Finite Group Databasebeta

← C2×#76393 #11430425

Subgroups — C2×#76393 #11430425

Order 768.

3046 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#939C211yesmaximal, characteristic
2C22×#889C211yesmaximal, characteristic, complemented
3C2×C3×#390C211yesmaximal, characteristic, complemented
4C2×#5222C211yesmaximal, characteristic, complemented
5C2×#4993C211yesmaximal, characteristic, complemented
6C2×#4959C211yesmaximal, characteristic, complemented
7C2×#4959C211yesmaximal, characteristic, complemented
8C2×#4948C211yesmaximal, characteristic, complemented
9C2×#4961C211yesmaximal, characteristic, complemented
10C2×#4957C211yesmaximal, characteristic, complemented
11C2×#4945C211yesmaximal, characteristic, complemented
12C2×#4946C211yesmaximal, characteristic, complemented
13C2×#4946C211yesmaximal, characteristic, complemented
14C2×#4940C211yesmaximal, characteristic, complemented
15C2×#4933C211yesmaximal, characteristic, complemented
16#76393C2116yesmaximal, direct product factor
17C2×#2711—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C24×Dic3C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C42C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C2×#939—28no—
34C2×#939C2218yes—
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×(C2×D3)⋊C4C2211yescharacteristic
38C22×(C2×D3)⋊C4C2211yescharacteristic
39C22×(C2×D3)⋊C4C2211yescharacteristic
40C22×C4⋊Dic3C2211yescharacteristic
41C22×Dic3⋊C4C2211yescharacteristic
42C22×Dic3⋊C4C2211yescharacteristic
43C22×Dic3⋊C4C2211yescharacteristic
44C22×Dic3⋊C4C2211yescharacteristic
45C22×Dic3⋊C4C2211yescharacteristic
46C22×Dic3⋊C4C2211yescharacteristic
47C22×Dic3⋊C4C2211yescharacteristic
48C22×C4×Dic3C2211yescharacteristic
49C2×#889—28no—
50C2×#889C2218yescomplemented
51C3×#390C2218yescomplemented
52#5222C2218yescomplemented
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59#4993C2218yescomplemented
60#4961C2218yescomplemented
61#4959C2218yescomplemented
62#4959C2218yescomplemented
63#4957C2218yescomplemented
64#4948C2218yescomplemented
65#4946C2218yescomplemented
66#4946C2218yescomplemented
67#4945C2218yescomplemented
68#4940C2218yescomplemented
69#4933C2218yescomplemented
70C22×#125—31no—
71C22×#121—31no—
72#2711—316no—
73C2×#399—31no—
74C2×#396—31no—
75C2×#394—31no—
76C2×#394—31no—
77C2×#394—31no—
78C2×#394—31no—
79C2×#390—31no—
80C2×#390D311yescharacteristic, complemented
81C2×#388—31no—
82C2×#388—31no—
83C2×#387—31no—
84C2×#385—31no—
85C2×#385—31no—
86C25×C3C2311yescharacteristic
87C25×C3C2311yescharacteristic
88C24×D3C2311yescharacteristic
89C22×C3×D4—24no—
90C22×C3×D4—24no—
91C22×C3×D4—42no—
92C22×C3×D4C2314yes—
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C22×#67—24no—
99C22×#67—24no—
100C22×#67—24no—
101C22×#67—42no—
