Finite Group Databasebeta

← #11783848

Subgroups — #11783848

Order 1152.

613 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63814C211yesmaximal, characteristic
2C3×#5132C211yesmaximal, characteristic
3C3×#5122C211yesmaximal, characteristic, complemented
4#10591231C211yesmaximal, characteristic
5#10591059C211yesmaximal, characteristic, complemented
6#10589425C211yesmaximal, characteristic, complemented
7#10589170C211yesmaximal, characteristic, complemented
8#70133—31nomaximal
9#69898—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3711C412yescomplemented
18#63814—21no—
19#63814—21no—
20#63814—21no—
21#63814—21no—
22C2×D3×C3⋊C8C412yescomplemented
23C3×#824C412yescomplemented
24C3×#823C412yescomplemented
25C3×#815—21no—
26C3×C8×Dic3—21no—
27#63580C414yes—
28#63555—21no—
29#63553—21no—
30C2×#948—31no—
31C2×#901—31no—
32C3×#413—31no—
33C3×#405—31no—
34#5240—31no—
35#5132D311yescharacteristic
36#5122—31no—
37#5122D311yescharacteristic, complemented
38#5101—31no—
39#5006—31no—
40#4559—31no—
41#4559—31no—
42#4559—31no—
43#4559—61no—
44#4533—31no—
45C22×C32×C4C2311yescharacteristic
46C2×C3×#67C2×C412yes—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235—21no—
50C3×#235—21no—
51C2×C3×D12C2×C411yescharacteristic
52C2×C3×C4×D3C2×C412yes—
53C2×C3×Dic6C2×C411yescharacteristic
54C32×M16—21no—
55C32×M16C2×C412yes—
56C2×C32×C8—21no—
57#3757C2×C412yes—
58C4⋊(C3⋊Dic3)—21no—
59C4×C3⋊Dic3—21no—
60#3748—21no—
61#3748—21no—
62C2×C3⋊(C3⋊C8)C2×C412yes—
63C3×#217C2×C412yes—
64C3×C4⋊Dic3—21no—
65C3×C4×Dic3—21no—
66C3×#208—21no—
67C3×#208C2×C412yes—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8C2×C411yescharacteristic
70C2×C3×C3⋊C8C2×C411yescharacteristic
71C2×C3×C3⋊C8D411yescharacteristic
72C2×C3×C3⋊C8D411yescharacteristic
73C2×C3×C3⋊C8D411yescharacteristic
74C2×C3×C3⋊C8D411yescharacteristic
75#3711—22no—
76#3711—22no—
77D3×C3⋊C8—22no—
78D3×C3⋊C8—22no—
79#1757—91noSylow
80C2×C3×#41—31no—
81C2×#235C2×D311yescharacteristic
82C2×C3×M16—21no—
83C2×C3×M16—31no—
84C2×C3×M16C2×D311yescharacteristic
85C2×C3×M16C2×D311yescharacteristic
86C22×C3×C8—31no—
87C3×#117—31no—
88#948—61no—
89#948—61no—
90#948—61no—
91#948—61no—
92#926—31no—
93#926—31no—
94#926—61no—
95#926C2×D311yescharacteristic
96C2×#208—31no—
97C2×#208—31no—
98C2×#208—32no—
99C2×#208—61no—
100C2×#208C2×D311yescharacteristic
101C22×C3⋊C8—32no—
102C22×C3⋊C8C2×D311yescharacteristic
103#901—61no—
104#901—61no—
105#901—61no—
106#901—61no—
107C2×ΓL(1,𝔽25)—32no—
108C2×D3×C8—32no—
109C3×#101—32no—
110C3×#100—32no—
111C3×#97—61no—
112C3×C4×C8—61no—
113#834—34no—
114#824Dic312yescomplemented
