Finite Group Databasebeta

← C3×#24399 #10643006

Subgroups — C3×#24399 #10643006

Order 768.

1450 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×AGL(1,ℤ/8)C211yesmaximal, characteristic
2C2×C3×#471C212yesmaximal, complemented
3C3×#3007C211yesmaximal, characteristic, complemented
4C2×C3×#450C211yesmaximal, characteristic, complemented
5C3×#2880C211yesmaximal, characteristic, complemented
6C3×#2051C212yesmaximal, complemented
7C3×#2019C212yesmaximal, complemented
8C3×#1907C212yesmaximal, complemented
9C3×#1901C211yesmaximal, characteristic, complemented
10C3×#1855C211yesmaximal, characteristic, complemented
11C3×#1783C211yesmaximal, characteristic, complemented
12#24399C311yesmaximal, characteristic, direct product factor, Sylow
13C22×C3×#41C2211yescharacteristic
14C23×C3×D4C2211yescharacteristic
15C2×C3×#137C2211yescharacteristic, complemented
16C2×C3×#137C2211yescharacteristic, complemented
17C2×C3×AGL(1,ℤ/8)—21no—
18C2×C3×AGL(1,ℤ/8)—21no—
19C2×C3×AGL(1,ℤ/8)—28no—
20C2×C3×AGL(1,ℤ/8)C2212yes—
21C2×C3×AGL(1,ℤ/8)C2212yes—
22C22×C3×SD16—21no—
23C22×C3×SD16C2212yescomplemented
24C22×C3×D8—21no—
25C2×C3×#131C2212yescomplemented
26C22×C3×M16C2211yescharacteristic
27C2×C3×C22⋊Q8C2211yescharacteristic
28C3×#471—28no—
29C3×#452—21no—
30C3×#452—21no—
31C3×#451—21no—
32C3×#450—21no—
33C3×#450—21no—
34C3×#450—21no—
35C3×#450—22no—
36C2×C3×#108C2212yescomplemented
37C3×#417C2211yescharacteristic, complemented
38C3×#417C2211yescharacteristic, complemented
39C2×C3×#102C2212yescomplemented
40C2×C3×#101C2212yescomplemented
41C2×C3×#100C2212yescomplemented
42C2×C3×#100C2212yescomplemented
43C3×#408—22no—
44C3×#408C2212yescomplemented
45C3×#407—21no—
46C3×#407C2211yescharacteristic
47C3×#407C2211yescharacteristic
48C2×C3×C22⋊C8—21no—
49C2×C3×C22⋊C8C2211yescharacteristic
50C3×#343C2212yescomplemented
51C3×#341C2212yescomplemented
52C22×AGL(1,ℤ/8)C2×C311yescharacteristic
53C2×#471C2×C312yescomplemented
54#3007C2×C311yescharacteristic, complemented
55C2×#450C2×C311yescharacteristic, complemented
56#2880C2×C311yescharacteristic, complemented
57#2051C2×C312yescomplemented
58#2019C2×C312yescomplemented
59#1907C2×C312yescomplemented
60#1901C2×C311yescharacteristic, complemented
61#1855C2×C311yescharacteristic, complemented
62#1783C2×C311yescharacteristic, complemented
63C25×C3—21no—
64C2×C3×#41—21no—
65C2×C3×#41—21no—
66C2×C3×#41—24no—
67C2×C3×#41—42no—
68C2×C3×#41D411yescharacteristic
69C2×C3×#41D411yescharacteristic
70C2×C3×#41C2311yescharacteristic
71C2×C3×#41C2311yescharacteristic
72C22×C3×Q8D411yescharacteristic
73C22×C3×Q8C2311yescharacteristic
74C22×C3×D4—24no—
75C22×C3×D4—21no—
76C22×C3×D4—21no—
