Finite Group Databasebeta

← C3×#30412 #10649019

Subgroups — C3×#30412 #10649019

Order 768.

1248 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#469C211yesmaximal, characteristic, complemented
2C2×C3×#447C211yesmaximal, characteristic, complemented
3C3×#2537C211yesmaximal, characteristic, complemented
4C3×#2408C211yesmaximal, characteristic, complemented
5C3×#2094C211yesmaximal, characteristic, complemented
6C3×#2077C211yesmaximal, characteristic, complemented
7C3×#2071C211yesmaximal, characteristic, complemented
8C3×#2034C211yesmaximal, characteristic, complemented
9C3×#2034C211yesmaximal, characteristic, complemented
10C3×#1999C211yesmaximal, characteristic, complemented
11C3×#1895C211yesmaximal, characteristic, complemented
12C3×#1879C211yesmaximal, characteristic, complemented
13C3×#1879C211yesmaximal, characteristic, complemented
14C3×#1870C211yesmaximal, characteristic, complemented
15C3×#1786C211yesmaximal, characteristic, complemented
16#30412C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×D4C2211yescharacteristic
18C22×C3×D8C2211yescharacteristic
19C22×C3×D8C2211yescharacteristic
20C22×C3×M16C2211yescharacteristic, complemented
21C2×C3×#121—21no—
22C2×C3×#121C2211yescharacteristic
23C2×C3×#121C2211yescharacteristic
24C2×C3×#121C2211yescharacteristic
25C2×C3×#121C2211yescharacteristic, complemented
26C2×C3×#120—21no—
27C2×C3×C4×D4C2211yescharacteristic
28C2×C3×C4×D4C2211yescharacteristic, complemented
29C3×#469—24no—
30C3×#447—24no—
31C2×C3×#106C2211yescharacteristic, complemented
32C2×C3×#106C2211yescharacteristic, complemented
33C2×C3×#102C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic, complemented
40C2×C3×#102C2211yescharacteristic, complemented
41C2×C3×C22⋊C8C2211yescharacteristic
42C2×C3×C22⋊C8C2211yescharacteristic
43C2×C3×C22⋊C8C2211yescharacteristic, complemented
44C3×#394—21no—
45C3×#394—21no—
46C3×#394—21no—
47C3×#392—21no—
48C3×#390C2211yescharacteristic
49C3×#390C2211yescharacteristic
50C3×#384C2211yescharacteristic, complemented
51C3×#380—21no—
52C3×#380C2211yescharacteristic
53C3×#380C2211yescharacteristic
54C3×#380C2211yescharacteristic, complemented
55C3×#379—21no—
56C3×#340C2211yescharacteristic, complemented
57C3×#340C2211yescharacteristic, complemented
58C3×#340C2211yescharacteristic, complemented
59C3×#340C2211yescharacteristic, complemented
60C3×#336C2211yescharacteristic, complemented
61C3×#336C2211yescharacteristic, complemented
62C2×#469C2×C311yescharacteristic, complemented
63C2×#447C2×C311yescharacteristic, complemented
64#2537C2×C311yescharacteristic, complemented
65#2408C2×C311yescharacteristic, complemented
66#2094C2×C311yescharacteristic, complemented
67#2077C2×C311yescharacteristic, complemented
68#2071C2×C311yescharacteristic, complemented
69#2034C2×C311yescharacteristic, complemented
70#2034C2×C311yescharacteristic, complemented
71#1999C2×C311yescharacteristic, complemented
72#1895C2×C311yescharacteristic, complemented
73#1879C2×C311yescharacteristic, complemented
74#1879C2×C311yescharacteristic, complemented
75#1870C2×C311yescharacteristic, complemented
76#1786C2×C311yescharacteristic, complemented
77C25×C3—21no—
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—21no—
81C22×C3×D4—21no—
82C22×C3×D4—21no—
83C22×C3×D4—21no—
84C22×C3×D4—21no—
85C22×C3×D4—41no—
86C22×C3×D4—41no—
87C22×C3×D4—41no—
88C22×C3×D4—41no—
89C22×C3×D4D411yescharacteristic
90C22×C3×D4C2311yescharacteristic
