Finite Group Databasebeta

← C2×#82873 #11429934

Subgroups — C2×#82873 #11429934

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×C3×#123C211yesmaximal, characteristic, complemented
2C22×#938C211yesmaximal, characteristic, complemented
3C22×#930C211yesmaximal, characteristic, complemented
4C22×#894C211yesmaximal, characteristic, complemented
5C2×#5223C211yesmaximal, characteristic, complemented
6C2×#5210C211yesmaximal, characteristic, complemented
7#82873C2116yesmaximal, direct product factor
8C2×#4994C211yesmaximal, characteristic, complemented
9C2×#4989C211yesmaximal, characteristic, complemented
10C2×#4984C211yesmaximal, characteristic, complemented
11C2×#4960C211yesmaximal, characteristic, complemented
12C2×#4948C211yesmaximal, characteristic, complemented
13C2×#4961C211yesmaximal, characteristic, complemented
14C2×#4961C211yesmaximal, characteristic, complemented
15C2×#4957C211yesmaximal, characteristic, complemented
16C2×#4957C211yesmaximal, characteristic, complemented
17C2×#2682—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C24×C3×C4C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×#67C2211yescharacteristic
22C23×#67C2211yescharacteristic
23C23×#67C2211yescharacteristic
24C23×D12C2211yescharacteristic
25C23×C4×D3C2211yescharacteristic
26C2×C3×#123—28no—
27C2×C3×#123C2218yescomplemented
28C22×C3×C4⋊C4C2211yescharacteristic
29C22×C3×C4⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×C3×C22⋊C4C2211yescharacteristic
32C22×C3×C22⋊C4C2211yescharacteristic
33C22×#217C2211yescharacteristic
34C22×#217C2211yescharacteristic
35C22×#217C2211yescharacteristic
36C22×#217C2211yescharacteristic
37C2×#938—28no—
38C2×#938C2218yescomplemented
39C2×#930—28no—
40C2×#930C2218yescomplemented
41C22×(C2×D3)⋊C4C2211yescharacteristic
42C22×(C2×D3)⋊C4C2211yescharacteristic
43C22×(C2×D3)⋊C4C2211yescharacteristic
44C22×(C2×D3)⋊C4C2211yescharacteristic
45C22×(C2×D3)⋊C4C2211yescharacteristic
46C22×(C2×D3)⋊C4C2211yescharacteristic
47C22×(C2×D3)⋊C4C2211yescharacteristic
48C22×C4⋊Dic3C2211yescharacteristic
49C22×C4⋊Dic3C2211yescharacteristic
50C22×C4⋊Dic3C2211yescharacteristic
51C22×Dic3⋊C4C2211yescharacteristic
52C22×Dic3⋊C4C2211yescharacteristic
53C22×Dic3⋊C4C2211yescharacteristic
54C22×C4×Dic3C2211yescharacteristic
55C2×#894—28no—
56C2×#894C2218yescomplemented
57#5223C2218yescomplemented
58#5210C2218yescomplemented
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61C2×C3⋊#95C2211yescharacteristic
62C2×C3⋊#95C2211yescharacteristic
63#4994C2218yescomplemented
64#4989C2218yescomplemented
65#4984C2218yescomplemented
66#4961C2218yescomplemented
67#4961C2218yescomplemented
68#4960C2218yescomplemented
69#4957C2218yescomplemented
70#4957C2218yescomplemented
71#4948C2218yescomplemented
72C22×#123—31no—
73C22×#123D311yescharacteristic, complemented
74C22×#121—31no—
75C22×#121—31no—
76#2682—316no—
77C2×#396—31no—
78C2×#396—31no—
79C2×#394—31no—
80C2×#394—31no—
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—24no—
94C22×C3×D4—42no—
95C22×C3×D4C2314yes—
96C23×C3×C4—24no—
97C23×C3×C4—24no—
98C23×C3×C4—42no—
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2314yes—
102C23×C3×C4C2311yescharacteristic
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C22×#67—24no—
106C22×#67—24no—
