Finite Group Databasebeta

← C2×#10593904 #11902675

Subgroups — C2×#10593904 #11902675

Order 1152.

3285 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×Dic6C212yesmaximal, complemented
2C2×C4×#634C211yesmaximal, characteristic, complemented
3C2×C3×C4×D12C211yesmaximal, characteristic
4C2×C3×#869C211yesmaximal, characteristic, complemented
5C2×#63919C212yesmaximal, complemented
6C2×#63899C214yesmaximal, complemented
7C2×#63898C212yesmaximal
8C2×#63856C212yesmaximal, complemented
9#10593904C2116yesmaximal, direct product factor
10C2×#5727—31nomaximal
11C2×D4×Dic6—31nomaximal
12C22×#634C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×C4×D3C2212yes—
15C22×C3×Dic6C2212yes—
16C22×#627C2214yes—
17C22×D3×Dic3C2214yes—
18C2×D3×Dic6—216no—
19C2×D3×Dic6C22116yescomplemented
20C2×C32×C42C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×#3750C2212yes—
23C2×C4×C3⋊Dic3C2212yes—
24C4×#634C2218yescomplemented
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×C4⋊Dic3C2212yes—
27C2×C3×C4⋊Dic3C2212yes—
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C3×C4×D12C2218yes—
30C3×#869C2218yescomplemented
31C2×#3724C2214yes—
32C2×(C2×D3)⋊Dic3C2214yes—
33#63919C22116yescomplemented
34#63899C22132yescomplemented
35#63898C22116yes—
36#63856C22116yescomplemented
37C22×D3×Q8—32no—
38C23×Dic6—32no—
39C2×C3×C4⋊Q8—31no—
40C2×C3×C4×D4—31no—
41C2×#946—32no—
42C2×D4×Dic3—32no—
43C2×#924—32no—
44#5727—316no—
45D4×Dic6—316no—
46C2×#896—34no—
47C2×#893—32no—
48C2×#888—32no—
49C2×#888—32no—
50C2×#878—34no—
51C2×C4×D12D311yescharacteristic
52C2×#869D311yescharacteristic, complemented
53C2×C4×Dic6—31no—
54C2×C4×Dic6—31no—
55C2×C4×Dic6—61no—
56C23×C3×D3C2312yes—
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3C2312yes—
61C22×C3⋊Dic3C2312yes—
62C2×#634D418yescomplemented
63C2×#634C2314yes—
64C22×C3×Dic3C2314yes—
65C22×C3×Dic3C2312yes—
66C2×C3×D12Q818yescomplemented
67C2×C3×D12C2314yes—
68C2×C3×C4×D3—28no—
69C2×C3×C4×D3C2318yes—
70C2×C3×Dic6—28no—
71C2×C3×Dic6C2318yes—
72C2×#627—216no—
73C2×#627C23116yes—
74C2×D3×Dic3—216no—
75C2×D3×Dic3C23116yes—
76D3×Dic6—264no—
77C32×C42C2314yes—
78C4⋊(C3⋊Dic3)C2314yes—
79#3750C2318yes—
80C4×C3⋊Dic3C2318yes—
81C3×(C2×D3)⋊C4C2318yes—
82C3×C4⋊Dic3C2318yes—
83C3×C4⋊Dic3C2318yes—
84C3×C4⋊Dic3C2314yes—
85#3724C23116yes—
86(C2×D3)⋊Dic3C23116yes—
87C2×D4×Q8—91noSylow
88C22×C3×Q8—32no—
89C22×C3×D4—31no—
