Finite Group Databasebeta

← #86283

Subgroups — #86283

Order 384.

992 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#533C211yesmaximal, characteristic, complemented
2#5728C211yesmaximal, characteristic, complemented
3#5728C211yesmaximal, characteristic, complemented
4#5728C211yesmaximal, characteristic, complemented
5D3×C4⋊Q8C211yesmaximal, characteristic, complemented
6#5694C212yesmaximal, complemented
7#5685C212yesmaximal, complemented
8#5641C212yesmaximal, complemented
9#5639C212yesmaximal, complemented
10#5628C212yesmaximal
11#5625C212yesmaximal, complemented
12#5583C212yesmaximal, complemented
13#5581C212yesmaximal, complemented
14#5572C212yesmaximal, complemented
15#5569C212yesmaximal, complemented
16#5533C212yesmaximal, complemented
17#5529C212yesmaximal, complemented
18C4×#235C211yesmaximal, characteristic
19#5470C211yesmaximal, characteristic, complemented
20#3509—31nomaximal, Sylow
21C2×D3×Q8C2212yes—
22C2×#235C2211yescharacteristic
23C3×C4⋊Q8C2211yescharacteristic
24C3×C4⋊Q8C2211yescharacteristic
25C3×#125C2212yes—
26C3×C22⋊Q8C2212yes—
27C3×C22⋊Q8C2212yes—
28C3×C4×Q8C2212yes—
29C3×C4×Q8C2212yes—
30C3×#117C2212yes—
31C2×C3×C42C2211yescharacteristic
32#946C2212yes—
33#946C2212yes—
34#946C2212yes—
35Q8×Dic3C2212yes—
36Q8×Dic3C2212yes—
37Q8×Dic3C2212yes—
38#944C2212yes—
39C4×#67C2211yescharacteristic
40C4×#67C2211yescharacteristic
41C4×#67C2211yescharacteristic
42C4×#67C2211yescharacteristic
43#926C2212yes—
44#926C2211yescharacteristic
45#924C2212yes—
46#924C2212yes—
47#898C2214yes—
48#897C2212yes—
49#897C2212yes—
50#897C2212yes—
51#894C2214yes—
52#892C2214yes—
53#892C2212yes—
54#892C2212yes—
55#892C2212yes—
56D3×C4⋊C4C2212yes—
57D3×C4⋊C4C2212yes—
58#890C2212yes—
59#890C2212yes—
60#890C2214yes—
61#890C2212yes—
62#889C2214yes—
63#889C2214yes—
64#888C2212yes—
65#888C2212yes—
66#888C2214yes—
67#887C2214yes—
68#887C2212yes—
69#887C2212yes—
70#887C2212yes—
71#885C2214yes—
72#883C2214yes—
73#879C2214yes—
74#879C2214yes—
75#876C2214yes—
76C4×D12C2211yescharacteristic
77C4×D12C2211yescharacteristic
78#872C2211yescharacteristic
79#872C2211yescharacteristic
80#872C2214yes—
81C42×D3C2211yescharacteristic
82C42×D3C2211yescharacteristic
83#870C2212yes—
84#870C2214yes—
85#869C2211yescharacteristic
86#869C2211yescharacteristic
87C4×Dic6C2211yescharacteristic
88C4×Dic6C2212yes—
89C4×Dic6C2212yes—
90C4×Dic6C2211yescharacteristic
91C4×Dic6C2214yes—
92#557—32no—
93#557—32no—
94#556—32no—
95#556—32no—
96#552—32no—
97#552—32no—
98#552—32no—
99#552—32no—
100#541—32no—
101#541—32no—
102#536—32no—
103#533—31no—
104#533—31no—
105#533—31no—
106#533—31no—
107#533D311yescharacteristic, complemented
108C2×C4⋊Q8—31no—
