Finite Group Databasebeta

← C2×#77007 #11429937

Subgroups — C2×#77007 #11429937

Order 768.

3934 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#939C211yesmaximal, characteristic, complemented
2C22×#883C211yesmaximal, characteristic, complemented
3C22×#884C211yesmaximal, characteristic, complemented
4C22×#886C211yesmaximal, characteristic, complemented
5C2×C3×#394C211yesmaximal, characteristic, complemented
6C2×#5223C211yesmaximal, characteristic, complemented
7C2×#4991C211yesmaximal, characteristic, complemented
8C2×#4972C211yesmaximal, characteristic, complemented
9C2×#4960C211yesmaximal, characteristic, complemented
10C2×#4948C211yesmaximal, characteristic, complemented
11C2×#4957C211yesmaximal, characteristic, complemented
12C2×#4957C211yesmaximal, characteristic, complemented
13C2×#4946C211yesmaximal, characteristic, complemented
14#77007C2116yesmaximal, direct product factor
15C2×#4676C211yesmaximal, characteristic, complemented
16C2×#4668C211yesmaximal, characteristic, complemented
17C2×#2682—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×#67C2211yescharacteristic
22C23×#67C2211yescharacteristic
23C24×Dic3C2211yescharacteristic
24C23×D12C2211yescharacteristic
25C23×C4×D3C2211yescharacteristic
26C22×C3×C4⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C22×#217C2211yescharacteristic
34C2×#939—28no—
35C2×#939C2218yescomplemented
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×C4⋊Dic3C2211yescharacteristic
45C22×Dic3⋊C4C2211yescharacteristic
46C22×Dic3⋊C4C2211yescharacteristic
47C22×Dic3⋊C4C2211yescharacteristic
48C22×Dic3⋊C4C2211yescharacteristic
49C22×Dic3⋊C4C2211yescharacteristic
50C22×C4×Dic3C2211yescharacteristic
51C2×#886—28no—
52C2×#886C2218yescomplemented
53C2×#884—28no—
54C2×#884C2218yescomplemented
55C2×#883—28no—
56C2×#883C2218yescomplemented
57C3×#394C2218yescomplemented
58C2×C3×#95C2211yescharacteristic
59#5223C2218yescomplemented
60C2×C3⋊#95C2211yescharacteristic
61C2×C3⋊#95C2211yescharacteristic
62C2×C3⋊#95C2211yescharacteristic
63#4991C2218yescomplemented
64#4972C2218yescomplemented
65#4960C2218yescomplemented
66#4957C2218yescomplemented
67#4957C2218yescomplemented
68#4948C2218yescomplemented
69#4946C2218yescomplemented
70#4676C2218yescomplemented
71#4668C2218yescomplemented
72C22×#123—31no—
73C22×#123—31no—
74C22×#121—31no—
75C22×#121—31no—
76#2682—316no—
77C2×#396—31no—
78C2×#396—31no—
79C2×#394—31no—
80C2×#394D311yescharacteristic, complemented
81C2×#392—31no—
82C2×#392—31no—
83C2×#390—31no—
84C2×#390—31no—
85C2×#389—31no—
86C2×#385—31no—
87C2×#385—31no—
88C25×C3C2311yescharacteristic
89C25×C3C2311yescharacteristic
90C24×D3C2311yescharacteristic
91C24×D3C2311yescharacteristic
92C22×C3×D4—24no—
93C22×C3×D4—42no—
94C22×C3×D4—42no—
95C22×C3×D4C2314yes—
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C22×#67—24no—
102C22×#67—24no—
