Finite Group Databasebeta

← C2×#74923 #11430019

Subgroups — C2×#74923 #11430019

Order 768.

3650 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#938C211yesmaximal, characteristic, complemented
2C22×#884C211yesmaximal, characteristic, complemented
3C2×C3×#386C211yesmaximal, characteristic, complemented
4C2×#5223C211yesmaximal, characteristic, complemented
5C2×#5213C211yesmaximal, characteristic, complemented
6C2×#5213C211yesmaximal, characteristic, complemented
7C2×#4959C211yesmaximal, characteristic, complemented
8C2×#4960C211yesmaximal, characteristic, complemented
9C2×#4956C211yesmaximal, characteristic, complemented
10C2×#4952C211yesmaximal, characteristic, complemented
11C2×#4952C211yesmaximal, characteristic, complemented
12#74923C2116yesmaximal, direct product factor
13C2×#4665C211yesmaximal, characteristic, complemented
14C2×#4668C211yesmaximal, characteristic, complemented
15C2×#4664C211yesmaximal, characteristic, complemented
16C2×#4660C211yesmaximal, characteristic, complemented
17C2×#2688—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C24×C3×C4C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×#67C2211yescharacteristic
22C23×#67C2211yescharacteristic
23C23×#67C2211yescharacteristic
24C23×D12C2211yescharacteristic
25C23×C4×D3C2211yescharacteristic
26C23×C4×D3C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C22×#217C2211yescharacteristic
34C2×#938—28no—
35C2×#938C2218yescomplemented
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×C4⋊Dic3C2211yescharacteristic
43C22×Dic3⋊C4C2211yescharacteristic
44C22×Dic3⋊C4C2211yescharacteristic
45C2×#884—28no—
46C2×#884C2218yescomplemented
47C3×#386C2218yescomplemented
48C2×C3×#95C2211yescharacteristic
49C2×C3×#95C2211yescharacteristic
50#5223C2218yescomplemented
51#5213C2218yescomplemented
52#5213C2218yescomplemented
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61#4960C2218yescomplemented
62#4959C2218yescomplemented
63#4956C2218yescomplemented
64#4952C2218yescomplemented
65#4952C2218yescomplemented
66#4668C2218yescomplemented
67#4665C2218yescomplemented
68#4664C2218yescomplemented
69#4660C2218yescomplemented
70C22×#121—31no—
71C22×#121—31no—
72#2688—316no—
73C2×#400—31no—
74C2×#397—31no—
75C2×#397—31no—
76C2×#394—31no—
77C2×#392—31no—
78C2×#392—31no—
79C2×#386—31no—
80C2×#386—31no—
81C2×#386—31no—
82C2×#386—31no—
83C2×#386D311yescharacteristic, complemented
84C2×#385—31no—
85C2×#381—31no—
86C25×C3C2311yescharacteristic
87C25×C3C2311yescharacteristic
88C24×D3C2311yescharacteristic
89C24×D3C2311yescharacteristic
90C22×C3×D4—24no—
91C22×C3×D4—24no—
92C22×C3×D4—42no—
93C22×C3×D4C2314yes—
94C23×C3×C4—42no—
95C23×C3×C4—42no—
96C23×C3×C4—42no—
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C2314yes—
103C22×#67—24no—
104C22×#67—24no—
105C22×#67—24no—
106C22×#67—24no—
107C22×#67—42no—
108C22×#67—42no—
