Finite Group Databasebeta

← #74877

Subgroups — #74877

Order 384.

696 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#938C211yesmaximal, characteristic
2C2×C4×#67C211yesmaximal, characteristic, complemented
3C2×#67⋊C4C211yesmaximal, characteristic, complemented
4C3×#386C211yesmaximal, characteristic, complemented
5#5220C211yesmaximal, characteristic, complemented
6#5210C211yesmaximal, characteristic, complemented
7#4956C211yesmaximal, characteristic, complemented
8#4956C211yesmaximal, characteristic, complemented
9#4946C211yesmaximal, characteristic, complemented
10#4945C211yesmaximal, characteristic, complemented
11#4944C211yesmaximal, characteristic, complemented
12#4667C211yesmaximal, characteristic, complemented
13D3×#95C211yesmaximal, characteristic, complemented
14#4654C211yesmaximal, characteristic, complemented
15#4653C211yesmaximal, characteristic, complemented
16#2325—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C23×C3×C4C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C23×Dic3C2211yescharacteristic
22C22×C4×D3C2211yescharacteristic
23C22×C4×D3C2211yescharacteristic
24C22×C4×D3C2211yescharacteristic
25C2×C3×C22⋊C4C2211yescharacteristic
26C2×C3×C22⋊C4C2211yescharacteristic
27C2×C3×C22⋊C4C2211yescharacteristic
28C2×#217C2211yescharacteristic
29C2×#217C2211yescharacteristic
30C2×#217C2211yescharacteristic
31C2×#217C2211yescharacteristic
32C2×#217C2211yescharacteristic
33#938C418yescomplemented
34C4×#67—24no—
35C2×(C2×D3)⋊C4C2211yescharacteristic
36C2×(C2×D3)⋊C4C2211yescharacteristic
37C2×C4⋊Dic3C2211yescharacteristic
38C2×Dic3⋊C4C2211yescharacteristic
39C2×Dic3⋊C4C2211yescharacteristic
40C2×Dic3⋊C4C2211yescharacteristic
41C2×Dic3⋊C4C2211yescharacteristic
42C2×C4×Dic3C2211yescharacteristic
43C2×C4×Dic3C2211yescharacteristic
44#67⋊C4—24no—
45C3×#95C2211yescharacteristic
46C3×#95C2211yescharacteristic
47C3⋊#95C2211yescharacteristic
48C3⋊#95C2211yescharacteristic
49C3⋊#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C3⋊#95C2211yescharacteristic
55C2×#121—31no—
56C2×C4×D4—31no—
57C2×C4×D4—31no—
58#388—31no—
59#388—31no—
60#387—31no—
61#387—31no—
62#386—31no—
63#386—31no—
64#386—31no—
65#386D311yescharacteristic, complemented
66#385—31no—
67#385—31no—
68#380—31no—
69C2×#95—31no—
70C24×C3C2311yescharacteristic
71C24×C3C2311yescharacteristic
72C23×D3C2311yescharacteristic
73C2×C3×D4—41no—
74C2×C3×D4—41no—
75C2×C3×D4C2×C414yescomplemented
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×#67C2×C414yescomplemented
89C2×#67C2×C414yescomplemented
90C22×Dic3—22no—
91C22×Dic3—41no—
92C22×Dic3—41no—
93C22×Dic3C2311yescharacteristic
94C22×Dic3C2311yescharacteristic
95C22×Dic3C2311yescharacteristic
96C22×Dic3C2311yescharacteristic
97C22×Dic3C2311yescharacteristic
98C22×Dic3C2311yescharacteristic
99C22×Dic3C2311yescharacteristic
100C2×C4×D3—22no—
101C2×C4×D3—41no—
102C2×C4×D3—41no—
103C2×C4×D3—41no—
104C2×C4×D3—41no—
105C2×C4×D3—41no—
106C2×C4×D3—41no—
107C2×C4×D3C2×C414yescomplemented
108C2×C4×D3D414yescomplemented
109C3×C22⋊C4—22no—
110C3×C22⋊C4—41no—
111C3×C22⋊C4—41no—
112#217—22no—
113#217—41no—
114#217—41no—
