Finite Group Databasebeta

← C2×#78113 #11429780

Subgroups — C2×#78113 #11429780

Order 768.

4042 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#894C211yesmaximal, characteristic, complemented
2C22×#895C211yesmaximal, characteristic, complemented
3C22×#884C211yesmaximal, characteristic, complemented
4C22×#884C211yesmaximal, characteristic, complemented
5C2×C3×#399C211yesmaximal, characteristic, complemented
6C2×#4991C211yesmaximal, characteristic, complemented
7C2×#4989C211yesmaximal, characteristic, complemented
8C2×#4987C211yesmaximal, characteristic, complemented
9C2×#4983C211yesmaximal, characteristic, complemented
10C2×#4959C211yesmaximal, characteristic, complemented
11C2×#4960C211yesmaximal, characteristic, complemented
12C2×#4956C211yesmaximal, characteristic, complemented
13C2×#4961C211yesmaximal, characteristic, complemented
14#78113C2116yesmaximal, direct product factor
15C2×#4665C211yesmaximal, characteristic, complemented
16C2×#4668C211yesmaximal, characteristic, complemented
17C2×#2671—31nomaximal, Sylow
18C23×#67C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×D12C2211yescharacteristic
22C23×D12C2211yescharacteristic
23C23×D12C2211yescharacteristic
24C23×C4×D3C2211yescharacteristic
25C23×C4×D3C2211yescharacteristic
26C23×C4×D3C2211yescharacteristic
27C22×C3×C4⋊C4C2211yescharacteristic
28C22×C3×C4⋊C4C2211yescharacteristic
29C22×C3×C4⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×C3×C22⋊C4C2211yescharacteristic
32C22×C3×C22⋊C4C2211yescharacteristic
33C22×#217C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
44C22×Dic3⋊C4C2211yescharacteristic
45C22×Dic3⋊C4C2211yescharacteristic
46C22×Dic3⋊C4C2211yescharacteristic
47C2×#895—28no—
48C2×#895C2218yescomplemented
49C2×#894—28no—
50C2×#894C2218yescomplemented
51C2×#884—28no—
52C2×#884—28no—
53C2×#884C2218yescomplemented
54C2×#884C2218yescomplemented
55C3×#399C2218yescomplemented
56C2×C3×#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61C2×C3⋊#95C2211yescharacteristic
62#4991C2218yescomplemented
63#4989C2218yescomplemented
64#4987C2218yescomplemented
65#4983C2218yescomplemented
66#4961C2218yescomplemented
67#4960C2218yescomplemented
68#4959C2218yescomplemented
69#4956C2218yescomplemented
70#4668C2218yescomplemented
71#4665C2218yescomplemented
72C22×#123—31no—
73C22×#121—31no—
74C22×#121—31no—
75C22×#121—31no—
76#2671—316no—
77C2×#399D311yescharacteristic, complemented
78C2×#398—31no—
79C2×#394—31no—
80C2×#394—31no—
81C2×#394—31no—
82C2×#392—31no—
83C2×#386—31no—
84C2×#386—31no—
85C2×#385—31no—
86C2×#385—31no—
87C2×#380—31no—
88C25×C3C2311yescharacteristic
89C24×D3C2311yescharacteristic
90C24×D3C2311yescharacteristic
