Finite Group Databasebeta

← #11784147

Subgroups — #11784147

Order 1152.

629 conjugacy classes of subgroups.

The subgroup lattice has 433 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63814C211yesmaximal, characteristic
2C3×#5113C211yesmaximal, characteristic
3C2×C3×#815C211yesmaximal, characteristic, complemented
4C2×#63569C211yesmaximal, characteristic
5#10591055C211yesmaximal, characteristic, complemented
6#10589418C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#70290—31nomaximal
9#69839—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3711—21no—
18#63814—22no—
19#63814C414yescomplemented
20C2×D3×C3⋊C8—21no—
21C3×#821C412yescomplemented
22C3×#816C412yescomplemented
23C3×#815—22no—
24#63569C414yescomplemented
25#63554—21no—
26Dic3×C3⋊C8—21no—
27C2×#948—31no—
28C2×#901—31no—
29C3×#416—31no—
30C2×C3×#97—31no—
31C2×#837—31no—
32#5113D311yescharacteristic
33#5101—31no—
34C2×#815D311yescharacteristic, complemented
35#4997—31no—
36C2×#805—31no—
37#4552—31no—
38#4552—31no—
39#4552—61no—
40#4532—31no—
41#4523—31no—
42C22×C32×C4C2311yescharacteristic
43C2×C3×#67—21no—
44C22×C3×Dic3—21no—
45C3×#235—21no—
46C3×#235—21no—
47C3×#235C2×C412yes—
48C3×#235C2×C412yes—
49C2×C3×D12C2×C411yescharacteristic
50C2×C3×C4×D3—21no—
51C2×C3×Dic6C2×C411yescharacteristic
52C2×C32×C8—21no—
53C2×C32×C8—21no—
54C2×C32×C8C2×C412yes—
55#3748—21no—
56#3748—21no—
57#3748C2×C412yes—
58#3748C2×C412yes—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C3×#217—21no—
62C3×C4⋊Dic3C2×C412yes—
63C3×C4×Dic3—21no—
64C3×C4×Dic3—21no—
65C3×C4×Dic3C2×C412yes—
66C2×C3×C3⋊C8C2×C412yes—
67C2×C3×C3⋊C8D411yescharacteristic
68C2×C3×C3⋊C8D411yescharacteristic
69C2×C3×C3⋊C8D412yes—
70#3711—24no—
71D3×C3⋊C8—24no—
72#1765—91noSylow
73C2×C3×#41—31no—
74C2×#235C2×D311yescharacteristic
75C22×C3×C8—21no—
76C22×C3×C8—31no—
77C22×C3×C8C2×D311yescharacteristic
78C22×C3×C8C2×D311yescharacteristic
79C3×#117—31no—
80C2×C3×C42—31no—
81#948—34no—
82#948—62no—
83#926C2×D311yescharacteristic
84C2×C4×Dic3C2×D311yescharacteristic
85C2×#208—31no—
86C2×#208—31no—
87C2×#208—31no—
88C2×#208—31no—
89C2×#208—61no—
90C2×#208—61no—
91C2×#208—61no—
92C22×C3⋊C8—61no—
93C22×C3⋊C8C2×D311yescharacteristic
94#901—34no—
95#901—62no—
96C2×ΓL(1,𝔽25)—61no—
97C2×D3×C8—61no—
98C3×#103—32no—
99C3×#102—32no—
100C3×#97—62no—
101#837—34no—
102#821Dic312yescomplemented
103#816Dic312yescomplemented
104#815—22no—
105#815—61no—
106C8×Dic3—61no—
107#805—34no—
108#803—61no—
109C4×C3⋊C8—61no—
110C23×C32#4111yescharacteristic
111C22×C3×D3—21no—
112C2×C32×C4C22×C411yescharacteristic
113C2×C32×C4C22×C411yescharacteristic
114C2×C32×C4C22×C411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C3×#67—22no—
119C3×#67—22no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—22no—
123C2×C3×Dic3—42no—
124C3×D12—21no—
125C3×D12C4212yes—
126C3×C4×D3—22no—
127C3×C4×D3—22no—
128C3×Dic6—21no—
129C3×Dic6C4212yes—
130C32×C8—22no—
131C3⋊(C3⋊C8)—22no—
132C3⋊(C3⋊C8)—22no—
133C3×C3⋊C8C22⋊C412yes—
134C3×C3⋊C8C22⋊C412yes—
135C2×#131—91no—
136C2×#104—91no—
137#416—31no—
138#405—91no—
139C2×#97—31no—
140#341—91no—
141#339—91no—
142C3×#41—32no—
143C3×#41—32no—
144C3×#41—61no—
145C3×#41—61no—
146C2×C3×Q8—31no—
147C2×C3×D4—31no—
