Finite Group Databasebeta

← #11860975

Subgroups — #11860975

Order 1152.

1034 conjugacy classes of subgroups.

The subgroup lattice has 495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63808C211yesmaximal, characteristic
2#10594327C212yesmaximal, complemented
3#10592568C211yesmaximal, characteristic, complemented
4C3×D3×#106C211yesmaximal, characteristic, complemented
5C3×#4853C211yesmaximal, characteristic, complemented
6#10590819C211yesmaximal, characteristic, complemented
7#10590768C211yesmaximal, characteristic, complemented
8#10590693C211yesmaximal, characteristic, complemented
9#10590609C212yesmaximal, complemented
10#10590483C212yesmaximal, complemented
11#10590458C212yesmaximal, complemented
12#79832—31nomaximal
13#79106—31nomaximal
14C2×#3799C2212yes—
15C2×#3745C2211yescharacteristic
16#64102C2212yes—
17C2×C3×Dic12C2211yescharacteristic
18C2×C3×D3×C8C2211yescharacteristic
19C3×D3×C4⋊C4C2212yes—
20C3×#887C2212yes—
21#63904—22no—
22C4×#626—22no—
23#63894C2212yes—
24#63883—22no—
25#63855C2211yescharacteristic
26#63843C2212yes—
27#63836—22no—
28C2×#3717C2212yes—
29C2×#3711C2211yescharacteristic
30#63808C418yescomplemented
31C32×#106C2211yescharacteristic
32#63642C2211yescharacteristic
33#63636C2212yes—
34C3×#817C2211yescharacteristic
35C3×#815C2211yescharacteristic
36C3×#810C2212yes—
37C3×#808C2212yes—
38#63565C2212yes—
39#63564C2212yes—
40#63553C2211yescharacteristic
41Dic3×C3⋊C8C2211yescharacteristic
42C2×#919—31no—
43C2×#904—31no—
44#5574—32no—
45#5504—32no—
46C3×#441—31no—
47C2×C3×#106—31no—
48#5184—31no—
49#5101—31no—
50C4×#215—32no—
51#4966—32no—
52#4869—31no—
53#4869—31no—
54#4869—31no—
55#4869—61no—
56D3×#106D311yescharacteristic, complemented
57#4853—31no—
58#4853D311yescharacteristic, complemented
59#4852—32no—
60#4852—32no—
61#4803—32no—
62#4788—32no—
63#4711—31no—
64#4708—31no—
65C2×C4⋊(C3⋊D3)C2312yes—
66C2×C4×C3⋊D3—22no—
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3C2311yescharacteristic
69C2×C3×Dic6C2312yes—
70C2×#626—22no—
71C2×#624—22no—
72C2×#624—22no—
73#3799—24no—
74#3799C2×C418yescomplemented
75C2×C32×C8C2311yescharacteristic
76C32×C4⋊C4C2312yes—
77#3752—22no—
78C4×C3⋊Dic3C2311yescharacteristic
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80#3745C2×C414yescomplemented
81C3×C4⋊Dic3C2312yes—
82C3×Dic3⋊C4—22no—
83C3×Dic3⋊C4—22no—
84C3×C4×Dic3—22no—
85C3×C4×Dic3C2311yescharacteristic
86C2×C3×C3⋊C8C2311yescharacteristic
87C2×C3×C3⋊C8C2311yescharacteristic
88C3×Dic12C2×C414yescomplemented
89C3×D3×C8C2×C414yescomplemented
90Dic3⋊Dic3—22no—
91Dic3⋊Dic3D412yes—
92#3722—22no—
93(C2×D3)⋊Dic3D412yes—
94Dic32—22no—
95#3717C2×C418yescomplemented
96#3711—22no—
