Finite Group Databasebeta

← C2×#10590727 #11859244

Subgroups — C2×#10590727 #11859244

Order 1152.

1229 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×C8C211yesmaximal, characteristic, complemented
2C2×C4×#626C211yesmaximal, characteristic
3C22×#3712C211yesmaximal, characteristic, complemented
4C2×#63647C211yesmaximal, characteristic, complemented
5C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
6C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
7C2×#63554C211yesmaximal, characteristic, complemented
8#10590727C218yesmaximal, direct product factor
9C2×#5111—31nomaximal
10C2×#4836—31nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C22×#626C411yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×C3×D3×C8—24no—
20C2×C3×D3×C8C2214yescomplemented
21C2×Dic3⋊Dic3C411yescharacteristic
22C2×#3722C411yescharacteristic
23C2×(C2×D3)⋊Dic3C411yescharacteristic
24C4×#626C414yes—
25C4×#626C2214yes—
26C2×#3712—24no—
27C2×#3712C2214yescomplemented
28#63647C2214yescomplemented
29C3×Dic3⋊C8C2214yescomplemented
30(C2×D3)⋊(C3⋊C8)C2214yescomplemented
31#63554C2214yescomplemented
32C23×C3×C8—31no—
33C2×C4×#67—31no—
34C22×ΓL(1,𝔽25)—31no—
35C22×ΓL(1,𝔽25)—31no—
36C22×D3×C8D311yescharacteristic, complemented
37C2×C4×D12—31no—
38C2×C3×C4⋊C8—31no—
39C2×#830—31no—
40#5111—38no—
41C2×(C2×D3)⋊C8—31no—
42C2×(C2×D3)⋊C8—31no—
43C2×(C2×D3)⋊C8—31no—
44C2×(C2×D3)⋊C8—61no—
45C2×#815—31no—
46C2×Dic3⋊C8D311yescharacteristic, complemented
47C2×#803—31no—
48#4836—38no—
49C23×C3⋊D3C2×C411yescharacteristic
50C23×C3×D3C2×C411yescharacteristic
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3C2×C411yescharacteristic
53C2×C4×C3⋊D3—22no—
54C2×C4×C3⋊D3—22no—
55C2×C4×C3⋊D3C2×C412yes—
56C2×C4×C3⋊D3C2312yes—
57C22×C3×Dic3C2×C411yescharacteristic
58C22×C3×Dic3C2×C411yescharacteristic
59C22×C3×Dic3C2×C411yescharacteristic
60C2×C3×C4×D3—22no—
61C2×C3×C4×D3—22no—
62C2×C3×C4×D3C2×C412yes—
63C2×C3×C4×D3C2312yes—
64C2×#626—24no—
65C2×#626C2×C414yes—
66C2×C32×C8—22no—
67C2×C32×C8C2312yes—
68C2×C3⋊(C3⋊C8)—22no—
69C2×C3⋊(C3⋊C8)C2312yes—
70C3×C4×Dic3C2×C412yes—
71C3×C4×Dic3C2312yes—
72C2×C3×C3⋊C8—22no—
73C2×C3×C3⋊C8D414yescomplemented
74C2×C3×C3⋊C8C2312yes—
75C2×C3×C3⋊C8C2312yes—
76C3×D3×C8—28no—
77Dic3⋊Dic3C2×C414yes—
78#3722C2×C414yes—
79(C2×D3)⋊Dic3C2×C414yes—
80#3712—28no—
81C2×#435—91noSylow
82C23×C3×C4—31no—
83C22×#67—31no—
84C22×D12—31no—
85C22×C4×D3—31no—
86C22×C4×D3—31no—
87C22×C4×D3—61no—
88C22×C4×D3C2×D311yescharacteristic
