Finite Group Databasebeta

← C3×#21874 #10640481

Subgroups — C3×#21874 #10640481

Order 768.

1598 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#525C211yesmaximal, characteristic
2C3×#2280C211yesmaximal, characteristic, complemented
3C2×C3×#380C211yesmaximal, characteristic, complemented
4C3×#1996C212yesmaximal, complemented
5C3×#1964C212yesmaximal, complemented
6C3×#1898C214yesmaximal, complemented
7C3×#1799C214yesmaximal, complemented
8#21874C311yesmaximal, characteristic, direct product factor, Sylow
9C22×C3×#41C411yescharacteristic, complemented
10C24×C3×C4C2211yescharacteristic
11C3×#525—21no—
12C3×#525—21no—
13C3×#525—21no—
14C3×#525—21no—
15C3×#525—21no—
16C3×#525—21no—
17C3×#525—21no—
18C3×#525—21no—
19C2×C3×#123C412yescomplemented
20C2×C3×C22⋊Q8C411yescharacteristic, complemented
21C2×C3×C22⋊Q8C2211yescharacteristic
22C2×C3×#121C411yescharacteristic, complemented
23C2×C3×#121C2211yescharacteristic
24C2×C3×#120C2212yes—
25C2×C3×C4×D4C412yescomplemented
26C2×C3×C4×D4C2212yes—
27C2×C3×#117—21no—
28C2×C3×#117C411yescharacteristic, complemented
29C22×C3×C4⋊C4—21no—
30C22×C3×C22⋊C4C2212yes—
31C2×C3×#99C2218yes—
32C3×#381—21no—
33C3×#380—21no—
34C3×#380—21no—
35C3×#380—21no—
36C3×#380C2212yes—
37C3×#380C2212yes—
38C3×#380C2212yes—
39C3×#379C2212yes—
40C3×C4×C22⋊C4—21no—
41C3×C4×C22⋊C4C2212yes—
42C2×C3×#95—21no—
43C3×#342C2218yes—
44C2×#525C2×C311yescharacteristic
45#2280C2×C311yescharacteristic, complemented
46C2×#380C2×C311yescharacteristic, complemented
47#1996C2×C312yescomplemented
48#1964C2×C312yescomplemented
49#1898C2×C314yescomplemented
50#1799C2×C314yescomplemented
51C25×C3C2311yescharacteristic
52C2×C3×#41—21no—
53C2×C3×#41—21no—
54C2×C3×#41—21no—
55C2×C3×#41—21no—
56C2×C3×#41—44no—
57C22×C3×Q8C2×C411yescharacteristic, complemented
58C22×C3×D4C2×C412yes—
59C22×C3×D4C2×C412yes—
60C22×C3×D4C2×C411yescharacteristic, complemented
61C22×C3×D4C2312yes—
62C23×C3×C4—22no—
63C23×C3×C4—44no—
64C23×C3×C4C2×C411yescharacteristic
65C23×C3×C4C2×C411yescharacteristic
66C23×C3×C4C2×C411yescharacteristic
67C23×C3×C4C2×C411yescharacteristic
68C23×C3×C4C2×C412yescomplemented
69C23×C3×C4D411yescharacteristic
70C23×C3×C4D411yescharacteristic
71C23×C3×C4D411yescharacteristic
72C23×C3×C4D411yescharacteristic
73C23×C3×C4D411yescharacteristic
74C23×C3×C4D411yescharacteristic
75C23×C3×C4D411yescharacteristic
76C23×C3×C4D411yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C3×#123—22no—
80C3×#123—22no—
81C3×#123—22no—
82C3×#123—22no—
83C3×C22⋊Q8—21no—
84C3×C22⋊Q8—21no—
85C3×C22⋊Q8—21no—
86C3×C22⋊Q8—21no—
87C3×C22⋊Q8—21no—
88C3×C22⋊Q8—21no—
89C3×C22⋊Q8—21no—
90C3×C22⋊Q8—21no—
91C3×#121—21no—
92C3×#121—21no—
93C3×#121—21no—
94C3×#121—21no—
95C3×#121—21no—
96C3×#121—21no—
97C3×#121—21no—
98C3×#121—21no—