148C2×C3×D4—61no—
149C22×C3×C4—21no—
150C22×C3×C4—61no—
151C22×C3×C4—61no—
152C22×C3×C4C22×D311yescharacteristic
153C22×C3×C4C22×D311yescharacteristic
154C2×#67—21no—
155C22×Dic3—21no—
156#235—21no—
157#235—21no—
158#235C4×D312yes—
159#235C4×D312yes—
160C2×D12C2×Dic311yescharacteristic
161C2×C4×D3—21no—
162C2×Dic6C2×Dic311yescharacteristic
163C2×C3×C8—21no—
164C2×C3×C8—21no—
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C2×C3×C8—22no—
168C2×C3×C8—32no—
169C2×C3×C8—31no—
170C2×C3×C8—31no—
171C2×C3×C8—32no—
172C2×C3×C8—41no—
173C2×C3×C8—41no—
174C2×C3×C8C4×D312yes—
175C2×C3×C8C2×Dic312yes—
176C3×C4⋊C4—32no—
177C3×C22⋊C4—61no—
178C3×C42—32no—
179C3×C42—61no—
180C3×C42—61no—
181#217—21no—
182C4⋊Dic3C2×Dic312yes—
183C4×Dic3—21no—
184C4×Dic3—21no—
185C4×Dic3C4×D312yes—
186#208—32no—
187#208—32no—
188#208—32no—
189#208—32no—
190#208—62no—
191#208—62no—
192#208—61no—
193#208—61no—
194#208—61no—
195#208—61no—
196#208—64no—
197#208—121no—
198#208—121no—
199C2×C3⋊C8—61no—
200C2×C3⋊C8—61no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8—61no—
203C2×C3⋊C8—64no—
204C2×C3⋊C8—121no—
205C2×C3⋊C8—121no—
206C2×C3⋊C8C4×D312yes—
207C2×C3⋊C8D1211yescharacteristic
208C2×C3⋊C8D1211yescharacteristic
209C2×C3⋊C8#6712yes—
210ΓL(1,𝔽25)—64no—
211D3×C8—64no—
212C22×C32—22no—
213C22×C32#11711yescharacteristic
214C22×C32C4×D411yescharacteristic
215C22×C32C4×D411yescharacteristic
216C2×C3×D3—22no—
217C2×C3×D3—42no—
218C32×C4C2×C4211yescharacteristic
219C32×C4C2×C22⋊C411yescharacteristic
220C32×C4C4×D411yescharacteristic
221C32×C4C4×D411yescharacteristic
222C3×Dic3—22no—
223C3×Dic3—42no—
224C3×Dic3—42no—
225C2×#41—31no—
226#131—94no—
227#131—182no—
228C2×M16—91no—
229C2×M16—91no—
230C2×M16—181no—
231C22×C8—31no—
232C22×C8—181no—
233C22×C8D3211yescharacteristic
234#117—31no—
235C2×C42—31no—
236#104—94no—
237#103—32no—
238#102—32no—
239#97—62no—
240#97—181no—
241C4×C8—181no—
242C23×C3—21no—
243C23×C3—61no—
244C23×C3#23511yescharacteristic
245C23×C3#23711yescharacteristic
246C22×D3—21no—
247C3×Q8—32no—
248C3×Q8—61no—
249C3×D4—32no—
250C3×D4—62no—
251C3×D4—62no—
252C3×D4—61no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—61no—
260C2×C3×C4—62no—
261C2×C3×C4—62no—
262C2×C3×C4—62no—
263C2×C3×C4—62no—
264C2×C3×C4—122no—
265C2×C3×C4C2×C4×D311yescharacteristic
266C2×C3×C4C2×C4×D311yescharacteristic
267C2×C3×C4C2×C4×D311yescharacteristic
268C2×C3×C4C2×C4×D311yescharacteristic
269C2×C3×C4C2×C4×D311yescharacteristic
270C2×C3×C4C2×D1211yescharacteristic
271C2×C3×C4#23511yescharacteristic
272C2×C3×C4D3×D411yescharacteristic
273C2×C3×C4D3×D411yescharacteristic
274C2×C3×C4#23711yescharacteristic
275C2×C3×C4C22×Dic311yescharacteristic
276C2×C3×C4C2×#6711yescharacteristic
277#67—22no—
278#67—22no—
279C2×Dic3—21no—
280C2×Dic3—22no—
281C2×Dic3—22no—
282C2×Dic3—42no—
283D12—21no—
284D12C4×Dic312yes—
285C4×D3—22no—
286C4×D3—22no—
287Dic6—21no—
288Dic6C4×Dic312yes—
289C3×C8—22no—
290C3×C8—22no—
291C3×C8—32no—
292C3×C8—32no—
293C3×C8—42no—
294C3⋊C8—62no—
295C3⋊C8—62no—
296C3⋊C8—62no—
297C3⋊C8—62no—
298C3⋊C8—122no—
299C3⋊C8—122no—
300C3⋊C8(C2×D3)⋊C412yes—
301C3⋊C8(C2×D3)⋊C412yes—
302C2×C32—21no—
303C2×C32—21no—
304C2×C32C4×C22⋊C411yescharacteristic
305C2×C32#44412yes—