109C22×#67—42no—
110C22×#67—42no—
111C22×#67—42no—
112C22×#67—42no—
113C22×#67—42no—
114C22×#67D418yescomplemented
115C22×#67C2314yes—
116C22×#67C2314yes—
117C22×#67C2314yes—
118C22×#67C2314yes—
119C23×Dic3C2311yescharacteristic
120C23×Dic3C2311yescharacteristic
121C23×Dic3C2311yescharacteristic
122C23×Dic3C2311yescharacteristic
123C23×Dic3C2311yescharacteristic
124C23×Dic3C2311yescharacteristic
125C22×D12—24no—
126C22×D12—24no—
127C22×D12—42no—
128C22×D12C2314yes—
129C22×C4×D3—24no—
130C22×C4×D3—24no—
131C22×C4×D3—24no—
132C22×C4×D3—42no—
133C22×C4×D3—42no—
134C22×C4×D3—42no—
135C22×C4×D3C2314yes—
136C22×C4×D3C2314yes—
137C2×C3×C22⋊C4—24no—
138C2×C3×C22⋊C4—42no—
139C2×C3×C22⋊C4—42no—
140C2×C3×C22⋊C4C2314yes—
141C2×C3×C22⋊C4C2314yes—
142C2×C3×C22⋊C4C2314yes—
143C2×#217—24no—
144C2×#217—24no—
145C2×#217—42no—
146C2×#217—42no—
147C2×#217C2314yes—
148C2×#217C2314yes—
149C2×#217C2314yes—
150C2×#217C2314yes—
151#938—232no—
152C2×(C2×D3)⋊C4—24no—
153C2×(C2×D3)⋊C4—24no—
154C2×(C2×D3)⋊C4—42no—
155C2×(C2×D3)⋊C4—42no—
156C2×(C2×D3)⋊C4—42no—
157C2×(C2×D3)⋊C4—42no—
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×C4⋊Dic3—24no—
165C2×C4⋊Dic3C2314yes—
166C2×Dic3⋊C4—24no—
167C2×Dic3⋊C4—42no—
168C2×Dic3⋊C4C2314yes—
169C2×Dic3⋊C4C2314yes—
170#884—232no—
171C3×#95C2314yes—
172C3×#95C2314yes—
173C3⋊#95C2314yes—
174C3⋊#95C2314yes—
175C3⋊#95C2314yes—
176C3⋊#95C2314yes—
177C3⋊#95C2314yes—
178C3⋊#95C2314yes—
179C3⋊#95C2314yes—
180C3⋊#95C2314yes—
181C23×D4—31no—
182C23×D4—31no—
183C23×D4—31no—
184C23×D4—31no—
185C23×D4—31no—
186C23×D4C2×D311yescharacteristic
187C24×C4—31no—
188C24×C4—31no—
189C24×C4C2×D311yescharacteristic
190C2×#121—38no—
191C2×#121—38no—
192C2×#121—68no—
193C2×#121—68no—
194C22×C4⋊C4—31no—
195C22×C4⋊C4—31no—
196C22×C4⋊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⋊C4C2×D311yescharacteristic
208C22×C22⋊C4C2×D311yescharacteristic
209C22×C22⋊C4C2×D311yescharacteristic
210#400—38no—
211#397—38no—
212#397—38no—
213#394—38no—
214#392—38no—
215#392—38no—
216#386—38no—
217#386—38no—
218#386—38no—
219#386—38no—
220#386C2×D318yescomplemented
221#385—38no—
222#381—38no—
223C2×#95—31no—
224C2×#95—31no—
225C2×#95—31no—
226C2×#95—31no—
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×C3—22no—
241C24×C3—22no—
242C24×C3—22no—
243C24×C3—22no—
244C24×C3—22no—
245C24×C3—22no—
246C24×C3C2×D414yes—
247C24×C3C2412yes—
248C24×C3C2412yes—
249C24×C3C2411yescharacteristic
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×D3C2×D414yes—
263C23×D3#4114yes—
264C23×D3C2412yes—
265C23×D3C2412yes—
266C2×C3×D4—28no—
267C2×C3×D4—28no—
268C2×C3×D4—44no—
269C2×C3×D4—416no—
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×C4—22no—
283C22×C3×C4—22no—
284C22×C3×C4—44no—
285C22×C3×C4—44no—
286C22×C3×C4—44no—
287C22×C3×C4—416no—
288C22×C3×C4#4114yes—
289C22×C3×C4C2412yes—
290C22×C3×C4C2412yes—
