Finite Group Databasebeta

← #74393

Subgroups — #74393

Order 384.

776 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×C4×#67C211yesmaximal, characteristic
2C22×Dic3⋊C4C211yesmaximal, characteristic, complemented
3C2×D3×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×#67⋊C4C211yesmaximal, characteristic
5C2×#67⋊C4C211yesmaximal, characteristic
6C3×#385C211yesmaximal, characteristic, complemented
7#4989C211yesmaximal, characteristic, complemented
8#4976C211yesmaximal, characteristic, complemented
9#4975C211yesmaximal, characteristic, complemented
10#4950C211yesmaximal, characteristic, complemented
11#4942C211yesmaximal, characteristic, complemented
12#4668C211yesmaximal, characteristic, complemented
13#4667C211yesmaximal, characteristic, complemented
14#4649C211yesmaximal, characteristic, complemented
15#4647C211yesmaximal, characteristic, complemented
16D4×C4⋊C4—31nomaximal, Sylow
17C23×C3×C4C2211yescharacteristic
18C22×#67C2211yescharacteristic
19C23×Dic3C2211yescharacteristic
20C23×Dic3C2211yescharacteristic
21C22×C4×D3C2211yescharacteristic
22C22×C4×D3C2211yescharacteristic
23C22×C4×D3C2211yescharacteristic
24C2×C3×C4⋊C4C2211yescharacteristic
25C2×C3×C4⋊C4C2211yescharacteristic
26C2×C3×C22⋊C4C2211yescharacteristic
27C2×C3×C22⋊C4C2211yescharacteristic
28C2×#217C2211yescharacteristic
29C4×#67—24no—
30C2×(C2×D3)⋊C4C2211yescharacteristic
31C2×(C2×D3)⋊C4C2211yescharacteristic
32C2×(C2×D3)⋊C4C2211yescharacteristic
33C2×C4⋊Dic3C2211yescharacteristic
34C2×C4⋊Dic3C2211yescharacteristic
35C2×Dic3⋊C4—24no—
36C2×Dic3⋊C4C2211yescharacteristic
37C2×Dic3⋊C4C2211yescharacteristic
38C2×Dic3⋊C4C2211yescharacteristic
39C2×Dic3⋊C4C2211yescharacteristic
40C2×Dic3⋊C4C2211yescharacteristic
41C2×Dic3⋊C4C2211yescharacteristic
42C2×Dic3⋊C4C2211yescharacteristic
43C2×Dic3⋊C4C2211yescharacteristic
44C2×Dic3⋊C4C2211yescharacteristic
45C2×C4×Dic3C2211yescharacteristic
46C2×C4×Dic3C2211yescharacteristic
47C2×C4×Dic3C2211yescharacteristic
48D3×C4⋊C4—24no—
49#67⋊C4—24no—
50#67⋊C4C418yescomplemented
51C3×#95C2211yescharacteristic
52C3×#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C3⋊#95C2211yescharacteristic
55C3⋊#95C2211yescharacteristic
56C3⋊#95C2211yescharacteristic
57C2×C4×D4—31no—
58C2×C4×D4—31no—
59C2×C4×D4—31no—
60C22×C4⋊C4—31no—
61C22×C4⋊C4—31no—
62#389—31no—
63#389—31no—
64#385—31no—
65#385—31no—
66#385—31no—
67#385D311yescharacteristic, complemented
68#384—31no—
69#380—31no—
70#380—31no—
71C4×C4⋊C4—31no—
72C24×C3C2311yescharacteristic
73C23×D3C2311yescharacteristic
74C22×C3×C4—22no—
