Finite Group Databasebeta

← C2×#10590725 #11859237

Subgroups — C2×#10590725 #11859237

Order 1152.

1201 conjugacy classes of subgroups.

The subgroup lattice has 519 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#625C211yesmaximal, characteristic
2C22×#3711C211yesmaximal, characteristic, complemented
3C22×D3×C3⋊C8C211yesmaximal, characteristic, complemented
4C2×#63642C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
6C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
7C2×#63572C211yesmaximal, characteristic, complemented
8#10590725C218yesmaximal, direct product factor
9C2×#4728—31nomaximal
10C2×#4730—31nomaximal
11C22×C3×C4×D3C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C22×#625C411yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×#3724C411yescharacteristic
20C2×(C2×D3)⋊Dic3C411yescharacteristic
21C2×(C2×D3)⋊Dic3C411yescharacteristic
22C4×#625C414yes—
23C4×#625C2214yes—
24C2×#3711—24no—
25C2×#3711C2214yescomplemented
26C2×D3×C3⋊C8—24no—
27C2×D3×C3⋊C8C2214yescomplemented
28#63642C2214yescomplemented
29C3×(C2×D3)⋊C8C2214yescomplemented
30C3×(C2×D3)⋊C8C2214yescomplemented
31#63572C2214yescomplemented
32C2×C4×#67—31no—
33C2×C4×#67—31no—
34C22×#208—31no—
35C23×C3⋊C8—31no—
36C22×ΓL(1,𝔽25)—31no—
37C22×D3×C8—31no—
38C2×C3×C22⋊C8—31no—
39C2×C3×C22⋊C8—31no—
40C2×(C2×D3)⋊C8D311yescharacteristic, complemented
41C2×(C2×D3)⋊C8D311yescharacteristic, complemented
42C2×#815—31no—
43C2×#815—31no—
44C2×#815—61no—
45C2×Dic3⋊C8—31no—
46C2×Dic3⋊C8—31no—
47#4730—38no—
48#4728—38no—
49C23×C3×D3C2×C411yescharacteristic
50C23×C3×D3C2×C411yescharacteristic
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3C2×C411yescharacteristic
53C22×C3⋊Dic3C2×C411yescharacteristic
54C22×C3×Dic3C2×C411yescharacteristic
55C22×C3×Dic3C2×C411yescharacteristic
56C2×C3×C4×D3—22no—
57C2×C3×C4×D3—22no—
58C2×C3×C4×D3—22no—
59C2×C3×C4×D3—22no—
60C2×C3×C4×D3C2×C412yes—
61C2×C3×C4×D3C2×C412yes—
62C2×C3×C4×D3C2312yes—
63C2×C3×C4×D3C2312yes—
64C2×#625—24no—
65C2×#625C2×C414yes—
66C2×C32×C8—22no—
67C2×C32×C8C2312yes—
68C4×C3⋊Dic3C2×C412yes—
69C4×C3⋊Dic3C2312yes—
70C2×C3⋊(C3⋊C8)D414yescomplemented
71C2×C3⋊(C3⋊C8)C2312yes—
72C2×C3×C3⋊C8—22no—
73C2×C3×C3⋊C8—22no—
74C2×C3×C3⋊C8C2312yes—
75C2×C3×C3⋊C8C2312yes—
76#3724C2×C414yes—
77(C2×D3)⋊Dic3C2×C414yes—
78(C2×D3)⋊Dic3C2×C414yes—
79#3711—28no—
80D3×C3⋊C8—28no—
81C2×#435—91noSylow
82C23×C3×C4—31no—
83C23×C3×C4—31no—
84C22×#67—31no—
85C22×#67—31no—
