Finite Group Databasebeta

← C3×#14205 #10632812

Subgroups — C3×#14205 #10632812

Order 768.

2038 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#394C211yesmaximal, characteristic
2C2×C3×#390C211yesmaximal, characteristic
3C2×C3×#389C211yesmaximal, characteristic, complemented
4C2×C3×#388C211yesmaximal, characteristic, complemented
5C2×C3×#388C211yesmaximal, characteristic, complemented
6C2×C3×#386C211yesmaximal, characteristic
7C2×C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
8C3×#1442C211yesmaximal, characteristic, complemented
9C3×#1439C211yesmaximal, characteristic, complemented
10C3×#1439C211yesmaximal, characteristic, complemented
11C3×#1437C211yesmaximal, characteristic, complemented
12C3×#1437C211yesmaximal, characteristic, complemented
13C3×#1436C211yesmaximal, characteristic, complemented
14C3×C22⋊#95C211yesmaximal, characteristic, complemented
15C3×C4×#95C211yesmaximal, characteristic, complemented
16#14205C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×C3×C22⋊C4C2211yescharacteristic
32C22×C3×C22⋊C4C2211yescharacteristic
33C22×C3×C22⋊C4C2211yescharacteristic
34C22×C3×C42C2211yescharacteristic
35C22×C3×C42C2211yescharacteristic
36C22×C3×C42C2211yescharacteristic
37C22×C3×C42C2211yescharacteristic
38C3×#394C418yescomplemented
39C3×#390—24no—
40C3×#389—24no—
41C3×#388—24no—
42C3×#388—24no—
43C3×#386—24no—
44C3×C4×C22⋊C4—24no—
45C2×C3×#95C2211yescharacteristic
46C2×C3×#95C2211yescharacteristic
47C2×C3×#95C2211yescharacteristic
48C2×C3×#95C2211yescharacteristic
49C2×C3×#95C2211yescharacteristic
50C2×C3×#95C2211yescharacteristic
51C2×C3×#95C2211yescharacteristic
52C2×C3×#95C2211yescharacteristic
53C2×C3×#95C2211yescharacteristic
54C2×C3×#95C2211yescharacteristic
55C2×C3×#95C2211yescharacteristic
56C2×C3×#95C2211yescharacteristic
57C2×C3×#95C2211yescharacteristic
58C2×C3×#95C2211yescharacteristic
59C2×#394C2×C311yescharacteristic
60C2×#390C2×C311yescharacteristic
61C2×#389C2×C311yescharacteristic, complemented
62C2×#388C2×C311yescharacteristic, complemented
63C2×#388C2×C311yescharacteristic, complemented
64C2×#386C2×C311yescharacteristic
65C2×C4×C22⋊C4C2×C311yescharacteristic, complemented
66#1442C2×C311yescharacteristic, complemented
67#1439C2×C311yescharacteristic, complemented
68#1439C2×C311yescharacteristic, complemented
69#1437C2×C311yescharacteristic, complemented
70#1437C2×C311yescharacteristic, complemented
71#1436C2×C311yescharacteristic, complemented
72C22⋊#95C2×C311yescharacteristic, complemented
73C4×#95C2×C311yescharacteristic, complemented
74C25×C3C2311yescharacteristic
75C25×C3C2311yescharacteristic
76C22×C3×D4—22no—
77C22×C3×D4—22no—
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—41no—
81C22×C3×D4—41no—
82C22×C3×D4C2×C414yes—
83C23×C3×C4—22no—
84C23×C3×C4—22no—
85C23×C3×C4—22no—
86C23×C3×C4—22no—
87C23×C3×C4—22no—
88C23×C3×C4—41no—
89C23×C3×C4—41no—
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C2311yescharacteristic
103C2×C3×C4⋊C4—22no—
104C2×C3×C4⋊C4—22no—
105C2×C3×C4⋊C4—22no—
106C2×C3×C4⋊C4—22no—
107C2×C3×C4⋊C4—22no—
108C2×C3×C4⋊C4—22no—
109C2×C3×C4⋊C4—22no—
110C2×C3×C4⋊C4—22no—
