Finite Group Databasebeta

← C2×#75712 #11430834

Subgroups — C2×#75712 #11430834

Order 768.

3390 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#885C211yesmaximal, characteristic, complemented
2C22×#875C211yesmaximal, characteristic, complemented
3C2×C3×#388C211yesmaximal, characteristic, complemented
4C2×#4988C211yesmaximal, characteristic, complemented
5C2×#4990C211yesmaximal, characteristic, complemented
6C2×#4959C211yesmaximal, characteristic, complemented
7C2×#4960C211yesmaximal, characteristic, complemented
8C2×#4960C211yesmaximal, characteristic, complemented
9C2×#4960C211yesmaximal, characteristic, complemented
10C2×#4957C211yesmaximal, characteristic, complemented
11C2×#4940C211yesmaximal, characteristic, complemented
12#75712C2116yesmaximal, direct product factor
13C2×#4671C211yesmaximal, characteristic, complemented
14C2×#4672C211yesmaximal, characteristic, complemented
15C2×#4646C211yesmaximal, characteristic, complemented
16C2×#4669C211yesmaximal, characteristic, complemented
17C2×#2733—31nomaximal, Sylow
18C23×#67C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×D12C2211yescharacteristic
22C23×D12C2211yescharacteristic
23C23×D12C2211yescharacteristic
24C23×Dic6C2211yescharacteristic
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C42C2211yescharacteristic
30C22×#217C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
42C22×(C2×D3)⋊C4C2211yescharacteristic
43C22×Dic3⋊C4C2211yescharacteristic
44C22×Dic3⋊C4C2211yescharacteristic
45C22×C4×Dic3C2211yescharacteristic
46C22×C4×Dic3C2211yescharacteristic
47C2×#885—28no—
48C2×#885C2218yescomplemented
49C2×#875—28no—
50C2×#875C2218yescomplemented
51C3×#388C2218yescomplemented
52C2×C3×#95C2211yescharacteristic
53C2×C3×#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58#4990C2218yescomplemented
59#4988C2218yescomplemented
60#4960C2218yescomplemented
61#4960C2218yescomplemented
62#4960C2218yescomplemented
63#4959C2218yescomplemented
64#4957C2218yescomplemented
65#4940C2218yescomplemented
66#4672C2218yescomplemented
67#4671C2218yescomplemented
68#4669C2218yescomplemented
69#4646C2218yescomplemented
70C22×#124—31no—
71C22×#124—31no—
72#2733—316no—
73C2×#394—31no—
74C2×#394—31no—
75C2×#392—31no—
76C2×#392—31no—
77C2×#392—31no—
78C2×#392—31no—
79C2×#391—31no—
80C2×#390—31no—
81C2×#390—31no—
82C2×#388—31no—
83C2×#388—31no—
84C2×#388—31no—
85C2×#388D311yescharacteristic, complemented
86C25×C3C2311yescharacteristic
87C24×D3C2311yescharacteristic
88C24×D3C2311yescharacteristic
89C24×D3C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C22×#67—24no—
