Finite Group Databasebeta

← C2×#11797801 #72255342

Subgroups — C2×#11797801 #72255342

Order 2304.

2394 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#63653C211yesmaximal, characteristic
2C2×D8×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×#10592571C211yesmaximal, characteristic, complemented
4#11797801C218yesmaximal, direct product factor
5C2×#10589356C211yesmaximal, characteristic, complemented
6C2×#10589375C211yesmaximal, characteristic, complemented
7C2×#10589368C211yesmaximal, characteristic, complemented
8C2×C32×#357C211yesmaximal, characteristic, complemented
9C2×#69177—34nomaximal
10C22×C32×D8C2211yescharacteristic
11C2×D4×C3⋊Dic3—21no—
12C22×#3745C2211yescharacteristic
13C2×#64102—21no—
14C22×C32×C16C2211yescharacteristic
15C2×C32×#107C2211yescharacteristic
16C2×#63659—21no—
17D8×C3⋊Dic3—22no—
18D8×C3⋊Dic3C2214yescomplemented
19C2×#63653C418yescomplemented
20C2×#63653C2214yes—
21C2×#63645C2211yescharacteristic
22C2×C8×C3⋊Dic3C2211yescharacteristic
23C22×C3⋊(C3⋊C16)C2211yescharacteristic
24C2×#63636—21no—
25#10592571—22no—
26#10592571C2214yescomplemented
27C32×#357C2214yescomplemented
28#10589375C2214yescomplemented
29#10589368C2214yescomplemented
30#10589356C2214yescomplemented
31C2×Dic3×D8—34no—
32C22×#826—34no—
33C2×#4872—34no—
34C2×C3×#357D314yescomplemented
35C2×#4509—34no—
36C2×#4502—34no—
37C2×#4490—34no—
38#69177—332no—
39C22×C32×D4—21no—
40C23×C3⋊Dic3—41no—
41C22×C4⋊(C3⋊D3)—21no—
42C22×C4×C3⋊D3—41no—
43C2×C32×D8—21no—
44C2×C32×D8—22no—
45C2×C32×D8C2×C414yescomplemented
46C2×C32×D8C2312yes—
47C22×C32×C8C2311yescharacteristic
48C2×C32×C4⋊C4—21no—
49C2×#3757—41no—
50D4×C3⋊Dic3—24no—
51D4×C3⋊Dic3—42no—
52C2×#3752—41no—
53C2×C4⋊(C3⋊Dic3)—21no—
54C2×C4×C3⋊Dic3D411yescharacteristic
55C22×C3⋊(C3⋊C8)D411yescharacteristic
56C2×#3745—21no—
57C2×#3745—22no—
58C2×#3745C2×C414yescomplemented
59C2×#3745C2312yes—
60#64102—24no—
61#64102—42no—
62C2×C32×C16—22no—
63C2×C32×C16C2312yes—
64C32×#107—21no—
65C32×#107C2312yes—
66#63659—24no—
67#63653C2×C4116yescomplemented
68#63645—21no—
69#63645C2312yes—
70C8×C3⋊Dic3D412yes—
71C8×C3⋊Dic3C2312yes—
72C2×C3⋊(C3⋊C16)C2×C414yescomplemented
73C2×C3⋊(C3⋊C16)C2312yes—
74#63636—24no—
75C2×#2177—91noSylow
76C22×C3×D8C2×D314yes—
77C2×D4×Dic3—64no—
78C22×D24—34no—
79C2×#893—64no—
80C22×C3×C16C2×D314yes—
81C2×C3×#107C2×D314yes—
82C2×#832—64no—
83Dic3×D8—316no—
84Dic3×D8—68no—
85C2×#826—332no—
