Finite Group Databasebeta

← #11860777

Subgroups — #11860777

Order 1152.

1049 conjugacy classes of subgroups.

The subgroup lattice has 451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#204C211yesmaximal, characteristic
2#10594982C211yesmaximal, characteristic
3#10594818C211yesmaximal, characteristic, complemented
4#10592800C211yesmaximal, characteristic, complemented
5C3×#5106C211yesmaximal, characteristic, complemented
6#10591099C211yesmaximal, characteristic, complemented
7#10591085C211yesmaximal, characteristic
8#10590779C214yesmaximal, complemented
9#10590775C214yesmaximal, complemented
10#83843—31nomaximal
11#79168—31nomaximal
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15#64135C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C3×#926C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C2×C3×#204C418yescomplemented
20C2×C3×#204C2212yes—
21C2×C3×#204C2212yes—
22D3×#217—22no—
23#63955—22no—
24#63898C2214yes—
25Dic3×D12—22no—
26#63843C2214yescomplemented
27Dic3×Dic6—22no—
28#63642C2212yescomplemented
29C8×C3⋊Dic3C2212yescomplemented
30C3×#818C2212yescomplemented
31C3×#817C2212yescomplemented
32#63565C2214yescomplemented
33#63562C2214yes—
34C22×C3×SD16—31no—
35#5812—31no—
36#5798—31no—
37C22×#204D311yescharacteristic
38#5521—31no—
39#5516—31no—
40C3×#427—31no—
41#5225—31no—
42#5215—31no—
43#5164—34no—
44Dic3×SD16—34no—
45#5106D311yescharacteristic, complemented
46#5101—31no—
47#5101—31no—
48#5101—61no—
49#5004—31no—
50#5001—31no—
51#4889—34no—
52#4852—34no—
53C23×C3×D3—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3×Dic3—21no—
56C2×C3×D12—21no—
57C2×C3×D12—22no—
58C2×C3×D12C2×C414yes—
59C2×C3×D12C2312yes—
60C2×C3×Dic6—21no—
61C2×C3×Dic6—22no—
62C2×C3×Dic6C2×C414yescomplemented
63C2×C3×Dic6C2312yes—
64C2×D3×Dic3—24no—
65C2×C32×C8C2×C414yescomplemented
66C2×C32×C8C2311yescharacteristic
67C2×C32×C8C2311yescharacteristic
68#3757D412yes—
69C4⋊(C3⋊Dic3)D412yes—
70C4×C3⋊Dic3C2312yes—
71#3748—22no—
72C2×C3⋊(C3⋊C8)C2312yes—
73C3×#217—21no—
74C3×#217—21no—
75C3×C4⋊Dic3C2312yes—
76C3×C4⋊Dic3C2312yes—
77C3×C4×Dic3—21no—
78C3×C4×Dic3—21no—
79C3×#204C2×C418yescomplemented
80C3×#204C2×C418yescomplemented
81Dic3⋊Dic3—24no—
82(C2×D3)⋊Dic3—24no—
83Dic32—24no—
84#2949—91noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—31no—
87C22×D12C2×D311yescharacteristic
88C22×Dic6C2×D311yescharacteristic
89C2×C3×SD16—38no—
90C2×C3×SD16—32no—
91C2×C3×SD16—32no—
92C22×C3×C8—21no—
93C22×C3×C8C2×D311yescharacteristic
94C22×C3×C8C2×D311yescharacteristic
95C3×#117—31no—
96C3×#117—31no—
97C2×#217—62no—
98Q8×Dic3—34no—
99Q8×Dic3—62no—
100D4×Dic3—34no—