97C22×#67—24no—
98C22×#67—42no—
99C22×#67—42no—
100C22×#67—42no—
101C22×#67—42no—
102C22×#67—42no—
103C22×#67—42no—
104C22×#67—42no—
105C22×#67C2314yes—
106C22×#67C2314yes—
107C22×#67C2314yes—
108C23×Dic3C2311yescharacteristic
109C23×Dic3C2311yescharacteristic
110C23×Dic3C2311yescharacteristic
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C22×D12—24no—
114C22×D12—24no—
115C22×D12—42no—
116C22×D12—42no—
117C22×D12—42no—
118C22×D12—42no—
119C22×D12—42no—
120C22×D12—42no—
121C22×D12—42no—
122C22×D12C2314yes—
123C22×D12C2314yes—
124C22×D12C2314yes—
125C22×Dic6—42no—
126C22×Dic6—42no—
127C22×Dic6D418yescomplemented
128C22×Dic6C2314yes—
129C2×C3×C4⋊C4—42no—
130C2×C3×C4⋊C4C2314yes—
131C2×C3×C22⋊C4—24no—
132C2×C3×C22⋊C4—24no—
133C2×C3×C22⋊C4—42no—
134C2×C3×C22⋊C4C2314yes—
135C2×C3×C22⋊C4C2314yes—
136C2×C3×C22⋊C4C2314yes—
137C2×C3×C42—24no—
138C2×C3×C42C2314yes—
139C2×#217—24no—
140C2×#217C2314yes—
141C2×(C2×D3)⋊C4—24no—
142C2×(C2×D3)⋊C4—24no—
143C2×(C2×D3)⋊C4—24no—
144C2×(C2×D3)⋊C4—24no—
145C2×(C2×D3)⋊C4—24no—
146C2×(C2×D3)⋊C4—24no—
147C2×(C2×D3)⋊C4—24no—
148C2×(C2×D3)⋊C4—24no—
149C2×(C2×D3)⋊C4—24no—
150C2×(C2×D3)⋊C4—42no—
151C2×(C2×D3)⋊C4—42no—
152C2×(C2×D3)⋊C4—42no—
153C2×(C2×D3)⋊C4C2314yes—
154C2×(C2×D3)⋊C4C2314yes—
155C2×(C2×D3)⋊C4C2314yes—
156C2×(C2×D3)⋊C4C2314yes—
157C2×(C2×D3)⋊C4C2314yes—
158C2×(C2×D3)⋊C4C2314yes—
159C2×(C2×D3)⋊C4C2314yes—
160C2×(C2×D3)⋊C4C2314yes—
161C2×(C2×D3)⋊C4C2314yes—
162C2×(C2×D3)⋊C4C2314yes—
163C2×(C2×D3)⋊C4C2314yes—
164C2×(C2×D3)⋊C4C2314yes—
165C2×Dic3⋊C4—42no—
166C2×Dic3⋊C4—42no—
167C2×Dic3⋊C4C2314yes—
168C2×Dic3⋊C4C2314yes—
169C2×C4×Dic3—24no—
170C2×C4×Dic3—42no—
171C2×C4×Dic3C2314yes—
172C2×C4×Dic3C2314yes—
173#885—232no—
174#875—232no—
175C3×#95C2314yes—
176C3×#95C2314yes—
177C3⋊#95C2314yes—
178C3⋊#95C2314yes—
179C3⋊#95C2314yes—
180C3⋊#95C2314yes—
181C23×Q8—31no—
182C23×D4—31no—
183C23×D4—31no—
184C23×D4—31no—
185C23×D4—31no—
186C23×D4—31no—
187C23×D4—31no—
188C2×#124—38no—
189C2×#124—38no—
190C2×#124—68no—
191C2×#124—68no—
192C22×C4⋊C4—31no—
193C22×C4⋊C4—31no—
194C22×C4⋊C4C2×D311yescharacteristic
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⋊C4—31no—
203C22×C22⋊C4—31no—
204C22×C22⋊C4—31no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4—31no—
208C22×C22⋊C4C2×D311yescharacteristic
209C22×C22⋊C4C2×D311yescharacteristic
210C22×C22⋊C4C2×D311yescharacteristic
211C22×C42—31no—
212C22×C42—31no—
213C22×C42C2×D311yescharacteristic
214#394—38no—
215#394—38no—
216#392—38no—
217#392—38no—
218#392—38no—
219#392—38no—
220#391—38no—
221#390—38no—
222#390—38no—
223#388—38no—
