Finite Group Databasebeta

← C2×#10592524 #11864813

Subgroups — C2×#10592524 #11864813

Order 1152.

2280 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64366C211yesmaximal, characteristic
2C2×#64160C211yesmaximal, characteristic, complemented
3C2×#64118C211yesmaximal, characteristic, complemented
4C2×#64084C211yesmaximal, characteristic, complemented
5C2×C32×#104C211yesmaximal, characteristic, complemented
6C2×#63650C211yesmaximal, characteristic, complemented
7C2×#63632C211yesmaximal, characteristic, complemented
8#10592524C218yesmaximal, direct product factor
9C2×#4825—34nomaximal
10C2×C32×#41C2211yescharacteristic
11#64366—22no—
12#64366—22no—
13#64366—22no—
14#64366C2214yes—
15C2×#3832—21no—
16C2×D4×C3⋊D3—21no—
17C2×D4×C3⋊D3—22no—
18C2×#3828—21no—
19C2×#3828C2211yescharacteristic
20C22×C4⋊(C3⋊D3)—21no—
21C22×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×#634C2211yescharacteristic, complemented
23C2×C32×M16C2211yescharacteristic, complemented
24C2×C32×C42C2211yescharacteristic, complemented
25#64160—22no—
26#64160C2214yescomplemented
27C2×#3756—21no—
28C2×#3754—21no—
29C2×#3752—22no—
30C2×#3748C2211yescharacteristic, complemented
31#64118—22no—
32#64118C2214yescomplemented
33C2×#3746—21no—
34C2×#3744—21no—
35#64084—22no—
36#64084C2214yescomplemented
37C32×#104C2214yescomplemented
38#63650C2214yescomplemented
39#63632C2214yescomplemented
40C2×#1009—34no—
41C2×#951—34no—
42C2×#909—34no—
43C2×#875—34no—
44C2×C3×#104D314yescomplemented
45C2×#823—34no—
46C2×#805—34no—
47#4825—332no—
48C23×C3⋊D3—22no—
49C23×C3⋊D3D412yes—
50C32×#41—21no—
51C32×#41—21no—
52C32×#41D412yes—
53C32×#41C2312yes—
54C2×C32×Q8D411yescharacteristic
55C2×C32×D4—21no—
56C2×C32×D4D411yescharacteristic
57C22×C32×C4—21no—
58C22×C32×C4—21no—
59C22×C32×C4C2311yescharacteristic
60C2×#638—22no—
61C2×#638—21no—
62C22×C3⋊Dic3—21no—
63#3832—24no—
64#3832—24no—
65D4×C3⋊D3—28no—
66D4×C3⋊D3—24no—
67D4×C3⋊D3—28no—
68D4×C3⋊D3—24no—
69#3828—24no—
70#3828—21no—
71#3828—21no—
72#3828—24no—
73#3828D412yes—
74#3828C2312yes—
75C2×C4⋊(C3⋊D3)—22no—
76C2×C4⋊(C3⋊D3)—24no—
77C2×C4⋊(C3⋊D3)—21no—
78C2×C4⋊(C3⋊D3)—21no—
79C2×C4⋊(C3⋊D3)—21no—
80C2×C4⋊(C3⋊D3)—21no—
81C2×C4⋊(C3⋊D3)—24no—
82C2×C4⋊(C3⋊D3)D412yes—
83C2×C4⋊(C3⋊D3)D411yescharacteristic
84C2×C4⋊(C3⋊D3)C2312yes—
85C2×C4×C3⋊D3—22no—
86C2×C4×C3⋊D3—21no—
87C2×#634—21no—
88C2×#634—21no—
89C2×#634—21no—
90C2×#634—21no—
91C2×#634—21no—
92C2×#634D411yescharacteristic
93C2×#634C2312yescomplemented
94C32×M16—21no—
95C32×M16C2312yescomplemented
96C2×C32×C8—21no—
97C32×C42—21no—
98C32×C42C2312yescomplemented
99#3756—24no—
100#3754—24no—
101#3752—28no—
102#3748—21no—
103#3748C2312yescomplemented
104C2×C3⋊(C3⋊C8)—21no—
105#3746—24no—
106#3744—24no—
107C2×#455—91noSylow
108C2×C3×#41C2×D314yes—
109#1009—316no—
110#1009—68no—
111#1009—68no—
112#1009—68no—
113C2×#239—64no—
114C2×D3×D4—68no—
115C2×D3×D4—64no—
116C2×#235—34no—
117C2×#235—64no—
118C22×D12—34no—
119C22×D12—64no—
120C22×Dic6—34no—
121C2×C3×M16C2×D314yescomplemented
