Finite Group Databasebeta

← C2×#74794 #11429924

Subgroups — C2×#74794 #11429924

Order 768.

3610 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#939C211yesmaximal, characteristic
2C22×#929C211yesmaximal, characteristic, complemented
3C22×#924C211yesmaximal, characteristic, complemented
4C22×#878C211yesmaximal, characteristic, complemented
5C2×C3×#386C211yesmaximal, characteristic, complemented
6C2×#5222C211yesmaximal, characteristic, complemented
7C2×#4961C211yesmaximal, characteristic, complemented
8C2×#4961C211yesmaximal, characteristic, complemented
9C2×#4957C211yesmaximal, characteristic, complemented
10C2×#4944C211yesmaximal, characteristic, complemented
11C2×#4946C211yesmaximal, characteristic, complemented
12#74794C2116yesmaximal, direct product factor
13C2×#4676C211yesmaximal, characteristic, complemented
14C2×#4673C211yesmaximal, characteristic, complemented
15C2×#4657C211yesmaximal, characteristic, complemented
16C2×#4647C211yesmaximal, characteristic, complemented
17C2×#2681—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C24×C3×C4C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×#67C2211yescharacteristic
22C24×Dic3C2211yescharacteristic
23C23×Dic6C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C2×#939—28no—
33C2×#939C2218yes—
34C2×#929—28no—
35C2×#929C2218yescomplemented
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×(C2×D3)⋊C4C2211yescharacteristic
38C22×(C2×D3)⋊C4C2211yescharacteristic
39C22×(C2×D3)⋊C4C2211yescharacteristic
40C22×(C2×D3)⋊C4C2211yescharacteristic
41C22×C4⋊Dic3C2211yescharacteristic
42C22×C4⋊Dic3C2211yescharacteristic
43C2×#924—28no—
44C2×#924C2218yescomplemented
45C22×Dic3⋊C4C2211yescharacteristic
46C22×Dic3⋊C4C2211yescharacteristic
47C22×Dic3⋊C4C2211yescharacteristic
48C22×Dic3⋊C4C2211yescharacteristic
49C22×Dic3⋊C4C2211yescharacteristic
50C22×Dic3⋊C4C2211yescharacteristic
51C22×Dic3⋊C4C2211yescharacteristic
52C22×C4×Dic3C2211yescharacteristic
53C2×#878—28no—
54C2×#878C2218yescomplemented
55C3×#386C2218yescomplemented
56C2×C3×#95C2211yescharacteristic
57C2×C3×#95C2211yescharacteristic
58#5222C2218yescomplemented
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61C2×C3⋊#95C2211yescharacteristic
62C2×C3⋊#95C2211yescharacteristic
63#4961C2218yescomplemented
64#4961C2218yescomplemented
65#4957C2218yescomplemented
66#4946C2218yescomplemented
67#4944C2218yescomplemented
68#4676C2218yescomplemented
69#4673C2218yescomplemented
70#4657C2218yescomplemented
71#4647C2218yescomplemented
72C22×#123—31no—
73C22×C22⋊Q8—31no—
74C22×C22⋊Q8—31no—
75C22×#121—31no—
76#2681—316no—
77C2×#398—31no—
78C2×#396—31no—
79C2×#394—31no—
80C2×#394—31no—
81C2×#394—31no—
82C2×#393—31no—
83C2×#390—31no—
84C2×#389—31no—
85C2×#388—31no—
86C2×#386D311yescharacteristic, complemented
87C2×#385—31no—
88C25×C3C2311yescharacteristic
89C25×C3C2311yescharacteristic
90C24×D3C2311yescharacteristic
91C22×C3×D4—24no—
92C22×C3×D4—24no—
93C22×C3×D4—42no—
94C22×C3×D4C2314yes—