224#388—38no—
225#388—38no—
226#388C2×D318yescomplemented
227C2×#95—31no—
228C2×#95—31no—
229C2×#95—31no—
230C2×#95—31no—
231C2×#95C2×D311yescharacteristic
232C2×#95C2×D311yescharacteristic
233C24×C3—22no—
234C24×C3—22no—
235C24×C3—22no—
236C24×C3—22no—
237C24×C3—22no—
238C24×C3—22no—
239C24×C3—22no—
240C24×C3C2412yes—
241C24×C3C2411yescharacteristic
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×D3—22no—
254C23×D3—22no—
255C23×D3—22no—
256C23×D3—22no—
257C23×D3—22no—
258C23×D3—22no—
259C23×D3—22no—
260C23×D3—22no—
261C23×D3—22no—
262C23×D3—22no—
263C23×D3C2412yes—
264C23×D3C2412yes—
265C23×D3C2412yes—
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×C4—22no—
275C22×C3×C4—22no—
276C22×C3×C4—22no—
277C22×C3×C4—22no—
278C22×C3×C4—22no—
279C22×C3×C4—22no—
280C22×C3×C4—22no—
281C22×C3×C4—22no—
282C22×C3×C4C2×D414yes—
283C22×C3×C4#4114yes—
284C22×C3×C4C2412yes—
285C22×C3×C4C2412yes—
286C22×C3×C4C2412yes—
287C22×C3×C4C2412yes—
288C22×C3×C4C2412yes—
289C22×C3×C4C2412yes—
290C2×#67—28no—
291C2×#67—28no—
292C2×#67—44no—
293C2×#67—44no—
294C2×#67—44no—
295C2×#67—44no—
296C2×#67—44no—
297C2×#67—44no—
298C2×#67—44no—
299C2×#67—416no—
300C2×#67—416no—
301C2×#67—416no—
302C22×Dic3—22no—
303C22×Dic3—22no—
304C22×Dic3—22no—
305C22×Dic3—22no—
306C22×Dic3—22no—
307C22×Dic3—22no—
308C22×Dic3—22no—
309C22×Dic3—22no—
310C22×Dic3—22no—
311C22×Dic3—22no—
312C22×Dic3—22no—
313C22×Dic3—22no—
314C22×Dic3C2×D414yes—
315C22×Dic3C2×D414yes—
316C22×Dic3#4114yes—
317C22×Dic3C2412yes—
318C22×Dic3C2412yes—
319C22×Dic3C2412yes—
320C22×Dic3C2412yes—
321C22×Dic3C2412yes—
322C2×D12—28no—
323C2×D12—28no—
324C2×D12—44no—
325C2×D12—44no—
326C2×D12—44no—
327C2×D12—44no—
328C2×D12—44no—
329C2×D12—44no—
330C2×D12—44no—
331C2×D12—416no—
332C2×D12—416no—
333C2×D12—416no—
334C2×Dic6—416no—
335C2×Dic6—44no—
336C2×Dic6—44no—
337C2×Dic6C2×D4116yescomplemented
338C3×C4⋊C4—44no—
339C3×C22⋊C4—28no—
340C3×C22⋊C4—28no—
341C3×C22⋊C4—44no—
342C3×C42—28no—
343#217—28no—
344(C2×D3)⋊C4—28no—
345(C2×D3)⋊C4—28no—
346(C2×D3)⋊C4—28no—
347(C2×D3)⋊C4—28no—
348(C2×D3)⋊C4—28no—
349(C2×D3)⋊C4—28no—
350(C2×D3)⋊C4—28no—
351(C2×D3)⋊C4—28no—
352(C2×D3)⋊C4—28no—
353(C2×D3)⋊C4—44no—
354(C2×D3)⋊C4—44no—
355(C2×D3)⋊C4—44no—
356Dic3⋊C4—44no—
357Dic3⋊C4—44no—
358C4×Dic3—28no—
359C4×Dic3—44no—
360C25—31no—
361C25—31no—
362C25—31no—
363C25C22×D311yescharacteristic
364C22×Q8—38no—
365C22×Q8—34no—
366C22×Q8—122no—
367C22×Q8—122no—
368C22×D4—34no—
369C22×D4—34no—
370C22×D4—34no—
371C22×D4—34no—
372C22×D4—34no—
373C22×D4—34no—
374C22×D4—64no—
375C22×D4—64no—
376C22×D4—64no—
