Finite Group Databasebeta

← #77284

Subgroups — #77284

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×#895C211yesmaximal, characteristic, complemented
2C2×#893C211yesmaximal, characteristic, complemented
3C2×D3×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×#884C211yesmaximal, characteristic, complemented
5C2×#884C211yesmaximal, characteristic, complemented
6C2×#884C211yesmaximal, characteristic, complemented
7C3×#396C211yesmaximal, characteristic, complemented
8#4994C211yesmaximal, characteristic, complemented
9#4991C211yesmaximal, characteristic, complemented
10#4976C211yesmaximal, characteristic, complemented
11#4961C211yesmaximal, characteristic, complemented
12#4957C211yesmaximal, characteristic, complemented
13#4956C211yesmaximal, characteristic, complemented
14#4667C211yesmaximal, characteristic, complemented
15#4665C211yesmaximal, characteristic, complemented
16#2416—31nomaximal, Sylow
17C22×#67C2211yescharacteristic
18C22×#67C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×D12C2211yescharacteristic
21C22×D12C2211yescharacteristic
22C22×D12C2211yescharacteristic
23C22×C4×D3C2211yescharacteristic
24C22×C4×D3C2211yescharacteristic
25C22×C4×D3C2211yescharacteristic
26C22×C4×D3C2211yescharacteristic
27C2×C3×C4⋊C4C2211yescharacteristic
28C2×C3×C4⋊C4C2211yescharacteristic
29C2×C3×C4⋊C4C2211yescharacteristic
30C2×C3×C22⋊C4C2211yescharacteristic
31C2×C3×C22⋊C4C2211yescharacteristic
32C2×C3×C22⋊C4C2211yescharacteristic
33C2×#217C2211yescharacteristic
34C2×(C2×D3)⋊C4C2211yescharacteristic
35C2×(C2×D3)⋊C4C2211yescharacteristic
36C2×(C2×D3)⋊C4C2211yescharacteristic
37C2×(C2×D3)⋊C4C2211yescharacteristic
38C2×(C2×D3)⋊C4C2211yescharacteristic
39C2×(C2×D3)⋊C4C2211yescharacteristic
40C2×(C2×D3)⋊C4C2211yescharacteristic
41C2×(C2×D3)⋊C4C2211yescharacteristic
42C2×C4⋊Dic3C2211yescharacteristic
43C2×Dic3⋊C4C2211yescharacteristic
44C2×Dic3⋊C4C2211yescharacteristic
45C2×Dic3⋊C4C2211yescharacteristic
46C2×Dic3⋊C4C2211yescharacteristic
47C2×C4×Dic3C2211yescharacteristic
48#895—24no—
49#893—24no—
50D3×C4⋊C4—24no—
51#884—24no—
52#884—24no—
53#884—24no—
54C3×#95C2211yescharacteristic
55C3⋊#95C2211yescharacteristic
56C3⋊#95C2211yescharacteristic
57C3⋊#95C2211yescharacteristic
58C2×#121—31no—
59C2×#121—31no—
60C2×#121—31no—
61C2×#121—31no—
62C2×C4×D4—31no—
63C22×C4⋊C4—31no—
64#396—31no—
65#396D311yescharacteristic, complemented
66#394—31no—
67#394—31no—
68#390—31no—
69#389—31no—
70#386—31no—
71#386—31no—
72#380—31no—
73C24×C3C2311yescharacteristic
74C23×D3C2311yescharacteristic
75C23×D3C2311yescharacteristic
76C23×D3C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C22×C3×C4C2311yescharacteristic
81C22×C3×C4C2311yescharacteristic
82C22×C3×C4C2311yescharacteristic
83C2×#67—22no—
84C2×#67—22no—
85C2×#67—22no—
86C2×#67—22no—
87C2×#67—22no—
88C2×#67—22no—
89C2×#67—22no—
90C2×#67—22no—
91C2×#67—41no—
92C22×Dic3C2311yescharacteristic
93C22×Dic3C2311yescharacteristic
94C22×Dic3C2311yescharacteristic
95C22×Dic3C2311yescharacteristic
96C22×Dic3C2311yescharacteristic
97C2×D12—22no—
98C2×D12—22no—
99C2×D12—22no—
100C2×D12—22no—
101C2×D12—22no—
102C2×D12—22no—
103C2×D12—22no—
104C2×D12—41no—
105C2×D12D414yescomplemented
106C2×C4×D3—22no—
107C2×C4×D3—22no—
108C2×C4×D3—22no—
109C2×C4×D3—22no—
110C2×C4×D3—22no—
111C2×C4×D3—22no—
112C2×C4×D3—22no—
