Finite Group Databasebeta

← C3×#14185 #10632792

Subgroups — C3×#14185 #10632792

Order 768.

2422 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×D4C211yesmaximal, characteristic
2C2×C3×#394C211yesmaximal, characteristic
3C2×C3×#389C211yesmaximal, characteristic, complemented
4C2×C3×#388C211yesmaximal, characteristic, complemented
5C2×C3×#385C211yesmaximal, characteristic, complemented
6C2×C3×#385C211yesmaximal, characteristic, complemented
7C2×C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
8C3×#1440C211yesmaximal, characteristic, complemented
9C3×#1439C211yesmaximal, characteristic, complemented
10C3×#1438C211yesmaximal, characteristic
11C3×#1437C211yesmaximal, characteristic, complemented
12C3×#1436C211yesmaximal, characteristic, complemented
13C3×#1436C211yesmaximal, characteristic, complemented
14C3×#1436C211yesmaximal, characteristic, complemented
15C3×C22⋊#95C211yesmaximal, characteristic, complemented
16#14185C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C24×C3×C4C2211yescharacteristic
20C2×C3×C4×D4—24no—
21C2×C3×C4×D4—24no—
22C2×C3×C4×D4—24no—
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×C3×C4⋊C4C2211yescharacteristic
27C22×C3×C4⋊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×C22⋊C4C2211yescharacteristic
35C22×C3×C22⋊C4C2211yescharacteristic
36C22×C3×C22⋊C4C2211yescharacteristic
37C22×C3×C22⋊C4C2211yescharacteristic
38C22×C3×C42C2211yescharacteristic
39C22×C3×C42C2211yescharacteristic
40C22×C3×C42C2211yescharacteristic
41C3×#394C418yescomplemented
42C3×#389—24no—
43C3×#388—24no—
44C3×#385—24no—
45C3×#385—24no—
46C3×C4×C22⋊C4—24no—
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×C3×#95C2211yescharacteristic
60C2×C3×#95C2211yescharacteristic
61C22×C4×D4C2×C311yescharacteristic
62C2×#394C2×C311yescharacteristic
63C2×#389C2×C311yescharacteristic, complemented
64C2×#388C2×C311yescharacteristic, complemented
65C2×#385C2×C311yescharacteristic, complemented
66C2×#385C2×C311yescharacteristic, complemented
67C2×C4×C22⋊C4C2×C311yescharacteristic, complemented
68#1440C2×C311yescharacteristic, complemented
69#1439C2×C311yescharacteristic, complemented
70#1438C2×C311yescharacteristic
71#1437C2×C311yescharacteristic, complemented
72#1436C2×C311yescharacteristic, complemented
73#1436C2×C311yescharacteristic, complemented
74#1436C2×C311yescharacteristic, complemented
75C22⋊#95C2×C311yescharacteristic, complemented
76C25×C3C2311yescharacteristic
77C25×C3C2311yescharacteristic
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—22no—
81C22×C3×D4—22no—
82C22×C3×D4—22no—
83C22×C3×D4—22no—
84C22×C3×D4C2×C414yes—
85C23×C3×C4—22no—
86C23×C3×C4—22no—
87C23×C3×C4—22no—
88C23×C3×C4—22no—
89C23×C3×C4—22no—
90C23×C3×C4—22no—
91C23×C3×C4—22no—
92C23×C3×C4—22no—
93C23×C3×C4—22no—
94C23×C3×C4—41no—
95C23×C3×C4—41no—
96C23×C3×C4—41no—
97C23×C3×C4—41no—
98C23×C3×C4D414yes—
