Finite Group Databasebeta

← C2×#10590362 #11860071

Subgroups — C2×#10590362 #11860071

Order 1152.

1301 conjugacy classes of subgroups.

The subgroup lattice has 507 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
3C22×#3717C211yesmaximal, characteristic
4C2×C3×#803C211yesmaximal, characteristic, complemented
5C2×#63575C211yesmaximal, characteristic, complemented
6C2×#63566C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic
8#10590362C218yesmaximal, direct product factor
9C2×#5026—31nomaximal
10C2×#4710—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C4×C3⋊D3—21no—
13C22×C3×Dic6C2211yescharacteristic
14C2×C32×C42C2211yescharacteristic
15C2×#3752—21no—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C4×C4⋊(C3⋊D3)—22no—
18C4×C4⋊(C3⋊D3)C2214yes—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×Dic3⋊C4—21no—
21C2×C3×C4×Dic3—21no—
22C22×C3×C3⋊C8C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C3×C4×Dic6—22no—
25C3×C4×Dic6C2214yescomplemented
26C2×#3717C418yescomplemented
27C2×#3717C2214yes—
28C3×#803C2214yescomplemented
29#63575C2214yescomplemented
30#63566C2214yescomplemented
31#63564C2214yes—
32C2×C3×C4×Q8—31no—
33C22×#215—31no—
34C22×#204—31no—
35C2×C4×D12—31no—
36C2×C4×D12—31no—
37C2×C4×D12—61no—
38C2×C4×Dic6D311yescharacteristic, complemented
39C2×C3×#97—31no—
40C2×#835—31no—
41C2×#821—31no—
42C2×#818—31no—
43C2×#816—31no—
44#5026—38no—
45C2×#809—31no—
46C2×#807—31no—
47C2×#803D311yescharacteristic, complemented
48#4710—38no—
49C23×C3⋊D3—21no—
50C22×C32×C4D411yescharacteristic
51C22×C32×C4D411yescharacteristic
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3—21no—
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)—22no—
56C2×C4⋊(C3⋊D3)C2×C414yes—
57C2×C4⋊(C3⋊D3)C2312yes—
58C2×C4×C3⋊D3—24no—
59C2×C4×C3⋊D3—44no—
60C22×C3×Dic3—21no—
61C22×C3×Dic3—21no—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—22no—
64C2×C3×Dic6C2×C414yescomplemented
65C2×C3×Dic6C2312yes—
66C32×C42D412yes—
67C32×C42C2312yes—
68#3752—24no—
69C4⋊(C3⋊Dic3)—21no—
70C4⋊(C3⋊Dic3)C2312yes—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3C2312yes—
73C3×Dic3⋊C4—24no—
74C3×C4×Dic3—24no—
75C2×C3×C3⋊C8—22no—
76C2×C3×C3⋊C8C2×C414yescomplemented
77C2×C3×C3⋊C8C2312yes—
78C2×C3×C3⋊C8C2312yes—
79#3717C2×C4116yescomplemented
80C2×#440—91noSylow
81C22×C3×Q8—31no—
82C22×D12—31no—
83C22×D12—31no—
84C22×D12—61no—
85C22×C4×D3—62no—
86C22×C4×D3—61no—
87C22×C4×D3—61no—
88C22×Dic6C2×D311yescharacteristic
89C22×C3×C8—31no—
90C22×C3×C8—31no—
91C3×C4×Q8—34no—
92C3×C4×Q8—62no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C4⋊C4—61no—
95C2×C3×C42—21no—
96C2×C3×C42—61no—
97C2×C3×C42C2×D311yescharacteristic
98C2×C3×C42C2×D311yescharacteristic
99C2×#215—38no—
100C2×#215—34no—
101C2×(C2×D3)⋊C4—62no—
102C2×(C2×D3)⋊C4—61no—
103C2×(C2×D3)⋊C4—61no—
104C2×C4⋊Dic3—31no—
105C2×C4⋊Dic3—31no—
106C2×C4⋊Dic3—61no—
107C2×C4⋊Dic3C2×D311yescharacteristic
108C2×Dic3⋊C4—21no—
109C2×C4×Dic3—21no—
110C22×C3⋊C8C2×D311yescharacteristic
111C22×C3⋊C8C2×D311yescharacteristic