99C3×#120—22no—
100C3×#120—22no—
101C3×#120—22no—
102C3×#120—22no—
103C3×C4×D4—22no—
104C3×C4×D4—22no—
105C3×C4×D4—22no—
106C3×C4×D4—22no—
107C3×C4×D4—22no—
108C3×C4×D4—22no—
109C3×C4×D4—22no—
110C3×C4×D4—22no—
111C3×#117—21no—
112C3×#117—21no—
113C3×#117—21no—
114C3×#117—21no—
115C3×#117—44no—
116C2×C3×C4⋊C4—22no—
117C2×C3×C4⋊C4—22no—
118C2×C3×C4⋊C4—22no—
119C2×C3×C4⋊C4—44no—
120C2×C3×C4⋊C4C2×C411yescharacteristic, complemented
121C2×C3×C4⋊C4C2×C411yescharacteristic, complemented
122C2×C3×C4⋊C4C2×C412yescomplemented
123C2×C3×C4⋊C4C2×C412yescomplemented
124C2×C3×C22⋊C4—22no—
125C2×C3×C22⋊C4—22no—
126C2×C3×C22⋊C4—22no—
127C2×C3×C22⋊C4—44no—
128C2×C3×C22⋊C4C2×C412yes—
129C2×C3×C22⋊C4C2×C412yes—
130C2×C3×C22⋊C4C2×C412yescomplemented
131C2×C3×C22⋊C4C2×C412yescomplemented
132C2×C3×C22⋊C4C2314yes—
133C2×C3×C22⋊C4C2314yes—
134C2×C3×C22⋊C4C2312yes—
135C2×C3×C42—22no—
136C2×C3×C42C2×C412yescomplemented
137C3×#99—48no—
138C3×#95—22no—
139C3×#95—22no—
140C3×#95—22no—
141C3×#95—22no—
142C22×#41C3×C411yescharacteristic, complemented
143C24×C4C22×C311yescharacteristic
144#525—21no—
145#525—21no—
146#525—21no—
147#525—21no—
148#525—21no—
149#525—21no—
150#525—21no—
151#525—21no—
152C2×#123C3×C412yescomplemented
153C2×C22⋊Q8C3×C411yescharacteristic, complemented
154C2×C22⋊Q8C22×C311yescharacteristic
155C2×#121C3×C411yescharacteristic, complemented
156C2×#121C22×C311yescharacteristic
157C2×#120C22×C312yes—
158C2×C4×D4C3×C412yescomplemented
159C2×C4×D4C22×C312yes—
160C2×#117—21no—
161C2×#117C3×C411yescharacteristic, complemented
162C22×C4⋊C4—21no—
163C22×C22⋊C4C22×C312yes—
164C2×#99C22×C318yes—
165#381—21no—
166#380—21no—
167#380—21no—
168#380—21no—
169#380C22×C312yes—
170#380C22×C312yes—
171#380C22×C312yes—
172#379C22×C312yes—
173C4×C22⋊C4—21no—
174C4×C22⋊C4C22×C312yes—
175C2×#95—21no—
176#342C22×C318yes—
177C24×C3—22no—
178C24×C3—22no—
179C24×C3—42no—
180C24×C3—42no—
181C24×C3C22×C411yescharacteristic
182C24×C3C22×C411yescharacteristic
183C24×C3C22×C412yes—
184C24×C3C2×D411yescharacteristic
185C24×C3C2×D411yescharacteristic
186C24×C3C2×D411yescharacteristic
187C24×C3C2×D411yescharacteristic
188C24×C3C2411yescharacteristic
189C3×#41—44no—
190C3×#41—44no—
191C3×#41—44no—
192C3×#41—44no—
193C2×C3×Q8—21no—
194C2×C3×Q8—21no—
195C2×C3×Q8—42no—
196C2×C3×D4—22no—
197C2×C3×D4—22no—
198C2×C3×D4—22no—
199C2×C3×D4—22no—
200C2×C3×D4—22no—
201C2×C3×D4—22no—
202C2×C3×D4—24no—
203C2×C3×D4—24no—
204C2×C3×D4—21no—
205C2×C3×D4—21no—
206C2×C3×D4—42no—
207C2×C3×D4—44no—
208C2×C3×D4—44no—
209C22×C3×C4—24no—
210C22×C3×C4—24no—
211C22×C3×C4—24no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—24no—
215C22×C3×C4—24no—
216C22×C3×C4—42no—
217C22×C3×C4—42no—
218C22×C3×C4—42no—
219C22×C3×C4—42no—
220C22×C3×C4—42no—
221C22×C3×C4—42no—
222C22×C3×C4—42no—
