Finite Group Databasebeta

← C2×#10590454 #11860066

Subgroups — C2×#10590454 #11860066

Order 1152.

1153 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#887C211yesmaximal, characteristic, complemented
2C2×Dic3×D12C211yesmaximal, characteristic
3C22×#3715C211yesmaximal, characteristic
4C2×#63634C211yesmaximal, characteristic, complemented
5C2×C3×#809C211yesmaximal, characteristic
6C2×#63566C211yesmaximal, characteristic, complemented
7C2×#63554C211yesmaximal, characteristic, complemented
8#10590454C218yesmaximal, direct product factor
9C2×#5026—31nomaximal
10C2×#4757—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×D3×Dic3—21no—
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×Dic3⋊C4—21no—
18C2×C3×C4×Dic3—21no—
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#887—22no—
22C3×#887C2214yescomplemented
23C2×(C2×D3)⋊Dic3—21no—
24Dic3×D12—22no—
25Dic3×D12C2214yes—
26C2×#3715C418yescomplemented
27C2×#3715C2214yes—
28#63634C2214yescomplemented
29C3×#809C2214yes—
30#63566C2214yescomplemented
31#63554C2214yescomplemented
32C2×C3×C4×Q8—31no—
33C22×#215—31no—
34C2×D4×Dic3—31no—
35C22×#214—31no—
36C2×#887D311yescharacteristic, complemented
37C2×C4×D12—31no—
38C2×C3×#102—31no—
39C2×#835—31no—
40C2×#816—31no—
41C2×#815—31no—
42#5026—38no—
43C2×#809D311yescharacteristic
44C2×#807—31no—
45C2×#807—31no—
46C2×#807—61no—
47C2×#803—31no—
48#4757—38no—
49C23×C3×D3—21no—
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C22×C3×Dic3D411yescharacteristic
56C2×C3×D12—21no—
57C2×C3×D12—22no—
58C2×C3×D12C2×C414yes—
59C2×C3×D12C2312yes—
60C2×C3×Dic6—21no—
61C2×C3×Dic6—22no—
62C2×C3×Dic6C2×C414yescomplemented
63C2×C3×Dic6C2312yes—
64C2×D3×Dic3—24no—
65C2×D3×Dic3—44no—
66C32×C4⋊C4—21no—
67C32×C4⋊C4C2312yes—
68C4⋊(C3⋊Dic3)—21no—
69C4⋊(C3⋊Dic3)C2312yes—
70C2×C3⋊(C3⋊C8)C2×C414yescomplemented
71C2×C3⋊(C3⋊C8)C2312yes—
72C3×Dic3⋊C4—24no—
73C3×C4×Dic3—24no—
74C3×C4×Dic3D412yes—
75C3×C4×Dic3C2312yes—
76C2×C3×C3⋊C8—22no—
77C2×C3×C3⋊C8C2312yes—
78(C2×D3)⋊Dic3—24no—
79#3715C2×C4116yescomplemented
80C2×#440—91noSylow
81C22×C3×Q8—31no—
82C22×C3×D4—31no—
83C23×Dic3—61no—
84C22×D12C2×D311yescharacteristic
85C22×C4×D3—61no—
86C22×Dic6C2×D311yescharacteristic
87C22×C3×C8—31no—
88C3×C4×Q8—34no—
89C3×C4×Q8—62no—
90C2×C3×C4⋊C4—21no—
91C2×C3×C4⋊C4—61no—
92C2×C3×C4⋊C4C2×D311yescharacteristic
93C2×C3×C4⋊C4C2×D311yescharacteristic
94C2×C3×C42—31no—
95C2×C3×C42—61no—
96C2×#217—61no—
97C2×#215—38no—
98C2×#215—34no—
99D4×Dic3—34no—
100D4×Dic3—62no—
101C2×#214—38no—
102C2×#214—34no—
103C2×(C2×D3)⋊C4—61no—
104C2×C4⋊Dic3—31no—
105C2×C4⋊Dic3—31no—
106C2×C4⋊Dic3—61no—
107C2×Dic3⋊C4—21no—
108C2×C4×Dic3—21no—