77C22×C3×D4—21no—
78C22×C3×D4—21no—
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4—42no—
82C22×C3×D4D411yescharacteristic
83C22×C3×D4C2312yes—
84C23×C3×C4—21no—
85C23×C3×C4C2311yescharacteristic
86C3×#137—24no—
87C3×#137—42no—
88C3×AGL(1,ℤ/8)—28no—
89C3×AGL(1,ℤ/8)—28no—
90C3×AGL(1,ℤ/8)—24no—
91C3×AGL(1,ℤ/8)—24no—
92C3×AGL(1,ℤ/8)—24no—
93C3×AGL(1,ℤ/8)D418yes—
94C2×C3×Q16—21no—
95C2×C3×Q16—21no—
96C2×C3×SD16—28no—
97C2×C3×SD16—22no—
98C2×C3×SD16—22no—
99C2×C3×SD16—24no—
100C2×C3×SD16—21no—
101C2×C3×SD16—21no—
102C2×C3×SD16—22no—
103C2×C3×SD16—22no—
104C2×C3×SD16—42no—
105C2×C3×D8—28no—
106C2×C3×D8—22no—
107C2×C3×D8—22no—
108C3×#131—24no—
109C3×#131—42no—
110C2×C3×M16—21no—
111C2×C3×M16—24no—
112C2×C3×M16—22no—
113C2×C3×M16C2312yes—
114C2×C3×M16C2311yescharacteristic
115C2×C3×M16C2311yescharacteristic
116C2×C3×M16C2312yes—
117C22×C3×C8—21no—
118C22×C3×C8—22no—
119C22×C3×C8C2312yes—
120C3×C22⋊Q8—21no—
121C3×C22⋊Q8—21no—
122C3×C22⋊Q8—21no—
123C3×C22⋊Q8—21no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C22⋊C4—21no—
127C3×#108—24no—
128C3×#103—21no—
129C3×#103—21no—
130C3×#102—21no—
131C3×#102—21no—
132C3×#102—22no—
133C3×#102—22no—
134C3×#101—24no—
135C3×#100—24no—
136C3×#100—42no—
137C3×C22⋊C8—21no—
138C3×C22⋊C8—21no—
139C3×C22⋊C8—21no—
140C3×C22⋊C8—21no—
141C3×C22⋊C8—22no—
142C3×C22⋊C8—22no—
143C3×C22⋊C8D411yescharacteristic
144C3×C22⋊C8D411yescharacteristic
145C3×C22⋊C8D412yes—
146C22×#41C22×C311yescharacteristic
147C23×D4C22×C311yescharacteristic
148C2×#137C22×C311yescharacteristic, complemented
149C2×#137C22×C311yescharacteristic, complemented
150C2×AGL(1,ℤ/8)—21no—
151C2×AGL(1,ℤ/8)—21no—
152C2×AGL(1,ℤ/8)—28no—
153C2×AGL(1,ℤ/8)C22×C312yes—
154C2×AGL(1,ℤ/8)C22×C312yes—
155C22×SD16—21no—
156C22×SD16C22×C312yescomplemented
157C22×D8—21no—
158C2×#131C22×C312yescomplemented
159C22×M16C22×C311yescharacteristic
160C2×C22⋊Q8C22×C311yescharacteristic
161#471—28no—
162#452—21no—
163#452—21no—
164#451—21no—
165#450—21no—
166#450—21no—
167#450—21no—
168#450—22no—
169C2×#108C22×C312yescomplemented
170#417C22×C311yescharacteristic, complemented
171#417C22×C311yescharacteristic, complemented
172C2×#102C22×C312yescomplemented
173C2×#101C22×C312yescomplemented
174C2×#100C22×C312yescomplemented
175C2×#100C22×C312yescomplemented
176#408—22no—
177#408C22×C312yescomplemented
178#407—21no—
179#407C22×C311yescharacteristic
180#407C22×C311yescharacteristic
181C2×C22⋊C8—21no—
182C2×C22⋊C8C22×C311yescharacteristic
183#343C22×C312yescomplemented
184#341C22×C312yescomplemented
185C24×C3—21no—
186C24×C3—22no—
187C24×C3—44no—
188C24×C3—41no—
189C24×C3—41no—
190C24×C3—82no—
191C24×C3—82no—
192C24×C3#4111yescharacteristic
