Finite Group Databasebeta

← C2×#10593647 #11923032

Subgroups — C2×#10593647 #11923032

Order 1152.

1686 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 1686 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3⋊S4C211yesmaximal, characteristic
2C22×C3×C4×A4C211yesmaximal, characteristic, complemented
3C22×C3⋊SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
4#10593647C214yesmaximal, direct product factor
5C2×(C2×S4)⋊C4—33nomaximal
6C2×#5213—31nomaximal
7C23×C3×A4C2211yescharacteristic
8C22×C3⋊S4—22no—
9C22×C3⋊S4—22no—
10C22×C3⋊S4C414yescomplemented
11C22×C3⋊S4C2212yes—
12C2×C3×C4×A4—22no—
13C2×C3×C4×A4C2212yescomplemented
14C2×C3⋊SL(2,ℤ/4)—22no—
15C2×C3⋊SL(2,ℤ/4)C2212yescomplemented
16C2×#3752—41nomaximal
17C23×S4—33no—
18C24×C3×C4D311yescharacteristic, complemented
19C23×#67—31no—
20C22×C4×A4D313yescomplemented
21C22×SL(2,ℤ/4)—33no—
22C22×#217—31no—
23C22×(C2×D3)⋊C4—31no—
24C22×(C2×D3)⋊C4—31no—
25(C2×S4)⋊C4—312no—
26#5213—34no—
27#5213—34no—
28C2×C3⋊#95—31no—
29C2×C3⋊#95—31no—
30C23×C3⋊D3—41no—
31C22×C3×A4C2×C412yes—
32C22×C3×A4D412yes—
33C22×C3×A4D412yes—
34C22×C3×A4C2311yescharacteristic
35C2×C3⋊S4—28no—
36C2×C3⋊S4—22no—
37C2×C3⋊S4—22no—
38C2×C3⋊S4C2×C414yescomplemented
39C22×C32×C4—41no—
40C22×C3⋊Dic3—41no—
41C3×C4×A4—22no—
42C3⋊SL(2,ℤ/4)—22no—
43#3752—44no—
44C2×#386—91noSylow
45C25×C3C2×D311yescharacteristic
46C24×D3—31no—
47C23×A4C2×D313yes—
48C22×S4—312no—
49C22×S4—36no—
50C22×S4—66no—
51C22×S4—66no—
52C23×C3×C4—22no—
53C23×C3×C4—31no—
54C23×C3×C4—31no—
55C23×C3×C4—32no—
56C23×C3×C4—62no—
57C23×C3×C4C2×D312yescomplemented
58C22×#67—34no—
59C22×#67—32no—
60C22×#67—34no—
61C22×#67—32no—
62C22×#67—62no—
63C22×#67—62no—
64C22×#67—62no—
65C22×#67—62no—
66C23×Dic3—31no—
67C23×Dic3—31no—
68C23×Dic3—31no—
69C2×C4×A4—26no—
70C2×C4×A4C2×D316yescomplemented
71C2×SL(2,ℤ/4)—36no—
72C2×SL(2,ℤ/4)—66no—
73C2×#217—32no—
74C2×#217—32no—
75C2×#217—62no—
76C2×#217—62no—
77C2×(C2×D3)⋊C4—34no—
78C2×(C2×D3)⋊C4—34no—
79C2×(C2×D3)⋊C4—64no—
80C2×(C2×D3)⋊C4—61no—
81C2×(C2×D3)⋊C4—62no—
82C2×(C2×D3)⋊C4—61no—
83C2×(C2×D3)⋊C4—123no—
84C3⋊#95—34no—
85C3⋊#95—34no—
86C23×C32—41no—
87C22×C3⋊D3—44no—
88C22×C3⋊D3—42no—
89C22×C3⋊D3—82no—
90C22×C3⋊D3—82no—
91C2×C3×A4C22⋊C414yescomplemented
92C2×C3×A4C22×C411yescharacteristic
93C2×C3×A4C2×D411yescharacteristic
94C2×C3×A4C2×D411yescharacteristic
95C3⋊S4—24no—
96C2×C32×C4—42no—
97C2×C32×C4—82no—
98C2×C3⋊Dic3—42no—
