Finite Group Databasebeta

← #74509

Subgroups — #74509

Order 384.

676 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×#930C211yesmaximal, characteristic, complemented
2C2×#897C211yesmaximal, characteristic, complemented
3C2×#885C211yesmaximal, characteristic, complemented
4C2×#884C211yesmaximal, characteristic, complemented
5C3×#385C211yesmaximal, characteristic, complemented
6#5213C211yesmaximal, characteristic, complemented
7#4994C211yesmaximal, characteristic, complemented
8#4991C211yesmaximal, characteristic, complemented
9#4988C211yesmaximal, characteristic, complemented
10#4961C211yesmaximal, characteristic, complemented
11#4960C211yesmaximal, characteristic, complemented
12#4673C211yesmaximal, characteristic, complemented
13#4671C211yesmaximal, characteristic, complemented
14#4665C211yesmaximal, characteristic, complemented
15#4653C211yesmaximal, characteristic, complemented
16#2676—31nomaximal, Sylow
17C23×C3×C4C2211yescharacteristic
18C22×#67C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×D12C2211yescharacteristic
22C22×D12C2211yescharacteristic
23C22×D12C2211yescharacteristic
24C22×C4×D3C2211yescharacteristic
25C22×Dic6C2211yescharacteristic
26C2×C3×C4⋊C4C2211yescharacteristic
27C2×C3×C4⋊C4C2211yescharacteristic
28C2×C3×C22⋊C4C2211yescharacteristic
29C2×C3×C22⋊C4C2211yescharacteristic
30C2×#217C2211yescharacteristic
31#930—24no—
32C2×(C2×D3)⋊C4C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
42C2×(C2×D3)⋊C4C2211yescharacteristic
43C2×C4⋊Dic3C2211yescharacteristic
44C2×C4⋊Dic3C2211yescharacteristic
45C2×Dic3⋊C4C2211yescharacteristic
46C2×C4×Dic3C2211yescharacteristic
47#897—24no—
48#885—24no—
49#884—24no—
50C3×#95C2211yescharacteristic
51C3×#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C3⋊#95C2211yescharacteristic
55C3⋊#95C2211yescharacteristic
56C2×#124—31no—
57C2×C22⋊Q8—31no—
58C2×#121—31no—
59C2×#121—31no—
60#396—31no—
61#394—31no—
62#394—31no—
63#393—31no—
64#392—31no—
65#392—31no—
66#390—31no—
67#387—31no—
68#386—31no—
69#386—31no—
70#385D311yescharacteristic, complemented
71C24×C3C2311yescharacteristic
72C23×D3C2311yescharacteristic
73C23×D3C2311yescharacteristic
74C23×D3C2311yescharacteristic
75C22×C3×C4—22no—
76C22×C3×C4—41no—
77C22×C3×C4—41no—
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C22×C3×C4C2311yescharacteristic
81C22×C3×C4C2311yescharacteristic
82C22×C3×C4C2311yescharacteristic
83C22×C3×C4C2311yescharacteristic
84C2×#67—22no—
85C2×#67—22no—
86C2×#67—22no—
87C2×#67—22no—
88C2×#67—22no—
89C2×#67—22no—
90C2×#67—41no—
91C2×#67—41no—
92C2×#67—41no—
93C22×Dic3C2311yescharacteristic
94C22×Dic3C2311yescharacteristic
95C22×Dic3C2311yescharacteristic
96C22×Dic3C2311yescharacteristic
97C22×Dic3C2311yescharacteristic
98C2×D12—22no—
99C2×D12—22no—
100C2×D12—22no—
101C2×D12—22no—
102C2×D12—41no—
103C2×D12—41no—
104C2×D12—41no—
105C2×D12—41no—
106C2×D12—41no—
107C2×C4×D3—22no—
108C2×C4×D3—22no—
109C2×C4×D3—41no—
110C2×Dic6—22no—
111C2×Dic6—22no—
112C2×Dic6—41no—
113C3×C4⋊C4—22no—
114C3×C4⋊C4—41no—
115C3×C22⋊C4—41no—
116C3×C22⋊C4D414yescomplemented
117#217—22no—
118(C2×D3)⋊C4—22no—
119(C2×D3)⋊C4—22no—
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—
126(C2×D3)⋊C4—41no—
127(C2×D3)⋊C4—41no—
128(C2×D3)⋊C4—41no—
129C4⋊Dic3—22no—
130C4⋊Dic3D414yescomplemented
131Dic3⋊C4—22no—
132C4×Dic3—22no—
133C22×Q8—31no—
134C22×D4—31no—
135C22×D4—31no—
136C22×D4—31no—
137C22×D4—31no—
138C22×D4—31no—
139C22×D4—31no—
140C23×C4—31no—
141C23×C4C2×D311yescharacteristic
142#124—64no—
143C22⋊Q8—64no—
144#121—64no—
145#121—64no—
146C2×C4⋊C4—31no—
147C2×C4⋊C4—31no—
148C2×C4⋊C4—31no—
149C2×C4⋊C4C2×D311yescharacteristic
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⋊C4—31no—
161C2×C22⋊C4—31no—
162C2×C22⋊C4—31no—
163C2×C22⋊C4C2×D311yescharacteristic
164C2×C22⋊C4C2×D311yescharacteristic
165C2×C42—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×C3C2×D412yes—
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×D3—21no—
198C22×D3—21no—
199C22×D3—21no—
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×C4—44no—
217C2×C3×C4C2×D412yes—
218C2×C3×C4C2×D412yes—
219C2×C3×C4C2×D412yes—
220#67—44no—
221#67—44no—
222#67—44no—
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×Dic3C2×D412yes—
237C2×Dic3C2×D412yes—
238D12—44no—
239D12—44no—
240D12—44no—