86C2×#826—316no—
87C2×#818—34no—
88C2×C8×Dic3—34no—
89C22×C3⋊C16—34no—
90C2×#809—64no—
91#4872—316no—
92#4872—68no—
93C3×#357C2×D3116yescomplemented
94#4509—316no—
95#4502—316no—
96#4490—316no—
97C24×C32—41no—
98C23×C3⋊D3—41no—
99C2×C32×D4—24no—
100C2×C32×D4—22no—
101C2×C32×D4—41no—
102C2×C32×D4—42no—
103C22×C32×C4—41no—
104C22×C32×C4C2×D411yescharacteristic
105C22×C3⋊Dic3—41no—
106C22×C3⋊Dic3—44no—
107C22×C3⋊Dic3—84no—
108C22×C3⋊Dic3D811yescharacteristic
109C22×C3⋊Dic3D811yescharacteristic
110C2×C4⋊(C3⋊D3)—24no—
111C2×C4⋊(C3⋊D3)—22no—
112C2×C4⋊(C3⋊D3)—41no—
113C2×C4⋊(C3⋊D3)—42no—
114C2×C4×C3⋊D3—44no—
115C2×C4×C3⋊D3—84no—
116C32×D8—24no—
117C32×D8—22no—
118C32×D8C22×C414yescomplemented
119C2×C32×C8C22×C412yes—
120C2×C32×C8C2×D411yescharacteristic
121C2×C32×C8#4112yes—
122C2×C32×C8C2411yescharacteristic
123C32×C4⋊C4—22no—
124C32×C4⋊C4—41no—
125#3757—44no—
126#3752—44no—
127C4⋊(C3⋊Dic3)—22no—
128C4⋊(C3⋊Dic3)—41no—
129C4×C3⋊Dic3D812yes—
130C4×C3⋊Dic3C2×D412yes—
131C2×C3⋊(C3⋊C8)—22no—
132C2×C3⋊(C3⋊C8)C2×D412yes—
133#3745—24no—
134#3745—22no—
135#3745C22×C414yescomplemented
136C32×C16—22no—
137C3⋊(C3⋊C16)C22×C414yescomplemented
138C22×D16—91no—
139C2×C4×D8—91no—
140C2×C4×D8—91no—
141#2177—98no—
142C2×#367—91no—
143C2×#357—91no—
144C2×#357C3⋊D311yescharacteristic, complemented
145C2×#346—91no—
146C22×C3×D4—24no—
147C23×Dic3—124no—
148C22×D12—64no—
149C22×C4×D3—124no—
150C2×C3×D8—24no—
151C2×C3×D8—28no—
152C2×C3×D8C4×D3116yescomplemented
153C2×C3×D8C22×D318yes—
154C22×C3×C8C22×D314yes—
155C2×C3×C4⋊C4—24no—
156C2×#217—124no—
157D4×Dic3—616no—
158D4×Dic3—128no—
159C2×(C2×D3)⋊C4—124no—
160C2×C4⋊Dic3—64no—
161C2×C4×Dic3—34no—
162C22×C3⋊C8—34no—
163C2×D24—316no—
164C2×D24—38no—
165C2×D24—64no—
166C2×D24—68no—
167#893—616no—
168#893—128no—
169C2×C3×C16—28no—
170C2×C3×C16C22×D318yes—
171C3×#107—24no—
172C3×#107C22×D318yes—
173#832—616no—
174#826—364no—
175#818—38no—
176#818—64no—
177C8×Dic3—38no—
178C8×Dic3—38no—
179C2×C3⋊C16—316no—
180C2×C3⋊C16—38no—
181#809—616no—
182C23×C32—42no—
183C23×C32—44no—
184C23×C32—82no—
185C23×C32—82no—
186C23×C32C2×D811yescharacteristic
187C22×C3⋊D3—42no—
188C22×C3⋊D3—44no—
189C22×C3⋊D3—82no—
190C22×C3⋊D3—82no—
191C32×D4—24no—
192C32×D4—42no—
193C32×D4—44no—
194C2×C32×C4—42no—
195C2×C32×C4—82no—
196C2×C32×C4C4×D412yes—
197C2×C32×C4C2×D811yescharacteristic
198C2×C32×C4#13512yes—
199C2×C32×C4C22×D411yescharacteristic
