Finite Group Databasebeta

← #11861234

Subgroups — #11861234

Order 1152.

1037 conjugacy classes of subgroups.

The subgroup lattice has 477 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64113C211yesmaximal, characteristic
2#10594780C212yesmaximal, complemented
3C2×C3×#819C211yesmaximal, characteristic, complemented
4C3×#5101C211yesmaximal, characteristic, complemented
5#10591113C212yesmaximal, complemented
6#10590918C214yesmaximal, complemented
7#10590917C214yesmaximal, complemented
8#79249—31nomaximal
9#78580—31nomaximal
10C2×#3828C2212yes—
11C22×C32×C8C2211yescharacteristic
12C2×#3746C411yescharacteristic, complemented
13#64113C412yescomplemented
14#64113C412yescomplemented
15#64113C2212yes—
16#64113C2212yes—
17C2×#3745C411yescharacteristic, complemented
18C2×#3744C412yescomplemented
19C3×#926C2211yescharacteristic
20C2×C3×#208C2212yes—
21C2×C3×#208C2211yescharacteristic
22#63818—24no—
23#63817—24no—
24#63817C2218yescomplemented
25C3×#819C2212yescomplemented
26C3×#819C2212yescomplemented
27C3×#815C2212yescomplemented
28C3×C8×Dic3C2212yescomplemented
29#63570C2218yescomplemented
30#5745—32no—
31#5745—32no—
32C2×#904—31no—
33C2×#904—31no—
34C2×#904—61no—
35C2×C3×#108—31no—
36C3×#405—31no—
37#5139—32no—
38C2×#819D311yescharacteristic, complemented
39#5101D311yescharacteristic, complemented
40#5005—32no—
41#4895—34no—
42#4894—34no—
43#4717—34no—
44#4700—34no—
45C22×C32×C4C2311yescharacteristic
46C2×#638—22no—
47#3828—22no—
48#3828—22no—
49#3828C2×C414yes—
50#3828C2314yes—
51C2×C4⋊(C3⋊D3)C2×C412yes—
52C2×C4×C3⋊D3—22no—
53C2×#634C2×C412yes—
54C2×C32×C8C2×C411yescharacteristic
55C2×C32×C8C2×C411yescharacteristic
56C2×C32×C8C2×C411yescharacteristic
57C2×C32×C8C2×C411yescharacteristic
58C2×C32×C8C2311yescharacteristic
59C2×C32×C8C2311yescharacteristic
60#3746C2×C412yes—
61#3746C2×C412yes—
62#3745C2×C412yes—
63#3745C2×C412yes—
64#3744C2×C414yes—
65#3744C2×C414yes—
66C3×#217—21no—
67C3×C4⋊Dic3—21no—
68C3×C4×Dic3C2312yes—
69C3×#208—22no—
70C3×#208D412yes—
71C3×#208D412yes—
72C3×#208C2314yes—
73C2×C3×C3⋊C8—22no—
74C2×C3×C3⋊C8C2312yes—
75#3712—28no—
76#3710—28no—
77#2957—91noSylow
78C2×#235—32no—
79C2×#235—32no—
80C2×#235—62no—
81C2×C3×M16—31no—
82C2×C3×M16—32no—
83C22×C3×C8—21no—
84C22×C3×C8C2×D311yescharacteristic
85C22×C3×C8C2×D311yescharacteristic
86C3×#117—31no—
87#926C2×D311yescharacteristic
88C2×#208C2×D312yes—
89C2×#208C2×D311yescharacteristic
90#907—38no—
91#907—64no—
92D3×M16—64no—
93D3×M16—64no—
94C2×Dic12—31no—
95C2×Dic12—31no—
96C2×Dic12—61no—
97#904—32no—
98#904—32no—
99#904—32no—
100#904—32no—
101#904—32no—
102#904—32no—
103#904—32no—
104#904—32no—
105#904—62no—
106#904—62no—
107#904—62no—
108#904—62no—
109C2×D24—31no—
110C2×D24—31no—
111C2×D24—61no—
112C2×#204—32no—
113C2×#204—32no—
114C2×#204—62no—
115#901—38no—
