Finite Group Databasebeta

← C2×#10594165 #11902953

Subgroups — C2×#10594165 #11902953

Order 1152.

2987 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64091C211yesmaximal, characteristic
2C2×C3×#879C212yesmaximal, complemented
3C2×#63975C211yesmaximal, characteristic, complemented
4C2×#63974C212yesmaximal, complemented
5C2×#63953C211yesmaximal, characteristic, complemented
6C2×#63897C212yesmaximal, complemented
7C2×#63895C212yesmaximal, complemented
8C2×#63894C212yesmaximal, complemented
9C2×#63836C212yesmaximal, complemented
10#10594165C2116yesmaximal, direct product factor
11C2×#5705—32nomaximal
12C24×C3⋊D3C2211yescharacteristic
13C22×#638C2211yescharacteristic
14C22×C4⋊(C3⋊D3)C2212yes—
15C22×#627C2211yescharacteristic, complemented
16C22×#624C2212yes—
17C22×#624C2212yes—
18C22×#624C2211yescharacteristic, complemented
19C2×C32×C22⋊C4C2211yescharacteristic
20C2×#3752C2212yes—
21#64091C2218yes—
22C2×C3×#217C2212yes—
23C2×C3×#217C2212yes—
24C2×C3×C4⋊Dic3C2212yescomplemented
25C2×C3×Dic3⋊C4C2212yescomplemented
26C2×C3×Dic3⋊C4C2212yescomplemented
27C2×C3×C4×Dic3C2212yescomplemented
28C3×#879C22116yescomplemented
29#63975C2218yescomplemented
30#63974C22116yescomplemented
31C2×Dic3⋊Dic3C2212yescomplemented
32C2×#3722C2212yes—
33C2×#3722C2212yes—
34C2×#3722C2212yescomplemented
35C2×#3722C2211yescharacteristic, complemented
36C2×Dic32C2211yescharacteristic, complemented
37#63953C2218yescomplemented
38#63897C22116yescomplemented
39#63895C22116yescomplemented
40#63894C22116yescomplemented
41#63836C22116yescomplemented
42C2×C3×#126—32no—
43#5705—332no—
44C2×#897—32no—
45C2×#896—32no—
46C2×#894—32no—
47C2×#894—32no—
48C2×#893—32no—
49C2×#892—32no—
50C2×#885—32no—
51C2×#883—32no—
52C2×#882—32no—
53C2×#882—61no—
54C2×D3×C22⋊C4—32no—
55C2×D3×C22⋊C4—32no—
56C2×#879D312yescomplemented
57C2×C4×D12—32no—
58C2×#872—32no—
59C24×C32C2311yescharacteristic
60C23×C3⋊D3—28no—
61C23×C3⋊D3—42no—
62C23×C3⋊D3C2311yescharacteristic
63C23×C3⋊D3C2314yes—
64C23×C3⋊D3C2312yes—
65C22×C32×C4C2312yes—
66C2×#638—42no—
67C2×#638C2314yes—
68C22×C3⋊Dic3C2311yescharacteristic
69C2×C4⋊(C3⋊D3)—28no—
70C2×C4⋊(C3⋊D3)C2318yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C2×#627—42no—
76C2×#627C2314yescomplemented
77C2×#624—28no—
78C2×#624—44no—
79C2×#624—42no—
80C2×#624C2318yes—
81C2×#624C2318yes—
82C2×#624C2314yescomplemented
83C32×C22⋊C4C2314yes—
84#3752C2318yes—
85C3×#217C2318yes—
86C3×#217C2318yes—
87C3×C4⋊Dic3C2318yescomplemented
88C3×Dic3⋊C4C2318yescomplemented
89C3×Dic3⋊C4C2318yescomplemented
90C3×C4×Dic3C2318yescomplemented
91Dic3⋊Dic3C2318yescomplemented