193C3×#41—22no—
194C3×#41—22no—
195C3×#41—22no—
196C3×#41—22no—
197C3×#41—22no—
198C3×#41—44no—
199C3×#41—41no—
200C3×#41—41no—
201C3×#41—44no—
202C3×#41C2×D414yes—
203C2×C3×Q8—21no—
204C2×C3×Q8—22no—
205C2×C3×Q8—22no—
206C2×C3×Q8—21no—
207C2×C3×Q8—21no—
208C2×C3×Q8—22no—
209C2×C3×Q8—41no—
210C2×C3×Q8C2×D411yescharacteristic
211C2×C3×Q8C2×D411yescharacteristic
212C2×C3×D4—21no—
213C2×C3×D4—24no—
214C2×C3×D4—24no—
215C2×C3×D4—22no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—22no—
221C2×C3×D4—22no—
222C2×C3×D4—22no—
223C2×C3×D4—22no—
224C2×C3×D4—22no—
225C2×C3×D4—41no—
226C2×C3×D4—44no—
227C2×C3×D4—44no—
228C2×C3×D4—44no—
229C2×C3×D4—42no—
230C2×C3×D4—42no—
231C2×C3×D4—44no—
232C2×C3×D4—41no—
233C2×C3×D4—41no—
234C2×C3×D4C2×D414yes—
235C2×C3×D4C2×D411yescharacteristic
236C2×C3×D4C2×D411yescharacteristic
237C22×C3×C4—21no—
238C22×C3×C4—22no—
239C22×C3×C4—22no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—44no—
247C22×C3×C4C2×D411yescharacteristic
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2×D411yescharacteristic
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4#4111yescharacteristic
252C22×C3×C4C2411yescharacteristic
253C3×Q16—42no—
254C3×Q16—42no—
255C3×SD16—28no—
256C3×SD16—28no—
257C3×SD16—44no—
258C3×SD16—44no—
259C3×SD16—42no—
260C3×SD16—42no—
261C3×D8—28no—
262C3×D8—28no—
263C3×M16—24no—
264C3×M16—22no—
265C3×M16—22no—
266C3×M16—22no—
267C3×M16—22no—
268C3×M16—22no—
269C3×M16—44no—
270C3×M16C2×D414yes—
271C2×C3×C8—24no—
272C2×C3×C8—22no—
273C2×C3×C8—22no—
274C2×C3×C8—22no—
275C2×C3×C8—22no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—44no—
279C2×C3×C8C2×D412yes—
280C2×C3×C8C2×D412yes—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—41no—
284C3×C4⋊C4—41no—
285C3×C22⋊C4—41no—
286C3×C22⋊C4—41no—
287C25—21no—
288C2×#41—21no—
289C2×#41—21no—
290C2×#41—24no—
291C2×#41—42no—
292C2×#41C3×D411yescharacteristic
293C2×#41C3×D411yescharacteristic
294C2×#41C23×C311yescharacteristic
295C2×#41C23×C311yescharacteristic
296C22×Q8C3×D411yescharacteristic
297C22×Q8C23×C311yescharacteristic
298C22×D4—24no—
299C22×D4—21no—
300C22×D4—21no—
301C22×D4—21no—
302C22×D4—21no—
303C22×D4—21no—
304C22×D4—21no—
305C22×D4—42no—
306C22×D4C3×D411yescharacteristic
307C22×D4C23×C312yes—
308C23×C4—21no—
309C23×C4C23×C311yescharacteristic
310#137—24no—
311#137—42no—
312AGL(1,ℤ/8)—28no—
313AGL(1,ℤ/8)—28no—
314AGL(1,ℤ/8)—24no—
315AGL(1,ℤ/8)—24no—
316AGL(1,ℤ/8)—24no—
317AGL(1,ℤ/8)C3×D418yes—
318C2×Q16—21no—
319C2×Q16—21no—
320C2×SD16—28no—
321C2×SD16—22no—
322C2×SD16—22no—
323C2×SD16—24no—
324C2×SD16—21no—
325C2×SD16—21no—
326C2×SD16—22no—
327C2×SD16—22no—
328C2×SD16—42no—
329C2×D8—28no—
