Finite Group Databasebeta

← C2×#10591392 #11808167

Subgroups — C2×#10591392 #11808167

Order 1152.

2841 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#626C211yesmaximal, characteristic
2C22×#3752C211yesmaximal, characteristic, complemented
3C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
5C22×#3722C211yesmaximal, characteristic, complemented
6C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
7C2×#63579C211yesmaximal, characteristic, complemented
8#10591392C218yesmaximal, direct product factor
9C2×#4991—31nomaximal
10C2×#4961—31nomaximal
11C24×C3⋊D3C2211yescharacteristic
12C24×C3×D3C2211yescharacteristic
13C23×C32×C4C2211yescharacteristic
14C23×C3⋊Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C22×#626—24no—
19C22×#626—24no—
20C22×#626—24no—
21C22×#626C2214yes—
22C2×#3752—24no—
23C2×#3752C2214yescomplemented
24C2×C3×(C2×D3)⋊C4—24no—
25C2×C3×(C2×D3)⋊C4C2214yescomplemented
26C2×C3×C4⋊Dic3—24no—
27C2×C3×C4⋊Dic3C2214yescomplemented
28C2×#3722—24no—
29C2×#3722C2214yescomplemented
30C2×(C2×D3)⋊Dic3—24no—
31C2×(C2×D3)⋊Dic3C2214yescomplemented
32#63579C2214yescomplemented
33C23×#67—31no—
34C23×D12—31no—
35C22×C3×C4⋊C4—31no—
36C22×C3×C22⋊C4—31no—
37C22×#217—31no—
38C22×(C2×D3)⋊C4—31no—
39C22×(C2×D3)⋊C4—31no—
40C22×(C2×D3)⋊C4—31no—
41C22×(C2×D3)⋊C4—31no—
42C22×(C2×D3)⋊C4—31no—
43C22×(C2×D3)⋊C4—61no—
44C22×(C2×D3)⋊C4D311yescharacteristic, complemented
45C22×C4⋊Dic3D311yescharacteristic, complemented
46C2×C3⋊#95—31no—
47C2×C3⋊#95—31no—
48#4991—38no—
49#4961—38no—
50C24×C32C2311yescharacteristic
51C23×C3⋊D3—22no—
52C23×C3⋊D3—22no—
53C23×C3⋊D3—22no—
54C23×C3⋊D3—22no—
55C23×C3⋊D3—22no—
56C23×C3⋊D3—22no—
57C23×C3⋊D3D414yes—
58C23×C3⋊D3C2312yes—
59C23×C3×D3—22no—
60C23×C3×D3—22no—
61C23×C3×D3—22no—
62C23×C3×D3—22no—
63C23×C3×D3—22no—
64C23×C3×D3—22no—
65C23×C3×D3D414yes—
66C23×C3×D3C2312yes—
67C22×C32×C4—22no—
68C22×C32×C4—22no—
69C22×C32×C4D414yescomplemented
70C22×C32×C4C2312yes—
71C22×C3⋊Dic3—22no—
72C22×C3⋊Dic3—22no—
73C22×C3⋊Dic3—22no—
74C22×C3⋊Dic3C2312yes—
75C22×C3×Dic3—22no—
76C22×C3×Dic3—22no—
77C22×C3×Dic3—22no—
78C22×C3×Dic3—22no—
79C22×C3×Dic3—22no—
80C22×C3×Dic3—22no—
81C22×C3×Dic3—22no—
82C22×C3×Dic3—22no—
83C22×C3×Dic3D414yes—
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2312yes—
87C2×#626—232no—
88C2×#626—28no—
89C2×#626—28no—
90C2×#626—28no—
91#3752—28no—
92C3×(C2×D3)⋊C4—28no—
93C3×C4⋊Dic3—28no—
94#3722—28no—
95(C2×D3)⋊Dic3—28no—
96C2×#394—91noSylow
97C25×C3—31no—
98C24×D3—31no—