103C22×#67—24no—
104C22×#67—24no—
105C22×#67—24no—
106C22×#67—42no—
107C22×#67—42no—
108C22×#67—42no—
109C22×#67—42no—
110C22×#67—42no—
111C22×#67—42no—
112C22×#67D418yescomplemented
113C22×#67C2314yes—
114C22×#67C2314yes—
115C22×#67C2314yes—
116C22×#67C2314yes—
117C23×Dic3—24no—
118C23×Dic3—24no—
119C23×Dic3—42no—
120C23×Dic3C2311yescharacteristic
121C23×Dic3C2311yescharacteristic
122C23×Dic3C2314yes—
123C23×Dic3C2311yescharacteristic
124C23×Dic3C2311yescharacteristic
125C23×Dic3C2311yescharacteristic
126C23×Dic3C2311yescharacteristic
127C22×D12—24no—
128C22×D12—42no—
129C22×D12—42no—
130C22×D12C2314yes—
131C22×C4×D3—24no—
132C22×C4×D3—24no—
133C22×C4×D3—42no—
134C22×C4×D3C2314yes—
135C2×C3×C4⋊C4—42no—
136C2×C3×C4⋊C4C2314yes—
137C2×C3×C22⋊C4—24no—
138C2×C3×C22⋊C4—24no—
139C2×C3×C22⋊C4—24no—
140C2×C3×C22⋊C4—42no—
141C2×C3×C22⋊C4C2314yes—
142C2×C3×C22⋊C4C2314yes—
143C2×C3×C22⋊C4C2314yes—
144C2×C3×C22⋊C4C2314yes—
145C2×#217—24no—
146C2×#217—24no—
147C2×#217—24no—
148C2×#217C2314yes—
149C2×#217C2314yes—
150C2×#217C2314yes—
151#939—232no—
152C2×(C2×D3)⋊C4—24no—
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—42no—
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×(C2×D3)⋊C4C2314yes—
166C2×C4⋊Dic3—24no—
167C2×C4⋊Dic3D418yescomplemented
168C2×C4⋊Dic3C2314yes—
169C2×C4⋊Dic3C2314yes—
170C2×Dic3⋊C4—24no—
171C2×Dic3⋊C4—24no—
172C2×Dic3⋊C4—24no—
173C2×Dic3⋊C4—42no—
174C2×Dic3⋊C4—42no—
175C2×Dic3⋊C4C2314yes—
176C2×Dic3⋊C4C2314yes—
177C2×Dic3⋊C4C2314yes—
178C2×Dic3⋊C4C2314yes—
179C2×Dic3⋊C4C2314yes—
180C2×C4×Dic3—42no—
181C2×C4×Dic3C2314yes—
182#886—232no—
183#884—232no—
184#883—232no—
185C3×#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C23×D4—31no—
190C23×D4—31no—
191C23×D4—31no—
192C23×D4—31no—
193C23×D4—31no—
194C23×D4C2×D311yescharacteristic
195C24×C4—31no—
196C24×C4—31no—
197C2×#123—38no—
198C2×#123—38no—
199C2×#123—68no—
200C2×#123—68no—
201C2×#121—38no—
202C2×#121—38no—
203C2×#121—68no—
204C2×#121—68no—
205C22×C4⋊C4—31no—
206C22×C4⋊C4—31no—
207C22×C4⋊C4—31no—
208C22×C4⋊C4—31no—
209C22×C4⋊C4—31no—
210C22×C4⋊C4—31no—
211C22×C4⋊C4—31no—
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
226C22×C22⋊C4C2×D311yescharacteristic
227C22×C42—31no—
228#396—38no—
229#396—38no—
230#394—38no—
231#394C2×D318yescomplemented
232#392—38no—
233#392—38no—
234#390—38no—
235#390—38no—
236#389—38no—
237#385—38no—
238#385—38no—
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×C3—22no—
251C24×C3—22no—
252C24×C3—22no—
253C24×C3—22no—
254C24×C3—22no—
255C24×C3—22no—
256C24×C3C2×D414yes—
257C24×C3C2412yes—
258C24×C3C2412yes—
259C24×C3C2411yescharacteristic
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×D3—22no—
271C23×D3—22no—
272C23×D3—22no—
273C23×D3C2×D414yes—
274C23×D3C2412yes—
275C23×D3C2412yes—
276C2×C3×D4—28no—
277C2×C3×D4—44no—
278C2×C3×D4—44no—
279C2×C3×D4—416no—
