Finite Group Databasebeta

← C3×#14141 #10632748

Subgroups — C3×#14141 #10632748

Order 768.

1938 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
1C2×C3×#390C211yesmaximal, characteristic
2C2×C3×#390C211yesmaximal, characteristic
3C2×C3×#390C211yesmaximal, characteristic
4C2×C3×#389C211yesmaximal, characteristic, complemented
5C2×C3×#388C212yesmaximal, complemented
6C2×C3×C4×C4⋊C4C211yesmaximal, characteristic, complemented
7C3×#1440C212yesmaximal, complemented
8C3×#1439C212yesmaximal, complemented
9C3×#1437C212yesmaximal, complemented
10C3×C4⋊#95C211yesmaximal, characteristic, complemented
11C3×C4×#95C211yesmaximal, characteristic, complemented
12#14141C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4C2211yescharacteristic
14C22×C3×C4⋊C4C2212yes—
15C22×C3×C4⋊C4C2211yescharacteristic
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2212yes—
19C22×C3×C22⋊C4C2212yes—
20C22×C3×C22⋊C4C2212yes—
21C22×C3×C22⋊C4C2212yes—
22C22×C3×C22⋊C4C2212yes—
23C22×C3×C22⋊C4C2212yes—
24C22×C3×C42C2211yescharacteristic
25C22×C3×C42C2211yescharacteristic
26C22×C3×C42C2212yes—
27C22×C3×C42C2211yescharacteristic
28C3×#390—24no—
29C3×#390—24no—
30C3×#390C418yescomplemented
31C3×#389—24no—
32C3×#388—28no—
33C3×C4×C4⋊C4—24no—
34C2×C3×#95C2212yes—
35C2×C3×#95C2212yes—
36C2×C3×#95C2212yes—
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2211yescharacteristic
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2212yes—
41C2×C3×#95C2211yescharacteristic
42C2×#390C2×C311yescharacteristic
43C2×#390C2×C311yescharacteristic
44C2×#390C2×C311yescharacteristic
45C2×#389C2×C311yescharacteristic, complemented
46C2×#388C2×C312yescomplemented
47C2×C4×C4⋊C4C2×C311yescharacteristic, complemented
48#1440C2×C312yescomplemented
49#1439C2×C312yescomplemented
50#1437C2×C312yescomplemented
51C4⋊#95C2×C311yescharacteristic, complemented
52C4×#95C2×C311yescharacteristic, complemented
53C25×C3C2312yes—
54C22×C3×D4—22no—
55C22×C3×D4—22no—
56C22×C3×D4—22no—
57C22×C3×D4—22no—
58C22×C3×D4—22no—
59C22×C3×D4—22no—
60C22×C3×D4C2×C414yes—
61C23×C3×C4C2311yescharacteristic
62C23×C3×C4C2312yes—
63C23×C3×C4C2311yescharacteristic
64C23×C3×C4C2312yes—
65C23×C3×C4C2312yes—
66C23×C3×C4C2311yescharacteristic
67C23×C3×C4C2311yescharacteristic
68C23×C3×C4C2311yescharacteristic
69C23×C3×C4C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C2×C3×C4⋊C4—22no—
72C2×C3×C4⋊C4—22no—
73C2×C3×C4⋊C4—22no—
74C2×C3×C4⋊C4—22no—
75C2×C3×C4⋊C4—22no—
76C2×C3×C4⋊C4—22no—
77C2×C3×C4⋊C4—24no—
78C2×C3×C4⋊C4—24no—
79C2×C3×C4⋊C4—42no—
80C2×C3×C4⋊C4C2×C414yes—
81C2×C3×C4⋊C4D414yes—
82C2×C3×C4⋊C4D414yes—
83C2×C3×C22⋊C4—24no—
84C2×C3×C22⋊C4—24no—
85C2×C3×C22⋊C4—24no—
86C2×C3×C22⋊C4—24no—
87C2×C3×C22⋊C4—24no—
88C2×C3×C22⋊C4—24no—
89C2×C3×C22⋊C4—24no—
90C2×C3×C22⋊C4—24no—
91C2×C3×C22⋊C4—24no—
92C2×C3×C22⋊C4—24no—
93C2×C3×C22⋊C4—42no—
94C2×C3×C22⋊C4—42no—
95C2×C3×C22⋊C4—42no—
96C2×C3×C22⋊C4—42no—
97C2×C3×C22⋊C4—42no—
98C2×C3×C22⋊C4—42no—
99C2×C3×C22⋊C4C2×C418yes—
100C2×C3×C22⋊C4C2×C418yes—
101C2×C3×C42—22no—
102C2×C3×C42—22no—
103C2×C3×C42—24no—
104C2×C3×C42—24no—
105C2×C3×C42—22no—
106C2×C3×C42—22no—
107C2×C3×C42—22no—