95C23×C3×C4—24no—
96C23×C3×C4—24no—
97C23×C3×C4—42no—
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C2314yes—
103C23×C3×C4C2311yescharacteristic
104C22×#67—24no—
105C22×#67—24no—
106C22×#67—24no—
107C22×#67—24no—
108C22×#67—42no—
109C22×#67—42no—
110C22×#67C2314yes—
111C22×#67C2314yes—
112C23×Dic3—24no—
113C23×Dic3—24no—
114C23×Dic3—42no—
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2311yescharacteristic
117C23×Dic3C2311yescharacteristic
118C23×Dic3C2314yes—
119C23×Dic3C2311yescharacteristic
120C23×Dic3C2311yescharacteristic
121C23×Dic3C2311yescharacteristic
122C23×Dic3C2311yescharacteristic
123C22×Dic6—24no—
124C22×Dic6—24no—
125C22×Dic6—42no—
126C22×Dic6C2314yes—
127C2×C3×C22⋊C4—24no—
128C2×C3×C22⋊C4—42no—
129C2×C3×C22⋊C4—42no—
130C2×C3×C22⋊C4C2314yes—
131C2×C3×C22⋊C4C2314yes—
132C2×C3×C22⋊C4C2314yes—
133C2×#217—24no—
134C2×#217—24no—
135C2×#217—24no—
136C2×#217—24no—
137C2×#217D418yes—
138C2×#217C2314yes—
139C2×#217C2314yes—
140C2×#217C2314yes—
141C2×#217C2314yes—
142C2×#217C2314yes—
143#939—232no—
144#929—232no—
145C2×(C2×D3)⋊C4—24no—
146C2×(C2×D3)⋊C4—24no—
147C2×(C2×D3)⋊C4—24no—
148C2×(C2×D3)⋊C4—42no—
149C2×(C2×D3)⋊C4—42no—
150C2×(C2×D3)⋊C4C2314yes—
151C2×(C2×D3)⋊C4C2314yes—
152C2×(C2×D3)⋊C4C2314yes—
153C2×(C2×D3)⋊C4C2314yes—
154C2×(C2×D3)⋊C4C2314yes—
155C2×C4⋊Dic3—24no—
156C2×C4⋊Dic3—24no—
157C2×C4⋊Dic3C2314yes—
158C2×C4⋊Dic3C2314yes—
159#924—232no—
160C2×Dic3⋊C4—24no—
161C2×Dic3⋊C4—24no—
162C2×Dic3⋊C4—24no—
163C2×Dic3⋊C4—24no—
164C2×Dic3⋊C4—24no—
165C2×Dic3⋊C4—42no—
166C2×Dic3⋊C4D418yescomplemented
167C2×Dic3⋊C4C2314yes—
168C2×Dic3⋊C4C2314yes—
169C2×Dic3⋊C4C2314yes—
170C2×Dic3⋊C4C2314yes—
171C2×Dic3⋊C4C2314yes—
172C2×Dic3⋊C4C2314yes—
173C2×Dic3⋊C4C2314yes—
174C2×C4×Dic3—42no—
175C2×C4×Dic3C2314yes—
176#878—232no—
177C3×#95C2314yes—
178C3×#95C2314yes—
179C3⋊#95C2314yes—
180C3⋊#95C2314yes—
181C3⋊#95C2314yes—
182C3⋊#95C2314yes—
183C23×Q8—31no—
184C23×D4—31no—
185C23×D4—31no—
186C23×D4C2×D311yescharacteristic
187C24×C4—31no—
188C24×C4C2×D311yescharacteristic
189C2×#123—38no—
190C2×#123—68no—
191C2×C22⋊Q8—38no—
192C2×C22⋊Q8—38no—
193C2×C22⋊Q8—68no—
194C2×C22⋊Q8—68no—
195C2×#121—38no—
196C2×#121—68no—
197C22×C4⋊C4—31no—
198C22×C4⋊C4—31no—
199C22×C4⋊C4—31no—
200C22×C4⋊C4—31no—
201C22×C4⋊C4—31no—
202C22×C4⋊C4—31no—
203C22×C4⋊C4—31no—
204C22×C4⋊C4—31no—
205C22×C4⋊C4—31no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4—31no—
210C22×C22⋊C4—31no—
211C22×C22⋊C4—31no—
212C22×C22⋊C4—31no—
213C22×C22⋊C4—31no—
214C22×C22⋊C4—31no—
215C22×C22⋊C4—31no—
216C22×C22⋊C4C2×D311yescharacteristic
217C22×C22⋊C4C2×D311yescharacteristic
218C22×C22⋊C4C2×D311yescharacteristic
219C22×C42—31no—
220#398—38no—
221#396—38no—
222#394—38no—
223#394—38no—
224#394—38no—
225#393—38no—
226#390—38no—
227#389—38no—
228#388—38no—
229#386C2×D318yescomplemented
230#385—38no—
231C2×#95—31no—
232C2×#95—31no—
233C2×#95—31no—
234C2×#95—31no—
235C2×#95C2×D311yescharacteristic
236C2×#95C2×D311yescharacteristic
