Finite Group Databasebeta

← C3×#33006 #10651613

Subgroups — C3×#33006 #10651613

Order 768.

1408 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#41C211yesmaximal, characteristic, complemented
2C2×C3×#482C211yesmaximal, characteristic, complemented
3C2×C3×#449C211yesmaximal, characteristic
4C3×#2854C211yesmaximal, characteristic, complemented
5C3×#1880C211yesmaximal, characteristic, complemented
6C3×#1880C211yesmaximal, characteristic, complemented
7C3×#1879C211yesmaximal, characteristic, complemented
8C3×#1879C211yesmaximal, characteristic, complemented
9C3×#1865C211yesmaximal, characteristic, complemented
10C3×#1864C211yesmaximal, characteristic, complemented
11C3×#1863C211yesmaximal, characteristic, complemented
12C3×#1862C211yesmaximal, characteristic, complemented
13C3×#1825C211yesmaximal, characteristic, complemented
14C3×#1817C211yesmaximal, characteristic, complemented
15C3×#1788C211yesmaximal, characteristic, complemented
16#33006C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×D8C2211yescharacteristic
20C2×C3×#123—21no—
21C2×C3×#121C2211yescharacteristic
22C3×C4×#41—24no—
23C3×C4×#41—24no—
24C2×C3×C4×Q8C2211yescharacteristic
25C2×C3×C4×Q8C2211yescharacteristic
26C2×C3×C4×D4—21no—
27C2×C3×C4×D4—21no—
28C2×C3×C4×D4C2211yescharacteristic
29C2×C3×C4×D4C2211yescharacteristic
30C2×C3×#117—21no—
31C2×C3×#117C2211yescharacteristic
32C22×C3×C42—21no—
33C22×C3×C42C2211yescharacteristic
34C3×#482—24no—
35C3×#449—24no—
36C2×C3×#107C2211yescharacteristic
37C2×C3×#106C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#102C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×C22⋊C8C2211yescharacteristic
47C2×C3×C22⋊C8C2211yescharacteristic
48C3×#390C2211yescharacteristic
49C3×#390C2211yescharacteristic
50C3×#389C2211yescharacteristic
51C3×#389C2211yescharacteristic
52C3×#388—21no—
53C3×#388—21no—
54C3×#386—21no—
55C3×#380C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×C4×#41C2×C311yescharacteristic, complemented
65C2×#482C2×C311yescharacteristic, complemented
66C2×#449C2×C311yescharacteristic
67#2854C2×C311yescharacteristic, complemented
68#1880C2×C311yescharacteristic, complemented
69#1880C2×C311yescharacteristic, complemented
70#1879C2×C311yescharacteristic, complemented
71#1879C2×C311yescharacteristic, complemented
72#1865C2×C311yescharacteristic, complemented
73#1864C2×C311yescharacteristic, complemented
74#1863C2×C311yescharacteristic, complemented
75#1862C2×C311yescharacteristic, complemented
76#1825C2×C311yescharacteristic, complemented
77#1817C2×C311yescharacteristic, complemented
78#1788C2×C311yescharacteristic, complemented
79C2×C3×#41—22no—
80C2×C3×#41—22no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41D414yes—
85C22×C3×Q8C2311yescharacteristic
86C22×C3×D4—21no—
87C22×C3×D4—21no—
88C22×C3×D4C2311yescharacteristic
89C22×C3×D4C2311yescharacteristic
90C23×C3×C4—21no—
91C23×C3×C4—21no—
92C23×C3×C4—21no—
93C23×C3×C4D411yescharacteristic
94C23×C3×C4D411yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C2×C3×SD16—22no—
