Finite Group Databasebeta

← C2×#82691 #11430213

Subgroups — C2×#82691 #11430213

Order 768.

3542 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#121C211yesmaximal, characteristic, complemented
2C22×#939C211yesmaximal, characteristic, complemented
3C2×#5223C211yesmaximal, characteristic, complemented
4C2×#5223C211yesmaximal, characteristic, complemented
5C2×#5222C211yesmaximal, characteristic, complemented
6C2×#5221C211yesmaximal, characteristic, complemented
7C2×#5220C211yesmaximal, characteristic, complemented
8C2×#5213C211yesmaximal, characteristic, complemented
9C2×#5211C211yesmaximal, characteristic, complemented
10#82691C2116yesmaximal, direct product factor
11C2×#4982C211yesmaximal, characteristic, complemented
12C2×#4990C211yesmaximal, characteristic, complemented
13C2×#4959C211yesmaximal, characteristic, complemented
14C2×#4961C211yesmaximal, characteristic, complemented
15C2×#4945C211yesmaximal, characteristic, complemented
16C2×#4943C211yesmaximal, characteristic, complemented
17C2×#2699—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C23×C3×D4C2211yescharacteristic
21C24×C3×C4C2211yescharacteristic
22C23×#67C2211yescharacteristic
23C23×#67C2211yescharacteristic
24C23×#67C2211yescharacteristic
25C24×Dic3C2211yescharacteristic
26C2×C3×#121—28no—
27C2×C3×#121C2218yescomplemented
28C22×C3×C4⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C22×#217C2211yescharacteristic
34C22×#217C2211yescharacteristic
35C22×#217C2211yescharacteristic
36C22×#217C2211yescharacteristic
37C22×#217C2211yescharacteristic
38C22×#217C2211yescharacteristic
39C2×#939—28no—
40C2×#939C2218yescomplemented
41C22×(C2×D3)⋊C4C2211yescharacteristic
42C22×(C2×D3)⋊C4C2211yescharacteristic
43C22×(C2×D3)⋊C4C2211yescharacteristic
44C22×(C2×D3)⋊C4C2211yescharacteristic
45C22×C4⋊Dic3C2211yescharacteristic
46C22×Dic3⋊C4C2211yescharacteristic
47C22×Dic3⋊C4C2211yescharacteristic
48C22×C4×Dic3C2211yescharacteristic
49#5223C2218yescomplemented
50#5223C2218yescomplemented
51#5222C2218yescomplemented
52#5221C2218yescomplemented
53#5220C2218yescomplemented
54#5213C2218yescomplemented
55#5211C2218yescomplemented
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61C2×C3⋊#95C2211yescharacteristic
62C2×C3⋊#95C2211yescharacteristic
63C2×C3⋊#95C2211yescharacteristic
64#4990C2218yescomplemented
65#4982C2218yescomplemented
66#4961C2218yescomplemented
67#4959C2218yescomplemented
68#4945C2218yescomplemented
69#4943C2218yescomplemented
70C22×#121—31no—
71C22×#121D311yescharacteristic, complemented
72#2699—316no—
73C2×#398—31no—
74C2×#394—31no—
75C2×#394—31no—
76C2×#394—31no—
77C2×#392—31no—
78C2×#392—31no—
79C2×#390—31no—
80C2×#388—31no—
81C2×#388—31no—
82C2×#386—31no—
83C2×#386—31no—
84C2×#381—31no—
85C2×#381—31no—
86C25×C3C2311yescharacteristic
87C25×C3C2311yescharacteristic
88C25×C3C2311yescharacteristic
89C24×D3C2311yescharacteristic