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×C4—22no—
293C22×C3×C4—22no—
294C22×C3×C4C2×D414yes—
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—416no—
306C2×#67—44no—
307C2×#67—44no—
308C2×#67—44no—
309C2×#67—44no—
310C2×#67—44no—
311C2×#67—44no—
312C2×#67—416no—
313C2×#67—416no—
314C2×#67—416no—
315C2×#67C2×D4116yescomplemented
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×Dic3—28no—
328C22×Dic3—22no—
329C22×Dic3—22no—
330C22×Dic3—22no—
331C22×Dic3—28no—
332C22×Dic3—44no—
333C22×Dic3—416no—
334C22×Dic3C2×D414yes—
335C22×Dic3C2×D414yes—
336C22×Dic3C2×D414yes—
337C22×Dic3#4114yes—
338C22×Dic3C2412yes—
339C22×Dic3C2412yes—
340C22×Dic3C2412yes—
341C22×Dic3C2412yes—
342C22×Dic3C2412yes—
343C22×Dic3C2412yes—
344C2×D12—28no—
345C2×D12—44no—
346C2×D12—44no—
347C2×D12—416no—
348C2×C4×D3—28no—
349C2×C4×D3—28no—
350C2×C4×D3—44no—
351C2×C4×D3—416no—
352C3×C4⋊C4—44no—
353C3×C22⋊C4—28no—
354C3×C22⋊C4—28no—
355C3×C22⋊C4—28no—
356C3×C22⋊C4—44no—
357#217—28no—
358#217—28no—
359#217—28no—
360(C2×D3)⋊C4—28no—
361(C2×D3)⋊C4—28no—
362(C2×D3)⋊C4—28no—
363(C2×D3)⋊C4—28no—
364(C2×D3)⋊C4—28no—
365(C2×D3)⋊C4—28no—
366(C2×D3)⋊C4—44no—
367C4⋊Dic3—28no—
368C4⋊Dic3C2×D4116yescomplemented
369Dic3⋊C4—28no—
370Dic3⋊C4—28no—
371Dic3⋊C4—28no—
372Dic3⋊C4—44no—
373Dic3⋊C4—44no—
374C4×Dic3—44no—
375C25—31no—
376C25—31no—
377C25C22×D311yescharacteristic
378C25C22×D311yescharacteristic
379C22×D4—24no—
380C22×D4—38no—
381C22×D4—34no—
382C22×D4—34no—
383C22×D4—34no—
384C22×D4—34no—
385C22×D4—34no—
386C22×D4—42no—
387C22×D4—42no—
388C22×D4—64no—
389C22×D4—64no—
390C22×D4—64no—
391C22×D4—64no—
392C22×D4—64no—
393C22×D4—64no—
394C22×D4—122no—
395C22×D4—122no—
396C22×D4—122no—
397C22×D4—122no—
398C22×D4—122no—
399C22×D4—122no—
400C22×D4—122no—
401C22×D4—122no—
402C22×D4C22×D314yes—
403C23×C4—31no—
404C23×C4—31no—
405C23×C4—31no—
406C23×C4—31no—
407C23×C4—31no—
408C23×C4—31no—
409C23×C4—34no—
410C23×C4—34no—
411C23×C4—64no—
412C23×C4—64no—
413C23×C4—64no—
414C23×C4—64no—
415C23×C4—122no—
416C23×C4—122no—
417C23×C4C22×D311yescharacteristic
418C23×C4C22×D311yescharacteristic
419C23×C4C22×D311yescharacteristic
420C23×C4C22×D311yescharacteristic
421C23×C4C22×D311yescharacteristic
422#123—632no—
423#123—632no—
424#121—632no—
425#121—632no—
426C2×C4⋊C4—38no—
427C2×C4⋊C4—34no—
428C2×C4⋊C4—34no—
429C2×C4⋊C4—34no—
430C2×C4⋊C4—34no—
431C2×C4⋊C4—34no—
432C2×C4⋊C4—34no—
433C2×C4⋊C4—34no—
434C2×C4⋊C4—42no—
435C2×C4⋊C4—64no—
436C2×C4⋊C4—64no—
437C2×C4⋊C4—64no—
438C2×C4⋊C4—64no—
439C2×C4⋊C4—122no—
440C2×C4⋊C4—122no—
441C2×C4⋊C4C22×D314yes—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—34no—
446C2×C22⋊C4—34no—
447C2×C22⋊C4—34no—
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—42no—
456C2×C22⋊C4—64no—
457C2×C22⋊C4—64no—
458C2×C22⋊C4—64no—
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⋊C4C22×D314yes—