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×C3C2×D414yes—
250C24×C3#4114yes—
251C24×C3C2412yes—
252C24×C3C2412yes—
253C24×C3C2411yescharacteristic
254C23×D3—22no—
255C23×D3—22no—
256C23×D3—22no—
257C23×D3—22no—
258C23×D3—22no—
259C23×D3—22no—
260C23×D3—22no—
261C23×D3C2412yes—
262C2×C3×D4—28no—
263C2×C3×D4—28no—
264C2×C3×D4—44no—
265C2×C3×D4—416no—
266C22×C3×C4—22no—
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—28no—
273C22×C3×C4—22no—
274C22×C3×C4—22no—
275C22×C3×C4—22no—
276C22×C3×C4—22no—
277C22×C3×C4—22no—
278C22×C3×C4—22no—
279C22×C3×C4—22no—
280C22×C3×C4—22no—
281C22×C3×C4—28no—
282C22×C3×C4—44no—
283C22×C3×C4—416no—
284C22×C3×C4C2×D414yes—
285C22×C3×C4C2412yes—
286C22×C3×C4C2412yes—
287C22×C3×C4C2412yes—
288C22×C3×C4C2412yes—
289C22×C3×C4C2412yes—
290C2×#67—28no—
291C2×#67—28no—
292C2×#67—28no—
293C2×#67—28no—
294C2×#67—44no—
295C2×#67—44no—
296C2×#67—416no—
297C2×#67—416no—
298C22×Dic3—22no—
299C22×Dic3—22no—
300C22×Dic3—22no—
301C22×Dic3—22no—
302C22×Dic3—22no—
303C22×Dic3—22no—
304C22×Dic3—22no—
305C22×Dic3—22no—
306C22×Dic3—22no—
307C22×Dic3—22no—
308C22×Dic3—22no—
309C22×Dic3—22no—
310C22×Dic3—22no—
311C22×Dic3—22no—
312C22×Dic3—22no—
313C22×Dic3—22no—
314C22×Dic3—22no—
315C22×Dic3—28no—
316C22×Dic3—28no—
317C22×Dic3—44no—
318C22×Dic3—416no—
319C22×Dic3C2×D414yes—
320C22×Dic3C2×D414yes—
321C22×Dic3C2×D414yes—
322C22×Dic3C2×D414yes—
323C22×Dic3C2412yes—
324C22×Dic3C2412yes—
325C22×Dic3C2412yes—
326C22×Dic3C2412yes—
327C22×Dic3C2412yes—
328C22×Dic3C2412yes—
329C22×Dic3C2412yes—
330C2×Dic6—28no—
331C2×Dic6—28no—
332C2×Dic6—44no—
333C2×Dic6—416no—
334C3×C22⋊C4—28no—
335C3×C22⋊C4—44no—
336C3×C22⋊C4—44no—
337#217—28no—
338#217—28no—
339#217—28no—
340#217—28no—
341#217C2×D4116yes—
342(C2×D3)⋊C4—28no—
343(C2×D3)⋊C4—28no—
344(C2×D3)⋊C4—28no—
345(C2×D3)⋊C4—44no—
346(C2×D3)⋊C4—44no—
347C4⋊Dic3—28no—
348C4⋊Dic3—28no—
349Dic3⋊C4—28no—
350Dic3⋊C4—28no—
351Dic3⋊C4—28no—
352Dic3⋊C4—28no—
353Dic3⋊C4—28no—
354Dic3⋊C4—44no—
355Dic3⋊C4C2×D4116yescomplemented
356C4×Dic3—44no—
357C25—31no—
358C25C22×D311yescharacteristic
359C25C22×D311yescharacteristic
360C22×Q8—34no—
361C22×Q8—64no—
362C22×Q8—64no—
363C22×Q8—122no—
364C22×D4—24no—
365C22×D4—24no—
366C22×D4—34no—
367C22×D4—34no—
368C22×D4—42no—
369C22×D4—64no—
370C22×D4—64no—
371C22×D4—64no—
372C22×D4—64no—
373C22×D4—122no—
374C22×D4—122no—
375C22×D4C22×D314yes—
376C23×C4—24no—
377C23×C4—24no—
378C23×C4—31no—
379C23×C4—31no—
380C23×C4—31no—
381C23×C4—31no—
382C23×C4—31no—
383C23×C4—31no—
384C23×C4—31no—
385C23×C4—34no—
386C23×C4—42no—
387C23×C4—64no—
388C23×C4—64no—
389C23×C4—122no—
390C23×C4C22×D311yescharacteristic
391C23×C4C22×D311yescharacteristic
392C23×C4C22×D311yescharacteristic
393C23×C4C22×D311yescharacteristic
394C23×C4C22×D314yes—
395C23×C4C22×D311yescharacteristic
396#123—632no—
397C22⋊Q8—632no—
398C22⋊Q8—632no—
399#121—632no—
400C2×C4⋊C4—38no—
401C2×C4⋊C4—34no—
402C2×C4⋊C4—34no—
403C2×C4⋊C4—34no—
404C2×C4⋊C4—34no—
