Finite Group Databasebeta

← #11783847

Subgroups — #11783847

Order 1152.

633 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#901C211yesmaximal, characteristic
2#10592800C211yesmaximal, characteristic, complemented
3C3×#5101C211yesmaximal, characteristic, complemented
4#10591231C211yesmaximal, characteristic
5#10591076C211yesmaximal, characteristic
6#10589171C211yesmaximal, characteristic, complemented
7#10589169C211yesmaximal, characteristic, complemented
8#72011—31nomaximal
9#69898—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#901—21no—
18C3×#901—21no—
19C3×#901—21no—
20C3×#901—21no—
21C2×C3×ΓL(1,𝔽25)C412yescomplemented
22C2×C3×D3×C8C412yescomplemented
23#63642—21no—
24C8×C3⋊Dic3—21no—
25C3×#815—21no—
26C3×C8×Dic3—21no—
27#63580C414yes—
28#63560C412yescomplemented
29#63558C412yescomplemented
30C2×C3×#131—31no—
31C2×#901D311yescharacteristic
32C3×#405—31no—
33#5240—31no—
34#5237—31no—
35#5132—31no—
36#5101—31no—
37#5101—31no—
38#5101—61no—
39#5101D311yescharacteristic, complemented
40#5006—31no—
41#4559—31no—
42#4556—31no—
43#4556—31no—
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
54C2×C32×C8C2×C411yescharacteristic
55C2×C32×C8C2×C411yescharacteristic
56C2×C32×C8D411yescharacteristic
57C2×C32×C8D411yescharacteristic
58C2×C32×C8D411yescharacteristic
59C2×C32×C8D411yescharacteristic
60#3757C2×C412yes—
61C4⋊(C3⋊Dic3)—21no—
62C4×C3⋊Dic3—21no—
63#3748—21no—
64#3748C2×C412yes—
65C2×C3⋊(C3⋊C8)—21no—
66C3×#217C2×C412yes—
67C3×C4⋊Dic3—21no—
68C3×C4×Dic3—21no—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208—21no—
72C3×#208C2×C412yes—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8C2×C412yes—
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—31no—
87C2×C3×M16—32no—
88C2×C3×M16—31no—
89C22×C3×C8—21no—
90C22×C3×C8—32no—
91C22×C3×C8C2×D311yescharacteristic
92C22×C3×C8C2×D311yescharacteristic
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
102C2×#208C2×D311yescharacteristic
103#901—21no—
104#901—21no—
105#901—21no—
106#901—21no—
107C2×ΓL(1,𝔽25)Dic312yescomplemented
108C2×D3×C8Dic312yescomplemented
109C3×#97—61no—
110C3×C4×C8—61no—
111#836—32no—
112#834—34no—
113#833—32no—
114#824—32no—
115#823—32no—
116#815—21no—
117#815—62no—
118#815—61no—
119#815—61no—
120C8×Dic3—21no—
121C8×Dic3—62no—
122C8×Dic3—61no—
123C8×Dic3—61no—
124#806—34no—
125C23×C32C22×C411yescharacteristic
126C22×C3×D3C4212yes—
127C2×C32×C4C22×C411yescharacteristic
128C2×C32×C4C22×C411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C3⋊Dic3—22no—
134C3×#67—22no—
135C3×#67—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3C4212yes—
138C3×D12—21no—
139C3×D12—21no—
140C3×C4×D3—22no—
141C3×C4×D3—22no—
142C3×Dic6—21no—
143C3×Dic6—21no—
144C32×C8C22⋊C411yescharacteristic
145C32×C8C22⋊C411yescharacteristic
146C32×C8C22⋊C411yescharacteristic
147C32×C8C22⋊C411yescharacteristic
148C3⋊(C3⋊C8)—22no—
149C3×C3⋊C8—22no—
150C3×C3⋊C8—22no—
151C2×#131—31no—
152#413—91no—
153#410—91no—
154#405—31no—
155#405—91no—
156#344—91no—
157#344—91no—
158C3×#41—61no—
159C3×#41—61no—
160C3×#41—61no—
161C3×#41—61no—
162C2×C3×Q8—31no—
163C2×C3×D4—32no—
164C2×C3×D4—31no—
165C22×C3×C4—21no—
166C22×C3×C4—32no—
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C2×#67C4×D312yes—
170#235—21no—
171#235—21no—
172#235—21no—
173#235—21no—
174C2×D12C4×D311yescharacteristic
175C2×C4×D3C2×Dic312yes—
176C2×Dic6C4×D311yescharacteristic
177C3×M16—32no—
178C3×M16—61no—
179C3×M16—61no—
180C3×M16—61no—
181C3×M16—62no—