90C22×C3×D4—24no—
91C22×C3×D4—24no—
92C22×C3×D4—24no—
93C22×C3×D4—42no—
94C22×C3×D4—42no—
95C22×C3×D4—42no—
96C22×C3×D4—42no—
97C22×C3×D4—42no—
98C22×C3×D4D418yescomplemented
99C22×C3×D4C2314yes—
100C22×C3×D4C2314yes—
101C22×C3×D4C2314yes—
102C23×C3×C4—24no—
103C23×C3×C4—24no—
104C23×C3×C4—42no—
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2314yes—
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2311yescharacteristic
110C22×#67—24no—
111C22×#67—24no—
112C22×#67—24no—
113C22×#67—42no—
114C22×#67—42no—
115C22×#67—42no—
116C22×#67—42no—
117C22×#67—42no—
118C22×#67—42no—
119C22×#67C2314yes—
120C22×#67C2314yes—
121C22×#67C2314yes—
122C23×Dic3—24no—
123C23×Dic3—24no—
124C23×Dic3—42no—
125C23×Dic3C2311yescharacteristic
126C23×Dic3C2311yescharacteristic
127C23×Dic3C2311yescharacteristic
128C23×Dic3C2311yescharacteristic
129C23×Dic3C2311yescharacteristic
130C23×Dic3C2311yescharacteristic
131C23×Dic3C2314yes—
132C23×Dic3C2311yescharacteristic
133C3×#121—232no—
134C2×C3×C4⋊C4—24no—
135C2×C3×C4⋊C4C2314yes—
136C2×C3×C22⋊C4—24no—
137C2×C3×C22⋊C4—24no—
138C2×C3×C22⋊C4C2314yes—
139C2×C3×C22⋊C4C2314yes—
140C2×#217—24no—
141C2×#217—24no—
142C2×#217—42no—
143C2×#217—42no—
144C2×#217—42no—
145C2×#217—42no—
146C2×#217—42no—
147C2×#217—42no—
148C2×#217C2314yes—
149C2×#217C2314yes—
150C2×#217C2314yes—
151C2×#217C2314yes—
152C2×#217C2314yes—
153C2×#217C2314yes—
154C2×#217C2314yes—
155C2×#217C2314yes—
156#939—232no—
157C2×(C2×D3)⋊C4—24no—
158C2×(C2×D3)⋊C4—24no—
159C2×(C2×D3)⋊C4—42no—
160C2×(C2×D3)⋊C4—42no—
161C2×(C2×D3)⋊C4C2314yes—
162C2×(C2×D3)⋊C4C2314yes—
163C2×(C2×D3)⋊C4C2314yes—
164C2×(C2×D3)⋊C4C2314yes—
165C2×C4⋊Dic3—42no—
166C2×C4⋊Dic3C2314yes—
167C2×Dic3⋊C4—24no—
168C2×Dic3⋊C4—42no—
169C2×Dic3⋊C4C2314yes—
170C2×Dic3⋊C4C2314yes—
171C2×C4×Dic3—42no—
172C2×C4×Dic3C2314yes—
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×D4C2×D311yescharacteristic
185C23×D4C2×D311yescharacteristic
186C23×D4C2×D311yescharacteristic
187C24×C4—31no—
188C24×C4C2×D311yescharacteristic
189C2×#121—28no—
190C2×#121—38no—
191C2×#121—68no—
192C2×#121C2×D318yescomplemented
193C22×C4⋊C4—31no—
194C22×C4⋊C4—31no—
195C22×C4⋊C4—31no—
196C22×C4⋊C4C2×D311yescharacteristic
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⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4C2×D311yescharacteristic
210C22×C22⋊C4C2×D311yescharacteristic
211C22×C42—31no—
212#398—38no—
213#394—38no—
214#394—38no—
215#394—38no—
216#392—38no—
217#392—38no—
218#390—38no—
219#388—38no—
220#388—38no—
221#386—38no—
222#386—38no—
223#381—38no—
224#381—38no—
225C2×#95—31no—
226C2×#95—31no—
227C2×#95—31no—
228C2×#95—31no—
229C2×#95—31no—
230C2×#95—31no—
231C2×#95—31no—
232C2×#95—31no—
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×C3—22no—
247C24×C3—22no—
248C24×C3—22no—
249C24×C3—22no—
250C24×C3—22no—
251C24×C3—22no—
252C24×C3C2×D414yes—
253C24×C3C2×D414yes—
