Finite Group Databasebeta

← C2×#10592901 #11864804

Subgroups — C2×#10592901 #11864804

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×C32×#137C211yesmaximal, characteristic, complemented
3C2×#64156C211yesmaximal, characteristic, complemented
4C2×#64151C211yesmaximal, characteristic, complemented
5C2×#63664C211yesmaximal, characteristic, complemented
6#10592901C218yesmaximal, direct product factor
7C2×#63652C211yesmaximal, characteristic, complemented
8C2×#63650C211yesmaximal, characteristic, complemented
9C2×#5202—34nomaximal
10C2×C32×#41C2211yescharacteristic
11C22×C32×Q8C2211yescharacteristic, complemented
12#64366—22no—
13#64366—22no—
14#64366—22no—
15#64366C2214yes—
16C2×#3832—21no—
17C2×D4×C3⋊D3—21no—
18C2×D4×C3⋊D3—22no—
19C2×#3828—21no—
20C2×#3828C2211yescharacteristic
21C22×C4⋊(C3⋊D3)—21no—
22C22×C4⋊(C3⋊D3)C2211yescharacteristic
23C32×#137—22no—
24C32×#137C2214yescomplemented
25C2×C32×Q16—21no—
26C2×C32×SD16—21no—
27C2×C32×M16C2211yescharacteristic, complemented
28#64156—22no—
29#64156C2214yescomplemented
30C2×#3756—21no—
31#64151—22no—
32#64151C2214yescomplemented
33C2×#3755—21no—
34C2×#3752—22no—
35C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
36C2×#3748C2211yescharacteristic, complemented
37#63664C2214yescomplemented
38#63652C2214yescomplemented
39#63650C2214yescomplemented
40C2×#1009—34no—
41C2×C3×#137D314yescomplemented
42C2×#947—34no—
43C2×#942—34no—
44C2×#837—34no—
45#5202—332no—
46C2×#825—34no—
47C2×#823—34no—
48C23×C3⋊D3—22no—
49C23×C3⋊D3D412yes—
50C32×#41—21no—
51C32×#41—21no—
52C32×#41D412yes—
53C32×#41C2312yes—
54C2×C32×Q8—21no—
55C2×C32×Q8—21no—
56C2×C32×Q8—21no—
57C2×C32×Q8—21no—
58C2×C32×Q8—21no—
59C2×C32×Q8D411yescharacteristic
60C2×C32×Q8C2312yescomplemented
61C2×C32×D4—21no—
62C2×C32×D4D411yescharacteristic
63C22×C32×C4—21no—
64C22×C32×C4—21no—
65C22×C32×C4C2311yescharacteristic
66C2×#638—22no—
67C2×#638—21no—
68C22×C3⋊Dic3—21no—
69#3832—24no—
70#3832—24no—
71D4×C3⋊D3—28no—
72D4×C3⋊D3—24no—
73D4×C3⋊D3—28no—
74D4×C3⋊D3—24no—
75#3828—24no—
76#3828—21no—
77#3828—21no—
78#3828—24no—
79#3828D412yes—
80#3828C2312yes—
81C2×C4⋊(C3⋊D3)—22no—
82C2×C4⋊(C3⋊D3)—24no—
83C2×C4⋊(C3⋊D3)—21no—
84C2×C4⋊(C3⋊D3)—21no—
85C2×C4⋊(C3⋊D3)—21no—
86C2×C4⋊(C3⋊D3)—21no—
87C2×C4⋊(C3⋊D3)—24no—
88C2×C4⋊(C3⋊D3)D412yes—
89C2×C4⋊(C3⋊D3)D411yescharacteristic
90C2×C4⋊(C3⋊D3)C2312yes—
91C2×C4×C3⋊D3—22no—
92C2×C4×C3⋊D3—21no—
93C2×#634D411yescharacteristic
94C32×Q16—24no—
95C32×SD16—24no—
96C32×M16—21no—
97C32×M16C2312yescomplemented
98C2×C32×C8—21no—
99#3756—24no—
100#3755—24no—
101#3752—28no—
102C4×C3⋊Dic3—21no—
103C4×C3⋊Dic3C2312yescomplemented
104#3748—21no—
105#3748C2312yescomplemented
106C2×C3⋊(C3⋊C8)—21no—
107C2×#455—91noSylow
108C2×C3×#41C2×D314yes—
109C22×C3×Q8C2×D314yescomplemented
110#1009—316no—
111#1009—68no—
112#1009—68no—
113#1009—68no—
114C2×#239—64no—
115C2×D3×D4—68no—
116C2×D3×D4—64no—
117C2×#235—34no—
118C2×#235—64no—
119C22×D12—34no—
120C22×D12—64no—
121C3×#137—28no—
122C3×#137C2×D3116yescomplemented
123C2×C3×Q16—24no—
124C2×C3×SD16—24no—
125C2×C3×M16C2×D314yescomplemented
126#947—316no—
127#947—68no—
128C2×#216—64no—
129#942—316no—
130#942—68no—
131C2×#215—64no—
132C2×(C2×D3)⋊C4—68no—
133C2×C4×Dic3—34no—
134C2×#208—34no—
135#837—316no—
136#825—316no—
137#823—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×Q8—22no—
