Finite Group Databasebeta

← #11803294

Subgroups — #11803294

Order 1152.

1829 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic, complemented
2C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
3C2×#63977C211yesmaximal, characteristic
4C3×C4×#217C211yesmaximal, characteristic, complemented
5#10591718C211yesmaximal, characteristic, complemented
6#10591711C211yesmaximal, characteristic, complemented
7#10591706C211yesmaximal, characteristic, complemented
8#10591387C212yesmaximal, complemented
9#10591383C212yesmaximal, complemented
10#10591287C212yesmaximal, complemented
11#10591280C212yesmaximal, complemented
12#82096—31nomaximal
13#73569—31nomaximal
14C24×C3×D3C2211yescharacteristic
15C23×C32×C4C2211yescharacteristic
16C22×#638C2211yescharacteristic
17C22×C4×C3⋊D3C2211yescharacteristic, complemented
18C23×C3×Dic3C2211yescharacteristic
19C22×#626C2212yes—
20C2×#3757C2211yescharacteristic
21C4×#638—24no—
22C2×#3752C2211yescharacteristic, complemented
23C2×#3750C2211yescharacteristic, complemented
24C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4—24no—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×C4×Dic3C2212yescomplemented
31#63977C418yescomplemented
32C2×Dic3⋊Dic3C2212yescomplemented
33C2×#3722C2212yescomplemented
34C2×(C2×D3)⋊Dic3C2212yes—
35C2×(C2×D3)⋊Dic3C2212yes—
36C2×(C2×D3)⋊Dic3C2212yes—
37C3×C3⋊#95C2212yescomplemented
38#63579C2212yescomplemented
39#63579C2212yescomplemented
40C22×C3×C22⋊C4—31no—
41C2×#953—31no—
42C2×C4×#67—31no—
43C2×C4×#67—31no—
44C2×C4×#67—61no—
45C22×(C2×D3)⋊C4D311yescharacteristic, complemented
46C2×#882—31no—
47C3×C4×C22⋊C4—31no—
48#5247—31no—
49#5213—31no—
50#5210—31no—
51C4×#217D311yescharacteristic, complemented
52#4958—31no—
53#4957—32no—
54#4956—32no—
55#4955—31no—
56#4950—31no—
57#4945—32no—
58#4944—32no—
59#4940—32no—
60#4939—32no—
61#4670—32no—
62#4665—32no—
63C24×C32C2311yescharacteristic
64C23×C3⋊D3C2311yescharacteristic
65C23×C3×D3—22no—
66C23×C3×D3—22no—
67C23×C3×D3—42no—
68C23×C3×D3—42no—
69C23×C3×D3C2×C414yescomplemented
70C23×C3×D3C2312yes—
71C22×C32×C4—42no—
72C22×C32×C4D414yescomplemented
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2311yescharacteristic
75C2×#638—22no—
76C2×#638—22no—
77C2×#638C2×C414yes—
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2311yescharacteristic
80C22×C3⋊Dic3C2311yescharacteristic
81C2×C4×C3⋊D3—22no—
82C2×C4×C3⋊D3—42no—
83C22×C3×Dic3—22no—
84C22×C3×Dic3—42no—
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2312yes—
88C2×#626—42no—
89C2×#626—42no—
90C2×#626C2×C418yescomplemented
91#3757—22no—
92#3752—22no—
93#3750—22no—
94C4×C3⋊Dic3—22no—
95C3×#217—22no—
96C3×#217C2×C414yescomplemented
97C3×(C2×D3)⋊C4—24no—
