Finite Group Databasebeta

← #11784959

Subgroups — #11784959

Order 1152.

1764 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64366C211yesmaximal, characteristic
2C32×#421C211yesmaximal, characteristic, complemented
3#10592935C211yesmaximal, characteristic, complemented
4#10592831C211yesmaximal, characteristic, complemented
5#10592830C211yesmaximal, characteristic, complemented
6#10592705C211yesmaximal, characteristic, complemented
7#10592700C211yesmaximal, characteristic, complemented
8#70414—34nomaximal
9C2×C32×#41C2211yescharacteristic
10#64366—22no—
11#64366—22no—
12#64366—22no—
13#64366—22no—
14C2×#3832C412yescomplemented
15C2×D4×C3⋊D3—22no—
16C2×D4×C3⋊D3C412yescomplemented
17C2×#3828—21no—
18C2×#3828C2211yescharacteristic
19C22×C4⋊(C3⋊D3)—21no—
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C32×M16C2211yescharacteristic, complemented
22C32×#117C2211yescharacteristic, complemented
23#64135C2211yescharacteristic, complemented
24C2×#3748C2211yescharacteristic, complemented
25C32×#104—22no—
26#63664—22no—
27#63651—21no—
28#63650—21no—
29#63648—22no—
30#63636—22no—
31#63633—22no—
32C2×#1009—34no—
33C3×#421D314yescomplemented
34#5236—34no—
35#5132—34no—
36#5131—34no—
37#5006—34no—
38#5001—34no—
39C23×C3⋊D3—21no—
40C23×C3⋊D3—22no—
41C32×#41—21no—
42C32×#41—21no—
43C32×#41D412yes—
44C32×#41D412yes—
45C2×C32×Q8C2×C411yescharacteristic
46C2×C32×D4—21no—
47C2×C32×D4C2×C411yescharacteristic
48C22×C32×C4—21no—
49C22×C32×C4C2311yescharacteristic
50C2×#638—22no—
51C2×#638D412yes—
52#3832—24no—
53#3832—24no—
54D4×C3⋊D3—28no—
55D4×C3⋊D3—28no—
56D4×C3⋊D3—24no—
57D4×C3⋊D3—24no—
58#3828—24no—
59#3828—24no—
60#3828—21no—
61#3828—21no—
62#3828—21no—
63#3828—21no—
64C2×C4⋊(C3⋊D3)—24no—
65C2×C4⋊(C3⋊D3)—24no—
66C2×C4⋊(C3⋊D3)—22no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)—21no—
70C2×C4⋊(C3⋊D3)C2×C412yes—
71C2×C4⋊(C3⋊D3)D411yescharacteristic
72C2×C4⋊(C3⋊D3)D412yes—
73C2×C4⋊(C3⋊D3)D412yes—
74C2×C4×C3⋊D3—22no—
75C2×C4×C3⋊D3C2×C412yes—
76C2×#634D411yescharacteristic
77C32×M16—21no—
78C32×M16—21no—
79C2×C32×C8—21no—
80C32×C4⋊C4—21no—
81C32×C22⋊C4—21no—
82C32×C42—21no—
83#3757—21no—
84C4⋊(C3⋊Dic3)—21no—
85C4×C3⋊Dic3—21no—
86#3748—21no—
87#3748—21no—
88C2×C3⋊(C3⋊C8)—21no—
89#1795—91noSylow
90C2×C3×#41C2×D314yes—
91#1009—68no—
92#1009—68no—
93#1009—68no—
94#1009—68no—
95C2×#239—38no—
96C2×D3×D4—38no—
97C2×D3×D4—68no—
98C2×#235—34no—
99C2×#235—64no—
100C22×D12—34no—
101C22×D12—64no—
102C2×C3×M16C2×D314yescomplemented
