Finite Group Databasebeta

← #11660639

Subgroups — #11660639

Order 768.

1772 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#529C211yesmaximal, characteristic
2#83133C214yesmaximal, complemented
3#83130C214yesmaximal, complemented
4#83128C214yesmaximal, complemented
5#83127C214yesmaximal, complemented
6#82436C212yesmaximal, complemented
7#82303C214yesmaximal, complemented
8#82302C212yesmaximal, complemented
9#82210C214yesmaximal, complemented
10#82049C211yesmaximal, characteristic, complemented
11C2×#4926C211yesmaximal, characteristic, complemented
12#60291—31nomaximal, Sylow
13C3×#529C412yes—
14C3×#529C412yes—
15C3×#529C412yes—
16C3×#529C412yes—
17C3×#529C2212yes—
18C3×#529C2212yes—
19C3×#529C2212yes—
20C3×#529C2212yes—
21C2×C3×#126C412yes—
22C2×C3×#125C411yescharacteristic
23C2×C3×#124C411yescharacteristic
24C2×C3×#123C412yes—
25C2×C3×C22⋊Q8C411yescharacteristic
26C2×C3×#121C411yescharacteristic
27C2×C3×C4×Q8C2211yescharacteristic
28C2×C3×C4×D4C2211yescharacteristic
29C2×C3×C4×D4C2212yes—
30C2×C3×#117C2212yes—
31C22×C3×C42C2211yescharacteristic
32#5207C2214yes—
33#5207C2212yes—
34C2×#830C2214yes—
35C2×#830C2212yes—
36#5024C2218yescomplemented
37#5024C2218yescomplemented
38#5012C2218yescomplemented
39#5011C2218yescomplemented
40#5011C2218yescomplemented
41#5011C2218yescomplemented
42#5011C2218yescomplemented
43D4×C3⋊C8C2218yescomplemented
44#5000C2218yescomplemented
45#5000C2218yescomplemented
46#4999C2218yescomplemented
47#4997C2218yescomplemented
48#4926C2214yes—
49#4926C2212yes—
50#4926C2212yes—
51#4926C2212yes—
52#4926C2212yescomplemented
53#4926C2212yescomplemented
54#4926C2212yescomplemented
55#4925C2214yes—
56#4925C2212yes—
57#4925C2212yescomplemented
58#4924C2212yescomplemented
59C2×C4⋊(C3⋊C8)C2212yescomplemented
60C4×#208C2212yescomplemented
61C2×#803C2212yescomplemented
62C2×#529D311yescharacteristic
63#2995—34no—
64#2992—34no—
65#2983—32no—
66#2974—34no—
67#2973—32no—
68#2968—34no—
69#2967—34no—
70#2924—34no—
71#2920—31no—
72C2×#432—31no—
73C22×C3×Q8C2×C411yescharacteristic
74C22×C3×D4C2×C412yes—
75C22×C3×D4C2×C411yescharacteristic
76C23×C3×C4C2×C411yescharacteristic
77C23×C3×C4C2×C411yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2312yes—
80C3×#126C2×C414yes—
81C3×#126C2×C414yes—
82C3×#126C2×C414yes—
83C3×#126C2×C414yes—
84C3×#125C2×C412yes—
85C3×#125C2×C412yes—
86C3×#125C2×C412yes—
87C3×#125C2×C412yes—
88C3×#124C2×C412yes—
89C3×#124C2×C412yes—
90C3×#124C2×C412yes—
91C3×#124C2×C412yes—
92C3×#123C2×C414yes—
93C3×#123C2×C414yes—
94C3×#123C2×C414yes—
95C3×#123C2×C414yes—
96C3×C22⋊Q8C2×C412yes—
97C3×C22⋊Q8C2×C412yes—
98C3×C22⋊Q8C2×C412yes—
99C3×C22⋊Q8C2×C412yes—
100C3×#121C2×C412yes—
101C3×#121C2×C412yes—
102C3×#121C2×C412yes—
103C3×#121C2×C412yes—
104C3×C4×Q8C2×C412yes—
