Finite Group Databasebeta

← #75955

Subgroups — #75955

Order 384.

508 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#388C211yesmaximal, characteristic, complemented
2#4992C211yesmaximal, characteristic, complemented
3#4991C211yesmaximal, characteristic, complemented
4#4961C211yesmaximal, characteristic, complemented
5#4960C211yesmaximal, characteristic, complemented
6#4960C211yesmaximal, characteristic, complemented
7#4960C211yesmaximal, characteristic, complemented
8#4959C211yesmaximal, characteristic, complemented
9#4959C211yesmaximal, characteristic, complemented
10#4940C211yesmaximal, characteristic, complemented
11#4939C211yesmaximal, characteristic, complemented
12#4675C211yesmaximal, characteristic, complemented
13#4672C211yesmaximal, characteristic, complemented
14#4671C211yesmaximal, characteristic, complemented
15#4660C211yesmaximal, characteristic, complemented
16#2828—31nomaximal, Sylow
17C22×#67C2211yescharacteristic
18C22×#67C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×D12C2211yescharacteristic
21C22×D12C2211yescharacteristic
22C22×D12C2211yescharacteristic
23C2×C3×C4⋊C4C2211yescharacteristic
24C2×C3×C22⋊C4C2211yescharacteristic
25C2×C3×C22⋊C4C2211yescharacteristic
26C2×C3×C22⋊C4C2211yescharacteristic
27C2×C3×C42C2211yescharacteristic
28C2×#217C2211yescharacteristic
29C2×(C2×D3)⋊C4C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
39C2×(C2×D3)⋊C4C2211yescharacteristic
40C2×(C2×D3)⋊C4C2211yescharacteristic
41C2×C4⋊Dic3C2211yescharacteristic
42C2×Dic3⋊C4C2211yescharacteristic
43C2×Dic3⋊C4C2211yescharacteristic
44C3×#95C2211yescharacteristic
45C3×#95C2211yescharacteristic
46C3⋊#95C2211yescharacteristic
47C3⋊#95C2211yescharacteristic
48C3⋊#95C2211yescharacteristic
49C3⋊#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52#400—31no—
53#397—31no—
54#397—31no—
55#394—31no—
56#394—31no—
57#394—31no—
58#394—31no—
59#394—31no—
60#392—31no—
61#392—31no—
62#392—31no—
63#392—31no—
64#390—31no—
65#388—31no—
66#388D311yescharacteristic, complemented
67C24×C3C2311yescharacteristic
68C23×D3C2311yescharacteristic
69C23×D3C2311yescharacteristic
70C23×D3C2311yescharacteristic
71C22×C3×C4C2311yescharacteristic
72C22×C3×C4C2311yescharacteristic
73C22×C3×C4C2311yescharacteristic
74C22×C3×C4C2311yescharacteristic
75C22×C3×C4C2311yescharacteristic
76C22×C3×C4C2311yescharacteristic
77C2×#67—41no—
78C2×#67—41no—
79C2×#67—41no—
80C2×#67—41no—
81C2×#67—41no—
82C2×#67—41no—
83C2×#67—41no—
84C2×#67—41no—
85C2×#67—41no—
86C22×Dic3C2311yescharacteristic
87C22×Dic3C2311yescharacteristic
88C22×Dic3C2311yescharacteristic
89C22×Dic3C2311yescharacteristic
90C22×Dic3C2311yescharacteristic
91C2×D12—22no—
92C2×D12—41no—
93C2×D12—41no—
94C2×D12—41no—
95C2×D12—41no—
96C2×D12—41no—
97C2×D12—41no—
98C2×D12—41no—
99C2×D12—41no—
100C3×C4⋊C4—41no—
101C3×C22⋊C4—22no—
102C3×C22⋊C4—41no—
103C3×C22⋊C4—41no—
104C3×C42—41no—
105#217—41no—
106(C2×D3)⋊C4—22no—
107(C2×D3)⋊C4—41no—
