Finite Group Databasebeta

← #11803839

Subgroups — #11803839

Order 1152.

2220 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64149C211yesmaximal, characteristic
2C2×C4×#638C211yesmaximal, characteristic, complemented
3C2×#64090C211yesmaximal, characteristic, complemented
4C32×#386C211yesmaximal, characteristic, complemented
5#10592919C211yesmaximal, characteristic, complemented
6#10592912C211yesmaximal, characteristic, complemented
7#10592657C211yesmaximal, characteristic, complemented
8#10592656C211yesmaximal, characteristic, complemented
9#10592656C211yesmaximal, characteristic, complemented
10#10592655C211yesmaximal, characteristic, complemented
11#10592655C211yesmaximal, characteristic, complemented
12#10592364C211yesmaximal, characteristic, complemented
13#10592364C211yesmaximal, characteristic, complemented
14#10592349C211yesmaximal, characteristic, complemented
15#10592347C211yesmaximal, characteristic, complemented
16#74667—34nomaximal
17C22×C32×D4C2211yescharacteristic
18C23×C32×C4C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C22×#638C2211yescharacteristic
23C23×C3⋊Dic3C2211yescharacteristic
24C22×C4⋊(C3⋊D3)C2211yescharacteristic
25C22×C4×C3⋊D3C2211yescharacteristic
26C22×C4×C3⋊D3C2211yescharacteristic
27C2×C32×C22⋊C4C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×#3757C2211yescharacteristic
31C2×#3757C2211yescharacteristic
32C2×#3757C2211yescharacteristic
33#64149C418yescomplemented
34C4×#638—24no—
35C2×#3752C2211yescharacteristic
36C2×#3752C2211yescharacteristic
37C2×#3752C2211yescharacteristic
38C2×#3752C2211yescharacteristic
39C2×#3752C2211yescharacteristic
40C2×#3752C2211yescharacteristic
41C2×#3750C2211yescharacteristic
42C2×#3750C2211yescharacteristic
43C2×C4×C3⋊Dic3C2211yescharacteristic
44C2×C4×C3⋊Dic3C2211yescharacteristic
45C2×C4×C3⋊Dic3C2211yescharacteristic
46#64090—24no—
47C32×#95C2211yescharacteristic
48C32×#95C2211yescharacteristic
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52#63658C2211yescharacteristic
53#63658C2211yescharacteristic
54#63658C2211yescharacteristic
55C2×#940—34no—
56C2×C4×#67—34no—
57C2×#67⋊C4—34no—
58C3×#386D314yescomplemented
59#5220—34no—
60#5213—34no—
61#4958—34no—
62#4957—34no—
63#4957—34no—
64#4956—34no—
65#4956—34no—
66#4665—34no—
67#4665—34no—
68#4650—34no—
69#4648—34no—
70C24×C32C2311yescharacteristic
71C24×C32C2311yescharacteristic
72C23×C3⋊D3C2311yescharacteristic
73C23×C3⋊D3C2311yescharacteristic
74C2×C32×D4—41no—
75C2×C32×D4—41no—
76C2×C32×D4C2×C414yescomplemented
77C22×C32×C4—22no—
78C22×C32×C4—41no—
79C22×C32×C4—41no—
80C22×C32×C4C2311yescharacteristic
