Finite Group Databasebeta

← C2×#10591477 #11873579

Subgroups — C2×#10591477 #11873579

Order 1152.

1077 conjugacy classes of subgroups.

The subgroup lattice has 517 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#940C211yesmaximal, characteristic
2C2×#63869C211yesmaximal, characteristic, complemented
3C2×#63659C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5#10591477C218yesmaximal, direct product factor
6C2×#63563C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic, complemented
8C2×#63554C211yesmaximal, characteristic, complemented
9C2×#5071—31nomaximal
10C2×#4764—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×C3×#67—21no—
13C22×C3×#67—21no—
14C22×C3×D12C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#940—22no—
18C3×#940C2214yes—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C2×#3724—21no—
23C2×Dic3⋊Dic3—21no—
24#63869—22no—
25#63869C2214yescomplemented
26#63659C2214yescomplemented
27C3×#832C2214yescomplemented
28#63563C2214yescomplemented
29#63562C2214yescomplemented
30#63554C2214yescomplemented
31C2×C3×#127—31no—
32C2×#940D311yescharacteristic
33C2×#890—31no—
34C2×#870—31no—
35C2×C3×#102—31no—
36C2×#832—31no—
37C2×#832—31no—
38C2×#832—31no—
39C2×#832—31no—
40C2×#832—61no—
41C2×#832D311yescharacteristic, complemented
42C2×#821—31no—
43C2×#815—31no—
44#5071—38no—
45C2×#809—31no—
46C2×#803—31no—
47#4764—38no—
48C24×C32—21no—
49C23×C3×D3—21no—
50C2×C32×D4—21no—
51C2×C32×D4—22no—
52C2×C32×D4—22no—
53C2×C32×D4C2312yes—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C2×C3×#67—24no—
57C2×C3×#67—24no—
58C2×C3×#67—44no—
59C2×C3×#67—44no—
60C22×C3×Dic3—21no—
61C22×C3×Dic3D411yescharacteristic
62C22×C3×Dic3D411yescharacteristic
63C2×C3×D12—22no—
64C2×C3×D12—22no—
65C2×C3×D12—21no—
66C2×C3×D12C2312yes—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)C2312yes—
69C2×C3⋊(C3⋊C8)—22no—
70C2×C3⋊(C3⋊C8)C2312yes—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3C2312yes—
73C3×C4×Dic3D412yes—
74C3×C4×Dic3C2312yes—
75C2×C3×C3⋊C8—22no—
76C2×C3×C3⋊C8C2312yes—
77#3724—24no—
78Dic3⋊Dic3—24no—
79C2×#490—91noSylow
80C22×C3×D4—21no—
81C22×C3×D4—31no—
82C22×C3×D4—61no—
83C22×C3×D4—61no—
84C22×C3×D4C2×D311yescharacteristic
85C22×C3×D4C2×D311yescharacteristic
86C22×#67—21no—
87C22×#67—21no—
88C22×D12C2×D311yescharacteristic
89C22×C3×C8—31no—
90C3×#127—34no—
91C3×#127—62no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C42—31no—
94#940—22no—
95#940C2×D314yes—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—31no—
98C2×C4⋊Dic3—61no—
99C2×C4⋊Dic3—61no—
100C2×C4⋊Dic3C2×D311yescharacteristic
101C2×Dic3⋊C4—61no—
102C2×Dic3⋊C4—61no—
103C2×Dic3⋊C4—61no—
104C2×C4×Dic3C2×D311yescharacteristic
105C22×C3⋊C8—31no—
106C22×C3⋊C8—31no—
107C22×C3⋊C8—61no—
108C22×C3⋊C8C2×D311yescharacteristic
109#890—34no—
110#890—62no—
111#870—34no—
112#870—62no—
113C3×#102—34no—