291C22×C3×C4C2412yes—
292C22×C3×C4C2412yes—
293C22×C3×C4C2412yes—
294C2×#67—28no—
295C2×#67—28no—
296C2×#67—28no—
297C2×#67—28no—
298C2×#67—416no—
299C2×#67—44no—
300C2×#67—44no—
301C2×#67—44no—
302C2×#67—44no—
303C2×#67—44no—
304C2×#67—44no—
305C2×#67—44no—
306C2×#67—416no—
307C2×#67—416no—
308C2×#67—416no—
309C2×#67C2×D4116yescomplemented
310C22×Dic3—22no—
311C22×Dic3—22no—
312C22×Dic3—22no—
313C22×Dic3—22no—
314C22×Dic3—22no—
315C22×Dic3—22no—
316C22×Dic3—22no—
317C22×Dic3—22no—
318C22×Dic3—22no—
319C22×Dic3—22no—
320C22×Dic3—22no—
321C22×Dic3—22no—
322C22×Dic3—22no—
323C22×Dic3—22no—
324C22×Dic3—22no—
325C22×Dic3—22no—
326C22×Dic3—22no—
327C22×Dic3C2×D414yes—
328C22×Dic3C2412yes—
329C22×Dic3C2412yes—
330C22×Dic3C2412yes—
331C22×Dic3C2412yes—
332C22×Dic3C2412yes—
333C22×Dic3C2412yes—
334C2×D12—28no—
335C2×D12—28no—
336C2×D12—44no—
337C2×D12—416no—
338C2×C4×D3—28no—
339C2×C4×D3—28no—
340C2×C4×D3—28no—
341C2×C4×D3—44no—
342C2×C4×D3—44no—
343C2×C4×D3—44no—
344C2×C4×D3—416no—
345C2×C4×D3—416no—
346C3×C22⋊C4—28no—
347C3×C22⋊C4—44no—
348C3×C22⋊C4—44no—
349#217—28no—
350#217—28no—
351#217—44no—
352#217—44no—
353(C2×D3)⋊C4—28no—
354(C2×D3)⋊C4—28no—
355(C2×D3)⋊C4—44no—
356(C2×D3)⋊C4—44no—
357(C2×D3)⋊C4—44no—
358(C2×D3)⋊C4—44no—
359C4⋊Dic3—28no—
360Dic3⋊C4—28no—
361Dic3⋊C4—44no—
362C25—31no—
363C25—31no—
364C25C22×D311yescharacteristic
365C25C22×D311yescharacteristic
366C22×D4—24no—
367C22×D4—24no—
368C22×D4—38no—
369C22×D4—34no—
370C22×D4—34no—
371C22×D4—34no—
372C22×D4—34no—
373C22×D4—34no—
374C22×D4—42no—
375C22×D4—64no—
376C22×D4—64no—
377C22×D4—64no—
378C22×D4—64no—
379C22×D4—64no—
380C22×D4—64no—
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×D4C22×D314yes—
390C23×C4—31no—
391C23×C4—31no—
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—31no—
395C23×C4—31no—
396C23×C4—34no—
397C23×C4—34no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4—64no—
402C23×C4—64no—
403C23×C4—64no—
404C23×C4—122no—
405C23×C4—122no—
406C23×C4—122no—
407C23×C4C22×D311yescharacteristic
408C23×C4C22×D311yescharacteristic
409C23×C4C22×D311yescharacteristic
410C23×C4C22×D311yescharacteristic
411C23×C4C22×D311yescharacteristic
412C23×C4C22×D314yes—
413#121—632no—
414#121—632no—
415C2×C4⋊C4—34no—
416C2×C4⋊C4—34no—
417C2×C4⋊C4—34no—
418C2×C4⋊C4—64no—
419C2×C4⋊C4—64no—
420C2×C4⋊C4—122no—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—34no—
423C2×C22⋊C4—34no—
424C2×C22⋊C4—34no—
425C2×C22⋊C4—34no—
426C2×C22⋊C4—34no—
427C2×C22⋊C4—34no—
428C2×C22⋊C4—34no—
429C2×C22⋊C4—34no—
430C2×C22⋊C4—34no—
431C2×C22⋊C4—34no—
432C2×C22⋊C4—42no—
433C2×C22⋊C4—42no—
434C2×C22⋊C4—64no—
435C2×C22⋊C4—64no—
436C2×C22⋊C4—64no—
437C2×C22⋊C4—64no—
438C2×C22⋊C4—122no—
439C2×C22⋊C4—122no—
440C2×C22⋊C4—122no—
441C2×C22⋊C4—122no—
442C2×C22⋊C4—122no—
443C2×C22⋊C4—122no—
444C2×C22⋊C4C22×D314yes—
445C2×C22⋊C4C22×D314yes—
