Finite Group Databasebeta

← C3×#30420 #10649027

Subgroups — C3×#30420 #10649027

Order 768.

1164 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#468C211yesmaximal, characteristic, complemented
2C2×C3×#450C211yesmaximal, characteristic, complemented
3C3×#2538C211yesmaximal, characteristic, complemented
4C3×#2408C211yesmaximal, characteristic
5C3×#2093C211yesmaximal, characteristic, complemented
6C3×#2076C211yesmaximal, characteristic, complemented
7C3×#2071C211yesmaximal, characteristic, complemented
8C3×#2036C211yesmaximal, characteristic, complemented
9C3×#2033C211yesmaximal, characteristic, complemented
10C3×#2000C211yesmaximal, characteristic, complemented
11C3×#1895C211yesmaximal, characteristic, complemented
12C3×#1880C211yesmaximal, characteristic, complemented
13C3×#1880C211yesmaximal, characteristic, complemented
14C3×#1870C211yesmaximal, characteristic, complemented
15C3×#1786C211yesmaximal, characteristic, complemented
16#30420C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×D4C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×C3×M16C2211yescharacteristic, complemented
21C2×C3×C22⋊Q8C2211yescharacteristic
22C2×C3×C22⋊Q8C2211yescharacteristic, complemented
23C2×C3×#121C2211yescharacteristic
24C2×C3×#121C2211yescharacteristic
25C2×C3×#120—21no—
26C2×C3×C4×Q8C2211yescharacteristic, complemented
27C2×C3×C4×D4C2211yescharacteristic
28C3×#468—24no—
29C3×#450—24no—
30C2×C3×#107C2211yescharacteristic, complemented
31C2×C3×#107C2211yescharacteristic, complemented
32C2×C3×#103C2211yescharacteristic, complemented
33C2×C3×#103C2211yescharacteristic, complemented
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic
41C2×C3×C22⋊C8C2211yescharacteristic
42C2×C3×C22⋊C8C2211yescharacteristic, complemented
43C3×#396—21no—
44C3×#396—21no—
45C3×#394—21no—
46C3×#392—21no—
47C3×#390—21no—
48C3×#390C2211yescharacteristic
49C3×#390C2211yescharacteristic
50C3×#389—21no—
51C3×#384C2211yescharacteristic, complemented
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×#468C2×C311yescharacteristic, complemented
63C2×#450C2×C311yescharacteristic, complemented
64#2538C2×C311yescharacteristic, complemented
65#2408C2×C311yescharacteristic
66#2093C2×C311yescharacteristic, complemented
67#2076C2×C311yescharacteristic, complemented
68#2071C2×C311yescharacteristic, complemented
69#2036C2×C311yescharacteristic, complemented
70#2033C2×C311yescharacteristic, complemented
71#2000C2×C311yescharacteristic, complemented
72#1895C2×C311yescharacteristic, complemented
73#1880C2×C311yescharacteristic, complemented
74#1880C2×C311yescharacteristic, complemented
75#1870C2×C311yescharacteristic, complemented
76#1786C2×C311yescharacteristic, complemented
77C25×C3—21no—
78C22×C3×Q8C2311yescharacteristic
79C22×C3×D4—22no—
80C22×C3×D4—22no—
81C22×C3×D4—21no—
82C22×C3×D4—21no—
83C22×C3×D4—21no—
84C22×C3×D4—41no—
85C22×C3×D4—41no—
86C22×C3×D4—41no—
87C22×C3×D4—41no—
88C22×C3×D4D411yescharacteristic
89C22×C3×D4C2311yescharacteristic
90C22×C3×D4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C2×C3×SD16—22no—
94C2×C3×SD16—22no—
95C2×C3×SD16—41no—
96C2×C3×SD16—41no—
97C2×C3×SD16—41no—
98C2×C3×SD16D414yescomplemented
99C2×C3×M16—22no—
100C2×C3×M16—41no—