109C2×C4×Dic3C2×D311yescharacteristic
110C22×C3⋊C8—31no—
111C22×C3⋊C8—31no—
112C22×C3⋊C8—61no—
113C22×C3⋊C8C2×D311yescharacteristic
114#887—22no—
115#887C2×D314yescomplemented
116C4×D12—34no—
117C4×D12—62no—
118C3×#102—34no—
119#835—34no—
120#816—34no—
121#815—34no—
122#809C2×D314yes—
123#807—34no—
124#807—34no—
125#807—64no—
126#803—34no—
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—42no—
134C2×C32×C4C22×C412yes—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4#4112yes—
137C2×C32×C4C2411yescharacteristic
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—42no—
140C2×C3×Dic3—24no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3C2×D412yes—
145C2×C3×Dic3C2×D412yes—
146C3×D12—24no—
147C3×D12—22no—
148C3×D12C22×C414yes—
149C3×Dic6—24no—
150C3×Dic6—22no—
151C3×Dic6C22×C414yescomplemented
152D3×Dic3—48no—
153C3⋊(C3⋊C8)C22×C414yescomplemented
154C3×C3⋊C8—22no—
155C22×SD16—91no—
156C2×C4×Q8—31no—
157C2×C4×D4—91no—
158#440—98no—
159C2×#107—91no—
160C2×#103—91no—
161C2×#102—31no—
162C2×#97—91no—
163C24×C3—61no—
164C23×D3—21no—
165C2×C3×Q8—34no—
166C2×C3×Q8—32no—
167C2×C3×Q8—61no—
168C2×C3×Q8—62no—
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—31no—
177C22×C3×C4—31no—
178C22×C3×C4—41no—
179C22×C3×C4—61no—
180C22×C3×C4C22×D311yescharacteristic
181C22×C3×C4C22×D311yescharacteristic
182C22×Dic3—21no—
183C22×Dic3—61no—
184C22×Dic3—61no—
185C22×Dic3—64no—
186C22×Dic3—121no—
187C22×Dic3—124no—
188C22×Dic3#6711yescharacteristic
189C22×Dic3#6711yescharacteristic
190C2×D12—21no—
191C2×D12—22no—
192C2×D12C4×D314yes—
193C2×D12C22×D312yes—
194C2×C4×D3—64no—
195C2×C4×D3—124no—
196C2×Dic6—22no—
197C2×Dic6—21no—
198C2×Dic6C4×D314yescomplemented
199C2×Dic6C22×D312yes—
200C2×C3×C8—32no—
201C2×C3×C8—62no—
202C3×C4⋊C4—21no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4—22no—
205C3×C4⋊C4—41no—
206C3×C4⋊C4—64no—
207C3×C4⋊C4C22×D312yes—
208C3×C4⋊C4C22×D312yes—
209C3×C42—32no—
210C3×C42—32no—
211C3×C42—64no—
212#217—64no—
213#215—316no—
214#214—316no—
215(C2×D3)⋊C4—64no—
216C4⋊Dic3—32no—
217C4⋊Dic3—32no—
218C4⋊Dic3—62no—
219C4⋊Dic3—61no—
220C4⋊Dic3—61no—
221C4⋊Dic3—121no—
222Dic3⋊C4—24no—
223C4×Dic3—24no—
224C4×Dic3#6712yes—
225C4×Dic3C22×D312yes—
226C2×C3⋊C8—22no—
227C2×C3⋊C8—34no—
228C2×C3⋊C8—34no—
229C2×C3⋊C8—32no—
230C2×C3⋊C8—32no—
231C2×C3⋊C8—62no—
232C2×C3⋊C8—64no—
233C2×C3⋊C8C22×D312yes—
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—42no—
243C32×C4C4×D412yes—
244C32×C4C23×C411yescharacteristic
245C32×C4C2×#4111yescharacteristic
246C3⋊Dic3—42no—
247C3×Dic3—24no—
248C3×Dic3—22no—
249C3×Dic3—22no—
250C22×Q8—31no—
251C22×D4—31no—
252C23×C4—181no—