105C3×C4×Q8C2×C412yes—
106C3×C4×Q8C2312yes—
107C3×C4×Q8C2312yes—
108C3×C4×D4C2×C412yes—
109C3×C4×D4C2×C412yes—
110C3×C4×D4C2×C414yes—
111C3×C4×D4C2×C414yes—
112C3×C4×D4C2314yes—
113C3×C4×D4C2312yes—
114C3×C4×D4C2312yes—
115C3×C4×D4C2314yes—
116C3×#117C2×C414yes—
117C3×#117C2×C414yes—
118C3×#117C2314yes—
119C3×#117C2314yes—
120C2×C3×C4⋊C4C2×C412yes—
121C2×C3×C4⋊C4C2×C412yes—
122C2×C3×C4⋊C4C2×C411yescharacteristic
123C2×C3×C4⋊C4C2×C412yes—
124C2×C3×C4⋊C4C2×C411yescharacteristic
125C2×C3×C4⋊C4C2×C412yes—
126C2×C3×C22⋊C4C2×C412yes—
127C2×C3×C22⋊C4C2×C412yes—
128C2×C3×C22⋊C4C2×C412yes—
129C2×C3×C22⋊C4C2×C412yes—
130C2×C3×C22⋊C4C2×C412yes—
131C2×C3×C42C2×C411yescharacteristic
132C2×C3×C42C2×C411yescharacteristic
133C2×C3×C42C2×C411yescharacteristic
134C2×C3×C42C2×C411yescharacteristic
135C2×C3×C42C2×C411yescharacteristic
136C2×C3×C42C2×C411yescharacteristic
137C2×C3×C42C2311yescharacteristic
138C2×C3×C42C2311yescharacteristic
139C2×C3×C42C2311yescharacteristic
140C2×C3×C42C2311yescharacteristic
141C2×C3×C42C2311yescharacteristic
142C2×C3×C42C2312yes—
143C2×C3×C42C2311yescharacteristic
144C2×#208C2314yes—
145C2×#208C2318yes—
146C22×C3⋊C8C2314yes—
147C22×C3⋊C8C2318yes—
148#830C2314yes—
149#830C2314yes—
150#830C2314yes—
151#830C2314yes—
152#830C2318yes—
153#830C2318yes—
154C4⋊(C3⋊C8)C2314yes—
155C4⋊(C3⋊C8)C2314yes—
156C4⋊(C3⋊C8)C2314yes—
157C4⋊(C3⋊C8)C2314yes—
158C4⋊(C3⋊C8)C2318yes—
159C4⋊(C3⋊C8)C2318yes—
160#803C2314yes—
161#803C2314yes—
162#803C2314yes—
163#803C2318yes—
164C4×C3⋊C8C2314yes—
165C4×C3⋊C8C2318yes—
166#529Dic312yes—
167#529Dic312yes—
168#529Dic312yes—
169#529Dic312yes—
170#529C2×D312yes—
171#529C2×D312yes—
172#529C2×D312yes—
173#529C2×D312yes—
174C2×#126Dic312yes—
175C2×#125Dic311yescharacteristic
176C2×#124Dic311yescharacteristic
177C2×#123Dic312yes—
178C2×C22⋊Q8Dic311yescharacteristic
179C2×#121Dic311yescharacteristic
180C2×C4×Q8C2×D311yescharacteristic
181C2×C4×D4C2×D311yescharacteristic
182C2×C4×D4C2×D312yes—
183C2×#117C2×D312yes—
184C22×C42C2×D311yescharacteristic
185#446—38no—
186#446—38no—
187#436—38no—
188#435—38no—
189#435—38no—
190#435—38no—
191#435—38no—
192C8×D4—38no—
193#433—38no—
194#433—38no—
195#432—32no—
196#432—32no—
197#432—32no—
198#432—34no—
199#432—32no—
200#432—32no—
201#432—32no—
202#431—32no—
203#431—34no—
204#431—32no—
205#424—38no—
206#423—32no—
207C2×C4⋊C8—32no—
208#407—32no—
209#407—34no—
210C2×C22⋊C8—32no—
211C2×C22⋊C8—34no—
212#405—38no—
213C4×M16—32no—
214C2×#97—32no—
215C24×C3C22×C411yescharacteristic
216C24×C3C22×C412yes—
217C2×C3×Q8—42no—
218C2×C3×Q8C22×C412yes—
219C2×C3×Q8C22×C412yes—
220C2×C3×D4—42no—
221C2×C3×D4—44no—
222C2×C3×D4C22×C414yes—
223C2×C3×D4C22×C414yes—
224C2×C3×D4C22×C412yes—
225C2×C3×D4C22×C412yes—
226C22×C3×C4—42no—
227C22×C3×C4—44no—
228C22×C3×C4—42no—
