Finite Group Databasebeta

← #74698

Subgroups — #74698

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×#930C211yesmaximal, characteristic, complemented
3C2×C4×#67C211yesmaximal, characteristic, complemented
4C2×#884C211yesmaximal, characteristic, complemented
5C2×#884C211yesmaximal, characteristic, complemented
6C2×#884C211yesmaximal, characteristic, complemented
7C3×#386C211yesmaximal, characteristic, complemented
8#5223C211yesmaximal, characteristic, complemented
9#4961C211yesmaximal, characteristic, complemented
10#4959C211yesmaximal, characteristic, complemented
11#4957C211yesmaximal, characteristic, complemented
12#4671C211yesmaximal, characteristic, complemented
13#4666C211yesmaximal, characteristic, complemented
14#4665C211yesmaximal, characteristic, complemented
15#4647C211yesmaximal, characteristic, complemented
16#2428—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C23×C3×C4C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C22×#67C2211yescharacteristic
23C22×#67C2211yescharacteristic
24C22×#67C2211yescharacteristic
25C22×D12C2211yescharacteristic
26C22×D12C2211yescharacteristic
27C22×D12C2211yescharacteristic
28C22×C4×D3C2211yescharacteristic
29C22×C4×D3C2211yescharacteristic
30C2×C3×C22⋊C4C2211yescharacteristic
31C2×C3×C22⋊C4C2211yescharacteristic
32C2×C3×C22⋊C4C2211yescharacteristic
33C2×#217C2211yescharacteristic
34C2×#217C2211yescharacteristic
35#940—24no—
36#930—24no—
37C4×#67—24no—
38C2×(C2×D3)⋊C4C2211yescharacteristic
39C2×(C2×D3)⋊C4C2211yescharacteristic
40C2×(C2×D3)⋊C4C2211yescharacteristic
41C2×(C2×D3)⋊C4C2211yescharacteristic
42C2×(C2×D3)⋊C4C2211yescharacteristic
43C2×(C2×D3)⋊C4C2211yescharacteristic
44C2×(C2×D3)⋊C4C2211yescharacteristic
45C2×C4⋊Dic3C2211yescharacteristic
46C2×Dic3⋊C4C2211yescharacteristic
47C2×Dic3⋊C4C2211yescharacteristic
48C2×Dic3⋊C4C2211yescharacteristic
49C2×C4×Dic3C2211yescharacteristic
50C2×C4×Dic3C2211yescharacteristic
51#884—24no—
52#884—24no—
53#884—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#392—31no—
68#390—31no—
69#389—31no—
70#386—31no—
71#386D311yescharacteristic, complemented
72C4×C22⋊C4—31no—
73C24×C3C2311yescharacteristic
74C24×C3C2311yescharacteristic
75C23×D3C2311yescharacteristic
76C23×D3C2311yescharacteristic
77C23×D3C2311yescharacteristic
78C2×C3×D4—22no—
79C2×C3×D4—22no—
80C2×C3×D4—41no—
81C22×C3×C4—22no—
82C22×C3×C4—22no—
83C22×C3×C4—41no—
84C22×C3×C4C2311yescharacteristic
85C22×C3×C4C2311yescharacteristic
86C22×C3×C4C2311yescharacteristic
87C22×C3×C4C2311yescharacteristic
88C22×C3×C4C2311yescharacteristic
89C2×#67—22no—
90C2×#67—22no—
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—41no—
103C2×#67—41no—
104C2×#67—41no—
105C2×#67—41no—
106C2×#67D414yescomplemented
107C22×Dic3C2311yescharacteristic
108C22×Dic3C2311yescharacteristic
109C22×Dic3C2311yescharacteristic
110C22×Dic3C2311yescharacteristic
111C22×Dic3C2311yescharacteristic
112C2×D12—22no—
113C2×D12—22no—
114C2×D12—22no—
115C2×D12—22no—
116C2×D12—22no—
117C2×D12—22no—
118C2×D12—41no—
119C2×D12—41no—
120C2×D12—41no—
121C2×C4×D3—22no—
122C2×C4×D3—22no—
123C2×C4×D3—22no—
124C2×C4×D3—22no—
125C2×C4×D3—22no—
126C2×C4×D3—41no—
127C3×C22⋊C4—22no—
128C3×C22⋊C4—22no—
129C3×C22⋊C4—22no—
130#217—22no—
131#217—41no—
132(C2×D3)⋊C4—22no—
133(C2×D3)⋊C4—22no—
134(C2×D3)⋊C4—22no—
135(C2×D3)⋊C4—22no—
136(C2×D3)⋊C4—22no—
137(C2×D3)⋊C4—41no—
138(C2×D3)⋊C4D414yescomplemented
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×D4—31no—
153C22×D4—31no—
154C22×D4C2×D311yescharacteristic
155C23×C4—31no—
156C23×C4—31no—
157C23×C4C2×D311yescharacteristic
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#95C2×D311yescharacteristic
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×C3C2×D412yes—
200C23×C3C2411yescharacteristic
201C22×D3—21no—
202C22×D3—21no—
203C22×D3—21no—
204C22×D3—21no—
205C22×D3—21no—
206C22×D3—21no—
207C22×D3—21no—
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×D3C2×D412yes—
221C22×D3C2×D412yes—
222C3×D4—44no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
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×C4—44no—
236C2×C3×C4C2×D412yes—
237C2×C3×C4C2×D412yes—
238C2×C3×C4#4112yes—
239#67—28no—
240#67—44no—
241#67—44no—
242#67—44no—
243#67—44no—
244#67—44no—
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×Dic3C2×D412yes—