405C2×C4⋊C4—34no—
406C2×C4⋊C4—34no—
407C2×C4⋊C4—34no—
408C2×C4⋊C4—34no—
409C2×C4⋊C4—34no—
410C2×C4⋊C4—64no—
411C2×C4⋊C4—64no—
412C2×C4⋊C4—64no—
413C2×C4⋊C4—64no—
414C2×C4⋊C4—64no—
415C2×C4⋊C4—64no—
416C2×C4⋊C4—64no—
417C2×C4⋊C4—122no—
418C2×C22⋊C4—24no—
419C2×C22⋊C4—38no—
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—42no—
431C2×C22⋊C4—42no—
432C2×C22⋊C4—64no—
433C2×C22⋊C4—64no—
434C2×C22⋊C4—64no—
435C2×C22⋊C4—64no—
436C2×C22⋊C4—64no—
437C2×C22⋊C4—64no—
438C2×C22⋊C4—64no—
439C2×C22⋊C4—122no—
440C2×C22⋊C4—122no—
441C2×C22⋊C4C22×D314yes—
442C2×C22⋊C4C22×D314yes—
443C2×C22⋊C4C22×D314yes—
444C2×C42—34no—
445C2×C42—122no—
446#95—34no—
447#95—34no—
448#95—34no—
449#95—34no—
450#95C22×D314yes—
451#95C22×D314yes—
452C23×C3—28no—
453C23×C3—28no—
454C23×C3—28no—
455C23×C3—28no—
456C23×C3—28no—
457C23×C3—28no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
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—44no—
471C23×C3—44no—
472C23×C3—44no—
473C23×C3—44no—
474C23×C3—44no—
475C23×C3—44no—
476C23×C3—44no—
477C23×C3—44no—
478C23×C3C22×D414yes—
479C23×C3C22×D412yes—
480C23×C3C22×D412yes—
481C23×C3C2×#4114yes—
482C23×C3C2×#4112yes—
483C23×C3H(5,𝔽2)12yes—
484C23×C3H(5,𝔽2)12yes—
485C23×C32−1+412yes—
486C23×C32−1+412yes—
487C23×C3C2511yescharacteristic
488C22×D3—22no—
489C22×D3—22no—
490C22×D3—22no—
491C22×D3—22no—
492C22×D3—22no—
493C22×D3—22no—
494C22×D3—22no—
495C22×D3—44no—
496C22×D3—44no—
497C22×D3—44no—
498C22×D3—44no—
499C22×D3—44no—
500C22×D3—44no—
501C22×D3—44no—
502C3×D4—416no—
503C2×C3×C4—28no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—416no—
519C2×C3×C4—44no—
520C2×C3×C4—44no—
521C2×C3×C4—44no—
522C2×C3×C4—44no—
523C2×C3×C4C22×D414yes—
524#67—416no—
525#67—416no—
526C2×Dic3—28no—
527C2×Dic3—28no—
528C2×Dic3—28no—
529C2×Dic3—28no—
530C2×Dic3—22no—
531C2×Dic3—22no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—22no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3—22no—
540C2×Dic3—22no—
541C2×Dic3—22no—
542C2×Dic3—22no—
543C2×Dic3—22no—
544C2×Dic3—22no—
545C2×Dic3—22no—
546C2×Dic3—22no—
547C2×Dic3—416no—
548C2×Dic3—44no—
549C2×Dic3—44no—
550C2×Dic3—44no—
551C2×Dic3C22×D414yes—
552C2×Dic3C22×D414yes—
553C2×Dic3C22×D414yes—
554C2×Dic3C22×D414yes—
555Dic6—416no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24—22no—
566C24—22no—
567C24—22no—
568C24—32no—
569C24—62no—
570C24—62no—
571C24—62no—
572C24—62no—
573C24—62no—
574C24—62no—
575C24—62no—
576C24#23514yes—
577C24D3×D414yes—
578C24C23×D312yes—
579C24C23×D312yes—
580C24C23×D311yescharacteristic
581C2×Q8—68no—
582C2×Q8—68no—
583C2×Q8—124no—
584C2×Q8—1216no—
585C2×D4—28no—
586C2×D4—28no—
587C2×D4—44no—
588C2×D4—416no—
589C2×D4—68no—
590C2×D4—68no—
591C2×D4—68no—
592C2×D4—68no—
593C2×D4—124no—
594C2×D4—124no—
595C2×D4—1216no—
596C2×D4—1216no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—28no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—28no—
613C22×C4—34no—
614C22×C4—34no—
615C22×C4—34no—