107C22×#67—24no—
108C22×#67—42no—
109C22×#67—42no—
110C22×#67—42no—
111C22×#67—42no—
112C22×#67—42no—
113C22×#67—42no—
114C22×#67—42no—
115C22×#67—42no—
116C22×#67D418yescomplemented
117C22×#67C2314yes—
118C22×#67C2314yes—
119C22×#67C2314yes—
120C22×#67C2314yes—
121C23×Dic3C2311yescharacteristic
122C23×Dic3C2311yescharacteristic
123C23×Dic3C2311yescharacteristic
124C23×Dic3C2311yescharacteristic
125C23×Dic3C2311yescharacteristic
126C23×Dic3C2311yescharacteristic
127C22×D12—24no—
128C22×D12—24no—
129C22×D12—42no—
130C22×D12C2314yes—
131C22×C4×D3—24no—
132C22×C4×D3—24no—
133C22×C4×D3—42no—
134C22×C4×D3C2314yes—
135C3×#123—232no—
136C2×C3×C4⋊C4—24no—
137C2×C3×C4⋊C4D418yescomplemented
138C2×C3×C4⋊C4C2314yes—
139C2×C3×C4⋊C4C2314yes—
140C2×C3×C22⋊C4—24no—
141C2×C3×C22⋊C4—24no—
142C2×C3×C22⋊C4—24no—
143C2×C3×C22⋊C4C2314yes—
144C2×C3×C22⋊C4C2314yes—
145C2×C3×C22⋊C4C2314yes—
146C2×#217—24no—
147C2×#217—24no—
148C2×#217—24no—
149C2×#217—42no—
150C2×#217C2314yes—
151C2×#217C2314yes—
152C2×#217C2314yes—
153C2×#217C2314yes—
154#938—232no—
155#930—232no—
156C2×(C2×D3)⋊C4—24no—
157C2×(C2×D3)⋊C4—24no—
158C2×(C2×D3)⋊C4—24no—
159C2×(C2×D3)⋊C4—24no—
160C2×(C2×D3)⋊C4—24no—
161C2×(C2×D3)⋊C4—24no—
162C2×(C2×D3)⋊C4—42no—
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×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—42no—
178C2×Dic3⋊C4—42no—
179C2×Dic3⋊C4C2314yes—
180C2×Dic3⋊C4C2314yes—
181C2×Dic3⋊C4C2314yes—
182C2×C4×Dic3—42no—
183C2×C4×Dic3C2314yes—
184#894—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×C4C2×D311yescharacteristic
197C2×#123—28no—
198C2×#123—38no—
199C2×#123—68no—
200C2×#123C2×D318yescomplemented
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⋊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⋊C4—31no—
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#394—38no—
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×#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×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—28no—
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—28no—
288C22×C3×C4—22no—
289C22×C3×C4—22no—
290C22×C3×C4—22no—
291C22×C3×C4—22no—
292C22×C3×C4—22no—
293C22×C3×C4—28no—
294C22×C3×C4—44no—
295C22×C3×C4—416no—
296C22×C3×C4C2×D414yes—
297C22×C3×C4C2×D414yes—
298C22×C3×C4C2×D414yes—
299C22×C3×C4C2412yes—
300C22×C3×C4C2412yes—
301C22×C3×C4C2412yes—
302C22×C3×C4C2412yes—
303C22×C3×C4C2412yes—
304C2×#67—28no—
305C2×#67—28no—
306C2×#67—28no—
307C2×#67—416no—
308C2×#67—44no—
309C2×#67—44no—
310C2×#67—44no—
311C2×#67—44no—
312C2×#67—44no—
313C2×#67—44no—
314C2×#67—44no—
315C2×#67—44no—
316C2×#67—416no—
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×Dic3C2×D414yes—
337C22×Dic3#4114yes—
338C22×Dic3C2412yes—
339C22×Dic3C2412yes—
340C22×Dic3C2412yes—
341C22×Dic3C2412yes—
342C22×Dic3C2412yes—
343C22×Dic3C2412yes—
344C2×D12—28no—
345C2×D12—28no—
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—28no—
353C3×C4⋊C4C2×D4116yescomplemented
354C3×C22⋊C4—28no—
355C3×C22⋊C4—28no—
356C3×C22⋊C4—28no—
357#217—28no—
358#217—28no—
359#217—28no—
360#217—44no—
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—28no—
367(C2×D3)⋊C4—44no—
368C4⋊Dic3—28no—
369C4⋊Dic3—28no—
370C4⋊Dic3—44no—
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—24no—