101D4×Dic3—62no—
102#926—31no—
103#926—31no—
104#926—61no—
105#926—62no—
106#926C2×D311yescharacteristic
107#926C2×D311yescharacteristic
108C2×#208—31no—
109C2×#208—31no—
110C2×#208—61no—
111C2×#204Dic318yescomplemented
112C2×#204C2×D312yes—
113C2×#204C2×D312yes—
114#893—34no—
115#887—34no—
116D3×C22⋊C4—62no—
117#877—62no—
118C4×D12—62no—
119C4×Dic6—62no—
120C3×#107—32no—
121C3×#106—32no—
122#835—34no—
123#832—34no—
124#818C2×D312yescomplemented
125#817C2×D312yescomplemented
126#815—32no—
127#815—32no—
128#815—62no—
129C8×Dic3—32no—
130C8×Dic3—32no—
131C8×Dic3—62no—
132#810—34no—
133#809—34no—
134C23×C32C2×D411yescharacteristic
135C22×C3×D3—22no—
136C22×C3×D3—24no—
137C22×C3×D3—82no—
138C2×C32×C4C22×C412yes—
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4#4112yes—
141C2×C32×C4C2411yescharacteristic
142C2×C3⋊Dic3C2×D414yes—
143C2×C3×Dic3—24no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C3×D12—24no—
148C3×D12—22no—
149C3×D12C22×C414yes—
150C3×Dic6—24no—
151C3×Dic6—22no—
152C3×Dic6C22×C414yes—
153D3×Dic3—84no—
154C32×C8C22×C412yes—
155C32×C8C22×C412yes—
156C3⋊(C3⋊C8)—22no—
157C22×SD16—31no—
158#519—91no—
159#518—91no—
160#440—94no—
161C4×SD16—94no—
162#427—31no—
163#419—91no—
164#418—91no—
165#405—91no—
166C24×C3—61no—
167C23×D3—21no—
168C2×C3×Q8—34no—
169C2×C3×Q8—32no—
170C2×C3×Q8—61no—
171C2×C3×Q8—62no—
172C2×C3×D4—34no—
173C2×C3×D4—32no—
174C2×C3×D4—61no—
175C2×C3×D4—62no—
176C22×C3×C4—21no—
177C22×C3×C4—61no—
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C22×D311yescharacteristic
180C22×Dic3—21no—
181C22×Dic3—64no—
182C2×D12—21no—
183C2×D12—22no—
184C2×D12C2×Dic314yes—
185C2×D12C22×D312yes—
186C2×C4×D3—64no—
187C2×Dic6—21no—
188C2×Dic6—22no—
189C2×Dic6C2×Dic314yescomplemented
190C2×Dic6C22×D312yes—
191C3×SD16—38no—
192C3×SD16—38no—
193C2×C3×C8—24no—
194C2×C3×C8—21no—
195C2×C3×C8—21no—
196C2×C3×C8C4×D314yescomplemented
197C2×C3×C8C2×Dic314yescomplemented
198C2×C3×C8C22×D311yescharacteristic
199C2×C3×C8C22×D311yescharacteristic
200C2×C3×C8C22×D311yescharacteristic
201C2×C3×C8C22×D311yescharacteristic
202C3×C4⋊C4—32no—
203C3×C4⋊C4—32no—
204C3×C22⋊C4—61no—
205C3×C22⋊C4—61no—
206C3×C42—61no—
207C3×C42—61no—
208#217—21no—
209#217—21no—
210#217—32no—
211#217—32no—
212#217—62no—
213#217—64no—
214(C2×D3)⋊C4—64no—
215C4⋊Dic3—32no—
216C4⋊Dic3—32no—
217C4⋊Dic3—62no—
218C4⋊Dic3—64no—
219C4⋊Dic3C22×D312yes—
220C4⋊Dic3C22×D312yes—
221Dic3⋊C4—64no—
222C4×Dic3—21no—
223C4×Dic3—21no—
224C4×Dic3—32no—
225C4×Dic3—32no—
226C4×Dic3—62no—
227C4×Dic3—64no—
228C4×Dic3—64no—
229#208—64no—
230#208—62no—
231#208—62no—
232C2×C3⋊C8—32no—
233C2×C3⋊C8—32no—
234C2×C3⋊C8—62no—
