Finite Group Databasebeta

← C2×#10595446 #11918895

Subgroups — C2×#10595446 #11918895

Order 1152.

3053 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×#1010C211yesmaximal, characteristic, complemented
2C2×C3×#1009C211yesmaximal, characteristic, complemented
3C2×#64157C211yesmaximal, characteristic, complemented
4#10595446C2116yesmaximal, direct product factor
5C2×#63827C213yesmaximal, complemented
6C22×#3715C213yesmaximal, complemented
7C2×#63823C213yesmaximal, complemented
8C2×#63822C213yesmaximal, complemented
9C2×#5837—31nomaximal
10C2×#5836—31nomaximal
11C2×C32×#41C2211yescharacteristic
12C3×#1010—24no—
13C3×#1010C2218yescomplemented
14C3×#1009—24no—
15C3×#1009C2218yescomplemented
16C2×C3×#239—21no—
17C2×C3×D3×Q8—21no—
18C2×C3×#237—23no—
19C2×C3×D3×D4—23no—
20C2×C3×#235C2213yes—
21C2×C3×#235C2213yescomplemented
22C22×C3×D12C2213yes—
23C22×C3×Dic6C2213yescomplemented
24#64157C2218yescomplemented
25C2×#3748C2213yescomplemented
26C22×C3⋊(C3⋊C8)C2213yescomplemented
27C2×#3718C2213yescomplemented
28#63827C22124yescomplemented
29C2×#3715C2211yescharacteristic, complemented
30C2×#3715C2213yescomplemented
31C2×#3715C2216yescomplemented
32C2×#3715C22124yescomplemented
33#63823C22124yescomplemented
34#63822C22124yescomplemented
35C2×#3713C2213yescomplemented
36C2×C3×2−1+4—31no—
37C2×C3×H(5,𝔽2)—31no—
38C2×#1010D311yescharacteristic, complemented
39C2×#1009D311yescharacteristic, complemented
40#5837—316no—
41#5836—316no—
42C2×#951—33no—
43C2×#950—33no—
44C2×#950—33no—
45C2×#949—33no—
46C2×#948—31no—
47C2×#948—31no—
48C2×#948—61no—
49C2×#942—33no—
50C22×#215—33no—
51C22×#214—33no—
52C2×#932—33no—
53C23×C3×D3—23no—
54C32×#41D414yes—
55C32×#41C2314yes—
56C2×C32×Q8D411yescharacteristic
57C2×C32×D4D413yes—
58C22×C32×C4C2313yes—
59C2×C3×#67—23no—
60C2×C3×#67—23no—
61C22×C3×Dic3—23no—
62C3×#239—28no—
63C3×D3×Q8—28no—
64C3×#237—224no—
65C3×D3×D4—224no—
66C3×#235—26no—
67C3×#235—26no—
68C3×#235C23112yes—
69C3×#235C23112yescomplemented
70C2×C3×D12—23no—
71C2×C3×D12—26no—
72C2×C3×D12C2311yescharacteristic
73C2×C3×D12C2313yes—
74C2×C3×D12C23112yes—
75C2×C3×C4×D3—23no—
76C2×C3×C4×D3—23no—
77C2×C3×Dic6—23no—
78C2×C3×Dic6—26no—
79C2×C3×Dic6C2313yes—
80C2×C3×Dic6C2311yescharacteristic
81C2×C3×Dic6C23112yescomplemented
82#3748C23112yescomplemented
83C2×C3⋊(C3⋊C8)C2313yes—
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C2×C3⋊(C3⋊C8)C23112yescomplemented
86#3718C23112yescomplemented
87#3715C2314yescomplemented
88#3715C23112yescomplemented
89#3715C23124yescomplemented
90#3713C23112yescomplemented
91C2×#577—91noSylow
92C3×2−1+4—38no—
93C3×2−1+4—64no—
94C3×H(5,𝔽2)—38no—
95C3×H(5,𝔽2)—64no—
96C2×C3×#41—21no—
97C2×C3×#41—33no—
98C2×C3×#41—33no—
99C2×C3×#41—61no—
100C2×C3×#41—63no—
101C2×C3×#41C2×D311yescharacteristic
102C2×C3×#41C2×D311yescharacteristic
103C22×C3×Q8—33no—
104C22×C3×Q8—61no—
105C22×C3×D4—33no—
106C22×C3×D4—63no—
107#1010—24no—
108#1010C2×D318yescomplemented
109#1009—24no—
110#1009C2×D318yescomplemented
111C2×#239—21no—
112C2×D3×Q8—21no—