241C4×D3—44no—
242Dic6—44no—
243C24—31no—
244C24—31no—
245C24—31no—
246C24C22×D311yescharacteristic
247C2×Q8—62no—
248C2×Q8—62no—
249C2×Q8—121no—
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—121no—
261C2×D4—121no—
262C2×D4—121no—
263C2×D4—121no—
264C2×D4—121no—
265C2×D4—121no—
266C2×D4—121no—
267C2×D4—121no—
268C22×C4—22no—
269C22×C4—31no—
270C22×C4—31no—
271C22×C4—31no—
272C22×C4—31no—
273C22×C4—31no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—62no—
277C22×C4—62no—
278C22×C4—121no—
279C22×C4C22×D311yescharacteristic
280C22×C4C22×D311yescharacteristic
281C22×C4C22×D311yescharacteristic
282C22×C4C22×D311yescharacteristic
283C22×C4C22×D311yescharacteristic
284C22×C4C22×D311yescharacteristic
285C4⋊C4—22no—
286C4⋊C4—34no—
287C4⋊C4—41no—
288C4⋊C4—62no—
289C4⋊C4—62no—
290C22⋊C4—41no—
291C22⋊C4—62no—
292C22⋊C4—62no—
293C22⋊C4—62no—
294C22⋊C4—62no—
295C22⋊C4—62no—
296C22⋊C4—62no—
297C22⋊C4—62no—
298C22⋊C4—62no—
299C22⋊C4—121no—
300C22⋊C4—121no—
301C22⋊C4—121no—
302C22⋊C4—121no—
303C22⋊C4D1214yescomplemented
304C42—62no—
305C22×C3—22no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3C22×D411yescharacteristic
313C22×C3C22×D411yescharacteristic
314C22×C3C2×#4111yescharacteristic
315C22×C3H(5,𝔽2)11yescharacteristic
316C22×C3H(5,𝔽2)11yescharacteristic
317C22×C3H(5,𝔽2)11yescharacteristic
318C22×C32−1+411yescharacteristic
319C2×D3—22no—
320C2×D3—22no—
321C2×D3—22no—
322C2×D3—41no—
323C2×D3—41no—
324C2×D3—41no—
325C2×D3—41no—
326C2×D3—41no—
327C2×D3—41no—
328C2×D3—41no—
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—
340C3×C4—22no—
341C3×C4—22no—
342C3×C4—22no—
343C3×C4—41no—
344C3×C4—41no—
345C3×C4—41no—
346Dic3—22no—
347Dic3—22no—
348Dic3—41no—
349Dic3—41no—
350Dic3—41no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—32no—
358C23—61no—
359C23—61no—
360C23—61no—
361C23—61no—
362C23—61no—
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—
378C23C2×D1212yes—
379C23C23×D311yescharacteristic
380Q8—124no—
381D4—124no—
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—44no—
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×C4C2×D1212yes—
420C2×C4C2×D1212yes—
421C2×C4D3×D412yes—
422C2×C3—42no—
423C2×C3#53511yescharacteristic
424C2×C3#53711yescharacteristic
425C2×C3#53811yescharacteristic
426C2×C3D4211yescharacteristic
427C2×C3#54611yescharacteristic
428C2×C3#54811yescharacteristic
429C2×C3#56211yescharacteristic
430D3—42no—
431D3—81no—
432D3—81no—
433C22—22no—
434C22—22no—
435C22—22no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—62no—
441C22—62no—
442C22—62no—
443C22—121no—
444C22—121no—
445C22—121no—
446C22—121no—
447C22—121no—
448C22—121no—
449C22—121no—
450C22—121no—
451C22—121no—
452C22—121no—
453C22—121no—
454C22—121no—
455C22—121no—
456C22—121no—
457C22—121no—
458C22—121no—
459C22—121no—
460C22—121no—
461C22C22×D1211yescharacteristic
462C22C2×D3×D411yescharacteristic
463C22#100411yescharacteristic
464C22#100411yescharacteristic
465C22#100711yescharacteristic
466C22D3×#4111yescharacteristic
467C22#100911yescharacteristic
468C4—22no—
469C4—22no—
470C4—22no—
471C4—41no—
472C4—41no—
473C4—41no—
474C4—62no—
475C4—62no—
476C4—121no—
477C4—121no—
478C4—121no—
479C3#267611yescharacteristic, complemented, Sylow
480C2—42no—
481C2—122no—
482C2—241no—
483C2—241no—
484C2#551011yescharacteristic
485C2D4×D1211yescharacteristic
486C2#555411yescharacteristic
487C2#559211yescharacteristic
488C2#563311yescharacteristic
489C2#564711yescharacteristic
490C2#565711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#385C2
hypercenter#385D3
hypocenterC3#2676
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#930C2semidirect
2. C2×#897C2semidirect
3. C2×#885C2semidirect
4. C2×#884C2semidirect
5. C3×#385C2semidirect
6. #5213C2semidirect
7. #4994C2semidirect
8. #4991C2semidirect
9. #4988C2semidirect
10. #4961C2semidirect
11. #4960C2semidirect
12. #4673C2semidirect
13. #4671C2semidirect
14. #4665C2semidirect
15. #4653C2semidirect
70. #385D3semidirect
116. C3×C22⋊C4D4semidirect
130. C4⋊Dic3D4semidirect
303. C22⋊C4D12semidirect
479. C3#2676semidirect

Maximal subgroups

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

subgroupindex
C2×#9302
C2×#8972
C2×#8852
C2×#8842
C3×#3852
#52132
#49942
#49912
#49882
#49612
#49602
#46732
#46712
#46652
#46532
#26763