Finite Group Databasebeta

← #11860220

Subgroups — #11860220

Order 1152.

1050 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
2C4×#3799C212yesmaximal, complemented
3#10592410C211yesmaximal, characteristic, complemented
4C3×#4716C211yesmaximal, characteristic, complemented
5C3×D3×#97C211yesmaximal, characteristic, complemented
6#10590812C211yesmaximal, characteristic, complemented
7#10590795C212yesmaximal, complemented
8#10590768C211yesmaximal, characteristic, complemented
9#10590706C211yesmaximal, characteristic, complemented
10#10590690C212yesmaximal, complemented
11#10590362C212yesmaximal, complemented
12#79828—31nomaximal
13#78494—31nomaximal
14C2×#3799C2212yes—
15C2×#3745C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C2212yes—
17C2×C3×Dic12C2211yescharacteristic
18C2×C3×D3×C8C2211yescharacteristic
19C2×C3×D3×C8C2211yescharacteristic
20C3×C42×D3C2211yescharacteristic
21C3×C4×Dic6C2212yes—
22#63904—22no—
23C4×#626—22no—
24#63894C2212yes—
25C4×#624—22no—
26Dic3×Dic6C2212yes—
27#63841C2212yes—
28#63836—22no—
29C2×#3717C2212yes—
30#63808C418yescomplemented
31C32×#97C2211yescharacteristic
32#63648C2212yes—
33#63644C2211yescharacteristic
34C3×#817C2211yescharacteristic
35C3×#816C2212yes—
36C3×#815C2211yescharacteristic
37C3×#815C2211yescharacteristic
38C3×#803C2211yescharacteristic
39#63575C2212yes—
40#63566C2212yes—
41#63564C2212yes—
42C2×#919—31no—
43C2×#904—31no—
44C4×#239—32no—
45C4×#235—32no—
46C3×#441—31no—
47C2×C3×#97—31no—
48#5184—31no—
49#5113—32no—
50#5106—31no—
51#5026—32no—
52#4869—31no—
53#4860—31no—
54#4817—32no—
55#4804—32no—
56#4716—31no—
57#4716D311yescharacteristic, complemented
58#4711—31no—
59#4711—31no—
60#4711—31no—
61#4711—61no—
62#4710—32no—
63#4710—32no—
64D3×#97D311yescharacteristic, complemented
65C2×C4⋊(C3⋊D3)C2312yes—
66C2×C4×C3⋊D3—22no—
67C2×C3×C4×D3D412yes—
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
76C2×C32×C8C2311yescharacteristic
77C32×C42C2311yescharacteristic
78#3752—22no—
79C4⋊(C3⋊Dic3)C2312yes—
80#3745C2×C414yescomplemented
81C3×C4⋊Dic3C2312yes—
82C3×Dic3⋊C4—22no—
83C3×C4×Dic3—22no—
84C3×C4×Dic3D412yes—
85C3×C4×Dic3C2311yescharacteristic
86C2×C3×C3⋊C8C2311yescharacteristic
87C2×C3×C3⋊C8C2311yescharacteristic
88C3×Dic12C2×C414yescomplemented
89C3×D3×C8—22no—
90C3×D3×C8C2×C414yescomplemented
91Dic3⋊Dic3—22no—
92#3722—22no—
93(C2×D3)⋊Dic3—22no—
94Dic32—22no—
95Dic32—22no—
96#3717C2×C418yescomplemented
97#2943—91noSylow
98C2×#239—32no—
99C2×#235—32no—
100C2×C3×Q16—31no—
101C22×C3×C8—31no—
102C22×C3×C8—31no—
103C3×C4×Q8—32no—
104C2×C3×C42—31no—
105Q8×Dic3—32no—
106C2×#215—32no—
107C4×#67—62no—
108C4×#67—62no—
109#926—32no—
110#919—38no—
111C2×Dic12C2×D311yescharacteristic
112#904—38no—
113C2×D24—31no—
114C2×D24—31no—
115C2×D24—61no—
116C2×#204—32no—
117C2×D3×C8C2×D311yescharacteristic
118C2×D3×C8C2×D311yescharacteristic
119#893—32no—
120#893—62no—
121#892—32no—
122#892—62no—
123C4×D12—32no—
124C4×D12—32no—
125C4×D12—32no—
126C4×D12—62no—
127C4×D12—62no—
128#872—62no—
129C42×D3—62no—
130C42×D3—62no—
131C42×D3C2×D311yescharacteristic
132C4×Dic6—32no—
133C4×Dic6C2×D312yes—
134C3×#106—31no—
135C3×#103—32no—
136C3×#97—21no—
137C3×#97—31no—
138C3×#97—31no—
139C3×#97—31no—
140C3×#97C2×D311yescharacteristic
141C3×#97C2×D311yescharacteristic
142#835—32no—
143#821—32no—
144#821—32no—
145#821—32no—
146#821—62no—
147#818—32no—
148#817—31no—
149#817—31no—
150#817—61no—
151#817C2×D311yescharacteristic
152#816—32no—
153#816C2×D312yes—
