Finite Group Databasebeta

← C2×#10593859 #11900845

Subgroups — C2×#10593859 #11900845

Order 1152.

2481 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64078C211yesmaximal, characteristic, complemented
2C2×C3×C42×D3C211yesmaximal, characteristic
3C2×C3×#869C211yesmaximal, characteristic, complemented
4C2×#63869C212yesmaximal, complemented
5C2×#63857C212yesmaximal
6C2×#63856C212yesmaximal
7C2×#63844C212yesmaximal, complemented
8C2×Dic3×Dic6C212yesmaximal, complemented
9C2×#63841C212yesmaximal
10#10593859C2116yesmaximal, direct product factor
11C2×#5728—31nomaximal
12C2×#5470—31nomaximal
13C22×#634C2212yes—
14C22×C3×C4×D3C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×C3×Dic6C2212yes—
18C2×C32×C42C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2212yes—
20C2×C4⋊(C3⋊Dic3)C2212yes—
21#64078C2218yescomplemented
22C2×C3×C4⋊Dic3C2212yes—
23C2×C3×C4⋊Dic3C2212yes—
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C3×C42×D3C2218yes—
28C3×#869C2218yescomplemented
29C2×#3724C2214yes—
30C2×Dic3⋊Dic3C2214yes—
31C2×(C2×D3)⋊Dic3C2214yes—
32C2×Dic32C2214yes—
33#63869C22116yescomplemented
34#63857C22116yes—
35#63856C22116yes—
36#63844C22116yescomplemented
37Dic3×Dic6C22116yescomplemented
38#63841C22116yes—
39C2×C3×C4⋊Q8—31no—
40C22×C3×C42—31no—
41C2×#946—32no—
42C2×Q8×Dic3—32no—
43C2×#926—32no—
44C2×#924—32no—
45C2×#924—32no—
46#5728—316no—
47C2×#897—32no—
48C2×#892—32no—
49C2×#890—32no—
50C2×#887—32no—
51C2×C42×D3D311yescharacteristic
52#5470—316no—
53C2×#870—32no—
54C2×#869—31no—
55C2×#869—31no—
56C2×#869—61no—
57C2×#869D311yescharacteristic, complemented
58C2×C4×Dic6—32no—
59C2×C4×Dic6—32no—
60C23×C3×D3C2311yescharacteristic
61C22×C32×C4C2311yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C3⋊Dic3C2314yes—
65C2×#634—28no—
66C2×#634C2318yes—
67C22×C3×Dic3C2311yescharacteristic
68C22×C3×Dic3C2311yescharacteristic
69C22×C3×Dic3C2314yes—
70C22×C3×Dic3C2311yescharacteristic
71C2×C3×C4×D3—24no—
72C2×C3×C4×D3—24no—
73C2×C3×C4×D3Q818yescomplemented
74C2×C3×C4×D3C2314yes—
75C2×C3×C4×D3C2314yes—
76C2×C3×C4×D3C2314yes—
77C2×C3×Dic6—28no—
78C2×C3×Dic6C2318yes—
79C32×C42C2314yes—
80C4⋊(C3⋊Dic3)C2318yes—
81C4⋊(C3⋊Dic3)C2318yes—
82C3×C4⋊Dic3C2318yes—
83C3×C4⋊Dic3C2318yes—
84C3×C4×Dic3C2314yes—
85C3×C4×Dic3C2314yes—
86C3×C4×Dic3C2314yes—
87#3724C23116yes—
88Dic3⋊Dic3C23116yes—
89(C2×D3)⋊Dic3C23116yes—
90Dic32C23116yes—
91C2×#533—91noSylow
92C22×C3×Q8—32no—
93C23×C3×C4—31no—
94C23×C3×C4—31no—
95C23×C3×C4—31no—
96C22×C4×D3C2×D311yescharacteristic
97C22×C4×D3C2×D311yescharacteristic
98C22×C4×D3C2×D311yescharacteristic
99C22×Dic6—32no—
100C22×Dic6—32no—
101C22×Dic6—62no—
102C22×Dic6C2×D312yes—
103C3×C4⋊Q8—38no—
104C2×C3×C4⋊C4—32no—
105C2×C3×C4⋊C4—32no—
106C2×C3×C42—21no—
107C2×C3×C42—31no—
108C2×C3×C42—31no—
109C2×C3×C42—31no—
110C2×C3×C42—38no—
111C2×C3×C42C2×D311yescharacteristic
112C2×C3×C42C2×D311yescharacteristic
113C2×#217—34no—
