Finite Group Databasebeta

← C2×#10590795 #11860073

Subgroups — C2×#10590795 #11860073

Order 1152.

1189 conjugacy classes of subgroups.

The subgroup lattice has 493 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63894C211yesmaximal, characteristic
2C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
3C22×#3717C211yesmaximal, characteristic
4C2×#63648C211yesmaximal, characteristic
5C2×C3×#816C211yesmaximal, characteristic, complemented
6C2×C3×#815C211yesmaximal, characteristic, complemented
7C2×#63575C211yesmaximal, characteristic, complemented
8#10590795C218yesmaximal, direct product factor
9C2×#4817—31nomaximal
10C2×#4710—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×#624—21no—
14C22×C32×C8C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4×Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×Dic3⋊Dic3—21no—
20C2×#3722—21no—
21C2×Dic32—21no—
22#63894—22no—
23#63894C2214yes—
24Dic3×Dic6—22no—
25Dic3×Dic6C2214yescomplemented
26C2×#3717C418yescomplemented
27C2×#3717C2214yes—
28#63648C2214yes—
29C3×#816C2214yescomplemented
30C3×#815C2214yescomplemented
31#63575C2214yescomplemented
32C2×Q8×Dic3—31no—
33C22×#215—31no—
34C22×#204—31no—
35C2×#893—31no—
36C2×C4×D12—31no—
37C2×C4×Dic6—31no—
38C2×C3×#103—31no—
39C2×C3×#97—31no—
40C2×#821—31no—
41C2×#821—31no—
42C2×#821—61no—
43C2×#818—31no—
44C2×#816D311yescharacteristic, complemented
45C2×#815D311yescharacteristic, complemented
46C2×#807—31no—
47#4817—38no—
48#4710—38no—
49C23×C3⋊D3—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—22no—
54C2×C4⋊(C3⋊D3)C2×C414yes—
55C2×C4⋊(C3⋊D3)C2312yes—
56C22×C3×Dic3—21no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3D411yescharacteristic
59C22×C3×Dic3D411yescharacteristic
60C2×C3×Dic6—21no—
61C2×C3×Dic6—22no—
62C2×C3×Dic6C2×C414yescomplemented
63C2×C3×Dic6C2312yes—
64C2×#624—24no—
65C2×#624—44no—
66C2×C32×C8—22no—
67C2×C32×C8C2312yes—
68C4⋊(C3⋊Dic3)—21no—
69C4⋊(C3⋊Dic3)C2312yes—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3C2312yes—
72C3×C4×Dic3D412yes—
73C3×C4×Dic3C2312yes—
74C2×C3×C3⋊C8C2×C414yescomplemented
75C2×C3×C3⋊C8C2312yes—
76Dic3⋊Dic3—24no—
77#3722—24no—
78Dic32—24no—
79#3717C2×C4116yescomplemented
80C2×#440—91noSylow
81C22×C3×Q8—31no—
82C22×D12—31no—
83C22×D12—31no—
84C22×D12—61no—
85C22×C4×D3—61no—
86C22×C4×D3—61no—
87C22×Dic6C2×D311yescharacteristic
88C22×C3×C8—21no—
89C22×C3×C8—31no—
90C22×C3×C8C2×D311yescharacteristic
91C22×C3×C8C2×D311yescharacteristic
92C2×C3×C4⋊C4—31no—
93C2×C3×C42—31no—
94Q8×Dic3—34no—
95Q8×Dic3—62no—
96C2×#215—38no—
97C2×#215—34no—
98C2×(C2×D3)⋊C4—61no—
99C2×(C2×D3)⋊C4—61no—
100C2×C4⋊Dic3—31no—
101C2×C4⋊Dic3—31no—
102C2×C4⋊Dic3—61no—
103C2×C4⋊Dic3—61no—
104C2×C4⋊Dic3C2×D311yescharacteristic
105C2×Dic3⋊C4—61no—
106C2×C4×Dic3—61no—
107C2×C4×Dic3—61no—
108C2×C4×Dic3C2×D311yescharacteristic
109C22×C3⋊C8C2×D311yescharacteristic
110C2×#204—38no—
