Finite Group Databasebeta

← #86339

Subgroups — #86339

Order 384.

1012 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#536C211yesmaximal, characteristic, complemented
2#5833C211yesmaximal, characteristic
3Dic3×#41C211yesmaximal, characteristic, complemented
4#5816C211yesmaximal, characteristic, complemented
5C2×Q8×Dic3C211yesmaximal, characteristic, complemented
6#5731C212yesmaximal, complemented
7#5728C212yesmaximal, complemented
8#5682C212yesmaximal, complemented
9#5680C212yesmaximal, complemented
10#5665C214yesmaximal, complemented
11#5649C214yesmaximal, complemented
12#5643C212yesmaximal, complemented
13#5625C212yesmaximal, complemented
14#5624C212yesmaximal, complemented
15#5622C212yesmaximal, complemented
16#5522C211yesmaximal, characteristic, complemented
17#5519C211yesmaximal, characteristic, complemented
18#3461—31nomaximal, Sylow
19C2×C3×#41C2211yescharacteristic
20C22×C3×Q8C2211yescharacteristic
21C2×#235C2211yescharacteristic
22C3×C4⋊Q8C2212yes—
23C3×#124C2212yes—
24C3×#123C2214yes—
25C3×C22⋊Q8C2212yes—
26C3×C22⋊Q8C2212yes—
27C3×#117C2211yescharacteristic
28#947C2212yes—
29#946C2212yes—
30#946C2212yes—
31#946C2212yes—
32Q8×Dic3C2212yes—
33Q8×Dic3C2212yes—
34Q8×Dic3C2212yes—
35Q8×Dic3C2211yescharacteristic
36Q8×Dic3C2211yescharacteristic
37Q8×Dic3C2212yes—
38#944C2212yes—
39#939C2214yes—
40#938C2212yes—
41D4×Dic3C2212yes—
42D4×Dic3C2212yes—
43D4×Dic3C2211yescharacteristic
44D4×Dic3C2211yescharacteristic
45#930C2212yes—
46#929C2214yes—
47#926C2212yes—
48#926C2211yescharacteristic
49C2×C4⋊Dic3C2212yes—
50C2×C4⋊Dic3C2211yescharacteristic
51#924C2212yes—
52C2×C4×Dic3C2212yes—
53C2×C4×Dic3C2211yescharacteristic
54C2×C4×Dic3C2212yes—
55#898C2214yes—
56#898C2214yes—
57#897C2214yes—
58#893C2211yescharacteristic
59#893C2211yescharacteristic
60#892C2214yes—
61#890C2214yes—
62#890C2212yes—
63#889C2214yes—
64#889C2214yes—
65#888C2212yes—
66#887C2214yes—
67#887C2211yescharacteristic
68#887C2211yescharacteristic
69#886C2214yes—
70#885C2214yes—
71#883C2214yes—
72#67⋊C4C2212yes—
73#67⋊C4C2214yes—
74#67⋊C4C2212yes—
75#879C2214yes—
76#879C2214yes—
77#878C2214yes—
78#878C2214yes—
79#877C2214yes—
80#872C2212yes—
81C42×D3C2212yes—
82#870C2212yes—
83#869C2212yes—
84#544—31no—
85#542—32no—
86#542—32no—
87#541—32no—
88#541—32no—
89#539—34no—
90#537—31no—
91#536—31no—
92#536D311yescharacteristic, complemented
93#533—32no—
94#533—32no—
95#529—32no—