91C22×C3×D4C2311yescharacteristic
92C22×C3×D4C2311yescharacteristic
93C23×C3×C4—21no—
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C2×C3×D8—22no—
97C2×C3×D8—22no—
98C2×C3×D8—41no—
99C2×C3×D8—41no—
100C2×C3×D8—41no—
101C2×C3×D8D414yescomplemented
102C2×C3×M16—22no—
103C2×C3×M16—41no—
104C2×C3×M16—41no—
105C22×C3×C8C2311yescharacteristic
106C22×C3×C8C2311yescharacteristic
107C22×C3×C8C2311yescharacteristic
108C22×C3×C8C2311yescharacteristic
109C3×#121—22no—
110C3×#121—22no—
111C3×#121—22no—
112C3×#121—22no—
113C3×#121—41no—
114C3×#121—41no—
115C3×#121—41no—
116C3×#121—41no—
117C3×#121—44no—
118C3×#120—44no—
119C3×C4×D4—41no—
120C3×C4×D4—41no—
121C3×C4×D4—41no—
122C3×C4×D4—41no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4D411yescharacteristic
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C22⋊C4—21no—
132C2×C3×C22⋊C4—21no—
133C2×C3×C22⋊C4—21no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C22⋊C4—21no—
136C2×C3×C22⋊C4—21no—
137C2×C3×C22⋊C4—21no—
138C2×C3×C22⋊C4—21no—
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4—21no—
141C2×C3×C22⋊C4—21no—
142C2×C3×C22⋊C4—21no—
143C2×C3×C22⋊C4D411yescharacteristic
144C2×C3×C22⋊C4D411yescharacteristic
145C2×C3×C42C2311yescharacteristic
146C3×#106—22no—
147C3×#106—41no—
148C3×#102—22no—
149C3×#102—22no—
150C3×#102—22no—
151C3×#102—22no—
152C3×#102—41no—
153C3×#102—41no—
154C3×#102—41no—
155C3×#102—41no—
156C3×C22⋊C8—22no—
157C3×C22⋊C8—41no—
158C3×C22⋊C8—41no—
159C3×#95—21no—
160C3×#95—21no—
161C3×#95—21no—
162C23×D4C22×C311yescharacteristic
163C22×D8C22×C311yescharacteristic
164C22×D8C22×C311yescharacteristic
165C22×M16C22×C311yescharacteristic, complemented
166C2×#121—21no—
167C2×#121C22×C311yescharacteristic
168C2×#121C22×C311yescharacteristic
169C2×#121C22×C311yescharacteristic
170C2×#121C22×C311yescharacteristic, complemented
171C2×#120—21no—
172C2×C4×D4C22×C311yescharacteristic
173C2×C4×D4C22×C311yescharacteristic, complemented
174#469—24no—
175#447—24no—
176C2×#106C22×C311yescharacteristic, complemented
177C2×#106C22×C311yescharacteristic, complemented
178C2×#102C22×C311yescharacteristic
179C2×#102C22×C311yescharacteristic
180C2×#102C22×C311yescharacteristic
181C2×#102C22×C311yescharacteristic
182C2×#102C22×C311yescharacteristic
183C2×#102C22×C311yescharacteristic
184C2×#102C22×C311yescharacteristic, complemented
185C2×#102C22×C311yescharacteristic, complemented
186C2×C22⋊C8C22×C311yescharacteristic
187C2×C22⋊C8C22×C311yescharacteristic
188C2×C22⋊C8C22×C311yescharacteristic, complemented
189#394—21no—
190#394—21no—
191#394—21no—
192#392—21no—
193#390C22×C311yescharacteristic
194#390C22×C311yescharacteristic
195#384C22×C311yescharacteristic, complemented
196#380—21no—
197#380C22×C311yescharacteristic
198#380C22×C311yescharacteristic
199#380C22×C311yescharacteristic, complemented
200#379—21no—
201#340C22×C311yescharacteristic, complemented
202#340C22×C311yescharacteristic, complemented
203#340C22×C311yescharacteristic, complemented
204#340C22×C311yescharacteristic, complemented
205#336C22×C311yescharacteristic, complemented
206#336C22×C311yescharacteristic, complemented
207C24×C3—21no—
208C24×C3—21no—
209C24×C3—21no—
210C24×C3—42no—
211C24×C3—42no—
212C24×C3—42no—
213C24×C3—42no—
214C24×C3—42no—
215C24×C3—81no—
216C24×C3—81no—
217C24×C3C2×D411yescharacteristic
218C24×C3C2×D411yescharacteristic
219C2×C3×D4—22no—
220C2×C3×D4—22no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—41no—
237C2×C3×D4—42no—