200C2×C3⋊Dic3—22no—
201C2×C3⋊Dic3—22no—
202C2×C3⋊Dic3—42no—
203C2×C3⋊Dic3—88no—
204C2×C3⋊Dic3—82no—
205C2×C3⋊Dic3C2×D812yes—
206C2×C3⋊Dic3C2×D812yes—
207C4⋊(C3⋊D3)—24no—
208C4⋊(C3⋊D3)—42no—
209C4⋊(C3⋊D3)—44no—
210C4×C3⋊D3—88no—
211C32×C8C4×D412yes—
212C32×C8C23×C411yescharacteristic
213C32×C8C2×#4111yescharacteristic
214C3⋊(C3⋊C8)—22no—
215C22×D8—91no—
216C22×D8C2×C3⋊D311yescharacteristic
217C2×C4×D4—181no—
218C2×C4×D4—181no—
219C2×D16—98no—
220C2×D16—94no—
221C22×C16—91no—
222C22×C16C2×C3⋊D311yescharacteristic
223C4×D8—94no—
224C4×D8—94no—
225C4×D8—182no—
226C4×D8—182no—
227C2×#107—91no—
228C2×#107C2×C3⋊D311yescharacteristic
229C2×#102—181no—
230C2×#102—181no—
231C2×C4×C8—91no—
232#367—94no—
233#357—94no—
234#357C2×C3⋊D314yescomplemented
235#346—94no—
236C24×C3—44no—
237C23×D3—124no—
238C2×C3×D4—216no—
239C2×C3×D4—28no—
240C2×C3×D4—44no—
241C2×C3×D4—48no—
242C22×C3×C4—44no—
243C22×C3×C4D3×D414yes—
244C22×Dic3—34no—
245C22×Dic3—34no—
246C22×Dic3—1216no—
247C22×Dic3—124no—
248C22×Dic3—2416no—
249C2×D12—616no—
250C2×D12—68no—
251C2×D12—124no—
252C2×D12—128no—
253C2×C4×D3—1216no—
254C2×C4×D3—2416no—
255C3×D8—216no—
256C3×D8—28no—
257C3×D8C2×C4×D3116yescomplemented
258C2×C3×C8C2×C4×D318yes—
259C2×C3×C8D3×D414yes—
260C2×C3×C8#23718yes—
261C2×C3×C8C23×D314yes—
262C3×C4⋊C4—28no—
263C3×C4⋊C4—44no—
264#217—1216no—
265(C2×D3)⋊C4—1216no—
266C4⋊Dic3—68no—
267C4⋊Dic3—124no—
268C4×Dic3—38no—
269C4×Dic3—38no—
270C2×C3⋊C8—38no—
271C2×C3⋊C8—68no—
272D24—316no—
273D24—616no—
274D24—68no—
275C3×C16—28no—
276C3⋊C16—316no—
277C22×C32—44no—
278C22×C32—82no—
279C22×C32—82no—
280C22×C32—88no—
281C22×C32C4×D812yes—
282C22×C32#50912yes—
283C22×C32#50912yes—
284C22×C32C22×D811yescharacteristic
285C2×C3⋊D3—44no—
286C2×C3⋊D3—82no—
287C2×C3⋊D3—82no—
288C2×C3⋊D3—88no—
289C32×C4—82no—
290C32×C4C4×D812yes—
291C32×C4C2×C4×D411yescharacteristic
292C32×C4C2×#13511yescharacteristic
293C3⋊Dic3—22no—
294C3⋊Dic3—22no—
295C3⋊Dic3—82no—
296C22×D4—21no—
297C22×D4—181no—
298C23×C4—361no—
299C23×C4—361no—
300C2×D8—21no—
301C2×D8—22no—
302C2×D8—92no—
303C2×D8—94no—
304C2×D8—181no—
305C2×D8—182no—
306C2×D8C4×C3⋊D314yescomplemented
307C2×D8C22×C3⋊D312yes—
308C22×C8—91no—
309C22×C8C22×C3⋊D311yescharacteristic
310C4×D4—184no—
311C4×D4—184no—
312C4×D4—362no—
313C4×D4—362no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—181no—
316C2×C22⋊C4—361no—
317C2×C22⋊C4—361no—
318C2×C42—91no—
