Finite Group Databasebeta

← #11861236

Subgroups — #11861236

Order 1152.

957 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
1C2×C3×#904C211yesmaximal, characteristic
2#10594776C212yesmaximal, complemented
3C2×#63646C211yesmaximal, characteristic, complemented
4C3×#5101C211yesmaximal, characteristic, complemented
5#10591111C212yesmaximal, complemented
6#10590916C214yesmaximal, complemented
7#10590915C214yesmaximal, complemented
8#83910—31nomaximal
9#78580—31nomaximal
10C2×C3×#235C2212yes—
11C22×C32×C8C2211yescharacteristic
12C2×#3748C2212yes—
13C3×#926C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×Dic12C411yescharacteristic, complemented
16C3×#904C412yescomplemented
17C3×#904C412yescomplemented
18C3×#904C2212yes—
19C3×#904C2212yes—
20C2×C3×D24C411yescharacteristic, complemented
21C2×C3×#204C412yescomplemented
22#63815—24no—
23#63814C2218yescomplemented
24D3×#208—24no—
25#63646C2212yescomplemented
26#63646C2212yescomplemented
27C3×#815C2212yescomplemented
28C3×C8×Dic3C2212yescomplemented
29#63569C2218yescomplemented
30C2×C3×#135—31no—
31#5819—32no—
32#5745—32no—
33C2×#904D311yescharacteristic
34C3×#405—31no—
35#5236—32no—
36#5197—34no—
37#5196—34no—
38C2×#819—31no—
39C2×#819—31no—
40C2×#819—61no—
41#5101D311yescharacteristic, complemented
42#5005—32no—
43#4717—34no—
44#4700—34no—
45C22×C32×C4C2311yescharacteristic
46C2×C3×#67—22no—
47C3×#235—22no—
48C3×#235—22no—
49C3×#235C2×C414yes—
50C3×#235C2314yes—
51C2×C3×D12C2×C412yes—
52C2×C3×C4×D3—22no—
53C2×C3×Dic6C2×C412yes—
54C2×C32×C8C2×C411yescharacteristic
55C2×C32×C8C2×C411yescharacteristic
56C2×C32×C8C2×C411yescharacteristic
57C2×C32×C8C2×C411yescharacteristic
58C2×C32×C8C2311yescharacteristic
59C2×C32×C8C2311yescharacteristic
60#3748—22no—
61#3748C2314yes—
62C2×C3⋊(C3⋊C8)—22no—
63C3×#217—21no—
64C3×C4⋊Dic3—21no—
65C3×C4×Dic3C2312yes—
66C3×#208D412yes—
67C3×#208D412yes—
68C2×C3×C3⋊C8C2312yes—
69C3×Dic12C2×C412yes—
70C3×Dic12C2×C412yes—
71C3×D24C2×C412yes—
72C3×D24C2×C412yes—
73C3×#204C2×C414yes—
74C3×#204C2×C414yes—
75#3711—28no—
76D3×C3⋊C8—28no—
77#2957—91noSylow
78C2×C3×#41—32no—
79C2×#235C2×D312yes—
80C3×#135—32no—
81C3×#135—32no—
82C3×#135—32no—
83C3×#135—32no—
84C2×C3×Q16—31no—
85C2×C3×SD16—32no—
86C2×C3×D8—31no—
87C2×C3×M16—31no—
88C22×C3×C8—21no—
89C22×C3×C8C2×D311yescharacteristic
90C22×C3×C8C2×D311yescharacteristic
91C3×#117—31no—
92#948—38no—
93#948—64no—
94#926C2×D311yescharacteristic
95C2×#208—32no—
96C2×#208—32no—
97C2×#208—62no—
98C2×#208—64no—
99C2×#208C2×D311yescharacteristic
100#907—64no—
101D3×M16—64no—
102C2×Dic12Dic311yescharacteristic, complemented
103#904Dic312yescomplemented
104#904Dic312yescomplemented
105#904C2×D312yes—
106#904C2×D312yes—
107C2×D24Dic311yescharacteristic, complemented
108C2×#204Dic312yescomplemented