75C22×C3×C4—22no—
76C22×C3×C4—41no—
77C22×C3×C4C2311yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C22×C3×C4C2311yescharacteristic
81C22×C3×C4C2311yescharacteristic
82C22×C3×C4C2311yescharacteristic
83C2×#67C2×C414yes—
84C2×#67D414yes—
85C2×#67Q814yes—
86C22×Dic3—22no—
87C22×Dic3—22no—
88C22×Dic3—22no—
89C22×Dic3—22no—
90C22×Dic3—41no—
91C22×Dic3C2×C414yescomplemented
92C22×Dic3C2311yescharacteristic
93C22×Dic3C2311yescharacteristic
94C22×Dic3C2311yescharacteristic
95C22×Dic3C2311yescharacteristic
96C22×Dic3C2311yescharacteristic
97C22×Dic3C2311yescharacteristic
98C22×Dic3C2311yescharacteristic
99C2×C4×D3—22no—
100C2×C4×D3—22no—
101C2×C4×D3—22no—
102C2×C4×D3—22no—
103C2×C4×D3—22no—
104C2×C4×D3—22no—
105C2×C4×D3—41no—
106C2×C4×D3—41no—
107C2×C4×D3C2×C414yescomplemented
108C3×C4⋊C4—22no—
109C3×C4⋊C4—41no—
110C3×C22⋊C4—22no—
111C3×C22⋊C4C2×C414yescomplemented
112#217—22no—
113(C2×D3)⋊C4—22no—
114(C2×D3)⋊C4—22no—
115(C2×D3)⋊C4C2×C414yescomplemented
116C4⋊Dic3—22no—
117C4⋊Dic3—41no—
118Dic3⋊C4—22no—
119Dic3⋊C4—22no—
120Dic3⋊C4—22no—
121Dic3⋊C4—22no—
122Dic3⋊C4—22no—
123Dic3⋊C4—22no—
124Dic3⋊C4—22no—
125Dic3⋊C4C2×C414yescomplemented
126Dic3⋊C4D414yescomplemented
127C4×Dic3—22no—
128C4×Dic3—22no—
129C4×Dic3C2×C414yescomplemented
130C22×D4—31no—
131C23×C4—31no—
132C23×C4—31no—
133C23×C4—31no—
134C23×C4—31no—
135C23×C4—31no—
136C23×C4C2×D311yescharacteristic
137C4×D4—38no—
138C4×D4—64no—
139C4×D4—64no—
140C2×C4⋊C4—31no—
141C2×C4⋊C4—31no—
142C2×C4⋊C4—31no—
143C2×C4⋊C4—31no—
144C2×C4⋊C4—31no—
145C2×C4⋊C4—31no—
146C2×C4⋊C4—31no—
147C2×C4⋊C4—31no—
148C2×C4⋊C4—31no—
149C2×C4⋊C4—31no—
150C2×C4⋊C4—31no—
151C2×C4⋊C4—64no—
152C2×C4⋊C4—64no—
153C2×C4⋊C4C2×D311yescharacteristic
154C2×C4⋊C4C2×D311yescharacteristic
155C2×C22⋊C4—31no—
156C2×C22⋊C4—31no—
157C2×C22⋊C4—31no—
158C2×C22⋊C4—31no—
159C2×C22⋊C4C2×D311yescharacteristic
160C2×C22⋊C4C2×D311yescharacteristic
161C2×C42—31no—
162C2×C42—31no—
163C2×C42—31no—
164#95—31no—
165#95—31no—
166#95—31no—
167#95—31no—
168#95C2×D311yescharacteristic
169#95C2×D311yescharacteristic
170C23×C3—21no—
171C23×C3—21no—
172C23×C3—21no—
173C23×C3—21no—
174C23×C3C22×C412yes—
175C23×C3C2×D412yes—
176C23×C3C2×Q812yes—
177C23×C3C2411yescharacteristic
178C22×D3—21no—
179C22×D3—21no—
180C22×D3—21no—
181C22×D3—21no—
182C22×D3C22×C412yes—
183C22×D3C2×D412yes—
184C22×D3C2×Q812yes—
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—44no—
201C2×C3×C4C22×C412yes—
202C2×C3×C4C22×C412yes—
203C2×C3×C4C2×D412yes—
204#67C4⋊C4116yescomplemented
205C2×Dic3—21no—
206C2×Dic3—21no—