111C2×#204—34no—
112#893—34no—
113#893—62no—
114C4×D12—34no—
115C4×D12—62no—
116C4×Dic6—34no—
117C4×Dic6—62no—
118C3×#103—34no—
119C3×#97—34no—
120#821—34no—
121#821—34no—
122#821—64no—
123#818—34no—
124#816C2×D314yescomplemented
125#815C2×D314yescomplemented
126#807—34no—
127C23×C32C2×D411yescharacteristic
128C22×C3⋊D3—24no—
129C22×C3⋊D3—22no—
130C22×C3⋊D3—42no—
131C22×C3⋊D3—42no—
132C2×C32×C4C22×C412yes—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4#4112yes—
135C2×C32×C4C2411yescharacteristic
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—42no—
138C4⋊(C3⋊D3)—24no—
139C4⋊(C3⋊D3)—22no—
140C4⋊(C3⋊D3)C22×C414yes—
141C2×C3×Dic3—24no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—42no—
147C2×C3×Dic3C2×D412yes—
148C2×C3×Dic3C2×D412yes—
149C3×Dic6—24no—
150C3×Dic6—22no—
151C3×Dic6C22×C414yescomplemented
152#624—48no—
153C32×C8—22no—
154C3×C3⋊C8C22×C414yescomplemented
155C22×SD16—91no—
156C2×C4×Q8—91no—
157C2×C4×D4—91no—
158#440—98no—
159C2×#107—91no—
160C2×#103—31no—
161C2×#102—91no—
162C2×#97—31no—
163C23×D3—61no—
164C23×D3—61no—
165C23×D3—121no—
166C2×C3×Q8—34no—
167C2×C3×Q8—32no—
168C2×C3×Q8—61no—
169C2×C3×Q8—62no—
170C22×C3×C4—21no—
171C22×C3×C4—31no—
172C22×C3×C4—31no—
173C22×C3×C4—61no—
174C22×C3×C4—61no—
175C22×C3×C4C22×D311yescharacteristic
176C22×C3×C4C22×D311yescharacteristic
177C22×Dic3—21no—
178C22×Dic3—21no—
179C22×Dic3—61no—
180C22×Dic3—61no—
181C22×Dic3—121no—
182C22×Dic3D1211yescharacteristic
183C22×Dic3D1211yescharacteristic
184C2×D12—34no—
185C2×D12—34no—
186C2×D12—32no—
187C2×D12—32no—
188C2×D12—62no—
189C2×D12—64no—
190C2×D12—61no—
191C2×D12—62no—
192C2×D12—61no—
193C2×D12—62no—
194C2×D12—121no—
195C2×D12—122no—
196C2×C4×D3—64no—
197C2×C4×D3—64no—
198C2×C4×D3—124no—
199C2×C4×D3—124no—
200C2×Dic6—21no—
201C2×Dic6—22no—
202C2×Dic6C4×D314yescomplemented
203C2×Dic6C22×D312yes—
204C2×C3×C8—22no—
205C2×C3×C8—22no—
206C2×C3×C8—22no—
207C2×C3×C8—34no—
208C2×C3×C8—32no—
209C2×C3×C8—42no—
210C2×C3×C8C22×D312yes—
211C2×C3×C8C22×D312yes—
212C3×C4⋊C4—32no—
213C3×C4⋊C4—61no—
214C3×C42—32no—
215C3×C42—32no—
216#215—316no—
217(C2×D3)⋊C4—64no—
218(C2×D3)⋊C4—64no—
219C4⋊Dic3—21no—
220C4⋊Dic3—32no—
221C4⋊Dic3—32no—
222C4⋊Dic3—62no—
223C4⋊Dic3—61no—
224C4⋊Dic3—61no—
225C4⋊Dic3—64no—
226C4⋊Dic3—121no—
227C4⋊Dic3C22×D312yes—
228Dic3⋊C4—64no—
229C4×Dic3—64no—
230C4×Dic3—64no—
231C4×Dic3D1212yes—
232C4×Dic3C22×D312yes—
233C2×C3⋊C8C4×D314yescomplemented
234C2×C3⋊C8C22×D312yes—
235#204—316no—
236C22×C32C4×D412yes—
237C22×C32AGL(1,ℤ/8)12yes—
238C22×C32#13712yes—
239C22×C32C22×D411yescharacteristic
240C2×C3⋊D3—24no—
241C2×C3⋊D3—42no—
242C2×C3⋊D3—42no—
243C2×C3⋊D3—48no—
244C32×C4C4×D412yes—
245C32×C4C23×C411yescharacteristic
246C32×C4C2×#4111yescharacteristic
247C3⋊Dic3—42no—
248C3×Dic3—24no—
249C3×Dic3—22no—
250C3×Dic3—22no—
251C3×Dic3—42no—
252C22×Q8—31no—
253C22×D4—91no—
254C23×C4—181no—
255C2×SD16—98no—
