Finite Group Databasebeta

← #11860221

Subgroups — #11860221

Order 1152.

1057 conjugacy classes of subgroups.

The subgroup lattice has 503 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63810C211yesmaximal, characteristic
2C4×#3796C212yesmaximal, complemented
3C3⋊D3×#97C211yesmaximal, characteristic, complemented
4C3×#4716C211yesmaximal, characteristic, complemented
5C3×#4711C211yesmaximal, characteristic, complemented
6#10590956C212yesmaximal, complemented
7#10590819C211yesmaximal, characteristic, complemented
8#10590781C211yesmaximal, characteristic, complemented
9#10590743C212yesmaximal, complemented
10#10590712C211yesmaximal, characteristic, complemented
11#10590358C212yesmaximal, complemented
12#79864—31nomaximal
13#79828—31nomaximal
14C2×#3796C2212yes—
15C2×C8×C3⋊D3C2211yescharacteristic
16C2×C8×C3⋊D3C2211yescharacteristic
17C42×C3⋊D3C2211yescharacteristic
18C2×C3×Dic12C2211yescharacteristic
19C2×C3×D24C2211yescharacteristic
20C3×C4×D12C2212yes—
21C3×C4×Dic6C2212yes—
22C4×#626—22no—
23#63898C2212yes—
24#63881—22no—
25#63878—22no—
26C4×D3×Dic3—22no—
27#63849C2212yes—
28#63843C2212yes—
29C2×#3715C2212yes—
30#63810C418yescomplemented
31C32×#97C2211yescharacteristic
32#63642C2211yescharacteristic
33#63642C2211yescharacteristic
34#63630C2211yescharacteristic
35C3×#821C2212yes—
36C3×#817C2211yescharacteristic
37C3×#817C2211yescharacteristic
38C3×#816C2212yes—
39#63576C2212yes—
40#63565C2212yes—
41#63562C2212yes—
42C2×#919—31no—
43C2×#912—31no—
44C4×#239—32no—
45C4×#237—32no—
46C3×#442—31no—
47C3×#441—31no—
48#5184—31no—
49#5152—31no—
50#5026—32no—
51#5018—32no—
52#4869—31no—
53#4860—31no—
54#4860—31no—
55#4853—31no—
56#4817—32no—
57#4804—32no—
58#4772—32no—
59#4757—32no—
60#4716D311yescharacteristic, complemented
61#4711D311yescharacteristic, complemented
62D3×#97—31no—
63D3×#97—31no—
64D3×#97—61no—
65C2×C4×C3⋊D3D412yes—
66C2×C4×C3⋊D3C2311yescharacteristic
67C2×C3×D12C2312yes—
68C2×C3×C4×D3—22no—
69C2×C3×Dic6C2312yes—
70C2×#626—22no—
71C2×D3×Dic3—22no—
72C2×D3×Dic3—22no—
73#3796—24no—
74#3796C2×C418yescomplemented
75C2×C32×C8C2311yescharacteristic
76C2×C32×C8C2311yescharacteristic
77C32×C42C2311yescharacteristic
78C4×C3⋊Dic3D412yes—
79C4×C3⋊Dic3C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C8×C3⋊D3—22no—
83C8×C3⋊D3C2×C414yescomplemented
84C3×(C2×D3)⋊C4—22no—
85C3×C4⋊Dic3C2312yes—
86C3×C4⋊Dic3C2312yes—
87C3×Dic3⋊C4—22no—
88C3×C4×Dic3—22no—
89C3×Dic12C2×C414yescomplemented
90C3×D24C2×C414yescomplemented
91Dic3⋊Dic3—22no—
92#3722—22no—
93(C2×D3)⋊Dic3—22no—
94Dic32—22no—
95Dic32—22no—
96#3715C2×C418yescomplemented
97#2943—91noSylow
98C2×#239—32no—
99C2×#237—32no—
100C2×C3×Q16—31no—
101C2×C3×D8—31no—
102C3×C4×Q8—32no—
103C3×C4×D4—32no—
104Q8×Dic3—32no—