229C22×C3×C4—42no—
230C22×C3×C4C22×C411yescharacteristic
231C22×C3×C4C22×C411yescharacteristic
232C22×C3×C4C22×C411yescharacteristic
233C22×C3×C4C22×C411yescharacteristic
234C22×C3×C4C22×C412yes—
235C22×C3×C4C22×C411yescharacteristic
236C22×C3×C4C22×C411yescharacteristic
237C22×C3×C4C22×C411yescharacteristic
238C22×C3×C4C22×C411yescharacteristic
239C22×C3×C4C22×C411yescharacteristic
240C22×C3×C4C22×C411yescharacteristic
241C22×C3×C4C22×C411yescharacteristic
242C22×C3×C4C22×C411yescharacteristic
243C22×C3×C4C22×C411yescharacteristic
244C22×C3×C4C22×C411yescharacteristic
245C22×C3×C4C22×C411yescharacteristic
246C22×C3×C4C22×C412yes—
247C22×C3×C4C22×C412yes—
248C22×C3×C4C22×C414yes—
249C22×C3×C4C2411yescharacteristic
250C22×C3×C4C2411yescharacteristic
251C22×C3×C4C2414yes—
252C22×C3×C4C2411yescharacteristic
253C3×C4⋊C4C22×C414yes—
254C3×C4⋊C4C22×C414yes—
255C3×C4⋊C4C22×C414yes—
256C3×C4⋊C4C22×C414yes—
257C3×C4⋊C4C22×C412yes—
258C3×C4⋊C4C22×C412yes—
259C3×C4⋊C4C22×C414yes—
260C3×C4⋊C4C22×C414yes—
261C3×C4⋊C4C22×C412yes—
262C3×C4⋊C4C22×C412yes—
263C3×C4⋊C4C22×C414yes—
264C3×C4⋊C4C22×C414yes—
265C3×C22⋊C4C22×C414yes—
266C3×C22⋊C4C22×C414yes—
267C3×C22⋊C4C22×C414yes—
268C3×C22⋊C4C22×C414yes—
269C3×C22⋊C4C22×C414yes—
270C3×C22⋊C4C22×C414yes—
271C3×C22⋊C4C22×C414yes—
272C3×C22⋊C4C22×C414yes—
273C3×C22⋊C4C22×C414yes—
274C3×C22⋊C4C22×C414yes—
275C3×C42C22×C411yescharacteristic
276C3×C42C22×C411yescharacteristic
277C3×C42C22×C411yescharacteristic
278C3×C42C22×C411yescharacteristic
279C3×C42C22×C411yescharacteristic
280C3×C42C22×C411yescharacteristic
281C3×C42C22×C411yescharacteristic
282C3×C42C22×C411yescharacteristic
283C3×C42C22×C411yescharacteristic
284C3×C42C22×C411yescharacteristic
285C3×C42C22×C411yescharacteristic
286C3×C42C22×C411yescharacteristic
287C3×C42C22×C414yes—
288C3×C42C2411yescharacteristic
289C3×C42C2414yes—
290C3×C42C2411yescharacteristic
291C3×C42C2411yescharacteristic
292C3×C42C2411yescharacteristic
293#208—48no—
294#208—44no—
295C2×C3⋊C8—44no—
296C2×C3⋊C8—48no—
297C2×C3⋊C8C2418yes—
298C2×C3⋊C8C2418yes—
299C22×Q8C2×Dic311yescharacteristic
300C22×D4C2×Dic312yes—
301C22×D4C2×Dic311yescharacteristic
302C23×C4C2×Dic311yescharacteristic
303C23×C4C2×Dic311yescharacteristic
304C23×C4C22×D312yes—
305C23×C4C22×D311yescharacteristic
306C2×M16—34no—
307C2×M16—38no—
308C22×C8—34no—
309C22×C8—38no—
310#126C2×Dic314yes—
311#126C2×Dic314yes—
312#126C2×Dic314yes—
313#126C2×Dic314yes—
314#125C2×Dic312yes—
315#125C2×Dic312yes—
316#125C2×Dic312yes—
317#125C2×Dic312yes—
318#124C2×Dic312yes—
319#124C2×Dic312yes—
320#124C2×Dic312yes—
321#124C2×Dic312yes—
322#123C2×Dic314yes—
323#123C2×Dic314yes—
324#123C2×Dic314yes—
325#123C2×Dic314yes—
326C22⋊Q8C2×Dic312yes—
327C22⋊Q8C2×Dic312yes—
328C22⋊Q8C2×Dic312yes—
