Finite Group Databasebeta

← #11859490

Subgroups — #11859490

Order 1152.

1063 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#907C211yesmaximal, characteristic, complemented
2#10595032C211yesmaximal, characteristic
3C2×#63814C211yesmaximal, characteristic, complemented
4#10592817C211yesmaximal, characteristic, complemented
5C3×#5129C211yesmaximal, characteristic, complemented
6#10591070C211yesmaximal, characteristic, complemented
7C2×#63553C211yesmaximal, characteristic, complemented
8#10590735C214yesmaximal, complemented
9#10590717C214yesmaximal, complemented
10#83786—31nomaximal
11#78657—31nomaximal
12C2×C3×#235C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C3×#907—24no—
20C2×C3×ΓL(1,𝔽25)C2212yes—
21C2×C3×D3×C8C2212yes—
22#63980C414yes—
23#63914C411yescharacteristic
24C4×#625C2214yes—
25#63873C411yescharacteristic
26#63863C411yescharacteristic
27#63863C411yescharacteristic
28C2×#3711C2212yes—
29#63814—24no—
30C2×D3×C3⋊C8C2212yes—
31#63641C2214yes—
32C3×(C2×D3)⋊C8C2214yes—
33(C2×D3)⋊(C3⋊C8)C2214yes—
34#63553C2212yes—
35#63553C2212yes—
36C2×C3×#131—31no—
37#5832—31no—
38#5832—31no—
39C2×#948—31no—
40C2×#907D311yescharacteristic, complemented
41C2×#901—31no—
42C3×#408—31no—
43#5234—31no—
44#5129D311yescharacteristic, complemented
45#5128—34no—
46#5118—31no—
47#5118—31no—
48#5118—61no—
49#5110—31no—
50C8×#67—34no—
51C2×C8×Dic3—31no—
52C2×C8×Dic3—31no—
53#4729—34no—
54#67⋊C8—34no—
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3C2×C412yes—
57C2×C3×#67C2×C412yes—
58C2×C3×#67C2×C412yes—
59C3×#235—22no—
60C3×#235—22no—
61C3×#235—22no—
62C3×#235—22no—
63C2×C3×D12C2×C411yescharacteristic
64C2×C3×D12C2×C411yescharacteristic
65C2×C3×C4×D3C2312yes—
66C2×C3×C4×D3C2312yes—
67C2×C3×Dic6C2×C411yescharacteristic
68C2×C3×Dic6C2×C411yescharacteristic
69C2×#625C2×C414yes—
70C32×M16—22no—
71C2×C32×C8C2312yes—
72C4×C3⋊Dic3C2×C411yescharacteristic
73C4×C3⋊Dic3C2×C411yescharacteristic
74C4×C3⋊Dic3C2312yes—
75#3748—22no—
76C2×C3⋊(C3⋊C8)C2312yes—
77C2×C3×C3⋊C8—22no—
78C2×C3×C3⋊C8D414yescomplemented
79C2×C3×C3⋊C8C2312yes—
80C2×C3×C3⋊C8C2311yescharacteristic
81C2×C3×C3⋊C8C2311yescharacteristic
82C3×ΓL(1,𝔽25)—24no—
83C3×D3×C8—24no—
84#3724C2×C414yes—
85(C2×D3)⋊Dic3C2×C414yes—
86(C2×D3)⋊Dic3C2×C414yes—
87#3711—24no—
88D3×C3⋊C8—24no—
89#2931—91noSylow
90C2×C3×#41—31no—
91C2×C3×#41—31no—
92C2×#235C2×D311yescharacteristic
93C2×#235C2×D311yescharacteristic
94C3×#131—64no—
95C2×C3×M16—21no—
96C2×C3×M16—32no—
97C2×C3×M16C2×D311yescharacteristic
98C2×C3×M16C2×D311yescharacteristic
99C22×C3×C8—31no—
100C22×C3×C8—31no—
101C22×C3×C8—32no—
102#948—64no—
103#947—31no—
104#947—31no—
105#944—31no—
106#944—31no—
107#940—31no—
108#940—31no—
109#939—34no—