238C2×C3×D4—42no—
239C2×C3×D4—42no—
240C2×C3×D4—44no—
241C2×C3×D4—44no—
242C2×C3×D4—44no—
243C2×C3×D4—44no—
244C2×C3×D4—42no—
245C2×C3×D4—42no—
246C2×C3×D4—42no—
247C2×C3×D4—42no—
248C2×C3×D4—42no—
249C2×C3×D4—42no—
250C2×C3×D4—42no—
251C2×C3×D4—42no—
252C2×C3×D4—81no—
253C2×C3×D4—81no—
254C2×C3×D4—81no—
255C2×C3×D4—81no—
256C2×C3×D4C2×D412yes—
257C2×C3×D4C2×D412yes—
258C2×C3×D4#4112yes—
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—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—42no—
277C22×C3×C4—42no—
278C22×C3×C4—42no—
279C22×C3×C4C2×D411yescharacteristic
280C22×C3×C4C2×D411yescharacteristic
281C22×C3×C4C2×D411yescharacteristic
282C22×C3×C4C2×D411yescharacteristic
283C22×C3×C4C2411yescharacteristic
284C3×D8—44no—
285C3×D8—44no—
286C3×M16—44no—
287C2×C3×C8—21no—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8—21no—
297C2×C3×C8—21no—
298C2×C3×C8C2×D412yes—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4—21no—
309C3×C4⋊C4—41no—
310C3×C4⋊C4—42no—
311C3×C4⋊C4—81no—
312C3×C22⋊C4—41no—
313C3×C22⋊C4—41no—
314C3×C22⋊C4—42no—
315C3×C22⋊C4—42no—
316C3×C22⋊C4—42no—
317C3×C22⋊C4—42no—
318C3×C22⋊C4—42no—
319C3×C22⋊C4—42no—
320C3×C22⋊C4—42no—
321C3×C22⋊C4—42no—
322C3×C22⋊C4—42no—
323C3×C22⋊C4—42no—
324C3×C22⋊C4—81no—
325C3×C22⋊C4—81no—
326C3×C42—21no—
327C3×C42—21no—
328C25—21no—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—21no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—41no—
337C22×D4—41no—
338C22×D4—41no—
339C22×D4—41no—
340C22×D4C3×D411yescharacteristic
341C22×D4C23×C311yescharacteristic
342C22×D4C23×C311yescharacteristic
343C22×D4C23×C311yescharacteristic
344C23×C4—21no—
345C23×C4C23×C311yescharacteristic
346C23×C4C23×C311yescharacteristic
347C2×D8—22no—
348C2×D8—22no—
349C2×D8—41no—
350C2×D8—41no—
351C2×D8—41no—
352C2×D8C3×D414yescomplemented
353C2×M16—22no—
354C2×M16—41no—
355C2×M16—41no—
356C22×C8C23×C311yescharacteristic
357C22×C8C23×C311yescharacteristic
358C22×C8C23×C311yescharacteristic
359C22×C8C23×C311yescharacteristic
360#121—22no—
361#121—22no—
362#121—22no—
363#121—22no—
364#121—41no—
365#121—41no—
366#121—41no—
367#121—41no—
368#121—44no—
369#120—44no—
370C4×D4—41no—
371C4×D4—41no—
372C4×D4—41no—
373C4×D4—41no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4C3×D411yescharacteristic
377C2×C4⋊C4C23×C311yescharacteristic
378C2×C4⋊C4C23×C311yescharacteristic
379C2×C4⋊C4C23×C311yescharacteristic
380C2×C4⋊C4C23×C311yescharacteristic
381C2×C4⋊C4C23×C311yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4C3×D411yescharacteristic
395C2×C22⋊C4C3×D411yescharacteristic
396C2×C42C23×C311yescharacteristic
397#106—22no—
398#106—41no—
399#102—22no—
400#102—22no—
401#102—22no—
402#102—22no—
403#102—41no—
404#102—41no—
405#102—41no—
406#102—41no—
407C22⋊C8—22no—
408C22⋊C8—41no—
409C22⋊C8—41no—
410#95—21no—
411#95—21no—
412#95—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—22no—
421C23×C3—22no—
422C23×C3—21no—
423C23×C3—22no—
424C23×C3—21no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—48no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3—41no—
437C23×C3—41no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3—41no—
443C23×C3—41no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3—84no—
449C23×C3—84no—
450C23×C3—84no—
451C23×C3—84no—
452C23×C3—84no—
453C23×C3—84no—
454C23×C3AGL(1,ℤ/8)12yes—
455C23×C3C22×D411yescharacteristic
456C3×D4—22no—
457C3×D4—22no—
458C3×D4—22no—
459C3×D4—22no—
460C3×D4—22no—
