Finite Group Databasebeta

← C2×#10590358 #11860072

Subgroups — C2×#10590358 #11860072

Order 1152.

1161 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×D12C211yesmaximal, characteristic
2C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
3C22×#3715C211yesmaximal, characteristic
4C2×#63630C211yesmaximal, characteristic, complemented
5C2×#63576C211yesmaximal, characteristic, complemented
6C2×#63565C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic
8#10590358C218yesmaximal, direct product factor
9C2×#5026—31nomaximal
10C2×#5018—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×C3×C4×D3—21no—
13C22×C3×Dic6C2211yescharacteristic
14C2×C32×C42C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×Dic3⋊C4—21no—
21C2×C3×C4×Dic3—21no—
22C3×C4×D12—22no—
23C3×C4×D12C2214yes—
24C3×C4×Dic6—22no—
25C3×C4×Dic6C2214yescomplemented
26C2×#3715C418yescomplemented
27C2×#3715C2214yes—
28#63630C2214yescomplemented
29#63576C2214yescomplemented
30#63565C2214yescomplemented
31#63562C2214yes—
32C2×C3×C4×Q8—31no—
33C2×C3×C4×D4—31no—
34C22×#215—31no—
35C22×#214—31no—
36C2×C4×D12D311yescharacteristic
37C2×C4×Dic6D311yescharacteristic, complemented
38C2×#835—31no—
39C2×#832—31no—
40#5026—38no—
41#5018—38no—
42C2×#810—31no—
43C2×#809—31no—
44C2×#807—31no—
45C2×#807—31no—
46C2×#803—31no—
47C2×#803—31no—
48C2×#803—61no—
49C23×C3×D3—21no—
50C22×C32×C4D411yescharacteristic
51C22×C32×C4D411yescharacteristic
52C22×C32×C4C2311yescharacteristic
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3—21no—
56C2×C3×D12—21no—
57C2×C3×D12—22no—
58C2×C3×D12C2×C414yes—
59C2×C3×D12C2312yes—
60C2×C3×C4×D3—24no—
61C2×C3×C4×D3—44no—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—22no—
64C2×C3×Dic6C2×C414yescomplemented
65C2×C3×Dic6C2312yes—
66C32×C42D412yes—
67C32×C42C2312yes—
68C2×C3⋊(C3⋊C8)—22no—
69C2×C3⋊(C3⋊C8)C2×C414yescomplemented
70C2×C3⋊(C3⋊C8)C2312yes—
71C2×C3⋊(C3⋊C8)C2312yes—
72C3×(C2×D3)⋊C4—24no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3C2312yes—
76C3×C4⋊Dic3C2312yes—
77C3×Dic3⋊C4—24no—
78C3×C4×Dic3—24no—
79#3715C2×C4116yescomplemented
80C2×#440—91noSylow
81C22×C3×Q8—31no—
82C22×C3×D4—31no—
83C23×C3×C4—61no—
84C22×D12C2×D311yescharacteristic
85C22×C4×D3—21no—
86C22×Dic6C2×D311yescharacteristic
87C3×C4×Q8—34no—
88C3×C4×Q8—62no—
89C3×C4×D4—34no—
90C3×C4×D4—62no—
91C2×C3×C4⋊C4—31no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C4⋊C4—61no—
94C2×C3×C22⋊C4—61no—
95C2×C3×C42—21no—
96C2×C3×C42—61no—
97C2×C3×C42C2×D311yescharacteristic
98C2×C3×C42C2×D311yescharacteristic
99C2×#215—38no—
100C2×#215—34no—
101C2×#214—38no—
102C2×#214—34no—
103C2×(C2×D3)⋊C4—21no—
104C2×C4⋊Dic3C2×D311yescharacteristic
105C2×C4⋊Dic3C2×D311yescharacteristic
106C2×Dic3⋊C4—21no—
107C2×C4×Dic3—21no—
108C22×C3⋊C8—31no—
109C22×C3⋊C8—31no—
110C22×C3⋊C8—31no—
111C22×C3⋊C8—31no—