89C22×C3×C8—21no—
90C22×C3×C8—31no—
91C22×C3×C8—31no—
92C22×C3×C8—34no—
93C22×C3×C8—64no—
94C22×C3×C8C2×D311yescharacteristic
95C22×C3×C8C2×D311yescharacteristic
96C2×C3×C42—31no—
97C2×#217—31no—
98C4×#67—34no—
99C4×#67—34no—
100C2×(C2×D3)⋊C4—31no—
101C2×(C2×D3)⋊C4—31no—
102C2×(C2×D3)⋊C4—31no—
103C2×C4⋊Dic3—31no—
104C2×Dic3⋊C4—31no—
105C2×C4×Dic3C2×D311yescharacteristic
106C22×C3⋊C8—31no—
107C22×C3⋊C8—31no—
108C22×C3⋊C8—61no—
109C22×C3⋊C8C2×D311yescharacteristic
110C22×C3⋊C8C2×D311yescharacteristic
111C2×ΓL(1,𝔽25)—34no—
112C2×ΓL(1,𝔽25)—34no—
113C2×ΓL(1,𝔽25)—64no—
114C2×ΓL(1,𝔽25)—64no—
115C2×D3×C8—24no—
116C2×D3×C8C2×D314yescomplemented
117C4×D12—34no—
118C4×D12—34no—
119C3×C4⋊C8—34no—
120#830—34no—
121(C2×D3)⋊C8—34no—
122(C2×D3)⋊C8—34no—
123(C2×D3)⋊C8—34no—
124(C2×D3)⋊C8—64no—
125#815—34no—
126Dic3⋊C8C2×D314yescomplemented
127#803—34no—
128C23×C32C22×C411yescharacteristic
129C22×C3⋊D3—22no—
130C22×C3⋊D3—22no—
131C22×C3⋊D3—22no—
132C22×C3⋊D3C22×C412yes—
133C22×C3×D3—22no—
134C22×C3×D3—22no—
135C22×C3×D3M1614yescomplemented
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⋊Dic3C22×C412yes—
143C4×C3⋊D3—24no—
144C4×C3⋊D3—22no—
145C4×C3⋊D3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3C22×C412yes—
150C2×C3×Dic3C22×C412yes—
151C2×C3×Dic3C22×C412yes—
152C3×C4×D3—24no—
153C3×C4×D3—22no—
154C3×C4×D3—22no—
155#626—28no—
156C32×C8—22no—
157C3⋊(C3⋊C8)—22no—
158C3×C3⋊C8—22no—
159C3×C3⋊C8C2×D414yescomplemented
160C22×M16—91no—
161C23×C8—31no—
162C2×C4×D4—91no—
163#435—98no—
164C2×C4⋊C8—31no—
165C2×C22⋊C8—91no—
166C2×C22⋊C8—91no—
167C2×#97—91no—
168C24×C3—31no—
169C23×D3—31no—
170C23×D3—31no—
171C23×D3—61no—
172C23×D3C4×D311yescharacteristic
173C22×C3×C4—21no—
174C22×C3×C4—31no—
175C22×C3×C4—31no—
176C22×C3×C4—31no—
177C22×C3×C4—32no—
178C22×C3×C4—32no—
179C22×C3×C4—62no—
180C22×C3×C4—62no—
181C22×C3×C4C22×D311yescharacteristic
182C22×C3×C4C22×D311yescharacteristic
183C2×#67—34no—
184C2×#67—64no—
185C22×Dic3—31no—
186C22×Dic3—31no—
187C22×Dic3—61no—
188C22×Dic3C4×D311yescharacteristic
189C22×Dic3C4×D311yescharacteristic
190C22×Dic3C4×D311yescharacteristic
191C2×D12—34no—
192C2×D12—64no—
193C2×C4×D3—22no—
194C2×C4×D3—22no—
195C2×C4×D3—32no—
196C2×C4×D3—32no—
197C2×C4×D3—32no—
198C2×C4×D3—32no—
199C2×C4×D3—62no—
200C2×C4×D3—62no—
201C2×C4×D3—62no—
202C2×C4×D3—62no—
203C2×C4×D3—62no—
204C2×C4×D3—62no—
205C2×C4×D3—122no—
206C2×C4×D3—122no—
207C2×C4×D3C4×D312yes—
208C2×C4×D3C22×D312yes—
209C2×C3×C8—22no—
210C2×C3×C8—22no—