81C22×C32×C4C2311yescharacteristic
82C22×C32×C4C2311yescharacteristic
83C22×C32×C4C2311yescharacteristic
84C22×C32×C4C2311yescharacteristic
85C2×#638—22no—
86C2×#638—22no—
87C2×#638—22no—
88C2×#638—22no—
89C2×#638—41no—
90C2×#638—41no—
91C2×#638—41no—
92C2×#638—41no—
93C2×#638C2×C414yescomplemented
94C2×#638C2×C414yescomplemented
95C2×#638C2×C414yescomplemented
96C2×#638C2×C414yescomplemented
97C22×C3⋊Dic3—22no—
98C22×C3⋊Dic3—41no—
99C22×C3⋊Dic3—41no—
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C22×C3⋊Dic3C2311yescharacteristic
106C2×C4⋊(C3⋊D3)—41no—
107C2×C4⋊(C3⋊D3)—41no—
108C2×C4⋊(C3⋊D3)C2×C414yescomplemented
109C2×C4×C3⋊D3—22no—
110C2×C4×C3⋊D3—22no—
111C2×C4×C3⋊D3—41no—
112C2×C4×C3⋊D3—41no—
113C2×C4×C3⋊D3—41no—
114C2×C4×C3⋊D3—41no—
115C32×C22⋊C4—22no—
116C32×C22⋊C4—41no—
117C32×C22⋊C4—41no—
118#3757—22no—
119#3757—41no—
120#3757—41no—
121#3752—22no—
122#3752—22no—
123#3752—41no—
124#3752—41no—
125#3752—41no—
126#3752—41no—
127#3750—22no—
128#3750—22no—
129C4×C3⋊Dic3—22no—
130C4×C3⋊Dic3C2×C414yescomplemented
131C4×C3⋊Dic3D414yescomplemented
132#2328—91noSylow
133C22×C3×D4C2×D314yes—
134C23×C3×C4C2×D314yes—
135C22×#67—34no—
136C22×#67—34no—
137C22×#67—34no—
138C22×#67—34no—
139C23×Dic3—34no—
140C22×D12—34no—
141C22×C4×D3—34no—
142C22×C4×D3—34no—
143C2×C3×C22⋊C4C2×D314yes—
144C2×C3×C22⋊C4C2×D314yes—
145C2×C3×C22⋊C4C2×D314yes—
146C2×#217—34no—
147C2×#217—34no—
148C2×#217—34no—
149#940—332no—
150C4×#67—616no—
151C2×(C2×D3)⋊C4—34no—
152C2×(C2×D3)⋊C4—34no—
153C2×(C2×D3)⋊C4—34no—
154C2×(C2×D3)⋊C4—34no—
155C2×(C2×D3)⋊C4—34no—
156C2×(C2×D3)⋊C4—34no—
157C2×Dic3⋊C4—34no—
158C2×Dic3⋊C4—34no—
159C2×C4×Dic3—34no—
160C2×C4×Dic3—34no—
161C2×C4×Dic3—34no—
162#67⋊C4—616no—
163C3×#95C2×D314yes—
164C3×#95C2×D314yes—
165C3⋊#95—34no—
166C3⋊#95—34no—
167C3⋊#95—34no—
168C3⋊#95—34no—
169C3⋊#95—34no—
170C3⋊#95—34no—
171C23×C32—21no—
172C23×C32—21no—
173C23×C32—21no—
174C23×C32—21no—
175C23×C32—21no—
176C23×C32—21no—
177C23×C32—21no—
178C23×C32—21no—
179C23×C32—21no—
180C23×C32—21no—
181C23×C32—21no—
182C23×C32—21no—
183C23×C32C22×C412yes—
184C23×C32C22×C412yes—
185C23×C32C2411yescharacteristic
186C22×C3⋊D3—21no—
187C22×C3⋊D3—21no—
188C22×C3⋊D3—21no—
189C22×C3⋊D3—21no—
190C22×C3⋊D3—21no—
191C22×C3⋊D3—21no—
192C22×C3⋊D3—21no—
193C22×C3⋊D3—21no—
194C22×C3⋊D3—21no—
195C22×C3⋊D3—21no—
196C22×C3⋊D3—21no—
197C22×C3⋊D3—21no—
198C22×C3⋊D3C22×C412yes—
199C22×C3⋊D3C22×C412yes—
200C32×D4—44no—
201C2×C32×C4—21no—
202C2×C32×C4—21no—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4—21no—
206C2×C32×C4—21no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4—21no—
