Finite Group Databasebeta

← C2×#10590535 #11873545

Subgroups — C2×#10590535 #11873545

Order 1152.

973 conjugacy classes of subgroups.

The subgroup lattice has 485 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#888C211yesmaximal, characteristic, complemented
2C2×#63864C211yesmaximal, characteristic
3C2×#63636C211yesmaximal, characteristic
4C2×C3×#810C211yesmaximal, characteristic, complemented
5C2×#63565C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic
7C2×#63554C211yesmaximal, characteristic, complemented
8#10590535C218yesmaximal, direct product factor
9C2×#5089—31nomaximal
10C2×#4794—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×Dic6—21no—
13C22×C3×Dic6C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×Dic3⋊C4—21no—
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C3×#888—22no—
21C3×#888C2214yescomplemented
22C2×#3722—21no—
23C2×#3722—21no—
24#63864—22no—
25#63864C2214yes—
26#63636C2214yes—
27C3×#810C2214yescomplemented
28#63565C2214yescomplemented
29#63564C2214yes—
30#63554C2214yescomplemented
31C2×C3×C4⋊Q8—31no—
32C2×#947—31no—
33C2×#888D311yescharacteristic, complemented
34C2×#875—31no—
35C2×C3×#103—31no—
36C2×#835—31no—
37C2×#821—31no—
38C2×#815—31no—
39#5089—38no—
40C2×#810—31no—
41C2×#810D311yescharacteristic, complemented
42C2×#809—31no—
43C2×#809—31no—
44C2×#809—31no—
45C2×#809—61no—
46C2×#803—31no—
47#4794—38no—
48C23×C3⋊D3—21no—
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C2×C4⋊(C3⋊D3)—22no—
52C2×C4⋊(C3⋊D3)—22no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)C2312yes—
55C22×C3×Dic3—21no—
56C22×C3×Dic3—21no—
57C22×C3×Dic3D411yescharacteristic
58C22×C3×Dic3D411yescharacteristic
59C2×C3×Dic6—22no—
60C2×C3×Dic6—22no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—24no—
63C2×C3×Dic6—44no—
64C2×C3×Dic6C2312yes—
65C32×C4⋊C4—21no—
66C32×C4⋊C4C2312yes—
67C2×C3⋊(C3⋊C8)—22no—
68C2×C3⋊(C3⋊C8)C2312yes—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3C2312yes—
71C3×Dic3⋊C4—24no—
72C3×C4×Dic3D412yes—
73C3×C4×Dic3C2312yes—
74C2×C3×C3⋊C8—22no—
75C2×C3×C3⋊C8C2312yes—
76#3722—24no—
77#3722—24no—
78C2×#489—91noSylow
79C22×C3×Q8—31no—
80C22×C3×Q8—61no—
81C22×D12—31no—
82C22×D12—31no—
83C22×D12—61no—
84C22×Dic6—21no—
85C22×Dic6C2×D311yescharacteristic
86C22×C3×C8—31no—
87C3×C4⋊Q8—34no—
88C3×C4⋊Q8—62no—
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C4⋊C4—61no—
92C2×C3×C4⋊C4C2×D311yescharacteristic
93C2×C3×C4⋊C4C2×D311yescharacteristic
94C2×C3×C42—31no—
95#947—34no—
96#947—62no—
97C2×(C2×D3)⋊C4—61no—
98C2×(C2×D3)⋊C4—61no—
99C2×(C2×D3)⋊C4—61no—
100C2×(C2×D3)⋊C4—61no—
101C2×C4⋊Dic3C2×D311yescharacteristic
102C2×Dic3⋊C4—21no—
103C2×C4×Dic3C2×D311yescharacteristic
104C22×C3⋊C8—31no—