90C23×C3×C4—32no—
91C23×Dic3—34no—
92C2×D3×Q8—316no—
93C2×D3×Q8—616no—
94C22×D12C2×D311yescharacteristic
95C22×C4×D3—34no—
96C22×C4×D3C2×D312yes—
97C22×Dic6—31no—
98C22×Dic6—31no—
99C22×Dic6—34no—
100C22×Dic6—34no—
101C22×Dic6—316no—
102C22×Dic6—61no—
103C22×Dic6—616no—
104C22×Dic6C2×D312yes—
105C3×C4⋊Q8—38no—
106C3×C4×D4—38no—
107C2×C3×C4⋊C4—31no—
108C2×C3×C4⋊C4—32no—
109C2×C3×C4⋊C4—32no—
110C2×C3×C22⋊C4—32no—
111C2×C3×C42—21no—
112C2×C3×C42C2×D311yescharacteristic
113C2×C3×C42C2×D311yescharacteristic
114C2×#217—34no—
115#946—316no—
116D4×Dic3—316no—
117C2×(C2×D3)⋊C4—34no—
118C2×(C2×D3)⋊C4C2×D312yes—
119C2×C4⋊Dic3—31no—
120C2×C4⋊Dic3—31no—
121C2×C4⋊Dic3—61no—
122C2×C4⋊Dic3C2×D312yes—
123C2×C4⋊Dic3C2×D312yes—
124C2×C4⋊Dic3C2×D311yescharacteristic
125#924—316no—
126C2×Dic3⋊C4—32no—
127C2×Dic3⋊C4—32no—
128C2×Dic3⋊C4—34no—
129C2×Dic3⋊C4—34no—
130C2×Dic3⋊C4—62no—
131C2×C4×Dic3—32no—
132C2×C4×Dic3—32no—
133C2×C4×Dic3—62no—
134#896—332no—
135#893—316no—
136#888—316no—
137#888—316no—
138#878—332no—
139C4×D12C2×D318yes—
140#869C2×D318yescomplemented
141C4×Dic6—38no—
142C4×Dic6—38no—
143C4×Dic6—68no—
144C23×C32C2411yescharacteristic
145C22×C3×D3—24no—
146C22×C3×D3—24no—
147C22×C3×D3C2×Q818yescomplemented
148C22×C3×D3C2414yes—
149C2×C32×C4—22no—
150C2×C32×C4C2×D414yes—
151C2×C32×C4C2×Q814yescomplemented
152C2×C32×C4C2412yes—
153C2×C32×C4C2412yes—
154C2×C32×C4C2412yes—
155C2×C3⋊Dic3—24no—
156C2×C3⋊Dic3C2×D418yes—
157C2×C3⋊Dic3C2414yes—
158C2×C3⋊Dic3C2414yes—
159#634C2×D4116yescomplemented
160C2×C3×Dic3—28no—
161C2×C3×Dic3—24no—
162C2×C3×Dic3C2418yes—
163C2×C3×Dic3C2414yes—
164C3×D12C2×Q8116yescomplemented
165C3×C4×D3—216no—
166C3×Dic6—216no—
167#627—232no—
168D3×Dic3—232no—
169C23×Q8—92no—
170D4×Q8—916no—
171C2×C4⋊Q8—31no—
172C2×C4⋊Q8—92no—
173C2×C22⋊Q8—94no—
174C2×C22⋊Q8—92no—
175C2×C4×Q8—91no—
176C2×C4×D4—31no—
177C2×C4×D4—92no—
178C24×C3—32no—
179C23×D3C22×D312yes—
180C2×C3×Q8—38no—
181C2×C3×Q8—68no—
182C2×C3×D4—38no—
183C2×C3×D4—34no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—32no—
188C22×C3×C4—34no—
189C22×C3×C4—38no—
190C22×C3×C4—68no—
191C22×C3×C4C22×D311yescharacteristic
192C22×C3×C4C22×D311yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C22×C3×C4C22×D311yescharacteristic
196C22×C3×C4C22×D311yescharacteristic
197C22×Dic3—32no—
198C22×Dic3—32no—
199C22×Dic3—32no—
200C22×Dic3—32no—
201C22×Dic3—316no—
