Finite Group Databasebeta

← #75882

Subgroups — #75882

Order 384.

724 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#895C211yesmaximal, characteristic, complemented
2C2×#884C211yesmaximal, characteristic, complemented
3C2×#884C211yesmaximal, characteristic, complemented
4C2×C4×D12C211yesmaximal, characteristic, complemented
5C3×#388C211yesmaximal, characteristic, complemented
6#4982C211yesmaximal, characteristic, complemented
7#4961C211yesmaximal, characteristic, complemented
8#4960C211yesmaximal, characteristic, complemented
9#4956C211yesmaximal, characteristic, complemented
10#4956C211yesmaximal, characteristic, complemented
11#4940C211yesmaximal, characteristic, complemented
12#4675C211yesmaximal, characteristic, complemented
13#4665C211yesmaximal, characteristic, complemented
14#4665C211yesmaximal, characteristic, complemented
15D3×#95C211yesmaximal, characteristic, complemented
16#2543—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×C22⋊C4C2211yescharacteristic
29C2×C3×C22⋊C4C2211yescharacteristic
30C2×C3×C22⋊C4C2211yescharacteristic
31C2×C3×C42C2211yescharacteristic
32C2×#217C2211yescharacteristic
33C2×(C2×D3)⋊C4C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
42C2×Dic3⋊C4C2211yescharacteristic
43C2×Dic3⋊C4C2211yescharacteristic
44#895—24no—
45#884—24no—
46#884—24no—
47C4×D12—24no—
48C3×#95C2211yescharacteristic
49C3×#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C3⋊#95C2211yescharacteristic
55C3⋊#95C2211yescharacteristic
56C2×#121—31no—
57C2×#121—31no—
58C2×#121—31no—
59C2×C4×D4—31no—
60#398—31no—
61#397—31no—
62#394—31no—
63#392—31no—
64#388—31no—
65#388D311yescharacteristic, complemented
66#386—31no—
67#386—31no—
68#386—31no—
69#386—31no—
70C2×#95—31no—
71C24×C3C2311yescharacteristic
72C23×D3C2311yescharacteristic
73C23×D3C2311yescharacteristic
74C23×D3C2311yescharacteristic
75C22×C3×C4C2311yescharacteristic
76C22×C3×C4C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C22×C3×C4C2311yescharacteristic
81C2×#67—22no—
82C2×#67—22no—
83C2×#67—22no—
84C2×#67—22no—
85C2×#67—22no—
86C2×#67—22no—
87C2×#67—41no—
88C2×#67—41no—
89C2×#67—41no—
90C22×Dic3C2311yescharacteristic
91C22×Dic3C2311yescharacteristic
92C22×Dic3C2311yescharacteristic
93C22×Dic3C2311yescharacteristic
94C22×Dic3C2311yescharacteristic
95C2×D12—22no—
96C2×D12—22no—
97C2×D12—22no—
98C2×D12—22no—
99C2×D12—22no—
100C2×D12—22no—
101C2×D12—22no—
102C2×D12—41no—
103C2×D12D414yescomplemented
104C2×C4×D3—22no—
105C2×C4×D3—22no—
106C2×C4×D3—22no—
107C2×C4×D3—22no—
108C2×C4×D3—22no—
109C2×C4×D3—41no—
110C2×C4×D3—41no—
111C2×C4×D3—41no—
112C2×C4×D3—41no—
113C2×C4×D3—41no—
114C2×C4×D3—41no—
115C2×C4×D3D414yescomplemented
116C3×C4⋊C4—22no—
117C3×C22⋊C4—22no—
118C3×C22⋊C4—22no—
119C3×C22⋊C4—22no—
120C3×C42—22no—
121#217—41no—
122(C2×D3)⋊C4—22no—
123(C2×D3)⋊C4—22no—
124(C2×D3)⋊C4—22no—
125(C2×D3)⋊C4—22no—
126(C2×D3)⋊C4—22no—
127(C2×D3)⋊C4—22no—
128(C2×D3)⋊C4—22no—
129(C2×D3)⋊C4—41no—
130C4⋊Dic3—22no—
131Dic3⋊C4—22no—
132Dic3⋊C4—22no—
133C22×D4—31no—
134C22×D4—31no—
135C22×D4—31no—
136C22×D4—31no—
137C22×D4—31no—
138C22×D4—31no—
139C23×C4—31no—
140C23×C4—31no—
141C23×C4—31no—
142C23×C4—31no—
143#121—64no—
144#121—64no—