211C2×C32×C4—21no—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4—44no—
215C2×C32×C4C22×C412yes—
216C2×C32×C4C2×D412yes—
217#638—28no—
218#638—28no—
219#638—44no—
220#638—44no—
221C2×C3⋊Dic3—21no—
222C2×C3⋊Dic3—21no—
223C2×C3⋊Dic3—21no—
224C2×C3⋊Dic3—21no—
225C2×C3⋊Dic3—21no—
226C2×C3⋊Dic3—21no—
227C2×C3⋊Dic3—21no—
228C2×C3⋊Dic3—21no—
229C2×C3⋊Dic3—21no—
230C2×C3⋊Dic3—21no—
231C2×C3⋊Dic3—21no—
232C2×C3⋊Dic3—21no—
233C2×C3⋊Dic3—21no—
234C2×C3⋊Dic3—44no—
235C2×C3⋊Dic3C22×C412yes—
236C2×C3⋊Dic3C22×C412yes—
237C2×C3⋊Dic3C2×D412yes—
238C2×C3⋊Dic3C2×D412yes—
239C2×C3⋊Dic3#4112yes—
240C4⋊(C3⋊D3)—44no—
241C4×C3⋊D3—44no—
242C4×C3⋊D3—44no—
243C2×#127—91no—
244C2×C4×D4—91no—
245C2×C4×D4—91no—
246#390—91no—
247#390—91no—
248#386—91no—
249#386—91no—
250#386—91no—
251#386—91no—
252#386—91no—
253#386—91no—
254#386—91no—
255#386C3⋊D311yescharacteristic, complemented
256#382—91no—
257#376—91no—
258C24×C3C22×D314yes—
259C24×C3C22×D314yes—
260C23×D3—34no—
261C23×D3—34no—
262C2×C3×D4—44no—
263C2×C3×D4—44no—
264C2×C3×D4C4×D3116yescomplemented
265C22×C3×C4—28no—
266C22×C3×C4—44no—
267C22×C3×C4—44no—
268C22×C3×C4C22×D314yes—
269C22×C3×C4C22×D314yes—
270C22×C3×C4C22×D314yes—
271C22×C3×C4C22×D314yes—
272C22×C3×C4C22×D314yes—
273C2×#67—316no—
274C2×#67—316no—
275C2×#67—316no—
276C2×#67—316no—
277C2×#67—68no—
278C2×#67—68no—
279C2×#67—68no—
280C2×#67—68no—
281C2×#67—124no—
282C2×#67—124no—
283C2×#67—124no—
284C2×#67—124no—
285C22×Dic3—34no—
286C22×Dic3—34no—
287C22×Dic3—34no—
288C22×Dic3—34no—
289C22×Dic3—34no—
290C22×Dic3—34no—
291C22×Dic3—68no—
292C22×Dic3—124no—
293C22×Dic3—124no—
294C2×D12—316no—
295C2×D12—124no—
296C2×D12—124no—
297C2×C4×D3—68no—
298C2×C4×D3—68no—
299C2×C4×D3—124no—
300C2×C4×D3—124no—
301C2×C4×D3—124no—
302C2×C4×D3—124no—
303C3×C22⋊C4—28no—
304C3×C22⋊C4—44no—
305C3×C22⋊C4—44no—
306#217—68no—
307#217—124no—
308#217—124no—
309(C2×D3)⋊C4—68no—
310(C2×D3)⋊C4—68no—
311(C2×D3)⋊C4—124no—
312(C2×D3)⋊C4—124no—
313(C2×D3)⋊C4—124no—
314(C2×D3)⋊C4—124no—
315Dic3⋊C4—68no—
316Dic3⋊C4—68no—
317C4×Dic3—316no—
318C4×Dic3—316no—
319C4×Dic3—68no—
320C22×C32—22no—
321C22×C32—22no—
322C22×C32—22no—
323C22×C32—22no—
324C22×C32—22no—
325C22×C32—22no—
326C22×C32—41no—
327C22×C32—41no—
328C22×C32—41no—
329C22×C32—41no—
330C22×C32—41no—
331C22×C32—41no—
332C22×C32—41no—
333C22×C32—41no—
334C22×C32C23×C411yescharacteristic
335C22×C32C22×D411yescharacteristic
336C22×C32C2×#4111yescharacteristic
337C22×C32H(5,𝔽2)11yescharacteristic
338C22×C32H(5,𝔽2)11yescharacteristic
339C22×C32H(5,𝔽2)11yescharacteristic
340C22×C32H(5,𝔽2)11yescharacteristic
341C2×C3⋊D3—22no—
342C2×C3⋊D3—22no—
343C2×C3⋊D3—22no—
344C2×C3⋊D3—22no—
