Finite Group Databasebeta

← C2×#77649 #11001534

Subgroups — C2×#77649 #11001534

Order 768.

2822 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#397C211yesmaximal, characteristic, complemented
2C2×#4991C211yesmaximal, characteristic, complemented
3C2×#4990C211yesmaximal, characteristic, complemented
4C2×#4959C211yesmaximal, characteristic, complemented
5C2×#4960C211yesmaximal, characteristic, complemented
6C2×#4960C211yesmaximal, characteristic, complemented
7C2×#4960C211yesmaximal, characteristic, complemented
8C2×#4961C211yesmaximal, characteristic, complemented
9C2×#4957C211yesmaximal, characteristic, complemented
10#77649C2116yesmaximal, direct product factor
11C2×#4671C211yesmaximal, characteristic, complemented
12C2×#4658C211yesmaximal, characteristic, complemented
13C2×#4674C211yesmaximal, characteristic, complemented
14C2×#4672C211yesmaximal, characteristic, complemented
15C2×#4672C211yesmaximal, characteristic, complemented
16C2×#4670C211yesmaximal, characteristic, complemented
17C2×#2828—31nomaximal, Sylow
18C23×#67C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×D12C2211yescharacteristic
22C23×D12C2211yescharacteristic
23C23×D12C2211yescharacteristic
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×(C2×D3)⋊C4C2211yescharacteristic
38C22×(C2×D3)⋊C4C2211yescharacteristic
39C22×(C2×D3)⋊C4C2211yescharacteristic
40C22×(C2×D3)⋊C4C2211yescharacteristic
41C22×C4⋊Dic3C2211yescharacteristic
42C22×Dic3⋊C4C2211yescharacteristic
43C22×Dic3⋊C4C2211yescharacteristic
44C22×C4×Dic3C2211yescharacteristic
45C3×#397C2218yescomplemented
46C2×C3×#95C2211yescharacteristic
47C2×C3×#95C2211yescharacteristic
48C2×C3×#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54#4991C2218yescomplemented
55#4990C2218yescomplemented
56#4961C2218yescomplemented
57#4960C2218yescomplemented
58#4960C2218yescomplemented
59#4960C2218yescomplemented
60#4959C2218yescomplemented
61#4957C2218yescomplemented
62#4674C2218yescomplemented
63#4672C2218yescomplemented
64#4672C2218yescomplemented
65#4671C2218yescomplemented
66#4670C2218yescomplemented
67#4658C2218yescomplemented
68#2828—316no—
69C2×#400—31no—
70C2×#397—31no—
71C2×#397D311yescharacteristic, complemented
72C2×#394—31no—
73C2×#394—31no—
74C2×#394—31no—
75C2×#394—31no—
76C2×#394—31no—
77C2×#392—31no—
78C2×#392—31no—
79C2×#392—31no—
80C2×#392—31no—
81C2×#390—31no—
82C2×#388—31no—
83C2×#388—31no—
84C25×C3C2311yescharacteristic
85C24×D3C2311yescharacteristic
86C24×D3C2311yescharacteristic
87C24×D3C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C22×#67—24no—
95C22×#67—42no—
96C22×#67—42no—
97C22×#67—42no—
98C22×#67—42no—
99C22×#67—42no—
100C22×#67—42no—
101C22×#67—42no—
102C22×#67—42no—
103C22×#67C2314yes—
104C22×#67C2314yes—
105C22×#67C2314yes—