114#832—34no—
115#832—34no—
116#832—34no—
117#832—34no—
118#832—64no—
119#832C2×D314yescomplemented
120#821—34no—
121#815—34no—
122#809—34no—
123#803—34no—
124C23×C32—22no—
125C23×C32—42no—
126C23×C32—42no—
127C23×C32—42no—
128C23×C32C2×D411yescharacteristic
129C22×C3×D3—22no—
130C22×C3×D3—42no—
131C22×C3×D3—42no—
132C22×C3×D3—42no—
133C32×D4—22no—
134C32×D4—22no—
135C32×D4—42no—
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4#4112yes—
138C2×C32×C4#4112yes—
139C2×C32×C4C2411yescharacteristic
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—42no—
142C3×#67—48no—
143C3×#67—48no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—42no—
148C2×C3×Dic3C2×D412yes—
149C2×C3×Dic3C2×D412yes—
150C3×D12—22no—
151C3×D12—22no—
152C3×D12—42no—
153C3⋊(C3⋊C8)—22no—
154C3×C3⋊C8—22no—
155C2×#127—31no—
156C2×#125—91no—
157#490—98no—
158C2×#102—31no—
159C2×#102—91no—
160C2×#102—91no—
161C2×#102—91no—
162C2×#97—91no—
163C24×C3—21no—
164C24×C3—21no—
165C24×C3—41no—
166C24×C3—61no—
167C23×D3—21no—
168C2×C3×D4—24no—
169C2×C3×D4—22no—
170C2×C3×D4—21no—
171C2×C3×D4—22no—
172C2×C3×D4—22no—
173C2×C3×D4—22no—
174C2×C3×D4—21no—
175C2×C3×D4—22no—
176C2×C3×D4—32no—
177C2×C3×D4—42no—
178C2×C3×D4—41no—
179C2×C3×D4—64no—
180C2×C3×D4—64no—
181C2×C3×D4—62no—
182C2×C3×D4—61no—
183C2×C3×D4—62no—
184C2×C3×D4—124no—
185C2×C3×D4—124no—
186C2×C3×D4C22×D312yes—
187C2×C3×D4C22×D312yes—
188C22×C3×C4—21no—
189C22×C3×C4—31no—
190C22×C3×C4—31no—
191C22×C3×C4—61no—
192C22×C3×C4C22×D311yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C2×#67—24no—
195C2×#67—24no—
196C2×#67—44no—
197C2×#67—44no—
198C22×Dic3—21no—
199C22×Dic3—61no—
200C22×Dic3—61no—
201C22×Dic3—121no—
202C22×Dic3#6711yescharacteristic
203C22×Dic3#6711yescharacteristic
204C2×D12—22no—
205C2×D12—22no—
206C2×D12—21no—
207C2×D12C22×D312yes—
208C2×C3×C8—32no—
209C2×C3×C8—62no—
210C3×C4⋊C4—32no—
211C3×C4⋊C4—61no—
212C3×C42—32no—
213C3×C42—32no—
214C4⋊Dic3—21no—
215C4⋊Dic3—32no—
216C4⋊Dic3—32no—
217C4⋊Dic3—62no—
218C4⋊Dic3—61no—
219C4⋊Dic3—61no—
220C4⋊Dic3—64no—
221C4⋊Dic3—121no—
222C4⋊Dic3C22×D312yes—
223Dic3⋊C4—64no—
224Dic3⋊C4—64no—
225Dic3⋊C4—64no—
226C4×Dic3#6712yes—
227C4×Dic3C22×D312yes—
228C2×C3⋊C8—22no—
229C2×C3⋊C8—32no—
230C2×C3⋊C8—32no—
231C2×C3⋊C8—62no—
232C2×C3⋊C8—62no—
233C2×C3⋊C8—62no—
234C2×C3⋊C8—122no—
235C2×C3⋊C8C22×D312yes—
236C22×C32—42no—
237C22×C32—42no—
238C22×C32—42no—
239C22×C32—84no—
240C22×C32#12412yes—
241C22×C32AGL(1,ℤ/8)12yes—
242C22×C32AGL(1,ℤ/8)12yes—
243C22×C32C22×D411yescharacteristic
244C2×C3×D3—42no—
245C2×C3×D3—42no—
246C2×C3×D3—42no—
247C2×C3×D3—84no—
248C32×C4#12412yes—
249C32×C4C2×#4111yescharacteristic
250C32×C4C2×#4111yescharacteristic
251C3⋊Dic3—42no—
252C3×Dic3—22no—
253C3×Dic3—22no—
254C3×Dic3—42no—
255C22×D4—31no—
256C22×D4—61no—
257C22×D4—61no—
258C22×D4D3211yescharacteristic
259C22×C8—31no—
260C22×C8—91no—
261#127—34no—
