Finite Group Databasebeta

← C2×#77433 #11429939

Subgroups — C2×#77433 #11429939

Order 768.

3438 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#896C211yesmaximal, characteristic, complemented
2C22×#897C211yesmaximal, characteristic, complemented
3C22×#878C211yesmaximal, characteristic, complemented
4C22×#878C211yesmaximal, characteristic, complemented
5C2×C3×#396C211yesmaximal, characteristic, complemented
6C2×#4994C211yesmaximal, characteristic, complemented
7C2×#4979C211yesmaximal, characteristic, complemented
8C2×#4976C211yesmaximal, characteristic, complemented
9C2×#4972C211yesmaximal, characteristic, complemented
10C2×#4956C211yesmaximal, characteristic
11C2×#4948C211yesmaximal, characteristic, complemented
12C2×#4957C211yesmaximal, characteristic
13C2×#4958C211yesmaximal, characteristic
14#77433C2116yesmaximal, direct product factor
15C2×#4676C211yesmaximal, characteristic, complemented
16C2×#4656C211yesmaximal, characteristic, complemented
17C2×#2683—31nomaximal, Sylow
18C23×#67C2211yescharacteristic
19C24×Dic3C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C23×Dic6C2211yescharacteristic
22C23×Dic6C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×Dic3⋊C4C2211yescharacteristic
41C22×Dic3⋊C4C2211yescharacteristic
42C22×Dic3⋊C4C2211yescharacteristic
43C22×Dic3⋊C4C2211yescharacteristic
44C22×Dic3⋊C4C2211yescharacteristic
45C22×Dic3⋊C4C2211yescharacteristic
46C22×C4×Dic3C2211yescharacteristic
47C2×#897—28no—
48C2×#897C2218yescomplemented
49C2×#896—28no—
50C2×#896C2218yescomplemented
51C2×#878—28no—
52C2×#878—28no—
53C2×#878C2218yescomplemented
54C2×#878C2218yescomplemented
55C3×#396C2218yescomplemented
56C2×C3×#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61C2×C3⋊#95C2211yescharacteristic
62#4994C2218yescomplemented
63#4979C2218yescomplemented
64#4976C2218yescomplemented
65#4972C2218yescomplemented
66#4958C2218yes—
67#4957C2218yes—
68#4956C2218yes—
69#4948C2218yescomplemented
70#4676C2218yescomplemented
71#4656C2218yescomplemented
72C22×C22⋊Q8—31no—
73C22×C22⋊Q8—31no—
74C22×C22⋊Q8—31no—
75C22×C22⋊Q8—31no—
76#2683—316no—
77C2×#396—31no—
78C2×#396—31no—
79C2×#396—31no—
80C2×#396D311yescharacteristic, complemented
81C2×#395—31no—
82C2×#395—31no—
83C2×#390—31no—
84C2×#389—31no—
85C2×#389—31no—
86C2×#386—31no—
87C2×#386—31no—
88C25×C3C2311yescharacteristic
89C24×D3C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C22×#67—42no—
97C22×#67—42no—
98C22×#67Q818yescomplemented
99C22×#67C2314yes—
100C23×Dic3—24no—
101C23×Dic3—24no—
102C23×Dic3—42no—
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2314yes—
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C23×Dic3C2311yescharacteristic
109C23×Dic3C2311yescharacteristic
