Finite Group Databasebeta

← C2×#82716 #11429770

Subgroups — C2×#82716 #11429770

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×C3×#121C211yesmaximal, characteristic, complemented
2C22×#938C211yesmaximal, characteristic, complemented
3C22×#939C211yesmaximal, characteristic, complemented
4C22×#883C211yesmaximal, characteristic, complemented
5C2×#5223C211yesmaximal, characteristic, complemented
6C2×#5222C211yesmaximal, characteristic, complemented
7C2×#5222C211yesmaximal, characteristic, complemented
8C2×#5220C211yesmaximal, characteristic, complemented
9C2×#5213C211yesmaximal, characteristic, complemented
10C2×#5212C211yesmaximal, characteristic, complemented
11#82716C2116yesmaximal, direct product factor
12C2×#4989C211yesmaximal, characteristic, complemented
13C2×#4982C211yesmaximal, characteristic, complemented
14C2×#4949C211yesmaximal, characteristic, complemented
15C2×#4961C211yesmaximal, characteristic, complemented
16C2×#4950C211yesmaximal, characteristic, complemented
17C2×#2671—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C23×C3×D4C2211yescharacteristic
21C24×C3×C4C2211yescharacteristic
22C23×#67C2211yescharacteristic
23C23×#67C2211yescharacteristic
24C23×#67C2211yescharacteristic
25C24×Dic3C2211yescharacteristic
26C23×C4×D3C2211yescharacteristic
27C2×C3×#121—28no—
28C2×C3×#121C2218yescomplemented
29C22×C3×C4⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×C3×C22⋊C4C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C22×#217C2211yescharacteristic
34C22×#217C2211yescharacteristic
35C22×#217C2211yescharacteristic
36C22×#217C2211yescharacteristic
37C22×#217C2211yescharacteristic
38C22×#217C2211yescharacteristic
39C22×#217C2211yescharacteristic
40C2×#939—28no—
41C2×#939C2218yescomplemented
42C2×#938—28no—
43C2×#938C2218yescomplemented
44C22×(C2×D3)⋊C4C2211yescharacteristic
45C22×(C2×D3)⋊C4C2211yescharacteristic
46C22×(C2×D3)⋊C4C2211yescharacteristic
47C22×C4⋊Dic3C2211yescharacteristic
48C22×C4⋊Dic3C2211yescharacteristic
49C22×C4⋊Dic3C2211yescharacteristic
50C22×Dic3⋊C4C2211yescharacteristic
51C22×Dic3⋊C4C2211yescharacteristic
52C22×Dic3⋊C4C2211yescharacteristic
53C2×#883—28no—
54C2×#883C2218yescomplemented
55#5223C2218yescomplemented
56#5222C2218yescomplemented
57#5222C2218yescomplemented
58#5220C2218yescomplemented
59#5213C2218yescomplemented
60#5212C2218yescomplemented
61C2×C3⋊#95C2211yescharacteristic
62C2×C3⋊#95C2211yescharacteristic
63C2×C3⋊#95C2211yescharacteristic
64C2×C3⋊#95C2211yescharacteristic
65C2×C3⋊#95C2211yescharacteristic
66C2×C3⋊#95C2211yescharacteristic
67#4989C2218yescomplemented
68#4982C2218yescomplemented