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C2311yescharacteristic
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2311yescharacteristic
110C23×C3×C4C2311yescharacteristic
111C23×C3×C4C2311yescharacteristic
112C3×C4×D4—232no—
113C2×C3×C4⋊C4—22no—
114C2×C3×C4⋊C4—22no—
115C2×C3×C4⋊C4—22no—
116C2×C3×C4⋊C4—22no—
117C2×C3×C4⋊C4—22no—
118C2×C3×C4⋊C4—22no—
119C2×C3×C4⋊C4—22no—
120C2×C3×C4⋊C4—22no—
121C2×C3×C4⋊C4—22no—
122C2×C3×C4⋊C4—22no—
123C2×C3×C4⋊C4—22no—
124C2×C3×C4⋊C4—22no—
125C2×C3×C4⋊C4—41no—
126C2×C3×C4⋊C4C2×C414yescomplemented
127C2×C3×C4⋊C4D414yes—
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—22no—
138C2×C3×C22⋊C4—22no—
139C2×C3×C22⋊C4—22no—
140C2×C3×C22⋊C4—22no—
141C2×C3×C22⋊C4—22no—
142C2×C3×C22⋊C4—22no—
143C2×C3×C22⋊C4—22no—
144C2×C3×C22⋊C4—22no—
145C2×C3×C22⋊C4—22no—
146C2×C3×C22⋊C4—22no—
147C2×C3×C22⋊C4—22no—
148C2×C3×C22⋊C4—22no—
149C2×C3×C22⋊C4—41no—
150C2×C3×C22⋊C4—41no—
151C2×C3×C22⋊C4—41no—
152C2×C3×C22⋊C4—41no—
153C2×C3×C22⋊C4C2×C414yescomplemented
154C2×C3×C22⋊C4C2×C414yescomplemented
155C2×C3×C22⋊C4C2×C414yescomplemented
156C2×C3×C22⋊C4C2×C414yescomplemented
157C2×C3×C22⋊C4D414yes—
158C2×C3×C42—22no—
159C2×C3×C42—22no—
160C2×C3×C42—22no—
161C2×C3×C42—22no—
162C2×C3×C42—22no—
163C2×C3×C42—22no—
164C2×C3×C42—22no—
165C2×C3×C42—41no—
166C2×C3×C42—41no—
167C3×#95—22no—
168C3×#95—22no—
169C3×#95—22no—
170C3×#95—22no—
171C3×#95—22no—
172C3×#95—22no—
173C3×#95—22no—
174C3×#95—22no—
175C3×#95—22no—
176C3×#95—22no—
177C3×#95—22no—
178C3×#95—41no—
179C3×#95C2×C414yescomplemented
180C3×#95D414yescomplemented
181C23×D4C22×C311yescharacteristic
182C24×C4C22×C311yescharacteristic
183C24×C4C22×C311yescharacteristic
184C2×C4×D4—24no—
185C2×C4×D4—24no—
186C2×C4×D4—24no—
187C22×C4⋊C4C22×C311yescharacteristic
188C22×C4⋊C4C22×C311yescharacteristic
189C22×C4⋊C4C22×C311yescharacteristic
190C22×C4⋊C4C22×C311yescharacteristic
191C22×C4⋊C4C22×C311yescharacteristic
192C22×C22⋊C4C22×C311yescharacteristic
193C22×C22⋊C4C22×C311yescharacteristic
194C22×C22⋊C4C22×C311yescharacteristic
195C22×C22⋊C4C22×C311yescharacteristic
196C22×C22⋊C4C22×C311yescharacteristic
197C22×C22⋊C4C22×C311yescharacteristic
198C22×C22⋊C4C22×C311yescharacteristic
199C22×C22⋊C4C22×C311yescharacteristic
200C22×C22⋊C4C22×C311yescharacteristic
201C22×C22⋊C4C22×C311yescharacteristic
202C22×C42C22×C311yescharacteristic
203C22×C42C22×C311yescharacteristic
204C22×C42C22×C311yescharacteristic
205#394C3×C418yescomplemented
206#389—24no—
207#388—24no—
208#385—24no—
209#385—24no—
210C4×C22⋊C4—24no—
211C2×#95C22×C311yescharacteristic
212C2×#95C22×C311yescharacteristic
213C2×#95C22×C311yescharacteristic
214C2×#95C22×C311yescharacteristic
215C2×#95C22×C311yescharacteristic
216C2×#95C22×C311yescharacteristic
217C2×#95C22×C311yescharacteristic
218C2×#95C22×C311yescharacteristic
219C2×#95C22×C311yescharacteristic