116#901—64no—
117C3×#108—32no—
118C3×#108—32no—
119C3×#97—32no—
120C3×C4×C8—32no—
121#825—38no—
122#819C2×D312yescomplemented
123#819C2×D312yescomplemented
124#815C2×D312yescomplemented
125C8×Dic3C2×D312yescomplemented
126#805—38no—
127C23×C32#4111yescharacteristic
128C22×C3⋊D3—22no—
129C2×C32×C4C22×C411yescharacteristic
130C2×C32×C4C22×C411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C32×C4C2411yescharacteristic
135#638—24no—
136#638—24no—
137C2×C3⋊Dic3—22no—
138C4⋊(C3⋊D3)—22no—
139C4⋊(C3⋊D3)C22×C414yes—
140C4×C3⋊D3—24no—
141C4×C3⋊D3—24no—
142#634—22no—
143#634C22×C414yes—
144C2×C3×Dic3—22no—
145C32×C8C22×C411yescharacteristic
146C32×C8C22×C411yescharacteristic
147C32×C8C22×C411yescharacteristic
148C32×C8C22×C411yescharacteristic
149C3×C3⋊C8—24no—
150C3×C3⋊C8C2×D414yes—
151C2×#135—91no—
152#568—92no—
153#444—94no—
154#443—94no—
155C2×#108—31no—
156#421—92no—
157#405—31no—
158C22×C3×C4—21no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C2×#67—62no—
162C2×#67—62no—
163C2×#67—122no—
164#235—34no—
165#235—34no—
166#235—34no—
167#235—34no—
168#235—64no—
169#235—64no—
170#235—62no—
171#235—62no—
172#235—62no—
173#235—62no—
174#235—122no—
175#235—122no—
176C2×D12—32no—
177C2×D12—32no—
178C2×D12—62no—
179C2×C4×D3—62no—
180C2×C4×D3—62no—
181C2×C4×D3—122no—
182C2×Dic6—32no—
183C2×Dic6—32no—
184C2×Dic6—62no—
185C3×M16—32no—
186C3×M16—32no—
187C3×M16—34no—
188C3×M16—62no—
189C2×C3×C8—21no—
190C2×C3×C8—21no—
191C2×C3×C8—21no—
192C2×C3×C8—21no—
193C2×C3×C8—21no—
194C2×C3×C8—21no—
195C2×C3×C8—32no—
196C2×C3×C8—62no—
197C2×C3×C8C4×D311yescharacteristic
198C2×C3×C8C4×D311yescharacteristic
199C2×C3×C8C4×D311yescharacteristic
200C2×C3×C8C4×D311yescharacteristic
201C2×C3×C8C4×D311yescharacteristic
202C2×C3×C8C4×D311yescharacteristic
203C2×C3×C8C4×D311yescharacteristic
204C2×C3×C8C4×D311yescharacteristic
205C2×C3×C8C22×D311yescharacteristic
206C2×C3×C8C22×D311yescharacteristic
207C2×C3×C8C22×D311yescharacteristic
208C2×C3×C8C22×D311yescharacteristic
209C3×C4⋊C4—61no—
210C3×C22⋊C4—61no—
211C3×C42—32no—
212#217—21no—
213C4⋊Dic3—21no—
214C4×Dic3C22×D312yes—
215#208—22no—
216#208D1212yes—
217#208D1212yes—
218#208C22×D314yes—
219C2×C3⋊C8—22no—
220C2×C3⋊C8C22×D312yes—
221Dic12—32no—
222Dic12—32no—
223Dic12—32no—
224Dic12—32no—
225Dic12—62no—
226Dic12—62no—
227D24—32no—
228D24—32no—
229D24—32no—
230D24—32no—
231D24—62no—
232D24—62no—
233#204—34no—
234#204—34no—
235#204—34no—
236#204—34no—
237#204—64no—
238#204—64no—
239ΓL(1,𝔽25)—68no—
240ΓL(1,𝔽25)—68no—
241D3×C8—68no—
242D3×C8—68no—
243C22×C32—41no—
244C22×C32C4×D411yescharacteristic
245C22×C32C4×D411yescharacteristic
246C22×C32C2×#4111yescharacteristic
247C2×C3⋊D3—24no—
248C2×C3⋊D3—82no—
249C32×C4C4×D411yescharacteristic
250C32×C4C4×D411yescharacteristic
251C32×C4C23×C411yescharacteristic