149C32×Q8—22no—
150C32×Q8—41no—
151C32×Q8—41no—
152C32×Q8C2×D412yes—
153C32×D4—22no—
154C32×D4—22no—
155C32×D4—21no—
156C32×D4C2×D412yes—
157C2×C32×C4—21no—
158C2×C32×C4—22no—
159C2×C32×C4—22no—
160C2×C32×C4—22no—
161C2×C32×C4—41no—
162C2×C32×C4—41no—
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2411yescharacteristic
169#638—28no—
170#638—22no—
171#638—22no—
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3—42no—
175C4⋊(C3⋊D3)—28no—
176C4⋊(C3⋊D3)—22no—
177C4⋊(C3⋊D3)—21no—
178C4⋊(C3⋊D3)—22no—
179C4⋊(C3⋊D3)—22no—
180C4⋊(C3⋊D3)—22no—
181C4⋊(C3⋊D3)C2×D412yes—
182C4×C3⋊D3—28no—
183C4×C3⋊D3—22no—
184C4×C3⋊D3—22no—
185#634—21no—
186#634C2×D412yes—
187C32×C8—22no—
188C3⋊(C3⋊C8)—22no—
189C2×H(5,𝔽2)—91no—
190C2×#137—91no—
191C2×#137C3⋊D311yescharacteristic, complemented
192C2×#124—91no—
193#455—98no—
194C2×#104—91no—
195C2×#104—91no—
196C2×#100—91no—
197C23×D3—38no—
198C23×D3—68no—
199C3×#41—24no—
200C3×#41—24no—
201C3×#41#6718yes—
202C3×#41C22×D318yes—
203C2×C3×Q8—24no—
204C2×C3×Q8—24no—
205C2×C3×Q8—24no—
206C2×C3×Q8—24no—
207C2×C3×Q8—24no—
208C2×C3×Q8#6714yes—
209C2×C3×Q8C22×D318yescomplemented
210C2×C3×D4—24no—
211C2×C3×D4#6714yes—
212C22×C3×C4—24no—
213C22×C3×C4—24no—
214C22×C3×C4C22×D314yes—
215C2×#67—68no—
216C2×#67—64no—
217C22×Dic3—64no—
218#239—616no—
219#239—616no—
220D3×D4—632no—
221D3×D4—632no—
222D3×D4—616no—
223D3×D4—616no—
224#235—38no—
225#235—38no—
226#235—616no—
227#235—616no—
228#235—64no—
229#235—64no—
230C2×D12—34no—
231C2×D12—38no—
232C2×D12—38no—
233C2×D12—616no—
234C2×D12—68no—
235C2×D12—616no—
236C2×D12—64no—
237C2×D12—64no—
238C2×D12—64no—
239C2×D12—64no—
240C2×C4×D3—68no—
241C2×C4×D3—64no—
242C2×Dic6—34no—
243C3×Q16—216no—
244C3×SD16—216no—
245C3×M16—24no—
246C3×M16C22×D318yescomplemented
247C2×C3×C8—24no—
248#216—616no—
249#215—616no—
250(C2×D3)⋊C4—632no—
251C4×Dic3—38no—
252C4×Dic3—64no—
253#208—38no—
254#208—64no—
255C2×C3⋊C8—64no—
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×Q8C2×C3⋊D311yescharacteristic, complemented
286C22×D4—91no—
287C22×D4—181no—
288C22×D4—182no—
289C22×D4—181no—
290#137—22no—
291#137—94no—
292#137—182no—
293#137C2×C3⋊D314yescomplemented
294C2×Q16—21no—
295C2×Q16—181no—
296C2×SD16—21no—
297C2×SD16—181no—
298C2×M16—91no—
299C2×M16C2×C3⋊D311yescharacteristic, complemented
300#124—94no—
301#124—182no—
302C2×C22⋊C4—182no—
303C2×C42—91no—
304#104—94no—
305#104—94no—
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×Q8—28no—
318C3×Q8—28no—
319C3×Q8—44no—
320C3×Q8—44no—
321C3×Q8C2×#6718yes—
322C3×D4—28no—
323C3×D4—28no—
324C3×D4—24no—
325C3×D4C2×#6718yes—
326C2×C3×C4—24no—
327C2×C3×C4—28no—
328C2×C3×C4—28no—
329C2×C3×C4—28no—
330C2×C3×C4—44no—
331C2×C3×C4—44no—
332C2×C3×C4D3×D414yes—
333C2×C3×C4D3×D414yes—
334C2×C3×C4D3×D414yes—
335C2×C3×C4C2×#6714yes—
336C2×C3×C4C2×#6714yes—
337C2×C3×C4C23×D314yes—
338#67—632no—
339#67—68no—
340#67—68no—
341C2×Dic3—64no—
342C2×Dic3—68no—
343C2×Dic3—128no—
344D12—38no—
345D12—632no—
346D12—64no—
347D12—68no—
348D12—68no—
349D12—68no—
350D12—68no—
351C4×D3—632no—
352C4×D3—68no—
353C4×D3—68no—
354Dic6—38no—
355Dic6—64no—
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#41#63812yes—
378#41C22×C3⋊D312yes—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—91no—
385C2×Q8#63811yescharacteristic
386C2×Q8C22×C3⋊D312yescomplemented
