Finite Group Databasebeta

← #11783841

Subgroups — #11783841

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×C3×#907C211yesmaximal, characteristic
2#10591231C211yesmaximal, characteristic
3#10591076C211yesmaximal, characteristic
4#10591059C211yesmaximal, characteristic, complemented
5#10591055C211yesmaximal, characteristic, complemented
6#10589422C211yesmaximal, characteristic, complemented
7C3×#4556C211yesmaximal, characteristic, complemented
8#72011—31nomaximal
9#69014—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C3×#907—21no—
18C3×#907—21no—
19C3×#907—21no—
20C3×#907—21no—
21C2×C3×ΓL(1,𝔽25)C412yescomplemented
22C2×C3×D3×C8C412yescomplemented
23#63580C414yes—
24#63560C412yescomplemented
25#63558C412yescomplemented
26#63555—21no—
27#63554—21no—
28#63553—21no—
29Dic3×C3⋊C8—21no—
30C2×C3×#131—31no—
31C2×#907D311yescharacteristic
32#5240—31no—
33#5237—31no—
34#5132—31no—
35#5122—31no—
36#5101—31no—
37#5101—31no—
38#5006—31no—
39#4997—31no—
40C3×#344—31no—
41#4556—31no—
42#4556—31no—
43#4556—61no—
44#4556D311yescharacteristic, complemented
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×M16—21no—
56C2×C32×C8C2×C412yes—
57#3757C2×C412yes—
58C4⋊(C3⋊Dic3)—21no—
59C4×C3⋊Dic3—21no—
60#3748—21no—
61#3748C2×C412yes—
62C2×C3⋊(C3⋊C8)—21no—
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
75C3×ΓL(1,𝔽25)—22no—
76C3×ΓL(1,𝔽25)—22no—
77C3×D3×C8—22no—
78C3×D3×C8—22no—
79#1757—91noSylow
80C2×C3×#41—31no—
81C2×#235C2×D311yescharacteristic
82C3×#131—61no—
83C3×#131—61no—
84C3×#131—61no—
85C3×#131—61no—
86C2×C3×M16—21no—
87C2×C3×M16—32no—
88C2×C3×M16—31no—
89C2×C3×M16C2×D311yescharacteristic
90C2×C3×M16C2×D311yescharacteristic
91C22×C3×C8—31no—
92C22×C3×C8—32no—
93C3×#117—31no—
94#926—31no—
95#926—31no—
96#926—61no—
97#926C2×D311yescharacteristic
98C2×#208—31no—
99C2×#208—31no—
100C2×#208—61no—
101C2×#208C2×D311yescharacteristic
102C22×C3⋊C8C2×D311yescharacteristic
103#907—21no—
104#907—21no—
105#907—21no—
106#907—21no—
107C2×ΓL(1,𝔽25)Dic312yescomplemented
108C2×D3×C8Dic312yescomplemented
109#836—32no—
110#834—34no—
111#833—32no—
112#824—32no—
113#823—32no—
114#815—61no—
115#815—61no—
116#815—61no—
117C8×Dic3—61no—
118C8×Dic3—61no—
119C8×Dic3—61no—
120#806—34no—
121#803—61no—
122C4×C3⋊C8—61no—
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—31no—
150#413—91no—
151#410—91no—
152#405—91no—
153#405—91no—
154#344—31no—
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×D12C4×D311yescharacteristic
173C2×C4×D3C2×Dic312yes—
174C2×Dic6C4×D311yescharacteristic
175C3×M16—21no—
176C3×M16—21no—
177C3×M16—21no—
178C3×M16—21no—
179C3×M16—32no—
180C3×M16—41no—
181C3×M16—41no—
182C3×M16—62no—
183C3×M16—62no—
184C3×M16—61no—
185C2×C3×C8—22no—
186C2×C3×C8—31no—
187C2×C3×C8—31no—
188C2×C3×C8—31no—
189C2×C3×C8—31no—
190C2×C3×C8—31no—
191C2×C3×C8—31no—
192C2×C3×C8—62no—
193C2×C3×C8—62no—
194C2×C3×C8—61no—
195C2×C3×C8C4×D312yes—
196C2×C3×C8C2×Dic312yes—
197C3×C4⋊C4—61no—
198C3×C22⋊C4—32no—
199C3×C42—61no—
200#217—32no—
201#217—32no—
202#217—62no—
203#217C4×D312yes—
204C4⋊Dic3—21no—
205C4⋊Dic3—61no—
206C4⋊Dic3—61no—
207C4⋊Dic3—121no—
208C4×Dic3—21no—
209C4×Dic3—61no—
210C4×Dic3—61no—
211C4×Dic3—121no—
212#208—21no—
213#208—32no—
214#208—32no—
215#208—62no—
216#208—61no—
217#208—61no—
218#208—121no—
219#208C4×D312yes—
220C2×C3⋊C8—21no—
221C2×C3⋊C8—61no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—121no—