113C2×#237—23no—
114C2×D3×D4—23no—
115C2×#235C2×D313yes—
116C2×#235C2×D313yescomplemented
117C22×D12C2×D313yes—
118C22×Dic6C2×D313yescomplemented
119#951—324no—
120#950—324no—
121#950—324no—
122#949—324no—
123#948—38no—
124#948—38no—
125#948—68no—
126C2×#216—33no—
127C2×#216—33no—
128#942—324no—
129C2×#215—33no—
130C2×#215—36no—
131C2×#215—324no—
132C2×#215—31no—
133C2×#214—36no—
134C2×#214—33no—
135C2×#214—31no—
136C2×#214—324no—
137#932—324no—
138C2×#213—33no—
139C2×#213—33no—
140C2×#208—33no—
141C2×#208—33no—
142C2×#208—63no—
143C22×C3⋊C8—33no—
144C22×C3⋊C8—33no—
145C22×C3⋊C8—63no—
146C23×C32C2×D413yes—
147C22×C3×D3—23no—
148C22×C3×D3—21no—
149C22×C3×D3—212no—
150C22×C3×D3—86no—
151C32×Q8C2×D414yes—
152C32×D4C2×D4112yes—
153C2×C32×C4C2×D413yes—
154C2×C32×C4C2×D416yes—
155C2×C32×C4C2411yescharacteristic
156C2×C32×C4C2416yes—
157C3×#67—212no—
158C3×#67—212no—
159C2×C3×Dic3—23no—
160C2×C3×Dic3—212no—
161C2×C3×Dic3—21no—
162C3×D12—23no—
163C3×D12—212no—
164C3×D12—21no—
165C3×D12C2412yes—
166C3×D12C2416yes—
167C3×C4×D3—212no—
168C3×C4×D3—212no—
169C3×Dic6—23no—
170C3×Dic6—212no—
171C3×Dic6—21no—
172C3×Dic6C2416yes—
173C3×Dic6C2412yes—
174C3⋊(C3⋊C8)C2416yes—
175C3⋊(C3⋊C8)C2412yes—
176C2×2−1+4—31no—
177C2×H(5,𝔽2)—31no—
178#577—916no—
179C2×#137—93no—
180C2×AGL(1,ℤ/8)—93no—
181C2×#135—93no—
182C22×SD16—93no—
183C2×#131—91no—
184C24×C3—63no—
185C23×D3—23no—
186C3×#41—24no—
187C3×#41—24no—
188C3×#41—312no—
189C3×#41—312no—
190C3×#41—68no—
191C3×#41—624no—
192C3×#41—66no—
193C3×#41—66no—
194C3×#41#6714yes—
195C3×#41#6714yes—
196C3×#41C22×D314yes—
197C3×#41C22×D314yes—
198C2×C3×Q8—21no—
199C2×C3×Q8—33no—
200C2×C3×Q8—312no—
201C2×C3×Q8—31no—
202C2×C3×Q8—68no—
203C2×C3×Q8—63no—
204C2×C3×Q8—66no—
205C2×C3×Q8#6711yescharacteristic
206C2×C3×Q8#6711yescharacteristic
207C2×C3×D4—23no—
208C2×C3×D4—31no—
209C2×C3×D4—33no—
210C2×C3×D4—312no—
211C2×C3×D4—63no—
212C2×C3×D4—63no—
213C2×C3×D4—624no—
214C2×C3×D4—63no—
215C2×C3×D4—66no—
216C2×C3×D4#6713yes—
217C2×C3×D4#6713yes—
218C22×C3×C4—23no—
219C22×C3×C4—63no—
220C22×C3×C4—63no—
221C22×C3×C4—63no—
222C22×C3×C4C22×D313yes—
223C22×C3×C4C22×D313yes—
224C2×#67—23no—
225C2×#67—23no—
226C22×Dic3—23no—
227#239—28no—
228D3×Q8—28no—
229#237—224no—
230D3×D4—224no—
231#235—26no—
232#235—26no—
233#235C22×D3112yes—
234#235C22×D3112yescomplemented
235C2×D12—23no—
236C2×D12—26no—
237C2×D12C22×D311yescharacteristic
238C2×D12C22×D313yes—
239C2×D12C22×D3112yes—
240C2×C4×D3—23no—
241C2×C4×D3—23no—
242C2×Dic6—23no—
243C2×Dic6—26no—
244C2×Dic6C22×D313yes—
245C2×Dic6C22×D311yescharacteristic
246C2×Dic6C22×D3112yescomplemented
247#216—312no—
248#216—312no—
249#215—312no—
250#215—324no—
251#215—34no—
252#214—324no—
253#214—312no—
254#214—34no—
255#213—312no—
256#213—312no—
257#208—312no—
258#208—312no—
259#208—612no—
260C2×C3⋊C8—31no—
261C2×C3⋊C8—31no—
262C2×C3⋊C8—33no—
263C2×C3⋊C8—33no—
264C2×C3⋊C8—312no—
265C2×C3⋊C8—312no—
266C2×C3⋊C8—61no—
267C2×C3⋊C8—63no—
268C2×C3⋊C8—612no—
269C22×C32—26no—
270C22×C32C22×D416yes—