110C23×Dic3C2311yescharacteristic
111C22×C4×D3—24no—
112C22×C4×D3—24no—
113C22×C4×D3—42no—
114C22×C4×D3C2314yes—
115C22×Dic6—24no—
116C22×Dic6—24no—
117C22×Dic6—24no—
118C22×Dic6—24no—
119C22×Dic6—42no—
120C22×Dic6—42no—
121C22×Dic6C2314yes—
122C22×Dic6C2314yes—
123C2×C3×C4⋊C4—24no—
124C2×C3×C4⋊C4—24no—
125C2×C3×C4⋊C4—42no—
126C2×C3×C4⋊C4C2314yes—
127C2×C3×C4⋊C4C2314yes—
128C2×C3×C4⋊C4C2314yes—
129C2×C3×C22⋊C4—24no—
130C2×C3×C22⋊C4—24no—
131C2×C3×C22⋊C4—42no—
132C2×C3×C22⋊C4C2314yes—
133C2×C3×C22⋊C4C2314yes—
134C2×C3×C22⋊C4C2314yes—
135C2×#217—24no—
136C2×#217—24no—
137C2×#217C2314yes—
138C2×#217C2314yes—
139C2×(C2×D3)⋊C4—24no—
140C2×(C2×D3)⋊C4—24no—
141C2×(C2×D3)⋊C4—24no—
142C2×(C2×D3)⋊C4—24no—
143C2×(C2×D3)⋊C4—42no—
144C2×(C2×D3)⋊C4C2314yes—
145C2×(C2×D3)⋊C4C2314yes—
146C2×(C2×D3)⋊C4C2314yes—
147C2×(C2×D3)⋊C4C2314yes—
148C2×(C2×D3)⋊C4C2314yes—
149C2×C4⋊Dic3—24no—
150C2×C4⋊Dic3—24no—
151C2×C4⋊Dic3D418yescomplemented
152C2×C4⋊Dic3C2314yes—
153C2×C4⋊Dic3C2314yes—
154C2×C4⋊Dic3C2314yes—
155C2×Dic3⋊C4—24no—
156C2×Dic3⋊C4—24no—
157C2×Dic3⋊C4—24no—
158C2×Dic3⋊C4—24no—
159C2×Dic3⋊C4—42no—
160C2×Dic3⋊C4—42no—
161C2×Dic3⋊C4D418yescomplemented
162C2×Dic3⋊C4C2314yes—
163C2×Dic3⋊C4C2314yes—
164C2×Dic3⋊C4C2314yes—
165C2×Dic3⋊C4C2314yes—
166C2×Dic3⋊C4C2314yes—
167C2×Dic3⋊C4C2314yes—
168C2×Dic3⋊C4C2314yes—
169C2×C4×Dic3—42no—
170C2×C4×Dic3C2314yes—
171#897—232no—
172#896—232no—
173#878—232no—
174#878—232no—
175C3×#95C2314yes—
176C3⋊#95C2314yes—
177C3⋊#95C2314yes—
178C3⋊#95C2314yes—
179C3⋊#95C2314yes—
180C3⋊#95C2314yes—
181C23×Q8—31no—
182C23×Q8—31no—
183C23×D4—31no—
184C24×C4—31no—
185C24×C4—31no—
186C2×C22⋊Q8—38no—
187C2×C22⋊Q8—38no—
188C2×C22⋊Q8—38no—
189C2×C22⋊Q8—38no—
190C2×C22⋊Q8—68no—
191C2×C22⋊Q8—68no—
192C2×C22⋊Q8—68no—
193C2×C22⋊Q8—68no—
194C22×C4⋊C4—31no—
195C22×C4⋊C4—31no—
196C22×C4⋊C4—31no—
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⋊C4C2×D311yescharacteristic
205C22×C4⋊C4C2×D311yescharacteristic
206C22×C4⋊C4C2×D311yescharacteristic
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⋊C4C2×D311yescharacteristic
215C22×C22⋊C4C2×D311yescharacteristic
216C22×C22⋊C4C2×D311yescharacteristic
217C22×C42—31no—
218#396—38no—
219#396—38no—
220#396—38no—
221#396C2×D318yescomplemented
222#395—38no—
223#395—38no—
224#390—38no—
225#389—38no—
226#389—38no—
227#386—38no—
228#386—38no—
229C2×#95—31no—
230C2×#95—31no—
231C2×#95—31no—
232C2×#95—31no—
233C2×#95—31no—
234C2×#95C2×D311yescharacteristic
235C24×C3—22no—
236C24×C3—22no—
237C24×C3—22no—
238C24×C3—22no—
239C24×C3—22no—
240C24×C3—22no—
241C24×C3C2×Q814yes—
242C24×C3C2412yes—
243C24×C3C2411yescharacteristic
244C23×D3—22no—
245C23×D3—22no—
246C23×D3—22no—
247C23×D3—22no—
248C23×D3—22no—
249C23×D3—22no—
250C23×D3C2×Q814yes—
251C23×D3C2412yes—