97#2952—91noSylow
98C2×#239—32no—
99C2×#235—32no—
100C2×C3×Q16—31no—
101C22×C3×C8—31no—
102C3×C4×Q8—32no—
103C2×C3×C4⋊C4—32no—
104Q8×Dic3—32no—
105C2×#215—32no—
106C4×#67—62no—
107C4×#67—62no—
108#926—31no—
109C2×#208—31no—
110#919—38no—
111C2×Dic12C2×D311yescharacteristic
112#904—38no—
113C2×D24—31no—
114C2×D24—31no—
115C2×D24—61no—
116C2×#204—32no—
117C2×ΓL(1,𝔽25)—31no—
118C2×D3×C8C2×D311yescharacteristic
119#893—32no—
120#893—32no—
121#893—32no—
122#893—62no—
123#893—62no—
124#892—62no—
125D3×C4⋊C4—62no—
126D3×C4⋊C4—62no—
127D3×C4⋊C4C2×D312yes—
128#887—32no—
129#887C2×D312yes—
130C4×D12—32no—
131C4×D12—62no—
132#872—31no—
133#872—62no—
134C3×#106—21no—
135C3×#106—31no—
136C3×#106—32no—
137C3×#106C2×D311yescharacteristic
138C3×#106C2×D311yescharacteristic
139C3×#103—32no—
140C3×#97—31no—
141#835—32no—
142#821—32no—
143#817C2×D311yescharacteristic
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#810C2×D312yes—
153#809—32no—
154#809—32no—
155#809—32no—
156#809—62no—
157#808C2×D312yes—
158C4×C3⋊C8—31no—
159C22×C3⋊D3—22no—
160C22×C3×D3C2×D411yescharacteristic
161C2×C32×C4—22no—
162C2×C32×C4C2411yescharacteristic
163C2×C3⋊Dic3C2×D412yes—
164C4⋊(C3⋊D3)—22no—
165C4⋊(C3⋊D3)C22×C414yes—
166C4×C3⋊D3—82no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3C2×D412yes—
170C2×C3×Dic3C2×D411yescharacteristic
171C3×C4×D3—82no—
172C3×C4×D3C22×C412yes—
173C3×C4×D3#4112yes—
174C3×Dic6—22no—
175C3×Dic6C22×C414yes—
176#626—28no—
177#624—28no—
178#624—82no—
179C32×C8C22×C412yes—
180C3⋊(C3⋊C8)—21no—
181C3×C3⋊C8—21no—
182C3×C3⋊C8C22×C412yes—
183C2×#135—91no—
184#520—92no—
185#442—91no—
186#442—91no—
187#441—31no—
188#441—91no—
189C4×SD16—92no—
190C4×SD16—92no—
191C2×#106—31no—
192#417—92no—
193#405—91no—
194C2×C3×Q8—32no—
195C22×C3×C4—31no—
196C22×C3×C4—62no—
197C2×#67—62no—
198#239—38no—
199#239—64no—
200#235—38no—
201#235—64no—
202C2×D12—32no—
203C2×D12—32no—
204C2×D12—62no—
205C2×D12—62no—
206C2×C4×D3—22no—
207C2×C4×D3—62no—
208C2×C4×D3—62no—
209C2×C4×D3—62no—
210C2×C4×D3—62no—
211C2×C4×D3—62no—
212C2×C4×D3—62no—
213C2×C4×D3—122no—
214C2×C4×D3C22×D311yescharacteristic
215C2×Dic6C22×D312yes—
216C3×Q16—34no—
217C2×C3×C8—21no—
218C2×C3×C8—31no—
219C2×C3×C8—34no—
220C2×C3×C8—31no—
221C2×C3×C8C22×D311yescharacteristic
222C2×C3×C8C22×D311yescharacteristic
223C3×C4⋊C4—22no—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—62no—
226C3×C4⋊C4—62no—
227C3×C4⋊C4C22×D312yes—
228C3×C4⋊C4C22×D312yes—
229C3×C42—31no—
230C3×C42—62no—
231#217—32no—
232#215—38no—
233(C2×D3)⋊C4—32no—
234(C2×D3)⋊C4—62no—
235(C2×D3)⋊C4—62no—
236(C2×D3)⋊C4—62no—
237(C2×D3)⋊C4—62no—
238(C2×D3)⋊C4—122no—
239C4⋊Dic3—32no—
240C4⋊Dic3—62no—