109#519—32no—
110C4×#41—31no—
111C2×C3×Q8C2312yes—
112C2×C3×Q8C2312yes—
113C22×C3×C4C2311yescharacteristic
114C22×C3×C4C2311yescharacteristic
115C22×C3×C4C2311yescharacteristic
116C2×#67C2311yescharacteristic
117C2×#67C2311yescharacteristic
118D3×Q8—28no—
119#235—24no—
120C2×D12C2311yescharacteristic
121C2×C4×D3C2311yescharacteristic
122C2×C4×D3C2311yescharacteristic
123C2×C4×D3C2311yescharacteristic
124C2×C4×D3C2311yescharacteristic
125C2×C4×D3C2311yescharacteristic
126C2×C4×D3C2314yes—
127C2×C4×D3C2311yescharacteristic
128C2×Dic6C2311yescharacteristic
129C2×Dic6C2312yes—
130C2×Dic6C2312yes—
131C2×Dic6C2314yes—
132C3×C4⋊C4C2312yes—
133C3×C4⋊C4C2314yes—
134C3×C4⋊C4C2312yes—
135C3×C4⋊C4C2312yes—
136C3×C4⋊C4C2314yes—
137C3×C4⋊C4C2312yes—
138C3×C22⋊C4C2314yes—
139C3×C42C2311yescharacteristic
140C3×C42C2311yescharacteristic
141C3×C42C2311yescharacteristic
142C3×C42C2314yes—
143C3×C42C2311yescharacteristic
144#217C2311yescharacteristic
145#217C2311yescharacteristic
146#217C2314yes—
147(C2×D3)⋊C4C2311yescharacteristic
148(C2×D3)⋊C4C2311yescharacteristic
149(C2×D3)⋊C4C2311yescharacteristic
150(C2×D3)⋊C4C2311yescharacteristic
151(C2×D3)⋊C4C2314yes—
152(C2×D3)⋊C4C2314yes—
153(C2×D3)⋊C4C2314yes—
154C4⋊Dic3C2312yes—
155C4⋊Dic3C2312yes—
156C4⋊Dic3C2311yescharacteristic
157C4⋊Dic3C2311yescharacteristic
158C4⋊Dic3C2314yes—
159C4⋊Dic3C2312yes—
160C4⋊Dic3C2312yes—
161C4⋊Dic3C2314yes—
162C4⋊Dic3C2314yes—
163Dic3⋊C4C2311yescharacteristic
164Dic3⋊C4C2314yes—
165Dic3⋊C4C2311yescharacteristic
166Dic3⋊C4C2314yes—
167Dic3⋊C4C2311yescharacteristic
168Dic3⋊C4C2311yescharacteristic
169Dic3⋊C4C2314yes—
170Dic3⋊C4C2314yes—
171Dic3⋊C4C2314yes—
172Dic3⋊C4C2314yes—
173Dic3⋊C4C2314yes—
174C4×Dic3C2314yes—
175C4×Dic3C2311yescharacteristic
176C4×Dic3C2311yescharacteristic
177C4×Dic3C2311yescharacteristic
178C4×Dic3C2311yescharacteristic
179C4×Dic3C2314yes—
180C4×Dic3C2314yes—
181C4×Dic3C2311yescharacteristic
182C4×Dic3C2311yescharacteristic
183C4×Dic3C2314yes—
184C2×#41—31no—
185C22×Q8—32no—
186C4⋊Q8—32no—
187C4⋊Q8—32no—
188C4⋊Q8—32no—
189C4⋊Q8—34no—
190C4⋊Q8—31no—
191C4⋊Q8—31no—
192C4⋊Q8C2×D311yescharacteristic
193C4⋊Q8C2×D311yescharacteristic
194#126—34no—
195#126—34no—
196#126—34no—
197#126—34no—
198#125—32no—
199#125—32no—
200#125—32no—
201#125—34no—
202#125—34no—
203#125—34no—
204#125—32no—
205#125—34no—
206#125C2×D312yes—
207#124—34no—
208#123—34no—
209#123—34no—
210C22⋊Q8—32no—
211C22⋊Q8—32no—
212C22⋊Q8—32no—
213C22⋊Q8—32no—
214C22⋊Q8—32no—
215C22⋊Q8—32no—
216C22⋊Q8—32no—
217C22⋊Q8—32no—
218C22⋊Q8C2×D312yes—
219C22⋊Q8C2×D312yes—
220C4×Q8—32no—
221C4×Q8—32no—
222C4×Q8—32no—
223C4×Q8—32no—
224C4×Q8—34no—
225C4×Q8—32no—
226C4×Q8—32no—