145#121—64no—
146C4×D4—64no—
147C2×C4⋊C4—31no—
148C2×C4⋊C4—31no—
149C2×C4⋊C4—31no—
150C2×C4⋊C4C2×D311yescharacteristic
151C2×C22⋊C4—31no—
152C2×C22⋊C4—31no—
153C2×C22⋊C4—31no—
154C2×C22⋊C4—31no—
155C2×C22⋊C4—31no—
156C2×C22⋊C4—31no—
157C2×C22⋊C4—31no—
158C2×C22⋊C4—31no—
159C2×C22⋊C4—31no—
160C2×C22⋊C4C2×D311yescharacteristic
161C2×C22⋊C4C2×D311yescharacteristic
162C2×C22⋊C4C2×D311yescharacteristic
163C2×C42C2×D311yescharacteristic
164#95—31no—
165#95—31no—
166#95—31no—
167#95—31no—
168#95—31no—
169#95—31no—
170#95C2×D311yescharacteristic
171#95C2×D311yescharacteristic
172C23×C3—21no—
173C23×C3—21no—
174C23×C3—21no—
175C23×C3—21no—
176C23×C3—21no—
177C23×C3—21no—
178C23×C3—21no—
179C23×C3C2411yescharacteristic
180C22×D3—21no—
181C22×D3—21no—
182C22×D3—21no—
183C22×D3—21no—
184C22×D3—21no—
185C22×D3—21no—
186C22×D3—21no—
187C22×D3—21no—
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×D3C2×D412yes—
198C22×D3C2×D412yes—
199C22×D3C2×D412yes—
200C22×D3#4112yes—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
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×C4C2×D412yes—
217C2×C3×C4C2×D412yes—
218C2×C3×C4#4112yes—
219#67—44no—
220#67—44no—
221#67—44no—
222C2×Dic3—21no—
223C2×Dic3—21no—
224C2×Dic3—21no—
225C2×Dic3—21no—
226C2×Dic3—21no—
227C2×Dic3—21no—
228C2×Dic3—21no—
229C2×Dic3—21no—
230C2×Dic3—21no—
231C2×Dic3—21no—
232C2×Dic3—21no—
233C2×Dic3—21no—
234C2×Dic3—21no—
235C2×Dic3C2×D412yes—
236C2×Dic3#4112yes—
237D12—28no—
238D12—44no—
239D12—44no—
240C4×D3—44no—
241C4×D3—44no—
242C4×D3—44no—
243C4×D3—44no—
244C24—31no—
245C24—31no—
246C24—31no—
247C24C22×D311yescharacteristic
248C2×D4—34no—
249C2×D4—62no—
250C2×D4—62no—
251C2×D4—62no—
252C2×D4—62no—
253C2×D4—62no—
254C2×D4—62no—
255C2×D4—62no—
256C2×D4—62no—
257C2×D4—62no—
258C2×D4—62no—
259C2×D4—62no—
260C2×D4—62no—
261C2×D4—62no—
262C2×D4—121no—
263C2×D4—121no—
264C2×D4—121no—
265C2×D4—121no—
266C22×C4—31no—
267C22×C4—31no—
268C22×C4—34no—
269C22×C4—31no—
270C22×C4—31no—
271C22×C4—31no—
272C22×C4—62no—
273C22×C4—62no—
274C22×C4—62no—
275C22×C4—62no—
276C22×C4—62no—
277C22×C4—121no—
278C22×C4—121no—
279C22×C4—121no—
280C22×C4—121no—
281C22×C4—121no—
282C22×C4—121no—
283C22×C4C22×D311yescharacteristic
284C22×C4C22×D311yescharacteristic
285C22×C4C22×D311yescharacteristic
286C22×C4C22×D311yescharacteristic
287C22×C4C22×D311yescharacteristic
288C22×C4C22×D311yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—62no—
291C4⋊C4—62no—
292C4⋊C4—62no—
293C22⋊C4—22no—
294C22⋊C4—22no—
295C22⋊C4—22no—
296C22⋊C4—62no—
297C22⋊C4—62no—
298C22⋊C4—62no—
299C22⋊C4—62no—
300C22⋊C4—62no—
301C22⋊C4—62no—
302C22⋊C4—62no—
303C22⋊C4—121no—
304C22⋊C4—121no—
305C42—22no—
306C22×C3—41no—
307C22×C3—41no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—41no—
313C22×C3C22×D411yescharacteristic
314C22×C3C22×D411yescharacteristic
315C22×C3C2×#4111yescharacteristic
316C22×C3C2×#4111yescharacteristic
317C22×C3C2×#4111yescharacteristic
318C22×C3H(5,𝔽2)11yescharacteristic
319C22×C3H(5,𝔽2)11yescharacteristic
320C2×D3—22no—
321C2×D3—22no—
322C2×D3—22no—
323C2×D3—22no—
324C2×D3—22no—
325C2×D3—22no—
326C2×D3—22no—
327C2×D3—22no—
328C2×D3—22no—
329C2×D3—41no—
330C2×D3—41no—