115#217C2×C414yescomplemented
116#217C2×C414yescomplemented
117(C2×D3)⋊C4—22no—
118(C2×D3)⋊C4—22no—
119C4⋊Dic3C2×C414yescomplemented
120Dic3⋊C4—22no—
121Dic3⋊C4—22no—
122Dic3⋊C4—41no—
123Dic3⋊C4—41no—
124C4×Dic3—22no—
125C4×Dic3—22no—
126C22×D4—31no—
127C22×D4—31no—
128C22×D4C2×D311yescharacteristic
129C23×C4—31no—
130C23×C4—31no—
131C23×C4—31no—
132C23×C4—31no—
133C23×C4C2×D311yescharacteristic
134#121—38no—
135C4×D4—64no—
136C4×D4—64no—
137C2×C4⋊C4—31no—
138C2×C4⋊C4—31no—
139C2×C4⋊C4—31no—
140C2×C4⋊C4—31no—
141C2×C4⋊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⋊C4C2×D311yescharacteristic
150C2×C22⋊C4C2×D311yescharacteristic
151C2×C22⋊C4C2×D311yescharacteristic
152C2×C42—31no—
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×C3C22×C412yes—
177C23×C3C22×C412yes—
178C23×C3C2411yescharacteristic
179C22×D3—21no—
180C22×D3—21no—
181C22×D3—21no—
182C22×D3—21no—
183C22×D3C22×C412yes—
184C22×D3C2×D412yes—
185C22×D3#4112yes—
186C3×D4—44no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
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—44no—
201C2×C3×C4C22×C412yes—
202C2×C3×C4C2×D412yes—
203#67—28no—
204#67—28no—
205C2×Dic3—21no—
206C2×Dic3—21no—
207C2×Dic3—21no—
208C2×Dic3—21no—
209C2×Dic3—21no—
210C2×Dic3—21no—
211C2×Dic3—21no—
212C2×Dic3—21no—
213C2×Dic3—21no—
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—44no—
223C2×Dic3C22×C412yes—
224C2×Dic3C22×C412yes—
225C2×Dic3C22×C412yes—
226C2×Dic3C2×D412yes—
227C4×D3—44no—
228C4×D3—44no—
229C4×D3—44no—
230C24—31no—
231C24C22×D311yescharacteristic
232C24C22×D311yescharacteristic
233C2×D4—34no—
234C2×D4—34no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—62no—
238C2×D4—62no—
239C2×D4—62no—
240C2×D4—62no—
241C2×D4C4×D314yescomplemented
242C22×C4—22no—
243C22×C4—31no—
244C22×C4—31no—
245C22×C4—31no—
246C22×C4—31no—
247C22×C4—34no—
248C22×C4—34no—
249C22×C4—31no—
250C22×C4—31no—
251C22×C4—31no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—62no—
255C22×C4—62no—
256C22×C4—121no—
257C22×C4—121no—
258C22×C4—121no—
259C22×C4—121no—
260C22×C4—121no—
261C22×C4—121no—
262C22×C4—121no—
263C22×C4—121no—
264C22×C4C22×D311yescharacteristic
265C22×C4C22×D311yescharacteristic
266C22×C4C22×D311yescharacteristic
267C22×C4C22×D311yescharacteristic
268C22×C4C22×D311yescharacteristic
269C4⋊C4—34no—
270C4⋊C4—62no—
271C4⋊C4—62no—
272C4⋊C4—121no—
273C4⋊C4—121no—
274C22⋊C4—22no—
275C22⋊C4—34no—
276C22⋊C4—34no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—62no—
280C22⋊C4—62no—
281C22⋊C4—62no—
282C22⋊C4—121no—
283C22⋊C4—121no—
284C42—62no—
285C42—62no—
286C22×C3—22no—
287C22×C3—22no—
288C22×C3—22no—
289C22×C3—22no—
290C22×C3—22no—
291C22×C3—22no—
292C22×C3—41no—
293C22×C3—41no—
294C22×C3—41no—
295C22×C3—41no—
296C22×C3—41no—
297C22×C3—41no—
298C22×C3—41no—
299C22×C3—41no—
300C22×C3C23×C411yescharacteristic
301C22×C3C22×D411yescharacteristic
302C22×C3C2×#4111yescharacteristic
303C22×C3H(5,𝔽2)11yescharacteristic
304C22×C3H(5,𝔽2)11yescharacteristic
305C22×C3H(5,𝔽2)11yescharacteristic
306C22×C32−1+411yescharacteristic
307C2×D3—22no—
308C2×D3—22no—
309C2×D3—22no—
310C2×D3—22no—
