Finite Group Databasebeta

← #11865299

Subgroups — #11865299

Order 1152.

2298 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596756C211yesmaximal, characteristic, complemented
2C32×#525C211yesmaximal, characteristic, complemented
3#10596262C212yesmaximal, complemented
4#10592939C211yesmaximal, characteristic, complemented
5#10592752C214yesmaximal, complemented
6#10592731C214yesmaximal, complemented
7#10592705C212yesmaximal, complemented
8#82936—34nomaximal
9C2×C32×#41C2211yescharacteristic
10C23×C32×C4C2211yescharacteristic, complemented
11#64367—22no—
12#64366—22no—
13#41×C3⋊D3—24no—
14#64364—21no—
15#64361—21no—
16#64361C2214yes—
17C2×#3828—22no—
18C2×#3828C2212yes—
19C32×#123C2212yescomplemented
20C32×C22⋊Q8—21no—
21C32×#121—21no—
22C32×#120C2212yescomplemented
23C32×C4×D4—22no—
24C32×#117C2211yescharacteristic, complemented
25#64162C2214yescomplemented
26#64139—22no—
27#64138C2214yescomplemented
28C4×#638—24no—
29#64135C2212yescomplemented
30#64133—22no—
31#63661C2214yescomplemented
32#63633C2218yescomplemented
33#5964—34no—
34C3×#525D314yescomplemented
35#5791—38no—
36#5240—34no—
37#5053—316no—
38#5032—316no—
39#5006—38no—
40C24×C32C2311yescharacteristic
41C32×#41—22no—
42C32×#41—22no—
43C2×C32×Q8D411yescharacteristic, complemented
44C2×C32×D4—22no—
45C2×C32×D4D411yescharacteristic, complemented
46C2×C32×D4C2312yes—
47C22×C32×C4—22no—
48C22×C32×C4—22no—
49C22×C32×C4—21no—
50C22×C32×C4—21no—
51C22×C32×C4D412yescomplemented
52C22×C32×C4C2311yescharacteristic
53C22×C32×C4C2311yescharacteristic
54C2×#638—24no—
55C2×#638—24no—
56C2×#638C2314yes—
57#3832—24no—
58Q8×C3⋊D3—24no—
59#3830—24no—
60#3830—28no—
61D4×C3⋊D3—24no—
62D4×C3⋊D3—28no—
63#3828—24no—
64#3828—24no—
65#3828—22no—
66#3828—24no—
67#3828—22no—
68#3828—22no—
69#3828—22no—
70C2×C4⋊(C3⋊D3)—22no—
71C2×C4⋊(C3⋊D3)D412yescomplemented
72C2×C4×C3⋊D3—24no—
73C2×C4×C3⋊D3D414yescomplemented
74C2×#634—22no—
75C2×#634D412yescomplemented
76C32×C4⋊C4—21no—
77C32×C4⋊C4—22no—
78C32×C22⋊C4—22no—
79C32×C22⋊C4—22no—
80C32×C22⋊C4C2312yes—
81C32×C42—21no—
82#3757—24no—
83#3757C2314yes—
84#3752—24no—
85C4⋊(C3⋊Dic3)—22no—
86#3750—24no—
87C4×C3⋊Dic3—22no—
88#3025—91noSylow
89C2×C3×#41C2×D314yes—
90C23×C3×C4C2×D314yescomplemented
91#1010—68no—
92#1009—68no—
93D3×#41—616no—
94#1007—64no—
95#1004—316no—
96#1004—64no—
97C2×#235—38no—
98C2×#235—68no—
99C3×#123C2×D318yescomplemented
100C3×C22⋊Q8—24no—
101C3×#121—24no—
102C3×#120C2×D318yescomplemented
103C3×C4×D4—28no—
104C3×#117C2×D314yescomplemented
105#953—316no—
