Finite Group Databasebeta

← #11784141

Subgroups — #11784141

Order 1152.

639 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63814C211yesmaximal, characteristic
2C3×#5002C211yesmaximal, characteristic
3C3×#4997C211yesmaximal, characteristic, complemented
4C2×#63568C211yesmaximal, characteristic
5C2×#63555C211yesmaximal, characteristic, complemented
6#10589398C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#70290—31nomaximal
9#69888—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C22×C3×C3⋊C8C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3711—21no—
18#63814—22no—
19#63814C414yescomplemented
20C2×D3×C3⋊C8—21no—
21C3×#810C412yescomplemented
22C3×#809C412yescomplemented
23C3×#803—21no—
24C3×C4×C3⋊C8—21no—
25#63568C414yescomplemented
26#63555—22no—
27C2×#948—31no—
28C2×#901—31no—
29C3×#416—31no—
30C3×#405—31no—
31C2×#837—31no—
32C2×#825—31no—
33C2×#815—31no—
34C2×#815—31no—
35#5002D311yescharacteristic
36#4997D311yescharacteristic, complemented
37#4558—31no—
38#4552—31no—
39#4532—31no—
40#4532—31no—
41#4532—61no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C2×C3×#67—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
52C32×C4⋊C4C2×C412yes—
53C32×C22⋊C4—21no—
54C32×C42—21no—
55C4×C3⋊Dic3—21no—
56C4×C3⋊Dic3C2×C412yes—
57#3748—21no—
58#3748C2×C412yes—
59C2×C3⋊(C3⋊C8)—21no—
60C3×#208—21no—
61C3×#208C2×C412yes—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8C2×C412yes—
66C2×C3×C3⋊C8C2×C412yes—
67C2×C3×C3⋊C8D412yes—
68C2×C3×C3⋊C8D411yescharacteristic
69C2×C3×C3⋊C8D411yescharacteristic
70#3711—24no—
71D3×C3⋊C8—24no—
72#1765—91noSylow
73C2×C3×#41—31no—
74C2×#235C2×D311yescharacteristic
75C2×C3×M16—31no—
76C22×C3×C8—31no—
77C22×C3×C8—31no—
78C3×#117—21no—
79C3×#117C2×D311yescharacteristic
80C3×#117C2×D311yescharacteristic
81#948—34no—
82#948—62no—
83C2×C4×Dic3—31no—
84C2×C4×Dic3—31no—
85C2×C4×Dic3—61no—
86C2×#208—31no—
87C2×#208—31no—
88C2×#208—61no—
89C2×#208—61no—
90C2×#208C2×D311yescharacteristic
91C22×C3⋊C8—61no—
92C22×C3⋊C8C2×D311yescharacteristic
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—61no—
101C3×C4×C8—61no—
102#837—34no—
103#825—34no—
104#815—62no—
105#815—62no—
106#810Dic312yescomplemented
107#809Dic312yescomplemented
108#803—21no—
109C4×C3⋊C8—21no—
110C23×C32#4111yescharacteristic
111C22×C3×D3—21no—
112C2×C32×C4—22no—
113C2×C32×C4C22×C411yescharacteristic
114C2×C32×C4C22×C411yescharacteristic
115C2×C32×C4C22×C411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3—42no—
121C3×#67—22no—
122C3×#67—22no—
123C2×C3×Dic3—21no—
124C3×D12—21no—
125C3×D12C4212yes—
126C3×C4×D3—22no—
127C3×C4×D3—22no—
128C3×Dic6—21no—
129C3×Dic6C4212yes—
130C3⋊(C3⋊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—31no—
139C2×#97—91no—
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×C4C22×D311yescharacteristic