69#4961C2218yescomplemented
70#4950C2218yescomplemented
71#4949C2218yescomplemented
72C22×#123—31no—
73C22×#121—31no—
74C22×#121—31no—
75C22×#121D311yescharacteristic, complemented
76#2671—316no—
77C2×#399—31no—
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
89C25×C3C2311yescharacteristic
90C25×C3C2311yescharacteristic
91C24×D3C2311yescharacteristic
92C22×C3×D4—24no—
93C22×C3×D4—24no—
94C22×C3×D4—24no—
95C22×C3×D4—24no—
96C22×C3×D4—24no—
97C22×C3×D4—24no—
98C22×C3×D4—42no—
99C22×C3×D4—42no—
100C22×C3×D4—42no—
101C22×C3×D4C2314yes—
102C22×C3×D4C2314yes—
103C22×C3×D4C2314yes—
104C23×C3×C4—24no—
105C23×C3×C4—24no—
106C23×C3×C4—42no—
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2314yes—
109C23×C3×C4C2311yescharacteristic
110C23×C3×C4C2311yescharacteristic
111C23×C3×C4C2311yescharacteristic
112C22×#67—24no—
113C22×#67—24no—
114C22×#67—24no—
115C22×#67—42no—
116C22×#67—42no—
117C22×#67—42no—
118C22×#67—42no—
119C22×#67—42no—
120C22×#67D418yescomplemented
121C22×#67C2314yes—
122C22×#67C2314yes—
123C22×#67C2314yes—
124C23×Dic3—24no—
125C23×Dic3—42no—
126C23×Dic3—42no—
127C23×Dic3C2311yescharacteristic
128C23×Dic3C2311yescharacteristic
129C23×Dic3C2311yescharacteristic
130C23×Dic3C2311yescharacteristic
131C23×Dic3C2311yescharacteristic
132C23×Dic3C2311yescharacteristic
133C23×Dic3C2311yescharacteristic
134C23×Dic3C2314yes—
135C22×C4×D3—24no—
136C22×C4×D3—24no—
137C22×C4×D3—42no—
138C22×C4×D3C2314yes—
139C3×#121—232no—
140C2×C3×C4⋊C4—24no—
141C2×C3×C4⋊C4C2314yes—
142C2×C3×C22⋊C4—24no—
143C2×C3×C22⋊C4D418yescomplemented
144C2×C3×C22⋊C4C2314yes—
145C2×C3×C22⋊C4C2314yes—
146C2×#217—24no—
147C2×#217—24no—
148C2×#217—24no—
149C2×#217—24no—
150C2×#217—42no—
151C2×#217—42no—
152C2×#217—42no—
153C2×#217—42no—
154C2×#217C2314yes—
155C2×#217C2314yes—
156C2×#217C2314yes—
157C2×#217C2314yes—
158C2×#217C2314yes—
159C2×#217C2314yes—
160C2×#217C2314yes—
161C2×#217C2314yes—
162#939—232no—
163#938—232no—
164C2×(C2×D3)⋊C4—24no—
165C2×(C2×D3)⋊C4—24no—
166C2×(C2×D3)⋊C4—24no—
167C2×(C2×D3)⋊C4C2314yes—
168C2×(C2×D3)⋊C4C2314yes—
169C2×(C2×D3)⋊C4C2314yes—
170C2×C4⋊Dic3—24no—
171C2×C4⋊Dic3—24no—
172C2×C4⋊Dic3—42no—
173C2×C4⋊Dic3C2314yes—
174C2×C4⋊Dic3C2314yes—
175C2×C4⋊Dic3C2314yes—
176C2×Dic3⋊C4—24no—
177C2×Dic3⋊C4—24no—
178C2×Dic3⋊C4—42no—
179C2×Dic3⋊C4C2314yes—
180C2×Dic3⋊C4C2314yes—
181C2×Dic3⋊C4C2314yes—
182#883—232no—
183C3⋊#95C2314yes—
184C3⋊#95C2314yes—
185C3⋊#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C23×D4—31no—
190C23×D4—31no—
191C23×D4—31no—
192C23×D4C2×D311yescharacteristic
193C23×D4C2×D311yescharacteristic
194C23×D4C2×D311yescharacteristic
