Finite Group Databasebeta

← #86676

Subgroups — #86676

Order 384.

1094 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#547C211yesmaximal, characteristic, complemented
2Dic3×#41C212yesmaximal, complemented
3#5824C212yesmaximal, complemented
4#5728C211yesmaximal, characteristic, complemented
5#5721C211yesmaximal, characteristic, complemented
6#5650C214yesmaximal, complemented
7#5649C214yesmaximal, complemented
8#5641C212yesmaximal, complemented
9#5622C212yesmaximal, complemented
10#5600C212yesmaximal, complemented
11#5598C212yesmaximal, complemented
12#5542C211yesmaximal, characteristic, complemented
13D4×Dic6C211yesmaximal, characteristic, complemented
14C4×#237C211yesmaximal, characteristic, complemented
15C4×#237C211yesmaximal, characteristic, complemented
16#5513C212yesmaximal, complemented
17C2×#887C212yesmaximal, complemented
18#3482—31nomaximal, Sylow
19C2×C3×#41C2212yes—
20C2×#237C2211yescharacteristic
21C2×#237C2211yescharacteristic
22C22×Dic6C2212yes—
23C3×C4⋊Q8C2211yescharacteristic
24C3×#123C2214yes—
25C3×C22⋊Q8C2212yes—
26C3×#121C2212yes—
27C3×C4×D4C2211yescharacteristic
28C3×C4×D4C2211yescharacteristic
29C2×C3×C4⋊C4C2212yes—
30#946C2212yes—
31Q8×Dic3C2212yes—
32Q8×Dic3C2212yes—
33#944C2212yes—
34#939C2214yes—
35#936C2212yes—
36#935C2214yes—
37D4×Dic3C2214yes—
38D4×Dic3C2214yes—
39D4×Dic3C2211yescharacteristic
40D4×Dic3C2211yescharacteristic
41D4×Dic3C2212yes—
42#929C2214yes—
43C4×#67C2212yes—
44C4×#67C2212yes—
45#926C2212yes—
46#926C2214yes—
47#924C2212yes—
48#924C2212yes—
49C2×Dic3⋊C4C2214yes—
50C2×C4×Dic3C2214yes—
51C2×C4×Dic3C2212yes—
52C2×C4×Dic3C2212yes—
53#898C2214yes—
54#897C2212yes—
55#892C2211yescharacteristic
56#892C2212yes—
57#892C2211yescharacteristic
58#890C2212yes—
59#890C2212yes—
60#889C2214yes—
61#889C2214yes—
62#888C2212yes—
63#887C2214yes—
64#887C2214yes—
65#887C2212yes—
66#887C2212yes—
67#887C2211yescharacteristic
68#887C2212yes—
69#887C2211yescharacteristic
70#885C2214yes—
71#67⋊C4C2212yes—
72#67⋊C4C2212yes—
73#879C2214yes—
74#879C2214yes—
75#878C2214yes—
76#878C2214yes—
77#877C2214yes—
78#877C2212yes—
79#877C2212yes—
80C42×D3C2211yescharacteristic
81#869C2211yescharacteristic
82C4×Dic6C2211yescharacteristic
83C4×Dic6C2211yescharacteristic
84#557—31no—
85#556—32no—
86#556—31no—
87#552—34no—
88#552—32no—
89D4×Q8—31no—
90#548—32no—
91#547—32no—
92#547D311yescharacteristic, complemented
93#533—31no—
94#533—32no—
95#529—34no—
96#529—32no—