114#946—316no—
115Q8×Dic3—316no—
116C2×(C2×D3)⋊C4—34no—
117#926—316no—
118C2×C4⋊Dic3—32no—
119C2×C4⋊Dic3—32no—
120C2×C4⋊Dic3—32no—
121C2×C4⋊Dic3—32no—
122C2×C4⋊Dic3—34no—
123C2×C4⋊Dic3—62no—
124C2×C4⋊Dic3—62no—
125C2×C4⋊Dic3C2×D312yes—
126C2×C4⋊Dic3C2×D312yes—
127#924—316no—
128#924—316no—
129C2×Dic3⋊C4—34no—
130C2×Dic3⋊C4—34no—
131C2×Dic3⋊C4—34no—
132C2×C4×Dic3—34no—
133C2×C4×Dic3—34no—
134C2×C4×Dic3C2×D311yescharacteristic
135C2×C4×Dic3C2×D311yescharacteristic
136C2×C4×Dic3C2×D311yescharacteristic
137#897—316no—
138#892—316no—
139#890—316no—
140#887—316no—
141C42×D3C2×D318yes—
142#870—316no—
143#869—38no—
144#869—38no—
145#869—68no—
146#869C2×D318yescomplemented
147C4×Dic6—316no—
148C4×Dic6—316no—
149C23×C32C2411yescharacteristic
150C22×C3×D3—22no—
151C22×C3×D3—22no—
152C22×C3×D3C2×Q814yes—
153C22×C3×D3C2412yes—
154C2×C32×C4C2×Q814yes—
155C2×C32×C4#4114yes—
156C2×C32×C4#4114yes—
157C2×C32×C4C2412yes—
158C2×C32×C4C2412yes—
159C2×C32×C4C2412yes—
160C2×C3⋊Dic3—28no—
161C2×C3⋊Dic3C2418yes—
162#634—216no—
163C2×C3×Dic3—28no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3C2×Q814yes—
167C2×C3×Dic3C2418yes—
168C2×C3×Dic3C2412yes—
169C2×C3×Dic3C2412yes—
170C2×C3×Dic3C2412yes—
171C3×C4×D3—28no—
172C3×C4×D3—28no—
173C3×C4×D3C2×Q8116yescomplemented
174C3×Dic6—216no—
175#533—916no—
176C2×C4⋊Q8—31no—
177C2×C4⋊Q8—91no—
178C2×#125—92no—
179C2×C22⋊Q8—92no—
180C2×C22⋊Q8—92no—
181C2×C4×Q8—92no—
182C2×C4×Q8—92no—
183C2×#117—92no—
184C22×C42—31no—
185C24×C3—31no—
186C23×D3C22×D311yescharacteristic
187C2×C3×Q8—38no—
188C2×C3×Q8—68no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—31no—
193C22×C3×C4—38no—
194C22×C3×C4—34no—
195C22×C3×C4—34no—
196C22×C3×C4—31no—
197C22×C3×C4—31no—
198C22×C3×C4—34no—
199C22×C3×C4—34no—
200C22×C3×C4—64no—
201C22×C3×C4—64no—
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D311yescharacteristic
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C22×D311yescharacteristic
208C22×Dic3—34no—
209C22×Dic3—34no—
210C22×Dic3—64no—
211C22×Dic3C22×D314yes—
212C22×Dic3C22×D311yescharacteristic
213C22×Dic3C22×D311yescharacteristic
214C22×Dic3C22×D311yescharacteristic
215C2×C4×D3—24no—
216C2×C4×D3—24no—
217C2×C4×D3Dic618yescomplemented
218C2×C4×D3C22×D314yes—
219C2×C4×D3C22×D314yes—
220C2×C4×D3C22×D314yes—
221C2×Dic6—28no—
222C2×Dic6—38no—
223C2×Dic6—38no—
224C2×Dic6—68no—
225C2×Dic6—68no—
226C2×Dic6—68no—
227C2×Dic6—128no—
228C2×Dic6C22×D318yes—
229C3×C4⋊C4—38no—
230C3×C4⋊C4—38no—
231C3×C42—24no—
232C3×C42—34no—
233C3×C42—34no—
234C3×C42—34no—
235C3×C42C22×D314yes—
236C3×C42C22×D314yes—
237#217—316no—
238(C2×D3)⋊C4—316no—
239C4⋊Dic3—38no—
240C4⋊Dic3—38no—
241C4⋊Dic3—38no—
242C4⋊Dic3—38no—
243C4⋊Dic3—316no—
244C4⋊Dic3—68no—
245C4⋊Dic3—68no—
246C4⋊Dic3C22×D318yes—
247C4⋊Dic3C22×D318yes—
248Dic3⋊C4—316no—
249Dic3⋊C4—316no—
250Dic3⋊C4—316no—
251C4×Dic3—316no—
252C4×Dic3—316no—
253C4×Dic3C22×D314yes—
254C4×Dic3C22×D314yes—