108C2×C3×C42—22no—
109C2×C3×C42—22no—
110C2×C3×C42—22no—
111C2×C3×C42—42no—
112C2×C3×C42C2×C414yes—
113C3×#95—24no—
114C3×#95—24no—
115C3×#95—24no—
116C3×#95—22no—
117C3×#95—22no—
118C3×#95—22no—
119C3×#95—42no—
120C3×#95D414yescomplemented
121C23×D4C22×C311yescharacteristic
122C22×C4⋊C4C22×C312yes—
123C22×C4⋊C4C22×C311yescharacteristic
124C22×C4⋊C4C22×C311yescharacteristic
125C22×C4⋊C4C22×C311yescharacteristic
126C22×C22⋊C4C22×C312yes—
127C22×C22⋊C4C22×C312yes—
128C22×C22⋊C4C22×C312yes—
129C22×C22⋊C4C22×C312yes—
130C22×C22⋊C4C22×C312yes—
131C22×C22⋊C4C22×C312yes—
132C22×C42C22×C311yescharacteristic
133C22×C42C22×C311yescharacteristic
134C22×C42C22×C312yes—
135C22×C42C22×C311yescharacteristic
136#390—24no—
137#390—24no—
138#390C3×C418yescomplemented
139#389—24no—
140#388—28no—
141C4×C4⋊C4—24no—
142C2×#95C22×C311yescharacteristic
143C2×#95C22×C311yescharacteristic
144C2×#95C22×C311yescharacteristic
145C2×#95C22×C312yes—
146C2×#95C22×C312yes—
147C2×#95C22×C312yes—
148C2×#95C22×C312yes—
149C2×#95C22×C311yescharacteristic
150C24×C3—22no—
151C24×C3—22no—
152C24×C3—22no—
153C24×C3—22no—
154C24×C3—22no—
155C24×C3—22no—
156C24×C3—22no—
157C24×C3—22no—
158C24×C3—22no—
159C24×C3—22no—
160C24×C3—22no—
161C24×C3—22no—
162C24×C3—22no—
163C24×C3—22no—
164C24×C3C22×C414yes—
165C24×C3C2411yescharacteristic
166C2×C3×D4—28no—
167C2×C3×D4—28no—
168C2×C3×D4—28no—
169C2×C3×D4—44no—
170C2×C3×D4—44no—
171C2×C3×D4—44no—
172C2×C3×D4—44no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—22no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—21no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4C22×C412yes—
226C22×C3×C4C22×C414yes—
227C22×C3×C4C22×C412yes—
228C22×C3×C4C22×C412yes—
229C22×C3×C4C2×D412yes—
230C22×C3×C4C2×D414yes—
231C22×C3×C4C2×D414yes—
232C22×C3×C4C2×D412yes—
233C22×C3×C4C2×D412yes—
234C22×C3×C4C2×D412yes—
235C22×C3×C4C2×D412yes—
236C22×C3×C4#4112yes—
237C22×C3×C4#4112yes—
238C22×C3×C4#4112yes—
239C22×C3×C4#4112yes—
240C22×C3×C4#4112yes—
241C22×C3×C4#4112yes—
242C22×C3×C4#4112yes—
243C3×C4⋊C4—28no—
244C3×C4⋊C4—28no—
245C3×C4⋊C4—28no—
246C3×C4⋊C4—48no—
247C3×C22⋊C4—216no—
248C3×C22⋊C4—48no—
249C3×C22⋊C4—48no—
250C3×C22⋊C4—48no—
251C3×C22⋊C4—48no—
252C3×C22⋊C4—48no—
253C3×C42—28no—
254C3×C42—48no—
255C3×C42—44no—
256C3×C42—44no—
257C25C23×C312yes—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4C2×C3×C414yes—
265C23×C4C23×C312yes—
266C23×C4C23×C311yescharacteristic
267C23×C4C23×C312yes—
268C23×C4C23×C311yescharacteristic
269C23×C4C23×C312yes—
270C23×C4C23×C311yescharacteristic
271C23×C4C23×C311yescharacteristic
272C23×C4C23×C311yescharacteristic
273C23×C4C23×C311yescharacteristic
274C23×C4C23×C311yescharacteristic
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4C2×C3×C414yes—
285C2×C4⋊C4C3×D414yes—
286C2×C4⋊C4C3×D414yes—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—24no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—24no—
291C2×C22⋊C4—24no—
292C2×C22⋊C4—24no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—42no—
298C2×C22⋊C4—42no—
299C2×C22⋊C4—42no—
300C2×C22⋊C4—42no—
301C2×C22⋊C4—42no—
302C2×C22⋊C4—42no—