97C4×#41—32no—
98C4×#41—31no—
99C4×#41—31no—
100C2×C4×Q8—32no—
101C3×#41—28no—
102C2×C3×Q8C2312yes—
103C2×C3×D4C2314yes—
104C2×C3×D4C2311yescharacteristic
105C2×C3×D4C2311yescharacteristic
106C22×C3×C4C2314yes—
107C22×C3×C4C2312yes—
108C22×C3×C4C2312yes—
109C2×#67C2312yes—
110C2×#67C2312yes—
111C22×Dic3C2312yes—
112C22×Dic3C2312yes—
113C22×Dic3C2312yes—
114C22×Dic3C2314yes—
115C22×Dic3C2312yes—
116#237—24no—
117#237—24no—
118C2×C4×D3C2311yescharacteristic
119C2×C4×D3C2311yescharacteristic
120C2×C4×D3C2311yescharacteristic
121C2×Dic6—28no—
122C2×Dic6C2311yescharacteristic
123C2×Dic6C2312yes—
124C2×Dic6C2314yes—
125C2×Dic6C2311yescharacteristic
126C3×C4⋊C4C2311yescharacteristic
127C3×C4⋊C4C2314yes—
128C3×C4⋊C4C2312yes—
129C3×C4⋊C4C2311yescharacteristic
130C3×C4⋊C4C2312yes—
131C3×C22⋊C4C2312yes—
132C3×C22⋊C4C2314yes—
133C3×C22⋊C4C2312yes—
134C3×C42C2311yescharacteristic
135#217C2314yes—
136#217C2312yes—
137#217C2312yes—
138#217C2314yes—
139#217C2314yes—
140(C2×D3)⋊C4C2312yes—
141(C2×D3)⋊C4C2312yes—
142(C2×D3)⋊C4C2314yes—
143C4⋊Dic3C2311yescharacteristic
144C4⋊Dic3C2311yescharacteristic
145C4⋊Dic3C2312yes—
146C4⋊Dic3C2312yes—
147C4⋊Dic3C2314yes—
148C4⋊Dic3C2314yes—
149Dic3⋊C4C2312yes—
150Dic3⋊C4C2312yes—
151Dic3⋊C4C2312yes—
152Dic3⋊C4C2314yes—
153Dic3⋊C4C2312yes—
154Dic3⋊C4C2314yes—
155Dic3⋊C4C2314yes—
156Dic3⋊C4C2314yes—
157Dic3⋊C4C2314yes—
158C4×Dic3C2312yes—
159C4×Dic3C2312yes—
160C4×Dic3C2311yescharacteristic
161C4×Dic3C2311yescharacteristic
162C4×Dic3C2311yescharacteristic
163C4×Dic3C2312yes—
164C4×Dic3C2312yes—
165C4×Dic3C2314yes—
166C4×Dic3C2312yes—
167C4×Dic3C2314yes—
168C4×Dic3C2312yes—
169C4×Dic3C2314yes—
170C2×#41—31no—
171C2×#41—31no—
172C2×#41C2×D312yes—
173C22×Q8—32no—
174C4⋊Q8—32no—
175C4⋊Q8—32no—
176C4⋊Q8—31no—
177C4⋊Q8C2×D311yescharacteristic
178#126—34no—
179#126—34no—
180#126—34no—
181#125—34no—
182#125—32no—
183#125—34no—
184#125—32no—
185#124—32no—
186#124—34no—
187#123—34no—
188#123—34no—
189#123C2×D314yes—
190C22⋊Q8—32no—
191C22⋊Q8—32no—
192C22⋊Q8—32no—
193C22⋊Q8—32no—
194C22⋊Q8—34no—
195C22⋊Q8—34no—
196C22⋊Q8C2×D312yes—
197#121—34no—
198#121C2×D312yes—
199C4×Q8—32no—
200C4×Q8—32no—
201C4×Q8—31no—
202C4×Q8—34no—
203C4×Q8—32no—
204C4×Q8—32no—
205C4×Q8—34no—
206C4×Q8—32no—
207C4×Q8—31no—
208C4×Q8—31no—
209C4×Q8—31no—
210C4×D4—31no—
211C4×D4—31no—
212C4×D4—34no—
213C4×D4—32no—
214C4×D4—34no—
215C4×D4—32no—
216C4×D4—32no—
217C4×D4—32no—
218C4×D4—32no—