112C22×C3⋊C8—61no—
113C22×C3⋊C8—61no—
114C4×D12—22no—
115C4×D12C2×D314yes—
116C4×Dic6—22no—
117C4×Dic6C2×D314yescomplemented
118#835—34no—
119#832—34no—
120#810—34no—
121#809—34no—
122#807—34no—
123#807—34no—
124#803—34no—
125#803—34no—
126#803—64no—
127C23×C32C2×D411yescharacteristic
128C22×C3×D3—24no—
129C22×C3×D3—22no—
130C22×C3×D3—42no—
131C22×C3×D3—42no—
132C2×C32×C4—22no—
133C2×C32×C4—22no—
134C2×C32×C4C22×C412yes—
135C2×C32×C4C2×D412yes—
136C2×C32×C4C2×D412yes—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4#4112yes—
139C2×C32×C4C2411yescharacteristic
140C2×C3×Dic3—24no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—42no—
145C2×C3×Dic3—42no—
146C3×D12—24no—
147C3×D12—22no—
148C3×D12C22×C414yes—
149C3×C4×D3—48no—
150C3×Dic6—24no—
151C3×Dic6—22no—
152C3×Dic6C22×C414yescomplemented
153C3⋊(C3⋊C8)—22no—
154C3⋊(C3⋊C8)C22×C414yescomplemented
155C22×SD16—91no—
156C2×C4×Q8—31no—
157C2×C4×D4—31no—
158#440—98no—
159C2×#107—91no—
160C2×#103—91no—
161C2×#102—91no—
162C2×#97—91no—
163C24×C3—61no—
164C23×D3—21no—
165C2×C3×Q8—34no—
166C2×C3×Q8—32no—
167C2×C3×Q8—62no—
168C2×C3×Q8—61no—
169C2×C3×D4—34no—
170C2×C3×D4—32no—
171C2×C3×D4—62no—
172C2×C3×D4—61no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—61no—
177C22×C3×C4—61no—
178C22×C3×C4—61no—
179C22×C3×C4—64no—
180C22×C3×C4—124no—
181C22×C3×C4#6711yescharacteristic
182C22×C3×C4#6711yescharacteristic
183C22×C3×C4#6711yescharacteristic
184C22×C3×C4#6711yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C22×Dic3—21no—
188C22×Dic3—21no—
189C22×Dic3—21no—
190C2×D12—22no—
191C2×D12—21no—
192C2×D12C4×D314yes—
193C2×D12C22×D312yes—
194C2×C4×D3—24no—
195C2×C4×D3—44no—
196C2×Dic6—22no—
197C2×Dic6—21no—
198C2×Dic6C4×D314yescomplemented
199C2×Dic6C22×D312yes—
200C3×C4⋊C4—32no—
201C3×C4⋊C4—32no—
202C3×C4⋊C4—64no—
203C3×C4⋊C4—61no—
204C3×C4⋊C4—61no—
205C3×C22⋊C4—64no—
206C3×C42—22no—
207C3×C42—22no—
208C3×C42—64no—
209C3×C42#6712yes—
210C3×C42#6712yes—
211C3×C42C22×D312yes—
212C3×C42C22×D312yes—
213#215—316no—
214#214—316no—
215(C2×D3)⋊C4—24no—
216C4⋊Dic3—21no—
217C4⋊Dic3—21no—
218C4⋊Dic3C22×D312yes—
219C4⋊Dic3C22×D312yes—
220Dic3⋊C4—24no—
221C4×Dic3—24no—
222C2×C3⋊C8—34no—
223C2×C3⋊C8—34no—
224C2×C3⋊C8—32no—
225C2×C3⋊C8—32no—
226C2×C3⋊C8—32no—
227C2×C3⋊C8—32no—
228C2×C3⋊C8—62no—
229C2×C3⋊C8—62no—
230C2×C3⋊C8—64no—
231C2×C3⋊C8—64no—
232C2×C3⋊C8—62no—
233C2×C3⋊C8—62no—
234C22×C32C4×D412yes—
235C22×C32AGL(1,ℤ/8)12yes—
236C22×C32#13712yes—
237C22×C32C22×D411yescharacteristic
238C2×C3×D3—24no—
239C2×C3×D3—42no—
240C2×C3×D3—42no—
241C2×C3×D3—48no—
242C32×C4—22no—
243C32×C4—22no—
244C32×C4C4×D412yes—
245C32×C4C23×C411yescharacteristic
246C32×C4C2×#4111yescharacteristic
247C3×Dic3—24no—
248C3×Dic3—42no—
249C3×Dic3—42no—
250C22×Q8—31no—
251C22×D4—31no—
252C23×C4—61no—
253C2×SD16—98no—
254C2×SD16—94no—