319D16—916no—
320C2×C16—22no—
321C2×C16—92no—
322C2×C16—94no—
323C2×C16C22×C3⋊D312yes—
324#107—21no—
325#107—92no—
326#107—181no—
327#107C22×C3⋊D312yes—
328#102—184no—
329#102—184no—
330C4×C8—92no—
331C4×C8—92no—
332C23×C3—48no—
333C23×C3—416no—
334C23×C3—88no—
335C23×C3—88no—
336C23×C3D3×D814yes—
337C22×D3—128no—
338C22×D3—1216no—
339C22×D3—248no—
340C22×D3—248no—
341C3×D4—216no—
342C3×D4—48no—
343C3×D4—416no—
344C2×C3×C4—48no—
345C2×C3×C4—88no—
346C2×C3×C4#67⋊C418yes—
347C2×C3×C4D3×D814yes—
348C2×C3×C4#91618yes—
349C2×C3×C4C2×D3×D414yes—
350C2×Dic3—38no—
351C2×Dic3—38no—
352C2×Dic3—68no—
353C2×Dic3—68no—
354C2×Dic3—128no—
355C2×Dic3—2432no—
356C2×Dic3—248no—
357D12—616no—
358D12—128no—
359D12—1216no—
360C4×D3—2432no—
361C3×C8#67⋊C418yes—
362C3×C8C22×C4×D314yes—
363C3×C8C2×#23714yes—
364C3⋊C8—68no—
365C2×C32—84no—
366C2×C32#217714yescomplemented
367C2×C32C2×C4×D811yescharacteristic
368C2×C32C2×#50911yescharacteristic
369C2×C32C2×#50911yescharacteristic
370C3⋊D3—84no—
371C24—41no—
372C24—361no—
373C2×D4—24no—
374C2×D4—22no—
375C2×D4—41no—
376C2×D4—42no—
377C2×D4—184no—
378C2×D4—182no—
379C2×D4—361no—
380C2×D4—362no—
381C22×C4—41no—
382C22×C4—91no—
383C22×C4—91no—
384C22×C4—364no—
385C22×C4—364no—
386C22×C4—361no—
387C22×C4—724no—
388C22×C4—724no—
389C22×C4D4×C3⋊D311yescharacteristic
390D8—24no—
391D8—22no—
392D8—94no—
393D8—184no—
394D8—182no—
395D8C2×C4×C3⋊D314yescomplemented
396C2×C8—92no—
397C2×C8—182no—
398C2×C8C2×C4×C3⋊D312yes—
399C2×C8D4×C3⋊D311yescharacteristic
400C2×C8#383012yes—
401C2×C8C23×C3⋊D311yescharacteristic
402C4⋊C4—22no—
403C4⋊C4—41no—
404C4⋊C4—182no—
405C4⋊C4—361no—
406C22⋊C4—364no—
407C22⋊C4—364no—
408C42—92no—
409C42—92no—
410C16—22no—
411C16—94no—
412C22×C3—416no—
413C22×C3—832no—
414C22×C3—88no—
415C22×C3—88no—
416C22×C3#475618yes—
417C22×C3#491118yes—
418C22×C3#491418yes—
419C22×C3C2×D3×D814yes—
420C2×D3—1216no—
421C2×D3—2432no—
422C2×D3—248no—
423C2×D3—248no—
424C3×C4—88no—
425C3×C4#475618yes—
426C3×C4C2×#67⋊C414yes—
427C3×C4C2×#91614yes—
428Dic3—68no—
429Dic3—68no—
430Dic3—248no—
431C32C2×#217711yescharacteristic, complemented, Sylow
432C23—42no—
433C23—44no—
434C23—82no—
435C23—82no—
436C23—362no—
437C23—364no—
438C23—722no—
439C23—722no—
440C23D8×C3⋊D311yescharacteristic
441D4—24no—
442D4—42no—
443D4—44no—
444D4—184no—
445D4—362no—
446D4—364no—
447C2×C4—42no—
448C2×C4—82no—
449C2×C4—92no—
450C2×C4—92no—