111C2×C3×C4⋊C4—41no—
112C2×C3×C4⋊C4—41no—
113C2×C3×C4⋊C4—41no—
114C2×C3×C4⋊C4C2×C414yescomplemented
115C2×C3×C22⋊C4—22no—
116C2×C3×C22⋊C4—22no—
117C2×C3×C22⋊C4—22no—
118C2×C3×C22⋊C4—22no—
119C2×C3×C22⋊C4—22no—
120C2×C3×C22⋊C4—22no—
121C2×C3×C22⋊C4—22no—
122C2×C3×C22⋊C4—22no—
123C2×C3×C22⋊C4—22no—
124C2×C3×C22⋊C4—22no—
125C2×C3×C22⋊C4—22no—
126C2×C3×C22⋊C4—22no—
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4—22no—
129C2×C3×C22⋊C4—22no—
130C2×C3×C22⋊C4—22no—
131C2×C3×C22⋊C4—22no—
132C2×C3×C22⋊C4—22no—
133C2×C3×C22⋊C4—22no—
134C2×C3×C22⋊C4—22no—
135C2×C3×C22⋊C4—22no—
136C2×C3×C22⋊C4—22no—
137C2×C3×C22⋊C4—41no—
138C2×C3×C22⋊C4—41no—
139C2×C3×C22⋊C4—41no—
140C2×C3×C22⋊C4—41no—
141C2×C3×C22⋊C4—41no—
142C2×C3×C22⋊C4—41no—
143C2×C3×C22⋊C4C2×C414yes—
144C2×C3×C22⋊C4C2×C414yes—
145C2×C3×C22⋊C4C2×C414yescomplemented
146C2×C3×C22⋊C4C2×C414yescomplemented
147C2×C3×C22⋊C4D414yes—
148C2×C3×C42—22no—
149C2×C3×C42—22no—
150C2×C3×C42—22no—
151C2×C3×C42—22no—
152C2×C3×C42—22no—
153C2×C3×C42—22no—
154C2×C3×C42—22no—
155C2×C3×C42—22no—
156C2×C3×C42—22no—
157C2×C3×C42—41no—
158C2×C3×C42—41no—
159C2×C3×C42—41no—
160C3×#95—22no—
161C3×#95—22no—
162C3×#95—22no—
163C3×#95—22no—
164C3×#95—22no—
165C3×#95—22no—
166C3×#95—22no—
167C3×#95—22no—
168C3×#95—22no—
169C3×#95—41no—
170C3×#95—41no—
171C3×#95C2×C414yescomplemented
172C3×#95D414yes—
173C3×#95D414yescomplemented
174C23×D4C22×C311yescharacteristic
175C24×C4C22×C311yescharacteristic
176C22×C4⋊C4C22×C311yescharacteristic
177C22×C4⋊C4C22×C311yescharacteristic
178C22×C4⋊C4C22×C311yescharacteristic
179C22×C4⋊C4C22×C311yescharacteristic
180C22×C22⋊C4C22×C311yescharacteristic
181C22×C22⋊C4C22×C311yescharacteristic
182C22×C22⋊C4C22×C311yescharacteristic
183C22×C22⋊C4C22×C311yescharacteristic
184C22×C22⋊C4C22×C311yescharacteristic
185C22×C22⋊C4C22×C311yescharacteristic
186C22×C22⋊C4C22×C311yescharacteristic
187C22×C22⋊C4C22×C311yescharacteristic
188C22×C22⋊C4C22×C311yescharacteristic
189C22×C22⋊C4C22×C311yescharacteristic
190C22×C22⋊C4C22×C311yescharacteristic
191C22×C42C22×C311yescharacteristic
192C22×C42C22×C311yescharacteristic
193C22×C42C22×C311yescharacteristic
194C22×C42C22×C311yescharacteristic
195#394C3×C418yescomplemented
196#390—24no—
197#389—24no—
198#388—24no—
199#388—24no—
200#386—24no—
201C4×C22⋊C4—24no—
202C2×#95C22×C311yescharacteristic
203C2×#95C22×C311yescharacteristic
204C2×#95C22×C311yescharacteristic
205C2×#95C22×C311yescharacteristic
206C2×#95C22×C311yescharacteristic
207C2×#95C22×C311yescharacteristic
208C2×#95C22×C311yescharacteristic
209C2×#95C22×C311yescharacteristic
210C2×#95C22×C311yescharacteristic
211C2×#95C22×C311yescharacteristic
212C2×#95C22×C311yescharacteristic
213C2×#95C22×C311yescharacteristic
214C2×#95C22×C311yescharacteristic
215C2×#95C22×C311yescharacteristic
216C24×C3—21no—
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—21no—
220C24×C3—21no—
221C24×C3—21no—
222C24×C3—21no—
223C24×C3—21no—
224C24×C3—21no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3—21no—
228C24×C3—21no—
229C24×C3—21no—
230C24×C3—21no—
231C24×C3—21no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—21no—