108(C2×D3)⋊C4—41no—
109(C2×D3)⋊C4—41no—
110(C2×D3)⋊C4—41no—
111(C2×D3)⋊C4—41no—
112(C2×D3)⋊C4—41no—
113(C2×D3)⋊C4—41no—
114(C2×D3)⋊C4—41no—
115(C2×D3)⋊C4—41no—
116(C2×D3)⋊C4—41no—
117(C2×D3)⋊C4—41no—
118C4⋊Dic3—41no—
119Dic3⋊C4—41no—
120Dic3⋊C4—41no—
121C22×D4—31no—
122C22×D4—31no—
123C22×D4—31no—
124C22×D4—31no—
125C22×D4—31no—
126C22×D4—31no—
127C2×C4⋊C4—31no—
128C2×C4⋊C4—31no—
129C2×C4⋊C4—31no—
130C2×C4⋊C4C2×D311yescharacteristic
131C2×C22⋊C4—31no—
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⋊C4—31no—
143C2×C22⋊C4—31no—
144C2×C22⋊C4C2×D311yescharacteristic
145C2×C22⋊C4C2×D311yescharacteristic
146C2×C22⋊C4C2×D311yescharacteristic
147C2×C42C2×D311yescharacteristic
148#95—31no—
149#95—31no—
150#95—31no—
151#95—31no—
152#95—31no—
153#95—31no—
154#95C2×D311yescharacteristic
155#95C2×D311yescharacteristic
156C23×C3—21no—
157C23×C3—21no—
158C23×C3—21no—
159C23×C3—21no—
160C23×C3—21no—
161C23×C3—21no—
162C23×C3—21no—
163C23×C3C2411yescharacteristic
164C22×D3—21no—
165C22×D3—21no—
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×D3—21no—
179C22×D3—21no—
180C22×D3—21no—
181C22×D3—21no—
182C22×D3—21no—
183C22×D3—21no—
184C22×D3—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×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#4112yes—
203#67—44no—
204#67—44no—
205#67—44no—
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—
221D12—44no—
222D12—44no—
223D12—44no—
224C24—31no—
225C24—31no—
226C24—31no—
227C24C22×D311yescharacteristic
228C2×D4—62no—
229C2×D4—121no—
230C2×D4—121no—
231C2×D4—121no—
232C2×D4—121no—
233C2×D4—121no—
234C2×D4—121no—
235C2×D4—121no—
236C2×D4—121no—
237C2×D4—121no—
238C2×D4—121no—
239C2×D4—121no—
240C2×D4—121no—
241C2×D4—121no—
242C2×D4—121no—
243C2×D4—121no—
244C2×D4—121no—
245C2×D4—121no—
246C22×C4—31no—
247C22×C4—31no—
248C22×C4—31no—
249C22×C4—31no—
250C22×C4—31no—
251C22×C4C22×D311yescharacteristic
252C22×C4C22×D311yescharacteristic
253C22×C4C22×D311yescharacteristic
254C22×C4C22×D311yescharacteristic
255C22×C4C22×D311yescharacteristic
256C22×C4C22×D311yescharacteristic
257C4⋊C4—41no—
258C4⋊C4—121no—
259C4⋊C4—121no—
260C4⋊C4—121no—
261C22⋊C4—22no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—62no—
265C22⋊C4—121no—
266C22⋊C4—121no—
267C22⋊C4—121no—
268C22⋊C4—121no—
269C22⋊C4—121no—
270C22⋊C4—121no—
271C22⋊C4—121no—
272C22⋊C4—121no—
273C22⋊C4—121no—
274C22⋊C4—121no—
275C22⋊C4—121no—
276C22⋊C4—121no—
277C42—41no—
278C22×C3—41no—
279C22×C3—41no—
280C22×C3—41no—
281C22×C3—41no—
282C22×C3—41no—
283C22×C3—41no—
284C22×C3—41no—
285C22×C3C2×#4111yescharacteristic
286C22×C3H(5,𝔽2)11yescharacteristic
287C22×C3H(5,𝔽2)11yescharacteristic
288C22×C3H(5,𝔽2)11yescharacteristic
289C22×C3H(5,𝔽2)11yescharacteristic
290C22×C3H(5,𝔽2)11yescharacteristic
291C22×C3H(5,𝔽2)11yescharacteristic
292C2×D3—41no—
293C2×D3—41no—
294C2×D3—41no—
295C2×D3—41no—
296C2×D3—41no—
297C2×D3—41no—
298C2×D3—41no—
299C2×D3—41no—
300C2×D3—41no—