461C3×D4—22no—
462C3×D4—44no—
463C3×D4—48no—
464C3×D4—41no—
465C3×D4—41no—
466C3×D4—41no—
467C3×D4—41no—
468C3×D4—41no—
469C3×D4—41no—
470C3×D4—84no—
471C3×D4—84no—
472C3×D4—84no—
473C3×D4—84no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—84no—
509C2×C3×C4AGL(1,ℤ/8)12yes—
510C2×C3×C4C22×D411yescharacteristic
511C2×C3×C4C2×#4111yescharacteristic
512C2×C3×C4H(5,𝔽2)11yescharacteristic
513C2×C3×C4H(5,𝔽2)11yescharacteristic
514C2×C3×C4H(5,𝔽2)11yescharacteristic
515C2×C3×C4H(5,𝔽2)11yescharacteristic
516C3×C8—22no—
517C3×C8—41no—
518C3×C8—41no—
519C3×C8—41no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—42no—
524C24—42no—
525C24—42no—
526C24—42no—
527C24—42no—
528C24—81no—
529C24—81no—
530C24C2×C3×D411yescharacteristic
531C24C2×C3×D411yescharacteristic
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—41no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—44no—
554C2×D4—44no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—81no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4C2×C3×D412yes—
570C2×D4C2×C3×D412yes—
571C2×D4C3×#4112yes—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4C2×C3×D411yescharacteristic
593C22×C4C2×C3×D411yescharacteristic
594C22×C4C2×C3×D411yescharacteristic
595C22×C4C2×C3×D411yescharacteristic
596C22×C4C24×C311yescharacteristic
597D8—44no—
598D8—44no—
599M16—44no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8C2×C3×D412yes—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—41no—
623C4⋊C4—42no—
624C4⋊C4—81no—
625C22⋊C4—41no—
626C22⋊C4—41no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—81no—
638C22⋊C4—81no—
639C42—21no—
640C42—21no—
641C22×C3—22no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—42no—
650C22×C3—42no—
651C22×C3—42no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—42no—
656C22×C3—42no—
657C22×C3—41no—
658C22×C3—42no—
659C22×C3—42no—
660C22×C3—41no—
661C22×C3—42no—
662C22×C3—41no—
663C22×C3—42no—
664C22×C3—816no—
665C22×C3—81no—
666C22×C3—81no—
667C22×C3—81no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—81no—
671C22×C3—81no—
672C22×C3—81no—
673C22×C3—81no—
674C22×C3—81no—
675C22×C3—81no—
676C22×C3—81no—
677C22×C3#53411yescharacteristic
678C22×C3D4211yescharacteristic
679C22×C3#54611yescharacteristic
680C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
681C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
682C22×C3#57611yescharacteristic
683C22×C3#57711yescharacteristic
684C3×C4—22no—
685C3×C4—41no—
686C3×C4—41no—
687C3×C4—41no—
688C3×C4—81no—
689C3×C4—81no—
690C3×C4—81no—
691C3×C4—81no—
692C3×C4—81no—
693C3×C4#53411yescharacteristic
694C3×C4#53811yescharacteristic
695C3×C4#54611yescharacteristic
696C3×C4#56011yescharacteristic
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—22no—
709C23—22no—
710C23—21no—
711C23—22no—
712C23—21no—
713C23—48no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—84no—
733C23—84no—
734C23—84no—
735C23—84no—
736C23—84no—
737C23—84no—
738C23C3×AGL(1,ℤ/8)12yes—
739C23C22×C3×D411yescharacteristic
740D4—22no—
741D4—22no—
742D4—22no—
743D4—22no—
744D4—22no—
745D4—22no—
746D4—44no—
747D4—48no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—84no—
755D4—84no—
756D4—84no—
757D4—84no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—84no—
793C2×C4C3×AGL(1,ℤ/8)12yes—
794C2×C4C22×C3×D411yescharacteristic
795C2×C4C2×C3×#4111yescharacteristic
796C2×C4C3×H(5,𝔽2)11yescharacteristic
797C2×C4C3×H(5,𝔽2)11yescharacteristic