252C32×C4C22×D411yescharacteristic
253C3⋊Dic3—24no—
254C3×Dic3—42no—
255C2×#41—92no—
256#135—92no—
257#135—92no—
258#135—92no—
259#135—92no—
260C2×Q16—91no—
261C2×SD16—92no—
262C2×D8—91no—
263#131—98no—
264#131—184no—
265C2×M16—31no—
266C2×M16—32no—
267C2×M16—184no—
268C22×C8D3211yescharacteristic
269#117—31no—
270#108—32no—
271#108—32no—
272#104—98no—
273#97—32no—
274C4×C8—32no—
275C23×C3—21no—
276C23×C3#23511yescharacteristic
277C23×C3#23911yescharacteristic
278C22×D3—62no—
279C22×D3—62no—
280C22×D3—122no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—62no—
288C2×C3×C4C2×C4×D311yescharacteristic
289C2×C3×C4C2×C4×D311yescharacteristic
290C2×C3×C4C2×C4×D311yescharacteristic
291C2×C3×C4C2×C4×D311yescharacteristic
292C2×C3×C4C2×D1211yescharacteristic
293C2×C3×C4C2×D1211yescharacteristic
294C2×C3×C4#23511yescharacteristic
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4#23911yescharacteristic
298C2×C3×C4C23×D311yescharacteristic
299C2×C3×C4C23×D311yescharacteristic
300#67—64no—
301#67—64no—
302#67—64no—
303#67—64no—
304#67—124no—
305#67—124no—
306C2×Dic3—22no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C2×Dic3—122no—
310D12—34no—
311D12—34no—
312D12—64no—
313D12—62no—
314D12—62no—
315D12—122no—
316C4×D3—64no—
317C4×D3—64no—
318C4×D3—64no—
319C4×D3—64no—
320C4×D3—124no—
321C4×D3—124no—
322Dic6—34no—
323Dic6—34no—
324Dic6—64no—
325Dic6—62no—
326Dic6—62no—
327Dic6—122no—
328C3×C8—21no—
329C3×C8—21no—
330C3×C8—21no—
331C3×C8—21no—
332C3×C8—34no—
333C3×C8—64no—
334C3×C8C2×C4×D311yescharacteristic
335C3×C8C2×C4×D311yescharacteristic
336C3×C8C2×C4×D311yescharacteristic
337C3×C8C2×C4×D311yescharacteristic
338C3×C8C2×C4×D311yescharacteristic
339C3×C8C2×C4×D311yescharacteristic
340C3×C8C2×C4×D311yescharacteristic
341C3×C8C2×C4×D311yescharacteristic
342C3⋊C8—24no—
343C3⋊C8C2×D1214yes—
344C2×C32—21no—
345C2×C32—21no—
346C2×C32—21no—
347C2×C32C2×C4×D411yescharacteristic
348C3⋊D3—44no—
349#41—94no—
350#41—94no—
351#41—182no—
352#41—182no—
353C2×Q8—92no—
354C2×D4—92no—
355C2×D4—182no—
356C22×C4—182no—
357C22×C4C2×D3211yescharacteristic
358Q16—92no—
359Q16—92no—
360SD16—94no—
361SD16—94no—
362D8—92no—
363D8—92no—
364M16—32no—
365M16—32no—
366M16—34no—
367M16—62no—
368M16—188no—
369C2×C8—32no—
370C2×C8—62no—
371C2×C8—188no—
372C2×C8#62411yescharacteristic
373C2×C8#62411yescharacteristic
374C2×C8#62411yescharacteristic
375C2×C8#62411yescharacteristic
376C2×C8C2×D3211yescharacteristic
377C2×C8C2×D3211yescharacteristic
378C4⋊C4—61no—
379C22⋊C4—61no—
380C42—32no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—41no—
385C22×C3—41no—
386C22×C3—42no—
387C22×C3C4×D1211yescharacteristic
388C22×C3C4×D1211yescharacteristic
389C22×C3#89311yescharacteristic
390C22×C3#89311yescharacteristic
391C22×C3C2×#23511yescharacteristic