105C2×#215—32no—
106D4×Dic3—32no—
107C2×#214—32no—
108C4×#67—62no—
109C2×C4×Dic3—62no—
110#919—38no—
111#912—38no—
112C2×Dic12C2×D311yescharacteristic
113C2×D24C2×D311yescharacteristic
114C2×D3×C8—31no—
115C2×D3×C8—31no—
116C2×D3×C8—31no—
117C2×D3×C8—31no—
118C2×D3×C8—61no—
119C2×D3×C8—61no—
120#893—32no—
121#893—62no—
122#892—32no—
123#892—32no—
124#892—62no—
125#887—32no—
126#67⋊C4—62no—
127#877—62no—
128C4×D12—62no—
129C4×D12C2×D312yes—
130C42×D3—31no—
131C42×D3—31no—
132C42×D3—61no—
133C42×D3—62no—
134C4×Dic6C2×D312yes—
135C3×#106—31no—
136C3×#106—31no—
137C3×#103—32no—
138C3×#102—32no—
139C3×#97—21no—
140C3×#97C2×D311yescharacteristic
141C3×#97C2×D311yescharacteristic
142#835—32no—
143#832—32no—
144#821C2×D312yes—
145#817C2×D311yescharacteristic
146#817C2×D311yescharacteristic
147#816C2×D312yes—
148#815—31no—
149#815—31no—
150#815—31no—
151#815—31no—
152#815—61no—
153#815—61no—
154#810—32no—
155#809—32no—
156#807—32no—
157#807—32no—
158#803—31no—
159#803—31no—
160#803—61no—
161C22×C3⋊D3C2×D411yescharacteristic
162C22×C3×D3—22no—
163C2×C32×C4C2×D412yes—
164C2×C32×C4C2411yescharacteristic
165C2×C3⋊Dic3C2×D412yes—
166C2×C3⋊Dic3C2×D411yescharacteristic
167C4×C3⋊D3—42no—
168C4×C3⋊D3C22×C412yes—
169C4×C3⋊D3#4112yes—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C3×D12—22no—
174C3×D12C22×C414yes—
175C3×C4×D3—44no—
176C3×Dic6—22no—
177C3×Dic6C22×C414yes—
178#626—28no—
179D3×Dic3—28no—
180D3×Dic3—44no—
181C32×C8—21no—
182C32×C8C22×C412yes—
183C3⋊(C3⋊C8)—21no—
184C3⋊(C3⋊C8)C22×C412yes—
185C2×#135—91no—
186C4×#41—92no—
187#442—31no—
188#442—91no—
189#441—31no—
190#441—91no—
191#440—92no—
192#440—92no—
193#427—91no—
194#416—92no—
195C2×#97—91no—
196C2×C3×Q8—32no—
197C2×C3×D4—32no—
198C22×C3×C4—62no—
199C2×#67—62no—
200C22×Dic3—62no—
201C22×Dic3—62no—
202#239—38no—
203#239—64no—
204#237—38no—
205#237—64no—
206C2×D12—62no—
207C2×D12C22×D312yes—
208C2×C4×D3—22no—
209C2×C4×D3—31no—
210C2×C4×D3—31no—
211C2×C4×D3—32no—
212C2×C4×D3—32no—
213C2×C4×D3—61no—
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×C4×D3—62no—
217C2×Dic6C22×D312yes—
218C3×Q16—34no—
219C3×D8—34no—
220C2×C3×C8—21no—
221C2×C3×C8—21no—
222C2×C3×C8C22×D311yescharacteristic
223C2×C3×C8C22×D311yescharacteristic
224C2×C3×C8C22×D311yescharacteristic
225C2×C3×C8C22×D311yescharacteristic
226C3×C4⋊C4—32no—
227C3×C4⋊C4—32no—
228C3×C4⋊C4—62no—
229C3×C22⋊C4—62no—
230C3×C42—21no—
231C3×C42—62no—
232C3×C42C22×D311yescharacteristic
233C3×C42C22×D311yescharacteristic
234#217—62no—
235#215—38no—
236#214—38no—
237(C2×D3)⋊C4—22no—
238(C2×D3)⋊C4—62no—
239(C2×D3)⋊C4—62no—
240(C2×D3)⋊C4—62no—
241C4⋊Dic3—62no—
242C4⋊Dic3C22×D312yes—
243C4⋊Dic3C22×D312yes—
244Dic3⋊C4—22no—
245Dic3⋊C4—62no—
246C4×Dic3—22no—
247C4×Dic3—32no—
248C4×Dic3—32no—