254C24×C3C2412yes—
255C24×C3C2412yes—
256C24×C3C2412yes—
257C24×C3C2411yescharacteristic
258C23×D3—22no—
259C23×D3—22no—
260C23×D3—22no—
261C23×D3—22no—
262C23×D3—22no—
263C23×D3—22no—
264C23×D3—22no—
265C23×D3C2412yes—
266C2×C3×D4—28no—
267C2×C3×D4—28no—
268C2×C3×D4—28no—
269C2×C3×D4—416no—
270C2×C3×D4—44no—
271C2×C3×D4—44no—
272C2×C3×D4—44no—
273C2×C3×D4—44no—
274C2×C3×D4—44no—
275C2×C3×D4—416no—
276C2×C3×D4—416no—
277C2×C3×D4C2×D4116yescomplemented
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—28no—
285C22×C3×C4—22no—
286C22×C3×C4—22no—
287C22×C3×C4—22no—
288C22×C3×C4—22no—
289C22×C3×C4—28no—
290C22×C3×C4—44no—
291C22×C3×C4—416no—
292C22×C3×C4C2×D414yes—
293C22×C3×C4#4114yes—
294C22×C3×C4C2412yes—
295C22×C3×C4C2412yes—
296C22×C3×C4C2412yes—
297C22×C3×C4C2412yes—
298C2×#67—28no—
299C2×#67—28no—
300C2×#67—28no—
301C2×#67—44no—
302C2×#67—44no—
303C2×#67—44no—
304C2×#67—44no—
305C2×#67—44no—
306C2×#67—44no—
307C2×#67—416no—
308C2×#67—416no—
309C2×#67—416no—
310C22×Dic3—22no—
311C22×Dic3—22no—
312C22×Dic3—22no—
313C22×Dic3—22no—
314C22×Dic3—28no—
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×Dic3—22no—
328C22×Dic3—22no—
329C22×Dic3—22no—
330C22×Dic3—22no—
331C22×Dic3—28no—
332C22×Dic3—44no—
333C22×Dic3—416no—
334C22×Dic3#4114yes—
335C22×Dic3C2412yes—
336C22×Dic3C2412yes—
337C22×Dic3C2412yes—
338C22×Dic3C2412yes—
339C22×Dic3C2412yes—
340C22×Dic3C2412yes—
341C22×Dic3C2412yes—
342C3×C4⋊C4—28no—
343C3×C22⋊C4—28no—
344C3×C22⋊C4—28no—
345#217—28no—
346#217—28no—
347#217—44no—
348#217—44no—
349#217—44no—
350#217—44no—
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—
357C4⋊Dic3—44no—
358Dic3⋊C4—28no—
359Dic3⋊C4—44no—
360C4×Dic3—44no—
361C25—31no—
362C25C22×D311yescharacteristic
363C25C22×D311yescharacteristic
364C25C22×D311yescharacteristic
365C22×D4—24no—
366C22×D4—24no—
367C22×D4—24no—
368C22×D4—34no—
369C22×D4—34no—
370C22×D4—34no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4—64no—
377C22×D4—64no—
378C22×D4—64no—
379C22×D4—122no—
380C22×D4—122no—
381C22×D4—122no—
382C22×D4—122no—
383C22×D4—122no—
384C22×D4—122no—
385C22×D4#6718yescomplemented
386C22×D4C22×D314yes—
387C22×D4C22×D314yes—
388C22×D4C22×D314yes—
389C23×C4—24no—
390C23×C4—24no—
391C23×C4—31no—
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—31no—
395C23×C4—31no—
396C23×C4—31no—
397C23×C4—31no—
398C23×C4—34no—
399C23×C4—42no—
400C23×C4—64no—
401C23×C4—64no—
402C23×C4—122no—
403C23×C4C22×D311yescharacteristic
404C23×C4C22×D311yescharacteristic
405C23×C4C22×D314yes—
406C23×C4C22×D311yescharacteristic
407C23×C4C22×D311yescharacteristic
408#121—232no—
409#121—632no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—34no—
412C2×C4⋊C4—34no—
413C2×C4⋊C4—34no—
414C2×C4⋊C4—64no—
415C2×C4⋊C4—122no—
416C2×C4⋊C4—122no—
417C2×C4⋊C4C22×D314yes—
418C2×C22⋊C4—24no—
419C2×C22⋊C4—24no—
420C2×C22⋊C4—34no—
421C2×C22⋊C4—34no—
