Finite Group Databasebeta

← #11803311

Subgroups — #11803311

Order 1152.

1733 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#882C211yesmaximal, characteristic
2C2×Dic3×#67C211yesmaximal, characteristic, complemented
3C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
4#10592649C211yesmaximal, characteristic, complemented
5C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
6#10591713C211yesmaximal, characteristic, complemented
7#10591706C211yesmaximal, characteristic, complemented
8#10591376C212yesmaximal, complemented
9#10591318C212yesmaximal, complemented
10#10591316C212yesmaximal, complemented
11#10591305C212yesmaximal, complemented
12#82578—31nomaximal
13#73569—31nomaximal
14C24×C3×D3C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C22×C3×#67C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C22×C3×D12C2212yes—
19C22×D3×Dic3C2211yescharacteristic, complemented
20C2×C32×C22⋊C4C2211yescharacteristic
21C2×#3757C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2212yescomplemented
23C2×C3×#217C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×C4×Dic3C2212yescomplemented
26C3×#882C418yescomplemented
27Dic3×#67—24no—
28C2×Dic3⋊Dic3C2211yescharacteristic, complemented
29C2×(C2×D3)⋊Dic3—24no—
30C2×(C2×D3)⋊Dic3C2212yes—
31C2×(C2×D3)⋊Dic3C2212yes—
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
35C2×(C2×D3)⋊Dic3C2212yescomplemented
36C2×Dic32C2211yescharacteristic, complemented
37#63658C2212yescomplemented
38C3×C3⋊#95C2212yescomplemented
39#63579C2212yescomplemented
40C2×C3×#120—31no—
41C22×#217—31no—
42C2×D4×Dic3—31no—
43C2×C4×#67—31no—
44C22×(C2×D3)⋊C4—31no—
45C2×#882D311yescharacteristic
46C3×C4×C22⋊C4—31no—
47#5247—31no—
48#5221—32no—
49#5220—31no—
50#5220—32no—
51#4958—31no—
52#4955—31no—
53#4951—32no—
54#4951—32no—
55#4950—31no—
56#4950—31no—
57#4950—61no—
58Dic3×C22⋊C4D311yescharacteristic, complemented
59#4940—32no—
60#4939—32no—
61#4670—32no—
62#4665—32no—
63C24×C32C2311yescharacteristic
64C23×C3×D3—22no—
65C23×C3×D3—22no—
66C23×C3×D3—42no—
67C23×C3×D3—42no—
68C23×C3×D3C2×C414yescomplemented
69C23×C3×D3C2312yes—
70C23×C3×D3C2311yescharacteristic
71C22×C32×C4C2312yes—
72C22×C3⋊Dic3—22no—
73C22×C3⋊Dic3—42no—
74C22×C3⋊Dic3C2311yescharacteristic
75C22×C3⋊Dic3C2312yes—
76C22×C3⋊Dic3C2311yescharacteristic
77C2×C3×#67—22no—
78C2×C3×#67—22no—
79C2×C3×#67C2×C414yes—
80C22×C3×Dic3—42no—
81C22×C3×Dic3D414yescomplemented
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2311yescharacteristic
86C2×C3×D12—42no—
87C2×C3×D12—42no—
88C2×C3×D12C2×C418yescomplemented
89C2×D3×Dic3—22no—
90C2×D3×Dic3—42no—
91C32×C22⋊C4C2×C414yescomplemented
92#3757—22no—
93C4⋊(C3⋊Dic3)—42no—
94C3×#217—22no—
