Finite Group Databasebeta

← #11792396

Subgroups — #11792396

Order 1152.

1182 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 179 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
1C32×#525C211yesmaximal, characteristic, complemented
2#10596293C211yesmaximal, characteristic, complemented
3#10596262C211yesmaximal, characteristic, complemented
4#10592935C211yesmaximal, characteristic, complemented
5#10592906C211yesmaximal, characteristic, complemented
6#10592704C211yesmaximal, characteristic, complemented
7#10589397C211yesmaximal, characteristic, complemented
8#71715—34nomaximal
9C2×C32×#41C2211yescharacteristic
10C23×C32×C4C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12C32×#123—21no—
13C32×C22⋊Q8—21no—
14C32×#121—21no—
15C32×#120—21no—
16C32×C4×D4—22no—
17C32×#117C2211yescharacteristic
18#64162—21no—
19#64160—21no—
20#64159—22no—
21#64158—21no—
22#64151—21no—
23#64141—21no—
24#64139—21no—
25#64138—21no—
26C4×#638—22no—
27#64135C2211yescharacteristic
28#64133—21no—
29C2×#3748C2211yescharacteristic
30C2×#3748C2211yescharacteristic
31#63664—22no—
32#63657—22no—
33#63632—22no—
34C3×#525D314yescomplemented
35#5822—34no—
36#5791—34no—
37#5236—34no—
38#5207—34no—
39#5005—34no—
40#4531—34no—
41C24×C32D411yescharacteristic
42C32×#41—21no—
43C32×#41—21no—
44C32×#41—21no—
45C32×#41—21no—
46C2×C32×Q8D411yescharacteristic, complemented
47C2×C32×D4—22no—
48C2×C32×D4—21no—
49C2×C32×D4D411yescharacteristic, complemented
50C22×C32×C4—21no—
51C22×C32×C4—21no—
52C22×C32×C4—21no—
53C22×C32×C4—21no—
54C22×C32×C4—21no—
55C22×C32×C4—21no—
56C22×C32×C4—21no—
57C22×C32×C4D411yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C2×#638—22no—
60C2×#638—21no—
61#3828—21no—
62#3828—21no—
63#3828—21no—
64#3828—21no—
65C2×C4⋊(C3⋊D3)D411yescharacteristic, complemented
66C2×C4×C3⋊D3—21no—
67C2×#634D411yescharacteristic, complemented
68C32×C4⋊C4—22no—
69C32×C4⋊C4—21no—
70C32×C22⋊C4—22no—
71C32×C22⋊C4—22no—
72C32×C22⋊C4—21no—
73C32×C42D412yescomplemented
74#3757—22no—
75#3757—21no—
76#3756—22no—
77#3755—22no—
78#3754—22no—
79#3753—22no—
80#3752—22no—
81C4⋊(C3⋊Dic3)—21no—
82#3750—22no—
83C4×C3⋊Dic3D412yescomplemented
84#3748—21no—
85#3748—21no—
86#3748—21no—
87#3748—21no—
88C2×C3⋊(C3⋊C8)—21no—
89C2×C3⋊(C3⋊C8)D412yescomplemented
90#2010—91noSylow
91C2×C3×#41C2×D314yes—
92C23×C3×C4C2×D314yes—
93C2×#235—34no—
94C3×#123—24no—
95C3×C22⋊Q8—24no—
96C3×#121—24no—
97C3×#120—24no—
98C3×C4×D4—28no—
99C3×#117C2×D314yes—
100#953—64no—
101#951—64no—
102#950—68no—
103#949—64no—
104#942—64no—
105#932—64no—
106#930—64no—
107#929—64no—
108C4×#67—68no—
109#926—34no—
110#924—64no—
111C2×#208—34no—
112C2×#208—34no—
113#837—68no—
114#830—68no—
115#805—68no—
116C23×C32—21no—
117C23×C32—21no—
118C23×C32—21no—
119C23×C32—21no—
120C23×C32—42no—
121C23×C32C2×D411yescharacteristic
122C22×C3⋊D3—21no—
123C32×Q8—21no—
124C32×Q8—21no—
125C32×D4—21no—
126C32×D4—21no—
127C32×D4—44no—
128C32×D4—41no—
129C32×D4—41no—
130C2×C32×C4—21no—
131C2×C32×C4—22no—
132C2×C32×C4—21no—
133C2×C32×C4—21no—
134C2×C32×C4—21no—
135C2×C32×C4—41no—
136C2×C32×C4—41no—
137C2×C32×C4—41no—
138C2×C32×C4—41no—
139C2×C32×C4—41no—
140C2×C32×C4—41no—
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4#4111yescharacteristic
147#638—44no—
148#638—41no—
149#638—41no—
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—21no—
