Finite Group Databasebeta

← #11860973

Subgroups — #11860973

Order 1152.

1022 conjugacy classes of subgroups.

The subgroup lattice has 491 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63807C211yesmaximal, characteristic
2#10594359C212yesmaximal, complemented
3#10592552C211yesmaximal, characteristic, complemented
4C3×#4869C211yesmaximal, characteristic, complemented
5C3×D3×#106C211yesmaximal, characteristic, complemented
6#10590810C211yesmaximal, characteristic, complemented
7#10590781C211yesmaximal, characteristic, complemented
8#10590693C211yesmaximal, characteristic, complemented
9#10590607C212yesmaximal, complemented
10#10590479C212yesmaximal, complemented
11#10590460C212yesmaximal, complemented
12#79868—31nomaximal
13#79106—31nomaximal
14C2×#3795C2212yes—
15C2×#3746C2211yescharacteristic
16#64096C2212yes—
17C2×C3×D24C2211yescharacteristic
18C2×C3×D3×C8C2211yescharacteristic
19C3×#893C2212yes—
20C3×D3×C4⋊C4C2212yes—
21C4×#625—22no—
22#63898C2212yes—
23#63879—22no—
24#63878—22no—
25D3×Dic3⋊C4—22no—
26#63855C2211yescharacteristic
27#63844C2212yes—
28C2×#3716C2212yes—
29C2×#3711C2211yescharacteristic
30#63807C418yescomplemented
31C32×#106C2211yescharacteristic
32#63642C2211yescharacteristic
33#63637C2212yes—
34C3×#817C2211yescharacteristic
35C3×#815C2211yescharacteristic
36C3×#809C2212yes—
37C3×#808C2212yes—
38#63567C2212yes—
39#63562C2212yes—
40#63553C2211yescharacteristic
41Dic3×C3⋊C8C2211yescharacteristic
42C2×#912—31no—
43C2×#904—31no—
44#5546—32no—
45#5504—32no—
46C3×#442—31no—
47C2×C3×#106—31no—
48#5152—31no—
49#5101—31no—
50C4×#214—32no—
51#4966—32no—
52#4869—31no—
53#4869D311yescharacteristic, complemented
54D3×#106D311yescharacteristic, complemented
55#4853—31no—
56#4853—31no—
57#4853—31no—
58#4853—61no—
59#4852—32no—
60#4852—32no—
61#4771—32no—
62#4758—32no—
63#4716—31no—
64#4708—31no—
65C2×#634C2312yes—
66C2×C3×D12C2312yes—
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3C2311yescharacteristic
70C2×#625—22no—
71C2×D3×Dic3—22no—
72C2×D3×Dic3—22no—
73#3795—24no—
74#3795C2×C418yescomplemented
75C2×C32×C8C2311yescharacteristic
76C32×C4⋊C4C2312yes—
77#3750—22no—
78C4×C3⋊Dic3—22no—
79C4×C3⋊Dic3C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81#3746C2×C414yescomplemented
82C3×(C2×D3)⋊C4—22no—
83C3×C4⋊Dic3C2312yes—
84C3×Dic3⋊C4—22no—
85C3×C4×Dic3C2311yescharacteristic
86C2×C3×C3⋊C8C2311yescharacteristic
87C2×C3×C3⋊C8C2311yescharacteristic
88C3×D24C2×C414yescomplemented
89C3×D3×C8C2×C414yescomplemented
90#3724—22no—
91Dic3⋊Dic3D412yes—
92(C2×D3)⋊Dic3—22no—
93(C2×D3)⋊Dic3D412yes—
94Dic32—22no—
95#3716C2×C418yescomplemented
96#3711—22no—
97#2952—91noSylow
98C2×#237—32no—
99C2×#235—32no—
100C2×C3×D8—31no—
101C22×C3×C8—31no—
102C3×C4×D4—32no—
