Finite Group Databasebeta

← C2×#72240977 #72344168

Subgroups — C2×#72240977 #72344168

Order 6144.

Only the 1356 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 397 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#72236824C211yesmaximal, characteristic, complemented
2C2×#72236792C211yesmaximal, characteristic, complemented
3C22×#60399⋊C3C211yesmaximal, characteristic, complemented
4C2×#72236802C212yesmaximal, complemented
5C2×#60401⋊C3C2211yescharacteristic, complemented
6C2×#72236799C212yesmaximal, complemented
7C2×#21484⋊C3C2212yescomplemented
8C2×#11710352C2211yescharacteristic, complemented
9C2×#72233783C211yesmaximal, characteristic, complemented
10C2×#72236859C211yesmaximal, characteristic, complemented
11C2×#72236874C212yesmaximal, complemented
12C2×#11710347C2211yescharacteristic, complemented
13C2×#32896⋊C3C2212yescomplemented
14C2×#32947⋊C3C2212yescomplemented
15C2×#72236864C212yesmaximal, complemented
16C22×#3025⋊C3C2211yescharacteristic
17C2×#21483⋊C3C2212yescomplemented
18C2×#32948⋊C3C2212yescomplemented
19C2×#72236755C211yesmaximal, characteristic, complemented
20C22×#3027⋊C3C2211yescharacteristic, complemented
21C2×#32894⋊C3C2212yescomplemented
22C2×#32894⋊C3C2212yescomplemented
23C2×#32895⋊C3C2212yescomplemented
24C2×#20612⋊C3C2211yescharacteristic, complemented
25C2×#72215685C211yesmaximal, characteristic, complemented
26C2×#11710873C2211yescharacteristic, complemented
27C2×#11710899C2212yescomplemented
28C2×#60398⋊C3C2211yescharacteristic, complemented
29C2×#11710937C2211yescharacteristic, complemented
30C22×#87547C2211yescharacteristic, complemented
31C2×#72236873C311yesmaximal, characteristic, complemented, Sylow
32C2×#6372744C2×C311yescharacteristic, complemented
33C2×#6573736C2×C312yescomplemented
34C2×#6573735C2×C312yescomplemented
35C2×#6628885C2×C311yescharacteristic, complemented
36C2×#6629045C2×C311yescharacteristic, complemented
37C2×#10574874C2×C311yescharacteristic, complemented
38C2×#10586999C2×C311yescharacteristic, complemented
39C2×#6628883C2×C311yescharacteristic, complemented
40C2×#6573730C2×C312yescomplemented
41C2×#6573729C2×C312yescomplemented
42#72240977C2116yesmaximal, direct product factor
43#72236874C22116yescomplemented
44#72236873C2×C3116yescomplemented
45#72236864C22116yescomplemented
46#72236859C2218yescomplemented
47#72236824C2218yescomplemented
48#72236802C22116yescomplemented
49#72236799C22116yescomplemented
50C2×#60399⋊C3C2212yescomplemented
51C2×#60399⋊C3C2212yescomplemented
52C2×#60399⋊C3C2218yescomplemented
53C2×#60399⋊C3C2211yescharacteristic, complemented
54#72236792C2218yescomplemented
55#72236755C2218yescomplemented
56C22×#60399C2×C311yescharacteristic, complemented
57#72233783C2218yescomplemented
58C2×#11710898C2212yescomplemented
59#72215685C2218yescomplemented
60#11710937C2314yescomplemented
61C2×#87548C2311yescharacteristic, complemented
