Finite Group Databasebeta

← #82642

Subgroups — #82642

Order 384.

788 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#121C211yesmaximal, characteristic, complemented
2C2×#939C211yesmaximal, characteristic, complemented
3C2×#939C211yesmaximal, characteristic, complemented
4C2×#939C211yesmaximal, characteristic, complemented
5C2×D4×Dic3C211yesmaximal, characteristic, complemented
6C22×Dic3⋊C4C211yesmaximal, characteristic, complemented
7#5222C211yesmaximal, characteristic, complemented
8#5220C211yesmaximal, characteristic, complemented
9#5213C211yesmaximal, characteristic, complemented
10#4994C211yesmaximal, characteristic, complemented
11#4976C211yesmaximal, characteristic, complemented
12#4959C211yesmaximal, characteristic, complemented
13#4957C211yesmaximal, characteristic, complemented
14#4948C211yesmaximal, characteristic, complemented
15#4942C211yesmaximal, characteristic, complemented
16#2416—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C22×C3×D4C2211yescharacteristic
19C22×C3×D4C2211yescharacteristic
20C23×C3×C4C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C22×#67C2211yescharacteristic
23C22×#67C2211yescharacteristic
24C23×Dic3C2211yescharacteristic
25C23×Dic3C2211yescharacteristic
26C23×Dic3C2211yescharacteristic
27C3×#121—24no—
28C2×C3×C4⋊C4C2211yescharacteristic
29C2×C3×C22⋊C4C2211yescharacteristic
30C2×C3×C22⋊C4C2211yescharacteristic
31C2×#217C2211yescharacteristic
32C2×#217C2211yescharacteristic
33C2×#217C2211yescharacteristic
34C2×#217C2211yescharacteristic
35C2×#217C2211yescharacteristic
36C2×#217C2211yescharacteristic
37#939—24no—
38#939—24no—
39#939—24no—
40D4×Dic3—24no—
41C2×(C2×D3)⋊C4C2211yescharacteristic
42C2×(C2×D3)⋊C4C2211yescharacteristic
43C2×(C2×D3)⋊C4C2211yescharacteristic
44C2×(C2×D3)⋊C4C2211yescharacteristic
45C2×C4⋊Dic3C2211yescharacteristic
46C2×Dic3⋊C4—24no—
47C2×Dic3⋊C4C2211yescharacteristic
48C2×Dic3⋊C4C2211yescharacteristic
49C2×Dic3⋊C4C2211yescharacteristic
50C2×Dic3⋊C4C2211yescharacteristic
51C2×Dic3⋊C4C2211yescharacteristic
52C2×Dic3⋊C4C2211yescharacteristic
53C2×C4×Dic3C2211yescharacteristic
54C3⋊#95C2211yescharacteristic
55C3⋊#95C2211yescharacteristic
56C3⋊#95C2211yescharacteristic
57C3⋊#95C2211yescharacteristic
58C2×#121—31no—
59C2×#121—31no—
60C2×#121—31no—
61C2×#121D311yescharacteristic, complemented
62C2×C4×D4—31no—
63C22×C4⋊C4—31no—
64#396—31no—
65#396—31no—
66#394—31no—
67#394—31no—
68#390—31no—
69#389—31no—
70#386—31no—
71#386—31no—
72#380—31no—
73C24×C3C2311yescharacteristic
74C24×C3C2311yescharacteristic
75C24×C3C2311yescharacteristic
76C23×D3C2311yescharacteristic
77C2×C3×D4—22no—
78C2×C3×D4—22no—
79C2×C3×D4—22no—
80C2×C3×D4—22no—
81C2×C3×D4—22no—