91C24×D3C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
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—24no—
102C22×#67—24no—
103C22×#67—42no—
104C22×#67—42no—
105C22×#67—42no—
106C22×#67—42no—
107C22×#67C2314yes—
108C22×#67C2314yes—
109C22×#67C2314yes—
110C23×Dic3C2311yescharacteristic
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C23×Dic3C2311yescharacteristic
114C23×Dic3C2311yescharacteristic
115C22×D12—24no—
116C22×D12—24no—
117C22×D12—24no—
118C22×D12—24no—
119C22×D12—42no—
120C22×D12—42no—
121C22×D12—42no—
122C22×D12—42no—
123C22×D12D418yescomplemented
124C22×D12C2314yes—
125C22×D12C2314yes—
126C22×D12C2314yes—
127C22×C4×D3—24no—
128C22×C4×D3—24no—
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×D3—42no—
136C22×C4×D3C2314yes—
137C22×C4×D3C2314yes—
138C22×C4×D3C2314yes—
139C2×C3×C4⋊C4—24no—
140C2×C3×C4⋊C4—24no—
141C2×C3×C4⋊C4—42no—
142C2×C3×C4⋊C4C2314yes—
143C2×C3×C4⋊C4C2314yes—
144C2×C3×C4⋊C4C2314yes—
145C2×C3×C22⋊C4—24no—
146C2×C3×C22⋊C4—24no—
147C2×C3×C22⋊C4—42no—
148C2×C3×C22⋊C4C2314yes—
149C2×C3×C22⋊C4C2314yes—
150C2×C3×C22⋊C4C2314yes—
151C2×#217—42no—
152C2×#217C2314yes—
153C2×(C2×D3)⋊C4—24no—
154C2×(C2×D3)⋊C4—24no—
155C2×(C2×D3)⋊C4—24no—
156C2×(C2×D3)⋊C4—24no—
157C2×(C2×D3)⋊C4—24no—
158C2×(C2×D3)⋊C4—24no—
159C2×(C2×D3)⋊C4—42no—
160C2×(C2×D3)⋊C4—42no—
161C2×(C2×D3)⋊C4D418yescomplemented
162C2×(C2×D3)⋊C4C2314yes—
163C2×(C2×D3)⋊C4C2314yes—
164C2×(C2×D3)⋊C4C2314yes—
165C2×(C2×D3)⋊C4C2314yes—
166C2×(C2×D3)⋊C4C2314yes—
167C2×(C2×D3)⋊C4C2314yes—
168C2×(C2×D3)⋊C4C2314yes—
169C2×(C2×D3)⋊C4C2314yes—
170C2×(C2×D3)⋊C4C2314yes—
171C2×C4⋊Dic3—42no—
172C2×C4⋊Dic3C2314yes—
173C2×Dic3⋊C4—24no—
174C2×Dic3⋊C4—24no—
175C2×Dic3⋊C4—24no—
176C2×Dic3⋊C4C2314yes—
177C2×Dic3⋊C4C2314yes—
178C2×Dic3⋊C4C2314yes—
179#895—232no—
180#894—232no—
181#884—232no—
182#884—232no—
183C3×#95C2314yes—
184C3⋊#95C2314yes—
185C3⋊#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C23×D4—31no—
190C23×D4—31no—
191C23×D4—31no—
192C23×D4—31no—
193C23×D4—31no—
194C23×D4—31no—
195C24×C4—31no—
196C24×C4—31no—
197C24×C4—31no—
198C2×#123—38no—
199C2×#123—68no—
200C2×#121—38no—
201C2×#121—38no—
202C2×#121—38no—
203C2×#121—68no—
204C2×#121—68no—
205C2×#121—68no—
206C22×C4⋊C4—31no—
207C22×C4⋊C4—31no—
208C22×C4⋊C4—31no—
209C22×C4⋊C4—31no—
210C22×C4⋊C4C2×D311yescharacteristic
211C22×C4⋊C4C2×D311yescharacteristic
212C22×C4⋊C4C2×D311yescharacteristic
213C22×C22⋊C4—31no—
214C22×C22⋊C4—31no—
215C22×C22⋊C4—31no—
216C22×C22⋊C4—31no—
217C22×C22⋊C4—31no—
218C22×C22⋊C4—31no—
219C22×C22⋊C4—31no—
220C22×C22⋊C4—31no—
221C22×C22⋊C4—31no—
222C22×C22⋊C4—31no—
223C22×C22⋊C4C2×D311yescharacteristic
224C22×C22⋊C4C2×D311yescharacteristic