202C22×Dic3—62no—
203C22×Dic3—62no—
204C22×Dic3—616no—
205C22×Dic3C22×D312yes—
206C22×Dic3C22×D314yes—
207D3×Q8—664no—
208C2×D12Dic618yescomplemented
209C2×D12C22×D314yes—
210C2×C4×D3—28no—
211C2×C4×D3—316no—
212C2×C4×D3—616no—
213C2×C4×D3C22×D318yes—
214C2×Dic6—28no—
215C2×Dic6—38no—
216C2×Dic6—38no—
217C2×Dic6—34no—
218C2×Dic6—34no—
219C2×Dic6—316no—
220C2×Dic6—316no—
221C2×Dic6—64no—
222C2×Dic6—68no—
223C2×Dic6—664no—
224C2×Dic6—616no—
225C2×Dic6—616no—
226C2×Dic6C22×D318yes—
227C3×C4⋊C4—34no—
228C3×C4⋊C4—38no—
229C3×C4⋊C4—38no—
230C3×C22⋊C4—38no—
231C3×C42—24no—
232C3×C42C22×D314yes—
233C3×C42C22×D314yes—
234#217—316no—
235(C2×D3)⋊C4—316no—
236(C2×D3)⋊C4C22×D318yes—
237C4⋊Dic3—34no—
238C4⋊Dic3—34no—
239C4⋊Dic3—64no—
240C4⋊Dic3C22×D318yes—
241C4⋊Dic3C22×D318yes—
242C4⋊Dic3C22×D314yes—
243Dic3⋊C4—38no—
244Dic3⋊C4—38no—
245Dic3⋊C4—316no—
246Dic3⋊C4—316no—
247Dic3⋊C4—68no—
248C4×Dic3—38no—
249C4×Dic3—38no—
250C4×Dic3—68no—
251C22×C32C22×D412yes—
252C22×C32C22×Q812yes—
253C22×C322−1+412yes—
254C22×C32C2511yescharacteristic
255C2×C3×D3—216no—
256C2×C3×D3—24no—
257C2×C3×D3—24no—
258C2×C3×D3C22×Q818yescomplemented
259C32×C4—22no—
260C32×C4C22×D414yes—
261C32×C4C22×Q814yescomplemented
262C3⋊Dic3—24no—
263C3⋊Dic3C22×D418yes—
264C3×Dic3—28no—
265C3×Dic3—24no—
266C22×Q8—32no—
267C22×Q8—94no—
268C22×Q8—916no—
269C22×Q8—91no—
270C22×Q8—1816no—
271C22×D4—31no—
272C23×C4—32no—
273C23×C4—94no—
274C4⋊Q8—38no—
275C4⋊Q8—916no—
276C22⋊Q8—932no—
277C22⋊Q8—916no—
278C4×Q8—98no—
279C4×D4—38no—
280C4×D4—916no—
281C2×C4⋊C4—31no—
282C2×C4⋊C4—32no—
283C2×C4⋊C4—32no—
284C2×C4⋊C4—94no—
285C2×C4⋊C4—92no—
286C2×C4⋊C4—91no—
287C2×C22⋊C4—32no—
288C2×C22⋊C4—94no—
289C2×C42—92no—
290C2×C42D3211yescharacteristic
291C23×C3—21no—
292C23×C3—38no—
293C23×C3—34no—
294C23×C3—64no—
295C23×C3—64no—
296C23×C3C23×D311yescharacteristic
297C23×C3C23×D311yescharacteristic
298C22×D3—24no—
299C22×D3—24no—
300C22×D3C2×Dic618yescomplemented
301C22×D3C23×D314yes—
302C3×Q8—616no—
303C3×D4—316no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—24no—
310C2×C3×C4—24no—
311C2×C3×C4—34no—
312C2×C3×C4—38no—
313C2×C3×C4—42no—
314C2×C3×C4—64no—
315C2×C3×C4—68no—
316C2×C3×C4—616no—
317C2×C3×C4C2×Dic614yescomplemented
318C2×C3×C4D3×D414yes—
319C2×C3×C4D3×D414yes—
320C2×C3×C4D3×Q814yescomplemented
321C2×C3×C4C23×D312yes—
322C2×C3×C4C23×D312yes—
323C2×C3×C4C23×D312yes—
324C2×C3×C4C23×D312yes—