106#930—68no—
107#929—316no—
108C4×#67—616no—
109#926—38no—
110#924—68no—
111#834—316no—
112#806—332no—
113C23×C32—22no—
114C23×C32—21no—
115C23×C32—42no—
116C23×C32C2×D412yes—
117C23×C32C2411yescharacteristic
118C22×C3⋊D3—24no—
119C22×C3⋊D3C2×D414yes—
120C32×Q8—22no—
121C32×D4—24no—
122C32×D4—22no—
123C32×D4—44no—
124C2×C32×C4—22no—
125C2×C32×C4—22no—
126C2×C32×C4—22no—
127C2×C32×C4—22no—
128C2×C32×C4—21no—
129C2×C32×C4—41no—
130C2×C32×C4—42no—
131C2×C32×C4—41no—
132C2×C32×C4C2×D412yes—
133C2×C32×C4C2×D412yes—
134C2×C32×C4C2×D412yes—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137#638—28no—
138#638—24no—
139#638—24no—
140#638—48no—
141C2×C3⋊Dic3—24no—
142C2×C3⋊Dic3—24no—
143C2×C3⋊Dic3C2×D414yes—
144C4⋊(C3⋊D3)—24no—
145C4⋊(C3⋊D3)—22no—
146C4⋊(C3⋊D3)—22no—
147C4×C3⋊D3—28no—
148C4×C3⋊D3—24no—
149C4×C3⋊D3—24no—
150#634—24no—
151#634—22no—
152#634—22no—
153#585—91no—
154#525—92no—
155#525C3⋊D311yescharacteristic, complemented
156#458—94no—
157B(4,𝔽2)—94no—
158#410—91no—
159#410—92no—
160C24×C3C22×D314yes—
161C3×#41—28no—
162C3×#41—28no—
163C2×C3×Q8#6714yescomplemented
164C2×C3×D4—28no—
165C2×C3×D4#6714yescomplemented
166C2×C3×D4C22×D318yes—
167C22×C3×C4—28no—
168C22×C3×C4—28no—
169C22×C3×C4—24no—
170C22×C3×C4—24no—
171C22×C3×C4#6718yescomplemented
172C22×C3×C4C22×D314yes—
173C22×C3×C4C22×D314yes—
174C2×#67—316no—
175C2×#67—616no—
176C2×#67—616no—
177#239—616no—
178D3×Q8—616no—
179#237—632no—
180#237—616no—
181D3×D4—632no—
182D3×D4—616no—
183#235—616no—
184#235—616no—
185#235—68no—
186#235—68no—
187#235—68no—
188#235—68no—
189#235—616no—
190C2×D12—38no—
191C2×D12—68no—
192C2×C4×D3—316no—
193C2×C4×D3—616no—
194C2×Dic6—38no—
195C2×Dic6—68no—
196C3×C4⋊C4—24no—
197C3×C4⋊C4—28no—
198C3×C22⋊C4—28no—
199C3×C22⋊C4—28no—
200C3×C22⋊C4C22×D318yes—
201C3×C42—24no—
202#217—316no—
203#217—616no—
204(C2×D3)⋊C4—616no—
205C4⋊Dic3—68no—
206Dic3⋊C4—616no—
207C4×Dic3—68no—
208C22×C32—24no—
209C22×C32—22no—
210C22×C32—22no—
211C22×C32—41no—
212C22×C32—42no—
213C22×C32—42no—
214C22×C32—41no—
215C22×C32—41no—
216C22×C32C22×D412yes—
217C22×C32C22×D411yescharacteristic
218C2×C3⋊D3—24no—
219C2×C3⋊D3—44no—
220C2×C3⋊D3—84no—
221C32×C4—22no—
222C32×C4—42no—
223C32×C4—41no—
224C32×C4#12011yescharacteristic
225C32×C4#12012yes—
226C32×C4#12011yescharacteristic
227C3⋊Dic3—24no—
228C3⋊Dic3—44no—
2292−1+4—182no—
2302−1+4—181no—
231H(5,𝔽2)—94no—
232H(5,𝔽2)—182no—
233H(5,𝔽2)—181no—
234C2×#41—92no—
235C2×#41—184no—
236C2×#41—182no—
237C2×#41C2×C3⋊D311yescharacteristic
238C23×C4C2×C3⋊D311yescharacteristic, complemented