82C2×C3×D4—22no—
83C2×C3×D4—22no—
84C2×C3×D4—41no—
85C2×C3×D4D414yescomplemented
86C22×C3×C4—22no—
87C22×C3×C4—22no—
88C22×C3×C4—41no—
89C22×C3×C4C2311yescharacteristic
90C22×C3×C4C2311yescharacteristic
91C22×C3×C4C2311yescharacteristic
92C22×C3×C4C2311yescharacteristic
93C2×#67—22no—
94C2×#67—22no—
95C2×#67—22no—
96C2×#67—22no—
97C2×#67—22no—
98C2×#67—22no—
99C2×#67—22no—
100C2×#67—22no—
101C2×#67—41no—
102C22×Dic3—22no—
103C22×Dic3—22no—
104C22×Dic3—22no—
105C22×Dic3—22no—
106C22×Dic3—22no—
107C22×Dic3—22no—
108C22×Dic3—22no—
109C22×Dic3—41no—
110C22×Dic3D414yescomplemented
111C22×Dic3C2311yescharacteristic
112C22×Dic3C2311yescharacteristic
113C22×Dic3C2311yescharacteristic
114C22×Dic3C2311yescharacteristic
115C22×Dic3C2311yescharacteristic
116C22×Dic3C2311yescharacteristic
117C22×Dic3C2311yescharacteristic
118C3×C4⋊C4—22no—
119C3×C22⋊C4—22no—
120C3×C22⋊C4—22no—
121#217—22no—
122#217—22no—
123#217—22no—
124#217—22no—
125#217—22no—
126#217—41no—
127(C2×D3)⋊C4—22no—
128(C2×D3)⋊C4—22no—
129(C2×D3)⋊C4—22no—
130(C2×D3)⋊C4—41no—
131C4⋊Dic3—22no—
132Dic3⋊C4—22no—
133Dic3⋊C4—22no—
134Dic3⋊C4—22no—
135Dic3⋊C4—22no—
136Dic3⋊C4—22no—
137Dic3⋊C4D414yescomplemented
138C4×Dic3—22no—
139C22×D4—31no—
140C22×D4—31no—
141C22×D4—31no—
142C22×D4C2×D311yescharacteristic
143C22×D4C2×D311yescharacteristic
144C22×D4C2×D311yescharacteristic
145C23×C4—31no—
146C23×C4—31no—
147C23×C4—31no—
148C23×C4C2×D311yescharacteristic
149#121—24no—
150#121—64no—
151#121—64no—
152#121—64no—
153C4×D4—64no—
154C2×C4⋊C4—31no—
155C2×C4⋊C4—31no—
156C2×C4⋊C4—31no—
157C2×C4⋊C4—31no—
158C2×C4⋊C4—31no—
159C2×C4⋊C4—31no—
160C2×C4⋊C4—31no—
161C2×C4⋊C4—64no—
162C2×C4⋊C4C2×D311yescharacteristic
163C2×C22⋊C4—31no—
164C2×C22⋊C4—31no—
165C2×C22⋊C4—31no—
166C2×C22⋊C4—31no—
167C2×C22⋊C4—31no—
168C2×C22⋊C4—31no—
169C2×C22⋊C4—31no—
170C2×C22⋊C4—31no—
171C2×C22⋊C4—31no—
172C2×C22⋊C4—31no—
173C2×C22⋊C4C2×D311yescharacteristic
174C2×C22⋊C4C2×D311yescharacteristic
175C2×C42—31no—
176#95—31no—
177#95—31no—
178#95—31no—
179#95—31no—
180C23×C3—21no—
181C23×C3—21no—
182C23×C3—21no—
183C23×C3—21no—
184C23×C3—21no—
185C23×C3—21no—
186C23×C3—21no—
187C23×C3—21no—
188C23×C3—21no—
189C23×C3—21no—
190C23×C3—21no—
191C23×C3—21no—
192C23×C3—21no—
193C23×C3—21no—
194C23×C3—21no—
195C23×C3—21no—
196C23×C3—21no—
197C23×C3C2×D412yes—
198C23×C3C2×D412yes—
199C23×C3C2×D412yes—
200C23×C3#4112yes—
201C23×C3C2411yescharacteristic
202C22×D3—21no—
203C22×D3—21no—
204C22×D3—21no—
205C22×D3—21no—
206C22×D3—21no—
207C22×D3—21no—
208C22×D3—21no—
209C3×D4—28no—
210C3×D4—44no—
211C3×D4—44no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—44no—
223C2×C3×C4C2×D412yes—
224C2×C3×C4C2×D412yes—
225#67—44no—