211C2×C3×C8—22no—
212C2×C3×C8—34no—
213C2×C3×C8—32no—
214C2×C3×C8—32no—
215C2×C3×C8—42no—
216C2×C3×C8—68no—
217C2×C3×C8—62no—
218C2×C3×C8C22×D312yes—
219C2×C3×C8C22×D312yes—
220C3×C42—32no—
221C3×C42—32no—
222#217—34no—
223(C2×D3)⋊C4—34no—
224(C2×D3)⋊C4—34no—
225(C2×D3)⋊C4—34no—
226C4⋊Dic3—34no—
227Dic3⋊C4—34no—
228C4×Dic3C4×D312yes—
229C4×Dic3C22×D312yes—
230C2×C3⋊C8—22no—
231C2×C3⋊C8—32no—
232C2×C3⋊C8—32no—
233C2×C3⋊C8—62no—
234C2×C3⋊C8—62no—
235C2×C3⋊C8—62no—
236C2×C3⋊C8—122no—
237C2×C3⋊C8#6714yescomplemented
238C2×C3⋊C8C22×D312yes—
239C2×C3⋊C8C22×D312yes—
240ΓL(1,𝔽25)—68no—
241ΓL(1,𝔽25)—68no—
242D3×C8—28no—
243C22×C32C4×D412yes—
244C22×C32C2×M1612yes—
245C22×C32#13112yes—
246C22×C32C23×C411yescharacteristic
247C2×C3⋊D3—22no—
248C2×C3⋊D3—22no—
249C2×C3⋊D3—22no—
250C2×C3⋊D3—44no—
251C2×C3×D3—22no—
252C2×C3×D3—22no—
253C2×C3×D3—28no—
254C2×C3×D3C2×M1614yescomplemented
255C32×C4C4×D412yes—
256C32×C4C22×D411yescharacteristic
257C32×C4C2×#4111yescharacteristic
258C3⋊Dic3—22no—
259C3×Dic3—22no—
260C3×Dic3—22no—
261C3×Dic3—22no—
262C22×D4—91no—
263C23×C4—31no—
264C23×C4—91no—
265C2×M16—94no—
266C2×M16—184no—
267C22×C8—31no—
268C22×C8—31no—
269C22×C8—34no—
270C22×C8—64no—
271C22×C8—91no—
272C22×C8D3211yescharacteristic
273C4×D4—94no—
274C4×D4—94no—
275C2×C4⋊C4—91no—
276C2×C22⋊C4—91no—
277C2×C22⋊C4—91no—
278C2×C42—31no—
279C4⋊C8—34no—
280C22⋊C8—94no—
281C22⋊C8—94no—
282#97—94no—
283C23×C3—21no—
284C23×C3—34no—
285C23×C3—32no—
286C23×C3—62no—
287C23×C3—62no—
288C23×C3C2×C4×D311yescharacteristic
289C23×C3C2×C4×D311yescharacteristic
290C22×D3—22no—
291C22×D3—22no—
292C22×D3—32no—
293C22×D3—32no—
294C22×D3—62no—
295C22×D3—64no—
296C22×D3—62no—
297C22×D3—62no—
298C22×D3—62no—
299C22×D3—62no—
300C22×D3—62no—
301C22×D3—62no—
302C22×D3—122no—
303C22×D3—122no—
304C22×D3ΓL(1,𝔽25)14yescomplemented
305C22×D3C2×C4×D312yes—
306C2×C3×C4—21no—
307C2×C3×C4—22no—
308C2×C3×C4—21no—
309C2×C3×C4—22no—
310C2×C3×C4—32no—
311C2×C3×C4—32no—
312C2×C3×C4—32no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4—64no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4C2×C4×D311yescharacteristic
320C2×C3×C4C2×C4×D311yescharacteristic
321C2×C3×C4#23512yes—
322C2×C3×C4D3×D412yes—
323C2×C3×C4#23912yes—
324C2×C3×C4C2×#6712yes—
325C2×C3×C4C23×D311yescharacteristic
326C2×C3×C4C23×D311yescharacteristic
327#67—68no—
328C2×Dic3—22no—
329C2×Dic3—22no—
330C2×Dic3—22no—
331C2×Dic3—32no—
332C2×Dic3—32no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—122no—
