Finite Group Databasebeta

← C3×#30416 #10649023

Subgroups — C3×#30416 #10649023

Order 768.

1220 conjugacy classes of subgroups.

The subgroup lattice has 880 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×#2535C211yesmaximal, characteristic, complemented
4C3×#2408C211yesmaximal, characteristic, complemented
5C3×#2092C211yesmaximal, characteristic, complemented
6C3×#2077C211yesmaximal, characteristic, complemented
7C3×#2073C211yesmaximal, characteristic, complemented
8C3×#2033C211yesmaximal, characteristic, complemented
9C3×#2033C211yesmaximal, 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#30416C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×D4C2211yescharacteristic
18C22×C3×D8C2211yescharacteristic
19C22×C3×D8C2211yescharacteristic
20C22×C3×M16C2211yescharacteristic, complemented
21C2×C3×#121C2211yescharacteristic
22C2×C3×#121C2211yescharacteristic
23C2×C3×#121C2211yescharacteristic
24C2×C3×#121C2211yescharacteristic, complemented
25C2×C3×#120—21no—
26C2×C3×C4×D4C2211yescharacteristic
27C2×C3×C4×D4C2211yescharacteristic, complemented
28C3×#469—24no—
29C3×#447—24no—
30C2×C3×#107C2211yescharacteristic, complemented
31C2×C3×#106C2211yescharacteristic, complemented
32C2×C3×#102C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic, complemented
39C2×C3×#102C2211yescharacteristic, complemented
40C2×C3×C22⋊C8C2211yescharacteristic
41C2×C3×C22⋊C8C2211yescharacteristic
42C2×C3×C22⋊C8C2211yescharacteristic, complemented
43C3×#397—21no—
44C3×#394—21no—
45C3×#392—21no—
46C3×#392—21no—
47C3×#390C2211yescharacteristic
48C3×#390C2211yescharacteristic
49C3×#386—21no—
50C3×#386—21no—
51C3×#382C2211yescharacteristic, 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×#469C2×C311yescharacteristic, complemented
63C2×#447C2×C311yescharacteristic, complemented
64#2535C2×C311yescharacteristic, complemented
65#2408C2×C311yescharacteristic, complemented
66#2092C2×C311yescharacteristic, complemented
67#2077C2×C311yescharacteristic, complemented
68#2073C2×C311yescharacteristic, complemented
69#2033C2×C311yescharacteristic, complemented
70#2033C2×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×#120—44no—
118C3×C4×D4—41no—
119C3×C4×D4—41no—
120C3×C4×D4—41no—
121C3×C4×D4—41no—
122C2×C3×C4⋊C4D411yescharacteristic
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C22⋊C4—21no—
129C2×C3×C22⋊C4—21no—
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⋊C4D411yescharacteristic
141C2×C3×C22⋊C4D411yescharacteristic
142C2×C3×C42C2311yescharacteristic
143C3×#107—41no—
144C3×#106—22no—
145C3×#102—22no—
146C3×#102—22no—
147C3×#102—22no—
148C3×#102—22no—
149C3×#102—41no—
150C3×#102—41no—
151C3×#102—41no—
152C3×#102—41no—
153C3×C22⋊C8—22no—
154C3×C22⋊C8—41no—
155C3×C22⋊C8—41no—
156C3×#95—21no—
157C3×#95—21no—
158C3×#95—21no—
159C3×#95—21no—
160C3×#95—21no—
161C23×D4C22×C311yescharacteristic
162C22×D8C22×C311yescharacteristic
163C22×D8C22×C311yescharacteristic
164C22×M16C22×C311yescharacteristic, complemented
165C2×#121C22×C311yescharacteristic
166C2×#121C22×C311yescharacteristic
167C2×#121C22×C311yescharacteristic
168C2×#121C22×C311yescharacteristic, complemented
169C2×#120—21no—
170C2×C4×D4C22×C311yescharacteristic
171C2×C4×D4C22×C311yescharacteristic, complemented
172#469—24no—
173#447—24no—
174C2×#107C22×C311yescharacteristic, complemented
175C2×#106C22×C311yescharacteristic, complemented
176C2×#102C22×C311yescharacteristic
177C2×#102C22×C311yescharacteristic
178C2×#102C22×C311yescharacteristic
179C2×#102C22×C311yescharacteristic
180C2×#102C22×C311yescharacteristic
181C2×#102C22×C311yescharacteristic
182C2×#102C22×C311yescharacteristic, complemented
