Finite Group Databasebeta

← C2×#10595476 #11902932

Subgroups — C2×#10595476 #11902932

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×#64162C211yesmaximal, characteristic
2C22×C3×#217C212yesmaximal, complemented
3C2×#63975C211yesmaximal, characteristic, complemented
4C2×#63966C212yesmaximal, complemented
5C2×#63964C212yesmaximal, complemented
6C2×#63956C212yesmaximal, complemented
7C2×#63955C212yesmaximal, complemented
8#10595476C2116yesmaximal, direct product factor
9C2×#63953C211yesmaximal, characteristic, complemented
10C2×#63952C212yesmaximal, complemented
11C2×#5495—32nomaximal
12C25×C32C2211yescharacteristic
13C22×#638C2212yes—
14C22×#638C2211yescharacteristic
15C23×C3×Dic3C2212yes—
16C23×C3×Dic3C2212yes—
17C22×#627C2211yescharacteristic, complemented
18C22×#624C2211yescharacteristic, complemented
19#64162C2218yes—
20C2×#3757C2212yes—
21C2×#3757C2211yescharacteristic
22C2×C3×#217C2212yes—
23C2×C3×#217C2212yes—
24C2×C3×#217C2212yes—
25C2×C3×#217C2212yes—
26C2×C3×#217C22116yescomplemented
27#63975C2218yescomplemented
28C2×#3724C2212yescomplemented
29#63966C22116yescomplemented
30C2×Dic3⋊Dic3C2212yescomplemented
31C2×Dic3⋊Dic3C2212yescomplemented
32C2×Dic3⋊Dic3C2212yescomplemented
33#63964C22116yescomplemented
34C2×#3722C2212yescomplemented
35C2×#3722C2211yescharacteristic, complemented
36#63956C22116yescomplemented
37#63955C22116yescomplemented
38C2×Dic32C2212yescomplemented
39C2×Dic32C2211yescharacteristic, complemented
40#63953C2218yescomplemented
41#63952C22116yescomplemented
42C22×C3×C22⋊C4—32no—
43C2×#953—32no—
44C2×#953—61no—
45C22×#217D312yescomplemented
46C2×#929—32no—
47C2×C4×#67—32no—
48C2×#926—32no—
49C2×#924—32no—
50#5495—332no—
51C2×#886—32no—
52C2×#885—32no—
53C2×#883—32no—
54C2×#67⋊C4—32no—
55C2×#879—32no—
56C2×#879—32no—
57C2×#878—32no—
58C2×#877—32no—
59C24×C32—28no—
60C24×C32—42no—
61C24×C32C2311yescharacteristic
62C24×C32C2314yes—
63C24×C32C2312yes—
64C23×C3⋊D3C2311yescharacteristic
65C2×#638—28no—
66C2×#638—42no—
67C2×#638C2318yes—
68C2×#638C2314yes—
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3⋊Dic3C2312yes—
71C22×C3×Dic3—28no—
72C22×C3×Dic3—44no—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2318yes—
78C22×C3×Dic3C2318yes—
79C2×#627—42no—
80C2×#627C2314yescomplemented
81C2×#624—42no—
82C2×#624C2314yescomplemented
83#3757C2318yes—
84#3757C2314yes—
85C3×#217C2318yes—
86C3×#217C2318yes—
87C3×#217C2318yes—
88C3×#217C2318yes—
89#3724C2318yescomplemented
90Dic3⋊Dic3C2318yescomplemented
