Finite Group Databasebeta

← #74783

Subgroups — #74783

Order 384.

628 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#67C211yesmaximal, characteristic, complemented
2C2×#885C211yesmaximal, characteristic, complemented
3C3×#386C211yesmaximal, characteristic, complemented
4#5223C211yesmaximal, characteristic, complemented
5#5223C211yesmaximal, characteristic, complemented
6#5213C211yesmaximal, characteristic, complemented
7#4960C211yesmaximal, characteristic, complemented
8#4960C211yesmaximal, characteristic, complemented
9#4956C211yesmaximal, characteristic, complemented
10#4952C211yesmaximal, characteristic, complemented
11#4947C211yesmaximal, characteristic, complemented
12#4675C211yesmaximal, characteristic, complemented
13#4673C211yesmaximal, characteristic, complemented
14#4665C211yesmaximal, characteristic, complemented
15#4651C211yesmaximal, characteristic, complemented
16#2631—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C23×C3×C4C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C22×#67C2211yescharacteristic
23C22×D12C2211yescharacteristic
24C22×C4×D3C2211yescharacteristic
25C22×Dic6C2211yescharacteristic
26C2×C3×C22⋊C4C2211yescharacteristic
27C2×C3×C22⋊C4C2211yescharacteristic
28C2×C3×C22⋊C4C2211yescharacteristic
29C2×#217C2211yescharacteristic
30C2×#217C2211yescharacteristic
31C2×#217C2211yescharacteristic
32C2×#217C2211yescharacteristic
33C4×#67—24no—
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×Dic3⋊C4C2211yescharacteristic
42C2×C4×Dic3C2211yescharacteristic
43#885—24no—
44C3×#95C2211yescharacteristic
45C3×#95C2211yescharacteristic
46C3⋊#95C2211yescharacteristic
47C3⋊#95C2211yescharacteristic
48C3⋊#95C2211yescharacteristic
49C3⋊#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C2×#124—31no—
55C2×C4×D4—31no—
56#397—31no—
57#397—31no—
58#393—31no—
59#393—31no—
60#392—31no—
61#392—31no—
62#392—31no—
63#392—31no—
64#386—31no—
65#386—31no—
66#386—31no—
67#386D311yescharacteristic, complemented
68#383—31no—
69C24×C3C2311yescharacteristic
70C24×C3C2311yescharacteristic
71C23×D3C2311yescharacteristic
72C23×D3C2311yescharacteristic
73C2×C3×D4—22no—
74C2×C3×D4—41no—
75C2×C3×D4—41no—
76C22×C3×C4—22no—
77C22×C3×C4—41no—
78C22×C3×C4—41no—
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—
93C2×#67—41no—
94C2×#67—41no—
95C2×#67—41no—
96C22×Dic3C2311yescharacteristic
97C22×Dic3C2311yescharacteristic
98C22×Dic3C2311yescharacteristic
99C22×Dic3C2311yescharacteristic
100C22×Dic3C2311yescharacteristic
101C22×Dic3C2311yescharacteristic
102C2×D12—22no—
103C2×D12—41no—
104C2×D12—41no—
105C2×C4×D3—22no—
106C2×C4×D3—41no—
107C2×C4×D3—41no—
108C2×Dic6—22no—
109C2×Dic6—41no—
110C2×Dic6—41no—
111C3×C22⋊C4—22no—
112C3×C22⋊C4—41no—
113C3×C22⋊C4—41no—
114#217—22no—
115#217—22no—
116#217—41no—
117#217—41no—
118(C2×D3)⋊C4—22no—
119(C2×D3)⋊C4—22no—
120(C2×D3)⋊C4—22no—
121(C2×D3)⋊C4—41no—
122(C2×D3)⋊C4—41no—
123(C2×D3)⋊C4—41no—
124(C2×D3)⋊C4—41no—
125Dic3⋊C4—22no—
126C4×Dic3D414yescomplemented
127C22×Q8—31no—