337C2×Dic3C2×C4×D312yes—
338C2×Dic3C2×C4×D312yes—
339C2×Dic3C2×C4×D312yes—
340D12—68no—
341C4×D3—24no—
342C4×D3—22no—
343C4×D3—22no—
344C4×D3—64no—
345C4×D3—64no—
346C4×D3—62no—
347C4×D3—62no—
348C4×D3—62no—
349C4×D3—62no—
350C4×D3—122no—
351C4×D3—122no—
352C4×D3—124no—
353C3×C8—22no—
354C3×C8—22no—
355C3×C8—34no—
356C3×C8—42no—
357C3×C8—62no—
358C3⋊C8—22no—
359C3⋊C8—62no—
360C3⋊C8—62no—
361C3⋊C8—122no—
362C3⋊C8C2×#6714yescomplemented
363C2×C32#43514yescomplemented
364C2×C32C2×C4×D411yescharacteristic
365C2×C32C22×M1611yescharacteristic
366C2×C32C2×#13111yescharacteristic
367C3⋊D3—42no—
368C3×D3—24no—
369C24—31no—
370C24—91no—
371C2×D4—94no—
372C2×D4—184no—
373C22×C4—31no—
374C22×C4—31no—
375C22×C4—31no—
376C22×C4—32no—
377C22×C4—32no—
378C22×C4—62no—
379C22×C4—62no—
380C22×C4—91no—
381C22×C4—92no—
382C22×C4—92no—
383C22×C4—182no—
384C22×C4—182no—
385C22×C4C2×D3211yescharacteristic
386M16—188no—
387C2×C8—22no—
388C2×C8—32no—
389C2×C8—34no—
390C2×C8—32no—
391C2×C8—68no—
392C2×C8—62no—
393C2×C8—92no—
394C2×C8—182no—
395C2×C8C2×D3212yes—
396C4⋊C4—94no—
397C22⋊C4—94no—
398C22⋊C4—94no—
399C42—32no—
400C42—32no—
401C22×C3—22no—
402C22×C3—21no—
403C22×C3—22no—
404C22×C3—22no—
405C22×C3—34no—
406C22×C3—62no—
407C22×C3—62no—
408C22×C3—68no—
409C22×C3#89312yes—
410C22×C3C2×ΓL(1,𝔽25)12yes—
411C22×C3#90112yes—
412C22×C3#90112yes—
413C22×C3D3×M1612yes—
414C22×C3C4×#6712yes—
415C22×C3C22×C4×D311yescharacteristic
416C22×C3C22×C4×D311yescharacteristic
417C2×D3—22no—
418C2×D3—22no—
419C2×D3—28no—
420C2×D3—64no—
421C2×D3—62no—
422C2×D3—62no—
423C2×D3—62no—
424C2×D3—62no—
425C2×D3—62no—
426C2×D3—62no—
427C2×D3—122no—
428C2×D3—122no—
429C2×D3—128no—
430C2×D3—124no—
431C2×D3—124no—
432C2×D3C2×ΓL(1,𝔽25)14yescomplemented
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—22no—
436C3×C4—62no—
437C3×C4—62no—
438C3×C4—62no—
439C3×C4#89312yes—
440C3×C4C4×#6712yes—
441C3×C4C2×#23511yescharacteristic
442C3×C4C2×D3×D411yescharacteristic
443C3×C4C2×#23911yescharacteristic
444C3×C4C22×#6711yescharacteristic
445Dic3—22no—
446Dic3—22no—
447Dic3—22no—
448Dic3—62no—
449Dic3—62no—
450Dic3—122no—
451C32C2×#43511yescharacteristic, complemented, Sylow
452C23—34no—
453C23—32no—
454C23—62no—
455C23—62no—
456C23—92no—
457C23—182no—
458C23—182no—
459C23—182no—
460C23C4×D3211yescharacteristic
461D4—188no—
462C2×C4—32no—
463C2×C4—32no—
464C2×C4—32no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—62no—
469C2×C4—62no—
470C2×C4—64no—
