Finite Group Databasebeta

← #76671

Subgroups — #76671

Order 384.

832 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#940C211yesmaximal, characteristic, complemented
2C2×#939C211yesmaximal, characteristic, complemented
3C2×#939C211yesmaximal, characteristic, complemented
4C2×#939C211yesmaximal, characteristic, complemented
5C2×#938C211yesmaximal, characteristic, complemented
6C2×#67⋊C4C211yesmaximal, characteristic, complemented
7C3×#392C211yesmaximal, characteristic, complemented
8#5220C211yesmaximal, characteristic, complemented
9#4961C211yesmaximal, characteristic, complemented
10#4960C211yesmaximal, characteristic, complemented
11#4959C211yesmaximal, characteristic, complemented
12#4957C211yesmaximal, characteristic, complemented
13Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
14#4665C211yesmaximal, characteristic, complemented
15#4647C211yesmaximal, characteristic, complemented
16#2428—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C22×C3×D4C2211yescharacteristic
19C22×C3×D4C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C22×#67C2211yescharacteristic
23C22×#67C2211yescharacteristic
24C22×#67C2211yescharacteristic
25C22×#67C2211yescharacteristic
26C23×Dic3C2211yescharacteristic
27C23×Dic3C2211yescharacteristic
28C22×D12C2211yescharacteristic
29C22×C4×D3C2211yescharacteristic
30C2×C3×C22⋊C4C2211yescharacteristic
31C2×C3×C22⋊C4C2211yescharacteristic
32C2×C3×C22⋊C4C2211yescharacteristic
33C2×#217C2211yescharacteristic
34C2×#217C2211yescharacteristic
35C2×#217C2211yescharacteristic
36C2×#217C2211yescharacteristic
37#940—24no—
38#939—24no—
39#939—24no—
40#939—24no—
41#938—24no—
42C2×(C2×D3)⋊C4C2211yescharacteristic
43C2×(C2×D3)⋊C4C2211yescharacteristic
44C2×(C2×D3)⋊C4C2211yescharacteristic
45C2×(C2×D3)⋊C4C2211yescharacteristic
46C2×(C2×D3)⋊C4C2211yescharacteristic
47C2×C4⋊Dic3C2211yescharacteristic
48C2×Dic3⋊C4C2211yescharacteristic
49C2×Dic3⋊C4C2211yescharacteristic
50C2×Dic3⋊C4C2211yescharacteristic
51C2×C4×Dic3C2211yescharacteristic
52C2×C4×Dic3C2211yescharacteristic
53#67⋊C4—24no—
54C3×#95C2211yescharacteristic
55C3⋊#95C2211yescharacteristic
56C3⋊#95C2211yescharacteristic
57C3⋊#95C2211yescharacteristic
58C2×#127—31no—
59C2×#121—31no—
60C2×#121—31no—
61C2×#121—31no—
62C2×#121—31no—
63C2×C4×D4—31no—
64#394—31no—
65#394—31no—
66#392—31no—
67#392D311yescharacteristic, complemented
68#390—31no—
69#389—31no—
70#386—31no—
71#386—31no—
72C4×C22⋊C4—31no—
73C24×C3C2311yescharacteristic
74C24×C3C2311yescharacteristic
75C24×C3C2311yescharacteristic
76C23×D3C2311yescharacteristic
77C23×D3C2311yescharacteristic
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×D4—41no—
86C2×C3×D4—41no—
87C22×C3×C4C2311yescharacteristic