122C2×C3×C42C2×D314yescomplemented
123#951—316no—
124#951—68no—
125C2×#216—64no—
126C2×#214—64no—
127C2×(C2×D3)⋊C4—68no—
128C2×#208—34no—
129#909—316no—
130#909—68no—
131C2×Dic12—64no—
132C2×#204—64no—
133#875—316no—
134#875—68no—
135C3×#104C2×D3116yescomplemented
136#823—316no—
137#805—316no—
138C23×C32—21no—
139C23×C32C2×D411yescharacteristic
140C22×C3⋊D3—21no—
141C22×C3⋊D3—22no—
142C22×C3⋊D3—28no—
143C22×C3⋊D3—22no—
144C22×C3⋊D3—44no—
145C22×C3⋊D3—84no—
146C22×C3⋊D3C2×D414yes—
147C32×Q8—21no—
148C32×Q8C2×D412yes—
149C32×D4—22no—
150C32×D4—22no—
151C32×D4—21no—
152C32×D4C2×D412yes—
153C2×C32×C4—21no—
154C2×C32×C4—22no—
155C2×C32×C4—22no—
156C2×C32×C4—22no—
157C2×C32×C4—42no—
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2411yescharacteristic
164#638—28no—
165#638—22no—
166#638—22no—
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—41no—
170C2×C3⋊Dic3—41no—
171C4⋊(C3⋊D3)—28no—
172C4⋊(C3⋊D3)—22no—
173C4⋊(C3⋊D3)—21no—
174C4⋊(C3⋊D3)—22no—
175C4⋊(C3⋊D3)—22no—
176C4⋊(C3⋊D3)—22no—
177C4⋊(C3⋊D3)C2×D412yes—
178C4×C3⋊D3—28no—
179C4×C3⋊D3—22no—
180C4×C3⋊D3—22no—
181#634—21no—
182#634—22no—
183#634—22no—
184#634—41no—
185#634—41no—
186#634C2×D412yes—
187C32×C8—22no—
188C3⋊(C3⋊C8)—22no—
189C2×H(5,𝔽2)—91no—
190C2×#137—91no—
191C2×#137—91no—
192C2×#124—91no—
193#455—98no—
194C2×#104—91no—
195C2×#104C3⋊D311yescharacteristic, complemented
196C2×#100—91no—
197C23×D3—38no—
198C23×D3—68no—
199C3×#41—24no—
200C3×#41—24no—
201C3×#41D1218yes—
202C3×#41C22×D318yes—
203C2×C3×Q8D1214yes—
204C2×C3×D4—24no—
205C2×C3×D4D1214yes—
206C22×C3×C4—24no—
207C22×C3×C4—24no—
208C22×C3×C4C22×D314yes—
209C2×#67—68no—
210C2×#67—64no—
211C22×Dic3—64no—
212#239—616no—
213#239—616no—
214D3×D4—632no—
215D3×D4—632no—
216D3×D4—616no—
217D3×D4—616no—
218#235—38no—
219#235—38no—
220#235—616no—
221#235—616no—
222#235—64no—
223#235—64no—
224C2×D12—34no—
225C2×D12—38no—
226C2×D12—38no—
227C2×D12—616no—
228C2×D12—68no—
229C2×D12—616no—
230C2×D12—64no—
231C2×D12—64no—
232C2×D12—64no—
233C2×D12—64no—
234C2×C4×D3—68no—
235C2×C4×D3—64no—
236C2×Dic6—34no—
237C2×Dic6—38no—
238C2×Dic6—64no—
239C2×Dic6—64no—
240C2×Dic6—64no—
241C2×Dic6—64no—
242C2×Dic6—64no—
243C3×M16—24no—
244C3×M16C22×D318yescomplemented
245C2×C3×C8—24no—
246C3×C42—24no—
247C3×C42C22×D318yescomplemented
248#216—616no—
249#214—616no—
250(C2×D3)⋊C4—632no—
251#208—38no—
252#208—64no—
253C2×C3⋊C8—64no—
254Dic12—616no—
255#204—616no—
256C22×C32—22no—
257C22×C32—22no—
258C22×C32—42no—
259C22×C32#12011yescharacteristic
260C22×C32#12011yescharacteristic
261C22×C32C22×D411yescharacteristic
262C2×C3⋊D3—24no—
263C2×C3⋊D3—22no—
264C2×C3⋊D3—44no—
265C2×C3⋊D3—42no—
266C2×C3⋊D3—44no—
267C2×C3⋊D3—82no—
268C2×C3⋊D3—88no—
269C32×C4—22no—
270C32×C4—42no—
271C32×C4#12011yescharacteristic
272C32×C4#12011yescharacteristic
273C32×C4C22×D411yescharacteristic
274C32×C4C22×D411yescharacteristic
275C3⋊Dic3—22no—
276C3⋊Dic3—42no—
277H(5,𝔽2)—94no—
278H(5,𝔽2)—182no—
279H(5,𝔽2)—182no—
280H(5,𝔽2)—182no—
281C2×#41—91no—
282C2×#41—181no—