128C22×D4—31no—
129C22×D4—31no—
130C22×D4—31no—
131C22×D4—31no—
132C22×D4—31no—
133C22×D4C2×D311yescharacteristic
134C23×C4—31no—
135C23×C4C2×D311yescharacteristic
136#124—64no—
137C4×D4—64no—
138C2×C4⋊C4—31no—
139C2×C22⋊C4—31no—
140C2×C22⋊C4—31no—
141C2×C22⋊C4—31no—
142C2×C22⋊C4—31no—
143C2×C22⋊C4—31no—
144C2×C22⋊C4—31no—
145C2×C22⋊C4—31no—
146C2×C22⋊C4—31no—
147C2×C22⋊C4—31no—
148C2×C22⋊C4—31no—
149C2×C22⋊C4—31no—
150C2×C22⋊C4C2×D311yescharacteristic
151C2×C22⋊C4C2×D311yescharacteristic
152C2×C22⋊C4C2×D311yescharacteristic
153C2×C42—31no—
154#95—31no—
155#95—31no—
156#95—31no—
157#95—31no—
158#95—31no—
159#95—31no—
160#95—31no—
161#95—31no—
162#95C2×D311yescharacteristic
163#95C2×D311yescharacteristic
164C23×C3—21no—
165C23×C3—21no—
166C23×C3—21no—
167C23×C3—21no—
168C23×C3—21no—
169C23×C3—21no—
170C23×C3—21no—
171C23×C3—21no—
172C23×C3—21no—
173C23×C3—21no—
174C23×C3—21no—
175C23×C3—21no—
176C23×C3—21no—
177C23×C3#4112yes—
178C23×C3C2411yescharacteristic
179C22×D3—21no—
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#4112yes—
193C3×D4—44no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
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—44no—
209C2×C3×C4C2×D412yes—
210#67—28no—
211#67—44no—
212#67—44no—
213#67—44no—
214C2×Dic3—21no—
215C2×Dic3—21no—
216C2×Dic3—21no—
217C2×Dic3—21no—
218C2×Dic3—21no—
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×Dic3C2×D412yes—
231C2×Dic3C2×D412yes—
232D12—44no—
233C4×D3—44no—
234Dic6—44no—
235C24—31no—
236C24—31no—
237C24C22×D311yescharacteristic
238C24C22×D311yescharacteristic
239C2×Q8—62no—
240C2×Q8—121no—
241C2×Q8—121no—
242C2×D4—22no—
243C2×D4—41no—
244C2×D4—41no—
245C2×D4—62no—
246C2×D4—62no—
247C2×D4—62no—
248C2×D4—62no—
249C2×D4—62no—
250C2×D4—62no—
251C2×D4—62no—
252C2×D4—121no—
253C2×D4—121no—
254C2×D4—121no—
255C2×D4—121no—
256C2×D4—121no—
257C2×D4—121no—
258C2×D4—121no—
259C2×D4—121no—
260C22×C4—22no—
261C22×C4—31no—
262C22×C4—31no—
263C22×C4—31no—
264C22×C4—31no—
265C22×C4—31no—
266C22×C4—31no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—62no—
270C22×C4—121no—
271C22×C4—121no—
272C22×C4C22×D311yescharacteristic
273C22×C4C22×D311yescharacteristic
274C22×C4C22×D311yescharacteristic
275C22×C4C22×D311yescharacteristic
276C22×C4C22×D311yescharacteristic
277C4⋊C4—62no—
278C22⋊C4—22no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—62no—
282C22⋊C4—62no—
283C22⋊C4—62no—
284C22⋊C4—62no—
285C22⋊C4—62no—
286C22⋊C4—121no—
287C22⋊C4—121no—
288C22⋊C4—121no—
289C22⋊C4—121no—
290C22⋊C4—121no—
291C22⋊C4—121no—
292C42—34no—
293C22×C3—22no—
294C22×C3—22no—
295C22×C3—22no—
296C22×C3—41no—
297C22×C3—41no—
298C22×C3—41no—
299C22×C3—41no—
300C22×C3—41no—
301C22×C3—41no—
302C22×C3—41no—
303C22×C3—41no—
304C22×C3—41no—
305C22×C3—41no—
306C22×C3—41no—
307C22×C3C22×D411yescharacteristic
308C22×C3C2×#4111yescharacteristic
309C22×C3C2×#4111yescharacteristic
310C22×C3H(5,𝔽2)11yescharacteristic
311C22×C3H(5,𝔽2)11yescharacteristic
312C22×C3H(5,𝔽2)11yescharacteristic