152C4⋊(C3⋊D3)—21no—
153C4⋊(C3⋊D3)—21no—
154C4×C3⋊D3—41no—
155C4×C3⋊D3—41no—
156#634—21no—
157#634—21no—
158C3⋊(C3⋊C8)—22no—
159C3⋊(C3⋊C8)—41no—
160#575—91no—
161#525—91no—
162#525C3⋊D311yescharacteristic, complemented
163#421—91no—
164#421—91no—
165#407—91no—
166H(3,ℤ/4)—91no—
167C24×C3#6714yes—
168C3×#41—24no—
169C3×#41—24no—
170C3×#41—24no—
171C3×#41—24no—
172C2×C3×Q8#6714yescomplemented
173C2×C3×D4—28no—
174C2×C3×D4—24no—
175C2×C3×D4#6714yescomplemented
176C22×C3×C4—24no—
177C22×C3×C4—24no—
178C22×C3×C4—24no—
179C22×C3×C4—24no—
180C22×C3×C4—24no—
181C22×C3×C4—24no—
182C22×C3×C4—24no—
183C22×C3×C4#6714yes—
184C22×C3×C4C22×D314yes—
185C2×#67—68no—
186C2×#67—64no—
187#235—64no—
188#235—64no—
189#235—64no—
190#235—64no—
191C2×D12—34no—
192C2×C4×D3—64no—
193C2×Dic6—34no—
194C3×C4⋊C4—28no—
195C3×C4⋊C4—24no—
196C3×C22⋊C4—28no—
197C3×C22⋊C4—28no—
198C3×C22⋊C4—24no—
199C3×C42#6718yescomplemented
200#217—68no—
201#217—64no—
202#216—68no—
203#215—68no—
204#214—68no—
205#213—68no—
206(C2×D3)⋊C4—68no—
207C4⋊Dic3—64no—
208Dic3⋊C4—68no—
209C4×Dic3—38no—
210#208—64no—
211#208—64no—
212#208—64no—
213#208—64no—
214C2×C3⋊C8—38no—
215C2×C3⋊C8—64no—
216C22×C32—22no—
217C22×C32—22no—
218C22×C32—22no—
219C22×C32—41no—
220C22×C32—41no—
221C22×C32—41no—
222C22×C32—41no—
223C22×C32—42no—
224C22×C32—41no—
225C22×C32—41no—
226C22×C32#12011yescharacteristic
227C22×C32#12011yescharacteristic
228C22×C32#12111yescharacteristic
229C2×C3⋊D3—42no—
230C2×C3⋊D3—41no—
231C32×C4—42no—
232C32×C4—41no—
233C32×C4—41no—
234C32×C4#12011yescharacteristic
235C32×C4#12111yescharacteristic
236C32×C4#12111yescharacteristic
237C32×C4#12711yescharacteristic
238C3⋊Dic3—42no—
239C3⋊Dic3—41no—
240C2×#41—91no—
241C2×#41C2×C3⋊D311yescharacteristic
242C23×C4C2×C3⋊D311yescharacteristic
243#137—181no—
244#137—181no—
245AGL(1,ℤ/8)—181no—
246AGL(1,ℤ/8)—181no—
247#135—182no—
248C2×M16—91no—
249C2×M16—91no—
250#123—21no—
251#123—181no—
252C22⋊Q8—21no—
253C22⋊Q8—181no—
254#121—21no—
255#121—181no—
256#120—21no—
257#120—181no—
258C4×D4—22no—
259C4×D4—182no—
260#117—91no—
261#117C2×C3⋊D311yescharacteristic
262#104—182no—
263#104—182no—
264C22⋊C8—182no—
265C23×C3—24no—
266C23×C3—24no—
267C23×C3—24no—
268C23×C3—24no—
269C23×C3—48no—
270C23×C3C2×#6714yes—
271C22×D3—64no—
272C3×Q8—24no—
273C3×Q8—24no—
274C3×D4—24no—
275C3×D4—24no—
276C3×D4—416no—
277C3×D4—44no—
278C3×D4—44no—
279C2×C3×C4—24no—
280C2×C3×C4—24no—
281C2×C3×C4—28no—
282C2×C3×C4—24no—
283C2×C3×C4—24no—
284C2×C3×C4—44no—
285C2×C3×C4—44no—
286C2×C3×C4—44no—
287C2×C3×C4—44no—
288C2×C3×C4—44no—
289C2×C3×C4—44no—
290C2×C3×C4D3×D414yes—
291C2×C3×C4D3×D414yes—
292C2×C3×C4D3×D414yes—
293C2×C3×C4#23714yes—
294C2×C3×C4C2×#6714yes—
295C2×C3×C4C2×#6714yes—
296#67—1216no—
297#67—124no—
298#67—124no—
299C2×Dic3—68no—
300C2×Dic3—64no—
301D12—64no—
302D12—64no—
303C4×D3—124no—
304C4×D3—124no—
305Dic6—64no—
306Dic6—64no—
307C3⋊C8—68no—
308C3⋊C8—124no—
309C2×C32—21no—
310C2×C32—21no—
311C2×C32—21no—
312C2×C32—42no—
313C2×C32—81no—
314C2×C32#39211yescharacteristic
315C3⋊D3—81no—
316C24#63811yescharacteristic
317#41—21no—
318#41—21no—
319#41—21no—
320#41—21no—
321#41—181no—
322#41—181no—
323#41—181no—
324#41—181no—
325C2×Q8—91no—
326C2×Q8#63811yescharacteristic, complemented
327C2×D4—22no—
328C2×D4—21no—
329C2×D4—91no—
330C2×D4—182no—
331C2×D4—181no—