798C2×C4C3×H(5,𝔽2)11yescharacteristic
799C2×C4C3×H(5,𝔽2)11yescharacteristic
800C8—22no—
801C8—41no—
802C8—41no—
803C8—41no—
804C2×C3—42no—
805C2×C3—81no—
806C2×C3—82no—
807C2×C3—82no—
808C2×C3—82no—
809C2×C3#266811yescharacteristic
810C2×C3#319211yescharacteristic
811C2×C3#319811yescharacteristic
812C2×C3#326411yescharacteristic
813C2×C3#327211yescharacteristic
814C2×C3#330611yescharacteristic
815C2×C3#332511yescharacteristic
816C22—22no—
817C22—22no—
818C22—22no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—41no—
836C22—42no—
837C22—41no—
838C22—42no—
839C22—816no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22C3×#53411yescharacteristic
853C22C3×D4211yescharacteristic
854C22C3×#54611yescharacteristic
855C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
856C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
857C22C3×#57611yescharacteristic
858C22C3×#57711yescharacteristic
859C4—22no—
860C4—41no—
861C4—41no—
862C4—41no—
863C4—81no—
864C4—81no—
865C4—81no—
866C4—81no—
867C4—81no—
868C4C3×#53411yescharacteristic
869C4C3×#53811yescharacteristic
870C4C3×#54611yescharacteristic
871C4C3×#56011yescharacteristic
872C3#3041211yescharacteristic, direct product factor, Sylow
873C2—42no—
874C2—81no—
875C2—82no—
876C2—82no—
877C2—82no—
878C2C3×#266811yescharacteristic
879C2C3×#319211yescharacteristic
880C2C3×#319811yescharacteristic
881C2C3×#326411yescharacteristic
882C2C3×#327211yescharacteristic
883C2C3×#330611yescharacteristic
884C2C3×#332511yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#469C2semidirect
2. C2×C3×#447C2semidirect
3. C3×#2537C2semidirect
4. C3×#2408C2semidirect
5. C3×#2094C2semidirect
6. C3×#2077C2semidirect
7. C3×#2071C2semidirect
8. C3×#2034C2semidirect
9. C3×#2034C2semidirect
10. C3×#1999C2semidirect
11. C3×#1895C2semidirect
12. C3×#1879C2semidirect
13. C3×#1879C2semidirect
14. C3×#1870C2semidirect
15. C3×#1786C2semidirect
16. #30412C3direct (N × H)
20. C22×C3×M16C22semidirect
25. C2×C3×#121C22semidirect
28. C2×C3×C4×D4C22semidirect
31. C2×C3×#106C22semidirect
32. C2×C3×#106C22semidirect
39. C2×C3×#102C22semidirect
40. C2×C3×#102C22semidirect
43. C2×C3×C22⋊C8C22semidirect
50. C3×#384C22semidirect
54. C3×#380C22semidirect
56. C3×#340C22semidirect
57. C3×#340C22semidirect
58. C3×#340C22semidirect
59. C3×#340C22semidirect
60. C3×#336C22semidirect
61. C3×#336C22semidirect
62. C2×#469C2×C3semidirect
63. C2×#447C2×C3semidirect
64. #2537C2×C3semidirect
65. #2408C2×C3semidirect
66. #2094C2×C3semidirect
67. #2077C2×C3semidirect
68. #2071C2×C3semidirect
69. #2034C2×C3semidirect
70. #2034C2×C3semidirect
71. #1999C2×C3semidirect
72. #1895C2×C3semidirect
73. #1879C2×C3semidirect
74. #1879C2×C3semidirect
75. #1870C2×C3semidirect
76. #1786C2×C3semidirect
101. C2×C3×D8D4semidirect
165. C22×M16C22×C3semidirect
170. C2×#121C22×C3semidirect
173. C2×C4×D4C22×C3semidirect
176. C2×#106C22×C3semidirect
177. C2×#106C22×C3semidirect
184. C2×#102C22×C3semidirect
185. C2×#102C22×C3semidirect
188. C2×C22⋊C8C22×C3semidirect
195. #384C22×C3semidirect
199. #380C22×C3semidirect
201. #340C22×C3semidirect
202. #340C22×C3semidirect
203. #340C22×C3semidirect
204. #340C22×C3semidirect
205. #336C22×C3semidirect
206. #336C22×C3semidirect
352. C2×D8C3×D4semidirect
872. C3#30412direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4692
C2×C3×#4472
C3×#25372
C3×#24082
C3×#20942
C3×#20772
C3×#20712
C3×#20342
C3×#19992
C3×#18952
C3×#18792
C3×#18702
C3×#17862
#304123