109#901—38no—
110C3×#97—32no—
111C3×C4×C8—32no—
112#837—38no—
113#819—32no—
114#819—32no—
115#819—32no—
116#819—32no—
117#819—62no—
118#819—62no—
119#815C2×D312yescomplemented
120C8×Dic3C2×D312yescomplemented
121#805—38no—
122C23×C32#4111yescharacteristic
123C22×C3×D3—22no—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C22×C411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C32×C4C2411yescharacteristic
130C3×#67—24no—
131C3×#67—24no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—22no—
134C3×D12—22no—
135C3×D12C22×C414yes—
136C3×C4×D3—24no—
137C3×C4×D3—24no—
138C3×Dic6—22no—
139C3×Dic6C22×C414yes—
140C32×C8C22×C411yescharacteristic
141C32×C8C22×C411yescharacteristic
142C32×C8C22×C411yescharacteristic
143C32×C8C22×C411yescharacteristic
144C3⋊(C3⋊C8)—24no—
145C3×C3⋊C8C2×D414yes—
146C2×#135—31no—
147#568—92no—
148#444—94no—
149#443—94no—
150C2×#108—91no—
151#421—92no—
152#405—31no—
153C3×#41—34no—
154C3×#41—34no—
155C3×#41—62no—
156C3×#41—62no—
157C2×C3×Q8—32no—
158C2×C3×D4—32no—
159C2×C3×D4—62no—
160C22×C3×C4—21no—
161C22×C3×C4—62no—
162C22×C3×C4C22×D311yescharacteristic
163C22×C3×C4C22×D311yescharacteristic
164C2×#67—22no—
165#235—22no—
166#235—22no—
167#235C2×Dic314yes—
168#235C22×D314yes—
169C2×D12C2×Dic312yes—
170C2×C4×D3—22no—
171C2×Dic6C2×Dic312yes—
172C3×Q16—32no—
173C3×Q16—32no—
174C3×SD16—34no—
175C3×SD16—34no—
176C3×D8—32no—
177C3×D8—32no—
178C3×M16—32no—
179C3×M16—32no—
180C2×C3×C8—21no—
181C2×C3×C8—21no—
182C2×C3×C8—21no—
183C2×C3×C8—21no—
184C2×C3×C8—21no—
185C2×C3×C8—21no—
186C2×C3×C8—32no—
187C2×C3×C8C4×D311yescharacteristic
188C2×C3×C8C4×D311yescharacteristic
189C2×C3×C8C4×D311yescharacteristic
190C2×C3×C8C4×D311yescharacteristic
191C2×C3×C8C2×Dic311yescharacteristic
192C2×C3×C8C2×Dic311yescharacteristic
193C2×C3×C8C2×Dic311yescharacteristic
194C2×C3×C8C2×Dic311yescharacteristic
195C2×C3×C8C22×D311yescharacteristic
196C2×C3×C8C22×D311yescharacteristic
197C2×C3×C8C22×D311yescharacteristic
198C2×C3×C8C22×D311yescharacteristic
199C3×C4⋊C4—61no—
200C3×C22⋊C4—61no—
201C3×C42—32no—
202#217—21no—
203C4⋊Dic3—21no—
204C4×Dic3C22×D312yes—
205#208—34no—
206#208—34no—
207#208—64no—
208#208—62no—
209#208—62no—
210#208—68no—
211#208—122no—
212#208D1212yes—
213#208D1212yes—
214C2×C3⋊C8—62no—
215C2×C3⋊C8—62no—
216C2×C3⋊C8—68no—
217C2×C3⋊C8—122no—
218C2×C3⋊C8C22×D312yes—
219Dic12C2×Dic312yes—
220Dic12C2×Dic312yes—
221D24C2×Dic312yes—
222D24C2×Dic312yes—
223#204C2×Dic314yes—
224#204C2×Dic314yes—
225ΓL(1,𝔽25)—68no—
226D3×C8—68no—
227C22×C32—41no—
228C22×C32C4×D411yescharacteristic
229C22×C32C4×D411yescharacteristic
230C22×C32C2×#4111yescharacteristic
231C2×C3×D3—24no—
232C2×C3×D3—82no—
233C32×C4C4×D411yescharacteristic
234C32×C4C4×D411yescharacteristic
235C32×C4C23×C411yescharacteristic