236C24×C3—21no—
237C24×C3—21no—
238C24×C3—21no—
239C24×C3—21no—
240C24×C3—21no—
241C24×C3—21no—
242C24×C3C22×C412yes—
243C24×C3C22×C412yes—
244C24×C3C2×D412yes—
245C24×C3#4112yes—
246C24×C3C2411yescharacteristic
247C2×C3×D4—28no—
248C2×C3×D4—28no—
249C2×C3×D4—44no—
250C2×C3×D4—44no—
251C2×C3×D4—44no—
252C2×C3×D4—44no—
253C2×C3×D4—44no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—28no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—44no—
328C22×C3×C4—44no—
329C22×C3×C4—44no—
330C22×C3×C4—44no—
331C22×C3×C4—44no—
332C22×C3×C4—44no—
333C22×C3×C4C22×C412yes—
334C22×C3×C4C22×C412yes—
335C22×C3×C4C22×C412yes—
336C22×C3×C4C22×C412yes—
337C22×C3×C4C22×C412yes—
338C22×C3×C4C2×D412yes—
339C22×C3×C4C2×D412yes—
340C22×C3×C4C2×D412yes—
341C22×C3×C4C2×D412yes—
342C22×C3×C4C2×D412yes—
343C22×C3×C4C2×D412yes—
344C22×C3×C4C2×D412yes—
345C22×C3×C4C2×D412yes—
346C22×C3×C4#4112yes—
347C22×C3×C4#4112yes—
348C22×C3×C4#4112yes—
349C22×C3×C4#4112yes—
350C22×C3×C4#4112yes—
351C22×C3×C4#4112yes—
352C3×C4⋊C4—28no—
353C3×C4⋊C4—44no—
354C3×C4⋊C4—44no—
355C3×C4⋊C4—44no—
356C3×C22⋊C4—28no—
357C3×C22⋊C4—28no—
358C3×C22⋊C4—28no—
359C3×C22⋊C4—28no—
360C3×C22⋊C4—44no—
361C3×C22⋊C4—44no—
362C3×C22⋊C4—44no—
363C3×C22⋊C4—44no—
364C3×C22⋊C4—44no—
365C3×C22⋊C4—44no—
366C3×C22⋊C4—44no—
367C3×C42—44no—
368C3×C42—44no—
369C3×C42—44no—
370C3×C42—44no—
371C25C23×C311yescharacteristic
372C25C23×C311yescharacteristic
373C22×D4—22no—
374C22×D4—22no—
375C22×D4—22no—
376C22×D4—22no—
377C22×D4—41no—
378C22×D4—41no—
379C22×D4C2×C3×C414yes—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—41no—
386C23×C4—41no—
387C23×C4C23×C311yescharacteristic
388C23×C4C23×C311yescharacteristic
389C23×C4C23×C311yescharacteristic
390C23×C4C23×C311yescharacteristic
391C23×C4C23×C311yescharacteristic
392C23×C4C23×C311yescharacteristic
393C23×C4C23×C311yescharacteristic
394C23×C4C23×C311yescharacteristic
395C23×C4C23×C311yescharacteristic
396C23×C4C23×C311yescharacteristic
397C23×C4C23×C311yescharacteristic
398C23×C4C23×C311yescharacteristic
399C23×C4C23×C311yescharacteristic
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—41no—
409C2×C4⋊C4—41no—
410C2×C4⋊C4—41no—
411C2×C4⋊C4C2×C3×C414yescomplemented
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—41no—
435C2×C22⋊C4—41no—
436C2×C22⋊C4—41no—
437C2×C22⋊C4—41no—
438C2×C22⋊C4—41no—
439C2×C22⋊C4—41no—
440C2×C22⋊C4C2×C3×C414yes—
441C2×C22⋊C4C2×C3×C414yes—
442C2×C22⋊C4C2×C3×C414yescomplemented
443C2×C22⋊C4C2×C3×C414yescomplemented
444C2×C22⋊C4C3×D414yes—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—22no—
451C2×C42—22no—
452C2×C42—22no—
453C2×C42—22no—
454C2×C42—41no—
455C2×C42—41no—
456C2×C42—41no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—41no—
467#95—41no—
468#95C2×C3×C414yescomplemented
469#95C3×D414yes—
470#95C3×D414yescomplemented
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—22no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—22no—
489C23×C3—22no—
490C23×C3—22no—
491C23×C3—22no—
492C23×C3—22no—
493C23×C3—22no—
494C23×C3—22no—
495C23×C3—22no—
496C23×C3—41no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—41no—