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C23×Dic3C2311yescharacteristic
109C23×Dic3C2311yescharacteristic
110C23×Dic3C2311yescharacteristic
111C22×D12—42no—
112C22×D12—42no—
113C22×D12—42no—
114C22×D12—42no—
115C22×D12—42no—
116C22×D12—42no—
117C22×D12—42no—
118C22×D12—42no—
119C22×D12—42no—
120C22×D12C2314yes—
121C22×D12C2314yes—
122C22×D12C2314yes—
123C2×C3×C4⋊C4—42no—
124C2×C3×C4⋊C4C2314yes—
125C2×C3×C22⋊C4—42no—
126C2×C3×C22⋊C4—42no—
127C2×C3×C22⋊C4—42no—
128C2×C3×C22⋊C4C2314yes—
129C2×C3×C22⋊C4C2314yes—
130C2×C3×C22⋊C4C2314yes—
131C2×#217—42no—
132C2×#217C2314yes—
133C2×(C2×D3)⋊C4—24no—
134C2×(C2×D3)⋊C4—24no—
135C2×(C2×D3)⋊C4—42no—
136C2×(C2×D3)⋊C4—42no—
137C2×(C2×D3)⋊C4—42no—
138C2×(C2×D3)⋊C4—42no—
139C2×(C2×D3)⋊C4—42no—
140C2×(C2×D3)⋊C4—42no—
141C2×(C2×D3)⋊C4—42no—
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×(C2×D3)⋊C4C2314yes—
151C2×(C2×D3)⋊C4C2314yes—
152C2×(C2×D3)⋊C4C2314yes—
153C2×(C2×D3)⋊C4C2314yes—
154C2×(C2×D3)⋊C4C2314yes—
155C2×(C2×D3)⋊C4C2314yes—
156C2×(C2×D3)⋊C4C2314yes—
157C2×C4⋊Dic3—42no—
158C2×C4⋊Dic3C2314yes—
159C2×Dic3⋊C4—42no—
160C2×Dic3⋊C4—42no—
161C2×Dic3⋊C4C2314yes—
162C2×Dic3⋊C4C2314yes—
163C2×C4×Dic3—42no—
164C2×C4×Dic3C2314yes—
165C3×#95C2314yes—
166C3×#95C2314yes—
167C3×#95C2314yes—
168C3⋊#95C2314yes—
169C3⋊#95C2314yes—
170C3⋊#95C2314yes—
171C3⋊#95C2314yes—
172C3⋊#95C2314yes—
173C23×D4—31no—
174C23×D4—31no—
175C23×D4—31no—
176C23×D4—31no—
177C23×D4—31no—
178C23×D4—31no—
179C22×C4⋊C4—31no—
180C22×C4⋊C4—31no—
181C22×C4⋊C4—31no—
182C22×C4⋊C4C2×D311yescharacteristic
183C22×C22⋊C4—31no—
184C22×C22⋊C4—31no—
185C22×C22⋊C4—31no—
186C22×C22⋊C4—31no—
187C22×C22⋊C4—31no—
188C22×C22⋊C4—31no—
189C22×C22⋊C4—31no—
190C22×C22⋊C4—31no—
191C22×C22⋊C4—31no—
192C22×C22⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4C2×D311yescharacteristic
197C22×C22⋊C4C2×D311yescharacteristic
198C22×C22⋊C4C2×D311yescharacteristic
199C22×C42—31no—
200#400—38no—
201#397—38no—
202#397C2×D318yescomplemented
203#394—38no—
204#394—38no—
205#394—38no—
206#394—38no—
207#394—38no—
208#392—38no—
209#392—38no—
210#392—38no—
211#392—38no—
212#390—38no—
213#388—38no—
214#388—38no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95—31no—
218C2×#95—31no—
219C2×#95—31no—
220C2×#95C2×D311yescharacteristic
221C2×#95C2×D311yescharacteristic
222C2×#95C2×D311yescharacteristic
223C24×C3—22no—
224C24×C3—22no—
225C24×C3—22no—
226C24×C3—22no—
227C24×C3—22no—
228C24×C3—22no—
229C24×C3—22no—
230C24×C3C2412yes—
231C24×C3C2411yescharacteristic
232C23×D3—22no—
233C23×D3—22no—
234C23×D3—22no—
235C23×D3—22no—
236C23×D3—22no—
237C23×D3—22no—
238C23×D3—22no—
239C23×D3—22no—
240C23×D3—22no—
241C23×D3—22no—
242C23×D3—22no—
243C23×D3—22no—
244C23×D3—22no—
245C23×D3—22no—
246C23×D3—22no—
247C23×D3—22no—
248C23×D3—22no—