303C2×C22⋊C4C2×C3×C418yes—
304C2×C22⋊C4C2×C3×C418yes—
305C2×C42—22no—
306C2×C42—22no—
307C2×C42—24no—
308C2×C42—24no—
309C2×C42—22no—
310C2×C42—22no—
311C2×C42—22no—
312C2×C42—22no—
313C2×C42—22no—
314C2×C42—22no—
315C2×C42—42no—
316C2×C42C2×C3×C414yes—
317#95—24no—
318#95—24no—
319#95—24no—
320#95—22no—
321#95—22no—
322#95—22no—
323#95—42no—
324#95C3×D414yescomplemented
325C23×C3—24no—
326C23×C3—24no—
327C23×C3—24no—
328C23×C3—24no—
329C23×C3—24no—
330C23×C3—24no—
331C23×C3—24no—
332C23×C3—42no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3—42no—
336C23×C3—42no—
337C23×C3—42no—
338C23×C3—42no—
339C23×C3—42no—
340C23×C3—42no—
341C23×C3—42no—
342C23×C3—42no—
343C23×C3—42no—
344C23×C3—42no—
345C23×C3—42no—
346C23×C3—42no—
347C23×C3—42no—
348C23×C3—42no—
349C23×C3—42no—
350C23×C3—42no—
351C23×C3—42no—
352C23×C3—42no—
353C23×C3—42no—
354C23×C3—42no—
355C23×C3—42no—
356C23×C3—42no—
357C23×C3—42no—
358C23×C3—42no—
359C23×C3—42no—
360C23×C3C23×C411yescharacteristic
361C23×C3C22×D411yescharacteristic
362C23×C3C22×D411yescharacteristic
363C23×C3C22×D411yescharacteristic
364C23×C3C2×#4111yescharacteristic
365C23×C3C2×#4111yescharacteristic
366C23×C3C2×#4111yescharacteristic
367C23×C3C2×#4111yescharacteristic
368C23×C3C2×#4111yescharacteristic
369C23×C3C2×#4111yescharacteristic
370C23×C3C2×#4111yescharacteristic
371C23×C3H(5,𝔽2)11yescharacteristic
372C23×C3H(5,𝔽2)11yescharacteristic
373C23×C3H(5,𝔽2)11yescharacteristic
374C23×C32−1+411yescharacteristic
375C3×D4—416no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—24no—
384C2×C3×C4—24no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—24no—
388C2×C3×C4—24no—
389C2×C3×C4—24no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—24no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—24no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—24no—
402C2×C3×C4—24no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—41no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—42no—
411C2×C3×C4—42no—
412C2×C3×C4—41no—
413C2×C3×C4—42no—
414C2×C3×C4—42no—
415C2×C3×C4—41no—
416C2×C3×C4—41no—
417C2×C3×C4—41no—
418C2×C3×C4—42no—
419C2×C3×C4—42no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—42no—
426C2×C3×C4—42no—
427C2×C3×C4—41no—
428C2×C3×C4—42no—
429C2×C3×C4—41no—
430C2×C3×C4—42no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—42no—
437C2×C3×C4—42no—
438C2×C3×C4#11714yes—
439C2×C3×C4C4×D414yes—
440C2×C3×C4C4×D414yes—
441C2×C3×C4C4×D414yes—
442C2×C3×C4#12114yes—
443C2×C3×C4#12314yes—
444C2×C3×C4#12414yes—
445C2×C3×C4#12614yes—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24C22×C3×C414yes—
461C24C24×C311yescharacteristic
462C2×D4—28no—
463C2×D4—28no—
464C2×D4—28no—
465C2×D4—44no—
466C2×D4—44no—
467C2×D4—44no—
468C2×D4—44no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4C22×C3×C412yes—
522C22×C4C22×C3×C414yes—
523C22×C4C22×C3×C412yes—
524C22×C4C22×C3×C412yes—
525C22×C4C2×C3×D412yes—
526C22×C4C2×C3×D414yes—
527C22×C4C2×C3×D414yes—
528C22×C4C2×C3×D412yes—
529C22×C4C2×C3×D412yes—
530C22×C4C2×C3×D412yes—
531C22×C4C2×C3×D412yes—
532C22×C4C3×#4112yes—
533C22×C4C3×#4112yes—