616C22×C4—34no—
617C22×C4—32no—
618C22×C4—32no—
619C22×C4—32no—
620C22×C4—32no—
621C22×C4—32no—
622C22×C4—32no—
623C22×C4—32no—
624C22×C4—44no—
625C22×C4—416no—
626C22×C4—68no—
627C22×C4—68no—
628C22×C4—62no—
629C22×C4—62no—
630C22×C4—62no—
631C22×C4—62no—
632C22×C4—62no—
633C22×C4—62no—
634C22×C4—62no—
635C22×C4—62no—
636C22×C4—62no—
637C22×C4—62no—
638C22×C4—62no—
639C22×C4—62no—
640C22×C4—62no—
641C22×C4—62no—
642C22×C4—62no—
643C22×C4—62no—
644C22×C4—62no—
645C22×C4—124no—
646C22×C4—1216no—
647C22×C4D3×D414yes—
648C22×C4C23×D312yes—
649C22×C4C23×D312yes—
650C22×C4C23×D312yes—
651C22×C4C23×D312yes—
652C22×C4C23×D312yes—
653C4⋊C4—316no—
654C4⋊C4—68no—
655C4⋊C4—68no—
656C4⋊C4—68no—
657C4⋊C4—68no—
658C4⋊C4—68no—
659C4⋊C4—68no—
660C4⋊C4—68no—
661C4⋊C4—124no—
662C22⋊C4—28no—
663C22⋊C4—316no—
664C22⋊C4—44no—
665C22⋊C4—44no—
666C22⋊C4—68no—
667C22⋊C4—68no—
668C22⋊C4—68no—
669C22⋊C4—68no—
670C22⋊C4—68no—
671C22⋊C4—68no—
672C22⋊C4—68no—
673C22⋊C4—124no—
674C22⋊C4—124no—
675C42—124no—
676C22×C3—24no—
677C22×C3—24no—
678C22×C3—24no—
679C22×C3—24no—
680C22×C3—24no—
681C22×C3—24no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3—42no—
685C22×C3—416no—
686C22×C3—416no—
687C22×C3—42no—
688C22×C3—42no—
689C22×C3—42no—
690C22×C3—42no—
691C22×C3—42no—
692C22×C3#53614yes—
693C22×C3#53714yes—
694C22×C3#53914yes—
695C22×C3D4214yes—
696C22×C3#54614yes—
697C22×C3#54814yes—
698C22×C3#56214yes—
699C22×C3C23×D411yescharacteristic
700C22×C3C23×D411yescharacteristic
701C22×C3C22×#4111yescharacteristic
702C22×C3C2×H(5,𝔽2)11yescharacteristic
703C22×C3C2×H(5,𝔽2)11yescharacteristic
704C22×C3C2×2−1+411yescharacteristic
705C22×C3C2×2−1+411yescharacteristic
706C2×D3—42no—
707C2×D3—42no—
708C2×D3—42no—
709C2×D3—42no—
710C2×D3—42no—
711C2×D3—42no—
712C2×D3—42no—
713C2×D3—88no—
714C3×C4—24no—
715C3×C4—42no—
716C3×C4—42no—
717C3×C4—42no—
718C3×C4—42no—
719Dic3—24no—
720Dic3—24no—
721Dic3—24no—
722Dic3—24no—
723Dic3—42no—
724Dic3—42no—
725Dic3—42no—
726C23—28no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—28no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—28no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—62no—
753C23—62no—
754C23—62no—
755C23—62no—
756C23—62no—
757C23—62no—
758C23—62no—
759C23—124no—
760C23—124no—
761C23—124no—
762C23—124no—
763C23—124no—
764C23—124no—
765C23—124no—
766C23C2×#23514yes—
767C23C2×#23512yes—
768C23C2×D3×D414yes—
769C23C2×D3×D412yes—
770C23C2×D3×D412yes—
771C23#100412yes—
772C23#100412yes—
773C23#101012yes—
774C23#101012yes—
775C23C24×D311yescharacteristic
776Q8—1216no—
777D4—416no—
778D4—1216no—
779D4—1216no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—28no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—34no—
796C2×C4—34no—
797C2×C4—34no—
798C2×C4—34no—
799C2×C4—416no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—62no—
805C2×C4—62no—
806C2×C4—62no—
807C2×C4—62no—
808C2×C4—62no—
809C2×C4—62no—
810C2×C4—62no—
811C2×C4—62no—
812C2×C4—68no—
813C2×C4—68no—