377C22×D4—64no—
378C22×D4—122no—
379C22×D4—122no—
380C22×D4—122no—
381C22×D4—122no—
382C22×D4—122no—
383C22×D4—122no—
384C22×D4—122no—
385C22×D4—122no—
386C22×D4—122no—
387C22×D4—122no—
388C22×D4—122no—
389C22×D4—122no—
390C22×D4—122no—
391C22×D4—122no—
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—31no—
395C23×C4—31no—
396C23×C4—31no—
397C23×C4C22×D311yescharacteristic
398C23×C4C22×D311yescharacteristic
399C23×C4C22×D311yescharacteristic
400C23×C4C22×D311yescharacteristic
401C23×C4C22×D311yescharacteristic
402C23×C4C22×D311yescharacteristic
403#124—632no—
404#124—632no—
405C2×C4⋊C4—34no—
406C2×C4⋊C4—34no—
407C2×C4⋊C4—42no—
408C2×C4⋊C4—122no—
409C2×C4⋊C4—122no—
410C2×C4⋊C4C22×D314yes—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—34no—
414C2×C22⋊C4—34no—
415C2×C22⋊C4—34no—
416C2×C22⋊C4—34no—
417C2×C22⋊C4—34no—
418C2×C22⋊C4—34no—
419C2×C22⋊C4—34no—
420C2×C22⋊C4—34no—
421C2×C22⋊C4—34no—
422C2×C22⋊C4—34no—
423C2×C22⋊C4—34no—
424C2×C22⋊C4—34no—
425C2×C22⋊C4—34no—
426C2×C22⋊C4—42no—
427C2×C22⋊C4—64no—
428C2×C22⋊C4—64no—
429C2×C22⋊C4—64no—
430C2×C22⋊C4—64no—
431C2×C22⋊C4—64no—
432C2×C22⋊C4—64no—
433C2×C22⋊C4—64no—
434C2×C22⋊C4—64no—
435C2×C22⋊C4—64no—
436C2×C22⋊C4—64no—
437C2×C22⋊C4—122no—
438C2×C22⋊C4—122no—
439C2×C22⋊C4—122no—
440C2×C22⋊C4C22×D314yes—
441C2×C22⋊C4C22×D314yes—
442C2×C22⋊C4C22×D314yes—
443C2×C42—24no—
444C2×C42—34no—
445C2×C42—34no—
446C2×C42—64no—
447C2×C42—122no—
448C2×C42C22×D314yes—
449#95—34no—
450#95—34no—
451#95—34no—
452#95—34no—
453#95C22×D314yes—
454#95C22×D314yes—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—44no—
463C23×C3—44no—
464C23×C3—44no—
465C23×C3—44no—
466C23×C3—44no—
467C23×C3—44no—
468C23×C3—44no—
469C23×C3C22×D412yes—
470C23×C3C2×#4112yes—
471C23×C3C2×#4112yes—
472C23×C3H(5,𝔽2)12yes—
473C23×C3H(5,𝔽2)12yes—
474C23×C3H(5,𝔽2)12yes—
475C23×C3H(5,𝔽2)12yes—
476C23×C3C2511yescharacteristic
477C22×D3—22no—
478C22×D3—22no—
479C22×D3—22no—
480C22×D3—22no—
481C22×D3—22no—
482C22×D3—22no—
483C22×D3—22no—
484C22×D3—22no—
485C22×D3—22no—
486C22×D3—22no—
487C22×D3—22no—
488C22×D3—22no—
489C22×D3—22no—
490C22×D3—22no—
491C22×D3—22no—
492C22×D3—22no—
493C22×D3—22no—
494C22×D3—22no—
495C22×D3—22no—
496C22×D3—22no—
497C22×D3—22no—
498C22×D3—44no—
499C22×D3—44no—
500C22×D3—44no—
501C22×D3—44no—
502C22×D3—44no—
503C22×D3—44no—
504C22×D3—44no—
505C22×D3—44no—
506C22×D3—44no—
507C22×D3—44no—
508C22×D3—44no—
509C22×D3—44no—
510C22×D3—44no—
511C22×D3—44no—
512C22×D3—44no—
513C22×D3—44no—
514C22×D3—44no—
515C22×D3—44no—
516C22×D3—44no—
517C22×D3—44no—
518C22×D3—44no—
519C2×C3×C4—28no—
