Finite Group Databasebeta

← #74913

Subgroups — #74913

Order 384.

682 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#938C211yesmaximal, characteristic, complemented
2C2×#930C211yesmaximal, characteristic, complemented
3C2×#884C211yesmaximal, characteristic, complemented
4C2×#883C211yesmaximal, characteristic, complemented
5C3×#386C211yesmaximal, characteristic, complemented
6#5223C211yesmaximal, characteristic, complemented
7#5210C211yesmaximal, characteristic, complemented
8#4961C211yesmaximal, characteristic, complemented
9#4959C211yesmaximal, characteristic, complemented
10#4959C211yesmaximal, characteristic, complemented
11#4949C211yesmaximal, characteristic, complemented
12#4668C211yesmaximal, characteristic, complemented
13#4667C211yesmaximal, characteristic, complemented
14#4665C211yesmaximal, characteristic, complemented
15#4661C211yesmaximal, characteristic, complemented
16#2671—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C23×C3×C4C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C22×#67C2211yescharacteristic
23C22×D12C2211yescharacteristic
24C22×C4×D3C2211yescharacteristic
25C22×C4×D3C2211yescharacteristic
26C2×C3×C22⋊C4C2211yescharacteristic
27C2×C3×C22⋊C4C2211yescharacteristic
28C2×C3×C22⋊C4C2211yescharacteristic
29C2×#217C2211yescharacteristic
30C2×#217C2211yescharacteristic
31C2×#217C2211yescharacteristic
32C2×#217C2211yescharacteristic
33#938—24no—
34#930—24no—
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×C4⋊Dic3C2211yescharacteristic
43C2×C4⋊Dic3C2211yescharacteristic
44C2×Dic3⋊C4C2211yescharacteristic
45C2×Dic3⋊C4C2211yescharacteristic
46C2×Dic3⋊C4C2211yescharacteristic
47C2×Dic3⋊C4C2211yescharacteristic
48#884—24no—
49#883—24no—
50C3×#95C2211yescharacteristic
51C3×#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C3⋊#95C2211yescharacteristic
55C3⋊#95C2211yescharacteristic
56C2×#123—31no—
57C2×#121—31no—
58C2×#121—31no—
59C2×#121—31no—
60#399—31no—
61#398—31no—
62#394—31no—
63#394—31no—
64#394—31no—
65#392—31no—
66#386—31no—
67#386D311yescharacteristic, complemented
68#385—31no—
69#385—31no—
70#380—31no—
71C24×C3C2311yescharacteristic
72C24×C3C2311yescharacteristic
73C23×D3C2311yescharacteristic
74C23×D3C2311yescharacteristic
75C2×C3×D4—22no—
76C2×C3×D4—22no—
77C2×C3×D4—41no—
78C22×C3×C4—22no—
79C22×C3×C4—41no—
80C22×C3×C4—41no—
81C22×C3×C4C2311yescharacteristic
82C22×C3×C4C2311yescharacteristic
83C22×C3×C4C2311yescharacteristic
84C22×C3×C4C2311yescharacteristic
85C22×C3×C4C2311yescharacteristic
86C2×#67—22no—
87C2×#67—22no—
88C2×#67—22no—
89C2×#67—22no—
90C2×#67—22no—
91C2×#67—22no—
92C2×#67—22no—
93C2×#67—41no—
94C2×#67—41no—
95C2×#67—41no—
96C2×#67—41no—
97C2×#67—41no—
98C22×Dic3C2311yescharacteristic
99C22×Dic3C2311yescharacteristic
100C22×Dic3C2311yescharacteristic
101C22×Dic3C2311yescharacteristic
102C22×Dic3C2311yescharacteristic
103C22×Dic3C2311yescharacteristic
104C2×D12—41no—
105C2×D12—41no—
106C2×D12D414yescomplemented
107C2×C4×D3—22no—
108C2×C4×D3—22no—
109C2×C4×D3—22no—
110C2×C4×D3—22no—
111C2×C4×D3—41no—
