Finite Group Databasebeta

← #75509

Subgroups — #75509

Order 384.

590 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#885C211yesmaximal, characteristic, complemented
2C2×C4×D12C211yesmaximal, characteristic, complemented
3C3×#388C211yesmaximal, characteristic, complemented
4#4991C211yesmaximal, characteristic, complemented
5#4980C211yesmaximal, characteristic, complemented
6#4961C211yesmaximal, characteristic, complemented
7#4960C211yesmaximal, characteristic
8#4956C211yesmaximal, characteristic, complemented
9#4956C211yesmaximal, characteristic, complemented
10#4951C211yesmaximal, characteristic, complemented
11#4929C211yesmaximal, characteristic, complemented
12#4673C211yesmaximal, characteristic, complemented
13#4670C211yesmaximal, characteristic, complemented
14#4666C211yesmaximal, characteristic, complemented
15#4664C211yesmaximal, characteristic, complemented
16#2459—31nomaximal, Sylow
17C22×#67C2211yescharacteristic
18C22×#67C2211yescharacteristic
19C22×D12C2211yescharacteristic
20C22×C4×D3C2211yescharacteristic
21C22×C4×D3C2211yescharacteristic
22C22×Dic6C2211yescharacteristic
23C2×C3×C4⋊C4C2211yescharacteristic
24C2×C3×C22⋊C4C2211yescharacteristic
25C2×C3×C22⋊C4C2211yescharacteristic
26C2×C3×C22⋊C4C2211yescharacteristic
27C2×C3×C42C2211yescharacteristic
28C2×#217C2211yescharacteristic
29C2×#217C2211yescharacteristic
30C2×(C2×D3)⋊C4C2211yescharacteristic
31C2×(C2×D3)⋊C4C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
39C2×C4⋊Dic3C2211yescharacteristic
40C2×C4×Dic3C2211yescharacteristic
41C2×C4×Dic3C2211yescharacteristic
42#885—24no—
43C4×D12—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#394—31no—
57#394—31no—
58#393—31no—
59#392—31no—
60#391—31no—
61#388—31no—
62#388—31no—
63#388D311yescharacteristic, complemented
64#387—31no—
65#386—31no—
66#386—31no—
67#381—31no—
68C4×C22⋊C4—31no—
69C24×C3C2311yescharacteristic
70C23×D3C2311yescharacteristic
71C23×D3C2311yescharacteristic
72C22×C3×C4C2311yescharacteristic
73C22×C3×C4C2311yescharacteristic
74C22×C3×C4C2311yescharacteristic
75C22×C3×C4C2311yescharacteristic
76C22×C3×C4C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C2×#67—22no—
79C2×#67—22no—
80C2×#67—22no—
81C2×#67—41no—
82C2×#67—41no—
83C2×#67—41no—
84C22×Dic3C2311yescharacteristic
85C22×Dic3C2311yescharacteristic
86C22×Dic3C2311yescharacteristic
87C22×Dic3C2311yescharacteristic
88C22×Dic3C2311yescharacteristic
89C22×Dic3C2311yescharacteristic
90C2×D12—22no—
91C2×D12—22no—
92C2×D12—22no—
93C2×C4×D3—22no—
94C2×C4×D3—22no—
95C2×C4×D3—22no—
96C2×C4×D3—22no—
97C2×C4×D3—41no—
98C2×C4×D3—41no—
99C2×Dic6—22no—
100C2×Dic6—22no—
101C2×Dic6—41no—
102C3×C4⋊C4—22no—
103C3×C22⋊C4—22no—
104C3×C22⋊C4—22no—
105C3×C22⋊C4—22no—
106C3×C42—22no—
107#217—22no—
108#217—41no—
109(C2×D3)⋊C4—22no—
110(C2×D3)⋊C4—22no—
111(C2×D3)⋊C4—22no—
112(C2×D3)⋊C4—22no—
113(C2×D3)⋊C4—41no—
114(C2×D3)⋊C4—41no—
115(C2×D3)⋊C4—41no—
116(C2×D3)⋊C4D414yescomplemented
117C4⋊Dic3—22no—