62C2×#87547C2312yes—
63C2×#87547C2314yescomplemented
64C2×#87547C2311yescharacteristic, complemented
65C22×#5950C2311yescharacteristic
66#11710899C2318yescomplemented
67#11710898C2318yescomplemented
68#11710873C2314yescomplemented
69C2×#85666C2312yescomplemented
70#11710352C2314yescomplemented
71#60401⋊C3C2314yescomplemented
72#11710347C2314yescomplemented
73#60399⋊C3C2318yescomplemented
74#60399⋊C3C2318yescomplemented
75#60399⋊C3C2314yescomplemented
76#60398⋊C3C2314yescomplemented
77C2×#3028⋊C3C2311yescharacteristic, complemented
78C2×#3027⋊C3C2312yes—
79C2×#3027⋊C3C2314yescomplemented
80C2×#3027⋊C3C2311yescharacteristic, complemented
81C2×#3025⋊C3D411yescharacteristic
82C2×#3025⋊C3D414yes—
83C2×#3025⋊C3D411yescharacteristic
84C2×#3025⋊C3C2311yescharacteristic
85C2×#3025⋊C3C2314yes—
86C2×#3025⋊C3C2311yescharacteristic
87C22×#458⋊C3D411yescharacteristic
88C22×B(4,𝔽2)⋊C3D411yescharacteristic
89#32948⋊C3C2318yescomplemented
90#32947⋊C3C2318yescomplemented
91#32896⋊C3C2318yescomplemented
92#32895⋊C3C2318yescomplemented
93#32894⋊C3C2318yescomplemented
94#32894⋊C3C2318yescomplemented
95#21484⋊C3C2318yescomplemented
96#21483⋊C3C2318yescomplemented
97#20612⋊C3C2314yescomplemented
98C2×#1791⋊C3C2312yescomplemented
99C2×#63103C22×C311yescharacteristic, complemented
100C22×H(7,𝔽2)C22×C311yescharacteristic, complemented
101#10586999C22×C318yescomplemented
102C2×#63092C22×C312yescomplemented
103C2×#63091C22×C312yescomplemented
104C24×AGL(1,ℤ/8)A411yescharacteristic, complemented
105C2×#63076C22×C311yescharacteristic, complemented
106C2×#60402C22×C311yescharacteristic, complemented
107C2×#60400C22×C311yescharacteristic, complemented
108C2×#60398C22×C311yescharacteristic, complemented
109C22×#3027C22×C311yescharacteristic, complemented
110C22×#3025C22×C311yescharacteristic
111#10574874C22×C318yescomplemented
112C2×#60401C22×C311yescharacteristic, complemented
113C2×#60399C22×C312yes—
114C2×#60399C22×C312yescomplemented
115C2×#60399C22×C318yescomplemented
116C2×#60399C22×C311yescharacteristic, complemented
117#6629045C22×C318yescomplemented
118C2×#32948C22×C312yescomplemented
119C2×#32947C22×C312yescomplemented
120#6628885C22×C318yescomplemented
121#6628883C22×C318yescomplemented
122C2×#32895C22×C312yescomplemented
123C2×#32896C22×C312yescomplemented
124C2×#32894C22×C312yescomplemented
125C2×#32894C22×C312yescomplemented
126#6573736C22×C3116yescomplemented
127#6573735C22×C3116yescomplemented
128#6573730C22×C3116yescomplemented
129#6573729C22×C3116yescomplemented
130#6372744C22×C318yescomplemented
131C2×#21484C22×C312yescomplemented
132C2×#21483C22×C312yescomplemented
133C2×#20612C22×C311yescharacteristic, complemented
134#87548C2412yescomplemented
135#87547C2414yes—
136#87547C2412yescomplemented
137C2×#5950C2×D411yescharacteristic
138C2×#5950C2×D412yes—
139C2×#5950C2411yescharacteristic
140C2×#5950C2412yes—
141C22×#997C2×D411yescharacteristic