98C3×(C2×D3)⋊C4—24no—
99C3×C4×Dic3—42no—
100Dic3⋊Dic3—42no—
101#3722—42no—
102(C2×D3)⋊Dic3—42no—
103(C2×D3)⋊Dic3—42no—
104(C2×D3)⋊Dic3C2×C418yescomplemented
105#2321—91noSylow
106C25×C3—31no—
107C24×D3C2×D311yescharacteristic
108C23×C3×C4—21no—
109C23×C3×C4—31no—
110C23×C3×C4C2×D311yescharacteristic
111C23×C3×C4C2×D311yescharacteristic
112C22×#67—31no—
113C22×#67—31no—
114C22×#67—32no—
115C22×#67—61no—
116C23×Dic3C2×D311yescharacteristic
117C22×D12—32no—
118C22×C4×D3—31no—
119C22×C4×D3—31no—
120C22×C4×D3—61no—
121C2×C3×C22⋊C4—31no—
122C2×C3×C22⋊C4—31no—
123C2×C3×C22⋊C4—32no—
124C2×C3×C22⋊C4—32no—
125C2×C3×C22⋊C4—64no—
126C2×C3×C42—32no—
127#953—38no—
128C2×#217—32no—
129C2×#217—31no—
130C2×#217—31no—
131C2×#217—32no—
132C2×#217—32no—
133C2×#217—61no—
134C2×#217C2×D311yescharacteristic
135C2×#217C2×D311yescharacteristic
136C4×#67—68no—
137C4×#67—64no—
138C4×#67—64no—
139C2×(C2×D3)⋊C4—24no—
140C2×(C2×D3)⋊C4—32no—
141C2×(C2×D3)⋊C4—31no—
142C2×(C2×D3)⋊C4—31no—
143C2×(C2×D3)⋊C4—32no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4—32no—
146C2×(C2×D3)⋊C4—32no—
147C2×(C2×D3)⋊C4—61no—
148C2×(C2×D3)⋊C4C2×D312yes—
149C2×(C2×D3)⋊C4C2×D312yes—
150C2×C4⋊Dic3—32no—
151C2×Dic3⋊C4—31no—
152C2×Dic3⋊C4—31no—
153C2×Dic3⋊C4—32no—
154C2×Dic3⋊C4—61no—
155C2×C4×Dic3—31no—
156C2×C4×Dic3—31no—
157C2×C4×Dic3—61no—
158C2×C4×Dic3C2×D312yescomplemented
159#882—38no—
160C3×#95—32no—
161C3⋊#95—32no—
162C3⋊#95—32no—
163C3⋊#95—32no—
164C3⋊#95—32no—
165C3⋊#95C2×D312yescomplemented
166C23×C32—22no—
167C23×C32—22no—
168C23×C32C22×C412yes—
169C23×C32C2×D412yes—
170C23×C32#4112yes—
171C23×C32C2411yescharacteristic
172C22×C3⋊D3—21no—
173C22×C3⋊D3—21no—
174C22×C3⋊D3—22no—
175C22×C3⋊D3—22no—
176C22×C3⋊D3C22×C412yes—
177C22×C3×D3—28no—
178C22×C3×D3—22no—
179C22×C3×D3—22no—
180C22×C3×D3—22no—
181C22×C3×D3—22no—
182C22×C3×D3—22no—
183C22×C3×D3—22no—
184C22×C3×D3—48no—
185C22×C3×D3—44no—
186C22×C3×D3—44no—
187C22×C3×D3—48no—
188C22×C3×D3C22×C414yes—
189C2×C32×C4—22no—
190C2×C32×C4—22no—
191C2×C32×C4—44no—
192C2×C32×C4C2×D412yes—
193C2×C32×C4C2×D412yes—
194#638—28no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—21no—
198C2×C3⋊Dic3—21no—
199C2×C3⋊Dic3—22no—
200C2×C3⋊Dic3—22no—
201C2×C3⋊Dic3C22×C412yes—
202C4×C3⋊D3—44no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—44no—
212C2×C3×Dic3C22×C414yes—
213#626—48no—
214C2×#120—91no—
215C2×C4×D4—91no—
216C22×C22⋊C4—31no—
217#390—92no—
218#388—92no—
219#388—92no—
220#386—92no—
221#386—91no—
222#385—91no—
223#379—91no—
224C4×C22⋊C4—31no—
225C24×C3—21no—
226C24×C3—32no—
227C24×C3—34no—
228C24×C3—62no—
229C24×C3—62no—
230C24×C3—122no—
231C24×C3—122no—
232C24×C3C22×D311yescharacteristic