102C22×#67—42no—
103C22×#67—42no—
104C22×#67C2314yes—
105C22×#67C2314yes—
106C23×Dic3—24no—
107C23×Dic3—42no—
108C23×Dic3—42no—
109C23×Dic3C2311yescharacteristic
110C23×Dic3C2311yescharacteristic
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C23×Dic3C2311yescharacteristic
114C23×Dic3C2311yescharacteristic
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2314yes—
117C2×C3×C4⋊C4—24no—
118C2×C3×C4⋊C4C2314yes—
119C2×C3×C22⋊C4—42no—
120C2×C3×C22⋊C4—42no—
121C2×C3×C22⋊C4—42no—
122C2×C3×C22⋊C4—42no—
123C2×C3×C22⋊C4C2314yes—
124C2×C3×C22⋊C4C2314yes—
125C2×C3×C22⋊C4C2314yes—
126C2×C3×C22⋊C4C2314yes—
127C2×C3×C42—42no—
128C2×C3×C42C2314yes—
129C2×#217—24no—
130C2×#217—24no—
131C2×#217—24no—
132C2×#217—24no—
133C2×#217—42no—
134C2×#217C2314yes—
135C2×#217C2314yes—
136C2×#217C2314yes—
137C2×#217C2314yes—
138C2×#217C2314yes—
139#939—232no—
140C2×(C2×D3)⋊C4—24no—
141C2×(C2×D3)⋊C4—24no—
142C2×(C2×D3)⋊C4—42no—
143C2×(C2×D3)⋊C4—42no—
144C2×(C2×D3)⋊C4—42no—
145C2×(C2×D3)⋊C4C2314yes—
146C2×(C2×D3)⋊C4C2314yes—
147C2×(C2×D3)⋊C4C2314yes—
148C2×(C2×D3)⋊C4C2314yes—
149C2×(C2×D3)⋊C4C2314yes—
150C2×C4⋊Dic3—24no—
151C2×C4⋊Dic3C2314yes—
152C2×Dic3⋊C4—24no—
153C2×Dic3⋊C4—24no—
154C2×Dic3⋊C4—24no—
155C2×Dic3⋊C4—42no—
156C2×Dic3⋊C4—42no—
157C2×Dic3⋊C4—42no—
158C2×Dic3⋊C4D418yes—
159C2×Dic3⋊C4C2314yes—
160C2×Dic3⋊C4C2314yes—
161C2×Dic3⋊C4C2314yes—
162C2×Dic3⋊C4C2314yes—
163C2×Dic3⋊C4C2314yes—
164C2×Dic3⋊C4C2314yes—
165C2×Dic3⋊C4C2314yes—
166C2×C4×Dic3—24no—
167C2×C4×Dic3C2314yes—
168#889—232no—
169C3⋊#95C2314yes—
170C3⋊#95C2314yes—
171C3⋊#95C2314yes—
172C3⋊#95C2314yes—
173C3⋊#95C2314yes—
174C3⋊#95C2314yes—
175C23×D4—31no—
176C23×D4—31no—
177C23×D4C2×D311yescharacteristic
178C24×C4—31no—
179C2×#125—38no—
180C2×#125—68no—
181C2×#121—38no—
182C2×#121—68no—
183C22×C4⋊C4—31no—
184C22×C4⋊C4—31no—
185C22×C4⋊C4—31no—
186C22×C4⋊C4—31no—
187C22×C4⋊C4—31no—
188C22×C4⋊C4—31no—
189C22×C4⋊C4—31no—
190C22×C4⋊C4—31no—
191C22×C4⋊C4C2×D311yescharacteristic
192C22×C22⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4—31no—
200C22×C22⋊C4—31no—
201C22×C22⋊C4—31no—
202C22×C22⋊C4C2×D311yescharacteristic
203C22×C22⋊C4C2×D311yescharacteristic
204C22×C22⋊C4C2×D311yescharacteristic
205C22×C22⋊C4C2×D311yescharacteristic
206C22×C42—31no—
207C22×C42C2×D311yescharacteristic
208#399—38no—
209#396—38no—
210#394—38no—
211#394—38no—
212#394—38no—
213#394—38no—
214#390—38no—
215#390C2×D318yescomplemented
216#388—38no—
217#388—38no—
218#387—38no—
219#385—38no—
220#385—38no—
221C2×#95—31no—
222C2×#95—31no—
223C2×#95—31no—
224C2×#95—31no—
225C2×#95—31no—
226C2×#95—31no—
227C24×C3—22no—
228C24×C3—22no—
229C24×C3—22no—
230C24×C3—22no—
231C24×C3—22no—
232C24×C3—22no—
233C24×C3—22no—
234C24×C3—22no—
235C24×C3—22no—
236C24×C3—22no—
237C24×C3—22no—
