Finite Group Databasebeta

← #83070

Subgroups — #83070

Order 384.

540 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#125C211yesmaximal, characteristic, complemented
2C2×#895C211yesmaximal, characteristic
3#4994C211yesmaximal, characteristic, complemented
4#4993C211yesmaximal, characteristic, complemented
5#4991C211yesmaximal, characteristic, complemented
6#4991C211yesmaximal, characteristic, complemented
7#4991C211yesmaximal, characteristic, complemented
8#4991C211yesmaximal, characteristic, complemented
9#4990C211yesmaximal, characteristic, complemented
10#4989C211yesmaximal, characteristic, complemented
11#4989C211yesmaximal, characteristic, complemented
12#4988C211yesmaximal, characteristic, complemented
13#4980C211yesmaximal, characteristic, complemented
14#4940C211yesmaximal, characteristic, complemented
15#4939C211yesmaximal, characteristic, complemented
16#2711—31nomaximal, Sylow
17C22×D12C2211yescharacteristic
18C22×D12C2211yescharacteristic
19C22×D12C2211yescharacteristic
20C22×C4×D3C2211yescharacteristic
21C3×#125—24no—
22C2×C3×C4⋊C4C2211yescharacteristic
23C2×C3×C4⋊C4C2211yescharacteristic
24C2×C3×C4⋊C4C2211yescharacteristic
25C2×C3×C4⋊C4C2211yescharacteristic
26C2×C3×C4⋊C4C2211yescharacteristic
27C2×C3×C4⋊C4C2211yescharacteristic
28C2×C3×C42C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
42C2×(C2×D3)⋊C4C2211yescharacteristic
43C2×C4⋊Dic3C2211yescharacteristic
44C2×Dic3⋊C4C2211yescharacteristic
45C2×Dic3⋊C4C2211yescharacteristic
46C2×C4×Dic3C2211yescharacteristic
47#895—24no—
48C3⋊#95C2211yescharacteristic
49C3⋊#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C2×#125D311yescharacteristic, complemented
55C2×#121—31no—
56#399—31no—
57#396—31no—
58#394—31no—
59#394—31no—
60#394—31no—
61#394—31no—
62#390—31no—
63#390—31no—
64#388—31no—
65#388—31no—
66#387—31no—
67#385—31no—
68#385—31no—
69C23×D3C2311yescharacteristic
70C23×D3C2311yescharacteristic
71C23×D3C2311yescharacteristic
72C22×C3×C4C2311yescharacteristic
73C22×C3×C4C2311yescharacteristic
74C22×C3×C4C2311yescharacteristic
75C22×C3×C4C2311yescharacteristic
76C22×C3×C4C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C22×Dic3C2311yescharacteristic
80C22×Dic3C2311yescharacteristic
81C22×Dic3C2311yescharacteristic
82C22×Dic3C2311yescharacteristic
83C22×Dic3C2311yescharacteristic
84C2×D12—22no—
85C2×D12—22no—
86C2×D12—22no—
87C2×D12—22no—
88C2×D12—22no—
89C2×D12—41no—
90C2×D12—41no—
91C2×D12—41no—
92C2×D12—41no—
93C2×C4×D3—22no—
94C2×C4×D3—41no—
95C2×C4×D3—41no—
96C3×C4⋊C4—22no—
97C3×C4⋊C4—22no—
98C3×C4⋊C4—22no—
99C3×C4⋊C4—22no—
100C3×C4⋊C4—22no—
101C3×C4⋊C4D414yes—
102C3×C42—22no—
103(C2×D3)⋊C4—22no—
104(C2×D3)⋊C4—22no—
105(C2×D3)⋊C4—22no—
106(C2×D3)⋊C4—22no—
107(C2×D3)⋊C4—22no—
108(C2×D3)⋊C4—22no—
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—
117C4⋊Dic3—41no—
118Dic3⋊C4—41no—
119Dic3⋊C4—41no—
120C4×Dic3—41no—
121C22×D4—31no—
122C22×D4—31no—
123C22×D4—31no—
124C23×C4—31no—
125#125—24no—
126#121—64no—
127C2×C4⋊C4—31no—
128C2×C4⋊C4—31no—
129C2×C4⋊C4—31no—
130C2×C4⋊C4C2×D311yescharacteristic
131C2×C4⋊C4C2×D311yescharacteristic
132C2×C4⋊C4C2×D311yescharacteristic
133C2×C4⋊C4C2×D311yescharacteristic
134C2×C4⋊C4C2×D311yescharacteristic
135C2×C4⋊C4C2×D311yescharacteristic
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⋊C4—31no—
145C2×C22⋊C4—31no—
146C2×C22⋊C4—31no—
147C2×C22⋊C4—31no—
148C2×C22⋊C4—31no—
149C2×C22⋊C4—31no—
150C2×C42—31no—
151C2×C42C2×D311yescharacteristic
152#95—31no—
153#95—31no—
154#95—31no—
155#95—31no—
156#95—31no—
157#95—31no—
158C23×C3C2411yescharacteristic
159C22×D3—21no—
160C22×D3—21no—
161C22×D3—21no—
162C22×D3—21no—
163C22×D3—21no—
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#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×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4C2×D412yes—
198C2×C3×C4C2×D412yes—
199C2×C3×C4C2×D412yes—
200C2×C3×C4#4112yes—
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—
216D12—44no—
217D12—44no—
218D12—44no—
219C4×D3—44no—
220C24—31no—
221C24—31no—
222C24—31no—
223C2×D4—62no—
224C2×D4—62no—
225C2×D4—62no—
226C2×D4—62no—