95C3×(C2×D3)⋊C4C2×C418yescomplemented
96C3×C4×Dic3—42no—
97Dic3⋊Dic3—22no—
98(C2×D3)⋊Dic3—24no—
99(C2×D3)⋊Dic3—24no—
100(C2×D3)⋊Dic3—22no—
101(C2×D3)⋊Dic3—42no—
102(C2×D3)⋊Dic3—42no—
103(C2×D3)⋊Dic3—42no—
104Dic32—22no—
105#2321—91noSylow
106C25×C3—31no—
107C24×D3C2×D311yescharacteristic
108C22×C3×D4—31no—
109C22×C3×D4—32no—
110C23×C3×C4—31no—
111C22×#67C2×D311yescharacteristic
112C23×Dic3—31no—
113C23×Dic3—31no—
114C23×Dic3—31no—
115C23×Dic3—61no—
116C23×Dic3C2×D311yescharacteristic
117C22×D12C2×D312yes—
118C22×C4×D3—31no—
119C3×#120—38no—
120C2×C3×C22⋊C4—21no—
121C2×C3×C22⋊C4—32no—
122C2×C3×C22⋊C4—31no—
123C2×C3×C22⋊C4C2×D311yescharacteristic
124C2×C3×C22⋊C4C2×D311yescharacteristic
125C2×C3×C42—32no—
126C2×#217—31no—
127C2×#217—31no—
128C2×#217—32no—
129C2×#217—32no—
130C2×#217—31no—
131C2×#217—32no—
132C2×#217—32no—
133C2×#217—32no—
134C2×#217—61no—
135C2×#217—64no—
136C2×#217C2×D311yescharacteristic
137D4×Dic3—64no—
138C4×#67—64no—
139C2×(C2×D3)⋊C4—32no—
140C2×(C2×D3)⋊C4—31no—
141C2×(C2×D3)⋊C4—32no—
142C2×(C2×D3)⋊C4—32no—
143C2×(C2×D3)⋊C4—32no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4—64no—
146C2×(C2×D3)⋊C4C2×D312yes—
147C2×C4⋊Dic3—31no—
148C2×C4⋊Dic3—32no—
149C2×C4⋊Dic3—32no—
150C2×C4⋊Dic3—62no—
151C2×Dic3⋊C4—31no—
152C2×C4×Dic3—31no—
153C2×C4×Dic3—31no—
154C2×C4×Dic3C2×D312yescomplemented
155#882Dic318yescomplemented
156C3×#95—32no—
157C3⋊#95—32no—
158C3⋊#95—32no—
159C3⋊#95—32no—
160C3⋊#95—32no—
161C3⋊#95—62no—
162C3⋊#95C2×D312yescomplemented
163C23×C32—22no—
164C23×C32—22no—
165C23×C32C22×C412yes—
166C23×C32C2×D412yes—
167C23×C32#4112yes—
168C23×C32C2411yescharacteristic
169C22×C3×D3—28no—
170C22×C3×D3—22no—
171C22×C3×D3—21no—
172C22×C3×D3—22no—
173C22×C3×D3—21no—
174C22×C3×D3—22no—
175C22×C3×D3—22no—
176C22×C3×D3—22no—
177C22×C3×D3—22no—
178C22×C3×D3—22no—
179C22×C3×D3—22no—
180C22×C3×D3—48no—
181C22×C3×D3—44no—
182C22×C3×D3—44no—
183C22×C3×D3—48no—
184C22×C3×D3C22×C414yes—
185C22×C3×D3C22×C412yes—
186C2×C32×C4—22no—
187C2×C32×C4—22no—
188C2×C32×C4C22×C414yes—
189C2×C3⋊Dic3—22no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—22no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—22no—
194C2×C3⋊Dic3—22no—
195C2×C3⋊Dic3—22no—
196C2×C3⋊Dic3—44no—
197C3×#67—28no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—44no—
206C2×C3×Dic3C22×C412yes—
207C2×C3×Dic3C2×D412yes—
208C2×C3×Dic3C2×D412yes—
209C3×D12—48no—
210D3×Dic3—44no—
211C2×#120—31no—
212C2×C4×D4—91no—
213C22×C22⋊C4—91no—
214#390—92no—
215#388—92no—
216#388—92no—
217#386—92no—
218#386—91no—
219#385—91no—
220#379—91no—
221C4×C22⋊C4—31no—
222C24×C3—21no—
223C24×C3—32no—
224C24×C3—31no—
225C24×C3—34no—
226C24×C3—62no—
227C24×C3—62no—