311C2×D3—22no—
312C2×D3—22no—
313C2×D3C4×D414yes—
314C3×C4—22no—
315C3×C4—22no—
316C3×C4—41no—
317C3×C4—41no—
318C3×C4—41no—
319Dic3—22no—
320Dic3—22no—
321Dic3—22no—
322Dic3—22no—
323Dic3—41no—
324Dic3—41no—
325Dic3—41no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—32no—
339C23—32no—
340C23—32no—
341C23—61no—
342C23—61no—
343C23—61no—
344C23—61no—
345C23C2×C4×D312yes—
346C23C2×C4×D312yes—
347C23C23×D311yescharacteristic
348D4—44no—
349D4—68no—
350D4—68no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—32no—
365C2×C4—32no—
366C2×C4—32no—
367C2×C4—32no—
368C2×C4—44no—
369C2×C4—61no—
370C2×C4—61no—
371C2×C4—61no—
372C2×C4—61no—
373C2×C4—61no—
374C2×C4—61no—
375C2×C4—61no—
376C2×C4—61no—
377C2×C4—61no—
378C2×C4—61no—
379C2×C4—61no—
380C2×C4—61no—
381C2×C4—61no—
382C2×C4—61no—
383C2×C4—61no—
384C2×C4—61no—
385C2×C4—61no—
386C2×C4—124no—
387C2×C4—124no—
388C2×C4—124no—
389C2×C4—124no—
390C2×C4C2×C4×D312yes—
391C2×C4D3×D412yes—
392C2×C3—42no—
393C2×C3—42no—
394C2×C3C2×C4×D411yescharacteristic
395C2×C3#51811yescharacteristic
396C2×C3#52011yescharacteristic
397C2×C3#53411yescharacteristic
398C2×C3#53711yescharacteristic
399C2×C3#53811yescharacteristic
400C2×C3#53911yescharacteristic
401D3—24no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—34no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—62no—
418C22—62no—
419C22—62no—
420C22—62no—
421C22—62no—
422C22—62no—
423C22C22×C4×D311yescharacteristic
424C22C2×D3×D411yescharacteristic
425C22#100411yescharacteristic
426C22#100411yescharacteristic
427C22#100411yescharacteristic
428C22D3×#4111yescharacteristic
429C22#101011yescharacteristic
430C4—22no—
431C4—22no—
432C4—41no—
433C4—41no—
434C4—41no—
435C4—62no—
436C4—62no—
437C4—62no—
438C4—62no—
439C4—121no—
440C4—121no—
441C4—121no—
442C3#232511yescharacteristic, complemented, Sylow
443C2—42no—
444C2—42no—
445C2—64no—
446C2#548611yescharacteristic
447C2C4×D3×D411yescharacteristic
448C2#554611yescharacteristic
449C2#558911yescharacteristic
450C2#560811yescharacteristic
451C2#561311yescharacteristic
452C2#566011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutatorC22×C3C23×C4
FittingC3×#386C2
socle, cosocleC23×C3C24
prime radicalC2×#938C2
hypercenter#386D3
hypocenterC3#2325
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×#67C2semidirect
3. C2×#67⋊C4C2semidirect
4. C3×#386C2semidirect
5. #5220C2semidirect
6. #5210C2semidirect
7. #4956C2semidirect
8. #4956C2semidirect
9. #4946C2semidirect
10. #4945C2semidirect
11. #4944C2semidirect
12. #4667C2semidirect
13. D3×#95C2semidirect
14. #4654C2semidirect
15. #4653C2semidirect
33. #938C4semidirect
65. #386D3semidirect
75. C2×C3×D4C2×C4semidirect
88. C2×#67C2×C4semidirect
89. C2×#67C2×C4semidirect
107. C2×C4×D3C2×C4semidirect
108. C2×C4×D3D4semidirect
115. #217C2×C4semidirect
116. #217C2×C4semidirect
119. C4⋊Dic3C2×C4semidirect
241. C2×D4C4×D3semidirect
442. C3#2325semidirect

Maximal subgroups

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

subgroupindex
C2×#9382
C2×C4×#672
C2×#67⋊C42
C3×#3862
#52202
#52102
#49562
#49462
#49452
#49442
#46672
D3×#952
#46542
#46532
#23253