325C2×C3×C4C23×D312yes—
326C2×C3×C4C23×D312yes—
327C2×Dic3—28no—
328C2×Dic3—24no—
329C2×Dic3—38no—
330C2×Dic3—38no—
331C2×Dic3—34no—
332C2×Dic3—34no—
333C2×Dic3—34no—
334C2×Dic3—34no—
335C2×Dic3—68no—
336C2×Dic3—64no—
337C2×Dic3—64no—
338C2×Dic3—632no—
339C2×Dic3—64no—
340C2×Dic3—64no—
341C2×Dic3—124no—
342C2×Dic3C23×D314yes—
343C2×Dic3C23×D318yes—
344D12C2×Dic6116yescomplemented
345C4×D3—216no—
346C4×D3—632no—
347Dic6—216no—
348Dic6—316no—
349Dic6—316no—
350Dic6—616no—
351Dic6—632no—
352Dic6—632no—
353C2×C32D4×Q814yescomplemented
354C2×C32C23×D411yescharacteristic
355C2×C32C23×Q811yescharacteristic
356C2×C32C2×2−1+411yescharacteristic
357C3×D3—28no—
358C24—32no—
359C2×Q8—38no—
360C2×Q8—68no—
361C2×Q8—916no—
362C2×Q8—94no—
363C2×Q8—98no—
364C2×Q8—1816no—
365C2×Q8—1864no—
366C2×D4—34no—
367C2×D4—38no—
368C22×C4—32no—
369C22×C4—34no—
370C22×C4—38no—
371C22×C4—68no—
372C22×C4—916no—
373C22×C4—92no—
374C22×C4—92no—
375C22×C4—1816no—
376C22×C4C2×D3211yescharacteristic
377C22×C4C2×D3211yescharacteristic
378C22×C4C2×D3211yescharacteristic
379C4⋊C4—34no—
380C4⋊C4—38no—
381C4⋊C4—38no—
382C4⋊C4—916no—
383C4⋊C4—98no—
384C4⋊C4—94no—
385C22⋊C4—38no—
386C22⋊C4—916no—
387C42—98no—
388C42C2×D3214yes—
389C22×C3—22no—
390C22×C3—22no—
391C22×C3—22no—
392C22×C3—21no—
393C22×C3—38no—
394C22×C3—64no—
395C22×C3—64no—
396C22×C3—616no—
397C22×C3C22×Dic612yes—
398C22×C3C2×D3×D412yes—
399C22×C3C2×D3×D412yes—
400C22×C3C2×D3×Q812yes—
401C22×C3#100712yes—
402C22×C3#101012yes—
403C22×C3C24×D311yescharacteristic
404C22×C3C24×D311yescharacteristic
405C2×D3—24no—
406C2×D3—24no—
407C2×D3—216no—
408C2×D3C22×Dic618yescomplemented
409C3×C4—22no—
410C3×C4—22no—
411C3×C4—24no—
412C3×C4—24no—
413C3×C4—42no—
414C3×C4—64no—
415C3×C4—68no—
416C3×C4C22×Dic614yescomplemented
417C3×C4C2×D3×D414yes—
418C3×C4C2×D3×D414yes—
419C3×C4C2×D3×Q814yescomplemented
420Dic3—28no—
421Dic3—24no—
422Dic3—38no—
423Dic3—38no—
424Dic3—68no—
425Dic3—64no—
426Dic3—64no—
427Dic3—124no—
428C32C2×D4×Q811yescharacteristic, complemented, Sylow
429C23—38no—
430C23—34no—
431C23—64no—
432C23—64no—
433C23C22×D3211yescharacteristic
434Q8—616no—
435Q8—916no—
436Q8—1832no—
437D4—316no—
438C2×C4—22no—
439C2×C4—34no—
440C2×C4—38no—
441C2×C4—64no—
442C2×C4—68no—
443C2×C4—616no—
444C2×C4—98no—
445C2×C4—94no—
446C2×C4—94no—
447C2×C4—1832no—
448C2×C4—184no—
449C2×C4D3×Dic614yescomplemented