226#67—44no—
227#67—44no—
228C2×Dic3—21no—
229C2×Dic3—21no—
230C2×Dic3—21no—
231C2×Dic3—21no—
232C2×Dic3—28no—
233C2×Dic3—21no—
234C2×Dic3—21no—
235C2×Dic3—21no—
236C2×Dic3—21no—
237C2×Dic3—21no—
238C2×Dic3—21no—
239C2×Dic3—21no—
240C2×Dic3—21no—
241C2×Dic3—21no—
242C2×Dic3—21no—
243C2×Dic3—21no—
244C2×Dic3—21no—
245C2×Dic3—44no—
246C2×Dic3—44no—
247C2×Dic3C2×D412yes—
248C2×Dic3C2×D412yes—
249C2×Dic3C2×D412yes—
250C2×Dic3C2×D412yes—
251C2×Dic3#4112yes—
252C24—31no—
253C24C22×D311yescharacteristic
254C24C22×D311yescharacteristic
255C24C22×D311yescharacteristic
256C2×D4—22no—
257C2×D4—22no—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4—22no—
263C2×D4—41no—
264C2×D4—62no—
265C2×D4—62no—
266C2×D4—62no—
267C2×D4—62no—
268C2×D4—62no—
269C2×D4—62no—
270C2×D4—62no—
271C2×D4—62no—
272C2×D4—121no—
273C2×D4#6714yescomplemented
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—31no—
277C22×C4—34no—
278C22×C4—31no—
279C22×C4—31no—
280C22×C4—31no—
281C22×C4—31no—
282C22×C4—31no—
283C22×C4—31no—
284C22×C4—41no—
285C22×C4—62no—
286C22×C4—62no—
287C22×C4—62no—
288C22×C4—62no—
289C22×C4—62no—
290C22×C4—62no—
291C22×C4—62no—
292C22×C4—121no—
293C22×C4C22×D311yescharacteristic
294C22×C4C22×D311yescharacteristic
295C22×C4C22×D311yescharacteristic
296C22×C4C22×D311yescharacteristic
297C4⋊C4—22no—
298C4⋊C4—34no—
299C4⋊C4—62no—
300C4⋊C4—62no—
301C4⋊C4—62no—
302C4⋊C4—62no—
303C4⋊C4—62no—
304C4⋊C4—62no—
305C22⋊C4—22no—
306C22⋊C4—22no—
307C22⋊C4—62no—
308C22⋊C4—62no—
309C22⋊C4—62no—
310C22⋊C4—62no—
311C22⋊C4—62no—
312C22⋊C4—62no—
313C22⋊C4—62no—
314C22⋊C4—62no—
315C22⋊C4—121no—
316C22⋊C4—121no—
317C42—62no—
318C22×C3—22no—
319C22×C3—22no—
320C22×C3—22no—
321C22×C3—22no—
322C22×C3—22no—
323C22×C3—22no—
324C22×C3—22no—
325C22×C3—22no—
326C22×C3—22no—
327C22×C3—41no—
328C22×C3—41no—
329C22×C3—41no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—41no—
333C22×C3—41no—
334C22×C3—41no—
335C22×C3—41no—
336C22×C3—41no—
337C22×C3—41no—
338C22×C3#12114yescomplemented
339C22×C3C22×D411yescharacteristic
340C22×C3C22×D411yescharacteristic
341C22×C3C22×D411yescharacteristic
342C22×C3C2×#4111yescharacteristic
343C22×C3C2×#4111yescharacteristic
344C22×C3H(5,𝔽2)11yescharacteristic
345C22×C32−1+411yescharacteristic
346C2×D3—41no—
347C2×D3—41no—
348C2×D3—41no—
349C2×D3—41no—
350C2×D3—41no—
351C2×D3—41no—
352C2×D3—41no—
353C3×C4—22no—
354C3×C4—22no—
355C3×C4—41no—
356C3×C4—41no—
357Dic3—22no—
358Dic3—22no—
359Dic3—41no—
360Dic3—41no—
361Dic3—41no—
362Dic3—41no—
363Dic3#12114yescomplemented
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—61no—
382C23—61no—
383C23—61no—
384C23—61no—
385C23—61no—
386C23—61no—
387C23—61no—
388C23D3×D412yes—