345C2×C3⋊D3—22no—
346C2×C3⋊D3—22no—
347C2×C3⋊D3—41no—
348C2×C3⋊D3—41no—
349C2×C3⋊D3—41no—
350C2×C3⋊D3—41no—
351C2×C3⋊D3—41no—
352C2×C3⋊D3—41no—
353C2×C3⋊D3—41no—
354C2×C3⋊D3—41no—
355C32×C4—22no—
356C32×C4—22no—
357C32×C4—41no—
358C32×C4—41no—
359C32×C4—41no—
360C3⋊Dic3—22no—
361C3⋊Dic3—22no—
362C3⋊Dic3—41no—
363C3⋊Dic3—41no—
364C3⋊Dic3—41no—
365C3⋊Dic3C4×D414yes—
366C22×D4—91no—
367C22×D4—91no—
368C22×D4—91no—
369C22×D4—91no—
370C22×D4—91no—
371C22×D4C2×C3⋊D311yescharacteristic
372C23×C4—91no—
373C23×C4—91no—
374C23×C4—91no—
375C23×C4C2×C3⋊D311yescharacteristic
376#127—98no—
377C4×D4—184no—
378C4×D4—184no—
379C2×C4⋊C4—91no—
380C2×C4⋊C4—91no—
381C2×C22⋊C4—91no—
382C2×C22⋊C4—91no—
383C2×C22⋊C4—91no—
384C2×C22⋊C4—91no—
385C2×C22⋊C4—91no—
386C2×C22⋊C4—91no—
387C2×C22⋊C4—91no—
388C2×C22⋊C4—91no—
389C2×C22⋊C4—91no—
390C2×C22⋊C4C2×C3⋊D311yescharacteristic
391C2×C22⋊C4C2×C3⋊D311yescharacteristic
392C2×C22⋊C4C2×C3⋊D311yescharacteristic
393C2×C42—91no—
394C2×C42—91no—
395C2×C42—91no—
396#95—91no—
397#95—91no—
398#95—91no—
399#95—91no—
400#95—91no—
401#95—91no—
402#95C2×C3⋊D311yescharacteristic
403#95C2×C3⋊D311yescharacteristic
404C23×C3—24no—
405C23×C3—24no—
406C23×C3—24no—
407C23×C3—24no—
408C23×C3—24no—
409C23×C3—24no—
410C23×C3—24no—
411C23×C3—24no—
412C23×C3—24no—
413C23×C3—24no—
414C23×C3—24no—
415C23×C3—24no—
416C23×C3C2×C4×D318yes—
417C23×C3C2×C4×D318yes—
418C23×C3C23×D314yes—
419C22×D3—38no—
420C22×D3—38no—
421C22×D3—64no—
422C22×D3—64no—
423C22×D3—64no—
424C22×D3—64no—
425C22×D3—64no—
426C22×D3—64no—
427C22×D3—64no—
428C22×D3—64no—
429C22×D3—64no—
430C22×D3—64no—
431C22×D3—64no—
432C22×D3—64no—
433C3×D4—416no—
434C2×C3×C4—24no—
435C2×C3×C4—24no—
436C2×C3×C4—24no—
437C2×C3×C4—24no—
438C2×C3×C4—24no—
439C2×C3×C4—24no—
440C2×C3×C4—24no—
441C2×C3×C4—24no—
442C2×C3×C4—24no—
443C2×C3×C4—24no—
444C2×C3×C4—24no—
445C2×C3×C4—24no—
446C2×C3×C4—24no—
447C2×C3×C4—416no—
448C2×C3×C4C2×C4×D318yes—
449C2×C3×C4D3×D418yes—
450#67—632no—
451#67—632no—
452#67—1216no—
453#67—1216no—
454C2×Dic3—38no—
455C2×Dic3—38no—
456C2×Dic3—38no—
457C2×Dic3—38no—
458C2×Dic3—38no—
459C2×Dic3—64no—
460C2×Dic3—64no—
461C2×Dic3—64no—
462C2×Dic3—64no—
463C2×Dic3—64no—
464C2×Dic3—64no—
465C2×Dic3—64no—
466C2×Dic3—64no—
467C2×Dic3—64no—
468C2×Dic3—64no—
469C2×Dic3—64no—
470C2×Dic3—64no—
471C2×Dic3—64no—
472C2×Dic3—1216no—
473D12—1216no—
474C4×D3—1216no—
475C4×D3—1216no—
476C2×C32—42no—
477C2×C32—42no—
478C2×C32C2×C4×D411yescharacteristic
479C2×C32#51811yescharacteristic
480C2×C32#51811yescharacteristic
481C2×C32#53511yescharacteristic
482C2×C32#53511yescharacteristic
483C2×C32#54011yescharacteristic