228C24×C3—122no—
229C24×C3—122no—
230C24×C3C22×D311yescharacteristic
231C24×C3C22×D311yescharacteristic
232C23×D3—22no—
233C23×D3—22no—
234C23×D3—42no—
235C23×D3—42no—
236C23×D3C2×Dic314yescomplemented
237C23×D3C22×D312yes—
238C23×D3C22×D311yescharacteristic
239C2×C3×D4—34no—
240C2×C3×D4—38no—
241C2×C3×D4—62no—
242C2×C3×D4—62no—
243C2×C3×D4—122no—
244C2×C3×D4—122no—
245C22×C3×C4—22no—
246C22×C3×C4—31no—
247C22×C3×C4—31no—
248C22×C3×C4—31no—
249C22×C3×C4—34no—
250C22×C3×C4—32no—
251C22×C3×C4—122no—
252C22×C3×C4C22×D312yes—
253C22×C3×C4C22×D312yes—
254C2×#67—22no—
255C2×#67—22no—
256C2×#67C2×Dic314yes—
257C22×Dic3—31no—
258C22×Dic3—32no—
259C22×Dic3—31no—
260C22×Dic3—32no—
261C22×Dic3—31no—
262C22×Dic3—31no—
263C22×Dic3—42no—
264C22×Dic3—62no—
265C22×Dic3—61no—
266C22×Dic3—61no—
267C22×Dic3—62no—
268C22×Dic3—62no—
269C22×Dic3—62no—
270C22×Dic3—122no—
271C22×Dic3—122no—
272C22×Dic3—122no—
273C22×Dic3—122no—
274C22×Dic3—124no—
275C22×Dic3D1214yescomplemented
276C22×Dic3C22×D312yes—
277C22×Dic3C22×D311yescharacteristic
278C22×Dic3C22×D311yescharacteristic
279C22×Dic3C22×D311yescharacteristic
280C2×D12—42no—
281C2×D12—42no—
282C2×D12C2×Dic318yescomplemented
283C2×C4×D3—62no—
284C2×C4×D3—122no—
285C3×C22⋊C4—24no—
286C3×C22⋊C4—38no—
287C3×C22⋊C4—62no—
288C3×C22⋊C4C4×D314yescomplemented
289C3×C22⋊C4C2×Dic314yescomplemented
290C3×C42—122no—
291#217—22no—
292#217—62no—
293#217—62no—
294#217—62no—
295#217—64no—
296#217—64no—
297#217—122no—
298#217—122no—
299#217—122no—
300#217—122no—
301(C2×D3)⋊C4—64no—
302(C2×D3)⋊C4—64no—
303(C2×D3)⋊C4—62no—
304(C2×D3)⋊C4—122no—
305(C2×D3)⋊C4—122no—
306(C2×D3)⋊C4—122no—
307(C2×D3)⋊C4C2×Dic318yescomplemented
308C4⋊Dic3—62no—
309C4⋊Dic3—122no—
310C4⋊Dic3—122no—
311C4⋊Dic3—124no—
312Dic3⋊C4—62no—
313C4×Dic3—42no—
314C4×Dic3—62no—
315C4×Dic3—62no—
316C22×C32—24no—
317C22×C32—22no—
318C22×C32—22no—
319C22×C32—24no—
320C22×C32C4×D414yes—
321C22×C32C23×C411yescharacteristic
322C22×C32C22×D411yescharacteristic
323C22×C32C2×#4111yescharacteristic
324C22×C32H(5,𝔽2)12yes—
325C22×C32H(5,𝔽2)12yes—
326C2×C3×D3—22no—
327C2×C3×D3—24no—
328C2×C3×D3—24no—
329C2×C3×D3—24no—
330C2×C3×D3—24no—
331C2×C3×D3—416no—
332C2×C3×D3—41no—
333C2×C3×D3—42no—
334C2×C3×D3—41no—
335C2×C3×D3—42no—
336C2×C3×D3—42no—
337C2×C3×D3—42no—
338C2×C3×D3—42no—
339C32×C4—24no—
340C3⋊Dic3—42no—
341C3⋊Dic3—41no—
342C3⋊Dic3—41no—
343C3×Dic3—22no—
344C3×Dic3—22no—
345C3×Dic3—22no—
346C3×Dic3—42no—
347C25—31no—
348C22×D4—31no—
349C22×D4—32no—
350C23×C4—31no—
351C23×C4—91no—
352C23×C4—91no—
353#120—38no—
354C4×D4—184no—
355C2×C4⋊C4—91no—
356C2×C4⋊C4—92no—
357C2×C22⋊C4—32no—
358C2×C22⋊C4—31no—
359C2×C22⋊C4—92no—
360C2×C22⋊C4—92no—