249C23×D3—22no—
250C23×D3—22no—
251C23×D3—22no—
252C23×D3—22no—
253C23×D3C2412yes—
254C23×D3C2412yes—
255C23×D3C2412yes—
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×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—22no—
274C22×C3×C4C2412yes—
275C22×C3×C4C2412yes—
276C22×C3×C4C2412yes—
277C22×C3×C4C2412yes—
278C22×C3×C4C2412yes—
279C22×C3×C4C2412yes—
280C2×#67—28no—
281C2×#67—44no—
282C2×#67—44no—
283C2×#67—44no—
284C2×#67—44no—
285C2×#67—44no—
286C2×#67—44no—
287C2×#67—44no—
288C2×#67—44no—
289C2×#67—416no—
290C2×#67—416no—
291C2×#67—416no—
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—22no—
303C22×Dic3—22no—
304C22×Dic3—22no—
305C22×Dic3—22no—
306C22×Dic3#4114yes—
307C22×Dic3C2412yes—
308C22×Dic3C2412yes—
309C22×Dic3C2412yes—
310C22×Dic3C2412yes—
311C22×Dic3C2412yes—
312C2×D12—44no—
313C2×D12—44no—
314C2×D12—44no—
315C2×D12—44no—
316C2×D12—44no—
317C2×D12—44no—
318C2×D12—44no—
319C2×D12—44no—
320C2×D12—44no—
321C2×D12—416no—
322C2×D12—416no—
323C2×D12—416no—
324C3×C4⋊C4—44no—
325C3×C22⋊C4—44no—
326C3×C22⋊C4—44no—
327C3×C22⋊C4—44no—
328#217—44no—
329(C2×D3)⋊C4—28no—
330(C2×D3)⋊C4—28no—
331(C2×D3)⋊C4—44no—
332(C2×D3)⋊C4—44no—
333(C2×D3)⋊C4—44no—
334(C2×D3)⋊C4—44no—
335(C2×D3)⋊C4—44no—
336(C2×D3)⋊C4—44no—
337(C2×D3)⋊C4—44no—
338(C2×D3)⋊C4—44no—
339(C2×D3)⋊C4—44no—
340(C2×D3)⋊C4—44no—
341C4⋊Dic3—44no—
342Dic3⋊C4—44no—
343Dic3⋊C4—44no—
344C4×Dic3—44no—
345C25—31no—
346C25—31no—
347C25—31no—
348C25C22×D311yescharacteristic
349C22×D4—34no—
350C22×D4—34no—
351C22×D4—34no—
352C22×D4—34no—
353C22×D4—34no—
354C22×D4—34no—
355C22×D4—64no—
356C22×D4—122no—
357C22×D4—122no—
358C22×D4—122no—
359C22×D4—122no—
360C22×D4—122no—
361C22×D4—122no—
362C22×D4—122no—
363C22×D4—122no—
364C22×D4—122no—
365C22×D4—122no—
366C22×D4—122no—
367C22×D4—122no—
368C22×D4—122no—
369C22×D4—122no—
370C22×D4—122no—
371C22×D4—122no—
372C22×D4—122no—
373C23×C4—31no—
374C23×C4—31no—
375C23×C4—31no—
376C23×C4—31no—
377C23×C4—31no—
378C23×C4C22×D311yescharacteristic
379C23×C4C22×D311yescharacteristic
380C23×C4C22×D311yescharacteristic
381C23×C4C22×D311yescharacteristic
382C23×C4C22×D311yescharacteristic
383C23×C4C22×D311yescharacteristic
384C2×C4⋊C4—34no—
385C2×C4⋊C4—34no—
386C2×C4⋊C4—34no—
387C2×C4⋊C4—42no—
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—34no—
403C2×C22⋊C4—34no—
404C2×C22⋊C4—34no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4—64no—
409C2×C22⋊C4—64no—
410C2×C22⋊C4—122no—
411C2×C22⋊C4—122no—
412C2×C22⋊C4—122no—
413C2×C22⋊C4—122no—
414C2×C22⋊C4—122no—
415C2×C22⋊C4—122no—
416C2×C22⋊C4—122no—
417C2×C22⋊C4—122no—
418C2×C22⋊C4—122no—
419C2×C22⋊C4—122no—
420C2×C22⋊C4—122no—
421C2×C22⋊C4C22×D314yes—
422C2×C22⋊C4C22×D314yes—
423C2×C22⋊C4C22×D314yes—
424C2×C42—34no—
425C2×C42—122no—
426#95—34no—
427#95—34no—