520C2×C3×C4—28no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—44no—
538C2×C3×C4—44no—
539C2×C3×C4—44no—
540C2×C3×C4—44no—
541C2×C3×C4C22×D414yes—
542C2×C3×C4C2×#4114yes—
543#67—416no—
544#67—416no—
545#67—416no—
546C2×Dic3—28no—
547C2×Dic3—28no—
548C2×Dic3—28no—
549C2×Dic3—22no—
550C2×Dic3—22no—
551C2×Dic3—22no—
552C2×Dic3—22no—
553C2×Dic3—22no—
554C2×Dic3—22no—
555C2×Dic3—22no—
556C2×Dic3—22no—
557C2×Dic3—22no—
558C2×Dic3—22no—
559C2×Dic3—22no—
560C2×Dic3—22no—
561C2×Dic3—44no—
562C2×Dic3—44no—
563C2×Dic3C22×D414yes—
564C2×Dic3C22×D414yes—
565C2×Dic3C2×#4114yes—
566D12—416no—
567D12—416no—
568D12—416no—
569Dic6—416no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—32no—
578C24—32no—
579C24—32no—
580C24—62no—
581C24—62no—
582C24—62no—
583C24—62no—
584C24—62no—
585C24—62no—
586C24—62no—
587C24—62no—
588C24—62no—
589C24—62no—
590C24—62no—
591C24—62no—
592C24—62no—
593C24—62no—
594C24—62no—
595C24—62no—
596C24—62no—
597C24—62no—
598C24—62no—
599C24—62no—
600C24—62no—
601C24C23×D312yes—
602C24C23×D311yescharacteristic
603C2×Q8—316no—
604C2×Q8—1216no—
605C2×Q8—124no—
606C2×Q8—124no—
607C2×D4—68no—
608C2×D4—68no—
609C2×D4—68no—
610C2×D4—68no—
611C2×D4—124no—
612C2×D4—124no—
613C2×D4—124no—
614C2×D4—124no—
615C2×D4—124no—
616C2×D4—124no—
617C2×D4—124no—
618C2×D4—1216no—
619C2×D4—1216no—
620C2×D4—1216no—
621C2×D4—124no—
622C2×D4—124no—
623C2×D4—124no—
624C2×D4—124no—
625C2×D4—124no—
626C2×D4—124no—
627C2×D4—124no—
628C2×D4—1216no—
629C2×D4—1216no—
630C2×D4—1216no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—34no—
648C22×C4—34no—
649C22×C4—34no—
650C22×C4—32no—
651C22×C4—32no—
652C22×C4—32no—
653C22×C4—32no—
654C22×C4—32no—
655C22×C4—62no—
656C22×C4—62no—
657C22×C4—62no—
658C22×C4—62no—
659C22×C4—62no—
660C22×C4—62no—
661C22×C4—62no—
662C22×C4—62no—
663C22×C4—62no—
664C22×C4—62no—
665C22×C4—62no—
666C22×C4—62no—
667C22×C4#23514yes—
668C22×C4D3×D414yes—
669C22×C4C23×D312yes—
670C22×C4C23×D312yes—
671C22×C4C23×D312yes—
672C22×C4C23×D312yes—
673C22×C4C23×D312yes—
674C22×C4C23×D312yes—
675C4⋊C4—44no—
676C4⋊C4—124no—
677C4⋊C4—124no—
678C22⋊C4—28no—
679C22⋊C4—28no—
680C22⋊C4—44no—
681C22⋊C4—68no—
682C22⋊C4—68no—
683C22⋊C4—68no—
684C22⋊C4—68no—
685C22⋊C4—68no—
686C22⋊C4—68no—
687C22⋊C4—68no—
688C22⋊C4—68no—
689C22⋊C4—68no—
690C22⋊C4—68no—
691C22⋊C4—124no—
692C22⋊C4—124no—
693C22⋊C4—124no—
694C42—28no—
695C42—68no—
696C42—124no—
697C22×C3—42no—
698C22×C3—42no—
699C22×C3—42no—
700C22×C3—42no—
701C22×C3—42no—
702C22×C3—42no—
703C22×C3—42no—
704C22×C3—88no—
705C22×C3#53414yes—
706C22×C3#53814yes—
707C22×C3#53814yes—
