Finite Group Databasebeta

← #76714

Subgroups — #76714

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×#939C211yesmaximal, characteristic, complemented
2C2×#939C211yesmaximal, characteristic, complemented
3C2×#936C211yesmaximal, characteristic, complemented
4C2×#878C211yesmaximal, characteristic, complemented
5C3×#392C211yesmaximal, characteristic, complemented
6#5223C211yesmaximal, characteristic, complemented
7#5220C211yesmaximal, characteristic, complemented
8#5220C211yesmaximal, characteristic, complemented
9#4961C211yesmaximal, characteristic, complemented
10#4959C211yesmaximal, characteristic, complemented
11#4957C211yesmaximal, characteristic, complemented
12#4948C211yesmaximal, characteristic, complemented
13#4946C211yesmaximal, characteristic, complemented
14#4673C211yesmaximal, characteristic, complemented
15#4652C211yesmaximal, characteristic, complemented
16#2676—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C22×C3×D4C2211yescharacteristic
19C22×C3×D4C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C22×#67C2211yescharacteristic
23C23×Dic3C2211yescharacteristic
24C23×Dic3C2211yescharacteristic
25C22×Dic6C2211yescharacteristic
26C2×C3×C22⋊C4C2211yescharacteristic
27C2×C3×C22⋊C4C2211yescharacteristic
28C2×C3×C22⋊C4C2211yescharacteristic
29C2×#217C2211yescharacteristic
30C2×#217C2211yescharacteristic
31C2×#217C2211yescharacteristic
32C2×#217C2211yescharacteristic
33C2×#217C2211yescharacteristic
34C2×#217C2211yescharacteristic
35C2×#217C2211yescharacteristic
36#939—24no—
37#939—24no—
38#936—24no—
39C2×(C2×D3)⋊C4C2211yescharacteristic
40C2×(C2×D3)⋊C4C2211yescharacteristic
41C2×(C2×D3)⋊C4C2211yescharacteristic
42C2×(C2×D3)⋊C4C2211yescharacteristic
43C2×C4⋊Dic3C2211yescharacteristic
44C2×Dic3⋊C4C2211yescharacteristic
45C2×Dic3⋊C4C2211yescharacteristic
46C2×Dic3⋊C4C2211yescharacteristic
47C2×Dic3⋊C4C2211yescharacteristic
48C2×C4×Dic3C2211yescharacteristic
49#878—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#392D311yescharacteristic, complemented
66#390—31no—
67#387—31no—
68#386—31no—
69#386—31no—
70#385—31no—
71C24×C3C2311yescharacteristic
72C24×C3C2311yescharacteristic
73C24×C3C2311yescharacteristic
74C23×D3C2311yescharacteristic
75C2×C3×D4—22no—
76C2×C3×D4—22no—
77C2×C3×D4—22no—
78C2×C3×D4—22no—
79C2×C3×D4—22no—
80C2×C3×D4—41no—
81C2×C3×D4—41no—
82C2×C3×D4—41no—
83C2×C3×D4—41no—
84C22×C3×C4C2311yescharacteristic
85C22×C3×C4C2311yescharacteristic
86C22×C3×C4C2311yescharacteristic
87C22×C3×C4C2311yescharacteristic
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—
97C22×Dic3—22no—
98C22×Dic3—22no—
99C22×Dic3—22no—
100C22×Dic3—41no—
101C22×Dic3—41no—
102C22×Dic3—41no—
103C22×Dic3C2311yescharacteristic
104C22×Dic3C2311yescharacteristic
105C22×Dic3C2311yescharacteristic
106C22×Dic3C2311yescharacteristic
107C22×Dic3C2311yescharacteristic
108C22×Dic3C2311yescharacteristic
109C22×Dic3C2311yescharacteristic
110C2×Dic6—22no—
111C2×Dic6—22no—
112C2×Dic6—41no—
113C3×C22⋊C4—22no—
114C3×C22⋊C4—41no—
115C3×C22⋊C4—41no—
116#217—22no—
117#217—22no—
118#217—22no—
119#217—22no—
120#217—22no—
121#217—41no—
122#217D414yescomplemented
123(C2×D3)⋊C4—22no—
124(C2×D3)⋊C4—22no—
125(C2×D3)⋊C4—41no—
126(C2×D3)⋊C4—41no—
127C4⋊Dic3—22no—
128Dic3⋊C4—22no—
129Dic3⋊C4—22no—
130Dic3⋊C4—41no—
131Dic3⋊C4D414yescomplemented
132C4×Dic3—22no—
133C22×Q8—31no—
134C22×D4—31no—
135C22×D4—31no—
136C22×D4—31no—
137C22×D4C2×D311yescharacteristic
138C22×D4C2×D311yescharacteristic
139C22×D4C2×D311yescharacteristic
140C23×C4—31no—
141C23×C4—31no—
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⋊C4—31no—
150C2×C4⋊C4—31no—
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⋊C4C2×D311yescharacteristic
163C2×C22⋊C4C2×D311yescharacteristic
164C2×C22⋊C4C2×D311yescharacteristic
165C2×C42—31no—
166#95—31no—
167#95—31no—
168#95—31no—
169#95—31no—
170#95—31no—
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×C3—21no—
186C23×C3—21no—
187C23×C3—21no—
188C23×C3—21no—
189C23×C3—21no—
190C23×C3—21no—
191C23×C3C2×D412yes—
192C23×C3#4112yes—
193C23×C3C2411yescharacteristic
194C22×D3—21no—
195C22×D3—21no—
196C22×D3—21no—
197C22×D3—21no—
198C22×D3—21no—
199C22×D3—21no—
200C22×D3—21no—
201C3×D4—44no—
202C3×D4—44no—
203C3×D4—44no—
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×C4C2×D412yes—
216#67—44no—
217#67—44no—
218#67—44no—
219C2×Dic3—21no—
220C2×Dic3—21no—