99C24×D3—31no—
100C24×D3—61no—
101C24×D3C2×D311yescharacteristic
102C23×C3×C4—21no—
103C23×C3×C4—31no—
104C23×C3×C4—31no—
105C23×C3×C4—31no—
106C23×C3×C4C2×D311yescharacteristic
107C23×C3×C4C2×D311yescharacteristic
108C22×#67—34no—
109C22×#67—64no—
110C22×#67—64no—
111C22×#67—64no—
112C23×Dic3—31no—
113C23×Dic3—31no—
114C23×Dic3—61no—
115C23×Dic3C2×D311yescharacteristic
116C23×Dic3C2×D311yescharacteristic
117C23×Dic3C2×D311yescharacteristic
118C22×D12—34no—
119C22×D12—64no—
120C22×D12—64no—
121C22×D12—64no—
122C2×C3×C4⋊C4—34no—
123C2×C3×C4⋊C4—64no—
124C2×C3×C22⋊C4—34no—
125C2×C3×C22⋊C4—64no—
126C2×#217—34no—
127C2×#217—64no—
128C2×(C2×D3)⋊C4—24no—
129C2×(C2×D3)⋊C4—34no—
130C2×(C2×D3)⋊C4—34no—
131C2×(C2×D3)⋊C4—34no—
132C2×(C2×D3)⋊C4—34no—
133C2×(C2×D3)⋊C4—34no—
134C2×(C2×D3)⋊C4—64no—
135C2×(C2×D3)⋊C4—64no—
136C2×(C2×D3)⋊C4—64no—
137C2×(C2×D3)⋊C4—68no—
138C2×(C2×D3)⋊C4—64no—
139C2×(C2×D3)⋊C4—64no—
140C2×(C2×D3)⋊C4—64no—
141C2×(C2×D3)⋊C4C2×D314yescomplemented
142C2×C4⋊Dic3—24no—
143C2×C4⋊Dic3C2×D314yescomplemented
144C3⋊#95—34no—
145C3⋊#95—34no—
146C23×C32C2×D412yes—
147C23×C32C2×D412yes—
148C23×C32C2×D412yes—
149C23×C32C2×D412yes—
150C23×C32#4112yes—
151C23×C32#4112yes—
152C23×C32#4112yes—
153C23×C32C2411yescharacteristic
154C22×C3⋊D3—28no—
155C22×C3⋊D3—22no—
156C22×C3⋊D3—22no—
157C22×C3⋊D3—28no—
158C22×C3⋊D3—28no—
159C22×C3⋊D3—22no—
160C22×C3⋊D3—22no—
161C22×C3⋊D3—22no—
162C22×C3⋊D3—22no—
163C22×C3⋊D3—44no—
164C22×C3⋊D3—44no—
165C22×C3⋊D3—44no—
166C22×C3⋊D3—44no—
167C22×C3⋊D3C2×D414yes—
168C22×C3×D3—28no—
169C22×C3×D3—28no—
170C22×C3×D3—28no—
171C22×C3×D3—22no—
172C22×C3×D3—22no—
173C22×C3×D3—22no—
174C22×C3×D3—22no—
175C22×C3×D3—22no—
176C22×C3×D3—22no—
177C22×C3×D3—44no—
178C22×C3×D3—44no—
179C22×C3×D3—44no—
180C22×C3×D3—44no—
181C22×C3×D3C2×D414yes—
182C2×C32×C4—28no—
183C2×C32×C4—22no—
184C2×C32×C4—22no—
185C2×C32×C4C2×D414yescomplemented
186C2×C3⋊Dic3—22no—
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3—22no—
189C2×C3⋊Dic3—44no—
190C2×C3×Dic3—28no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—44no—
200C2×C3×Dic3—44no—
201C2×C3×Dic3C2×D414yes—
202#626—232no—
203C23×D4—91no—
204C22×C4⋊C4—31no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—91no—
207C22×C22⋊C4—91no—
208C22×C22⋊C4—91no—
209#394—98no—
210C2×#95—91no—
211C24×C3—21no—
212C24×C3—34no—
213C24×C3—32no—
214C24×C3—62no—
215C24×C3—62no—
216C24×C3—62no—
217C24×C3—62no—
218C24×C3—62no—
219C24×C3—62no—
220C24×C3C22×D311yescharacteristic
