Finite Group Databasebeta

← #11784139

Subgroups — #11784139

Order 1152.

657 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#901C211yesmaximal, characteristic
2C2×#63642C211yesmaximal, characteristic, complemented
3C3×#5101C211yesmaximal, characteristic, complemented
4C2×#63568C211yesmaximal, characteristic
5#10591083C211yesmaximal, characteristic
6#10589165C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#72009—31nomaximal
9#69888—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#901—22no—
18C3×#901C414yescomplemented
19C2×C3×ΓL(1,𝔽25)—21no—
20C2×C3×D3×C8—21no—
21#63642—22no—
22C3×#815—21no—
23C3×C8×Dic3—21no—
24#63568C414yescomplemented
25#63565C412yescomplemented
26#63562C412yescomplemented
27C2×C3×#131—31no—
28C2×#901D311yescharacteristic
29C3×#405—31no—
30C2×#837—31no—
31#5233—31no—
32C2×#825—31no—
33#5101D311yescharacteristic, complemented
34C2×#815—31no—
35C2×#815—31no—
36C2×#815—61no—
37#5002—31no—
38#4558—31no—
39#4558—31no—
40#4555—31no—
41#4532—31no—
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
52C2×C32×C8C2×C412yes—
53C2×C32×C8D412yes—
54C2×C32×C8D411yescharacteristic
55C2×C32×C8D411yescharacteristic
56C4×C3⋊Dic3—21no—
57C4×C3⋊Dic3C2×C412yes—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)C2×C412yes—
61C3×#217—21no—
62C3×C4⋊Dic3C2×C412yes—
63C3×C4×Dic3—21no—
64C3×#208—21no—
65C3×#208—21no—
66C3×#208C2×C412yes—
67C3×#208C2×C412yes—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
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—31no—
78C2×C3×M16—31no—
79C2×C3×M16—61no—
80C22×C3×C8—21no—
81C22×C3×C8—61no—
82C22×C3×C8C2×D311yescharacteristic
83C22×C3×C8C2×D311yescharacteristic
84C3×#117—31no—
85#926C2×D311yescharacteristic
86C2×C4×Dic3—31no—
87C2×C4×Dic3—31no—
88C2×C4×Dic3—61no—
89C2×#208C2×D311yescharacteristic
90C2×#208C2×D311yescharacteristic
91C22×C3⋊C8—31no—
92C22×C3⋊C8—31no—
93C22×C3⋊C8—61no—
94#901—22no—
95#901Dic314yescomplemented
96C2×ΓL(1,𝔽25)—21no—
97C2×D3×C8—21no—
98C3×#97—61no—
99C3×C4×C8—61no—
100#837—34no—
101#835—32no—
102#832—32no—
103#825—34no—
104#815—21no—
105#815—64no—
106#815—62no—
107#815—62no—
108C8×Dic3—21no—
109#810—32no—
110#809—32no—
111C23×C32#4111yescharacteristic
112C22×C3×D3—21no—
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—
124C2×C3×Dic3—22no—
125C3×D12—21no—
126C3×D12C4212yes—
127C3×C4×D3—22no—
128C3×C4×D3—22no—
129C3×Dic6—21no—
130C3×Dic6C4212yes—
131C32×C8C22⋊C412yes—
132C32×C8C22⋊C412yes—
133C3⋊(C3⋊C8)—22no—
134C3×C3⋊C8—22no—
135C3×C3⋊C8—22no—
136C2×#131—31no—
137C2×#104—91no—
138#416—91no—
139#405—31no—
140C2×#97—91no—
141#341—91no—
142#339—91no—
143C3×#41—32no—
144C3×#41—32no—
145C3×#41—61no—
146C3×#41—61no—
147C2×C3×Q8—31no—
148C2×C3×D4—31no—
149C2×C3×D4—61no—
150C22×C3×C4—21no—
151C22×C3×C4—61no—
152C22×C3×C4C22×D311yescharacteristic
153C22×C3×C4C22×D311yescharacteristic
154C2×#67—21no—
155C22×Dic3—62no—
156C22×Dic3—61no—
157C22×Dic3—61no—
158#235—21no—
159#235—21no—
160#235C4×D312yes—
161#235C2×Dic312yes—