91Dic3⋊Dic3C2318yescomplemented
92Dic3⋊Dic3C2318yescomplemented
93#3722C2318yescomplemented
94#3722C2314yescomplemented
95Dic32C2318yescomplemented
96Dic32C2314yescomplemented
97C2×#551—91noSylow
98C25×C3—21no—
99C25×C3C2×D312yes—
100C23×C3×C4—32no—
101C23×C3×C4—32no—
102C22×#67—32no—
103C22×#67—32no—
104C22×#67—32no—
105C22×#67—62no—
106C22×#67—61no—
107C23×Dic3C2×D312yes—
108C23×Dic3C2×D312yes—
109C22×C4×D3—32no—
110C22×Dic6—32no—
111C2×C3×C22⋊C4—32no—
112C2×C3×C22⋊C4—32no—
113C2×C3×C22⋊C4—32no—
114C2×C3×C22⋊C4—32no—
115C2×C3×C22⋊C4—316no—
116#953—316no—
117#953—68no—
118C2×#217—32no—
119C2×#217—32no—
120C2×#217—32no—
121C2×#217—62no—
122C2×#217—61no—
123C2×#217C2×D312yes—
124C2×#217C2×D312yes—
125C2×#217C2×D312yes—
126C2×#217C2×D312yes—
127C2×#217C2×D3116yescomplemented
128#929—316no—
129C4×#67—316no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133#926—316no—
134C2×C4⋊Dic3—32no—
135C2×C4⋊Dic3—32no—
136C2×C4⋊Dic3—32no—
137#924—316no—
138C2×Dic3⋊C4—32no—
139C2×Dic3⋊C4—32no—
140C2×Dic3⋊C4—32no—
141C2×Dic3⋊C4—32no—
142C2×Dic3⋊C4—32no—
143C2×C4×Dic3—32no—
144C2×C4×Dic3—32no—
145C2×C4×Dic3—32no—
146#886—316no—
147#885—316no—
148#883—316no—
149#67⋊C4—316no—
150#879—316no—
151#879—316no—
152#878—316no—
153#877—316no—
154C23×C32—22no—
155C23×C32—24no—
156C23×C32—24no—
157C23×C32—216no—
158C23×C32—24no—
159C23×C32—44no—
160C23×C32—416no—
161C23×C32#4118yes—
162C23×C32C2412yes—
163C23×C32C2414yes—
164C23×C32C2411yescharacteristic
165C22×C3⋊D3—24no—
166C22×C3⋊D3—22no—
167C22×C3⋊D3C2412yes—
168#638—216no—
169#638—44no—
170C2×C3⋊Dic3—24no—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3C2414yes—
173C2×C3⋊Dic3C2412yes—
174C2×C3×Dic3—216no—
175C2×C3×Dic3—24no—
176C2×C3×Dic3—24no—
177C2×C3×Dic3—24no—
178C2×C3×Dic3—24no—
179C2×C3×Dic3—48no—
180C2×C3×Dic3C2414yes—
181C2×C3×Dic3C2414yes—
182C2×C3×Dic3C2414yes—
183C2×C3×Dic3C2414yes—
184#627—44no—
185#624—44no—
186#551—916no—
187C2×#126—92no—
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—32no—
196C24×C3—28no—
197C24×C3—28no—
198C24×C3—21no—
199C24×C3—22no—
200C24×C3—24no—
201C24×C3—48no—
202C24×C3—44no—
203C24×C3—44no—
204C24×C3C22×D312yes—
205C24×C3C22×D318yes—
206C24×C3C22×D312yes—
207C24×C3C22×D312yes—
208C23×D3—32no—
209C23×D3—61no—
210C22×C3×C4—32no—
211C22×C3×C4—32no—
212C22×C3×C4—32no—
213C22×C3×C4—32no—
214C22×C3×C4—38no—
215C22×C3×C4—38no—
216C22×C3×C4—68no—
217C22×C3×C4—124no—
218C2×#67—38no—
219C2×#67—38no—
220C2×#67—38no—
221C2×#67—68no—
222C2×#67—64no—