484C2×C32#54011yescharacteristic
485C3⋊D3—42no—
486C3⋊D3—42no—
487C24—91no—
488C24—91no—
489C24C22×C3⋊D311yescharacteristic
490C24C22×C3⋊D311yescharacteristic
491C2×D4—41no—
492C2×D4—41no—
493C2×D4—94no—
494C2×D4—94no—
495C2×D4—94no—
496C2×D4—94no—
497C2×D4—94no—
498C2×D4—182no—
499C2×D4—182no—
500C2×D4—182no—
501C2×D4—182no—
502C2×D4—361no—
503C2×D4—361no—
504C2×D4—361no—
505C2×D4—361no—
506C2×D4—361no—
507C2×D4—361no—
508C2×D4C4×C3⋊D314yescomplemented
509C22×C4—22no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—91no—
513C22×C4—91no—
514C22×C4—91no—
515C22×C4—91no—
516C22×C4—91no—
517C22×C4—91no—
518C22×C4—182no—
519C22×C4—182no—
520C22×C4—182no—
521C22×C4—361no—
522C22×C4—361no—
523C22×C4—361no—
524C22×C4—361no—
525C22×C4—361no—
526C22×C4—361no—
527C22×C4C22×C3⋊D311yescharacteristic
528C22×C4C22×C3⋊D311yescharacteristic
529C22×C4C22×C3⋊D311yescharacteristic
530C22×C4C22×C3⋊D311yescharacteristic
531C22×C4C22×C3⋊D311yescharacteristic
532C4⋊C4—182no—
533C4⋊C4—182no—
534C22⋊C4—22no—
535C22⋊C4—41no—
536C22⋊C4—41no—
537C22⋊C4—182no—
538C22⋊C4—182no—
539C22⋊C4—182no—
540C22⋊C4—361no—
541C22⋊C4—361no—
542C22⋊C4—361no—
543C22⋊C4—361no—
544C22⋊C4—361no—
545C22⋊C4—361no—
546C42—94no—
547C42—94no—
548C42—182no—
549C22×C3—28no—
550C22×C3—28no—
551C22×C3—28no—
552C22×C3—28no—
553C22×C3—28no—
554C22×C3—28no—
555C22×C3—44no—
556C22×C3—44no—
557C22×C3—44no—
558C22×C3—44no—
559C22×C3—44no—
560C22×C3—44no—
561C22×C3—44no—
562C22×C3—44no—
563C22×C3C22×C4×D314yes—
564C22×C3C2×D3×D414yes—
565C22×C3#100414yes—
566C22×C3#100414yes—
567C22×C3#100414yes—
568C22×C3D3×#4114yes—
569C22×C3#100914yes—
570C2×D3—68no—
571C2×D3—68no—
572C2×D3—68no—
573C2×D3—68no—
574C2×D3—68no—
575C2×D3—68no—
576C2×D3—124no—
577C2×D3—124no—
578C2×D3—124no—
579C2×D3—124no—
580C2×D3—124no—
581C2×D3—124no—
582C2×D3—124no—
583C2×D3—124no—
584C3×C4—28no—
585C3×C4—28no—
586C3×C4—44no—
587C3×C4—44no—
588C3×C4—44no—
589Dic3—316no—
590Dic3—68no—
591Dic3—68no—
592Dic3—124no—
593Dic3—124no—
594Dic3—124no—
595C32#232811yescharacteristic, complemented, Sylow
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—92no—
609C23—92no—
610C23—181no—
611C23—181no—
612C23—181no—
613C23—181no—
614C23—181no—
615C23—181no—
616C23—181no—
617C23—181no—
618C23—181no—
619C23—181no—
620C23—181no—
621C23—181no—
622C23C2×C4×C3⋊D312yes—
623C23C2×C4×C3⋊D312yes—
624C23C23×C3⋊D311yescharacteristic
625D4—44no—
626D4—188no—
627D4—188no—
628D4—364no—
629D4—364no—
630D4—364no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—44no—
645C2×C4—92no—
646C2×C4—92no—
647C2×C4—92no—
648C2×C4—92no—
649C2×C4—92no—
650C2×C4—181no—
