Finite Group Databasebeta

← #16855446

Subgroups — #16855446

Order 3968.

446 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521848C211yesmaximal, characteristic
2C2×#11758495C211yesmaximal, characteristic, complemented
3#137×D31C211yesmaximal, characteristic, complemented
4#14521814C211yesmaximal, characteristic, complemented
5#14521323C211yesmaximal, characteristic, complemented
6#14521322C211yesmaximal, characteristic, complemented
7#14521321C211yesmaximal, characteristic, complemented
8#14521315C211yesmaximal, characteristic, complemented
9#14521314C211yesmaximal, characteristic, complemented
10#14521313C211yesmaximal, characteristic, complemented
11#14521312C211yesmaximal, characteristic, complemented
12#14521096C211yesmaximal, characteristic, complemented
13#14521032C211yesmaximal, characteristic, complemented
14#101×D31C211yesmaximal, characteristic, complemented
15C31×#473C211yesmaximal, characteristic, complemented
16#41×D31C2211yescharacteristic
17C2×#92499C2211yescharacteristic
18C2×Q8×D31C2211yescharacteristic
19C31×#137C2211yescharacteristic
20C31×#137C2211yescharacteristic
21C2×Q16×C31C2211yescharacteristic, complemented
22C31×#131C2211yescharacteristic
23#11758528C2211yescharacteristic
24#11758526C2211yescharacteristic
25#11758525C2211yescharacteristic
26C2×#92482C2211yescharacteristic, complemented
27#11758519C2211yescharacteristic
28#11758519C2211yescharacteristic
29C2×#92481C2211yescharacteristic, complemented
30#11758496—21no—
31#11758495—21no—
32#11758495—21no—
33#11758495—21no—
34#11758495—21no—
35#11758495—21no—
36#11758495—21no—
37Q16×D31—21no—
38#11758493—21no—
39#11758492—21no—
40#11758491—21no—
41SD16×D31—21no—
42#11758486C2211yescharacteristic
43#11758485C2211yescharacteristic
44#11758484—21no—
45#11758484C2211yescharacteristic
46M16×D31—21no—
47M16×D31C2211yescharacteristic
48M16×D31C2211yescharacteristic
49M16×D31C2211yescharacteristic
50C2×#92470C2211yescharacteristic, complemented
51#11758478—21no—
52#11758478C2211yescharacteristic
53C2×#92469—21no—
54C2×#92469C2211yescharacteristic
55C31×#108C2211yescharacteristic, complemented
56C31×#101C2211yescharacteristic, complemented
57C31×#101C2211yescharacteristic, complemented
58#11758424C2211yescharacteristic, complemented
59#11758424C2211yescharacteristic, complemented
60#11758412C2211yescharacteristic, complemented
61#11758412C2211yescharacteristic, complemented
62#11758411C2211yescharacteristic, complemented
63#11758411C2211yescharacteristic, complemented
64#11758410C2211yescharacteristic, complemented
65#11758410C2211yescharacteristic, complemented
66#11758407C2211yescharacteristic, complemented
67#41×C31C2311yescharacteristic
68C2×Q8×C31C2311yescharacteristic
69C2×Q8×C31C2311yescharacteristic
70#92499—21no—
71#92499—21no—
72#92499—21no—
73#92499—21no—
74#92499D411yescharacteristic
75Q8×D31—21no—
76Q8×D31—21no—
77Q8×D31—21no—
78Q8×D31—21no—
79Q8×D31D411yescharacteristic
80#92497—21no—
81#92497D411yescharacteristic
82D4×D31—21no—
83D4×D31D411yescharacteristic
84#92495—21no—
85#92495C2311yescharacteristic
86C2×D124—21no—
87C2×D124C2311yescharacteristic
88C2×C4×D31—21no—
89C2×C4×D31—21no—
90C2×C4×D31—21no—
91C2×C4×D31C2311yescharacteristic
92C2×Dic62—21no—
93C2×Dic62C2311yescharacteristic
94Q16×C31—21no—
95Q16×C31—21no—
96Q16×C31—21no—
97Q16×C31—21no—
98SD16×C31—21no—
99SD16×C31—21no—
