Finite Group Databasebeta

← #11788893

Subgroups — #11788893

Order 1152.

725 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5525C211yesmaximal, characteristic
2#10594776C211yesmaximal, characteristic, complemented
3#10591076C211yesmaximal, characteristic, complemented
4C2×#63558C211yesmaximal, characteristic, complemented
5C2×#63558C211yesmaximal, characteristic, complemented
6#10589399C211yesmaximal, characteristic, complemented
7C3×#4533C211yesmaximal, characteristic, complemented
8#71855—31nomaximal
9#69040—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C32×#117C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#895—22no—
18C3×#882C414yes—
19C3×#875—21no—
20C3×#874—21no—
21#63815—22no—
22#63814—22no—
23D3×#208—22no—
24#63560—21no—
25#63558—21no—
26#63558—22no—
27#63558—22no—
28C3×#535—31no—
29#5819—31no—
30#5745—31no—
31#5525D311yescharacteristic
32#5237—31no—
33C2×#833—31no—
34C2×#833—31no—
35#5132—31no—
36C2×#823—31no—
37C2×#823—31no—
38C3×#344—31no—
39#4533—31no—
40#4533—31no—
41#4533—61no—
42#4533D311yescharacteristic, complemented
43C23×C3×D3C2×C412yes—
44C22×C32×C4C2311yescharacteristic
45C2×C3×#67C2×C412yes—
46C3×#235—21no—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—24no—
57C2×C3×D12D411yescharacteristic
58C2×C3×C4×D3D412yes—
59C2×C3×Dic6D411yescharacteristic
60C32×C4⋊C4—21no—
61C32×C22⋊C4C2×C412yes—
62C32×C42—21no—
63#3748—21no—
64#3748—21no—
65#3748—21no—
66#3748D412yescomplemented
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C3×(C2×D3)⋊C4—24no—
70C3×#208—21no—
71C3×#208—21no—
72C3×#208—21no—
73C3×#208D412yescomplemented
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76#3711—24no—
77D3×C3⋊C8—24no—
78#1914—91noSylow
79C2×C3×#41—31no—
80C22×C3×D4—31no—
81C2×#235C2×D311yescharacteristic
82C22×D12C2×D311yescharacteristic
83C2×C3×M16—31no—
84C2×C3×M16—31no—
85C3×#127—61no—
86C3×#124—61no—
87C3×#121—62no—
88C3×#120—34no—
89C3×#117—21no—
90C3×#117C2×D311yescharacteristic
91C3×#117C2×D311yescharacteristic
92#948—62no—
93#948—62no—
94C2×#208—31no—
95C2×#208—31no—
96C2×#208—31no—
97C2×#208—31no—
98C2×#208—61no—
99C2×#208—61no—
100C2×#208—62no—
101C2×#208C2×D311yescharacteristic
102C2×#208C2×D311yescharacteristic
103#907—62no—
104D3×M16—62no—
105#901—62no—
106#895—22no—
107#882Dic314yes—
108#875—21no—
109#874—21no—
110#836—61no—
111#833—62no—
112#833—61no—
113#833—62no—
114#824—61no—
115#823—62no—
116#823—62no—
117#823—61no—
118C23×C32C22×C411yescharacteristic
119C22×C3×D3—22no—
120C22×C3×D3—22no—
121C22×C3×D3—22no—
122C22×C3×D3—82no—
123C22×C3×D3C22⋊C412yes—
124C2×C32×C4—22no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C3×#67—22no—
132C3×#67—22no—
133C2×C3×Dic3C22⋊C412yes—
134C3×D12—21no—
135C3×D12—21no—
136C3×D12—41no—
137C3×D12—41no—
138C3×D12—41no—
139C3×D12—41no—
140C3×D12—84no—
141C3×C4×D3—22no—
142C3×C4×D3—22no—
143C3×Dic6—21no—
144C3×Dic6—21no—
145C3⋊(C3⋊C8)—22no—
146C3⋊(C3⋊C8)—41no—
147C3×C3⋊C8—22no—
148C3×C3⋊C8—41no—
149#568—91no—
150#535—31no—
151#413—91no—
152C2×#100—91no—
153C2×#100—91no—
154#344—31no—
155#344—91no—
156C24×C3—32no—
157C23×D3C2×Dic312yes—
158C3×#41—61no—
159C3×#41—61no—
160C3×#41—61no—
161C3×#41—61no—
162C2×C3×Q8—31no—
163C2×C3×D4—32no—
164C2×C3×D4—31no—
165C2×C3×D4—64no—
166C2×C3×D4—61no—
167C2×C3×D4—61no—
168C2×C3×D4—61no—
169C2×C3×D4—61no—
170C2×C3×D4—61no—
171C2×C3×D4—61no—
172C22×C3×C4—21no—