225C22×C22⋊C4C2×D311yescharacteristic
226#399C2×D318yescomplemented
227#398—38no—
228#394—38no—
229#394—38no—
230#394—38no—
231#392—38no—
232#386—38no—
233#386—38no—
234#385—38no—
235#385—38no—
236#380—38no—
237C2×#95—31no—
238C2×#95—31no—
239C2×#95—31no—
240C2×#95—31no—
241C2×#95—31no—
242C2×#95C2×D311yescharacteristic
243C24×C3—22no—
244C24×C3—22no—
245C24×C3—22no—
246C24×C3—22no—
247C24×C3—22no—
248C24×C3—22no—
249C24×C3—22no—
250C24×C3C2412yes—
251C24×C3C2411yescharacteristic
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×D3—22no—
264C23×D3—22no—
265C23×D3—22no—
266C23×D3—22no—
267C23×D3—22no—
268C23×D3—22no—
269C23×D3—22no—
270C23×D3C2×D414yes—
271C23×D3C2×D414yes—
272C23×D3C2×D414yes—
273C23×D3C2412yes—
274C23×D3C2412yes—
275C23×D3C2412yes—
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—22no—
285C22×C3×C4—22no—
286C22×C3×C4—22no—
287C22×C3×C4—22no—
288C22×C3×C4—22no—
289C22×C3×C4—22no—
290C22×C3×C4—22no—
291C22×C3×C4—22no—
292C22×C3×C4C2×D414yes—
293C22×C3×C4C2×D414yes—
294C22×C3×C4C2412yes—
295C22×C3×C4C2412yes—
296C22×C3×C4C2412yes—
297C22×C3×C4C2412yes—
298C22×C3×C4C2412yes—
299C22×C3×C4C2412yes—
300C2×#67—28no—
301C2×#67—28no—
302C2×#67—28no—
303C2×#67—28no—
304C2×#67—28no—
305C2×#67—44no—
306C2×#67—44no—
307C2×#67—44no—
308C2×#67—44no—
309C2×#67—416no—
310C2×#67—416no—
311C2×#67—416no—
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×Dic3C2×D414yes—
326C22×Dic3#4114yes—
327C22×Dic3C2412yes—
328C22×Dic3C2412yes—
329C22×Dic3C2412yes—
330C22×Dic3C2412yes—
331C22×Dic3C2412yes—
332C2×D12—28no—
333C2×D12—28no—
334C2×D12—28no—
335C2×D12—28no—
336C2×D12—416no—
337C2×D12—44no—
338C2×D12—44no—
339C2×D12—44no—
340C2×D12—44no—
341C2×D12—416no—
342C2×D12—416no—
343C2×D12C2×D4116yescomplemented
344C2×C4×D3—28no—
345C2×C4×D3—28no—
346C2×C4×D3—28no—
347C2×C4×D3—28no—
348C2×C4×D3—28no—
349C2×C4×D3—44no—
350C2×C4×D3—44no—
351C2×C4×D3—44no—
352C2×C4×D3—44no—
353C2×C4×D3—416no—
354C2×C4×D3—416no—
355C2×C4×D3—416no—
356C3×C4⋊C4—28no—
357C3×C4⋊C4—28no—
358C3×C4⋊C4—44no—
359C3×C22⋊C4—28no—
360C3×C22⋊C4—28no—
361C3×C22⋊C4—44no—
362#217—44no—
363(C2×D3)⋊C4—28no—
364(C2×D3)⋊C4—28no—
365(C2×D3)⋊C4—28no—
366(C2×D3)⋊C4—28no—
367(C2×D3)⋊C4—28no—
368(C2×D3)⋊C4—28no—
369(C2×D3)⋊C4—44no—
370(C2×D3)⋊C4—44no—
371(C2×D3)⋊C4C2×D4116yescomplemented
372C4⋊Dic3—44no—
373Dic3⋊C4—28no—
374Dic3⋊C4—28no—
375Dic3⋊C4—28no—
376C25—31no—
377C25—31no—
378C25—31no—
379C25C22×D311yescharacteristic
380C22×D4—34no—
381C22×D4—34no—
382C22×D4—34no—
383C22×D4—38no—
384C22×D4—34no—
385C22×D4—34no—
386C22×D4—34no—
387C22×D4—64no—
388C22×D4—64no—
389C22×D4—64no—
390C22×D4—64no—
391C22×D4—64no—
392C22×D4—64no—