110#939—34no—
111#936—31no—
112#936—31no—
113C4×#67—34no—
114C4×#67—34no—
115C2×C4×Dic3—31no—
116C2×C4×Dic3—31no—
117C2×C4×Dic3—61no—
118C2×#208—31no—
119C2×#208—31no—
120C2×#208—32no—
121C2×#208—61no—
122C22×C3⋊C8—32no—
123C22×C3⋊C8C2×D311yescharacteristic
124C22×C3⋊C8C2×D311yescharacteristic
125#907—24no—
126#901—64no—
127C2×ΓL(1,𝔽25)—32no—
128C2×ΓL(1,𝔽25)C2×D312yes—
129C2×D3×C8—32no—
130C2×D3×C8C2×D312yes—
131C3×C22⋊C8—34no—
132#830—34no—
133(C2×D3)⋊C8—34no—
134(C2×D3)⋊C8C2×D314yes—
135Dic3⋊C8—34no—
136Dic3⋊C8—34no—
137Dic3⋊C8—64no—
138C8×Dic3—32no—
139C8×Dic3—32no—
140C8×Dic3—32no—
141C8×Dic3—32no—
142C23×C32C22×C411yescharacteristic
143C22×C3×D3C22×C412yes—
144C22×C3×D3C22×C412yes—
145C2×C32×C4C22×C411yescharacteristic
146C2×C32×C4C2×D412yes—
147C2×C32×C4#4112yes—
148C2×C32×C4C2411yescharacteristic
149C2×C3⋊Dic3—24no—
150C2×C3⋊Dic3C22×C412yes—
151C2×C3⋊Dic3C22×C412yes—
152C3×#67—24no—
153C3×#67—24no—
154C2×C3×Dic3C22×C412yes—
155C2×C3×Dic3C22×C412yes—
156C3×D12—22no—
157C3×D12—22no—
158C3×C4×D3—22no—
159C3×C4×D3—22no—
160C3×C4×D3—22no—
161C3×C4×D3—22no—
162C3×Dic6—22no—
163C3×Dic6—22no—
164#625—28no—
165C32×C8—22no—
166C3⋊(C3⋊C8)—22no—
167C3×C3⋊C8—22no—
168C3×C3⋊C8C2×D412yes—
169C3×C3⋊C8C2×D412yes—
170C2×#131—31no—
171C2×#131—91no—
172#532—91no—
173#436—94no—
174C8×D4—94no—
175#423—91no—
176#408—31no—
177#408—91no—
178C2×C4×C8—91no—
179C3×#41—62no—
180C3×#41—62no—
181C3×#41—62no—
182C3×#41—62no—
183C2×C3×Q8—31no—
184C2×C3×Q8—31no—
185C2×C3×D4—32no—
186C2×C3×D4—32no—
187C2×C3×D4—31no—
188C2×C3×D4—31no—
189C22×C3×C4—21no—
190C22×C3×C4—32no—
191C22×C3×C4—32no—
192C22×C3×C4C22×D311yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C2×#67—34no—
195C2×#67—34no—
196C2×#67C4×D312yes—
197C2×#67C4×D312yes—
198C22×Dic3—32no—
199C22×Dic3—32no—
200C22×Dic3—62no—
201#235—22no—
202#235—22no—
203#235—22no—
204#235—22no—
205C2×D12C4×D311yescharacteristic
206C2×D12C4×D311yescharacteristic
207C2×C4×D3C22×D312yes—
208C2×C4×D3C22×D312yes—
209C2×Dic6C4×D311yescharacteristic
210C2×Dic6C4×D311yescharacteristic
211C3×M16—22no—
212C3×M16—22no—
213C3×M16—42no—
214C3×M16—64no—
215C2×C3×C8—22no—
216C2×C3×C8—34no—
217C2×C3×C8—31no—
218C2×C3×C8—31no—
219C2×C3×C8—32no—
220C2×C3×C8—64no—
221C2×C3×C8—62no—
222C2×C3×C8C22×D312yes—
223C2×C3×C8C22×D312yes—
224#217—34no—
225#217—34no—
226(C2×D3)⋊C4—34no—
227(C2×D3)⋊C4—34no—
228Dic3⋊C4—34no—
229Dic3⋊C4—34no—
230C4×Dic3—31no—
231C4×Dic3—31no—
232C4×Dic3—31no—
233C4×Dic3—31no—
234C4×Dic3—32no—
235C4×Dic3—32no—
236C4×Dic3—62no—
237C4×Dic3—61no—
238C4×Dic3—61no—
239#208—62no—
240#208—62no—
241#208—64no—
242#208—122no—
243C2×C3⋊C8—22no—
244C2×C3⋊C8—32no—
245C2×C3⋊C8—32no—
246C2×C3⋊C8—62no—
247C2×C3⋊C8—64no—
248C2×C3⋊C8#6714yescomplemented