236C32×C4C22×D411yescharacteristic
237C3×Dic3—24no—
238C3×Dic3—42no—
239C2×#41—32no—
240#135—32no—
241#135—32no—
242#135—32no—
243#135—32no—
244C2×Q16—31no—
245C2×SD16—32no—
246C2×D8—31no—
247#131—98no—
248#131—184no—
249C2×M16—31no—
250C2×M16—92no—
251C2×M16—184no—
252C22×C8D3211yescharacteristic
253#117—31no—
254#108—92no—
255#108—92no—
256#104—98no—
257#97—32no—
258C4×C8—32no—
259C23×C3—21no—
260C23×C3—62no—
261C23×C3#23511yescharacteristic
262C23×C3#23711yescharacteristic
263C22×D3—22no—
264C3×Q8—34no—
265C3×Q8—62no—
266C3×D4—34no—
267C3×D4—64no—
268C3×D4—64no—
269C3×D4—62no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—62no—
277C2×C3×C4—64no—
278C2×C3×C4—64no—
279C2×C3×C4—62no—
280C2×C3×C4C2×C4×D311yescharacteristic
281C2×C3×C4C2×C4×D311yescharacteristic
282C2×C3×C4C2×D1211yescharacteristic
283C2×C3×C4C2×D1211yescharacteristic
284C2×C3×C4#23511yescharacteristic
285C2×C3×C4D3×D411yescharacteristic
286C2×C3×C4D3×D411yescharacteristic
287C2×C3×C4#23711yescharacteristic
288C2×C3×C4C22×Dic311yescharacteristic
289C2×C3×C4C22×Dic311yescharacteristic
290C2×C3×C4C23×D311yescharacteristic
291C2×C3×C4C23×D311yescharacteristic
292#67—24no—
293#67—24no—
294C2×Dic3—22no—
295C2×Dic3—22no—
296D12—22no—
297D12C22×Dic314yes—
298C4×D3—24no—
299C4×D3—24no—
300Dic6—22no—
301Dic6C22×Dic314yes—
302C3×C8—21no—
303C3×C8—21no—
304C3×C8—21no—
305C3×C8—21no—
306C3×C8—34no—
307C3×C8C2×C4×D311yescharacteristic
308C3×C8C2×C4×D311yescharacteristic
309C3×C8C2×C4×D311yescharacteristic
310C3×C8C2×C4×D311yescharacteristic
311C3×C8C22×Dic311yescharacteristic
312C3×C8C22×Dic311yescharacteristic
313C3×C8C22×Dic311yescharacteristic
314C3×C8C22×Dic311yescharacteristic
315C3⋊C8—64no—
316C3⋊C8—64no—
317C3⋊C8—124no—
318C3⋊C8C2×D1214yes—
319C2×C32—21no—
320C2×C32—21no—
321C2×C32—21no—
322C2×C32C2×C4×D411yescharacteristic
323C3×D3—44no—
324#41—34no—
325#41—34no—
326#41—62no—
327#41—62no—
328C2×Q8—32no—
329C2×D4—32no—
330C2×D4—62no—
331C22×C4—62no—
332C22×C4C2×D3211yescharacteristic
333Q16—32no—
334Q16—32no—
335SD16—34no—
336SD16—34no—
337D8—32no—
338D8—32no—
339M16—32no—
340M16—32no—
341M16—94no—
342M16—188no—
343M16—182no—
344C2×C8—32no—
345C2×C8—188no—
346C2×C8—182no—
347C2×C8D3×Dic311yescharacteristic
348C2×C8D3×Dic311yescharacteristic
349C2×C8D3×Dic311yescharacteristic
350C2×C8D3×Dic311yescharacteristic
351C2×C8C2×D3211yescharacteristic
352C2×C8C2×D3211yescharacteristic
353C4⋊C4—61no—
354C22⋊C4—61no—
355C42—32no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—41no—
360C22×C3—41no—
361C22×C3—42no—
362C22×C3—64no—
363C22×C3—242no—
364C22×C3C4×D1211yescharacteristic
365C22×C3C4×D1211yescharacteristic
366C22×C3D4×Dic311yescharacteristic
367C22×C3D4×Dic311yescharacteristic
368C22×C3C2×#23511yescharacteristic
369C22×C3C2×#23711yescharacteristic