183C2×#102C22×C311yescharacteristic, complemented
184C2×C22⋊C8C22×C311yescharacteristic
185C2×C22⋊C8C22×C311yescharacteristic
186C2×C22⋊C8C22×C311yescharacteristic, complemented
187#397—21no—
188#394—21no—
189#392—21no—
190#392—21no—
191#390C22×C311yescharacteristic
192#390C22×C311yescharacteristic
193#386—21no—
194#386—21no—
195#382C22×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—21no—
209C24×C3—42no—
210C24×C3—42no—
211C24×C3—42no—
212C24×C3—42no—
213C24×C3—42no—
214C24×C3—81no—
215C24×C3—81no—
216C24×C3C2×D411yescharacteristic
217C24×C3C2×D411yescharacteristic
218C2×C3×D4—22no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
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—41no—
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—42no—
248C2×C3×D4—42no—
249C2×C3×D4—42no—
250C2×C3×D4—42no—
251C2×C3×D4—81no—
252C2×C3×D4—81no—
253C2×C3×D4—81no—
254C2×C3×D4—81no—
255C2×C3×D4C2×D412yes—
256C2×C3×D4C2×D412yes—
257C2×C3×D4#4112yes—
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—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—42no—
276C22×C3×C4—81no—
277C22×C3×C4—81no—
278C22×C3×C4C2×D411yescharacteristic
279C22×C3×C4C2×D411yescharacteristic
280C22×C3×C4C2×D411yescharacteristic
281C22×C3×C4C2×D411yescharacteristic
282C22×C3×C4C2411yescharacteristic
283C3×D8—44no—
284C3×D8—44no—
285C3×M16—44no—
286C2×C3×C8—21no—
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×C8C2×D412yes—
298C3×C4⋊C4—21no—
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—41no—
309C3×C22⋊C4—41no—
310C3×C22⋊C4—41no—
311C3×C22⋊C4—42no—
312C3×C22⋊C4—42no—
313C3×C22⋊C4—42no—
314C3×C22⋊C4—42no—
315C3×C22⋊C4—42no—
316C3×C22⋊C4—42no—
317C3×C22⋊C4—42no—
318C3×C22⋊C4—42no—
319C3×C22⋊C4—81no—
320C3×C22⋊C4—81no—
321C3×C22⋊C4—81no—
322C3×C22⋊C4—81no—
323C3×C42—21no—
324C3×C42—21no—
325C25—21no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—21no—
329C22×D4—21no—
330C22×D4—21no—
331C22×D4—21no—
332C22×D4—21no—
333C22×D4—41no—
334C22×D4—41no—
335C22×D4—41no—
336C22×D4—41no—
337C22×D4C3×D411yescharacteristic
338C22×D4C23×C311yescharacteristic
339C22×D4C23×C311yescharacteristic
340C22×D4C23×C311yescharacteristic
341C23×C4—21no—
342C23×C4C23×C311yescharacteristic
343C23×C4C23×C311yescharacteristic
344C2×D8—22no—
345C2×D8—22no—
346C2×D8—41no—
347C2×D8—41no—
348C2×D8—41no—
349C2×D8C3×D414yescomplemented
350C2×M16—22no—
351C2×M16—41no—
352C2×M16—41no—
353C22×C8C23×C311yescharacteristic
354C22×C8C23×C311yescharacteristic
355C22×C8C23×C311yescharacteristic
356C22×C8C23×C311yescharacteristic
357#121—22no—
358#121—22no—
359#121—22no—
360#121—22no—
361#121—41no—
362#121—41no—
363#121—41no—
364#121—41no—
365#120—44no—
366C4×D4—41no—
367C4×D4—41no—
368C4×D4—41no—
369C4×D4—41no—
370C2×C4⋊C4C3×D411yescharacteristic
371C2×C4⋊C4C23×C311yescharacteristic
372C2×C4⋊C4C23×C311yescharacteristic
373C2×C4⋊C4C23×C311yescharacteristic
374C2×C4⋊C4C23×C311yescharacteristic
375C2×C4⋊C4C23×C311yescharacteristic
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⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4C3×D411yescharacteristic
389C2×C22⋊C4C3×D411yescharacteristic
390C2×C42C23×C311yescharacteristic
391#107—41no—
392#106—22no—
393#102—22no—
394#102—22no—
395#102—22no—
396#102—22no—
397#102—41no—
398#102—41no—
399#102—41no—
400#102—41no—
401C22⋊C8—22no—
402C22⋊C8—41no—
403C22⋊C8—41no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—22no—
417C23×C3—22no—
418C23×C3—21no—
419C23×C3—22no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—48no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
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—84no—