233C24×C3C22×D311yescharacteristic
234C23×D3—22no—
235C23×D3—22no—
236C23×D3—31no—
237C23×D3—31no—
238C23×D3—42no—
239C23×D3—42no—
240C23×D3—61no—
241C23×D3C4×D314yescomplemented
242C23×D3C22×D312yes—
243C22×C3×C4—24no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—32no—
247C22×C3×C4—32no—
248C22×C3×C4—32no—
249C22×C3×C4—42no—
250C22×C3×C4—42no—
251C22×C3×C4—44no—
252C22×C3×C4—62no—
253C22×C3×C4—122no—
254C22×C3×C4D1214yescomplemented
255C22×C3×C4#6714yescomplemented
256C22×C3×C4C22×D311yescharacteristic
257C22×C3×C4C22×D311yescharacteristic
258C22×C3×C4C22×D311yescharacteristic
259C22×C3×C4C22×D311yescharacteristic
260C2×#67—34no—
261C2×#67—34no—
262C2×#67—38no—
263C2×#67—64no—
264C2×#67—64no—
265C2×#67—64no—
266C2×#67—62no—
267C2×#67—62no—
268C2×#67—62no—
269C2×#67—62no—
270C2×#67—122no—
271C2×#67—122no—
272C22×Dic3—22no—
273C22×Dic3—31no—
274C22×Dic3—31no—
275C22×Dic3—31no—
276C22×Dic3—31no—
277C22×Dic3—31no—
278C22×Dic3—31no—
279C22×Dic3—42no—
280C22×Dic3—61no—
281C22×Dic3—61no—
282C22×Dic3—61no—
283C22×Dic3C22×D312yes—
284C22×Dic3C22×D312yes—
285C22×Dic3C22×D312yes—
286C2×D12—38no—
287C2×D12—122no—
288C2×D12—122no—
289C2×C4×D3—64no—
290C2×C4×D3—62no—
291C2×C4×D3—62no—
292C2×C4×D3—122no—
293C2×C4×D3—122no—
294C2×C4×D3—124no—
295C3×C22⋊C4—34no—
296C3×C22⋊C4—62no—
297C3×C22⋊C4—64no—
298C3×C22⋊C4—64no—
299C3×C42—122no—
300#217—22no—
301#217—38no—
302#217—64no—
303#217—62no—
304#217—62no—
305#217—122no—
306#217—122no—
307#217C4×D314yescomplemented
308(C2×D3)⋊C4—24no—
309(C2×D3)⋊C4—24no—
310(C2×D3)⋊C4—38no—
311(C2×D3)⋊C4—64no—
312(C2×D3)⋊C4—62no—
313(C2×D3)⋊C4—62no—
314(C2×D3)⋊C4—122no—
315(C2×D3)⋊C4—122no—
316(C2×D3)⋊C4—122no—
317(C2×D3)⋊C4—122no—
318C4⋊Dic3—122no—
319Dic3⋊C4—64no—
320Dic3⋊C4—62no—
321Dic3⋊C4—62no—
322Dic3⋊C4—122no—
323C4×Dic3—42no—
324C4×Dic3—64no—
325C4×Dic3—62no—
326C4×Dic3—62no—
327C22×C32—24no—
328C22×C32—22no—
329C22×C32—22no—
330C22×C32—24no—
331C22×C32C4×D414yes—
332C22×C32C23×C411yescharacteristic
333C22×C32C22×D411yescharacteristic
334C22×C32C2×#4111yescharacteristic
335C22×C32H(5,𝔽2)12yes—
336C22×C32H(5,𝔽2)12yes—
337C2×C3⋊D3—22no—
338C2×C3⋊D3—24no—
339C2×C3⋊D3—41no—
340C2×C3⋊D3—41no—
341C2×C3⋊D3—42no—
342C2×C3×D3—24no—
343C2×C3×D3—24no—
344C2×C3×D3—24no—
345C2×C3×D3—416no—
346C2×C3×D3—42no—
347C2×C3×D3—42no—
348C2×C3×D3—42no—
349C2×C3×D3—42no—
350C32×C4—22no—
351C32×C4—22no—
352C3⋊Dic3—22no—
353C3⋊Dic3—41no—
354C3⋊Dic3—41no—
355C3×Dic3—24no—
356C3×Dic3—42no—
357C3×Dic3—42no—
358C25—31no—
359C22×D4—92no—
360C22×D4—91no—
361C23×C4—31no—
362C23×C4—91no—
363C23×C4D3211yescharacteristic
364#120—98no—
365C4×D4—184no—
366C2×C4⋊C4—91no—
367C2×C4⋊C4—92no—
368C2×C22⋊C4—31no—
369C2×C22⋊C4—31no—
