Finite Group Databasebeta

← C2×#77969 #11429908

Subgroups — C2×#77969 #11429908

Order 768.

3286 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#894C211yesmaximal, characteristic
2C22×#894C211yesmaximal, characteristic
3C22×#896C211yesmaximal, characteristic, complemented
4C22×#897C211yesmaximal, characteristic, complemented
5C2×C3×#398C211yesmaximal, characteristic, complemented
6C2×#4989C211yesmaximal, characteristic, complemented
7C2×#4979C211yesmaximal, characteristic, complemented
8C2×#4990C211yesmaximal, characteristic, complemented
9C2×#4975C211yesmaximal, characteristic, complemented
10#77969C2116yesmaximal, direct product factor
11C2×#4675C211yesmaximal, characteristic, complemented
12C2×#4668C211yesmaximal, characteristic, complemented
13C2×#4657C211yesmaximal, characteristic, complemented
14C2×#4674C211yesmaximal, characteristic, complemented
15C2×#4672C211yesmaximal, characteristic
16C2×#4669C211yesmaximal, characteristic, complemented
17C2×#2680—31nomaximal, Sylow
18C23×D12C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C23×Dic6C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×C4⋊Dic3C2211yescharacteristic
37C22×C4⋊Dic3C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×Dic3⋊C4C2211yescharacteristic
41C22×Dic3⋊C4C2211yescharacteristic
42C22×Dic3⋊C4C2211yescharacteristic
43C22×Dic3⋊C4C2211yescharacteristic
44C22×C4×Dic3C2211yescharacteristic
45C2×#897—28no—
46C2×#897C2218yescomplemented
47C2×#896—28no—
48C2×#896C2218yescomplemented
49C2×#894—28no—
50C2×#894—28no—
51C2×#894C2218yes—
52C2×#894C2218yes—
53C3×#398C2218yescomplemented
54C2×C3×#95C2211yescharacteristic
55C2×C3×#95C2211yescharacteristic
56C2×C3×#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61C2×C3⋊#95C2211yescharacteristic
62#4990C2218yescomplemented
63#4989C2218yescomplemented
64#4979C2218yescomplemented
65#4975C2218yescomplemented
66#4675C2218yescomplemented
67#4674C2218yescomplemented
68#4672C2218yes—
69#4669C2218yescomplemented
70#4668C2218yescomplemented
71#4657C2218yescomplemented
72C22×#123—31no—
73C22×#123—31no—
74C22×C22⋊Q8—31no—
75C22×C22⋊Q8—31no—
76#2680—316no—
77C2×#398—31no—
78C2×#398D311yescharacteristic, complemented
79C2×#397—31no—
80C2×#397—31no—
81C2×#395—31no—
82C2×#394—31no—
83C2×#388—31no—
84C2×#388—31no—
85C2×#385—31no—
86C2×#385—31no—
87C2×#384—31no—
88C24×D3C2311yescharacteristic
89C24×D3C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C22×D12—24no—
104C22×D12—24no—
105C22×D12—42no—
106C22×D12C2314yes—
107C22×C4×D3—24no—
108C22×C4×D3—24no—
109C22×C4×D3—24no—
110C22×C4×D3—24no—
111C22×C4×D3—42no—
112C22×C4×D3—42no—
113C22×C4×D3C2314yes—
114C22×C4×D3C2314yes—