651C2×C4—181no—
652C2×C4—181no—
653C2×C4—181no—
654C2×C4—181no—
655C2×C4—181no—
656C2×C4—181no—
657C2×C4—181no—
658C2×C4—181no—
659C2×C4—181no—
660C2×C4—181no—
661C2×C4—181no—
662C2×C4—181no—
663C2×C4—364no—
664C2×C4—364no—
665C2×C4—364no—
666C2×C4C2×C4×C3⋊D312yes—
667C2×C4D4×C3⋊D312yes—
668C2×C3—48no—
669C2×C3—48no—
670C2×C3#548614yes—
671C2×C3C4×D3×D414yes—
672C2×C3#554514yes—
673C2×C3#559214yes—
674C2×C3#560714yes—
675C2×C3#561514yes—
676C2×C3#566314yes—
677D3—128no—
678D3—128no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—182no—
694C22—182no—
695C22—182no—
696C22—182no—
697C22—182no—
698C22—182no—
699C22—361no—
700C22—361no—
701C22—361no—
702C22—361no—
703C22—361no—
704C22—361no—
705C22—361no—
706C22—361no—
707C22C22×C4×C3⋊D311yescharacteristic
708C22C2×D4×C3⋊D311yescharacteristic
709C22#6436111yescharacteristic
710C22#6436111yescharacteristic
711C22#6436111yescharacteristic
712C22#41×C3⋊D311yescharacteristic
713C22#6436611yescharacteristic
714C4—22no—
715C4—22no—
716C4—41no—
717C4—41no—
718C4—41no—
719C4—94no—
720C4—182no—
721C4—182no—
722C4—361no—
723C4—361no—
724C4—361no—
725C3#7466714yescomplemented
726C2—42no—
727C2—42no—
728C2—362no—
729C2—362no—
730C2#1059595711yescharacteristic
731C2C4×D4×C3⋊D311yescharacteristic
732C2#1059601611yescharacteristic
733C2#1059606311yescharacteristic
734C2#1059607811yescharacteristic
735C2#1059608611yescharacteristic
736C2#1059613411yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#386C2
socle, cosocleC23×C32C24
prime radicalC2×#64149C2
hypercenter#386C3⋊D3
hypocenterC32#2328
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×#638C2semidirect
3. C2×#64090C2semidirect
4. C32×#386C2semidirect
5. #10592919C2semidirect
6. #10592912C2semidirect
7. #10592657C2semidirect
8. #10592656C2semidirect
9. #10592656C2semidirect
10. #10592655C2semidirect
11. #10592655C2semidirect
12. #10592364C2semidirect
13. #10592364C2semidirect
14. #10592349C2semidirect
15. #10592347C2semidirect
33. #64149C4semidirect
58. C3×#386D3semidirect
76. C2×C32×D4C2×C4semidirect
93. C2×#638C2×C4semidirect
94. C2×#638C2×C4semidirect
95. C2×#638C2×C4semidirect
96. C2×#638C2×C4semidirect
108. C2×C4⋊(C3⋊D3)C2×C4semidirect
130. C4×C3⋊Dic3C2×C4semidirect
131. C4×C3⋊Dic3D4semidirect
255. #386C3⋊D3semidirect
264. C2×C3×D4C4×D3semidirect
508. C2×D4C4×C3⋊D3semidirect
595. C32#2328semidirect
725. C3#74667semidirect

Maximal subgroups

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

subgroupindex
C2×#641492
C2×C4×#6382
C2×#640902
C32×#3862
#105929192
#105929122
#105926572
#105926562
#105926552
#105923642
#105923492
#105923472
#746673