306C3×D3—42no—
307#41—32no—
308#41—32no—
309#41—61no—
310#41—61no—
311C2×Q8—31no—
312C2×D4—31no—
313C2×D4—61no—
314C22×C4—61no—
315C22×C4—61no—
316C22×C4C2×D3211yescharacteristic
317M16—92no—
318M16—92no—
319M16—184no—
320M16—181no—
321M16—181no—
322C2×C8—21no—
323C2×C8—21no—
324C2×C8—32no—
325C2×C8—31no—
326C2×C8—31no—
327C2×C8—32no—
328C2×C8—184no—
329C2×C8—181no—
330C2×C8—181no—
331C2×C8D3×Dic312yes—
332C4⋊C4—32no—
333C22⋊C4—61no—
334C42—32no—
335C42—61no—
336C42—61no—
337C22×C3—22no—
338C22×C3—22no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—42no—
343C22×C3—62no—
344C22×C3—122no—
345C22×C3#87211yescharacteristic
346C22×C3C4×D1211yescharacteristic
347C22×C3#87711yescharacteristic
348C22×C3#67⋊C411yescharacteristic
349C22×C3C4×#6711yescharacteristic
350C22×C3D4×Dic311yescharacteristic
351C2×D3—22no—
352C2×D3—42no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—62no—
358C3×C4—122no—
359C3×C4—122no—
360C3×C4C42×D311yescharacteristic
361C3×C4C4×D1211yescharacteristic
362C3×C4D3×C22⋊C411yescharacteristic
363C3×C4#67⋊C411yescharacteristic
364C3×C4C2×C4×Dic311yescharacteristic
365C3×C4C2×(C2×D3)⋊C411yescharacteristic
366C3×C4C4×#6711yescharacteristic
367C3×C4D4×Dic311yescharacteristic
368Dic3—22no—
369Dic3—42no—
370Dic3—42no—
371C32#176511yescharacteristic, complemented, Sylow
372C23—61no—
373C23#379511yescharacteristic
374Q8—32no—
375Q8—61no—
376D4—32no—
377D4—62no—
378D4—62no—
379D4—61no—
380C2×C4—61no—
381C2×C4—62no—
382C2×C4—62no—
383C2×C4—62no—
384C2×C4—62no—
385C2×C4—122no—
386C2×C4C4×D3211yescharacteristic
387C2×C4C4×D3211yescharacteristic
388C2×C4D3×D1211yescharacteristic
389C2×C4C2×D3×Dic311yescharacteristic
390C2×C4#380411yescharacteristic
391C2×C4D3×#6711yescharacteristic
392C8—22no—
393C8—32no—
394C8—32no—
395C8—182no—
396C8—182no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—22no—
403C2×C3—41no—
404C2×C3—41no—
405C2×C3—122no—
406C2×C3#471712yes—
407C2×C3C4×(C2×D3)⋊C411yescharacteristic
408C2×C3Dic3×C22⋊C411yescharacteristic
409C2×C3#519712yes—
410D3—42no—
411C22—22no—
412C22—62no—
413C22—122no—
414C22#6387711yescharacteristic
415C22#6387911yescharacteristic
416C22Dic3×D1211yescharacteristic
417C4—62no—
418C4—122no—
419C4—122no—
420C4C4×D3×Dic311yescharacteristic
421C4#6388011yescharacteristic
422C4D3×(C2×D3)⋊C411yescharacteristic
423C4Dic3×#6711yescharacteristic
424C3—21no—
425C3#6983911yescharacteristic, complemented
426C3#7029011yescharacteristic, complemented
427C2—21no—
428C2—21no—
429C2—122no—
430C2#1059091612yes—
431C2Dic3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC22×C32C4×D4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1765
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. C2×C3×#815C2semidirect
5. #10591055C2semidirect
6. #10589418C2semidirect
7. #10589161C2semidirect
19. #63814C4semidirect
21. C3×#821C4semidirect
22. C3×#816C4semidirect
24. #63569C4semidirect
34. C2×#815D3semidirect
102. #821Dic3semidirect
103. #816Dic3semidirect
371. C32#1765semidirect
425. C3#69839semidirect
426. C3#70290semidirect

Maximal subgroups

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

subgroupindex
C2×#638142
C3×#51132
C2×C3×#8152
C2×#635692
#105910552
#105894182
#105891612
#702903
#698393