88C22×C3×C4C2311yescharacteristic
89C22×C3×C4C2311yescharacteristic
90C22×C3×C4C2311yescharacteristic
91C2×#67—22no—
92C2×#67—22no—
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—22no—
102C2×#67—22no—
103C2×#67—22no—
104C2×#67—41no—
105C2×#67—41no—
106C2×#67—41no—
107C2×#67—41no—
108C2×#67D414yescomplemented
109C22×Dic3—22no—
110C22×Dic3—22no—
111C22×Dic3—22no—
112C22×Dic3—22no—
113C22×Dic3—22no—
114C22×Dic3—41no—
115C22×Dic3C2311yescharacteristic
116C22×Dic3C2311yescharacteristic
117C22×Dic3C2311yescharacteristic
118C22×Dic3C2311yescharacteristic
119C22×Dic3C2311yescharacteristic
120C22×Dic3C2311yescharacteristic
121C2×D12—22no—
122C2×D12—22no—
123C2×D12—41no—
124C2×C4×D3—22no—
125C2×C4×D3—22no—
126C2×C4×D3—41no—
127C3×C22⋊C4—22no—
128C3×C22⋊C4—22no—
129C3×C22⋊C4—41no—
130#217—22no—
131#217—22no—
132#217—22no—
133#217D414yescomplemented
134(C2×D3)⋊C4—22no—
135(C2×D3)⋊C4—22no—
136(C2×D3)⋊C4—22no—
137(C2×D3)⋊C4—22no—
138(C2×D3)⋊C4—41no—
139C4⋊Dic3—22no—
140Dic3⋊C4—22no—
141Dic3⋊C4—22no—
142Dic3⋊C4D414yescomplemented
143C4×Dic3—22no—
144C4×Dic3—22no—
145C22×D4—31no—
146C22×D4—31no—
147C22×D4—31no—
148C22×D4—31no—
149C22×D4—31no—
150C22×D4—31no—
151C22×D4—31no—
152C22×D4C2×D311yescharacteristic
153C22×D4C2×D311yescharacteristic
154C22×D4C2×D311yescharacteristic
155C23×C4—31no—
156C23×C4—31no—
157C23×C4—31no—
158#127—64no—
159#121—64no—
160#121—64no—
161#121—64no—
162#121—64no—
163C4×D4—64no—
164C2×C4⋊C4—31no—
165C2×C4⋊C4—31no—
166C2×C4⋊C4—31no—
167C2×C4⋊C4—31no—
168C2×C22⋊C4—31no—
169C2×C22⋊C4—31no—
170C2×C22⋊C4—31no—
171C2×C22⋊C4—31no—
172C2×C22⋊C4—31no—
173C2×C22⋊C4—31no—
174C2×C22⋊C4—31no—
175C2×C22⋊C4—31no—
176C2×C22⋊C4—31no—
177C2×C22⋊C4C2×D311yescharacteristic
178C2×C22⋊C4C2×D311yescharacteristic
179C2×C22⋊C4C2×D311yescharacteristic
180C2×C42—31no—
181C2×C42—31no—
182#95—31no—
183#95—31no—
184#95—31no—
185#95C2×D311yescharacteristic
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×C3—21no—
198C23×C3—21no—
199C23×C3—21no—
200C23×C3—21no—
201C23×C3—21no—
202C23×C3—21no—
203C23×C3—21no—
204C23×C3—21no—
205C23×C3C2×D412yes—
206C23×C3C2×D412yes—
207C23×C3C2411yescharacteristic
208C22×D3—21no—
209C22×D3—21no—
210C22×D3—21no—
211C22×D3—21no—
212C22×D3—21no—
213C22×D3—21no—
214C22×D3—21no—
215C22×D3—21no—
216C22×D3—21no—
217C22×D3—21no—
218C22×D3—21no—
219C22×D3—21no—
220C22×D3—21no—
221C22×D3C2×D412yes—
222C3×D4—44no—
223C3×D4—44no—
224C3×D4—44no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4C2×D412yes—
236C2×C3×C4#4112yes—
237#67—28no—
238#67—44no—
239#67—44no—
240#67—44no—
241#67—44no—
242#67—44no—
243C2×Dic3—21no—
244C2×Dic3—21no—
245C2×Dic3—21no—
246C2×Dic3—21no—
247C2×Dic3—21no—
248C2×Dic3—21no—
249C2×Dic3—21no—