814C2×C4—68no—
815C2×C4—68no—
816C2×C4—62no—
817C2×C4—62no—
818C2×C4—62no—
819C2×C4—62no—
820C2×C4—62no—
821C2×C4—62no—
822C2×C4—62no—
823C2×C4—62no—
824C2×C4—62no—
825C2×C4—1216no—
826C2×C4—124no—
827C2×C4—124no—
828C2×C4—124no—
829C2×C4C2×D3×D414yes—
830C2×C3—44no—
831C2×C3—44no—
832C2×C3#268118yescomplemented
833C2×C3C2×#53611yescharacteristic
834C2×C3C2×#53711yescharacteristic
835C2×C3C2×#53911yescharacteristic
836C2×C3C2×D4211yescharacteristic
837C2×C3C2×#54611yescharacteristic
838C2×C3C2×#54811yescharacteristic
839C2×C3C2×#56211yescharacteristic
840D3—82no—
841C22—24no—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—416no—
848C22—416no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—122no—
858C22—122no—
859C22—122no—
860C22—122no—
861C22—122no—
862C22—122no—
863C22—122no—
864C22—248no—
865C22#549014yes—
866C22#555214yes—
867C22#556414yes—
868C22#559014yes—
869C22#560814yes—
870C22#562114yes—
871C22#564814yes—
872C22C22×#23511yescharacteristic
873C22C22×D3×D411yescharacteristic
874C22C22×D3×D411yescharacteristic
875C22C2×#100411yescharacteristic
876C22C2×#100411yescharacteristic
877C22C2×#101011yescharacteristic
878C22C2×#101011yescharacteristic
879C4—24no—
880C4—42no—
881C4—42no—
882C4—42no—
883C4—42no—
884C4—64no—
885C4—64no—
886C4—64no—
887C4—64no—
888C4—122no—
889C4—122no—
890C4—122no—
891C3C2×#268111yescharacteristic, complemented, Sylow
892C2—44no—
893C2—44no—
894C2—242no—
895C2#7479418yesdirect product factor
896C2C2×#549011yescharacteristic
897C2C2×#556411yescharacteristic
898C2C2×#555211yescharacteristic
899C2C2×#559011yescharacteristic
900C2C2×#560811yescharacteristic
901C2C2×#562111yescharacteristic
902C2C2×#564811yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#386C2
socleC24×C3C24
prime radicalC22×#939C2
hypercenterC2×#386D3
hypocenterC3C2×#2681
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×#929C2semidirect
3. C22×#924C2semidirect
4. C22×#878C2semidirect
5. C2×C3×#386C2semidirect
6. C2×#5222C2semidirect
7. C2×#4961C2semidirect
8. C2×#4961C2semidirect
9. C2×#4957C2semidirect
10. C2×#4944C2semidirect
11. C2×#4946C2semidirect
12. #74794C2direct (N × H)
13. C2×#4676C2semidirect
14. C2×#4673C2semidirect
15. C2×#4657C2semidirect
16. C2×#4647C2semidirect
35. C2×#929C22semidirect
44. C2×#924C22semidirect
54. C2×#878C22semidirect
55. C3×#386C22semidirect
58. #5222C22semidirect
63. #4961C22semidirect
64. #4961C22semidirect
65. #4957C22semidirect
66. #4946C22semidirect
67. #4944C22semidirect
68. #4676C22semidirect
69. #4673C22semidirect
70. #4657C22semidirect
71. #4647C22semidirect
86. C2×#386D3semidirect
166. C2×Dic3⋊C4D4semidirect
229. #386C2×D3semidirect
355. Dic3⋊C4C2×D4semidirect
832. C2×C3#2681semidirect
891. C3C2×#2681semidirect
895. C2#74794direct (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×#9292
C22×#9242
C22×#8782
C2×C3×#3862
C2×#52222
C2×#49612
C2×#49572
C2×#49442
C2×#49462
#747942
C2×#46762
C2×#46732
C2×#46572
C2×#46472
C2×#26813