152C22×C3×C4C22×D311yescharacteristic
153C2×#67—21no—
154C22×Dic3—61no—
155C22×Dic3—61no—
156C22×Dic3—121no—
157#235—21no—
158#235—21no—
159#235C4×D312yes—
160#235C4×D312yes—
161C2×D12C2×Dic311yescharacteristic
162C2×C4×D3—21no—
163C2×Dic6C2×Dic311yescharacteristic
164C3×M16—32no—
165C3×M16—61no—
166C2×C3×C8—32no—
167C2×C3×C8—32no—
168C2×C3×C8—31no—
169C2×C3×C8—31no—
170C2×C3×C8—32no—
171C2×C3×C8—61no—
172C2×C3×C8—61no—
173C2×C3×C8—61no—
174C3×C4⋊C4—22no—
175C3×C4⋊C4C4×D312yes—
176C3×C4⋊C4C2×Dic312yes—
177C3×C22⋊C4—21no—
178C3×C22⋊C4—21no—
179C3×C22⋊C4—41no—
180C3×C42—21no—
181C3×C42—21no—
182C3×C42—41no—
183C4×Dic3—32no—
184C4×Dic3—32no—
185C4×Dic3—62no—
186C4×Dic3—61no—
187C4×Dic3—61no—
188C4×Dic3—121no—
189#208—21no—
190#208—32no—
191#208—32no—
192#208—62no—
193#208—61no—
194#208—61no—
195#208—64no—
196#208—121no—
197#208C4×D312yes—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—21no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8—61no—
203C2×C3⋊C8—64no—
204C2×C3⋊C8—121no—
205C2×C3⋊C8C4×D312yes—
206C2×C3⋊C8D1212yes—
207C2×C3⋊C8C2×Dic312yes—
208C2×C3⋊C8#6711yescharacteristic
209C2×C3⋊C8#6711yescharacteristic
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×C4—42no—
219C32×C4C2×C4211yescharacteristic
220C32×C4C2×C22⋊C411yescharacteristic
221C32×C4C4×D411yescharacteristic
222C32×C4C4×D411yescharacteristic
223C3⋊Dic3—42no—
224C3×Dic3—22no—
225C2×#41—31no—
226#131—94no—
227#131—182no—
228C2×M16—31no—
229C2×M16—91no—
230C2×M16—181no—
231C22×C8—31no—
232C22×C8—31no—
233C22×C8—181no—
234#117D3211yescharacteristic
235C2×C42—91no—
236#104—94no—
237#103—32no—
238#102—32no—
239#97—61no—
240#97—182no—
241C4×C8—61no—
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—22no—
254C2×C3×C4—22no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—42no—
262C2×C3×C4—61no—
263C2×C3×C4—62no—
264C2×C3×C4—62no—
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—62no—
281C2×Dic3—62no—
282C2×Dic3—122no—
283C2×Dic3—122no—
284C2×Dic3—122no—
285C2×Dic3—124no—
286D12—21no—
287D12C4×Dic312yes—
288C4×D3—22no—
289C4×D3—22no—
290Dic6—21no—
291Dic6C4×Dic312yes—
292C3×C8—32no—
293C3×C8—32no—
294C3×C8—62no—
295C3×C8—62no—
296C3⋊C8—22no—
297C3⋊C8—22no—
298C3⋊C8—62no—
299C3⋊C8—62no—
300C3⋊C8—122no—
301C3⋊C8(C2×D3)⋊C412yes—
302C3⋊C8(C2×D3)⋊C412yes—
303C2×C32—21no—
304C2×C32—21no—
305C2×C32C4×C22⋊C411yescharacteristic
306C2×C32#44412yes—
307C3×D3—42no—
308#41—32no—
309#41—32no—
310#41—61no—
311#41—61no—
312C2×Q8—31no—
313C2×D4—31no—
314C2×D4—61no—
315C22×C4—61no—
316C22×C4—181no—
317C22×C4C2×D3211yescharacteristic
318M16—32no—
319M16—61no—
320M16—92no—
321M16—184no—
322M16—181no—
323C2×C8—32no—
324C2×C8—32no—
325C2×C8—31no—
326C2×C8—31no—
327C2×C8—32no—
328C2×C8—61no—
329C2×C8—61no—
330C2×C8—61no—
331C2×C8—184no—
332C2×C8—181no—