92#3722C2318yes—
93#3722C2318yes—
94#3722C2318yescomplemented
95#3722C2314yescomplemented
96Dic32C2314yescomplemented
97C2×#551—91noSylow
98C24×D3—32no—
99C24×D3—61no—
100C22×#67—32no—
101C22×#67—61no—
102C22×D12—32no—
103C22×D12—32no—
104C22×D12—62no—
105C22×C4×D3—32no—
106C22×C4×D3—32no—
107C22×C4×D3—32no—
108C22×C4×D3—32no—
109C22×C4×D3—32no—
110C22×Dic6—32no—
111C3×#126—316no—
112C2×C3×C4⋊C4—32no—
113C2×C3×C4⋊C4—32no—
114C2×C3×C4⋊C4—32no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—32no—
117C2×C3×C22⋊C4—32no—
118C2×C3×C22⋊C4C2×D312yes—
119C2×C3×C42—32no—
120C2×#217C2×D312yes—
121C2×#217C2×D312yes—
122C2×(C2×D3)⋊C4—32no—
123C2×(C2×D3)⋊C4—32no—
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4—32no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4—32no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—62no—
132C2×C4⋊Dic3—32no—
133C2×C4⋊Dic3C2×D312yescomplemented
134C2×Dic3⋊C4—32no—
135C2×Dic3⋊C4C2×D312yescomplemented
136C2×Dic3⋊C4C2×D312yescomplemented
137C2×C4×Dic3—32no—
138C2×C4×Dic3C2×D312yescomplemented
139#897—316no—
140#896—316no—
141#894—316no—
142#894—316no—
143#893—316no—
144#892—316no—
145#885—316no—
146#883—316no—
147#882—316no—
148#882—68no—
149D3×C22⋊C4—316no—
150D3×C22⋊C4—316no—
151#879C2×D3116yescomplemented
152C4×D12—316no—
153#872—316no—
154C23×C32—22no—
155C23×C32—24no—
156C23×C32C2412yes—
157C23×C32C2411yescharacteristic
158C22×C3⋊D3—24no—
159C22×C3⋊D3—24no—
160C22×C3⋊D3—24no—
161C22×C3⋊D3—22no—
162C22×C3⋊D3—216no—
163C22×C3⋊D3—44no—
164C22×C3⋊D3—416no—
165C22×C3⋊D3#4118yes—
166C22×C3⋊D3C2412yes—
167C22×C3⋊D3C2414yes—
168C2×C32×C4—24no—
169C2×C32×C4C2414yes—
170#638—44no—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3C2412yes—
173C4⋊(C3⋊D3)—216no—
174C2×C3×Dic3—24no—
175C2×C3×Dic3—24no—
176C2×C3×Dic3—24no—
177C2×C3×Dic3—24no—
178C2×C3×Dic3C2414yes—
179C2×C3×Dic3C2414yes—
180C2×C3×Dic3C2414yes—
181C2×C3×Dic3C2414yes—
182#627—44no—
183#624—216no—
184#624—48no—
185#624—44no—
186#551—916no—
187C2×#126—32no—
188C2×#124—91no—
189C2×#123—91no—
190C2×#123—92no—
191C2×C22⋊Q8—92no—
192C2×#120—91no—
193C2×C4×D4—92no—
194C2×#117—92no—
195C22×C22⋊C4—92no—
196C24×C3—21no—
197C24×C3C22×D312yes—
198C23×D3—32no—
199C23×D3—32no—
200C23×D3—32no—
201C23×D3—38no—
202C23×D3—62no—
203C23×D3—64no—
204C23×D3—61no—
205C23×D3—68no—
206C23×D3—68no—
207C23×D3—128no—
208C23×D3—124no—
209C23×D3—124no—
210C22×C3×C4—22no—
211C22×C3×C4—32no—
212C22×C3×C4—32no—
213C22×C3×C4—32no—
214C22×C3×C4—32no—
215C22×C3×C4C22×D312yes—
216C22×C3×C4C22×D312yes—
217C2×#67—38no—
218C2×#67—64no—
219C2×#67—124no—