329C22⋊Q8C2×Dic312yes—
330#121C2×Dic312yes—
331#121C2×Dic312yes—
332#121C2×Dic312yes—
333#121C2×Dic312yes—
334C4×Q8C2×Dic312yes—
335C4×Q8C2×Dic312yes—
336C4×Q8C22×D312yes—
337C4×Q8C22×D312yes—
338C4×D4C2×Dic312yes—
339C4×D4C2×Dic312yes—
340C4×D4C2×Dic314yes—
341C4×D4C2×Dic314yes—
342C4×D4C22×D314yes—
343C4×D4C22×D312yes—
344C4×D4C22×D312yes—
345C4×D4C22×D314yes—
346#117C2×Dic314yes—
347#117C2×Dic314yes—
348#117C22×D314yes—
349#117C22×D314yes—
350C2×C4⋊C4C2×Dic312yes—
351C2×C4⋊C4C2×Dic312yes—
352C2×C4⋊C4C2×Dic311yescharacteristic
353C2×C4⋊C4C2×Dic312yes—
354C2×C4⋊C4C2×Dic311yescharacteristic
355C2×C4⋊C4C2×Dic312yes—
356C2×C22⋊C4C2×Dic312yes—
357C2×C22⋊C4C2×Dic312yes—
358C2×C22⋊C4C2×Dic312yes—
359C2×C22⋊C4C2×Dic312yes—
360C2×C22⋊C4C2×Dic312yes—
361C2×C42C2×Dic311yescharacteristic
362C2×C42C2×Dic311yescharacteristic
363C2×C42C2×Dic311yescharacteristic
364C2×C42C2×Dic311yescharacteristic
365C2×C42C2×Dic311yescharacteristic
366C2×C42C2×Dic311yescharacteristic
367C2×C42C22×D311yescharacteristic
368C2×C42C22×D312yes—
369C2×C42C22×D311yescharacteristic
370C2×C42C22×D311yescharacteristic
371C2×C42C22×D311yescharacteristic
372C2×C42C22×D311yescharacteristic
373C2×C42C22×D311yescharacteristic
374C4⋊C8—34no—
375C4⋊C8—34no—
376C4⋊C8—34no—
377C4⋊C8—34no—
378C4⋊C8—38no—
379C4⋊C8—38no—
380C22⋊C8—34no—
381C22⋊C8—34no—
382C22⋊C8—34no—
383C22⋊C8—38no—
384C22⋊C8—34no—
385C22⋊C8—38no—
386#97—34no—
387#97—34no—
388#97—34no—
389#97—38no—
390C4×C8—34no—
391C4×C8—38no—
392C23×C3—22no—
393C23×C3—22no—
394C23×C3—24no—
395C23×C3—41no—
396C23×C3—42no—
397C23×C3—42no—
398C23×C3C23×C414yes—
399C23×C3C23×C411yescharacteristic
400C23×C3C23×C411yescharacteristic
401C23×C3C23×C411yescharacteristic
402C3×Q8—42no—
403C3×Q8—42no—
404C3×D4—28no—
405C3×D4—42no—
406C3×D4—42no—
407C3×D4—44no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—24no—
413C2×C3×C4—22no—
414C2×C3×C4—28no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—41no—
418C2×C3×C4—41no—
419C2×C3×C4—44no—
420C2×C3×C4—41no—
421C2×C3×C4—42no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—42no—
431C2×C3×C4C23×C411yescharacteristic
432C2×C3×C4C23×C411yescharacteristic
433C2×C3×C4C23×C411yescharacteristic
434C2×C3×C4C23×C411yescharacteristic
435C2×C3×C4C23×C411yescharacteristic
436C2×C3×C4C23×C411yescharacteristic
437C2×C3×C4C23×C411yescharacteristic
438C2×C3×C4C23×C411yescharacteristic
439C2×C3×C4C23×C411yescharacteristic
440C2×C3×C4C23×C411yescharacteristic
441C2×C3×C4C23×C411yescharacteristic
442C2×C3×C4C23×C414yes—
443C2×C3×C4C23×C414yes—
444C2×C3×C4C23×C414yes—
445C2×C3×C4C2511yescharacteristic
446C3⋊C8—28no—
447C3⋊C8—28no—
448C24C22×Dic311yescharacteristic
449C24C22×Dic312yes—
450C2×Q8—42no—
451C2×Q8C22×Dic312yes—
452C2×Q8C22×Dic312yes—
453C2×D4—42no—
454C2×D4—44no—