118C4⋊Dic3—41no—
119C4×Dic3—22no—
120C4×Dic3—41no—
121C22×Q8—31no—
122C22×D4—31no—
123C22×D4—31no—
124C22×D4—31no—
125C23×C4—31no—
126C23×C4—31no—
127#124—64no—
128C4×D4—64no—
129C2×C4⋊C4—31no—
130C2×C4⋊C4—31no—
131C2×C4⋊C4C2×D311yescharacteristic
132C2×C22⋊C4—31no—
133C2×C22⋊C4—31no—
134C2×C22⋊C4—31no—
135C2×C22⋊C4—31no—
136C2×C22⋊C4—31no—
137C2×C22⋊C4—31no—
138C2×C22⋊C4—31no—
139C2×C22⋊C4—31no—
140C2×C22⋊C4—31no—
141C2×C22⋊C4—31no—
142C2×C22⋊C4C2×D311yescharacteristic
143C2×C22⋊C4C2×D311yescharacteristic
144C2×C22⋊C4C2×D311yescharacteristic
145C2×C42—31no—
146C2×C42—31no—
147C2×C42C2×D311yescharacteristic
148#95—31no—
149#95—31no—
150#95—31no—
151#95—31no—
152#95—31no—
153#95—31no—
154#95—31no—
155#95—31no—
156#95C2×D311yescharacteristic
157#95C2×D311yescharacteristic
158C23×C3—21no—
159C23×C3—21no—
160C23×C3—21no—
161C23×C3—21no—
162C23×C3—21no—
163C23×C3—21no—
164C23×C3—21no—
165C23×C3C2411yescharacteristic
166C22×D3—21no—
167C22×D3—21no—
168C22×D3—21no—
169C22×D3—21no—
170C22×D3—21no—
171C22×D3—21no—
172C22×D3—21no—
173C22×D3—21no—
174C22×D3—21no—
175C22×D3—21no—
176C22×D3—21no—
177C22×D3—21no—
178C22×D3C2×D412yes—
179C22×D3#4112yes—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
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×C4C2×D412yes—
196C2×C3×C4#4112yes—
197C2×C3×C4#4112yes—
198#67—44no—
199#67—44no—
200C2×Dic3—21no—
201C2×Dic3—21no—
202C2×Dic3—21no—
203C2×Dic3—21no—
204C2×Dic3—21no—
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×Dic3C2×D412yes—
217C2×Dic3#4112yes—
218D12—28no—
219C4×D3—44no—
220C4×D3—44no—
221Dic6—44no—
222C24—31no—
223C24—31no—
224C24C22×D311yescharacteristic
225C2×Q8—62no—
226C2×Q8—62no—
227C2×Q8—121no—
228C2×D4—62no—
229C2×D4—62no—
230C2×D4—62no—
231C2×D4—62no—
232C2×D4—62no—
233C2×D4—62no—
234C2×D4—121no—
235C2×D4—121no—
236C2×D4—121no—
237C22×C4—31no—
238C22×C4—31no—
239C22×C4—31no—
240C22×C4—31no—
241C22×C4—31no—
242C22×C4—31no—
243C22×C4—62no—
244C22×C4—62no—
245C22×C4—62no—
246C22×C4—62no—
247C22×C4—121no—
248C22×C4—121no—
249C22×C4C22×D311yescharacteristic
250C22×C4C22×D311yescharacteristic
251C22×C4C22×D311yescharacteristic
252C22×C4C22×D311yescharacteristic
253C22×C4C22×D311yescharacteristic
254C22×C4C22×D311yescharacteristic
255C4⋊C4—22no—
256C4⋊C4—62no—
257C4⋊C4—121no—
258C22⋊C4—22no—
259C22⋊C4—22no—
260C22⋊C4—22no—
261C22⋊C4—34no—
262C22⋊C4—62no—
263C22⋊C4—62no—
264C22⋊C4—62no—
265C22⋊C4—62no—
266C22⋊C4—62no—
267C22⋊C4—121no—
268C22⋊C4—121no—
269C22⋊C4—121no—
270C22⋊C4—121no—
271C42—22no—
272C42—62no—
273C42—121no—
274C22×C3—41no—
275C22×C3—41no—
276C22×C3—41no—
277C22×C3—41no—
278C22×C3—41no—
279C22×C3—41no—
280C22×C3—41no—
281C22×C3C22×D411yescharacteristic
282C22×C3C2×#4111yescharacteristic
283C22×C3C2×#4111yescharacteristic
284C22×C3C2×#4111yescharacteristic
285C22×C3C2×#4111yescharacteristic
286C22×C3H(5,𝔽2)11yescharacteristic
287C22×C3H(5,𝔽2)11yescharacteristic
288C2×D3—22no—
289C2×D3—22no—
290C2×D3—22no—
291C2×D3—22no—