221C24×C3C22×D311yescharacteristic
222C23×D3—22no—
223C23×D3—22no—
224C23×D3—22no—
225C23×D3—22no—
226C23×D3—22no—
227C23×D3—22no—
228C23×D3—34no—
229C23×D3—34no—
230C23×D3—32no—
231C23×D3—32no—
232C23×D3—64no—
233C23×D3—62no—
234C23×D3—64no—
235C23×D3—64no—
236C23×D3—62no—
237C23×D3—62no—
238C23×D3—62no—
239C23×D3—62no—
240C23×D3—62no—
241C23×D3—62no—
242C23×D3—62no—
243C23×D3—62no—
244C23×D3—62no—
245C23×D3—62no—
246C23×D3—62no—
247C23×D3—62no—
248C23×D3—122no—
249C23×D3—122no—
250C23×D3—122no—
251C23×D3—122no—
252C23×D3D1214yes—
253C23×D3C22×D312yes—
254C22×C3×C4—22no—
255C22×C3×C4—22no—
256C22×C3×C4—22no—
257C22×C3×C4—22no—
258C22×C3×C4—24no—
259C22×C3×C4—22no—
260C22×C3×C4—34no—
261C22×C3×C4—32no—
262C22×C3×C4—32no—
263C22×C3×C4—32no—
264C22×C3×C4—42no—
265C22×C3×C4—42no—
266C22×C3×C4—62no—
267C22×C3×C4—62no—
268C22×C3×C4—62no—
269C22×C3×C4—62no—
270C22×C3×C4—62no—
271C22×C3×C4—62no—
272C22×C3×C4—62no—
273C22×C3×C4—62no—
274C22×C3×C4D1214yescomplemented
275C22×C3×C4#6714yescomplemented
276C22×C3×C4C22×D312yes—
277C22×C3×C4C22×D312yes—
278C2×#67—68no—
279C2×#67—68no—
280C2×#67—632no—
281C2×#67—68no—
282C22×Dic3—22no—
283C22×Dic3—22no—
284C22×Dic3—22no—
285C22×Dic3—22no—
286C22×Dic3—22no—
287C22×Dic3—22no—
288C22×Dic3—22no—
289C22×Dic3—22no—
290C22×Dic3—32no—
291C22×Dic3—32no—
292C22×Dic3—62no—
293C22×Dic3—64no—
294C22×Dic3—62no—
295C22×Dic3—62no—
296C22×Dic3—62no—
297C22×Dic3—62no—
298C22×Dic3—62no—
299C22×Dic3—62no—
300C22×Dic3—122no—
301C22×Dic3—122no—
302C22×Dic3#6714yes—
303C22×Dic3C22×D312yes—
304C22×Dic3C22×D312yes—
305C22×Dic3C22×D312yes—
306C2×D12—68no—
307C2×D12—68no—
308C2×D12—632no—
309C2×D12—68no—
310C3×C4⋊C4—68no—
311C3×C22⋊C4—68no—
312#217—68no—
313(C2×D3)⋊C4—28no—
314(C2×D3)⋊C4—68no—
315(C2×D3)⋊C4—68no—
316(C2×D3)⋊C4—616no—
317(C2×D3)⋊C4—68no—
318(C2×D3)⋊C4—68no—
319(C2×D3)⋊C4—68no—
320C4⋊Dic3—28no—
321C22×C32#12014yes—
322C22×C32#12114yes—
323C22×C32#12114yes—
324C22×C32#12114yes—
325C22×C32#12314yes—
326C22×C32#12314yes—
327C22×C32#12414yes—
328C22×C32C22×D411yescharacteristic
329C22×C32C22×D411yescharacteristic
330C22×C32C22×D411yescharacteristic
331C22×C32C22×D411yescharacteristic
332C22×C32C2×#4111yescharacteristic
333C22×C32C2×#4111yescharacteristic
334C22×C32C2×#4111yescharacteristic
335C2×C3⋊D3—24no—
336C2×C3⋊D3—24no—
337C2×C3⋊D3—24no—
338C2×C3⋊D3—42no—
339C2×C3⋊D3—42no—
340C2×C3⋊D3—42no—
341C2×C3⋊D3—42no—
342C2×C3⋊D3—416no—
343C2×C3×D3—24no—
344C2×C3×D3—24no—
345C2×C3×D3—24no—