467C2×C22⋊C4C22×D314yes—
468C2×C22⋊C4C22×D314yes—
469C2×C22⋊C4C22×D314yes—
470C2×C42—34no—
471C2×C42—122no—
472#95—34no—
473#95—34no—
474#95—34no—
475#95C22×D314yes—
476C23×C3—28no—
477C23×C3—28no—
478C23×C3—28no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—22no—
489C23×C3—22no—
490C23×C3—22no—
491C23×C3—22no—
492C23×C3—44no—
493C23×C3—44no—
494C23×C3—44no—
495C23×C3—44no—
496C23×C3—44no—
497C23×C3—44no—
498C23×C3—44no—
499C23×C3—44no—
500C23×C3—44no—
501C23×C3—44no—
502C23×C3—44no—
503C23×C3C22×D414yes—
504C23×C3C22×D412yes—
505C23×C3C22×D412yes—
506C23×C3C2×#4112yes—
507C23×C3H(5,𝔽2)12yes—
508C23×C3H(5,𝔽2)12yes—
509C23×C3H(5,𝔽2)12yes—
510C23×C32−1+412yes—
511C23×C3C2511yescharacteristic
512C22×D3—28no—
513C22×D3—28no—
514C22×D3—28no—
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—22no—
527C22×D3—22no—
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×D3—44no—
539C22×D3C22×D414yes—
540C3×D4—416no—
541C2×C3×C4—28no—
542C2×C3×C4—22no—
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—44no—
557C2×C3×C4—44no—
558C2×C3×C4—44no—
559C2×C3×C4—44no—
560C2×C3×C4C22×D414yes—
561#67—416no—
562#67—416no—
563#67—416no—
564#67—416no—
565C2×Dic3—28no—
566C2×Dic3—28no—
567C2×Dic3—28no—
568C2×Dic3—28no—
569C2×Dic3—22no—
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—416no—
584C2×Dic3—44no—
585C2×Dic3—44no—
586C2×Dic3C22×D414yes—
587C2×Dic3C22×D414yes—
588C2×Dic3C22×D414yes—
589C2×Dic3C2×#4114yes—
590D12—416no—
591C4×D3—416no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—34no—
606C24—32no—
607C24—32no—
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—
621C24D3×D414yes—
622C24C23×D312yes—
623C24C23×D312yes—
624C24C23×D311yescharacteristic
625C2×D4—28no—
626C2×D4—316no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—416no—
630C2×D4—68no—
631C2×D4—68no—
632C2×D4—68no—
633C2×D4—68no—
634C2×D4—68no—
635C2×D4—68no—
636C2×D4—124no—
637C2×D4—124no—
638C2×D4—1216no—
639C2×D4—124no—
640C2×D4—124no—
641C2×D4—124no—
642C2×D4—124no—
643C2×D4—124no—
644C2×D4—124no—
645C2×D4—1216no—
646C2×D4—1216no—
647C2×D4—1216no—
648C2×D4—1216no—
649C22×C4—22no—
650C22×C4—22no—
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—34no—
664C22×C4—34no—
665C22×C4—34no—
666C22×C4—34no—
667C22×C4—32no—
668C22×C4—32no—
669C22×C4—32no—
670C22×C4—32no—
671C22×C4—32no—
672C22×C4—32no—
673C22×C4—68no—
674C22×C4—68no—
675C22×C4—68no—
676C22×C4—62no—
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—68no—
688C22×C4—62no—
689C22×C4—62no—
690C22×C4—62no—
691C22×C4—124no—
692C22×C4—1216no—
693C22×C4—124no—
694C22×C4—1216no—
695C22×C4D3×D414yes—
696C22×C4C23×D312yes—
697C22×C4C23×D312yes—
698C22×C4C23×D312yes—
699C22×C4C23×D312yes—
700C22×C4C23×D312yes—
701C4⋊C4—316no—
702C4⋊C4—44no—
703C4⋊C4—68no—
704C4⋊C4—68no—
705C4⋊C4—68no—
706C4⋊C4—68no—
707C4⋊C4—124no—
708C4⋊C4—124no—
709C22⋊C4—28no—