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×C4—22no—
268C22×C3×C4C2×D414yes—
269C22×C3×C4C2×D414yes—
270C22×C3×C4C2412yes—
271C22×C3×C4C2412yes—
272C22×C3×C4C2412yes—
273C22×C3×C4C2412yes—
274C22×C3×C4C2412yes—
275C22×C3×C4C2412yes—
276C2×#67—416no—
277C2×#67—44no—
278C2×#67—44no—
279C2×#67C2×Q8116yescomplemented
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×Dic3—22no—
292C22×Dic3—22no—
293C22×Dic3—22no—
294C22×Dic3—22no—
295C22×Dic3—22no—
296C22×Dic3—28no—
297C22×Dic3—28no—
298C22×Dic3—44no—
299C22×Dic3—416no—
300C22×Dic3C2×D414yes—
301C22×Dic3C2×D414yes—
302C22×Dic3C2×D414yes—
303C22×Dic3C2×D414yes—
304C22×Dic3C2×Q814yes—
305C22×Dic3C2412yes—
306C22×Dic3C2412yes—
307C22×Dic3C2412yes—
308C22×Dic3C2412yes—
309C22×Dic3C2412yes—
310C22×Dic3C2412yes—
311C22×Dic3C2412yes—
312C2×C4×D3—28no—
313C2×C4×D3—28no—
314C2×C4×D3—44no—
315C2×C4×D3—416no—
316C2×Dic6—28no—
317C2×Dic6—28no—
318C2×Dic6—28no—
319C2×Dic6—28no—
320C2×Dic6—44no—
321C2×Dic6—44no—
322C2×Dic6—416no—
323C2×Dic6—416no—
324C3×C4⋊C4—28no—
325C3×C4⋊C4—28no—
326C3×C4⋊C4—44no—
327C3×C22⋊C4—28no—
328C3×C22⋊C4—28no—
329C3×C22⋊C4—44no—
330#217—28no—
331#217—28no—
332(C2×D3)⋊C4—28no—
333(C2×D3)⋊C4—28no—
334(C2×D3)⋊C4—28no—
335(C2×D3)⋊C4—28no—
336(C2×D3)⋊C4—44no—
337C4⋊Dic3—28no—
338C4⋊Dic3—28no—
339C4⋊Dic3C2×D4116yescomplemented
340Dic3⋊C4—28no—
341Dic3⋊C4—28no—
342Dic3⋊C4—28no—
343Dic3⋊C4—28no—
344Dic3⋊C4—44no—
345Dic3⋊C4—44no—
346Dic3⋊C4C2×D4116yescomplemented
347C4×Dic3—44no—
348C25—31no—
349C25C22×D311yescharacteristic
350C22×Q8—34no—
351C22×Q8—34no—
352C22×Q8—64no—
353C22×Q8—64no—
354C22×Q8—64no—
355C22×Q8—64no—
356C22×Q8—122no—
357C22×Q8—122no—
358C22×D4—38no—
359C22×D4—34no—
360C22×D4—122no—
361C22×D4—122no—
362C23×C4—31no—
363C23×C4—31no—
364C23×C4—31no—
365C23×C4—31no—
366C23×C4—31no—
367C23×C4—31no—
368C23×C4—31no—
369C23×C4—34no—
370C23×C4—34no—
371C23×C4—64no—
372C23×C4—64no—
373C23×C4—64no—
374C23×C4—64no—
375C23×C4—122no—
376C23×C4—122no—
377C23×C4C22×D311yescharacteristic
378C23×C4C22×D311yescharacteristic
379C23×C4C22×D311yescharacteristic
380C23×C4C22×D311yescharacteristic
381C23×C4C22×D311yescharacteristic
382C23×C4C22×D311yescharacteristic
383C22⋊Q8—632no—
384C22⋊Q8—632no—
385C22⋊Q8—632no—
386C22⋊Q8—632no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—38no—
390C2×C4⋊C4—38no—
391C2×C4⋊C4—34no—
392C2×C4⋊C4—34no—
393C2×C4⋊C4—34no—
394C2×C4⋊C4—34no—
395C2×C4⋊C4—34no—
396C2×C4⋊C4—34no—
397C2×C4⋊C4—34no—
398C2×C4⋊C4—34no—
399C2×C4⋊C4—34no—
400C2×C4⋊C4—34no—
401C2×C4⋊C4—42no—
402C2×C4⋊C4—64no—
403C2×C4⋊C4—64no—
404C2×C4⋊C4—64no—
405C2×C4⋊C4—64no—
406C2×C4⋊C4—64no—
407C2×C4⋊C4—64no—
408C2×C4⋊C4—122no—
409C2×C4⋊C4—122no—
410C2×C4⋊C4C22×D314yes—
411C2×C4⋊C4C22×D314yes—