103C2×C3×C4⋊C4—32no—
104D4×Dic3—32no—
105C2×#214—32no—
106C4×#67—62no—
107C4×#67—62no—
108C4×#67—62no—
109#926—31no—
110C2×Dic3⋊C4—62no—
111C2×#208—31no—
112#912—38no—
113C2×Dic12—31no—
114C2×Dic12—31no—
115C2×Dic12—61no—
116#904—38no—
117C2×D24C2×D311yescharacteristic
118C2×#204—32no—
119C2×ΓL(1,𝔽25)—31no—
120C2×D3×C8C2×D311yescharacteristic
121#893—32no—
122#893C2×D312yes—
123#892—62no—
124D3×C4⋊C4—62no—
125D3×C4⋊C4C2×D312yes—
126#887—32no—
127#887—32no—
128#887—32no—
129#887—62no—
130#67⋊C4—62no—
131#877—62no—
132#872—31no—
133C4×Dic6—32no—
134C3×#106—21no—
135C3×#106—31no—
136C3×#106—32no—
137C3×#106C2×D311yescharacteristic
138C3×#106C2×D311yescharacteristic
139C3×#102—32no—
140C3×#97—31no—
141#832—32no—
142#817C2×D311yescharacteristic
143#816—32no—
144#815—31no—
145#815—31no—
146#815—61no—
147#815C2×D311yescharacteristic
148C8×Dic3—31no—
149C8×Dic3—31no—
150C8×Dic3—31no—
151#810—32no—
152#810—32no—
153#810—32no—
154#810—62no—
155#809—32no—
156#809C2×D312yes—
157#808C2×D312yes—
158C4×C3⋊C8—31no—
159C22×C3×D3—22no—
160C22×C3×D3C2×D411yescharacteristic
161C2×C32×C4—22no—
162C2×C32×C4C2411yescharacteristic
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3C2×D412yes—
165#634—22no—
166#634C22×C414yes—
167C2×C3×Dic3—22no—
168C2×C3×Dic3C2×D412yes—
169C2×C3×Dic3C2×D411yescharacteristic
170C3×D12—22no—
171C3×D12C22×C414yes—
172C3×C4×D3—82no—
173C3×C4×D3—82no—
174C3×C4×D3C22×C412yes—
175C3×C4×D3#4112yes—
176#625—28no—
177D3×Dic3—28no—
178D3×Dic3—82no—
179C32×C8C22×C412yes—
180C3⋊(C3⋊C8)—21no—
181C3×C3⋊C8—21no—
182C3×C3⋊C8C22×C412yes—
183C2×#135—91no—
184#520—92no—
185#442—31no—
186#442—91no—
187#441—91no—
188#441—91no—
189C4×SD16—92no—
190C4×SD16—92no—
191C2×#106—31no—
192#417—92no—
193#405—91no—
194C2×C3×D4—32no—
195C22×C3×C4—31no—
196C22×C3×C4—62no—
197C22×C3×C4—62no—
198C2×#67—62no—
199C2×#67—62no—
200C22×Dic3—62no—
201C22×Dic3—62no—
202#237—38no—
203#237—64no—
204#235—38no—
205#235—64no—
206C2×D12C22×D312yes—
207C2×C4×D3—22no—
208C2×C4×D3—22no—
209C2×C4×D3—62no—
210C2×C4×D3—62no—
211C2×C4×D3C22×D311yescharacteristic
212C2×Dic6—32no—
213C2×Dic6—32no—
214C2×Dic6—62no—
215C3×D8—34no—
216C2×C3×C8—21no—
217C2×C3×C8—31no—
218C2×C3×C8—34no—
219C2×C3×C8—31no—
220C2×C3×C8C22×D311yescharacteristic
221C2×C3×C8C22×D311yescharacteristic
222C3×C4⋊C4—22no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4—62no—
225C3×C4⋊C4C22×D312yes—
226C3×C4⋊C4C22×D312yes—
227C3×C22⋊C4—62no—
228C3×C42—31no—
229#217—32no—
230#217—62no—
231#214—38no—
232(C2×D3)⋊C4—22no—
233(C2×D3)⋊C4—32no—
234(C2×D3)⋊C4—62no—
235C4⋊Dic3—32no—
236C4⋊Dic3C22×D312yes—
237Dic3⋊C4—22no—
238Dic3⋊C4—32no—
239Dic3⋊C4—62no—
240Dic3⋊C4—62no—
241Dic3⋊C4—62no—
242Dic3⋊C4—62no—
243Dic3⋊C4—122no—
244C4×Dic3—31no—
245C4×Dic3—31no—