262#127—62no—
263#125—94no—
264#125—182no—
265C2×C4⋊C4—31no—
266C2×C4⋊C4—91no—
267C2×C4⋊C4—181no—
268C2×C4⋊C4—181no—
269C2×C42—31no—
270#102—34no—
271#102—94no—
272#102—94no—
273#102—94no—
274#97—94no—
275C23×C3—22no—
276C23×C3—22no—
277C23×C3—21no—
278C23×C3—42no—
279C23×C3—44no—
280C23×C3—42no—
281C23×C3—42no—
282C23×C3—42no—
283C23×C3—42no—
284C23×C3—42no—
285C23×C3—42no—
286C23×C3—62no—
287C23×C3—82no—
288C23×C3—82no—
289C23×C3—122no—
290C23×C3—122no—
291C23×C3—122no—
292C23×C3D3×D411yescharacteristic
293C23×C3C2×#6711yescharacteristic
294C22×D3—22no—
295C22×D3—42no—
296C22×D3—42no—
297C22×D3—42no—
298C3×D4—24no—
299C3×D4—22no—
300C3×D4—22no—
301C3×D4—22no—
302C3×D4—22no—
303C3×D4—42no—
304C3×D4—44no—
305C3×D4—42no—
306C3×D4—42no—
307C3×D4—62no—
308C3×D4—62no—
309C3×D4—128no—
310C3×D4—128no—
311C3×D4—122no—
312C2×C3×C4—21no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—21no—
316C2×C3×C4—32no—
317C2×C3×C4—32no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4—122no—
322C2×C3×C4#23512yes—
323C2×C3×C4D3×D411yescharacteristic
324C2×C3×C4#23712yes—
325C2×C3×C4#23712yes—
326C2×C3×C4#23712yes—
327C2×C3×C4C2×#6711yescharacteristic
328C2×C3×C4C23×D311yescharacteristic
329C2×C3×C4C23×D311yescharacteristic
330#67—48no—
331#67—48no—
332C2×Dic3—22no—
333C2×Dic3—22no—
334C2×Dic3—22no—
335C2×Dic3—42no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—122no—
339C2×Dic3—122no—
340C2×Dic3—122no—
341C2×Dic3—242no—
342C2×Dic3C2×#6712yes—
343C2×Dic3C2×#6712yes—
344D12—22no—
345D12—22no—
346D12—42no—
347C3×C8—62no—
348C3⋊C8—22no—
349C3⋊C8—62no—
350C3⋊C8—62no—
351C3⋊C8—122no—
352C2×C32—82no—
353C2×C32#49014yescomplemented
354C2×C32C2×#12411yescharacteristic
355C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
356C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
357C3×D3—82no—
358C24—21no—
359C24—61no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—21no—
363C2×D4—32no—
364C2×D4—64no—
365C2×D4—64no—
366C2×D4—62no—
367C2×D4—62no—
368C2×D4—61no—
369C2×D4—124no—
370C2×D4—124no—
371C2×D4C2×D3212yes—
372C22×C4—31no—
373C22×C4—31no—
374C22×C4—61no—
375C22×C4—181no—
376C22×C4C2×D3211yescharacteristic
377C2×C8—32no—
378C2×C8—62no—
379C2×C8—92no—
380C2×C8—182no—
381C4⋊C4—32no—
382C4⋊C4—61no—
383C4⋊C4—92no—
384C4⋊C4—184no—
385C4⋊C4—184no—
386C4⋊C4—181no—
387C42—32no—
388C42—32no—
389C22×C3—21no—
390C22×C3—22no—
391C22×C3—22no—
392C22×C3—22no—
393C22×C3—44no—
394C22×C3—42no—
395C22×C3—42no—
396C22×C3—42no—
397C22×C3—42no—
398C22×C3—42no—
399C22×C3—42no—
400C22×C3—82no—
401C22×C3—82no—
402C22×C3—88no—
403C22×C3—84no—
404C22×C3—84no—
405C22×C3—122no—
406C22×C3—122no—
407C22×C3—122no—
408C22×C3—244no—
409C22×C3#88512yes—
410C22×C3#91112yes—
411C22×C3#91412yes—
412C22×C3#93212yes—
413C22×C3#93212yes—
414C22×C3#93612yes—
415C22×C3C2×D3×D411yescharacteristic
416C22×C3C22×#6711yescharacteristic