223C2×#67—68no—
224C2×#67—68no—
225C2×#67—128no—
226C2×#67—124no—
227C2×#67—124no—
228C22×Dic3—28no—
229C22×Dic3—32no—
230C22×Dic3—32no—
231C22×Dic3—32no—
232C22×Dic3—44no—
233C22×Dic3—62no—
234C22×Dic3—61no—
235C22×Dic3C22×D318yes—
236C22×Dic3C22×D312yes—
237C22×Dic3C22×D312yes—
238C22×Dic3C22×D312yes—
239C22×Dic3C22×D312yes—
240C22×Dic3C22×D318yes—
241C2×C4×D3—38no—
242C2×C4×D3—124no—
243C2×Dic6—38no—
244C2×Dic6—124no—
245C3×C22⋊C4—38no—
246C3×C22⋊C4—38no—
247C3×C22⋊C4—38no—
248C3×C22⋊C4—38no—
249#217—38no—
250#217—38no—
251#217—38no—
252#217—68no—
253#217—64no—
254#217C22×D318yes—
255#217C22×D318yes—
256#217C22×D318yes—
257#217C22×D318yes—
258(C2×D3)⋊C4—38no—
259(C2×D3)⋊C4—38no—
260(C2×D3)⋊C4—38no—
261C4⋊Dic3—38no—
262C4⋊Dic3—38no—
263C4⋊Dic3—38no—
264Dic3⋊C4—38no—
265Dic3⋊C4—38no—
266Dic3⋊C4—38no—
267Dic3⋊C4—38no—
268Dic3⋊C4—38no—
269C4×Dic3—38no—
270C4×Dic3—38no—
271C4×Dic3—38no—
272C22×C32—22no—
273C22×C32—216no—
274C22×C32—24no—
275C22×C32—24no—
276C22×C32—24no—
277C22×C32—416no—
278C22×C32—44no—
279C22×C32C2×#4118yes—
280C22×C32C2×#4114yes—
281C22×C32H(5,𝔽2)12yes—
282C22×C32C2511yescharacteristic
283C2×C3⋊D3—24no—
284C2×C3⋊D3—22no—
285C2×C3⋊D3—44no—
286C3⋊Dic3—24no—
287C3⋊Dic3—22no—
288C3×Dic3—24no—
289C3×Dic3—24no—
290C3×Dic3—24no—
291C3×Dic3—24no—
292C25D3211yescharacteristic
293C22×Q8—91no—
294C22×D4—92no—
295C22×D4—91no—
296C23×C4—32no—
297C23×C4—32no—
298C23×C4—91no—
299#126—916no—
300#124—98no—
301#123—98no—
302#123—916no—
303C22⋊Q8—916no—
304#120—98no—
305C4×D4—916no—
306#117—916no—
307C2×C4⋊C4—92no—
308C2×C4⋊C4—92no—
309C2×C4⋊C4—92no—
310C2×C4⋊C4—92no—
311C2×C22⋊C4—32no—
312C2×C22⋊C4—32no—
313C2×C22⋊C4—32no—
314C2×C22⋊C4—32no—
315C2×C22⋊C4—316no—
316C2×C22⋊C4—92no—
317C2×C22⋊C4—91no—
318C2×C22⋊C4—92no—
319C2×C22⋊C4—91no—
320C2×C42—91no—
321C2×C42—92no—
322C23×C3—24no—
323C23×C3—24no—
324C23×C3—24no—
325C23×C3—24no—
326C23×C3—24no—
327C23×C3—216no—
328C23×C3—24no—
329C23×C3—216no—
330C23×C3—24no—
331C23×C3—24no—
332C23×C3—22no—
333C23×C3—24no—
334C23×C3—21no—
335C23×C3—28no—
336C23×C3—44no—
337C23×C3—44no—
338C23×C3—44no—
339C23×C3—416no—
340C23×C3—48no—
341C23×C3—432no—
342C23×C3—48no—
343C23×C3—432no—
344C23×C3#23518yes—
345C23×C3#23718yes—
346C23×C3C23×D314yes—
347C23×C3C23×D314yes—
348C23×C3C23×D314yes—
349C23×C3C23×D312yes—
350C22×D3—34no—
351C22×D3—62no—
352C22×D3—64no—
353C22×D3—64no—
354C22×D3—64no—
355C22×D3—124no—
356C22×D3—122no—
357C2×C3×C4—34no—
358C2×C3×C4—34no—
359C2×C3×C4—34no—
360C2×C3×C4—34no—