86C22×C4×D3C2×D311yescharacteristic
87C22×C4×D3C2×D311yescharacteristic
88C22×C3×C8—21no—
89C22×C3×C8—31no—
90C22×C3×C8—31no—
91C22×C3×C8C2×D311yescharacteristic
92C22×C3×C8C2×D311yescharacteristic
93C2×#217—31no—
94C2×#217—31no—
95C4×#67—34no—
96C4×#67—34no—
97C4×#67—34no—
98C4×#67—34no—
99C2×(C2×D3)⋊C4—31no—
100C2×(C2×D3)⋊C4—31no—
101C2×Dic3⋊C4—31no—
102C2×Dic3⋊C4—31no—
103C2×C4×Dic3—31no—
104C2×C4×Dic3—31no—
105C2×C4×Dic3—61no—
106C2×#208—34no—
107C2×#208—64no—
108C22×C3⋊C8—31no—
109C22×C3⋊C8—31no—
110C22×C3⋊C8—34no—
111C22×C3⋊C8—61no—
112C22×C3⋊C8—64no—
113C22×C3⋊C8C2×D311yescharacteristic
114C22×C3⋊C8C2×D311yescharacteristic
115C2×ΓL(1,𝔽25)—34no—
116C2×ΓL(1,𝔽25)—64no—
117C2×D3×C8—34no—
118C2×D3×C8—64no—
119C3×C22⋊C8—34no—
120C3×C22⋊C8—34no—
121(C2×D3)⋊C8C2×D314yescomplemented
122(C2×D3)⋊C8C2×D314yescomplemented
123#815—34no—
124#815—34no—
125#815—64no—
126Dic3⋊C8—34no—
127Dic3⋊C8—34no—
128C23×C32C22×C411yescharacteristic
129C22×C3×D3—22no—
130C22×C3×D3—22no—
131C22×C3×D3—22no—
132C22×C3×D3—22no—
133C22×C3×D3—22no—
134C22×C3×D3M1614yescomplemented
135C22×C3×D3C22×C412yes—
136C22×C3×D3C22×C412yes—
137C2×C32×C4C22×C411yescharacteristic
138C2×C32×C4C2×D412yes—
139C2×C32×C4#4112yes—
140C2×C32×C4C2411yescharacteristic
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3C22×C412yes—
144C2×C3⋊Dic3C22×C412yes—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3C22×C412yes—
148C2×C3×Dic3C22×C412yes—
149C3×C4×D3—24no—
150C3×C4×D3—24no—
151C3×C4×D3—22no—
152C3×C4×D3—22no—
153C3×C4×D3—22no—
154C3×C4×D3—22no—
155#625—28no—
156C32×C8—22no—
157C3⋊(C3⋊C8)C2×D414yescomplemented
158C3×C3⋊C8—22no—
159C3×C3⋊C8—22no—
160C22×M16—91no—
161C23×C8—91no—
162C2×C4×D4—91no—
163#435—98no—
164C2×C4⋊C8—91no—
165C2×C22⋊C8—31no—
166C2×C22⋊C8—31no—
167C2×#97—91no—
168C24×C3—31no—
169C24×C3—31no—
170C23×D3C4×D311yescharacteristic
171C23×D3C4×D311yescharacteristic
172C22×C3×C4—21no—
173C22×C3×C4—31no—
174C22×C3×C4—31no—
175C22×C3×C4—32no—
176C22×C3×C4—32no—
177C22×C3×C4—32no—
178C22×C3×C4—32no—
179C22×C3×C4—62no—
180C22×C3×C4—62no—
181C22×C3×C4—62no—
182C22×C3×C4—62no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C2×#67—34no—
186C2×#67—34no—
187C2×#67—64no—
188C2×#67—64no—
189C22×Dic3—31no—
190C22×Dic3—31no—
191C22×Dic3—31no—
192C22×Dic3—31no—
193C22×Dic3—61no—
194C22×Dic3—61no—
195C22×Dic3C4×D311yescharacteristic
196C22×Dic3C4×D311yescharacteristic
197C2×C4×D3—22no—
198C2×C4×D3—22no—
199C2×C4×D3—22no—