534C22×C4C3×#4112yes—
535C22×C4C3×#4112yes—
536C22×C4C3×#4112yes—
537C22×C4C3×#4112yes—
538C22×C4C3×#4112yes—
539C4⋊C4—28no—
540C4⋊C4—28no—
541C4⋊C4—28no—
542C4⋊C4—48no—
543C22⋊C4—216no—
544C22⋊C4—48no—
545C22⋊C4—48no—
546C22⋊C4—48no—
547C22⋊C4—48no—
548C22⋊C4—48no—
549C42—28no—
550C42—48no—
551C42—44no—
552C42—44no—
553C22×C3—44no—
554C22×C3—44no—
555C22×C3—44no—
556C22×C3—44no—
557C22×C3—44no—
558C22×C3—44no—
559C22×C3—44no—
560C22×C3—82no—
561C22×C3—82no—
562C22×C3—82no—
563C22×C3—82no—
564C22×C3—82no—
565C22×C3—82no—
566C22×C3—82no—
567C22×C3—82no—
568C22×C3C2×#11711yescharacteristic
569C22×C3C2×C4×D411yescharacteristic
570C22×C3C2×C4×D411yescharacteristic
571C22×C3C2×C4×D411yescharacteristic
572C22×C3C4×#4111yescharacteristic
573C22×C3#51811yescharacteristic
574C22×C3#52011yescharacteristic
575C22×C3C2×#12111yescharacteristic
576C22×C3C2×#12311yescharacteristic
577C22×C3C2×#12411yescharacteristic
578C22×C3C2×#12611yescharacteristic
579C22×C3#52911yescharacteristic
580C22×C3#52911yescharacteristic
581C22×C3#53211yescharacteristic
582C22×C3#53211yescharacteristic
583C22×C3#54011yescharacteristic
584C22×C3#54011yescharacteristic
585C22×C3#54211yescharacteristic
586C22×C3#54211yescharacteristic
587C22×C3D4211yescharacteristic
588C22×C3D4211yescharacteristic
589C22×C3#54611yescharacteristic
590C22×C3#54611yescharacteristic
591C22×C3#54711yescharacteristic
592C22×C3#54811yescharacteristic
593C22×C3#54811yescharacteristic
594C22×C3#55011yescharacteristic
595C22×C3#55011yescharacteristic
596C22×C3#55011yescharacteristic
597C22×C3#55311yescharacteristic
598C22×C3#55311yescharacteristic
599C22×C3#55511yescharacteristic
600C22×C3#55611yescharacteristic
601C22×C3#55911yescharacteristic
602C22×C3#55911yescharacteristic
603C3×C4—24no—
604C3×C4—42no—
605C3×C4—44no—
606C3×C4—42no—
607C3×C4—44no—
608C3×C4—42no—
609C3×C4—44no—
610C3×C4—42no—
611C3×C4—42no—
612C3×C4#38818yescomplemented
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23C23×C3×C411yescharacteristic
649C23C22×C3×D411yescharacteristic
650C23C22×C3×D411yescharacteristic
651C23C22×C3×D411yescharacteristic
652C23C2×C3×#4111yescharacteristic
653C23C2×C3×#4111yescharacteristic
654C23C2×C3×#4111yescharacteristic
655C23C2×C3×#4111yescharacteristic
656C23C2×C3×#4111yescharacteristic
657C23C2×C3×#4111yescharacteristic
658C23C2×C3×#4111yescharacteristic
659C23C3×H(5,𝔽2)11yescharacteristic
660C23C3×H(5,𝔽2)11yescharacteristic
661C23C3×H(5,𝔽2)11yescharacteristic
662C23C3×2−1+411yescharacteristic
663D4—416no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4C3×#11714yes—
727C2×C4C3×C4×D414yes—
728C2×C4C3×C4×D414yes—
729C2×C4C3×C4×D414yes—
730C2×C4C3×#12114yes—
731C2×C4C3×#12314yes—
732C2×C4C3×#12414yes—
733C2×C4C3×#12614yes—
734C2×C3—84no—
735C2×C3C2×#38811yescharacteristic
736C2×C3#229311yescharacteristic
737C2×C3#231911yescharacteristic
738C2×C3#236111yescharacteristic
739C2×C3#236311yescharacteristic
740C2×C3#236611yescharacteristic
741C2×C3#236711yescharacteristic
742C2×C3#242611yescharacteristic
743C2×C3#242811yescharacteristic
744C2×C3#244511yescharacteristic
745C2×C3#244811yescharacteristic