238C24×C3—22no—
239C24×C3—22no—
240C24×C3#4114yes—
241C24×C3C2412yes—
242C24×C3C2412yes—
243C24×C3C2411yescharacteristic
244C23×D3—22no—
245C23×D3—22no—
246C23×D3—22no—
247C23×D3—22no—
248C23×D3—22no—
249C23×D3—22no—
250C23×D3—22no—
251C23×D3C2412yes—
252C2×C3×D4—28no—
253C2×C3×D4—28no—
254C2×C3×D4—44no—
255C2×C3×D4—416no—
256C22×C3×C4—22no—
257C22×C3×C4—22no—
258C22×C3×C4—22no—
259C22×C3×C4—22no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—22no—
264C22×C3×C4—22no—
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4C2×D414yes—
271C22×C3×C4C2412yes—
272C22×C3×C4C2412yes—
273C22×C3×C4C2412yes—
274C22×C3×C4C2412yes—
275C22×C3×C4C2412yes—
276C2×#67—28no—
277C2×#67—28no—
278C2×#67—28no—
279C2×#67—44no—
280C2×#67—44no—
281C2×#67—44no—
282C2×#67—416no—
283C2×#67—416no—
284C22×Dic3—22no—
285C22×Dic3—22no—
286C22×Dic3—22no—
287C22×Dic3—22no—
288C22×Dic3—22no—
289C22×Dic3—22no—
290C22×Dic3—22no—
291C22×Dic3—22no—
292C22×Dic3—22no—
293C22×Dic3—22no—
294C22×Dic3—22no—
295C22×Dic3—22no—
296C22×Dic3—22no—
297C22×Dic3—22no—
298C22×Dic3—22no—
299C22×Dic3—22no—
300C22×Dic3—22no—
301C22×Dic3—22no—
302C22×Dic3—28no—
303C22×Dic3—44no—
304C22×Dic3—44no—
305C22×Dic3—416no—
306C22×Dic3C2×D414yes—
307C22×Dic3C2×D414yes—
308C22×Dic3#4114yes—
309C22×Dic3C2412yes—
310C22×Dic3C2412yes—
311C22×Dic3C2412yes—
312C22×Dic3C2412yes—
313C22×Dic3C2412yes—
314C22×Dic3C2412yes—
315C22×Dic3C2412yes—
316C3×C4⋊C4—28no—
317C3×C22⋊C4—44no—
318C3×C22⋊C4—44no—
319C3×C22⋊C4—44no—
320C3×C22⋊C4—44no—
321C3×C42—44no—
322#217—28no—
323#217—28no—
324#217—28no—
325#217—28no—
326#217—44no—
327(C2×D3)⋊C4—28no—
328(C2×D3)⋊C4—28no—
329(C2×D3)⋊C4—44no—
330(C2×D3)⋊C4—44no—
331(C2×D3)⋊C4—44no—
332C4⋊Dic3—28no—
333Dic3⋊C4—28no—
334Dic3⋊C4—28no—
335Dic3⋊C4—28no—
336Dic3⋊C4—44no—
337Dic3⋊C4—44no—
338Dic3⋊C4—44no—
339Dic3⋊C4C2×D4116yes—
340C4×Dic3—28no—
341C25—31no—
342C25C22×D311yescharacteristic
343C25C22×D311yescharacteristic
344C22×D4—24no—
345C22×D4—24no—
346C22×D4—34no—
347C22×D4—34no—
348C22×D4—42no—
349C22×D4—64no—
350C22×D4—64no—
351C22×D4—64no—
352C22×D4—122no—
353C22×D4—122no—
354C22×D4—122no—
355C22×D4C22×D314yes—
356C23×C4—31no—
357C23×C4—31no—
358C23×C4—31no—
359C23×C4—31no—
360C23×C4—31no—
361C23×C4—31no—
362C23×C4—31no—
363C23×C4—34no—
364C23×C4—64no—
365C23×C4—122no—
366C23×C4—122no—
367C23×C4C22×D311yescharacteristic
368C23×C4C22×D311yescharacteristic
369C23×C4C22×D311yescharacteristic
370C23×C4C22×D311yescharacteristic
371C23×C4C22×D311yescharacteristic
372#125—632no—
373#121—632no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—38no—
376C2×C4⋊C4—34no—
377C2×C4⋊C4—34no—
378C2×C4⋊C4—34no—
379C2×C4⋊C4—34no—
380C2×C4⋊C4—34no—
381C2×C4⋊C4—34no—
382C2×C4⋊C4—34no—
383C2×C4⋊C4—34no—
384C2×C4⋊C4—64no—
385C2×C4⋊C4—64no—