219C4×D4C2×D311yescharacteristic
220C4×D4C2×D311yescharacteristic
221#117—34no—
222#117—32no—
223#117—31no—
224#117—31no—
225#117—32no—
226#117—32no—
227#117—32no—
228#117—34no—
229C2×C4⋊C4—34no—
230C2×C4⋊C4C2×D312yes—
231C2×C42—32no—
232C2×C42—34no—
233C2×C42—32no—
234C2×C42—31no—
235C23×C3C2412yes—
236C23×C3C2412yes—
237C22×D3C2411yescharacteristic
238C3×Q8—24no—
239C3×D4—28no—
240C3×D4—22no—
241C3×D4#4114yescomplemented
242C2×C3×C4—28no—
243C2×C3×C4—24no—
244C2×C3×C4—24no—
245C2×C3×C4C2412yes—
246C2×C3×C4C2414yes—
247C2×C3×C4C2412yes—
248C2×C3×C4C2411yescharacteristic
249C2×C3×C4C2411yescharacteristic
250C2×C3×C4C2411yescharacteristic
251#67—24no—
252#67—24no—
253C2×Dic3—24no—
254C2×Dic3—28no—
255C2×Dic3—24no—
256C2×Dic3—24no—
257C2×Dic3—24no—
258C2×Dic3C2412yes—
259C2×Dic3C2411yescharacteristic
260C2×Dic3C2411yescharacteristic
261C2×Dic3C2412yes—
262C2×Dic3C2412yes—
263C2×Dic3C2414yes—
264C2×Dic3C2412yes—
265C2×Dic3C2411yescharacteristic
266C4×D3—22no—
267C4×D3—22no—
268C4×D3—22no—
269Dic6—24no—
270Dic6—22no—
271Dic6—28no—
272Dic6#4114yescomplemented
273#41—28no—
274#41—64no—
275#41—64no—
276C2×Q8—31no—
277C2×Q8—34no—
278C2×Q8—32no—
279C2×Q8—31no—
280C2×Q8—68no—
281C2×Q8C22×D312yes—
282C2×D4—32no—
283C2×D4—32no—
284C2×D4C22×D314yes—
285C2×D4C22×D311yescharacteristic
286C2×D4C22×D311yescharacteristic
287C22×C4—32no—
288C22×C4—32no—
289C22×C4—34no—
290C22×C4—32no—
291C22×C4—32no—
292C22×C4—31no—
293C22×C4—31no—
294C22×C4—31no—
295C22×C4C22×D314yes—
296C22×C4C22×D312yes—
297C22×C4C22×D312yes—
298C4⋊C4—32no—
299C4⋊C4—34no—
300C4⋊C4—34no—
301C4⋊C4—34no—
302C4⋊C4—31no—
303C4⋊C4—32no—
304C4⋊C4—32no—
305C4⋊C4—34no—
306C4⋊C4—31no—
307C4⋊C4—32no—
308C4⋊C4—32no—
309C4⋊C4—34no—
310C4⋊C4—34no—
311C4⋊C4—32no—
312C4⋊C4—34no—
313C4⋊C4C22×D311yescharacteristic
314C4⋊C4C22×D312yes—
315C4⋊C4C22×D314yes—
316C4⋊C4C22×D311yescharacteristic
317C4⋊C4C22×D312yes—
318C22⋊C4—32no—
319C22⋊C4—34no—
320C22⋊C4—32no—
321C22⋊C4—34no—
322C22⋊C4—34no—
323C22⋊C4—32no—
324C22⋊C4—32no—
325C22⋊C4—34no—
326C22⋊C4C22×D312yes—
327C22⋊C4C22×D312yes—
328C22⋊C4C22×D314yes—
329C42—32no—
330C42—31no—
331C42—31no—
332C42—31no—
333C42—32no—
334C42—34no—
335C42—32no—
336C42—32no—
337C42—34no—
338C42—32no—
339C42—34no—
340C42—32no—
341C42C22×D311yescharacteristic
342C22×C3—22no—
343C22×C3—22no—
344C22×C3—22no—
345C22×C3—22no—
346C22×C3—22no—
347C22×C3C2×#4114yes—
348C22×C3C2511yescharacteristic
349C2×D3—21no—
350C2×D3—21no—
351C2×D3—21no—