101C2×C3×M16—41no—
102C22×C3×C8C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C22×C3×C8C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C3×C22⋊Q8—22no—
107C3×C22⋊Q8—22no—
108C3×C22⋊Q8—41no—
109C3×C22⋊Q8—41no—
110C3×#121—22no—
111C3×#121—22no—
112C3×#121—41no—
113C3×#121—41no—
114C3×#120—44no—
115C3×C4×Q8—41no—
116C3×C4×Q8—41no—
117C3×C4×D4—41no—
118C3×C4×D4—41no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4D411yescharacteristic
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C22⋊C4—21no—
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⋊C4D411yescharacteristic
142C2×C3×C22⋊C4D411yescharacteristic
143C2×C3×C42—21no—
144C2×C3×C42C2311yescharacteristic
145C3×#107—22no—
146C3×#107—41no—
147C3×#103—22no—
148C3×#103—41no—
149C3×#102—22no—
150C3×#102—22no—
151C3×#102—22no—
152C3×#102—41no—
153C3×#102—41no—
154C3×#102—41no—
155C3×C22⋊C8—22no—
156C3×C22⋊C8—41no—
157C3×C22⋊C8—41no—
158C3×#95—21no—
159C3×#95—21no—
160C3×#95—21no—
161C23×D4C22×C311yescharacteristic
162C22×SD16C22×C311yescharacteristic
163C22×SD16C22×C311yescharacteristic
164C22×M16C22×C311yescharacteristic, complemented
165C2×C22⋊Q8C22×C311yescharacteristic
166C2×C22⋊Q8C22×C311yescharacteristic, complemented
167C2×#121C22×C311yescharacteristic
168C2×#121C22×C311yescharacteristic
169C2×#120—21no—
170C2×C4×Q8C22×C311yescharacteristic, complemented
171C2×C4×D4C22×C311yescharacteristic
172#468—24no—
173#450—24no—
174C2×#107C22×C311yescharacteristic, complemented
175C2×#107C22×C311yescharacteristic, complemented
176C2×#103C22×C311yescharacteristic, complemented
177C2×#103C22×C311yescharacteristic, complemented
178C2×#102C22×C311yescharacteristic
179C2×#102C22×C311yescharacteristic
180C2×#102C22×C311yescharacteristic
181C2×#102C22×C311yescharacteristic
182C2×#102C22×C311yescharacteristic
183C2×#102C22×C311yescharacteristic
184C2×C22⋊C8C22×C311yescharacteristic
185C2×C22⋊C8C22×C311yescharacteristic
186C2×C22⋊C8C22×C311yescharacteristic, complemented
187#396—21no—
188#396—21no—
189#394—21no—
190#392—21no—
191#390—21no—
192#390C22×C311yescharacteristic
193#390C22×C311yescharacteristic
194#389—21no—
195#384C22×C311yescharacteristic, complemented
196#380C22×C311yescharacteristic
197#380C22×C311yescharacteristic
198#380C22×C311yescharacteristic, complemented
199#379—21no—
200#340C22×C311yescharacteristic, complemented
201#340C22×C311yescharacteristic, complemented
202#340C22×C311yescharacteristic, complemented
203#340C22×C311yescharacteristic, complemented
204#336C22×C311yescharacteristic, complemented
205#336C22×C311yescharacteristic, complemented
206C24×C3—21no—
207C24×C3—21no—
208C24×C3—42no—
209C24×C3—42no—
210C24×C3—42no—
211C24×C3—42no—
212C24×C3—42no—
213C24×C3—81no—
214C24×C3—81no—
215C24×C3C2×D411yescharacteristic
216C24×C3C2×D411yescharacteristic
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8C2×D412yes—
223C2×C3×D4—22no—
224C2×C3×D4—22no—
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—41no—
236C2×C3×D4—42no—
237C2×C3×D4—42no—
238C2×C3×D4—42no—
239C2×C3×D4—44no—
240C2×C3×D4—44no—
241C2×C3×D4—44no—
242C2×C3×D4—44no—
243C2×C3×D4—42no—
244C2×C3×D4—42no—
245C2×C3×D4—42no—
246C2×C3×D4—42no—
247C2×C3×D4—81no—
248C2×C3×D4—81no—
249C2×C3×D4C2×D412yes—