115C22×Dic6—24no—
116C22×Dic6—24no—
117C22×Dic6—42no—
118C22×Dic6C2314yes—
119C2×C3×C4⋊C4—24no—
120C2×C3×C4⋊C4—24no—
121C2×C3×C4⋊C4—24no—
122C2×C3×C4⋊C4—24no—
123C2×C3×C4⋊C4C2314yes—
124C2×C3×C4⋊C4C2314yes—
125C2×C3×C4⋊C4C2314yes—
126C2×C3×C4⋊C4C2314yes—
127C2×(C2×D3)⋊C4—24no—
128C2×(C2×D3)⋊C4—24no—
129C2×(C2×D3)⋊C4—24no—
130C2×(C2×D3)⋊C4—24no—
131C2×(C2×D3)⋊C4—24no—
132C2×(C2×D3)⋊C4—24no—
133C2×(C2×D3)⋊C4—24no—
134C2×(C2×D3)⋊C4—24no—
135C2×(C2×D3)⋊C4D418yes—
136C2×(C2×D3)⋊C4D418yes—
137C2×(C2×D3)⋊C4C2314yes—
138C2×(C2×D3)⋊C4C2314yes—
139C2×(C2×D3)⋊C4C2314yes—
140C2×(C2×D3)⋊C4C2314yes—
141C2×(C2×D3)⋊C4C2314yes—
142C2×(C2×D3)⋊C4C2314yes—
143C2×(C2×D3)⋊C4C2314yes—
144C2×(C2×D3)⋊C4C2314yes—
145C2×(C2×D3)⋊C4C2314yes—
146C2×(C2×D3)⋊C4C2314yes—
147C2×C4⋊Dic3—24no—
148C2×C4⋊Dic3—24no—
149C2×C4⋊Dic3C2314yes—
150C2×C4⋊Dic3C2314yes—
151C2×Dic3⋊C4—24no—
152C2×Dic3⋊C4—24no—
153C2×Dic3⋊C4—24no—
154C2×Dic3⋊C4—24no—
155C2×Dic3⋊C4—42no—
156C2×Dic3⋊C4—42no—
157C2×Dic3⋊C4C2314yes—
158C2×Dic3⋊C4C2314yes—
159C2×Dic3⋊C4C2314yes—
160C2×Dic3⋊C4C2314yes—
161C2×Dic3⋊C4C2314yes—
162C2×Dic3⋊C4C2314yes—
163C2×C4×Dic3—24no—
164C2×C4×Dic3C2314yes—
165#897—232no—
166#896—232no—
167#894—232no—
168#894—232no—
169C3×#95C2314yes—
170C3×#95C2314yes—
171C3×#95C2314yes—
172C3⋊#95C2314yes—
173C3⋊#95C2314yes—
174C3⋊#95C2314yes—
175C3⋊#95C2314yes—
176C3⋊#95C2314yes—
177C23×Q8—31no—
178C23×D4—31no—
179C24×C4—31no—
180C24×C4—31no—
181C2×#123—38no—
182C2×#123—38no—
183C2×#123—68no—
184C2×#123—68no—
185C2×C22⋊Q8—38no—
186C2×C22⋊Q8—38no—
187C2×C22⋊Q8—68no—
188C2×C22⋊Q8—68no—
189C22×C4⋊C4—31no—
190C22×C4⋊C4—31no—
191C22×C4⋊C4—31no—
192C22×C4⋊C4—31no—
193C22×C4⋊C4—31no—
194C22×C4⋊C4—31no—
195C22×C4⋊C4—31no—
196C22×C4⋊C4—31no—
197C22×C4⋊C4C2×D311yescharacteristic
198C22×C4⋊C4C2×D311yescharacteristic
199C22×C4⋊C4C2×D311yescharacteristic
200C22×C4⋊C4C2×D311yescharacteristic
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⋊C4—31no—
210C22×C22⋊C4—31no—
211C22×C42—31no—
212#398—38no—
213#398C2×D318yescomplemented
214#397—38no—
215#397—38no—
216#395—38no—
217#394—38no—
218#388—38no—
219#388—38no—
220#385—38no—
221#385—38no—
222#384—38no—
223C2×#95—31no—
224C2×#95—31no—
225C2×#95—31no—
226C2×#95—31no—
227C2×#95—31no—
228C2×#95C2×D311yescharacteristic
229C2×#95C2×D311yescharacteristic
230C2×#95C2×D311yescharacteristic
231C24×C3C2411yescharacteristic
232C23×D3—22no—
233C23×D3—22no—
234C23×D3—22no—
235C23×D3—22no—
236C23×D3—22no—
237C23×D3—22no—
238C23×D3—22no—
239C23×D3—22no—
240C23×D3—22no—
241C23×D3—22no—
242C23×D3—22no—
243C23×D3—22no—
244C23×D3C2×D414yes—
245C23×D3C2×D414yes—
246C23×D3C2412yes—
247C23×D3C2412yes—