207C2×Dic3—21no—
208C2×Dic3—21no—
209C2×Dic3—28no—
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—44no—
220C2×Dic3C22×C412yes—
221C2×Dic3C22×C412yes—
222C2×Dic3C22×C412yes—
223C2×Dic3C2×D412yes—
224C2×Dic3C2×D412yes—
225C2×Dic3C2×D412yes—
226C2×Dic3C2×Q812yes—
227C2×Dic3#4112yes—
228C4×D3—28no—
229C4×D3—44no—
230C4×D3—44no—
231C24—31no—
232C24C22×D311yescharacteristic
233C2×D4—34no—
234C2×D4—34no—
235C2×D4—34no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—31no—
239C22×C4—31no—
240C22×C4—34no—
241C22×C4—31no—
242C22×C4—31no—
243C22×C4—34no—
244C22×C4—31no—
245C22×C4—31no—
246C22×C4—31no—
247C22×C4—41no—
248C22×C4—62no—
249C22×C4—62no—
250C22×C4—62no—
251C22×C4—62no—
252C22×C4—62no—
253C22×C4—62no—
254C22×C4—62no—
255C22×C4—62no—
256C22×C4—62no—
257C22×C4—62no—
258C22×C4—121no—
259C22×C4—121no—
260C22×C4—121no—
261C22×C4C22×D311yescharacteristic
262C22×C4C22×D311yescharacteristic
263C22×C4C22×D311yescharacteristic
264C22×C4C22×D311yescharacteristic
265C22×C4C22×D311yescharacteristic
266C22×C4C22×D311yescharacteristic
267C4⋊C4—22no—
268C4⋊C4—34no—
269C4⋊C4—34no—
270C4⋊C4—41no—
271C4⋊C4—62no—
272C4⋊C4—62no—
273C4⋊C4—62no—
274C4⋊C4—62no—
275C4⋊C4—62no—
276C4⋊C4—62no—
277C4⋊C4—62no—
278C4⋊C4—62no—
279C4⋊C4—121no—
280C22⋊C4—22no—
281C22⋊C4—34no—
282C22⋊C4—62no—
283C22⋊C4—62no—
284C22⋊C4—62no—
285C22⋊C4C4×D314yescomplemented
286C42—34no—
287C42—62no—
288C42—62no—
289C22×C3—22no—
290C22×C3—22no—
291C22×C3—22no—
292C22×C3—22no—
293C22×C3—22no—
294C22×C3—22no—
295C22×C3C2×C4⋊C414yescomplemented
296C22×C3C23×C411yescharacteristic
297C22×C3C22×D411yescharacteristic
298C22×C3C22×D411yescharacteristic
299C22×C3C22×Q811yescharacteristic
300C22×C3C2×#4111yescharacteristic
301C22×C3H(5,𝔽2)11yescharacteristic
302C22×C32−1+411yescharacteristic
303C2×D3—22no—
304C2×D3—22no—
305C2×D3—22no—
306C2×D3—22no—
307C2×D3—22no—
308C2×D3—22no—
309C2×D3C2×C4⋊C414yescomplemented
310C3×C4—22no—
311C3×C4—22no—
312C3×C4—22no—
313C3×C4—41no—
314C3×C4—41no—
315C3×C4—41no—
316Dic3—22no—
317Dic3—22no—
318Dic3—41no—
319Dic3—41no—
320Dic3—41no—
321Dic3C2×C4⋊C414yescomplemented
322Dic3C4×D414yescomplemented
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—32no—
328C23—32no—
329C23—32no—
330C23—61no—
331C23—61no—
332C23—61no—
333C23—61no—
334C23C2×C4×D312yes—
335C23D3×D412yes—
336C23D3×Q812yes—
337C23C23×D311yescharacteristic
338D4—316no—
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—32no—
355C2×C4—32no—
356C2×C4—32no—
357C2×C4—32no—
358C2×C4—32no—
359C2×C4—32no—
360C2×C4—32no—
361C2×C4—32no—
