Finite Group Databasebeta

← C2×#10593903 #11902674

Subgroups — C2×#10593903 #11902674

Order 1152.

3349 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3797C212yesmaximal, complemented
2C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
3C2×C3×#869C211yesmaximal, characteristic, complemented
4C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
5C2×#63918C212yesmaximal, complemented
6C2×#63895C214yesmaximal, complemented
7C2×#63894C212yesmaximal
8C2×#63871C212yesmaximal, complemented
9#10593903C2116yesmaximal, direct product factor
10C2×#5727—31nomaximal
11C2×Q8×D12—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C4×C3⋊D3C2212yes—
14C22×C3×Dic6C2212yes—
15C22×C3×Dic6C2211yescharacteristic
16C22×#627C2214yes—
17C22×#624C2214yes—
18C2×#3797—216no—
19C2×#3797C22116yescomplemented
20C2×C32×C42C2211yescharacteristic
21C2×#3752C2212yes—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C4×C4⋊(C3⋊D3)C2218yes—
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic3C2212yes—
26C2×C3×C4⋊Dic3C2212yes—
27C2×C3×Dic3⋊C4C2212yes—
28C2×C3×C4×Dic3C2212yes—
29C3×#869C2218yescomplemented
30C3×C4×Dic6C2218yescomplemented
31C2×Dic3⋊Dic3C2214yes—
32C2×#3722C2214yes—
33#63918C22116yescomplemented
34#63895C22132yescomplemented
35#63894C22116yes—
36#63871C22116yescomplemented
37C22×D3×Q8—32no—
38C22×D3×Q8—32no—
39C2×C3×C4⋊Q8—31no—
40C2×C3×C4×Q8—31no—
41C2×#946—32no—
42#5727—316no—
43Q8×D12—316no—
44C2×#897—32no—
45C2×#897—34no—
46C2×#896—34no—
47C2×#893—32no—
48C2×#888—32no—
49C2×C4×D12—31no—
50C2×C4×D12—31no—
51C2×C4×D12—32no—
52C2×C4×D12—61no—
53C2×#869—32no—
54C2×#869D311yescharacteristic, complemented
55C2×C4×Dic6D311yescharacteristic, complemented
56C23×C3⋊D3C2312yes—
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3C2312yes—
61C2×C4⋊(C3⋊D3)Q818yescomplemented
62C2×C4⋊(C3⋊D3)C2314yes—
63C2×C4×C3⋊D3—28no—
64C2×C4×C3⋊D3C2318yes—
65C22×C3×Dic3C2312yes—
66C22×C3×Dic3C2314yes—
67C22×C3×Dic3C2312yes—
68C2×C3×Dic6—28no—
69C2×C3×Dic6D418yescomplemented
70C2×C3×Dic6C2318yes—
71C2×C3×Dic6C2314yes—
72C2×#627—216no—
73C2×#627C23116yes—
74C2×#624—216no—
75C2×#624C23116yes—
76#3797—264no—
77C32×C42C2314yes—
78#3752C2318yes—
79C4⋊(C3⋊Dic3)C2314yes—
80C3×C4⋊Dic3C2314yes—
81C3×C4⋊Dic3C2318yes—
82C3×C4⋊Dic3C2318yes—
83C3×Dic3⋊C4C2318yes—
84C3×C4×Dic3C2318yes—
85Dic3⋊Dic3C23116yes—
86#3722C23116yes—
87C2×D4×Q8—91noSylow
88C22×C3×Q8—31no—
89C22×C3×Q8—32no—
90C2×D3×Q8—316no—
91C2×D3×Q8—316no—
92C2×D3×Q8—616no—
93C2×D3×Q8—616no—
94C22×D12—31no—
95C22×D12—31no—
96C22×D12—61no—
97C22×C4×D3—32no—
98C22×C4×D3—32no—
99C22×C4×D3—34no—
100C22×C4×D3—34no—
101C22×C4×D3—62no—
102C22×Dic6—34no—
103C22×Dic6—34no—
104C22×Dic6C2×D312yes—
105C22×Dic6C2×D311yescharacteristic
106C3×C4⋊Q8—38no—
107C3×C4×Q8—38no—
108C2×C3×C4⋊C4—32no—
109C2×C3×C4⋊C4—32no—
110C2×C3×C4⋊C4—32no—
111C2×C3×C4⋊C4—31no—
112C2×C3×C42—21no—
113C2×C3×C42—32no—