500C23×C3—41no—
501C23×C3—41no—
502C23×C3—41no—
503C23×C3—41no—
504C23×C3—41no—
505C23×C3—41no—
506C23×C3—41no—
507C23×C3—41no—
508C23×C3—41no—
509C23×C3—41no—
510C23×C3—41no—
511C23×C3—41no—
512C23×C3—41no—
513C23×C3—41no—
514C23×C3—41no—
515C23×C3—41no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—41no—
539C23×C3—41no—
540C23×C3C4×D414yes—
541C23×C3C23×C411yescharacteristic
542C23×C3C22×D411yescharacteristic
543C23×C3C22×D411yescharacteristic
544C23×C3C22×D411yescharacteristic
545C23×C3C2×#4111yescharacteristic
546C23×C3C2×#4111yescharacteristic
547C23×C3C2×#4111yescharacteristic
548C23×C3C2×#4111yescharacteristic
549C23×C3C2×#4111yescharacteristic
550C23×C3C2×#4111yescharacteristic
551C23×C3C2×#4111yescharacteristic
552C23×C3H(5,𝔽2)11yescharacteristic
553C23×C3H(5,𝔽2)11yescharacteristic
554C23×C3H(5,𝔽2)11yescharacteristic
555C23×C32−1+411yescharacteristic
556C3×D4—416no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—416no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—41no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—41no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—41no—
626C2×C3×C4—41no—
627C2×C3×C4—41no—
628C2×C3×C4—41no—
629C2×C3×C4—41no—
630C2×C3×C4—41no—
631C2×C3×C4—41no—
632C2×C3×C4—41no—
633C2×C3×C4—41no—
634C2×C3×C4—41no—
635C2×C3×C4—41no—
636C2×C3×C4—41no—
637C2×C3×C4—41no—
638C2×C3×C4—41no—
639C2×C3×C4—41no—
640C2×C3×C4—41no—
641C2×C3×C4—41no—
642C2×C3×C4—41no—
643C2×C3×C4—41no—
644C2×C3×C4—41no—
645C2×C3×C4C4×D414yes—
646C2×C3×C4C4×D414yes—
647C2×C3×C4#12114yes—
648C2×C3×C4#12414yes—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24C22×C3×C412yes—
676C24C22×C3×C412yes—
677C24C2×C3×D412yes—
678C24C3×#4112yes—
679C24C24×C311yescharacteristic
680C2×D4—28no—
681C2×D4—28no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—44no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—28no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4C22×C3×C412yes—
767C22×C4C22×C3×C412yes—
768C22×C4C22×C3×C412yes—
769C22×C4C22×C3×C412yes—
770C22×C4C22×C3×C412yes—
771C22×C4C2×C3×D412yes—
772C22×C4C2×C3×D412yes—
773C22×C4C2×C3×D412yes—
774C22×C4C2×C3×D412yes—
775C22×C4C2×C3×D412yes—
776C22×C4C2×C3×D412yes—
777C22×C4C2×C3×D412yes—
778C22×C4C2×C3×D412yes—
779C22×C4C3×#4112yes—
780C22×C4C3×#4112yes—
781C22×C4C3×#4112yes—
782C22×C4C3×#4112yes—
783C22×C4C3×#4112yes—
784C22×C4C3×#4112yes—
785C4⋊C4—28no—
786C4⋊C4—44no—
787C4⋊C4—44no—
788C4⋊C4—44no—
789C22⋊C4—28no—
790C22⋊C4—28no—
791C22⋊C4—28no—
792C22⋊C4—28no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C22⋊C4—44no—
796C22⋊C4—44no—
797C22⋊C4—44no—
798C22⋊C4—44no—
799C22⋊C4—44no—
800C42—44no—
801C42—44no—
802C42—44no—
803C42—44no—
804C22×C3—24no—
805C22×C3—24no—
806C22×C3—24no—
807C22×C3—42no—
808C22×C3—42no—
809C22×C3—42no—
810C22×C3—42no—
811C22×C3—42no—
812C22×C3—42no—
813C22×C3—42no—
814C22×C3—42no—
815C22×C3—42no—
816C22×C3—42no—
817C22×C3—42no—
818C22×C3—42no—
819C22×C3—42no—
820C22×C3—42no—
821C22×C3—42no—
822C22×C3—42no—
823C22×C3—42no—
824C22×C3—42no—
825C22×C3—42no—
826C22×C3—81no—
827C22×C3—81no—
828C22×C3—81no—