386C2×C4⋊C4—64no—
387C2×C4⋊C4—64no—
388C2×C4⋊C4—122no—
389C2×C4⋊C4—122no—
390C2×C4⋊C4—122no—
391C2×C4⋊C4C22×D314yes—
392C2×C22⋊C4—34no—
393C2×C22⋊C4—34no—
394C2×C22⋊C4—34no—
395C2×C22⋊C4—34no—
396C2×C22⋊C4—34no—
397C2×C22⋊C4—34no—
398C2×C22⋊C4—34no—
399C2×C22⋊C4—34no—
400C2×C22⋊C4—34no—
401C2×C22⋊C4—34no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—64no—
407C2×C22⋊C4—64no—
408C2×C22⋊C4—64no—
409C2×C22⋊C4—64no—
410C2×C22⋊C4—64no—
411C2×C22⋊C4—64no—
412C2×C22⋊C4—122no—
413C2×C22⋊C4—122no—
414C2×C22⋊C4—122no—
415C2×C22⋊C4—122no—
416C2×C22⋊C4C22×D314yes—
417C2×C22⋊C4C22×D314yes—
418C2×C22⋊C4C22×D314yes—
419C2×C22⋊C4C22×D314yes—
420C2×C42—34no—
421C2×C42—42no—
422C2×C42—64no—
423C2×C42C22×D314yes—
424#95—34no—
425#95—34no—
426#95—34no—
427#95—34no—
428#95—34no—
429#95—34no—
430C23×C3—28no—
431C23×C3—28no—
432C23×C3—28no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—44no—
447C23×C3—44no—
448C23×C3—44no—
449C23×C3—44no—
450C23×C3—44no—
451C23×C3—44no—
452C23×C3—44no—
453C23×C3—44no—
454C23×C3—44no—
455C23×C3—44no—
456C23×C3—44no—
457C23×C3C22×D412yes—
458C23×C3C2×#4114yes—
459C23×C3C2×#4112yes—
460C23×C3C2×#4112yes—
461C23×C3H(5,𝔽2)12yes—
462C23×C3H(5,𝔽2)12yes—
463C23×C3H(5,𝔽2)12yes—
464C23×C32−1+412yes—
465C23×C3C2511yescharacteristic
466C22×D3—22no—
467C22×D3—22no—
468C22×D3—22no—
469C22×D3—22no—
470C22×D3—22no—
471C22×D3—22no—
472C22×D3—22no—
473C22×D3—44no—
474C22×D3—44no—
475C22×D3—44no—
476C22×D3—44no—
477C22×D3—44no—
478C22×D3—44no—
479C22×D3—44no—
480C3×D4—416no—
481C2×C3×C4—28no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—44no—
497C2×C3×C4—44no—
498C2×C3×C4—44no—
499C2×C3×C4—44no—
500C2×C3×C4C22×D414yes—
501#67—416no—
502#67—416no—
503C2×Dic3—28no—
504C2×Dic3—28no—
505C2×Dic3—28no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3—22no—
516C2×Dic3—22no—
517C2×Dic3—22no—
518C2×Dic3—22no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—22no—
524C2×Dic3—416no—
525C2×Dic3—44no—
526C2×Dic3—44no—
527C2×Dic3—44no—
528C2×Dic3—44no—
529C2×Dic3C22×D414yes—
530C2×Dic3C22×D414yes—
531C2×Dic3C2×#4114yes—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—32no—
546C24—62no—
547C24—62no—
548C24—62no—
549C24—62no—
550C24—62no—
551C24—62no—
552C24—62no—
553C24#23514yes—
554C24C23×D312yes—
555C24C23×D312yes—
556C24C23×D311yescharacteristic
557C2×D4—28no—
558C2×D4—28no—
559C2×D4—44no—
560C2×D4—416no—
561C2×D4—68no—
562C2×D4—68no—
563C2×D4—68no—
564C2×D4—124no—
565C2×D4—124no—
566C2×D4—124no—
567C2×D4—1216no—
568C2×D4—1216no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—34no—
584C22×C4—34no—
585C22×C4—34no—
586C22×C4—32no—
587C22×C4—32no—
588C22×C4—32no—
589C22×C4—32no—
590C22×C4—32no—
591C22×C4—32no—
592C22×C4—32no—
593C22×C4—68no—
594C22×C4—62no—
595C22×C4—62no—