455C2×D4C22×Dic314yes—
456C2×D4C22×Dic314yes—
457C2×D4C22×Dic312yes—
458C2×D4C22×Dic312yes—
459C22×C4—42no—
460C22×C4—44no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4C22×Dic311yescharacteristic
464C22×C4C22×Dic311yescharacteristic
465C22×C4C22×Dic311yescharacteristic
466C22×C4C22×Dic311yescharacteristic
467C22×C4C22×Dic312yes—
468C22×C4C22×Dic311yescharacteristic
469C22×C4C22×Dic311yescharacteristic
470C22×C4C22×Dic311yescharacteristic
471C22×C4C22×Dic311yescharacteristic
472C22×C4C22×Dic311yescharacteristic
473C22×C4C22×Dic311yescharacteristic
474C22×C4C22×Dic311yescharacteristic
475C22×C4C22×Dic311yescharacteristic
476C22×C4C22×Dic311yescharacteristic
477C22×C4C22×Dic311yescharacteristic
478C22×C4C22×Dic311yescharacteristic
479C22×C4C22×Dic312yes—
480C22×C4C22×Dic312yes—
481C22×C4C22×Dic314yes—
482C22×C4C23×D311yescharacteristic
483C22×C4C23×D311yescharacteristic
484C22×C4C23×D311yescharacteristic
485C22×C4C23×D314yes—
486M16—128no—
487M16—124no—
488C2×C8—38no—
489C2×C8—38no—
490C2×C8—124no—
491C2×C8—128no—
492C4⋊C4C22×Dic314yes—
493C4⋊C4C22×Dic314yes—
494C4⋊C4C22×Dic314yes—
495C4⋊C4C22×Dic314yes—
496C4⋊C4C22×Dic312yes—
497C4⋊C4C22×Dic312yes—
498C4⋊C4C22×Dic314yes—
499C4⋊C4C22×Dic314yes—
500C4⋊C4C22×Dic312yes—
501C4⋊C4C22×Dic312yes—
502C4⋊C4C22×Dic314yes—
503C4⋊C4C22×Dic314yes—
504C22⋊C4C22×Dic314yes—
505C22⋊C4C22×Dic314yes—
506C22⋊C4C22×Dic314yes—
507C22⋊C4C22×Dic314yes—
508C22⋊C4C22×Dic314yes—
509C22⋊C4C22×Dic314yes—
510C22⋊C4C22×Dic314yes—
511C22⋊C4C22×Dic314yes—
512C22⋊C4C22×Dic314yes—
513C22⋊C4C22×Dic314yes—
514C42C22×Dic311yescharacteristic
515C42C22×Dic311yescharacteristic
516C42C22×Dic311yescharacteristic
517C42C22×Dic311yescharacteristic
518C42C22×Dic311yescharacteristic
519C42C22×Dic311yescharacteristic
520C42C22×Dic311yescharacteristic
521C42C22×Dic311yescharacteristic
522C42C22×Dic311yescharacteristic
523C42C22×Dic311yescharacteristic
524C42C22×Dic311yescharacteristic
525C42C22×Dic311yescharacteristic
526C42C22×Dic314yes—
527C42C23×D311yescharacteristic
528C42C23×D314yes—
529C42C23×D311yescharacteristic
530C42C23×D311yescharacteristic
531C42C23×D311yescharacteristic
532C22×C3—21no—
533C22×C3—21no—
534C22×C3—21no—
535C22×C3—21no—
536C22×C3—21no—
537C22×C3—24no—
538C22×C3—21no—
539C22×C3—21no—
540C22×C3—24no—
541C22×C3—24no—
542C22×C3—44no—
543C22×C3—84no—
544C22×C3#56812yes—
545C22×C3#56812yes—
546C22×C3C24×C411yescharacteristic
547C3×C4—21no—
548C3×C4—21no—
549C3×C4—24no—
550C3×C4—21no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4—21no—
554C3×C4—21no—
555C3×C4—21no—
556C3×C4—21no—
557C3×C4—21no—
558C3×C4—21no—
559C3×C4—24no—
560C3×C4—24no—
561C3×C4#58512yes—
562C23—22no—
563C23—22no—
564C23—24no—
565C23—41no—
566C23—42no—
567C23—42no—
568C23C23×Dic314yes—
569C23C23×Dic311yescharacteristic