105C22×C3⋊C8—31no—
106C22×C3⋊C8—61no—
107C22×C3⋊C8C2×D311yescharacteristic
108#888—22no—
109#888C2×D314yescomplemented
110#875—34no—
111#875—62no—
112C3×#103—34no—
113#835—34no—
114#821—34no—
115#815—34no—
116#810—34no—
117#810C2×D314yescomplemented
118#809—34no—
119#809—34no—
120#809—34no—
121#809—64no—
122#803—34no—
123C23×C32C2×D411yescharacteristic
124C22×C3⋊D3—22no—
125C22×C3⋊D3—42no—
126C22×C3⋊D3—42no—
127C22×C3⋊D3—42no—
128C2×C32×C4—22no—
129C2×C32×C4—42no—
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4#4112yes—
132C2×C32×C4#4112yes—
133C2×C32×C4C2411yescharacteristic
134C4⋊(C3⋊D3)—22no—
135C4⋊(C3⋊D3)—22no—
136C4⋊(C3⋊D3)—42no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—42no—
142C2×C3×Dic3—42no—
143C2×C3×Dic3C2×D412yes—
144C2×C3×Dic3C2×D412yes—
145C3×Dic6—22no—
146C3×Dic6—22no—
147C3×Dic6—48no—
148C3×Dic6—42no—
149C3⋊(C3⋊C8)—22no—
150C3×C3⋊C8—22no—
151C2×C4⋊Q8—31no—
152C2×#124—91no—
153#489—98no—
154C2×#103—31no—
155C2×#103—91no—
156C2×#102—91no—
157C2×#102—91no—
158C2×#97—91no—
159C23×D3—61no—
160C23×D3—61no—
161C23×D3—121no—
162C2×C3×Q8—32no—
163C2×C3×Q8—64no—
164C2×C3×Q8—61no—
165C2×C3×Q8—62no—
166C2×C3×Q8—62no—
167C2×C3×Q8—124no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—31no—
172C22×C3×C4—31no—
173C22×C3×C4—41no—
174C22×C3×C4—61no—
175C22×C3×C4—61no—
176C22×C3×C4C22×D311yescharacteristic
177C22×C3×C4C22×D311yescharacteristic
178C22×Dic3—21no—
179C22×Dic3—21no—
180C22×Dic3#6711yescharacteristic
181C22×Dic3#6711yescharacteristic
182C2×D12—32no—
183C2×D12—32no—
184C2×D12—62no—
185C2×D12—64no—
186C2×D12—62no—
187C2×D12—62no—
188C2×D12—62no—
189C2×D12—62no—
190C2×D12—61no—
191C2×D12—61no—
192C2×D12—122no—
193C2×D12—121no—
194C2×Dic6—22no—
195C2×Dic6—22no—
196C2×Dic6—21no—
197C2×Dic6—24no—
198C2×Dic6—44no—
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—32no—
206C3×C4⋊C4—41no—
207C3×C4⋊C4—64no—
208C3×C4⋊C4—61no—
209C3×C4⋊C4C22×D312yes—
210C3×C4⋊C4C22×D312yes—
211C3×C42—32no—
212C3×C42—32no—
213(C2×D3)⋊C4—64no—
214(C2×D3)⋊C4—64no—
215(C2×D3)⋊C4—64no—
216(C2×D3)⋊C4—64no—
217C4⋊Dic3—21no—
218C4⋊Dic3C22×D312yes—
219Dic3⋊C4—24no—
220C4×Dic3#6712yes—
221C4×Dic3C22×D312yes—
222C2×C3⋊C8—22no—
223C2×C3⋊C8—32no—
224C2×C3⋊C8—32no—
225C2×C3⋊C8—62no—
226C2×C3⋊C8—62no—
227C2×C3⋊C8—62no—
228C2×C3⋊C8—122no—
229C2×C3⋊C8C22×D312yes—
230C22×C32#12412yes—
231C22×C32AGL(1,ℤ/8)12yes—
232C22×C32#13712yes—
233C22×C32C22×D411yescharacteristic
234C2×C3⋊D3—42no—
235C2×C3⋊D3—42no—
236C2×C3⋊D3—42no—
237C2×C3⋊D3—84no—
238C32×C4—42no—
239C32×C4#12412yes—
240C32×C4C2×#4111yescharacteristic
241C32×C4C2×#4111yescharacteristic
242C3×Dic3—22no—
243C3×Dic3—22no—
244C3×Dic3—42no—
245C3×Dic3—42no—
246C22×Q8—31no—
247C22×Q8—61no—