200C2×C4×D3—22no—
201C2×C4×D3C4×D312yes—
202C2×C4×D3C4×D312yes—
203C2×C4×D3C22×D312yes—
204C2×C4×D3C22×D312yes—
205C2×C3×C8—24no—
206C2×C3×C8—22no—
207C2×C3×C8—22no—
208C2×C3×C8—22no—
209C2×C3×C8—32no—
210C2×C3×C8—32no—
211C2×C3×C8—62no—
212C2×C3×C8—62no—
213C2×C3×C8C22×D312yes—
214C2×C3×C8C22×D312yes—
215#217—34no—
216#217—34no—
217(C2×D3)⋊C4—34no—
218(C2×D3)⋊C4—34no—
219Dic3⋊C4—34no—
220Dic3⋊C4—34no—
221C4×Dic3—32no—
222C4×Dic3—32no—
223C4×Dic3—32no—
224C4×Dic3—32no—
225C4×Dic3—62no—
226C4×Dic3—62no—
227#208—68no—
228C2×C3⋊C8—22no—
229C2×C3⋊C8—22no—
230C2×C3⋊C8—34no—
231C2×C3⋊C8—34no—
232C2×C3⋊C8—32no—
233C2×C3⋊C8—32no—
234C2×C3⋊C8—62no—
235C2×C3⋊C8—64no—
236C2×C3⋊C8—68no—
237C2×C3⋊C8C22×D312yes—
238C2×C3⋊C8C22×D312yes—
239ΓL(1,𝔽25)—68no—
240D3×C8—68no—
241C22×C32C4×D412yes—
242C22×C32C2×M1612yes—
243C22×C32#13112yes—
244C22×C32C23×C411yescharacteristic
245C2×C3×D3—22no—
246C2×C3×D3—22no—
247C2×C3×D3—28no—
248C2×C3×D3—22no—
249C2×C3×D3—22no—
250C2×C3×D3—22no—
251C2×C3×D3—44no—
252C2×C3×D3C2×M1614yescomplemented
253C32×C4C4×D412yes—
254C32×C4C22×D411yescharacteristic
255C32×C4C2×#4111yescharacteristic
256C3⋊Dic3—22no—
257C3⋊Dic3—22no—
258C3×Dic3—22no—
259C3×Dic3—22no—
260C22×D4—91no—
261C23×C4—31no—
262C23×C4—31no—
263C2×M16—94no—
264C2×M16—184no—
265C22×C8—31no—
266C22×C8—31no—
267C22×C8—94no—
268C22×C8—91no—
269C22×C8—184no—
270C22×C8D3211yescharacteristic
271C4×D4—94no—
272C4×D4—94no—
273C2×C4⋊C4—91no—
274C2×C22⋊C4—91no—
275C2×C22⋊C4—91no—
276C2×C42—91no—
277C4⋊C8—94no—
278C22⋊C8—34no—
279C22⋊C8—34no—
280#97—94no—
281C23×C3—21no—
282C23×C3—34no—
283C23×C3—32no—
284C23×C3—32no—
285C23×C3—62no—
286C23×C3—62no—
287C23×C3—62no—
288C23×C3—62no—
289C23×C3—62no—
290C23×C3C2×C4×D311yescharacteristic
291C23×C3C2×C4×D311yescharacteristic
292C22×D3—22no—
293C22×D3—22no—
294C22×D3—22no—
295C22×D3—22no—
296C22×D3—22no—
297C22×D3ΓL(1,𝔽25)14yescomplemented
298C22×D3C2×C4×D312yes—
299C22×D3C2×C4×D312yes—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—32no—
305C2×C3×C4—32no—
306C2×C3×C4—62no—
307C2×C3×C4—62no—
308C2×C3×C4—64no—
309C2×C3×C4—64no—
310C2×C3×C4—62no—
311C2×C3×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4C2×C4×D311yescharacteristic
315C2×C3×C4C2×C4×D311yescharacteristic
316C2×C3×C4D3×D412yes—
317C2×C3×C4D3×D412yes—
318C2×C3×C4#23712yes—
319C2×C3×C4#23712yes—
320C2×C3×C4C23×D311yescharacteristic
321C2×C3×C4C23×D311yescharacteristic
322#67—68no—
323#67—68no—
324C2×Dic3—22no—
