Finite Group Databasebeta

← #11803600

Subgroups — #11803600

Order 1152.

1433 conjugacy classes of subgroups.

The subgroup lattice has 703 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#895C211yesmaximal, characteristic
2C2×#63898C211yesmaximal, characteristic, complemented
3C2×#63855C211yesmaximal, characteristic, complemented
4C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C3×#4984C211yesmaximal, characteristic, complemented
6#10591377C212yesmaximal, complemented
7#10591376C212yesmaximal, complemented
8#10591323C212yesmaximal, complemented
9#10591318C211yesmaximal, characteristic, complemented
10#10591313C211yesmaximal, characteristic, complemented
11#10591286C212yesmaximal, complemented
12#82633—31nomaximal
13#76198—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C22×C3×D12C2212yes—
16C22×C3×C4×D3C2211yescharacteristic
17C22×D3×Dic3C2212yes—
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C4×C3⋊Dic3C2212yes—
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2212yes—
25C2×C3×C4×Dic3C2211yescharacteristic
26C3×#895C418yescomplemented
27C2×Dic3⋊Dic3C2211yescharacteristic
28C2×Dic3⋊Dic3C2211yescharacteristic
29C2×(C2×D3)⋊Dic3C2211yescharacteristic
30C2×(C2×D3)⋊Dic3C2211yescharacteristic
31C2×(C2×D3)⋊Dic3C2212yes—
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×(C2×D3)⋊Dic3C2212yes—
35#63898—24no—
36#63855—24no—
37#63658C2212yes—
38C3×C3⋊#95C2212yes—
39#63579C2212yes—
40C2×C3×#121—31no—
41C2×D4×Dic3—31no—
42C2×#926—31no—
43C2×#895D311yescharacteristic
44C2×#893—31no—
45C2×#872—31no—
46C3×#389—31no—
47#5221—32no—
48#5221—31no—
49#5220—32no—
50#5212—31no—
51#4989—32no—
52#4988—32no—
53#4987—31no—
54#4984D311yescharacteristic, complemented
55Dic3×C4⋊C4—31no—
56Dic3×C4⋊C4—31no—
57Dic3×C4⋊C4—61no—
58#4951—32no—
59#4950—32no—
60#4939—31no—
61#4669—32no—
62#4665—32no—
63C23×C3×D3C2312yes—
64C23×C3×D3C2311yescharacteristic
65C22×C32×C4C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3C2312yes—
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C2×C3×D12—22no—
75C2×C3×D12—22no—
76C2×C3×D12—42no—
77C2×C3×D12—42no—
78C2×C3×D12C2×C414yes—
79C2×C3×D12C2×C418yescomplemented
80C2×C3×C4×D3—22no—
81C2×C3×C4×D3—22no—
82C2×C3×C4×D3C2×C414yescomplemented
83C2×D3×Dic3—24no—
84C2×D3×Dic3—42no—
85C2×D3×Dic3—42no—
86C32×C4⋊C4C2×C414yescomplemented
87C4⋊(C3⋊Dic3)—22no—
88C4×C3⋊Dic3—42no—
89C4×C3⋊Dic3D414yescomplemented
90C3×(C2×D3)⋊C4C2×C418yescomplemented
91C3×C4⋊Dic3—22no—
92C3×C4⋊Dic3—42no—
93C3×C4×Dic3—22no—
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97(C2×D3)⋊Dic3—22no—