112C2×#204—38no—
113C2×#204—34no—
114C4×D12—34no—
115C4×D12—34no—
116C4×D12—64no—
117C4×D12—64no—
118C4×D12—62no—
119C4×D12—62no—
120C4×Dic6—22no—
121C4×Dic6C2×D314yescomplemented
122C3×#97—34no—
123#835—34no—
124#821—34no—
125#818—34no—
126#816—34no—
127#809—34no—
128#807—34no—
129#803C2×D314yescomplemented
130C23×C32C2×D411yescharacteristic
131C22×C3⋊D3—24no—
132C22×C3⋊D3—22no—
133C22×C3⋊D3—42no—
134C22×C3⋊D3—42no—
135C2×C32×C4—22no—
136C2×C32×C4—22no—
137C2×C32×C4C22×C412yes—
138C2×C32×C4C2×D412yes—
139C2×C32×C4C2×D412yes—
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4112yes—
142C2×C32×C4C2411yescharacteristic
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—42no—
145C4⋊(C3⋊D3)—24no—
146C4⋊(C3⋊D3)—22no—
147C4⋊(C3⋊D3)C22×C414yes—
148C4×C3⋊D3—48no—
149C2×C3×Dic3—24no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—42no—
153C3×Dic6—24no—
154C3×Dic6—22no—
155C3×Dic6C22×C414yescomplemented
156C3×C3⋊C8—22no—
157C3×C3⋊C8C22×C414yescomplemented
158C22×SD16—91no—
159C2×C4×Q8—31no—
160C2×C4×D4—91no—
161#440—98no—
162C2×#107—91no—
163C2×#103—91no—
164C2×#102—91no—
165C2×#97—31no—
166C23×D3—62no—
167C23×D3—61no—
168C23×D3—61no—
169C2×C3×Q8—34no—
170C2×C3×Q8—32no—
171C2×C3×Q8—61no—
172C2×C3×Q8—62no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—61no—
177C22×C3×C4—61no—
178C22×C3×C4D1211yescharacteristic
179C22×C3×C4D1211yescharacteristic
180C22×C3×C4#6711yescharacteristic
181C22×C3×C4#6711yescharacteristic
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C22×Dic3—21no—
185C22×Dic3—21no—
186C22×Dic3—62no—
187C22×Dic3—61no—
188C22×Dic3—61no—
189C2×D12—34no—
190C2×D12—34no—
191C2×D12—32no—
192C2×D12—32no—
193C2×D12—62no—
194C2×D12—64no—
195C2×D12—62no—
196C2×D12—64no—
197C2×D12—61no—
198C2×D12—62no—
199C2×D12—62no—
200C2×D12—61no—
201C2×C4×D3—68no—
202C2×C4×D3—64no—
203C2×C4×D3—64no—
204C2×C4×D3—128no—
205C2×C4×D3—124no—
206C2×C4×D3—124no—
207C2×Dic6—22no—
208C2×Dic6—21no—
209C2×Dic6C4×D314yescomplemented
210C2×Dic6C22×D312yes—
211C2×C3×C8—34no—
212C2×C3×C8—32no—
213C2×C3×C8—32no—
214C2×C3×C8—62no—
215C3×C4⋊C4—32no—
216C3×C4⋊C4—64no—
217C3×C4⋊C4—61no—
218C3×C42—22no—
219C3×C42—22no—
220C3×C42—64no—
221C3×C42D1212yes—
222C3×C42#6712yes—
223C3×C42C22×D312yes—
224C3×C42C22×D312yes—
225#215—316no—
226(C2×D3)⋊C4—68no—
227(C2×D3)⋊C4—64no—
228(C2×D3)⋊C4—64no—
229C4⋊Dic3—21no—
230C4⋊Dic3—32no—
231C4⋊Dic3—32no—
232C4⋊Dic3—62no—
233C4⋊Dic3—62no—
234C4⋊Dic3—61no—
235C4⋊Dic3—61no—
236C4⋊Dic3C22×D312yes—
237Dic3⋊C4—24no—
238C4×Dic3—24no—
239C2×C3⋊C8—22no—
240C2×C3⋊C8C4×D314yescomplemented
241C2×C3⋊C8C22×D312yes—
242C2×C3⋊C8C22×D312yes—
243#204—316no—
244C22×C32C4×D412yes—
245C22×C32AGL(1,ℤ/8)12yes—
246C22×C32#13712yes—
247C22×C32C22×D411yescharacteristic
248C2×C3⋊D3—24no—
249C2×C3⋊D3—42no—
250C2×C3⋊D3—42no—
251C2×C3⋊D3—48no—
252C32×C4—22no—
253C32×C4—22no—
254C32×C4C4×D412yes—
255C32×C4C23×C411yescharacteristic
256C32×C4C2×#4111yescharacteristic
257C3⋊Dic3—42no—
258C3×Dic3—24no—
259C3×Dic3—42no—
260C22×Q8—31no—
261C22×D4—91no—