162C2×D12C4×D311yescharacteristic
163C2×C4×D3—21no—
164C2×Dic6C4×D311yescharacteristic
165C3×M16—32no—
166C3×M16—32no—
167C3×M16—61no—
168C3×M16—61no—
169C3×M16—64no—
170C2×C3×C8—22no—
171C2×C3×C8—21no—
172C2×C3×C8—21no—
173C2×C3×C8—22no—
174C2×C3×C8—61no—
175C2×C3×C8—61no—
176C2×C3×C8—64no—
177C2×C3×C8C4×D312yes—
178C2×C3×C8D1212yes—
179C2×C3×C8C2×Dic312yes—
180C2×C3×C8#6711yescharacteristic
181C2×C3×C8#6711yescharacteristic
182C2×C3×C8#6711yescharacteristic
183C2×C3×C8#6711yescharacteristic
184C2×C3×C8#6712yes—
185C3×C4⋊C4—32no—
186C3×C22⋊C4—61no—
187C3×C42—61no—
188#217—21no—
189C4⋊Dic3C4×D312yes—
190C4×Dic3—21no—
191C4×Dic3—32no—
192C4×Dic3—32no—
193C4×Dic3—62no—
194C4×Dic3—62no—
195C4×Dic3—61no—
196C4×Dic3—61no—
197#208—21no—
198#208—21no—
199#208C4×D312yes—
200#208C2×Dic312yes—
201C2×C3⋊C8—21no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—32no—
204C2×C3⋊C8—32no—
205C2×C3⋊C8—62no—
206C2×C3⋊C8—62no—
207C2×C3⋊C8—62no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—61no—
210C2×C3⋊C8—61no—
211C2×C3⋊C8—61no—
212ΓL(1,𝔽25)—24no—
213D3×C8—24no—
214C22×C32—22no—
215C22×C32#11711yescharacteristic
216C22×C32C4×D411yescharacteristic
217C22×C32C4×D411yescharacteristic
218C2×C3×D3—22no—
219C2×C3×D3—42no—
220C32×C4C2×C4211yescharacteristic
221C32×C4C2×C22⋊C411yescharacteristic
222C32×C4C4×D411yescharacteristic
223C32×C4C4×D411yescharacteristic
224C3⋊Dic3—42no—
225C3×Dic3—22no—
226C3×Dic3—42no—
227C2×#41—31no—
228#131—34no—
229#131—62no—
230C2×M16—31no—
231C2×M16—31no—
232C2×M16—61no—
233C22×C8—61no—
234C22×C8—91no—
235C22×C8D3211yescharacteristic
236#117—31no—
237C2×C42—91no—
238#104—94no—
239#103—92no—
240#102—92no—
241#97—61no—
242#97—182no—
243C4×C8—61no—
244C23×C3—21no—
245C23×C3—61no—
246C23×C3#23511yescharacteristic
247C23×C3#23511yescharacteristic
248C22×D3—21no—
249C3×Q8—32no—
250C3×Q8—61no—
251C3×D4—32no—
252C3×D4—62no—
253C3×D4—62no—
254C3×D4—61no—
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—61no—
262C2×C3×C4—62no—
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×C4#23511yescharacteristic
273C2×C3×C4C22×Dic311yescharacteristic
274C2×C3×C4C2×#6711yescharacteristic
275C2×C3×C4C2×#6711yescharacteristic
276C2×C3×C4C2×#6711yescharacteristic
277#67—22no—
278#67—22no—
279C2×Dic3—21no—
280C2×Dic3—22no—
281C2×Dic3—64no—
282C2×Dic3—62no—
283C2×Dic3—62no—
284C2×Dic3—124no—
285C2×Dic3—122no—
286C2×Dic3—122no—
287D12—21no—
288D12C4×Dic312yes—
289C4×D3—22no—
290C4×D3—22no—
291Dic6—21no—
292Dic6C4×Dic312yes—
293C3×C8—22no—
294C3×C8—22no—
295C3×C8—62no—
296C3×C8—62no—
297C3×C8(C2×D3)⋊C412yes—
298C3×C8(C2×D3)⋊C412yes—
299C3×C8#21712yes—
300C3×C8#21712yes—
301C3⋊C8—22no—
302C3⋊C8—22no—
303C3⋊C8—64no—
304C3⋊C8—62no—
305C3⋊C8—62no—
306C2×C32—21no—
307C2×C32—21no—
308C2×C32C4×C22⋊C411yescharacteristic
309C2×C32#44412yes—
310C3×D3—42no—
311#41—32no—
312#41—32no—
313#41—61no—
314#41—61no—
315C2×Q8—31no—
316C2×D4—31no—
317C2×D4—61no—
318C22×C4—61no—
319C22×C4—181no—
320C22×C4C2×D3211yescharacteristic
321M16—32no—
322M16—32no—