248C22×D4—91no—
249C22×C8—31no—
250C22×C8—91no—
251C4⋊Q8—34no—
252C4⋊Q8—62no—
253#124—94no—
254#124—182no—
255C2×C4⋊C4—31no—
256C2×C4⋊C4—61no—
257C2×C4⋊C4D3211yescharacteristic
258C2×C22⋊C4—181no—
259C2×C22⋊C4—181no—
260C2×C42—31no—
261#103—34no—
262#103—94no—
263#102—94no—
264#102—94no—
265#97—94no—
266C23×C3—21no—
267C23×C3D3×D411yescharacteristic
268C23×C3C2×#6711yescharacteristic
269C22×D3—62no—
270C22×D3—62no—
271C22×D3—122no—
272C22×D3—124no—
273C22×D3—122no—
274C22×D3—122no—
275C22×D3—122no—
276C22×D3—122no—
277C22×D3—122no—
278C22×D3—122no—
279C22×D3—242no—
280C22×D3—242no—
281C3×Q8—62no—
282C3×Q8—62no—
283C3×Q8—128no—
284C3×Q8—122no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—21no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—21no—
291C2×C3×C4—32no—
292C2×C3×C4—32no—
293C2×C3×C4—42no—
294C2×C3×C4—42no—
295C2×C3×C4—42no—
296C2×C3×C4—62no—
297C2×C3×C4—62no—
298C2×C3×C4—62no—
299C2×C3×C4—62no—
300C2×C3×C4—82no—
301C2×C3×C4—122no—
302C2×C3×C4—122no—
303C2×C3×C4#23512yes—
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4#23712yes—
306C2×C3×C4#23912yes—
307C2×C3×C4#23912yes—
308C2×C3×C4C2×#6711yescharacteristic
309C2×C3×C4C23×D311yescharacteristic
310C2×C3×C4C23×D311yescharacteristic
311C2×Dic3—22no—
312C2×Dic3—22no—
313C2×Dic3—22no—
314C2×Dic3—22no—
315C2×Dic3—42no—
316C2×Dic3—42no—
317C2×Dic3C2×#6712yes—
318C2×Dic3C2×#6712yes—
319D12—64no—
320D12—62no—
321D12—62no—
322D12—62no—
323D12—62no—
324D12—122no—
325D12—124no—
326D12—122no—
327D12—122no—
328Dic6—22no—
329Dic6—22no—
330Dic6—48no—
331Dic6—42no—
332C3×C8—62no—
333C3⋊C8—22no—
334C3⋊C8—62no—
335C3⋊C8—62no—
336C3⋊C8—122no—
337C2×C32#48914yescomplemented
338C2×C32C2×#12411yescharacteristic
339C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
340C2×C32C2×#13711yescharacteristic
341C3⋊D3—82no—
342C24—181no—
343C2×Q8—32no—
344C2×Q8—64no—
345C2×Q8—61no—
346C2×Q8—62no—
347C2×Q8—62no—
348C2×Q8—124no—
349C2×D4—92no—
350C2×D4—182no—
351C2×D4—182no—
352C2×D4—181no—
353C22×C4—21no—
354C22×C4—31no—
355C22×C4—31no—
356C22×C4—61no—
357C22×C4—61no—
358C22×C4C2×D3211yescharacteristic
359C2×C8—32no—
360C2×C8—62no—
361C2×C8—92no—
362C2×C8—182no—
363C4⋊C4—21no—
364C4⋊C4—32no—
365C4⋊C4—64no—
366C4⋊C4—61no—
367C4⋊C4C2×D3212yes—
368C22⋊C4—184no—
369C22⋊C4—184no—
370C42—32no—
371C42—32no—
372C22×C3—21no—
373C22×C3—22no—
374C22×C3—22no—
375C22×C3—22no—
376C22×C3#88512yes—
377C22×C3#91412yes—
378C22×C3#91812yes—
379C22×C3#93212yes—
380C22×C3#94212yes—
381C22×C3#94712yes—
382C22×C3C2×D3×D411yescharacteristic
383C22×C3C22×#6711yescharacteristic
384C2×D3—124no—
385C2×D3—122no—
386C2×D3—122no—
387C2×D3—122no—
388C2×D3—122no—
389C2×D3—122no—
390C2×D3—122no—
391C2×D3—242no—