113C2×C4×D3—22no—
114C2×C4×D3—22no—
115C2×C4×D3—41no—
116C2×C4×D3—41no—
117C2×C4×D3D414yescomplemented
118C3×C4⋊C4—22no—
119C3×C4⋊C4—22no—
120C3×C4⋊C4—22no—
121C3×C22⋊C4—22no—
122C3×C22⋊C4—22no—
123C3×C22⋊C4—22no—
124#217—41no—
125(C2×D3)⋊C4—22no—
126(C2×D3)⋊C4—22no—
127(C2×D3)⋊C4—22no—
128(C2×D3)⋊C4—22no—
129(C2×D3)⋊C4—22no—
130(C2×D3)⋊C4—22no—
131(C2×D3)⋊C4—22no—
132(C2×D3)⋊C4—41no—
133C4⋊Dic3—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×D4—31no—
143C22×D4—31no—
144C22×D4—31no—
145C23×C4—31no—
146C23×C4—31no—
147C23×C4—31no—
148C23×C4—31no—
149#121—64no—
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—64no—
160C2×C4⋊C4C2×D311yescharacteristic
161C2×C4⋊C4C2×D311yescharacteristic
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⋊C4C2×D311yescharacteristic
173C2×C22⋊C4C2×D311yescharacteristic
174C2×C22⋊C4C2×D311yescharacteristic
175C2×C42—31no—
176#95—31no—
177#95—31no—
178#95—31no—
179#95C2×D311yescharacteristic
180C23×C3—21no—
181C23×C3—21no—
182C23×C3—21no—
183C23×C3—21no—
184C23×C3—21no—
185C23×C3—21no—
186C23×C3—21no—
187C23×C3C2411yescharacteristic
188C22×D3—21no—
189C22×D3—21no—
190C22×D3—21no—
191C22×D3—21no—
192C22×D3—21no—
193C22×D3—21no—
194C22×D3—21no—
195C22×D3—21no—
196C22×D3—21no—
197C22×D3—21no—
198C22×D3—21no—
199C22×D3—21no—
200C22×D3—21no—
201C22×D3—21no—
202C22×D3—21no—
203C22×D3—21no—
204C22×D3—21no—
205C22×D3C2×D412yes—
206C22×D3C2×D412yes—
207C22×D3C2×D412yes—
208C22×D3#4112yes—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
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—21no—
223C2×C3×C4—21no—
224C2×C3×C4C2×D412yes—
225C2×C3×C4C2×D412yes—
226C2×C3×C4C2×D412yes—
227#67—44no—
228#67—44no—
229#67—44no—
230C2×Dic3—21no—
231C2×Dic3—21no—
232C2×Dic3—21no—
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×Dic3C2×D412yes—
242C2×Dic3C2×D412yes—
243C2×Dic3C2×D412yes—
244C2×Dic3#4112yes—
245D12—28no—
246D12—44no—
247D12—44no—
248C4×D3—28no—
249C4×D3—44no—
250C4×D3—44no—
251C4×D3—44no—
252C24—31no—
253C24—31no—
254C24—31no—
255C24C22×D311yescharacteristic
256C2×D4—34no—
257C2×D4—62no—
258C2×D4—62no—
259C2×D4—62no—
260C2×D4—62no—
261C2×D4—62no—
262C2×D4—62no—
263C2×D4—62no—
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—121no—
274C22×C4—31no—
275C22×C4—31no—
276C22×C4—34no—
277C22×C4—31no—
278C22×C4—31no—
279C22×C4—31no—
280C22×C4—62no—
281C22×C4—62no—
282C22×C4—62no—
283C22×C4—62no—
284C22×C4—62no—
285C22×C4—62no—
286C22×C4—62no—
287C22×C4—62no—
288C22×C4—62no—
289C22×C4—121no—
290C22×C4—121no—
291C22×C4C22×D311yescharacteristic
292C22×C4C22×D311yescharacteristic
293C22×C4C22×D311yescharacteristic
294C22×C4C22×D311yescharacteristic
295C22×C4C22×D311yescharacteristic
296C22×C4C22×D311yescharacteristic
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—34no—
301C4⋊C4—62no—
302C4⋊C4—62no—
303C4⋊C4—62no—
304C4⋊C4—62no—
305C22⋊C4—22no—
306C22⋊C4—22no—
307C22⋊C4—22no—
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—41no—
319C22×C3—41no—
320C22×C3—41no—
321C22×C3—41no—
322C22×C3—41no—
323C22×C3—41no—
324C22×C3—41no—
325C22×C3C22×D411yescharacteristic
326C22×C3C22×D411yescharacteristic
327C22×C3C22×D411yescharacteristic
328C22×C3C2×#4111yescharacteristic
329C22×C3C2×#4111yescharacteristic
330C22×C3H(5,𝔽2)11yescharacteristic
331C22×C32−1+411yescharacteristic
332C2×D3—22no—
333C2×D3—22no—
334C2×D3—22no—