195C24×C4—31no—
196C24×C4—31no—
197C24×C4C2×D311yescharacteristic
198C2×#123—38no—
199C2×#123—68no—
200C2×#121—28no—
201C2×#121—38no—
202C2×#121—38no—
203C2×#121—68no—
204C2×#121—68no—
205C2×#121C2×D318yescomplemented
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⋊C4—31no—
224C22×C22⋊C4C2×D311yescharacteristic
225C22×C22⋊C4C2×D311yescharacteristic
226#399—38no—
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×#95—31no—
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×C3—22no—
257C24×C3—22no—
258C24×C3—22no—
259C24×C3—22no—
260C24×C3—22no—
261C24×C3—22no—
262C24×C3C2×D414yes—
263C24×C3C2×D414yes—
264C24×C3C2412yes—
265C24×C3C2412yes—
266C24×C3C2412yes—
267C24×C3C2411yescharacteristic
268C23×D3—22no—
269C23×D3—22no—
270C23×D3—22no—
271C23×D3—22no—
272C23×D3—22no—
273C23×D3—22no—
274C23×D3C2×D414yes—
275C23×D3C2412yes—
276C2×C3×D4—28no—
277C2×C3×D4—28no—
278C2×C3×D4—28no—
279C2×C3×D4—28no—
280C2×C3×D4—28no—
281C2×C3×D4—28no—
282C2×C3×D4—44no—
283C2×C3×D4—44no—
284C2×C3×D4—44no—
285C2×C3×D4—416no—
286C2×C3×D4—416no—
287C2×C3×D4—416no—
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×C4—22no—
295C22×C3×C4—22no—
296C22×C3×C4—22no—
297C22×C3×C4—28no—
298C22×C3×C4—28no—
299C22×C3×C4—44no—
300C22×C3×C4—416no—
301C22×C3×C4C2×D414yes—
302C22×C3×C4C2×D414yes—
303C22×C3×C4#4114yes—
304C22×C3×C4C2412yes—
305C22×C3×C4C2412yes—
306C22×C3×C4C2412yes—
307C22×C3×C4C2412yes—
308C2×#67—28no—
309C2×#67—28no—
310C2×#67—28no—
311C2×#67—416no—
312C2×#67—44no—
313C2×#67—44no—
314C2×#67—44no—
315C2×#67—44no—
316C2×#67—44no—
317C2×#67—416no—
318C2×#67—416no—
319C2×#67C2×D4116yescomplemented
320C22×Dic3—22no—
321C22×Dic3—22no—
322C22×Dic3—22no—
323C22×Dic3—22no—
324C22×Dic3—22no—
325C22×Dic3—22no—
326C22×Dic3—22no—
327C22×Dic3—22no—
328C22×Dic3—22no—
329C22×Dic3—22no—
330C22×Dic3—22no—
331C22×Dic3—22no—
332C22×Dic3—22no—
333C22×Dic3—22no—
334C22×Dic3—22no—
335C22×Dic3—22no—
336C22×Dic3—22no—
337C22×Dic3—22no—
338C22×Dic3—22no—
339C22×Dic3—22no—
340C22×Dic3—28no—
341C22×Dic3—44no—
342C22×Dic3—44no—
343C22×Dic3—416no—
344C22×Dic3C2×D414yes—
345C22×Dic3C2412yes—
346C22×Dic3C2412yes—
347C22×Dic3C2412yes—
348C22×Dic3C2412yes—
349C22×Dic3C2412yes—
350C22×Dic3C2412yes—
351C22×Dic3C2412yes—
352C2×C4×D3—28no—
353C2×C4×D3—28no—
354C2×C4×D3—44no—
355C2×C4×D3—416no—
356C3×C4⋊C4—28no—
357C3×C22⋊C4—28no—
358C3×C22⋊C4C2×D4116yescomplemented
359#217—28no—
360#217—28no—
361#217—28no—
362#217—28no—
363#217—44no—
364#217—44no—
365#217—44no—
366#217—44no—
367(C2×D3)⋊C4—28no—
368(C2×D3)⋊C4—28no—
369(C2×D3)⋊C4—28no—
370C4⋊Dic3—28no—
371C4⋊Dic3—28no—
