Finite Group Databasebeta

← #80933

Subgroups — #80933

Order 384.

448 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5779C211yesmaximal, characteristic, complemented
2#5775C211yesmaximal, characteristic, complemented
3#5762C211yesmaximal, characteristic, complemented
4#5753C211yesmaximal, characteristic, complemented
5C3×#471C211yesmaximal, characteristic, complemented
6#5205C211yesmaximal, characteristic, complemented
7#5201C211yesmaximal, characteristic, complemented
8#5167C211yesmaximal, characteristic, complemented
9#5145C211yesmaximal, characteristic, complemented
10#4896C211yesmaximal, characteristic, complemented
11#4894C211yesmaximal, characteristic, complemented
12#4755C211yesmaximal, characteristic, complemented
13#4752C211yesmaximal, characteristic, complemented
14#4748C211yesmaximal, characteristic, complemented
15#4746C211yesmaximal, characteristic, complemented
16#3289—31nomaximal, Sylow
17#1010C2211yescharacteristic
18#1010C2211yescharacteristic, complemented
19#1007C2211yescharacteristic
20#1004C2211yescharacteristic
21C3×#137C2211yescharacteristic, complemented
22C3×AGL(1,ℤ/8)C2211yescharacteristic
23C2×C3×SD16C2211yescharacteristic
24C3×#131C2211yescharacteristic, complemented
25#950C2211yescharacteristic
26#944C2211yescharacteristic, complemented
27C2×#216C2211yescharacteristic, complemented
28#942C2211yescharacteristic
29#936C2211yescharacteristic
30C2×#214C2211yescharacteristic
31#932C2211yescharacteristic
32#918—21no—
33D3×Q16—21no—
34#916—21no—
35#916—21no—
36#915—21no—
37#915—21no—
38#915—21no—
39#914—21no—
40D3×SD16—21no—
41D3×SD16—21no—
42#912—21no—
43#911—21no—
44#909—21no—
45#909—21no—
46#909C2211yescharacteristic
47#909C2211yescharacteristic
48#909C2211yescharacteristic
49#909C2211yescharacteristic, complemented
50#907C2211yescharacteristic
51#907C2211yescharacteristic, complemented
52C2×Dic12—21no—
53C2×Dic12C2211yescharacteristic, complemented
54#904—21no—
55#904C2211yescharacteristic
56#901C2211yescharacteristic
57C3×#108C2211yescharacteristic, complemented
58C3×#101C2211yescharacteristic, complemented
59C3×#100C2211yescharacteristic
60#837C2211yescharacteristic, complemented
61#825C2211yescharacteristic
62#825C2211yescharacteristic
63#825C2211yescharacteristic, complemented
64#824C2211yescharacteristic, complemented
65#824C2211yescharacteristic, complemented
66#822C2211yescharacteristic, complemented
67#815C2211yescharacteristic, complemented
68#578—31no—
69#578—31no—
70#577—31no—
71#577—31no—
72#497—31no—
73#473—31no—
74#473—31no—
75#471—31no—
76#471D311yescharacteristic, complemented
77#456—31no—
78#456—31no—
79#455—31no—
80#454—31no—
81#444—31no—
82#444—31no—
83C3×#41C2311yescharacteristic
84C2×C3×Q8C2311yescharacteristic
85C2×C3×D4C2311yescharacteristic
86C2×#67—41no—
87#239—21no—
88#239—21no—
89D3×Q8—21no—
90D3×Q8—21no—
91D3×Q8—21no—
92D3×Q8—21no—
93#237—21no—
94#237—21no—
95#237—21no—
96#237—21no—
97#237—41no—
98#237—41no—
99D3×D4—21no—
100D3×D4—21no—
101#235—21no—
102#235—21no—
103#235—41no—
104#235C2311yescharacteristic
105#235C2311yescharacteristic
106#235C2311yescharacteristic
107C2×Dic6—21no—
108C2×Dic6—21no—
109C2×Dic6C2311yescharacteristic
110C2×Dic6C2311yescharacteristic
111C3×Q16—21no—
112C3×SD16—21no—
113C3×SD16—21no—
114C3×SD16—21no—
115C3×SD16—21no—
116C3×D8—21no—
117C3×M16—21no—
118C3×M16C2311yescharacteristic
119C3×M16C2311yescharacteristic
120C3×M16C2311yescharacteristic
121C2×C3×C8—21no—