262C23×C4—181no—
263C2×SD16—98no—
264C2×SD16—94no—
265C22×C8—31no—
266C22×C8—31no—
267C4×Q8—34no—
268C4×Q8—62no—
269C4×D4—94no—
270C4×D4—182no—
271C2×C4⋊C4—31no—
272C2×C4⋊C4—61no—
273C2×C4⋊C4—91no—
274C2×C22⋊C4—181no—
275C2×C42—61no—
276C2×C42D3211yescharacteristic
277#107—94no—
278#103—94no—
279#102—94no—
280#97—34no—
281C23×C3—21no—
282C23×C3C2×D1211yescharacteristic
283C23×C3C2×#6711yescharacteristic
284C22×D3—64no—
285C22×D3—68no—
286C22×D3—64no—
287C22×D3—64no—
288C22×D3—62no—
289C22×D3—62no—
290C22×D3—124no—
291C22×D3—124no—
292C22×D3—122no—
293C22×D3—122no—
294C22×D3—122no—
295C22×D3—122no—
296C3×Q8—34no—
297C3×Q8—64no—
298C3×Q8—62no—
299C2×C3×C4—24no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—21no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—21no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—42no—
311C2×C3×C4—64no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4—122no—
315C2×C3×C4C2×C4×D312yes—
316C2×C3×C4C2×C4×D312yes—
317C2×C3×C4C2×D1212yes—
318C2×C3×C4C2×D1212yes—
319C2×C3×C4C2×D1211yescharacteristic
320C2×C3×C4#23512yes—
321C2×C3×C4#23512yes—
322C2×C3×C4C2×#6712yes—
323C2×C3×C4C2×#6712yes—
324C2×C3×C4C2×#6711yescharacteristic
325C2×C3×C4C23×D311yescharacteristic
326C2×C3×C4C23×D311yescharacteristic
327C2×Dic3—24no—
328C2×Dic3—22no—
329C2×Dic3—22no—
330C2×Dic3—42no—
331C2×Dic3—64no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—124no—
335C2×Dic3—122no—
336C2×Dic3—122no—
337D12—34no—
338D12—34no—
339D12—64no—
340D12—64no—
341D12—68no—
342D12—64no—
343D12—64no—
344D12—62no—
345D12—62no—
346C4×D3—1216no—
347C4×D3—128no—
348C4×D3—128no—
349Dic6—24no—
350Dic6—22no—
351Dic6C2×C4×D314yescomplemented
352C3×C8—34no—
353C3×C8—62no—
354C3⋊C8—22no—
355C3⋊C8C2×C4×D314yescomplemented
356C2×C32#44014yescomplemented
357C2×C32C2×C4×D411yescharacteristic
358C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
359C2×C32C2×#13711yescharacteristic
360C3⋊D3—44no—
361C24—181no—
362C2×Q8—32no—
363C2×Q8—34no—
364C2×Q8—62no—
365C2×Q8—61no—
366C2×D4—92no—
367C2×D4—94no—
368C2×D4—182no—
369C2×D4—181no—
370C22×C4—61no—
371C22×C4—61no—
372C22×C4—181no—
373C22×C4—184no—
374C22×C4—364no—
375C22×C4#62611yescharacteristic
376C22×C4#62611yescharacteristic
377C22×C4C2×D3211yescharacteristic
378SD16—916no—
379C2×C8—32no—
380C2×C8—34no—
381C2×C8—32no—
382C2×C8—62no—
383C4⋊C4—32no—
384C4⋊C4—61no—
385C4⋊C4—64no—
386C4⋊C4—92no—
387C4⋊C4—181no—
388C22⋊C4—184no—
389C42—64no—
390C42#62612yes—
391C42C2×D3212yes—
392C22×C3—21no—
393C22×C3—22no—
394C22×C3—22no—
395C22×C3—22no—
396C22×C3C4×D1212yes—
397C22×C3#90812yes—
398C22×C3#90912yes—
399C22×C3C4×#6712yes—
400C22×C3#94212yes—
401C22×C3#94912yes—
402C22×C3C22×D1211yescharacteristic
403C22×C3C22×#6711yescharacteristic
404C2×D3—68no—
405C2×D3—64no—
406C2×D3—64no—
407C2×D3—124no—
408C2×D3—1216no—
409C2×D3—124no—
410C2×D3—128no—
411C2×D3—122no—
412C2×D3—122no—
413C2×D3—128no—
414C2×D3—122no—
415C2×D3—122no—
416C3×C4—24no—
417C3×C4—22no—
418C3×C4—22no—
419C3×C4—22no—