372C4⋊Dic3—44no—
373Dic3⋊C4—28no—
374Dic3⋊C4—28no—
375Dic3⋊C4—44no—
376C25—31no—
377C25C22×D311yescharacteristic
378C25C22×D311yescharacteristic
379C25C22×D311yescharacteristic
380C22×D4—24no—
381C22×D4—24no—
382C22×D4—24no—
383C22×D4—24no—
384C22×D4—24no—
385C22×D4—24no—
386C22×D4—38no—
387C22×D4—34no—
388C22×D4—34no—
389C22×D4—34no—
390C22×D4—42no—
391C22×D4—42no—
392C22×D4—42no—
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×D4C22×D314yes—
402C22×D4C22×D314yes—
403C22×D4C22×D314yes—
404C23×C4—24no—
405C23×C4—24no—
406C23×C4—31no—
407C23×C4—31no—
408C23×C4—31no—
409C23×C4—31no—
410C23×C4—31no—
411C23×C4—31no—
412C23×C4—31no—
413C23×C4—34no—
414C23×C4—34no—
415C23×C4—42no—
416C23×C4—64no—
417C23×C4—64no—
418C23×C4—64no—
419C23×C4—122no—
420C23×C4—122no—
421C23×C4—122no—
422C23×C4C22×D311yescharacteristic
423C23×C4C22×D314yes—
424C23×C4C22×D311yescharacteristic
425C23×C4C22×D311yescharacteristic
426C23×C4C22×D311yescharacteristic
427#123—632no—
428#121—232no—
429#121—632no—
430#121—632no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—34no—
433C2×C4⋊C4—34no—
434C2×C4⋊C4—34no—
435C2×C4⋊C4—34no—
436C2×C4⋊C4—34no—
437C2×C4⋊C4—34no—
438C2×C4⋊C4—64no—
439C2×C4⋊C4—64no—
440C2×C4⋊C4—64no—
441C2×C4⋊C4—64no—
442C2×C4⋊C4—122no—
443C2×C4⋊C4—122no—
444C2×C4⋊C4C22×D314yes—
445C2×C22⋊C4—24no—
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—34no—
456C2×C22⋊C4—34no—
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—122no—
465C2×C22⋊C4—122no—
466C2×C22⋊C4—122no—
467C2×C22⋊C4—122no—
468C2×C22⋊C4#6718yescomplemented
469C2×C22⋊C4C22×D314yes—
470C2×C22⋊C4C22×D314yes—
471#95—34no—
472#95—34no—
473#95—34no—
474#95—34no—
475#95—34no—
476#95—34no—
477C23×C3—28no—
478C23×C3—28no—
479C23×C3—28no—
480C23×C3—28no—
481C23×C3—28no—
482C23×C3—28no—
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—22no—
493C23×C3—22no—
494C23×C3—22no—
495C23×C3—22no—
496C23×C3—22no—
497C23×C3—22no—
498C23×C3—22no—
499C23×C3—22no—
500C23×C3—22no—
501C23×C3—22no—
502C23×C3—44no—
503C23×C3—44no—
504C23×C3—44no—
505C23×C3—44no—
506C23×C3—44no—
507C23×C3—44no—
508C23×C3—44no—
509C23×C3—44no—
510C23×C3—44no—
511C23×C3—44no—
512C23×C3—44no—
513C23×C3—44no—
514C23×C3—44no—
515C23×C3—44no—
516C23×C3—44no—
517C23×C3C22×D414yes—
518C23×C3C22×D412yes—
519C23×C3C22×D414yes—
520C23×C3C22×D412yes—
521C23×C3C2×#4112yes—
522C23×C3H(5,𝔽2)12yes—
523C23×C3H(5,𝔽2)12yes—
524C23×C3H(5,𝔽2)12yes—
525C23×C32−1+412yes—
526C23×C3C2511yescharacteristic
527C22×D3—28no—
528C22×D3—28no—
529C22×D3—28no—
530C22×D3—22no—
531C22×D3—22no—
532C22×D3—22no—
533C22×D3—22no—
534C22×D3—22no—
535C22×D3—22no—