227C2×D4—62no—
228C2×D4—121no—
229C2×D4—121no—
230C2×D4—121no—
231C2×D4—121no—
232C22×C4—31no—
233C22×C4—31no—
234C22×C4—31no—
235C22×C4—31no—
236C22×C4—31no—
237C22×C4—62no—
238C22×C4—121no—
239C22×C4—121no—
240C22×C4C22×D311yescharacteristic
241C22×C4C22×D311yescharacteristic
242C22×C4C22×D311yescharacteristic
243C22×C4C22×D311yescharacteristic
244C22×C4C22×D311yescharacteristic
245C22×C4C22×D311yescharacteristic
246C22×C4C22×D311yescharacteristic
247C4⋊C4—22no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—121no—
253C4⋊C4—121no—
254C4⋊C4—121no—
255C4⋊C4#6714yes—
256C22⋊C4—62no—
257C22⋊C4—62no—
258C22⋊C4—62no—
259C22⋊C4—62no—
260C22⋊C4—62no—
261C22⋊C4—62no—
262C22⋊C4—121no—
263C22⋊C4—121no—
264C22⋊C4—121no—
265C22⋊C4—121no—
266C22⋊C4—121no—
267C22⋊C4—121no—
268C22⋊C4—121no—
269C22⋊C4—121no—
270C42—22no—
271C42—121no—
272C22×C3C22×D411yescharacteristic
273C22×C3C2×#4111yescharacteristic
274C22×C3C2×#4111yescharacteristic
275C22×C3H(5,𝔽2)11yescharacteristic
276C22×C3H(5,𝔽2)11yescharacteristic
277C22×C3H(5,𝔽2)11yescharacteristic
278C22×C32−1+411yescharacteristic
279C2×D3—22no—
280C2×D3—22no—
281C2×D3—22no—
282C2×D3—41no—
283C2×D3—41no—
284C2×D3—41no—
285C2×D3—41no—
286C2×D3—41no—
287C2×D3—41no—
288C2×D3—41no—
289C2×D3—41no—
290C2×D3—41no—
291C2×D3—41no—
292C2×D3—41no—
293C2×D3—41no—
294C2×D3—41no—
295C2×D3—41no—
296C2×D3—41no—
297C2×D3—41no—
298C2×D3—41no—
299C2×D3—41no—
300C3×C4—22no—
301C3×C4—22no—
302C3×C4—22no—
303C3×C4—22no—
304C3×C4—41no—
305C3×C4—41no—
306C3×C4—41no—
307Dic3—41no—
308Dic3—41no—
309Dic3—41no—
310Dic3—41no—
311Dic3—41no—
312C23—32no—
313C23—61no—
314C23—61no—
315C23—61no—
316C23—61no—
317C23—61no—
318C23—61no—
319C23—61no—
320C23—61no—
321C23—61no—
322C23—61no—
323C23—61no—
324C23—61no—
325C23—61no—
326C23—61no—
327C23—61no—
328C23—61no—
329C23—61no—
330C23—61no—
331C23—61no—
332C23—61no—
333C23C23×D311yescharacteristic
334D4—124no—
335D4—124no—
336D4—124no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
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—61no—
355C2×C4—61no—
356C2×C4—61no—
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—124no—
370C2×C4#23912yes—
371C2×C4C2×#6712yes—
372C2×C4C2×#6712yes—
373C2×C4C2×#6712yes—
374C2×C3#53511yescharacteristic
375C2×C3#53911yescharacteristic
376C2×C3#54011yescharacteristic
377C2×C3#54611yescharacteristic
378C2×C3#54811yescharacteristic
379C2×C3#55311yescharacteristic
380C2×C3#56211yescharacteristic
381D3—42no—
382D3—81no—
383D3—81no—
384C22—62no—
385C22—62no—
386C22—62no—
387C22—121no—
388C22—121no—
389C22—121no—
390C22—121no—
391C22—121no—
392C22—121no—
393C22—121no—
394C22—121no—
395C22—121no—
396C22—121no—
397C22—121no—
398C22—121no—
399C22—121no—
400C22—121no—
401C22—121no—
402C22—121no—
403C22—121no—
404C22—121no—
405C22C2×#23911yescharacteristic
406C22#100711yescharacteristic
407C22D3×#4111yescharacteristic
408C22#100911yescharacteristic
409C22#100911yescharacteristic
410C22#100911yescharacteristic
411C22C22×#6711yescharacteristic
412C4—22no—
413C4—22no—
414C4—22no—
415C4—22no—
416C4—41no—
417C4—41no—
418C4—41no—
419C4—121no—
420C4—121no—
421C4—121no—
422C4—121no—
423C4—121no—
424C3#271111yescharacteristic, complemented, Sylow
425C2—122no—
426C2—241no—
427C2—241no—
428C2#569211yescharacteristic
429C2#569511yescharacteristic
430C2#569711yescharacteristic
431C2#570011yescharacteristic
432C2#581711yescharacteristic
433C2#582911yescharacteristic
434C2#583011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC2×C3×#125C2
prime radicalC2×#895C2
hypercenterC2×#125D3
hypocenterC3#2711
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. C2×C3×#125C2semidirect
3. #4994C2semidirect
4. #4993C2semidirect
5. #4991C2semidirect
6. #4991C2semidirect
7. #4991C2semidirect
8. #4991C2semidirect
9. #4990C2semidirect
10. #4989C2semidirect
11. #4989C2semidirect
12. #4988C2semidirect
13. #4980C2semidirect
14. #4940C2semidirect
15. #4939C2semidirect
54. C2×#125D3semidirect
424. C3#2711semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#1252
C2×#8952
#49942
#49932
#49912
#49902
#49892
#49882
#49802
#49402
#49392
#27113