8D411yescharacteristic
45C2×C3×C42C2311yescharacteristic
46C2×(C2×D3)⋊C4—21no—
47C2×C4⋊Dic3—21no—
48C2×C4⋊Dic3—21no—
49C2×C4⋊Dic3—21no—
50C2×C4⋊Dic3D411yescharacteristic
51C22×C3⋊C8—21no—
52C2×D24—24no—
53C2×D24—42no—
54C2×D24—42no—
55C2×D3×C8—24no—
56C2×D3×C8—42no—
57C2×D3×C8—42no—
58#874—21no—
59#874—21no—
60#874—21no—
61#874C2×C412yes—
62C4×D12—21no—
63C4×D12—21no—
64C4×D12C2×C412yes—
65C4×D12D412yes—
66C3×C4⋊C8—21no—
67C3×C4⋊C8—21no—
68C3×C4⋊C8—21no—
69C3×C4⋊C8C2×C412yes—
70C3×C4×C8—21no—
71C3×C4×C8—21no—
72#821—24no—
73#821—42no—
74#821—42no—
75#821—42no—
76(C2×D3)⋊C8—24no—
77C4⋊(C3⋊C8)—21no—
78C4⋊(C3⋊C8)D412yes—
79C22×D8—61no—
80C23×C8—61no—
81C2×#127—31no—
82C2×C4×D4—31no—
83#459—34no—
84#459—62no—
85C8×D4—62no—
86C8×D4—62no—
87C2×C4⋊C8—31no—
88C2×C4⋊C8C2×D311yescharacteristic
89C2×C4⋊C8C2×D311yescharacteristic
90C2×#102—61no—
91C2×#102—61no—
92C2×#102—61no—
93C2×#102—61no—
94C2×C22⋊C8—61no—
95C2×C4×C8C2×D311yescharacteristic
96#384—31no—
97#340—61no—
98#331—62no—
99C23×D3—21no—
100C23×D3—41no—
101C22×C3×C4C2×D411yescharacteristic
102C22×C3×C4C2×D411yescharacteristic
103C22×C3×C4#4111yescharacteristic
104C22×Dic3—21no—
105C22×Dic3—41no—
106C2×D12—21no—
107C2×D12—21no—
108C2×D12—21no—
109C2×D12—22no—
110C2×D12—22no—
111C2×D12—22no—
112C2×D12—41no—
113C2×D12—41no—
114C2×D12—41no—
115C2×D12—41no—
116C2×D12—41no—
117C2×D12—41no—
118C2×D12—41no—
119C2×D12—41no—
120C2×D12—41no—
121C2×D12—41no—
122C2×D12—41no—
123C2×D12—81no—
124C2×D12—81no—
125C2×D12C22⋊C412yes—
126C2×D12D812yes—
127C2×D12SD1612yes—
128C2×C4×D3—22no—
129C2×C4×D3—22no—
130C2×C4×D3—41no—
131C2×C4×D3—41no—
132C2×C4×D3—41no—
133C2×C4×D3—41no—
134C2×C3×C8—21no—
135C2×C3×C8—21no—
136C2×C3×C8—22no—
137C2×C3×C8—21no—
138C2×C3×C8—21no—
139C2×C3×C8—21no—
140C2×C3×C8—41no—
141C2×C3×C8—41no—
142C2×C3×C8—41no—
143C2×C3×C8—41no—
144C2×C3×C8—41no—
145C2×C3×C8D812yescomplemented
146C3×C42C22×C411yescharacteristic
147C3×C42C2×D411yescharacteristic
148C3×C42C2×D411yescharacteristic
149C3×C42#4111yescharacteristic
150(C2×D3)⋊C4—22no—
151(C2×D3)⋊C4—22no—
152C4⋊Dic3—21no—
153C4⋊Dic3—41no—
154C4⋊Dic3—41no—
155C4⋊Dic3—41no—
156C4⋊Dic3—41no—
157C4⋊Dic3—81no—
158C4⋊Dic3C22⋊C412yes—
159C2×C3⋊C8—22no—
160C2×C3⋊C8—41no—
161C2×C3⋊C8—41no—
162D24—48no—
163D3×C8—48no—
164C22×D4—31no—
165C22×D4—61no—
166C22×D4—61no—
167C22×D4—61no—
168C23×C4—61no—
169C2×D8—64no—
170C2×D8—122no—
171C2×D8—122no—
172C22×C8—21no—
173C22×C8—21no—
174C22×C8—64no—
175C22×C8—61no—
176C22×C8—122no—
177C22×C8—122no—
178C22×C8D1211yescharacteristic
179C22×C8D1211yescharacteristic
180#127—32no—
181#127—61no—
182#127—61no—
183#127—61no—
184C4×D4—32no—
185C4×D4—32no—
186C4×D4—61no—
187C4×D4—61no—
188C2×C4⋊C4—31no—
189C2×C4⋊C4—61no—
190C2×C4⋊C4—61no—
191C2×C4⋊C4—61no—
192C2×C22⋊C4—61no—
193C2×C42C22×D311yescharacteristic
194C4⋊C8—21no—
195C4⋊C8—21no—
196C4⋊C8—21no—
197C4⋊C8—32no—
198C4⋊C8—61no—
199C4⋊C8C4×D312yes—
200#102—64no—
201#102—122no—
202#102—122no—
203#102—122no—
204C22⋊C8—64no—
205C4×C8—21no—
206C4×C8—21no—
207C23×C3#12111yescharacteristic
208C22×D3—22no—
209C22×D3—22no—
210C22×D3—22no—