248C22×C3×C4—22no—
249C22×C3×C4—22no—
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—22no—
253C22×C3×C4—22no—
254C22×C3×C4—22no—
255C22×C3×C4—22no—
256C22×C3×C4—22no—
257C22×C3×C4—22no—
258C22×C3×C4—22no—
259C22×C3×C4—22no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—22no—
264C22×C3×C4—22no—
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4C2×D414yes—
268C22×C3×C4C2×D414yes—
269C22×C3×C4C2412yes—
270C22×C3×C4C2412yes—
271C22×C3×C4C2412yes—
272C22×C3×C4C2412yes—
273C22×C3×C4C2412yes—
274C22×C3×C4C2412yes—
275C22×C3×C4C2412yes—
276C22×Dic3—22no—
277C22×Dic3—22no—
278C22×Dic3—22no—
279C22×Dic3—22no—
280C22×Dic3—22no—
281C22×Dic3—22no—
282C22×Dic3—22no—
283C22×Dic3—22no—
284C22×Dic3—22no—
285C22×Dic3—22no—
286C22×Dic3—22no—
287C22×Dic3—22no—
288C22×Dic3—22no—
289C22×Dic3—22no—
290C22×Dic3—22no—
291C22×Dic3C2×D414yes—
292C22×Dic3C2×D414yes—
293C22×Dic3#4114yes—
294C22×Dic3C2412yes—
295C22×Dic3C2412yes—
296C22×Dic3C2412yes—
297C22×Dic3C2412yes—
298C22×Dic3C2412yes—
299C22×Dic3C2412yes—
300C2×D12—28no—
301C2×D12—28no—
302C2×D12—44no—
303C2×D12—416no—
304C2×C4×D3—28no—
305C2×C4×D3—28no—
306C2×C4×D3—28no—
307C2×C4×D3—28no—
308C2×C4×D3—44no—
309C2×C4×D3—44no—
310C2×C4×D3—416no—
311C2×C4×D3—416no—
312C2×Dic6—28no—
313C2×Dic6—28no—
314C2×Dic6—44no—
315C2×Dic6—416no—
316C3×C4⋊C4—28no—
317C3×C4⋊C4—28no—
318C3×C4⋊C4—28no—
319C3×C4⋊C4—28no—
320(C2×D3)⋊C4—28no—
321(C2×D3)⋊C4—28no—
322(C2×D3)⋊C4—28no—
323(C2×D3)⋊C4—28no—
324(C2×D3)⋊C4—28no—
325(C2×D3)⋊C4—28no—
326(C2×D3)⋊C4—28no—
327(C2×D3)⋊C4—28no—
328(C2×D3)⋊C4C2×D4116yes—
329(C2×D3)⋊C4C2×D4116yes—
330C4⋊Dic3—28no—
331C4⋊Dic3—28no—
332Dic3⋊C4—28no—
333Dic3⋊C4—28no—
334Dic3⋊C4—28no—
335Dic3⋊C4—28no—
336Dic3⋊C4—44no—
337Dic3⋊C4—44no—
338C4×Dic3—28no—
339C25—31no—
340C25—31no—
341C22×Q8—34no—
342C22×Q8—64no—
343C22×Q8—64no—
344C22×Q8—122no—
345C22×D4—34no—
346C22×D4—64no—
347C22×D4—64no—
348C22×D4—122no—
349C23×C4—31no—
350C23×C4—31no—
351C23×C4—31no—
352C23×C4—31no—
353C23×C4—31no—
354C23×C4—31no—
355C23×C4—34no—
356C23×C4—34no—
357C23×C4—64no—
358C23×C4—64no—
359C23×C4—64no—
360C23×C4—64no—
361C23×C4—122no—
362C23×C4—122no—
363C23×C4C22×D311yescharacteristic
364C23×C4C22×D311yescharacteristic
365C23×C4C22×D311yescharacteristic
366C23×C4C22×D311yescharacteristic
367C23×C4C22×D311yescharacteristic
368C23×C4C22×D311yescharacteristic
369C23×C4C22×D311yescharacteristic
370#123—632no—
371#123—632no—
372C22⋊Q8—632no—
373C22⋊Q8—632no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—34no—
379C2×C4⋊C4—34no—
380C2×C4⋊C4—34no—
381C2×C4⋊C4—34no—
382C2×C4⋊C4—34no—
383C2×C4⋊C4—34no—
384C2×C4⋊C4—34no—
385C2×C4⋊C4—34no—
386C2×C4⋊C4—64no—