710C22⋊C4—28no—
711C22⋊C4—28no—
712C22⋊C4—44no—
713C22⋊C4—68no—
714C22⋊C4—68no—
715C22⋊C4—68no—
716C22⋊C4—68no—
717C22⋊C4—68no—
718C22⋊C4—68no—
719C22⋊C4—68no—
720C22⋊C4—68no—
721C22⋊C4—68no—
722C22⋊C4—124no—
723C42—124no—
724C22×C3—24no—
725C22×C3—24no—
726C22×C3—24no—
727C22×C3—42no—
728C22×C3—416no—
729C22×C3—42no—
730C22×C3—42no—
731C22×C3—42no—
732C22×C3—42no—
733C22×C3—42no—
734C22×C3—42no—
735C22×C3—42no—
736C22×C3—42no—
737C22×C3—42no—
738C22×C3—42no—
739C22×C3—88no—
740C22×C3#53414yes—
741C22×C3#53714yes—
742C22×C3#53814yes—
743C22×C3D4214yes—
744C22×C3#54714yes—
745C22×C3#55014yes—
746C22×C3#56214yes—
747C22×C3C23×D411yescharacteristic
748C22×C3C23×D411yescharacteristic
749C22×C3C22×#4111yescharacteristic
750C22×C3C2×H(5,𝔽2)11yescharacteristic
751C22×C3C2×H(5,𝔽2)11yescharacteristic
752C22×C3C2×H(5,𝔽2)11yescharacteristic
753C22×C3C2×2−1+411yescharacteristic
754C2×D3—24no—
755C2×D3—24no—
756C2×D3—24no—
757C2×D3—42no—
758C2×D3—416no—
759C2×D3—42no—
760C2×D3—42no—
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—88no—
770C3×C4—24no—
771C3×C4—42no—
772C3×C4—42no—
773C3×C4—42no—
774C3×C4—42no—
775Dic3—24no—
776Dic3—24no—
777Dic3—24no—
778Dic3—24no—
779Dic3—42no—
780Dic3—42no—
781C23—28no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—28no—
789C23—28no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—34no—
798C23—44no—
799C23—44no—
800C23—44no—
801C23—44no—
802C23—44no—
803C23—44no—
804C23—44no—
805C23—44no—
806C23—44no—
807C23—44no—
808C23—44no—
809C23—68no—
810C23—62no—
811C23—62no—
812C23—62no—
813C23—62no—
814C23—62no—
815C23—62no—
816C23—68no—
817C23—68no—
818C23—62no—
819C23—62no—
820C23—62no—
821C23—62no—
822C23—62no—
823C23—62no—
824C23—62no—
825C23—124no—
826C23—124no—
827C23—124no—
828C23—124no—
829C23—124no—
830C23—124no—
831C23—124no—
832C23—124no—
833C23—124no—
834C23—124no—
835C23—124no—
836C23C2×D3×D414yes—
837C23C2×D3×D412yes—
838C23C2×D3×D412yes—
839C23#100412yes—
840C23#100412yes—
841C23D3×#4112yes—
842C23#100912yes—
843C23#101012yes—
844C23C24×D311yescharacteristic
845D4—416no—
846D4—1216no—
847D4—1216no—
848D4—1216no—
849D4—1216no—
850D4—1216no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—28no—
854C2×C4—22no—
855C2×C4—22no—
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—34no—
867C2×C4—34no—
868C2×C4—34no—
869C2×C4—34no—
870C2×C4—44no—
871C2×C4—44no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—68no—
875C2×C4—62no—
876C2×C4—62no—
877C2×C4—62no—
878C2×C4—62no—
879C2×C4—62no—
880C2×C4—62no—
881C2×C4—62no—
882C2×C4—62no—
883C2×C4—68no—
884C2×C4—68no—
885C2×C4—68no—
886C2×C4—62no—
887C2×C4—62no—
888C2×C4—62no—
889C2×C4—62no—
890C2×C4—62no—
891C2×C4—62no—
892C2×C4—1216no—
893C2×C4—1216no—
894C2×C4—124no—
895C2×C4—124no—
896C2×C4C2×D3×D414yes—
897C2×C3—44no—
898C2×C3—82no—
899C2×C3#268218yescomplemented