292C2×D3—22no—
293C2×D3—22no—
294C2×D3—41no—
295C2×D3—41no—
296C2×D3—41no—
297C2×D3—41no—
298C2×D3—41no—
299C2×D3—41no—
300C2×D3—41no—
301C2×D3—41no—
302C3×C4—22no—
303C3×C4—22no—
304C3×C4—22no—
305C3×C4—41no—
306C3×C4—41no—
307C3×C4—41no—
308Dic3—22no—
309Dic3—22no—
310Dic3—41no—
311Dic3—41no—
312Dic3—41no—
313Dic3—41no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—32no—
322C23—32no—
323C23—61no—
324C23—61no—
325C23—61no—
326C23—61no—
327C23—61no—
328C23—61no—
329C23—61no—
330C23—61no—
331C23—61no—
332C23—61no—
333C23—61no—
334C23—61no—
335C23C23×D311yescharacteristic
336Q8—124no—
337D4—68no—
338D4—124no—
339D4—124no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—32no—
356C2×C4—32no—
357C2×C4—61no—
358C2×C4—61no—
359C2×C4—61no—
360C2×C4—61no—
361C2×C4—61no—
362C2×C4—61no—
363C2×C4—61no—
364C2×C4—61no—
365C2×C4—61no—
366C2×C4—61no—
367C2×C4—61no—
368C2×C4—61no—
369C2×C4—61no—
370C2×C4—61no—
371C2×C4—61no—
372C2×C4—61no—
373C2×C4—124no—
374C2×C4—124no—
375C2×C4#23512yes—
376C2×C4D3×D412yes—
377C2×C4#23712yes—
378C2×C3—81no—
379C2×C3#52511yescharacteristic
380C2×C3#52911yescharacteristic
381C2×C3#53811yescharacteristic
382C2×C3#54611yescharacteristic
383C2×C3#54611yescharacteristic
384C2×C3#55511yescharacteristic
385C2×C3#55911yescharacteristic
386D3—42no—
387D3—42no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—62no—
396C22—62no—
397C22—62no—
398C22—62no—
399C22—62no—
400C22—62no—
401C22—121no—
402C22—121no—
403C22—121no—
404C22—121no—
405C22—121no—
406C22—121no—
407C22—121no—
408C22—121no—
409C22C2×#23511yescharacteristic
410C22C2×D3×D411yescharacteristic
411C22C2×#23711yescharacteristic
412C22D3×#4111yescharacteristic
413C22D3×#4111yescharacteristic
414C22#100911yescharacteristic
415C22#100911yescharacteristic
416C4—22no—
417C4—22no—
418C4—22no—
419C4—41no—
420C4—41no—
421C4—41no—
422C4—62no—
423C4—62no—
424C4—121no—
425C4—121no—
426C4—121no—
427C4—121no—
428C3#245911yescharacteristic, complemented, Sylow
429C2—81no—
430C2—122no—
431C2—122no—
432C2#552811yescharacteristic
433C2#555011yescharacteristic
434C2#556311yescharacteristic
435C2#560611yescharacteristic
436C2#565411yescharacteristic
437C2#568111yescharacteristic
438C2#570411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#388C2
prime radical#4960C2
hypercenter#388D3
hypocenterC3#2459
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#885C2semidirect
2. C2×C4×D12C2semidirect
3. C3×#388C2semidirect
4. #4991C2semidirect
5. #4980C2semidirect
6. #4961C2semidirect
8. #4956C2semidirect
9. #4956C2semidirect
10. #4951C2semidirect
11. #4929C2semidirect
12. #4673C2semidirect
13. #4670C2semidirect
14. #4666C2semidirect
15. #4664C2semidirect
63. #388D3semidirect
116. (C2×D3)⋊C4D4semidirect
428. C3#2459semidirect

Maximal subgroups

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

subgroupindex
C2×#8852
C2×C4×D122
C3×#3882
#49912
#49802
#49612
#49602
#49562
#49512
#49292
#46732
#46702
#46662
#46642
#24593