122C2×C3×C8C2311yescharacteristic
123#217—41no—
124#216—21no—
125#216—21no—
126#216—21no—
127#216D411yescharacteristic
128#215—21no—
129#215D411yescharacteristic
130#214—21no—
131#214—21no—
132#214—21no—
133#214D411yescharacteristic
134#213—21no—
135#213D411yescharacteristic
136Dic3⋊C4—41no—
137C4×Dic3C2311yescharacteristic
138#208C2311yescharacteristic
139C2×C3⋊C8C2311yescharacteristic
140Dic12—21no—
141Dic12—21no—
142Dic12—21no—
143Dic12—21no—
144Dic12—21no—
145Dic12—21no—
146Dic12D411yescharacteristic
147D24D411yescharacteristic
148#204—21no—
149#204—21no—
150#204—21no—
151#204—21no—
152#204D411yescharacteristic
153#204D411yescharacteristic
154ΓL(1,𝔽25)—21no—
155ΓL(1,𝔽25)—21no—
156ΓL(1,𝔽25)—21no—
157D3×C8—21no—
158D3×C8—21no—
159D3×C8—21no—
1602−1+4—31no—
1612−1+4—31no—
1622−1+4—31no—
163H(5,𝔽2)—31no—
164#137—31no—
165#137—31no—
166#137—31no—
167#137—31no—
168#137—31no—
169#137—61no—
170#137—61no—
171#137—61no—
172#137—61no—
173#137—61no—
174#137—61no—
175#137C2×D311yescharacteristic, complemented
176AGL(1,ℤ/8)—31no—
177AGL(1,ℤ/8)—61no—
178AGL(1,ℤ/8)—61no—
179AGL(1,ℤ/8)C2×D311yescharacteristic
180#135—31no—
181#135—31no—
182#135—61no—
183#135—61no—
184#135—61no—
185#135—61no—
186C2×Q16—31no—
187C2×Q16—31no—
188C2×Q16—61no—
189C2×Q16—61no—
190C2×SD16—31no—
191C2×SD16—61no—
192C2×SD16—61no—
193C2×SD16C2×D311yescharacteristic
194#131—31no—
195#131—31no—
196#131—31no—
197#131C2×D311yescharacteristic, complemented
198C4⋊Q8—31no—
199#124—31no—
200#108—31no—
201#108C2×D311yescharacteristic, complemented
202#104—31no—
203#104—31no—
204#104—31no—
205#104—31no—
206#101—31no—
207#101—31no—
208#101C2×D311yescharacteristic, complemented
209#100C2×D311yescharacteristic
210#97—31no—
211C23×C3—21no—
212C22×D3—41no—
213C3×Q8—21no—
214C3×Q8—21no—
215C3×Q8C2×D411yescharacteristic
216C3×D4—21no—
217C3×D4—21no—
218C3×D4—21no—
219C3×D4C2×D411yescharacteristic
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4C2411yescharacteristic
223#67—21no—
224#67—21no—
225#67—21no—
226#67—41no—
227#67—41no—
228#67—41no—
229#67—41no—
230C2×Dic3—21no—
231C2×Dic3—21no—
232C2×Dic3—21no—
233C2×Dic3—41no—
234C2×Dic3—41no—
235C2×Dic3—41no—
236D12—41no—
237D12C2×D411yescharacteristic
238D12C2×D411yescharacteristic
239D12C2×D411yescharacteristic
240C4×D3—21no—
241C4×D3—21no—
242C4×D3—21no—
243C4×D3—41no—
244C4×D3—41no—
245C4×D3—41no—
246C4×D3—41no—
247Dic6—21no—
248Dic6—21no—
249Dic6—21no—
250Dic6—21no—
251Dic6—41no—
252Dic6—41no—
253Dic6—41no—
254Dic6C2×D411yescharacteristic
255Dic6C2×D411yescharacteristic
256Dic6C2×D411yescharacteristic
257C3×C8—21no—
258C3×C8—21no—
259C3×C8—21no—
260C3×C8C2×D411yescharacteristic
261C3×C8C2×D411yescharacteristic
262C3⋊C8—21no—
263C3⋊C8C2×D411yescharacteristic
264C3⋊C8C2×D411yescharacteristic
265#41—31no—
266#41—31no—
267#41—31no—
268#41—61no—
269#41—61no—
270#41—61no—
271#41—61no—
272#41—61no—
273#41—61no—
274#41—61no—
275#41—61no—
276#41—121no—
277#41—121no—
278#41—121no—
279#41C22×D311yescharacteristic
280C2×Q8—31no—
281C2×Q8—31no—
282C2×Q8—61no—
283C2×Q8—61no—
284C2×Q8—61no—
285C2×Q8—61no—
286C2×Q8—61no—
287C2×Q8—61no—
288C2×Q8C22×D311yescharacteristic
289C2×D4—61no—
290C2×D4—61no—
291C2×D4—121no—
292C2×D4C22×D311yescharacteristic
293Q16—21no—
294Q16—31no—
295Q16—31no—
296Q16—61no—
297Q16—61no—
298Q16—61no—
299Q16—61no—
300Q16—61no—
301Q16—61no—
302Q16—61no—
303Q16—61no—
304Q16—61no—
305SD16—21no—
306SD16—21no—
307SD16—21no—
308SD16—21no—
309SD16—31no—
310SD16—31no—
311SD16—31no—