361C2×C22⋊C4—91no—
362C2×C22⋊C4—91no—
363C2×C22⋊C4—92no—
364C2×C22⋊C4—92no—
365C2×C22⋊C4—92no—
366C2×C22⋊C4—184no—
367C2×C22⋊C4D3211yescharacteristic
368C2×C42—32no—
369C2×C42—91no—
370#95—32no—
371#95—92no—
372#95—92no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3—22no—
376C23×C3—22no—
377C23×C3—21no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—34no—
382C23×C3—32no—
383C23×C3—42no—
384C23×C3—42no—
385C23×C3—68no—
386C23×C3—62no—
387C23×C3—61no—
388C23×C3—61no—
389C23×C3—62no—
390C23×C3—62no—
391C23×C3—62no—
392C23×C3—62no—
393C23×C3—62no—
394C23×C3—62no—
395C23×C3—62no—
396C23×C3—128no—
397C23×C3—124no—
398C23×C3—124no—
399C23×C3—128no—
400C23×C3C2×C4×D312yes—
401C23×C3C2×D1212yes—
402C23×C3#23512yes—
403C23×C3D3×D412yes—
404C23×C3#23712yes—
405C23×C3C22×Dic312yes—
406C23×C3C23×D311yescharacteristic
407C23×C3C23×D311yescharacteristic
408C22×D3—28no—
409C22×D3—22no—
410C22×D3—21no—
411C22×D3—21no—
412C22×D3—22no—
413C22×D3—22no—
414C22×D3—22no—
415C22×D3—22no—
416C22×D3—22no—
417C22×D3—22no—
418C22×D3—22no—
419C22×D3—48no—
420C22×D3—44no—
421C22×D3—44no—
422C22×D3—48no—
423C22×D3C22×Dic314yes—
424C22×D3C22×Dic312yes—
425C3×D4—68no—
426C3×D4—128no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—24no—
432C2×C3×C4—32no—
433C2×C3×C4—32no—
434C2×C3×C4—32no—
435C2×C3×C4—42no—
436C2×C3×C4—42no—
437C2×C3×C4—61no—
438C2×C3×C4—61no—
439C2×C3×C4—62no—
440C2×C3×C4—62no—
441C2×C3×C4—62no—
442C2×C3×C4—62no—
443C2×C3×C4—62no—
444C2×C3×C4—124no—
445C2×C3×C4C2×C4×D314yes—
446C2×C3×C4C22×Dic314yes—
447#67—28no—
448C2×Dic3—21no—
449C2×Dic3—21no—
450C2×Dic3—22no—
451C2×Dic3—22no—
452C2×Dic3—22no—
453C2×Dic3—22no—
454C2×Dic3—22no—
455C2×Dic3—44no—
456C2×Dic3—64no—
457C2×Dic3—61no—
458C2×Dic3—61no—
459C2×Dic3—62no—
460C2×Dic3—61no—
461C2×Dic3—61no—
462C2×Dic3—62no—
463C2×Dic3—62no—
464C2×Dic3—62no—
465C2×Dic3—62no—
466C2×Dic3—62no—
467C2×Dic3—62no—
468C2×Dic3—62no—
469C2×Dic3—62no—
470C2×Dic3—62no—
471C2×Dic3—122no—
472C2×Dic3—122no—
473C2×Dic3—122no—
474C2×Dic3—121no—
475C2×Dic3—121no—
476C2×Dic3—122no—
477C2×Dic3—124no—
478C2×Dic3—124no—
479C2×Dic3—124no—
480C2×Dic3—128no—
481C2×Dic3C2×D1212yes—
482C2×Dic3C2×D1212yes—
483C2×Dic3C22×Dic312yes—
484D12—48no—
485C4×D3—124no—
486C2×C32—24no—
487C2×C32C2×C4×D411yescharacteristic
488C2×C32#51812yes—
489C2×C32#53411yescharacteristic
490C2×C32#53511yescharacteristic
491C2×C32#53812yes—
492C3×D3—42no—
493C3×D3—44no—
494C24—32no—
495C24—31no—
496C24—34no—
497C24—62no—
498C24—62no—
499C24—122no—
500C24—122no—
501C24C2×D3211yescharacteristic
502C2×D4—34no—
503C2×D4—38no—
504C2×D4—62no—
505C2×D4—62no—
506C2×D4—122no—
507C2×D4—122no—
508C22×C4—31no—
509C22×C4—31no—
510C22×C4—31no—