333C4⋊C4D3×Dic312yes—
334C22⋊C4—21no—
335C42—21no—
336C42—92no—
337C42—181no—
338C22×C3—22no—
339C22×C3—22no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—42no—
344C22×C3—62no—
345C22×C3—122no—
346C22×C3#87211yescharacteristic
347C22×C3C4×D1211yescharacteristic
348C22×C3#87711yescharacteristic
349C22×C3#67⋊C411yescharacteristic
350C22×C3C4×#6711yescharacteristic
351C22×C3D4×Dic311yescharacteristic
352C2×D3—22no—
353C2×D3—42no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—42no—
359C3×C4—42no—
360C3×C4—62no—
361C3×C4—82no—
362C3×C4C42×D311yescharacteristic
363C3×C4C4×D1211yescharacteristic
364C3×C4D3×C22⋊C411yescharacteristic
365C3×C4#67⋊C411yescharacteristic
366C3×C4C2×C4×Dic311yescharacteristic
367C3×C4C2×(C2×D3)⋊C411yescharacteristic
368C3×C4C4×#6711yescharacteristic
369C3×C4D4×Dic311yescharacteristic
370Dic3—22no—
371Dic3—122no—
372Dic3—122no—
373Dic3—124no—
374C32#176511yescharacteristic, complemented, Sylow
375C23—61no—
376C23#380411yescharacteristic
377Q8—32no—
378Q8—61no—
379D4—32no—
380D4—62no—
381D4—62no—
382D4—61no—
383C2×C4—22no—
384C2×C4—61no—
385C2×C4—62no—
386C2×C4—62no—
387C2×C4—182no—
388C2×C4—362no—
389C2×C4#379511yescharacteristic
390C2×C4C4×D3211yescharacteristic
391C2×C4C4×D3211yescharacteristic
392C2×C4D3×D1211yescharacteristic
393C2×C4C2×D3×Dic311yescharacteristic
394C2×C4D3×#6711yescharacteristic
395C8—32no—
396C8—32no—
397C8—62no—
398C8—62no—
399C8—182no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—22no—
406C2×C3—41no—
407C2×C3—41no—
408C2×C3—122no—
409C2×C3C4×(C2×D3)⋊C411yescharacteristic
410C2×C3Dic3×C22⋊C411yescharacteristic
411C2×C3#514512yes—
412C2×C3#519712yes—
413D3—42no—
414C22—22no—
415C22—62no—
416C22—122no—
417C22#6387711yescharacteristic
418C22#6388011yescharacteristic
419C22Dic3×#6711yescharacteristic
420C4—42no—
421C4—62no—
422C4—362no—
423C4C4×D3×Dic311yescharacteristic
424C4#6387911yescharacteristic
425C4Dic3×D1211yescharacteristic
426C4D3×(C2×D3)⋊C411yescharacteristic
427C3—21no—
428C3#6988811yescharacteristic, complemented
429C3#7029011yescharacteristic, complemented
430C2—21no—
431C2—21no—
432C2—122no—
433C2Dic3×(C2×D3)⋊C411yescharacteristic
434C2#1059167412yes—
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32C4×D4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1765
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. C3×#4997C2semidirect
5. C2×#63555C2semidirect
6. #10589398C2semidirect
7. #10589166C2semidirect
19. #63814C4semidirect
21. C3×#810C4semidirect
22. C3×#809C4semidirect
25. #63568C4semidirect
36. #4997D3semidirect
106. #810Dic3semidirect
107. #809Dic3semidirect
374. C32#1765semidirect
428. C3#69888semidirect
429. 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×#50022
C3×#49972
C2×#635682
C2×#635552
#105893982
#105891662
#702903
#698883