220C2×#67—124no—
221C22×Dic3—32no—
222C22×Dic3—61no—
223C22×Dic3C22×D312yes—
224C22×Dic3C22×D312yes—
225C22×Dic3C22×D312yes—
226C22×Dic3C22×D312yes—
227C2×D12—38no—
228C2×D12—38no—
229C2×D12—68no—
230C2×D12—68no—
231C2×D12—68no—
232C2×D12—128no—
233C2×C4×D3—38no—
234C2×C4×D3—38no—
235C2×C4×D3—38no—
236C2×C4×D3—38no—
237C2×C4×D3—38no—
238C2×C4×D3—68no—
239C2×C4×D3—68no—
240C2×C4×D3—124no—
241C2×C4×D3—124no—
242C2×C4×D3—124no—
243C2×Dic6—38no—
244C2×Dic6—124no—
245C3×C4⋊C4—38no—
246C3×C4⋊C4—38no—
247C3×C4⋊C4—38no—
248C3×C22⋊C4—24no—
249C3×C22⋊C4—38no—
250C3×C22⋊C4—38no—
251C3×C22⋊C4C22×D318yes—
252C3×C42—38no—
253#217C22×D318yes—
254#217C22×D318yes—
255(C2×D3)⋊C4—38no—
256(C2×D3)⋊C4—38no—
257(C2×D3)⋊C4—38no—
258(C2×D3)⋊C4—38no—
259(C2×D3)⋊C4—38no—
260(C2×D3)⋊C4—38no—
261(C2×D3)⋊C4—38no—
262(C2×D3)⋊C4—38no—
263(C2×D3)⋊C4—38no—
264(C2×D3)⋊C4—68no—
265C4⋊Dic3—38no—
266C4⋊Dic3C22×D318yescomplemented
267Dic3⋊C4—38no—
268Dic3⋊C4C22×D318yescomplemented
269Dic3⋊C4C22×D318yescomplemented
270C4×Dic3—38no—
271C4×Dic3C22×D318yescomplemented
272C22×C32—22no—
273C22×C32—24no—
274C22×C32—44no—
275C22×C32C2×#4114yes—
276C22×C32H(5,𝔽2)12yes—
277C22×C32C2511yescharacteristic
278C2×C3⋊D3—216no—
279C2×C3⋊D3—24no—
280C2×C3⋊D3—24no—
281C2×C3⋊D3—24no—
282C2×C3⋊D3—22no—
283C2×C3⋊D3—416no—
284C2×C3⋊D3—44no—
285C2×C3⋊D3C2×#4118yes—
286C32×C4—24no—
287C3⋊Dic3—22no—
288C3×Dic3—24no—
289C3×Dic3—24no—
290C3×Dic3—24no—
291C3×Dic3—24no—
292C25—91no—
293C22×Q8—91no—
294C22×D4—91no—
295C22×D4—92no—
296C23×C4—92no—
297C23×C4—92no—
298C23×C4—91no—
299#126—316no—
300#124—98no—
301#123—98no—
302#123—916no—
303C22⋊Q8—916no—
304#120—98no—
305C4×D4—916no—
306#117—916no—
307C2×C4⋊C4—32no—
308C2×C4⋊C4—32no—
309C2×C4⋊C4—32no—
310C2×C4⋊C4—92no—
311C2×C22⋊C4—32no—
312C2×C22⋊C4—32no—
313C2×C22⋊C4—916no—
314C2×C22⋊C4—92no—
315C2×C22⋊C4—92no—
316C2×C22⋊C4—92no—
317C2×C22⋊C4—91no—
318C2×C22⋊C4—92no—
319C2×C22⋊C4D3211yescharacteristic
320C2×C42—32no—
321C2×C42—91no—
322C23×C3—24no—
323C23×C3—24no—
324C23×C3—24no—
325C23×C3—24no—
326C23×C3—22no—
327C23×C3—21no—
328C23×C3—44no—
329C23×C3C23×D314yes—
330C23×C3C23×D312yes—
331C22×D3—38no—
332C22×D3—38no—
333C22×D3—34no—
334C22×D3—34no—
335C22×D3—34no—
336C22×D3—68no—
337C22×D3—64no—
338C22×D3—62no—
339C22×D3—616no—
340C22×D3—616no—
341C22×D3—64no—
342C22×D3—64no—
343C22×D3—64no—
344C22×D3—64no—
345C22×D3—64no—
346C22×D3—64no—
347C22×D3—64no—
348C22×D3—1216no—
349C22×D3—124no—
350C22×D3—124no—
351C22×D3—124no—
352C22×D3—122no—
353C22×D3—128no—
354C22×D3—1232no—
355C22×D3—128no—
356C22×D3—1232no—
357C2×C3×C4—24no—