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—64no—
433C2×C22⋊C4—64no—
434C2×C22⋊C4—64no—
435C2×C22⋊C4—64no—
436C2×C22⋊C4—122no—
437C2×C22⋊C4—122no—
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×C42—34no—
447C2×C42—122no—
448#95—34no—
449#95—34no—
450#95—34no—
451#95—34no—
452#95—34no—
453#95—34no—
454#95—34no—
455#95—34no—
456C23×C3—28no—
457C23×C3—28no—
458C23×C3—28no—
459C23×C3—28no—
460C23×C3—28no—
461C23×C3—28no—
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—22no—
474C23×C3—22no—
475C23×C3—22no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—44no—
482C23×C3—44no—
483C23×C3—44no—
484C23×C3—44no—
485C23×C3—44no—
486C23×C3—44no—
487C23×C3—44no—
488C23×C3—44no—
489C23×C3—44no—
490C23×C3—44no—
491C23×C3—44no—
492C23×C3—44no—
493C23×C3—44no—
494C23×C3—44no—
495C23×C3—44no—
496C23×C3C22×D414yes—
497C23×C3C22×D414yes—
498C23×C3C22×D412yes—
499C23×C3C2×#4112yes—
500C23×C3C2×#4112yes—
501C23×C3H(5,𝔽2)12yes—
502C23×C3H(5,𝔽2)12yes—
503C23×C3H(5,𝔽2)12yes—
504C23×C3H(5,𝔽2)12yes—
505C23×C3C2511yescharacteristic
506C22×D3—22no—
507C22×D3—22no—
508C22×D3—22no—
509C22×D3—22no—
510C22×D3—22no—
511C22×D3—22no—
512C22×D3—22no—
513C22×D3—44no—
514C22×D3—44no—
515C22×D3—44no—
516C22×D3—44no—
517C22×D3—44no—
518C22×D3—44no—
519C22×D3—44no—
520C3×D4—416no—
521C3×D4—416no—
522C3×D4—416no—
523C2×C3×C4—28no—
524C2×C3×C4—28no—
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—416no—
536C2×C3×C4—44no—
537C2×C3×C4—44no—
538C2×C3×C4C22×D414yes—
539C2×C3×C4C2×#4114yes—
540#67—416no—
541#67—416no—
542#67—416no—
543C2×Dic3—28no—
544C2×Dic3—22no—
545C2×Dic3—22no—
546C2×Dic3—22no—
547C2×Dic3—22no—
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—416no—
565C2×Dic3—44no—
566C2×Dic3—44no—
567C2×Dic3—44no—
568C2×Dic3—44no—
569C2×Dic3—44no—
570C2×Dic3—44no—
571C2×Dic3C2×#4114yes—
572C24—22no—
573C24—22no—
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—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—32no—
592C24—62no—
593C24—62no—
594C24—62no—
595C24—62no—
596C24—62no—
597C24—62no—
598C24—62no—
599C24C2×#6714yes—
600C24C2×#6714yes—
601C24C23×D312yes—
602C24C23×D312yes—
603C24C23×D312yes—
604C24C23×D311yescharacteristic
605C2×D4—28no—
606C2×D4—28no—
607C2×D4—28no—
608C2×D4—416no—
609C2×D4—44no—
610C2×D4—44no—
611C2×D4—44no—
612C2×D4—44no—
613C2×D4—44no—
614C2×D4—416no—
615C2×D4—416no—
616C2×D4—68no—
617C2×D4—68no—
618C2×D4—68no—
619C2×D4—124no—
620C2×D4—124no—
621C2×D4—124no—
622C2×D4—124no—
623C2×D4—124no—
624C2×D4—124no—
625C2×D4—1216no—
626C2×D4—1216no—
627C2×D4—1216no—
628C2×D4C2×#67116yescomplemented
629C22×C4—22no—
630C22×C4—22no—
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—28no—
640C22×C4—28no—
641C22×C4—34no—
642C22×C4—32no—
643C22×C4—32no—
644C22×C4—32no—
645C22×C4—32no—
646C22×C4—32no—
647C22×C4—32no—
648C22×C4—32no—
649C22×C4—44no—
650C22×C4—416no—
651C22×C4—68no—
652C22×C4—62no—