536C22×D3—44no—
537C22×D3—44no—
538C22×D3—44no—
539C22×D3—44no—
540C22×D3C22×D414yes—
541C3×D4—416no—
542C3×D4—416no—
543C3×D4—416no—
544C2×C3×C4—28no—
545C2×C3×C4—28no—
546C2×C3×C4—28no—
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—416no—
557C2×C3×C4—44no—
558C2×C3×C4C22×D414yes—
559C2×C3×C4C22×D414yes—
560C2×C3×C4C2×#4114yes—
561#67—416no—
562#67—416no—
563#67—416no—
564C2×Dic3—28no—
565C2×Dic3—22no—
566C2×Dic3—22no—
567C2×Dic3—22no—
568C2×Dic3—22no—
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—22no—
584C2×Dic3—22no—
585C2×Dic3—416no—
586C2×Dic3—44no—
587C2×Dic3—44no—
588C2×Dic3—44no—
589C2×Dic3—44no—
590C2×Dic3—44no—
591C2×Dic3—44no—
592C2×Dic3C22×D414yes—
593C4×D3—416no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—34no—
614C24—32no—
615C24—62no—
616C24—62no—
617C24—62no—
618C24—62no—
619C24—62no—
620C24—62no—
621C24D3×D414yes—
622C24C2×#6714yes—
623C24C23×D312yes—
624C24C23×D312yes—
625C24C23×D312yes—
626C24C23×D311yescharacteristic
627C2×D4—28no—
628C2×D4—28no—
629C2×D4—28no—
630C2×D4—28no—
631C2×D4—28no—
632C2×D4—28no—
633C2×D4—316no—
634C2×D4—44no—
635C2×D4—44no—
636C2×D4—44no—
637C2×D4—416no—
638C2×D4—416no—
639C2×D4—416no—
640C2×D4—68no—
641C2×D4—68no—
642C2×D4—68no—
643C2×D4—124no—
644C2×D4—124no—
645C2×D4—1216no—
646C2×D4—124no—
647C2×D4—124no—
648C2×D4—124no—
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—28no—
661C22×C4—28no—
662C22×C4—34no—
663C22×C4—32no—
664C22×C4—32no—
665C22×C4—32no—
666C22×C4—32no—
667C22×C4—32no—
668C22×C4—32no—
669C22×C4—32no—
670C22×C4—44no—
671C22×C4—416no—
672C22×C4—68no—
673C22×C4—68no—
674C22×C4—62no—
675C22×C4—62no—
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—62no—
688C22×C4—62no—
689C22×C4—62no—
690C22×C4—62no—
691C22×C4—62no—
692C22×C4—62no—
693C22×C4—62no—
694C22×C4—68no—
695C22×C4—124no—
696C22×C4—1216no—
697C22×C4—124no—
698C22×C4—124no—
699C22×C4—1216no—
700C22×C4#23714yes—
701C22×C4C2×#6714yes—
702C22×C4C2×#6714yes—
703C22×C4C23×D312yes—
704C22×C4C23×D312yes—
705C22×C4C23×D312yes—
706C22×C4C23×D312yes—
707C4⋊C4—28no—
708C4⋊C4—68no—
709C4⋊C4—68no—
710C4⋊C4—68no—
711C4⋊C4—68no—
712C4⋊C4—124no—
713C4⋊C4—124no—
714C22⋊C4—28no—
715C22⋊C4—68no—
716C22⋊C4—68no—
717C22⋊C4—68no—
718C22⋊C4—68no—
719C22⋊C4—68no—
720C22⋊C4—68no—
721C22⋊C4—68no—
722C22⋊C4—124no—
723C22⋊C4—124no—
724C22⋊C4—124no—
725C22⋊C4—124no—
726C22⋊C4C2×#67116yescomplemented
727C22×C3—24no—
728C22×C3—24no—
729C22×C3—24no—
730C22×C3—24no—
731C22×C3—24no—
732C22×C3—24no—
733C22×C3—416no—
734C22×C3—416no—
735C22×C3—42no—
736C22×C3—42no—
737C22×C3—42no—
738C22×C3—42no—
739C22×C3—42no—
740C22×C3—42no—