98(C2×D3)⋊Dic3—24no—
99(C2×D3)⋊Dic3—42no—
100(C2×D3)⋊Dic3—42no—
101(C2×D3)⋊Dic3—42no—
102#2324—91noSylow
103C22×C3×D4—31no—
104C22×C3×D4—32no—
105C23×C3×C4—31no—
106C23×Dic3—32no—
107C22×D12C2×D311yescharacteristic
108C22×D12C2×D312yes—
109C22×C4×D3—32no—
110C22×C4×D3C2×D311yescharacteristic
111C3×#121—38no—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4—31no—
114C2×C3×C4⋊C4—32no—
115C2×C3×C4⋊C4C2×D311yescharacteristic
116C2×C3×C4⋊C4C2×D311yescharacteristic
117C2×C3×C22⋊C4—32no—
118C2×C3×C42—31no—
119C2×#217—32no—
120C2×#217—31no—
121C2×#217—31no—
122C2×#217—32no—
123C2×#217—32no—
124C2×#217—32no—
125D4×Dic3—64no—
126C2×(C2×D3)⋊C4—31no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4—31no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4C2×D312yes—
133#926—64no—
134C2×C4⋊Dic3—31no—
135C2×C4⋊Dic3—31no—
136C2×C4⋊Dic3—31no—
137C2×C4⋊Dic3—31no—
138C2×C4⋊Dic3—61no—
139C2×C4⋊Dic3C2×D311yescharacteristic
140C2×C4⋊Dic3C2×D312yes—
141C2×Dic3⋊C4—31no—
142C2×Dic3⋊C4—31no—
143C2×C4×Dic3—31no—
144C2×C4×Dic3—31no—
145C2×C4×Dic3—32no—
146C2×C4×Dic3—32no—
147C2×C4×Dic3—61no—
148C2×C4×Dic3—62no—
149C2×C4×Dic3C2×D311yescharacteristic
150#895Dic318yescomplemented
151#893—64no—
152#872—64no—
153C3×#95—32no—
154C3⋊#95—32no—
155C3⋊#95—32no—
156C3⋊#95—32no—
157C3⋊#95—32no—
158C3⋊#95—62no—
159C3⋊#95C2×D312yes—
160C23×C32C2411yescharacteristic
161C22×C3×D3—21no—
162C22×C3×D3—22no—
163C22×C3×D3—21no—
164C22×C3×D3—22no—
165C22×C3×D3—21no—
166C22×C3×D3—22no—
167C22×C3×D3—22no—
168C22×C3×D3—22no—
169C22×C3×D3—21no—
170C22×C3×D3—21no—
171C22×C3×D3—22no—
172C22×C3×D3—21no—
173C22×C3×D3C22×C414yes—
174C22×C3×D3C22×C412yes—
175C2×C32×C4—22no—
176C2×C32×C4—22no—
177C2×C32×C4C22×C414yes—
178C2×C32×C4C22×C412yes—
179C2×C32×C4C2×D412yes—
180C2×C32×C4#4112yes—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—22no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—22no—
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3C2×D412yes—
189C2×C3⋊Dic3C2×D412yes—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3C22×C412yes—
202C3×D12—28no—
203C3×D12—48no—
204C3×C4×D3—28no—
205D3×Dic3—48no—
206C2×#121—31no—
207C2×C4×D4—91no—
208C2×#117—91no—
209#390—91no—
210#390—92no—
211#389—31no—
212#388—92no—
213#386—92no—
214#385—92no—
215#380—91no—
216C4×C4⋊C4—91no—
217C24×C3—31no—
218C24×C3—32no—
219C23×D3C22×D311yescharacteristic
220C23×D3C22×D312yes—
221C2×C3×D4—34no—
222C2×C3×D4—38no—
223C2×C3×D4—62no—
224C2×C3×D4—62no—
225C2×C3×D4—122no—
226C2×C3×D4—122no—
227C22×C3×C4—21no—
228C22×C3×C4—22no—
229C22×C3×C4—31no—