96#529—34no—
97#529—32no—
98C4×#41—31no—
99C4×#41—31no—
100C2×C4×Q8—31no—
101C3×#41—24no—
102C2×C3×Q8—24no—
103C2×C3×Q8C2312yes—
104C2×C3×Q8C2312yes—
105C2×C3×Q8C2311yescharacteristic
106C2×C3×D4C2311yescharacteristic
107C2×C3×D4C2312yes—
108C22×C3×C4C2312yes—
109C22×C3×C4C2312yes—
110C22×C3×C4C2311yescharacteristic
111C2×#67C2312yes—
112C2×#67C2314yes—
113C22×Dic3C2312yes—
114C22×Dic3C2311yescharacteristic
115C22×Dic3C2312yes—
116C22×Dic3C2312yes—
117C22×Dic3C2311yescharacteristic
118#235—24no—
119C2×D12C2311yescharacteristic
120C2×C4×D3C2312yes—
121C2×C4×D3C2312yes—
122C2×C4×D3C2312yes—
123C2×Dic6C2311yescharacteristic
124C2×Dic6C2314yes—
125C3×C4⋊C4C2311yescharacteristic
126C3×C4⋊C4C2314yes—
127C3×C4⋊C4C2311yescharacteristic
128C3×C4⋊C4C2314yes—
129C3×C22⋊C4C2314yes—
130C3×C22⋊C4C2312yes—
131C3×C22⋊C4C2314yes—
132C3×C42C2312yes—
133#217C2314yes—
134#217C2312yes—
135#217C2312yes—
136#217C2312yes—
137(C2×D3)⋊C4C2312yes—
138(C2×D3)⋊C4C2312yes—
139(C2×D3)⋊C4C2314yes—
140(C2×D3)⋊C4C2314yes—
141(C2×D3)⋊C4C2314yes—
142C4⋊Dic3C2311yescharacteristic
143C4⋊Dic3C2312yes—
144C4⋊Dic3C2314yes—
145C4⋊Dic3C2311yescharacteristic
146C4⋊Dic3C2314yes—
147C4⋊Dic3C2314yes—
148C4⋊Dic3C2312yes—
149C4⋊Dic3C2312yes—
150C4⋊Dic3C2312yes—
151Dic3⋊C4C2314yes—
152Dic3⋊C4C2314yes—
153Dic3⋊C4C2312yes—
154Dic3⋊C4C2312yes—
155Dic3⋊C4C2314yes—
156Dic3⋊C4C2314yes—
157Dic3⋊C4C2314yes—
158C4×Dic3C2311yescharacteristic
159C4×Dic3C2312yes—
160C4×Dic3C2312yes—
161C4×Dic3C2311yescharacteristic
162C4×Dic3C2314yes—
163C4×Dic3C2314yes—
164C4×Dic3C2312yes—
165C4×Dic3C2311yescharacteristic
166C4×Dic3C2311yescharacteristic
167C4×Dic3C2312yes—
168C4×Dic3C2312yes—
169C2×#41—31no—
170C2×#41C2×D311yescharacteristic
171C22×Q8C2×D311yescharacteristic
172C4⋊Q8—32no—
173C4⋊Q8—32no—
174C4⋊Q8—32no—
175C4⋊Q8C2×D312yes—
176#126—34no—
177#126—34no—
178#126—34no—
179#126—34no—
180#125—34no—
181#125—32no—
182#125—34no—
183#125—34no—
184#125—32no—
185#124—32no—
186#124—34no—
187#124C2×D312yes—
188#123—34no—
189#123—34no—
190#123—34no—
191#123C2×D314yes—
192C22⋊Q8—32no—
193C22⋊Q8—32no—
194C22⋊Q8—32no—
195C22⋊Q8—32no—
196C22⋊Q8—34no—
197C22⋊Q8—34no—
198C22⋊Q8—34no—
199C22⋊Q8C2×D312yes—
200C22⋊Q8C2×D312yes—
201#121—34no—
202#121—32no—
203#121—32no—
204C4×Q8—32no—
205C4×Q8—32no—
206C4×Q8—32no—
207C4×Q8—32no—
208C4×Q8—31no—
209C4×Q8—31no—
210C4×Q8—31no—
211C4×Q8—31no—
212C4×Q8—34no—
213C4×D4—31no—
214C4×D4—32no—
