Finite Group Databasebeta

← #11803300

Subgroups — #11803300

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×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#937C211yesmaximal, characteristic
3C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
4C3×#5220C211yesmaximal, characteristic, complemented
5#10591718C211yesmaximal, characteristic, complemented
6#10591713C212yesmaximal, complemented
7#10591707C212yesmaximal, complemented
8#10591706C211yesmaximal, characteristic, complemented
9#10591705C211yesmaximal, characteristic, complemented
10#10591316C212yesmaximal, complemented
11#10591286C212yesmaximal, complemented
12#82578—31nomaximal
13#74875—31nomaximal
14C24×C3×D3C2211yescharacteristic
15C22×C32×D4C2211yescharacteristic
16C23×C3⋊Dic3C2211yescharacteristic
17C23×C3⋊Dic3C2211yescharacteristic, complemented
18C22×C3×#67C2212yes—
19C23×C3×Dic3C2211yescharacteristic
20C2×#3757C2211yescharacteristic
21C2×#3757C2211yescharacteristic, complemented
22D4×C3⋊Dic3—24no—
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
24C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2212yescomplemented
28C3×#937C418yescomplemented
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×Dic3⋊Dic3C2212yescomplemented
31C2×(C2×D3)⋊Dic3—24no—
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×(C2×D3)⋊Dic3C2212yes—
35C2×(C2×D3)⋊Dic3C2212yes—
36C2×Dic32C2212yescomplemented
37C3×C3⋊#95C2212yescomplemented
38#63579C2212yescomplemented
39#63579C2212yescomplemented
40C2×C3×#120—31no—
41C22×#217—31no—
42C2×#937D311yescharacteristic
43C2×D4×Dic3—31no—
44C2×D4×Dic3—31no—
45C2×D4×Dic3—61no—
46C22×(C2×D3)⋊C4—31no—
47C3×#386—31no—
48#5247—31no—
49#5221—32no—
50#5220—32no—
51#5220D311yescharacteristic, complemented
52#5210—31no—
53#4958—32no—
54#4957—32no—
55#4955—31no—
56#4951—32no—
57#4951—32no—
58#4950—31no—
59Dic3×C22⋊C4—31no—
60Dic3×C22⋊C4—31no—
61#4670—32no—
62#4669—32no—
63C24×C32C2311yescharacteristic
64C24×C32C2311yescharacteristic
65C23×C3×D3—22no—
66C23×C3×D3—22no—
67C23×C3×D3—42no—
68C23×C3×D3—42no—
69C23×C3×D3C2×C414yescomplemented
70C23×C3×D3C2312yes—
71C2×C32×D4—22no—
72C2×C32×D4—22no—
73C2×C32×D4C2×C414yes—
74C22×C32×C4C2311yescharacteristic
75C22×C3⋊Dic3—22no—
76C22×C3⋊Dic3—42no—
77C22×C3⋊Dic3—42no—
78C22×C3⋊Dic3D414yescomplemented
79C22×C3⋊Dic3C2311yescharacteristic
80C22×C3⋊Dic3C2311yescharacteristic
81C22×C3⋊Dic3C2311yescharacteristic
82C22×C3⋊Dic3C2311yescharacteristic
83C2×C3×#67—42no—
84C2×C3×#67—42no—
85C2×C3×#67C2×C418yescomplemented
86C22×C3×Dic3—22no—
87C22×C3×Dic3—42no—
88C22×C3×Dic3C2312yes—
89C22×C3×Dic3C2312yes—
90C22×C3×Dic3C2312yes—