256C2×SD16—94no—
257C22×C8—31no—
258C22×C8D3211yescharacteristic
259C4×Q8—94no—
260C4×Q8—182no—
261C4×D4—94no—
262C4×D4—182no—
263C2×C4⋊C4—31no—
264C2×C4⋊C4—91no—
265C2×C4⋊C4—181no—
266C2×C22⋊C4—181no—
267C2×C42—31no—
268C2×C42—181no—
269#107—94no—
270#103—34no—
271#102—94no—
272#97—34no—
273C23×C3—21no—
274C23×C3C2×D1211yescharacteristic
275C23×C3D3×D411yescharacteristic
276C22×D3—64no—
277C22×D3—64no—
278C22×D3—62no—
279C22×D3—62no—
280C22×D3—122no—
281C22×D3—124no—
282C22×D3—122no—
283C22×D3—122no—
284C22×D3—122no—
285C22×D3—122no—
286C22×D3—242no—
287C22×D3—242no—
288C3×Q8—34no—
289C3×Q8—64no—
290C3×Q8—62no—
291C2×C3×C4—21no—
292C2×C3×C4—22no—
293C2×C3×C4—21no—
294C2×C3×C4—22no—
295C2×C3×C4—32no—
296C2×C3×C4—32no—
297C2×C3×C4—64no—
298C2×C3×C4—62no—
299C2×C3×C4—62no—
300C2×C3×C4—62no—
301C2×C3×C4—62no—
302C2×C3×C4—122no—
303C2×C3×C4C2×C4×D312yes—
304C2×C3×C4C2×C4×D312yes—
305C2×C3×C4C2×D1211yescharacteristic
306C2×C3×C4#23512yes—
307C2×C3×C4D3×D411yescharacteristic
308C2×C3×C4#23712yes—
309C2×C3×C4C23×D311yescharacteristic
310C2×C3×C4C23×D311yescharacteristic
311C2×Dic3—24no—
312C2×Dic3—22no—
313C2×Dic3—22no—
314C2×Dic3—22no—
315C2×Dic3—22no—
316C2×Dic3—42no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—122no—
320C2×Dic3—122no—
321C2×Dic3—122no—
322C2×Dic3—242no—
323C2×Dic3C2×D1212yes—
324C2×Dic3C2×D1212yes—
325D12—34no—
326D12—34no—
327D12—64no—
328D12—64no—
329D12—64no—
330D12—62no—
331D12—62no—
332D12—122no—
333D12—124no—
334C4×D3—128no—
335C4×D3—128no—
336Dic6—24no—
337Dic6—22no—
338Dic6C2×C4×D314yescomplemented
339C3×C8—22no—
340C3×C8—22no—
341C3×C8—34no—
342C3×C8—42no—
343C3⋊C8C2×C4×D314yescomplemented
344C2×C32#44014yescomplemented
345C2×C32C2×C4×D411yescharacteristic
346C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
347C2×C32C2×#13711yescharacteristic
348C3⋊D3—44no—
349C24—181no—
350C2×Q8—32no—
351C2×Q8—34no—
352C2×Q8—61no—
353C2×Q8—62no—
354C2×D4—92no—
355C2×D4—94no—
356C2×D4—181no—
357C2×D4—182no—
358C22×C4—31no—
359C22×C4—31no—
360C22×C4—61no—
361C22×C4—61no—
362C22×C4—184no—
363C22×C4—181no—
364C22×C4—364no—
365C22×C4C2×D3211yescharacteristic
366SD16—916no—
367C2×C8—22no—
368C2×C8—32no—
369C2×C8—34no—
370C2×C8C2×D3212yes—
371C4⋊C4—32no—
372C4⋊C4—61no—
373C4⋊C4—92no—
374C4⋊C4—184no—
375C4⋊C4—181no—
376C22⋊C4—184no—
377C42—32no—
378C42—32no—
379C42—184no—
380C22×C3—21no—
381C22×C3—22no—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3C4×D1212yes—
385C22×C3#67⋊C412yes—
386C22×C3#90812yes—
387C22×C3#90912yes—
388C22×C3#91412yes—
389C22×C3#91812yes—
390C22×C3C22×D1211yescharacteristic
391C22×C3C2×D3×D411yescharacteristic
392C2×D3—64no—
393C2×D3—64no—
394C2×D3—124no—
395C2×D3—128no—
396C2×D3—122no—
397C2×D3—122no—
398C2×D3—122no—
399C2×D3—122no—
400C2×D3—128no—
401C2×D3—248no—
402C2×D3—242no—
403C2×D3—242no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—22no—