100M16×C31—21no—
101M16×C31C2311yescharacteristic
102M16×C31C2311yescharacteristic
103M16×C31C2311yescharacteristic
104C2×C8×C31—21no—
105C2×C8×C31C2311yescharacteristic
106#92482—21no—
107#92482—21no—
108#92482—21no—
109#92482—21no—
110#92482—21no—
111#92481—21no—
112#92481—21no—
113#92481—21no—
114#92481—21no—
115#92481—21no—
116#92480—21no—
117#92479—21no—
118#92474—21no—
119#92474C2311yescharacteristic
120#92474C2311yescharacteristic
121#92474C2311yescharacteristic
122C2×C31⋊C8—21no—
123C2×C31⋊C8C2311yescharacteristic
124Dic124—21no—
125D248—21no—
126#92470—21no—
127#92470—21no—
128#92470—21no—
129#92470—21no—
130#92469—21no—
131#92469—21no—
132#92469—21no—
133#92469—21no—
134#92469—21no—
135#92469D411yescharacteristic
136#92469D411yescharacteristic
137#92469D411yescharacteristic
138#92469D411yescharacteristic
139C8×D31—21no—
140C8×D31—21no—
141C8×D31—21no—
142C8×D31—21no—
143C8×D31—21no—
144C22×D31—21no—
145C22×D31—21no—
146C22×D31#4111yescharacteristic
147Q8×C31—21no—
148Q8×C31—21no—
149Q8×C31—21no—
150Q8×C31—21no—
151Q8×C31C2×D411yescharacteristic
152D4×C31—21no—
153D4×C31C2×D411yescharacteristic
154C2×C4×C31—21no—
155C2×C4×C31—21no—
156C2×C4×C31—21no—
157C2×C4×C31C2411yescharacteristic
158C22⋊D31—21no—
159C22⋊D31—21no—
160C22⋊D31—21no—
161C2×Dic31—21no—
162C2×Dic31—21no—
163C2×Dic31#4111yescharacteristic
164D124—21no—
165D124—21no—
166D124—21no—
167D124—41no—
168D124—41no—
169D124C2×D411yescharacteristic
170C4×D31—21no—
171C4×D31—21no—
172C4×D31—21no—
173C4×D31—41no—
174C4×D31—41no—
175C4×D31—41no—
176C4×D31—41no—
177C4×D31C2×D411yescharacteristic
178C4×D31C2×D411yescharacteristic
179C4×D31C2×D411yescharacteristic
180C4×D31C2×D411yescharacteristic
181Dic62—21no—
182Dic62—21no—
183Dic62—21no—
184Dic62—41no—
185Dic62—41no—
186Dic62C2×D411yescharacteristic
187C8×C31—21no—
188C8×C31—21no—
189C8×C31—21no—
190C8×C31C2×D411yescharacteristic
191C8×C31C2×D411yescharacteristic
192C31⋊C8—21no—
193C31⋊C8—21no—
194C31⋊C8—21no—
195C31⋊C8C2×D411yescharacteristic
196C31⋊C8C2×D411yescharacteristic
197#3069—311nomaximal, Sylow
198C22×C31—21no—
199C22×C31C2×#4111yescharacteristic
200C2×D31—21no—
201C2×D31—41no—
202C2×D31—41no—
203C2×D31—81no—
204C2×D31—81no—
205C2×D31#12111yescharacteristic
206C2×D31#12111yescharacteristic
207C4×C31—21no—
208C4×C31—41no—
209C4×C31—41no—
210C4×C31C22×D411yescharacteristic
211C4×C31C22×D411yescharacteristic
212Dic31—21no—
213Dic31—41no—
214Dic31#12111yescharacteristic
215Dic31#12111yescharacteristic
216#575—311no—
217C2×#137—311no—
218C2×#137—311no—
219#568—311no—
220#473—311no—
221#473—311no—
222#473—311no—
223#473D3111yescharacteristic, complemented
224#471—311no—
225#471—311no—
226#471—311no—
227#471—311no—
228#430—311no—
229#413—311no—
230C2×#101—311no—
231C2×C31—21no—
232C2×C31—41no—
233C2×C31C2×#12111yescharacteristic
234D31—21no—
235D31—21no—
236D31—41no—
237D31—81no—
238C2×#41—311no—
239C2×#41—311no—
240C22×Q8—311no—
241#137—311no—
242#137—311no—
243#137—311no—
244#137—311no—
245#137—621no—
246#137—621no—
247#137—621no—
248#137—621no—
249#137—621no—
250#137—621no—
251#137—621no—
252#137C2×D3111yescharacteristic
253#137C2×D3111yescharacteristic
254AGL(1,ℤ/8)—311no—
255AGL(1,ℤ/8)—311no—
256AGL(1,ℤ/8)—621no—
257#135—621no—
258#135—621no—
259C2×Q16—311no—
260C2×Q16—621no—
261C2×Q16C2×D3111yescharacteristic, complemented
262C2×SD16—311no—