412C2×C4⋊C4C22×D314yes—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—34no—
416C2×C22⋊C4—34no—
417C2×C22⋊C4—34no—
418C2×C22⋊C4—34no—
419C2×C22⋊C4—34no—
420C2×C22⋊C4—34no—
421C2×C22⋊C4—34no—
422C2×C22⋊C4—42no—
423C2×C22⋊C4—64no—
424C2×C22⋊C4—64no—
425C2×C22⋊C4—64no—
426C2×C22⋊C4—64no—
427C2×C22⋊C4—64no—
428C2×C22⋊C4—64no—
429C2×C22⋊C4—122no—
430C2×C22⋊C4C22×D314yes—
431C2×C22⋊C4C22×D314yes—
432C2×C22⋊C4C22×D314yes—
433C2×C42—34no—
434C2×C42—122no—
435#95—34no—
436#95—34no—
437#95—34no—
438#95—34no—
439#95—34no—
440#95C22×D314yes—
441C23×C3—28no—
442C23×C3—28no—
443C23×C3—28no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—44no—
451C23×C3—44no—
452C23×C3—44no—
453C23×C3—44no—
454C23×C3C22×D412yes—
455C23×C3C22×D412yes—
456C23×C3C22×Q814yes—
457C23×C3C22×Q812yes—
458C23×C3H(5,𝔽2)12yes—
459C23×C3H(5,𝔽2)12yes—
460C23×C32−1+412yes—
461C23×C32−1+412yes—
462C23×C3C2511yescharacteristic
463C22×D3—28no—
464C22×D3—28no—
465C22×D3—28no—
466C22×D3—22no—
467C22×D3—22no—
468C22×D3—22no—
469C22×D3—22no—
470C22×D3—22no—
471C22×D3—22no—
472C22×D3—44no—
473C22×D3—44no—
474C22×D3—44no—
475C22×D3—44no—
476C22×D3C22×Q814yes—
477C2×C3×C4—28no—
478C2×C3×C4—28no—
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—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—44no—
496C2×C3×C4—44no—
497C2×C3×C4—44no—
498C2×C3×C4—44no—
499C2×C3×C4C22×D414yes—
500C2×C3×C4C22×D414yes—
501#67—416no—
502C2×Dic3—28no—
503C2×Dic3—28no—
504C2×Dic3—28no—
505C2×Dic3—28no—
506C2×Dic3—28no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3—22no—
516C2×Dic3—22no—
517C2×Dic3—22no—
518C2×Dic3—22no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—416no—
524C2×Dic3—44no—
525C2×Dic3—44no—
526C2×Dic3C22×D414yes—
527C2×Dic3C22×D414yes—
528C2×Dic3C22×D414yes—
529C2×Dic3C22×D414yes—
530C2×Dic3C22×Q814yes—
531C4×D3—416no—
532Dic6—416no—
533Dic6—416no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—34no—
541C24—32no—
542C24—62no—
543C24—62no—
544C24—62no—
545C24—62no—
546C24—62no—
547C24—62no—
548C24D3×Q814yes—
549C24C23×D312yes—
550C24C23×D311yescharacteristic
551C2×Q8—68no—
552C2×Q8—68no—
553C2×Q8—68no—
554C2×Q8—68no—
555C2×Q8—124no—
556C2×Q8—124no—
557C2×Q8—1216no—
558C2×Q8—1216no—
559C2×D4—316no—
560C2×D4—1216no—
561C2×D4—124no—
562C2×D4—124no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—34no—
580C22×C4—34no—
581C22×C4—34no—
582C22×C4—34no—
583C22×C4—34no—
584C22×C4—32no—
585C22×C4—32no—
586C22×C4—32no—
587C22×C4—32no—
588C22×C4—32no—
589C22×C4—32no—
590C22×C4—32no—
591C22×C4—68no—
592C22×C4—68no—
593C22×C4—68no—
594C22×C4—62no—
595C22×C4—62no—
596C22×C4—62no—
597C22×C4—62no—
598C22×C4—62no—
599C22×C4—62no—
600C22×C4—62no—
601C22×C4—62no—
602C22×C4—62no—
603C22×C4—62no—
604C22×C4—62no—