241C4⋊Dic3C22×D312yes—
242Dic3⋊C4—22no—
243Dic3⋊C4—22no—
244Dic3⋊C4—32no—
245Dic3⋊C4—62no—
246C4×Dic3—22no—
247C4×Dic3—31no—
248C4×Dic3—31no—
249C4×Dic3—61no—
250C4×Dic3—62no—
251C4×Dic3—62no—
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
259Dic12C4×D314yescomplemented
260D24—34no—
261D24—34no—
262D24—64no—
263#204—38no—
264ΓL(1,𝔽25)—62no—
265D3×C8C4×D314yescomplemented
266C22×C32C22×D411yescharacteristic
267C2×C3⋊D3—24no—
268C2×C3⋊D3—42no—
269C2×C3⋊D3—42no—
270C2×C3×D3—22no—
271C2×C3×D3C4×D412yes—
272C32×C4—42no—
273C32×C4C23×C411yescharacteristic
274C32×C4C2×#4111yescharacteristic
275C3⋊Dic3—22no—
276C3×Dic3—24no—
277C3×Dic3—22no—
278C3×Dic3—42no—
279C3×Dic3C4×D412yes—
280C2×#41—92no—
281#135—98no—
282C2×Q16—31no—
283C2×SD16—92no—
284C2×D8—91no—
285C2×M16—91no—
286C22×C8—31no—
287C4×Q8—32no—
288C4×Q8—92no—
289C4×D4—92no—
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—32no—
301#103—92no—
302#102—92no—
303#102—92no—
304#97—31no—
305#97—91no—
306C4×C8—91no—
307C4×C8—91no—
308C23×C3—31no—
309C22×D3—62no—
310C22×D3—62no—
311C22×D3—122no—
312C22×D3D3×D411yescharacteristic
313C3×Q8—34no—
314C3×Q8—62no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—21no—
318C2×C3×C4—31no—
319C2×C3×C4—32no—
320C2×C3×C4—32no—
321C2×C3×C4—32no—
322C2×C3×C4—42no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—242no—
326C2×C3×C4C23×D311yescharacteristic
327C2×C3×C4C23×D311yescharacteristic
328#67—68no—
329C2×Dic3—22no—
330C2×Dic3—22no—
331C2×Dic3—32no—
332C2×Dic3—32no—
333C2×Dic3—62no—
334C2×Dic3D3×D412yes—
335C2×Dic3D3×D411yescharacteristic
336D12—34no—
337D12—34no—
338D12—64no—
339D12—68no—
340D12—62no—
341D12—62no—
342D12—122no—
343C4×D3—68no—
344C4×D3—68no—
345C4×D3—82no—
346C4×D3—242no—
347C4×D3—242no—
348C4×D3—242no—
349C4×D3—242no—
350C4×D3—244no—
351C4×D3C2×C4×D312yes—
352C4×D3#23912yes—
353Dic6—22no—
354Dic6C2×C4×D314yes—
355C3×C8—22no—
356C3×C8—32no—
357C3×C8—61no—
358C3×C8C2×C4×D312yes—
359C3×C8C2×C4×D312yes—
360C3⋊C8—21no—
361C3⋊C8—61no—
362C3⋊C8—61no—
363C3⋊C8—121no—
364C3⋊C8C2×C4×D312yes—
365C2×C32C2×C4×D411yescharacteristic
366C2×C32#57712yes—
367C3⋊D3—44no—
368C3×D3—22no—
369#41—98no—
370#41—184no—
371C2×Q8—32no—
372C2×D4—92no—
373C2×D4—182no—
374C22×C4—31no—
375C22×C4—62no—
376C22×C4—182no—
377C22×C4—182no—
378C22×C4—182no—
379Q16—34no—
380SD16—98no—
381D8—94no—
382M16—182no—
383C2×C8—31no—
384C2×C8—34no—
385C2×C8—31no—
386C2×C8—91no—
387C2×C8C2×D3211yescharacteristic
388C4⋊C4—32no—
389C4⋊C4—62no—
390C4⋊C4—62no—
391C4⋊C4—92no—
392C4⋊C4—182no—
393C4⋊C4C2×D3212yes—
394C22⋊C4—92no—
395C22⋊C4—182no—
396C22⋊C4—182no—
397C42—31no—
398C42—62no—
399C42—91no—
400C42—182no—
401C22×C3—21no—