331C2×D3—41no—
332C2×D3—41no—
333C2×D3—41no—
334C2×D3—41no—
335C2×D3—41no—
336C2×D3—41no—
337C2×D3—41no—
338C2×D3—41no—
339C2×D3—41no—
340C2×D3#12114yes—
341C3×C4—22no—
342C3×C4—22no—
343C3×C4—22no—
344C3×C4—41no—
345C3×C4—41no—
346C3×C4—41no—
347Dic3—22no—
348Dic3—22no—
349Dic3—41no—
350Dic3—41no—
351Dic3—41no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—32no—
360C23—32no—
361C23—32no—
362C23—32no—
363C23—61no—
364C23—61no—
365C23—61no—
366C23—61no—
367C23—61no—
368C23—61no—
369C23—61no—
370C23—61no—
371C23—61no—
372C23—61no—
373C23—61no—
374C23—61no—
375C23—61no—
376C23—61no—
377C23—61no—
378C23—61no—
379C23—61no—
380C23C23×D311yescharacteristic
381D4—68no—
382D4—124no—
383D4—124no—
384D4—124no—
385D4—124no—
386D4—124no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—32no—
403C2×C4—32no—
404C2×C4—61no—
405C2×C4—61no—
406C2×C4—61no—
407C2×C4—61no—
408C2×C4—61no—
409C2×C4—61no—
410C2×C4—61no—
411C2×C4—61no—
412C2×C4—61no—
413C2×C4—61no—
414C2×C4—61no—
415C2×C4—61no—
416C2×C4—61no—
417C2×C4—124no—
418C2×C4—124no—
419C2×C4—124no—
420C2×C4—124no—
421C2×C4#23512yes—
422C2×C4D3×D412yes—
423C2×C4D3×D412yes—
424C2×C3—81no—
425C2×C3C2×#12111yescharacteristic
426C2×C3#53211yescharacteristic
427C2×C3#53411yescharacteristic
428C2×C3#54611yescharacteristic
429C2×C3#54611yescharacteristic
430C2×C3#55311yescharacteristic
431C2×C3#55311yescharacteristic
432D3—24no—
433D3—42no—
434D3—81no—
435C22—34no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—62no—
444C22—62no—
445C22—62no—
446C22—62no—
447C22—62no—
448C22—62no—
449C22—62no—
450C22—62no—
451C22—62no—
452C22—121no—
453C22—121no—
454C22—121no—
455C22—121no—
456C22—121no—
457C22—121no—
458C22—121no—
459C22—121no—
460C22—121no—
461C22—121no—
462C22—121no—
463C22C2×#23511yescharacteristic
464C22C2×D3×D411yescharacteristic
465C22C2×D3×D411yescharacteristic
466C22D3×#4111yescharacteristic
467C22D3×#4111yescharacteristic
468C22#100911yescharacteristic
469C22#100911yescharacteristic
470C4—22no—
471C4—22no—
472C4—22no—
473C4—41no—
474C4—41no—
475C4—41no—
476C4—62no—
477C4—62no—
478C4—121no—
479C4—121no—
480C4—121no—
481C3#254311yescharacteristic, complemented, Sylow
482C2—64no—
483C2—81no—
484C2—122no—
485C2—241no—
486C2#553011yescharacteristic
487C2#554811yescharacteristic
488C2#555011yescharacteristic
489C2D3×#12111yescharacteristic
490C2#565311yescharacteristic
491C2#567611yescharacteristic
492C2#570911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#388C2
hypercenter#388D3
hypocenterC3#2543
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#895C2semidirect
2. C2×#884C2semidirect
3. C2×#884C2semidirect
4. C2×C4×D12C2semidirect
5. C3×#388C2semidirect
6. #4982C2semidirect
7. #4961C2semidirect
8. #4960C2semidirect
9. #4956C2semidirect
10. #4956C2semidirect
11. #4940C2semidirect
12. #4675C2semidirect
13. #4665C2semidirect
14. #4665C2semidirect
15. D3×#95C2semidirect
65. #388D3semidirect
103. C2×D12D4semidirect
115. C2×C4×D3D4semidirect
481. C3#2543semidirect

Maximal subgroups

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

subgroupindex
C2×#8952
C2×#8842
C2×C4×D122
C3×#3882
#49822
#49612
#49602
#49562
#49402
#46752
#46652
D3×#952
#25433