215C4×D4—32no—
216C4×D4—31no—
217C4×D4—31no—
218C4×D4—31no—
219C4×D4—32no—
220C4×D4—32no—
221C4×D4—34no—
222#117—31no—
223#117—32no—
224#117—34no—
225#117—34no—
226#117—32no—
227#117C2×D311yescharacteristic
228C2×C4⋊C4—31no—
229C2×C4⋊C4—32no—
230C2×C42—31no—
231C2×C42—32no—
232C2×C42—32no—
233C2×C42—32no—
234C23×C3C2412yes—
235C23×C3C2411yescharacteristic
236C22×D3C2412yes—
237C3×Q8—24no—
238C3×Q8—24no—
239C3×Q8—22no—
240C3×D4—24no—
241C3×D4—22no—
242C2×C3×C4—24no—
243C2×C3×C4—24no—
244C2×C3×C4#4114yes—
245C2×C3×C4C2414yes—
246C2×C3×C4C2412yes—
247C2×C3×C4C2412yes—
248C2×C3×C4C2412yes—
249C2×C3×C4C2411yescharacteristic
250C2×C3×C4C2411yescharacteristic
251#67—24no—
252#67—44no—
253C2×Dic3—22no—
254C2×Dic3—24no—
255C2×Dic3—42no—
256C2×Dic3—42no—
257C2×Dic3—41no—
258C2×Dic3C2411yescharacteristic
259C2×Dic3C2411yescharacteristic
260C2×Dic3C2411yescharacteristic
261C2×Dic3C2412yes—
262C2×Dic3C2412yes—
263C2×Dic3C2414yes—
264C2×Dic3C2412yes—
265C2×Dic3C2411yescharacteristic
266D12—22no—
267C4×D3—24no—
268C4×D3—24no—
269C4×D3—42no—
270Dic6—22no—
271Dic6—44no—
272#41—24no—
273#41—64no—
274C2×Q8—24no—
275C2×Q8—31no—
276C2×Q8—34no—
277C2×Q8C22×D312yes—
278C2×Q8C22×D311yescharacteristic
279C2×Q8C22×D312yes—
280C2×D4—32no—
281C2×D4—34no—
282C2×D4—31no—
283C2×D4C22×D312yes—
284C2×D4C22×D311yescharacteristic
285C22×C4—31no—
286C22×C4—32no—
287C22×C4—31no—
288C22×C4—32no—
289C22×C4—32no—
290C22×C4—32no—
291C22×C4—32no—
292C22×C4—32no—
293C22×C4C22×D312yes—
294C22×C4C22×D312yes—
295C22×C4C22×D311yescharacteristic
296C4⋊C4—32no—
297C4⋊C4—32no—
298C4⋊C4—34no—
299C4⋊C4—34no—
300C4⋊C4—32no—
301C4⋊C4—32no—
302C4⋊C4—31no—
303C4⋊C4—31no—
304C4⋊C4—32no—
305C4⋊C4—32no—
306C4⋊C4—34no—
307C4⋊C4—34no—
308C4⋊C4—34no—
309C4⋊C4—34no—
310C4⋊C4—34no—
311C4⋊C4—34no—
312C4⋊C4C22×D314yes—
313C4⋊C4C22×D311yescharacteristic
314C4⋊C4C22×D311yescharacteristic
315C4⋊C4C22×D314yes—
316C22⋊C4—32no—
317C22⋊C4—32no—
318C22⋊C4—32no—
319C22⋊C4—34no—
320C22⋊C4—32no—
321C22⋊C4—32no—
322C22⋊C4—34no—
323C22⋊C4—34no—
324C22⋊C4—34no—
325C22⋊C4C22×D314yes—
326C22⋊C4C22×D312yes—
327C22⋊C4C22×D314yes—
328C42—31no—
329C42—31no—
330C42—32no—
331C42—34no—
332C42—32no—
333C42—31no—
334C42—31no—
335C42—32no—
336C42—32no—
337C42—32no—
338C42—34no—
339C42C22×D312yes—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—22no—
343C22×C3—22no—
344C22×C3—22no—
345C22×C3C2×#4112yes—
346C22×C3C2511yescharacteristic
