Finite Group Databasebeta

← #74198

Subgroups — #74198

Order 384.

554 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#894C211yesmaximal, characteristic, complemented
2C2×#894C211yesmaximal, characteristic, complemented
3C3×#382C211yesmaximal, characteristic, complemented
4#4993C211yesmaximal, characteristic, complemented
5#4992C211yesmaximal, characteristic, complemented
6#4940C211yesmaximal, characteristic, complemented
7#4939C211yesmaximal, characteristic, complemented
8#4676C211yesmaximal, characteristic, complemented
9#4672C211yesmaximal, characteristic, complemented
10#4671C211yesmaximal, characteristic
11#4668C211yesmaximal, characteristic, complemented
12#4667C211yesmaximal, characteristic, complemented
13#4665C211yesmaximal, characteristic, complemented
14#4665C211yesmaximal, characteristic, complemented
15#4657C211yesmaximal, characteristic, complemented
16#2706—31nomaximal, Sylow
17C22×D12C2211yescharacteristic
18C22×D12C2211yescharacteristic
19C22×D12C2211yescharacteristic
20C22×C4×D3C2211yescharacteristic
21C22×C4×D3C2211yescharacteristic
22C2×C3×C4⋊C4C2211yescharacteristic
23C2×C3×C4⋊C4C2211yescharacteristic
24C2×C3×C42C2211yescharacteristic
25C2×(C2×D3)⋊C4C2211yescharacteristic
26C2×(C2×D3)⋊C4C2211yescharacteristic
27C2×(C2×D3)⋊C4C2211yescharacteristic
28C2×(C2×D3)⋊C4C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
39C2×Dic3⋊C4C2211yescharacteristic
40C2×Dic3⋊C4C2211yescharacteristic
41C2×Dic3⋊C4C2211yescharacteristic
42C2×Dic3⋊C4C2211yescharacteristic
43C2×Dic3⋊C4C2211yescharacteristic
44#894—24no—
45#894—24no—
46C3×#95C2211yescharacteristic
47C3×#95C2211yescharacteristic
48C3×#95C2211yescharacteristic
49C3×#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C2×#123—31no—
55C2×#123—31no—
56#399—31no—
57#398—31no—
58#397—31no—
59#396—31no—
60#394—31no—
61#392—31no—
62#390—31no—
63#388—31no—
64#386—31no—
65#386—31no—
66#385—31no—
67#382D311yescharacteristic, complemented
68#380—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—22no—
95C2×C4×D3—22no—
96C2×C4×D3—41no—
97C2×C4×D3—41no—
98C2×C4×D3—41no—
99C3×C4⋊C4—22no—
100C3×C4⋊C4—22no—
101C3×C42—22no—
102(C2×D3)⋊C4—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—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)⋊C4D414yescomplemented
115C4⋊Dic3—41no—
116Dic3⋊C4—22no—
117Dic3⋊C4—22no—
118Dic3⋊C4—41no—
119Dic3⋊C4—41no—
120Dic3⋊C4—41no—
121C22×D4—31no—
122C22×D4—31no—
123C22×D4—31no—
124C23×C4—31no—
125C23×C4—31no—
126#123—64no—
127#123—64no—
128C2×C4⋊C4—31no—
129C2×C4⋊C4—31no—
130C2×C4⋊C4—31no—
131C2×C4⋊C4—31no—
132C2×C4⋊C4—31no—
133C2×C4⋊C4—31no—
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×C42C2×D311yescharacteristic
150#95—31no—
151#95—31no—
152#95—31no—
153#95—31no—
154#95C2×D311yescharacteristic
155#95C2×D311yescharacteristic
156#95C2×D311yescharacteristic
157#95C2×D311yescharacteristic
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×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×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
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×Dic3C2×D412yes—
216D12—44no—
217D12—44no—
218D12—44no—
219C4×D3—44no—
220C4×D3—44no—
221C24—31no—
222C24—31no—
223C24—31no—
224C2×D4—62no—
225C2×D4—62no—
226C2×D4—62no—
227C2×D4—62no—
228C2×D4—62no—
229C2×D4—121no—
230C2×D4—121no—
231C2×D4—121no—
232C2×D4—121no—
233C22×C4—31no—
234C22×C4—31no—
235C22×C4—31no—
236C22×C4—31no—
237C22×C4—31no—
238C22×C4—62no—
239C22×C4—62no—
240C22×C4—62no—