446C2×C22⋊C4C22×D314yes—
447#95—34no—
448#95—34no—
449#95—34no—
450#95—34no—
451#95—34no—
452#95—34no—
453#95—34no—
454#95—34no—
455#95C22×D314yes—
456#95C22×D314yes—
457C23×C3—28no—
458C23×C3—28no—
459C23×C3—28no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—44no—
474C23×C3—44no—
475C23×C3—44no—
476C23×C3—44no—
477C23×C3—44no—
478C23×C3—44no—
479C23×C3—44no—
480C23×C3—44no—
481C23×C3—44no—
482C23×C3—44no—
483C23×C3—44no—
484C23×C3C22×D414yes—
485C23×C3C22×D412yes—
486C23×C3C2×#4112yes—
487C23×C3C2×#4112yes—
488C23×C3H(5,𝔽2)12yes—
489C23×C3H(5,𝔽2)12yes—
490C23×C3H(5,𝔽2)12yes—
491C23×C3H(5,𝔽2)12yes—
492C23×C3C2511yescharacteristic
493C22×D3—28no—
494C22×D3—28no—
495C22×D3—28no—
496C22×D3—28no—
497C22×D3—28no—
498C22×D3—28no—
499C22×D3—22no—
500C22×D3—22no—
501C22×D3—22no—
502C22×D3—22no—
503C22×D3—22no—
504C22×D3—22no—
505C22×D3—22no—
506C22×D3—22no—
507C22×D3—22no—
508C22×D3—22no—
509C22×D3—22no—
510C22×D3—22no—
511C22×D3—44no—
512C22×D3—44no—
513C22×D3—44no—
514C22×D3—44no—
515C22×D3—44no—
516C22×D3—44no—
517C22×D3—44no—
518C22×D3—44no—
519C22×D3C22×D414yes—
520C22×D3C2×#4114yes—
521C3×D4—416no—
522C2×C3×C4—28no—
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—416no—
538C2×C3×C4—44no—
539C2×C3×C4—44no—
540C2×C3×C4—44no—
541C2×C3×C4—44no—
542C2×C3×C4C2×#4114yes—
543#67—416no—
544#67—416no—
545#67—416no—
546#67—416no—
547C2×Dic3—28no—
548C2×Dic3—22no—
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—22no—
562C2×Dic3—22no—
563C2×Dic3—22no—
564C2×Dic3—22no—
565C2×Dic3—44no—
566C2×Dic3—44no—
567C2×Dic3—44no—
568C2×Dic3—44no—
569C2×Dic3—44no—
570C2×Dic3C22×D414yes—
571D12—416no—
572C4×D3—416no—
573C4×D3—416no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—34no—
588C24—34no—
589C24—32no—
590C24—32no—
591C24—62no—
592C24—62no—
593C24—62no—
594C24—62no—
595C24—62no—
596C24—62no—
597C24—62no—
598C24—62no—
599C24—62no—
600C24—62no—
601C24—62no—
602C24—62no—
603C24D3×D414yes—
604C24C23×D312yes—
605C24C23×D312yes—
606C24C23×D311yescharacteristic
607C2×D4—28no—
608C2×D4—28no—
609C2×D4—316no—
610C2×D4—44no—
611C2×D4—416no—
612C2×D4—68no—
613C2×D4—68no—
614C2×D4—68no—
615C2×D4—68no—
616C2×D4—68no—
617C2×D4—68no—
618C2×D4—124no—
619C2×D4—1216no—
620C2×D4—124no—
621C2×D4—124no—
622C2×D4—1216no—
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—34no—
646C22×C4—32no—
647C22×C4—32no—
648C22×C4—32no—
649C22×C4—32no—
650C22×C4—32no—
651C22×C4—32no—
652C22×C4—44no—
653C22×C4—44no—
654C22×C4—44no—
655C22×C4—416no—
656C22×C4—68no—
657C22×C4—68no—
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—62no—
668C22×C4—62no—
669C22×C4—62no—
670C22×C4—62no—
671C22×C4—62no—
672C22×C4—62no—
673C22×C4—62no—
674C22×C4—62no—
675C22×C4—68no—
676C22×C4—124no—
677C22×C4—124no—
678C22×C4—124no—
679C22×C4—1216no—
680C22×C4—1216no—
681C22×C4#23514yes—
682C22×C4C23×D312yes—
