Finite Group Databasebeta

← C2×#10590929 #11867934

Subgroups — C2×#10590929 #11867934

Order 1152.

1109 conjugacy classes of subgroups.

The subgroup lattice has 499 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64110C211yesmaximal, characteristic, complemented
2C22×C3×D24C211yesmaximal, characteristic, complemented
3C2×#63830C212yesmaximal, complemented
4C2×C3×#819C211yesmaximal, characteristic, complemented
5C2×#63558C212yesmaximal, complemented
6#10590929C218yesmaximal, direct product factor
7C2×#5160—31nomaximal
8C2×#4897—31nomaximal
9C2×#3828C2211yescharacteristic
10C22×C3×D12C2212yes—
11C22×C32×C8C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13#64110—22no—
14#64110C2214yescomplemented
15C2×#3743—21no—
16C2×C8×C3⋊D3—21no—
17C2×C3×#208C2212yes—
18C2×C3×D24—21no—
19C2×C3×D24—21no—
20C2×C3×D24—22no—
21C2×C3×D24C2214yescomplemented
22#63830—24no—
23#63830C2218yescomplemented
24C2×#3716—22no—
25C2×#3714—22no—
26C3×#819C2214yescomplemented
27#63558C2218yescomplemented
28C22×C3×D8—31no—
29C2×#932—32no—
30C2×#908—32no—
31C22×D24D311yescharacteristic, complemented
32C2×#901—31no—
33C2×#901—31no—
34C2×#901—61no—
35C2×C3×#108—31no—
36C2×#833—32no—
37#5160—38no—
38C2×#823—32no—
39C2×#819D311yescharacteristic, complemented
40#4897—38no—
41C23×C3×D3—22no—
42C22×C32×C4C2311yescharacteristic
43C2×#638—21no—
44#3828—21no—
45#3828—21no—
46#3828D412yes—
47#3828C2312yes—
48C2×C4⋊(C3⋊D3)D411yescharacteristic
49C2×C4×C3⋊D3—21no—
50C2×#634D411yescharacteristic
51C2×C3×D12—22no—
52C2×C3×D12—22no—
53C2×C3×D12—22no—
54C2×C3×D12—22no—
55C2×C3×D12—22no—
56C2×C3×D12C2314yes—
57C2×C32×C8D411yescharacteristic
58C2×C32×C8D411yescharacteristic
59C2×C32×C8D412yes—
60C2×C32×C8C2312yes—
61#3748—21no—
62#3748C2312yes—
63C2×C3⋊(C3⋊C8)—21no—
64#3743—24no—
65C8×C3⋊D3—24no—
66C3×#208—22no—
67C3×#208C2314yes—
68C2×C3×C3⋊C8—22no—
69C3×D24—24no—
70C3×D24—24no—
71#3716—28no—
72#3714—28no—
73C2×#472—91noSylow
74C22×C3×D4—32no—
75C2×#235—31no—
76C2×#235—31no—
77C2×#235—61no—
78C22×D12C2×D312yes—
79C2×C3×D8—34no—
80C2×C3×D8—61no—
81C2×C3×D8—61no—
82C2×C3×D8—62no—
83C2×C3×M16—32no—
84C22×C3×C8—21no—
85C22×C3×C8C2×D311yescharacteristic
86C22×C3×C8C2×D311yescharacteristic
87C2×#214—62no—
88#932—38no—
89#932—64no—
90C2×#213—62no—
91C2×#208—31no—
92C2×#208—31no—
93C2×#208—61no—
94C2×#208C2×D312yes—
95#908—38no—
96#908—64no—
97C2×D24—21no—
98C2×D24—21no—
99C2×D24—22no—
100C2×D24—62no—
101C2×D24C2×D314yescomplemented
102C2×#204—62no—
103#901—34no—
104#901—34no—
105#901—64no—
106#901—64no—
107#901—62no—
108#901—62no—
109C2×ΓL(1,𝔽25)—62no—
110C2×ΓL(1,𝔽25)—61no—
111C2×ΓL(1,𝔽25)—61no—
112C2×D3×C8—62no—
113C2×D3×C8—61no—
114C2×D3×C8—61no—
115C3×#108—34no—