91#3757—22no—
92#3757—22no—
93C4⋊(C3⋊Dic3)—22no—
94C4×C3⋊Dic3—22no—
95C3×#217—22no—
96C3×#217—42no—
97C3×#217C2×C414yescomplemented
98C3×(C2×D3)⋊C4C2×C418yescomplemented
99Dic3⋊Dic3—42no—
100(C2×D3)⋊Dic3—24no—
101(C2×D3)⋊Dic3—24no—
102(C2×D3)⋊Dic3—42no—
103(C2×D3)⋊Dic3—42no—
104Dic32—42no—
105#2321—91noSylow
106C25×C3—31no—
107C24×D3C2×D311yescharacteristic
108C22×C3×D4—21no—
109C22×C3×D4—32no—
110C22×C3×D4C2×D311yescharacteristic
111C22×C3×D4C2×D311yescharacteristic
112C23×C3×C4—31no—
113C22×#67C2×D312yes—
114C23×Dic3—31no—
115C23×Dic3—31no—
116C23×Dic3—31no—
117C23×Dic3—31no—
118C23×Dic3—61no—
119C23×Dic3—61no—
120C23×Dic3C2×D311yescharacteristic
121C3×#120—38no—
122C2×C3×C22⋊C4—31no—
123C2×C3×C22⋊C4—32no—
124C2×C3×C22⋊C4—31no—
125C2×C3×C22⋊C4—32no—
126C2×#217—31no—
127C2×#217—31no—
128C2×#217—31no—
129C2×#217—31no—
130C2×#217—32no—
131C2×#217—32no—
132C2×#217—32no—
133C2×#217—32no—
134C2×#217—61no—
135C2×#217—61no—
136C2×#217—64no—
137C2×#217C2×D311yescharacteristic
138C2×#217C2×D311yescharacteristic
139C2×#217C2×D312yescomplemented
140#937Dic318yescomplemented
141D4×Dic3—64no—
142D4×Dic3—64no—
143D4×Dic3—68no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4—32no—
146C2×(C2×D3)⋊C4—32no—
147C2×(C2×D3)⋊C4—32no—
148C2×(C2×D3)⋊C4—64no—
149C2×(C2×D3)⋊C4C2×D312yes—
150C2×C4⋊Dic3—31no—
151C2×C4⋊Dic3—31no—
152C2×C4⋊Dic3—32no—
153C2×C4⋊Dic3—61no—
154C2×Dic3⋊C4—32no—
155C2×C4×Dic3—31no—
156C2×C4×Dic3—31no—
157C2×C4×Dic3—32no—
158C2×C4×Dic3—32no—
159C2×C4×Dic3—61no—
160C3×#95—32no—
161C3⋊#95—32no—
162C3⋊#95—32no—
163C3⋊#95—32no—
164C3⋊#95—32no—
165C3⋊#95C2×D312yescomplemented
166C23×C32—21no—
167C23×C32—21no—
168C23×C32—22no—
169C23×C32—22no—
170C23×C32—22no—
171C23×C32—22no—
172C23×C32C22×C412yes—
173C23×C32C22×C412yes—
174C23×C32C2×D412yes—
175C23×C32#4112yes—
176C23×C32C2411yescharacteristic
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—
189C32×D4—28no—
190C2×C32×C4—21no—
191C2×C32×C4—21no—
192C2×C32×C4C22×C412yes—
193C2×C3⋊Dic3—22no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—22no—
197C2×C3⋊Dic3—22no—
198C2×C3⋊Dic3—22no—
199C2×C3⋊Dic3—44no—
200C2×C3⋊Dic3—44no—
201C2×C3⋊Dic3C2×D412yes—
202C2×C3⋊Dic3C2×D412yes—
203C3×#67—48no—
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—22no—
212C2×C3×Dic3—44no—
213C2×C3×Dic3C22×C414yes—
214C2×#120—31no—
215C2×C4×D4—91no—
216C22×C22⋊C4—91no—
217#390—92no—
218#388—92no—
219#388—92no—
220#386—31no—
221#386—92no—
222#385—91no—
223#379—91no—
224C4×C22⋊C4—91no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3—32no—
228C24×C3—34no—
229C24×C3—62no—
230C24×C3—62no—
231C24×C3—122no—
232C24×C3—122no—