271C22×C32C22×D411yescharacteristic
272C2×C3×D3—22no—
273C2×C3×D3—26no—
274C2×C3×D3—42no—
275C2×C3×D3—46no—
276C2×C3×D3—812no—
277C32×C4C22×D411yescharacteristic
278C32×C4C22×D416yes—
279C32×C4C2511yescharacteristic
280C3×Dic3—26no—
281C3×Dic3—22no—
2822−1+4—38no—
2832−1+4—64no—
284H(5,𝔽2)—38no—
285H(5,𝔽2)—64no—
286C2×#41—33no—
287C2×#41—33no—
288C2×#41—61no—
289C2×#41—63no—
290C2×#41D3211yescharacteristic
291C22×Q8—33no—
292C22×Q8—61no—
293C22×D4—33no—
294C22×D4—63no—
295#137—924no—
296AGL(1,ℤ/8)—924no—
297#135—924no—
298C2×Q16—93no—
299C2×SD16—93no—
300C2×SD16—96no—
301C2×SD16—924no—
302C2×SD16—91no—
303C2×D8—93no—
304#131—98no—
305C2×M16—93no—
306C22×C8—93no—
307C23×C3—23no—
308C23×C3—61no—
309C23×C3—63no—
310C23×C3—612no—
311C23×C3—246no—
312C23×C3C2×#6713yes—
313C23×C3C2×#6713yes—
314C22×D3—21no—
315C22×D3—23no—
316C22×D3—212no—
317C22×D3—86no—
318C3×Q8—24no—
319C3×Q8—36no—
320C3×Q8—32no—
321C3×Q8—63no—
322C3×Q8—612no—
323C3×Q8—61no—
324C3×Q8C2×#6714yes—
325C3×Q8C2×#6714yes—
326C3×D4—212no—
327C3×D4—32no—
328C3×D4—36no—
329C3×D4—612no—
330C3×D4—612no—
331C3×D4—63no—
332C3×D4—612no—
333C3×D4—61no—
334C3×D4C2×#67112yes—
335C3×D4C2×#67112yes—
336C2×C3×C4—21no—
337C2×C3×C4—26no—
338C2×C3×C4—23no—
339C2×C3×C4—26no—
340C2×C3×C4—61no—
341C2×C3×C4—63no—
342C2×C3×C4—612no—
343C2×C3×C4—612no—
344C2×C3×C4—612no—
345C2×C3×C4C2×#6713yes—
346C2×C3×C4C2×#6716yes—
347C2×C3×C4C2×#6713yes—
348C2×C3×C4C2×#6716yes—
349C2×C3×C4C23×D311yescharacteristic
350C2×C3×C4C23×D311yescharacteristic
351C2×C3×C4C23×D316yes—
352C2×C3×C4C23×D316yes—
353#67—212no—
354#67—212no—
355C2×Dic3—23no—
356C2×Dic3—212no—
357C2×Dic3—21no—
358D12—23no—
359D12—212no—
360D12—21no—
361D12C23×D312yes—
362D12C23×D316yes—
363C4×D3—212no—
364C4×D3—212no—
365Dic6—23no—
366Dic6—212no—
367Dic6—21no—
368Dic6C23×D316yes—
369Dic6C23×D312yes—
370C3⋊C8—32no—
371C3⋊C8—32no—
372C3⋊C8—36no—
373C3⋊C8—36no—
374C3⋊C8—62no—
375C3⋊C8—66no—
376C2×C32—26no—
377C2×C32#57712yescomplemented
378C2×C32C23×D411yescharacteristic
379C3×D3—42no—
380C3×D3—46no—
381C24—63no—
382#41—312no—
383#41—312no—
384#41—68no—
385#41—624no—
386#41—66no—
387#41—66no—
388#41#62514yes—
389#41C2×D3214yes—
390C2×Q8—33no—
391C2×Q8—312no—
392C2×Q8—31no—
393C2×Q8—68no—
394C2×Q8—63no—
395C2×Q8—66no—
396C2×Q8#62511yescharacteristic
397C2×D4—31no—
398C2×D4—33no—
399C2×D4—312no—
400C2×D4—63no—
401C2×D4—63no—
402C2×D4—624no—
403C2×D4—63no—
404C2×D4—66no—
405C2×D4#62513yes—
406C22×C4—63no—
407C22×C4—63no—
408C22×C4—63no—
409C22×C4C2×D3213yes—
410Q16—912no—
411SD16—912no—
412SD16—924no—
413SD16—94no—
414D8—912no—
415M16—912no—
416C2×C8—91no—
417C2×C8—93no—
418C2×C8—912no—
419C22×C3—26no—
420C22×C3—26no—
421C22×C3—26no—
422C22×C3—21no—
423C22×C3—46no—
424C22×C3—62no—
425C22×C3—66no—
426C22×C3—122no—
427C22×C3—126no—
428C22×C3—2412no—
429C22×C3C22×#6716yes—
430C22×C3C22×#6716yes—
431C22×C3C22×#6711yescharacteristic
432C22×C3C22×#6711yescharacteristic
433C2×D3—22no—
434C2×D3—26no—
435C2×D3—46no—
436C2×D3—42no—
437C2×D3—812no—