173C22×C3×C4—32no—
174C22×C3×C4C22×D311yescharacteristic
175C22×C3×C4C22×D311yescharacteristic
176C2×#67C2×Dic312yes—
177#235—21no—
178#235—21no—
179#235—21no—
180#235—21no—
181C2×D12—21no—
182C2×D12—21no—
183C2×D12—21no—
184C2×D12—21no—
185C2×D12—21no—
186C2×D12—21no—
187C2×D12—24no—
188C2×D12#6711yescharacteristic
189C2×C4×D3#6712yes—
190C2×Dic6#6711yescharacteristic
191C3×M16—32no—
192C3×M16—61no—
193C3×M16—61no—
194C3×M16—61no—
195C2×C3×C8—61no—
196C2×C3×C8—61no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—41no—
200C3×C22⋊C4—22no—
201C3×C22⋊C4—64no—
202C3×C22⋊C4C4×D312yes—
203C3×C22⋊C4C2×Dic312yes—
204C3×C42—21no—
205C3×C42—21no—
206C3×C42—41no—
207(C2×D3)⋊C4—24no—
208#208—21no—
209#208—21no—
210#208—21no—
211#208—32no—
212#208—32no—
213#208—62no—
214#208—64no—
215#208—61no—
216#208—61no—
217#208—61no—
218#208—61no—
219#208—61no—
220#208—61no—
221#208—121no—
222#208—121no—
223#208—121no—
224#208D1212yescomplemented
225C2×C3⋊C8—21no—
226C2×C3⋊C8—21no—
227C2×C3⋊C8—64no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—61no—
230C2×C3⋊C8—62no—
231C2×C3⋊C8—61no—
232C2×C3⋊C8—61no—
233C2×C3⋊C8—121no—
234ΓL(1,𝔽25)—64no—
235D3×C8—64no—
236C22×C32—41no—
237C22×C32C2×C22⋊C411yescharacteristic
238C22×C32C4×D411yescharacteristic
239C22×C32C4×D411yescharacteristic
240C2×C3×D3—22no—
241C2×C3×D3—42no—
242C2×C3×D3—44no—
243C2×C3×D3—42no—
244C2×C3×D3—82no—
245C2×C3×D3—82no—
246C32×C4—42no—
247C32×C4#12011yescharacteristic
248C32×C4#12111yescharacteristic
249C32×C4#12111yescharacteristic
250C32×C4#12311yescharacteristic
251C3×Dic3—22no—
252C2×#41—31no—
253C22×D4—31no—
254#131—182no—
255#131—182no—
256C2×M16—31no—
257C2×M16—31no—
258C2×M16—91no—
259C2×M16—91no—
260C2×M16—182no—
261#127—61no—
262#124—61no—
263#121—62no—
264#120—34no—
265#117D3211yescharacteristic
266#101—181no—
267#100—182no—
268#100—182no—
269#100—181no—
270C23×C3—21no—
271C23×C3—32no—
272C23×C3—62no—
273C23×C3—62no—
274C23×C3—62no—
275C23×C3—242no—
276C23×C3C2×C4×D311yescharacteristic
277C23×C3C22×Dic311yescharacteristic
278C22×D3—22no—
279C22×D3—22no—
280C22×D3—22no—
281C22×D3—82no—
282C22×D3#21712yes—
283C3×Q8—61no—
284C3×Q8—61no—
285C3×D4—62no—
286C3×D4—62no—
287C3×D4—61no—
288C3×D4—61no—
289C3×D4—121no—
290C3×D4—121no—
291C3×D4—121no—
292C3×D4—121no—
293C3×D4—244no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—32no—
303C2×C3×C4—42no—
304C2×C3×C4—62no—
305C2×C3×C4—62no—
306C2×C3×C4C2×D1211yescharacteristic
307C2×C3×C4#23511yescharacteristic
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4D3×D411yescharacteristic
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4#23711yescharacteristic
314C2×C3×C4#23711yescharacteristic
315C2×C3×C4#23911yescharacteristic
316C2×C3×C4C2×#6711yescharacteristic
317C2×C3×C4C2×#6711yescharacteristic
318#67—22no—
319#67—22no—
320C2×Dic3#21712yes—
321D12—21no—
322D12—21no—
323D12—41no—
324D12—41no—
325D12—41no—
326D12—41no—
327D12—84no—
328C4×D3—22no—
329C4×D3—22no—
330Dic6—21no—
331Dic6—21no—
332C3×C8—62no—
333C3×C8—121no—
334C3⋊C8—22no—
335C3⋊C8—41no—
336C3⋊C8—62no—
337C3⋊C8—62no—
338C3⋊C8—122no—
339C3⋊C8—122no—
340C3⋊C8—121no—
341C3⋊C8—121no—
342C2×C32—21no—
343C2×C32—21no—
344C2×C32—21no—
345C2×C32#38611yescharacteristic
346C3×D3—42no—
347C3×D3—82no—
348C24—32no—
349#41—61no—
350#41—61no—
351#41—61no—
352#41—61no—
353C2×Q8—31no—
354C2×D4—32no—
355C2×D4—31no—