381C22×D4—38no—
382C22×D4—34no—
383C22×D4—34no—
384C22×D4—34no—
385C22×D4—34no—
386C22×D4—34no—
387C22×D4—42no—
388C22×D4—64no—
389C22×D4—64no—
390C22×D4—64no—
391C22×D4—64no—
392C22×D4—64no—
393C22×D4—122no—
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—24no—
404C23×C4—24no—
405C23×C4—31no—
406C23×C4—31no—
407C23×C4—31no—
408C23×C4—31no—
409C23×C4—31no—
410C23×C4—31no—
411C23×C4—34no—
412C23×C4—42no—
413C23×C4—64no—
414C23×C4—64no—
415C23×C4—122no—
416C23×C4C22×D311yescharacteristic
417C23×C4C22×D311yescharacteristic
418C23×C4C22×D314yes—
419C23×C4C22×D311yescharacteristic
420C23×C4C22×D311yescharacteristic
421C23×C4C22×D311yescharacteristic
422#123—232no—
423#123—632no—
424#121—632no—
425#121—632no—
426C2×C4⋊C4—24no—
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—64no—
434C2×C4⋊C4—64no—
435C2×C4⋊C4—64no—
436C2×C4⋊C4—122no—
437C2×C4⋊C4—122no—
438C2×C4⋊C4—122no—
439C2×C4⋊C4#6718yescomplemented
440C2×C4⋊C4C22×D314yes—
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—34no—
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⋊C4—122no—
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#95—34no—
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—28no—
543C2×C3×C4—28no—
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—416no—
557C2×C3×C4—44no—
558C2×C3×C4—44no—
559C2×C3×C4C22×D414yes—
560C2×C3×C4C22×D414yes—
561C2×C3×C4C22×D414yes—
562#67—416no—
563#67—416no—
564#67—416no—
565#67—416no—
566C2×Dic3—28no—
567C2×Dic3—28no—
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—44no—
585C2×Dic3—44no—
586C2×Dic3—44no—
587C2×Dic3—44no—
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—28no—
627C2×D4—316no—
628C2×D4—44no—
629C2×D4—416no—
630C2×D4—68no—
631C2×D4—68no—
632C2×D4—68no—
633C2×D4—68no—
634C2×D4—68no—
635C2×D4—124no—
636C2×D4—1216no—
637C2×D4—1216no—
638C2×D4—124no—
639C2×D4—124no—
640C2×D4—124no—
641C2×D4—124no—
642C2×D4—124no—
643C2×D4—124no—
644C2×D4—124no—
645C2×D4—124no—
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—28no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—28no—
663C22×C4—34no—
664C22×C4—34no—
665C22×C4—32no—
666C22×C4—32no—
667C22×C4—32no—
668C22×C4—32no—
669C22×C4—32no—
670C22×C4—32no—
671C22×C4—44no—
672C22×C4—416no—
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—68no—
691C22×C4—124no—
692C22×C4—1216no—
693C22×C4C2×#6714yes—
694C22×C4C2×#6714yes—
695C22×C4C2×#6714yes—
696C22×C4C23×D312yes—
697C22×C4C23×D312yes—
698C22×C4C23×D312yes—
699C22×C4C23×D312yes—
700C22×C4C23×D312yes—
701C4⋊C4—28no—
702C4⋊C4—68no—
703C4⋊C4—68no—
704C4⋊C4—68no—
705C4⋊C4—124no—
706C4⋊C4—124no—
707C4⋊C4—124no—
708C4⋊C4C2×#67116yescomplemented
709C22⋊C4—28no—
710C22⋊C4—28no—
711C22⋊C4—28no—
712C22⋊C4—68no—
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—124no—
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—24no—
772C3×C4—24no—
773C3×C4—42no—
774C3×C4—42no—
775Dic3—24no—
776Dic3—24no—
777Dic3—42no—
778Dic3—42no—
779Dic3—42no—
780Dic3—42no—
781C23—28no—
782C23—28no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
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—68no—
811C23—62no—
812C23—62no—
813C23—62no—
814C23—62no—
815C23—62no—
816C23—62no—
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—