230C22×C3×C4—34no—
231C22×C3×C4—32no—
232C22×C3×C4—31no—
233C22×C3×C4—31no—
234C22×C3×C4—62no—
235C22×C3×C4—62no—
236C22×C3×C4C22×D312yes—
237C22×C3×C4C22×D312yes—
238C22×C3×C4C22×D311yescharacteristic
239C22×C3×C4C22×D311yescharacteristic
240C22×Dic3—31no—
241C22×Dic3—31no—
242C22×Dic3—31no—
243C22×Dic3—31no—
244C22×Dic3—32no—
245C22×Dic3—32no—
246C22×Dic3—61no—
247C22×Dic3—61no—
248C22×Dic3—62no—
249C22×Dic3—64no—
250C22×Dic3—122no—
251C22×Dic3—122no—
252C22×Dic3C22×D312yes—
253C22×Dic3C22×D311yescharacteristic
254C22×Dic3C22×D311yescharacteristic
255C22×Dic3C22×D311yescharacteristic
256C2×D12—22no—
257C2×D12—22no—
258C2×D12—42no—
259C2×D12—42no—
260C2×D12C2×Dic314yes—
261C2×D12C2×Dic318yescomplemented
262C2×C4×D3—22no—
263C2×C4×D3—22no—
264C2×C4×D3—64no—
265C2×C4×D3—122no—
266C2×C4×D3—122no—
267C2×C4×D3C2×Dic314yescomplemented
268C3×C4⋊C4—24no—
269C3×C4⋊C4—62no—
270C3×C4⋊C4—122no—
271C3×C4⋊C4C4×D314yescomplemented
272C3×C4⋊C4C2×Dic314yescomplemented
273C3×C22⋊C4—38no—
274C3×C42—62no—
275#217—62no—
276#217—62no—
277#217—64no—
278#217—122no—
279#217—122no—
280#217—122no—
281(C2×D3)⋊C4—62no—
282(C2×D3)⋊C4—62no—
283(C2×D3)⋊C4—64no—
284(C2×D3)⋊C4—122no—
285(C2×D3)⋊C4—122no—
286(C2×D3)⋊C4—122no—
287(C2×D3)⋊C4C2×Dic318yescomplemented
288C4⋊Dic3—22no—
289C4⋊Dic3—42no—
290C4⋊Dic3—62no—
291C4⋊Dic3—62no—
292C4⋊Dic3—64no—
293C4⋊Dic3—62no—
294C4⋊Dic3—62no—
295Dic3⋊C4—62no—
296Dic3⋊C4—62no—
297C4×Dic3—22no—
298C4×Dic3—34no—
299C4×Dic3—34no—
300C4×Dic3—64no—
301C4×Dic3—122no—
302C4×Dic3—122no—
303C4×Dic3—124no—
304C22×C32C23×C411yescharacteristic
305C22×C32C22×D411yescharacteristic
306C22×C32C2×#4111yescharacteristic
307C22×C32H(5,𝔽2)11yescharacteristic
308C22×C32H(5,𝔽2)11yescharacteristic
309C22×C32H(5,𝔽2)11yescharacteristic
310C22×C322−1+411yescharacteristic
311C2×C3×D3—22no—
312C2×C3×D3—24no—
313C2×C3×D3—22no—
314C2×C3×D3—24no—
315C2×C3×D3—22no—
316C2×C3×D3—24no—
317C2×C3×D3—42no—
318C2×C3×D3—41no—
319C2×C3×D3—41no—
320C2×C3×D3—42no—
321C2×C3×D3—41no—
322C2×C3×D3—42no—
323C2×C3×D3—41no—
324C2×C3×D3—42no—
325C32×C4—24no—
326C32×C4C4×D414yes—
327C3⋊Dic3—22no—
328C3⋊Dic3—22no—
329C3⋊Dic3—42no—
330C3×Dic3—22no—
331C3×Dic3—42no—
332C3×Dic3—41no—
333C3×Dic3—41no—
334C22×D4—31no—
335C22×D4—32no—
336C23×C4—31no—
337C23×C4—92no—
338#121—38no—
339C4×D4—184no—
340#117—184no—
341C2×C4⋊C4—31no—
342C2×C4⋊C4—32no—
343C2×C4⋊C4—91no—
344C2×C4⋊C4—91no—
345C2×C4⋊C4—91no—
346C2×C4⋊C4D3211yescharacteristic
347C2×C22⋊C4—32no—
348C2×C22⋊C4—91no—
349C2×C22⋊C4—91no—
350C2×C22⋊C4—92no—
351C2×C22⋊C4—92no—
352C2×C22⋊C4—92no—
353C2×C22⋊C4—92no—