250C2×C3×D4#4112yes—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
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×C4C2×D411yescharacteristic
270C22×C3×C4C2×D411yescharacteristic
271C22×C3×C4C2×D411yescharacteristic
272C22×C3×C4C2×D411yescharacteristic
273C22×C3×C4C2411yescharacteristic
274C3×SD16—44no—
275C3×SD16—44no—
276C3×M16—44no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8—21no—
288C2×C3×C8C2×D412yes—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—21no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—41no—
300C3×C4⋊C4—42no—
301C3×C4⋊C4—42no—
302C3×C4⋊C4—42no—
303C3×C4⋊C4—42no—
304C3×C4⋊C4—81no—
305C3×C22⋊C4—41no—
306C3×C22⋊C4—41no—
307C3×C22⋊C4—42no—
308C3×C22⋊C4—42no—
309C3×C22⋊C4—42no—
310C3×C22⋊C4—42no—
311C3×C22⋊C4—42no—
312C3×C22⋊C4—42no—
313C3×C22⋊C4—42no—
314C3×C22⋊C4—81no—
315C3×C22⋊C4—81no—
316C3×C22⋊C4—81no—
317C3×C22⋊C4—81no—
318C3×C42—21no—
319C3×C42—21no—
320C3×C42—42no—
321C25—21no—
322C22×Q8C23×C311yescharacteristic
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—21no—
328C22×D4—41no—
329C22×D4—41no—
330C22×D4—41no—
331C22×D4—41no—
332C22×D4C3×D411yescharacteristic
333C22×D4C23×C311yescharacteristic
334C22×D4C23×C311yescharacteristic
335C23×C4C23×C311yescharacteristic
336C23×C4C23×C311yescharacteristic
337C2×SD16—22no—
338C2×SD16—22no—
339C2×SD16—41no—
340C2×SD16—41no—
341C2×SD16—41no—
342C2×SD16C3×D414yescomplemented
343C2×M16—22no—
344C2×M16—41no—
345C2×M16—41no—
346C22×C8C23×C311yescharacteristic
347C22×C8C23×C311yescharacteristic
348C22×C8C23×C311yescharacteristic
349C22×C8C23×C311yescharacteristic
350C22⋊Q8—22no—
351C22⋊Q8—22no—
352C22⋊Q8—41no—
353C22⋊Q8—41no—
354#121—22no—
355#121—22no—
356#121—41no—
357#121—41no—
358#120—44no—
359C4×Q8—41no—
360C4×Q8—41no—
361C4×D4—41no—
362C4×D4—41no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4C3×D411yescharacteristic
369C2×C4⋊C4C23×C311yescharacteristic
370C2×C4⋊C4C23×C311yescharacteristic
371C2×C4⋊C4C23×C311yescharacteristic
372C2×C4⋊C4C23×C311yescharacteristic
373C2×C4⋊C4C23×C311yescharacteristic
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4C3×D411yescharacteristic
386C2×C22⋊C4C3×D411yescharacteristic
387C2×C42—21no—
388C2×C42C23×C311yescharacteristic
389#107—22no—
390#107—41no—
391#103—22no—
392#103—41no—
393#102—22no—
394#102—22no—
395#102—22no—
396#102—41no—
397#102—41no—
398#102—41no—
399C22⋊C8—22no—
400C22⋊C8—41no—
401C22⋊C8—41no—
402#95—21no—
403#95—21no—
404#95—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—48no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3—84no—
434C23×C3—84no—
435C23×C3—84no—
436C23×C3—84no—
437C23×C3—84no—
438C23×C3—84no—
439C23×C3#13712yes—
440C23×C3C22×D411yescharacteristic
441C3×Q8—22no—
442C3×Q8—22no—
443C3×Q8—41no—
444C3×Q8—41no—
445C3×D4—22no—
446C3×D4—22no—
447C3×D4—22no—
448C3×D4—22no—
449C3×D4—44no—
450C3×D4—48no—
451C3×D4—41no—
452C3×D4—41no—
453C3×D4—41no—
454C3×D4—41no—
455C3×D4—84no—
456C3×D4—84no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—22no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
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×C4AGL(1,ℤ/8)12yes—
495C2×C3×C4C22×D411yescharacteristic
496C2×C3×C4C2×#4111yescharacteristic
