Finite Group Databasebeta

← #11788887

Subgroups — #11788887

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×#5745C211yesmaximal, characteristic, complemented
2#10595040C211yesmaximal, characteristic
3C2×C3×#823C211yesmaximal, characteristic, complemented
4#10591076C211yesmaximal, characteristic, complemented
5C2×#63558C211yesmaximal, characteristic, complemented
6#10589425C211yesmaximal, characteristic, complemented
7#10589171C211yesmaximal, characteristic, complemented
8#72030—31nomaximal
9#70089—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13#64135C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#907—22no—
18C3×D3×M16—22no—
19C3×#901—22no—
20#63976C414yes—
21#63914—21no—
22#63908—22no—
23#63863—21no—
24C3×#823—22no—
25#63560—21no—
26#63558—21no—
27#63558—22no—
28C3×#568—31no—
29#5830—31no—
30#5805—31no—
31#5745D311yescharacteristic, complemented
32C2×C3×#100—31no—
33#5237—31no—
34C2×#833—31no—
35#5132—31no—
36C2×#823—31no—
37C2×#823D311yescharacteristic, complemented
38#4559—31no—
39#4559—31no—
40#4559—31no—
41#4559—61no—
42#4556—31no—
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×D12D411yescharacteristic
57C2×C3×C4×D3D412yes—
58C2×C3×Dic6D411yescharacteristic
59C2×#625—24no—
60C32×M16—21no—
61C32×M16D412yescomplemented
62C2×C32×C8—21no—
63#3757C2×C412yes—
64C4⋊(C3⋊Dic3)—21no—
65C4×C3⋊Dic3—21no—
66#3748—21no—
67#3748—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208—21no—
72C3×#208D412yescomplemented
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C3×ΓL(1,𝔽25)—24no—
76C3×D3×C8—24no—
77(C2×D3)⋊Dic3—24no—
78#1914—91noSylow
79C2×C3×#41—31no—
80C22×C3×D4—31no—
81C2×#235C2×D311yescharacteristic
82C22×D12C2×D311yescharacteristic
83C3×#131—62no—
84C3×#131—62no—
85C2×C3×M16—21no—
86C2×C3×M16—31no—
87C2×C3×M16—31no—
88C2×C3×M16—62no—
89C2×C3×M16C2×D311yescharacteristic
90C2×C3×M16C2×D311yescharacteristic
91#953—34no—
92#947—61no—
93#940—61no—
94#940—61no—
95#938—62no—
96#937—34no—
97#936—61no—
98#930—62no—
99#926—31no—
100#926—31no—
101#926—61no—
102C2×#208—31no—
103C2×#208—31no—
104C2×#208—61no—
105C2×#208C2×D311yescharacteristic
106C2×#208C2×D311yescharacteristic
107#907—22no—
108D3×M16—22no—
109#901—22no—
110C3×#100—62no—
111#836—61no—
112#833—61no—
113#833—62no—
114#824—61no—
115#823—22no—
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×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C3⋊Dic3—22no—
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×C4×D3—22no—
141C3×C4×D3—22no—
142C3×Dic6—21no—
143C3×Dic6—21no—
144#625—84no—
145C32×C8—22no—
146C3⋊(C3⋊C8)—41no—
147C3×C3⋊C8—22no—
148C3×C3⋊C8—41no—
149#568—31no—
150#535—91no—
151#413—91no—
152C2×#100—31no—
153C2×#100—91no—
154#344—91no—
155#344—91no—
156C24×C3—32no—
157C23×D3C4×D312yes—
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—61no—
166C2×C3×D4—61no—
167C2×C3×D4—61no—
168C2×C3×D4—61no—
169C2×C3×D4—61no—
170C2×C3×D4—61no—
171C22×C3×C4—21no—
172C22×C3×C4—32no—