354C2×C42—31no—
355C2×C42—91no—
356C2×C42—92no—
357#95—32no—
358#95—92no—
359#95—92no—
360C23×C3—21no—
361C23×C3—34no—
362C23×C3—32no—
363C23×C3—61no—
364C23×C3—62no—
365C23×C3—62no—
366C23×C3—61no—
367C23×C3—61no—
368C23×C3—62no—
369C23×C3—61no—
370C23×C3—62no—
371C23×C3—61no—
372C23×C3—62no—
373C23×C3—62no—
374C23×C3—61no—
375C23×C3C23×D311yescharacteristic
376C23×C3C23×D311yescharacteristic
377C22×D3—21no—
378C22×D3—22no—
379C22×D3—21no—
380C22×D3—22no—
381C22×D3—22no—
382C22×D3—22no—
383C22×D3—21no—
384C22×D3—21no—
385C22×D3—21no—
386C22×D3—22no—
387C22×D3—21no—
388C22×D3—22no—
389C22×D3C22×Dic314yes—
390C22×D3C22×Dic312yes—
391C3×D4—68no—
392C3×D4—128no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—24no—
401C2×C3×C4—32no—
402C2×C3×C4—42no—
403C2×C3×C4—42no—
404C2×C3×C4—61no—
405C2×C3×C4—61no—
406C2×C3×C4—68no—
407C2×C3×C4—61no—
408C2×C3×C4—61no—
409C2×C3×C4—62no—
410C2×C3×C4—61no—
411C2×C3×C4—61no—
412C2×C3×C4—62no—
413C2×C3×C4—61no—
414C2×C3×C4—62no—
415C2×C3×C4—61no—
416C2×C3×C4C2×C4×D314yes—
417C2×C3×C4C2×C4×D312yes—
418C2×C3×C4D3×D412yes—
419C2×C3×C4D3×D412yes—
420C2×C3×C4#23712yes—
421C2×C3×C4#23912yes—
422C2×C3×C4C22×Dic314yes—
423C2×C3×C4C22×Dic312yes—
424C2×Dic3—21no—
425C2×Dic3—21no—
426C2×Dic3—21no—
427C2×Dic3—21no—
428C2×Dic3—22no—
429C2×Dic3—21no—
430C2×Dic3—22no—
431C2×Dic3—21no—
432C2×Dic3—21no—
433C2×Dic3—21no—
434C2×Dic3—22no—
435C2×Dic3—32no—
436C2×Dic3—32no—
437C2×Dic3—32no—
438C2×Dic3—32no—
439C2×Dic3—62no—
440C2×Dic3—62no—
441C2×Dic3—62no—
442C2×Dic3—62no—
443C2×Dic3—61no—
444C2×Dic3—61no—
445C2×Dic3—61no—
446C2×Dic3—61no—
447C2×Dic3—61no—
448C2×Dic3—61no—
449C2×Dic3—61no—
450C2×Dic3—61no—
451C2×Dic3—64no—
452C2×Dic3—62no—
453C2×Dic3—62no—
454C2×Dic3—62no—
455C2×Dic3—62no—
456C2×Dic3—62no—
457C2×Dic3—62no—
458C2×Dic3—122no—
459C2×Dic3—121no—
460C2×Dic3—121no—
461C2×Dic3—122no—
462C2×Dic3—128no—
463C2×Dic3C22×Dic312yes—
464D12—28no—
465D12—48no—
466C4×D3—28no—
467C4×D3—128no—
468C2×C32C2×C4×D411yescharacteristic
469C2×C32#51811yescharacteristic
470C2×C32#52011yescharacteristic
471C2×C32#53511yescharacteristic
472C2×C32#53711yescharacteristic
473C2×C32#54011yescharacteristic
474C2×C32#54211yescharacteristic
475C3×D3—42no—
476C3×D3—44no—
477C24—32no—
478C24—31no—
479C2×D4—34no—
480C2×D4—38no—
481C2×D4—62no—
482C2×D4—62no—
483C2×D4—122no—
484C2×D4—122no—
485C22×C4—31no—
486C22×C4—34no—
487C22×C4—31no—
488C22×C4—32no—
489C22×C4—31no—
490C22×C4—62no—
491C22×C4—62no—
492C22×C4—91no—
493C22×C4—91no—
494C22×C4—92no—
495C22×C4—184no—
496C22×C4—362no—
497C22×C4—362no—
498C22×C4C2×D3212yes—