387C2×C4⋊C4—64no—
388C2×C4⋊C4—64no—
389C2×C4⋊C4—64no—
390C2×C4⋊C4—64no—
391C2×C4⋊C4—64no—
392C2×C4⋊C4—122no—
393C2×C4⋊C4—122no—
394C2×C4⋊C4C22×D314yes—
395C2×C4⋊C4C22×D314yes—
396C2×C4⋊C4C22×D314yes—
397C2×C4⋊C4C22×D314yes—
398C2×C22⋊C4—38no—
399C2×C22⋊C4—38no—
400C2×C22⋊C4—34no—
401C2×C22⋊C4—34no—
402C2×C22⋊C4—34no—
403C2×C22⋊C4—34no—
404C2×C22⋊C4—34no—
405C2×C22⋊C4—34no—
406C2×C22⋊C4—34no—
407C2×C22⋊C4—34no—
408C2×C22⋊C4—34no—
409C2×C22⋊C4—34no—
410C2×C22⋊C4—64no—
411C2×C22⋊C4—64no—
412C2×C22⋊C4—64no—
413C2×C22⋊C4—64no—
414C2×C22⋊C4—64no—
415C2×C22⋊C4—64no—
416C2×C22⋊C4—64no—
417C2×C22⋊C4—64no—
418C2×C42—34no—
419C2×C42—64no—
420#95—34no—
421#95—34no—
422#95—34no—
423#95—34no—
424#95—34no—
425#95C22×D314yes—
426#95C22×D314yes—
427#95C22×D314yes—
428C23×C3C22×D412yes—
429C23×C3C22×D412yes—
430C23×C3C2×#4112yes—
431C23×C3H(5,𝔽2)12yes—
432C23×C32−1+412yes—
433C23×C32−1+412yes—
434C23×C32−1+412yes—
435C23×C3C2511yescharacteristic
436C22×D3—28no—
437C22×D3—28no—
438C22×D3—28no—
439C22×D3—28no—
440C22×D3—28no—
441C22×D3—28no—
442C22×D3—22no—
443C22×D3—22no—
444C22×D3—22no—
445C22×D3—22no—
446C22×D3—22no—
447C22×D3—22no—
448C22×D3—22no—
449C22×D3—22no—
450C22×D3—22no—
451C22×D3—22no—
452C22×D3—22no—
453C22×D3—22no—
454C22×D3—44no—
455C22×D3—44no—
456C22×D3—44no—
457C22×D3—44no—
458C22×D3—44no—
459C22×D3—44no—
460C22×D3—44no—
461C22×D3—44no—
462C22×D3C22×D414yes—
463C22×D3C22×D414yes—
464C2×C3×C4—28no—
465C2×C3×C4—28no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—44no—
486C2×C3×C4—44no—
487C2×C3×C4—44no—
488C2×C3×C4—44no—
489C2×C3×C4—44no—
490C2×C3×C4C22×D414yes—
491C2×C3×C4C22×D414yes—
492C2×Dic3—28no—
493C2×Dic3—28no—
494C2×Dic3—28no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—44no—
511C2×Dic3—44no—
512C2×Dic3—44no—
513C2×Dic3C22×D414yes—
514C2×Dic3C22×D414yes—
515C2×Dic3C2×#4114yes—
516D12—416no—
517C4×D3—416no—
518C4×D3—416no—
519Dic6—416no—
520C24—34no—
521C24—34no—
522C24—32no—
523C24—32no—
524C24—62no—
525C24—62no—
526C24—62no—
527C24—62no—
528C24—62no—
529C24—62no—
530C24—62no—
531C24—62no—
532C24—62no—
533C24—62no—
534C24—62no—
535C24—62no—
536C24C23×D311yescharacteristic
537C2×Q8—68no—
538C2×Q8—68no—
539C2×Q8—124no—
540C2×Q8—1216no—
541C2×D4—68no—
542C2×D4—68no—
543C2×D4—124no—
544C2×D4—1216no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—34no—
565C22×C4—34no—
566C22×C4—34no—
567C22×C4—32no—
568C22×C4—32no—
569C22×C4—32no—
570C22×C4—32no—
571C22×C4—32no—
572C22×C4—32no—
573C22×C4—68no—
574C22×C4—68no—
575C22×C4—68no—
576C22×C4—62no—
577C22×C4—62no—
578C22×C4—62no—
579C22×C4—62no—
580C22×C4—62no—
581C22×C4—62no—
582C22×C4—62no—
583C22×C4—62no—