605C22×C4—62no—
606C22×C4—62no—
607C22×C4—62no—
608C22×C4—62no—
609C22×C4—62no—
610C22×C4—68no—
611C22×C4—124no—
612C22×C4—1216no—
613C22×C4—124no—
614C22×C4—1216no—
615C22×C4D3×D414yes—
616C22×C4D3×D414yes—
617C22×C4C23×D312yes—
618C22×C4C23×D312yes—
619C22×C4C23×D312yes—
620C22×C4C23×D312yes—
621C22×C4C23×D312yes—
622C22×C4C23×D312yes—
623C4⋊C4—28no—
624C4⋊C4—28no—
625C4⋊C4—316no—
626C4⋊C4—316no—
627C4⋊C4—44no—
628C4⋊C4—68no—
629C4⋊C4—68no—
630C4⋊C4—68no—
631C4⋊C4—68no—
632C4⋊C4—68no—
633C4⋊C4—68no—
634C4⋊C4—124no—
635C4⋊C4—124no—
636C22⋊C4—28no—
637C22⋊C4—28no—
638C22⋊C4—44no—
639C22⋊C4—68no—
640C22⋊C4—68no—
641C22⋊C4—68no—
642C22⋊C4—68no—
643C22⋊C4—68no—
644C22⋊C4—68no—
645C22⋊C4—124no—
646C42—124no—
647C22×C3—24no—
648C22×C3—24no—
649C22×C3—24no—
650C22×C3—42no—
651C22×C3—42no—
652C22×C3—416no—
653C22×C3—42no—
654C22×C3—42no—
655C22×C3#53714yes—
656C22×C3#53714yes—
657C22×C3#54314yes—
658C22×C3D4214yes—
659C22×C3D4×Q814yes—
660C22×C3D4×Q814yes—
661C22×C3#56314yes—
662C22×C3C23×D411yescharacteristic
663C22×C3C23×D411yescharacteristic
664C22×C3C23×Q811yescharacteristic
665C22×C3C2×H(5,𝔽2)11yescharacteristic
666C22×C3C2×H(5,𝔽2)11yescharacteristic
667C22×C3C2×2−1+411yescharacteristic
668C22×C3C2×2−1+411yescharacteristic
669C2×D3—24no—
670C2×D3—24no—
671C2×D3—24no—
672C2×D3—42no—
673C2×D3—42no—
674C2×D3—416no—
675C2×D3—42no—
676C2×D3—42no—
677C3×C4—24no—
678C3×C4—24no—
679C3×C4—42no—
680C3×C4—42no—
681C3×C4—42no—
682C3×C4—42no—
683Dic3—24no—
684Dic3—24no—
685Dic3—24no—
686Dic3—24no—
687Dic3—24no—
688Dic3—42no—
689Dic3—42no—
690C23—28no—
691C23—28no—
692C23—28no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—34no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—68no—
705C23—68no—
706C23—68no—
707C23—62no—
708C23—62no—
709C23—62no—
710C23—62no—
711C23—62no—
712C23—62no—
713C23—124no—
714C23—124no—
715C23—124no—
716C23—124no—
717C23C2×D3×D412yes—
718C23C2×D3×D412yes—
719C23#100412yes—
720C23C2×D3×Q814yes—
721C23C2×D3×Q812yes—
722C23#100912yes—
723C23#101012yes—
724C23#101012yes—
725C23C24×D311yescharacteristic
726Q8—1216no—
727Q8—1216no—
728D4—1216no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—28no—
734C2×C4—28no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—34no—
748C2×C4—34no—
749C2×C4—34no—
750C2×C4—34no—
751C2×C4—34no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—68no—
757C2×C4—62no—
758C2×C4—62no—
759C2×C4—62no—
760C2×C4—62no—
761C2×C4—62no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—62no—
765C2×C4—62no—
766C2×C4—62no—
767C2×C4—68no—
768C2×C4—68no—
769C2×C4—68no—
770C2×C4—68no—
771C2×C4—62no—
772C2×C4—62no—
773C2×C4—62no—
774C2×C4—62no—
775C2×C4—62no—
776C2×C4—62no—
777C2×C4—1216no—
778C2×C4—1216no—
779C2×C4—124no—
780C2×C4—124no—