220C2×#95C22×C311yescharacteristic
221C2×#95C22×C311yescharacteristic
222C2×#95C22×C311yescharacteristic
223C2×#95C22×C311yescharacteristic
224C2×#95C22×C311yescharacteristic
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×C3—21no—
243C24×C3—21no—
244C24×C3—21no—
245C24×C3—21no—
246C24×C3—21no—
247C24×C3—21no—
248C24×C3—21no—
249C24×C3C22×C412yes—
250C24×C3C22×C412yes—
251C24×C3C2×D412yes—
252C24×C3C2×D412yes—
253C24×C3#4112yes—
254C24×C3#4112yes—
255C24×C3C2411yescharacteristic
256C2×C3×D4—28no—
257C2×C3×D4—28no—
258C2×C3×D4—28no—
259C2×C3×D4—28no—
260C2×C3×D4—28no—
261C2×C3×D4—28no—
262C2×C3×D4—28no—
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—21no—
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—28no—
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—28no—
323C22×C3×C4—28no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—21no—
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C22×C3×C4—44no—
339C22×C3×C4—44no—
340C22×C3×C4—44no—
341C22×C3×C4—44no—
342C22×C3×C4—44no—
343C22×C3×C4—44no—
344C22×C3×C4—44no—
345C22×C3×C4—44no—
346C22×C3×C4—44no—
347C22×C3×C4—44no—
348C22×C3×C4—44no—
349C22×C3×C4C22×C412yes—
350C22×C3×C4C22×C412yes—
351C22×C3×C4C22×C412yes—
352C22×C3×C4C22×C412yes—
353C22×C3×C4C22×C412yes—
354C22×C3×C4C2×D412yes—
355C22×C3×C4C2×D412yes—
356C22×C3×C4C2×D412yes—
357C22×C3×C4C2×D412yes—
358C22×C3×C4C2×D412yes—
359C22×C3×C4C2×D412yes—
360C22×C3×C4C2×D412yes—
361C22×C3×C4C2×D412yes—
362C22×C3×C4C2×D412yes—
363C22×C3×C4C2×D412yes—
364C22×C3×C4#4112yes—
365C22×C3×C4#4112yes—
366C22×C3×C4#4112yes—
367C22×C3×C4#4112yes—
368C3×C4⋊C4—28no—
369C3×C4⋊C4—28no—
370C3×C4⋊C4—44no—
371C3×C4⋊C4—44no—
372C3×C4⋊C4—44no—
373C3×C22⋊C4—28no—
374C3×C22⋊C4—28no—
375C3×C22⋊C4—28no—
376C3×C22⋊C4—28no—
377C3×C22⋊C4—28no—
378C3×C22⋊C4—28no—
379C3×C22⋊C4—28no—
380C3×C22⋊C4—44no—
381C3×C22⋊C4—44no—
382C3×C22⋊C4—44no—
383C3×C42—28no—
384C3×C42—44no—
385C3×C42—44no—
386C25C23×C311yescharacteristic
387C25C23×C311yescharacteristic
388C22×D4—22no—
389C22×D4—22no—
390C22×D4—22no—
391C22×D4—22no—
392C22×D4—22no—
393C22×D4—22no—
394C22×D4C2×C3×C414yes—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—41no—
405C23×C4—41no—
406C23×C4—41no—
407C23×C4—41no—
408C23×C4C3×D414yes—
409C23×C4C23×C311yescharacteristic
410C23×C4C23×C311yescharacteristic
411C23×C4C23×C311yescharacteristic
412C23×C4C23×C311yescharacteristic
413C23×C4C23×C311yescharacteristic
414C23×C4C23×C311yescharacteristic
415C23×C4C23×C311yescharacteristic
416C23×C4C23×C311yescharacteristic
417C23×C4C23×C311yescharacteristic
418C23×C4C23×C311yescharacteristic
419C23×C4C23×C311yescharacteristic
420C23×C4C23×C311yescharacteristic
421C23×C4C23×C311yescharacteristic
422C4×D4—232no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—41no—
436C2×C4⋊C4C2×C3×C414yescomplemented
437C2×C4⋊C4C3×D414yes—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—41no—