223C22×C3×C4—42no—
224C22×C3×C4—42no—
225C22×C3×C4—42no—
226C22×C3×C4—42no—
227C22×C3×C4—44no—
228C22×C3×C4—44no—
229C22×C3×C4—44no—
230C22×C3×C4—44no—
231C22×C3×C4C22⋊C411yescharacteristic
232C22×C3×C4C22⋊C411yescharacteristic
233C22×C3×C4C22⋊C411yescharacteristic
234C22×C3×C4C22⋊C411yescharacteristic
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⋊C411yescharacteristic
247C22×C3×C4C22×C412yes—
248C22×C3×C4C22×C411yescharacteristic
249C22×C3×C4C22×C411yescharacteristic
250C22×C3×C4C22×C412yes—
251C22×C3×C4C22×C412yes—
252C22×C3×C4C22×C411yescharacteristic
253C22×C3×C4C22×C411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2×D411yescharacteristic
261C22×C3×C4C2×D411yescharacteristic
262C3×C4⋊C4—21no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4—22no—
267C3×C4⋊C4—22no—
268C3×C4⋊C4—22no—
269C3×C4⋊C4—22no—
270C3×C4⋊C4—44no—
271C3×C4⋊C4—44no—
272C3×C4⋊C4—44no—
273C3×C22⋊C4—22no—
274C3×C22⋊C4—22no—
275C3×C22⋊C4—22no—
276C3×C22⋊C4—22no—
277C3×C22⋊C4—22no—
278C3×C22⋊C4—22no—
279C3×C22⋊C4—22no—
280C3×C22⋊C4—22no—
281C3×C22⋊C4—22no—
282C3×C22⋊C4—22no—
283C3×C22⋊C4—24no—
284C3×C22⋊C4—28no—
285C3×C22⋊C4—24no—
286C3×C22⋊C4—44no—
287C3×C22⋊C4—44no—
288C3×C22⋊C4—44no—
289C3×C42—22no—
290C3×C42—22no—
291C3×C42—44no—
292C25C23×C311yescharacteristic
293C2×#41—21no—
294C2×#41—21no—
295C2×#41—21no—
296C2×#41—21no—
297C2×#41—44no—
298C22×Q8C2×C3×C411yescharacteristic, complemented
299C22×D4C2×C3×C412yes—
300C22×D4C2×C3×C412yes—
301C22×D4C2×C3×C411yescharacteristic, complemented
302C22×D4C23×C312yes—
303C23×C4—22no—
304C23×C4—44no—
305C23×C4C2×C3×C411yescharacteristic
306C23×C4C2×C3×C411yescharacteristic
307C23×C4C2×C3×C411yescharacteristic
308C23×C4C2×C3×C411yescharacteristic
309C23×C4C2×C3×C412yescomplemented
310C23×C4C3×D411yescharacteristic
311C23×C4C3×D411yescharacteristic
312C23×C4C3×D411yescharacteristic
313C23×C4C3×D411yescharacteristic
314C23×C4C3×D411yescharacteristic
315C23×C4C3×D411yescharacteristic
316C23×C4C3×D411yescharacteristic
317C23×C4C3×D411yescharacteristic
318C23×C4C23×C311yescharacteristic
319C23×C4C23×C311yescharacteristic
320#123—22no—
321#123—22no—
322#123—22no—
323#123—22no—
324C22⋊Q8—21no—
325C22⋊Q8—21no—
326C22⋊Q8—21no—
327C22⋊Q8—21no—
328C22⋊Q8—21no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331C22⋊Q8—21no—
332#121—21no—
333#121—21no—
334#121—21no—
335#121—21no—
336#121—21no—
337#121—21no—
338#121—21no—
339#121—21no—
340#120—22no—
341#120—22no—
342#120—22no—
343#120—22no—
344C4×D4—22no—
345C4×D4—22no—
346C4×D4—22no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4—22no—
352#117—21no—
353#117—21no—
354#117—21no—
355#117—21no—
356#117—44no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4C2×C3×C411yescharacteristic, complemented
362C2×C4⋊C4C2×C3×C411yescharacteristic, complemented