182C3×M16—62no—
183C2×C3×C8—21no—
184C2×C3×C8—21no—
185C2×C3×C8—21no—
186C2×C3×C8—21no—
187C2×C3×C8—21no—
188C2×C3×C8—21no—
189C2×C3×C8—32no—
190C2×C3×C8—61no—
191C2×C3×C8—62no—
192C2×C3×C8—62no—
193C2×C3×C8C4×D311yescharacteristic
194C2×C3×C8C4×D311yescharacteristic
195C2×C3×C8D1211yescharacteristic
196C2×C3×C8D1211yescharacteristic
197C2×C3×C8C2×Dic311yescharacteristic
198C2×C3×C8C2×Dic311yescharacteristic
199C2×C3×C8#6711yescharacteristic
200C2×C3×C8#6711yescharacteristic
201C2×C3×C8#6711yescharacteristic
202C2×C3×C8#6711yescharacteristic
203C2×C3×C8#6711yescharacteristic
204C2×C3×C8#6711yescharacteristic
205C3×C4⋊C4—61no—
206C3×C22⋊C4—32no—
207C3×C42—61no—
208#217—32no—
209#217—32no—
210#217—62no—
211#217C4×D312yes—
212C4⋊Dic3—21no—
213C4⋊Dic3—62no—
214C4⋊Dic3—61no—
215C4⋊Dic3—61no—
216C4×Dic3—21no—
217C4×Dic3—62no—
218C4×Dic3—61no—
219C4×Dic3—61no—
220#208—21no—
221#208—21no—
222#208—21no—
223#208—32no—
224#208—32no—
225#208—62no—
226#208—62no—
227#208—61no—
228#208—61no—
229#208C4×D312yes—
230C2×C3⋊C8—21no—
231C2×C3⋊C8—62no—
232C2×C3⋊C8—61no—
233C2×C3⋊C8—61no—
234C2×C3⋊C8C2×Dic312yes—
235ΓL(1,𝔽25)—22no—
236ΓL(1,𝔽25)—22no—
237D3×C8—22no—
238D3×C8—22no—
239C22×C32—41no—
240C22×C32C2×C4211yescharacteristic
241C22×C32C4×D411yescharacteristic
242C22×C32C4×D411yescharacteristic
243C2×C3×D3—22no—
244C2×C3×D3—42no—
245C32×C4C2×C22⋊C411yescharacteristic
246C32×C4#11711yescharacteristic
247C32×C4C4×D411yescharacteristic
248C32×C4C4×D411yescharacteristic
249C3⋊Dic3—42no—
250C3×Dic3—22no—
251C3×Dic3—42no—
252C2×#41—31no—
253#131—61no—
254#131—61no—
255#131—61no—
256#131—61no—
257C2×M16—31no—
258C2×M16—32no—
259C2×M16—31no—
260C2×M16—91no—
261C22×C8—32no—
262C22×C8D3211yescharacteristic
263#117—31no—
264#117—91no—
265#101—92no—
266#100—92no—
267#99—94no—
268#97—61no—
269#97—181no—
270C4×C8—61no—
271C4×C8—181no—
272C23×C3—21no—
273C23×C3—32no—
274C23×C3C2×C4×D311yescharacteristic
275C23×C3C2×C4×D311yescharacteristic
276C22×D3C4×Dic312yes—
277C3×Q8—61no—
278C3×Q8—61no—
279C3×D4—62no—
280C3×D4—62no—
281C3×D4—61no—
282C3×D4—61no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—32no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4C2×C4×D311yescharacteristic
294C2×C3×C4C2×C4×D311yescharacteristic
295C2×C3×C4C2×C4×D311yescharacteristic
296C2×C3×C4C2×D1211yescharacteristic
297C2×C3×C4#23511yescharacteristic
298C2×C3×C4#23511yescharacteristic
299C2×C3×C4#23511yescharacteristic
300C2×C3×C4#23511yescharacteristic
301C2×C3×C4C22×Dic311yescharacteristic
302C2×C3×C4C2×#6711yescharacteristic
303C2×C3×C4C2×#6711yescharacteristic
304C2×C3×C4C2×#6711yescharacteristic
305#67—22no—
306#67—22no—
307C2×Dic3—22no—
308C2×Dic3—64no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3C4×Dic312yes—
312D12—21no—
313D12—21no—
314C4×D3—22no—
315C4×D3—22no—
316Dic6—21no—
317Dic6—21no—
318C3×C8—21no—
319C3×C8—21no—
320C3×C8—21no—
321C3×C8—21no—
322C3×C8—62no—
323C3×C8—62no—
324C3×C8(C2×D3)⋊C411yescharacteristic
325C3×C8(C2×D3)⋊C411yescharacteristic
326C3×C8(C2×D3)⋊C411yescharacteristic
327C3×C8(C2×D3)⋊C411yescharacteristic
328C3×C8#21711yescharacteristic
329C3×C8#21711yescharacteristic
330C3×C8#21711yescharacteristic
331C3×C8#21711yescharacteristic
332C3⋊C8—22no—
333C3⋊C8—22no—
334C3⋊C8—64no—
335C3⋊C8—62no—
336C3⋊C8—62no—
337C2×C32—21no—
338C2×C32—21no—
339C2×C32—21no—
340C2×C32C4×C22⋊C411yescharacteristic
341C3×D3—42no—
342#41—61no—
343#41—61no—
344#41—61no—
345#41—61no—
346C2×Q8—31no—