255C22×C8—91no—
256C22×C8—91no—
257C4×Q8—34no—
258C4×Q8—62no—
259C4×D4—34no—
260C4×D4—62no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4—31no—
263C2×C4⋊C4—61no—
264C2×C22⋊C4—61no—
265C2×C42—61no—
266C2×C42D3211yescharacteristic
267#107—94no—
268#103—94no—
269#102—94no—
270#97—94no—
271C23×C3—21no—
272C23×C3—64no—
273C23×C3—62no—
274C23×C3—122no—
275C23×C3—122no—
276C23×C3C2×#6711yescharacteristic
277C23×C3C2×#6711yescharacteristic
278C22×D3—24no—
279C22×D3—22no—
280C22×D3—42no—
281C22×D3—42no—
282C3×Q8—34no—
283C3×Q8—64no—
284C3×Q8—62no—
285C3×D4—34no—
286C3×D4—64no—
287C3×D4—62no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—21no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—21no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—42no—
299C2×C3×C4—42no—
300C2×C3×C4—64no—
301C2×C3×C4—62no—
302C2×C3×C4—62no—
303C2×C3×C4—62no—
304C2×C3×C4—128no—
305C2×C3×C4—122no—
306C2×C3×C4—122no—
307C2×C3×C4C2×C4×D312yes—
308C2×C3×C4C2×C4×D312yes—
309C2×C3×C4#23512yes—
310C2×C3×C4#23512yes—
311C2×C3×C4C2×#6712yes—
312C2×C3×C4C2×#6712yes—
313C2×C3×C4C2×#6712yes—
314C2×C3×C4C2×#6712yes—
315C2×C3×C4C2×#6711yescharacteristic
316C2×C3×C4C2×#6711yescharacteristic
317C2×C3×C4C23×D311yescharacteristic
318C2×C3×C4C23×D311yescharacteristic
319C2×Dic3—24no—
320C2×Dic3—22no—
321C2×Dic3—22no—
322C2×Dic3—22no—
323C2×Dic3—42no—
324C2×Dic3—42no—
325D12—24no—
326D12—22no—
327D12C2×C4×D314yes—
328C4×D3—48no—
329Dic6—24no—
330Dic6—22no—
331Dic6C2×C4×D314yescomplemented
332C3⋊C8—34no—
333C3⋊C8—34no—
334C3⋊C8—64no—
335C3⋊C8—64no—
336C3⋊C8—62no—
337C3⋊C8—62no—
338C2×C32#44014yescomplemented
339C2×C32C2×C4×D411yescharacteristic
340C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
341C2×C32C2×#13711yescharacteristic
342C3×D3—44no—
343C24—61no—
344C2×Q8—32no—
345C2×Q8—34no—
346C2×Q8—62no—
347C2×Q8—61no—
348C2×D4—32no—
349C2×D4—34no—
350C2×D4—62no—
351C2×D4—61no—
352C22×C4—61no—
353C22×C4—61no—
354C22×C4—61no—
355C22×C4—64no—
356C22×C4—124no—
357C22×C4#62511yescharacteristic
358C22×C4#62511yescharacteristic
359C22×C4C2×D3211yescharacteristic
360SD16—916no—
361C2×C8—92no—
362C2×C8—94no—
363C2×C8—92no—
364C2×C8—182no—
365C4⋊C4—32no—
366C4⋊C4—32no—
367C4⋊C4—61no—
368C4⋊C4—61no—
369C4⋊C4—64no—
370C22⋊C4—64no—
371C42—64no—
372C42#62512yes—
373C42C2×D3212yes—
374C22×C3—21no—
375C22×C3—22no—
376C22×C3—22no—
377C22×C3—22no—
378C22×C3—64no—
379C22×C3—128no—
380C22×C3—122no—
381C22×C3—122no—
382C22×C3C4×#6712yes—
383C22×C3C4×#6712yes—
384C22×C3#93212yes—
385C22×C3#94212yes—
386C22×C3#94912yes—
387C22×C3#95112yes—
388C22×C3C22×#6711yescharacteristic
389C22×C3C22×#6711yescharacteristic
390C2×D3—24no—
391C2×D3—48no—
392C2×D3—42no—
393C2×D3—42no—
394C3×C4—22no—
395C3×C4—22no—
396C3×C4—22no—
397C3×C4—22no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—22no—