221C2×Dic3—21no—
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—44no—
237C2×Dic3—44no—
238C2×Dic3C2×D412yes—
239C2×Dic3C2×D412yes—
240C2×Dic3C2×D412yes—
241C2×Dic3C2×D412yes—
242Dic6—44no—
243C24—31no—
244C24C22×D311yescharacteristic
245C24C22×D311yescharacteristic
246C24C22×D311yescharacteristic
247C2×Q8—62no—
248C2×Q8—62no—
249C2×Q8—121no—
250C2×D4—22no—
251C2×D4—22no—
252C2×D4—22no—
253C2×D4—22no—
254C2×D4—22no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—62no—
260C2×D4—62no—
261C2×D4—62no—
262C2×D4—62no—
263C2×D4—62no—
264C2×D4—121no—
265C2×D4—121no—
266C2×D4—121no—
267C2×D4—121no—
268C22×C4—31no—
269C22×C4—31no—
270C22×C4—31no—
271C22×C4—31no—
272C22×C4—31no—
273C22×C4—31no—
274C22×C4—31no—
275C22×C4—62no—
276C22×C4—62no—
277C22×C4—62no—
278C22×C4—121no—
279C22×C4—121no—
280C22×C4—121no—
281C22×C4C22×D311yescharacteristic
282C22×C4C22×D311yescharacteristic
283C22×C4C22×D311yescharacteristic
284C22×C4C22×D311yescharacteristic
285C4⋊C4—34no—
286C4⋊C4—62no—
287C4⋊C4—62no—
288C4⋊C4—62no—
289C4⋊C4—121no—
290C22⋊C4—22no—
291C22⋊C4—34no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—62no—
295C22⋊C4—62no—
296C22⋊C4—62no—
297C22⋊C4—62no—
298C22⋊C4—62no—
299C22⋊C4—62no—
300C22⋊C4—62no—
301C22⋊C4—121no—
302C22⋊C4—121no—
303C22⋊C4—121no—
304C42—62no—
305C22×C3—22no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—22no—
309C22×C3—22no—
310C22×C3—22no—
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×C3—41no—
320C22×C3—41no—
321C22×C3—41no—
322C22×C3—41no—
323C22×C3—41no—
324C22×C3—41no—
325C22×C3—41no—
326C22×C3C22×D411yescharacteristic
327C22×C3C22×D411yescharacteristic
328C22×C3C2×#4111yescharacteristic
329C22×C3H(5,𝔽2)11yescharacteristic
330C22×C3H(5,𝔽2)11yescharacteristic
331C22×C3H(5,𝔽2)11yescharacteristic
332C22×C32−1+411yescharacteristic
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—41no—
342C3×C4—41no—
343C3×C4—41no—
344Dic3—22no—
345Dic3—22no—
346Dic3—22no—
347Dic3—22no—
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—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—61no—
371C23—61no—
372C23—61no—
373C23—61no—
374C23—61no—
375C23—61no—
376C23—61no—
377C23D3×D412yes—
378C23#23712yes—
379C23C23×D311yescharacteristic
380Q8—124no—
381D4—44no—
382D4—44no—
383D4—44no—
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—32no—
399C2×C4—32no—
400C2×C4—32no—
401C2×C4—32no—
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—61no—
419C2×C4—124no—
420C2×C4—124no—
421C2×C4D3×D412yes—
422C2×C3—42no—
423C2×C3—42no—
424C2×C3—81no—
425C2×C3#53511yescharacteristic
426C2×C3#53711yescharacteristic
427C2×C3#53811yescharacteristic
428C2×C3D4211yescharacteristic
429C2×C3#54611yescharacteristic
430C2×C3#54811yescharacteristic
431C2×C3#56211yescharacteristic
432D3—81no—
433C22—22no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—121no—
455C22—121no—
456C22—121no—
457C22—121no—
458C22—121no—
459C22—121no—
460C22—121no—
461C22C2×D3×D411yescharacteristic
462C22C2×D3×D411yescharacteristic
463C22C2×#23711yescharacteristic
464C22#100411yescharacteristic
465C22#100411yescharacteristic
466C22#100411yescharacteristic
467C22#101011yescharacteristic
468C4—22no—
469C4—41no—
470C4—41no—
471C4—41no—
472C4—62no—
473C4—62no—
474C4—62no—
475C4—62no—
476C4—121no—
477C4—121no—
478C4—121no—
479C3#267611yescharacteristic, complemented, Sylow
480C2—42no—
481C2—42no—
482C2—81no—
483C2—241no—
484C2#559011yescharacteristic
485C2#559111yescharacteristic
486C2#559311yescharacteristic
487C2#559711yescharacteristic
488C2#559811yescharacteristic
489C2#562111yescharacteristic
490C2#571511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#392C2
hypercenter#392D3
hypocenterC3#2676
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#939C2semidirect
2. C2×#939C2semidirect
3. C2×#936C2semidirect
4. C2×#878C2semidirect
5. C3×#392C2semidirect
6. #5223C2semidirect
7. #5220C2semidirect
8. #5220C2semidirect
9. #4961C2semidirect
10. #4959C2semidirect
11. #4957C2semidirect
12. #4948C2semidirect
13. #4946C2semidirect
14. #4673C2semidirect
15. #4652C2semidirect
65. #392D3semidirect
122. #217D4semidirect
131. Dic3⋊C4D4semidirect
479. C3#2676semidirect

Maximal subgroups

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

subgroupindex
C2×#9392
C2×#9362
C2×#8782
C3×#3922
#52232
#52202
#49612
#49592
#49572
#49482
#49462
#46732
#46522
#26763