283C2×#41—181no—
284C2×#41C2×C3⋊D311yescharacteristic
285C22×Q8—91no—
286C22×D4—91no—
287C22×D4—181no—
288C22×D4—182no—
289C22×D4—181no—
290#137—94no—
291#137—94no—
292#137—182no—
293#137—182no—
294C2×Q16—181no—
295C2×Q16—181no—
296C2×SD16—181no—
297C2×SD16—181no—
298C2×M16—91no—
299C2×M16C2×C3⋊D311yescharacteristic, complemented
300#124—94no—
301#124—182no—
302C2×C22⋊C4—182no—
303C2×C42C2×C3⋊D311yescharacteristic, complemented
304#104—94no—
305#104C2×C3⋊D314yescomplemented
306#100—94no—
307C23×C3—24no—
308C23×C3D3×D414yes—
309C22×D3—316no—
310C22×D3—64no—
311C22×D3—68no—
312C22×D3—632no—
313C22×D3—68no—
314C22×D3—1216no—
315C22×D3—2416no—
316C3×Q8—24no—
317C3×Q8C2×D1218yes—
318C3×D4—28no—
319C3×D4—28no—
320C3×D4—24no—
321C3×D4C2×D1218yes—
322C2×C3×C4—24no—
323C2×C3×C4—28no—
324C2×C3×C4—28no—
325C2×C3×C4—28no—
326C2×C3×C4—48no—
327C2×C3×C4C2×D1214yes—
328C2×C3×C4C2×D1214yes—
329C2×C3×C4D3×D414yes—
330C2×C3×C4D3×D414yes—
331C2×C3×C4D3×D414yes—
332C2×C3×C4C23×D314yes—
333#67—632no—
334#67—68no—
335#67—68no—
336C2×Dic3—64no—
337C2×Dic3—68no—
338C2×Dic3—124no—
339C2×Dic3—124no—
340D12—38no—
341D12—632no—
342D12—64no—
343D12—68no—
344D12—68no—
345D12—68no—
346D12—68no—
347C4×D3—632no—
348C4×D3—68no—
349C4×D3—68no—
350Dic6—38no—
351Dic6—64no—
352Dic6—68no—
353Dic6—68no—
354Dic6—124no—
355Dic6—124no—
356C3×C8—28no—
357C3⋊C8—68no—
358C2×C32—21no—
359C2×C32—21no—
360C2×C32—42no—
361C2×C32#45512yescomplemented
362C2×C32C2×#12011yescharacteristic
363C3⋊D3—44no—
364C3⋊D3—42no—
365C24—92no—
366C24—182no—
367#41—21no—
368#41—21no—
369#41—92no—
370#41—92no—
371#41—184no—
372#41—184no—
373#41—184no—
374#41—184no—
375#41—181no—
376#41—181no—
377#41C4⋊(C3⋊D3)12yes—
378#41C22×C3⋊D312yes—
379C2×Q8—92no—
380C2×Q8—91no—
381C2×Q8—181no—
382C2×Q8—181no—
383C2×Q8—181no—
384C2×Q8—181no—
385C2×Q8—181no—
386C2×Q8C4⋊(C3⋊D3)11yescharacteristic
387C2×D4—21no—
388C2×D4—92no—
389C2×D4—91no—
390C2×D4—92no—
391C2×D4—184no—
392C2×D4—182no—
393C2×D4—184no—
394C2×D4—188no—
395C2×D4—188no—
396C2×D4—184no—
397C2×D4—182no—
398C2×D4—181no—
399C2×D4—184no—
400C2×D4—181no—
401C2×D4—181no—
402C2×D4—181no—
403C2×D4—181no—
404C2×D4C4⋊(C3⋊D3)11yescharacteristic
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—182no—
408C22×C4—181no—
409C22×C4—181no—
410C22×C4C22×C3⋊D311yescharacteristic
411Q16—184no—
412Q16—184no—
413SD16—184no—
414SD16—184no—
415M16—21no—
416M16—92no—
417M16—181no—
418M16C22×C3⋊D312yescomplemented
419C2×C8—21no—
420C2×C8—181no—
421C22⋊C4—188no—
422C42—21no—
423C42C22×C3⋊D312yescomplemented
424C22×C3—28no—
425C22×C3—28no—
426C22×C3—48no—
427C22×C3#88214yes—
428C22×C3#88214yes—
429C22×C3C2×D3×D414yes—
430C2×D3—68no—
431C2×D3—616no—
432C2×D3—1216no—
433C2×D3—128no—
434C2×D3—1216no—
435C2×D3—248no—
436C2×D3—2432no—
437C3×C4—28no—
438C3×C4—48no—
439C3×C4#88214yes—
440C3×C4#88214yes—
441C3×C4C22×D1214yes—
442C3×C4C2×D3×D414yes—
443Dic3—68no—
444Dic3—128no—
445C32C2×#45511yescharacteristic, complemented, Sylow
446C23—21no—
447C23—94no—
448C23—188no—