330C2×D8—22no—
331C2×D8—22no—
332#131—24no—
333#131—42no—
334C2×M16—21no—
335C2×M16—24no—
336C2×M16—22no—
337C2×M16C23×C312yes—
338C2×M16C23×C311yescharacteristic
339C2×M16C23×C311yescharacteristic
340C2×M16C23×C312yes—
341C22×C8—21no—
342C22×C8—22no—
343C22×C8C23×C312yes—
344C22⋊Q8—21no—
345C22⋊Q8—21no—
346C22⋊Q8—21no—
347C22⋊Q8—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4C23×C311yescharacteristic
350C2×C22⋊C4—21no—
351#108—24no—
352#103—21no—
353#103—21no—
354#102—21no—
355#102—21no—
356#102—22no—
357#102—22no—
358#101—24no—
359#100—24no—
360#100—42no—
361C22⋊C8—21no—
362C22⋊C8—21no—
363C22⋊C8—21no—
364C22⋊C8—21no—
365C22⋊C8—22no—
366C22⋊C8—22no—
367C22⋊C8C3×D411yescharacteristic
368C22⋊C8C3×D411yescharacteristic
369C22⋊C8C3×D412yes—
370C23×C3—21no—
371C23×C3—22no—
372C23×C3—22no—
373C23×C3—21no—
374C23×C3—24no—
375C23×C3—41no—
376C23×C3—42no—
377C23×C3—44no—
378C23×C3—44no—
379C23×C3—42no—
380C23×C3—42no—
381C23×C3—42no—
382C23×C3—81no—
383C23×C3—82no—
384C23×C3—82no—
385C23×C3—82no—
386C23×C3—82no—
387C23×C3—82no—
388C23×C3—816no—
389C23×C3—82no—
390C23×C3#12111yescharacteristic
391C23×C3#12111yescharacteristic
392C23×C3C2×#4111yescharacteristic
393C3×Q8—21no—
394C3×Q8—21no—
395C3×Q8—21no—
396C3×Q8—42no—
397C3×Q8—41no—
398C3×Q8—41no—
399C3×Q8—42no—
400C3×Q8#12012yes—
401C3×D4—24no—
402C3×D4—21no—
403C3×D4—24no—
404C3×D4—21no—
405C3×D4—21no—
406C3×D4—24no—
407C3×D4—42no—
408C3×D4—42no—
409C3×D4—44no—
410C3×D4—44no—
411C3×D4—42no—
412C3×D4—42no—
413C3×D4—42no—
414C3×D4—42no—
415C3×D4#12012yes—
416C2×C3×C4—21no—
417C2×C3×C4—22no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—24no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—21no—
426C2×C3×C4—42no—
427C2×C3×C4—42no—
428C2×C3×C4—42no—
429C2×C3×C4—42no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—42no—
433C2×C3×C4—81no—
434C2×C3×C4#12111yescharacteristic
435C2×C3×C4#12111yescharacteristic
436C2×C3×C4C22×D411yescharacteristic
437C2×C3×C4C22×D412yes—
438C2×C3×C4C22×D411yescharacteristic
439C2×C3×C4H(5,𝔽2)12yes—
440C3×C8—24no—
441C3×C8—22no—
442C3×C8—22no—
443C3×C8—41no—
444C3×C8—41no—
445C3×C8—42no—
446C24—21no—
447C24—22no—
448C24—44no—
449C24—41no—
450C24—41no—
451C24—82no—
452C24—82no—
453C24C3×#4111yescharacteristic
454#41—22no—
455#41—22no—
456#41—22no—
457#41—22no—
458#41—22no—
459#41—44no—
460#41—41no—
461#41—41no—
462#41—44no—
463#41C2×C3×D414yes—
464C2×Q8—21no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—22no—
470C2×Q8—41no—
471C2×Q8C2×C3×D411yescharacteristic
472C2×Q8C2×C3×D411yescharacteristic
473C2×D4—21no—
474C2×D4—24no—
475C2×D4—24no—