346C2×C3×D3—42no—
347C2×C3×D3—42no—
348C2×C3×D3—42no—
349C2×C3×D3—42no—
350C2×C3×D3—416no—
351C32×C4—24no—
352C3⋊Dic3—42no—
353C3×Dic3—24no—
354C3×Dic3—42no—
355C3×Dic3—42no—
356C25—31no—
357C25—91no—
358C22×D4—94no—
359C22×D4—184no—
360C22×D4—184no—
361C22×D4—184no—
362C23×C4—31no—
363C23×C4—31no—
364C23×C4—31no—
365C23×C4—91no—
366C23×C4D3211yescharacteristic
367C2×C4⋊C4—34no—
368C2×C4⋊C4—64no—
369C2×C22⋊C4—34no—
370C2×C22⋊C4—64no—
371C2×C22⋊C4—94no—
372C2×C22⋊C4—94no—
373C2×C22⋊C4—94no—
374C2×C22⋊C4—184no—
375C2×C22⋊C4—184no—
376C2×C22⋊C4—184no—
377#95—94no—
378C23×C3—21no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—22no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—34no—
387C23×C3—68no—
388C23×C3—68no—
389C23×C3—68no—
390C23×C3—62no—
391C23×C3—62no—
392C23×C3—62no—
393C23×C3—62no—
394C23×C3—62no—
395C23×C3—62no—
396C23×C3—124no—
397C23×C3—124no—
398C23×C3—124no—
399C23×C3—124no—
400C23×C3C2×D1212yes—
401C23×C3C2×D1212yes—
402C23×C3#23512yes—
403C23×C3#23512yes—
404C23×C3D3×D412yes—
405C23×C3D3×D412yes—
406C23×C3D3×D412yes—
407C23×C3D3×D412yes—
408C23×C3#23712yes—
409C23×C3#23712yes—
410C23×C3#23912yes—
411C23×C3#23912yes—
412C23×C3C2×#6712yes—
413C23×C3C2×#6712yes—
414C23×C3C23×D311yescharacteristic
415C23×C3C23×D311yescharacteristic
416C22×D3—28no—
417C22×D3—28no—
418C22×D3—28no—
419C22×D3—22no—
420C22×D3—22no—
421C22×D3—22no—
422C22×D3—22no—
423C22×D3—22no—
424C22×D3—22no—
425C22×D3—34no—
426C22×D3—34no—
427C22×D3—44no—
428C22×D3—44no—
429C22×D3—44no—
430C22×D3—44no—
431C22×D3—64no—
432C22×D3—64no—
433C22×D3—64no—
434C22×D3—616no—
435C22×D3—68no—
436C22×D3—68no—
437C22×D3—68no—
438C22×D3—68no—
439C22×D3—68no—
440C22×D3—68no—
441C22×D3—62no—
442C22×D3—62no—
443C22×D3—62no—
444C22×D3—62no—
445C22×D3—62no—
446C22×D3—62no—
447C22×D3—62no—
448C22×D3—62no—
449C22×D3—62no—
450C22×D3—62no—
451C22×D3—62no—
452C22×D3—62no—
453C22×D3—122no—
454C22×D3—122no—
455C22×D3—122no—
456C22×D3—122no—
457C22×D3—128no—
458C22×D3—128no—
459C22×D3—128no—
460C22×D3—128no—
461C22×D3—128no—
462C22×D3—128no—
463C22×D3—124no—
464C22×D3—124no—
465C22×D3—124no—
466C22×D3—124no—
467C22×D3—124no—
468C22×D3—124no—
469C22×D3—124no—
470C22×D3—124no—
471C22×D3C2×D1214yes—
472C2×C3×C4—28no—
473C2×C3×C4—28no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—24no—
479C2×C3×C4—34no—
480C2×C3×C4—42no—
481C2×C3×C4—42no—
482C2×C3×C4—48no—
483C2×C3×C4—68no—
484C2×C3×C4—62no—
485C2×C3×C4—62no—
486C2×C3×C4—62no—
487C2×C3×C4—62no—