233C24×C3C22×D311yescharacteristic
234C24×C3C22×D311yescharacteristic
235C24×C3C22×D311yescharacteristic
236C24×C3C22×D311yescharacteristic
237C23×D3—22no—
238C23×D3—22no—
239C23×D3—42no—
240C23×D3—42no—
241C23×D3C2×Dic314yescomplemented
242C23×D3C22×D312yes—
243C2×C3×D4—24no—
244C2×C3×D4—24no—
245C2×C3×D4—22no—
246C2×C3×D4—22no—
247C2×C3×D4—22no—
248C2×C3×D4—22no—
249C2×C3×D4—24no—
250C2×C3×D4—38no—
251C2×C3×D4—122no—
252C2×C3×D4—122no—
253C2×C3×D4C4×D314yes—
254C2×C3×D4C2×Dic314yes—
255C22×C3×C4—21no—
256C22×C3×C4—32no—
257C22×C3×C4—32no—
258C22×C3×C4—32no—
259C22×C3×C4—62no—
260C22×C3×C4—122no—
261C22×C3×C4C22×D311yescharacteristic
262C22×C3×C4C22×D311yescharacteristic
263C2×#67—42no—
264C2×#67—42no—
265C2×#67C2×Dic318yescomplemented
266C22×Dic3—22no—
267C22×Dic3—31no—
268C22×Dic3—31no—
269C22×Dic3—31no—
270C22×Dic3—31no—
271C22×Dic3—34no—
272C22×Dic3—34no—
273C22×Dic3—31no—
274C22×Dic3—31no—
275C22×Dic3—31no—
276C22×Dic3—31no—
277C22×Dic3—42no—
278C22×Dic3—61no—
279C22×Dic3—61no—
280C22×Dic3—61no—
281C22×Dic3—61no—
282C22×Dic3—64no—
283C22×Dic3—62no—
284C22×Dic3—62no—
285C22×Dic3—64no—
286C22×Dic3—122no—
287C22×Dic3—122no—
288C22×Dic3—122no—
289C22×Dic3—122no—
290C22×Dic3—124no—
291C22×Dic3—124no—
292C22×Dic3C22×D312yes—
293C22×Dic3C22×D312yes—
294C22×Dic3C22×D312yes—
295C3×C22⋊C4—34no—
296C3×C22⋊C4—38no—
297C3×C22⋊C4—62no—
298C3×C22⋊C4—122no—
299#217—22no—
300#217—42no—
301#217—64no—
302#217—64no—
303#217—62no—
304#217—62no—
305#217—64no—
306#217—64no—
307#217—62no—
308#217—62no—
309#217—122no—
310#217—122no—
311#217C2×Dic314yescomplemented
312(C2×D3)⋊C4—64no—
313(C2×D3)⋊C4—64no—
314(C2×D3)⋊C4—122no—
315(C2×D3)⋊C4—122no—
316(C2×D3)⋊C4C2×Dic318yescomplemented
317C4⋊Dic3—62no—
318C4⋊Dic3—62no—
319C4⋊Dic3—64no—
320C4⋊Dic3—122no—
321Dic3⋊C4—122no—
322C4×Dic3—62no—
323C4×Dic3—62no—
324C4×Dic3—64no—
325C4×Dic3—122no—
326C4×Dic3—122no—
327C22×C32—22no—
328C22×C32—24no—
329C22×C32—22no—
330C22×C32—22no—
331C22×C32—24no—
332C22×C32—24no—
333C22×C32—41no—
334C22×C32—41no—
335C22×C32—42no—
336C22×C32C4×D414yes—
337C22×C32C23×C411yescharacteristic
338C22×C32C22×D411yescharacteristic
339C22×C32C2×#4111yescharacteristic
340C22×C32H(5,𝔽2)12yes—
341C22×C32H(5,𝔽2)12yes—
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—
351C3⋊Dic3—22no—
352C3⋊Dic3—22no—
353C3⋊Dic3—41no—
354C3⋊Dic3—41no—
355C3×Dic3—24no—
356C3×Dic3—42no—
357C3×Dic3—42no—
358C25—31no—
359C22×D4—32no—
360C22×D4D3211yescharacteristic
361C23×C4—31no—
362C23×C4—91no—
363C23×C4—91no—
364#120—38no—
365C4×D4—184no—
366C2×C4⋊C4—91no—
367C2×C4⋊C4—92no—
368C2×C22⋊C4—31no—
369C2×C22⋊C4—32no—
370C2×C22⋊C4—31no—