116#833—38no—
117#823—38no—
118#819C2×D314yescomplemented
119C23×C32#4111yescharacteristic
120C22×C3⋊D3—21no—
121C22×C3×D3—24no—
122C22×C3×D3—42no—
123C22×C3×D3—42no—
124C22×C3×D3—84no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C32×C4C2411yescharacteristic
131#638—22no—
132#638—22no—
133C2×C3⋊Dic3—21no—
134C4⋊(C3⋊D3)—21no—
135C4⋊(C3⋊D3)C2×D412yes—
136C4×C3⋊D3—22no—
137C4×C3⋊D3—22no—
138#634—21no—
139#634C2×D412yes—
140C3×D12—24no—
141C3×D12—24no—
142C3×D12—42no—
143C3×D12—42no—
144C32×C8C2×D412yes—
145C32×C8C2×D412yes—
146C3⋊(C3⋊C8)—22no—
147C3×C3⋊C8—24no—
148C2×AGL(1,ℤ/8)—92no—
149C22×D8—31no—
150C2×#131—91no—
151#472—98no—
152C2×#108—31no—
153C2×#100—92no—
154C24×C3—62no—
155C23×D3—22no—
156C2×C3×D4—34no—
157C2×C3×D4—62no—
158C2×C3×D4—62no—
159C2×C3×D4—62no—
160C2×C3×D4—62no—
161C2×C3×D4—62no—
162C22×C3×C4—21no—
163C22×C3×C4C22×D311yescharacteristic
164C22×C3×C4C22×D311yescharacteristic
165C2×#67—62no—
166C2×#67—61no—
167C2×#67—61no—
168#235—32no—
169#235—32no—
170#235—32no—
171#235—32no—
172#235—62no—
173#235—62no—
174#235—62no—
175#235—62no—
176#235—61no—
177#235—61no—
178#235—61no—
179#235—61no—
180C2×D12—22no—
181C2×D12—22no—
182C2×D12—22no—
183C2×D12—22no—
184C2×D12—22no—
185C2×D12—31no—
186C2×D12—31no—
187C2×D12—61no—
188C2×D12C22×D314yes—
189C2×C4×D3—62no—
190C2×C4×D3—61no—
191C2×C4×D3—61no—
192C2×Dic6—31no—
193C2×Dic6—31no—
194C2×Dic6—61no—
195C3×D8—64no—
196C3×D8—64no—
197C3×M16—34no—
198C3×M16—62no—
199C2×C3×C8—21no—
200C2×C3×C8—21no—
201C2×C3×C8—22no—
202C2×C3×C8—22no—
203C2×C3×C8—62no—
204C2×C3×C8D1211yescharacteristic
205C2×C3×C8D1211yescharacteristic
206C2×C3×C8D1212yes—
207C2×C3×C8#6711yescharacteristic
208C2×C3×C8#6711yescharacteristic
209C2×C3×C8#6712yes—
210C2×C3×C8C22×D312yes—
211C2×C3×C8C22×D312yes—
212#214—68no—
213#213—68no—
214#208—22no—
215#208—32no—
216#208—32no—
217#208—62no—
218#208—62no—
219#208—61no—
220#208—61no—
221#208C22×D314yes—
222C2×C3⋊C8—22no—
223C2×C3⋊C8—62no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226D24—24no—
227D24—24no—
228D24—68no—
229#204—68no—
230ΓL(1,𝔽25)—68no—
231ΓL(1,𝔽25)—64no—
232ΓL(1,𝔽25)—64no—
233D3×C8—68no—
234D3×C8—64no—
235D3×C8—64no—
236C22×C32—22no—
237C22×C32#12111yescharacteristic
238C22×C32#12111yescharacteristic
239C22×C32C2×#4111yescharacteristic
240C2×C3⋊D3—22no—
241C2×C3⋊D3—42no—
242C2×C3×D3—44no—
243C2×C3×D3—84no—
244C2×C3×D3—84no—
245C2×C3×D3—84no—
246C32×C4#12111yescharacteristic
247C32×C4#12111yescharacteristic
248C32×C4C22×D411yescharacteristic
249C32×C4C22×D411yescharacteristic
250C3⋊Dic3—22no—
251C2×#41—91no—
252C22×D4—32no—
253AGL(1,ℤ/8)—98no—
254AGL(1,ℤ/8)—184no—
255C2×SD16—182no—
256C2×D8—34no—
257C2×D8—61no—
258C2×D8—61no—
259C2×D8—62no—