741C22×C3—42no—
742C22×C3—42no—
743C22×C3—42no—
744C22×C3—42no—
745C22×C3—42no—
746C22×C3—42no—
747C22×C3—42no—
748C22×C3—42no—
749C22×C3—42no—
750C22×C3—88no—
751C22×C3#53414yes—
752C22×C3#53714yes—
753C22×C3#54014yes—
754C22×C3D4214yes—
755C22×C3#54614yes—
756C22×C3#54714yes—
757C22×C3#56214yes—
758C22×C3C23×D411yescharacteristic
759C22×C3C23×D411yescharacteristic
760C22×C3C22×#4111yescharacteristic
761C22×C3C2×H(5,𝔽2)11yescharacteristic
762C22×C3C2×H(5,𝔽2)11yescharacteristic
763C22×C3C2×H(5,𝔽2)11yescharacteristic
764C22×C3C2×2−1+411yescharacteristic
765C2×D3—24no—
766C2×D3—24no—
767C2×D3—24no—
768C2×D3—416no—
769C2×D3—42no—
770C2×D3—42no—
771C2×D3—42no—
772C2×D3—42no—
773C3×C4—24no—
774C3×C4—24no—
775C3×C4—24no—
776C3×C4—42no—
777Dic3—24no—
778Dic3—42no—
779Dic3—42no—
780Dic3—42no—
781Dic3—42no—
782Dic3—42no—
783Dic3—42no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—28no—
797C23—28no—
798C23—28no—
799C23—28no—
800C23—28no—
801C23—28no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—34no—
810C23—44no—
811C23—44no—
812C23—44no—
813C23—44no—
814C23—44no—
815C23—44no—
816C23—44no—
817C23—44no—
818C23—44no—
819C23—44no—
820C23—44no—
821C23—44no—
822C23—44no—
823C23—44no—
824C23—44no—
825C23—62no—
826C23—62no—
827C23—62no—
828C23—62no—
829C23—62no—
830C23—62no—
831C23—68no—
832C23—68no—
833C23—68no—
834C23—124no—
835C23—124no—
836C23—124no—
837C23—124no—
838C23C2×D3×D414yes—
839C23C2×D3×D412yes—
840C23C2×#23712yes—
841C23#100412yes—
842C23#100412yes—
843C23#100912yes—
844C23#101012yes—
845C23C22×#6714yes—
846C23C22×#6712yes—
847C23C24×D311yescharacteristic
848D4—416no—
849D4—416no—
850D4—416no—
851D4—1216no—
852D4—1216no—
853D4—1216no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—28no—
861C2×C4—28no—
862C2×C4—28no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—34no—
867C2×C4—416no—
868C2×C4—44no—
869C2×C4—62no—
870C2×C4—62no—
871C2×C4—68no—
872C2×C4—62no—
873C2×C4—62no—
874C2×C4—62no—
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—62no—
884C2×C4—62no—
885C2×C4—62no—
886C2×C4—62no—
887C2×C4—62no—
888C2×C4—62no—
889C2×C4—62no—
890C2×C4—1216no—
891C2×C4—1216no—
892C2×C4—124no—
893C2×C4—124no—
894C2×C4—124no—
895C2×C4—124no—
896C2×C4—124no—
897C2×C4—124no—
898C2×C4C2×#23714yes—
899C2×C4C22×#6714yes—
900C2×C4C22×#6714yes—
901C2×C3—44no—
902C2×C3—44no—
903C2×C3—82no—
904C2×C3#267118yescomplemented
905C2×C3C2×#53411yescharacteristic
906C2×C3C2×#53711yescharacteristic
907C2×C3C2×#54011yescharacteristic
908C2×C3C2×D4211yescharacteristic
909C2×C3C2×#54611yescharacteristic
910C2×C3C2×#54711yescharacteristic
911C2×C3C2×#56211yescharacteristic