99C2×C3⋊Dic3—82no—
100C23×D4—91no—
101C24×C4C3⋊D311yescharacteristic, complemented
102C22×C22⋊C4—91no—
103C22×C22⋊C4—91no—
104C22×C22⋊C4—91no—
105#386—94no—
106#386—94no—
107C2×#95—91no—
108C2×#95—91no—
109C24×C3—31no—
110C24×C3—31no—
111C24×C3—32no—
112C24×C3—32no—
113C24×C3—32no—
114C24×C3C4×D312yes—
115C24×C3D1212yes—
116C24×C3#6712yes—
117C24×C3C22×D311yescharacteristic
118C23×D3—32no—
119C23×D3—34no—
120C23×D3—62no—
121C23×D3—61no—
122C23×D3—62no—
123C23×D3—62no—
124C23×D3—62no—
125C23×D3—62no—
126C23×D3—61no—
127C23×D3—123no—
128C22×A4C4×D316yes—
129C22×A4D1216yes—
130C22×A4#6716yes—
131C22×A4C22×D313yes—
132C2×S4—312no—
133C2×S4—624no—
134C2×S4—66no—
135C2×S4—66no—
136C22×C3×C4—22no—
137C22×C3×C4—32no—
138C22×C3×C4—34no—
139C22×C3×C4—31no—
140C22×C3×C4—32no—
141C22×C3×C4—32no—
142C22×C3×C4—43no—
143C22×C3×C4—62no—
144C22×C3×C4—62no—
145C22×C3×C4—61no—
146C22×C3×C4—62no—
147C22×C3×C4—64no—
148C22×C3×C4—64no—
149C22×C3×C4—62no—
150C22×C3×C4S411yescharacteristic, complemented
151C2×#67—38no—
152C2×#67—34no—
153C2×#67—34no—
154C2×#67—64no—
155C2×#67—62no—
156C2×#67—64no—
157C2×#67—62no—
158C2×#67—68no—
159C2×#67—68no—
160C2×#67—68no—
161C2×#67—68no—
162C2×#67—62no—
163C2×#67—62no—
164C22×Dic3—32no—
165C22×Dic3—34no—
166C22×Dic3—32no—
167C22×Dic3—32no—
168C22×Dic3—62no—
169C22×Dic3—62no—
170C22×Dic3—62no—
171C22×Dic3—61no—
172C22×Dic3—62no—
173C22×Dic3—62no—
174C22×Dic3—62no—
175C22×Dic3—62no—
176C22×Dic3—61no—
177C22×Dic3—123no—
178C4×A4—26no—
179SL(2,ℤ/4)—66no—
180#217—64no—
181#217—62no—
182#217—62no—
183(C2×D3)⋊C4—68no—
184(C2×D3)⋊C4—64no—
185(C2×D3)⋊C4—64no—
186(C2×D3)⋊C4—1212no—
187C22×C32—42no—
188C22×C32—42no—
189C22×C32—42no—
190C22×C32—41no—
191C2×C3⋊D3—44no—
192C2×C3⋊D3—82no—
193C2×C3⋊D3—88no—
194C2×C3⋊D3—82no—
195C3×A4C2×C22⋊C411yescharacteristic, complemented
196C32×C4—82no—
197C3⋊Dic3—82no—
198C25—91no—
199C25C2×C3⋊D311yescharacteristic
200C22×D4—92no—
201C22×D4—94no—
202C22×D4—94no—
203C22×D4—92no—
204C22×D4—182no—
205C22×D4—182no—
206C22×D4—182no—
207C22×D4—182no—
208C23×C4—22no—
209C23×C4—31no—
210C23×C4—31no—
211C23×C4—32no—
212C23×C4—62no—
213C23×C4—91no—
214C23×C4—91no—
215C23×C4—91no—
216C23×C4C2×C3⋊D312yescomplemented
217C2×C22⋊C4—94no—
218C2×C22⋊C4—94no—
219C2×C22⋊C4—92no—
220C2×C22⋊C4—92no—
221C2×C22⋊C4—184no—
222C2×C22⋊C4—181no—
223C2×C22⋊C4—182no—
224C2×C22⋊C4—182no—
225C2×C22⋊C4—182no—
226C2×C22⋊C4—181no—
227#95—94no—