389C23#23712yes—
390C23C2×#6712yes—
391C23C2×#6712yes—
392C23C23×D311yescharacteristic
393D4—28no—
394D4—44no—
395D4—44no—
396D4—124no—
397D4—124no—
398D4—124no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—32no—
410C2×C4—32no—
411C2×C4—32no—
412C2×C4—32no—
413C2×C4—32no—
414C2×C4—44no—
415C2×C4—68no—
416C2×C4—61no—
417C2×C4—61no—
418C2×C4—61no—
419C2×C4—61no—
420C2×C4—61no—
421C2×C4—61no—
422C2×C4—61no—
423C2×C4—61no—
424C2×C4—61no—
425C2×C4—61no—
426C2×C4—61no—
427C2×C4—61no—
428C2×C4—61no—
429C2×C4—61no—
430C2×C4—61no—
431C2×C4—61no—
432C2×C4—124no—
433C2×C4—124no—
434C2×C4D3×D412yes—
435C2×C4C2×#6712yes—
436C2×C3—24no—
437C2×C3—42no—
438C2×C3—81no—
439C2×C3C2×#12111yescharacteristic
440C2×C3C2×#12111yescharacteristic
441C2×C3#53711yescharacteristic
442C2×C3D4211yescharacteristic
443C2×C3#54711yescharacteristic
444C2×C3#54811yescharacteristic
445C2×C3#55311yescharacteristic
446D3—81no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—22no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—121no—
468C22—121no—
469C22—121no—
470C22—121no—
471C22—121no—
472C22—121no—
473C22—121no—
474C22#93914yescomplemented
475C22C2×D3×D411yescharacteristic
476C22C2×D3×D411yescharacteristic
477C22C2×#23711yescharacteristic
478C22#100411yescharacteristic
479C22D3×#4111yescharacteristic
480C22#101011yescharacteristic
481C22C22×#6711yescharacteristic
482C4—22no—
483C4—22no—
484C4—34no—
485C4—41no—
486C4—41no—
487C4—62no—
488C4—62no—
489C4—121no—
490C4—121no—
491C4—121no—
492C4—121no—
493C3#241611yescharacteristic, complemented, Sylow
494C2—24no—
495C2—42no—
496C2—81no—
497C2—241no—
498C2#559711yescharacteristic
499C2#559811yescharacteristic
500C2#560111yescharacteristic
501C2D3×#12111yescharacteristic
502C2D4×#6711yescharacteristic
503C2C2×#93911yescharacteristic
504C2#582411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC2×C3×#121C2
hypercenterC2×#121D3
hypocenterC3#2416
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×C3×#121C2semidirect
2. C2×#939C2semidirect
3. C2×#939C2semidirect
4. C2×#939C2semidirect
5. C2×D4×Dic3C2semidirect
6. C22×Dic3⋊C4C2semidirect
7. #5222C2semidirect
8. #5220C2semidirect
9. #5213C2semidirect
10. #4994C2semidirect
11. #4976C2semidirect
12. #4959C2semidirect
13. #4957C2semidirect
14. #4948C2semidirect
15. #4942C2semidirect
61. C2×#121D3semidirect
85. C2×C3×D4D4semidirect
110. C22×Dic3D4semidirect
137. Dic3⋊C4D4semidirect
273. C2×D4#67semidirect
338. C22×C3#121semidirect
363. Dic3#121semidirect
474. C22#939semidirect
493. C3#2416semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#1212
C2×#9392
C2×D4×Dic32
C22×Dic3⋊C42
#52222
#52202
#52132
#49942
#49762
#49592
#49572
#49482
#49422
#24163