103C3×#117C2×D314yescomplemented
104#926—34no—
105C2×#208—34no—
106C3×#104—28no—
107#837—68no—
108#824—64no—
109#823—64no—
110#821—68no—
111#809—68no—
112#806—68no—
113C23×C32—21no—
114C23×C32C2×D411yescharacteristic
115C22×C3⋊D3—22no—
116C22×C3⋊D3—28no—
117C22×C3⋊D3—22no—
118C22×C3⋊D3—22no—
119C22×C3⋊D3—82no—
120C22×C3⋊D3—84no—
121C22×C3⋊D3C22⋊C412yes—
122C32×Q8—21no—
123C32×Q8C22⋊C412yes—
124C32×D4—22no—
125C32×D4—22no—
126C32×D4—21no—
127C32×D4C22⋊C412yes—
128C2×C32×C4—21no—
129C2×C32×C4—22no—
130C2×C32×C4—22no—
131C2×C32×C4—41no—
132C2×C32×C4C22×C411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138#638—28no—
139#638—22no—
140#638—22no—
141C2×C3⋊Dic3—41no—
142C2×C3⋊Dic3C22⋊C412yes—
143C4⋊(C3⋊D3)—28no—
144C4⋊(C3⋊D3)—22no—
145C4⋊(C3⋊D3)—21no—
146C4⋊(C3⋊D3)—22no—
147C4⋊(C3⋊D3)—21no—
148C4⋊(C3⋊D3)—22no—
149C4⋊(C3⋊D3)C22⋊C414yes—
150C4×C3⋊D3—28no—
151C4×C3⋊D3—22no—
152C4×C3⋊D3—22no—
153#634—21no—
154#634—21no—
155C32×C8—41no—
156C3⋊(C3⋊C8)—41no—
157C2×H(5,𝔽2)—91no—
158#421—91no—
159#421C3⋊D311yescharacteristic, complemented
160#418—91no—
161#418—91no—
162#413—91no—
163#410—91no—
164C23×D3—68no—
165C23×D3—64no—
166C3×#41—24no—
167C3×#41—24no—
168C3×#41D1218yes—
169C3×#41#6718yes—
170C2×C3×Q8C4×D314yes—
171C2×C3×D4—24no—
172C2×C3×D4C4×D314yes—
173C22×C3×C4—24no—
174C22×C3×C4C22×D314yes—
175C2×#67—38no—
176C2×#67—68no—
177#239—616no—
178#239—616no—
179D3×D4—616no—
180D3×D4—632no—
181D3×D4—632no—
182D3×D4—616no—
183#235—616no—
184#235—616no—
185#235—64no—
186#235—64no—
187#235—64no—
188#235—64no—
189C2×D12—38no—
190C2×D12—38no—
191C2×D12—38no—
192C2×D12—34no—
193C2×D12—68no—
194C2×D12—616no—
195C2×D12—616no—
196C2×D12—64no—
197C2×D12—64no—
198C2×D12—64no—
199C2×C4×D3—38no—
200C2×C4×D3—68no—
201C2×Dic6—34no—
202C3×M16—24no—
203C3×M16—24no—
204C2×C3×C8—24no—
205C3×C4⋊C4—24no—
206C3×C22⋊C4—24no—
207C3×C42—24no—
208#217—64no—
209C4⋊Dic3—64no—
210C4×Dic3—64no—
211#208—64no—
212#208—64no—
213C2×C3⋊C8—64no—
214C22×C32—22no—
215C22×C32—41no—
216C22×C32—42no—
217C22×C32C2×C22⋊C411yescharacteristic
218C22×C32#12011yescharacteristic
219C22×C32#12011yescharacteristic
220C2×C3⋊D3—22no—
221C2×C3⋊D3—24no—
222C2×C3⋊D3—44no—
223C2×C3⋊D3—42no—
224C2×C3⋊D3—82no—
225C2×C3⋊D3—82no—
226C2×C3⋊D3—88no—
227C32×C4—22no—
228C32×C4—81no—
229C32×C4C2×C22⋊C411yescharacteristic
230C32×C4C2×C22⋊C411yescharacteristic
231C32×C4#12011yescharacteristic
232C32×C4#12011yescharacteristic
233C3⋊Dic3—22no—
234C3⋊Dic3—81no—
235H(5,𝔽2)—182no—
236H(5,𝔽2)—182no—
237H(5,𝔽2)—182no—