228#95—94no—
229C23×C3—32no—
230C23×C3—32no—
231C23×C3—32no—
232C23×C3—32no—
233C23×C3—32no—
234C23×C3—32no—
235C23×C3—31no—
236C23×C3—31no—
237C23×C3—32no—
238C23×C3—31no—
239C23×C3—32no—
240C23×C3—31no—
241C23×C3—32no—
242C23×C3—31no—
243C23×C3—34no—
244C23×C3—34no—
245C23×C3—34no—
246C23×C3—43no—
247C23×C3—61no—
248C23×C3—61no—
249C23×C3—61no—
250C23×C3—64no—
251C23×C3(C2×D3)⋊C414yescomplemented
252C23×C3C2×C4×D311yescharacteristic
253C23×C3C2×D1211yescharacteristic
254C23×C3C2×#6711yescharacteristic
255C23×C3C2×S411yescharacteristic
256C22×D3—34no—
257C22×D3—62no—
258C22×D3—62no—
259C22×D3—68no—
260C22×D3—62no—
261C22×D3—62no—
262C22×D3—68no—
263C22×D3—62no—
264C22×D3—64no—
265C22×D3—64no—
266C22×D3—62no—
267C22×D3—126no—
268C22×D3—1212no—
269C22×D3—122no—
270C22×D3—124no—
271C22×D3—124no—
272C22×D3—122no—
273C22×D3—122no—
274C22×D3—122no—
275C22×D3—246no—
276C22×D3—246no—
277C2×A4(C2×D3)⋊C4112yescomplemented
278C2×A4C2×C4×D313yes—
279C2×A4C2×D1213yes—
280C2×A4C2×#6713yes—
281S4—612no—
282C2×C3×C4—22no—
283C2×C3×C4—34no—
284C2×C3×C4—32no—
285C2×C3×C4—46no—
286C2×C3×C4—62no—
287C2×C3×C4—62no—
288C2×C3×C4—64no—
289C2×C3×C4—64no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—86no—
293C2×C3×C4C2×S412yescomplemented
294#67—616no—
295#67—64no—
296#67—64no—
297#67—64no—
298#67—64no—
299C2×Dic3—34no—
300C2×Dic3—62no—
301C2×Dic3—68no—
302C2×Dic3—62no—
303C2×Dic3—62no—
304C2×Dic3—62no—
305C2×Dic3—62no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C2×Dic3—126no—
310C2×Dic3—124no—
311C2×Dic3—122no—
312C2×Dic3—122no—
313C2×Dic3—246no—
314C2×C32—41no—
315C2×C32—41no—
316C2×C32—44no—
317C2×C32—41no—
318C3⋊D3—84no—
319C24—31no—
320C24—31no—
321C24—32no—
322C24—32no—
323C24—32no—
324C24—92no—
325C24—94no—
326C24—182no—
327C24—181no—
328C24—182no—
329C24—182no—
330C24—182no—
331C24—182no—
332C24—181no—
333C24C4×C3⋊D312yes—
334C24C4⋊(C3⋊D3)12yes—
335C24#63812yes—
336C24C22×C3⋊D311yescharacteristic
337C2×D4—98no—
338C2×D4—94no—
339C2×D4—94no—
340C2×D4—184no—
341C2×D4—182no—
342C2×D4—184no—
343C2×D4—182no—
344C2×D4—188no—
345C2×D4—188no—
346C2×D4—188no—
347C2×D4—188no—
348C2×D4—182no—
349C2×D4—182no—
350C22×C4—22no—
351C22×C4—32no—
352C22×C4—34no—
353C22×C4—31no—
354C22×C4—32no—
355C22×C4—32no—
356C22×C4—62no—
357C22×C4—62no—
358C22×C4—61no—
359C22×C4—62no—
360C22×C4—64no—
361C22×C4—64no—
362C22×C4—62no—
363C22×C4—92no—
364C22×C4—94no—
365C22×C4—92no—