450C2×C4#380214yes—
451C2×C4C22×D3212yes—
452C2×C4C22×D3212yes—
453C2×C4C22×D3212yes—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—24no—
458C2×C3—68no—
459C2×C3D4×Dic614yescomplemented
460C2×C3#572714yescomplemented
461C2×C3C23×Dic611yescharacteristic
462C2×C3C22×D3×D411yescharacteristic
463C2×C3C22×D3×D411yescharacteristic
464C2×C3C22×D3×Q811yescharacteristic
465C2×C3C2×#100711yescharacteristic
466C2×C3C2×#101011yescharacteristic
467D3—28no—
468C22—38no—
469C22—64no—
470C22—64no—
471C22—616no—
472C22C2×D3×Dic612yes—
473C22#6429712yes—
474C22C2×#380212yes—
475C22C23×D3211yescharacteristic
476C4—22no—
477C4—64no—
478C4—68no—
479C4—98no—
480C4—184no—
481C4C2×D3×Dic614yescomplemented
482C4C2×#380214yes—
483C3—21no—
484C3C2×D4×Dic611yescharacteristic, complemented
485C3C2×#572711yescharacteristic, complemented
486C2—68no—
487C2#1059390414yesdirect product factor
488C2C22×D3×Dic611yescharacteristic
489C2C2×#6429711yescharacteristic
490C2C22×#380211yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32C2×D4×Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C22×D3×Dic6C2semidirect
2. C2×C4×#634C2semidirect
4. C2×C3×#869C2semidirect
5. C2×#63919C2semidirect
6. C2×#63899C2semidirect
8. C2×#63856C2semidirect
9. #10593904C2direct (N × H)
19. C2×D3×Dic6C22semidirect
24. C4×#634C22semidirect
30. C3×#869C22semidirect
33. #63919C22semidirect
34. #63899C22semidirect
36. #63856C22semidirect
52. C2×#869D3semidirect
62. C2×#634D4semidirect
66. C2×C3×D12Q8semidirect
140. #869C2×D3semidirect
147. C22×C3×D3C2×Q8semidirect
151. C2×C32×C4C2×Q8semidirect
159. #634C2×D4semidirect
164. C3×D12C2×Q8semidirect
208. C2×D12Dic6semidirect
258. C2×C3×D3C22×Q8semidirect
261. C32×C4C22×Q8semidirect
300. C22×D3C2×Dic6semidirect
317. C2×C3×C4C2×Dic6semidirect
320. C2×C3×C4D3×Q8semidirect
344. D12C2×Dic6semidirect
353. C2×C32D4×Q8semidirect
408. C2×D3C22×Dic6semidirect
416. C3×C4C22×Dic6semidirect
419. C3×C4C2×D3×Q8semidirect
428. C32C2×D4×Q8semidirect
449. C2×C4D3×Dic6semidirect
459. C2×C3D4×Dic6semidirect
460. C2×C3#5727semidirect
481. C4C2×D3×Dic6semidirect
484. C3C2×D4×Dic6semidirect
485. C3C2×#5727semidirect
487. C2#10593904direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×Dic62
C2×C4×#6342
C2×C3×C4×D122
C2×C3×#8692
C2×#639192
C2×#638992
C2×#638982
C2×#638562
#105939042
C2×#57273
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