401C3×C4—42no—
402C3×C4—42no—
403C3×C4—64no—
404C3×C4—122no—
405C3×C4—122no—
406C3×C4C4×#6712yes—
407C3×C4C4×#6712yes—
408C3×C4C22×C4×D311yescharacteristic
409C3×C4C22×C4×D311yescharacteristic
410C3×C4C2×#23511yescharacteristic
411C3×C4C2×#23511yescharacteristic
412Dic3—24no—
413Dic3—42no—
414Dic3—42no—
415C32C2×#44011yescharacteristic, complemented, Sylow
416C23—62no—
417C23—64no—
418C23—122no—
419C23—122no—
420C23C2×#62511yescharacteristic
421Q8—34no—
422Q8—62no—
423Q8—64no—
424D4—34no—
425D4—62no—
426D4—64no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—62no—
430C2×C4—64no—
431C2×C4—62no—
432C2×C4—62no—
433C2×C4—128no—
434C2×C4—122no—
435C2×C4—122no—
436C2×C4#379812yes—
437C2×C4C4×D3212yes—
438C2×C4C2×#62512yes—
439C2×C4C2×#62512yes—
440C2×C4C2×#62511yescharacteristic
441C2×C4C22×D3211yescharacteristic
442C8—94no—
443C8—182no—
444C2×C3—24no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—124no—
449C2×C3#501814yescomplemented
450C2×C3#502614yescomplemented
451C2×C3C2×C4×#6711yescharacteristic
452C2×C3C2×C4×#6711yescharacteristic
453C2×C3C2×#93211yescharacteristic
454C2×C3C2×#94211yescharacteristic
455C2×C3C2×#94911yescharacteristic
456C2×C3C2×#95111yescharacteristic
457D3—44no—
458C22—64no—
459C22—128no—
460C22—122no—
461C22—122no—
462C22#6382312yes—
463C22#6382712yes—
464C22C4×#62512yes—
465C22C22×#62511yescharacteristic
466C4—22no—
467C4—22no—
468C4—64no—
469C4—122no—
470C4—122no—
471C4C4×#62512yes—
472C4C2×#379811yescharacteristic
473C4C2×C4×D3211yescharacteristic
474C3—21no—
475C3C2×#501811yescharacteristic, complemented
476C3C2×#502611yescharacteristic, complemented
477C2—124no—
478C2#1059035814yesdirect product factor
479C2C2×#6382311yescharacteristic
480C2C2×#6382711yescharacteristic
481C2C2×C4×#62511yescharacteristic
subgroupG/H
centerC23C2×#625
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC2×C32×C4C24
hypercenterC2×C42D32
hypocenterC32C2×#440
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×Dic6C2semidirect
4. C2×#63630C2semidirect
5. C2×#63576C2semidirect
6. C2×#63565C2semidirect
8. #10590358C2direct (N × H)
25. C3×C4×Dic6C22semidirect
26. C2×#3715C4semidirect
28. #63630C22semidirect
29. #63576C22semidirect
30. #63565C22semidirect
37. C2×C4×Dic6D3semidirect
64. C2×C3×Dic6C2×C4semidirect
69. C2×C3⋊(C3⋊C8)C2×C4semidirect
79. #3715C2×C4semidirect
117. C4×Dic6C2×D3semidirect
152. C3×Dic6C22×C4semidirect
154. C3⋊(C3⋊C8)C22×C4semidirect
198. C2×Dic6C4×D3semidirect
331. Dic6C2×C4×D3semidirect
338. C2×C32#440semidirect
415. C32C2×#440semidirect
449. C2×C3#5018semidirect
450. C2×C3#5026semidirect
475. C3C2×#5018semidirect
476. C3C2×#5026semidirect
478. C2#10590358direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×D122
C2×C3×C4×Dic62
C22×#37152
C2×#636302
C2×#635762
C2×#635652
C2×#635622
#105903582
C2×#50263
C2×#50183