428#95—34no—
429#95—34no—
430#95—34no—
431#95C22×D314yes—
432#95C22×D314yes—
433#95C22×D314yes—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—44no—
442C23×C3—44no—
443C23×C3—44no—
444C23×C3—44no—
445C23×C3—44no—
446C23×C3—44no—
447C23×C3—44no—
448C23×C3C2×#4112yes—
449C23×C3H(5,𝔽2)12yes—
450C23×C3H(5,𝔽2)12yes—
451C23×C3H(5,𝔽2)12yes—
452C23×C3H(5,𝔽2)12yes—
453C23×C3H(5,𝔽2)12yes—
454C23×C3H(5,𝔽2)12yes—
455C23×C3C2511yescharacteristic
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—22no—
468C22×D3—22no—
469C22×D3—22no—
470C22×D3—22no—
471C22×D3—22no—
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—44no—
478C22×D3—44no—
479C22×D3—44no—
480C22×D3—44no—
481C22×D3—44no—
482C22×D3—44no—
483C22×D3—44no—
484C22×D3—44no—
485C22×D3—44no—
486C22×D3—44no—
487C22×D3—44no—
488C22×D3—44no—
489C22×D3—44no—
490C22×D3—44no—
491C22×D3—44no—
492C22×D3—44no—
493C22×D3—44no—
494C22×D3—44no—
495C22×D3—44no—
496C22×D3—44no—
497C22×D3—44no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—44no—
517C2×C3×C4—44no—
518C2×C3×C4—44no—
519C2×C3×C4—44no—
520C2×C3×C4—44no—
521C2×C3×C4—44no—
522#67—416no—
523#67—416no—
524#67—416no—
525C2×Dic3—28no—
526C2×Dic3—22no—
527C2×Dic3—22no—
528C2×Dic3—22no—
529C2×Dic3—22no—
530C2×Dic3—22no—
531C2×Dic3—22no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—22no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3—22no—
540C2×Dic3—44no—
541C2×Dic3—44no—
542C2×Dic3—44no—
543C2×Dic3—44no—
544C2×Dic3C2×#4114yes—
545D12—416no—
546D12—416no—
547D12—416no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—32no—
556C24—32no—
557C24—32no—
558C24—62no—
559C24—62no—
560C24—62no—
561C24—62no—
562C24—62no—
563C24—62no—
564C24—62no—
565C24—62no—
566C24—62no—
567C24—62no—
568C24—62no—
569C24—62no—
570C24—62no—
571C24—62no—
572C24—62no—
573C24—62no—
574C24—62no—
575C24—62no—
576C24—62no—
577C24—62no—
578C24—62no—
579C24C23×D312yes—
580C24C23×D311yescharacteristic
581C2×D4—68no—
582C2×D4—124no—
583C2×D4—124no—
584C2×D4—124no—
585C2×D4—124no—
586C2×D4—124no—
587C2×D4—124no—
588C2×D4—124no—
589C2×D4—124no—
590C2×D4—124no—
591C2×D4—1216no—
592C2×D4—1216no—
593C2×D4—1216no—
594C2×D4—124no—
595C2×D4—124no—
596C2×D4—124no—
597C2×D4—124no—
598C2×D4—124no—
599C2×D4—124no—
600C2×D4—124no—
601C2×D4—124no—
602C2×D4—1216no—
603C2×D4—1216no—
604C2×D4—1216no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—34no—
624C22×C4—32no—
625C22×C4—32no—
626C22×C4—32no—
627C22×C4—32no—
628C22×C4—32no—
629C22×C4—62no—
630C22×C4—62no—
631C22×C4—62no—
632C22×C4—62no—
633C22×C4—62no—
634C22×C4—62no—
635C22×C4—62no—
636C22×C4—62no—
637C22×C4—62no—
638C22×C4—62no—
639C22×C4—62no—
640C22×C4—62no—
641C22×C4—62no—
642C22×C4—62no—
643C22×C4C23×D312yes—
644C22×C4C23×D312yes—
645C22×C4C23×D312yes—
646C22×C4C23×D312yes—