246C4×Dic3—61no—
247C4×Dic3—62no—
248C4×Dic3—62no—
249C4×Dic3—62no—
250C4×Dic3—62no—
251C4×Dic3—122no—
252C4×Dic3C22×D311yescharacteristic
253#208—62no—
254C2×C3⋊C8—31no—
255C2×C3⋊C8—31no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8C22×D311yescharacteristic
258C2×C3⋊C8C22×D311yescharacteristic
259Dic12—34no—
260Dic12—34no—
261Dic12—64no—
262D24C4×D314yescomplemented
263#204—38no—
264ΓL(1,𝔽25)—62no—
265D3×C8C4×D314yescomplemented
266C22×C32C22×D411yescharacteristic
267C2×C3×D3—22no—
268C2×C3×D3—24no—
269C2×C3×D3—42no—
270C2×C3×D3—42no—
271C2×C3×D3C4×D412yes—
272C32×C4—42no—
273C32×C4C23×C411yescharacteristic
274C32×C4C2×#4111yescharacteristic
275C3⋊Dic3—24no—
276C3⋊Dic3—22no—
277C3×Dic3—22no—
278C3×Dic3—42no—
279C3×Dic3C4×D412yes—
280C2×#41—92no—
281#135—98no—
282C2×Q16—91no—
283C2×SD16—92no—
284C2×D8—31no—
285C2×M16—91no—
286C22×C8—31no—
287C4×Q8—92no—
288C4×Q8—92no—
289C4×D4—32no—
290C4×D4—92no—
291C4×D4—182no—
292C4×D4—182no—
293#117—91no—
294#117—182no—
295C2×C4⋊C4—32no—
296C2×C4⋊C4—182no—
297#106—31no—
298#106—32no—
299#106D3211yescharacteristic
300#103—92no—
301#103—92no—
302#102—32no—
303#102—92no—
304#97—31no—
305#97—91no—
306C4×C8—91no—
307C4×C8—91no—
308C23×C3—31no—
309C23×C3—62no—
310C22×D3—22no—
311C22×D3D3×D411yescharacteristic
312C3×D4—34no—
313C3×D4—62no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—21no—
317C2×C3×C4—31no—
318C2×C3×C4—32no—
319C2×C3×C4—32no—
320C2×C3×C4—32no—
321C2×C3×C4—42no—
322C2×C3×C4—62no—
323C2×C3×C4—242no—
324C2×C3×C4—242no—
325C2×C3×C4C23×D311yescharacteristic
326C2×C3×C4C23×D311yescharacteristic
327#67—68no—
328#67—68no—
329C2×Dic3—22no—
330C2×Dic3—32no—
331C2×Dic3—32no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—68no—
336C2×Dic3—122no—
337C2×Dic3—242no—
338C2×Dic3D3×D412yes—
339C2×Dic3D3×D411yescharacteristic
340D12—22no—
341D12C2×C4×D314yes—
342C4×D3—68no—
343C4×D3—82no—
344C4×D3—82no—
345C4×D3—242no—
346C4×D3C2×C4×D312yes—
347C4×D3#23912yes—
348Dic6—34no—
349Dic6—34no—
350Dic6—64no—
351Dic6—62no—
352Dic6—62no—
353Dic6—122no—
354C3×C8—22no—
355C3×C8—32no—
356C3×C8—61no—
357C3×C8C2×C4×D312yes—
358C3×C8C2×C4×D312yes—
359C3⋊C8—21no—
360C3⋊C8—61no—
361C3⋊C8—61no—
362C3⋊C8—121no—
363C3⋊C8C2×C4×D312yes—
364C2×C32C2×C4×D411yescharacteristic
365C2×C32#57712yes—
366C3×D3—22no—
367C3×D3—44no—
368#41—98no—
369#41—184no—
370C2×Q8—92no—
371C2×D4—32no—
372C2×D4—182no—
373C22×C4—31no—
374C22×C4—62no—
375C22×C4—62no—
376C22×C4—182no—
377C22×C4—182no—
378Q16—94no—
379SD16—98no—
380D8—34no—
381M16—182no—
382C2×C8—31no—
383C2×C8—34no—
384C2×C8—31no—
385C2×C8—91no—
386C2×C8C2×D3211yescharacteristic
387C4⋊C4—32no—
388C4⋊C4—62no—
389C4⋊C4—92no—
390C4⋊C4—182no—
391C4⋊C4—182no—
392C4⋊C4C2×D3212yes—
393C22⋊C4—62no—
394C22⋊C4—92no—
395C22⋊C4—182no—