570C23C23×Dic311yescharacteristic
571C23C23×Dic311yescharacteristic
572Q8—42no—
573Q8—42no—
574D4—28no—
575D4—42no—
576D4—42no—
577D4—44no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—24no—
583C2×C4—22no—
584C2×C4—28no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—44no—
598C2×C4—41no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4C23×Dic311yescharacteristic
602C2×C4C23×Dic311yescharacteristic
603C2×C4C23×Dic311yescharacteristic
604C2×C4C23×Dic311yescharacteristic
605C2×C4C23×Dic311yescharacteristic
606C2×C4C23×Dic311yescharacteristic
607C2×C4C23×Dic311yescharacteristic
608C2×C4C23×Dic311yescharacteristic
609C2×C4C23×Dic311yescharacteristic
610C2×C4C23×Dic311yescharacteristic
611C2×C4C23×Dic311yescharacteristic
612C2×C4C23×Dic314yes—
613C2×C4C23×Dic314yes—
614C2×C4C23×Dic314yes—
615C2×C4C24×D311yescharacteristic
616C8—68no—
617C8—68no—
618C2×C3—22no—
619C2×C3—22no—
620C2×C3—41no—
621C2×C3—44no—
622C2×C3#342811yescharacteristic
623C2×C3C2×#56811yescharacteristic
624C2×C3C2×#56811yescharacteristic
625C22—21no—
626C22—21no—
627C22—21no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—24no—
632C22—24no—
633C22—21no—
634C22—24no—
635C22—44no—
636C22—84no—
637C22#581912yes—
638C22#581912yes—
639C22C24×Dic311yescharacteristic
640C4—21no—
641C4—21no—
642C4—21no—
643C4—21no—
644C4—21no—
645C4—21no—
646C4—21no—
647C4—21no—
648C4—24no—
649C4—24no—
650C4—21no—
651C4—21no—
652C4—24no—
653C4—21no—
654C4#596412yes—
655C3#6029111yescharacteristic, complemented, Sylow
656C2—22no—
657C2—22no—
658C2—41no—
659C2—44no—
660C2C2×#581911yescharacteristic
661C2C2×#581911yescharacteristic
662C2#8726011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D3
commutator, socleC22×C3C24×C4
FittingC2×C3×#529C2
prime radicalC2×C3×#121C4
cosocleC2×C3×C4C25
hypercenterC2×#529D3
hypocenterC3#60291
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
2. #83133C2semidirect
3. #83130C2semidirect
4. #83128C2semidirect
5. #83127C2semidirect
6. #82436C2semidirect
7. #82303C2semidirect
8. #82302C2semidirect
9. #82210C2semidirect
10. #82049C2semidirect
11. C2×#4926C2semidirect
36. #5024C22semidirect
37. #5024C22semidirect
38. #5012C22semidirect
39. #5011C22semidirect
40. #5011C22semidirect
41. #5011C22semidirect
42. #5011C22semidirect
43. D4×C3⋊C8C22semidirect
44. #5000C22semidirect
45. #5000C22semidirect
46. #4999C22semidirect
47. #4997C22semidirect
52. #4926C22semidirect
53. #4926C22semidirect
54. #4926C22semidirect
57. #4925C22semidirect
58. #4924C22semidirect
59. C2×C4⋊(C3⋊C8)C22semidirect
60. C4×#208C22semidirect
61. C2×#803C22semidirect
655. C3#60291semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5292
#831332
#831302
#831282
#831272
#824362
#823032
#823022
#822102
#820492
C2×#49262
#602913