476C2×D4—22no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—41no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—44no—
493C2×D4—41no—
494C2×D4—41no—
495C2×D4C2×C3×D414yes—
496C2×D4C2×C3×D411yescharacteristic
497C2×D4C2×C3×D411yescharacteristic
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—44no—
508C22×C4C2×C3×D411yescharacteristic
509C22×C4C2×C3×D411yescharacteristic
510C22×C4C2×C3×D411yescharacteristic
511C22×C4C2×C3×D411yescharacteristic
512C22×C4C3×#4111yescharacteristic
513C22×C4C24×C311yescharacteristic
514Q16—42no—
515Q16—42no—
516SD16—28no—
517SD16—28no—
518SD16—44no—
519SD16—44no—
520SD16—42no—
521SD16—42no—
522D8—28no—
523D8—28no—
524M16—24no—
525M16—22no—
526M16—22no—
527M16—22no—
528M16—22no—
529M16—22no—
530M16—44no—
531M16C2×C3×D414yes—
532C2×C8—24no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—44no—
540C2×C8C2×C3×D412yes—
541C2×C8C2×C3×D412yes—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—41no—
545C4⋊C4—41no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22×C3—21no—
549C22×C3—21no—
550C22×C3—21no—
551C22×C3—21no—
552C22×C3—21no—
553C22×C3—22no—
554C22×C3—21no—
555C22×C3—21no—
556C22×C3—44no—
557C22×C3—41no—
558C22×C3—41no—
559C22×C3—41no—
560C22×C3—44no—
561C22×C3—41no—
562C22×C3—41no—
563C22×C3—84no—
564C22×C3—84no—
565C22×C3—88no—
566C22×C3—84no—
567C22×C3—88no—
568C22×C3—82no—
569C22×C3—82no—
570C22×C3#47112yescomplemented
571C22×C3C2×#12111yescharacteristic
572C22×C3#54612yes—
573C3×C4—21no—
574C3×C4—21no—
575C3×C4—22no—
576C3×C4—41no—
577C3×C4—81no—
578C3×C4—81no—
579C3×C4C2×#12011yescharacteristic
580C3×C4#53411yescharacteristic
581C3×C4D4212yes—
582C23—21no—
583C23—22no—
584C23—22no—
585C23—21no—
586C23—24no—
587C23—41no—
588C23—42no—
589C23—44no—
590C23—44no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—81no—
595C23—82no—
596C23—82no—
597C23—82no—
598C23—82no—
599C23—82no—
600C23—816no—
601C23—82no—
602C23C3×#12111yescharacteristic
603C23C3×#12111yescharacteristic
604C23C2×C3×#4111yescharacteristic
605Q8—21no—
606Q8—21no—
607Q8—21no—
608Q8—42no—
609Q8—41no—
610Q8—41no—
611Q8—42no—
612Q8C3×#12012yes—
613D4—24no—
614D4—21no—
615D4—24no—
616D4—21no—
617D4—21no—
618D4—24no—
619D4—42no—
620D4—42no—
621D4—44no—
622D4—44no—
623D4—42no—
624D4—42no—
625D4—42no—
626D4—42no—
627D4C3×#12012yes—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—24no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—42no—
645C2×C4—81no—
646C2×C4C3×#12111yescharacteristic
647C2×C4C3×#12111yescharacteristic
648C2×C4C22×C3×D411yescharacteristic
649C2×C4C22×C3×D412yes—
650C2×C4C22×C3×D411yescharacteristic
651C2×C4C3×H(5,𝔽2)12yes—
652C8—24no—
653C8—22no—
654C8—22no—
655C8—41no—
656C8—41no—
657C8—42no—