392C22×C3C2×#23911yescharacteristic
393C2×D3—64no—
394C2×D3—64no—
395C2×D3—124no—
396C2×D3—242no—
397C2×D3—242no—
398C2×D3—244no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—122no—
404C3×C4C4×D1211yescharacteristic
405C3×C4C4×D1211yescharacteristic
406C3×C4#89311yescharacteristic
407C3×C4#89311yescharacteristic
408C3×C4C22×C4×D311yescharacteristic
409C3×C4C22×C4×D311yescharacteristic
410C3×C4C22×D1211yescharacteristic
411C3×C4C2×D3×D411yescharacteristic
412Dic3—42no—
413Dic3—64no—
414Dic3—64no—
415Dic3—124no—
416C32#295711yescharacteristic, complemented, Sylow
417C23—182no—
418C23#379911yescharacteristic
419Q8—94no—
420Q8—182no—
421D4—94no—
422D4—184no—
423D4—184no—
424D4—182no—
425C2×C4—62no—
426C2×C4—182no—
427C2×C4—184no—
428C2×C4—184no—
429C2×C4#379911yescharacteristic
430C2×C4D3×D1211yescharacteristic
431C2×C4D3×D1211yescharacteristic
432C2×C4C2×#62411yescharacteristic
433C2×C4C2×#62411yescharacteristic
434C2×C4C22×D3211yescharacteristic
435C8—34no—
436C8—64no—
437C8C2×#62411yescharacteristic
438C8C2×#62411yescharacteristic
439C8C2×#62411yescharacteristic
440C8C2×#62411yescharacteristic
441C2×C3—22no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—41no—
450C2×C3—41no—
451C2×C3C2×C4×D1211yescharacteristic
452C2×C3C2×#89311yescharacteristic
453D3—124no—
454D3—124no—
455D3—244no—
456C22—41no—
457C22—184no—
458C22—722no—
459C22#6389411yescharacteristic
460C22#6389411yescharacteristic
461C22C2×#379911yescharacteristic
462C4—122no—
463C4—184no—
464C4#6389411yescharacteristic
465C4#6389411yescharacteristic
466C4C2×D3×D1211yescharacteristic
467C4C22×#62411yescharacteristic
468C3—21no—
469C3#7858011yescharacteristic, complemented
470C3#7924911yescharacteristic, complemented
471C2—21no—
472C2—21no—
473C2—21no—
474C2—364no—
475C2C2×#6389411yescharacteristic
subgroupG/H
centerC4C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC2×C32C2×C4×D4
prime radicalC2×#64113C2
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. #10594780C2semidirect
3. C2×C3×#819C2semidirect
4. C3×#5101C2semidirect
5. #10591113C2semidirect
6. #10590918C2semidirect
7. #10590917C2semidirect
12. C2×#3746C4semidirect
13. #64113C4semidirect
14. #64113C4semidirect
17. C2×#3745C4semidirect
18. C2×#3744C4semidirect
24. #63817C22semidirect
25. C3×#819C22semidirect
26. C3×#819C22semidirect
27. C3×#815C22semidirect
28. C3×C8×Dic3C22semidirect
29. #63570C22semidirect
38. C2×#819D3semidirect
39. #5101D3semidirect
122. #819C2×D3semidirect
123. #819C2×D3semidirect
124. #815C2×D3semidirect
125. C8×Dic3C2×D3semidirect
416. C32#2957semidirect
469. C3#78580semidirect
470. C3#79249semidirect

Maximal subgroups

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

subgroupindex
C2×#641132
#105947802
C2×C3×#8192
C3×#51012
#105911132
#105909182
#105909172
#792493
#785803