584C22×C4—62no—
585C22×C4—62no—
586C22×C4—62no—
587C22×C4—62no—
588C22×C4—62no—
589C22×C4—62no—
590C22×C4—62no—
591C22×C4—68no—
592C22×C4—124no—
593C22×C4—124no—
594C22×C4—1216no—
595C22×C4—1216no—
596C22×C4D3×D414yes—
597C22×C4D3×D414yes—
598C22×C4C23×D312yes—
599C22×C4C23×D312yes—
600C22×C4C23×D312yes—
601C22×C4C23×D312yes—
602C22×C4C23×D312yes—
603C22×C4C23×D312yes—
604C22×C4C23×D312yes—
605C4⋊C4—28no—
606C4⋊C4—28no—
607C4⋊C4—28no—
608C4⋊C4—28no—
609C4⋊C4—68no—
610C4⋊C4—68no—
611C4⋊C4—68no—
612C4⋊C4—68no—
613C4⋊C4—68no—
614C4⋊C4—68no—
615C4⋊C4—124no—
616C4⋊C4—124no—
617C22⋊C4—316no—
618C22⋊C4—316no—
619C22⋊C4—68no—
620C22⋊C4—68no—
621C22⋊C4—68no—
622C22⋊C4—68no—
623C22⋊C4—68no—
624C22⋊C4—68no—
625C22⋊C4—68no—
626C22⋊C4—68no—
627C42—68no—
628C22×C3#53614yes—
629C22×C3#53614yes—
630C22×C3#53914yes—
631C22×C3D4214yes—
632C22×C3#54714yes—
633C22×C3#54714yes—
634C22×C3#56314yes—
635C22×C3C23×D411yescharacteristic
636C22×C3C23×D411yescharacteristic
637C22×C3C22×#4111yescharacteristic
638C22×C3C2×H(5,𝔽2)11yescharacteristic
639C22×C3C2×2−1+411yescharacteristic
640C22×C3C2×2−1+411yescharacteristic
641C22×C3C2×2−1+411yescharacteristic
642C2×D3—24no—
643C2×D3—24no—
644C2×D3—24no—
645C2×D3—24no—
646C2×D3—24no—
647C2×D3—24no—
648C2×D3—42no—
649C2×D3—42no—
650C2×D3—416no—
651C2×D3—416no—
652C2×D3—42no—
653C2×D3—42no—
654C2×D3—42no—
655C2×D3—42no—
656C2×D3—42no—
657C2×D3—42no—
658C3×C4—24no—
659C3×C4—24no—
660C3×C4—42no—
661C3×C4—42no—
662C3×C4—42no—
663C3×C4—42no—
664C3×C4—42no—
665Dic3—24no—
666Dic3—24no—
667Dic3—24no—
668Dic3—42no—
669Dic3—42no—
670Dic3—42no—
671C23—34no—
672C23—34no—
673C23—68no—
674C23—62no—
675C23—62no—
676C23—62no—
677C23—62no—
678C23—62no—
679C23—62no—
680C23—62no—
681C23—62no—
682C23—62no—
683C23—62no—
684C23—62no—
685C23—62no—
686C23—68no—
687C23—68no—
688C23—68no—
689C23—68no—
690C23—68no—
691C23—124no—
692C23—124no—
693C23—124no—
694C23—124no—
695C23—124no—
696C23—124no—
697C23—124no—
698C23—124no—
699C23C2×D3×D412yes—
700C23C2×D3×D412yes—
701C23#100712yes—
702C23#100712yes—
703C23D3×#4112yes—
704C23#100912yes—
705C23#101012yes—
706C23C24×D311yescharacteristic
707Q8—1216no—
708D4—1216no—
709C2×C4—28no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—28no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—34no—
731C2×C4—34no—
732C2×C4—34no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—68no—
739C2×C4—62no—
740C2×C4—62no—
741C2×C4—62no—
742C2×C4—62no—
743C2×C4—62no—
744C2×C4—62no—
745C2×C4—68no—
746C2×C4—68no—
747C2×C4—62no—
748C2×C4—62no—
749C2×C4—62no—
750C2×C4—62no—
751C2×C4—62no—
752C2×C4—62no—
753C2×C4—62no—
754C2×C4—62no—
755C2×C4—62no—
756C2×C4—1216no—