241C22×C4—121no—
242C22×C4—121no—
243C22×C4—121no—
244C22×C4C22×D311yescharacteristic
245C22×C4C22×D311yescharacteristic
246C22×C4C22×D311yescharacteristic
247C22×C4C22×D311yescharacteristic
248C22×C4C22×D311yescharacteristic
249C22×C4C22×D311yescharacteristic
250C22×C4C22×D311yescharacteristic
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—62no—
254C4⋊C4—62no—
255C4⋊C4—121no—
256C4⋊C4—121no—
257C4⋊C4—121no—
258C4⋊C4—121no—
259C22⋊C4—34no—
260C22⋊C4—62no—
261C22⋊C4—62no—
262C22⋊C4—62no—
263C22⋊C4—62no—
264C22⋊C4—62no—
265C22⋊C4—121no—
266C22⋊C4—121no—
267C22⋊C4—121no—
268C22⋊C4—121no—
269C22⋊C4—121no—
270C22⋊C4—121no—
271C22⋊C4—121no—
272C42—22no—
273C22×C3C22×D411yescharacteristic
274C22×C3C2×#4111yescharacteristic
275C22×C3C2×#4111yescharacteristic
276C22×C3H(5,𝔽2)11yescharacteristic
277C22×C3H(5,𝔽2)11yescharacteristic
278C22×C3H(5,𝔽2)11yescharacteristic
279C22×C32−1+411yescharacteristic
280C2×D3—22no—
281C2×D3—22no—
282C2×D3—22no—
283C2×D3—22no—
284C2×D3—22no—
285C2×D3—22no—
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—
300C2×D3—41no—
301C3×C4—22no—
302C3×C4—22no—
303C3×C4—41no—
304C3×C4—41no—
305C3×C4—41no—
306C3×C4—41no—
307C3×C4—41no—
308Dic3—22no—
309Dic3—41no—
310Dic3—41no—
311Dic3—41no—
312Dic3—41no—
313C23—32no—
314C23—32no—
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—
333C23—61no—
334C23C23×D311yescharacteristic
335D4—124no—
336D4—124no—
337D4—124no—
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—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—32no—
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—124no—
373C2×C4—124no—
374C2×C4#23512yes—
375C2×C4D3×D412yes—
376C2×C3#53511yescharacteristic
377C2×C3#53911yescharacteristic
378C2×C3#54011yescharacteristic
379C2×C3#54611yescharacteristic
380C2×C3#54711yescharacteristic
381C2×C3#55111yescharacteristic
382C2×C3#56211yescharacteristic
383D3—42no—
384D3—42no—
385D3—81no—
386C22—62no—
387C22—62no—
388C22—62no—
389C22—62no—
390C22—62no—
391C22—62no—
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—
405C22—121no—
406C22—121no—
407C22C2×#23511yescharacteristic
408C22C2×D3×D411yescharacteristic
409C22#100711yescharacteristic
410C22D3×#4111yescharacteristic
411C22#100911yescharacteristic
412C22#100911yescharacteristic
413C22#100911yescharacteristic
414C4—22no—
415C4—22no—
416C4—41no—
417C4—41no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—62no—
422C4—121no—
423C4—121no—
424C4—121no—
425C4—121no—
426C3#270611yescharacteristic, complemented, Sylow
427C2—122no—
428C2—122no—
429C2—241no—
430C2#550711yescharacteristic
431C2#552711yescharacteristic
432C2#553511yescharacteristic
433C2#567411yescharacteristic
434C2#567611yescharacteristic
435C2#569211yescharacteristic
436C2#570011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#382C2
prime radical#4671C2
hypercenter#382D3
hypocenterC3#2706
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
1. C2×#894C2semidirect
2. C2×#894C2semidirect
3. C3×#382C2semidirect
4. #4993C2semidirect
5. #4992C2semidirect
6. #4940C2semidirect
7. #4939C2semidirect
8. #4676C2semidirect
9. #4672C2semidirect
11. #4668C2semidirect
12. #4667C2semidirect
13. #4665C2semidirect
14. #4665C2semidirect
15. #4657C2semidirect
67. #382D3semidirect
114. (C2×D3)⋊C4D4semidirect
426. C3#2706semidirect

Maximal subgroups

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

subgroupindex
C2×#8942
C3×#3822
#49932
#49922
#49402
#49392
#46762
#46722
#46712
#46682
#46672
#46652
#46572
#27063