115#823Dic312yescomplemented
116#815—21no—
117#815—61no—
118#815—61no—
119C8×Dic3—21no—
120C8×Dic3—61no—
121C8×Dic3—61no—
122#806—34no—
123C23×C32C22×C411yescharacteristic
124C22×C3×D3C4212yes—
125C2×C32×C4C22×C411yescharacteristic
126C2×C32×C4C22×C411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C3⋊Dic3—22no—
132C3×#67—22no—
133C3×#67—22no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3C4212yes—
136C3×D12—21no—
137C3×D12—21no—
138C3×C4×D3—22no—
139C3×C4×D3—22no—
140C3×Dic6—21no—
141C3×Dic6—21no—
142C32×C8—22no—
143C3⋊(C3⋊C8)—22no—
144C3×C3⋊C8—22no—
145C3×C3⋊C8C22⋊C411yescharacteristic
146C3×C3⋊C8C22⋊C411yescharacteristic
147C3×C3⋊C8C22⋊C411yescharacteristic
148C3×C3⋊C8C22⋊C411yescharacteristic
149C2×#131—91no—
150#413—31no—
151#410—91no—
152#405—31no—
153#405—91no—
154#344—91no—
155#344—91no—
156C3×#41—61no—
157C3×#41—61no—
158C3×#41—61no—
159C3×#41—61no—
160C2×C3×Q8—31no—
161C2×C3×D4—32no—
162C2×C3×D4—31no—
163C22×C3×C4—21no—
164C22×C3×C4—32no—
165C22×C3×C4C22×D311yescharacteristic
166C22×C3×C4C22×D311yescharacteristic
167C2×#67C4×D312yes—
168#235—21no—
169#235—21no—
170#235—21no—
171#235—21no—
172C2×D12C2×Dic311yescharacteristic
173C2×C4×D3C4×D312yes—
174C2×Dic6C2×Dic311yescharacteristic
175C3×M16—21no—
176C3×M16—21no—
177C3×M16—22no—
178C3×M16—32no—
179C3×M16—41no—
180C3×M16—61no—
181C3×M16C4×D312yes—
182C3×M16C2×Dic312yes—
183C2×C3×C8—21no—
184C2×C3×C8—21no—
185C2×C3×C8—31no—
186C2×C3×C8—31no—
187C2×C3×C8—31no—
188C2×C3×C8—31no—
189C2×C3×C8—31no—
190C2×C3×C8—31no—
191C2×C3×C8—41no—
192C2×C3×C8—61no—
193C3×C4⋊C4—61no—
194C3×C22⋊C4—32no—
195C3×C42—61no—
196#217—32no—
197#217—32no—
198#217—62no—
199#217C4×D312yes—
200C4⋊Dic3—21no—
201C4⋊Dic3—61no—
202C4⋊Dic3—61no—
203C4⋊Dic3—121no—
204C4×Dic3—21no—
205C4×Dic3—61no—
206C4×Dic3—61no—
207C4×Dic3—121no—
208#208—21no—
209#208—61no—
210#208—61no—
211#208—61no—
212#208—61no—
213#208—62no—
214#208—62no—
215#208—121no—
216#208—121no—
217#208C2×Dic312yes—
218C2×C3⋊C8—21no—
219C2×C3⋊C8—32no—
220C2×C3⋊C8—32no—
221C2×C3⋊C8—62no—
222C2×C3⋊C8—62no—
223C2×C3⋊C8—62no—
224C2×C3⋊C8C4×D311yescharacteristic
225C2×C3⋊C8C4×D311yescharacteristic
226C2×C3⋊C8D1211yescharacteristic
227C2×C3⋊C8D1211yescharacteristic
228C2×C3⋊C8#6711yescharacteristic
229C2×C3⋊C8#6711yescharacteristic
230ΓL(1,𝔽25)—62no—
231ΓL(1,𝔽25)—62no—
232D3×C8—62no—
233D3×C8—62no—
234C22×C32—41no—
235C22×C32C2×C4211yescharacteristic
236C22×C32C4×D411yescharacteristic
237C22×C32C4×D411yescharacteristic
238C2×C3×D3—22no—
239C2×C3×D3—42no—
240C32×C4C2×C22⋊C411yescharacteristic
241C32×C4#11711yescharacteristic