97C2×C3×SD16—22no—
98C2×C3×SD16—22no—
99C2×C3×D8—22no—
100C2×C3×D8—22no—
101C2×C3×D8—22no—
102C22×C3×C8C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C22×C3×C8C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C3×#123—44no—
107C3×#121—22no—
108C3×#121—22no—
109C3×C4×Q8—22no—
110C3×C4×Q8—22no—
111C3×C4×Q8—22no—
112C3×C4×Q8—22no—
113C3×C4×D4—28no—
114C3×C4×D4—28no—
115C3×C4×D4—22no—
116C3×C4×D4—22no—
117C3×C4×D4—22no—
118C3×C4×D4—22no—
119C3×#117—28no—
120C3×#117—22no—
121C3×#117D414yes—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4—21no—
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×C42—28no—
141C2×C3×C42—21no—
142C2×C3×C42—21no—
143C2×C3×C42—21no—
144C2×C3×C42—22no—
145C2×C3×C42—22no—
146C2×C3×C42D411yescharacteristic
147C2×C3×C42D411yescharacteristic
148C2×C3×C42C2311yescharacteristic
149C2×C3×C42C2311yescharacteristic
150C3×#107—22no—
151C3×#106—22no—
152C3×#103—22no—
153C3×#103—22no—
154C3×#103—22no—
155C3×#102—22no—
156C3×#102—22no—
157C3×#102—22no—
158C3×#102—22no—
159C3×#102—22no—
160C3×C22⋊C8—22no—
161C3×C22⋊C8—22no—
162C3×#95—21no—
163C3×#95—21no—
164C3×#95—21no—
165C22×#41C22×C311yescharacteristic
166C22×SD16C22×C311yescharacteristic
167C22×D8C22×C311yescharacteristic
168C2×#123—21no—
169C2×#121C22×C311yescharacteristic
170C4×#41—24no—
171C4×#41—24no—
172C2×C4×Q8C22×C311yescharacteristic
173C2×C4×Q8C22×C311yescharacteristic
174C2×C4×D4—21no—
175C2×C4×D4—21no—
176C2×C4×D4C22×C311yescharacteristic
177C2×C4×D4C22×C311yescharacteristic
178C2×#117—21no—
179C2×#117C22×C311yescharacteristic
180C22×C42—21no—
181C22×C42C22×C311yescharacteristic
182#482—24no—
183#449—24no—
184C2×#107C22×C311yescharacteristic
185C2×#106C22×C311yescharacteristic
186C2×#103C22×C311yescharacteristic
187C2×#103C22×C311yescharacteristic
188C2×#103C22×C311yescharacteristic
189C2×#102C22×C311yescharacteristic
190C2×#102C22×C311yescharacteristic
191C2×#102C22×C311yescharacteristic
192C2×#102C22×C311yescharacteristic
193C2×#102C22×C311yescharacteristic
194C2×C22⋊C8C22×C311yescharacteristic
195C2×C22⋊C8C22×C311yescharacteristic
196#390C22×C311yescharacteristic
197#390C22×C311yescharacteristic
198#389C22×C311yescharacteristic
199#389C22×C311yescharacteristic
200#388—21no—
201#388—21no—
202#386—21no—
203#380C22×C311yescharacteristic
204#340C22×C311yescharacteristic
205#340C22×C311yescharacteristic
206#340C22×C311yescharacteristic
207#340C22×C311yescharacteristic
208#336C22×C311yescharacteristic
209#336C22×C311yescharacteristic
210#336C22×C311yescharacteristic
211#336C22×C311yescharacteristic
212C24×C3—21no—
213C24×C3—21no—
214C24×C3C2×D411yescharacteristic
215C3×#41—28no—
216C3×#41—28no—
217C3×#41—28no—
218C3×#41—28no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8C2×D412yes—
223C2×C3×Q8#4112yes—
224C2×C3×Q8#4112yes—
225C2×C3×D4—24no—
226C2×C3×D4—24no—
227C2×C3×D4—24no—
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—21no—
237C2×C3×D4—42no—
238C2×C3×D4—42no—
239C2×C3×D4—42no—
240C2×C3×D4C2×D412yes—
241C2×C3×D4#4112yes—