253C2×SD16—98no—
254C2×SD16—94no—
255C22×C8—31no—
256C22×C8—91no—
257C4×Q8—34no—
258C4×Q8—62no—
259C4×D4—94no—
260C4×D4—182no—
261C2×C4⋊C4—61no—
262C2×C4⋊C4—91no—
263C2×C4⋊C4D3211yescharacteristic
264C2×C22⋊C4—181no—
265C2×C42—31no—
266C2×C42—61no—
267#107—94no—
268#103—94no—
269#102—34no—
270#97—94no—
271C23×C3—21no—
272C23×C3—64no—
273C23×C3—62no—
274C23×C3—122no—
275C23×C3—122no—
276C23×C3D3×D411yescharacteristic
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—21no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—21no—
294C2×C3×C4—32no—
295C2×C3×C4—32no—
296C2×C3×C4—42no—
297C2×C3×C4—42no—
298C2×C3×C4—42no—
299C2×C3×C4—64no—
300C2×C3×C4—62no—
301C2×C3×C4—62no—
302C2×C3×C4—62no—
303C2×C3×C4—82no—
304C2×C3×C4C2×C4×D312yes—
305C2×C3×C4C2×C4×D312yes—
306C2×C3×C4#23512yes—
307C2×C3×C4D3×D411yescharacteristic
308C2×C3×C4#23712yes—
309C2×C3×C4C2×#6711yescharacteristic
310C2×C3×C4C23×D311yescharacteristic
311C2×C3×C4C23×D311yescharacteristic
312C2×Dic3—24no—
313C2×Dic3—22no—
314C2×Dic3—22no—
315C2×Dic3—22no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—122no—
319C2×Dic3—128no—
320C2×Dic3—122no—
321C2×Dic3—122no—
322C2×Dic3—242no—
323C2×Dic3C2×#6712yes—
324C2×Dic3C2×#6712yes—
325D12—24no—
326D12—22no—
327D12C2×C4×D314yes—
328C4×D3—128no—
329Dic6—24no—
330Dic6—22no—
331Dic6C2×C4×D314yescomplemented
332C3×C8—62no—
333C3⋊C8—22no—
334C3⋊C8—34no—
335C3⋊C8—34no—
336C3⋊C8—64no—
337C2×C32#44014yescomplemented
338C2×C32C2×C4×D411yescharacteristic
339C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
340C2×C32C2×#13711yescharacteristic
341C3×D3—44no—
342C24—61no—
343C2×Q8—32no—
344C2×Q8—34no—
345C2×Q8—62no—
346C2×Q8—61no—
347C2×D4—32no—
348C2×D4—34no—
349C2×D4—62no—
350C2×D4—61no—
351C22×C4—21no—
352C22×C4—31no—
353C22×C4—31no—
354C22×C4—61no—
355C22×C4—184no—
356C22×C4—181no—
357C22×C4—364no—
358C22×C4C2×D3211yescharacteristic
359SD16—916no—
360C2×C8—32no—
361C2×C8—62no—
362C2×C8—92no—
363C2×C8—94no—
364C4⋊C4—21no—
365C4⋊C4—64no—
366C4⋊C4—92no—
367C4⋊C4—181no—
368C4⋊C4C2×D3212yes—
369C22⋊C4—184no—
370C42—32no—
371C42—32no—
372C42—64no—
373C22×C3—21no—
374C22×C3—22no—
375C22×C3—22no—
376C22×C3—22no—
377C22×C3—64no—
378C22×C3—128no—
379C22×C3—122no—
380C22×C3—122no—
381C22×C3#67⋊C412yes—
382C22×C3#91112yes—
383C22×C3#91512yes—
384C22×C3C4×#6712yes—
385C22×C3#94212yes—
386C22×C3#94912yes—
387C22×C3C2×D3×D411yescharacteristic
388C22×C3C22×#6711yescharacteristic
389C2×D3—24no—
390C2×D3—42no—
391C2×D3—42no—
392C2×D3—48no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—22no—
396C3×C4—42no—
397C3×C4—42no—
398C3×C4—64no—
399C3×C4—62no—
400C3×C4—62no—
401C3×C4—82no—
402C3×C4#67⋊C412yes—