249C4×Dic3—31no—
250C4×Dic3—31no—
251C4×Dic3—61no—
252C4×Dic3—62no—
253C4×Dic3—62no—
254C4×Dic3—62no—
255C4×Dic3—62no—
256C4×Dic3—62no—
257C2×C3⋊C8—31no—
258C2×C3⋊C8—31no—
259C2×C3⋊C8—31no—
260C2×C3⋊C8—31no—
261C2×C3⋊C8—61no—
262C2×C3⋊C8—61no—
263Dic12C4×D314yescomplemented
264D24C4×D314yescomplemented
265D3×C8—34no—
266D3×C8—34no—
267D3×C8—64no—
268D3×C8—62no—
269D3×C8—62no—
270D3×C8—64no—
271C22×C32C22×D411yescharacteristic
272C2×C3⋊D3—22no—
273C2×C3⋊D3C4×D412yes—
274C2×C3×D3—24no—
275C2×C3×D3—42no—
276C2×C3×D3—42no—
277C32×C4—22no—
278C32×C4C23×C411yescharacteristic
279C32×C4C2×#4111yescharacteristic
280C3⋊Dic3—22no—
281C3⋊Dic3C4×D412yes—
282C3×Dic3—24no—
283C3×Dic3—42no—
284C3×Dic3—42no—
285C2×#41—92no—
286#135—98no—
287C2×Q16—31no—
288C2×SD16—92no—
289C2×D8—31no—
290C22×C8—91no—
291C22×C8—91no—
292C4×Q8—32no—
293C4×Q8—92no—
294C4×D4—32no—
295C4×D4—92no—
296C4×D4—182no—
297C4×D4—182no—
298#117—92no—
299#117—182no—
300C2×C42—91no—
301C2×C42—182no—
302#107—92no—
303#106—31no—
304#106—31no—
305#103—32no—
306#103—92no—
307#102—32no—
308#102—92no—
309#97—91no—
310#97—91no—
311#97—91no—
312#97D3211yescharacteristic
313C23×C3—62no—
314C22×D3—22no—
315C22×D3—31no—
316C22×D3—31no—
317C22×D3—61no—
318C3×Q8—34no—
319C3×Q8—62no—
320C3×D4—34no—
321C3×D4—62no—
322C2×C3×C4—21no—
323C2×C3×C4—22no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—124no—
328C2×C3×C4D3×D412yes—
329C2×C3×C4D3×D412yes—
330C2×C3×C4C23×D311yescharacteristic
331C2×C3×C4C23×D311yescharacteristic
332#67—68no—
333C2×Dic3—22no—
334C2×Dic3—22no—
335C2×Dic3—22no—
336C2×Dic3—31no—
337C2×Dic3—31no—
338C2×Dic3—32no—
339C2×Dic3—32no—
340C2×Dic3—61no—
341C2×Dic3—62no—
342C2×Dic3—68no—
343C2×Dic3—124no—
344D12—22no—
345D12—68no—
346D12C2×C4×D314yes—
347C4×D3—32no—
348C4×D3—32no—
349C4×D3—32no—
350C4×D3—32no—
351C4×D3—44no—
352C4×D3—62no—
353C4×D3—62no—
354C4×D3—68no—
355C4×D3—122no—
356C4×D3—122no—
357C4×D3—124no—
358C4×D3—124no—
359Dic6—22no—
360Dic6C2×C4×D314yes—
361C3×C8—22no—
362C3×C8—21no—
363C3×C8—21no—
364C3×C8—22no—
365C3×C8C2×C4×D312yes—
366C3×C8C2×C4×D312yes—
367C3⋊C8—32no—
368C3⋊C8—32no—
369C3⋊C8—62no—
370C3⋊C8—62no—
371C3⋊C8—61no—
372C3⋊C8—61no—
373C2×C32C2×C4×D411yescharacteristic
374C2×C32#57512yes—
375C3⋊D3—22no—
376C3×D3—44no—
377#41—98no—
378#41—184no—
379C2×Q8—32no—
380C2×D4—32no—
381C2×D4—182no—
382C22×C4—62no—
383C22×C4—91no—
384C22×C4—92no—
385C22×C4—182no—
386C22×C4—182no—
387Q16—34no—
388SD16—98no—
389D8—34no—
390C2×C8—91no—
391C2×C8—94no—
392C2×C8—91no—
393C2×C8—182no—
394C2×C8C2×D3211yescharacteristic
395C2×C8C2×D3211yescharacteristic
396C4⋊C4—32no—
397C4⋊C4—32no—
398C4⋊C4—62no—
399C4⋊C4—182no—
400C22⋊C4—62no—
401C22⋊C4—182no—
402C22⋊C4—182no—
403C42—62no—
404C42—91no—
405C42—92no—