325C2×Dic3—22no—
326C2×Dic3—32no—
327C2×Dic3—32no—
328C2×Dic3—32no—
329C2×Dic3—32no—
330C2×Dic3—62no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—122no—
337C2×Dic3—122no—
338C2×Dic3C2×C4×D312yes—
339C2×Dic3C2×C4×D312yes—
340C4×D3—24no—
341C4×D3—24no—
342C4×D3—22no—
343C4×D3—22no—
344C4×D3—22no—
345C4×D3—22no—
346C3×C8—24no—
347C3×C8—22no—
348C3×C8—22no—
349C3×C8—62no—
350C3×C8—62no—
351C3⋊C8—22no—
352C3⋊C8—22no—
353C3⋊C8—34no—
354C3⋊C8—34no—
355C3⋊C8—64no—
356C2×C32#43514yescomplemented
357C2×C32C2×C4×D411yescharacteristic
358C2×C32C22×M1611yescharacteristic
359C2×C32C2×#13111yescharacteristic
360C3×D3—24no—
361C3×D3—42no—
362C24—31no—
363C24—31no—
364C2×D4—94no—
365C2×D4—184no—
366C22×C4—31no—
367C22×C4—31no—
368C22×C4—32no—
369C22×C4—32no—
370C22×C4—32no—
371C22×C4—32no—
372C22×C4—62no—
373C22×C4—62no—
374C22×C4—62no—
375C22×C4—62no—
376C22×C4—91no—
377C22×C4—91no—
378C22×C4C2×D3211yescharacteristic
379M16—188no—
380C2×C8—22no—
381C2×C8—32no—
382C2×C8—32no—
383C2×C8—62no—
384C2×C8—62no—
385C2×C8—92no—
386C2×C8—94no—
387C2×C8—188no—
388C2×C8C2×D3212yes—
389C4⋊C4—94no—
390C22⋊C4—94no—
391C22⋊C4—94no—
392C42—92no—
393C42—92no—
394C22×C3—22no—
395C22×C3—21no—
396C22×C3—22no—
397C22×C3—22no—
398C22×C3—34no—
399C22×C3—62no—
400C22×C3—62no—
401C22×C3—68no—
402C22×C3—62no—
403C22×C3—62no—
404C22×C3—62no—
405C22×C3—124no—
406C22×C3#67⋊C412yes—
407C22×C3#67⋊C412yes—
408C22×C3C2×ΓL(1,𝔽25)12yes—
409C22×C3#90112yes—
410C22×C3D3×M1612yes—
411C22×C3#90712yes—
412C22×C3C22×C4×D311yescharacteristic
413C22×C3C22×C4×D311yescharacteristic
414C2×D3—22no—
415C2×D3—22no—
416C2×D3—28no—
417C2×D3—22no—
418C2×D3—22no—
419C2×D3—22no—
420C2×D3—44no—
421C2×D3C2×ΓL(1,𝔽25)14yescomplemented
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—22no—
425C3×C4—62no—
426C3×C4—62no—
427C3×C4#67⋊C412yes—
428C3×C4#67⋊C412yes—
429C3×C4C2×D3×D411yescharacteristic
430C3×C4C2×D3×D411yescharacteristic
431C3×C4C2×#23711yescharacteristic
432C3×C4C2×#23711yescharacteristic
433Dic3—22no—
434Dic3—22no—
435Dic3—62no—
436Dic3—62no—
437Dic3—62no—
438Dic3—62no—
439Dic3—122no—
440Dic3—122no—
441C32C2×#43511yescharacteristic, complemented, Sylow
442C23—34no—
443C23—32no—
444C23—32no—
445C23—62no—
446C23—62no—
447C23—62no—
448C23—62no—
449C23—62no—
450C23C4×D3211yescharacteristic
451D4—188no—
452C2×C4—32no—
453C2×C4—32no—
454C2×C4—62no—
455C2×C4—62no—
456C2×C4—62no—
457C2×C4—62no—
458C2×C4—62no—
459C2×C4—62no—
460C2×C4—64no—