647C22×C4C23×D312yes—
648C22×C4C23×D312yes—
649C4⋊C4—44no—
650C4⋊C4—124no—
651C4⋊C4—124no—
652C4⋊C4—124no—
653C22⋊C4—44no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—68no—
657C22⋊C4—68no—
658C22⋊C4—124no—
659C22⋊C4—124no—
660C22⋊C4—124no—
661C22⋊C4—124no—
662C22⋊C4—124no—
663C22⋊C4—124no—
664C22⋊C4—124no—
665C22⋊C4—124no—
666C22⋊C4—124no—
667C22⋊C4—124no—
668C22⋊C4—124no—
669C42—124no—
670C22×C3—42no—
671C22×C3—42no—
672C22×C3—42no—
673C22×C3—42no—
674C22×C3—42no—
675C22×C3—42no—
676C22×C3—42no—
677C22×C3—88no—
678C22×C3#53814yes—
679C22×C3#54014yes—
680C22×C3#54014yes—
681C22×C3#56014yes—
682C22×C3#56014yes—
683C22×C3#56014yes—
684C22×C3H(3,𝔽4)14yes—
685C22×C3C22×#4111yescharacteristic
686C22×C3C2×H(5,𝔽2)11yescharacteristic
687C22×C3C2×H(5,𝔽2)11yescharacteristic
688C22×C3C2×H(5,𝔽2)11yescharacteristic
689C22×C3C2×H(5,𝔽2)11yescharacteristic
690C22×C3C2×H(5,𝔽2)11yescharacteristic
691C22×C3C2×H(5,𝔽2)11yescharacteristic
692C2×D3—42no—
693C2×D3—42no—
694C2×D3—42no—
695C2×D3—42no—
696C2×D3—42no—
697C2×D3—42no—
698C2×D3—42no—
699C2×D3—42no—
700C2×D3—42no—
701C2×D3—42no—
702C2×D3—42no—
703C2×D3—42no—
704C2×D3—42no—
705C2×D3—42no—
706C2×D3—42no—
707C2×D3—42no—
708C2×D3—42no—
709C2×D3—42no—
710C2×D3—42no—
711C2×D3—42no—
712C2×D3—42no—
713C2×D3—88no—
714C2×D3—88no—
715C2×D3—88no—
716C3×C4—42no—
717C3×C4—42no—
718C3×C4—42no—
719C3×C4—42no—
720C3×C4—42no—
721C3×C4—42no—
722Dic3—24no—
723Dic3—42no—
724Dic3—42no—
725Dic3—42no—
726Dic3—42no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—62no—
742C23—62no—
743C23—62no—
744C23—62no—
745C23—62no—
746C23—62no—
747C23—62no—
748C23—62no—
749C23—62no—
750C23—62no—
751C23—62no—
752C23—62no—
753C23—62no—
754C23—62no—
755C23—62no—
756C23—62no—
757C23—62no—
758C23—62no—
759C23—62no—
760C23—62no—
761C23—62no—
762C23—124no—
763C23—124no—
764C23—124no—
765C23—124no—
766C23—124no—
767C23—124no—
768C23—124no—
769C23—124no—
770C23—124no—
771C23—124no—
772C23—124no—
773C23—124no—
774C23—124no—
775C23—124no—
776C23—124no—
777C23—124no—
778C23—124no—
779C23—124no—
780C23—124no—
781C23—124no—
782C23—124no—
783C23#100412yes—
784C23#100412yes—
785C23D3×#4112yes—
786C23#100912yes—
787C23#100912yes—
788C23#100912yes—
789C23#100912yes—
790C23C24×D311yescharacteristic
791D4—1216no—
792D4—1216no—
793D4—1216no—
794D4—1216no—
795D4—1216no—
796D4—1216no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—34no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—68no—
823C2×C4—62no—
824C2×C4—62no—
825C2×C4—62no—
826C2×C4—62no—
827C2×C4—62no—
828C2×C4—62no—
829C2×C4—62no—
830C2×C4—62no—
831C2×C4—62no—
832C2×C4—62no—
833C2×C4—62no—
834C2×C4—62no—
835C2×C4—62no—
836C2×C4—62no—
837C2×C4—124no—
838C2×C4—124no—
839C2×C4—124no—
840C2×C4—124no—
841C2×C3—82no—
842C2×C3#282818yescomplemented