451C2×C4—182no—
452C2×C4—182no—
453C2×C4—362no—
454C2×C4—728no—
455C2×C4—728no—
456C2×C4—722no—
457C2×C4#6409012yes—
458C2×C4D8×C3⋊D311yescharacteristic
459C2×C4#6412512yes—
460C2×C4C2×D4×C3⋊D311yescharacteristic
461C8—182no—
462C8#6409012yes—
463C8C22×C4×C3⋊D311yescharacteristic
464C8C2×#383011yescharacteristic
465C2×C3—816no—
466C2×C3#69177116yescomplemented
467C2×C3C2×#475614yes—
468C2×C3C2×#491114yes—
469C2×C3C2×#491414yes—
470D3—2416no—
471C22—44no—
472C22—88no—
473C22—82no—
474C22—82no—
475C22—364no—
476C22—728no—
477C22—722no—
478C22—722no—
479C22#1059245512yes—
480C22#1059261012yes—
481C22#1059261312yes—
482C22C2×D8×C3⋊D311yescharacteristic
483C4—82no—
484C4—182no—
485C4—182no—
486C4—722no—
487C4#1059245512yes—
488C4C2×#6409011yescharacteristic
489C4C2×#6412511yescharacteristic
490C3C2×#6917714yescomplemented
491C2—84no—
492C2—724no—
493C2#1179780114yesdirect product factor
494C2C2×#1059245511yescharacteristic
495C2C2×#1059261011yescharacteristic
496C2C2×#1059261311yescharacteristic
subgroupG/H
centerC23D8×C3⋊D3
commutatorC32×C8C23×C4
FrattiniC2×C8C23×C3⋊D3
FittingC2×C32×#357C2
socleC23×C32C2×D8
prime radicalC22×#63653C2
cosocleC2×C32×C8C24
hypercenterC2×#357C3⋊D3
hypocenterC32C2×#2177
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C2×D8×C3⋊Dic3C2semidirect
3. C2×#10592571C2semidirect
4. #11797801C2direct (N × H)
5. C2×#10589356C2semidirect
6. C2×#10589375C2semidirect
7. C2×#10589368C2semidirect
8. C2×C32×#357C2semidirect
18. D8×C3⋊Dic3C22semidirect
19. C2×#63653C4semidirect
26. #10592571C22semidirect
27. C32×#357C22semidirect
28. #10589375C22semidirect
29. #10589368C22semidirect
30. #10589356C22semidirect
34. C2×C3×#357D3semidirect
45. C2×C32×D8C2×C4semidirect
58. C2×#3745C2×C4semidirect
67. #63653C2×C4semidirect
72. C2×C3⋊(C3⋊C16)C2×C4semidirect
93. C3×#357C2×D3semidirect
118. C32×D8C22×C4semidirect
135. #3745C22×C4semidirect
137. C3⋊(C3⋊C16)C22×C4semidirect
144. C2×#357C3⋊D3semidirect
152. C2×C3×D8C4×D3semidirect
234. #357C2×C3⋊D3semidirect
257. C3×D8C2×C4×D3semidirect
306. C2×D8C4×C3⋊D3semidirect
366. C2×C32#2177semidirect
395. D8C2×C4×C3⋊D3semidirect
431. C32C2×#2177semidirect
466. C2×C3#69177semidirect
490. C3C2×#69177semidirect
493. C2#11797801direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#636532
C2×D8×C3⋊Dic32
C2×#105925712
#117978012
C2×#105893562
C2×#105893752
C2×#105893682
C2×C32×#3572
C2×#691773