235#204C2×Dic318yescomplemented
236#204C2×Dic318yescomplemented
237C22×C32—22no—
238C22×C32C4×D412yes—
239C22×C32C22×D411yescharacteristic
240C2×C3×D3—24no—
241C2×C3×D3—44no—
242C2×C3×D3—84no—
243C32×C4C4×D412yes—
244C32×C4C23×C411yescharacteristic
245C32×C4C2×#4111yescharacteristic
246C3⋊Dic3—24no—
247C3×Dic3—24no—
248C3×Dic3—42no—
249C3×Dic3—42no—
250C22×Q8—31no—
251C22×D4—31no—
252C2×SD16—38no—
253C2×SD16—32no—
254C2×SD16—32no—
255C2×M16—91no—
256C22×C8D3211yescharacteristic
257C4×Q8—94no—
258C4×Q8—182no—
259C4×D4—94no—
260C4×D4—182no—
261#117—31no—
262#117—31no—
263#117—91no—
264#117—182no—
265C2×C22⋊C4—182no—
266#107—32no—
267#106—32no—
268#103—94no—
269#102—94no—
270#97—92no—
271C4×C8—92no—
272C23×C3—21no—
273C23×C3—62no—
274C23×C3—64no—
275C23×C3—242no—
276C23×C3D3×D411yescharacteristic
277C23×C3D3×D411yescharacteristic
278C22×D3—22no—
279C22×D3—24no—
280C22×D3—82no—
281C3×Q8—34no—
282C3×Q8—64no—
283C3×Q8—62no—
284C3×D4—34no—
285C3×D4—64no—
286C3×D4—62no—
287C2×C3×C4—21no—
288C2×C3×C4—22no—
289C2×C3×C4—21no—
290C2×C3×C4—22no—
291C2×C3×C4—64no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4C2×C4×D312yes—
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4#23712yes—
299C2×C3×C4#23912yes—
300C2×C3×C4C22×Dic312yes—
301C2×C3×C4C23×D311yescharacteristic
302C2×C3×C4C23×D311yescharacteristic
303C2×Dic3—24no—
304C2×Dic3—22no—
305C2×Dic3—22no—
306C2×Dic3—22no—
307C2×Dic3—34no—
308C2×Dic3—34no—
309C2×Dic3—64no—
310C2×Dic3—244no—
311D12—24no—
312D12—22no—
313D12C22×Dic314yes—
314C4×D3—244no—
315Dic6—24no—
316Dic6—22no—
317Dic6C22×Dic314yes—
318C3×C8—22no—
319C3×C8—22no—
320C3×C8C2×C4×D312yes—
321C3×C8C2×C4×D312yes—
322C3×C8C22×Dic312yes—
323C3×C8C22×Dic312yes—
324C3⋊C8—64no—
325C3⋊C8—62no—
326C3⋊C8—62no—
327C2×C32—22no—
328C2×C32C2×C4×D411yescharacteristic
329C2×C32#57712yes—
330C3×D3—44no—
331C24—61no—
332C2×Q8—32no—
333C2×Q8—34no—
334C2×Q8—62no—
335C2×Q8—61no—
336C2×D4—32no—
337C2×D4—34no—
338C2×D4—62no—
339C2×D4—61no—
340C22×C4—61no—
341C22×C4—184no—
342C22×C4C2×D3211yescharacteristic
343SD16—38no—
344SD16—38no—
345M16—182no—
346C2×C8—92no—
347C2×C8D3×Dic314yescomplemented
348C2×C8C2×D3211yescharacteristic
349C2×C8C2×D3211yescharacteristic
350C4⋊C4—32no—
351C4⋊C4—32no—
352C4⋊C4—92no—
353C4⋊C4—184no—
354C22⋊C4—61no—
355C22⋊C4—61no—
356C22⋊C4—92no—
357C22⋊C4—184no—
358C42—61no—
359C42—61no—
360C42—92no—
361C42—184no—
362C22×C3—22no—
363C22×C3—22no—
364C22×C3—21no—
365C22×C3—22no—
366C22×C3—42no—
367C22×C3—64no—
368C22×C3—124no—
369C22×C3—244no—
370C22×C3#89312yes—
371C22×C3D4×Dic312yes—
372C22×C3C2×D3×D411yescharacteristic
373C22×C3C2×D3×D411yescharacteristic