371C2×C22⋊C4—32no—
372C2×C22⋊C4—92no—
373C2×C22⋊C4—92no—
374C2×C22⋊C4—91no—
375C2×C22⋊C4—91no—
376C2×C22⋊C4—92no—
377C2×C22⋊C4—92no—
378C2×C22⋊C4—184no—
379C2×C42—91no—
380C2×C42—92no—
381#95—32no—
382#95—92no—
383#95—92no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—21no—
393C23×C3—21no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—21no—
399C23×C3—22no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—34no—
404C23×C3—42no—
405C23×C3—42no—
406C23×C3—42no—
407C23×C3—42no—
408C23×C3—68no—
409C23×C3—62no—
410C23×C3—62no—
411C23×C3—62no—
412C23×C3—62no—
413C23×C3—62no—
414C23×C3—62no—
415C23×C3—128no—
416C23×C3—124no—
417C23×C3—124no—
418C23×C3—128no—
419C23×C3C2×C4×D312yes—
420C23×C3C2×C4×D312yes—
421C23×C3D3×D412yes—
422C23×C3D3×D412yes—
423C23×C3#23712yes—
424C23×C3#23712yes—
425C23×C3C22×Dic312yes—
426C23×C3C22×Dic312yes—
427C23×C3C23×D311yescharacteristic
428C23×C3C23×D311yescharacteristic
429C22×D3—28no—
430C22×D3—22no—
431C22×D3—22no—
432C22×D3—22no—
433C22×D3—22no—
434C22×D3—22no—
435C22×D3—22no—
436C22×D3—48no—
437C22×D3—44no—
438C22×D3—44no—
439C22×D3—48no—
440C22×D3C22×Dic314yes—
441C3×D4—216no—
442C3×D4—28no—
443C3×D4—28no—
444C3×D4—128no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—22no—
452C2×C3×C4—34no—
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×C4×D312yes—
463C2×C3×C4C22×Dic312yes—
464#67—48no—
465C2×Dic3—22no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—22no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—22no—
473C2×Dic3—32no—
474C2×Dic3—32no—
475C2×Dic3—32no—
476C2×Dic3—32no—
477C2×Dic3—44no—
478C2×Dic3—62no—
479C2×Dic3—62no—
480C2×Dic3—64no—
481C2×Dic3—62no—
482C2×Dic3—62no—
483C2×Dic3—62no—
484C2×Dic3—62no—
485C2×Dic3—62no—
486C2×Dic3—62no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—62no—
492C2×Dic3—62no—
493C2×Dic3—62no—
494C2×Dic3—62no—
495C2×Dic3—122no—
496C2×Dic3—122no—
497C2×Dic3—122no—
498C2×Dic3—124no—
499C2×Dic3—124no—
500C2×Dic3—128no—
501C2×Dic3—128no—
502C2×Dic3—124no—
503C2×Dic3—124no—
504C2×Dic3C22×Dic314yes—
505C2×C32—24no—
506C2×C32—42no—
507C2×C32C2×C4×D411yescharacteristic
508C2×C32#51812yes—
509C2×C32#53411yescharacteristic
510C2×C32#53511yescharacteristic
511C2×C32#53812yes—
512C3×D3—44no—
513C24—32no—
514C24—34no—
515C24—62no—
516C24—62no—
517C24—122no—
518C24—122no—
519C24C2×D3211yescharacteristic
520C24C2×D3211yescharacteristic
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—38no—
524C2×D4—122no—
525C2×D4—122no—
526C2×D4D3×Dic314yes—
527C22×C4—32no—
528C22×C4—32no—
529C22×C4—32no—
530C22×C4—62no—
531C22×C4—91no—
532C22×C4—91no—
533C22×C4—94no—