224C2×C3⋊C8C2×Dic311yescharacteristic
225C2×C3⋊C8C2×Dic311yescharacteristic
226C2×C3⋊C8#6711yescharacteristic
227C2×C3⋊C8#6711yescharacteristic
228C2×C3⋊C8#6711yescharacteristic
229C2×C3⋊C8#6711yescharacteristic
230ΓL(1,𝔽25)—22no—
231ΓL(1,𝔽25)—22no—
232D3×C8—22no—
233D3×C8—22no—
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—61no—
249#131—61no—
250#131—61no—
251#131—61no—
252C2×M16—32no—
253C2×M16—31no—
254C2×M16—91no—
255C2×M16D3211yescharacteristic
256C22×C8—31no—
257C22×C8—32no—
258#117—31no—
259#117—91no—
260#101—92no—
261#100—92no—
262#99—94no—
263#97—181no—
264#97—181no—
265C4×C8—181no—
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×C4#23511yescharacteristic
292C2×C3×C4#23511yescharacteristic
293C2×C3×C4D3×D411yescharacteristic
294C2×C3×C4D3×D411yescharacteristic
295C2×C3×C4#23711yescharacteristic
296C2×C3×C4#23911yescharacteristic
297C2×C3×C4C22×Dic311yescharacteristic
298C2×C3×C4C2×#6711yescharacteristic
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#21711yescharacteristic
326C3⋊C8#21711yescharacteristic
327C3⋊C8#21711yescharacteristic
328C3⋊C8#21711yescharacteristic
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—21no—
345M16—32no—
346M16—62no—
347M16—62no—
348M16—61no—
349M16—92no—
350M16—181no—
351C2×C8—31no—
352C2×C8—31no—
353C2×C8—31no—
354C2×C8—31no—
355C2×C8—31no—
356C2×C8—31no—
357C2×C8—62no—
358C2×C8—62no—
359C2×C8—61no—
360C2×C8—181no—
361C2×C8D3×Dic312yes—
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×C3#67⋊C411yescharacteristic
378C22×C3#89311yescharacteristic
379C22×C3C2×C4×Dic311yescharacteristic
380C22×C3C4×#6711yescharacteristic
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×C4D3×C22⋊C411yescharacteristic
391C3×C4#67⋊C411yescharacteristic
392C3×C4#89211yescharacteristic
393C3×C4#89311yescharacteristic
394C3×C4#92611yescharacteristic
395C3×C4C4×#6711yescharacteristic
396C3×C4C4×#6711yescharacteristic
397C3×C4C2×#21711yescharacteristic
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×C4#379911yescharacteristic
419C2×C4C4×D3211yescharacteristic
420C2×C4C2×D3×Dic311yescharacteristic
421C2×C4D3×#6711yescharacteristic
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×C3#466611yescharacteristic
442C2×C3C4×#21711yescharacteristic
443D3—42no—
444C22—41no—
445C22—62no—
446C22—122no—
447C22C4×D3×Dic311yescharacteristic
448C22#6387911yescharacteristic
449C22#6390411yescharacteristic
450C4—62no—
451C4—122no—
452C4—362no—
453C4#6384111yescharacteristic
454C4#6387911yescharacteristic
455C4#6390411yescharacteristic
456C4D3×#21711yescharacteristic
457C3—21no—
458C3#6901411yescharacteristic, complemented
459C3#7201111yescharacteristic, complemented
460C2—21no—
461C2—21no—
462C2—21no—
463C2—122no—
464C2#1059123711yescharacteristic
subgroupG/H
centerC4D3×#217
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
4. #10591059C2semidirect
5. #10591055C2semidirect
6. #10589422C2semidirect
7. C3×#4556C2semidirect
21. C2×C3×ΓL(1,𝔽25)C4semidirect
22. C2×C3×D3×C8C4semidirect
24. #63560C4semidirect
25. #63558C4semidirect
44. #4556D3semidirect
107. C2×ΓL(1,𝔽25)Dic3semidirect
108. C2×D3×C8Dic3semidirect
403. C32#1757semidirect
458. C3#69014semidirect
459. C3#72011semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9072
#105912312
#105910762
#105910592
#105910552
#105894222
C3×#45562
#720113
#690143