361C2×C3×C4—616no—
362C2×C3×C4—64no—
363C2×C3×C4—64no—
364C2×C3×C4—64no—
365C2×C3×C4—64no—
366C2×C3×C4—128no—
367#67—616no—
368#67—616no—
369#67—1216no—
370#67—128no—
371#67—128no—
372C2×Dic3—216no—
373C2×Dic3—24no—
374C2×Dic3—24no—
375C2×Dic3—24no—
376C2×Dic3—24no—
377C2×Dic3—34no—
378C2×Dic3—34no—
379C2×Dic3—34no—
380C2×Dic3—48no—
381C2×Dic3—64no—
382C2×Dic3—62no—
383C2×Dic3—64no—
384C2×Dic3—64no—
385C2×Dic3—64no—
386C2×Dic3—124no—
387C2×Dic3—122no—
388C2×Dic3C23×D314yes—
389C2×Dic3C23×D314yes—
390C2×Dic3C23×D314yes—
391C2×Dic3C23×D314yes—
392C4×D3—128no—
393Dic6—128no—
394C2×C32—28no—
395C2×C32—42no—
396C2×C32#55114yescomplemented
397C2×C32C22×#4112yes—
398C2×C32C2×H(5,𝔽2)11yescharacteristic
399C3⋊D3—42no—
400C24—28no—
401C24—42no—
402C24—91no—
403C24C2×D3211yescharacteristic
404C24C2×D3214yes—
405C24C2×D3212yes—
406C2×Q8—94no—
407C2×Q8—362no—
408C2×D4—98no—
409C2×D4—94no—
410C2×D4—188no—
411C2×D4—362no—
412C22×C4—38no—
413C22×C4—32no—
414C22×C4—32no—
415C22×C4—32no—
416C22×C4—32no—
417C22×C4—38no—
418C22×C4—68no—
419C22×C4—94no—
420C22×C4—92no—
421C22×C4—91no—
422C22×C4—124no—
423C22×C4—362no—
424C4⋊C4—98no—
425C4⋊C4—98no—
426C4⋊C4—98no—
427C4⋊C4—98no—
428C22⋊C4—38no—
429C22⋊C4—38no—
430C22⋊C4—38no—
431C22⋊C4—38no—
432C22⋊C4—98no—
433C22⋊C4—94no—
434C22⋊C4—98no—
435C22⋊C4—94no—
436C42—94no—
437C42—98no—
438C22×C3—24no—
439C22×C3—24no—
440C22×C3—24no—
441C22×C3—24no—
442C22×C3—216no—
443C22×C3—216no—
444C22×C3—24no—
445C22×C3—24no—
446C22×C3—24no—
447C22×C3—24no—
448C22×C3—24no—
449C22×C3—28no—
450C22×C3—22no—
451C22×C3—21no—
452C22×C3—44no—
453C22×C3—44no—
454C22×C3—416no—
455C22×C3—44no—
456C22×C3—432no—
457C22×C3—48no—
458C22×C3—432no—
459C22×C3—48no—
460C22×C3C2×#23518yes—
461C22×C3C2×#23514yes—
462C22×C3C2×#23718yes—
463C22×C3C2×#23714yes—
464C22×C3#100414yes—
465C22×C3C24×D312yes—
466C2×D3—64no—
467C2×D3—64no—
468C2×D3—64no—
469C2×D3—124no—
470C2×D3—122no—
471C2×D3—128no—
472C2×D3—244no—
473C3×C4—64no—
474C3×C4—64no—
475C3×C4—64no—
476C3×C4—64no—
477Dic3—24no—
478Dic3—24no—
479Dic3—24no—
480Dic3—24no—
481Dic3—64no—
482Dic3—64no—
483Dic3—64no—
484Dic3—124no—
485Dic3—122no—
486C32C2×#55111yescharacteristic, complemented, Sylow
487C23—24no—
488C23—24no—
489C23—216no—
490C23—24no—
491C23—22no—
492C23—44no—
493C23—416no—
494C23—92no—
495C23—184no—
496C23—182no—
497C23#380418yes—
498C23C22×D3212yes—
499C23C22×D3214yes—
500C23C22×D3211yescharacteristic
501Q8—364no—
502D4—1816no—
503D4—364no—
504C2×C4—34no—
505C2×C4—34no—