142#85666C2414yescomplemented
143#3028⋊C3C2412yescomplemented
144#3027⋊C3C2414yes—
145#3027⋊C3C2412yescomplemented
146#3025⋊C3C2×D412yes—
147#3025⋊C3C2×D414yes—
148#3025⋊C3C2×D414yes—
149#3025⋊C3C2×D412yes—
150#3025⋊C3C2412yes—
151#3025⋊C3C2412yes—
152C2×#458⋊C3C2×D411yescharacteristic
153C2×#458⋊C3C2×D414yes—
154C2×#458⋊C3C2×D411yescharacteristic
155C2×B(4,𝔽2)⋊C3C2×D411yescharacteristic
156C2×B(4,𝔽2)⋊C3C2×D414yes—
157C2×B(4,𝔽2)⋊C3C2×D411yescharacteristic
158#1791⋊C3C2414yescomplemented
159#63103C23×C314yescomplemented
160C2×2−1+6C23×C311yescharacteristic, complemented
161C2×H(7,𝔽2)C23×C312yes—
162C2×H(7,𝔽2)C23×C314yescomplemented
163C2×H(7,𝔽2)C23×C311yescharacteristic, complemented
164C22×#585C23×C311yescharacteristic
165C24×#41C2×A411yescharacteristic, complemented
166C25×D4C2×A411yescharacteristic, complemented
167#63092C23×C318yescomplemented
168#63091C23×C318yescomplemented
169C23×AGL(1,ℤ/8)C2×A411yescharacteristic
170C23×AGL(1,ℤ/8)C2×A411yescharacteristic, complemented
171C23×AGL(1,ℤ/8)C2×A411yescharacteristic, complemented
172C23×AGL(1,ℤ/8)C2×A411yescharacteristic, complemented
173C23×AGL(1,ℤ/8)C2×A412yescomplemented
174C23×AGL(1,ℤ/8)C2×A412yescomplemented
175C23×AGL(1,ℤ/8)C2×A4116yescomplemented
176C24×SD16C2×A412yescomplemented
177C24×D8C2×A412yescomplemented
178#63076C23×C314yescomplemented
179C2×#3573C23×C312yescomplemented
180C24×M16C2×A411yescharacteristic, complemented
181#60402C23×C314yescomplemented
182#60401C23×C314yescomplemented
183#60400C23×C314yescomplemented
184#60399C23×C318yes—
185#60399C23×C318yescomplemented
186#60399C23×C314yescomplemented
187#60398C23×C314yescomplemented
188C2×#3028C23×C311yescharacteristic, complemented
189C2×#3027C23×C312yes—
190C2×#3027C23×C314yescomplemented
191C2×#3027C23×C311yescharacteristic, complemented
192C2×#3025C3×D411yescharacteristic
193C2×#3025C3×D411yescharacteristic
194C2×#3025C3×D414yes—
195C2×#3025C23×C311yescharacteristic
196C2×#3025C23×C311yescharacteristic
197C2×#3025C23×C314yes—
198C22×#458C3×D411yescharacteristic
199C22×B(4,𝔽2)C3×D411yescharacteristic
200#32948C23×C318yescomplemented
201#32947C23×C318yescomplemented
202#32896C23×C318yescomplemented
203#32895C23×C318yescomplemented
204#32894C23×C318yescomplemented
205#32894C23×C318yescomplemented
206#21484C23×C318yescomplemented
207#21483C23×C318yescomplemented
208#20612C23×C314yescomplemented
209C2×#1791C23×C312yescomplemented
210#5950C22×D411yescharacteristic
211#5950C22×D412yes—
212#5950C2511yescharacteristic
213C2×#997C22×D411yescharacteristic
214C2×#997C22×D412yes—
215#458⋊C3C22×D412yes—
216#458⋊C3C22×D412yes—
217B(4,𝔽2)⋊C3C22×D412yes—
218B(4,𝔽2)⋊C3C22×D412yes—
2192−1+6C24×C312yescomplemented
220H(7,𝔽2)C24×C314yes—
221H(7,𝔽2)C24×C312yescomplemented
222C2×#585C2×C3×D412yes—
223C2×#585C2×C3×D411yescharacteristic
224C2×#585C24×C311yescharacteristic
225C2×#585C24×C312yes—