499C22×C4C2×D3211yescharacteristic
500C4⋊C4—62no—
501C4⋊C4—122no—
502C4⋊C4—182no—
503C4⋊C4—182no—
504C4⋊C4—182no—
505C4⋊C4D3×Dic314yescomplemented
506C22⋊C4—38no—
507C22⋊C4—182no—
508C22⋊C4—182no—
509C22⋊C4—184no—
510C22⋊C4—362no—
511C22⋊C4—362no—
512C22⋊C4—362no—
513C42—62no—
514C42—94no—
515C42—362no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—21no—
520C22×C3—21no—
521C22×C3—21no—
522C22×C3—21no—
523C22×C3—62no—
524C22×C3—64no—
525C22×C3—62no—
526C22×C3—64no—
527C22×C3—64no—
528C22×C3—62no—
529C22×C3—121no—
530C22×C3—122no—
531C22×C3—122no—
532C22×C3—121no—
533C22×C3—122no—
534C22×C3—121no—
535C22×C3—121no—
536C22×C3—122no—
537C22×C3C22×C4×D311yescharacteristic
538C22×C3C2×D3×D411yescharacteristic
539C22×C3C2×D3×D411yescharacteristic
540C22×C3C2×#23711yescharacteristic
541C22×C3#100411yescharacteristic
542C22×C3#100411yescharacteristic
543C22×C3#100411yescharacteristic
544C22×C3C2×#23911yescharacteristic
545C22×C3#100711yescharacteristic
546C22×C3#100911yescharacteristic
547C22×C3#100911yescharacteristic
548C22×C3#100911yescharacteristic
549C22×C3#101011yescharacteristic
550C22×C3C23×Dic311yescharacteristic
551C2×D3—22no—
552C2×D3—24no—
553C2×D3—22no—
554C2×D3—24no—
555C2×D3—22no—
556C2×D3—24no—
557C2×D3—41no—
558C2×D3—42no—
559C2×D3—42no—
560C2×D3—41no—
561C2×D3—41no—
562C2×D3—42no—
563C2×D3—41no—
564C2×D3—42no—
565C3×C4—24no—
566C3×C4—24no—
567C3×C4—24no—
568C3×C4—44no—
569C3×C4—62no—
570C3×C4—122no—
571C3×C4—121no—
572C3×C4—121no—
573C3×C4#89314yes—
574C3×C4D4×Dic314yes—
575Dic3—22no—
576Dic3—42no—
577Dic3—41no—
578Dic3—41no—
579Dic3—64no—
580Dic3—62no—
581Dic3—62no—
582Dic3—62no—
583Dic3—62no—
584Dic3—122no—
585Dic3—124no—
586Dic3—122no—
587Dic3—122no—
588C32#232411yescharacteristic, complemented, Sylow
589C23—34no—
590C23—32no—
591C23—61no—
592C23—62no—
593C23—61no—
594C23—62no—
595C23—62no—
596C23—61no—
597C23—62no—
598C23—61no—
599C23—62no—
600C23—61no—
601C23—61no—
602C23—62no—
603C23C22×D3211yescharacteristic
604D4—68no—
605D4—128no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—32no—
609C2×C4—61no—
610C2×C4—61no—
611C2×C4—68no—
612C2×C4—61no—
613C2×C4—61no—
614C2×C4—62no—
615C2×C4—61no—
616C2×C4—62no—
617C2×C4—61no—
618C2×C4—61no—
619C2×C4—61no—
620C2×C4—62no—
621C2×C4—92no—
622C2×C4—92no—
623C2×C4—181no—
624C2×C4—181no—
625C2×C4—181no—
626C2×C4—181no—
627C2×C4—182no—
628C2×C4—182no—
629C2×C4—182no—
630C2×C4—368no—
631C2×C4#379612yes—
632C2×C4#380212yes—
633C2×C4C2×D3×Dic314yes—
634C2×C4C2×D3×Dic312yes—
635C2×C3—21no—
636C2×C3—21no—
637C2×C3—21no—