370C2×C22⋊C4—32no—
371C2×C22⋊C4—32no—
372C2×C22⋊C4—64no—
373C2×C22⋊C4—92no—
374C2×C22⋊C4—91no—
375C2×C22⋊C4—91no—
376C2×C22⋊C4—92no—
377C2×C22⋊C4—92no—
378C2×C22⋊C4—92no—
379C2×C42—32no—
380C2×C42—91no—
381#95—32no—
382#95—92no—
383#95—92no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—21no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—34no—
393C23×C3—42no—
394C23×C3—42no—
395C23×C3—68no—
396C23×C3—62no—
397C23×C3—62no—
398C23×C3—62no—
399C23×C3—62no—
400C23×C3—62no—
401C23×C3—62no—
402C23×C3—128no—
403C23×C3—124no—
404C23×C3—124no—
405C23×C3—128no—
406C23×C3C2×C4×D312yes—
407C23×C3C2×C4×D312yes—
408C23×C3C2×D1212yes—
409C23×C3#23512yes—
410C23×C3#23512yes—
411C23×C3C2×#6712yes—
412C23×C3C23×D311yescharacteristic
413C23×C3C23×D311yescharacteristic
414C22×D3—28no—
415C22×D3—22no—
416C22×D3—22no—
417C22×D3—22no—
418C22×D3—22no—
419C22×D3—22no—
420C22×D3—22no—
421C22×D3—32no—
422C22×D3—32no—
423C22×D3—48no—
424C22×D3—48no—
425C22×D3—44no—
426C22×D3—44no—
427C22×D3—62no—
428C22×D3—62no—
429C22×D3—62no—
430C22×D3—61no—
431C22×D3—61no—
432C22×D3—61no—
433C22×D3—62no—
434C22×D3—62no—
435C22×D3—62no—
436C22×D3—62no—
437C22×D3—61no—
438C22×D3—122no—
439C22×D3—122no—
440C22×D3C2×C4×D314yes—
441C2×C3×C4—24no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—34no—
449C2×C3×C4—42no—
450C2×C3×C4—44no—
451C2×C3×C4—44no—
452C2×C3×C4—48no—
453C2×C3×C4—62no—
454C2×C3×C4—62no—
455C2×C3×C4—62no—
456C2×C3×C4—62no—
457C2×C3×C4—62no—
458C2×C3×C4—62no—
459C2×C3×C4—62no—
460C2×C3×C4—62no—
461C2×C3×C4—124no—
462C2×C3×C4C2×D1212yes—
463C2×C3×C4C2×D1212yes—
464C2×C3×C4C2×#6712yes—
465C2×C3×C4C2×#6712yes—
466#67—616no—
467#67—68no—
468#67—68no—
469#67—128no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—22no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—32no—
479C2×Dic3—32no—
480C2×Dic3—44no—
481C2×Dic3—62no—
482C2×Dic3—62no—
483C2×Dic3—62no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—62no—
489C2×Dic3—62no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—62no—
493C2×Dic3—62no—
494C2×Dic3—62no—
495C2×Dic3—62no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—122no—
499C2×Dic3—122no—
500C2×Dic3C2×C4×D314yes—
501D12—128no—
502C4×D3—128no—
503C4×D3—124no—
504C4×D3—124no—
505C2×C32—24no—
506C2×C32C2×C4×D411yescharacteristic
507C2×C32#51812yes—
508C2×C32#53411yescharacteristic
509C2×C32#53511yescharacteristic
510C2×C32#53812yes—
511C3⋊D3—42no—
512C3×D3—44no—
513C24—32no—
514C24—34no—
515C24—62no—
516C24—62no—
517C24—91no—
518C24—122no—
519C24—122no—
520C24C2×D3211yescharacteristic
521C2×D4—98no—
522C2×D4—94no—
523C2×D4—182no—
524C2×D4—182no—
525C2×D4—362no—
526C2×D4—362no—
527C22×C4—32no—
528C22×C4—32no—