260C2×D8—182no—
261#131—94no—
262#131—182no—
263C2×M16—32no—
264C2×M16—91no—
265C2×M16—181no—
266C22×C8—181no—
267C22×C8D3211yescharacteristic
268#108—34no—
269#100—98no—
270C23×C3—21no—
271C23×C3—64no—
272C23×C3—122no—
273C23×C3—122no—
274C23×C3—244no—
275C23×C3#23711yescharacteristic
276C23×C3#23911yescharacteristic
277C22×D3—24no—
278C22×D3—42no—
279C22×D3—42no—
280C22×D3—62no—
281C22×D3—61no—
282C22×D3—61no—
283C22×D3—84no—
284C3×D4—64no—
285C3×D4—64no—
286C3×D4—122no—
287C3×D4—122no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4C2×D1211yescharacteristic
295C2×C3×C4C2×D1211yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4#23711yescharacteristic
301C2×C3×C4#23911yescharacteristic
302C2×C3×C4C2×#6711yescharacteristic
303C2×C3×C4C2×#6711yescharacteristic
304C2×C3×C4C23×D311yescharacteristic
305C2×C3×C4C23×D311yescharacteristic
306#67—64no—
307#67—64no—
308#67—62no—
309#67—62no—
310#67—62no—
311#67—62no—
312C2×Dic3—62no—
313C2×Dic3—61no—
314C2×Dic3—61no—
315D12—24no—
316D12—24no—
317D12—32no—
318D12—32no—
319D12—42no—
320D12—42no—
321D12—62no—
322D12—62no—
323D12—61no—
324D12—61no—
325C4×D3—64no—
326C4×D3—64no—
327C4×D3—62no—
328C4×D3—62no—
329C4×D3—62no—
330C4×D3—62no—
331Dic6—32no—
332Dic6—32no—
333Dic6—62no—
334Dic6—62no—
335Dic6—61no—
336Dic6—61no—
337C3×C8—22no—
338C3×C8—22no—
339C3×C8—64no—
340C3×C8C2×D1212yes—
341C3×C8C2×D1212yes—
342C3×C8C2×#6712yes—
343C3×C8C2×#6712yes—
344C3⋊C8—24no—
345C3⋊C8—64no—
346C3⋊C8—62no—
347C3⋊C8—62no—
348C2×C32—21no—
349C2×C32—21no—
350C2×C32#47212yescomplemented
351C2×C32C2×#12111yescharacteristic
352C3⋊D3—42no—
353C3×D3—84no—
354C24—62no—
355#41—92no—
356#41—92no—
357#41—181no—
358#41—181no—
359C2×Q8—91no—
360C2×D4—34no—
361C2×D4—62no—
362C2×D4—62no—
363C2×D4—62no—
364C2×D4—62no—
365C2×D4—62no—
366C2×D4—91no—
367C2×D4—181no—
368C22×C4—181no—
369C22×C4C2×D3211yescharacteristic
370SD16—188no—
371D8—64no—
372D8—64no—
373D8—188no—
374M16—34no—
375M16—62no—
376M16—92no—
377M16—181no—
378M16—184no—
379C2×C8—62no—
380C2×C8—181no—
381C2×C8—184no—
382C2×C8#62611yescharacteristic
383C2×C8#62611yescharacteristic
384C2×C8#62612yes—
385C2×C8C2×D3212yes—
386C22×C3—22no—
387C22×C3—22no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—42no—
392C22×C3—124no—
393C22×C3—244no—
394C22×C3—244no—
395C22×C3—244no—
396C22×C3#89511yescharacteristic
397C22×C3#89511yescharacteristic
398C22×C3#93811yescharacteristic
399C22×C3#93811yescharacteristic
400C22×C3C2×#23711yescharacteristic
401C22×C3C2×#23911yescharacteristic
402C2×D3—44no—
403C2×D3—64no—
404C2×D3—62no—
405C2×D3—62no—
406C2×D3—84no—
407C2×D3—84no—
408C2×D3—84no—
409C2×D3—124no—
410C2×D3—122no—