407C3×C4—64no—
408C3×C4—62no—
409C3×C4—62no—
410C3×C4—122no—
411C3×C4C4×D1212yes—
412C3×C4#67⋊C412yes—
413C3×C4C22×C4×D311yescharacteristic
414C3×C4C22×C4×D311yescharacteristic
415C3×C4C2×#23511yescharacteristic
416C3×C4C2×#23711yescharacteristic
417Dic3—24no—
418Dic3—22no—
419Dic3—22no—
420Dic3—42no—
421Dic3—122no—
422Dic3—122no—
423Dic3—242no—
424C32C2×#44011yescharacteristic, complemented, Sylow
425C23—182no—
426C23—184no—
427C23—362no—
428C23—362no—
429C23D3×D1211yescharacteristic
430Q8—34no—
431Q8—62no—
432Q8—64no—
433D4—94no—
434D4—182no—
435D4—184no—
436C2×C4—32no—
437C2×C4—32no—
438C2×C4—62no—
439C2×C4—62no—
440C2×C4—62no—
441C2×C4—64no—
442C2×C4—62no—
443C2×C4—122no—
444C2×C4—182no—
445C2×C4—368no—
446C2×C4—362no—
447C2×C4C4×D3212yes—
448C2×C4D3×D1211yescharacteristic
449C2×C4#380412yes—
450C2×C4C22×D3211yescharacteristic
451C8—22no—
452C8—34no—
453C2×C3—21no—
454C2×C3—24no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3#471014yescomplemented
458C2×C3#481714yescomplemented
459C2×C3C2×C4×D1211yescharacteristic
460C2×C3C2×#67⋊C411yescharacteristic
461C2×C3C2×#90811yescharacteristic
462C2×C3C2×#90911yescharacteristic
463C2×C3C2×#91411yescharacteristic
464C2×C3C2×#91811yescharacteristic
465D3—124no—
466D3—124no—
467D3—244no—
468C22—184no—
469C22—368no—
470C22—362no—
471C22—362no—
472C22#6379412yes—
473C22#6380112yes—
474C22#6388012yes—
475C22C2×D3×D1211yescharacteristic
476C4—64no—
477C4—62no—
478C4—62no—
479C4—122no—
480C4—362no—
481C4#6388012yes—
482C4C2×C4×D3211yescharacteristic
483C4C2×#380411yescharacteristic
484C3—21no—
485C3C2×#471011yescharacteristic, complemented
486C3C2×#481711yescharacteristic, complemented
487C2—364no—
488C2#1059079514yesdirect product factor
489C2C2×#6379411yescharacteristic
490C2C2×#6380111yescharacteristic
491C2C2×#6388011yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C2×#440
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×Dic3×Dic6C2semidirect
5. C2×C3×#816C2semidirect
6. C2×C3×#815C2semidirect
7. C2×#63575C2semidirect
8. #10590795C2direct (N × H)
25. Dic3×Dic6C22semidirect
26. C2×#3717C4semidirect
29. C3×#816C22semidirect
30. C3×#815C22semidirect
31. #63575C22semidirect
44. C2×#816D3semidirect
45. C2×#815D3semidirect
62. C2×C3×Dic6C2×C4semidirect
74. C2×C3×C3⋊C8C2×C4semidirect
79. #3717C2×C4semidirect
124. #816C2×D3semidirect
125. #815C2×D3semidirect
151. C3×Dic6C22×C4semidirect
154. C3×C3⋊C8C22×C4semidirect
202. C2×Dic6C4×D3semidirect
233. C2×C3⋊C8C4×D3semidirect
338. Dic6C2×C4×D3semidirect
343. C3⋊C8C2×C4×D3semidirect
344. C2×C32#440semidirect
424. C32C2×#440semidirect
457. C2×C3#4710semidirect
458. C2×C3#4817semidirect
485. C3C2×#4710semidirect
486. C3C2×#4817semidirect
488. C2#10590795direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#638942
C2×Dic3×Dic62
C22×#37172
C2×#636482
C2×C3×#8162
C2×C3×#8152
C2×#635752
#105907952
C2×#48173
C2×#47103