255C4×Dic3C22×D314yes—
256C22×C32C22×Q812yes—
257C22×C32C2×#4112yes—
258C22×C32C2×#4112yes—
259C22×C32C2511yescharacteristic
260C2×C3×D3—28no—
261C2×C3×D3—22no—
262C2×C3×D3—22no—
263C2×C3×D3C22×Q814yes—
264C32×C4C22×Q814yes—
265C32×C4C2×#4114yes—
266C32×C4C2×#4114yes—
267C3⋊Dic3—28no—
268C3×Dic3—28no—
269C3×Dic3—22no—
270C3×Dic3—22no—
271C3×Dic3C22×Q814yes—
272C22×Q8—32no—
273C22×Q8—92no—
274C23×C4—31no—
275C23×C4—31no—
276C23×C4—31no—
277C4⋊Q8—38no—
278C4⋊Q8—98no—
279#125—916no—
280C22⋊Q8—916no—
281C22⋊Q8—916no—
282C4×Q8—916no—
283C4×Q8—916no—
284#117—916no—
285C2×C4⋊C4—32no—
286C2×C4⋊C4—32no—
287C2×C4⋊C4—94no—
288C2×C4⋊C4—94no—
289C2×C4⋊C4—92no—
290C2×C4⋊C4—92no—
291C2×C22⋊C4—94no—
292C2×C42—31no—
293C2×C42—31no—
294C2×C42—31no—
295C2×C42—38no—
296C2×C42—94no—
297C2×C42D3211yescharacteristic
298C23×C3—21no—
299C23×C3—34no—
300C23×C3—32no—
301C23×C3—62no—
302C23×C3—62no—
303C23×C3C23×D311yescharacteristic
304C23×C3C23×D311yescharacteristic
305C22×D3—22no—
306C22×D3—22no—
307C22×D3C2×Dic614yes—
308C22×D3C23×D312yes—
309C3×Q8—616no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—24no—
314C2×C3×C4—24no—
315C2×C3×C4—24no—
316C2×C3×C4—34no—
317C2×C3×C4—32no—
318C2×C3×C4—316no—
319C2×C3×C4—38no—
320C2×C3×C4—32no—
321C2×C3×C4—32no—
322C2×C3×C4—68no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—68no—
326C2×C3×C4—68no—
327C2×C3×C4C2×Dic614yes—
328C2×C3×C4#23514yes—
329C2×C3×C4#23514yes—
330C2×C3×C4#23714yes—
331C2×C3×C4D3×Q814yes—
332C2×C3×C4#23914yes—
333C2×C3×C4C23×D312yes—
334C2×C3×C4C23×D312yes—
335C2×C3×C4C23×D312yes—
336C2×C3×C4C23×D312yes—
337C2×C3×C4C23×D312yes—
338C2×C3×C4C23×D312yes—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—28no—
342C2×Dic3—38no—
343C2×Dic3—38no—
344C2×Dic3—68no—
345C2×Dic3—68no—
346C2×Dic3—68no—
347C2×Dic3—128no—
348C2×Dic3C2×Dic614yes—
349C2×Dic3C23×D318yes—
350C2×Dic3C23×D312yes—
351C2×Dic3C23×D312yes—
352C2×Dic3C23×D312yes—
353C4×D3—28no—
354C4×D3—28no—
355C4×D3C2×Dic6116yescomplemented
356Dic6—216no—
357Dic6—616no—
358Dic6—616no—
359Dic6—1216no—
360C2×C32#53314yescomplemented
361C2×C32C23×Q811yescharacteristic
362C2×C32C22×#4111yescharacteristic
363C2×C32C22×#4111yescharacteristic
364C3×D3—24no—
365C24—31no—
366C2×Q8—38no—
367C2×Q8—68no—
368C2×Q8—98no—
369C2×Q8—188no—
370C22×C4—31no—
371C22×C4—34no—
372C22×C4—38no—
373C22×C4—31no—
374C22×C4—31no—
375C22×C4—34no—
376C22×C4—34no—
377C22×C4—34no—
378C22×C4—64no—
379C22×C4—64no—
380C22×C4—94no—
381C22×C4C2×D3211yescharacteristic
382C22×C4C2×D3211yescharacteristic
383C22×C4C2×D3211yescharacteristic
384C4⋊C4—38no—
385C4⋊C4—38no—
386C4⋊C4—916no—
387C4⋊C4—916no—
388C4⋊C4—98no—
389C4⋊C4—98no—
390C22⋊C4—916no—
391C42—34no—
392C42—34no—
393C42—34no—
394C42—916no—
395C42C2×D3214yes—
396C22×C3—22no—
397C22×C3—22no—
398C22×C3—22no—
399C22×C3—21no—
400C22×C3—34no—
401C22×C3—62no—
402C22×C3—62no—
403C22×C3—68no—
404C22×C3C22×Dic612yes—