332C2×D4#63811yescharacteristic, complemented
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—181no—
341C22×C4#63811yescharacteristic
342C22×C4C22×C3⋊D311yescharacteristic
343Q16—182no—
344SD16—182no—
345SD16—182no—
346D8—182no—
347M16—181no—
348M16—181no—
349M16—181no—
350M16—181no—
351C2×C8—92no—
352C2×C8—181no—
353C4⋊C4—22no—
354C4⋊C4—21no—
355C4⋊C4—182no—
356C4⋊C4—181no—
357C22⋊C4—22no—
358C22⋊C4—22no—
359C22⋊C4—21no—
360C22⋊C4—182no—
361C22⋊C4—182no—
362C22⋊C4—181no—
363C42—92no—
364C42#63812yescomplemented
365C22×C3—28no—
366C22×C3—28no—
367C22×C3—28no—
368C22×C3—44no—
369C22×C3—44no—
370C22×C3—44no—
371C22×C3—44no—
372C22×C3—48no—
373C22×C3—44no—
374C22×C3—44no—
375C22×C3#93714yes—
376C22×C3#93914yes—
377C22×C3#95314yes—
378C2×D3—128no—
379C2×D3—124no—
380C3×C4—48no—
381C3×C4—44no—
382C3×C4—44no—
383C3×C4#93714yes—
384C3×C4#93814yes—
385C3×C4#93914yes—
386C3×C4#94014yes—
387Dic3—128no—
388Dic3—124no—
389C32#201011yescharacteristic, complemented, Sylow
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—42no—
395C23—181no—
396C23C2×#63811yescharacteristic
397Q8—21no—
398Q8—21no—
399Q8—181no—
400Q8—181no—
401D4—21no—
402D4—21no—
403D4—44no—
404D4—41no—
405D4—41no—
406D4—181no—
407D4—181no—
408D4—364no—
409D4—361no—
410D4—361no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—22no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—182no—
423C2×C4—181no—
424C2×C4—361no—
425C2×C4—361no—
426C2×C4D4×C3⋊D311yescharacteristic
427C2×C4D4×C3⋊D311yescharacteristic
428C2×C4D4×C3⋊D311yescharacteristic
429C2×C4#383011yescharacteristic
430C2×C4C2×#63811yescharacteristic
431C2×C4C2×#63811yescharacteristic
432C8—182no—
433C8—361no—
434C2×C3—24no—
435C2×C3—24no—
436C2×C3—24no—
437C2×C3—48no—
438C2×C3—84no—
439C2×C3#522314yes—
440D3—244no—
441C22—22no—
442C22—22no—
443C22—22no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—42no—
449C22—41no—
450C22—41no—
451C22—362no—
452C22—361no—
453C22#6414611yescharacteristic
454C22#6414811yescharacteristic
455C22#6416211yescharacteristic
456C4—42no—
457C4—41no—
458C4—41no—
459C4—362no—
460C4—361no—
461C4#6414611yescharacteristic
462C4#6414711yescharacteristic
463C4#6414811yescharacteristic
464C4#6414911yescharacteristic
465C3#7171514yescomplemented
466C2—21no—
467C2—21no—
468C2—21no—
469C2—42no—
470C2—81no—
471C2—721no—
472C2#1059292211yescharacteristic
subgroupG/H
centerC4#64149
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#525C2
socleC2×C32#392
hypercenter#525C3⋊D3
hypocenterC32#2010
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C32×#525C2semidirect
2. #10596293C2semidirect
3. #10596262C2semidirect
4. #10592935C2semidirect
5. #10592906C2semidirect
6. #10592704C2semidirect
7. #10589397C2semidirect
34. C3×#525D3semidirect
46. C2×C32×Q8D4semidirect
49. C2×C32×D4D4semidirect
65. C2×C4⋊(C3⋊D3)D4semidirect
67. C2×#634D4semidirect
73. C32×C42D4semidirect
83. C4×C3⋊Dic3D4semidirect
89. C2×C3⋊(C3⋊C8)D4semidirect
162. #525C3⋊D3semidirect
172. C2×C3×Q8#67semidirect
175. C2×C3×D4#67semidirect
199. C3×C42#67semidirect
326. C2×Q8#638semidirect
332. C2×D4#638semidirect
364. C42#638semidirect
389. C32#2010semidirect
465. C3#71715semidirect

Maximal subgroups

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

subgroupindex
C32×#5252
#105962932
#105962622
#105929352
#105929062
#105927042
#105893972
#717153