497C2×C3×C4H(5,𝔽2)11yescharacteristic
498C2×C3×C4H(5,𝔽2)11yescharacteristic
499C2×C3×C4H(5,𝔽2)11yescharacteristic
500C2×C3×C4H(5,𝔽2)11yescharacteristic
501C3×C8—22no—
502C3×C8—41no—
503C3×C8—41no—
504C3×C8—41no—
505C24—21no—
506C24—21no—
507C24—42no—
508C24—42no—
509C24—42no—
510C24—42no—
511C24—42no—
512C24—81no—
513C24—81no—
514C24C2×C3×D411yescharacteristic
515C24C2×C3×D411yescharacteristic
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8C2×C3×D412yes—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—41no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—44no—
539C2×D4—44no—
540C2×D4—44no—
541C2×D4—44no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—81no—
547C2×D4—81no—
548C2×D4C2×C3×D412yes—
549C2×D4C3×#4112yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4C2×C3×D411yescharacteristic
569C22×C4C2×C3×D411yescharacteristic
570C22×C4C2×C3×D411yescharacteristic
571C22×C4C2×C3×D411yescharacteristic
572C22×C4C24×C311yescharacteristic
573SD16—44no—
574SD16—44no—
575M16—44no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8C2×C3×D412yes—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—41no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—81no—
604C22⋊C4—41no—
605C22⋊C4—41no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—81no—
614C22⋊C4—81no—
615C22⋊C4—81no—
616C22⋊C4—81no—
617C42—21no—
618C42—21no—
619C42—42no—
620C22×C3—22no—
621C22×C3—22no—
622C22×C3—22no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—42no—
629C22×C3—42no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—42no—
634C22×C3—41no—
635C22×C3—42no—
636C22×C3—41no—
637C22×C3—42no—
638C22×C3—41no—
639C22×C3—42no—
640C22×C3—816no—
641C22×C3—81no—
642C22×C3—81no—
643C22×C3—81no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3—81no—
647C22×C3—81no—
648C22×C3—81no—
649C22×C3#53411yescharacteristic
650C22×C3D4211yescharacteristic
651C22×C3#54611yescharacteristic
652C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
653C22×C3C2×#13711yescharacteristic
654C22×C3#57611yescharacteristic
655C22×C3#57711yescharacteristic
656C3×C4—22no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—42no—
660C3×C4—41no—
661C3×C4—81no—
662C3×C4—81no—
663C3×C4—81no—
664C3×C4—81no—
665C3×C4—81no—
666C3×C4#53411yescharacteristic
667C3×C4#53811yescharacteristic
668C3×C4#54611yescharacteristic
669C3×C4#56011yescharacteristic
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—22no—
683C23—22no—
684C23—21no—
685C23—48no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23—84no—
702C23—84no—
703C23—84no—
704C23C3×#13712yes—
705C23C22×C3×D411yescharacteristic
706Q8—22no—
707Q8—22no—
708Q8—41no—
709Q8—41no—
710D4—22no—
711D4—22no—
712D4—22no—
713D4—22no—
714D4—44no—
715D4—48no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—84no—
721D4—84no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4C3×AGL(1,ℤ/8)12yes—
760C2×C4C22×C3×D411yescharacteristic
761C2×C4C2×C3×#4111yescharacteristic
762C2×C4C3×H(5,𝔽2)11yescharacteristic
763C2×C4C3×H(5,𝔽2)11yescharacteristic
764C2×C4C3×H(5,𝔽2)11yescharacteristic
765C2×C4C3×H(5,𝔽2)11yescharacteristic
766C8—22no—
767C8—41no—
768C8—41no—
769C8—41no—
770C2×C3—42no—
771C2×C3—81no—
772C2×C3—82no—
773C2×C3—82no—