242C2×C3×D4#4112yes—
243C22×C3×C4—24no—
244C22×C3×C4—24no—
245C22×C3×C4—21no—
246C22×C3×C4—24no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—24no—
252C22×C3×C4—24no—
253C22×C3×C4—22no—
254C22×C3×C4—22no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—22no—
258C22×C3×C4—22no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—41no—
263C22×C3×C4—41no—
264C22×C3×C4—42no—
265C22×C3×C4—42no—
266C22×C3×C4—42no—
267C22×C3×C4—42no—
268C22×C3×C4C2×D411yescharacteristic
269C22×C3×C4C2×D411yescharacteristic
270C22×C3×C4C2×D411yescharacteristic
271C22×C3×C4C2×D412yes—
272C22×C3×C4C2×D412yes—
273C22×C3×C4C2×D411yescharacteristic
274C22×C3×C4C2×D411yescharacteristic
275C22×C3×C4C2411yescharacteristic
276C3×SD16—44no—
277C3×D8—44no—
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×C8—21no—
289C2×C3×C8—21no—
290C3×C4⋊C4—24no—
291C3×C4⋊C4—24no—
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—21no—
300C3×C4⋊C4—42no—
301C3×C4⋊C4—42no—
302C3×C4⋊C4C2×D412yes—
303C3×C4⋊C4C2×D412yes—
304C3×C22⋊C4—24no—
305C3×C22⋊C4—24no—
306C3×C22⋊C4—24no—
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×C42—24no—
314C3×C42—24no—
315C3×C42—22no—
316C3×C42—24no—
317C3×C42—22no—
318C3×C42—21no—
319C3×C42—21no—
320C3×C42—21no—
321C3×C42—21no—
322C2×#41—22no—
323C2×#41—22no—
324C2×#41—22no—
325C2×#41—22no—
326C2×#41—22no—
327C2×#41C3×D414yes—
328C22×Q8C23×C311yescharacteristic
329C22×D4—21no—
330C22×D4—21no—
331C22×D4C23×C311yescharacteristic
332C22×D4C23×C311yescharacteristic
333C23×C4—21no—
334C23×C4—21no—
335C23×C4—21no—
336C23×C4C3×D411yescharacteristic
337C23×C4C3×D411yescharacteristic
338C23×C4C23×C311yescharacteristic
339C2×SD16—22no—
340C2×SD16—22no—
341C2×SD16—22no—
342C2×D8—22no—
343C2×D8—22no—
344C2×D8—22no—
345C22×C8C23×C311yescharacteristic
346C22×C8C23×C311yescharacteristic
347C22×C8C23×C311yescharacteristic
348C22×C8C23×C311yescharacteristic
349#123—44no—
350#121—22no—
351#121—22no—
352C4×Q8—22no—
353C4×Q8—22no—
354C4×Q8—22no—
355C4×Q8—22no—
356C4×D4—28no—
357C4×D4—28no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—22no—
362#117—28no—
363#117—22no—
364#117C3×D414yes—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
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×C42—28no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42C3×D411yescharacteristic
390C2×C42C3×D411yescharacteristic
391C2×C42C23×C311yescharacteristic
392C2×C42C23×C311yescharacteristic
393#107—22no—
394#106—22no—
395#103—22no—
396#103—22no—
397#103—22no—
398#102—22no—
399#102—22no—
400#102—22no—
401#102—22no—
402#102—22no—
403C22⋊C8—22no—
404C22⋊C8—22no—
405#95—21no—
406#95—21no—
407#95—21no—
408C23×C3—22no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3#12012yes—
429C23×C3C22×D411yescharacteristic
430C3×Q8—22no—
431C3×Q8—22no—
432C3×Q8—22no—
433C3×Q8#12314yescomplemented
434C3×D4—216no—
435C3×D4—22no—
436C3×D4—22no—
437C3×D4—22no—
438C3×D4—41no—
439C3×D4—41no—
440C3×D4—41no—
441C3×D4—41no—
442C3×D4—84no—
443C3×D4#12314yescomplemented