347C2×D3—22no—
348C2×D3—22no—
349C2×D3—22no—
350C3×C4—22no—
351C3×C4—24no—
352C3×C4—22no—
353C3×C4—22no—
354C3×C4C2×#4112yes—
355C3×C4C2×#4112yes—
356Dic3—22no—
357Dic3—21no—
358Dic3—22no—
359Dic3—22no—
360Dic3—24no—
361Dic3—21no—
362Dic3—21no—
363Dic32−1+412yes—
364C23—32no—
365C23C23×D312yes—
366C23C23×D311yescharacteristic
367Q8—24no—
368Q8—24no—
369Q8—22no—
370Q8—62no—
371Q8—124no—
372D4—24no—
373D4—22no—
374D4—64no—
375D4—62no—
376D4—124no—
377C2×C4—24no—
378C2×C4—24no—
379C2×C4—31no—
380C2×C4—31no—
381C2×C4—31no—
382C2×C4—31no—
383C2×C4—32no—
384C2×C4—32no—
385C2×C4—32no—
386C2×C4—34no—
387C2×C4—64no—
388C2×C4—62no—
389C2×C4—64no—
390C2×C4—64no—
391C2×C4—122no—
392C2×C4—121no—
393C2×C4—122no—
394C2×C4—122no—
395C2×C4#23714yes—
396C2×C4C23×D314yes—
397C2×C4C23×D312yes—
398C2×C4C23×D312yes—
399C2×C4C23×D312yes—
400C2×C4C23×D311yescharacteristic
401C2×C4C23×D311yescharacteristic
402C2×C3—22no—
403C2×C3—42no—
404C2×C3C22×#4111yescharacteristic
405C2×C3C2×2−1+411yescharacteristic
406C2×C3#58511yescharacteristic
407D3—42no—
408C22—21no—
409C22—21no—
410C22—22no—
411C22—22no—
412C22—22no—
413C22—62no—
414C22—62no—
415C22—62no—
416C22C2×#23712yes—
417C22C24×D311yescharacteristic
418C4—22no—
419C4—24no—
420C4—22no—
421C4—22no—
422C4—32no—
423C4—62no—
424C4—61no—
425C4—62no—
426C4—61no—
427C4—61no—
428C4—64no—
429C4—62no—
430C4C2×#23712yes—
431C4C2×#23712yes—
432C3#346111yescharacteristic, complemented, Sylow
433C2—22no—
434C2—42no—
435C2—122no—
436C2C22×#23711yescharacteristic
437C2D3×2−1+411yescharacteristic
438C2#596811yescharacteristic
subgroupG/H
center, FrattiniC22C24×D3
commutator, socle, cosocleC22×C3C25
FittingC3×#536C2
prime radical#5833C2
hypercenter#536D3
hypocenterC3#3461
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C3×#536C2semidirect
3. Dic3×#41C2semidirect
4. #5816C2semidirect
5. C2×Q8×Dic3C2semidirect
6. #5731C2semidirect
7. #5728C2semidirect
8. #5682C2semidirect
9. #5680C2semidirect
10. #5665C2semidirect
11. #5649C2semidirect
12. #5643C2semidirect
13. #5625C2semidirect
14. #5624C2semidirect
15. #5622C2semidirect
16. #5522C2semidirect
17. #5519C2semidirect
92. #536D3semidirect
432. C3#3461semidirect

Maximal subgroups

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

subgroupindex
C3×#5362
#58332
Dic3×#412
#58162
C2×Q8×Dic32
#57312
#57282
#56822
#56802
#56652
#56492
#56432
#56252
#56242
#56222
#55222
#55192
#34613