843C2×C3C2×#53811yescharacteristic
844C2×C3C2×#54011yescharacteristic
845C2×C3C2×#54011yescharacteristic
846C2×C3C2×#56011yescharacteristic
847C2×C3C2×#56011yescharacteristic
848C2×C3C2×#56011yescharacteristic
849C2×C3C2×H(3,𝔽4)11yescharacteristic
850D3—82no—
851D3—82no—
852D3—82no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—88no—
861C22—122no—
862C22—122no—
863C22—122no—
864C22—122no—
865C22—122no—
866C22—122no—
867C22—122no—
868C22—122no—
869C22—122no—
870C22—122no—
871C22—122no—
872C22—122no—
873C22—122no—
874C22—122no—
875C22—122no—
876C22—122no—
877C22—122no—
878C22—122no—
879C22—122no—
880C22—122no—
881C22—122no—
882C22—248no—
883C22—248no—
884C22—248no—
885C22#562014yes—
886C22#566314yes—
887C22#566314yes—
888C22#566614yes—
889C22#568314yes—
890C22#570414yes—
891C22#571114yes—
892C22C2×#100411yescharacteristic
893C22C2×#100411yescharacteristic
894C22C2×D3×#4111yescharacteristic
895C22C2×#100911yescharacteristic
896C22C2×#100911yescharacteristic
897C22C2×#100911yescharacteristic
898C22C2×#100911yescharacteristic
899C4—42no—
900C4—42no—
901C4—42no—
902C4—42no—
903C4—42no—
904C4—42no—
905C4—64no—
906C4—122no—
907C4—122no—
908C4—122no—
909C4—122no—
910C3C2×#282811yescharacteristic, complemented, Sylow
911C2—82no—
912C2—242no—
913C2—242no—
914C2—242no—
915C2#7764918yesdirect product factor
916C2C2×#562011yescharacteristic
917C2C2×#566311yescharacteristic
918C2C2×#566311yescharacteristic
919C2C2×#566611yescharacteristic
920C2C2×#568311yescharacteristic
921C2C2×#570411yescharacteristic
922C2C2×#571111yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#397C2
socleC24×C3C24
hypercenterC2×#397D3
hypocenterC3C2×#2828
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C2×C3×#397C2semidirect
2. C2×#4991C2semidirect
3. C2×#4990C2semidirect
4. C2×#4959C2semidirect
5. C2×#4960C2semidirect
6. C2×#4960C2semidirect
7. C2×#4960C2semidirect
8. C2×#4961C2semidirect
9. C2×#4957C2semidirect
10. #77649C2direct (N × H)
11. C2×#4671C2semidirect
12. C2×#4658C2semidirect
13. C2×#4674C2semidirect
14. C2×#4672C2semidirect
15. C2×#4672C2semidirect
16. C2×#4670C2semidirect
45. C3×#397C22semidirect
54. #4991C22semidirect
55. #4990C22semidirect
56. #4961C22semidirect
57. #4960C22semidirect
58. #4960C22semidirect
59. #4960C22semidirect
60. #4959C22semidirect
61. #4957C22semidirect
62. #4674C22semidirect
63. #4672C22semidirect
64. #4672C22semidirect
65. #4671C22semidirect
66. #4670C22semidirect
67. #4658C22semidirect
71. C2×#397D3semidirect
202. #397C2×D3semidirect
842. C2×C3#2828semidirect
910. C3C2×#2828semidirect
915. C2#77649direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3972
C2×#49912
C2×#49902
C2×#49592
C2×#49602
C2×#49612
C2×#49572
#776492
C2×#46712
C2×#46582
C2×#46742
C2×#46722
C2×#46702
C2×#28283