393C22×D4—64no—
394C22×D4—64no—
395C22×D4—64no—
396C22×D4—122no—
397C22×D4—122no—
398C22×D4—122no—
399C22×D4—122no—
400C22×D4—122no—
401C22×D4—122no—
402C22×D4—122no—
403C22×D4—122no—
404C23×C4—31no—
405C23×C4—31no—
406C23×C4—31no—
407C23×C4—31no—
408C23×C4—31no—
409C23×C4—34no—
410C23×C4—34no—
411C23×C4—34no—
412C23×C4—64no—
413C23×C4—64no—
414C23×C4—64no—
415C23×C4—64no—
416C23×C4—64no—
417C23×C4—122no—
418C23×C4—122no—
419C23×C4—122no—
420C23×C4—122no—
421C23×C4C22×D311yescharacteristic
422C23×C4C22×D311yescharacteristic
423C23×C4C22×D311yescharacteristic
424C23×C4C22×D311yescharacteristic
425C23×C4C22×D311yescharacteristic
426C23×C4C22×D311yescharacteristic
427#123—632no—
428#121—632no—
429#121—632no—
430#121—632no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—34no—
434C2×C4⋊C4—34no—
435C2×C4⋊C4—34no—
436C2×C4⋊C4—34no—
437C2×C4⋊C4—42no—
438C2×C4⋊C4—64no—
439C2×C4⋊C4—64no—
440C2×C4⋊C4—64no—
441C2×C4⋊C4—122no—
442C2×C4⋊C4C22×D314yes—
443C2×C4⋊C4C22×D314yes—
444C2×C4⋊C4C22×D314yes—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—38no—
448C2×C22⋊C4—34no—
449C2×C22⋊C4—34no—
450C2×C22⋊C4—34no—
451C2×C22⋊C4—34no—
452C2×C22⋊C4—34no—
453C2×C22⋊C4—34no—
454C2×C22⋊C4—34no—
455C2×C22⋊C4—34no—
456C2×C22⋊C4—34no—
457C2×C22⋊C4—34no—
458C2×C22⋊C4—42no—
459C2×C22⋊C4—64no—
460C2×C22⋊C4—64no—
461C2×C22⋊C4—64no—
462C2×C22⋊C4—64no—
463C2×C22⋊C4—64no—
464C2×C22⋊C4—64no—
465C2×C22⋊C4—122no—
466C2×C22⋊C4—122no—
467C2×C22⋊C4—122no—
468C2×C22⋊C4C22×D314yes—
469C2×C22⋊C4C22×D314yes—
470C2×C22⋊C4C22×D314yes—
471#95—34no—
472#95—34no—
473#95—34no—
474#95—34no—
475#95—34no—
476#95C22×D314yes—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—44no—
485C23×C3—44no—
486C23×C3—44no—
487C23×C3—44no—
488C23×C3—44no—
489C23×C3—44no—
490C23×C3—44no—
491C23×C3C22×D412yes—
492C23×C3C22×D412yes—
493C23×C3C2×#4112yes—
494C23×C3H(5,𝔽2)12yes—
495C23×C3H(5,𝔽2)12yes—
496C23×C3H(5,𝔽2)12yes—
497C23×C32−1+412yes—
498C23×C3C2511yescharacteristic
499C22×D3—28no—
500C22×D3—28no—
501C22×D3—28no—
502C22×D3—28no—
503C22×D3—28no—
504C22×D3—28no—
505C22×D3—28no—
506C22×D3—28no—
507C22×D3—28no—
508C22×D3—22no—
509C22×D3—22no—
510C22×D3—22no—
511C22×D3—22no—
512C22×D3—22no—
513C22×D3—22no—
514C22×D3—22no—
515C22×D3—22no—
516C22×D3—22no—
517C22×D3—22no—
518C22×D3—22no—
519C22×D3—22no—
520C22×D3—22no—
521C22×D3—22no—
522C22×D3—22no—
523C22×D3—22no—
524C22×D3—22no—
525C22×D3—22no—
526C22×D3—44no—
527C22×D3—44no—
528C22×D3—44no—
529C22×D3—44no—
530C22×D3—44no—
531C22×D3—44no—
532C22×D3—44no—
533C22×D3—44no—
534C22×D3—44no—
535C22×D3—44no—
536C22×D3—44no—
537C22×D3—44no—
538C22×D3C22×D414yes—
539C22×D3C22×D414yes—
540C22×D3C22×D414yes—
