Finite Group Databasebeta

← #11867014

Subgroups — #11867014

Order 1152.

1133 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 1133 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M16×C3⋊D3C211yesmaximal, characteristic
2#10594925C212yesmaximal
3C2×#63802C211yesmaximal, characteristic, complemented
4C3×#5137C212yesmaximal, complemented
5#10591189C212yesmaximal, complemented
6#10590858C212yesmaximal, complemented
7#10590856C212yesmaximal, complemented
8#10590685C211yesmaximal, characteristic, complemented
9#10590672C212yesmaximal, complemented
10D3×#470—32nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C2×#3797C2212yes—
13C2×C32×M16C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15M16×C3⋊D3—24no—
16C2×#3743C2211yescharacteristic
17C2×#3743C2211yescharacteristic
18C2×C8×C3⋊D3C2211yescharacteristic
19C2×C8×C3⋊D3C2211yescharacteristic
20C3×#924C2214yes—
21C2×C3×Dic12C2212yescomplemented
22#63982—22no—
23#63974—22no—
24#63900C2212yes—
25#63883—22no—
26#63871C2214yes—
27#63865—22no—
28C2×#3718C2212yescomplemented
29#63802—24no—
30C3×#817C2212yescomplemented
31C3×#816C2214yescomplemented
32#63574C2212yescomplemented
33#63565C2214yescomplemented
34C2×D3×Q16—32no—
35C2×D3×M16—32no—
36C2×D3×M16—61no—
37D3×C22⋊Q8—34no—
38C3×#470—32no—
39#5189—32no—
40#5137D312yescomplemented
41#5052—34no—
42#4867—32no—
43D3×#106—32no—
44#4816—34no—
45D3×#103—34no—
46C23×C3⋊D3D411yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3D411yescharacteristic
49C2×C4×C3⋊D3—22no—
50C2×C4×C3⋊D3—22no—
51C2×C4×C3⋊D3D411yescharacteristic
52C2×C4×C3⋊D3D411yescharacteristic
53C2×C4×C3⋊D3C2311yescharacteristic
54C2×C4×C3⋊D3C2311yescharacteristic
55C2×C3×Dic6C2314yes—
56C2×#627—22no—
57C2×#624—22no—
58C2×#624—22no—
59#3797—24no—
60#3797—24no—
61C32×M16—22no—
62C2×C32×C8C2311yescharacteristic
63C2×C32×C8C2311yescharacteristic
64#3748—22no—
65C2×C3⋊(C3⋊C8)C2311yescharacteristic
66C2×C3⋊(C3⋊C8)C2311yescharacteristic
67#3743—22no—
68#3743—22no—
69C8×C3⋊D3—22no—
70C8×C3⋊D3D414yes—
71C3×#217—24no—
72C3×C4⋊Dic3C2314yes—
73C3×Dic3⋊C4—24no—
74C3×Dic12—24no—
75#3724—22no—
76Dic3⋊Dic3—24no—
77#3722—24no—
78#3718—24no—
79C2×#470—91noSylow
80C2×D3×Q8—34no—
81C22×C4×D3—32no—
82C22×C4×D3—61no—
83C2×C3×Q16—32no—
84C2×C3×M16—21no—
85C2×C3×M16C2×D312yes—
86C3×C22⋊Q8—34no—
87#946—34no—
88C2×#216—34no—
89#924C2×D314yes—
90C2×#208—32no—
91C2×#208—61no—
92D3×Q16—68no—
93D3×M16—68no—
94D3×M16—68no—
95C2×Dic12C2×D312yescomplemented
96C2×ΓL(1,𝔽25)—32no—
97C2×ΓL(1,𝔽25)—32no—
98C2×ΓL(1,𝔽25)—61no—
99C2×ΓL(1,𝔽25)—61no—
100C2×D3×C8—32no—
101C2×D3×C8—32no—
102C2×D3×C8—61no—
103C2×D3×C8—61no—
104#897—34no—
105#896—64no—
106D3×C4⋊C4—34no—
107D3×C4⋊C4—64no—
108D3×C22⋊C4—64no—
109#878—64no—
110C3×#106—32no—
111C3×#103—34no—
112#835—34no—
113#817C2×D312yescomplemented
114#816C2×D314yescomplemented
115#810—34no—
116#808—34no—
117C23×C32C2×D411yescharacteristic
118C22×C3⋊D3—22no—
119C22×C3⋊D3—24no—
120C22×C3⋊D3C2×D411yescharacteristic
121C22×C3⋊D3C2×D411yescharacteristic
122C2×C32×C4—21no—
123C2×C32×C4—21no—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2411yescharacteristic
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3C2×D411yescharacteristic