838C23#100412yes—
839C23D3×#4112yes—
840C23#100912yes—
841C23#100912yes—
842C23#101012yes—
843C23C22×#6712yes—
844C23C24×D311yescharacteristic
845D4—416no—
846D4—1216no—
847D4—1216no—
848D4—1216no—
849D4—1216no—
850D4—1216no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—28no—
858C2×C4—28no—
859C2×C4—28no—
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—416no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—68no—
872C2×C4—68no—
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—1216no—
890C2×C4—124no—
891C2×C4—124no—
892C2×C4—124no—
893C2×C4—124no—
894C2×C4C22×#6714yes—
895C2×C4C22×#6714yes—
896C2×C4C22×#6714yes—
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—416no—
913C22—42no—
914C22—42no—
915C22—42no—
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—1216no—
929C22—122no—
930C22—122no—
931C22—122no—
932C22—122no—
933C22—122no—
934C22—122no—
935C22—122no—
936C22—122no—
937C22—122no—
938C22—122no—
939C22—122no—
940C22—248no—
941C22#565314yes—
942C22#565514yes—
943C22#565714yes—
944C22#566714yes—
945C22D4×#6714yes—
946C22#583314yes—
947C22#583414yes—
948C22C22×D3×D411yescharacteristic
949C22C2×#100411yescharacteristic
950C22C2×D3×#4111yescharacteristic
951C22C2×#100911yescharacteristic
952C22C2×#100911yescharacteristic
953C22C2×#101011yescharacteristic
954C22C23×#6711yescharacteristic
955C4—24no—
956C4—24no—
957C4—24no—
958C4—42no—
959C4—42no—
960C4—64no—
961C4—64no—
962C4—122no—
963C4—122no—
964C4—122no—
965C4—122no—
966C3C2×#268211yescharacteristic, complemented, Sylow
967C2—44no—
968C2—82no—
969C2—124no—
970C2—242no—
971C2#8287318yesdirect product factor
972C2C2×#565311yescharacteristic
973C2C2×#565711yescharacteristic
974C2C2×#565511yescharacteristic
975C2C2×#566711yescharacteristic
976C2C2×D4×#6711yescharacteristic
977C2C2×#583311yescharacteristic
978C2C2×#583411yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC22×C3×#123C2
socleC24×C3C24
hypercenterC22×#123D3
hypocenterC3C2×#2682
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×C3×#123C2semidirect
2. C22×#938C2semidirect
3. C22×#930C2semidirect
4. C22×#894C2semidirect
5. C2×#5223C2semidirect
6. C2×#5210C2semidirect
7. #82873C2direct (N × H)
8. C2×#4994C2semidirect
9. C2×#4989C2semidirect
10. C2×#4984C2semidirect
11. C2×#4960C2semidirect
12. C2×#4948C2semidirect
13. C2×#4961C2semidirect
14. C2×#4961C2semidirect
15. C2×#4957C2semidirect
16. C2×#4957C2semidirect
27. C2×C3×#123C22semidirect
38. C2×#938C22semidirect
40. C2×#930C22semidirect
56. C2×#894C22semidirect
57. #5223C22semidirect
58. #5210C22semidirect
63. #4994C22semidirect
64. #4989C22semidirect
65. #4984C22semidirect
66. #4961C22semidirect
67. #4961C22semidirect
68. #4960C22semidirect
69. #4957C22semidirect
70. #4957C22semidirect
71. #4948C22semidirect
73. C22×#123D3semidirect
116. C22×#67D4semidirect
137. C2×C3×C4⋊C4D4semidirect
200. C2×#123C2×D3semidirect
319. C2×#67C2×D4semidirect
353. C3×C4⋊C4C2×D4semidirect
439. C2×C4⋊C4#67semidirect
708. C4⋊C4C2×#67semidirect
899. C2×C3#2682semidirect
966. C3C2×#2682semidirect
971. C2#82873direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1232
C22×#9382
C22×#9302
C22×#8942
C2×#52232
C2×#52102
#828732
C2×#49942
C2×#49892
C2×#49842
C2×#49602
C2×#49482
C2×#49612
C2×#49572
C2×#26823