511C22×C4—34no—
512C22×C4—32no—
513C22×C4—92no—
514C22×C4—91no—
515C22×C4—91no—
516C22×C4—122no—
517C22×C4—182no—
518C22×C4—182no—
519C22×C4—362no—
520C22×C4—362no—
521C22×C4C2×D3212yes—
522C4⋊C4—182no—
523C4⋊C4—362no—
524C22⋊C4—38no—
525C22⋊C4—62no—
526C22⋊C4—184no—
527C22⋊C4—184no—
528C22⋊C4—182no—
529C22⋊C4—182no—
530C22⋊C4—362no—
531C22⋊C4—362no—
532C22⋊C4—362no—
533C22⋊C4D3×Dic314yescomplemented
534C42—122no—
535C42—182no—
536C22×C3—22no—
537C22×C3—22no—
538C22×C3—24no—
539C22×C3—24no—
540C22×C3—24no—
541C22×C3—22no—
542C22×C3—22no—
543C22×C3—24no—
544C22×C3—21no—
545C22×C3—21no—
546C22×C3—22no—
547C22×C3—22no—
548C22×C3—21no—
549C22×C3—24no—
550C22×C3—42no—
551C22×C3—44no—
552C22×C3—44no—
553C22×C3—42no—
554C22×C3—62no—
555C22×C3—64no—
556C22×C3—64no—
557C22×C3—64no—
558C22×C3—64no—
559C22×C3—1216no—
560C22×C3—121no—
561C22×C3—122no—
562C22×C3—122no—
563C22×C3—121no—
564C22×C3—122no—
565C22×C3—122no—
566C22×C3—122no—
567C22×C3C4×D1214yes—
568C22×C3D4×Dic314yes—
569C22×C3C22×C4×D311yescharacteristic
570C22×C3C22×D1211yescharacteristic
571C22×C3C2×#23511yescharacteristic
572C22×C3C2×D3×D411yescharacteristic
573C22×C3C2×#23711yescharacteristic
574C22×C3#100412yes—
575C22×C3#100412yes—
576C22×C3#100412yes—
577C22×C3#100912yes—
578C22×C3C23×Dic311yescharacteristic
579C2×D3—22no—
580C2×D3—24no—
581C2×D3—24no—
582C2×D3—24no—
583C2×D3—24no—
584C2×D3—416no—
585C2×D3—41no—
586C2×D3—42no—
587C2×D3—42no—
588C2×D3—41no—
589C2×D3—42no—
590C2×D3—42no—
591C2×D3—42no—
592C3×C4—24no—
593C3×C4—24no—
594C3×C4—44no—
595C3×C4—62no—
596C3×C4—62no—
597C3×C4—62no—
598C3×C4—122no—
599Dic3—22no—
600Dic3—22no—
601Dic3—22no—
602Dic3—42no—
603Dic3—124no—
604Dic3—121no—
605Dic3—122no—
606Dic3—121no—
607Dic3—121no—
608Dic3—122no—
609Dic3—121no—
610Dic3—241no—
611Dic3—241no—
612C32#232111yescharacteristic, complemented, Sylow
613C23—22no—
614C23—22no—
615C23—34no—
616C23—32no—
617C23—61no—
618C23—62no—
619C23—62no—
620C23—61no—
621C23—62no—
622C23—62no—
623C23—62no—
624C23—62no—
625C23—62no—
626C23—62no—
627C23—68no—
628C23—128no—
629C23—124no—
630C23—128no—
631C23—124no—
632C23#379512yes—
633C23D3×D1212yes—
634C23C2×D3×Dic312yes—
635C23C22×D3211yescharacteristic
636D4—68no—
637D4—128no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—32no—
641C2×C4—32no—
642C2×C4—32no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—62no—
646C2×C4—62no—
647C2×C4—62no—
648C2×C4—62no—
649C2×C4—62no—
650C2×C4—124no—
651C2×C4—181no—
652C2×C4—182no—
653C2×C4—181no—
654C2×C4—182no—
655C2×C4—182no—
656C2×C4—182no—
657C2×C4—182no—
658C2×C4—364no—
659C2×C4—364no—
660C2×C4C2×D3×Dic314yes—
661C2×C3—24no—
662C2×C3—24no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—22no—