392C2×D3—242no—
393C2×D3—248no—
394C2×D3—244no—
395C2×D3—244no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—22no—
399C3×C4—42no—
400C3×C4—42no—
401C3×C4—62no—
402C3×C4—62no—
403C3×C4—82no—
404C3×C4—122no—
405C3×C4—122no—
406C3×C4#88512yes—
407C3×C4#94712yes—
408C3×C4C2×#23511yescharacteristic
409C3×C4C2×#23711yescharacteristic
410C3×C4C2×#23911yescharacteristic
411C3×C4C2×#23911yescharacteristic
412Dic3—22no—
413Dic3—22no—
414Dic3—42no—
415Dic3—42no—
416C32C2×#48911yescharacteristic, complemented, Sylow
417C23—182no—
418C23—362no—
419C23—362no—
420C23—362no—
421C23D3×#6711yescharacteristic
422Q8—62no—
423Q8—62no—
424Q8—128no—
425Q8—122no—
426D4—182no—
427D4—182no—
428D4—362no—
429C2×C4—22no—
430C2×C4—32no—
431C2×C4—32no—
432C2×C4—42no—
433C2×C4—62no—
434C2×C4—62no—
435C2×C4—62no—
436C2×C4—62no—
437C2×C4—122no—
438C2×C4—122no—
439C2×C4#379612yes—
440C2×C4#379912yes—
441C2×C4D3×#6711yescharacteristic
442C2×C4C22×D3211yescharacteristic
443C8—62no—
444C8—182no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—24no—
448C2×C3—21no—
449C2×C3#479414yescomplemented
450C2×C3#508914yescomplemented
451C2×C3C2×#88511yescharacteristic
452C2×C3C2×#91411yescharacteristic
453C2×C3C2×#91811yescharacteristic
454C2×C3C2×#93211yescharacteristic
455C2×C3C2×#94211yescharacteristic
456C2×C3C2×#94711yescharacteristic
457D3—244no—
458D3—242no—
459D3—242no—
460C22—362no—
461C22—362no—
462C22—362no—
463C22—724no—
464C22#6390712yes—
465C22#6393412yes—
466C22#6394812yes—
467C22C2×D3×#6711yescharacteristic
468C4—42no—
469C4—62no—
470C4—62no—
471C4—122no—
472C4—122no—
473C4#6390712yes—
474C4C2×#379611yescharacteristic
475C4C2×#379911yescharacteristic
476C3—21no—
477C3C2×#479411yescharacteristic, complemented
478C3C2×#508911yescharacteristic, complemented
479C2—722no—
480C2#1059053514yesdirect product factor
481C2C2×#6390711yescharacteristic
482C2C2×#6393411yescharacteristic
483C2C2×#6394811yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#489
LCSG ▷ C2×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×#888C2semidirect
4. C2×C3×#810C2semidirect
5. C2×#63565C2semidirect
7. C2×#63554C2semidirect
8. #10590535C2direct (N × H)
21. C3×#888C22semidirect
27. C3×#810C22semidirect
28. #63565C22semidirect
30. #63554C22semidirect
33. C2×#888D3semidirect
41. C2×#810D3semidirect
109. #888C2×D3semidirect
117. #810C2×D3semidirect
337. C2×C32#489semidirect
416. C32C2×#489semidirect
449. C2×C3#4794semidirect
450. C2×C3#5089semidirect
477. C3C2×#4794semidirect
478. C3C2×#5089semidirect
480. C2#10590535direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8882
C2×#638642
C2×#636362
C2×C3×#8102
C2×#635652
C2×#635642
C2×#635542
#105905352
C2×#50893
C2×#47943