Finite Group Databasebeta

← #11784132

Subgroups — #11784132

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×C3×#907C211yesmaximal, characteristic
2C2×#63568C211yesmaximal, characteristic
3#10591084C211yesmaximal, characteristic
4C2×#63555C211yesmaximal, characteristic, complemented
5#10591059C211yesmaximal, characteristic, complemented
6#10589421C211yesmaximal, characteristic, complemented
7C3×#4558C211yesmaximal, characteristic, complemented
8#72009—31nomaximal
9#68927—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C22×C3×C3⋊C8C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C3×#907—22no—
18C3×#907C414yescomplemented
19C2×C3×ΓL(1,𝔽25)—21no—
20C2×C3×D3×C8—21no—
21#63568C414yescomplemented
22#63566C412yescomplemented
23#63563C412yescomplemented
24#63555—21no—
25#63555—22no—
26#63553—21no—
27C2×C3×#131—31no—
28C2×#907D311yescharacteristic
29C2×#837—31no—
30#5233—31no—
31C2×#825—31no—
32#5122—31no—
33#5113—31no—
34#5101—31no—
35C2×#815—31no—
36C2×#815—31no—
37C3×#341—31no—
38#4558D311yescharacteristic, complemented
39#4555—31no—
40#4555—31no—
41#4555—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×M16—21no—
53C32×M16C2×C412yes—
54C2×C32×C8—21no—
55#3757—21no—
56C4⋊(C3⋊Dic3)C2×C412yes—
57C4×C3⋊Dic3—21no—
58C4×C3⋊Dic3—21no—
59C4×C3⋊Dic3C2×C412yes—
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⋊C8D411yescharacteristic
68C2×C3×C3⋊C8D411yescharacteristic
69C2×C3×C3⋊C8D412yes—
70C3×ΓL(1,𝔽25)—24no—
71C3×D3×C8—24no—
72#1765—91noSylow
73C2×C3×#41—31no—
74C2×#235C2×D311yescharacteristic
75C3×#131—34no—
76C3×#131—62no—
77C2×C3×M16—21no—
78C2×C3×M16—31no—
79C2×C3×M16—61no—
80C2×C3×M16C2×D311yescharacteristic
81C2×C3×M16C2×D311yescharacteristic
82C22×C3×C8—31no—
83C22×C3×C8—31no—
84C22×C3×C8—61no—
85#926—31no—
86#926—31no—
87#926—61no—
88C2×C4×Dic3—31no—
89C2×C4×Dic3—31no—
90C2×C4×Dic3—61no—
91C2×#208C2×D311yescharacteristic
92C22×C3⋊C8C2×D311yescharacteristic
93C22×C3⋊C8C2×D311yescharacteristic
94#907—22no—
95#907Dic314yescomplemented
96C2×ΓL(1,𝔽25)—21no—
97C2×D3×C8—21no—
98#837—34no—
99#835—32no—
100#832—32no—
101#825—34no—
102#821—32no—
103#816—32no—
104#815—62no—
105#815—61no—
106#815—61no—
107#815—62no—
108C8×Dic3—61no—
109C8×Dic3—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
118C2×C3⋊Dic3—22no—
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—
130C32×C8—22no—
131C3×C3⋊C8—22no—
132C3×C3⋊C8—22no—
133C3×C3⋊C8C22⋊C412yes—
134C3×C3⋊C8C22⋊C412yes—
135C2×#131—31no—
136C2×#104—91no—
137#416—91no—
138#405—91no—
139C2×#97—91no—
140#341—31no—
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#235C2×Dic312yes—
161C2×D12C4×D311yescharacteristic
162C2×C4×D3—21no—
163C2×Dic6C4×D311yescharacteristic
164C3×M16—21no—
165C3×M16—21no—
166C3×M16—22no—
167C3×M16—32no—
168C3×M16—41no—
169C3×M16—64no—
170C3×M16—61no—
171C3×M16C4×D312yes—
172C3×M16C2×Dic312yes—
173C2×C3×C8—21no—
174C2×C3×C8—21no—
175C2×C3×C8—32no—
176C2×C3×C8—31no—
177C2×C3×C8—31no—
178C2×C3×C8—32no—
179C2×C3×C8—32no—
180C2×C3×C8—41no—
181C2×C3×C8—64no—
182C2×C3×C8—61no—
183C2×C3×C8—61no—
184C2×C3×C8—61no—
185#217—61no—
186#217—61no—
187#217—121no—
188C4⋊Dic3—32no—
189C4⋊Dic3—32no—
190C4⋊Dic3—62no—
191C4×Dic3—32no—
192C4×Dic3—32no—
193C4×Dic3—62no—
194C4×Dic3—61no—
195C4×Dic3—61no—
196C4×Dic3—61no—
197C4×Dic3—61no—
198C4×Dic3—121no—
199C4×Dic3—121no—
200#208—21no—
201#208C4×D312yes—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—21no—
204C2×C3⋊C8—21no—
205C2×C3⋊C8C4×D312yes—
206C2×C3⋊C8C2×Dic312yes—
207C2×C3⋊C8#6711yescharacteristic
208C2×C3⋊C8#6711yescharacteristic
209C2×C3⋊C8#6712yes—
210ΓL(1,𝔽25)—24no—
211D3×C8—24no—
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—42no—
223C3⋊Dic3—42no—
224C3×Dic3—22no—
225C2×#41—31no—
226#131—34no—
227#131—62no—
228C2×M16—31no—
229C2×M16—61no—
230C2×M16D3211yescharacteristic
231C22×C8—31no—
232C22×C8—31no—
233C22×C8—61no—
234#117—91no—