488C2×C3×C4—62no—
489C2×C3×C4—62no—
490C2×C3×C4—62no—
491C2×C3×C4—62no—
492C2×C3×C4—124no—
493C2×C3×C4—124no—
494C2×C3×C4C2×D1214yescomplemented
495C2×C3×C4C2×#6714yescomplemented
496#67—632no—
497C2×Dic3—28no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—44no—
507C2×Dic3—44no—
508C2×Dic3—64no—
509C2×Dic3—62no—
510C2×Dic3—62no—
511C2×Dic3—62no—
512C2×Dic3—62no—
513C2×Dic3—62no—
514C2×Dic3—62no—
515C2×Dic3—122no—
516C2×Dic3—122no—
517C2×Dic3—128no—
518C2×Dic3—124no—
519C2×Dic3—124no—
520C2×Dic3C2×#6714yes—
521D12—632no—
522C2×C32#39418yescomplemented
523C2×C32C2×#12011yescharacteristic
524C2×C32C2×#12111yescharacteristic
525C2×C32C2×#12111yescharacteristic
526C2×C32C2×#12111yescharacteristic
527C2×C32C2×#12311yescharacteristic
528C2×C32C2×#12311yescharacteristic
529C2×C32C2×#12411yescharacteristic
530C3⋊D3—44no—
531C3×D3—44no—
532C24—32no—
533C24—34no—
534C24—62no—
535C24—62no—
536C24—62no—
537C24—62no—
538C24—62no—
539C24—62no—
540C24—92no—
541C24—94no—
542C24—182no—
543C24—182no—
544C24—182no—
545C24—182no—
546C24—182no—
547C24—182no—
548C24C2×D3211yescharacteristic
549C2×D4—188no—
550C2×D4—188no—
551C2×D4—188no—
552C2×D4—1832no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—32no—
556C22×C4—34no—
557C22×C4—32no—
558C22×C4—32no—
559C22×C4—62no—
560C22×C4—62no—
561C22×C4—62no—
562C22×C4—62no—
563C22×C4—62no—
564C22×C4—62no—
565C22×C4—62no—
566C22×C4—62no—
567C22×C4—92no—
568C22×C4—182no—
569C22×C4—182no—
570C22×C4—182no—
571C22×C4#62614yescomplemented
572C22×C4C2×D3212yes—
573C4⋊C4—68no—
574C22⋊C4—68no—
575C22⋊C4—188no—
576C22⋊C4—188no—
577C22⋊C4—188no—
578C22×C3—21no—
579C22×C3—21no—
580C22×C3—21no—
581C22×C3—21no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—24no—
586C22×C3—24no—
587C22×C3—24no—
588C22×C3—24no—
589C22×C3—24no—
590C22×C3—24no—
591C22×C3—24no—
592C22×C3—64no—
593C22×C3—64no—
594C22×C3—64no—
595C22×C3—1216no—
596C22×C3—122no—
597C22×C3—122no—
598C22×C3—122no—
599C22×C3—122no—
600C22×C3#88214yes—
601C22×C3#88314yes—
602C22×C3#88514yes—
603C22×C3#88614yes—
604C22×C3#89414yes—
605C22×C3#89414yes—
606C22×C3#89514yes—
607C22×C3#89514yes—
608C22×C3#93014yes—
609C22×C3#93014yes—
610C22×C3#93714yes—
611C22×C3#93814yes—
612C22×C3#93914yes—
613C22×C3#94714yes—
614C22×C3C22×D1211yescharacteristic
615C22×C3C22×D1211yescharacteristic
616C22×C3C2×#23511yescharacteristic
617C22×C3C2×#23511yescharacteristic
618C22×C3C2×D3×D411yescharacteristic
619C22×C3C2×D3×D411yescharacteristic
620C22×C3C2×D3×D411yescharacteristic