227C4×Q8—31no—
228C4×Q8—31no—
229C4×Q8—32no—
230C4×Q8—34no—
231C4×Q8—32no—
232C4×Q8C2×D312yes—
233C4×Q8C2×D312yes—
234C4×D4—31no—
235C4×D4—31no—
236C4×D4—31no—
237C4×D4—31no—
238C4×D4—31no—
239C4×D4—31no—
240#117—31no—
241#117—32no—
242#117—32no—
243#117—34no—
244#117—32no—
245#117—32no—
246#117—31no—
247#117—31no—
248#117—34no—
249#117C2×D312yes—
250C2×C4⋊C4—32no—
251C2×C4⋊C4—32no—
252C2×C42—31no—
253C2×C42—31no—
254C2×C42C2×D311yescharacteristic
255C23×C3C2411yescharacteristic
256C22×D3C2411yescharacteristic
257C22×D3C2411yescharacteristic
258C3×Q8—24no—
259C3×Q8—24no—
260C2×C3×C4—22no—
261C2×C3×C4—22no—
262C2×C3×C4—22no—
263C2×C3×C4C2411yescharacteristic
264C2×C3×C4C2414yes—
265C2×C3×C4C2414yes—
266C2×C3×C4C2411yescharacteristic
267C2×C3×C4C2411yescharacteristic
268C2×C3×C4C2411yescharacteristic
269C2×C3×C4C2411yescharacteristic
270C2×C3×C4C2411yescharacteristic
271#67—22no—
272#67—22no—
273C2×Dic3C2411yescharacteristic
274C2×Dic3C2411yescharacteristic
275C2×Dic3C2414yes—
276C2×Dic3C2411yescharacteristic
277C2×Dic3C2411yescharacteristic
278C2×Dic3C2411yescharacteristic
279C2×Dic3C2414yes—
280C2×Dic3C2411yescharacteristic
281D12—22no—
282C4×D3—28no—
283C4×D3—22no—
284C4×D3—22no—
285C4×D3—22no—
286C4×D3—22no—
287C4×D3—22no—
288C4×D3#4114yes—
289Dic6—24no—
290Dic6—24no—
291Dic6—22no—
292Dic6—28no—
293#41—64no—
294C2×Q8—32no—
295C2×Q8—32no—
296C2×Q8—34no—
297C2×Q8—31no—
298C2×Q8—68no—
299C2×Q8C22×D312yes—
300C2×Q8C22×D312yes—
301C2×D4—31no—
302C2×D4—31no—
303C2×D4—31no—
304C22×C4—31no—
305C22×C4—31no—
306C22×C4—31no—
307C22×C4—31no—
308C22×C4—31no—
309C22×C4—31no—
310C22×C4—34no—
311C22×C4C22×D311yescharacteristic
312C22×C4C22×D311yescharacteristic
313C22×C4C22×D311yescharacteristic
314C4⋊C4—32no—
315C4⋊C4—32no—
316C4⋊C4—34no—
317C4⋊C4—34no—
318C4⋊C4—32no—
319C4⋊C4—31no—
320C4⋊C4—31no—
321C4⋊C4—31no—
322C4⋊C4—31no—
323C4⋊C4—31no—
324C4⋊C4—31no—
325C4⋊C4—32no—
326C4⋊C4—34no—
327C4⋊C4—34no—
328C4⋊C4—34no—
329C4⋊C4—34no—
330C4⋊C4—34no—
331C4⋊C4—34no—
332C4⋊C4—34no—
333C4⋊C4—34no—
334C4⋊C4C22×D312yes—
335C4⋊C4C22×D312yes—
336C4⋊C4C22×D312yes—
337C4⋊C4C22×D312yes—
338C4⋊C4C22×D314yes—
339C4⋊C4C22×D314yes—
340C22⋊C4—31no—
341C22⋊C4—31no—
342C22⋊C4—34no—
343C22⋊C4—31no—
344C22⋊C4—31no—
345C22⋊C4—34no—
346C22⋊C4—31no—
347C22⋊C4—31no—
348C22⋊C4—34no—
349C22⋊C4—34no—
350C22⋊C4C22×D314yes—
351C42—31no—
352C42—31no—
353C42—31no—
354C42—31no—
355C42—31no—
356C42—31no—
357C42—34no—
358C42—34no—
359C42—34no—
360C42—34no—
361C42C22×D311yescharacteristic
362C42C22×D311yescharacteristic
363C42C22×D311yescharacteristic
364C42C22×D311yescharacteristic
365C42C22×D314yes—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3C2511yescharacteristic