358C2×C3×C4—24no—
359C2×C3×C4—24no—
360C2×C3×C4—34no—
361C2×C3×C4—34no—
362C2×C3×C4—34no—
363C2×C3×C4—34no—
364C2×C3×C4—44no—
365C2×C3×C4—64no—
366C2×C3×C4—64no—
367C2×C3×C4—64no—
368C2×C3×C4—64no—
369C2×C3×C4C23×D314yes—
370C2×C3×C4C23×D314yes—
371#67—128no—
372#67—128no—
373C2×Dic3—24no—
374C2×Dic3—24no—
375C2×Dic3—24no—
376C2×Dic3—24no—
377C2×Dic3—34no—
378C2×Dic3—62no—
379C2×Dic3—64no—
380C2×Dic3—122no—
381C2×Dic3C23×D314yes—
382C2×Dic3C23×D314yes—
383C2×Dic3C23×D314yes—
384C2×Dic3C23×D314yes—
385D12—616no—
386D12—616no—
387D12—1216no—
388C4×D3—616no—
389C4×D3—616no—
390C4×D3—128no—
391C4×D3—128no—
392C4×D3—128no—
393Dic6—128no—
394C2×C32—42no—
395C2×C32#55114yescomplemented
396C2×C32C22×#4112yes—
397C2×C32C2×H(5,𝔽2)11yescharacteristic
398C3⋊D3—28no—
399C3⋊D3—42no—
400C24—92no—
401C24—91no—
402C24—94no—
403C24—188no—
404C24—362no—
405C24C2×D3211yescharacteristic
406C2×Q8—94no—
407C2×Q8—362no—
408C2×D4—94no—
409C2×D4—98no—
410C2×D4—188no—
411C2×D4—362no—
412C22×C4—32no—
413C22×C4—32no—
414C22×C4—32no—
415C22×C4—32no—
416C22×C4—98no—
417C22×C4—98no—
418C22×C4—94no—
419C22×C4—91no—
420C22×C4—188no—
421C22×C4—362no—
422C22×C4—364no—
423C22×C4C2×D3212yes—
424C4⋊C4—38no—
425C4⋊C4—38no—
426C4⋊C4—38no—
427C4⋊C4—98no—
428C22⋊C4—38no—
429C22⋊C4—38no—
430C22⋊C4—98no—
431C22⋊C4—98no—
432C22⋊C4—98no—
433C22⋊C4—94no—
434C22⋊C4—98no—
435C22⋊C4C2×D3214yes—
436C42—38no—
437C42—94no—
438C22×C3—24no—
439C22×C3—24no—
440C22×C3—24no—
441C22×C3—24no—
442C22×C3—22no—
443C22×C3—24no—
444C22×C3—21no—
445C22×C3—44no—
446C22×C3—48no—
447C22×C3—48no—
448C22×C3D3×#4114yes—
449C22×C3D3×#4114yes—
450C22×C3#100914yes—
451C22×C3C24×D312yes—
452C2×D3—38no—
453C2×D3—38no—
454C2×D3—68no—
455C2×D3—616no—
456C2×D3—616no—
457C2×D3—64no—
458C2×D3—64no—
459C2×D3—64no—
460C2×D3—64no—
461C2×D3—64no—
462C2×D3—64no—
463C2×D3—64no—
464C2×D3—124no—
465C2×D3—124no—
466C2×D3—1216no—
467C2×D3—124no—
468C2×D3—122no—
469C2×D3—1232no—
470C2×D3—1232no—
471C2×D3—128no—
472C2×D3—244no—
473C3×C4—24no—
474C3×C4—24no—
475C3×C4—44no—
476C3×C4—64no—
477C3×C4—64no—
478C3×C4—64no—
479C3×C4—64no—
480Dic3—24no—
481Dic3—24no—
482Dic3—24no—
483Dic3—24no—
484Dic3—64no—
485Dic3—122no—
486C32C2×#55111yescharacteristic, complemented, Sylow
487C23—22no—
488C23—24no—
489C23—98no—
490C23—94no—
491C23—92no—
492C23—1816no—
493C23—184no—
494C23—184no—
495C23—182no—
496C23—184no—
497C23—364no—
498C23—3616no—
499C23C22×D3212yes—
500C23C22×D3211yescharacteristic
501Q8—364no—
502D4—1816no—
503D4—364no—
504C2×C4—24no—
505C2×C4—34no—
506C2×C4—34no—
507C2×C4—34no—
508C2×C4—34no—
509C2×C4—64no—
510C2×C4—64no—