363C2×C4⋊C4C2×C3×C412yescomplemented
364C2×C4⋊C4C2×C3×C412yescomplemented
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4C2×C3×C412yes—
370C2×C22⋊C4C2×C3×C412yes—
371C2×C22⋊C4C2×C3×C412yescomplemented
372C2×C22⋊C4C2×C3×C412yescomplemented
373C2×C22⋊C4C23×C314yes—
374C2×C22⋊C4C23×C314yes—
375C2×C22⋊C4C23×C312yes—
376C2×C42—22no—
377C2×C42C2×C3×C412yescomplemented
378#99—48no—
379#95—22no—
380#95—22no—
381#95—22no—
382#95—22no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—22no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—24no—
399C23×C3—41no—
400C23×C3—41no—
401C23×C3—41no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—48no—
408C23×C3—48no—
409C23×C3—42no—
410C23×C3—42no—
411C23×C3C2×C22⋊C411yescharacteristic
412C23×C3C2×C22⋊C411yescharacteristic
413C23×C3C2×C22⋊C411yescharacteristic
414C23×C3C2×C22⋊C411yescharacteristic
415C23×C3C23×C411yescharacteristic
416C23×C3C22×D411yescharacteristic
417C23×C3C22×D411yescharacteristic
418C23×C3H(5,𝔽2)12yes—
419C23×C32−1+412yes—
420C3×Q8—42no—
421C3×Q8—42no—
422C3×D4—42no—
423C3×D4—44no—
424C3×D4—44no—
425C3×D4—42no—
426C3×D4—42no—
427C3×D4—44no—
428C3×D4—44no—
429C3×D4—44no—
430C3×D4—42no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—24no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—44no—
463C2×C3×C4—44no—
464C2×C3×C4—42no—
465C2×C3×C4—42no—
466C2×C3×C4—44no—
467C2×C3×C4—44no—
468C2×C3×C4—44no—
469C2×C3×C4—44no—
470C2×C3×C4—44no—
471C2×C3×C4—44no—
472C2×C3×C4—88no—
473C2×C3×C4#9914yescomplemented
474C2×C3×C4C2×C22⋊C411yescharacteristic
475C2×C3×C4C2×C22⋊C411yescharacteristic
476C2×C3×C4C2×C22⋊C411yescharacteristic
477C2×C3×C4C2×C22⋊C411yescharacteristic
478C2×C3×C4C2×C22⋊C411yescharacteristic
479C2×C3×C4C2×C22⋊C411yescharacteristic
480C2×C3×C4C2×C22⋊C411yescharacteristic
481C2×C3×C4C2×C22⋊C411yescharacteristic
482C24—22no—
483C24—22no—
484C24—42no—
485C24—42no—
486C24C22×C3×C411yescharacteristic
487C24C22×C3×C411yescharacteristic
488C24C22×C3×C412yes—
489C24C2×C3×D411yescharacteristic
490C24C2×C3×D411yescharacteristic
491C24C2×C3×D411yescharacteristic
492C24C2×C3×D411yescharacteristic
493C24C24×C311yescharacteristic
494#41—44no—
495#41—44no—
496#41—44no—
497#41—44no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—42no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—24no—
508C2×D4—24no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—42no—
512C2×D4—44no—
513C2×D4—44no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4C3×C22⋊C411yescharacteristic
537C22×C4C3×C22⋊C411yescharacteristic
538C22×C4C3×C22⋊C411yescharacteristic
539C22×C4C3×C22⋊C411yescharacteristic
540C22×C4C3×C22⋊C411yescharacteristic
541C22×C4C3×C22⋊C411yescharacteristic
542C22×C4C3×C22⋊C411yescharacteristic
543C22×C4C3×C22⋊C411yescharacteristic