323M16—61no—
324M16—61no—
325M16—64no—
326C2×C8—61no—
327C2×C8—61no—
328C2×C8—64no—
329C2×C8—92no—
330C2×C8—181no—
331C2×C8—181no—
332C2×C8D3×Dic312yes—
333C2×C8#62511yescharacteristic
334C2×C8#62511yescharacteristic
335C2×C8#62612yes—
336C4⋊C4—32no—
337C22⋊C4—61no—
338C42—61no—
339C42—92no—
340C42—181no—
341C22×C3—24no—
342C22×C3—22no—
343C22×C3—22no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—62no—
348C22×C3—122no—
349C22×C3#87211yescharacteristic
350C22×C3C4×D1211yescharacteristic
351C22×C3#92611yescharacteristic
352C22×C3C4×#6711yescharacteristic
353C22×C3C4×#6711yescharacteristic
354C22×C3C4×#6711yescharacteristic
355C2×D3—22no—
356C2×D3—42no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—62no—
362C3×C4—122no—
363C3×C4C42×D311yescharacteristic
364C3×C4C4×D1211yescharacteristic
365C3×C4C2×C4×Dic311yescharacteristic
366C3×C4C2×(C2×D3)⋊C411yescharacteristic
367C3×C4C4×#6711yescharacteristic
368C3×C4C4×#6711yescharacteristic
369C3×C4C4×#6711yescharacteristic
370C3×C4C2×#21711yescharacteristic
371Dic3—22no—
372Dic3—42no—
373Dic3—124no—
374Dic3—122no—
375Dic3—122no—
376C32#176511yescharacteristic, complemented, Sylow
377C23—61no—
378C23#379811yescharacteristic
379Q8—32no—
380Q8—61no—
381D4—32no—
382D4—62no—
383D4—62no—
384D4—61no—
385C2×C4—61no—
386C2×C4—62no—
387C2×C4—62no—
388C2×C4—62no—
389C2×C4—182no—
390C2×C4—362no—
391C2×C4#379811yescharacteristic
392C2×C4C4×D3211yescharacteristic
393C2×C4C4×D3211yescharacteristic
394C2×C4C2×D3×Dic311yescharacteristic
395C2×C4C2×#62511yescharacteristic
396C2×C4C2×#62611yescharacteristic
397C8—62no—
398C8—62no—
399C8—182no—
400C8(C2×D3)⋊Dic312yes—
401C8(C2×D3)⋊Dic312yes—
402C2×C3—22no—
403C2×C3—22no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—22no—
410C2×C3—122no—
411C2×C3C4×(C2×D3)⋊C411yescharacteristic
412C2×C3#514512yes—
413C2×C3#514512yes—
414C2×C3C4×#21711yescharacteristic
415D3—42no—
416C22—22no—
417C22—62no—
418C22—122no—
419C22#6385511yescharacteristic
420C22C4×#62511yescharacteristic
421C22C4×#62611yescharacteristic
422C4—62no—
423C4—122no—
424C4—362no—
425C4C4×D3×Dic311yescharacteristic
426C4C4×#62511yescharacteristic
427C4C4×#62611yescharacteristic
428C4C2×(C2×D3)⋊Dic311yescharacteristic
429C3—21no—
430C3#6988811yescharacteristic, complemented
431C3#7200911yescharacteristic, complemented
432C2—21no—
433C2—21no—
434C2—122no—
435C2#1059092212yes—
436C2C4×(C2×D3)⋊Dic311yescharacteristic
subgroupG/H
centerC2×C4C2×#625
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×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63642C2semidirect
3. C3×#5101C2semidirect
6. #10589165C2semidirect
7. #10589160C2semidirect
18. C3×#901C4semidirect
24. #63568C4semidirect
25. #63565C4semidirect
26. #63562C4semidirect
33. #5101D3semidirect
95. #901Dic3semidirect
376. C32#1765semidirect
430. C3#69888semidirect
431. C3#72009semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9012
C2×#636422
C3×#51012
C2×#635682
#105910832
#105891652
#105891602
#720093
#698883