347C2×D4—32no—
348C2×D4—31no—
349C22×C4—32no—
350C22×C4C2×D3211yescharacteristic
351M16—32no—
352M16—61no—
353M16—61no—
354M16—61no—
355M16—62no—
356M16—62no—
357M16—92no—
358M16—181no—
359C2×C8—32no—
360C2×C8—61no—
361C2×C8—62no—
362C2×C8—62no—
363C2×C8—181no—
364C2×C8D3×Dic311yescharacteristic
365C2×C8D3×Dic311yescharacteristic
366C2×C8#62511yescharacteristic
367C2×C8#62511yescharacteristic
368C2×C8#62611yescharacteristic
369C2×C8#62611yescharacteristic
370C4⋊C4—61no—
371C4⋊C4—181no—
372C22⋊C4—32no—
373C22⋊C4—92no—
374C42—61no—
375C42—181no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3—42no—
382C22×C3—62no—
383C22×C3—122no—
384C22×C3C42×D311yescharacteristic
385C22×C3C4×D1211yescharacteristic
386C22×C3C2×C4×Dic311yescharacteristic
387C22×C3C4×#6711yescharacteristic
388C22×C3C4×#6711yescharacteristic
389C22×C3C4×#6711yescharacteristic
390C2×D3—22no—
391C2×D3—42no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—62no—
397C3×C4—122no—
398C3×C4#87211yescharacteristic
399C3×C4C4×D1211yescharacteristic
400C3×C4#92611yescharacteristic
401C3×C4C2×(C2×D3)⋊C411yescharacteristic
402C3×C4C4×#6711yescharacteristic
403C3×C4C4×#6711yescharacteristic
404C3×C4C4×#6711yescharacteristic
405C3×C4C2×#21711yescharacteristic
406Dic3—22no—
407Dic3—42no—
408Dic3—124no—
409Dic3—122no—
410Dic3—122no—
411C32#175711yescharacteristic, complemented, Sylow
412C23—32no—
413C23C4×D3211yescharacteristic
414Q8—61no—
415Q8—61no—
416D4—62no—
417D4—62no—
418D4—61no—
419D4—61no—
420C2×C4—32no—
421C2×C4—62no—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4—182no—
425C2×C4#379811yescharacteristic
426C2×C4#379811yescharacteristic
427C2×C4C4×D3211yescharacteristic
428C2×C4C2×D3×Dic311yescharacteristic
429C2×C4C2×#62511yescharacteristic
430C2×C4C2×#62611yescharacteristic
431C8—62no—
432C8—62no—
433C8—182no—
434C8(C2×D3)⋊Dic311yescharacteristic
435C8(C2×D3)⋊Dic311yescharacteristic
436C8(C2×D3)⋊Dic311yescharacteristic
437C8(C2×D3)⋊Dic311yescharacteristic
438C2×C3—22no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—41no—
447C2×C3—41no—
448C2×C3—122no—
449C2×C3C4×(C2×D3)⋊C411yescharacteristic
450C2×C3C4×#21711yescharacteristic
451D3—42no—
452C22—41no—
453C22—62no—
454C22—122no—
455C22C4×D3×Dic311yescharacteristic
456C22C4×#62511yescharacteristic
457C22C4×#62611yescharacteristic
458C4—62no—
459C4—122no—
460C4—362no—
461C4#6385511yescharacteristic
462C4C4×#62511yescharacteristic
463C4C4×#62611yescharacteristic
464C4C2×(C2×D3)⋊Dic311yescharacteristic
465C3—21no—
466C3#6989811yescharacteristic, complemented
467C3#7201111yescharacteristic, complemented
468C2—21no—
469C2—21no—
470C2—21no—
471C2—122no—
472C2C4×(C2×D3)⋊Dic311yescharacteristic
subgroupG/H
centerC8(C2×D3)⋊Dic3
commutatorC22×C32C2×C42
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC2×C32C4×C22⋊C4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1757
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C8 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #10592800C2semidirect
3. C3×#5101C2semidirect
6. #10589171C2semidirect
7. #10589169C2semidirect
21. C2×C3×ΓL(1,𝔽25)C4semidirect
22. C2×C3×D3×C8C4semidirect
28. #63560C4semidirect
29. #63558C4semidirect
39. #5101D3semidirect
107. C2×ΓL(1,𝔽25)Dic3semidirect
108. C2×D3×C8Dic3semidirect
411. C32#1757semidirect
466. C3#69898semidirect
467. C3#72011semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9012
#105928002
C3×#51012
#105912312
#105910762
#105891712
#105891692
#720113
#698983