746C2×C3#249011yescharacteristic
747C2×C3#249111yescharacteristic
748C2×C3#251211yescharacteristic
749C2×C3#251311yescharacteristic
750C22—44no—
751C22—44no—
752C22—44no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—44no—
757C22—82no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22C2×C3×#11711yescharacteristic
766C22C2×C3×C4×D411yescharacteristic
767C22C2×C3×C4×D411yescharacteristic
768C22C2×C3×C4×D411yescharacteristic
769C22C3×C4×#4111yescharacteristic
770C22C3×#51811yescharacteristic
771C22C3×#52011yescharacteristic
772C22C2×C3×#12111yescharacteristic
773C22C2×C3×#12311yescharacteristic
774C22C2×C3×#12411yescharacteristic
775C22C2×C3×#12611yescharacteristic
776C22C3×#52911yescharacteristic
777C22C3×#52911yescharacteristic
778C22C3×#53211yescharacteristic
779C22C3×#53211yescharacteristic
780C22C3×#54011yescharacteristic
781C22C3×#54011yescharacteristic
782C22C3×#54211yescharacteristic
783C22C3×#54211yescharacteristic
784C22C3×D4211yescharacteristic
785C22C3×D4211yescharacteristic
786C22C3×#54611yescharacteristic
787C22C3×#54611yescharacteristic
788C22C3×#54711yescharacteristic
789C22C3×#54811yescharacteristic
790C22C3×#54811yescharacteristic
791C22C3×#55011yescharacteristic
792C22C3×#55011yescharacteristic
793C22C3×#55011yescharacteristic
794C22C3×#55311yescharacteristic
795C22C3×#55311yescharacteristic
796C22C3×#55511yescharacteristic
797C22C3×#55611yescharacteristic
798C22C3×#55911yescharacteristic
799C22C3×#55911yescharacteristic
800C4—24no—
801C4—42no—
802C4—44no—
803C4—42no—
804C4—44no—
805C4—42no—
806C4—44no—
807C4—42no—
808C4—42no—
809C4C3×#38818yescomplemented
810C3#1414111yescharacteristic, direct product factor, Sylow
811C2—84no—
812C2C2×C3×#38811yescharacteristic
813C2C3×#229311yescharacteristic
814C2C3×#231911yescharacteristic
815C2C3×#236111yescharacteristic
816C2C3×#236311yescharacteristic
817C2C3×#236611yescharacteristic
818C2C3×#236711yescharacteristic
819C2C3×#242611yescharacteristic
820C2C3×#242811yescharacteristic
821C2C3×#244511yescharacteristic
822C2C3×#244811yescharacteristic
823C2C3×#249011yescharacteristic
824C2C3×#249111yescharacteristic
825C2C3×#251211yescharacteristic
826C2C3×#251311yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutatorC23C23×C3×C4
Frattini, cosocleC24C24×C3
prime radicalC23×C3×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C3×#389C2semidirect
5. C2×C3×#388C2semidirect
6. C2×C3×C4×C4⋊C4C2semidirect
7. C3×#1440C2semidirect
8. C3×#1439C2semidirect
9. C3×#1437C2semidirect
10. C3×C4⋊#95C2semidirect
11. C3×C4×#95C2semidirect
12. #14141C3direct (N × H)
30. C3×#390C4semidirect
45. C2×#389C2×C3semidirect
46. C2×#388C2×C3semidirect
47. C2×C4×C4⋊C4C2×C3semidirect
48. #1440C2×C3semidirect
49. #1439C2×C3semidirect
50. #1437C2×C3semidirect
51. C4⋊#95C2×C3semidirect
52. C4×#95C2×C3semidirect
120. C3×#95D4semidirect
138. #390C3×C4semidirect
324. #95C3×D4semidirect
612. C3×C4#388semidirect
809. C4C3×#388semidirect
810. C3#14141direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3902
C2×C3×#3892
C2×C3×#3882
C2×C3×C4×C4⋊C42
C3×#14402
C3×#14392
C3×#14372
C3×C4⋊#952
C3×C4×#952
#141413