112C2×C4×D3—41no—
113C3×C22⋊C4—22no—
114C3×C22⋊C4—22no—
115C3×C22⋊C4—41no—
116#217—22no—
117#217—41no—
118#217—41no—
119#217D414yescomplemented
120(C2×D3)⋊C4—22no—
121(C2×D3)⋊C4—22no—
122(C2×D3)⋊C4—22no—
123(C2×D3)⋊C4—22no—
124(C2×D3)⋊C4—22no—
125(C2×D3)⋊C4—41no—
126C4⋊Dic3—22no—
127C4⋊Dic3—22no—
128C4⋊Dic3—22no—
129Dic3⋊C4—22no—
130Dic3⋊C4—22no—
131Dic3⋊C4—41no—
132Dic3⋊C4—41no—
133C22×D4—31no—
134C22×D4—31no—
135C22×D4—31no—
136C22×D4—31no—
137C22×D4—31no—
138C22×D4C2×D311yescharacteristic
139C23×C4—31no—
140C23×C4—31no—
141C23×C4C2×D311yescharacteristic
142#123—64no—
143#121—64no—
144#121—64no—
145#121—64no—
146C2×C4⋊C4—31no—
147C2×C4⋊C4—31no—
148C2×C4⋊C4—31no—
149C2×C4⋊C4—31no—
150C2×C4⋊C4—31no—
151C2×C4⋊C4—31no—
152C2×C4⋊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⋊C4—31no—
161C2×C22⋊C4—31no—
162C2×C22⋊C4—31no—
163C2×C22⋊C4C2×D311yescharacteristic
164C2×C22⋊C4C2×D311yescharacteristic
165C2×C22⋊C4C2×D311yescharacteristic
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×C3—21no—
180C23×C3—21no—
181C23×C3—21no—
182C23×C3—21no—
183C23×C3—21no—
184C23×C3—21no—
185C23×C3C2×D412yes—
186C23×C3C2411yescharacteristic
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×D3—21no—
198C22×D3—21no—
199C22×D3C2×D412yes—
200C22×D3C2×D412yes—
201C3×D4—44no—
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—44no—
216C2×C3×C4C2×D412yes—
217C2×C3×C4#4112yes—
218#67—44no—
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×Dic3—21no—
236C2×Dic3—21no—
237C2×Dic3—21no—
238C2×Dic3C2×D412yes—
239C2×Dic3C2×D412yes—
240D12—44no—
241C4×D3—44no—
242C4×D3—44no—
243C24—31no—
244C24—31no—
245C24C22×D311yescharacteristic
246C24C22×D311yescharacteristic
247C2×D4—22no—
248C2×D4—22no—
249C2×D4—34no—
250C2×D4—41no—
251C2×D4—62no—
252C2×D4—62no—
253C2×D4—62no—
254C2×D4—62no—
255C2×D4—62no—
256C2×D4—62no—
257C2×D4—62no—
258C2×D4—121no—
259C2×D4—121no—
260C2×D4—121no—
261C2×D4—121no—
262C2×D4—121no—
263C2×D4—121no—
264C2×D4—121no—
265C22×C4—22no—
266C22×C4—31no—
267C22×C4—31no—
268C22×C4—31no—
269C22×C4—31no—
270C22×C4—31no—
271C22×C4—31no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—62no—
275C22×C4—62no—
276C22×C4—62no—
277C22×C4—62no—
278C22×C4—121no—
279C22×C4—121no—
280C22×C4C22×D311yescharacteristic
281C22×C4C22×D311yescharacteristic
282C22×C4C22×D311yescharacteristic
283C22×C4C22×D311yescharacteristic
284C22×C4C22×D311yescharacteristic
285C4⋊C4—62no—
286C4⋊C4—62no—
287C4⋊C4—62no—
288C4⋊C4—62no—
289C4⋊C4—62no—
290C4⋊C4—121no—
291C4⋊C4—121no—
292C22⋊C4—22no—
293C22⋊C4—22no—
294C22⋊C4—34no—
295C22⋊C4—41no—
296C22⋊C4—62no—
297C22⋊C4—62no—
298C22⋊C4—62no—
299C22⋊C4—62no—
300C22⋊C4—62no—
301C22⋊C4—62no—
302C22⋊C4—121no—
303C22⋊C4—121no—
304C22⋊C4—121no—
305C22×C3—22no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—41no—
313C22×C3—41no—
314C22×C3—41no—
315C22×C3—41no—
316C22×C3—41no—
317C22×C3—41no—
318C22×C3—41no—
319C22×C3C22×D411yescharacteristic
320C22×C3C22×D411yescharacteristic
321C22×C3C2×#4111yescharacteristic
322C22×C3H(5,𝔽2)11yescharacteristic
323C22×C3H(5,𝔽2)11yescharacteristic