239#123—94no—
240#123C2×C3⋊D312yescomplemented
241C22⋊Q8—21no—
242C22⋊Q8—182no—
243#121—21no—
244#121—182no—
245#120—94no—
246#120C2×C3⋊D312yescomplemented
247C4×D4—22no—
248C4×D4—184no—
249#117—92no—
250#117C2×C3⋊D311yescharacteristic, complemented
251#99—94no—
252#99—98no—
253C23×C3—28no—
254C23×C3—24no—
255C23×C3—48no—
256C23×C3C2×#6718yes—
257C23×C3C23×D314yes—
258C22×D3—316no—
259C22×D3—616no—
260C3×Q8—28no—
261C3×D4—216no—
262C3×D4—28no—
263C3×D4—416no—
264C2×C3×C4—28no—
265C2×C3×C4—28no—
266C2×C3×C4—28no—
267C2×C3×C4—28no—
268C2×C3×C4—24no—
269C2×C3×C4—44no—
270C2×C3×C4—48no—
271C2×C3×C4—44no—
272C2×C3×C4D3×D418yes—
273C2×C3×C4D3×D418yes—
274C2×C3×C4C2×#6718yes—
275C2×C3×C4C2×#6714yes—
276C2×C3×C4C2×#6714yes—
277#67—632no—
278#67—616no—
279#67—616no—
280#67—1232no—
281C2×Dic3—316no—
282C2×Dic3—616no—
283C2×Dic3—616no—
284D12—616no—
285D12—68no—
286D12—68no—
287C4×D3—632no—
288C4×D3—616no—
289C4×D3—616no—
290Dic6—616no—
291Dic6—68no—
292Dic6—68no—
293C2×C32—22no—
294C2×C32—21no—
295C2×C32—42no—
296C2×C32—42no—
297C2×C32C2×#12011yescharacteristic
298C3⋊D3—44no—
299C24C22×C3⋊D311yescharacteristic
300#41—22no—
301#41—22no—
302#41—184no—
303#41—184no—
304#41—188no—
305#41—184no—
306#41—184no—
307#41—182no—
308#41—182no—
309#41—182no—
310#41—182no—
311#41—184no—
312C2×Q8—92no—
313C2×Q8—182no—
314C2×Q8—184no—
315C2×Q8#63811yescharacteristic, complemented
316C2×D4—22no—
317C2×D4—94no—
318C2×D4—92no—
319C2×D4—182no—
320C2×D4—188no—
321C2×D4—184no—
322C2×D4—184no—
323C2×D4—184no—
324C2×D4#63811yescharacteristic, complemented
325C2×D4C22×C3⋊D312yes—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—94no—
331C22×C4—184no—
332C22×C4#63812yescomplemented
333C22×C4C22×C3⋊D311yescharacteristic
334C22×C4C22×C3⋊D311yescharacteristic
335C4⋊C4—21no—
336C4⋊C4—22no—
337C4⋊C4—184no—
338C4⋊C4—182no—
339C22⋊C4—22no—
340C22⋊C4—22no—
341C22⋊C4—94no—
342C22⋊C4—184no—
343C22⋊C4—184no—
344C22⋊C4C22×C3⋊D312yes—
345C42—21no—
346C42—182no—
347C22×C3—216no—
348C22×C3—28no—
349C22×C3—28no—
350C22×C3—44no—
351C22×C3—48no—
352C22×C3—48no—
353C22×C3—44no—
354C22×C3—44no—
355C22×C3C2×D3×D418yes—
356C22×C3C22×#6714yes—
357C2×D3—616no—
358C2×D3—1216no—
359C2×D3—2416no—
360C3×C4—28no—
361C3×C4—48no—
362C3×C4—44no—
363C3×C4#93714yes—
364C3×C4#93718yes—
365C3×C4#93714yes—
366Dic3—616no—
367Dic3—1216no—
368C32#302511yescharacteristic, complemented, Sylow
369C23—22no—
370C23—21no—
371C23—42no—
372C23—94no—
373C23—184no—
374C23C2×#63812yes—
375C23C23×C3⋊D311yescharacteristic
376Q8—22no—