411C2×D3—122no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4#89511yescharacteristic
417C3×C4#89511yescharacteristic
418C3×C4#93811yescharacteristic
419C3×C4#93811yescharacteristic
420C3×C4C22×D1211yescharacteristic
421C3×C4C2×D3×D411yescharacteristic
422C3×C4C2×D3×D411yescharacteristic
423C3×C4C22×#6711yescharacteristic
424Dic3—64no—
425Dic3—62no—
426Dic3—62no—
427C32C2×#47211yescharacteristic, complemented, Sylow
428C23—64no—
429C23—122no—
430C23—122no—
431C23—181no—
432C23—244no—
433C23#379611yescharacteristic
434Q8—92no—
435Q8—181no—
436D4—64no—
437D4—64no—
438D4—92no—
439D4—122no—
440D4—122no—
441D4—182no—
442D4—182no—
443D4—181no—
444C2×C4—181no—
445C2×C4—182no—
446C2×C4—182no—
447C2×C4#379611yescharacteristic
448C2×C4#380211yescharacteristic
449C2×C4#380211yescharacteristic
450C2×C4C2×#62611yescharacteristic
451C2×C4C2×#62611yescharacteristic
452C2×C4C22×D3211yescharacteristic
453C8—64no—
454C8—182no—
455C8C2×#62612yes—
456C8C2×#62612yes—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—22no—
463C2×C3—41no—
464C2×C3—41no—
465C2×C3—244no—
466C2×C3#489712yescomplemented
467C2×C3#516012yescomplemented
468C2×C3C2×#89511yescharacteristic
469C2×C3C2×#93811yescharacteristic
470D3—84no—
471D3—124no—
472D3—122no—
473D3—122no—
474C22—22no—
475C22—124no—
476C22—182no—
477C22—244no—
478C22—244no—
479C22—244no—
480C22—362no—
481C22#6391611yescharacteristic
482C22#6391611yescharacteristic
483C22C2×#379611yescharacteristic
484C4—182no—
485C4#6391611yescharacteristic
486C4#6391611yescharacteristic
487C4C2×#380211yescharacteristic
488C4C22×#62611yescharacteristic
489C3—21no—
490C3C2×#489711yescharacteristic, complemented
491C3C2×#516011yescharacteristic, complemented
492C2—21no—
493C2—21no—
494C2—244no—
495C2—362no—
496C2#1059092912yesdirect product factor
497C2C2×#6391611yescharacteristic
subgroupG/H
centerC22#63916
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32#121
hypercenterC22×C8D32
hypocenterC32C2×#472
LCSG ▷ C2×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
1. C2×#64110C2semidirect
2. C22×C3×D24C2semidirect
3. C2×#63830C2semidirect
4. C2×C3×#819C2semidirect
5. C2×#63558C2semidirect
6. #10590929C2direct (N × H)
14. #64110C22semidirect
21. C2×C3×D24C22semidirect
23. #63830C22semidirect
26. C3×#819C22semidirect
27. #63558C22semidirect
31. C22×D24D3semidirect
39. C2×#819D3semidirect
101. C2×D24C2×D3semidirect
118. #819C2×D3semidirect
350. C2×C32#472semidirect
427. C32C2×#472semidirect
466. C2×C3#4897semidirect
467. C2×C3#5160semidirect
490. C3C2×#4897semidirect
491. C3C2×#5160semidirect
496. C2#10590929direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641102
C22×C3×D242
C2×#638302
C2×C3×#8192
C2×#635582
#105909292
C2×#51603
C2×#48973