757C2×C4—1216no—
758C2×C4—124no—
759C2×C4—124no—
760C2×C4—124no—
761C2×C4C2×D3×D414yes—
762C2×C4C2×D3×D414yes—
763C2×C3#268018yescomplemented
764C2×C3C2×#53611yescharacteristic
765C2×C3C2×#53611yescharacteristic
766C2×C3C2×#53911yescharacteristic
767C2×C3C2×D4211yescharacteristic
768C2×C3C2×#54711yescharacteristic
769C2×C3C2×#54711yescharacteristic
770C2×C3C2×#56311yescharacteristic
771D3—44no—
772D3—44no—
773C22—64no—
774C22—64no—
775C22—64no—
776C22—64no—
777C22—64no—
778C22—64no—
779C22—122no—
780C22—122no—
781C22—122no—
782C22—122no—
783C22—1216no—
784C22—1216no—
785C22—122no—
786C22—122no—
787C22—122no—
788C22—122no—
789C22#560914yes—
790C22#562814yes—
791C22#563114yes—
792C22#565514yes—
793C22#569214yes—
794C22#569914yes—
795C22#572414yes—
796C22C22×D3×D411yescharacteristic
797C22C22×D3×D411yescharacteristic
798C22C2×#100711yescharacteristic
799C22C2×#100711yescharacteristic
800C22C2×D3×#4111yescharacteristic
801C22C2×#100911yescharacteristic
802C22C2×#101011yescharacteristic
803C4—24no—
804C4—24no—
805C4—42no—
806C4—42no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—64no—
811C4—64no—
812C4—64no—
813C4—122no—
814C4—122no—
815C4—122no—
816C3C2×#268011yescharacteristic, complemented, Sylow
817C2—124no—
818C2—124no—
819C2#7796918yesdirect product factor
820C2C2×#560911yescharacteristic
821C2C2×#562811yescharacteristic
822C2C2×#563111yescharacteristic
823C2C2×#565511yescharacteristic
824C2C2×#569211yescharacteristic
825C2C2×#569911yescharacteristic
826C2C2×#572411yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#398C2
socleC24×C3C24
prime radicalC23×D12C22
hypercenterC2×#398D3
hypocenterC3C2×#2680
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
3. C22×#896C2semidirect
4. C22×#897C2semidirect
5. C2×C3×#398C2semidirect
6. C2×#4989C2semidirect
7. C2×#4979C2semidirect
8. C2×#4990C2semidirect
9. C2×#4975C2semidirect
10. #77969C2direct (N × H)
11. C2×#4675C2semidirect
12. C2×#4668C2semidirect
13. C2×#4657C2semidirect
14. C2×#4674C2semidirect
16. C2×#4669C2semidirect
46. C2×#897C22semidirect
48. C2×#896C22semidirect
53. C3×#398C22semidirect
62. #4990C22semidirect
63. #4989C22semidirect
64. #4979C22semidirect
65. #4975C22semidirect
66. #4675C22semidirect
67. #4674C22semidirect
69. #4669C22semidirect
70. #4668C22semidirect
71. #4657C22semidirect
78. C2×#398D3semidirect
213. #398C2×D3semidirect
763. C2×C3#2680semidirect
816. C3C2×#2680semidirect
819. C2#77969direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#8942
C22×#8962
C22×#8972
C2×C3×#3982
C2×#49892
C2×#49792
C2×#49902
C2×#49752
#779692
C2×#46752
C2×#46682
C2×#46572
C2×#46742
C2×#46722
C2×#46692
C2×#26803