708C22×C3#55014yes—
709C22×C3#55014yes—
710C22×C3#55514yes—
711C22×C3H(3,𝔽4)14yes—
712C22×C3C23×D411yescharacteristic
713C22×C3C22×#4111yescharacteristic
714C22×C3C22×#4111yescharacteristic
715C22×C3C2×H(5,𝔽2)11yescharacteristic
716C22×C3C2×H(5,𝔽2)11yescharacteristic
717C22×C3C2×H(5,𝔽2)11yescharacteristic
718C22×C3C2×H(5,𝔽2)11yescharacteristic
719C2×D3—42no—
720C2×D3—42no—
721C2×D3—42no—
722C2×D3—42no—
723C2×D3—42no—
724C2×D3—42no—
725C2×D3—42no—
726C2×D3—42no—
727C2×D3—42no—
728C2×D3—42no—
729C2×D3—42no—
730C2×D3—42no—
731C2×D3—42no—
732C2×D3—42no—
733C2×D3—42no—
734C2×D3—42no—
735C2×D3—42no—
736C2×D3—42no—
737C2×D3—42no—
738C2×D3—42no—
739C2×D3—42no—
740C2×D3—88no—
741C2×D3—88no—
742C2×D3—88no—
743C3×C4—24no—
744C3×C4—24no—
745C3×C4—42no—
746C3×C4—42no—
747C3×C4—42no—
748C3×C4—42no—
749Dic3—24no—
750Dic3—24no—
751Dic3—24no—
752Dic3—42no—
753Dic3—42no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—62no—
769C23—62no—
770C23—62no—
771C23—62no—
772C23—62no—
773C23—62no—
774C23—62no—
775C23—62no—
776C23—62no—
777C23—62no—
778C23—62no—
779C23—62no—
780C23—62no—
781C23—62no—
782C23—62no—
783C23—62no—
784C23—62no—
785C23—62no—
786C23—62no—
787C23—62no—
788C23—62no—
789C23—124no—
790C23—124no—
791C23—124no—
792C23—124no—
793C23—124no—
794C23—124no—
795C23—124no—
796C23—124no—
797C23—124no—
798C23—124no—
799C23—124no—
800C23—124no—
801C23—124no—
802C23—124no—
803C23—124no—
804C23—124no—
805C23—124no—
806C23—124no—
807C23—124no—
808C23—124no—
809C23—124no—
810C23C2×#23512yes—
811C23C2×D3×D412yes—
812C23#100412yes—
813C23D3×#4112yes—
814C23#100912yes—
815C23#100912yes—
816C23#100912yes—
817C23C24×D311yescharacteristic
818Q8—1216no—
819D4—1216no—
820D4—1216no—
821D4—1216no—
822D4—1216no—
823D4—1216no—
824D4—1216no—
825C2×C4—28no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—28no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—34no—
844C2×C4—34no—
845C2×C4—34no—
846C2×C4—44no—
847C2×C4—44no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—68no—
851C2×C4—68no—
852C2×C4—68no—
853C2×C4—62no—
854C2×C4—62no—
855C2×C4—62no—
856C2×C4—62no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—62no—
862C2×C4—62no—
863C2×C4—62no—
864C2×C4—62no—
865C2×C4—124no—
866C2×C4—124no—
867C2×C4C2×#23514yes—
868C2×C4C2×D3×D414yes—
869C2×C3—82no—
870C2×C3#273318yescomplemented
871C2×C3C2×#53411yescharacteristic
872C2×C3C2×#53811yescharacteristic
873C2×C3C2×#53811yescharacteristic
874C2×C3C2×#55011yescharacteristic
875C2×C3C2×#55011yescharacteristic
876C2×C3C2×#55511yescharacteristic
877C2×C3C2×H(3,𝔽4)11yescharacteristic
878D3—82no—