356C2×D4—64no—
357C2×D4—61no—
358C2×D4—61no—
359C2×D4—61no—
360C2×D4—61no—
361C2×D4—61no—
362C2×D4—61no—
363C22×C4—32no—
364C22×C4C2×D3211yescharacteristic
365M16—32no—
366M16—61no—
367M16—61no—
368M16—61no—
369M16—92no—
370M16—184no—
371M16—181no—
372M16—181no—
373M16—181no—
374C2×C8—61no—
375C2×C8—61no—
376C2×C8—184no—
377C2×C8—181no—
378C2×C8—181no—
379C4⋊C4—21no—
380C22⋊C4—64no—
381C22⋊C4D3×Dic312yes—
382C42—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—41no—
387C22×C3—41no—
388C22×C3—62no—
389C22×C3—81no—
390C22×C3—122no—
391C22×C3—124no—
392C22×C3—122no—
393C22×C3—242no—
394C22×C3—242no—
395C22×C3C4×D1211yescharacteristic
396C22×C3D3×C22⋊C411yescharacteristic
397C22×C3#89311yescharacteristic
398C22×C3D4×Dic311yescharacteristic
399C22×C3D4×Dic311yescharacteristic
400C22×C3C2×#21711yescharacteristic
401C2×D3—22no—
402C2×D3—42no—
403C2×D3—44no—
404C2×D3—42no—
405C2×D3—82no—
406C2×D3—82no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—42no—
412C3×C4—42no—
413C3×C4—62no—
414C3×C4—82no—
415C3×C4#88211yescharacteristic
416C3×C4#88411yescharacteristic
417C3×C4#89411yescharacteristic
418C3×C4#89511yescharacteristic
419C3×C4#93511yescharacteristic
420C3×C4#93711yescharacteristic
421C3×C4#93911yescharacteristic
422C3×C4#93911yescharacteristic
423Dic3—22no—
424C32#191411yescharacteristic, complemented, Sylow
425C23—32no—
426C23—62no—
427C23—62no—
428C23—62no—
429C23—242no—
430C23C2×D3×Dic311yescharacteristic
431Q8—61no—
432Q8—61no—
433D4—62no—
434D4—62no—
435D4—61no—
436D4—61no—
437D4—121no—
438D4—121no—
439D4—121no—
440D4—121no—
441D4—244no—
442C2×C4—22no—
443C2×C4—32no—
444C2×C4—62no—
445C2×C4—62no—
446C2×C4#379511yescharacteristic
447C2×C4#379611yescharacteristic
448C2×C4D3×D1211yescharacteristic
449C2×C4#380211yescharacteristic
450C2×C4D3×#6711yescharacteristic
451C2×C4D3×#6711yescharacteristic
452C8—62no—
453C8—121no—
454C8—182no—
455C8—361no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—41no—
464C2×C3—41no—
465C2×C3—41no—
466C2×C3—122no—
467C2×C3—242no—
468C2×C3#466511yescharacteristic
469C2×C3#522011yescharacteristic
470D3—42no—
471D3—82no—
472C22—41no—
473C22—62no—
474C22—122no—
475C22—124no—
476C22—122no—
477C22—242no—
478C22—242no—
479C22Dic3×D1211yescharacteristic
480C22#6389811yescharacteristic
481C22D3×#21711yescharacteristic
482C4—42no—
483C4—62no—
484C4#6388411yescharacteristic
485C4#6388511yescharacteristic
486C4#6388611yescharacteristic
487C4#6392211yescharacteristic
488C3—21no—
489C3#6904011yescharacteristic, complemented
490C3#7185511yescharacteristic, complemented
491C2—21no—
492C2—21no—
493C2—21no—
494C2—122no—
495C2—242no—
496C2#1059137611yescharacteristic
subgroupG/H
centerC2#10591376
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#386
prime radicalC3×#5525C2
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1914
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10594776C2semidirect
3. #10591076C2semidirect
4. C2×#63558C2semidirect
5. C2×#63558C2semidirect
6. #10589399C2semidirect
7. C3×#4533C2semidirect
42. #4533D3semidirect
66. #3748D4semidirect
73. C3×#208D4semidirect
224. #208D12semidirect
424. C32#1914semidirect
489. C3#69040semidirect
490. C3#71855semidirect

Maximal subgroups

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

subgroupindex
C3×#55252
#105947762
#105910762
C2×#635582
#105893992
C3×#45332
#718553
#690403