242C32×C4C4×D411yescharacteristic
243C32×C4C4×D411yescharacteristic
244C3⋊Dic3—42no—
245C3×Dic3—22no—
246C3×Dic3—42no—
247C2×#41—31no—
248#131—181no—
249#131—181no—
250#131—181no—
251#131—181no—
252C2×M16—31no—
253C2×M16—92no—
254C2×M16—91no—
255C2×M16D3211yescharacteristic
256C22×C8—31no—
257C22×C8—92no—
258#117—31no—
259#117—91no—
260#101—32no—
261#100—32no—
262#99—94no—
263#97—61no—
264#97—181no—
265C4×C8—61no—
266C4×C8—181no—
267C23×C3—21no—
268C23×C3—32no—
269C23×C3C2×C4×D311yescharacteristic
270C23×C3C2×C4×D311yescharacteristic
271C22×D3C4×Dic312yes—
272C3×Q8—61no—
273C3×Q8—61no—
274C3×D4—62no—
275C3×D4—62no—
276C3×D4—61no—
277C3×D4—61no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—32no—
285C2×C3×C4—62no—
286C2×C3×C4—62no—
287C2×C3×C4—62no—
288C2×C3×C4C2×C4×D311yescharacteristic
289C2×C3×C4C2×C4×D311yescharacteristic
290C2×C3×C4C2×C4×D311yescharacteristic
291C2×C3×C4C2×D1211yescharacteristic
292C2×C3×C4#23511yescharacteristic
293C2×C3×C4#23511yescharacteristic
294C2×C3×C4D3×D411yescharacteristic
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4#23711yescharacteristic
297C2×C3×C4#23711yescharacteristic
298C2×C3×C4C22×Dic311yescharacteristic
299C2×C3×C4C2×#6711yescharacteristic
300#67—22no—
301#67—22no—
302C2×Dic3—22no—
303C2×Dic3—62no—
304C2×Dic3—62no—
305C2×Dic3—122no—
306C2×Dic3C4×Dic312yes—
307D12—21no—
308D12—21no—
309C4×D3—22no—
310C4×D3—22no—
311Dic6—21no—
312Dic6—21no—
313C3×C8—22no—
314C3×C8—22no—
315C3×C8—31no—
316C3×C8—31no—
317C3×C8—31no—
318C3×C8—31no—
319C3×C8—42no—
320C3×C8—62no—
321C3⋊C8—22no—
322C3⋊C8—62no—
323C3⋊C8—62no—
324C3⋊C8—122no—
325C3⋊C8(C2×D3)⋊C411yescharacteristic
326C3⋊C8(C2×D3)⋊C411yescharacteristic
327C3⋊C8(C2×D3)⋊C411yescharacteristic
328C3⋊C8(C2×D3)⋊C411yescharacteristic
329C2×C32—21no—
330C2×C32—21no—
331C2×C32—21no—
332C2×C32C4×C22⋊C411yescharacteristic
333C3×D3—42no—
334#41—61no—
335#41—61no—
336#41—61no—
337#41—61no—
338C2×Q8—31no—
339C2×D4—32no—
340C2×D4—31no—
341C22×C4—32no—
342C22×C4C2×D3211yescharacteristic
343M16—21no—
344M16—32no—
345M16—61no—
346M16—182no—
347M16—182no—
348M16—181no—
349M16—181no—
350M16D3×Dic312yes—
351C2×C8—21no—
352C2×C8—31no—
353C2×C8—31no—
354C2×C8—31no—
355C2×C8—31no—
356C2×C8—31no—
357C2×C8—31no—
358C2×C8—61no—
359C2×C8—92no—
360C2×C8—182no—
361C2×C8—182no—
362C4⋊C4—61no—
363C4⋊C4—181no—
364C22⋊C4—32no—
365C22⋊C4—92no—
366C42—61no—
367C42—181no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—41no—
372C22×C3—41no—
373C22×C3—62no—
374C22×C3—81no—
375C22×C3—122no—
376C22×C3C42×D311yescharacteristic
377C22×C3C4×D1211yescharacteristic