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×D4#63811yescharacteristic
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—182no—
408C22×C4—181no—
409C22×C4—181no—
410C22×C4C22×C3⋊D311yescharacteristic
411Q16—24no—
412Q16—184no—
413SD16—24no—
414SD16—184no—
415M16—21no—
416M16—92no—
417M16—181no—
418M16C22×C3⋊D312yescomplemented
419C2×C8—21no—
420C2×C8—181no—
421C22⋊C4—188no—
422C42—92no—
423C42—181no—
424C22×C3—28no—
425C22×C3—28no—
426C22×C3—48no—
427C22×C3#93714yes—
428C22×C3#93714yes—
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#93714yes—
440C3×C4#93714yes—
441C3×C4C2×D3×D414yes—
442C3×C4C22×#6714yes—
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—22no—
457Q8—22no—
458Q8—41no—
459Q8—41no—
460Q8—92no—
461Q8—181no—
462Q8C2×#63812yes—
463D4—22no—
464D4—22no—
465D4—21no—
466D4—92no—
467D4—188no—
468D4—188no—
469D4—182no—
470D4—182no—
471D4—182no—
472D4—182no—
473D4—181no—
474D4—182no—
475D4—182no—
476D4C2×#63812yes—
477C2×C4—21no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—188no—
484C2×C4—181no—
485C2×C4—182no—
486C2×C4—182no—
487C2×C4—182no—
488C2×C4—362no—
489C2×C4D4×C3⋊D311yescharacteristic
490C2×C4D4×C3⋊D311yescharacteristic
491C2×C4D4×C3⋊D311yescharacteristic
492C2×C4C2×#63811yescharacteristic
493C2×C4C2×#63811yescharacteristic
494C2×C4C23×C3⋊D311yescharacteristic
495C8—22no—
496C8—182no—
497C2×C3—24no—
498C2×C3—24no—
499C2×C3—48no—
500C2×C3#520218yescomplemented
501C2×C3C2×#93714yes—
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#6414611yescharacteristic
515C22#6414611yescharacteristic
516C22C2×D4×C3⋊D311yescharacteristic
517C4—22no—
518C4—42no—
519C4—182no—
520C4—362no—
521C4#6414611yescharacteristic
522C4#6414611yescharacteristic
523C4C2×D4×C3⋊D311yescharacteristic
524C4C22×#63811yescharacteristic
525C3C2×#520214yescomplemented
526C2—21no—
527C2—21no—
528C2—42no—
529C2—364no—
530C2—362no—
531C2#1059290112yesdirect product factor
532C2C2×#6414611yescharacteristic
subgroupG/H
centerC22#64146
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#137C2
socleC22×C32#120
prime radicalC2×#64366C2
hypercenterC2×#137C3⋊D3
hypocenterC32C2×#455
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
2. C2×C32×#137C2semidirect
3. C2×#64156C2semidirect
4. C2×#64151C2semidirect
5. C2×#63664C2semidirect
6. #10592901C2direct (N × H)
7. C2×#63652C2semidirect
8. C2×#63650C2semidirect
11. C22×C32×Q8C22semidirect
24. C32×#137C22semidirect
27. C2×C32×M16C22semidirect
29. #64156C22semidirect
32. #64151C22semidirect
35. C2×C4×C3⋊Dic3C22semidirect
36. C2×#3748C22semidirect
37. #63664C22semidirect
38. #63652C22semidirect
39. #63650C22semidirect
41. C2×C3×#137D3semidirect
60. C2×C32×Q8C23semidirect
97. C32×M16C23semidirect
103. C4×C3⋊Dic3C23semidirect
105. #3748C23semidirect
109. C22×C3×Q8C2×D3semidirect
122. C3×#137C2×D3semidirect
125. C2×C3×M16C2×D3semidirect
191. C2×#137C3⋊D3semidirect
209. C2×C3×Q8C22×D3semidirect
246. C3×M16C22×D3semidirect
285. C22×Q8C2×C3⋊D3semidirect
293. #137C2×C3⋊D3semidirect
299. C2×M16C2×C3⋊D3semidirect
361. C2×C32#455semidirect
386. C2×Q8C22×C3⋊D3semidirect
418. M16C22×C3⋊D3semidirect
445. C32C2×#455semidirect
500. C2×C3#5202semidirect
525. C3C2×#5202semidirect
531. C2#10592901direct (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×C32×#1372
C2×#641562
C2×#641512
C2×#636642
#105929012
C2×#636522
C2×#636502
C2×#52023