114C2×C3×C42C2×D311yescharacteristic
115C2×C3×C42C2×D311yescharacteristic
116#946—316no—
117C2×(C2×D3)⋊C4—32no—
118C2×(C2×D3)⋊C4—32no—
119C2×(C2×D3)⋊C4—34no—
120C2×(C2×D3)⋊C4—34no—
121C2×(C2×D3)⋊C4—62no—
122C2×C4⋊Dic3—31no—
123C2×C4⋊Dic3—31no—
124C2×C4⋊Dic3—34no—
125C2×C4⋊Dic3—61no—
126C2×C4⋊Dic3C2×D311yescharacteristic
127C2×C4⋊Dic3C2×D312yes—
128C2×C4⋊Dic3C2×D312yes—
129C2×Dic3⋊C4—34no—
130C2×Dic3⋊C4C2×D312yes—
131C2×C4×Dic3C2×D312yes—
132#897—316no—
133#897—332no—
134#896—332no—
135#893—316no—
136#888—316no—
137C4×D12—38no—
138C4×D12—38no—
139C4×D12—316no—
140C4×D12—68no—
141#869—316no—
142#869C2×D318yescomplemented
143C4×Dic6C2×D318yescomplemented
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⋊Dic3C2414yes—
157C4⋊(C3⋊D3)C2×Q8116yescomplemented
158C4×C3⋊D3—216no—
159C2×C3×Dic3—28no—
160C2×C3×Dic3—24no—
161C2×C3×Dic3C2×D418yes—
162C2×C3×Dic3C2414yes—
163C2×C3×Dic3C2418yes—
164C2×C3×Dic3C2414yes—
165C3×Dic6—216no—
166C3×Dic6C2×D4116yescomplemented
167#627—232no—
168#624—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—31no—
176C2×C4×D4—92no—
177C2×C4×D4—91no—
178C23×D3—32no—
179C23×D3—32no—
180C23×D3—62no—
181C2×C3×Q8—38no—
182C2×C3×Q8—34no—
183C2×C3×Q8—38no—
184C2×C3×Q8—68no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—32no—
189C22×C3×C4—34no—
190C22×C3×C4—32no—
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—62no—
200C22×Dic3C22×D312yes—
201C22×Dic3C22×D314yes—
202C22×Dic3C22×D312yes—
203D3×Q8—664no—
204D3×Q8—664no—
205C2×D12—38no—
206C2×D12—38no—
207C2×D12—34no—
208C2×D12—34no—
209C2×D12—64no—
210C2×D12—68no—
211C2×C4×D3—38no—
212C2×C4×D3—38no—
213C2×C4×D3—316no—
214C2×C4×D3—316no—
215C2×C4×D3—68no—
216C2×C4×D3—616no—
217C2×C4×D3—68no—
218C2×C4×D3—68no—
219C2×C4×D3—616no—
220C2×C4×D3—128no—
221C2×Dic6—28no—
222C2×Dic6—316no—
223C2×Dic6—316no—
224C2×Dic6—616no—
225C2×Dic6—616no—
226C2×Dic6D1218yescomplemented
227C2×Dic6C22×D318yes—
228C2×Dic6C22×D314yes—
229C3×C4⋊C4—38no—
230C3×C4⋊C4—38no—
231C3×C4⋊C4—38no—
232C3×C4⋊C4—34no—
233C3×C42—24no—
234C3×C42—38no—
235C3×C42C22×D314yes—
236C3×C42C22×D314yes—
237(C2×D3)⋊C4—38no—
238(C2×D3)⋊C4—38no—
239(C2×D3)⋊C4—316no—
240(C2×D3)⋊C4—316no—
241(C2×D3)⋊C4—68no—
242C4⋊Dic3—34no—
243C4⋊Dic3—34no—
244C4⋊Dic3—316no—
245C4⋊Dic3—64no—
246C4⋊Dic3C22×D314yes—
247C4⋊Dic3C22×D318yes—
248C4⋊Dic3C22×D318yes—
249Dic3⋊C4—316no—
250Dic3⋊C4C22×D318yes—
251C4×Dic3C22×D318yes—
252C22×C32C22×D412yes—
253C22×C32C22×Q812yes—
254C22×C322−1+412yes—
255C22×C32C2511yescharacteristic
256C2×C3⋊D3—216no—
257C2×C3⋊D3—24no—
258C2×C3⋊D3—24no—
259C2×C3⋊D3C22×Q818yescomplemented
260C32×C4—22no—
261C32×C4C22×D414yes—
262C32×C4C22×Q814yescomplemented
263C3⋊Dic3—24no—
264C3×Dic3—28no—
265C3×Dic3—24no—
266C3×Dic3C22×D418yes—
267C22×Q8—31no—
268C22×Q8—32no—
269C22×Q8—94no—
270C22×Q8—916no—
271C22×Q8—1816no—
272C22×D4—91no—
273C23×C4—94no—
274C23×C4—92no—
275C4⋊Q8—38no—