405C22×C3C2×#23512yes—
406C22×C3C2×#23512yes—
407C22×C3C2×#23712yes—
408C22×C3C2×D3×Q812yes—
409C22×C3C2×#23912yes—
410C22×C3C24×D311yescharacteristic
411C22×C3C24×D311yescharacteristic
412C2×D3—22no—
413C2×D3—22no—
414C2×D3—28no—
415C2×D3C22×Dic614yes—
416C3×C4—24no—
417C3×C4—24no—
418C3×C4—24no—
419C3×C4—34no—
420C3×C4—68no—
421C3×C4—62no—
422C3×C4—62no—
423C3×C4C22×Dic614yes—
424C3×C4C2×#23514yes—
425C3×C4C2×#23514yes—
426C3×C4C2×#23714yes—
427C3×C4C2×D3×Q814yes—
428C3×C4C2×#23914yes—
429Dic3—22no—
430Dic3—22no—
431Dic3—28no—
432Dic3—68no—
433Dic3—68no—
434Dic3—128no—
435Dic3C22×Dic614yes—
436C32C2×#53311yescharacteristic, complemented, Sylow
437C23—34no—
438C23—32no—
439C23—62no—
440C23—62no—
441C23C22×D3211yescharacteristic
442Q8—616no—
443Q8—1816no—
444C2×C4—34no—
445C2×C4—32no—
446C2×C4—316no—
447C2×C4—32no—
448C2×C4—32no—
449C2×C4—38no—
450C2×C4—62no—
451C2×C4—68no—
452C2×C4—62no—
453C2×C4—68no—
454C2×C4—68no—
455C2×C4—98no—
456C2×C4—188no—
457C2×C4D3×Dic614yes—
458C2×C4#379514yes—
459C2×C4#379914yes—
460C2×C4C22×D3212yes—
461C2×C4C22×D3212yes—
462C2×C4C22×D3212yes—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—24no—
467C2×C3—64no—
468C2×C3#547014yescomplemented
469C2×C3#572814yescomplemented
470C2×C3C23×Dic611yescharacteristic
471C2×C3C22×#23511yescharacteristic
472C2×C3C22×#23511yescharacteristic
473C2×C3C22×#23711yescharacteristic
474C2×C3C22×D3×Q811yescharacteristic
475C2×C3C22×#23911yescharacteristic
476D3—24no—
477C22—34no—
478C22—62no—
479C22—62no—
480C22—68no—
481C22C2×D3×Dic612yes—
482C22C2×#379512yes—
483C22C2×#379912yes—
484C22C23×D3211yescharacteristic
485C4—34no—
486C4—62no—
487C4—68no—
488C4—62no—
489C4—188no—
490C4C2×D3×Dic614yes—
491C4C2×#379514yes—
492C4C2×#379914yes—
493C3—21no—
494C3C2×#547011yescharacteristic, complemented
495C3C2×#572811yescharacteristic, complemented
496C2—64no—
497C2#1059385914yesdirect product factor
498C2C22×D3×Dic611yescharacteristic
499C2C22×#379511yescharacteristic
500C2C22×#379911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32C2×#533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64078C2semidirect
3. C2×C3×#869C2semidirect
4. C2×#63869C2semidirect
7. C2×#63844C2semidirect
8. C2×Dic3×Dic6C2semidirect
10. #10593859C2direct (N × H)
21. #64078C22semidirect
28. C3×#869C22semidirect
33. #63869C22semidirect
36. #63844C22semidirect
37. Dic3×Dic6C22semidirect
57. C2×#869D3semidirect
73. C2×C3×C4×D3Q8semidirect
146. #869C2×D3semidirect
173. C3×C4×D3C2×Q8semidirect
217. C2×C4×D3Dic6semidirect
355. C4×D3C2×Dic6semidirect
360. C2×C32#533semidirect
436. C32C2×#533semidirect
468. C2×C3#5470semidirect
469. C2×C3#5728semidirect
494. C3C2×#5470semidirect
495. C3C2×#5728semidirect
497. C2#10593859direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640782
C2×C3×C42×D32
C2×C3×#8692
C2×#638692
C2×#638572
C2×#638562
C2×#638442
C2×Dic3×Dic62
C2×#638412
#105938592
C2×#57283
C2×#54703