396C42—31no—
397C42—91no—
398C42—182no—
399C42—182no—
400C22×C3—21no—
401C22×C3—32no—
402C22×C3—62no—
403C22×C3—64no—
404C22×C3—122no—
405C22×C3—122no—
406C22×C3C2×D3×D411yescharacteristic
407C22×C3C2×D3×D411yescharacteristic
408C2×D3—22no—
409C2×D3—24no—
410C2×D3—42no—
411C2×D3—42no—
412C2×D3#89312yes—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—32no—
416C3×C4—42no—
417C3×C4—42no—
418C3×C4—62no—
419C3×C4—82no—
420C3×C4—122no—
421C3×C4C22×C4×D311yescharacteristic
422C3×C4C22×C4×D311yescharacteristic
423C3×C4C2×#23911yescharacteristic
424C3×C4D3×#4111yescharacteristic
425Dic3—22no—
426Dic3—42no—
427Dic3—64no—
428Dic3—62no—
429Dic3—62no—
430Dic3—64no—
431Dic3—124no—
432Dic3—122no—
433Dic3#89312yes—
434C32#295211yescharacteristic, complemented, Sylow
435C23—31no—
436C23—62no—
437Q8—94no—
438Q8—182no—
439D4—34no—
440D4—62no—
441D4—188no—
442C2×C4—22no—
443C2×C4—31no—
444C2×C4—32no—
445C2×C4—32no—
446C2×C4—32no—
447C2×C4—62no—
448C2×C4—92no—
449C2×C4—188no—
450C2×C4—182no—
451C2×C4—242no—
452C2×C4—242no—
453C2×C4—722no—
454C2×C4C22×D3211yescharacteristic
455C8—32no—
456C8—61no—
457C8—181no—
458C8C4×D3212yes—
459C2×C3—21no—
460C2×C3—22no—
461C2×C3—62no—
462C2×C3—124no—
463C2×C3C2×#89311yescharacteristic
464C2×C3C4×D3×D411yescharacteristic
465C2×C3#576212yes—
466C2×C3#577512yes—
467D3—22no—
468D3—44no—
469C22—32no—
470C22—62no—
471C22—64no—
472C22—122no—
473C22—122no—
474C22D32×D411yescharacteristic
475C4—32no—
476C4—42no—
477C4—62no—
478C4—122no—
479C4—184no—
480C4—182no—
481C4C2×C4×D3211yescharacteristic
482C4D3×#23911yescharacteristic
483C3—21no—
484C3#7910611yescharacteristic, complemented
485C3#7986811yescharacteristic, complemented
486C2—62no—
487C2—124no—
488C2D3×#89311yescharacteristic
489C2#1059474912yes—
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×#63807C2
cosocleC2×C32×C4C24
hypercenter#106D32
hypocenterC32#2952
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #10594359C2semidirect
3. #10592552C2semidirect
4. C3×#4869C2semidirect
5. C3×D3×#106C2semidirect
6. #10590810C2semidirect
7. #10590781C2semidirect
8. #10590693C2semidirect
9. #10590607C2semidirect
10. #10590479C2semidirect
11. #10590460C2semidirect
30. #63807C4semidirect
53. #4869D3semidirect
54. D3×#106D3semidirect
74. #3795C2×C4semidirect
81. #3746C2×C4semidirect
88. C3×D24C2×C4semidirect
89. C3×D3×C8C2×C4semidirect
95. #3716C2×C4semidirect
262. D24C4×D3semidirect
265. D3×C8C4×D3semidirect
434. C32#2952semidirect
484. C3#79106semidirect
485. C3#79868semidirect

Maximal subgroups

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

subgroupindex
C2×#638072
#105943592
#105925522
C3×#48692
C3×D3×#1062
#105908102
#105907812
#105906932
#105906072
#105904792
#105904602
#798683
#791063