461C2×C4—64no—
462C2×C4—92no—
463C2×C4—92no—
464C2×C4—182no—
465C2×C4—182no—
466C2×C4C4×D3211yescharacteristic
467C2×C4#380212yes—
468C2×C4#380512yes—
469C2×C4C22×D3211yescharacteristic
470C8—22no—
471C8—62no—
472C8—62no—
473C8—94no—
474C2×C3—24no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—64no—
479C2×C3—122no—
480C2×C3#472814yescomplemented
481C2×C3#473014yescomplemented
482C2×C3C2×#67⋊C411yescharacteristic
483C2×C3C2×#67⋊C411yescharacteristic
484C2×C3C22×ΓL(1,𝔽25)11yescharacteristic
485C2×C3C2×#90111yescharacteristic
486C2×C3C2×D3×M1611yescharacteristic
487C2×C3C2×#90711yescharacteristic
488D3—24no—
489D3—42no—
490C22—34no—
491C22—68no—
492C22—62no—
493C22—62no—
494C22—62no—
495C22—62no—
496C22—62no—
497C22—124no—
498C22D3×ΓL(1,𝔽25)12yes—
499C22#6380412yes—
500C22#6390212yes—
501C22C2×C4×D3211yescharacteristic
502C4—62no—
503C4—62no—
504C4—182no—
505C4—182no—
506C4#6390212yes—
507C4C2×#380211yescharacteristic
508C4C2×#380511yescharacteristic
509C3—21no—
510C3C2×#473011yescharacteristic, complemented
511C3C2×#472811yescharacteristic, complemented
512C2—64no—
513C2—122no—
514C2#1059072514yesdirect product factor
515C2C2×D3×ΓL(1,𝔽25)11yescharacteristic
516C2C2×#6380411yescharacteristic
517C2C2×#6390211yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C22×C4
prime radicalC22×#625C4
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C2×#435
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C22×#3711C2semidirect
3. C22×D3×C3⋊C8C2semidirect
4. C2×#63642C2semidirect
5. C2×C3×(C2×D3)⋊C8C2semidirect
6. C2×C3×(C2×D3)⋊C8C2semidirect
7. C2×#63572C2semidirect
8. #10590725C2direct (N × H)
25. C2×#3711C22semidirect
27. C2×D3×C3⋊C8C22semidirect
28. #63642C22semidirect
29. C3×(C2×D3)⋊C8C22semidirect
30. C3×(C2×D3)⋊C8C22semidirect
31. #63572C22semidirect
40. C2×(C2×D3)⋊C8D3semidirect
41. C2×(C2×D3)⋊C8D3semidirect
70. C2×C3⋊(C3⋊C8)D4semidirect
121. (C2×D3)⋊C8C2×D3semidirect
122. (C2×D3)⋊C8C2×D3semidirect
134. C22×C3×D3M16semidirect
157. C3⋊(C3⋊C8)C2×D4semidirect
252. C2×C3×D3C2×M16semidirect
297. C22×D3ΓL(1,𝔽25)semidirect
356. C2×C32#435semidirect
421. C2×D3C2×ΓL(1,𝔽25)semidirect
441. C32C2×#435semidirect
480. C2×C3#4728semidirect
481. C2×C3#4730semidirect
510. C3C2×#4730semidirect
511. C3C2×#4728semidirect
514. C2#10590725direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#6252
C22×#37112
C22×D3×C3⋊C82
C2×#636422
C2×C3×(C2×D3)⋊C82
C2×#635722
#105907252
C2×#47283
C2×#47303