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—21no—
641C2×C3—21no—
642C2×C3—122no—
643C2×C3—124no—
644C2×C3C2×#89311yescharacteristic
645C2×C3#554511yescharacteristic
646C2×C3#557411yescharacteristic
647C2×C3#560311yescharacteristic
648C2×C3#560711yescharacteristic
649C2×C3#560711yescharacteristic
650C2×C3#560811yescharacteristic
651C2×C3#561911yescharacteristic
652C2×C3#562911yescharacteristic
653C2×C3#569711yescharacteristic
654C2×C3#573311yescharacteristic
655C2×C3C2×D4×Dic311yescharacteristic
656C2×C3#579811yescharacteristic
657C2×C3#582711yescharacteristic
658D3—42no—
659D3—44no—
660C22—64no—
661C22—62no—
662C22—62no—
663C22—64no—
664C22—62no—
665C22—64no—
666C22—122no—
667C22—121no—
668C22—121no—
669C22—122no—
670C22—121no—
671C22—122no—
672C22—121no—
673C22—122no—
674C22C2×#379611yescharacteristic
675C22C2×#380211yescharacteristic
676C22#6431311yescharacteristic
677C22#6431411yescharacteristic
678C22#6431511yescharacteristic
679C22#6432011yescharacteristic
680C22C22×D3×Dic311yescharacteristic
681C4—24no—
682C4—62no—
683C4—122no—
684C4—121no—
685C4—121no—
686C4—182no—
687C4—182no—
688C4—362no—
689C4#6389814yes—
690C3—21no—
691C3#7619811yescharacteristic, complemented
692C3#8263311yescharacteristic, complemented
693C2—122no—
694C2—124no—
695C2#1059449411yescharacteristic
696C2#1059450111yescharacteristic
697C2#1059452811yescharacteristic
698C2#1059463411yescharacteristic
699C2C2×#6389811yescharacteristic
700C2#1059521511yescharacteristic
701C2#1059539411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×C3×#895C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2324
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63898C2semidirect
3. C2×#63855C2semidirect
4. C4⋊C4×C3⋊Dic3C2semidirect
5. C3×#4984C2semidirect
6. #10591377C2semidirect
7. #10591376C2semidirect
8. #10591323C2semidirect
9. #10591318C2semidirect
10. #10591313C2semidirect
11. #10591286C2semidirect
26. C3×#895C4semidirect
54. #4984D3semidirect
79. C2×C3×D12C2×C4semidirect
82. C2×C3×C4×D3C2×C4semidirect
86. C32×C4⋊C4C2×C4semidirect
89. C4×C3⋊Dic3D4semidirect
90. C3×(C2×D3)⋊C4C2×C4semidirect
150. #895Dic3semidirect
261. C2×D12C2×Dic3semidirect
267. C2×C4×D3C2×Dic3semidirect
271. C3×C4⋊C4C4×D3semidirect
272. C3×C4⋊C4C2×Dic3semidirect
287. (C2×D3)⋊C4C2×Dic3semidirect
505. C4⋊C4D3×Dic3semidirect
588. C32#2324semidirect
691. C3#76198semidirect
692. C3#82633semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8952
C2×#638982
C2×#638552
C4⋊C4×C3⋊Dic32
C3×#49842
#105913772
#105913762
#105913232
#105913182
#105913132
#105912862
#826333
#761983