445C23×C3—84no—
446C23×C3—84no—
447C23×C3—84no—
448C23×C3—84no—
449C23×C3—84no—
450C23×C3AGL(1,ℤ/8)12yes—
451C23×C3C22×D411yescharacteristic
452C3×D4—22no—
453C3×D4—22no—
454C3×D4—22no—
455C3×D4—22no—
456C3×D4—22no—
457C3×D4—22no—
458C3×D4—44no—
459C3×D4—48no—
460C3×D4—41no—
461C3×D4—41no—
462C3×D4—41no—
463C3×D4—41no—
464C3×D4—41no—
465C3×D4—41no—
466C3×D4—84no—
467C3×D4—84no—
468C3×D4—84no—
469C3×D4—84no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
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—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×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—84no—
506C2×C3×C4C22×D411yescharacteristic
507C2×C3×C4C2×#4111yescharacteristic
508C2×C3×C4H(5,𝔽2)11yescharacteristic
509C2×C3×C4H(5,𝔽2)11yescharacteristic
510C2×C3×C4H(5,𝔽2)11yescharacteristic
511C2×C3×C4H(5,𝔽2)11yescharacteristic
512C3×C8—22no—
513C3×C8—41no—
514C3×C8—41no—
515C3×C8—41no—
516C24—21no—
517C24—21no—
518C24—21no—
519C24—42no—
520C24—42no—
521C24—42no—
522C24—42no—
523C24—42no—
524C24—81no—
525C24—81no—
526C24C2×C3×D411yescharacteristic
527C24C2×C3×D411yescharacteristic
528C2×D4—22no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
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—41no—
545C2×D4—41no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—44no—
550C2×D4—44no—
551C2×D4—44no—
552C2×D4—44no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—81no—
564C2×D4—81no—
565C2×D4C2×C3×D412yes—
566C2×D4C2×C3×D412yes—
567C2×D4C3×#4112yes—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
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—42no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4C2×C3×D411yescharacteristic
589C22×C4C2×C3×D411yescharacteristic
590C22×C4C2×C3×D411yescharacteristic
591C22×C4C2×C3×D411yescharacteristic
592C22×C4C24×C311yescharacteristic
593D8—44no—
594D8—44no—
595M16—44no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8C2×C3×D412yes—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—41no—
619C22⋊C4—41no—
620C22⋊C4—41no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C42—21no—
634C42—21no—
635C22×C3—22no—
636C22×C3—22no—
637C22×C3—22no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—42no—
644C22×C3—42no—
645C22×C3—42no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—42no—
650C22×C3—42no—
651C22×C3—41no—
652C22×C3—42no—
653C22×C3—42no—
654C22×C3—41no—
655C22×C3—42no—
656C22×C3—41no—
657C22×C3—42no—
658C22×C3—816no—
659C22×C3—81no—
660C22×C3—81no—
661C22×C3—81no—
662C22×C3—81no—
663C22×C3—81no—
664C22×C3—81no—
665C22×C3—81no—
666C22×C3—81no—
667C22×C3—81no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—81no—
671C22×C3#53411yescharacteristic
672C22×C3D4211yescharacteristic
673C22×C3#54611yescharacteristic
674C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
675C22×C3#57511yescharacteristic
676C22×C3#57611yescharacteristic
677C22×C3#57611yescharacteristic
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—81no—
683C3×C4—81no—
684C3×C4—81no—
685C3×C4—81no—
686C3×C4—81no—
687C3×C4#53411yescharacteristic
688C3×C4#53811yescharacteristic
689C3×C4#54611yescharacteristic
690C3×C4#56011yescharacteristic
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—22no—
703C23—22no—
704C23—21no—
705C23—22no—
706C23—21no—
707C23—48no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
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—84no—
727C23—84no—
728C23—84no—
729C23—84no—
730C23—84no—
731C23—84no—
732C23C3×AGL(1,ℤ/8)12yes—
733C23C22×C3×D411yescharacteristic
734D4—22no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—44no—