541C2×C3×C4—28no—
542C2×C3×C4—28no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—44no—
560C2×C3×C4—44no—
561C2×C3×C4—44no—
562C2×C3×C4—44no—
563C2×C3×C4C22×D414yes—
564C2×C3×C4C22×D414yes—
565#67—416no—
566#67—416no—
567#67—416no—
568C2×Dic3—28no—
569C2×Dic3—28no—
570C2×Dic3—22no—
571C2×Dic3—22no—
572C2×Dic3—22no—
573C2×Dic3—22no—
574C2×Dic3—22no—
575C2×Dic3—22no—
576C2×Dic3—22no—
577C2×Dic3—22no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—44no—
584C2×Dic3—44no—
585C2×Dic3—44no—
586C2×Dic3C22×D414yes—
587C2×Dic3C2×#4114yes—
588D12—416no—
589D12—416no—
590D12—416no—
591C4×D3—416no—
592C4×D3—416no—
593C4×D3—416no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—34no—
602C24—34no—
603C24—34no—
604C24—32no—
605C24—32no—
606C24—32no—
607C24—62no—
608C24—62no—
609C24—62no—
610C24—62no—
611C24—62no—
612C24—62no—
613C24—62no—
614C24—62no—
615C24—62no—
616C24—62no—
617C24—62no—
618C24—62no—
619C24—62no—
620C24—62no—
621C24—62no—
622C24—62no—
623C24—62no—
624C24—62no—
625C24C23×D312yes—
626C24C23×D311yescharacteristic
627C2×D4—316no—
628C2×D4—68no—
629C2×D4—68no—
630C2×D4—68no—
631C2×D4—68no—
632C2×D4—68no—
633C2×D4—68no—
634C2×D4—68no—
635C2×D4—68no—
636C2×D4—68no—
637C2×D4—1216no—
638C2×D4—124no—
639C2×D4—124no—
640C2×D4—124no—
641C2×D4—124no—
642C2×D4—1216no—
643C2×D4—1216no—
644C2×D4—124no—
645C2×D4—124no—
646C2×D4—124no—
647C2×D4—124no—
648C2×D4—1216no—
649C2×D4—1216no—
650C2×D4—1216no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—34no—
668C22×C4—34no—
669C22×C4—32no—
670C22×C4—32no—
671C22×C4—32no—
672C22×C4—32no—
673C22×C4—32no—
674C22×C4—68no—
675C22×C4—68no—
676C22×C4—68no—
677C22×C4—62no—
678C22×C4—62no—
679C22×C4—62no—
680C22×C4—62no—
681C22×C4—62no—
682C22×C4—62no—
683C22×C4—62no—
684C22×C4—62no—
685C22×C4—62no—
686C22×C4—62no—
687C22×C4—62no—
688C22×C4—62no—
689C22×C4—62no—
690C22×C4—68no—
691C22×C4—68no—
692C22×C4—124no—
693C22×C4—124no—
694C22×C4—124no—
695C22×C4—124no—
696C22×C4—1216no—
697C22×C4—1216no—
698C22×C4—1216no—
699C22×C4D3×D414yes—
700C22×C4D3×D414yes—
701C22×C4C23×D312yes—
702C22×C4C23×D312yes—
703C22×C4C23×D312yes—
704C22×C4C23×D312yes—
705C22×C4C23×D312yes—
706C22×C4C23×D312yes—
707C4⋊C4—28no—
708C4⋊C4—28no—
709C4⋊C4—44no—
710C4⋊C4—68no—
711C4⋊C4—68no—
712C4⋊C4—68no—
713C4⋊C4—124no—
714C22⋊C4—28no—
715C22⋊C4—28no—
716C22⋊C4—316no—
717C22⋊C4—44no—
718C22⋊C4—68no—
719C22⋊C4—68no—
720C22⋊C4—68no—
721C22⋊C4—68no—
722C22⋊C4—68no—
723C22⋊C4—68no—
724C22⋊C4—124no—
725C22⋊C4—124no—
726C22⋊C4—124no—
727C22×C3—42no—
728C22×C3—42no—
729C22×C3—42no—
730C22×C3—42no—
731C22×C3—42no—
732C22×C3—42no—
733C22×C3—42no—
734C22×C3—88no—
735C22×C3#53414yes—
736C22×C3#53714yes—