276C4⋊Q8—916no—
277C22⋊Q8—932no—
278C22⋊Q8—916no—
279C4×Q8—38no—
280C4×D4—916no—
281C4×D4—98no—
282C2×C4⋊C4—32no—
283C2×C4⋊C4—32no—
284C2×C4⋊C4—31no—
285C2×C4⋊C4—32no—
286C2×C4⋊C4—94no—
287C2×C4⋊C4—91no—
288C2×C22⋊C4—94no—
289C2×C22⋊C4—92no—
290C2×C42—32no—
291C2×C42D3211yescharacteristic
292C23×C3—21no—
293C23×C3C23×D311yescharacteristic
294C23×C3C23×D311yescharacteristic
295C22×D3—38no—
296C22×D3—38no—
297C22×D3—34no—
298C22×D3—34no—
299C22×D3—68no—
300C22×D3—64no—
301C22×D3—64no—
302C22×D3—64no—
303C22×D3—64no—
304C22×D3—64no—
305C22×D3—124no—
306C22×D3—124no—
307C3×Q8—316no—
308C3×Q8—616no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—24no—
315C2×C3×C4—24no—
316C2×C3×C4—38no—
317C2×C3×C4—34no—
318C2×C3×C4—38no—
319C2×C3×C4—34no—
320C2×C3×C4—42no—
321C2×C3×C4—68no—
322C2×C3×C4—64no—
323C2×C3×C4C2×D1214yes—
324C2×C3×C4D3×D414yes—
325C2×C3×C4D3×Q814yescomplemented
326C2×C3×C4D3×Q814yescomplemented
327C2×C3×C4C23×D312yes—
328C2×C3×C4C23×D312yes—
329C2×C3×C4C23×D312yes—
330C2×C3×C4C23×D312yes—
331C2×C3×C4C23×D312yes—
332C2×C3×C4C23×D312yes—
333C2×Dic3—28no—
334C2×Dic3—24no—
335C2×Dic3—34no—
336C2×Dic3—34no—
337C2×Dic3—64no—
338C2×Dic3—64no—
339C2×Dic3—64no—
340C2×Dic3—124no—
341C2×Dic3C2×D1218yes—
342C2×Dic3C23×D314yes—
343C2×Dic3C23×D318yes—
344C2×Dic3C23×D314yes—
345D12—316no—
346D12—316no—
347D12—616no—
348C4×D3—632no—
349C4×D3—616no—
350C4×D3—616no—
351C4×D3—632no—
352C4×D3—1216no—
353Dic6—216no—
354Dic6—632no—
355Dic6—632no—
356Dic6C2×D12116yescomplemented
357C2×C32D4×Q814yescomplemented
358C2×C32C23×D411yescharacteristic
359C2×C32C23×Q811yescharacteristic
360C2×C32C2×2−1+411yescharacteristic
361C3⋊D3—28no—
362C24—92no—
363C2×Q8—34no—
364C2×Q8—38no—
365C2×Q8—38no—
366C2×Q8—68no—
367C2×Q8—916no—
368C2×Q8—1816no—
369C2×Q8—1864no—
370C2×D4—94no—
371C2×D4—98no—
372C22×C4—32no—
373C22×C4—32no—
374C22×C4—34no—
375C22×C4—916no—
376C22×C4—92no—
377C22×C4—98no—
378C22×C4—1816no—
379C22×C4—188no—
380C22×C4C2×D3211yescharacteristic
381C22×C4C2×D3211yescharacteristic
382C22×C4C2×D3211yescharacteristic
383C4⋊C4—38no—
384C4⋊C4—38no—
385C4⋊C4—34no—
386C4⋊C4—38no—
387C4⋊C4—916no—
388C4⋊C4—94no—
389C22⋊C4—916no—
390C22⋊C4—98no—
391C42—38no—
392C42C2×D3214yes—
393C22×C3—22no—
394C22×C3—22no—
395C22×C3—22no—
396C22×C3—21no—
397C22×C3C22×D1212yes—
398C22×C3C2×D3×D412yes—
399C22×C3C2×D3×Q812yes—
400C22×C3C2×D3×Q812yes—
401C22×C3#100712yes—
402C22×C3#101012yes—
403C22×C3C24×D311yescharacteristic
404C22×C3C24×D311yescharacteristic
405C2×D3—38no—
406C2×D3—38no—
407C2×D3—68no—
408C2×D3—64no—
409C2×D3—64no—
410C2×D3—64no—
411C2×D3—64no—
412C2×D3—616no—
413C2×D3—616no—
414C2×D3—124no—
415C2×D3—124no—
416C2×D3—1216no—
417C3×C4—22no—
418C3×C4—22no—
419C3×C4—24no—
420C3×C4—24no—
421C3×C4—38no—
422C3×C4—42no—
423C3×C4—68no—
424C3×C4—64no—
425C3×C4C22×D1214yes—
426C3×C4C2×D3×D414yes—
427C3×C4C2×D3×Q814yescomplemented