226C22×H(5,𝔽2)C2×C3×D411yescharacteristic
227C23×#41C22×A411yescharacteristic
228C23×#41C22×A411yescharacteristic
229C23×#41C22×A411yescharacteristic, complemented
230C23×#41C22×A411yescharacteristic, complemented
231C23×#41C22×A418yescomplemented
232C24×Q8C22×A411yescharacteristic, complemented
233C24×D4C22×A412yes—
234C24×D4C22×A412yes—
235C24×D4C22×A411yescharacteristic
236C24×D4C22×A411yescharacteristic
237C24×D4C22×A418yescomplemented
238C24×D4C22×A411yescharacteristic, complemented
239C25×C4C22×A411yescharacteristic
240C22×AGL(1,ℤ/8)C22×A418yes—
241C22×AGL(1,ℤ/8)C22×A418yescomplemented
242C22×AGL(1,ℤ/8)C22×A418yescomplemented
243C22×AGL(1,ℤ/8)C22×A418yescomplemented
244C22×AGL(1,ℤ/8)C22×A4116yescomplemented
245C22×AGL(1,ℤ/8)C22×A4116yescomplemented
246C23×SD16C22×A412yes—
247C23×SD16C22×A412yes—
248C23×SD16C22×A412yescomplemented
249C23×SD16C22×A412yescomplemented
250C23×SD16C22×A4116yescomplemented
251C23×D8C22×A412yes—
252C23×D8C22×A412yes—
253C23×D8C22×A412yescomplemented
254C23×D8C22×A412yescomplemented
255C23×D8C22×A4116yescomplemented
256#3573C24×C314yescomplemented
257C23×M16C22×A411yescharacteristic
258C23×M16C22×A411yescharacteristic
259C23×M16C22×A412yescomplemented
260C23×M16C22×A418yescomplemented
261C24×C8C22×A412yescomplemented
262#3028C24×C312yescomplemented
263#3027C24×C314yes—
264#3027C24×C312yescomplemented
265#3025C2×C3×D412yes—
266#3025C2×C3×D412yes—
267#3025C2×C3×D414yes—
268#3025C2×C3×D414yes—
269#3025C24×C312yes—
270#3025C24×C312yes—
271C2×#458C2×C3×D411yescharacteristic
272C2×#458C2×C3×D411yescharacteristic
273C2×#458C2×C3×D414yes—
274C2×B(4,𝔽2)C2×C3×D411yescharacteristic
275C2×B(4,𝔽2)C2×C3×D411yescharacteristic
276C2×B(4,𝔽2)C2×C3×D414yes—
277#1791C24×C314yescomplemented
278#997C23×D411yescharacteristic
279C26D4×A411yescharacteristic
280#585C22×C3×D411yescharacteristic
281#585C22×C3×D412yes—
282#585C25×C311yescharacteristic
283C2×H(5,𝔽2)C22×C3×D412yes—
284C2×H(5,𝔽2)C22×C3×D411yescharacteristic
285C22×#41C23×A414yes—
286C22×#41C23×A414yes—
287C22×#41C23×A414yescomplemented
288C22×#41C23×A414yescomplemented
289C23×Q8C23×A411yescharacteristic
290C23×Q8C23×A411yescharacteristic
291C23×Q8C23×A414yescomplemented
292C23×D4C23×A412yes—
293C23×D4C23×A414yes—
294C23×D4C23×A411yescharacteristic
295C23×D4C23×A412yes—
296C23×D4C23×A414yes—
297C23×D4C23×A418yes—
298C23×D4C23×A418yes—
299C23×D4C23×A411yescharacteristic
300C23×D4C23×A414yescomplemented
301C24×C4D4×A411yescharacteristic
302C24×C4D4×A414yes—
303C24×C4D4×A411yescharacteristic
304C24×C4D4×A411yescharacteristic
305C24×C4C23×A411yescharacteristic
306C24×C4C23×A411yescharacteristic
307C24×C4C23×A411yescharacteristic
308C24×C4C23×A414yes—
309C2×AGL(1,ℤ/8)#120⋊C311yescharacteristic
310C22×SD16C23×A418yes—
311C22×SD16C23×A418yes—
312C22×SD16C23×A418yescomplemented
313C22×SD16C23×A418yescomplemented
314C22×D8C23×A418yes—
315C22×D8C23×A418yes—
316C22×D8C23×A418yescomplemented