596C22×C4—62no—
597C22×C4—62no—
598C22×C4—62no—
599C22×C4—62no—
600C22×C4—62no—
601C22×C4—62no—
602C22×C4—62no—
603C22×C4—62no—
604C22×C4—62no—
605C22×C4—62no—
606C22×C4—62no—
607C22×C4—62no—
608C22×C4—62no—
609C22×C4—62no—
610C22×C4—62no—
611C22×C4—62no—
612C22×C4—124no—
613C22×C4—124no—
614C22×C4—1216no—
615C22×C4D3×D414yes—
616C22×C4C23×D312yes—
617C22×C4C23×D312yes—
618C22×C4C23×D312yes—
619C22×C4C23×D312yes—
620C22×C4C23×D312yes—
621C4⋊C4—28no—
622C4⋊C4—316no—
623C4⋊C4—68no—
624C4⋊C4—68no—
625C4⋊C4—68no—
626C4⋊C4—68no—
627C4⋊C4—124no—
628C4⋊C4—124no—
629C4⋊C4—124no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C22⋊C4—68no—
635C22⋊C4—68no—
636C22⋊C4—68no—
637C22⋊C4—68no—
638C22⋊C4—68no—
639C22⋊C4—68no—
640C22⋊C4—124no—
641C22⋊C4—124no—
642C22⋊C4—124no—
643C22⋊C4—124no—
644C42—44no—
645C42—68no—
646C22×C3—24no—
647C22×C3—24no—
648C22×C3—24no—
649C22×C3—42no—
650C22×C3—42no—
651C22×C3—42no—
652C22×C3—416no—
653C22×C3—42no—
654C22×C3—42no—
655C22×C3—42no—
656C22×C3—42no—
657C22×C3—42no—
658C22×C3—42no—
659C22×C3—42no—
660C22×C3—42no—
661C22×C3—88no—
662C22×C3#53514yes—
663C22×C3#53914yes—
664C22×C3#54014yes—
665C22×C3#54614yes—
666C22×C3#54814yes—
667C22×C3#55314yes—
668C22×C3#56214yes—
669C22×C3C23×D411yescharacteristic
670C22×C3C22×#4111yescharacteristic
671C22×C3C22×#4111yescharacteristic
672C22×C3C2×H(5,𝔽2)11yescharacteristic
673C22×C3C2×H(5,𝔽2)11yescharacteristic
674C22×C3C2×H(5,𝔽2)11yescharacteristic
675C22×C3C2×2−1+411yescharacteristic
676C2×D3—42no—
677C2×D3—42no—
678C2×D3—42no—
679C2×D3—42no—
680C2×D3—42no—
681C2×D3—42no—
682C2×D3—42no—
683C2×D3—88no—
684C3×C4—24no—
685C3×C4—42no—
686C3×C4—42no—
687C3×C4—42no—
688C3×C4—42no—
689Dic3—24no—
690Dic3—24no—
691Dic3—24no—
692Dic3—42no—
693Dic3—42no—
694Dic3—42no—
695Dic3—42no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—28no—
703C23—28no—
704C23—28no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—62no—
724C23—62no—
725C23—62no—
726C23—62no—
727C23—62no—
728C23—62no—
729C23—62no—
730C23—124no—
731C23—124no—
732C23—124no—
733C23—124no—
734C23—124no—
735C23—124no—
736C23—124no—
737C23C2×#23514yes—
738C23C2×#23512yes—
739C23C2×D3×D412yes—
740C23#100412yes—
741C23#100412yes—
742C23#100412yes—
743C23D3×#4112yes—
744C23#101012yes—
745C23C24×D311yescharacteristic
746D4—416no—
747D4—1216no—
748D4—1216no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—28no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—34no—
765C2×C4—34no—
766C2×C4—34no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—68no—
772C2×C4—62no—
773C2×C4—62no—
774C2×C4—62no—
775C2×C4—62no—
776C2×C4—62no—
777C2×C4—62no—
778C2×C4—68no—
779C2×C4—68no—
780C2×C4—62no—
781C2×C4—62no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4—62no—
790C2×C4—62no—