428C3×C4C2×D3×Q814yescomplemented
429Dic3—28no—
430Dic3—24no—
431Dic3—64no—
432Dic3—64no—
433Dic3—124no—
434Dic3C22×D1218yes—
435C32C2×D4×Q811yescharacteristic, complemented, Sylow
436C23—98no—
437C23—94no—
438C23—184no—
439C23—184no—
440C23C22×D3211yescharacteristic
441Q8—316no—
442Q8—616no—
443Q8—1832no—
444D4—916no—
445C2×C4—22no—
446C2×C4—38no—
447C2×C4—34no—
448C2×C4—34no—
449C2×C4—38no—
450C2×C4—64no—
451C2×C4—68no—
452C2×C4—94no—
453C2×C4—1832no—
454C2×C4—184no—
455C2×C4—1816no—
456C2×C4#379714yescomplemented
457C2×C4D3×D1214yes—
458C2×C4C22×D3212yes—
459C2×C4C22×D3212yes—
460C2×C4C22×D3212yes—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—24no—
465C2×C3Q8×D1214yescomplemented
466C2×C3#572714yescomplemented
467C2×C3C23×D1211yescharacteristic
468C2×C3C22×D3×D411yescharacteristic
469C2×C3C22×D3×Q811yescharacteristic
470C2×C3C22×D3×Q811yescharacteristic
471C2×C3C2×#100711yescharacteristic
472C2×C3C2×#101011yescharacteristic
473D3—68no—
474D3—68no—
475D3—128no—
476C22—98no—
477C22—184no—
478C22—184no—
479C22—1816no—
480C22#6429712yes—
481C22C2×#379712yes—
482C22C2×D3×D1212yes—
483C22C23×D3211yescharacteristic
484C4—22no—
485C4—38no—
486C4—64no—
487C4—68no—
488C4—184no—
489C4C2×#379714yescomplemented
490C4C2×D3×D1214yes—
491C3—21no—
492C3C2×Q8×D1211yescharacteristic, complemented
493C3C2×#572711yescharacteristic, complemented
494C2—188no—
495C2#1059390314yesdirect product factor
496C2C2×#6429711yescharacteristic
497C2C22×#379711yescharacteristic
498C2C22×D3×D1211yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC22×C4⋊(C3⋊D3)C22
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×#3797C2semidirect
3. C2×C3×#869C2semidirect
4. C2×C3×C4×Dic6C2semidirect
5. C2×#63918C2semidirect
6. C2×#63895C2semidirect
8. C2×#63871C2semidirect
9. #10593903C2direct (N × H)
19. C2×#3797C22semidirect
29. C3×#869C22semidirect
30. C3×C4×Dic6C22semidirect
33. #63918C22semidirect
34. #63895C22semidirect
36. #63871C22semidirect
54. C2×#869D3semidirect
55. C2×C4×Dic6D3semidirect
61. C2×C4⋊(C3⋊D3)Q8semidirect
69. C2×C3×Dic6D4semidirect
142. #869C2×D3semidirect
143. C4×Dic6C2×D3semidirect
147. C22×C3⋊D3C2×Q8semidirect
151. C2×C32×C4C2×Q8semidirect
157. C4⋊(C3⋊D3)C2×Q8semidirect
166. C3×Dic6C2×D4semidirect
226. C2×Dic6D12semidirect
259. C2×C3⋊D3C22×Q8semidirect
262. C32×C4C22×Q8semidirect
325. C2×C3×C4D3×Q8semidirect
326. C2×C3×C4D3×Q8semidirect
356. Dic6C2×D12semidirect
357. C2×C32D4×Q8semidirect
427. C3×C4C2×D3×Q8semidirect
428. C3×C4C2×D3×Q8semidirect
435. C32C2×D4×Q8semidirect
456. C2×C4#3797semidirect
465. C2×C3Q8×D12semidirect
466. C2×C3#5727semidirect
489. C4C2×#3797semidirect
492. C3C2×Q8×D12semidirect
493. C3C2×#5727semidirect
495. C2#10593903direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37972
C2×C4×C4⋊(C3⋊D3)2
C2×C3×#8692
C2×C3×C4×Dic62
C2×#639182
C2×#638952
C2×#638942
C2×#638712
#105939032
C2×#57273
C2×Q8×D123