211C22×D3—41no—
212C22×D3—41no—
213C22×D3—41no—
214C22×D3—41no—
215C22×D3—42no—
216C22×D3—81no—
217C22×D3—81no—
218C22×D3—81no—
219C22×D3—81no—
220C22×D3—81no—
221C22×D3—81no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4C2×C22⋊C411yescharacteristic
225C2×C3×C4C4×D411yescharacteristic
226C2×C3×C4C4×D411yescharacteristic
227C2×C3×C4#12011yescharacteristic
228C2×C3×C4#12111yescharacteristic
229C2×C3×C4#12311yescharacteristic
230C2×C3×C4C2×D811yescharacteristic
231C2×C3×C4C2×D811yescharacteristic
232C2×C3×C4C2×SD1611yescharacteristic
233C2×C3×C4#13511yescharacteristic
234C2×C3×C4#13511yescharacteristic
235C2×C3×C4#13511yescharacteristic
236C2×C3×C4AGL(1,ℤ/8)11yescharacteristic
237C2×C3×C4AGL(1,ℤ/8)11yescharacteristic
238C2×Dic3—22no—
239C2×Dic3—41no—
240C2×Dic3—41no—
241C2×Dic3—81no—
242C2×Dic3—81no—
243C2×Dic3—81no—
244D12—22no—
245D12—22no—
246D12—22no—
247D12—42no—
248D12—42no—
249D12—42no—
250D12—42no—
251D12—82no—
252D12—82no—
253D12—81no—
254D12—81no—
255D12—81no—
256D12—81no—
257D12#10214yescomplemented
258C4×D3—42no—
259C4×D3—42no—
260C4×D3—42no—
261C4×D3—42no—
262C3×C8—22no—
263C3×C8—42no—
264C3×C8—41no—
265C3×C8—81no—
266C3⋊C8—42no—
267C24—61no—
268C24—121no—
269C2×D4—32no—
270C2×D4—32no—
271C2×D4—32no—
272C2×D4—62no—
273C2×D4—62no—
274C2×D4—61no—
275C2×D4—62no—
276C2×D4—61no—
277C2×D4—61no—
278C2×D4—121no—
279C2×D4—121no—
280C2×D4—121no—
281C2×D4—121no—
282C2×D4—121no—
283C2×D4—121no—
284C2×D4—121no—
285C2×D4—121no—
286C2×D4—121no—
287C2×D4—121no—
288C2×D4—121no—
289C2×D4—241no—
290C2×D4—241no—
291C22×C4—61no—
292C22×C4—62no—
293C22×C4—62no—
294C22×C4—121no—
295C22×C4—121no—
296C22×C4—121no—
297C22×C4—121no—
298C22×C4—121no—
299C22×C4C2×D1211yescharacteristic
300C22×C4D3×D411yescharacteristic
301C22×C4#23911yescharacteristic
302D8—128no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—22no—
306C2×C8—21no—
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—62no—
315C2×C8—128no—
316C2×C8—121no—
317C2×C8—121no—
318C2×C8D2412yescomplemented
319C4⋊C4—32no—
320C4⋊C4—61no—
321C4⋊C4—121no—
322C4⋊C4—121no—
323C4⋊C4—121no—
324C4⋊C4—121no—
325C4⋊C4—241no—
326C22⋊C4—62no—
327C22⋊C4—62no—
328C42C2×C4×D311yescharacteristic
329C42#23511yescharacteristic
330C42D3×D411yescharacteristic
331C42D3×D411yescharacteristic
332C22×C3#38611yescharacteristic
333C22×C3#45911yescharacteristic
334C22×C3#46311yescharacteristic
335C22×C3#46511yescharacteristic
336C22×C3#46611yescharacteristic
337C22×C3#47111yescharacteristic
338C22×C3#47211yescharacteristic
339C2×D3—24no—
340C2×D3—42no—
341C2×D3—42no—
342C2×D3—42no—
343C2×D3—42no—
344C2×D3—42no—
345C2×D3—42no—
346C2×D3—82no—
347C2×D3—82no—
348C2×D3—82no—
349C2×D3—161no—
350C2×D3—161no—
351C2×D3—161no—
352C2×D3—161no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4C2×#10211yescharacteristic
356C3×C4#41611yescharacteristic
357C3×C4C4×D811yescharacteristic
358C3×C4#44211yescharacteristic
359C3×C4#44711yescharacteristic
360C3×C4#44911yescharacteristic
361C3×C4#46511yescharacteristic
362C3×C4#46611yescharacteristic
363Dic3—42no—
364Dic3—161no—
365C23—62no—