366C22×C4—92no—
367C22×C4—182no—
368C22×C4—182no—
369C22×C4—182no—
370C22×C4—182no—
371C22×C4—182no—
372C22×C4—181no—
373C22×C4—182no—
374C22×C4—182no—
375C22×C4—181no—
376C22×C4C3⋊S411yescharacteristic, complemented
377C22⋊C4—188no—
378C22⋊C4—184no—
379C22⋊C4—184no—
380C22⋊C4—182no—
381C22⋊C4—182no—
382C22⋊C4—184no—
383C22×C3—34no—
384C22×C3—31no—
385C22×C3—31no—
386C22×C3—31no—
387C22×C3—31no—
388C22×C3—31no—
389C22×C3—32no—
390C22×C3—31no—
391C22×C3—31no—
392C22×C3—32no—
393C22×C3—34no—
394C22×C3—34no—
395C22×C3—34no—
396C22×C3—34no—
397C22×C3—31no—
398C22×C3—31no—
399C22×C3—32no—
400C22×C3—46no—
401C22×C3—46no—
402C22×C3—46no—
403C22×C3—43no—
404C22×C3—61no—
405C22×C3—62no—
406C22×C3—62no—
407C22×C3—62no—
408C22×C3C2×(C2×D3)⋊C411yescharacteristic, complemented
409C22×C3C4×S412yes—
410C22×C3C4⋊S412yes—
411C22×C3GL(2,ℤ/4)12yes—
412C22×C3C22×S411yescharacteristic
413C2×D3—64no—
414C2×D3—64no—
415C2×D3—64no—
416C2×D3—1212no—
417C2×D3—122no—
418C2×D3—128no—
419C2×D3—122no—
420C2×D3—122no—
421C2×D3—128no—
422C2×D3—122no—
423C2×D3—2424no—
424C2×D3—246no—
425C2×D3—246no—
426A4C2×(C2×D3)⋊C413yescomplemented
427C3×C4—22no—
428C3×C4—62no—
429C3×C4—86no—
430Dic3—64no—
431Dic3—122no—
432Dic3—122no—
433Dic3—246no—
434C32—41noSylow
435C23—32no—
436C23—32no—
437C23—32no—
438C23—32no—
439C23—32no—
440C23—32no—
441C23—31no—
442C23—31no—
443C23—32no—
444C23—31no—
445C23—32no—
446C23—31no—
447C23—32no—
448C23—31no—
449C23—34no—
450C23—34no—
451C23—34no—
452C23—61no—
453C23—64no—
454C23—61no—
455C23—61no—
456C23—94no—
457C23—182no—
458C23—188no—
459C23—182no—
460C23—182no—
461C23—188no—
462C23—182no—
463C23—184no—
464C23—182no—
465C23—184no—
466C23—182no—
467C23—364no—
468C23—364no—
469C23—362no—
470C23—362no—
471C23—362no—
472C23—362no—
473C23#375214yescomplemented
474C23C2×C4×C3⋊D311yescharacteristic
475C23C2×C4⋊(C3⋊D3)11yescharacteristic
476C23C2×#63811yescharacteristic
477C23C2×C3⋊S411yescharacteristic
478D4—1816no—
479D4—184no—
480D4—184no—
481D4—184no—
482D4—184no—
483C2×C4—22no—
484C2×C4—34no—
485C2×C4—32no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—64no—
489C2×C4—64no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—94no—
493C2×C4—188no—
494C2×C4—182no—
495C2×C4—182no—
496C2×C4—182no—
497C2×C4—182no—
498C2×C4—182no—
499C2×C4—182no—
500C2×C4—182no—
501C2×C4—182no—
502C2×C4—364no—
503C2×C4—362no—
504C2×C4—362no—
505C2×C4C2×C3⋊S412yescomplemented