529C22×C4—32no—
530C22×C4—42no—
531C22×C4—62no—
532C22×C4—91no—
533C22×C4—91no—
534C22×C4—91no—
535C22×C4—122no—
536C22×C4—182no—
537C22×C4—362no—
538C22×C4#62614yescomplemented
539C22×C4C2×D3211yescharacteristic
540C22×C4C2×D3211yescharacteristic
541C4⋊C4—182no—
542C4⋊C4—362no—
543C22⋊C4—34no—
544C22⋊C4—62no—
545C22⋊C4—64no—
546C22⋊C4—64no—
547C22⋊C4—98no—
548C22⋊C4—182no—
549C22⋊C4—182no—
550C22⋊C4—362no—
551C22⋊C4—362no—
552C22⋊C4—362no—
553C42—122no—
554C42—182no—
555C22×C3—24no—
556C22×C3—22no—
557C22×C3—24no—
558C22×C3—22no—
559C22×C3—24no—
560C22×C3—22no—
561C22×C3—22no—
562C22×C3—24no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—22no—
566C22×C3—21no—
567C22×C3—22no—
568C22×C3—24no—
569C22×C3—42no—
570C22×C3—44no—
571C22×C3—42no—
572C22×C3—44no—
573C22×C3—64no—
574C22×C3—64no—
575C22×C3—64no—
576C22×C3—1216no—
577C22×C3—122no—
578C22×C3—122no—
579C22×C3—122no—
580C22×C3—122no—
581C22×C3C4×D1214yes—
582C22×C3C4×#6714yes—
583C22×C3C22×C4×D311yescharacteristic
584C22×C3C22×C4×D311yescharacteristic
585C22×C3C22×D1211yescharacteristic
586C22×C3C2×#23511yescharacteristic
587C22×C3C2×#23511yescharacteristic
588C22×C3#100412yes—
589C22×C3#100412yes—
590C22×C3#100412yes—
591C22×C3#100912yes—
592C22×C3C22×#6711yescharacteristic
593C2×D3—24no—
594C2×D3—24no—
595C2×D3—24no—
596C2×D3—416no—
597C2×D3—42no—
598C2×D3—42no—
599C2×D3—42no—
600C2×D3—42no—
601C2×D3—64no—
602C2×D3—62no—
603C2×D3—64no—
604C2×D3—62no—
605C2×D3—64no—
606C2×D3—124no—
607C2×D3—122no—
608C2×D3—124no—
609C2×D3—122no—
610C2×D3—121no—
611C2×D3—122no—
612C2×D3—121no—
613C2×D3—121no—
614C2×D3—121no—
615C2×D3—122no—
616C3×C4—24no—
617C3×C4—22no—
618C3×C4—22no—
619C3×C4—22no—
620C3×C4—22no—
621C3×C4—42no—
622C3×C4—64no—
623C3×C4—122no—
624C3×C4—122no—
625Dic3—24no—
626Dic3—42no—
627Dic3—42no—
628Dic3—64no—
629Dic3—62no—
630Dic3—62no—
631Dic3—122no—
632Dic3—122no—
633Dic3—121no—
634Dic3—121no—
635Dic3—121no—
636Dic3—121no—
637C32#232111yescharacteristic, complemented, Sylow
638C23—22no—
639C23—22no—
640C23—34no—
641C23—62no—
642C23—62no—
643C23—62no—
644C23—62no—
645C23—62no—
646C23—62no—
647C23—68no—
648C23—92no—
649C23—128no—
650C23—124no—
651C23—128no—
652C23—124no—
653C23—181no—
654C23—182no—
655C23—181no—
656C23—182no—
657C23#379812yes—
658C23C4×D3212yes—
659C23C2×#62612yes—
660C23C22×D3211yescharacteristic
661D4—188no—
662D4—368no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—34no—
666C2×C4—44no—
667C2×C4—62no—
668C2×C4—62no—
669C2×C4—62no—
670C2×C4—62no—
671C2×C4—62no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—62no—
675C2×C4—92no—
676C2×C4—124no—
677C2×C4—181no—
678C2×C4—181no—
679C2×C4—182no—
680C2×C4—181no—
681C2×C4—181no—