621C22×C3C2×D3×D411yescharacteristic
622C22×C3C2×#23711yescharacteristic
623C22×C3C2×#23711yescharacteristic
624C22×C3C2×#23911yescharacteristic
625C22×C3C2×#23911yescharacteristic
626C22×C3C22×#6711yescharacteristic
627C22×C3C22×#6711yescharacteristic
628C2×D3—24no—
629C2×D3—24no—
630C2×D3—24no—
631C2×D3—416no—
632C2×D3—42no—
633C2×D3—42no—
634C2×D3—42no—
635C2×D3—42no—
636C2×D3—68no—
637C2×D3—64no—
638C2×D3—64no—
639C2×D3—64no—
640C2×D3—64no—
641C2×D3—64no—
642C2×D3—64no—
643C2×D3—124no—
644C2×D3—124no—
645C2×D3—124no—
646C2×D3—1232no—
647C2×D3—124no—
648C2×D3—124no—
649C2×D3—124no—
650C2×D3—1216no—
651C2×D3—122no—
652C2×D3—122no—
653C2×D3—1216no—
654C2×D3—122no—
655C2×D3—122no—
656C2×D3—122no—
657C2×D3—122no—
658C2×D3—122no—
659C2×D3—122no—
660C3×C4—24no—
661C3×C4—24no—
662C3×C4—44no—
663C3×C4—64no—
664C3×C4—122no—
665C3×C4—122no—
666Dic3—24no—
667Dic3—42no—
668Dic3—42no—
669Dic3—124no—
670Dic3—122no—
671Dic3—122no—
672C32C2×#39411yescharacteristic, complemented, Sylow
673C23—34no—
674C23—62no—
675C23—62no—
676C23—62no—
677C23—62no—
678C23—62no—
679C23—62no—
680C23—68no—
681C23—68no—
682C23—68no—
683C23—94no—
684C23—124no—
685C23—124no—
686C23—124no—
687C23—124no—
688C23—182no—
689C23—182no—
690C23—182no—
691C23—182no—
692C23—182no—
693C23—182no—
694C23—188no—
695C23—188no—
696C23—188no—
697C23—364no—
698C23—364no—
699C23—364no—
700C23—364no—
701C23#379612yes—
702C23#379912yes—
703C23D3×D1212yes—
704C23#380212yes—
705C23#380412yes—
706C23C2×#62612yes—
707C23D3×#6712yes—
708C23C22×D3211yescharacteristic
709D4—1832no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—28no—
713C2×C4—34no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—68no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—124no—
724C2×C4—124no—
725C2×C4—182no—
726C2×C4—182no—
727C2×C4—182no—
728C2×C4—364no—
729C2×C4C2×#62614yescomplemented
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—28no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—124no—
739C2×C3#496118yescomplemented
740C2×C3#499118yescomplemented
741C2×C3C2×#88211yescharacteristic
742C2×C3C2×#88311yescharacteristic
743C2×C3C2×#88511yescharacteristic
744C2×C3C2×#88611yescharacteristic
745C2×C3C2×#89411yescharacteristic
746C2×C3C2×#89411yescharacteristic
747C2×C3C2×#89511yescharacteristic
748C2×C3C2×#89511yescharacteristic
749C2×C3C2×#93011yescharacteristic
750C2×C3C2×#93011yescharacteristic
751C2×C3C2×#93711yescharacteristic
752C2×C3C2×#93811yescharacteristic