737C22×C3#54014yes—
738C22×C3D4214yes—
739C22×C3#54614yes—
740C22×C3#54714yes—
741C22×C3#56214yes—
742C22×C3C23×D411yescharacteristic
743C22×C3C23×D411yescharacteristic
744C22×C3C22×#4111yescharacteristic
745C22×C3C2×H(5,𝔽2)11yescharacteristic
746C22×C3C2×H(5,𝔽2)11yescharacteristic
747C22×C3C2×H(5,𝔽2)11yescharacteristic
748C22×C3C2×2−1+411yescharacteristic
749C2×D3—24no—
750C2×D3—24no—
751C2×D3—24no—
752C2×D3—24no—
753C2×D3—24no—
754C2×D3—24no—
755C2×D3—24no—
756C2×D3—24no—
757C2×D3—24no—
758C2×D3—416no—
759C2×D3—416no—
760C2×D3—416no—
761C2×D3—42no—
762C2×D3—42no—
763C2×D3—42no—
764C2×D3—42no—
765C2×D3—42no—
766C2×D3—42no—
767C2×D3—42no—
768C2×D3—42no—
769C2×D3—42no—
770C2×D3—42no—
771C2×D3—42no—
772C2×D3—42no—
773C3×C4—24no—
774C3×C4—24no—
775C3×C4—42no—
776C3×C4—42no—
777C3×C4—42no—
778C3×C4—42no—
779Dic3—24no—
780Dic3—24no—
781Dic3—42no—
782Dic3—42no—
783Dic3—42no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—34no—
792C23—34no—
793C23—34no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—44no—
798C23—44no—
799C23—44no—
800C23—44no—
801C23—68no—
802C23—68no—
803C23—68no—
804C23—62no—
805C23—62no—
806C23—62no—
807C23—62no—
808C23—62no—
809C23—62no—
810C23—62no—
811C23—62no—
812C23—62no—
813C23—62no—
814C23—62no—
815C23—62no—
816C23—62no—
817C23—62no—
818C23—62no—
819C23—62no—
820C23—62no—
821C23—62no—
822C23—68no—
823C23—68no—
824C23—68no—
825C23—68no—
826C23—68no—
827C23—68no—
828C23—124no—
829C23—124no—
830C23—124no—
831C23—124no—
832C23—124no—
833C23—124no—
834C23—124no—
835C23—124no—
836C23—124no—
837C23—124no—
838C23—124no—
839C23—124no—
840C23C2×D3×D412yes—
841C23C2×D3×D412yes—
842C23#100412yes—
843C23#100712yes—
844C23D3×#4112yes—
845C23#100912yes—
846C23#100912yes—
847C23C24×D311yescharacteristic
848D4—1216no—
849D4—1216no—
850D4—1216no—
851D4—1216no—
852D4—1216no—
853D4—1216no—
854C2×C4—28no—
855C2×C4—28no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—34no—
873C2×C4—34no—
874C2×C4—44no—
875C2×C4—44no—
876C2×C4—44no—
877C2×C4—44no—
878C2×C4—68no—
879C2×C4—62no—
880C2×C4—62no—
881C2×C4—62no—
882C2×C4—62no—
883C2×C4—68no—
884C2×C4—62no—
885C2×C4—62no—
886C2×C4—62no—
887C2×C4—62no—
888C2×C4—62no—
889C2×C4—62no—
890C2×C4—62no—
891C2×C4—62no—
892C2×C4—62no—
893C2×C4—1216no—
894C2×C4—1216no—
895C2×C4—1216no—
896C2×C4—124no—
897C2×C4—124no—
898C2×C4—124no—
899C2×C4C2×D3×D414yes—
900C2×C4C2×D3×D414yes—
901C2×C3—82no—
902C2×C3#267118yescomplemented
903C2×C3C2×#53411yescharacteristic
904C2×C3C2×#53711yescharacteristic
905C2×C3C2×#54011yescharacteristic
906C2×C3C2×D4211yescharacteristic
907C2×C3C2×#54611yescharacteristic
908C2×C3C2×#54711yescharacteristic
909C2×C3C2×#56211yescharacteristic