263C2×SD16—311no—
264C2×SD16—621no—
265#131—311no—
266#131—311no—
267#131—311no—
268#131—621no—
269#131—621no—
270#131C2×D3111yescharacteristic
271C2×M16—311no—
272C2×M16—311no—
273C2×M16—311no—
274C2×M16—311no—
275C2×M16—621no—
276C2×M16—621no—
277#108—311no—
278#108—311no—
279#108—311no—
280#108C2×D3111yescharacteristic, complemented
281#101—311no—
282#101—311no—
283#101—311no—
284#101—311no—
285#101C2×D3111yescharacteristic, complemented
286#101C2×D3111yescharacteristic, complemented
287#100—311no—
288#100—311no—
289C31#306911yescharacteristic, complemented, Sylow
290#41—311no—
291#41—311no—
292#41—311no—
293#41—621no—
294#41—621no—
295#41—621no—
296#41—621no—
297#41—621no—
298#41—621no—
299#41C22×D3111yescharacteristic
300C2×Q8—311no—
301C2×Q8—311no—
302C2×Q8—621no—
303C2×Q8—621no—
304C2×Q8—621no—
305C2×Q8—621no—
306C2×Q8—621no—
307C2×Q8C22×D3111yescharacteristic
308C2×Q8C22×D3111yescharacteristic
309C2×D4—311no—
310C2×D4—311no—
311C2×D4—621no—
312C2×D4—621no—
313C22×C4—311no—
314C22×C4—621no—
315C22×C4—621no—
316C22×C4—621no—
317Q16—21no—
318Q16—21no—
319Q16—21no—
320Q16—21no—
321Q16—621no—
322Q16—621no—
323Q16—621no—
324Q16—621no—
325Q16—621no—
326Q16—621no—
327SD16—21no—
328SD16—21no—
329SD16—621no—
330SD16—621no—
331SD16—621no—
332SD16—621no—
333SD16—621no—
334SD16—621no—
335SD16—621no—
336SD16—621no—
337SD16—621no—
338SD16—621no—
339D8—621no—
340D8—621no—
341M16—21no—
342M16—311no—
343M16—311no—
344M16—311no—
345M16—311no—
346M16—311no—
347M16—311no—
348M16—311no—
349M16—621no—
350M16—621no—
351M16—621no—
352M16—621no—
353M16—621no—
354M16—621no—
355M16C22×D3111yescharacteristic
356M16C22×D3111yescharacteristic
357M16C22×D3111yescharacteristic
358C2×C8—21no—
359C2×C8—311no—
360C2×C8—621no—
361C2×C8—621no—
362C2×C8—621no—
363C2×C8—621no—
364C2×C8—621no—
365C2×C8—621no—
366C2×C8C22×D3111yescharacteristic
367C23—311no—
368C23—621no—
369C23—621no—
370Q8—21no—
371Q8—21no—
372Q8—21no—
373Q8—21no—
374Q8—311no—
375Q8—621no—
376Q8—621no—
377Q8—621no—
378Q8—1241no—
379Q8—1241no—
380Q8D4×D3111yescharacteristic
381D4—21no—
382D4—311no—
383D4—621no—
384D4—621no—
385D4—621no—
386D4—621no—
387D4—621no—
388D4—621no—
389D4—1241no—
390D4—1241no—
391D4D4×D3111yescharacteristic
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—311no—
396C2×C4—311no—
397C2×C4—311no—
398C2×C4—311no—
399C2×C4—311no—
400C2×C4—621no—
401C2×C4—621no—
402C2×C4—621no—
403C2×C4—621no—
404C2×C4—621no—
405C2×C4—1241no—
406C2×C4—1241no—
407C2×C4—1241no—
408C2×C4—1241no—
409C2×C4C23×D3111yescharacteristic
410C8—21no—
411C8—21no—
412C8—21no—
413C8—311no—
414C8—311no—
415C8—621no—
416C8—621no—
417C8—621no—
418C8D4×D3111yescharacteristic
419C8D4×D3111yescharacteristic
420C22—21no—
421C22—311no—
422C22—311no—
423C22—621no—
424C22—1241no—
425C22—1241no—
426C22—2481no—
427C22—2481no—
428C22#41×D3111yescharacteristic
429C4—21no—
430C4—41no—
431C4—41no—
432C4—311no—
433C4—311no—
434C4—621no—
435C4—1241no—
436C4C2×D4×D3111yescharacteristic
437C4C2×D4×D3111yescharacteristic
438C2—21no—
439C2—41no—
440C2—621no—
441C2—621no—
442C2—1241no—
443C2—2481no—
444C2#121×D3111yescharacteristic
subgroupG/H
centerC2#121×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#473C2
socleC2×C31C2×#121
prime radical#14521848C2
hypercenter#473D31
hypocenterC31#3069
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ #473