370C2×D3—24no—
371C2×D3—82no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—64no—
377C3×C4—122no—
378C3×C4C4×D1211yescharacteristic
379C3×C4C4×D1211yescharacteristic
380C3×C4D4×Dic311yescharacteristic
381C3×C4D4×Dic311yescharacteristic
382C3×C4C22×C4×D311yescharacteristic
383C3×C4C22×D1211yescharacteristic
384C3×C4C2×D3×D411yescharacteristic
385C3×C4C23×Dic311yescharacteristic
386Dic3—24no—
387Dic3—42no—
388C32#295711yescharacteristic, complemented, Sylow
389C23—62no—
390C23#379511yescharacteristic
391Q8—34no—
392Q8—62no—
393D4—34no—
394D4—64no—
395D4—64no—
396D4—62no—
397C2×C4—62no—
398C2×C4—64no—
399C2×C4—64no—
400C2×C4—62no—
401C2×C4#379511yescharacteristic
402C2×C4D3×D1211yescharacteristic
403C2×C4D3×D1211yescharacteristic
404C2×C4C2×D3×Dic311yescharacteristic
405C2×C4C2×D3×Dic311yescharacteristic
406C2×C4C22×D3211yescharacteristic
407C8—34no—
408C8—184no—
409C8C2×D3×Dic311yescharacteristic
410C8C2×D3×Dic311yescharacteristic
411C8C2×D3×Dic311yescharacteristic
412C8C2×D3×Dic311yescharacteristic
413C2×C3—22no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—41no—
422C2×C3—41no—
423C2×C3—124no—
424C2×C3C2×C4×D1211yescharacteristic
425C2×C3C2×D4×Dic311yescharacteristic
426D3—44no—
427C22—41no—
428C22—64no—
429C22—242no—
430C22Dic3×D1211yescharacteristic
431C22Dic3×D1211yescharacteristic
432C22C2×#379511yescharacteristic
433C4—64no—
434C4—122no—
435C4Dic3×D1211yescharacteristic
436C4Dic3×D1211yescharacteristic
437C4C2×D3×D1211yescharacteristic
438C4C22×D3×Dic311yescharacteristic
439C3—21no—
440C3#7858011yescharacteristic, complemented
441C3#8391011yescharacteristic, complemented
442C2—21no—
443C2—21no—
444C2—21no—
445C2—124no—
446C2C2×Dic3×D1211yescharacteristic
subgroupG/H
centerC4C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC2×C32C2×C4×D4
prime radicalC2×C3×#904C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2957
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #10594776C2semidirect
3. C2×#63646C2semidirect
4. C3×#5101C2semidirect
5. #10591111C2semidirect
6. #10590916C2semidirect
7. #10590915C2semidirect
15. C2×C3×Dic12C4semidirect
16. C3×#904C4semidirect
17. C3×#904C4semidirect
20. C2×C3×D24C4semidirect
21. C2×C3×#204C4semidirect
23. #63814C22semidirect
25. #63646C22semidirect
26. #63646C22semidirect
27. C3×#815C22semidirect
28. C3×C8×Dic3C22semidirect
29. #63569C22semidirect
41. #5101D3semidirect
102. C2×Dic12Dic3semidirect
103. #904Dic3semidirect
104. #904Dic3semidirect
107. C2×D24Dic3semidirect
108. C2×#204Dic3semidirect
119. #815C2×D3semidirect
120. C8×Dic3C2×D3semidirect
388. C32#2957semidirect
440. C3#78580semidirect
441. C3#83910semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9042
#105947762
C2×#636462
C3×#51012
#105911112
#105909162
#105909152
#839103
#785803