370C2×D3—21no—
371C2×D3—21no—
372C2×D3—21no—
373C2×D3—21no—
374C2×D3—21no—
375C2×D3C2×#4112yes—
376C3×C4—24no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—24no—
381C3×C4C2×#4112yes—
382C3×C42−1+412yes—
383C3×C42−1+412yes—
384Dic3—24no—
385Dic3—21no—
386Dic3—24no—
387Dic3—21no—
388Dic3—21no—
389Dic3—21no—
390Dic3—21no—
391Dic3C2×#4112yes—
392C23—31no—
393C23—31no—
394C23C23×D311yescharacteristic
395Q8—24no—
396Q8—24no—
397Q8—68no—
398Q8—62no—
399Q8—64no—
400Q8—64no—
401D4—62no—
402D4—62no—
403D4—62no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—31no—
408C2×C4—34no—
409C2×C4—31no—
410C2×C4—31no—
411C2×C4—34no—
412C2×C4—31no—
413C2×C4—31no—
414C2×C4—34no—
415C2×C4—31no—
416C2×C4—68no—
417C2×C4—62no—
418C2×C4—62no—
419C2×C4—62no—
420C2×C4—62no—
421C2×C4—62no—
422C2×C4C23×D311yescharacteristic
423C2×C4C23×D314yes—
424C2×C4C23×D314yes—
425C2×C4C23×D311yescharacteristic
426C2×C4C23×D311yescharacteristic
427C2×C4C23×D311yescharacteristic
428C2×C4C23×D311yescharacteristic
429C2×C4C23×D311yescharacteristic
430C2×C3—41no—
431C2×C3C22×#4111yescharacteristic
432C2×C3C2×2−1+411yescharacteristic
433C2×C3C2×2−1+411yescharacteristic
434D3—22no—
435D3—41no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—32no—
440C22—61no—
441C22—61no—
442C22—61no—
443C22—61no—
444C22—61no—
445C22C24×D311yescharacteristic
446C4—21no—
447C4—21no—
448C4—24no—
449C4—21no—
450C4—24no—
451C4—32no—
452C4—61no—
453C4—61no—
454C4—64no—
455C4—61no—
456C4—64no—
457C4—61no—
458C4—61no—
459C4#100712yes—
460C4D3×#4112yes—
461C4#101012yes—
462C3#350911yescharacteristic, complemented, Sylow
463C2—41no—
464C2—62no—
465C2—121no—
466C2C2×#100711yescharacteristic
467C2C2×D3×#4111yescharacteristic
468C2C2×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C24×D3
commutator, socle, cosocleC22×C3C25
FittingC3×#533C2
prime radicalC2×#235C22
hypercenter#533D3
hypocenterC3#3509
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #533

Complements

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

NH ≅ G/Ntype
1. C3×#533C2semidirect
2. #5728C2semidirect
3. #5728C2semidirect
4. #5728C2semidirect
5. D3×C4⋊Q8C2semidirect
6. #5694C2semidirect
7. #5685C2semidirect
8. #5641C2semidirect
9. #5639C2semidirect
11. #5625C2semidirect
12. #5583C2semidirect
13. #5581C2semidirect
14. #5572C2semidirect
15. #5569C2semidirect
16. #5533C2semidirect
17. #5529C2semidirect
19. #5470C2semidirect
107. #533D3semidirect
462. C3#3509semidirect

Maximal subgroups

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

subgroupindex
C3×#5332
#57282
D3×C4⋊Q82
#56942
#56852
#56412
#56392
#56282
#56252
#55832
#55812
#55722
#55692
#55332
#55292
C4×#2352
#54702
#35093