313C22×C3H(5,𝔽2)11yescharacteristic
314C2×D3—22no—
315C2×D3—22no—
316C2×D3—22no—
317C2×D3—41no—
318C2×D3—41no—
319C2×D3—41no—
320C2×D3—41no—
321C2×D3—41no—
322C2×D3—41no—
323C2×D3—41no—
324C2×D3—41no—
325C2×D3—41no—
326C2×D3—41no—
327C2×D3—41no—
328C3×C4—22no—
329C3×C4—41no—
330C3×C4—41no—
331C3×C4—41no—
332C3×C4—41no—
333Dic3—22no—
334Dic3—22no—
335Dic3—41no—
336Dic3—41no—
337Dic3—41no—
338Dic3—41no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—32no—
353C23—61no—
354C23—61no—
355C23—61no—
356C23—61no—
357C23—61no—
358C23—61no—
359C23—61no—
360C23—61no—
361C23—61no—
362C23—61no—
363C23—61no—
364C23—61no—
365C23—61no—
366C23#23512yes—
367C23C23×D311yescharacteristic
368Q8—124no—
369D4—44no—
370D4—68no—
371D4—124no—
372D4—124no—
373D4—124no—
374D4—124no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—32no—
390C2×C4—32no—
391C2×C4—44no—
392C2×C4—61no—
393C2×C4—61no—
394C2×C4—61no—
395C2×C4—61no—
396C2×C4—61no—
397C2×C4—61no—
398C2×C4—61no—
399C2×C4—61no—
400C2×C4—61no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—61no—
405C2×C4—61no—
406C2×C4—61no—
407C2×C4—61no—
408C2×C4—124no—
409C2×C4D3×D412yes—
410C2×C3—42no—
411C2×C3—81no—
412C2×C3#52511yescharacteristic
413C2×C3#53511yescharacteristic
414C2×C3#53511yescharacteristic
415C2×C3#53811yescharacteristic
416C2×C3#53811yescharacteristic
417C2×C3#53811yescharacteristic
418C2×C3#53811yescharacteristic
419D3—42no—
420D3—81no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—62no—
436C22—62no—
437C22—62no—
438C22—121no—
439C22—121no—
440C22—121no—
441C22—121no—
442C22—121no—
443C22—121no—
444C22—121no—
445C22—121no—
446C22—121no—
447C22—121no—
448C22—121no—
449C22C2×#23511yescharacteristic
450C22C2×D3×D411yescharacteristic
451C22#100411yescharacteristic
452C22#100411yescharacteristic
453C22#100411yescharacteristic
454C22D3×#4111yescharacteristic
455C22#100911yescharacteristic
456C4—22no—
457C4—41no—
458C4—41no—
459C4—41no—
460C4—41no—
461C4—62no—
462C4—62no—
463C4—121no—
464C4—121no—
465C4—121no—
466C4—121no—
467C3#263111yescharacteristic, complemented, Sylow
468C2—42no—
469C2—81no—
470C2—122no—
471C2—241no—
472C2#549411yescharacteristic
473C2#554711yescharacteristic
474C2#556011yescharacteristic
475C2#559211yescharacteristic
476C2#560711yescharacteristic
477C2#561311yescharacteristic
478C2#565711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#386C2
hypercenter#386D3
hypocenterC3#2631
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×C4×#67C2semidirect
2. C2×#885C2semidirect
3. C3×#386C2semidirect
4. #5223C2semidirect
5. #5223C2semidirect
6. #5213C2semidirect
7. #4960C2semidirect
8. #4960C2semidirect
9. #4956C2semidirect
10. #4952C2semidirect
11. #4947C2semidirect
12. #4675C2semidirect
13. #4673C2semidirect
14. #4665C2semidirect
15. #4651C2semidirect
67. #386D3semidirect
126. C4×Dic3D4semidirect
467. C3#2631semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#672
C2×#8852
C3×#3862
#52232
#52132
#49602
#49562
#49522
#49472
#46752
#46732
#46652
#46512
#26313