173C22×C3×C4C22×D311yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C2×#67—64no—
176C2×#67—64no—
177C2×#67C4×D312yes—
178#235—21no—
179#235—21no—
180#235—21no—
181#235—21no—
182C2×D12—21no—
183C2×D12—21no—
184C2×D12—21no—
185C2×D12—21no—
186C2×D12—21no—
187C2×D12—21no—
188C2×D12D1211yescharacteristic
189C2×C4×D3#6712yes—
190C2×Dic6D1211yescharacteristic
191C3×M16—21no—
192C3×M16—21no—
193C3×M16—22no—
194C3×M16—32no—
195C3×M16—41no—
196C3×M16—64no—
197C3×M16—61no—
198C3×M16—61no—
199C3×M16—61no—
200C3×M16#6712yescomplemented
201C3×M16#6712yescomplemented
202C2×C3×C8—21no—
203C2×C3×C8—21no—
204C2×C3×C8—41no—
205C2×C3×C8—64no—
206C2×C3×C8—61no—
207C2×C3×C8—61no—
208#217—32no—
209#217—32no—
210#217—62no—
211#217—64no—
212(C2×D3)⋊C4—64no—
213C4⋊Dic3—61no—
214C4⋊Dic3—61no—
215C4⋊Dic3—121no—
216C4×Dic3—61no—
217C4×Dic3—61no—
218C4×Dic3—121no—
219#208—21no—
220#208—21no—
221#208—21no—
222#208—61no—
223#208—61no—
224#208—61no—
225#208—61no—
226#208—121no—
227#208—121no—
228#208#6712yescomplemented
229C2×C3⋊C8—21no—
230C2×C3⋊C8—21no—
231C2×C3⋊C8—62no—
232C2×C3⋊C8—61no—
233C2×C3⋊C8—61no—
234ΓL(1,𝔽25)—24no—
235D3×C8—24no—
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#12011yescharacteristic
247C32×C4#12111yescharacteristic
248C32×C4#12111yescharacteristic
249C32×C4#12311yescharacteristic
250C3⋊Dic3—42no—
251C3×Dic3—22no—
252C2×#41—31no—
253C22×D4—31no—
254#131—62no—
255#131—62no—
256C2×M16—31no—
257C2×M16—31no—
258C2×M16—62no—
259C2×M16—91no—
260C2×M16D3211yescharacteristic
261#127—181no—
262#124—181no—
263#121—182no—
264#120—94no—
265#117—91no—
266#101—181no—
267#100—62no—
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×C3C2×C4×D311yescharacteristic
278C22×D3—22no—
279C22×D3—22no—
280C22×D3—22no—
281C22×D3—82no—
282C22×D3(C2×D3)⋊C412yes—
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—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—32no—
300C2×C3×C4—62no—
301C2×C3×C4—62no—
302C2×C3×C4C2×D1211yescharacteristic
303C2×C3×C4#23511yescharacteristic
304C2×C3×C4#23511yescharacteristic
305C2×C3×C4#23511yescharacteristic
306C2×C3×C4D3×D411yescharacteristic
307C2×C3×C4D3×D411yescharacteristic
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4#23711yescharacteristic
310C2×C3×C4C2×#6711yescharacteristic
311C2×C3×C4C2×#6711yescharacteristic
312C2×C3×C4C2×#6711yescharacteristic
313C2×C3×C4C2×#6711yescharacteristic
314#67—22no—
315#67—22no—
316#67—244no—
317#67—244no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—122no—
321C2×Dic3(C2×D3)⋊C412yes—
322D12—21no—
323D12—21no—
324D12—41no—
325D12—41no—
326D12—41no—
327D12—41no—
328C4×D3—22no—
329C4×D3—22no—
330Dic6—21no—
331Dic6—21no—
332C3×C8—22no—
333C3×C8—22no—
334C3×C8—42no—
335C3×C8—62no—
336C3×C8—121no—
337C3⋊C8—22no—
338C3⋊C8—41no—
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—61no—
357C2×D4—61no—
358C2×D4—61no—
359C2×D4—61no—
360C2×D4—61no—
361C2×D4—61no—
362C2×D4—184no—
363C22×C4—32no—
364C22×C4C2×D3211yescharacteristic
365M16—21no—
366M16—32no—
367M16—64no—