317C22×D8C23×A418yescomplemented
318C22×M16C23×A414yes—
319C22×M16C23×A414yes—
320C22×M16C23×A418yescomplemented
321C23×C8C23×A412yes—
322C23×C8C23×A412yes—
323C23×C8C23×A418yescomplemented
324#458C22×C3×D412yes—
325#458C22×C3×D412yes—
326B(4,𝔽2)C22×C3×D412yes—
327B(4,𝔽2)C22×C3×D412yes—
328C25C2×D4×A411yescharacteristic
329C25C2×D4×A414yes—
330C25C2×D4×A411yescharacteristic
331C25C2×D4×A411yescharacteristic
332H(5,𝔽2)C23×C3×D411yescharacteristic
333C2×#41C2×#120⋊C311yescharacteristic
334C22×Q8C24×A412yes—
335C22×Q8C24×A412yes—
336C22×D4C2×#120⋊C311yescharacteristic
337C22×D4C24×A414yes—
338C22×D4C24×A412yes—
339C22×D4C24×A412yes—
340C22×D4C24×A414yes—
341C23×C4C2×D4×A412yes—
342C23×C4C2×D4×A411yescharacteristic
343C23×C4C2×D4×A414yes—
344C23×C4C2×D4×A411yescharacteristic
345C23×C4C2×D4×A411yescharacteristic
346C23×C4C2×D4×A412yes—
347C23×C4C2×D4×A412yes—
348C23×C4C2×D4×A414yes—
349C23×C4C2×D4×A414yes—
350C23×C4C24×A411yescharacteristic
351C23×C4C24×A412yes—
352C23×C4C24×A412yes—
353C23×C4C24×A412yes—
354AGL(1,ℤ/8)C2×#120⋊C318yes—
355C2×SD16C2×#120⋊C312yes—
356C2×D8C2×#120⋊C312yes—
357C2×M16C2×#120⋊C311yescharacteristic
358C22×C8C24×A414yes—
359C22×C8C24×A414yes—
360C24C22×D4×A412yes—
361C24C22×D4×A411yescharacteristic
362C24C22×D4×A412yes—
363C24C22×D4×A412yes—
364#41C22×#120⋊C314yes—
365C2×Q8C22×#120⋊C311yescharacteristic
366C2×D4C22×#120⋊C311yescharacteristic
367C2×D4C22×#120⋊C312yes—
368C2×D4C22×#120⋊C314yes—
369C22×C4C22×#120⋊C311yescharacteristic
370C22×C4C22×D4×A411yescharacteristic
371C22×C4C22×D4×A412yes—
372C22×C4C22×D4×A412yes—
373C22×C4C22×D4×A412yes—
374C22×C4C25×A411yescharacteristic
375SD16C22×#120⋊C318yes—
376D8C22×#120⋊C318yes—
377M16C22×#120⋊C314yes—
378C2×C8C22×#120⋊C312yes—
379C23D4×#120⋊C311yescharacteristic
380C23C23×D4×A411yescharacteristic
381Q8C23×#120⋊C312yes—
382D4C23×#120⋊C312yes—
383D4C23×#120⋊C314yes—
384C2×C4D4×#120⋊C312yes—
385C2×C4D4×#120⋊C311yescharacteristic
386C2×C4C23×#120⋊C312yes—
387C2×C4C23×#120⋊C311yescharacteristic
388C8C23×#120⋊C314yes—
389C22C2×D4×#120⋊C312yes—
390C22C2×D4×#120⋊C311yescharacteristic
391C4C2×D4×#120⋊C311yescharacteristic
392C4C2×D4×#120⋊C312yes—
393C4C24×#120⋊C311yescharacteristic
394C2#7224097712yesdirect product factor
395C2C22×D4×#120⋊C311yescharacteristic
subgroupG/H
center, socleC22C2×D4×#120⋊C3
commutator, cosocle#585C25×C3
FrattiniC22×C4C25×A4
FittingC2×#72236873C3
hypercenterC2×AGL(1,ℤ/8)#120⋊C3
hypocenterH(5,𝔽2)C23×C3×D4
LCSG ▷ #585 ▷ H(5,𝔽2)
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#72236824C2semidirect
2. C2×#72236792C2semidirect
3. C22×#60399⋊C3C2semidirect
4. C2×#72236802C2semidirect
5. C2×#60401⋊C3C22semidirect
6. C2×#72236799C2semidirect
7. C2×#21484⋊C3C22semidirect
8. C2×#11710352C22semidirect
9. C2×#72233783C2semidirect
10. C2×#72236859C2semidirect
11. C2×#72236874C2semidirect
12. C2×#11710347C22semidirect