460C2×C22⋊C4—41no—
461C2×C22⋊C4—41no—
462C2×C22⋊C4—41no—
463C2×C22⋊C4C2×C3×C414yescomplemented
464C2×C22⋊C4C2×C3×C414yescomplemented
465C2×C22⋊C4C2×C3×C414yescomplemented
466C2×C22⋊C4C2×C3×C414yescomplemented
467C2×C22⋊C4C3×D414yes—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42—22no—
472C2×C42—22no—
473C2×C42—22no—
474C2×C42—22no—
475C2×C42—41no—
476C2×C42—41no—
477#95—22no—
478#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—22no—
485#95—22no—
486#95—22no—
487#95—22no—
488#95—41no—
489#95C2×C3×C414yescomplemented
490#95C3×D414yescomplemented
491C23×C3—22no—
492C23×C3—22no—
493C23×C3—22no—
494C23×C3—22no—
495C23×C3—22no—
496C23×C3—22no—
497C23×C3—22no—
498C23×C3—22no—
499C23×C3—22no—
500C23×C3—22no—
501C23×C3—22no—
502C23×C3—22no—
503C23×C3—22no—
504C23×C3—22no—
505C23×C3—22no—
506C23×C3—22no—
507C23×C3—22no—
508C23×C3—22no—
509C23×C3—22no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—22no—
514C23×C3—22no—
515C23×C3—22no—
516C23×C3—22no—
517C23×C3—22no—
518C23×C3—22no—
519C23×C3—22no—
520C23×C3—22no—
521C23×C3—22no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
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×C3—41no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—41no—
546C23×C3—41no—
547C23×C3—41no—
548C23×C3—41no—
549C23×C3—41no—
550C23×C3—41no—
551C23×C3—41no—
552C23×C3—41no—
553C23×C3—41no—
554C23×C3—41no—
555C23×C3—41no—
556C23×C3—41no—
557C23×C3—41no—
558C23×C3—41no—
559C23×C3C4×D414yes—
560C23×C3C4×D414yes—
561C23×C3C23×C411yescharacteristic
562C23×C3C22×D411yescharacteristic
563C23×C3C22×D411yescharacteristic
564C23×C3C22×D411yescharacteristic
565C23×C3C22×D411yescharacteristic
566C23×C3C2×#4111yescharacteristic
567C23×C3C2×#4111yescharacteristic
568C23×C3C2×#4111yescharacteristic
569C23×C3C2×#4111yescharacteristic
570C23×C3C2×#4111yescharacteristic
571C23×C3C2×#4111yescharacteristic
572C23×C3H(5,𝔽2)11yescharacteristic
573C23×C3H(5,𝔽2)11yescharacteristic
574C23×C32−1+411yescharacteristic
575C23×C32−1+411yescharacteristic
576C3×D4—232no—
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—22no—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—22no—
606C2×C3×C4—22no—
607C2×C3×C4—22no—
608C2×C3×C4—22no—
609C2×C3×C4—22no—
610C2×C3×C4—22no—
611C2×C3×C4—22no—
612C2×C3×C4—22no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—22no—
617C2×C3×C4—22no—
618C2×C3×C4—22no—
619C2×C3×C4—22no—
620C2×C3×C4—22no—
621C2×C3×C4—22no—
622C2×C3×C4—416no—
623C2×C3×C4—416no—
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×C4—41no—
646C2×C3×C4—41no—
647C2×C3×C4—41no—
648C2×C3×C4—41no—
649C2×C3×C4—41no—
650C2×C3×C4—41no—
651C2×C3×C4—41no—
652C2×C3×C4—41no—
653C2×C3×C4—41no—
654C2×C3×C4—41no—
655C2×C3×C4—41no—
656C2×C3×C4—41no—
657C2×C3×C4—41no—
658C2×C3×C4—41no—
659C2×C3×C4—41no—
660C2×C3×C4—41no—
661C2×C3×C4—41no—