506C2×C4—34no—
507C2×C4—34no—
508C2×C4—616no—
509C2×C4—64no—
510C2×C4—64no—
511C2×C4—64no—
512C2×C4—64no—
513C2×C4—94no—
514C2×C4—92no—
515C2×C4—128no—
516C2×C4—184no—
517C2×C4—182no—
518C2×C4—364no—
519C2×C3—28no—
520C2×C3—28no—
521C2×C3—22no—
522C2×C3—21no—
523C2×C3—24no—
524C2×C3—48no—
525C2×C3—44no—
526C2×C3—44no—
527C2×C3#549518yescomplemented
528C2×C3C22×#23512yes—
529C2×C3C22×#23712yes—
530C2×C3C2×#100412yes—
531D3—124no—
532D3—242no—
533C22—24no—
534C22—24no—
535C22—216no—
536C22—24no—
537C22—22no—
538C22—416no—
539C22—44no—
540C22—184no—
541C22—182no—
542C22—364no—
543C22C2×#380418yes—
544C22C2×#380414yes—
545C22#6433012yes—
546C22C23×D3211yescharacteristic
547C4—64no—
548C4—64no—
549C4—64no—
550C4—64no—
551C4—184no—
552C4—182no—
553C3—21no—
554C3C2×#549512yescomplemented
555C2—28no—
556C2—42no—
557C2—362no—
558C2#1059547614yesdirect product factor
559C2C22×#380412yes—
560C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC25×C32C22
socleC23×C32C24
prime radicalC2×#64162C2
hypercenterC25D32
hypocenterC32C2×#551
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C25

Complements

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

NH ≅ G/Ntype
2. C22×C3×#217C2semidirect
3. C2×#63975C2semidirect
4. C2×#63966C2semidirect
5. C2×#63964C2semidirect
6. C2×#63956C2semidirect
7. C2×#63955C2semidirect
8. #10595476C2direct (N × H)
9. C2×#63953C2semidirect
10. C2×#63952C2semidirect
17. C22×#627C22semidirect
18. C22×#624C22semidirect
26. C2×C3×#217C22semidirect
27. #63975C22semidirect
28. C2×#3724C22semidirect
29. #63966C22semidirect
30. C2×Dic3⋊Dic3C22semidirect
31. C2×Dic3⋊Dic3C22semidirect
32. C2×Dic3⋊Dic3C22semidirect
33. #63964C22semidirect
34. C2×#3722C22semidirect
35. C2×#3722C22semidirect
36. #63956C22semidirect
37. #63955C22semidirect
38. C2×Dic32C22semidirect
39. C2×Dic32C22semidirect
40. #63953C22semidirect
41. #63952C22semidirect
45. C22×#217D3semidirect
80. C2×#627C23semidirect
82. C2×#624C23semidirect
89. #3724C23semidirect
90. Dic3⋊Dic3C23semidirect
91. Dic3⋊Dic3C23semidirect
92. Dic3⋊Dic3C23semidirect
93. #3722C23semidirect
94. #3722C23semidirect
95. Dic32C23semidirect
96. Dic32C23semidirect
127. C2×#217C2×D3semidirect
396. C2×C32#551semidirect
486. C32C2×#551semidirect
527. C2×C3#5495semidirect
554. C3C2×#5495semidirect
558. C2#10595476direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641622
C22×C3×#2172
C2×#639752
C2×#639662
C2×#639642
C2×#639562
C2×#639552
#105954762
C2×#639532
C2×#639522
C2×#54953