13. C2×#32896⋊C3C22semidirect
14. C2×#32947⋊C3C22semidirect
15. C2×#72236864C2semidirect
17. C2×#21483⋊C3C22semidirect
18. C2×#32948⋊C3C22semidirect
19. C2×#72236755C2semidirect
20. C22×#3027⋊C3C22semidirect
21. C2×#32894⋊C3C22semidirect
22. C2×#32894⋊C3C22semidirect
23. C2×#32895⋊C3C22semidirect
24. C2×#20612⋊C3C22semidirect
25. C2×#72215685C2semidirect
26. C2×#11710873C22semidirect
27. C2×#11710899C22semidirect
28. C2×#60398⋊C3C22semidirect
29. C2×#11710937C22semidirect
30. C22×#87547C22semidirect
31. C2×#72236873C3semidirect
32. C2×#6372744C2×C3semidirect
33. C2×#6573736C2×C3semidirect
34. C2×#6573735C2×C3semidirect
35. C2×#6628885C2×C3semidirect
36. C2×#6629045C2×C3semidirect
37. C2×#10574874C2×C3semidirect
38. C2×#10586999C2×C3semidirect
39. C2×#6628883C2×C3semidirect
40. C2×#6573730C2×C3semidirect
41. C2×#6573729C2×C3semidirect
42. #72240977C2direct (N × H)
43. #72236874C22semidirect
44. #72236873C2×C3semidirect
45. #72236864C22semidirect
46. #72236859C22semidirect
47. #72236824C22semidirect
48. #72236802C22semidirect
49. #72236799C22semidirect
50. C2×#60399⋊C3C22semidirect
51. C2×#60399⋊C3C22semidirect
52. C2×#60399⋊C3C22semidirect
53. C2×#60399⋊C3C22semidirect
54. #72236792C22semidirect
55. #72236755C22semidirect
56. C22×#60399C2×C3semidirect
57. #72233783C22semidirect
58. C2×#11710898C22semidirect
59. #72215685C22semidirect
60. #11710937C23semidirect
61. C2×#87548C23semidirect
63. C2×#87547C23semidirect
64. C2×#87547C23semidirect
66. #11710899C23semidirect
67. #11710898C23semidirect
68. #11710873C23semidirect
69. C2×#85666C23semidirect
70. #11710352C23semidirect
71. #60401⋊C3C23semidirect
72. #11710347C23semidirect
73. #60399⋊C3C23semidirect
74. #60399⋊C3C23semidirect
75. #60399⋊C3C23semidirect
76. #60398⋊C3C23semidirect
77. C2×#3028⋊C3C23semidirect
79. C2×#3027⋊C3C23semidirect
80. C2×#3027⋊C3C23semidirect
89. #32948⋊C3C23semidirect
90. #32947⋊C3C23semidirect
91. #32896⋊C3C23semidirect
92. #32895⋊C3C23semidirect
93. #32894⋊C3C23semidirect
94. #32894⋊C3C23semidirect
95. #21484⋊C3C23semidirect
96. #21483⋊C3C23semidirect
97. #20612⋊C3C23semidirect
98. C2×#1791⋊C3C23semidirect
99. C2×#63103C22×C3semidirect
100. C22×H(7,𝔽2)C22×C3semidirect
101. #10586999C22×C3semidirect
102. C2×#63092C22×C3semidirect
103. C2×#63091C22×C3semidirect
104. C24×AGL(1,ℤ/8)A4semidirect
105. C2×#63076C22×C3semidirect
106. C2×#60402C22×C3semidirect
107. C2×#60400C22×C3semidirect
108. C2×#60398C22×C3semidirect
109. C22×#3027C22×C3semidirect
111. #10574874C22×C3semidirect
112. C2×#60401C22×C3semidirect
114. C2×#60399C22×C3semidirect
115. C2×#60399C22×C3semidirect
116. C2×#60399C22×C3semidirect
117. #6629045C22×C3semidirect
118. C2×#32948C22×C3semidirect
119. C2×#32947C22×C3semidirect
120. #6628885C22×C3semidirect
121. #6628883C22×C3semidirect
122. C2×#32895C22×C3semidirect
123. C2×#32896C22×C3semidirect
124. C2×#32894C22×C3semidirect
125. C2×#32894C22×C3semidirect