534C22×C4—91no—
535C22×C4—91no—
536C22×C4—122no—
537C22×C4—182no—
538C22×C4—362no—
539C22×C4—362no—
540C22×C4C2×D3211yescharacteristic
541C4⋊C4—182no—
542C4⋊C4—362no—
543C22⋊C4—34no—
544C22⋊C4—38no—
545C22⋊C4—62no—
546C22⋊C4—122no—
547C22⋊C4—184no—
548C22⋊C4—184no—
549C22⋊C4—182no—
550C22⋊C4—182no—
551C22⋊C4—362no—
552C22⋊C4—362no—
553C42—182no—
554C42—362no—
555C22×C3—22no—
556C22×C3—24no—
557C22×C3—24no—
558C22×C3—22no—
559C22×C3—22no—
560C22×C3—22no—
561C22×C3—24no—
562C22×C3—24no—
563C22×C3—24no—
564C22×C3—22no—
565C22×C3—22no—
566C22×C3—24no—
567C22×C3—24no—
568C22×C3—22no—
569C22×C3—22no—
570C22×C3—21no—
571C22×C3—21no—
572C22×C3—21no—
573C22×C3—24no—
574C22×C3—42no—
575C22×C3—44no—
576C22×C3—42no—
577C22×C3—44no—
578C22×C3—44no—
579C22×C3—42no—
580C22×C3—42no—
581C22×C3—44no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—42no—
587C22×C3—42no—
588C22×C3—64no—
589C22×C3—64no—
590C22×C3—64no—
591C22×C3—1216no—
592C22×C3—122no—
593C22×C3—122no—
594C22×C3—122no—
595C22×C3—122no—
596C22×C3#67⋊C414yes—
597C22×C3D4×Dic314yes—
598C22×C3C22×C4×D311yescharacteristic
599C22×C3C2×D3×D411yescharacteristic
600C22×C3C2×D3×D411yescharacteristic
601C22×C3C2×#23711yescharacteristic
602C22×C3C2×#23711yescharacteristic
603C22×C3#100412yes—
604C22×C3#100412yes—
605C22×C3#100412yes—
606C22×C3#100912yes—
607C22×C3C23×Dic311yescharacteristic
608C2×D3—24no—
609C2×D3—24no—
610C2×D3—24no—
611C2×D3—416no—
612C2×D3—42no—
613C2×D3—42no—
614C2×D3—42no—
615C2×D3—42no—
616C3×C4—24no—
617C3×C4—22no—
618C3×C4—22no—
619C3×C4—64no—
620C3×C4—122no—
621C3×C4—122no—
622Dic3—24no—
623Dic3—42no—
624Dic3—42no—
625Dic3—64no—
626Dic3—62no—
627Dic3—62no—
628Dic3—62no—
629Dic3—62no—
630Dic3—122no—
631Dic3—122no—
632Dic3—122no—
633Dic3—121no—
634Dic3—121no—
635Dic3—121no—
636Dic3—121no—
637C32#232111yescharacteristic, complemented, Sylow
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—21no—
643C23—21no—
644C23—34no—
645C23—62no—
646C23—62no—
647C23—62no—
648C23—62no—
649C23—62no—
650C23—62no—
651C23—68no—
652C23—128no—
653C23—124no—
654C23—124no—
655C23—128no—
656C23C2×D3×Dic312yes—
657C23C2×D3×Dic312yes—
658C23#380512yes—
659C23#381112yes—
660C23C22×D3211yescharacteristic
661D4—28no—
662D4—128no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—34no—
666C2×C4—62no—
667C2×C4—62no—
668C2×C4—62no—
669C2×C4—62no—
670C2×C4—62no—
671C2×C4—62no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—92no—
675C2×C4—92no—
676C2×C4—124no—
677C2×C4—182no—
678C2×C4—182no—
679C2×C4—182no—
680C2×C4—182no—
681C2×C4—181no—
682C2×C4—181no—
683C2×C4—364no—
684C2×C4—364no—
685C2×C4C2×D3×Dic312yes—