438C3×C4—21no—
439C3×C4—26no—
440C3×C4—21no—
441C3×C4—62no—
442C3×C4—66no—
443C3×C4C22×#6711yescharacteristic
444C3×C4C22×#6716yes—
445C3×C4C22×#6711yescharacteristic
446C3×C4C22×#6716yes—
447C3×C4C24×D311yescharacteristic
448C3×C4C24×D311yescharacteristic
449Dic3—26no—
450Dic3—22no—
451C32C2×#57711yescharacteristic, complemented, Sylow
452C23—61no—
453C23—63no—
454C23—612no—
455C23—246no—
456C23C2×#62513yes—
457Q8—36no—
458Q8—32no—
459Q8—612no—
460Q8—63no—
461Q8—61no—
462Q8C2×#62514yes—
463D4—32no—
464D4—36no—
465D4—612no—
466D4—612no—
467D4—612no—
468D4—63no—
469D4—61no—
470D4C2×#625112yes—
471C2×C4—612no—
472C2×C4—61no—
473C2×C4—63no—
474C2×C4—612no—
475C2×C4—612no—
476C2×C4C2×#62516yes—
477C2×C4C2×#62513yes—
478C2×C4C22×D3216yes—
479C2×C4C22×D3211yescharacteristic
480C8—92no—
481C8—96no—
482C2×C3—26no—
483C2×C3—26no—
484C2×C3—21no—
485C2×C3—22no—
486C2×C3—46no—
487C2×C3—122no—
488C2×C3—126no—
489C2×C3#583612yescomplemented
490C2×C3#583712yescomplemented
491C2×C3C23×#6711yescharacteristic
492C2×C3C23×#6711yescharacteristic
493D3—46no—
494D3—42no—
495C22—26no—
496C22—62no—
497C22—66no—
498C22—126no—
499C22—122no—
500C22—2412no—
501C22C22×#62516yes—
502C22C22×#62511yescharacteristic
503C4—62no—
504C4—66no—
505C4C22×#62516yes—
506C4C22×#62511yescharacteristic
507C4C23×D3211yescharacteristic
508C3—21no—
509C3C2×#583611yescharacteristic, complemented
510C3C2×#583711yescharacteristic, complemented
511C2—26no—
512C2—126no—
513C2—122no—
514C2#1059544612yesdirect product factor
515C2C23×#62511yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32C2×#577
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. C2×C3×#1009C2semidirect
3. C2×#64157C2semidirect
4. #10595446C2direct (N × H)
5. C2×#63827C2semidirect
6. C22×#3715C2semidirect
7. C2×#63823C2semidirect
8. C2×#63822C2semidirect
13. C3×#1010C22semidirect
15. C3×#1009C22semidirect
21. C2×C3×#235C22semidirect
23. C22×C3×Dic6C22semidirect
24. #64157C22semidirect
25. C2×#3748C22semidirect
26. C22×C3⋊(C3⋊C8)C22semidirect
27. C2×#3718C22semidirect
28. #63827C22semidirect
29. C2×#3715C22semidirect
30. C2×#3715C22semidirect
31. C2×#3715C22semidirect
32. C2×#3715C22semidirect
33. #63823C22semidirect
34. #63822C22semidirect
35. C2×#3713C22semidirect
38. C2×#1010D3semidirect
39. C2×#1009D3semidirect
69. C3×#235C23semidirect
81. C2×C3×Dic6C23semidirect
82. #3748C23semidirect
85. C2×C3⋊(C3⋊C8)C23semidirect
86. #3718C23semidirect
87. #3715C23semidirect
88. #3715C23semidirect
89. #3715C23semidirect
90. #3713C23semidirect
108. #1010C2×D3semidirect
110. #1009C2×D3semidirect
116. C2×#235C2×D3semidirect
118. C22×Dic6C2×D3semidirect
234. #235C22×D3semidirect
246. C2×Dic6C22×D3semidirect
377. C2×C32#577semidirect
451. C32C2×#577semidirect
489. C2×C3#5836semidirect
490. C2×C3#5837semidirect
509. C3C2×#5836semidirect
510. C3C2×#5837semidirect
514. C2#10595446direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C2×C3×#10092
C2×#641572
#105954462
C2×#638272
C22×#37152
C2×#638232
C2×#638222
C2×#58373
C2×#58363