126. #6573736C22×C3semidirect
127. #6573735C22×C3semidirect
128. #6573730C22×C3semidirect
129. #6573729C22×C3semidirect
130. #6372744C22×C3semidirect
131. C2×#21484C22×C3semidirect
132. C2×#21483C22×C3semidirect
133. C2×#20612C22×C3semidirect
134. #87548C24semidirect
136. #87547C24semidirect
142. #85666C24semidirect
143. #3028⋊C3C24semidirect
145. #3027⋊C3C24semidirect
158. #1791⋊C3C24semidirect
159. #63103C23×C3semidirect
160. C2×2−1+6C23×C3semidirect
162. C2×H(7,𝔽2)C23×C3semidirect
163. C2×H(7,𝔽2)C23×C3semidirect
165. C24×#41C2×A4semidirect
166. C25×D4C2×A4semidirect
167. #63092C23×C3semidirect
168. #63091C23×C3semidirect
170. C23×AGL(1,ℤ/8)C2×A4semidirect
171. C23×AGL(1,ℤ/8)C2×A4semidirect
172. C23×AGL(1,ℤ/8)C2×A4semidirect
173. C23×AGL(1,ℤ/8)C2×A4semidirect
174. C23×AGL(1,ℤ/8)C2×A4semidirect
175. C23×AGL(1,ℤ/8)C2×A4semidirect
176. C24×SD16C2×A4semidirect
177. C24×D8C2×A4semidirect
178. #63076C23×C3semidirect
179. C2×#3573C23×C3semidirect
180. C24×M16C2×A4semidirect
181. #60402C23×C3semidirect
182. #60401C23×C3semidirect
183. #60400C23×C3semidirect
185. #60399C23×C3semidirect
186. #60399C23×C3semidirect
187. #60398C23×C3semidirect
188. C2×#3028C23×C3semidirect
190. C2×#3027C23×C3semidirect
191. C2×#3027C23×C3semidirect
200. #32948C23×C3semidirect
201. #32947C23×C3semidirect
202. #32896C23×C3semidirect
203. #32895C23×C3semidirect
204. #32894C23×C3semidirect
205. #32894C23×C3semidirect
206. #21484C23×C3semidirect
207. #21483C23×C3semidirect
208. #20612C23×C3semidirect
209. C2×#1791C23×C3semidirect
219. 2−1+6C24×C3semidirect
221. H(7,𝔽2)C24×C3semidirect
229. C23×#41C22×A4semidirect
230. C23×#41C22×A4semidirect
231. C23×#41C22×A4semidirect
232. C24×Q8C22×A4semidirect
237. C24×D4C22×A4semidirect
238. C24×D4C22×A4semidirect
241. C22×AGL(1,ℤ/8)C22×A4semidirect
242. C22×AGL(1,ℤ/8)C22×A4semidirect
243. C22×AGL(1,ℤ/8)C22×A4semidirect
244. C22×AGL(1,ℤ/8)C22×A4semidirect
245. C22×AGL(1,ℤ/8)C22×A4semidirect
248. C23×SD16C22×A4semidirect
249. C23×SD16C22×A4semidirect
250. C23×SD16C22×A4semidirect
253. C23×D8C22×A4semidirect
254. C23×D8C22×A4semidirect
255. C23×D8C22×A4semidirect
256. #3573C24×C3semidirect
259. C23×M16C22×A4semidirect
260. C23×M16C22×A4semidirect
261. C24×C8C22×A4semidirect
262. #3028C24×C3semidirect
264. #3027C24×C3semidirect
277. #1791C24×C3semidirect
287. C22×#41C23×A4semidirect
288. C22×#41C23×A4semidirect
291. C23×Q8C23×A4semidirect
300. C23×D4C23×A4semidirect
312. C22×SD16C23×A4semidirect
313. C22×SD16C23×A4semidirect
316. C22×D8C23×A4semidirect
317. C22×D8C23×A4semidirect
320. C22×M16C23×A4semidirect
323. C23×C8C23×A4semidirect
394. C2#72240977direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#722368242
C2×#722367922
C22×#60399⋊C32
C2×#722368022
C2×#722367992
C2×#722337832
C2×#722368592
C2×#722368742
C2×#722368642
C2×#722367552
C2×#722156852
C2×#722368733
#722409772
C22×A4×AGL(1,ℤ/8)4