791C2×C4—62no—
792C2×C4—1216no—
793C2×C4—124no—
794C2×C4—124no—
795C2×C4—124no—
796C2×C4—124no—
797C2×C4C2×D3×D414yes—
798C2×C3—44no—
799C2×C3—82no—
800C2×C3#271118yescomplemented
801C2×C3C2×#53511yescharacteristic
802C2×C3C2×#53911yescharacteristic
803C2×C3C2×#54011yescharacteristic
804C2×C3C2×#54611yescharacteristic
805C2×C3C2×#54811yescharacteristic
806C2×C3C2×#55311yescharacteristic
807C2×C3C2×#56211yescharacteristic
808D3—82no—
809C22—24no—
810C22—24no—
811C22—24no—
812C22—42no—
813C22—416no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—88no—
825C22—122no—
826C22—122no—
827C22—122no—
828C22—122no—
829C22—122no—
830C22—122no—
831C22—122no—
832C22—248no—
833C22#549014yes—
834C22#554014yes—
835C22#556414yes—
836C22#561514yes—
837C22#562114yes—
838C22#567714yes—
839C22#571514yes—
840C22C22×#23511yescharacteristic
841C22C22×D3×D411yescharacteristic
842C22C2×#100411yescharacteristic
843C22C2×#100411yescharacteristic
844C22C2×#100411yescharacteristic
845C22C2×D3×#4111yescharacteristic
846C22C2×#101011yescharacteristic
847C4—24no—
848C4—42no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—64no—
853C4—64no—
854C4—64no—
855C4—122no—
856C4—122no—
857C4—122no—
858C4—122no—
859C3C2×#271111yescharacteristic, complemented, Sylow
860C2—44no—
861C2—82no—
862C2—242no—
863C2#7639318yesdirect product factor
864C2C2×#549011yescharacteristic
865C2C2×#556411yescharacteristic
866C2C2×#554011yescharacteristic
867C2C2×#561511yescharacteristic
868C2C2×#562111yescharacteristic
869C2C2×#567711yescharacteristic
870C2C2×#571511yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#390C2
socleC24×C3C24
prime radicalC22×#939C2
hypercenterC2×#390D3
hypocenterC3C2×#2711
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C22×#889C2semidirect
3. C2×C3×#390C2semidirect
4. C2×#5222C2semidirect
5. C2×#4993C2semidirect
6. C2×#4959C2semidirect
7. C2×#4959C2semidirect
8. C2×#4948C2semidirect
9. C2×#4961C2semidirect
10. C2×#4957C2semidirect
11. C2×#4945C2semidirect
12. C2×#4946C2semidirect
13. C2×#4946C2semidirect
14. C2×#4940C2semidirect
15. C2×#4933C2semidirect
16. #76393C2direct (N × H)
50. C2×#889C22semidirect
51. C3×#390C22semidirect
52. #5222C22semidirect
59. #4993C22semidirect
60. #4961C22semidirect
61. #4959C22semidirect
62. #4959C22semidirect
63. #4957C22semidirect
64. #4948C22semidirect
65. #4946C22semidirect
66. #4946C22semidirect
67. #4945C22semidirect
68. #4940C22semidirect
69. #4933C22semidirect
80. C2×#390D3semidirect
215. #390C2×D3semidirect
800. C2×C3#2711semidirect
859. C3C2×#2711semidirect
863. C2#76393direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#9392
C22×#8892
C2×C3×#3902
C2×#52222
C2×#49932
C2×#49592
C2×#49482
C2×#49612
C2×#49572
C2×#49452
C2×#49462
C2×#49402
C2×#49332
#763932
C2×#27113