658C2×C3—22no—
659C2×C3—22no—
660C2×C3—41no—
661C2×C3—42no—
662C2×C3—81no—
663C2×C3—84no—
664C2×C3#241011yescharacteristic
665C2×C3C2×#47111yescharacteristic
666C2×C3#306811yescharacteristic
667C22—21no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—22no—
673C22—21no—
674C22—21no—
675C22—44no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—44no—
680C22—41no—
681C22—41no—
682C22—84no—
683C22—84no—
684C22—88no—
685C22—84no—
686C22—88no—
687C22—82no—
688C22—82no—
689C22C3×#47112yescomplemented
690C22C2×C3×#12111yescharacteristic
691C22C3×#54612yes—
692C4—21no—
693C4—21no—
694C4—22no—
695C4—41no—
696C4—81no—
697C4—81no—
698C4C2×C3×#12011yescharacteristic
699C4C3×#53411yescharacteristic
700C4C3×D4212yes—
701C3#2439911yescharacteristic, direct product factor, Sylow
702C2—22no—
703C2—22no—
704C2—41no—
705C2—42no—
706C2—81no—
707C2—84no—
708C2C3×#241011yescharacteristic
709C2C2×C3×#47111yescharacteristic
710C2C3×#306811yescharacteristic
subgroupG/H
center, socleC22×C3C2×#121
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×AGL(1,ℤ/8)C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#471C2semidirect
3. C3×#3007C2semidirect
4. C2×C3×#450C2semidirect
5. C3×#2880C2semidirect
6. C3×#2051C2semidirect
7. C3×#2019C2semidirect
8. C3×#1907C2semidirect
9. C3×#1901C2semidirect
10. C3×#1855C2semidirect
11. C3×#1783C2semidirect
12. #24399C3direct (N × H)
15. C2×C3×#137C22semidirect
16. C2×C3×#137C22semidirect
23. C22×C3×SD16C22semidirect
25. C2×C3×#131C22semidirect
36. C2×C3×#108C22semidirect
37. C3×#417C22semidirect
38. C3×#417C22semidirect
39. C2×C3×#102C22semidirect
40. C2×C3×#101C22semidirect
41. C2×C3×#100C22semidirect
42. C2×C3×#100C22semidirect
44. C3×#408C22semidirect
50. C3×#343C22semidirect
51. C3×#341C22semidirect
53. C2×#471C2×C3semidirect
54. #3007C2×C3semidirect
55. C2×#450C2×C3semidirect
56. #2880C2×C3semidirect
57. #2051C2×C3semidirect
58. #2019C2×C3semidirect
59. #1907C2×C3semidirect
60. #1901C2×C3semidirect
61. #1855C2×C3semidirect
62. #1783C2×C3semidirect
148. C2×#137C22×C3semidirect
149. C2×#137C22×C3semidirect
156. C22×SD16C22×C3semidirect
158. C2×#131C22×C3semidirect
169. C2×#108C22×C3semidirect
170. #417C22×C3semidirect
171. #417C22×C3semidirect
172. C2×#102C22×C3semidirect
173. C2×#101C22×C3semidirect
174. C2×#100C22×C3semidirect
175. C2×#100C22×C3semidirect
177. #408C22×C3semidirect
183. #343C22×C3semidirect
184. #341C22×C3semidirect
570. C22×C3#471semidirect
689. C22C3×#471semidirect
701. C3#24399direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×AGL(1,ℤ/8)2
C2×C3×#4712
C3×#30072
C2×C3×#4502
C3×#28802
C3×#20512
C3×#20192
C3×#19072
C3×#19012
C3×#18552
C3×#17832
#243993