374C2×D3—24no—
375C2×D3—44no—
376C2×D3—84no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—22no—
380C3×C4—64no—
381C3×C4—122no—
382C3×C4—122no—
383C3×C4#89312yes—
384C3×C4D4×Dic312yes—
385C3×C4C22×C4×D311yescharacteristic
386C3×C4C2×#23711yescharacteristic
387C3×C4C2×#23911yescharacteristic
388C3×C4C23×Dic311yescharacteristic
389Dic3—24no—
390Dic3—42no—
391Dic3—42no—
392Dic3—64no—
393Dic3—64no—
394Dic3—124no—
395C32#294911yescharacteristic, complemented, Sylow
396C23—62no—
397C23—64no—
398C23—242no—
399C23#380211yescharacteristic
400Q8—34no—
401Q8—62no—
402Q8—64no—
403D4—34no—
404D4—62no—
405D4—64no—
406C2×C4—62no—
407C2×C4—64no—
408C2×C4—62no—
409C2×C4—62no—
410C2×C4—94no—
411C2×C4—724no—
412C2×C4#379612yes—
413C2×C4#380211yescharacteristic
414C2×C4C2×D3×Dic312yes—
415C2×C4C22×D3211yescharacteristic
416C8—182no—
417C8C2×D3×Dic312yes—
418C8C2×D3×Dic312yes—
419C2×C3—22no—
420C2×C3—22no—
421C2×C3—21no—
422C2×C3—22no—
423C2×C3—42no—
424C2×C3—124no—
425C2×C3C2×#89311yescharacteristic
426C2×C3#576212yes—
427C2×C3#577012yes—
428C2×C3C2×D4×Dic311yescharacteristic
429D3—44no—
430C22—22no—
431C22—64no—
432C22—124no—
433C22—244no—
434C22#6389812yes—
435C22C2×#380211yescharacteristic
436C4—64no—
437C4—122no—
438C4—122no—
439C4—184no—
440C4#6389812yes—
441C4C2×#379611yescharacteristic
442C4C22×D3×Dic311yescharacteristic
443C3—21no—
444C3#7916811yescharacteristic, complemented
445C3#8384311yescharacteristic, complemented
446C2—22no—
447C2—124no—
448C2#1059468612yes—
449C2C2×#6389811yescharacteristic
subgroupG/H
centerC22C2×#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2949
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. #10594818C2semidirect
4. #10592800C2semidirect
5. C3×#5106C2semidirect
6. #10591099C2semidirect
8. #10590779C2semidirect
9. #10590775C2semidirect
19. C2×C3×#204C4semidirect
26. #63843C22semidirect
28. #63642C22semidirect
29. C8×C3⋊Dic3C22semidirect
30. C3×#818C22semidirect
31. C3×#817C22semidirect
32. #63565C22semidirect
45. #5106D3semidirect
62. C2×C3×Dic6C2×C4semidirect
65. C2×C32×C8C2×C4semidirect
79. C3×#204C2×C4semidirect
80. C3×#204C2×C4semidirect
111. C2×#204Dic3semidirect
124. #818C2×D3semidirect
125. #817C2×D3semidirect
189. C2×Dic6C2×Dic3semidirect
196. C2×C3×C8C4×D3semidirect
197. C2×C3×C8C2×Dic3semidirect
235. #204C2×Dic3semidirect
236. #204C2×Dic3semidirect
347. C2×C8D3×Dic3semidirect
395. C32#2949semidirect
444. C3#79168semidirect
445. C3#83843semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2042
#105949822
#105948182
#105928002
C3×#51062
#105910992
#105910852
#105907792
#105907752
#838433
#791683