471C2×C4—92no—
472C2×C4—182no—
473C2×C4—182no—
474C2×C4—182no—
475C2×C4—184no—
476C2×C4#379912yes—
477C2×C4C4×D3211yescharacteristic
478C2×C4D3×#6712yes—
479C2×C4C22×D3211yescharacteristic
480C8—22no—
481C8—34no—
482C8—62no—
483C8—182no—
484C2×C3—24no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—64no—
489C2×C3#483614yescomplemented
490C2×C3#511114yescomplemented
491C2×C3C2×#89311yescharacteristic
492C2×C3C22×ΓL(1,𝔽25)11yescharacteristic
493C2×C3C2×#90111yescharacteristic
494C2×C3C2×#90111yescharacteristic
495C2×C3C2×D3×M1611yescharacteristic
496C2×C3C2×C4×#6711yescharacteristic
497D3—24no—
498D3—124no—
499D3—122no—
500D3—122no—
501C22—34no—
502C22—68no—
503C22—62no—
504C22—62no—
505C22—182no—
506C22—182no—
507C22—182no—
508C22—364no—
509C22D3×ΓL(1,𝔽25)12yes—
510C22#6380312yes—
511C22#6390412yes—
512C22C2×C4×D3211yescharacteristic
513C4—62no—
514C4—62no—
515C4—62no—
516C4—182no—
517C4#6390412yes—
518C4C2×#379911yescharacteristic
519C4C2×D3×#6711yescharacteristic
520C3—21no—
521C3C2×#483611yescharacteristic, complemented
522C3C2×#511111yescharacteristic, complemented
523C2—64no—
524C2—362no—
525C2#1059072714yesdirect product factor
526C2C2×D3×ΓL(1,𝔽25)11yescharacteristic
527C2C2×#6380311yescharacteristic
528C2C2×#6390411yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C22×C4
prime radicalC22×#626C4
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
1. C22×C3×D3×C8C2semidirect
3. C22×#3712C2semidirect
4. C2×#63647C2semidirect
5. C2×C3×Dic3⋊C8C2semidirect
6. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
7. C2×#63554C2semidirect
8. #10590727C2direct (N × H)
20. C2×C3×D3×C8C22semidirect
27. C2×#3712C22semidirect
28. #63647C22semidirect
29. C3×Dic3⋊C8C22semidirect
30. (C2×D3)⋊(C3⋊C8)C22semidirect
31. #63554C22semidirect
36. C22×D3×C8D3semidirect
46. C2×Dic3⋊C8D3semidirect
73. C2×C3×C3⋊C8D4semidirect
116. C2×D3×C8C2×D3semidirect
126. Dic3⋊C8C2×D3semidirect
135. C22×C3×D3M16semidirect
159. C3×C3⋊C8C2×D4semidirect
237. C2×C3⋊C8#67semidirect
254. C2×C3×D3C2×M16semidirect
304. C22×D3ΓL(1,𝔽25)semidirect
362. C3⋊C8C2×#67semidirect
363. C2×C32#435semidirect
432. C2×D3C2×ΓL(1,𝔽25)semidirect
451. C32C2×#435semidirect
489. C2×C3#4836semidirect
490. C2×C3#5111semidirect
521. C3C2×#4836semidirect
522. C3C2×#5111semidirect
525. C2#10590727direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×C82
C2×C4×#6262
C22×#37122
C2×#636472
C2×C3×Dic3⋊C82
C2×(C2×D3)⋊(C3⋊C8)2
C2×#635542
#105907272
C2×#51113
C2×#48363