653C22×C4—62no—
654C22×C4—62no—
655C22×C4—62no—
656C22×C4—62no—
657C22×C4—62no—
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—68no—
673C22×C4—124no—
674C22×C4—1216no—
675C22×C4#23714yes—
676C22×C4C2×#6714yes—
677C22×C4C23×D312yes—
678C22×C4C23×D312yes—
679C22×C4C23×D312yes—
680C22×C4C23×D312yes—
681C4⋊C4—28no—
682C4⋊C4—68no—
683C4⋊C4—124no—
684C4⋊C4—124no—
685C22⋊C4—28no—
686C22⋊C4—28no—
687C22⋊C4—68no—
688C22⋊C4—68no—
689C22⋊C4—68no—
690C22⋊C4—68no—
691C22⋊C4—124no—
692C22⋊C4—124no—
693C22⋊C4—124no—
694C22⋊C4—124no—
695C22⋊C4—124no—
696C22⋊C4—124no—
697C22⋊C4—124no—
698C22⋊C4—124no—
699C42—124no—
700C22×C3—24no—
701C22×C3—24no—
702C22×C3—24no—
703C22×C3—24no—
704C22×C3—24no—
705C22×C3—24no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—42no—
709C22×C3—42no—
710C22×C3—416no—
711C22×C3—416no—
712C22×C3—42no—
713C22×C3—42no—
714C22×C3—42no—
715C22×C3—42no—
716C22×C3—42no—
717C22×C3—42no—
718C22×C3—42no—
719C22×C3—42no—
720C22×C3—42no—
721C22×C3—42no—
722C22×C3—42no—
723C22×C3—88no—
724C22×C3#53414yes—
725C22×C3#54014yes—
726C22×C3#54014yes—
727C22×C3#54614yes—
728C22×C3#54614yes—
729C22×C3#55514yes—
730C22×C3#56014yes—
731C22×C3C23×D411yescharacteristic
732C22×C3C22×#4111yescharacteristic
733C22×C3C22×#4111yescharacteristic
734C22×C3C2×H(5,𝔽2)11yescharacteristic
735C22×C3C2×H(5,𝔽2)11yescharacteristic
736C22×C3C2×H(5,𝔽2)11yescharacteristic
737C22×C3C2×H(5,𝔽2)11yescharacteristic
738C2×D3—42no—
739C2×D3—42no—
740C2×D3—42no—
741C2×D3—42no—
742C2×D3—42no—
743C2×D3—42no—
744C2×D3—42no—
745C2×D3—88no—
746C3×C4—24no—
747C3×C4—24no—
748C3×C4—42no—
749C3×C4—42no—
750Dic3—24no—
751Dic3—42no—
752Dic3—42no—
753Dic3—42no—
754Dic3—42no—
755Dic3—42no—
756Dic3—42no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—28no—
770C23—28no—
771C23—28no—
772C23—28no—
773C23—28no—
774C23—28no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—44no—
789C23—44no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—62no—
798C23—62no—
799C23—62no—
800C23—62no—
801C23—62no—
802C23—62no—
803C23—62no—
804C23—124no—
805C23—124no—
806C23—124no—
807C23—124no—
808C23—124no—
809C23—124no—
810C23—124no—
811C23C2×#23712yes—
812C23#100412yes—
813C23#100412yes—
814C23#100412yes—
815C23D3×#4112yes—
816C23#100912yes—
817C23C22×#6714yes—
818C23C22×#6714yes—
819C23C22×#6712yes—
820C23C24×D311yescharacteristic
821D4—416no—
822D4—416no—
823D4—416no—
824D4—1216no—
825D4—1216no—
826D4—1216no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—28no—
832C2×C4—28no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—34no—
840C2×C4—416no—
841C2×C4—44no—
842C2×C4—44no—
843C2×C4—62no—
844C2×C4—62no—
845C2×C4—68no—
846C2×C4—62no—
847C2×C4—62no—
848C2×C4—62no—
849C2×C4—62no—
850C2×C4—62no—
851C2×C4—62no—
852C2×C4—62no—
853C2×C4—62no—
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—1216no—
865C2×C4—124no—
866C2×C4—124no—
867C2×C4—124no—