335C2×D3—22no—
336C2×D3—22no—
337C2×D3—22no—
338C2×D3—22no—
339C2×D3—22no—
340C2×D3—22no—
341C2×D3—41no—
342C2×D3—41no—
343C2×D3—41no—
344C2×D3—41no—
345C2×D3—41no—
346C2×D3—41no—
347C2×D3—41no—
348C2×D3—41no—
349C2×D3—41no—
350C2×D3—41no—
351C2×D3—41no—
352C2×D3#12114yescomplemented
353C3×C4—22no—
354C3×C4—22no—
355C3×C4—22no—
356C3×C4—41no—
357C3×C4—41no—
358C3×C4—41no—
359Dic3—22no—
360Dic3—41no—
361Dic3—41no—
362Dic3—41no—
363Dic3#12114yescomplemented
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—32no—
372C23—32no—
373C23—32no—
374C23—32no—
375C23—61no—
376C23—61no—
377C23—61no—
378C23—61no—
379C23—61no—
380C23—61no—
381C23—61no—
382C23—61no—
383C23—61no—
384C23—61no—
385C23—61no—
386C23—61no—
387C23—61no—
388C23—61no—
389C23—61no—
390C23—61no—
391C23—61no—
392C23C23×D311yescharacteristic
393D4—68no—
394D4—124no—
395D4—124no—
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—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—32no—
415C2×C4—32no—
416C2×C4—32no—
417C2×C4—32no—
418C2×C4—68no—
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—124no—
431C2×C4—124no—
432C2×C4—124no—
433C2×C4D3×D412yes—
434C2×C4D3×D412yes—
435C2×C4D3×D412yes—
436C2×C3—81no—
437C2×C3C2×#12111yescharacteristic
438C2×C3C2×#12111yescharacteristic
439C2×C3#53711yescharacteristic
440C2×C3D4211yescharacteristic
441C2×C3#54711yescharacteristic
442C2×C3#54811yescharacteristic
443C2×C3#55311yescharacteristic
444D3—24no—
445D3—42no—
446D3—81no—
447C22—34no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—62no—
456C22—62no—
457C22—62no—
458C22—62no—
459C22—62no—
460C22—62no—
461C22—62no—
462C22—62no—
463C22—62no—
464C22—121no—
465C22—121no—
466C22—121no—
467C22—121no—
468C22—121no—
469C22—121no—
470C22—121no—
471C22—121no—
472C22—121no—
473C22—121no—
474C22—121no—
475C22C2×D3×D411yescharacteristic
476C22C2×D3×D411yescharacteristic
477C22C2×D3×D411yescharacteristic
478C22#100711yescharacteristic
479C22D3×#4111yescharacteristic
480C22D3×#4111yescharacteristic
481C22#100911yescharacteristic
482C4—22no—
483C4—22no—
484C4—22no—
485C4—34no—
486C4—41no—
487C4—41no—
488C4—41no—
489C4—62no—
490C4—121no—
491C4—121no—
492C4—121no—
493C3#241611yescharacteristic, complemented, Sylow
494C2—64no—
495C2—81no—
496C2—122no—
497C2—241no—
498C2D3×#12111yescharacteristic
499C2D3×#12111yescharacteristic
500C2#560911yescharacteristic
501C2#562911yescharacteristic
502C2#563111yescharacteristic
503C2#563311yescharacteristic
504C2#570911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#396C2
hypercenter#396D3
hypocenterC3#2416
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#895C2semidirect
2. C2×#893C2semidirect
3. C2×D3×C4⋊C4C2semidirect
4. C2×#884C2semidirect
5. C2×#884C2semidirect
6. C2×#884C2semidirect
7. C3×#396C2semidirect
8. #4994C2semidirect
9. #4991C2semidirect
10. #4976C2semidirect
11. #4961C2semidirect
12. #4957C2semidirect
13. #4956C2semidirect
14. #4667C2semidirect
15. #4665C2semidirect
65. #396D3semidirect
105. C2×D12D4semidirect
117. C2×C4×D3D4semidirect
137. Dic3⋊C4D4semidirect
352. C2×D3#121semidirect
363. Dic3#121semidirect
493. C3#2416semidirect

Maximal subgroups

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

subgroupindex
C2×#8952
C2×#8932
C2×D3×C4⋊C42
C2×#8842
C3×#3962
#49942
#49912
#49762
#49612
#49572
#49562
#46672
#46652
#24163