511C2×C4—64no—
512C2×C4—64no—
513C2×C4—92no—
514C2×C4—1816no—
515C2×C4—182no—
516C2×C4—364no—
517C2×C4—368no—
518C2×C4C22×D3214yes—
519C2×C3—21no—
520C2×C3—22no—
521C2×C3—24no—
522C2×C3—44no—
523C2×C3—44no—
524C2×C3#570518yescomplemented
525C2×C3C2×D3×#4112yes—
526C2×C3C2×D3×#4112yes—
527C2×C3C2×#100912yes—
528D3—68no—
529D3—68no—
530D3—128no—
531D3—124no—
532D3—242no—
533C22—22no—
534C22—24no—
535C22—44no—
536C22—98no—
537C22—184no—
538C22—184no—
539C22—1816no—
540C22—182no—
541C22—184no—
542C22—3616no—
543C22—364no—
544C22#6430812yes—
545C22#6431214yes—
546C22C23×D3211yescharacteristic
547C4—24no—
548C4—64no—
549C4—64no—
550C4—64no—
551C4—64no—
552C4—182no—
553C3—21no—
554C3C2×#570512yescomplemented
555C2—42no—
556C2—188no—
557C2—362no—
558C2#1059416514yesdirect product factor
559C2C2×#6430811yescharacteristic
560C2C2×#6431212yes—
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC2×#64091C2
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#551
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#879C2semidirect
3. C2×#63975C2semidirect
4. C2×#63974C2semidirect
5. C2×#63953C2semidirect
6. C2×#63897C2semidirect
7. C2×#63895C2semidirect
8. C2×#63894C2semidirect
9. C2×#63836C2semidirect
10. #10594165C2direct (N × H)
15. C22×#627C22semidirect
18. C22×#624C22semidirect
24. C2×C3×C4⋊Dic3C22semidirect
25. C2×C3×Dic3⋊C4C22semidirect
26. C2×C3×Dic3⋊C4C22semidirect
27. C2×C3×C4×Dic3C22semidirect
28. C3×#879C22semidirect
29. #63975C22semidirect
30. #63974C22semidirect
31. C2×Dic3⋊Dic3C22semidirect
34. C2×#3722C22semidirect
35. C2×#3722C22semidirect
36. C2×Dic32C22semidirect
37. #63953C22semidirect
38. #63897C22semidirect
39. #63895C22semidirect
40. #63894C22semidirect
41. #63836C22semidirect
56. C2×#879D3semidirect
76. C2×#627C23semidirect
82. C2×#624C23semidirect
87. C3×C4⋊Dic3C23semidirect
88. C3×Dic3⋊C4C23semidirect
89. C3×Dic3⋊C4C23semidirect
90. C3×C4×Dic3C23semidirect
91. Dic3⋊Dic3C23semidirect
94. #3722C23semidirect
95. #3722C23semidirect
96. Dic32C23semidirect
133. C2×C4⋊Dic3C2×D3semidirect
135. C2×Dic3⋊C4C2×D3semidirect
136. C2×Dic3⋊C4C2×D3semidirect
138. C2×C4×Dic3C2×D3semidirect
151. #879C2×D3semidirect
266. C4⋊Dic3C22×D3semidirect
268. Dic3⋊C4C22×D3semidirect
269. Dic3⋊C4C22×D3semidirect
271. C4×Dic3C22×D3semidirect
395. C2×C32#551semidirect
486. C32C2×#551semidirect
524. C2×C3#5705semidirect
554. C3C2×#5705semidirect
558. C2#10594165direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640912
C2×C3×#8792
C2×#639752
C2×#639742
C2×#639532
C2×#638972
C2×#638952
C2×#638942
C2×#638362
#105941652
C2×#57053