741D4—48no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—84no—
749D4—84no—
750D4—84no—
751D4—84no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
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—84no—
788C2×C4C22×C3×D411yescharacteristic
789C2×C4C2×C3×#4111yescharacteristic
790C2×C4C3×H(5,𝔽2)11yescharacteristic
791C2×C4C3×H(5,𝔽2)11yescharacteristic
792C2×C4C3×H(5,𝔽2)11yescharacteristic
793C2×C4C3×H(5,𝔽2)11yescharacteristic
794C8—22no—
795C8—41no—
796C8—41no—
797C8—41no—
798C2×C3—42no—
799C2×C3—81no—
800C2×C3—82no—
801C2×C3—82no—
802C2×C3—82no—
803C2×C3#266811yescharacteristic
804C2×C3#319411yescharacteristic
805C2×C3#319911yescharacteristic
806C2×C3#326411yescharacteristic
807C2×C3#327311yescharacteristic
808C2×C3#331811yescharacteristic
809C2×C3#332211yescharacteristic
810C22—22no—
811C22—22no—
812C22—22no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—42no—
826C22—41no—
827C22—42no—
828C22—42no—
829C22—41no—
830C22—42no—
831C22—41no—
832C22—42no—
833C22—816no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22C3×#53411yescharacteristic
847C22C3×D4211yescharacteristic
848C22C3×#54611yescharacteristic
849C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
850C22C3×#57511yescharacteristic
851C22C3×#57611yescharacteristic
852C22C3×#57611yescharacteristic
853C4—41no—
854C4—41no—
855C4—41no—
856C4—41no—
857C4—81no—
858C4—81no—
859C4—81no—
860C4—81no—
861C4—81no—
862C4C3×#53411yescharacteristic
863C4C3×#53811yescharacteristic
864C4C3×#54611yescharacteristic
865C4C3×#56011yescharacteristic
866C3#3041611yescharacteristic, direct product factor, Sylow
867C2—42no—
868C2—81no—
869C2—82no—
870C2—82no—
871C2—82no—
872C2C3×#266811yescharacteristic
873C2C3×#319411yescharacteristic
874C2C3×#319911yescharacteristic
875C2C3×#326411yescharacteristic
876C2C3×#327311yescharacteristic
877C2C3×#331811yescharacteristic
878C2C3×#332211yescharacteristic
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×#2535C2semidirect
4. C3×#2408C2semidirect
5. C3×#2092C2semidirect
6. C3×#2077C2semidirect
7. C3×#2073C2semidirect
8. C3×#2033C2semidirect
9. C3×#2033C2semidirect
10. C3×#1999C2semidirect
11. C3×#1895C2semidirect
12. C3×#1879C2semidirect
13. C3×#1879C2semidirect
14. C3×#1870C2semidirect
15. C3×#1786C2semidirect
16. #30416C3direct (N × H)
20. C22×C3×M16C22semidirect
24. C2×C3×#121C22semidirect
27. C2×C3×C4×D4C22semidirect
30. C2×C3×#107C22semidirect
31. C2×C3×#106C22semidirect
38. C2×C3×#102C22semidirect
39. C2×C3×#102C22semidirect
42. C2×C3×C22⋊C8C22semidirect
51. C3×#382C22semidirect
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. #2535C2×C3semidirect
65. #2408C2×C3semidirect
66. #2092C2×C3semidirect
67. #2077C2×C3semidirect
68. #2073C2×C3semidirect
69. #2033C2×C3semidirect
70. #2033C2×C3semidirect
71. #1999C2×C3semidirect
72. #1895C2×C3semidirect
73. #1879C2×C3semidirect
74. #1879C2×C3semidirect
75. #1870C2×C3semidirect
76. #1786C2×C3semidirect
101. C2×C3×D8D4semidirect
164. C22×M16C22×C3semidirect
168. C2×#121C22×C3semidirect
171. C2×C4×D4C22×C3semidirect
174. C2×#107C22×C3semidirect
175. C2×#106C22×C3semidirect
182. C2×#102C22×C3semidirect
183. C2×#102C22×C3semidirect
186. C2×C22⋊C8C22×C3semidirect
195. #382C22×C3semidirect
198. #380C22×C3semidirect
200. #340C22×C3semidirect
201. #340C22×C3semidirect
202. #340C22×C3semidirect
203. #340C22×C3semidirect
204. #336C22×C3semidirect
205. #336C22×C3semidirect
349. C2×D8C3×D4semidirect
866. C3#30416direct (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×#25352
C3×#24082
C3×#20922
C3×#20772
C3×#20732
C3×#20332
C3×#19992
C3×#18952
C3×#18792
C3×#18702
C3×#17862
#304163