417C2×D3—42no—
418C2×D3—42no—
419C2×D3—42no—
420C2×D3—84no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—22no—
424C3×C4—62no—
425C3×C4—62no—
426C3×C4—122no—
427C3×C4#88512yes—
428C3×C4#93612yes—
429C3×C4C2×#23511yescharacteristic
430C3×C4C2×#23711yescharacteristic
431C3×C4C2×#23711yescharacteristic
432C3×C4C2×#23711yescharacteristic
433Dic3—22no—
434Dic3—22no—
435Dic3—42no—
436Dic3—122no—
437Dic3—122no—
438Dic3—242no—
439C32C2×#49011yescharacteristic, complemented, Sylow
440C23—22no—
441C23—42no—
442C23—42no—
443C23—42no—
444C23—62no—
445C23—122no—
446C23—122no—
447C23—122no—
448C23D3×#6711yescharacteristic
449D4—22no—
450D4—22no—
451D4—42no—
452D4—62no—
453D4—62no—
454D4—128no—
455D4—128no—
456D4—122no—
457C2×C4—32no—
458C2×C4—32no—
459C2×C4—62no—
460C2×C4—62no—
461C2×C4—62no—
462C2×C4—122no—
463C2×C4—182no—
464C2×C4—362no—
465C2×C4#380412yes—
466C2×C4#380512yes—
467C2×C4D3×#6711yescharacteristic
468C2×C4C22×D3211yescharacteristic
469C8—62no—
470C8—182no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—24no—
475C2×C3—84no—
476C2×C3—82no—
477C2×C3—82no—
478C2×C3—242no—
479C2×C3#476414yescomplemented
480C2×C3#507114yescomplemented
481C2×C3C2×#88511yescharacteristic
482C2×C3C2×#91111yescharacteristic
483C2×C3C2×#91411yescharacteristic
484C2×C3C2×#93211yescharacteristic
485C2×C3C2×#93211yescharacteristic
486C2×C3C2×#93611yescharacteristic
487D3—82no—
488C22—42no—
489C22—42no—
490C22—42no—
491C22—84no—
492C22—122no—
493C22—122no—
494C22—122no—
495C22—244no—
496C22#6393212yes—
497C22#6393412yes—
498C22#6395912yes—
499C22C2×D3×#6711yescharacteristic
500C4—62no—
501C4—62no—
502C4—122no—
503C4—362no—
504C4#6395912yes—
505C4C2×#380411yescharacteristic
506C4C2×#380511yescharacteristic
507C3—21no—
508C3C2×#476411yescharacteristic, complemented
509C3C2×#507111yescharacteristic, complemented
510C2—82no—
511C2—242no—
512C2#1059147714yesdirect product factor
513C2C2×#6393211yescharacteristic
514C2C2×#6393411yescharacteristic
515C2C2×#6395911yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC2×C3×#940C2
hypercenterC22×D4D32
hypocenterC32C2×#490
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63869C2semidirect
3. C2×#63659C2semidirect
4. C2×C3×#832C2semidirect
5. #10591477C2direct (N × H)
6. C2×#63563C2semidirect
7. C2×#63562C2semidirect
8. C2×#63554C2semidirect
25. #63869C22semidirect
26. #63659C22semidirect
27. C3×#832C22semidirect
28. #63563C22semidirect
29. #63562C22semidirect
30. #63554C22semidirect
41. C2×#832D3semidirect
119. #832C2×D3semidirect
353. C2×C32#490semidirect
439. C32C2×#490semidirect
479. C2×C3#4764semidirect
480. C2×C3#5071semidirect
508. C3C2×#4764semidirect
509. C3C2×#5071semidirect
512. C2#10591477direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9402
C2×#638692
C2×#636592
C2×C3×#8322
#105914772
C2×#635632
C2×#635622
C2×#635542
C2×#50713
C2×#47643