377Q8—184no—
378Q8—182no—
379Q8—182no—
380D4—24no—
381D4—22no—
382D4—44no—
383D4—184no—
384D4—188no—
385D4—184no—
386D4—184no—
387D4—182no—
388D4—182no—
389D4—368no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—21no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—41no—
398C2×C4—94no—
399C2×C4—188no—
400C2×C4—184no—
401C2×C4—184no—
402C2×C4—184no—
403C2×C4—184no—
404C2×C4D4×C3⋊D312yes—
405C2×C4D4×C3⋊D312yes—
406C2×C4C2×#63812yes—
407C2×C4C2×#63811yescharacteristic
408C2×C4C2×#63811yescharacteristic
409C2×C3—28no—
410C2×C3—24no—
411C2×C3—48no—
412C2×C3—48no—
413C2×C3C2×#93714yes—
414D3—1216no—
415C22—22no—
416C22—24no—
417C22—22no—
418C22—41no—
419C22—42no—
420C22—41no—
421C22—42no—
422C22—41no—
423C22—184no—
424C22—364no—
425C22—724no—
426C22C2×D4×C3⋊D312yes—
427C22C22×#63811yescharacteristic
428C4—22no—
429C4—42no—
430C4—41no—
431C4—184no—
432C4—364no—
433C4#6414611yescharacteristic
434C4#6414612yes—
435C4#6414611yescharacteristic
436C3#8293614yescomplemented
437C2—21no—
438C2—22no—
439C2—42no—
440C2—42no—
441C2—364no—
442C2C2×#6414611yescharacteristic
subgroupG/H
centerC4#64146
commutator, cosocleC23×C32C24
FrattiniC23C23×C3⋊D3
FittingC32×#525C2
socleC2×C32C2×#120
hypercenter#525C3⋊D3
hypocenterC32#3025
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #10596756C2semidirect
2. C32×#525C2semidirect
3. #10596262C2semidirect
4. #10592939C2semidirect
5. #10592752C2semidirect
6. #10592731C2semidirect
7. #10592705C2semidirect
10. C23×C32×C4C22semidirect
19. C32×#123C22semidirect
22. C32×#120C22semidirect
24. C32×#117C22semidirect
25. #64162C22semidirect
27. #64138C22semidirect
29. #64135C22semidirect
31. #63661C22semidirect
32. #63633C22semidirect
34. C3×#525D3semidirect
43. C2×C32×Q8D4semidirect
45. C2×C32×D4D4semidirect
51. C22×C32×C4D4semidirect
71. C2×C4⋊(C3⋊D3)D4semidirect
73. C2×C4×C3⋊D3D4semidirect
75. C2×#634D4semidirect
90. C23×C3×C4C2×D3semidirect
99. C3×#123C2×D3semidirect
102. C3×#120C2×D3semidirect
104. C3×#117C2×D3semidirect
155. #525C3⋊D3semidirect
163. C2×C3×Q8#67semidirect
165. C2×C3×D4#67semidirect
171. C22×C3×C4#67semidirect
238. C23×C4C2×C3⋊D3semidirect
240. #123C2×C3⋊D3semidirect
246. #120C2×C3⋊D3semidirect
250. #117C2×C3⋊D3semidirect
315. C2×Q8#638semidirect
324. C2×D4#638semidirect
332. C22×C4#638semidirect
368. C32#3025semidirect
436. C3#82936semidirect

Maximal subgroups

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

subgroupindex
#105967562
C32×#5252
#105962622
#105929392
#105927522
#105927312
#105927052
#829363