868C2×C4—124no—
869C2×C4—124no—
870C2×C4—124no—
871C2×C4C2×#23714yes—
872C2×C4C22×#6714yes—
873C2×C3—44no—
874C2×C3—44no—
875C2×C3—82no—
876C2×C3#269918yescomplemented
877C2×C3C2×#53411yescharacteristic
878C2×C3C2×#54011yescharacteristic
879C2×C3C2×#54011yescharacteristic
880C2×C3C2×#54611yescharacteristic
881C2×C3C2×#54611yescharacteristic
882C2×C3C2×#55511yescharacteristic
883C2×C3C2×#56011yescharacteristic
884D3—82no—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—416no—
892C22—416no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—88no—
909C22—122no—
910C22—122no—
911C22—122no—
912C22—122no—
913C22—122no—
914C22—122no—
915C22—122no—
916C22—248no—
917C22#561514yes—
918C22#561614yes—
919C22#561914yes—
920C22#562014yes—
921C22#580414yes—
922C22#580614yes—
923C22#582914yes—
924C22C22×#23711yescharacteristic
925C22C2×#100411yescharacteristic
926C22C2×#100411yescharacteristic
927C22C2×#100411yescharacteristic
928C22C2×D3×#4111yescharacteristic
929C22C2×#100911yescharacteristic
930C22C23×#6711yescharacteristic
931C4—24no—
932C4—24no—
933C4—42no—
934C4—42no—
935C4—64no—
936C4—122no—
937C4—122no—
938C4—122no—
939C4—122no—
940C4—122no—
941C4—122no—
942C3C2×#269911yescharacteristic, complemented, Sylow
943C2—44no—
944C2—44no—
945C2—82no—
946C2—242no—
947C2#8269118yesdirect product factor
948C2C2×#561911yescharacteristic
949C2C2×#561511yescharacteristic
950C2C2×#561611yescharacteristic
951C2C2×#562011yescharacteristic
952C2C2×#580611yescharacteristic
953C2C2×#580411yescharacteristic
954C2C2×#582911yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC22×C3×#121C2
socleC24×C3C24
hypercenterC22×#121D3
hypocenterC3C2×#2699
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×#939C2semidirect
3. C2×#5223C2semidirect
4. C2×#5223C2semidirect
5. C2×#5222C2semidirect
6. C2×#5221C2semidirect
7. C2×#5220C2semidirect
8. C2×#5213C2semidirect
9. C2×#5211C2semidirect
10. #82691C2direct (N × H)
11. C2×#4982C2semidirect
12. C2×#4990C2semidirect
13. C2×#4959C2semidirect
14. C2×#4961C2semidirect
15. C2×#4945C2semidirect
16. C2×#4943C2semidirect
27. C2×C3×#121C22semidirect
40. C2×#939C22semidirect
49. #5223C22semidirect
50. #5223C22semidirect
51. #5222C22semidirect
52. #5221C22semidirect
53. #5220C22semidirect
54. #5213C22semidirect
55. #5211C22semidirect
64. #4990C22semidirect
65. #4982C22semidirect
66. #4961C22semidirect
67. #4959C22semidirect
68. #4945C22semidirect
69. #4943C22semidirect
71. C22×#121D3semidirect
98. C22×C3×D4D4semidirect
192. C2×#121C2×D3semidirect
277. C2×C3×D4C2×D4semidirect
385. C22×D4#67semidirect
628. C2×D4C2×#67semidirect
876. C2×C3#2699semidirect
942. C3C2×#2699semidirect
947. C2#82691direct (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×#9392
C2×#52232
C2×#52222
C2×#52212
C2×#52202
C2×#52132
C2×#52112
#826912
C2×#49822
C2×#49902
C2×#49592
C2×#49612
C2×#49452
C2×#49432
C2×#26993