301C2×D3—41no—
302C2×D3—41no—
303C2×D3—41no—
304C2×D3—41no—
305C2×D3—41no—
306C2×D3—41no—
307C2×D3—41no—
308C2×D3—41no—
309C2×D3—41no—
310C2×D3—41no—
311C2×D3—41no—
312C2×D3—41no—
313C3×C4—22no—
314C3×C4—41no—
315C3×C4—41no—
316C3×C4—41no—
317C3×C4—41no—
318C3×C4—41no—
319Dic3—41no—
320Dic3—41no—
321Dic3—41no—
322Dic3—41no—
323Dic3—41no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—61no—
332C23—61no—
333C23—61no—
334C23—61no—
335C23—61no—
336C23—61no—
337C23—61no—
338C23—61no—
339C23—61no—
340C23—61no—
341C23—61no—
342C23—61no—
343C23—61no—
344C23—61no—
345C23—61no—
346C23—61no—
347C23—61no—
348C23—61no—
349C23—61no—
350C23—61no—
351C23—61no—
352C23C23×D311yescharacteristic
353D4—124no—
354D4—124no—
355D4—124no—
356D4—124no—
357D4—124no—
358D4—124no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
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—61no—
387C2×C4—61no—
388C2×C4—61no—
389C2×C4—61no—
390C2×C4—61no—
391C2×C4#23512yes—
392C2×C3—81no—
393C2×C3#53811yescharacteristic
394C2×C3#54011yescharacteristic
395C2×C3#54011yescharacteristic
396C2×C3#56011yescharacteristic
397C2×C3#56011yescharacteristic
398C2×C3#56011yescharacteristic
399C2×C3H(3,𝔽4)11yescharacteristic
400D3—81no—
401D3—81no—
402D3—81no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—121no—
411C22—121no—
412C22—121no—
413C22—121no—
414C22—121no—
415C22—121no—
416C22—121no—
417C22—121no—
418C22—121no—
419C22—121no—
420C22—121no—
421C22—121no—
422C22—121no—
423C22—121no—
424C22—121no—
425C22—121no—
426C22—121no—
427C22—121no—
428C22—121no—
429C22—121no—
430C22—121no—
431C22C2×#23511yescharacteristic
432C22#100411yescharacteristic
433C22#100411yescharacteristic
434C22#100911yescharacteristic
435C22#100911yescharacteristic
436C22#100911yescharacteristic
437C22#100911yescharacteristic
438C4—22no—
439C4—41no—
440C4—41no—
441C4—41no—
442C4—41no—
443C4—41no—
444C4—121no—
445C4—121no—
446C4—121no—
447C4—121no—
448C4—121no—
449C3#282811yescharacteristic, complemented, Sylow
450C2—81no—
451C2—241no—
452C2—241no—
453C2—241no—
454C2#553511yescharacteristic
455C2#556011yescharacteristic
456C2#556211yescharacteristic
457C2#562011yescharacteristic
458C2#566611yescharacteristic
459C2#568311yescharacteristic
460C2#571111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#388C2
hypercenter#388D3
hypocenterC3#2828
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C3×#388C2semidirect
2. #4992C2semidirect
3. #4991C2semidirect
4. #4961C2semidirect
5. #4960C2semidirect
6. #4960C2semidirect
7. #4960C2semidirect
8. #4959C2semidirect
9. #4959C2semidirect
10. #4940C2semidirect
11. #4939C2semidirect
12. #4675C2semidirect
13. #4672C2semidirect
14. #4671C2semidirect
15. #4660C2semidirect
66. #388D3semidirect
449. C3#2828semidirect

Maximal subgroups

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

subgroupindex
C3×#3882
#49922
#49912
#49612
#49602
#49592
#49402
#49392
#46752
#46722
#46712
#46602
#28283