666C2×C3—22no—
667C2×C3—21no—
668C2×C3—44no—
669C2×C3—124no—
670C2×C3—122no—
671C2×C3C2×C4×D1211yescharacteristic
672C2×C3#549311yescharacteristic
673C2×C3#552511yescharacteristic
674C2×C3#554512yes—
675C2×C3#556012yes—
676C2×C3#558911yescharacteristic
677C2×C3#559211yescharacteristic
678C2×C3#559312yes—
679C2×C3C2×D4×Dic311yescharacteristic
680C2×C3#579812yes—
681D3—44no—
682D3—42no—
683C22—22no—
684C22—24no—
685C22—24no—
686C22—22no—
687C22—62no—
688C22—64no—
689C22—64no—
690C22—64no—
691C22—64no—
692C22—1216no—
693C22—122no—
694C22—121no—
695C22—122no—
696C22—122no—
697C22—122no—
698C22—121no—
699C22—122no—
700C22Dic3×D1214yes—
701C22C2×#379511yescharacteristic
702C22C2×D3×D1211yescharacteristic
703C22#6431312yes—
704C22#6431412yes—
705C22C22×D3×Dic311yescharacteristic
706C4—24no—
707C4—62no—
708C4—62no—
709C4—62no—
710C4—122no—
711C4—362no—
712C4—361no—
713C4—361no—
714C3—21no—
715C3#7356911yescharacteristic, complemented
716C3#8257811yescharacteristic, complemented
717C2—24no—
718C2—124no—
719C2—122no—
720C2#1059408011yescharacteristic
721C2#1059423812yes—
722C2#1059429011yescharacteristic
723C2C2×Dic3×D1211yescharacteristic
724C2#1059521512yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×C3×#882C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2321
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×Dic3×#67C2semidirect
3. C22×(C2×D3)⋊Dic3C2semidirect
4. #10592649C2semidirect
5. C3×Dic3×C22⋊C4C2semidirect
6. #10591713C2semidirect
7. #10591706C2semidirect
8. #10591376C2semidirect
9. #10591318C2semidirect
10. #10591316C2semidirect
11. #10591305C2semidirect
19. C22×D3×Dic3C22semidirect
22. C2×C4⋊(C3⋊Dic3)C22semidirect
25. C2×C3×C4×Dic3C22semidirect
26. C3×#882C4semidirect
28. C2×Dic3⋊Dic3C22semidirect
34. C2×(C2×D3)⋊Dic3C22semidirect
35. C2×(C2×D3)⋊Dic3C22semidirect
36. C2×Dic32C22semidirect
37. #63658C22semidirect
38. C3×C3⋊#95C22semidirect
39. #63579C22semidirect
58. Dic3×C22⋊C4D3semidirect
68. C23×C3×D3C2×C4semidirect
81. C22×C3×Dic3D4semidirect
88. C2×C3×D12C2×C4semidirect
91. C32×C22⋊C4C2×C4semidirect
95. C3×(C2×D3)⋊C4C2×C4semidirect
154. C2×C4×Dic3C2×D3semidirect
155. #882Dic3semidirect
162. C3⋊#95C2×D3semidirect
236. C23×D3C2×Dic3semidirect
275. C22×Dic3D12semidirect
282. C2×D12C2×Dic3semidirect
288. C3×C22⋊C4C4×D3semidirect
289. C3×C22⋊C4C2×Dic3semidirect
307. (C2×D3)⋊C4C2×Dic3semidirect
533. C22⋊C4D3×Dic3semidirect
612. C32#2321semidirect
715. C3#73569semidirect
716. C3#82578semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8822
C2×Dic3×#672
C22×(C2×D3)⋊Dic32
#105926492
C3×Dic3×C22⋊C42
#105917132
#105917062
#105913762
#105913182
#105913162
#105913052
#825783
#735693