682C2×C4—182no—
683C2×C4—364no—
684C2×C4C2×#62612yes—
685C2×C4C2×#62612yes—
686C2×C3—24no—
687C2×C3—24no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—22no—
691C2×C3—21no—
692C2×C3—22no—
693C2×C3—44no—
694C2×C3—124no—
695C2×C3C2×C4×D1211yescharacteristic
696C2×C3#548612yes—
697C2×C3#549311yescharacteristic
698C2×C3#549412yes—
699C2×C3#552511yescharacteristic
700C2×C3#554512yes—
701C2×C3#556012yes—
702C2×C3C2×C4×#6711yescharacteristic
703C2×C3#580411yescharacteristic
704C2×C3#580511yescharacteristic
705D3—44no—
706D3—124no—
707D3—122no—
708D3—122no—
709C22—22no—
710C22—24no—
711C22—22no—
712C22—24no—
713C22—64no—
714C22—64no—
715C22—64no—
716C22—1216no—
717C22—122no—
718C22—122no—
719C22—122no—
720C22—122no—
721C22—182no—
722C22—184no—
723C22—361no—
724C22—362no—
725C22—361no—
726C22C4×#62614yes—
727C22C2×#379811yescharacteristic
728C22C2×C4×D3211yescharacteristic
729C22#6430712yes—
730C22C22×#62611yescharacteristic
731C22#6433012yes—
732C4—22no—
733C4—22no—
734C4—64no—
735C4—122no—
736C4—122no—
737C4—182no—
738C4—361no—
739C4—361no—
740C3—21no—
741C3#7356911yescharacteristic, complemented
742C3#8209611yescharacteristic, complemented
743C2—24no—
744C2—124no—
745C2—362no—
746C2C2×C4×#62611yescharacteristic
747C2#1059503612yes—
748C2#1059504211yescharacteristic
749C2#1059505612yes—
750C2#1059551911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63977C2
hypercenterC23×C4D32
hypocenterC32#2321
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×#638C2semidirect
2. C22×C3×(C2×D3)⋊C4C2semidirect
4. C3×C4×#217C2semidirect
5. #10591718C2semidirect
6. #10591711C2semidirect
7. #10591706C2semidirect
8. #10591387C2semidirect
9. #10591383C2semidirect
10. #10591287C2semidirect
11. #10591280C2semidirect
17. C22×C4×C3⋊D3C22semidirect
22. C2×#3752C22semidirect
23. C2×#3750C22semidirect
24. C2×C4×C3⋊Dic3C22semidirect
30. C2×C3×C4×Dic3C22semidirect
31. #63977C4semidirect
32. C2×Dic3⋊Dic3C22semidirect
33. C2×#3722C22semidirect
37. C3×C3⋊#95C22semidirect
38. #63579C22semidirect
39. #63579C22semidirect
45. C22×(C2×D3)⋊C4D3semidirect
51. C4×#217D3semidirect
69. C23×C3×D3C2×C4semidirect
72. C22×C32×C4D4semidirect
90. C2×#626C2×C4semidirect
96. C3×#217C2×C4semidirect
104. (C2×D3)⋊Dic3C2×C4semidirect
158. C2×C4×Dic3C2×D3semidirect
165. C3⋊#95C2×D3semidirect
241. C23×D3C4×D3semidirect
254. C22×C3×C4D12semidirect
255. C22×C3×C4#67semidirect
307. #217C4×D3semidirect
538. C22×C4#626semidirect
637. C32#2321semidirect
741. C3#73569semidirect
742. C3#82096semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C22×C3×(C2×D3)⋊C42
C2×#639772
C3×C4×#2172
#105917182
#105917112
#105917062
#105913872
#105913832
#105912872
#105912802
#820963
#735693