449C23—181no—
450C23—182no—
451C23—182no—
452C23—364no—
453C23—724no—
454C23D4×C3⋊D311yescharacteristic
455Q8—21no—
456Q8—92no—
457Q8—181no—
458Q8—182no—
459Q8—182no—
460Q8—361no—
461Q8—361no—
462Q8C2×C4⋊(C3⋊D3)12yes—
463D4—22no—
464D4—22no—
465D4—21no—
466D4—92no—
467D4—188no—
468D4—188no—
469D4—182no—
470D4—182no—
471D4—181no—
472D4—182no—
473D4—182no—
474D4—182no—
475D4—182no—
476D4C2×C4⋊(C3⋊D3)12yes—
477C2×C4—21no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—42no—
482C2×C4—188no—
483C2×C4—181no—
484C2×C4—182no—
485C2×C4—182no—
486C2×C4—182no—
487C2×C4—361no—
488C2×C4—361no—
489C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
490C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
491C2×C4D4×C3⋊D311yescharacteristic
492C2×C4D4×C3⋊D311yescharacteristic
493C2×C4D4×C3⋊D311yescharacteristic
494C2×C4C23×C3⋊D311yescharacteristic
495C8—22no—
496C8—182no—
497C2×C3—24no—
498C2×C3—24no—
499C2×C3—48no—
500C2×C3#482518yescomplemented
501C2×C3C2×#88214yes—
502D3—1216no—
503D3—128no—
504C22—22no—
505C22—22no—
506C22—42no—
507C22—182no—
508C22—184no—
509C22—364no—
510C22—364no—
511C22—362no—
512C22—722no—
513C22—728no—
514C22#6409111yescharacteristic
515C22#6409111yescharacteristic
516C22C2×D4×C3⋊D311yescharacteristic
517C4—22no—
518C4—42no—
519C4—182no—
520C4—362no—
521C4#6409111yescharacteristic
522C4#6409111yescharacteristic
523C4C22×C4⋊(C3⋊D3)11yescharacteristic
524C4C2×D4×C3⋊D311yescharacteristic
525C3C2×#482514yescomplemented
526C2—21no—
527C2—21no—
528C2—42no—
529C2—364no—
530C2—362no—
531C2#1059252412yesdirect product factor
532C2C2×#6409111yescharacteristic
subgroupG/H
centerC22#64091
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#104C2
socleC22×C32#120
prime radicalC2×#64366C2
hypercenterC2×#104C3⋊D3
hypocenterC32C2×#455
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#64160C2semidirect
3. C2×#64118C2semidirect
4. C2×#64084C2semidirect
5. C2×C32×#104C2semidirect
6. C2×#63650C2semidirect
7. C2×#63632C2semidirect
8. #10592524C2direct (N × H)
22. C22×#634C22semidirect
23. C2×C32×M16C22semidirect
24. C2×C32×C42C22semidirect
26. #64160C22semidirect
30. C2×#3748C22semidirect
32. #64118C22semidirect
36. #64084C22semidirect
37. C32×#104C22semidirect
38. #63650C22semidirect
39. #63632C22semidirect
44. C2×C3×#104D3semidirect
93. C2×#634C23semidirect
95. C32×M16C23semidirect
98. C32×C42C23semidirect
103. #3748C23semidirect
121. C2×C3×M16C2×D3semidirect
122. C2×C3×C42C2×D3semidirect
135. C3×#104C2×D3semidirect
195. C2×#104C3⋊D3semidirect
244. C3×M16C22×D3semidirect
247. C3×C42C22×D3semidirect
299. C2×M16C2×C3⋊D3semidirect
303. C2×C42C2×C3⋊D3semidirect
305. #104C2×C3⋊D3semidirect
361. C2×C32#455semidirect
418. M16C22×C3⋊D3semidirect
423. C42C22×C3⋊D3semidirect
445. C32C2×#455semidirect
500. C2×C3#4825semidirect
525. C3C2×#4825semidirect
531. C2#10592524direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643662
C2×#641602
C2×#641182
C2×#640842
C2×C32×#1042
C2×#636502
C2×#636322
#105925242
C2×#48253