444C2×C3×C4—216no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—22no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—44no—
467C2×C3×C4—44no—
468C2×C3×C4—48no—
469C2×C3×C4—48no—
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#12012yes—
484C2×C3×C4#13512yes—
485C2×C3×C4AGL(1,ℤ/8)12yes—
486C2×C3×C4C22×D411yescharacteristic
487C2×C3×C4C22×D411yescharacteristic
488C2×C3×C4C2×#4111yescharacteristic
489C2×C3×C4C2×#4111yescharacteristic
490C2×C3×C4C2×#4111yescharacteristic
491C2×C3×C4C2×#4111yescharacteristic
492C3×C8—41no—
493C3×C8—41no—
494C3×C8—41no—
495C3×C8—41no—
496C24—21no—
497C24—21no—
498C24C2×C3×D411yescharacteristic
499#41—28no—
500#41—28no—
501#41—28no—
502#41—28no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8C2×C3×D412yes—
507C2×Q8C3×#4112yes—
508C2×Q8C3×#4112yes—
509C2×D4—24no—
510C2×D4—24no—
511C2×D4—24no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4C2×C3×D412yes—
525C2×D4C3×#4112yes—
526C2×D4C3×#4112yes—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—21no—
530C22×C4—24no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4C2×C3×D411yescharacteristic
553C22×C4C2×C3×D411yescharacteristic
554C22×C4C2×C3×D411yescharacteristic
555C22×C4C2×C3×D412yes—
556C22×C4C2×C3×D412yes—
557C22×C4C2×C3×D411yescharacteristic
558C22×C4C2×C3×D411yescharacteristic
559C22×C4C24×C311yescharacteristic
560SD16—44no—
561D8—44no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4C2×C3×D412yes—
587C4⋊C4C2×C3×D412yes—
588C22⋊C4—24no—
589C22⋊C4—24no—
590C22⋊C4—24no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C42—24no—
598C42—24no—
599C42—22no—
600C42—24no—
601C42—22no—
602C42—21no—
603C42—21no—
604C42—21no—
605C42—21no—
606C22×C3—22no—
607C22×C3—24no—
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—41no—
611C22×C3—42no—
612C22×C3—41no—
613C22×C3—42no—
614C22×C3—41no—
615C22×C3—42no—
616C22×C3—41no—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—42no—
620C22×C3—81no—
621C22×C3—81no—
622C22×C3—81no—
623C22×C3—81no—
624C22×C3—81no—
625C22×C3—81no—
626C22×C3—81no—
627C22×C3C2×#12011yescharacteristic
628C22×C3#52511yescharacteristic
629C22×C3#52511yescharacteristic
630C22×C3C2×#13511yescharacteristic
631C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
632C22×C3#57511yescharacteristic
633C22×C3#57511yescharacteristic
634C3×C4—22no—
635C3×C4—24no—
636C3×C4—22no—
637C3×C4—22no—
638C3×C4—41no—
639C3×C4—42no—
640C3×C4—41no—
641C3×C4—42no—
642C3×C4—81no—
643C3×C4—81no—
644C3×C4—81no—
645C3×C4C2×#12311yescharacteristic
646C3×C4C2×#12311yescharacteristic
647C3×C4#52511yescharacteristic
648C3×C4#52511yescharacteristic
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—21no—
655C23—21no—
656C23—22no—
657C23—22no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23C3×#12012yes—
670C23C22×C3×D411yescharacteristic
671Q8—22no—
672Q8—22no—
673Q8—22no—
674Q8C3×#12314yescomplemented
675D4—216no—
676D4—22no—
677D4—22no—
678D4—22no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—84no—
684D4C3×#12314yescomplemented