128C2×C3⋊Dic3C2×D411yescharacteristic
129C4×C3⋊D3—22no—
130C4×C3⋊D3—21no—
131C4×C3⋊D3—21no—
132C4×C3⋊D3—22no—
133C4×C3⋊D3C2×D412yes—
134C4×C3⋊D3#4112yes—
135C2×C3×Dic3—24no—
136C2×C3×Dic3—24no—
137C3×Dic6—24no—
138C3×Dic6—24no—
139#627—44no—
140#624—44no—
141#624—44no—
142C32×C8—21no—
143C32×C8C2×D412yes—
144C3⋊(C3⋊C8)—21no—
145C3⋊(C3⋊C8)C2×D412yes—
146C22×Q16—91no—
147C22×M16—91no—
148C2×C22⋊Q8—92no—
149#470—32no—
150#470—92no—
151#470—92no—
152#470—92no—
153C2×#106—91no—
154C2×#103—92no—
155C23×D3—32no—
156C23×D3—61no—
157C2×C3×Q8—34no—
158C22×C3×C4—21no—
159C22×C3×C4C22×D312yes—
160C22×Dic3—32no—
161C22×Dic3—61no—
162D3×Q8—68no—
163D3×Q8—68no—
164C2×C4×D3—32no—
165C2×C4×D3—32no—
166C2×C4×D3—32no—
167C2×C4×D3—32no—
168C2×C4×D3—61no—
169C2×C4×D3—61no—
170C2×C4×D3—61no—
171C2×C4×D3—61no—
172C2×C4×D3—64no—
173C2×C4×D3—64no—
174C2×C4×D3—64no—
175C2×C4×D3—64no—
176C2×C4×D3—64no—
177C2×C4×D3—64no—
178C2×Dic6—64no—
179C2×Dic6C22×D314yes—
180C3×Q16—64no—
181C3×M16—24no—
182C3×M16—24no—
183C2×C3×C8—21no—
184C2×C3×C8—21no—
185C2×C3×C8C22×D312yes—
186C2×C3×C8C22×D312yes—
187C3×C4⋊C4—34no—
188C3×C4⋊C4—64no—
189C3×C22⋊C4—64no—
190#217—24no—
191#216—68no—
192(C2×D3)⋊C4—64no—
193(C2×D3)⋊C4—64no—
194C4⋊Dic3—64no—
195C4⋊Dic3C22×D314yes—
196Dic3⋊C4—24no—
197Dic3⋊C4—64no—
198Dic3⋊C4—64no—
199#208—64no—
200#208—64no—
201C2×C3⋊C8—32no—
202C2×C3⋊C8—32no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—61no—
205Dic12—24no—
206ΓL(1,𝔽25)—64no—
207ΓL(1,𝔽25)—64no—
208ΓL(1,𝔽25)—64no—
209ΓL(1,𝔽25)—64no—
210D3×C8—38no—
211D3×C8—64no—
212D3×C8—64no—
213D3×C8—64no—
214C22×C32—21no—
215C22×C32—22no—
216C22×C32C22×D411yescharacteristic
217C2×C3⋊D3—21no—
218C2×C3⋊D3—22no—
219C2×C3⋊D3—44no—
220C2×C3⋊D3#12112yes—
221C2×C3⋊D3#13714yes—
222C32×C4—21no—
223C32×C4C22×D411yescharacteristic
224C32×C4C2×#4111yescharacteristic
225C3⋊Dic3—21no—
226C3⋊Dic3#12112yes—
227C3×Dic3—44no—
228C3×Dic3—44no—
229C22×Q8—92no—
230C23×C4—91no—
231C2×Q16—32no—
232C2×Q16—92no—
233C2×Q16—184no—
234C2×M16—91no—
235C2×M16—91no—
236C2×M16—91no—
237C2×M16—184no—
238C2×M16D3211yescharacteristic
239C22×C8—91no—
240C22×C8—91no—
241C22⋊Q8—34no—
242C22⋊Q8—94no—
243C22⋊Q8—182no—
244C22⋊Q8—182no—
245C2×C4⋊C4—92no—
246C2×C4⋊C4—182no—
247C2×C22⋊C4—182no—
248#106—32no—
249#106—92no—
250#103—34no—
251#103—94no—
252C23×C3—21no—
253C23×C3D3×D412yes—
254C22×D3—32no—
255C22×D3—32no—
256C22×D3—61no—
257C22×D3—61no—
258C22×D3—64no—
259C22×D3—68no—
260C22×D3—64no—
261C22×D3—124no—
262C3×Q8—64no—
263C3×Q8—64no—
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—64no—
271C2×C3×C4—64no—
272C2×C3×C4D3×D412yes—
273C2×C3×C4C23×D312yes—
274C2×Dic3—24no—
275C2×Dic3—24no—
276C2×Dic3—32no—
277C2×Dic3—32no—
278C2×Dic3—61no—
279C2×Dic3—61no—
280C2×Dic3—64no—
281C2×Dic3—64no—
282C4×D3—34no—
283C4×D3—34no—
284C4×D3—62no—
285C4×D3—62no—
286C4×D3—64no—
287C4×D3—64no—
288C4×D3—62no—
289C4×D3—64no—
290C4×D3—64no—
291C4×D3—62no—
292C4×D3—62no—
293C4×D3—62no—
294C4×D3—128no—
295C4×D3—128no—
296Dic6—24no—
297Dic6—24no—
298Dic6—128no—
299C3×C8—22no—
300C3×C8—22no—
301C3×C8—22no—
302C3×C8D3×D414yes—
303C3⋊C8—34no—
304C3⋊C8—62no—