368M16—61no—
369M16—61no—
370M16—61no—
371M16—181no—
372M16—181no—
373M16#62512yescomplemented
374C2×C8—21no—
375C2×C8—64no—
376C2×C8—61no—
377C2×C8—61no—
378C2×C8—181no—
379C4⋊C4—181no—
380C22⋊C4—92no—
381C22⋊C4—184no—
382C42—181no—
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×C3D3×C22⋊C411yescharacteristic
396C22×C3#67⋊C411yescharacteristic
397C22×C3C2×(C2×D3)⋊C411yescharacteristic
398C22×C3C4×#6711yescharacteristic
399C22×C3C4×#6711yescharacteristic
400C22×C3C4×#6711yescharacteristic
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—62no—
412C3×C4#88311yescharacteristic
413C3×C4#88411yescharacteristic
414C3×C4#92911yescharacteristic
415C3×C4#93011yescharacteristic
416C3×C4#93011yescharacteristic
417C3×C4#93711yescharacteristic
418C3×C4#93811yescharacteristic
419C3×C4#95311yescharacteristic
420Dic3—22no—
421Dic3—122no—
422Dic3—122no—
423Dic3—242no—
424C32#191411yescharacteristic, complemented, Sylow
425C23—32no—
426C23—62no—
427C23—62no—
428C23—62no—
429C23—242no—
430C23C4×D3211yescharacteristic
431Q8—61no—
432Q8—61no—
433D4—62no—
434D4—62no—
435D4—61no—
436D4—61no—
437D4—121no—
438D4—121no—
439D4—121no—
440D4—121no—
441D4—724no—
442C2×C4—32no—
443C2×C4—62no—
444C2×C4—62no—
445C2×C4—182no—
446C2×C4#379511yescharacteristic
447C2×C4#379811yescharacteristic
448C2×C4D3×D1211yescharacteristic
449C2×C4C2×#62511yescharacteristic
450C2×C4D3×#6711yescharacteristic
451C2×C4D3×#6711yescharacteristic
452C8—22no—
453C8—62no—
454C8—121no—
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#495611yescharacteristic
469C2×C3#521311yescharacteristic
470D3—42no—
471D3—82no—
472C22—41no—
473C22—62no—
474C22—122no—
475C22—124no—
476C22—122no—
477C22—242no—
478C22—242no—
479C22#6387911yescharacteristic
480C22C4×#62511yescharacteristic
481C22D3×(C2×D3)⋊C411yescharacteristic
482C4—62no—
483C4—362no—
484C4#6390511yescharacteristic
485C4#6390611yescharacteristic
486C4#6390811yescharacteristic
487C4#6397611yescharacteristic
488C3—21no—
489C3#7008911yescharacteristic, complemented
490C3#7203011yescharacteristic, complemented
491C2—21no—
492C2—21no—
493C2—21no—
494C2—122no—
495C2—242no—
496C2#1059138111yescharacteristic
subgroupG/H
centerC2#10591381
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#386
prime radical#10595040C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1914
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C3×#5745C2semidirect
3. C2×C3×#823C2semidirect
4. #10591076C2semidirect
5. C2×#63558C2semidirect
6. #10589425C2semidirect
7. #10589171C2semidirect
31. #5745D3semidirect
37. C2×#823D3semidirect
61. C32×M16D4semidirect
72. C3×#208D4semidirect
200. C3×M16#67semidirect
201. C3×M16#67semidirect
228. #208#67semidirect
373. M16#625semidirect
424. C32#1914semidirect
489. C3#70089semidirect
490. C3#72030semidirect

Maximal subgroups

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

subgroupindex
C3×#57452
#105950402
C2×C3×#8232
#105910762
C2×#635582
#105894252
#105891712
#720303
#700893