662C2×C3×C4—41no—
663C2×C3×C4—41no—
664C2×C3×C4—41no—
665C2×C3×C4—41no—
666C2×C3×C4C4×D414yes—
667C2×C3×C4C4×D414yescomplemented
668C2×C3×C4#12014yes—
669C2×C3×C4#12114yes—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—21no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24C22×C3×C412yes—
695C24C22×C3×C412yes—
696C24C2×C3×D412yes—
697C24C2×C3×D412yes—
698C24C3×#4112yes—
699C24C3×#4112yes—
700C24C24×C311yescharacteristic
701C2×D4—28no—
702C2×D4—28no—
703C2×D4—28no—
704C2×D4—28no—
705C2×D4—28no—
706C2×D4—28no—
707C2×D4—28no—
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—28no—
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—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—28no—
768C22×C4—28no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—44no—
784C22×C4—44no—
785C22×C4—44no—
786C22×C4—44no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—44no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4C22×C3×C412yes—
795C22×C4C22×C3×C412yes—
796C22×C4C22×C3×C412yes—
797C22×C4C22×C3×C412yes—
798C22×C4C22×C3×C412yes—
799C22×C4C2×C3×D412yes—
800C22×C4C2×C3×D412yes—
801C22×C4C2×C3×D412yes—
802C22×C4C2×C3×D412yes—
803C22×C4C2×C3×D412yes—
804C22×C4C2×C3×D412yes—
805C22×C4C2×C3×D412yes—
806C22×C4C2×C3×D412yes—
807C22×C4C2×C3×D412yes—
808C22×C4C2×C3×D412yes—
809C22×C4C3×#4112yes—
810C22×C4C3×#4112yes—
811C22×C4C3×#4112yes—
812C22×C4C3×#4112yes—
813C4⋊C4—28no—
814C4⋊C4—28no—
815C4⋊C4—44no—
816C4⋊C4—44no—
817C4⋊C4—44no—
818C22⋊C4—28no—
819C22⋊C4—28no—
820C22⋊C4—28no—
821C22⋊C4—28no—
822C22⋊C4—28no—
823C22⋊C4—28no—
824C22⋊C4—28no—
825C22⋊C4—44no—
826C22⋊C4—44no—
827C22⋊C4—44no—
828C42—28no—
829C42—44no—
830C42—44no—
831C22×C3—24no—
832C22×C3—24no—
833C22×C3—24no—
834C22×C3—24no—
835C22×C3—24no—
836C22×C3—24no—
837C22×C3—42no—
838C22×C3—42no—
839C22×C3—42no—
840C22×C3—42no—
841C22×C3—42no—
842C22×C3—42no—
843C22×C3—42no—
844C22×C3—42no—
845C22×C3—42no—
846C22×C3—42no—
847C22×C3—42no—
848C22×C3—42no—
849C22×C3—42no—
850C22×C3—42no—
851C22×C3—42no—
852C22×C3—42no—
853C22×C3—42no—
854C22×C3—42no—
855C22×C3—42no—
856C22×C3—42no—
857C22×C3—42no—
858C22×C3—42no—
859C22×C3—42no—
860C22×C3—42no—
861C22×C3C2×C4×D411yescharacteristic
862C22×C3C2×C4×D411yescharacteristic
863C22×C3C2×C4×D411yescharacteristic
864C22×C3C2×C4×D411yescharacteristic
865C22×C3C4×#4111yescharacteristic
866C22×C3#52011yescharacteristic
867C22×C3#52011yescharacteristic
868C22×C3C2×#12011yescharacteristic
869C22×C3C2×#12111yescharacteristic
870C22×C3#52511yescharacteristic
871C22×C3#52511yescharacteristic
872C22×C3#52511yescharacteristic
873C22×C3#52511yescharacteristic
874C22×C3#52911yescharacteristic
875C22×C3#53211yescharacteristic
876C22×C3#53411yescharacteristic
877C22×C3#53611yescharacteristic
878C22×C3#53911yescharacteristic
879C22×C3#53911yescharacteristic
880C22×C3D4211yescharacteristic
881C22×C3D4211yescharacteristic