305C3⋊C8—62no—
306C3⋊C8—62no—
307C2×C32—41no—
308C2×C32C2×#12111yescharacteristic
309C2×C32C2×#13712yes—
310C3⋊D3—41no—
311C3⋊D3#47014yescomplemented
312C24—91no—
313C2×Q8—34no—
314C2×Q8—182no—
315C2×Q8—184no—
316C2×Q8—184no—
317C22×C4—91no—
318C22×C4—91no—
319C22×C4—91no—
320C22×C4—91no—
321C22×C4—91no—
322C22×C4—182no—
323C22×C4—182no—
324C22×C4—182no—
325C22×C4—182no—
326C22×C4C2×D3211yescharacteristic
327Q16—64no—
328Q16—184no—
329M16—22no—
330M16—182no—
331M16—182no—
332M16—182no—
333C2×C8—91no—
334C2×C8—94no—
335C2×C8—91no—
336C2×C8—182no—
337C2×C8C2×D3211yescharacteristic
338C2×C8C2×D3211yescharacteristic
339C4⋊C4—34no—
340C4⋊C4—64no—
341C4⋊C4—182no—
342C4⋊C4—184no—
343C22⋊C4—64no—
344C22⋊C4—184no—
345C22×C3—22no—
346C22×C3—24no—
347C22×C3—22no—
348C22×C3—21no—
349C22×C3—42no—
350C22×C3C2×D3×D412yes—
351C2×D3—38no—
352C2×D3—34no—
353C2×D3—62no—
354C2×D3—64no—
355C2×D3—62no—
356C2×D3—64no—
357C2×D3—62no—
358C2×D3—122no—
359C2×D3—128no—
360C2×D3—128no—
361C3×C4—22no—
362C3×C4—22no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—124no—
366C3×C4—124no—
367C3×C4C2×D3×D412yes—
368C3×C4D3×#4112yes—
369Dic3—34no—
370Dic3—44no—
371Dic3—44no—
372Dic3—62no—
373Dic3—62no—
374Dic3—62no—
375C32C2×#47011yescharacteristic, complemented, Sylow
376C23—91no—
377C23—91no—
378C23—182no—
379C23—184no—
380C23#380211yescharacteristic
381Q8—64no—
382Q8—64no—
383Q8—364no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—64no—
387C2×C4—64no—
388C2×C4—91no—
389C2×C4—92no—
390C2×C4—92no—
391C2×C4—91no—
392C2×C4—182no—
393C2×C4—182no—
394C2×C4—182no—
395C2×C4—181no—
396C2×C4—181no—
397C2×C4—364no—
398C2×C4—364no—
399C2×C4#380211yescharacteristic
400C2×C4C22×D3211yescharacteristic
401C8—21no—
402C8—92no—
403C8—181no—
404C8#381112yes—
405C2×C3—21no—
406C2×C3—22no—
407C2×C3—42no—
408C2×C3—42no—
409C2×C3D3×#12112yes—
410C2×C3D3×#13714yes—
411D3—38no—
412D3—64no—
413D3—122no—
414D3—122no—
415C22—21no—
416C22—22no—
417C22—92no—
418C22—94no—
419C22—181no—
420C22—182no—
421C22—364no—
422C22C2×#380211yescharacteristic
423C4—21no—
424C4—92no—
425C4—124no—
426C4—124no—
427C4—181no—
428C4#6430611yescharacteristic
429C4C2×#381111yescharacteristic
430C3—21no—
431C3D3×#47012yescomplemented
432C2—41no—
433C2—94no—
434C2—361no—
435C2#1059471712yes—
436C2#1059508111yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC23×C3⋊D3D4
hypercenterC2×M16D32
hypocenterC32C2×#470
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C2×#63802C2semidirect
4. C3×#5137C2semidirect
5. #10591189C2semidirect
6. #10590858C2semidirect
7. #10590856C2semidirect
8. #10590685C2semidirect
9. #10590672C2semidirect
21. C2×C3×Dic12C22semidirect
28. C2×#3718C22semidirect
30. C3×#817C22semidirect
31. C3×#816C22semidirect
32. #63574C22semidirect
33. #63565C22semidirect
40. #5137D3semidirect
95. C2×Dic12C2×D3semidirect
113. #817C2×D3semidirect
114. #816C2×D3semidirect
311. C3⋊D3#470semidirect
375. C32C2×#470semidirect
431. C3D3×#470semidirect

Maximal subgroups

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

subgroupindex
C2×M16×C3⋊D32
#105949252
C2×#638022
C3×#51372
#105911892
#105908582
#105908562
#105906852
#105906722
D3×#4703