829C22×C3—81no—
830C22×C3—81no—
831C22×C3—81no—
832C22×C3—81no—
833C22×C3—81no—
834C22×C3C2×C4×D411yescharacteristic
835C22×C3C2×C4×D411yescharacteristic
836C22×C3C2×C4×D411yescharacteristic
837C22×C3C4×#4111yescharacteristic
838C22×C3C4×#4111yescharacteristic
839C22×C3#51811yescharacteristic
840C22×C3#52011yescharacteristic
841C22×C3C2×#12111yescharacteristic
842C22×C3#52511yescharacteristic
843C22×C3C2×#12411yescharacteristic
844C22×C3#52911yescharacteristic
845C22×C3#52911yescharacteristic
846C22×C3#52911yescharacteristic
847C22×C3#53211yescharacteristic
848C22×C3#53211yescharacteristic
849C22×C3#53811yescharacteristic
850C22×C3#53911yescharacteristic
851C22×C3#54011yescharacteristic
852C22×C3#54211yescharacteristic
853C22×C3D4211yescharacteristic
854C22×C3D4211yescharacteristic
855C22×C3#54611yescharacteristic
856C22×C3#54611yescharacteristic
857C22×C3#54611yescharacteristic
858C22×C3#54611yescharacteristic
859C22×C3#54711yescharacteristic
860C22×C3#54711yescharacteristic
861C22×C3#54811yescharacteristic
862C22×C3#55011yescharacteristic
863C22×C3#55111yescharacteristic
864C22×C3#55111yescharacteristic
865C22×C3#55211yescharacteristic
866C22×C3#55311yescharacteristic
867C22×C3#55311yescharacteristic
868C22×C3#55511yescharacteristic
869C3×C4—24no—
870C3×C4—24no—
871C3×C4—24no—
872C3×C4—24no—
873C3×C4—42no—
874C3×C4—42no—
875C3×C4—42no—
876C3×C4—42no—
877C3×C4—42no—
878C3×C4—42no—
879C3×C4—42no—
880C3×C4—81no—
881C3×C4—81no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23C3×C4×D414yes—
952C23C23×C3×C411yescharacteristic
953C23C22×C3×D411yescharacteristic
954C23C22×C3×D411yescharacteristic
955C23C22×C3×D411yescharacteristic
956C23C2×C3×#4111yescharacteristic
957C23C2×C3×#4111yescharacteristic
958C23C2×C3×#4111yescharacteristic
959C23C2×C3×#4111yescharacteristic
960C23C2×C3×#4111yescharacteristic
961C23C2×C3×#4111yescharacteristic
962C23C2×C3×#4111yescharacteristic
963C23C3×H(5,𝔽2)11yescharacteristic
964C23C3×H(5,𝔽2)11yescharacteristic
965C23C3×H(5,𝔽2)11yescharacteristic
966C23C3×2−1+411yescharacteristic
967D4—416no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—416no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4C3×C4×D414yes—
1057C2×C4C3×C4×D414yes—
1058C2×C4C3×#12114yes—
1059C2×C4C3×#12414yes—
1060C2×C3—44no—
1061C2×C3—82no—
1062C2×C3C4×#12111yescharacteristic
1063C2×C3C4×#12411yescharacteristic
1064C2×C3#233511yescharacteristic
1065C2×C3#235811yescharacteristic
1066C2×C3#235911yescharacteristic
1067C2×C3#236111yescharacteristic
1068C2×C3#236311yescharacteristic
1069C2×C3#242511yescharacteristic
1070C2×C3#242811yescharacteristic
1071C2×C3#247211yescharacteristic
1072C2×C3#247911yescharacteristic
1073C2×C3#249111yescharacteristic
1074C2×C3#252611yescharacteristic
1075C2×C3#255811yescharacteristic
1076C2×C3#255911yescharacteristic
1077C22—24no—
1078C22—24no—
1079C22—24no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—81no—
1100C22—81no—
1101C22—81no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22C2×C3×C4×D411yescharacteristic
1108C22C2×C3×C4×D411yescharacteristic
1109C22C2×C3×C4×D411yescharacteristic