249C2×C3⋊C8C22×D312yes—
250C2×C3⋊C8C22×D311yescharacteristic
251C2×C3⋊C8C22×D311yescharacteristic
252ΓL(1,𝔽25)—24no—
253ΓL(1,𝔽25)—64no—
254D3×C8—24no—
255D3×C8—64no—
256C22×C32—22no—
257C22×C32C4×D412yes—
258C22×C32C23×C411yescharacteristic
259C2×C3×D3—22no—
260C2×C3×D3—22no—
261C2×C3×D3—24no—
262C2×C3×D3—24no—
263C32×C4C4×D412yes—
264C32×C4C22×D411yescharacteristic
265C32×C4C2×#4111yescharacteristic
266C3⋊Dic3—22no—
267C3⋊Dic3#13114yescomplemented
268C3×Dic3—22no—
269C3×Dic3—22no—
270C2×#41—31no—
271C2×#41—31no—
272#131—64no—
273#131—184no—
274C2×M16—32no—
275C2×M16—92no—
276C2×M16—91no—
277C2×M16D3211yescharacteristic
278C22×C8—31no—
279C22×C8—31no—
280C22×C8—32no—
281C22×C8—92no—
282C4⋊Q8—91no—
283#127—91no—
284#124—91no—
285#124—91no—
286#121—94no—
287C4×D4—94no—
288C2×C42—91no—
289C4⋊C8—94no—
290C22⋊C8—34no—
291C22⋊C8—94no—
292C4×C8—92no—
293C4×C8—92no—
294C23×C3—21no—
295C23×C3—32no—
296C23×C3—32no—
297C23×C3C2×C4×D311yescharacteristic
298C23×C3C2×C4×D311yescharacteristic
299C22×D3C2×C4×D312yes—
300C22×D3C2×C4×D312yes—
301C3×Q8—62no—
302C3×Q8—62no—
303C3×D4—64no—
304C3×D4—64no—
305C3×D4—62no—
306C3×D4—62no—
307C2×C3×C4—21no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—22no—
311C2×C3×C4—32no—
312C2×C3×C4—32no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4C2×C4×D311yescharacteristic
318C2×C3×C4C2×C4×D311yescharacteristic
319C2×C3×C4#23512yes—
320C2×C3×C4D3×D412yes—
321C2×C3×C4#23712yes—
322C2×C3×C4C2×#6712yes—
323C2×C3×C4C23×D311yescharacteristic
324C2×C3×C4C23×D311yescharacteristic
325#67—24no—
326#67—24no—
327#67—68no—
328#67—68no—
329C2×Dic3—32no—
330C2×Dic3—32no—
331C2×Dic3—32no—
332C2×Dic3—32no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—64no—
336C2×Dic3—64no—
337C2×Dic3—124no—
338C2×Dic3C2×C4×D312yes—
339C2×Dic3C2×C4×D312yes—
340D12—22no—
341D12—22no—
342C4×D3—22no—
343C4×D3—22no—
344C4×D3—22no—
345C4×D3—22no—
346Dic6—22no—
347Dic6—22no—
348C3×C8—22no—
349C3×C8—22no—
350C3×C8—32no—
351C3×C8—32no—
352C3×C8—42no—
353C3×C8—62no—
354C3⋊C8—22no—
355C3⋊C8—62no—
356C3⋊C8—62no—
357C3⋊C8—122no—
358C3⋊C8C2×#6712yes—
359C3⋊C8C2×#6712yes—
360C2×C32—22no—
361C2×C32C2×C4×D411yescharacteristic
362C2×C32C2×#13112yes—
363C3×D3—42no—
364C3×D3—42no—
365#41—62no—
366#41—62no—
367#41—62no—
368#41—62no—
369C2×Q8—31no—
370C2×Q8—31no—
371C2×D4—32no—
372C2×D4—32no—
373C2×D4—31no—
374C2×D4—31no—
375C2×D4—94no—
376C22×C4—32no—
377C22×C4—32no—
378C22×C4—92no—
379C22×C4C2×D3211yescharacteristic
380M16—22no—
381M16—64no—
382M16—184no—
383M16—182no—
384C2×C8—31no—
385C2×C8—31no—
386C2×C8—34no—
387C2×C8—32no—
388C2×C8—64no—
389C2×C8—62no—
390C2×C8—92no—
391C2×C8—184no—
392C2×C8C2×D3212yes—
393C4⋊C4—94no—
394C22⋊C4—94no—