900C2×C3C2×#53411yescharacteristic
901C2×C3C2×#53711yescharacteristic
902C2×C3C2×#53811yescharacteristic
903C2×C3C2×D4211yescharacteristic
904C2×C3C2×#54711yescharacteristic
905C2×C3C2×#55011yescharacteristic
906C2×C3C2×#56211yescharacteristic
907D3—44no—
908D3—82no—
909C22—24no—
910C22—24no—
911C22—24no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—416no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—64no—
925C22—64no—
926C22—64no—
927C22—88no—
928C22—122no—
929C22—122no—
930C22—122no—
931C22—1216no—
932C22—122no—
933C22—122no—
934C22—122no—
935C22—122no—
936C22—122no—
937C22—122no—
938C22—122no—
939C22—122no—
940C22—248no—
941C22#558914yes—
942C22#559714yes—
943C22#559914yes—
944C22#560914yes—
945C22#565514yes—
946C22#566714yes—
947C22#567814yes—
948C22C22×D3×D411yescharacteristic
949C22C22×D3×D411yescharacteristic
950C22C2×#100411yescharacteristic
951C22C2×#100411yescharacteristic
952C22C2×D3×#4111yescharacteristic
953C22C2×#100911yescharacteristic
954C22C2×#101011yescharacteristic
955C4—24no—
956C4—42no—
957C4—42no—
958C4—42no—
959C4—42no—
960C4—64no—
961C4—64no—
962C4—64no—
963C4—64no—
964C4—122no—
965C4—122no—
966C3C2×#268211yescharacteristic, complemented, Sylow
967C2—44no—
968C2—82no—
969C2—124no—
970C2—242no—
971C2#7700718yesdirect product factor
972C2C2×#558911yescharacteristic
973C2C2×#559711yescharacteristic
974C2C2×#559911yescharacteristic
975C2C2×#560911yescharacteristic
976C2C2×#565511yescharacteristic
977C2C2×#566711yescharacteristic
978C2C2×#567811yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#394C2
socleC24×C3C24
hypercenterC2×#394D3
hypocenterC3C2×#2682
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#939C2semidirect
2. C22×#883C2semidirect
3. C22×#884C2semidirect
4. C22×#886C2semidirect
5. C2×C3×#394C2semidirect
6. C2×#5223C2semidirect
7. C2×#4991C2semidirect
8. C2×#4972C2semidirect
9. C2×#4960C2semidirect
10. C2×#4948C2semidirect
11. C2×#4957C2semidirect
12. C2×#4957C2semidirect
13. C2×#4946C2semidirect
14. #77007C2direct (N × H)
15. C2×#4676C2semidirect
16. C2×#4668C2semidirect
35. C2×#939C22semidirect
52. C2×#886C22semidirect
54. C2×#884C22semidirect
56. C2×#883C22semidirect
57. C3×#394C22semidirect
59. #5223C22semidirect
63. #4991C22semidirect
64. #4972C22semidirect
65. #4960C22semidirect
66. #4957C22semidirect
67. #4957C22semidirect
68. #4948C22semidirect
69. #4946C22semidirect
70. #4676C22semidirect
71. #4668C22semidirect
80. C2×#394D3semidirect
112. C22×#67D4semidirect
167. C2×C4⋊Dic3D4semidirect
231. #394C2×D3semidirect
315. C2×#67C2×D4semidirect
368. C4⋊Dic3C2×D4semidirect
899. C2×C3#2682semidirect
966. C3C2×#2682semidirect
971. C2#77007direct (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×#8832
C22×#8842
C22×#8862
C2×C3×#3942
C2×#52232
C2×#49912
C2×#49722
C2×#49602
C2×#49482
C2×#49572
C2×#49462
#770072
C2×#46762
C2×#46682
C2×#26823