366C23—62no—
367C23—62no—
368C23—121no—
369C23—121no—
370C23—121no—
371C23—121no—
372C23—122no—
373C23—241no—
374C23—241no—
375C23—241no—
376C23—241no—
377C23—241no—
378C23—241no—
379C23#89511yescharacteristic
380D4—34no—
381D4—62no—
382D4—62no—
383D4—62no—
384D4—122no—
385D4—122no—
386D4—122no—
387D4—122no—
388D4—242no—
389D4—242no—
390D4—241no—
391D4—241no—
392D4—241no—
393D4—241no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—62no—
397C2×C4—121no—
398C2×C4—121no—
399C2×C4—122no—
400C2×C4—122no—
401C2×C4—122no—
402C2×C4—122no—
403C2×C4—241no—
404C2×C4—241no—
405C2×C4—241no—
406C2×C4C4×D1211yescharacteristic
407C2×C4D3×C22⋊C411yescharacteristic
408C2×C4#88211yescharacteristic
409C2×C4#88411yescharacteristic
410C2×C4#89311yescharacteristic
411C2×C4#89411yescharacteristic
412C2×C4C2×D2411yescharacteristic
413C2×C4#90411yescharacteristic
414C2×C4#90811yescharacteristic
415C2×C4#90811yescharacteristic
416C2×C4D3×D811yescharacteristic
417C2×C4D3×SD1611yescharacteristic
418C2×C4#91611yescharacteristic
419C2×C4#91911yescharacteristic
420C8—22no—
421C8—41no—
422C8—42no—
423C8—81no—
424C8—122no—
425C2×C3#166511yescharacteristic
426C2×C3#166711yescharacteristic
427C2×C3#167711yescharacteristic
428C2×C3#168111yescharacteristic
429C2×C3#187911yescharacteristic
430C2×C3#189311yescharacteristic
431C2×C3#190711yescharacteristic
432D3—44no—
433D3—162no—
434C22—64no—
435C22—122no—
436C22—122no—
437C22—122no—
438C22—122no—
439C22—122no—
440C22—122no—
441C22—242no—
442C22—242no—
443C22—242no—
444C22—481no—
445C22—481no—
446C22—481no—
447C22—481no—
448C22#466511yescharacteristic
449C22#484311yescharacteristic
450C22#484411yescharacteristic
451C22#486411yescharacteristic
452C22#488311yescharacteristic
453C22#489711yescharacteristic
454C22#489811yescharacteristic
455C4—21no—
456C4—21no—
457C4—122no—
458C4—481no—
459C4C4×D2411yescharacteristic
460C4#471111yescharacteristic
461C4#473211yescharacteristic
462C4#473411yescharacteristic
463C4D3×#10211yescharacteristic
464C4#477511yescharacteristic
465C4#480411yescharacteristic
466C4#480711yescharacteristic
467C3#922111yescharacteristic, complemented, Sylow
468C2—124no—
469C2—482no—
470C2#6853611yescharacteristic
471C2#6853811yescharacteristic
472C2#6857611yescharacteristic
473C2#6858011yescharacteristic
474C2#6867311yescharacteristic
475C2#6888311yescharacteristic
476C2#6894811yescharacteristic
subgroupG/H
centerC23#895
commutatorC3×C42C22×C4
FrattiniC2×C42C22×D3
FittingC3×#1277C2
socleC23×C3#121
prime radicalC2×#4843C2
cosocleC2×C3×C42C23
hypercenter#1277D3
hypocenterC3#9221
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
2. C2×C8×D12C2semidirect
3. #70479C2semidirect
4. C2×#4485C2semidirect
5. #69772C2semidirect
6. C3×#1277C2semidirect
7. #67702C2semidirect
24. #4843C4semidirect
35. #1277D3semidirect
145. C2×C3×C8D8semidirect
257. D12#102semidirect
318. C2×C8D24semidirect
467. C3#9221semidirect

Maximal subgroups

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

subgroupindex
C2×#48432
C2×C8×D122
#704792
C2×#44852
#697722
C3×#12772
#677022
#92213