683C22×C4C23×D312yes—
684C22×C4C23×D312yes—
685C22×C4C23×D312yes—
686C22×C4C23×D312yes—
687C4⋊C4—68no—
688C4⋊C4—68no—
689C4⋊C4—124no—
690C22⋊C4—28no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—68no—
694C22⋊C4—68no—
695C22⋊C4—68no—
696C22⋊C4—68no—
697C22⋊C4—124no—
698C22⋊C4—124no—
699C22⋊C4—124no—
700C22⋊C4—124no—
701C22⋊C4—124no—
702C22⋊C4—124no—
703C22×C3—24no—
704C22×C3—24no—
705C22×C3—24no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—416no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—42no—
713C22×C3—42no—
714C22×C3—42no—
715C22×C3—42no—
716C22×C3—42no—
717C22×C3—42no—
718C22×C3—88no—
719C22×C3#53414yes—
720C22×C3#53814yes—
721C22×C3#54014yes—
722C22×C3#54614yes—
723C22×C3#54614yes—
724C22×C3#55314yes—
725C22×C3#56014yes—
726C22×C3C23×D411yescharacteristic
727C22×C3C22×#4111yescharacteristic
728C22×C3C22×#4111yescharacteristic
729C22×C3C2×H(5,𝔽2)11yescharacteristic
730C22×C3C2×H(5,𝔽2)11yescharacteristic
731C22×C3C2×H(5,𝔽2)11yescharacteristic
732C22×C3C2×H(5,𝔽2)11yescharacteristic
733C2×D3—24no—
734C2×D3—24no—
735C2×D3—24no—
736C2×D3—24no—
737C2×D3—24no—
738C2×D3—24no—
739C2×D3—42no—
740C2×D3—42no—
741C2×D3—42no—
742C2×D3—42no—
743C2×D3—416no—
744C2×D3—416no—
745C2×D3—42no—
746C2×D3—42no—
747C2×D3—42no—
748C2×D3—42no—
749C3×C4—24no—
750C3×C4—42no—
751C3×C4—42no—
752C3×C4—42no—
753C3×C4—42no—
754Dic3—24no—
755Dic3—42no—
756Dic3—42no—
757Dic3—42no—
758Dic3—42no—
759Dic3—42no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—28no—
767C23—28no—
768C23—28no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—34no—
777C23—34no—
778C23—44no—
779C23—44no—
780C23—44no—
781C23—44no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—44no—
789C23—68no—
790C23—62no—
791C23—62no—
792C23—62no—
793C23—62no—
794C23—62no—
795C23—62no—
796C23—62no—
797C23—62no—
798C23—62no—
799C23—62no—
800C23—62no—
801C23—62no—
802C23—68no—
803C23—68no—
804C23—68no—
805C23—68no—
806C23—68no—
807C23—124no—
808C23—124no—
809C23—124no—
810C23—124no—
811C23—124no—
812C23—124no—
813C23—124no—
814C23—124no—
815C23C2×#23512yes—
816C23C2×D3×D414yes—
817C23C2×D3×D412yes—
818C23#100412yes—
819C23#100412yes—
820C23#100412yes—
821C23D3×#4112yes—
822C23#100912yes—
823C23C24×D311yescharacteristic
824D4—416no—
825D4—1216no—
826D4—1216no—
827D4—1216no—
828D4—1216no—
829D4—1216no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—28no—
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—22no—
844C2×C4—22no—
845C2×C4—34no—
846C2×C4—416no—
847C2×C4—44no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—62no—
852C2×C4—62no—
853C2×C4—68no—
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—62no—
866C2×C4—62no—
867C2×C4—62no—
868C2×C4—62no—
869C2×C4—1216no—
870C2×C4—1216no—
871C2×C4—124no—
872C2×C4—124no—
873C2×C4—124no—
874C2×C4—124no—
875C2×C4—124no—
876C2×C4C2×#23514yes—
877C2×C3—44no—