403C3×C4C4×#6712yes—
404C3×C4C22×C4×D311yescharacteristic
405C3×C4C22×C4×D311yescharacteristic
406C3×C4C2×#23511yescharacteristic
407C3×C4C2×#23711yescharacteristic
408Dic3—24no—
409Dic3—22no—
410Dic3—22no—
411Dic3—122no—
412Dic3—122no—
413Dic3—242no—
414C32C2×#44011yescharacteristic, complemented, Sylow
415C23—62no—
416C23—64no—
417C23—122no—
418C23—122no—
419C23D3×#6711yescharacteristic
420Q8—34no—
421Q8—62no—
422Q8—64no—
423D4—34no—
424D4—62no—
425D4—64no—
426C2×C4—22no—
427C2×C4—32no—
428C2×C4—32no—
429C2×C4—42no—
430C2×C4—62no—
431C2×C4—64no—
432C2×C4—62no—
433C2×C4—62no—
434C2×C4—182no—
435C2×C4—368no—
436C2×C4—362no—
437C2×C4#379512yes—
438C2×C4C4×D3212yes—
439C2×C4D3×#6711yescharacteristic
440C2×C4C22×D3211yescharacteristic
441C8—62no—
442C8—94no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—24no—
447C2×C3—124no—
448C2×C3#475714yescomplemented
449C2×C3#502614yescomplemented
450C2×C3C2×#67⋊C411yescharacteristic
451C2×C3C2×#91111yescharacteristic
452C2×C3C2×#91511yescharacteristic
453C2×C3C2×C4×#6711yescharacteristic
454C2×C3C2×#94211yescharacteristic
455C2×C3C2×#94911yescharacteristic
456D3—44no—
457C22—64no—
458C22—122no—
459C22—122no—
460C22—128no—
461C22#6387912yes—
462C22#6392512yes—
463C22#6394612yes—
464C22C2×D3×#6711yescharacteristic
465C4—42no—
466C4—62no—
467C4—62no—
468C4—64no—
469C4—362no—
470C4#6387912yes—
471C4C2×#379511yescharacteristic
472C4C2×C4×D3211yescharacteristic
473C3—21no—
474C3C2×#475711yescharacteristic, complemented
475C3C2×#502611yescharacteristic, complemented
476C2—124no—
477C2#1059045414yesdirect product factor
478C2C2×#6387911yescharacteristic
479C2C2×#6392511yescharacteristic
480C2C2×#6394611yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#440
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#887C2semidirect
4. C2×#63634C2semidirect
6. C2×#63566C2semidirect
7. C2×#63554C2semidirect
8. #10590454C2direct (N × H)
22. C3×#887C22semidirect
26. C2×#3715C4semidirect
28. #63634C22semidirect
30. #63566C22semidirect
31. #63554C22semidirect
36. C2×#887D3semidirect
62. C2×C3×Dic6C2×C4semidirect
70. C2×C3⋊(C3⋊C8)C2×C4semidirect
79. #3715C2×C4semidirect
115. #887C2×D3semidirect
151. C3×Dic6C22×C4semidirect
153. C3⋊(C3⋊C8)C22×C4semidirect
198. C2×Dic6C4×D3semidirect
331. Dic6C2×C4×D3semidirect
337. C2×C32#440semidirect
414. C32C2×#440semidirect
448. C2×C3#4757semidirect
449. C2×C3#5026semidirect
474. C3C2×#4757semidirect
475. C3C2×#5026semidirect
477. C2#10590454direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8872
C2×Dic3×D122
C22×#37152
C2×#636342
C2×C3×#8092
C2×#635662
C2×#635542
#105904542
C2×#50263
C2×#47573