882C22×C3#54611yescharacteristic
883C22×C3#54611yescharacteristic
884C22×C3#54711yescharacteristic
885C22×C3#54711yescharacteristic
886C22×C3#54711yescharacteristic
887C22×C3#54811yescharacteristic
888C22×C3#54811yescharacteristic
889C22×C3#54811yescharacteristic
890C22×C3#55111yescharacteristic
891C22×C3#55211yescharacteristic
892C22×C3#55311yescharacteristic
893C22×C3#55311yescharacteristic
894C22×C3#55611yescharacteristic
895C22×C3#55911yescharacteristic
896C3×C4—24no—
897C3×C4—24no—
898C3×C4—24no—
899C3×C4—24no—
900C3×C4—42no—
901C3×C4—42no—
902C3×C4—42no—
903C3×C4—42no—
904C3×C4—42no—
905C3×C4—42no—
906C3×C4—42no—
907C3×C4—81no—
908C3×C4—81no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23C3×C4×D414yes—
978C23C3×C4×D414yes—
979C23C23×C3×C411yescharacteristic
980C23C22×C3×D411yescharacteristic
981C23C22×C3×D411yescharacteristic
982C23C22×C3×D411yescharacteristic
983C23C22×C3×D411yescharacteristic
984C23C2×C3×#4111yescharacteristic
985C23C2×C3×#4111yescharacteristic
986C23C2×C3×#4111yescharacteristic
987C23C2×C3×#4111yescharacteristic
988C23C2×C3×#4111yescharacteristic
989C23C2×C3×#4111yescharacteristic
990C23C3×H(5,𝔽2)11yescharacteristic
991C23C3×H(5,𝔽2)11yescharacteristic
992C23C3×2−1+411yescharacteristic
993C23C3×2−1+411yescharacteristic
994D4—232no—
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—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—416no—
1041C2×C4—416no—
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×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4C3×C4×D414yes—
1085C2×C4C3×C4×D414yescomplemented
1086C2×C4C3×#12014yes—
1087C2×C4C3×#12114yes—
1088C2×C3—44no—
1089C2×C3—44no—
1090C2×C3C4×#12011yescharacteristic
1091C2×C3C4×#12111yescharacteristic
1092C2×C3#232211yescharacteristic
1093C2×C3#235911yescharacteristic
1094C2×C3#236111yescharacteristic
1095C2×C3#236111yescharacteristic
1096C2×C3#236711yescharacteristic
1097C2×C3#241011yescharacteristic
1098C2×C3#241511yescharacteristic
1099C2×C3#243211yescharacteristic
1100C2×C3#245511yescharacteristic
1101C2×C3#246011yescharacteristic
1102C2×C3#246311yescharacteristic
1103C2×C3#246611yescharacteristic
1104C2×C3#260211yescharacteristic
1105C22—24no—
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—24no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22C2×C3×C4×D411yescharacteristic
1136C22C2×C3×C4×D411yescharacteristic
1137C22C2×C3×C4×D411yescharacteristic
1138C22C2×C3×C4×D411yescharacteristic
1139C22C3×C4×#4111yescharacteristic
1140C22C3×#52011yescharacteristic
1141C22C3×#52011yescharacteristic
1142C22C2×C3×#12011yescharacteristic
1143C22C2×C3×#12111yescharacteristic
1144C22C3×#52511yescharacteristic
1145C22C3×#52511yescharacteristic
1146C22C3×#52511yescharacteristic
1147C22C3×#52511yescharacteristic
1148C22C3×#52911yescharacteristic
1149C22C3×#53211yescharacteristic