362C2×C4—44no—
363C2×C4—68no—
364C2×C4—68no—
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—61no—
374C2×C4—61no—
375C2×C4—61no—
376C2×C4—61no—
377C2×C4—61no—
378C2×C4—124no—
379C2×C4—124no—
380C2×C4—124no—
381C2×C4C2×C4×D312yes—
382C2×C4C2×C4×D312yes—
383C2×C4D3×D412yes—
384C2×C3—24no—
385C2×C3C22×C4⋊C411yescharacteristic
386C2×C3C2×C4×D411yescharacteristic
387C2×C3#52011yescharacteristic
388C2×C3D4211yescharacteristic
389C2×C3#54711yescharacteristic
390C2×C3D4×Q811yescharacteristic
391C2×C3#55411yescharacteristic
392D3—24no—
393C22—22no—
394C22—22no—
395C22—22no—
396C22—22no—
397C22—22no—
398C22—22no—
399C22—34no—
400C22—62no—
401C22—62no—
402C22—62no—
403C22—62no—
404C22—62no—
405C22—62no—
406C22D3×C4⋊C414yescomplemented
407C22C22×C4×D311yescharacteristic
408C22C2×D3×D411yescharacteristic
409C22C2×D3×D411yescharacteristic
410C22#100411yescharacteristic
411C22C2×D3×Q811yescharacteristic
412C22D3×#4111yescharacteristic
413C22#101011yescharacteristic
414C4—22no—
415C4—22no—
416C4—22no—
417C4—34no—
418C4—34no—
419C4—41no—
420C4—41no—
421C4—41no—
422C4—62no—
423C4—62no—
424C4—121no—
425C4—121no—
426C4—121no—
427C3D4×C4⋊C411yescharacteristic, complemented, Sylow
428C2—24no—
429C2—64no—
430C2C2×D3×C4⋊C411yescharacteristic
431C2C4×D3×D411yescharacteristic
432C2#554611yescharacteristic
433C2#559011yescharacteristic
434C2#563211yescharacteristic
435C2#563611yescharacteristic
436C2#565511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutatorC22×C3C23×C4
FittingC3×#385C2
socle, cosocleC23×C3C24
prime radicalC22×#67C22
hypercenter#385D3
hypocenterC3D4×C4⋊C4
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C22×Dic3⋊C4C2semidirect
3. C2×D3×C4⋊C4C2semidirect
6. C3×#385C2semidirect
7. #4989C2semidirect
8. #4976C2semidirect
9. #4975C2semidirect
10. #4950C2semidirect
11. #4942C2semidirect
12. #4668C2semidirect
13. #4667C2semidirect
14. #4649C2semidirect
15. #4647C2semidirect
50. #67⋊C4C4semidirect
67. #385D3semidirect
91. C22×Dic3C2×C4semidirect
107. C2×C4×D3C2×C4semidirect
111. C3×C22⋊C4C2×C4semidirect
115. (C2×D3)⋊C4C2×C4semidirect
125. Dic3⋊C4C2×C4semidirect
126. Dic3⋊C4D4semidirect
129. C4×Dic3C2×C4semidirect
204. #67C4⋊C4semidirect
285. C22⋊C4C4×D3semidirect
295. C22×C3C2×C4⋊C4semidirect
309. C2×D3C2×C4⋊C4semidirect
321. Dic3C2×C4⋊C4semidirect
322. Dic3C4×D4semidirect
406. C22D3×C4⋊C4semidirect
427. C3D4×C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#672
C22×Dic3⋊C42
C2×D3×C4⋊C42
C2×#67⋊C42
C3×#3852
#49892
#49762
#49752
#49502
#49422
#46682
#46672
#46492
#46472
D4×C4⋊C43