238H(5,𝔽2)—182no—
239C2×#41—91no—
240C2×#41—92no—
241C2×#41—181no—
242C2×#41C2×C3⋊D311yescharacteristic
243C22×D4—92no—
244C22×D4—91no—
245C22×D4—181no—
246C22×D4—182no—
247C2×M16—91no—
248C2×M16C2×C3⋊D311yescharacteristic, complemented
249#117—91no—
250#117C2×C3⋊D311yescharacteristic, complemented
251#104—22no—
252#104—182no—
253#102—182no—
254#102—182no—
255#101—181no—
256#100—181no—
257#99—182no—
258C23×C3—24no—
259C23×C3D3×D414yes—
260C22×D3—38no—
261C22×D3—68no—
262C22×D3—632no—
263C22×D3—68no—
264C22×D3—68no—
265C22×D3—248no—
266C22×D3—2416no—
267C3×Q8—24no—
268C3×Q8(C2×D3)⋊C418yes—
269C3×D4—28no—
270C3×D4—28no—
271C3×D4—24no—
272C3×D4(C2×D3)⋊C418yes—
273C2×C3×C4—24no—
274C2×C3×C4—28no—
275C2×C3×C4—28no—
276C2×C3×C4—44no—
277C2×C3×C4C2×C4×D314yes—
278C2×C3×C4C2×D1214yes—
279C2×C3×C4D3×D414yes—
280C2×C3×C4D3×D414yes—
281C2×C3×C4D3×D414yes—
282C2×C3×C4C2×#6714yes—
283#67—632no—
284#67—68no—
285#67—68no—
286C2×Dic3—38no—
287C2×Dic3—124no—
288D12—316no—
289D12—632no—
290D12—68no—
291D12—64no—
292D12—68no—
293D12—68no—
294D12—64no—
295C4×D3—632no—
296C4×D3—68no—
297C4×D3—68no—
298Dic6—64no—
299Dic6—64no—
300C3×C8—44no—
301C3⋊C8—124no—
302C2×C32—21no—
303C2×C32—21no—
304C2×C32—21no—
305C2×C32—42no—
306C2×C32#37911yescharacteristic
307C3⋊D3—44no—
308C3⋊D3—42no—
309C24—182no—
310C24—181no—
311#41—21no—
312#41—21no—
313#41—184no—
314#41—184no—
315#41—184no—
316#41—184no—
317#41—181no—
318#41—181no—
319#41—181no—
320#41—181no—
321#41C4⋊(C3⋊D3)12yes—
322#41#63812yes—
323C2×Q8—91no—
324C2×Q8C4×C3⋊D311yescharacteristic
325C2×D4—21no—
326C2×D4—92no—
327C2×D4—92no—
328C2×D4—92no—
329C2×D4—92no—
330C2×D4—91no—
331C2×D4—182no—
332C2×D4—184no—
333C2×D4—184no—
334C2×D4—182no—
335C2×D4—184no—
336C2×D4—188no—
337C2×D4—188no—
338C2×D4—184no—
339C2×D4—181no—
340C2×D4—181no—
341C2×D4—181no—
342C2×D4C4×C3⋊D311yescharacteristic
343C22×C4—21no—
344C22×C4—92no—
345C22×C4—182no—
346C22×C4C22×C3⋊D311yescharacteristic
347M16—21no—
348M16—21no—
349M16—181no—
350M16—181no—
351C2×C8—21no—
352C2×C8—181no—
353C4⋊C4—21no—
354C4⋊C4—181no—
355C22⋊C4—21no—
356C22⋊C4—181no—
357C42—21no—
358C42—181no—
359C22×C3—28no—
360C22×C3—44no—
361C22×C3—48no—
362C22×C3D3×C22⋊C414yes—
363C22×C3#88214yes—
364C22×C3#93714yes—
365C2×D3—616no—
366C2×D3—68no—
367C2×D3—1216no—
368C2×D3—128no—
369C2×D3—248no—
370C2×D3—248no—
371C2×D3—2432no—
372C3×C4—28no—
373C3×C4—84no—
374C3×C4D3×C22⋊C414yes—
375C3×C4#88214yes—
376C3×C4C2×(C2×D3)⋊C414yes—
377C3×C4#93714yes—
378Dic3—68no—