402C22×C3—32no—
403C22×C3—62no—
404C22×C3C2×D3×D411yescharacteristic
405C22×C3C2×D3×D411yescharacteristic
406C2×D3—22no—
407C2×D3—64no—
408C2×D3—64no—
409C2×D3—124no—
410C2×D3—122no—
411C2×D3—122no—
412C2×D3—122no—
413C2×D3—122no—
414C2×D3—242no—
415C2×D3—242no—
416C2×D3#89312yes—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—32no—
420C3×C4—42no—
421C3×C4—42no—
422C3×C4—64no—
423C3×C4—62no—
424C3×C4—82no—
425C3×C4—122no—
426C3×C4C22×C4×D311yescharacteristic
427C3×C4C22×C4×D311yescharacteristic
428C3×C4C2×#23911yescharacteristic
429C3×C4D3×#4111yescharacteristic
430Dic3—22no—
431Dic3—24no—
432Dic3—42no—
433Dic3—62no—
434Dic3—62no—
435Dic3—122no—
436Dic3#89312yes—
437C32#295211yescharacteristic, complemented, Sylow
438C23—31no—
439C23—182no—
440Q8—34no—
441Q8—62no—
442D4—94no—
443D4—188no—
444D4—182no—
445C2×C4—22no—
446C2×C4—31no—
447C2×C4—32no—
448C2×C4—32no—
449C2×C4—32no—
450C2×C4—62no—
451C2×C4—62no—
452C2×C4—92no—
453C2×C4—188no—
454C2×C4—242no—
455C2×C4—722no—
456C2×C4—722no—
457C2×C4C22×D3211yescharacteristic
458C8—32no—
459C8—61no—
460C8—181no—
461C8C4×D3212yes—
462C2×C3—21no—
463C2×C3—22no—
464C2×C3—62no—
465C2×C3C2×#89311yescharacteristic
466C2×C3C4×D3×D411yescharacteristic
467C2×C3#576212yes—
468C2×C3#577812yes—
469D3—22no—
470D3—124no—
471D3—124no—
472D3—244no—
473C22—32no—
474C22—62no—
475C22—184no—
476C22—362no—
477C22—362no—
478C22D32×D411yescharacteristic
479C4—32no—
480C4—42no—
481C4—64no—
482C4—62no—
483C4—122no—
484C4—182no—
485C4C2×C4×D3211yescharacteristic
486C4D3×#23911yescharacteristic
487C3—21no—
488C3#7910611yescharacteristic, complemented
489C3#7983211yescharacteristic, complemented
490C2—62no—
491C2—364no—
492C2D3×#89311yescharacteristic
493C2#1059475112yes—
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×#63808C2
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. #10594327C2semidirect
3. #10592568C2semidirect
4. C3×D3×#106C2semidirect
5. C3×#4853C2semidirect
6. #10590819C2semidirect
7. #10590768C2semidirect
8. #10590693C2semidirect
9. #10590609C2semidirect
10. #10590483C2semidirect
11. #10590458C2semidirect
30. #63808C4semidirect
56. D3×#106D3semidirect
58. #4853D3semidirect
74. #3799C2×C4semidirect
80. #3745C2×C4semidirect
88. C3×Dic12C2×C4semidirect
89. C3×D3×C8C2×C4semidirect
95. #3717C2×C4semidirect
259. Dic12C4×D3semidirect
265. D3×C8C4×D3semidirect
437. C32#2952semidirect
488. C3#79106semidirect
489. C3#79832semidirect

Maximal subgroups

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

subgroupindex
C2×#638082
#105943272
#105925682
C3×D3×#1062
C3×#48532
#105908192
#105907682
#105906932
#105906092
#105904832
#105904582
#798323
#791063