312SD16—31no—
313SD16—61no—
314SD16—61no—
315SD16—61no—
316SD16—61no—
317SD16—61no—
318SD16—61no—
319SD16—61no—
320SD16—61no—
321D8—21no—
322D8—31no—
323D8—31no—
324D8—61no—
325M16—21no—
326M16—31no—
327M16—61no—
328M16—61no—
329M16—61no—
330M16C22×D311yescharacteristic
331M16C22×D311yescharacteristic
332M16C22×D311yescharacteristic
333C2×C8—21no—
334C2×C8—31no—
335C2×C8—61no—
336C2×C8—61no—
337C2×C8—61no—
338C2×C8C22×D311yescharacteristic
339C4⋊C4—121no—
340C22⋊C4—121no—
341C42—31no—
342C22×C3—21no—
343C22×C3—41no—
344C22×C3—81no—
345C22×C3H(5,𝔽2)11yescharacteristic
346C2×D3—21no—
347C2×D3—21no—
348C2×D3—21no—
349C2×D3—161no—
350C3×C4—21no—
351C3×C4—41no—
352C3×C4C22×D411yescharacteristic
353C3×C4C22×D411yescharacteristic
354Dic3—21no—
355Dic3—21no—
356Dic3—21no—
357Dic3—41no—
358Dic3—41no—
359Dic3—41no—
360C23—21no—
361C23—121no—
362Q8—21no—
363Q8—21no—
364Q8—31no—
365Q8—31no—
366Q8—31no—
367Q8—61no—
368Q8—61no—
369Q8—61no—
370Q8—61no—
371Q8—121no—
372Q8—121no—
373Q8—121no—
374Q8D3×D411yescharacteristic
375D4—21no—
376D4—21no—
377D4—21no—
378D4—31no—
379D4—31no—
380D4—31no—
381D4—61no—
382D4—61no—
383D4—61no—
384D4—121no—
385D4—121no—
386D4—121no—
387D4—121no—
388D4—121no—
389D4D3×D411yescharacteristic
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—61no—
393C2×C4—61no—
394C2×C4—61no—
395C2×C4—61no—
396C2×C4—61no—
397C2×C4—61no—
398C2×C4—121no—
399C2×C4—121no—
400C2×C4—121no—
401C2×C4—121no—
402C2×C4—121no—
403C2×C4—121no—
404C2×C4—121no—
405C2×C4C23×D311yescharacteristic
406C8—21no—
407C8—21no—
408C8—21no—
409C8—31no—
410C8—31no—
411C8—61no—
412C8D3×D411yescharacteristic
413C8D3×D411yescharacteristic
414C2×C3—21no—
415C2×C3—41no—
416C2×C3—81no—
417C2×C3D4211yescharacteristic
418D3—41no—
419D3—41no—
420D3—41no—
421C22—21no—
422C22—41no—
423C22—61no—
424C22—61no—
425C22—61no—
426C22—81no—
427C22—481no—
428C22#100911yescharacteristic
429C4—21no—
430C4—41no—
431C4—61no—
432C4—61no—
433C4—61no—
434C4—121no—
435C4—121no—
436C4—121no—
437C4C2×D3×D411yescharacteristic
438C4C2×D3×D411yescharacteristic
439C3#328911yescharacteristic, complemented, Sylow
440C2—21no—
441C2—41no—
442C2—81no—
443C2—121no—
444C2—121no—
445C2—121no—
446C2#560911yescharacteristic
subgroupG/H
centerC2#5609
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#471C2
socleC2×C3D42
hypercenter#471D3
hypocenterC3#3289
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #5779C2semidirect
2. #5775C2semidirect
3. #5762C2semidirect
4. #5753C2semidirect
5. C3×#471C2semidirect
6. #5205C2semidirect
7. #5201C2semidirect
8. #5167C2semidirect
9. #5145C2semidirect
10. #4896C2semidirect
11. #4894C2semidirect
12. #4755C2semidirect
13. #4752C2semidirect
14. #4748C2semidirect
15. #4746C2semidirect
18. #1010C22semidirect
21. C3×#137C22semidirect
24. C3×#131C22semidirect
26. #944C22semidirect
27. C2×#216C22semidirect
49. #909C22semidirect
51. #907C22semidirect
53. C2×Dic12C22semidirect
57. C3×#108C22semidirect
58. C3×#101C22semidirect
60. #837C22semidirect
63. #825C22semidirect
64. #824C22semidirect
65. #824C22semidirect
66. #822C22semidirect
67. #815C22semidirect
76. #471D3semidirect
175. #137C2×D3semidirect
197. #131C2×D3semidirect
201. #108C2×D3semidirect
208. #101C2×D3semidirect
439. C3#3289semidirect

Maximal subgroups

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

subgroupindex
#57792
#57752
#57622
#57532
C3×#4712
#52052
#52012
#51672
#51452
#48962
#48942
#47552
#47522
#47482
#47462
#32893