686C2×C3—24no—
687C2×C3—24no—
688C2×C3—22no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—22no—
693C2×C3—44no—
694C2×C3—44no—
695C2×C3—42no—
696C2×C3—42no—
697C2×C3—124no—
698C2×C3C2×#67⋊C411yescharacteristic
699C2×C3#554512yes—
700C2×C3#558911yescharacteristic
701C2×C3#559211yescharacteristic
702C2×C3#559211yescharacteristic
703C2×C3#559312yes—
704C2×C3#561712yes—
705C2×C3#565311yescharacteristic
706C2×C3C2×D4×Dic311yescharacteristic
707C2×C3#579812yes—
708D3—44no—
709C22—24no—
710C22—22no—
711C22—22no—
712C22—24no—
713C22—24no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—42no—
718C22—64no—
719C22—64no—
720C22—64no—
721C22—1216no—
722C22—122no—
723C22—122no—
724C22—122no—
725C22—122no—
726C22#67⋊Dic314yes—
727C22#6431312yes—
728C22#6431412yes—
729C22C22×D3×Dic311yescharacteristic
730C22C2×#380511yescharacteristic
731C22C2×#381111yescharacteristic
732C4—22no—
733C4—64no—
734C4—122no—
735C4—122no—
736C4—182no—
737C4—182no—
738C4—361no—
739C4—361no—
740C3—21no—
741C3#7487511yescharacteristic, complemented
742C3#8257811yescharacteristic, complemented
743C2—24no—
744C2—42no—
745C2—124no—
746C2#1059521512yes—
747C2#1059523911yescharacteristic
748C2#1059524211yescharacteristic
749C2#1059526712yes—
750C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×D4C22
socle, cosocleC23×C32C24
prime radicalC2×C3×#937C2
hypercenterC22×D4D32
hypocenterC32#2321
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊Dic3C2semidirect
3. C22×(C2×D3)⋊Dic3C2semidirect
4. C3×#5220C2semidirect
5. #10591718C2semidirect
6. #10591713C2semidirect
7. #10591707C2semidirect
8. #10591706C2semidirect
9. #10591705C2semidirect
10. #10591316C2semidirect
11. #10591286C2semidirect
17. C23×C3⋊Dic3C22semidirect
21. C2×#3757C22semidirect
23. C2×C4⋊(C3⋊Dic3)C22semidirect
24. C2×C4×C3⋊Dic3C22semidirect
27. C2×C3×#217C22semidirect
28. C3×#937C4semidirect
30. C2×Dic3⋊Dic3C22semidirect
36. C2×Dic32C22semidirect
37. C3×C3⋊#95C22semidirect
38. #63579C22semidirect
39. #63579C22semidirect
51. #5220D3semidirect
69. C23×C3×D3C2×C4semidirect
78. C22×C3⋊Dic3D4semidirect
85. C2×C3×#67C2×C4semidirect
97. C3×#217C2×C4semidirect
98. C3×(C2×D3)⋊C4C2×C4semidirect
139. C2×#217C2×D3semidirect
140. #937Dic3semidirect
165. C3⋊#95C2×D3semidirect
241. C23×D3C2×Dic3semidirect
265. C2×#67C2×Dic3semidirect
311. #217C2×Dic3semidirect
316. (C2×D3)⋊C4C2×Dic3semidirect
637. C32#2321semidirect
741. C3#74875semidirect
742. C3#82578semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C2×C3×#9372
C22×(C2×D3)⋊Dic32
C3×#52202
#105917182
#105917132
#105917072
#105917062
#105917052
#105913162
#105912862
#825783
#748753