154#815C2×D311yescharacteristic
155#815C2×D311yescharacteristic
156#809—32no—
157#807—32no—
158#803C2×D311yescharacteristic
159C22×C3⋊D3—22no—
160C22×C3×D3C2×D411yescharacteristic
161C2×C32×C4C2×D412yes—
162C2×C32×C4C2411yescharacteristic
163C2×C3⋊Dic3—22no—
164C4⋊(C3⋊D3)—22no—
165C4⋊(C3⋊D3)C22×C414yes—
166C4×C3⋊D3—44no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3C2×D412yes—
170C2×C3×Dic3C2×D411yescharacteristic
171C3×C4×D3—42no—
172C3×C4×D3C22×C412yes—
173C3×C4×D3#4112yes—
174C3×Dic6—22no—
175C3×Dic6C22×C414yes—
176#626—28no—
177#624—28no—
178#624—44no—
179C32×C8—21no—
180C32×C8C22×C412yes—
181C3×C3⋊C8—21no—
182C3×C3⋊C8C22×C412yes—
183C2×#135—91no—
184C4×#41—92no—
185#442—91no—
186#442—91no—
187#441—31no—
188#441—91no—
189#440—92no—
190#440—92no—
191#427—91no—
192#416—92no—
193C2×#97—31no—
194C2×C3×Q8—32no—
195C22×C3×C4—31no—
196C22×C3×C4—32no—
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—62no—
207C2×C4×D3—62no—
208C2×C4×D3—62no—
209C2×C4×D3—62no—
210C2×C4×D3—62no—
211C2×C4×D3—62no—
212C2×C4×D3—122no—
213C2×C4×D3D1212yes—
214C2×C4×D3C22×D311yescharacteristic
215C2×Dic6C22×D312yes—
216C3×Q16—34no—
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—31no—
220C2×C3×C8—34no—
221C2×C3×C8—31no—
222C2×C3×C8—62no—
223C2×C3×C8C22×D311yescharacteristic
224C2×C3×C8C22×D311yescharacteristic
225C2×C3×C8C22×D311yescharacteristic
226C2×C3×C8C22×D311yescharacteristic
227C3×C4⋊C4—32no—
228C3×C4⋊C4—62no—
229C3×C42—21no—
230C3×C42—32no—
231C3×C42—31no—
232C3×C42—62no—
233C3×C42C22×D311yescharacteristic
234C3×C42C22×D311yescharacteristic
235#217—62no—
236#215—38no—
237(C2×D3)⋊C4—62no—
238(C2×D3)⋊C4—62no—
239(C2×D3)⋊C4—62no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—62no—
242(C2×D3)⋊C4—122no—
243C4⋊Dic3—32no—
244C4⋊Dic3—32no—
245C4⋊Dic3—62no—
246C4⋊Dic3—62no—
247C4⋊Dic3C22×D312yes—
248Dic3⋊C4—22no—
249Dic3⋊C4—62no—
250C4×Dic3—22no—
251C4×Dic3—62no—
252C4×Dic3—62no—
253C4×Dic3—62no—
254C4×Dic3—62no—
255C4×Dic3D1212yes—
256C4×Dic3C22×D311yescharacteristic
257C2×C3⋊C8C22×D311yescharacteristic
258C2×C3⋊C8C22×D311yescharacteristic
259Dic12C4×D314yescomplemented
260D24—34no—
261D24—34no—
262D24—64no—
263#204—38no—
264D3×C8—22no—
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—22no—
273C32×C4C23×C411yescharacteristic
274C32×C4C2×#4111yescharacteristic
275C3⋊Dic3—42no—
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—
285C22×C8—31no—
286C22×C8—31no—
287C4×Q8—32no—
288C4×Q8—92no—
289C4×D4—92no—
290C4×D4—92no—
291C4×D4—182no—
292C4×D4—182no—
293#117—92no—
294#117—182no—
295C2×C42—31no—
296C2×C42—182no—
297#107—92no—
298#106—31no—
299#106—91no—
300#103—32no—
301#103—92no—
302#102—92no—
303#102—92no—
304#97—31no—
305#97—31no—
306#97—31no—
307#97D3211yescharacteristic
308C23×C3—31no—
309C22×D3—62no—
310C22×D3—62no—
311C22×D3—122no—
312C22×D3C2×D1211yescharacteristic
313C3×Q8—34no—
314C3×Q8—62no—
315C2×C3×C4—21no—
316C2×C3×C4—22no—
317C2×C3×C4—31no—
318C2×C3×C4—32no—
319C2×C3×C4—32no—
320C2×C3×C4—32no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—122no—
324C2×C3×C4C2×D1212yes—
325C2×C3×C4D3×D412yes—
326C2×C3×C4C23×D311yescharacteristic
327C2×C3×C4C23×D311yescharacteristic
328#67—68no—
329C2×Dic3—22no—
330C2×Dic3—22no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—122no—
334C2×Dic3C2×D1212yes—
335C2×Dic3C2×D1211yescharacteristic
336D12—34no—
337D12—34no—
338D12—64no—
339D12—68no—
340D12—62no—
341D12—62no—
342D12—122no—
343C4×D3—42no—
344C4×D3—68no—
345C4×D3—68no—
346C4×D3—124no—