781C2×C4C2×D3×D414yes—
782C2×C4C2×D3×D414yes—
783C2×C3—44no—
784C2×C3#268318yescomplemented
785C2×C3C2×#53711yescharacteristic
786C2×C3C2×#53711yescharacteristic
787C2×C3C2×#54311yescharacteristic
788C2×C3C2×D4211yescharacteristic
789C2×C3C2×D4×Q811yescharacteristic
790C2×C3C2×D4×Q811yescharacteristic
791C2×C3C2×#56311yescharacteristic
792D3—44no—
793C22—24no—
794C22—24no—
795C22—24no—
796C22—42no—
797C22—416no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—64no—
802C22—64no—
803C22—64no—
804C22—122no—
805C22—1216no—
806C22—122no—
807C22—122no—
808C22—122no—
809C22#559714yes—
810C22#560814yes—
811C22#560914yes—
812C22#563214yes—
813C22#563214yes—
814C22#563414yes—
815C22#571214yes—
816C22C22×D3×D411yescharacteristic
817C22C22×D3×D411yescharacteristic
818C22C2×#100411yescharacteristic
819C22C22×D3×Q811yescharacteristic
820C22C2×#100911yescharacteristic
821C22C2×#101011yescharacteristic
822C22C2×#101011yescharacteristic
823C4—24no—
824C4—24no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—64no—
830C4—64no—
831C4—64no—
832C4—64no—
833C4—64no—
834C4—122no—
835C4—122no—
836C3C2×#268311yescharacteristic, complemented, Sylow
837C2—44no—
838C2—124no—
839C2#7743318yesdirect product factor
840C2C2×#559711yescharacteristic
841C2C2×#560811yescharacteristic
842C2C2×#560911yescharacteristic
843C2C2×#563211yescharacteristic
844C2C2×#563211yescharacteristic
845C2C2×#563411yescharacteristic
846C2C2×#571211yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#396C2
socleC24×C3C24
prime radicalC23×#67C22
hypercenterC2×#396D3
hypocenterC3C2×#2683
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#896C2semidirect
2. C22×#897C2semidirect
3. C22×#878C2semidirect
4. C22×#878C2semidirect
5. C2×C3×#396C2semidirect
6. C2×#4994C2semidirect
7. C2×#4979C2semidirect
8. C2×#4976C2semidirect
9. C2×#4972C2semidirect
11. C2×#4948C2semidirect
14. #77433C2direct (N × H)
15. C2×#4676C2semidirect
16. C2×#4656C2semidirect
48. C2×#897C22semidirect
50. C2×#896C22semidirect
53. C2×#878C22semidirect
54. C2×#878C22semidirect
55. C3×#396C22semidirect
62. #4994C22semidirect
63. #4979C22semidirect
64. #4976C22semidirect
65. #4972C22semidirect
69. #4948C22semidirect
70. #4676C22semidirect
71. #4656C22semidirect
80. C2×#396D3semidirect
98. C22×#67Q8semidirect
151. C2×C4⋊Dic3D4semidirect
161. C2×Dic3⋊C4D4semidirect
221. #396C2×D3semidirect
279. C2×#67C2×Q8semidirect
339. C4⋊Dic3C2×D4semidirect
346. Dic3⋊C4C2×D4semidirect
784. C2×C3#2683semidirect
836. C3C2×#2683semidirect
839. C2#77433direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#8962
C22×#8972
C22×#8782
C2×C3×#3962
C2×#49942
C2×#49792
C2×#49762
C2×#49722
C2×#49562
C2×#49482
C2×#49572
C2×#49582
#774332
C2×#46762
C2×#46562
C2×#26833