395C22⋊C4—94no—
396C42—92no—
397C42—91no—
398C42—91no—
399C22×C3—22no—
400C22×C3—22no—
401C22×C3—21no—
402C22×C3—22no—
403C22×C3—42no—
404C22×C3—62no—
405C22×C3—64no—
406C22×C3—64no—
407C22×C3—62no—
408C22×C3#67⋊C412yes—
409C22×C3C4×#6712yes—
410C22×C3C22×C4×D311yescharacteristic
411C22×C3C22×C4×D311yescharacteristic
412C2×D3—22no—
413C2×D3—24no—
414C2×D3—24no—
415C2×D3—22no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—22no—
419C3×C4—62no—
420C3×C4—62no—
421C3×C4#67⋊C412yes—
422C3×C4C4×#6712yes—
423C3×C4C2×#23511yescharacteristic
424C3×C4C2×D3×D411yescharacteristic
425C3×C4C2×#23711yescharacteristic
426C3×C4C22×#6711yescharacteristic
427Dic3—22no—
428Dic3—22no—
429Dic3—34no—
430Dic3—34no—
431Dic3—64no—
432Dic3—62no—
433Dic3—62no—
434Dic3—122no—
435C32#293111yescharacteristic, complemented, Sylow
436C23—32no—
437C23—32no—
438C23C4×D3211yescharacteristic
439Q8—62no—
440Q8—62no—
441D4—64no—
442D4—64no—
443D4—62no—
444D4—62no—
445D4—188no—
446C2×C4—32no—
447C2×C4—32no—
448C2×C4—62no—
449C2×C4—62no—
450C2×C4—62no—
451C2×C4—62no—
452C2×C4—92no—
453C2×C4—92no—
454C2×C4—184no—
455C2×C4#379512yes—
456C2×C4C4×D3211yescharacteristic
457C2×C4D3×#6712yes—
458C2×C4C22×D3211yescharacteristic
459C8—22no—
460C8—32no—
461C8—32no—
462C8—62no—
463C8—182no—
464C2×C3—22no—
465C2×C3—22no—
466C2×C3—21no—
467C2×C3—22no—
468C2×C3—42no—
469C2×C3—122no—
470C2×C3—122no—
471C2×C3C2×#67⋊C411yescharacteristic
472C2×C3D3×#13112yes—
473C2×C3D3×#13112yes—
474C2×C3C2×C4×#6711yescharacteristic
475D3—42no—
476D3—42no—
477C22—22no—
478C22—62no—
479C22—62no—
480C22—64no—
481C22—64no—
482C22#6387912yes—
483C22C2×C4×D3211yescharacteristic
484C4—62no—
485C4—62no—
486C4—94no—
487C4—182no—
488C4#6387912yes—
489C4C2×#379511yescharacteristic
490C4C2×D3×#6711yescharacteristic
491C3—21no—
492C3#7865711yescharacteristic, complemented
493C3#8378611yescharacteristic, complemented
494C2—22no—
495C2—122no—
496C2—122no—
497C2#1059470712yes—
498C2C2×#6387911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC2×C32×M16C22
prime radical#10595032C2
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2931
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#907C2semidirect
3. C2×#63814C2semidirect
4. #10592817C2semidirect
5. C3×#5129C2semidirect
6. #10591070C2semidirect
7. C2×#63553C2semidirect
8. #10590735C2semidirect
9. #10590717C2semidirect
40. C2×#907D3semidirect
44. #5129D3semidirect
78. C2×C3×C3⋊C8D4semidirect
248. C2×C3⋊C8#67semidirect
267. C3⋊Dic3#131semidirect
435. C32#2931semidirect
492. C3#78657semidirect
493. C3#83786semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9072
#105950322
C2×#638142
#105928172
C3×#51292
#105910702
C2×#635532
#105907352
#105907172
#837863
#786573