774C2×C3#266811yescharacteristic
775C2×C3#319311yescharacteristic
776C2×C3#319811yescharacteristic
777C2×C3#326611yescharacteristic
778C2×C3#327411yescharacteristic
779C2×C3#331411yescharacteristic
780C2×C3#332411yescharacteristic
781C22—22no—
782C22—22no—
783C22—22no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—42no—
790C22—42no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—42no—
795C22—41no—
796C22—42no—
797C22—41no—
798C22—42no—
799C22—41no—
800C22—42no—
801C22—816no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22C3×#53411yescharacteristic
811C22C3×D4211yescharacteristic
812C22C3×#54611yescharacteristic
813C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
814C22C2×C3×#13711yescharacteristic
815C22C3×#57611yescharacteristic
816C22C3×#57711yescharacteristic
817C4—22no—
818C4—41no—
819C4—41no—
820C4—42no—
821C4—41no—
822C4—81no—
823C4—81no—
824C4—81no—
825C4—81no—
826C4—81no—
827C4C3×#53411yescharacteristic
828C4C3×#53811yescharacteristic
829C4C3×#54611yescharacteristic
830C4C3×#56011yescharacteristic
831C3#3042011yescharacteristic, direct product factor, Sylow
832C2—42no—
833C2—81no—
834C2—82no—
835C2—82no—
836C2C3×#266811yescharacteristic
837C2C3×#319311yescharacteristic
838C2C3×#319811yescharacteristic
839C2C3×#326611yescharacteristic
840C2C3×#327411yescharacteristic
841C2C3×#331411yescharacteristic
842C2C3×#332411yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#2408C2
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×#468C2semidirect
2. C2×C3×#450C2semidirect
3. C3×#2538C2semidirect
5. C3×#2093C2semidirect
6. C3×#2076C2semidirect
7. C3×#2071C2semidirect
8. C3×#2036C2semidirect
9. C3×#2033C2semidirect
10. C3×#2000C2semidirect
11. C3×#1895C2semidirect
12. C3×#1880C2semidirect
13. C3×#1880C2semidirect
14. C3×#1870C2semidirect
15. C3×#1786C2semidirect
16. #30420C3direct (N × H)
20. C22×C3×M16C22semidirect
22. C2×C3×C22⋊Q8C22semidirect
26. C2×C3×C4×Q8C22semidirect
30. C2×C3×#107C22semidirect
31. C2×C3×#107C22semidirect
32. C2×C3×#103C22semidirect
33. C2×C3×#103C22semidirect
42. C2×C3×C22⋊C8C22semidirect
51. 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×#468C2×C3semidirect
63. C2×#450C2×C3semidirect
64. #2538C2×C3semidirect
66. #2093C2×C3semidirect
67. #2076C2×C3semidirect
68. #2071C2×C3semidirect
69. #2036C2×C3semidirect
70. #2033C2×C3semidirect
71. #2000C2×C3semidirect
72. #1895C2×C3semidirect
73. #1880C2×C3semidirect
74. #1880C2×C3semidirect
75. #1870C2×C3semidirect
76. #1786C2×C3semidirect
98. C2×C3×SD16D4semidirect
164. C22×M16C22×C3semidirect
166. C2×C22⋊Q8C22×C3semidirect
170. C2×C4×Q8C22×C3semidirect
174. C2×#107C22×C3semidirect
175. C2×#107C22×C3semidirect
176. C2×#103C22×C3semidirect
177. C2×#103C22×C3semidirect
186. C2×C22⋊C8C22×C3semidirect
195. #384C22×C3semidirect
198. #380C22×C3semidirect
200. #340C22×C3semidirect
201. #340C22×C3semidirect
202. #340C22×C3semidirect
203. #340C22×C3semidirect
204. #336C22×C3semidirect
205. #336C22×C3semidirect
342. C2×SD16C3×D4semidirect
831. C3#30420direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4682
C2×C3×#4502
C3×#25382
C3×#24082
C3×#20932
C3×#20762
C3×#20712
C3×#20362
C3×#20332
C3×#20002
C3×#18952
C3×#18802
C3×#18702
C3×#17862
#304203