753C2×C3C2×#93911yescharacteristic
754C2×C3C2×#94711yescharacteristic
755D3—44no—
756D3—128no—
757D3—124no—
758D3—124no—
759C22—64no—
760C22—64no—
761C22—64no—
762C22—122no—
763C22—1216no—
764C22—122no—
765C22—122no—
766C22—122no—
767C22—184no—
768C22—184no—
769C22—184no—
770C22—362no—
771C22—3616no—
772C22—362no—
773C22—362no—
774C22—362no—
775C22#6385414yes—
776C22#6389014yes—
777C22#6390714yes—
778C22#6390914yes—
779C22#6391614yes—
780C22#6392214yes—
781C22#6397814yes—
782C22C2×#379611yescharacteristic
783C22C2×#379911yescharacteristic
784C22C2×D3×D1211yescharacteristic
785C22C2×#380211yescharacteristic
786C22C2×#380411yescharacteristic
787C22C22×#62611yescharacteristic
788C22C2×D3×#6711yescharacteristic
789C4—24no—
790C4—64no—
791C4—122no—
792C4—122no—
793C4—362no—
794C3—21no—
795C3C2×#496111yescharacteristic, complemented
796C3C2×#499111yescharacteristic, complemented
797C2—124no—
798C2—364no—
799C2#1059139218yesdirect product factor
800C2C2×#6385411yescharacteristic
801C2C2×#6389011yescharacteristic
802C2C2×#6390711yescharacteristic
803C2C2×#6390911yescharacteristic
804C2C2×#6391611yescharacteristic
805C2C2×#6392211yescharacteristic
806C2C2×#6397811yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC23×C32×C4C22
socleC24×C32C23
prime radicalC23×#626C2
hypercenterC23×C4D32
hypocenterC32C2×#394
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×#3752C2semidirect
3. C22×C3×(C2×D3)⋊C4C2semidirect
4. C22×C3×C4⋊Dic3C2semidirect
5. C22×#3722C2semidirect
6. C22×(C2×D3)⋊Dic3C2semidirect
7. C2×#63579C2semidirect
8. #10591392C2direct (N × H)
23. C2×#3752C22semidirect
25. C2×C3×(C2×D3)⋊C4C22semidirect
27. C2×C3×C4⋊Dic3C22semidirect
29. C2×#3722C22semidirect
31. C2×(C2×D3)⋊Dic3C22semidirect
32. #63579C22semidirect
44. C22×(C2×D3)⋊C4D3semidirect
45. C22×C4⋊Dic3D3semidirect
69. C22×C32×C4D4semidirect
141. C2×(C2×D3)⋊C4C2×D3semidirect
143. C2×C4⋊Dic3C2×D3semidirect
185. C2×C32×C4C2×D4semidirect
274. C22×C3×C4D12semidirect
275. C22×C3×C4#67semidirect
494. C2×C3×C4C2×D12semidirect
495. C2×C3×C4C2×#67semidirect
522. C2×C32#394semidirect
571. C22×C4#626semidirect
672. C32C2×#394semidirect
729. C2×C4C2×#626semidirect
739. C2×C3#4961semidirect
740. C2×C3#4991semidirect
795. C3C2×#4961semidirect
796. C3C2×#4991semidirect
799. C2#10591392direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6262
C22×#37522
C22×C3×(C2×D3)⋊C42
C22×C3×C4⋊Dic32
C22×#37222
C22×(C2×D3)⋊Dic32
C2×#635792
#105913922
C2×#49913
C2×#49613