352C3×C4—22no—
353C3×C4—22no—
354C3×C4—24no—
355C3×C4—21no—
356C3×C4C2×#4112yes—
357C3×C4C2×#4112yes—
358Dic3—24no—
359Dic3—22no—
360Dic3—21no—
361Dic3—21no—
362Dic3—22no—
363Dic3—22no—
364Dic3C2×#4114yes—
365Dic32−1+412yes—
366C23—31no—
367C23C23×D312yes—
368C23C23×D312yes—
369Q8—24no—
370Q8—34no—
371Q8—68no—
372Q8—62no—
373Q8—64no—
374D4—28no—
375D4—22no—
376D4—64no—
377D4—64no—
378D4#23714yescomplemented
379C2×C4—28no—
380C2×C4—24no—
381C2×C4—24no—
382C2×C4—31no—
383C2×C4—32no—
384C2×C4—32no—
385C2×C4—31no—
386C2×C4—31no—
387C2×C4—32no—
388C2×C4—34no—
389C2×C4—32no—
390C2×C4—62no—
391C2×C4—68no—
392C2×C4—64no—
393C2×C4—64no—
394C2×C4—64no—
395C2×C4—64no—
396C2×C4—62no—
397C2×C4—62no—
398C2×C4C23×D312yes—
399C2×C4C23×D312yes—
400C2×C4C23×D314yes—
401C2×C4C23×D311yescharacteristic
402C2×C4C23×D311yescharacteristic
403C2×C4C23×D311yescharacteristic
404C2×C3—24no—
405C2×C3—42no—
406C2×C3C22×#4111yescharacteristic
407C2×C3C22×#4111yescharacteristic
408C2×C3C2×2−1+411yescharacteristic
409D3—41no—
410C22—22no—
411C22—22no—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—61no—
416C22—61no—
417C22—61no—
418C22C2×#23714yes—
419C22C24×D311yescharacteristic
420C4—22no—
421C4—24no—
422C4—22no—
423C4—21no—
424C4—34no—
425C4—32no—
426C4—61no—
427C4—62no—
428C4—61no—
429C4—64no—
430C4—62no—
431C4—62no—
432C4C2×#23712yes—
433C4D3×#4112yes—
434C3#348211yescharacteristic, complemented, Sylow
435C2—24no—
436C2—42no—
437C2—121no—
438C2C22×#23711yescharacteristic
439C2C2×D3×#4111yescharacteristic
440C2D3×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D3
commutator, socle, cosocleC22×C3C25
FittingC3×#547C2
hypercenter#547D3
hypocenterC3#3482
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C3×#547C2semidirect
2. Dic3×#41C2semidirect
3. #5824C2semidirect
4. #5728C2semidirect
5. #5721C2semidirect
6. #5650C2semidirect
7. #5649C2semidirect
8. #5641C2semidirect
9. #5622C2semidirect
10. #5600C2semidirect
11. #5598C2semidirect
12. #5542C2semidirect
13. D4×Dic6C2semidirect
14. C4×#237C2semidirect
15. C4×#237C2semidirect
16. #5513C2semidirect
17. C2×#887C2semidirect
92. #547D3semidirect
241. C3×D4#41semidirect
272. Dic6#41semidirect
378. D4#237semidirect
434. C3#3482semidirect

Maximal subgroups

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

subgroupindex
C3×#5472
Dic3×#412
#58242
#57282
#57212
#56502
#56492
#56412
#56222
#56002
#55982
#55422
D4×Dic62
C4×#2372
#55132
C2×#8872
#34823