347C4×D3—124no—
348C4×D3—124no—
349C4×D3—124no—
350C4×D3—244no—
351C4×D3C2×C4×D312yes—
352C4×D3#23512yes—
353Dic6—22no—
354Dic6C2×C4×D314yes—
355C3×C8—21no—
356C3×C8—21no—
357C3×C8—22no—
358C3×C8—32no—
359C3×C8—41no—
360C3×C8—61no—
361C3×C8C2×C4×D312yes—
362C3×C8C2×C4×D312yes—
363C3⋊C8—21no—
364C3⋊C8C2×C4×D312yes—
365C2×C32C2×C4×D411yescharacteristic
366C2×C32#57512yes—
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—32no—
376C22×C4—182no—
377C22×C4—182no—
378C22×C4—182no—
379Q16—34no—
380SD16—98no—
381D8—94no—
382C2×C8—31no—
383C2×C8—34no—
384C2×C8—31no—
385C2×C8—62no—
386C2×C8C2×D3211yescharacteristic
387C2×C8C2×D3211yescharacteristic
388C4⋊C4—32no—
389C4⋊C4—62no—
390C4⋊C4—92no—
391C4⋊C4—182no—
392C22⋊C4—182no—
393C22⋊C4—182no—
394C22⋊C4—182no—
395C42—31no—
396C42—32no—
397C42—62no—
398C42—182no—
399C42—182no—
400C42C2×D3211yescharacteristic
401C22×C3—21no—
402C22×C3—32no—
403C22×C3—62no—
404C22×C3C22×D1211yescharacteristic
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×D3C4×D1212yes—
417C3×C4—22no—
418C3×C4—22no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—32no—
422C3×C4—42no—
423C3×C4—64no—
424C3×C4—62no—
425C3×C4—122no—
426C3×C4C22×C4×D311yescharacteristic
427C3×C4C22×C4×D311yescharacteristic
428C3×C4C2×#23511yescharacteristic
429C3×C4D3×#4111yescharacteristic
430Dic3—22no—
431Dic3—24no—
432Dic3—42no—
433Dic3—122no—
434Dic3—122no—
435Dic3—242no—
436Dic3C4×D1212yes—
437C32#294311yescharacteristic, complemented, Sylow
438C23—31no—
439C23—182no—
440Q8—34no—
441Q8—62no—
442D4—94no—
443D4—188no—
444D4—182no—
445C2×C4—31no—
446C2×C4—32no—
447C2×C4—32no—
448C2×C4—32no—
449C2×C4—62no—
450C2×C4—62no—
451C2×C4—122no—
452C2×C4—188no—
453C2×C4—182no—
454C2×C4—364no—
455C2×C4—364no—
456C2×C4D3×D1212yes—
457C2×C4C22×D3211yescharacteristic
458C8—21no—
459C8—32no—
460C8—61no—
461C8C4×D3212yes—
462C2×C3—22no—
463C2×C3—21no—
464C2×C3—62no—
465C2×C3C2×C4×D1211yescharacteristic
466C2×C3C4×D3×D411yescharacteristic
467C2×C3#574812yes—
468C2×C3#577712yes—
469D3—22no—
470D3—124no—
471D3—124no—
472D3—244no—
473C22—32no—
474C22—62no—
475C22—184no—
476C22—362no—
477C22—362no—
478C22C2×D3×D1211yescharacteristic
479C4—22no—
480C4—32no—
481C4—62no—
482C4—64no—
483C4—122no—
484C4—362no—
485C4C2×C4×D3211yescharacteristic
486C4D3×#23511yescharacteristic
487C3—21no—
488C3#7849411yescharacteristic, complemented
489C3#7982811yescharacteristic, complemented
490C2—62no—
491C2—364no—
492C2C4×D3×D1211yescharacteristic
493C2#1059471112yes—
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radicalC2×#63808C2
cosocleC2×C32×C4C24
hypercenter#97D32
hypocenterC32#2943
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. C4×#3799C2semidirect
3. #10592410C2semidirect
4. C3×#4716C2semidirect
5. C3×D3×#97C2semidirect
6. #10590812C2semidirect
7. #10590795C2semidirect
8. #10590768C2semidirect
9. #10590706C2semidirect
10. #10590690C2semidirect
11. #10590362C2semidirect
30. #63808C4semidirect
57. #4716D3semidirect
64. D3×#97D3semidirect
74. #3799C2×C4semidirect
80. #3745C2×C4semidirect
88. C3×Dic12C2×C4semidirect
90. C3×D3×C8C2×C4semidirect
96. #3717C2×C4semidirect
259. Dic12C4×D3semidirect
265. D3×C8C4×D3semidirect
437. C32#2943semidirect
488. C3#78494semidirect
489. C3#79828semidirect

Maximal subgroups

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

subgroupindex
C2×#638082
C4×#37992
#105924102
C3×#47162
C3×D3×#972
#105908122
#105907952
#105907682
#105907062
#105906902
#105903622
#798283
#784943