879D3—82no—
880D3—82no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—88no—
889C22—122no—
890C22—122no—
891C22—122no—
892C22—122no—
893C22—122no—
894C22—122no—
895C22—122no—
896C22—122no—
897C22—122no—
898C22—122no—
899C22—122no—
900C22—122no—
901C22—122no—
902C22—122no—
903C22—122no—
904C22—122no—
905C22—122no—
906C22—122no—
907C22—122no—
908C22—122no—
909C22—122no—
910C22—248no—
911C22—248no—
912C22—248no—
913C22#553214yes—
914C22#555314yes—
915C22#556014yes—
916C22#559914yes—
917C22#565314yes—
918C22#568314yes—
919C22#570414yes—
920C22C22×#23511yescharacteristic
921C22C22×D3×D411yescharacteristic
922C22C2×#100411yescharacteristic
923C22C2×D3×#4111yescharacteristic
924C22C2×#100911yescharacteristic
925C22C2×#100911yescharacteristic
926C22C2×#100911yescharacteristic
927C4—24no—
928C4—24no—
929C4—42no—
930C4—42no—
931C4—42no—
932C4—42no—
933C4—64no—
934C4—64no—
935C4—64no—
936C4—122no—
937C4—122no—
938C3C2×#273311yescharacteristic, complemented, Sylow
939C2—82no—
940C2—242no—
941C2—242no—
942C2—242no—
943C2#7571218yesdirect product factor
944C2C2×#553211yescharacteristic
945C2C2×#555311yescharacteristic
946C2C2×#556011yescharacteristic
947C2C2×#559911yescharacteristic
948C2C2×#565311yescharacteristic
949C2C2×#568311yescharacteristic
950C2C2×#570411yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#388C2
socleC24×C3C24
hypercenterC2×#388D3
hypocenterC3C2×#2733
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#885C2semidirect
2. C22×#875C2semidirect
3. C2×C3×#388C2semidirect
4. C2×#4988C2semidirect
5. C2×#4990C2semidirect
6. C2×#4959C2semidirect
7. C2×#4960C2semidirect
8. C2×#4960C2semidirect
9. C2×#4960C2semidirect
10. C2×#4957C2semidirect
11. C2×#4940C2semidirect
12. #75712C2direct (N × H)
13. C2×#4671C2semidirect
14. C2×#4672C2semidirect
15. C2×#4646C2semidirect
16. C2×#4669C2semidirect
48. C2×#885C22semidirect
50. C2×#875C22semidirect
51. C3×#388C22semidirect
58. #4990C22semidirect
59. #4988C22semidirect
60. #4960C22semidirect
61. #4960C22semidirect
62. #4960C22semidirect
63. #4959C22semidirect
64. #4957C22semidirect
65. #4940C22semidirect
66. #4672C22semidirect
67. #4671C22semidirect
68. #4669C22semidirect
69. #4646C22semidirect
85. C2×#388D3semidirect
127. C22×Dic6D4semidirect
226. #388C2×D3semidirect
337. C2×Dic6C2×D4semidirect
870. C2×C3#2733semidirect
938. C3C2×#2733semidirect
943. C2#75712direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#8852
C22×#8752
C2×C3×#3882
C2×#49882
C2×#49902
C2×#49592
C2×#49602
C2×#49572
C2×#49402
#757122
C2×#46712
C2×#46722
C2×#46462
C2×#46692
C2×#27333