544C22×C4C3×C22⋊C411yescharacteristic
545C22×C4C3×C22⋊C411yescharacteristic
546C22×C4C3×C22⋊C411yescharacteristic
547C22×C4C3×C22⋊C411yescharacteristic
548C22×C4C3×C22⋊C411yescharacteristic
549C22×C4C3×C22⋊C411yescharacteristic
550C22×C4C3×C22⋊C411yescharacteristic
551C22×C4C3×C22⋊C411yescharacteristic
552C22×C4C22×C3×C412yes—
553C22×C4C22×C3×C411yescharacteristic
554C22×C4C22×C3×C411yescharacteristic
555C22×C4C22×C3×C412yes—
556C22×C4C22×C3×C412yes—
557C22×C4C22×C3×C411yescharacteristic
558C22×C4C22×C3×C411yescharacteristic
559C22×C4C2×C3×D411yescharacteristic
560C22×C4C2×C3×D411yescharacteristic
561C22×C4C2×C3×D411yescharacteristic
562C22×C4C2×C3×D411yescharacteristic
563C22×C4C2×C3×D411yescharacteristic
564C22×C4C2×C3×D411yescharacteristic
565C22×C4C2×C3×D411yescharacteristic
566C22×C4C2×C3×D411yescharacteristic
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C4⋊C4—44no—
578C22⋊C4—22no—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—24no—
589C22⋊C4—28no—
590C22⋊C4—24no—
591C22⋊C4—44no—
592C22⋊C4—44no—
593C22⋊C4—44no—
594C42—22no—
595C42—22no—
596C42—44no—
597C22×C3—24no—
598C22×C3—24no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—42no—
616C22×C3—42no—
617C22×C3—44no—
618C22×C3—44no—
619C22×C3—44no—
620C22×C3—44no—
621C22×C3—42no—
622C22×C3—42no—
623C22×C3—42no—
624C22×C3—42no—
625C22×C3—42no—
626C22×C3—84no—
627C22×C3C2×#9912yes—
628C22×C3#41012yes—
629C22×C3C22×C22⋊C411yescharacteristic
630C22×C3#52012yes—
631C22×C3#53511yescharacteristic
632C22×C3#53611yescharacteristic
633C22×C3#53712yes—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—42no—
641C3×C4—42no—
642C3×C4—42no—
643C3×C4—84no—
644C3×C4—84no—
645C3×C4C2×#9912yes—
646C3×C4C2×#9912yes—
647C23—22no—
648C23—22no—
649C23—21no—
650C23—21no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—21no—
658C23—21no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—24no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—48no—
672C23—48no—
673C23—42no—
674C23—42no—
675C23C2×C3×C22⋊C411yescharacteristic
676C23C2×C3×C22⋊C411yescharacteristic
677C23C2×C3×C22⋊C411yescharacteristic
678C23C2×C3×C22⋊C411yescharacteristic
679C23C23×C3×C411yescharacteristic
680C23C22×C3×D411yescharacteristic
681C23C22×C3×D411yescharacteristic
682C23C3×H(5,𝔽2)12yes—
683C23C3×2−1+412yes—
684Q8—42no—
685Q8—42no—
686D4—42no—
687D4—44no—
688D4—44no—
689D4—44no—
690D4—44no—
691D4—42no—
692D4—42no—
693D4—44no—
694D4—42no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—88no—
737C2×C4C3×#9914yescomplemented
738C2×C4C2×C3×C22⋊C411yescharacteristic
739C2×C4C2×C3×C22⋊C411yescharacteristic
740C2×C4C2×C3×C22⋊C411yescharacteristic
741C2×C4C2×C3×C22⋊C411yescharacteristic
742C2×C4C2×C3×C22⋊C411yescharacteristic
743C2×C4C2×C3×C22⋊C411yescharacteristic