Complements

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

NH ≅ G/Ntype
2. C2×#11758495C2semidirect
3. #137×D31C2semidirect
4. #14521814C2semidirect
5. #14521323C2semidirect
6. #14521322C2semidirect
7. #14521321C2semidirect
8. #14521315C2semidirect
9. #14521314C2semidirect
10. #14521313C2semidirect
11. #14521312C2semidirect
12. #14521096C2semidirect
13. #14521032C2semidirect
14. #101×D31C2semidirect
15. C31×#473C2semidirect
21. C2×Q16×C31C22semidirect
26. C2×#92482C22semidirect
29. C2×#92481C22semidirect
50. C2×#92470C22semidirect
55. C31×#108C22semidirect
56. C31×#101C22semidirect
57. C31×#101C22semidirect
58. #11758424C22semidirect
59. #11758424C22semidirect
60. #11758412C22semidirect
61. #11758412C22semidirect
62. #11758411C22semidirect
63. #11758411C22semidirect
64. #11758410C22semidirect
65. #11758410C22semidirect
66. #11758407C22semidirect
223. #473D31semidirect
261. C2×Q16C2×D31semidirect
280. #108C2×D31semidirect
285. #101C2×D31semidirect
286. #101C2×D31semidirect
289. C31#3069semidirect

Maximal subgroups

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

subgroupindex
#145218482
C2×#117584952
#137×D312
#145218142
#145213232
#145213222
#145213212
#145213152
#145213142
#145213132
#145213122
#145210962
#145210322
#101×D312
C31×#4732
#306931