250C2×Dic3—21no—
251C2×Dic3—21no—
252C2×Dic3—21no—
253C2×Dic3—21no—
254C2×Dic3—21no—
255C2×Dic3—44no—
256C2×Dic3—44no—
257C2×Dic3C2×D412yes—
258C2×Dic3C2×D412yes—
259C2×Dic3C2×D412yes—
260C2×Dic3C2×D412yes—
261C2×Dic3C2×D412yes—
262C2×Dic3#4112yes—
263D12—44no—
264C4×D3—44no—
265C24—31no—
266C24—31no—
267C24C22×D311yescharacteristic
268C24C22×D311yescharacteristic
269C24C22×D311yescharacteristic
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—22no—
274C2×D4—22no—
275C2×D4—22no—
276C2×D4—34no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—62no—
281C2×D4—62no—
282C2×D4—62no—
283C2×D4—62no—
284C2×D4—62no—
285C2×D4—62no—
286C2×D4—62no—
287C2×D4—62no—
288C2×D4—62no—
289C2×D4—62no—
290C2×D4—62no—
291C2×D4—62no—
292C2×D4—62no—
293C2×D4—62no—
294C2×D4—62no—
295C2×D4—121no—
296C2×D4—121no—
297C2×D4—121no—
298C2×D4—121no—
299C2×D4—121no—
300C22×C4—31no—
301C22×C4—31no—
302C22×C4—31no—
303C22×C4—31no—
304C22×C4—31no—
305C22×C4—31no—
306C22×C4—62no—
307C22×C4—62no—
308C22×C4—62no—
309C22×C4—62no—
310C22×C4—62no—
311C22×C4—62no—
312C22×C4—62no—
313C22×C4—121no—
314C22×C4—121no—
315C22×C4C22×D311yescharacteristic
316C22×C4C22×D311yescharacteristic
317C22×C4C22×D311yescharacteristic
318C22×C4C22×D311yescharacteristic
319C4⋊C4—34no—
320C4⋊C4—62no—
321C4⋊C4—62no—
322C4⋊C4—62no—
323C22⋊C4—22no—
324C22⋊C4—22no—
325C22⋊C4—34no—
326C22⋊C4—41no—
327C22⋊C4—62no—
328C22⋊C4—62no—
329C22⋊C4—62no—
330C22⋊C4—62no—
331C22⋊C4—62no—
332C22⋊C4—62no—
333C22⋊C4—62no—
334C22⋊C4—121no—
335C42—62no—
336C42—62no—
337C22×C3—22no—
338C22×C3—22no—
339C22×C3—22no—
340C22×C3—22no—
341C22×C3—22no—
342C22×C3—22no—
343C22×C3—41no—
344C22×C3—41no—
345C22×C3—41no—
346C22×C3—41no—
347C22×C3—41no—
348C22×C3—41no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—41no—
357C22×C3—41no—
358C22×C3C22×D411yescharacteristic
359C22×C3C22×D411yescharacteristic
360C22×C3C22×D411yescharacteristic
361C22×C3C2×#4111yescharacteristic
362C22×C3C2×#4111yescharacteristic
363C22×C3H(5,𝔽2)11yescharacteristic
364C22×C3H(5,𝔽2)11yescharacteristic
365C2×D3—22no—
366C2×D3—22no—
367C2×D3—22no—
368C2×D3—41no—
369C2×D3—41no—
370C2×D3—41no—
371C2×D3—41no—
372C2×D3—41no—
373C2×D3—41no—
374C2×D3—41no—
375C2×D3—41no—
376C2×D3—41no—
377C2×D3—41no—
378C2×D3—41no—
379C3×C4—22no—
380C3×C4—22no—
381C3×C4—41no—
382C3×C4—41no—
383Dic3—22no—
384Dic3—22no—
385Dic3—22no—
386Dic3—41no—
387Dic3—41no—
388Dic3#12114yescomplemented
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—32no—
409C23—61no—
410C23—61no—
411C23—61no—
412C23—61no—
413C23—61no—
414C23—61no—
415C23—61no—
416C23—61no—
417C23—61no—
418C23—61no—
419C23—61no—
420C23—61no—
421C23—61no—
422C23D3×D412yes—
423C23D3×D412yes—
424C23C23×D311yescharacteristic