324C22×C3H(5,𝔽2)11yescharacteristic
325C22×C32−1+411yescharacteristic
326C2×D3—22no—
327C2×D3—22no—
328C2×D3—22no—
329C2×D3—22no—
330C2×D3—22no—
331C2×D3—22no—
332C2×D3—41no—
333C2×D3—41no—
334C2×D3—41no—
335C2×D3—41no—
336C2×D3—41no—
337C2×D3—41no—
338C2×D3—41no—
339C2×D3—41no—
340C3×C4—22no—
341C3×C4—22no—
342C3×C4—41no—
343C3×C4—41no—
344C3×C4—41no—
345Dic3—22no—
346Dic3—22no—
347Dic3—41no—
348Dic3—41no—
349Dic3—41no—
350Dic3—41no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—32no—
365C23—32no—
366C23—61no—
367C23—61no—
368C23—61no—
369C23—61no—
370C23—61no—
371C23—61no—
372C23—61no—
373C23—61no—
374C23—61no—
375C23—61no—
376C23—61no—
377C23—61no—
378C23D3×D412yes—
379C23C23×D311yescharacteristic
380D4—44no—
381D4—124no—
382D4—124no—
383D4—124no—
384D4—124no—
385D4—124no—
386C2×C4—21no—
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—32no—
400C2×C4—32no—
401C2×C4—44no—
402C2×C4—61no—
403C2×C4—61no—
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—61no—
418C2×C4—124no—
419C2×C4—124no—
420C2×C4#23512yes—
421C2×C4D3×D412yes—
422C2×C3—42no—
423C2×C3—81no—
424C2×C3#53411yescharacteristic
425C2×C3#53711yescharacteristic
426C2×C3#54011yescharacteristic
427C2×C3D4211yescharacteristic
428C2×C3#54611yescharacteristic
429C2×C3#54711yescharacteristic
430C2×C3#56211yescharacteristic
431D3—42no—
432D3—42no—
433C22—22no—
434C22—22no—
435C22—22no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—62no—
448C22—62no—
449C22—62no—
450C22—62no—
451C22—62no—
452C22—62no—
453C22—121no—
454C22—121no—
455C22—121no—
456C22—121no—
457C22—121no—
458C22—121no—
459C22—121no—
460C22—121no—
461C22C2×#23511yescharacteristic
462C22C2×D3×D411yescharacteristic
463C22C2×D3×D411yescharacteristic
464C22#100411yescharacteristic
465C22#100411yescharacteristic
466C22#100911yescharacteristic
467C22#101011yescharacteristic
468C4—22no—
469C4—22no—
470C4—41no—
471C4—41no—
472C4—41no—
473C4—62no—
474C4—62no—
475C4—121no—
476C4—121no—
477C4—121no—
478C4—121no—
479C3#267111yescharacteristic, complemented, Sylow
480C2—42no—
481C2—81no—
482C2—122no—
483C2—122no—
484C2#549011yescharacteristic
485C2#555111yescharacteristic
486C2#556211yescharacteristic
487C2#558911yescharacteristic
488C2#559711yescharacteristic
489C2#560911yescharacteristic
490C2#566711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#386C2
hypercenter#386D3
hypocenterC3#2671
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#938C2semidirect
2. C2×#930C2semidirect
3. C2×#884C2semidirect
4. C2×#883C2semidirect
5. C3×#386C2semidirect
6. #5223C2semidirect
7. #5210C2semidirect
8. #4961C2semidirect
9. #4959C2semidirect
10. #4959C2semidirect
11. #4949C2semidirect
12. #4668C2semidirect
13. #4667C2semidirect
14. #4665C2semidirect
15. #4661C2semidirect
67. #386D3semidirect
106. C2×D12D4semidirect
119. #217D4semidirect
479. C3#2671semidirect

Maximal subgroups

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

subgroupindex
C2×#9382
C2×#9302
C2×#8842
C2×#8832
C3×#3862
#52232
#52102
#49612
#49592
#49492
#46682
#46672
#46652
#46612
#26713