406C42—182no—
407C42—182no—
408C42C2×D3211yescharacteristic
409C22×C3—21no—
410C22×C3—64no—
411C22×C3—122no—
412C22×C3—122no—
413C22×C3C2×D3×D411yescharacteristic
414C22×C3C2×D3×D411yescharacteristic
415C2×D3—24no—
416C2×D3—32no—
417C2×D3—32no—
418C2×D3—42no—
419C2×D3—42no—
420C2×D3—62no—
421C2×D3—64no—
422C2×D3—62no—
423C2×D3—62no—
424C3×C4—22no—
425C3×C4—22no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—42no—
429C3×C4—64no—
430C3×C4—122no—
431C3×C4—122no—
432C3×C4C22×C4×D311yescharacteristic
433C3×C4C22×C4×D311yescharacteristic
434C3×C4D3×#4111yescharacteristic
435C3×C4D3×#4111yescharacteristic
436Dic3—24no—
437Dic3—32no—
438Dic3—32no—
439Dic3—42no—
440Dic3—42no—
441Dic3—62no—
442Dic3—62no—
443Dic3—62no—
444Dic3—122no—
445C32#294311yescharacteristic, complemented, Sylow
446C23—62no—
447C23—91no—
448Q8—34no—
449Q8—62no—
450D4—34no—
451D4—62no—
452D4—188no—
453C2×C4—62no—
454C2×C4—62no—
455C2×C4—62no—
456C2×C4—91no—
457C2×C4—92no—
458C2×C4—92no—
459C2×C4—92no—
460C2×C4—124no—
461C2×C4—188no—
462C2×C4—362no—
463C2×C4—364no—
464C2×C4#380212yes—
465C2×C4C22×D3211yescharacteristic
466C8—21no—
467C8—92no—
468C8—181no—
469C8C4×D3212yes—
470C2×C3—22no—
471C2×C3—21no—
472C2×C3—124no—
473C2×C3C4×D3×D411yescharacteristic
474C2×C3C4×D3×D411yescharacteristic
475C2×C3#577312yes—
476C2×C3#577712yes—
477D3—44no—
478D3—64no—
479D3—62no—
480D3—62no—
481C22—64no—
482C22—92no—
483C22—122no—
484C22—122no—
485C22—182no—
486C22C2×#380211yescharacteristic
487C4—22no—
488C4—64no—
489C4—92no—
490C4—122no—
491C4—122no—
492C4—182no—
493C4C2×C4×D3211yescharacteristic
494C4#6430611yescharacteristic
495C3—21no—
496C3#7982811yescharacteristic, complemented
497C3#7986411yescharacteristic, complemented
498C2—124no—
499C2—182no—
500C2C4×#380211yescharacteristic
501C2#1059471812yes—
subgroupG/H
centerC22C2×#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radicalC2×#63810C2
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×#3796C2semidirect
3. C3⋊D3×#97C2semidirect
4. C3×#4716C2semidirect
5. C3×#4711C2semidirect
6. #10590956C2semidirect
7. #10590819C2semidirect
8. #10590781C2semidirect
9. #10590743C2semidirect
10. #10590712C2semidirect
11. #10590358C2semidirect
30. #63810C4semidirect
60. #4716D3semidirect
61. #4711D3semidirect
74. #3796C2×C4semidirect
83. C8×C3⋊D3C2×C4semidirect
89. C3×Dic12C2×C4semidirect
90. C3×D24C2×C4semidirect
96. #3715C2×C4semidirect
263. Dic12C4×D3semidirect
264. D24C4×D3semidirect
445. C32#2943semidirect
496. C3#79828semidirect
497. C3#79864semidirect

Maximal subgroups

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

subgroupindex
C2×#638102
C4×#37962
C3⋊D3×#972
C3×#47162
C3×#47112
#105909562
#105908192
#105907812
#105907432
#105907122
#105903582
#798643
#798283