425D4—44no—
426D4—44no—
427D4—44no—
428D4—68no—
429D4—124no—
430D4—124no—
431D4—124no—
432D4—124no—
433D4—124no—
434D4—124no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—32no—
446C2×C4—32no—
447C2×C4—32no—
448C2×C4—32no—
449C2×C4—32no—
450C2×C4—32no—
451C2×C4—61no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—61no—
455C2×C4—61no—
456C2×C4—61no—
457C2×C4—61no—
458C2×C4—61no—
459C2×C4—61no—
460C2×C4—61no—
461C2×C4—61no—
462C2×C4—61no—
463C2×C4—124no—
464C2×C4—124no—
465C2×C4—124no—
466C2×C4D3×D412yes—
467C2×C4#23712yes—
468C2×C3—42no—
469C2×C3—42no—
470C2×C3—81no—
471C2×C3C2×#12111yescharacteristic
472C2×C3#53211yescharacteristic
473C2×C3#54011yescharacteristic
474C2×C3D4211yescharacteristic
475C2×C3D4211yescharacteristic
476C2×C3#54611yescharacteristic
477C2×C3#55011yescharacteristic
478D3—42no—
479D3—81no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—22no—
484C22—22no—
485C22—22no—
486C22—41no—
487C22—41no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—62no—
502C22—62no—
503C22—62no—
504C22—121no—
505C22—121no—
506C22—121no—
507C22—121no—
508C22—121no—
509C22—121no—
510C22—121no—
511C22—121no—
512C22—121no—
513C22—121no—
514C22—121no—
515C22C2×D3×D411yescharacteristic
516C22C2×D3×D411yescharacteristic
517C22C2×D3×D411yescharacteristic
518C22C2×#23711yescharacteristic
519C22#100411yescharacteristic
520C22#100411yescharacteristic
521C22D3×#4111yescharacteristic
522C4—22no—
523C4—22no—
524C4—34no—
525C4—41no—
526C4—41no—
527C4—62no—
528C4—62no—
529C4—62no—
530C4—121no—
531C4—121no—
532C3#242811yescharacteristic, complemented, Sylow
533C2—42no—
534C2—42no—
535C2—81no—
536C2—122no—
537C2—241no—
538C2#559011yescharacteristic
539C2#559011yescharacteristic
540C2#559111yescharacteristic
541C2#559611yescharacteristic
542C2D3×#12111yescharacteristic
543C2#561511yescharacteristic
544C2#571811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#392C2
hypercenter#392D3
hypocenterC3#2428
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#940C2semidirect
2. C2×#939C2semidirect
3. C2×#939C2semidirect
4. C2×#939C2semidirect
5. C2×#938C2semidirect
6. C2×#67⋊C4C2semidirect
7. C3×#392C2semidirect
8. #5220C2semidirect
9. #4961C2semidirect
10. #4960C2semidirect
11. #4959C2semidirect
12. #4957C2semidirect
13. Dic3×C22⋊C4C2semidirect
14. #4665C2semidirect
15. #4647C2semidirect
67. #392D3semidirect
108. C2×#67D4semidirect
133. #217D4semidirect
142. Dic3⋊C4D4semidirect
388. Dic3#121semidirect
532. C3#2428semidirect

Maximal subgroups

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

subgroupindex
C2×#9402
C2×#9392
C2×#9382
C2×#67⋊C42
C3×#3922
#52202
#49612
#49602
#49592
#49572
Dic3×C22⋊C42
#46652
#46472
#24283