506C2×C3—31no—
507C2×C3—31no—
508C2×C3—31no—
509C2×C3—34no—
510C2×C3—31no—
511C2×C3—412no—
512C2×C3—43no—
513C2×C3—43no—
514C2×C3—43no—
515C2×C3(C2×S4)⋊C414yescomplemented
516C2×C3C2×C4×S411yescharacteristic
517C2×C3C2×C4⋊S411yescharacteristic
518C2×C3C2×GL(2,ℤ/4)11yescharacteristic
519D3—124no—
520D3—2412no—
521C22—34no—
522C22—31no—
523C22—31no—
524C22—31no—
525C22—34no—
526C22—34no—
527C22—34no—
528C22—34no—
529C22—31no—
530C22—31no—
531C22—32no—
532C22—31no—
533C22—31no—
534C22—32no—
535C22—31no—
536C22—31no—
537C22—32no—
538C22—61no—
539C22—62no—
540C22—62no—
541C22—62no—
542C22—184no—
543C22—184no—
544C22—184no—
545C22—362no—
546C22—368no—
547C22—362no—
548C22—368no—
549C22—362no—
550C22—362no—
551C22C2×#375211yescharacteristic, complemented
552C22C4×C3⋊S412yes—
553C22C4⋊(C3⋊S4)12yes—
554C22#6426912yes—
555C22C22×C3⋊S411yescharacteristic
556C4—22no—
557C4—62no—
558C4—184no—
559C4—362no—
560C4—362no—
561C3—43no—
562C3C2×(C2×S4)⋊C411yescharacteristic, complemented
563C2—31no—
564C2—31no—
565C2—31no—
566C2—34no—
567C2—31no—
568C2—364no—
569C2#1059364714yesdirect product factor
570C2C2×C4×C3⋊S411yescharacteristic
571C2C2×C4⋊(C3⋊S4)11yescharacteristic
572C2C2×#6426911yescharacteristic
subgroupG/H
centerC23C2×C3⋊S4
commutatorC2×C3×A4C22×C4
FrattiniC22C22×C3⋊S4
FittingC24×C3×C4D3
socleC25×C3C2×D3
prime radicalC23×C3⋊S4C2
cosocleC22×C3×A4C23
hypercenterC22×C4C3⋊S4
hypocenterC3×A4C2×C22⋊C4
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4×A4C2semidirect
3. C22×C3⋊SL(2,ℤ/4)C2semidirect
4. #10593647C2direct (N × H)
10. C22×C3⋊S4C4semidirect
13. C2×C3×C4×A4C22semidirect
15. C2×C3⋊SL(2,ℤ/4)C22semidirect
18. C24×C3×C4D3semidirect
20. C22×C4×A4D3semidirect
38. C2×C3⋊S4C2×C4semidirect
57. C23×C3×C4C2×D3semidirect
70. C2×C4×A4C2×D3semidirect
91. C2×C3×A4C22⋊C4semidirect
101. C24×C4C3⋊D3semidirect
150. C22×C3×C4S4semidirect
195. C3×A4C2×C22⋊C4semidirect
216. C23×C4C2×C3⋊D3semidirect
251. C23×C3(C2×D3)⋊C4semidirect
277. C2×A4(C2×D3)⋊C4semidirect
293. C2×C3×C4C2×S4semidirect
376. C22×C4C3⋊S4semidirect
408. C22×C3C2×(C2×D3)⋊C4semidirect
426. A4C2×(C2×D3)⋊C4semidirect
473. C23#3752semidirect
505. C2×C4C2×C3⋊S4semidirect
515. C2×C3(C2×S4)⋊C4semidirect
551. C22C2×#3752semidirect
562. C3C2×(C2×S4)⋊C4semidirect
569. C2#10593647direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3⋊S42
C22×C3×C4×A42
C22×C3⋊SL(2,ℤ/4)2
#105936472
C2×(C2×S4)⋊C43
C2×#52133
C2×#37524