685C2×C4—216no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—48no—
710C2×C4—48no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4C3×#12012yes—
725C2×C4C3×#13512yes—
726C2×C4C3×AGL(1,ℤ/8)12yes—
727C2×C4C22×C3×D411yescharacteristic
728C2×C4C22×C3×D411yescharacteristic
729C2×C4C2×C3×#4111yescharacteristic
730C2×C4C2×C3×#4111yescharacteristic
731C2×C4C2×C3×#4111yescharacteristic
732C2×C4C2×C3×#4111yescharacteristic
733C8—41no—
734C8—41no—
735C8—41no—
736C8—41no—
737C2×C3—42no—
738C2×C3—44no—
739C2×C3—161no—
740C2×C3#284911yescharacteristic
741C2×C3#300211yescharacteristic
742C2×C3#300611yescharacteristic
743C2×C3#310211yescharacteristic
744C2×C3#310611yescharacteristic
745C2×C3#311111yescharacteristic
746C2×C3#311511yescharacteristic
747C22—22no—
748C22—22no—
749C22—22no—
750C22—24no—
751C22—42no—
752C22—42no—
753C22—41no—
754C22—42no—
755C22—41no—
756C22—42no—
757C22—41no—
758C22—42no—
759C22—41no—
760C22—42no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22C2×C3×#12011yescharacteristic
769C22C3×#52511yescharacteristic
770C22C3×#52511yescharacteristic
771C22C2×C3×#13511yescharacteristic
772C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
773C22C3×#57511yescharacteristic
774C22C3×#57511yescharacteristic
775C4—22no—
776C4—22no—
777C4—22no—
778C4—24no—
779C4—41no—
780C4—42no—
781C4—41no—
782C4—42no—
783C4—81no—
784C4—81no—
785C4—81no—
786C4C2×C3×#12311yescharacteristic
787C4C2×C3×#12311yescharacteristic
788C4C3×#52511yescharacteristic
789C4C3×#52511yescharacteristic
790C3#3300611yescharacteristic, direct product factor, Sylow
791C2—42no—
792C2—44no—
793C2—161no—
794C2C3×#284911yescharacteristic
795C2C3×#300211yescharacteristic
796C2C3×#300611yescharacteristic
797C2C3×#310211yescharacteristic
798C2C3×#310611yescharacteristic
799C2C3×#311111yescharacteristic
800C2C3×#311511yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#449C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C22×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×#41C2semidirect
2. C2×C3×#482C2semidirect
4. C3×#2854C2semidirect
5. C3×#1880C2semidirect
6. C3×#1880C2semidirect
7. C3×#1879C2semidirect
8. C3×#1879C2semidirect
9. C3×#1865C2semidirect
10. C3×#1864C2semidirect
11. C3×#1863C2semidirect
12. C3×#1862C2semidirect
13. C3×#1825C2semidirect
14. C3×#1817C2semidirect
15. C3×#1788C2semidirect
16. #33006C3direct (N × H)
64. C2×C4×#41C2×C3semidirect
65. C2×#482C2×C3semidirect
67. #2854C2×C3semidirect
68. #1880C2×C3semidirect
69. #1880C2×C3semidirect
70. #1879C2×C3semidirect
71. #1879C2×C3semidirect
72. #1865C2×C3semidirect
73. #1864C2×C3semidirect
74. #1863C2×C3semidirect
75. #1862C2×C3semidirect
76. #1825C2×C3semidirect
77. #1817C2×C3semidirect
78. #1788C2×C3semidirect
433. C3×Q8#123semidirect
443. C3×D4#123semidirect
674. Q8C3×#123semidirect
684. D4C3×#123semidirect
790. C3#33006direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×#412
C2×C3×#4822
C2×C3×#4492
C3×#28542
C3×#18802
C3×#18792
C3×#18652
C3×#18642
C3×#18632
C3×#18622
C3×#18252
C3×#18172
C3×#17882
#330063