379Dic3—244no—
380C32#179511yescharacteristic, complemented, Sylow
381C23—21no—
382C23—92no—
383C23—188no—
384C23—182no—
385C23—182no—
386C23—182no—
387C23—722no—
388C23—724no—
389C23D4×C3⋊D311yescharacteristic
390Q8—21no—
391Q8—181no—
392Q8—181no—
393Q8#375212yes—
394D4—22no—
395D4—22no—
396D4—21no—
397D4—94no—
398D4—188no—
399D4—188no—
400D4—182no—
401D4—182no—
402D4—182no—
403D4—181no—
404D4—182no—
405D4—182no—
406D4—181no—
407D4#375212yes—
408C2×C4—21no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—41no—
412C2×C4—92no—
413C2×C4—188no—
414C2×C4—182no—
415C2×C4—182no—
416C2×C4—361no—
417C2×C4C2×C4×C3⋊D311yescharacteristic
418C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
419C2×C4D4×C3⋊D311yescharacteristic
420C2×C4D4×C3⋊D311yescharacteristic
421C2×C4D4×C3⋊D311yescharacteristic
422C2×C4C2×#63811yescharacteristic
423C8—41no—
424C8—361no—
425C2×C3—24no—
426C2×C3—24no—
427C2×C3—24no—
428C2×C3—48no—
429C2×C3#495514yes—
430D3—1216no—
431D3—128no—
432C22—22no—
433C22—41no—
434C22—42no—
435C22—184no—
436C22—182no—
437C22—362no—
438C22—364no—
439C22—722no—
440C22—722no—
441C22—728no—
442C22C22⋊C4×C3⋊D311yescharacteristic
443C22#6409111yescharacteristic
444C22#6414611yescharacteristic
445C4—22no—
446C4—81no—
447C4—182no—
448C4—721no—
449C4C22⋊C4×C3⋊D311yescharacteristic
450C4#6409111yescharacteristic
451C4C2×#375211yescharacteristic
452C4#6414611yescharacteristic
453C3#7041414yescomplemented
454C2—21no—
455C2—21no—
456C2—21no—
457C2—42no—
458C2—364no—
459C2—362no—
460C2#1059265411yescharacteristic
subgroupG/H
centerC2#10592654
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#421C2
socleC2×C32#379
prime radicalC2×#64366C2
cosocleC22×C32×C4C23
hypercenter#421C3⋊D3
hypocenterC32#1795
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. C32×#421C2semidirect
3. #10592935C2semidirect
4. #10592831C2semidirect
5. #10592830C2semidirect
6. #10592705C2semidirect
7. #10592700C2semidirect
14. C2×#3832C4semidirect
16. C2×D4×C3⋊D3C4semidirect
21. C2×C32×M16C22semidirect
22. C32×#117C22semidirect
23. #64135C22semidirect
24. C2×#3748C22semidirect
33. C3×#421D3semidirect
102. C2×C3×M16C2×D3semidirect
103. C3×#117C2×D3semidirect
159. #421C3⋊D3semidirect
248. C2×M16C2×C3⋊D3semidirect
250. #117C2×C3⋊D3semidirect
380. C32#1795semidirect
453. C3#70414semidirect

Maximal subgroups

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

subgroupindex
C2×#643662
C32×#4212
#105929352
#105928312
#105928302
#105927052
#105927002
#704143