910D3—44no—
911D3—44no—
912D3—44no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—64no—
921C22—64no—
922C22—64no—
923C22—64no—
924C22—64no—
925C22—64no—
926C22—64no—
927C22—64no—
928C22—64no—
929C22—88no—
930C22—1216no—
931C22—1216no—
932C22—1216no—
933C22—122no—
934C22—122no—
935C22—122no—
936C22—122no—
937C22—122no—
938C22—122no—
939C22—122no—
940C22—122no—
941C22—122no—
942C22—122no—
943C22—122no—
944C22—122no—
945C22#562914yes—
946C22#563114yes—
947C22#564714yes—
948C22#565314yes—
949C22#565414yes—
950C22#566314yes—
951C22#571714yes—
952C22C22×D3×D411yescharacteristic
953C22C22×D3×D411yescharacteristic
954C22C2×#100411yescharacteristic
955C22C2×#100711yescharacteristic
956C22C2×D3×#4111yescharacteristic
957C22C2×#100911yescharacteristic
958C22C2×#100911yescharacteristic
959C4—24no—
960C4—24no—
961C4—42no—
962C4—42no—
963C4—42no—
964C4—42no—
965C4—64no—
966C4—64no—
967C4—122no—
968C4—122no—
969C4—122no—
970C3C2×#267111yescharacteristic, complemented, Sylow
971C2—82no—
972C2—124no—
973C2—124no—
974C2—124no—
975C2#7811318yesdirect product factor
976C2C2×#562911yescharacteristic
977C2C2×#563111yescharacteristic
978C2C2×#564711yescharacteristic
979C2C2×#566311yescharacteristic
980C2C2×#565311yescharacteristic
981C2C2×#565411yescharacteristic
982C2C2×#571711yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#399C2
socleC24×C3C24
hypercenterC2×#399D3
hypocenterC3C2×#2671
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C22×#894C2semidirect
2. C22×#895C2semidirect
3. C22×#884C2semidirect
4. C22×#884C2semidirect
5. C2×C3×#399C2semidirect
6. C2×#4991C2semidirect
7. C2×#4989C2semidirect
8. C2×#4987C2semidirect
9. C2×#4983C2semidirect
10. C2×#4959C2semidirect
11. C2×#4960C2semidirect
12. C2×#4956C2semidirect
13. C2×#4961C2semidirect
14. #78113C2direct (N × H)
15. C2×#4665C2semidirect
16. C2×#4668C2semidirect
48. C2×#895C22semidirect
50. C2×#894C22semidirect
53. C2×#884C22semidirect
54. C2×#884C22semidirect
55. C3×#399C22semidirect
62. #4991C22semidirect
63. #4989C22semidirect
64. #4987C22semidirect
65. #4983C22semidirect
66. #4961C22semidirect
67. #4960C22semidirect
68. #4959C22semidirect
69. #4956C22semidirect
70. #4668C22semidirect
71. #4665C22semidirect
77. C2×#399D3semidirect
123. C22×D12D4semidirect
161. C2×(C2×D3)⋊C4D4semidirect
226. #399C2×D3semidirect
343. C2×D12C2×D4semidirect
371. (C2×D3)⋊C4C2×D4semidirect
902. C2×C3#2671semidirect
970. C3C2×#2671semidirect
975. C2#78113direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#8942
C22×#8952
C22×#8842
C2×C3×#3992
C2×#49912
C2×#49892
C2×#49872
C2×#49832
C2×#49592
C2×#49602
C2×#49562
C2×#49612
#781132
C2×#46652
C2×#46682
C2×#26713