744C2×C4C2×C3×C22⋊C411yescharacteristic
745C2×C4C2×C3×C22⋊C411yescharacteristic
746C2×C3—21no—
747C2×C3—22no—
748C2×C3—21no—
749C2×C3—22no—
750C2×C3—22no—
751C2×C3—22no—
752C2×C3—41no—
753C2×C3—41no—
754C2×C3—82no—
755C2×C3#231111yescharacteristic
756C2×C3C22×#9911yescharacteristic
757C2×C3C2×#41011yescharacteristic
758C22—24no—
759C22—24no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—42no—
777C22—42no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—84no—
788C22C2×C3×#9912yes—
789C22C3×#41012yes—
790C22C22×C3×C22⋊C411yescharacteristic
791C22C3×#52012yes—
792C22C3×#53511yescharacteristic
793C22C3×#53611yescharacteristic
794C22C3×#53712yes—
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—84no—
805C4—84no—
806C4C2×C3×#9912yes—
807C4C2×C3×#9912yes—
808C3#2187411yescharacteristic, direct product factor, Sylow
809C2—21no—
810C2—22no—
811C2—22no—
812C2—22no—
813C2—21no—
814C2—22no—
815C2—41no—
816C2—41no—
817C2—82no—
818C2C3×#231111yescharacteristic
819C2C22×C3×#9911yescharacteristic
820C2C2×C3×#41011yescharacteristic
subgroupG/H
center, socleC22×C3C22×C22⋊C4
commutatorC23C23×C3×C4
Frattini, cosocleC24C24×C3
prime radicalC2×C3×#525C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C24×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#2280C2semidirect
3. C2×C3×#380C2semidirect
4. C3×#1996C2semidirect
5. C3×#1964C2semidirect
6. C3×#1898C2semidirect
7. C3×#1799C2semidirect
8. #21874C3direct (N × H)
9. C22×C3×#41C4semidirect
19. C2×C3×#123C4semidirect
20. C2×C3×C22⋊Q8C4semidirect
22. C2×C3×#121C4semidirect
25. C2×C3×C4×D4C4semidirect
28. C2×C3×#117C4semidirect
45. #2280C2×C3semidirect
46. C2×#380C2×C3semidirect
47. #1996C2×C3semidirect
48. #1964C2×C3semidirect
49. #1898C2×C3semidirect
50. #1799C2×C3semidirect
57. C22×C3×Q8C2×C4semidirect
60. C22×C3×D4C2×C4semidirect
68. C23×C3×C4C2×C4semidirect
120. C2×C3×C4⋊C4C2×C4semidirect
121. C2×C3×C4⋊C4C2×C4semidirect
122. C2×C3×C4⋊C4C2×C4semidirect
123. C2×C3×C4⋊C4C2×C4semidirect
130. C2×C3×C22⋊C4C2×C4semidirect
131. C2×C3×C22⋊C4C2×C4semidirect
136. C2×C3×C42C2×C4semidirect
142. C22×#41C3×C4semidirect
152. C2×#123C3×C4semidirect
153. C2×C22⋊Q8C3×C4semidirect
155. C2×#121C3×C4semidirect
158. C2×C4×D4C3×C4semidirect
161. C2×#117C3×C4semidirect
298. C22×Q8C2×C3×C4semidirect
301. C22×D4C2×C3×C4semidirect
309. C23×C4C2×C3×C4semidirect
361. C2×C4⋊C4C2×C3×C4semidirect
362. C2×C4⋊C4C2×C3×C4semidirect
363. C2×C4⋊C4C2×C3×C4semidirect
364. C2×C4⋊C4C2×C3×C4semidirect
371. C2×C22⋊C4C2×C3×C4semidirect
372. C2×C22⋊C4C2×C3×C4semidirect
377. C2×C42C2×C3×C4semidirect
473. C2×C3×C4#99semidirect
737. C2×C4C3×#99semidirect
808. C3#21874direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5252
C3×#22802
C2×C3×#3802
C3×#19962
C3×#19642
C3×#18982
C3×#17992
#218743