878C2×C3—82no—
879C2×C3#268818yescomplemented
880C2×C3C2×#53411yescharacteristic
881C2×C3C2×#53811yescharacteristic
882C2×C3C2×#54011yescharacteristic
883C2×C3C2×#54611yescharacteristic
884C2×C3C2×#54611yescharacteristic
885C2×C3C2×#55311yescharacteristic
886C2×C3C2×#56011yescharacteristic
887D3—44no—
888D3—44no—
889C22—24no—
890C22—24no—
891C22—24no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—416no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—64no—
905C22—64no—
906C22—64no—
907C22—64no—
908C22—64no—
909C22—64no—
910C22—88no—
911C22—122no—
912C22—122no—
913C22—122no—
914C22—122no—
915C22—122no—
916C22—1216no—
917C22—1216no—
918C22—122no—
919C22—122no—
920C22—122no—
921C22#549014yes—
922C22#555814yes—
923C22#556214yes—
924C22#559514yes—
925C22#560514yes—
926C22#561014yes—
927C22#565714yes—
928C22C22×#23511yescharacteristic
929C22C22×D3×D411yescharacteristic
930C22C2×#100411yescharacteristic
931C22C2×#100411yescharacteristic
932C22C2×#100411yescharacteristic
933C22C2×D3×#4111yescharacteristic
934C22C2×#100911yescharacteristic
935C4—24no—
936C4—42no—
937C4—42no—
938C4—42no—
939C4—42no—
940C4—64no—
941C4—122no—
942C4—122no—
943C4—122no—
944C4—122no—
945C4—122no—
946C3C2×#268811yescharacteristic, complemented, Sylow
947C2—44no—
948C2—82no—
949C2—124no—
950C2—124no—
951C2#7492318yesdirect product factor
952C2C2×#549011yescharacteristic
953C2C2×#556211yescharacteristic
954C2C2×#555811yescharacteristic
955C2C2×#559511yescharacteristic
956C2C2×#560511yescharacteristic
957C2C2×#561011yescharacteristic
958C2C2×#565711yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#386C2
socleC24×C3C24
hypercenterC2×#386D3
hypocenterC3C2×#2688
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#938C2semidirect
2. C22×#884C2semidirect
3. C2×C3×#386C2semidirect
4. C2×#5223C2semidirect
5. C2×#5213C2semidirect
6. C2×#5213C2semidirect
7. C2×#4959C2semidirect
8. C2×#4960C2semidirect
9. C2×#4956C2semidirect
10. C2×#4952C2semidirect
11. C2×#4952C2semidirect
12. #74923C2direct (N × H)
13. C2×#4665C2semidirect
14. C2×#4668C2semidirect
15. C2×#4664C2semidirect
16. C2×#4660C2semidirect
35. C2×#938C22semidirect
46. C2×#884C22semidirect
47. C3×#386C22semidirect
50. #5223C22semidirect
51. #5213C22semidirect
52. #5213C22semidirect
61. #4960C22semidirect
62. #4959C22semidirect
63. #4956C22semidirect
64. #4952C22semidirect
65. #4952C22semidirect
66. #4668C22semidirect
67. #4665C22semidirect
68. #4664C22semidirect
69. #4660C22semidirect
83. C2×#386D3semidirect
114. C22×#67D4semidirect
220. #386C2×D3semidirect
309. C2×#67C2×D4semidirect
879. C2×C3#2688semidirect
946. C3C2×#2688semidirect
951. C2#74923direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#9382
C22×#8842
C2×C3×#3862
C2×#52232
C2×#52132
C2×#49592
C2×#49602
C2×#49562
C2×#49522
#749232
C2×#46652
C2×#46682
C2×#46642
C2×#46602
C2×#26883