378C22×C3#67⋊C411yescharacteristic
379C22×C3#67⋊C411yescharacteristic
380C22×C3C2×C4×Dic311yescharacteristic
381C22×C3C4×#6711yescharacteristic
382C2×D3—22no—
383C2×D3—42no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—62no—
389C3×C4—122no—
390C3×C4#87211yescharacteristic
391C3×C4C4×D1211yescharacteristic
392C3×C4#87711yescharacteristic
393C3×C4D3×C22⋊C411yescharacteristic
394C3×C4C2×(C2×D3)⋊C411yescharacteristic
395C3×C4C4×#6711yescharacteristic
396C3×C4D4×Dic311yescharacteristic
397C3×C4D4×Dic311yescharacteristic
398Dic3—22no—
399Dic3—42no—
400Dic3—122no—
401Dic3—122no—
402Dic3—242no—
403C32#175711yescharacteristic, complemented, Sylow
404C23—32no—
405C23C4×D3211yescharacteristic
406Q8—61no—
407Q8—61no—
408D4—62no—
409D4—62no—
410D4—61no—
411D4—61no—
412C2×C4—32no—
413C2×C4—62no—
414C2×C4—62no—
415C2×C4—62no—
416C2×C4—182no—
417C2×C4#379511yescharacteristic
418C2×C4C4×D3211yescharacteristic
419C2×C4D3×D1211yescharacteristic
420C2×C4C2×D3×Dic311yescharacteristic
421C2×C4#380411yescharacteristic
422C2×C4D3×#6711yescharacteristic
423C8—22no—
424C8—31no—
425C8—31no—
426C8—31no—
427C8—31no—
428C8—62no—
429C8—182no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—41no—
438C2×C3—41no—
439C2×C3—41no—
440C2×C3—122no—
441C2×C3C4×(C2×D3)⋊C411yescharacteristic
442C2×C3Dic3×C22⋊C411yescharacteristic
443D3—42no—
444C22—41no—
445C22—62no—
446C22—122no—
447C22C4×D3×Dic311yescharacteristic
448C22#6387911yescharacteristic
449C22#6388011yescharacteristic
450C4—62no—
451C4—122no—
452C4—362no—
453C4#6387711yescharacteristic
454C4Dic3×D1211yescharacteristic
455C4D3×(C2×D3)⋊C411yescharacteristic
456C4Dic3×#6711yescharacteristic
457C3—21no—
458C3#6989811yescharacteristic, complemented
459C3#7013311yescharacteristic, complemented
460C2—21no—
461C2—21no—
462C2—21no—
463C2—122no—
464C2Dic3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC4D3×(C2×D3)⋊C4
commutatorC22×C32C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32C4×C22⋊C4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1757
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C3×#5122C2semidirect
5. #10591059C2semidirect
6. #10589425C2semidirect
7. #10589170C2semidirect
17. C2×#3711C4semidirect
22. C2×D3×C3⋊C8C4semidirect
23. C3×#824C4semidirect
24. C3×#823C4semidirect
37. #5122D3semidirect
114. #824Dic3semidirect
115. #823Dic3semidirect
403. C32#1757semidirect
458. C3#69898semidirect
459. C3#70133semidirect

Maximal subgroups

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

subgroupindex
C2×#638142
C3×#51322
C3×#51222
#105912312
#105910592
#105894252
#105891702
#701333
#698983