1150C22C3×#53411yescharacteristic
1151C22C3×#53611yescharacteristic
1152C22C3×#53911yescharacteristic
1153C22C3×#53911yescharacteristic
1154C22C3×D4211yescharacteristic
1155C22C3×D4211yescharacteristic
1156C22C3×#54611yescharacteristic
1157C22C3×#54611yescharacteristic
1158C22C3×#54711yescharacteristic
1159C22C3×#54711yescharacteristic
1160C22C3×#54711yescharacteristic
1161C22C3×#54811yescharacteristic
1162C22C3×#54811yescharacteristic
1163C22C3×#54811yescharacteristic
1164C22C3×#55111yescharacteristic
1165C22C3×#55211yescharacteristic
1166C22C3×#55311yescharacteristic
1167C22C3×#55311yescharacteristic
1168C22C3×#55611yescharacteristic
1169C22C3×#55911yescharacteristic
1170C4—24no—
1171C4—24no—
1172C4—24no—
1173C4—24no—
1174C4—42no—
1175C4—42no—
1176C4—42no—
1177C4—42no—
1178C4—42no—
1179C4—42no—
1180C4—42no—
1181C4—81no—
1182C4—81no—
1183C3#1418511yescharacteristic, direct product factor, Sylow
1184C2—44no—
1185C2—44no—
1186C2C3×C4×#12011yescharacteristic
1187C2C3×C4×#12111yescharacteristic
1188C2C3×#232211yescharacteristic
1189C2C3×#235911yescharacteristic
1190C2C3×#236111yescharacteristic
1191C2C3×#236111yescharacteristic
1192C2C3×#236711yescharacteristic
1193C2C3×#241011yescharacteristic
1194C2C3×#241511yescharacteristic
1195C2C3×#243211yescharacteristic
1196C2C3×#245511yescharacteristic
1197C2C3×#246011yescharacteristic
1198C2C3×#246311yescharacteristic
1199C2C3×#246611yescharacteristic
1200C2C3×#260211yescharacteristic
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×#385C2semidirect
6. C2×C3×#385C2semidirect
7. C2×C3×C4×C22⋊C4C2semidirect
8. C3×#1440C2semidirect
9. C3×#1439C2semidirect
11. C3×#1437C2semidirect
12. C3×#1436C2semidirect
13. C3×#1436C2semidirect
14. C3×#1436C2semidirect
15. C3×C22⋊#95C2semidirect
16. #14185C3direct (N × H)
41. C3×#394C4semidirect
63. C2×#389C2×C3semidirect
64. C2×#388C2×C3semidirect
65. C2×#385C2×C3semidirect
66. C2×#385C2×C3semidirect
67. C2×C4×C22⋊C4C2×C3semidirect
68. #1440C2×C3semidirect
69. #1439C2×C3semidirect
71. #1437C2×C3semidirect
72. #1436C2×C3semidirect
73. #1436C2×C3semidirect
74. #1436C2×C3semidirect
75. C22⋊#95C2×C3semidirect
126. C2×C3×C4⋊C4C2×C4semidirect
153. C2×C3×C22⋊C4C2×C4semidirect
154. C2×C3×C22⋊C4C2×C4semidirect
155. C2×C3×C22⋊C4C2×C4semidirect
156. C2×C3×C22⋊C4C2×C4semidirect
179. C3×#95C2×C4semidirect
180. C3×#95D4semidirect
205. #394C3×C4semidirect
436. C2×C4⋊C4C2×C3×C4semidirect
463. C2×C22⋊C4C2×C3×C4semidirect
464. C2×C22⋊C4C2×C3×C4semidirect
465. C2×C22⋊C4C2×C3×C4semidirect
466. C2×C22⋊C4C2×C3×C4semidirect
489. #95C2×C3×C4semidirect
490. #95C3×D4semidirect
667. C2×C3×C4C4×D4semidirect
1085. C2×C4C3×C4×D4semidirect
1183. C3#14185direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4×D42
C2×C3×#3942
C2×C3×#3892
C2×C3×#3882
C2×C3×#3852
C2×C3×C4×C22⋊C42
C3×#14402
C3×#14392
C3×#14382
C3×#14372
C3×#14362
C3×C22⋊#952
#141853