235C2×C42—91no—
236#104—94no—
237#103—92no—
238#102—92no—
239#97—182no—
240#97—181no—
241C4×C8—181no—
242C23×C3—21no—
243C23×C3—61no—
244C23×C3#23511yescharacteristic
245C23×C3#23911yescharacteristic
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×C4C2×C4×D311yescharacteristic
263C2×C3×C4C2×C4×D311yescharacteristic
264C2×C3×C4C2×C4×D311yescharacteristic
265C2×C3×C4C2×C4×D311yescharacteristic
266C2×C3×C4C2×C4×D311yescharacteristic
267C2×C3×C4#23511yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4#23711yescharacteristic
271C2×C3×C4C22×Dic311yescharacteristic
272C2×C3×C4C2×#6711yescharacteristic
273C2×C3×C4C2×#6711yescharacteristic
274#67—22no—
275#67—22no—
276C2×Dic3—21no—
277C2×Dic3—62no—
278C2×Dic3—62no—
279C2×Dic3—62no—
280C2×Dic3—62no—
281C2×Dic3—122no—
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—22no—
293C3×C8—22no—
294C3×C8—32no—
295C3×C8—32no—
296C3×C8—42no—
297C3×C8—62no—
298C3×C8—62no—
299C3⋊C8—22no—
300C3⋊C8—22no—
301C3⋊C8#21712yes—
302C3⋊C8#21712yes—
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—21no—
319M16—32no—
320M16—64no—
321M16—61no—
322M16D3×Dic312yes—
323C2×C8—21no—
324C2×C8—32no—
325C2×C8—32no—
326C2×C8—31no—
327C2×C8—31no—
328C2×C8—32no—
329C2×C8—64no—
330C2×C8—61no—
331C2×C8—61no—
332C2×C8—61no—
333C4⋊C4—92no—
334C22⋊C4—181no—
335C42—92no—
336C42—181no—
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#89211yescharacteristic
347C22×C3#89311yescharacteristic
348C22×C3#89311yescharacteristic
349C22×C3#92611yescharacteristic
350C22×C3C4×#6711yescharacteristic
351C22×C3C4×#6711yescharacteristic
352C2×D3—22no—
353C2×D3—42no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—62no—
359C3×C4C42×D311yescharacteristic
360C3×C4D3×C22⋊C411yescharacteristic
361C3×C4#67⋊C411yescharacteristic
362C3×C4#67⋊C411yescharacteristic
363C3×C4C2×C4×Dic311yescharacteristic
364C3×C4C4×#6711yescharacteristic
365C3×C4C4×#6711yescharacteristic
366C3×C4C2×#21711yescharacteristic
367Dic3—22no—
368Dic3—122no—
369Dic3—122no—
370Dic3—124no—
371Dic3—122no—
372Dic3—122no—
373Dic3—242no—
374C32#176511yescharacteristic, complemented, Sylow
375C23—61no—
376C23#379911yescharacteristic
377Q8—32no—
378Q8—61no—
379D4—32no—
380D4—62no—
381D4—62no—
382D4—61no—
383C2×C4—61no—
384C2×C4—62no—
385C2×C4—62no—
386C2×C4—182no—
387C2×C4—182no—
388C2×C4—362no—
389C2×C4#379511yescharacteristic
390C2×C4C4×D3211yescharacteristic
391C2×C4C4×D3211yescharacteristic
392C2×C4C2×D3×Dic311yescharacteristic
393C2×C4D3×#6711yescharacteristic
394C2×C4D3×#6711yescharacteristic
395C8—22no—
396C8—32no—
397C8—32no—
398C8—62no—
399C8—62no—
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×C3#466611yescharacteristic
410C2×C3#489412yes—
411C2×C3#514512yes—
412C2×C3C4×#21711yescharacteristic
413D3—42no—
414C22—22no—
415C22—62no—
416C22—122no—
417C22#6384111yescharacteristic
418C22#6390411yescharacteristic
419C22#6390411yescharacteristic
420C4—62no—
421C4—362no—
422C4—362no—
423C4C4×D3×Dic311yescharacteristic
424C4#6387911yescharacteristic
425C4#6387911yescharacteristic
426C4D3×#21711yescharacteristic
427C3—21no—
428C3#6892711yescharacteristic, complemented
429C3#7200911yescharacteristic, complemented
430C2—21no—
431C2—21no—
432C2—122no—
433C2#1059099412yes—
434C2#1059123711yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C4×D4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1765
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. C2×#63555C2semidirect
5. #10591059C2semidirect
6. #10589421C2semidirect
7. C3×#4558C2semidirect
18. C3×#907C4semidirect
21. #63568C4semidirect
22. #63566C4semidirect
23. #63563C4semidirect
38. #4558D3semidirect
95. #907Dic3semidirect
374. C32#1765semidirect
428. C3#68927semidirect
429. C3#72009semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9072
C2×#635682
#105910842
C2×#635552
#105910592
#105894212
C3×#45582
#720093
#689273