256C2×Dic3C2×D412yes—
257C2×Dic3C2×D412yes—
258C2×Dic3C2×D412yes—
259C2×Dic3#4112yes—
260D12—44no—
261D12—44no—
262D12—44no—
263C4×D3—44no—
264C4×D3—44no—
265C24—31no—
266C24—31no—
267C24—31no—
268C24C22×D311yescharacteristic
269C24C22×D311yescharacteristic
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—34no—
273C2×D4—41no—
274C2×D4—62no—
275C2×D4—62no—
276C2×D4—62no—
277C2×D4—62no—
278C2×D4—62no—
279C2×D4—62no—
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—121no—
294C2×D4—121no—
295C2×D4—121no—
296C2×D4—121no—
297C2×D4—121no—
298C2×D4—121no—
299C2×D4—121no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—31no—
303C22×C4—31no—
304C22×C4—31no—
305C22×C4—31no—
306C22×C4—31no—
307C22×C4—41no—
308C22×C4—62no—
309C22×C4—62no—
310C22×C4—62no—
311C22×C4—62no—
312C22×C4—62no—
313C22×C4—121no—
314C22×C4C22×D311yescharacteristic
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—22no—
326C22⋊C4—34no—
327C22⋊C4—62no—
328C22⋊C4—62no—
329C22⋊C4—62no—
330C22⋊C4—62no—
331C22⋊C4—62no—
332C22⋊C4—62no—
333C22⋊C4—121no—
334C22⋊C4—121no—
335C42—62no—
336C42—62no—
337C22×C3—22no—
338C22×C3—22no—
339C22×C3—22no—
340C22×C3—41no—
341C22×C3—41no—
342C22×C3—41no—
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×C3C22×D411yescharacteristic
352C22×C3C22×D411yescharacteristic
353C22×C3C22×D411yescharacteristic
354C22×C3C2×#4111yescharacteristic
355C22×C3C2×#4111yescharacteristic
356C22×C3H(5,𝔽2)11yescharacteristic
357C22×C3H(5,𝔽2)11yescharacteristic
358C2×D3—22no—
359C2×D3—22no—
360C2×D3—22no—
361C2×D3—22no—
362C2×D3—22no—
363C2×D3—22no—
364C2×D3—41no—
365C2×D3—41no—
366C2×D3—41no—
367C2×D3—41no—
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—22no—
382C3×C4—41no—
383C3×C4—41no—
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—32no—
403C23—32no—
404C23—61no—
405C23—61no—
406C23—61no—
407C23—61no—
408C23—61no—
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—
422C23—61no—
423C23D3×D412yes—
424C23C23×D311yescharacteristic
425D4—44no—
426D4—68no—
427D4—124no—
428D4—124no—
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—21no—
446C2×C4—21no—
447C2×C4—32no—
448C2×C4—32no—
449C2×C4—32no—
450C2×C4—32no—
451C2×C4—32no—
452C2×C4—44no—
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#23512yes—
466C2×C4D3×D412yes—
467C2×C4D3×D412yes—
468C2×C3—42no—
469C2×C3—81no—
470C2×C3C2×#12111yescharacteristic
471C2×C3#53211yescharacteristic
472C2×C3#54011yescharacteristic
473C2×C3D4211yescharacteristic
474C2×C3D4211yescharacteristic
475C2×C3#54611yescharacteristic
476C2×C3#55011yescharacteristic
477D3—42no—
478D3—42no—
479D3—81no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—62no—
495C22—62no—
496C22—62no—
497C22—62no—
498C22—62no—
499C22—62no—
500C22—121no—
501C22—121no—
502C22—121no—
503C22—121no—
504C22—121no—
505C22—121no—
506C22—121no—
507C22—121no—
508C22—121no—
509C22—121no—
510C22—121no—
511C22—121no—
512C22—121no—
513C22—121no—
514C22—121no—
515C22C2×#23511yescharacteristic
516C22C2×D3×D411yescharacteristic
517C22C2×D3×D411yescharacteristic
518C22C2×D3×D411yescharacteristic
519C22#100411yescharacteristic
520C22D3×#4111yescharacteristic
521C22#100911yescharacteristic
522C4—22no—
523C4—22no—
524C4—22no—
525C4—34no—
526C4—41no—
527C4—41no—
528C4—62no—
529C4—62no—
530C4—121no—
531C4—121no—
532C3#242811yescharacteristic, complemented, Sylow
533C2—42no—
534C2—81no—
535C2—122no—
536C2—122no—
537C2—241no—
538C2#549011yescharacteristic
539C2#554811yescharacteristic
540C2#555311yescharacteristic
541C2#559011yescharacteristic
542C2D3×#12111yescharacteristic
543C2#560911yescharacteristic
544C2#566311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#386C2
hypercenter#386D3
hypocenterC3#2428
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#940C2semidirect
2. C2×#930C2semidirect
3. C2×C4×#67C2semidirect
4. C2×#884C2semidirect
5. C2×#884C2semidirect
6. C2×#884C2semidirect
7. C3×#386C2semidirect
8. #5223C2semidirect
9. #4961C2semidirect
10. #4959C2semidirect
11. #4957C2semidirect
12. #4671C2semidirect
13. #4666C2semidirect
14. #4665C2semidirect
15. #4647C2semidirect
71. #386D3semidirect
106. C2×#67D4semidirect
138. (C2×D3)⋊C4D4semidirect
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×#9302
C2×C4×#672
C2×#8842
C3×#3862
#52232
#49612
#49592
#49572
#46712
#46662
#46652
#46472
#24283