1110C22C3×C4×#4111yescharacteristic
1111C22C3×C4×#4111yescharacteristic
1112C22C3×#51811yescharacteristic
1113C22C3×#52011yescharacteristic
1114C22C2×C3×#12111yescharacteristic
1115C22C3×#52511yescharacteristic
1116C22C2×C3×#12411yescharacteristic
1117C22C3×#52911yescharacteristic
1118C22C3×#52911yescharacteristic
1119C22C3×#52911yescharacteristic
1120C22C3×#53211yescharacteristic
1121C22C3×#53211yescharacteristic
1122C22C3×#53811yescharacteristic
1123C22C3×#53911yescharacteristic
1124C22C3×#54011yescharacteristic
1125C22C3×#54211yescharacteristic
1126C22C3×D4211yescharacteristic
1127C22C3×D4211yescharacteristic
1128C22C3×#54611yescharacteristic
1129C22C3×#54611yescharacteristic
1130C22C3×#54611yescharacteristic
1131C22C3×#54611yescharacteristic
1132C22C3×#54711yescharacteristic
1133C22C3×#54711yescharacteristic
1134C22C3×#54811yescharacteristic
1135C22C3×#55011yescharacteristic
1136C22C3×#55111yescharacteristic
1137C22C3×#55111yescharacteristic
1138C22C3×#55211yescharacteristic
1139C22C3×#55311yescharacteristic
1140C22C3×#55311yescharacteristic
1141C22C3×#55511yescharacteristic
1142C4—24no—
1143C4—24no—
1144C4—24no—
1145C4—24no—
1146C4—42no—
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—81no—
1154C4—81no—
1155C3#1420511yescharacteristic, direct product factor, Sylow
1156C2—44no—
1157C2—82no—
1158C2C3×C4×#12111yescharacteristic
1159C2C3×C4×#12411yescharacteristic
1160C2C3×#233511yescharacteristic
1161C2C3×#235811yescharacteristic
1162C2C3×#235911yescharacteristic
1163C2C3×#236111yescharacteristic
1164C2C3×#236311yescharacteristic
1165C2C3×#242511yescharacteristic
1166C2C3×#242811yescharacteristic
1167C2C3×#247211yescharacteristic
1168C2C3×#247911yescharacteristic
1169C2C3×#249111yescharacteristic
1170C2C3×#252611yescharacteristic
1171C2C3×#255811yescharacteristic
1172C2C3×#255911yescharacteristic
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
3. C2×C3×#389C2semidirect
4. C2×C3×#388C2semidirect
5. C2×C3×#388C2semidirect
7. C2×C3×C4×C22⋊C4C2semidirect
8. C3×#1442C2semidirect
9. C3×#1439C2semidirect
10. C3×#1439C2semidirect
11. C3×#1437C2semidirect
12. C3×#1437C2semidirect
13. C3×#1436C2semidirect
14. C3×C22⋊#95C2semidirect
15. C3×C4×#95C2semidirect
16. #14205C3direct (N × H)
38. C3×#394C4semidirect
61. C2×#389C2×C3semidirect
62. C2×#388C2×C3semidirect
63. C2×#388C2×C3semidirect
65. C2×C4×C22⋊C4C2×C3semidirect
66. #1442C2×C3semidirect
67. #1439C2×C3semidirect
68. #1439C2×C3semidirect
69. #1437C2×C3semidirect
70. #1437C2×C3semidirect
71. #1436C2×C3semidirect
72. C22⋊#95C2×C3semidirect
73. C4×#95C2×C3semidirect
114. C2×C3×C4⋊C4C2×C4semidirect
145. C2×C3×C22⋊C4C2×C4semidirect
146. C2×C3×C22⋊C4C2×C4semidirect
171. C3×#95C2×C4semidirect
173. C3×#95D4semidirect
195. #394C3×C4semidirect
411. C2×C4⋊C4C2×C3×C4semidirect
442. C2×C22⋊C4C2×C3×C4semidirect
443. C2×C22⋊C4C2×C3×C4semidirect
468. #95C2×C3×C4semidirect
470. #95C3×D4semidirect
1155. C3#14205direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3942
C2×C3×#3902
C2×C3×#3892
C2×C3×#3882
C2×C3×#3862
C2×C3×C4×C22⋊C42
C3×#14422
C3×#14392
C3×#14372
C3×#14362
C3×C22⋊#952
C3×C4×#952
#142053