912D3—44no—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—24no—
917C22—24no—
918C22—24no—
919C22—416no—
920C22—416no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—64no—
937C22—64no—
938C22—64no—
939C22—88no—
940C22—1216no—
941C22—122no—
942C22—122no—
943C22—122no—
944C22—122no—
945C22#560514yes—
946C22#561114yes—
947C22#561914yes—
948C22#562114yes—
949C22D4×#6714yes—
950C22#580614yes—
951C22#583314yes—
952C22C22×D3×D411yescharacteristic
953C22C22×#23711yescharacteristic
954C22C2×#100411yescharacteristic
955C22C2×#100411yescharacteristic
956C22C2×#100911yescharacteristic
957C22C2×#101011yescharacteristic
958C22C23×#6711yescharacteristic
959C4—24no—
960C4—24no—
961C4—24no—
962C4—42no—
963C4—64no—
964C4—122no—
965C4—122no—
966C4—122no—
967C4—122no—
968C4—122no—
969C4—122no—
970C3C2×#267111yescharacteristic, complemented, Sylow
971C2—44no—
972C2—44no—
973C2—82no—
974C2—124no—
975C2#8271618yesdirect product factor
976C2C2×#561911yescharacteristic
977C2C2×#561111yescharacteristic
978C2C2×#560511yescharacteristic
979C2C2×#562111yescharacteristic
980C2C2×#580611yescharacteristic
981C2C2×D4×#6711yescharacteristic
982C2C2×#583311yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC22×C3×#121C2
socleC24×C3C24
hypercenterC22×#121D3
hypocenterC3C2×#2671
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×C3×#121C2semidirect
2. C22×#938C2semidirect
3. C22×#939C2semidirect
4. C22×#883C2semidirect
5. C2×#5223C2semidirect
6. C2×#5222C2semidirect
7. C2×#5222C2semidirect
8. C2×#5220C2semidirect
9. C2×#5213C2semidirect
10. C2×#5212C2semidirect
11. #82716C2direct (N × H)
12. C2×#4989C2semidirect
13. C2×#4982C2semidirect
14. C2×#4949C2semidirect
15. C2×#4961C2semidirect
16. C2×#4950C2semidirect
28. C2×C3×#121C22semidirect
41. C2×#939C22semidirect
43. C2×#938C22semidirect
54. C2×#883C22semidirect
55. #5223C22semidirect
56. #5222C22semidirect
57. #5222C22semidirect
58. #5220C22semidirect
59. #5213C22semidirect
60. #5212C22semidirect
67. #4989C22semidirect
68. #4982C22semidirect
69. #4961C22semidirect
70. #4950C22semidirect
71. #4949C22semidirect
75. C22×#121D3semidirect
120. C22×#67D4semidirect
143. C2×C3×C22⋊C4D4semidirect
205. C2×#121C2×D3semidirect
319. C2×#67C2×D4semidirect
358. C3×C22⋊C4C2×D4semidirect
468. C2×C22⋊C4#67semidirect
726. C22⋊C4C2×#67semidirect
904. C2×C3#2671semidirect
970. C3C2×#2671semidirect
975. C2#82716direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1212
C22×#9382
C22×#9392
C22×#8832
C2×#52232
C2×#52222
C2×#52202
C2×#52132
C2×#52122
#827162
C2×#49892
C2×#49822
C2×#49492
C2×#49612
C2×#49502
C2×#26713