420C3×C4—22no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—22no—
424C3×C4—42no—
425C3×C4—64no—
426C3×C4—122no—
427C3×C4C4×D1212yes—
428C3×C4C4×#6712yes—
429C3×C4C22×C4×D311yescharacteristic
430C3×C4C22×C4×D311yescharacteristic
431C3×C4C2×#23511yescharacteristic
432C3×C4C2×#23511yescharacteristic
433Dic3—24no—
434Dic3—42no—
435Dic3—124no—
436Dic3—122no—
437Dic3—122no—
438C32C2×#44011yescharacteristic, complemented, Sylow
439C23—182no—
440C23—184no—
441C23—362no—
442C23—362no—
443C23C2×#62611yescharacteristic
444Q8—34no—
445Q8—62no—
446Q8—64no—
447D4—94no—
448D4—182no—
449D4—184no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—62no—
453C2×C4—64no—
454C2×C4—62no—
455C2×C4—122no—
456C2×C4—182no—
457C2×C4—368no—
458C2×C4—362no—
459C2×C4#379812yes—
460C2×C4C4×D3212yes—
461C2×C4C2×#62612yes—
462C2×C4C2×#62612yes—
463C2×C4C2×#62611yescharacteristic
464C2×C4C22×D3211yescharacteristic
465C8—34no—
466C8—62no—
467C2×C3—24no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3#471014yescomplemented
472C2×C3#502614yescomplemented
473C2×C3C2×C4×D1211yescharacteristic
474C2×C3C2×#90811yescharacteristic
475C2×C3C2×#90911yescharacteristic
476C2×C3C2×C4×#6711yescharacteristic
477C2×C3C2×#94211yescharacteristic
478C2×C3C2×#94911yescharacteristic
479D3—128no—
480D3—124no—
481D3—124no—
482C22—184no—
483C22—368no—
484C22—362no—
485C22—362no—
486C22#6382512yes—
487C22#6383312yes—
488C22C4×#62612yes—
489C22C22×#62611yescharacteristic
490C4—22no—
491C4—22no—
492C4—64no—
493C4—122no—
494C4—362no—
495C4C4×#62612yes—
496C4C2×#379811yescharacteristic
497C4C2×C4×D3211yescharacteristic
498C3—21no—
499C3C2×#471011yescharacteristic, complemented
500C3C2×#502611yescharacteristic, complemented
501C2—364no—
502C2#1059036214yesdirect product factor
503C2C2×#6382511yescharacteristic
504C2C2×#6383311yescharacteristic
505C2C2×C4×#62611yescharacteristic
subgroupG/H
centerC23C2×#626
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC2×C32×C4C24
hypercenterC2×C42D32
hypocenterC32C2×#440
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×Dic6C2semidirect
4. C2×C3×#803C2semidirect
5. C2×#63575C2semidirect
6. C2×#63566C2semidirect
8. #10590362C2direct (N × H)
25. C3×C4×Dic6C22semidirect
26. C2×#3717C4semidirect
28. C3×#803C22semidirect
29. #63575C22semidirect
30. #63566C22semidirect
38. C2×C4×Dic6D3semidirect
47. C2×#803D3semidirect
64. C2×C3×Dic6C2×C4semidirect
76. C2×C3×C3⋊C8C2×C4semidirect
79. #3717C2×C4semidirect
121. C4×Dic6C2×D3semidirect
129. #803C2×D3semidirect
155. C3×Dic6C22×C4semidirect
157. C3×C3⋊C8C22×C4semidirect
209. C2×Dic6C4×D3semidirect
240. C2×C3⋊C8C4×D3semidirect
351. Dic6C2×C4×D3semidirect
355. C3⋊C8C2×C4×D3semidirect
356. C2×C32#440semidirect
438. C32C2×#440semidirect
471. C2×C3#4710semidirect
472. C2×C3#5026semidirect
499. C3C2×#4710semidirect
500. C3C2×#5026semidirect
502. C2#10590362direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊(C3⋊D3)2
C2×C3×C4×Dic62
C22×#37172
C2×C3×#8032
C2×#635752
C2×#635662
C2×#635642
#105903622
C2×#50263
C2×#47103