Finite Group Databasebeta

← C3×#23575 #10642182

Subgroups — C3×#23575 #10642182

Order 768.

1260 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#529C211yesmaximal, characteristic, complemented
2C2×C3×#442C211yesmaximal, characteristic, complemented
3C2×C3×#440C211yesmaximal, characteristic, complemented
4C3×C4×#121C211yesmaximal, characteristic, complemented
5C3×#2059C211yesmaximal, characteristic, complemented
6C3×#2042C211yesmaximal, characteristic, complemented
7C3×#2035C211yesmaximal, characteristic, complemented
8C3×#2033C211yesmaximal, characteristic, complemented
9C3×#2025C211yesmaximal, characteristic, complemented
10C3×#2012C211yesmaximal, characteristic, complemented
11C3×#2000C211yesmaximal, characteristic, complemented
12C3×#1999C211yesmaximal, characteristic
13C3×#1763C211yesmaximal, characteristic, complemented
14C3×#1762C211yesmaximal, characteristic, complemented
15C3×#1749C211yesmaximal, characteristic, complemented
16#23575C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×D8C2211yescharacteristic
19C3×#529—24no—
20C3×#529—24no—
21C2×C3×#126—21no—
22C2×C3×#125C2211yescharacteristic
23C2×C3×#124C2211yescharacteristic
24C2×C3×#123—21no—
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×C3×#121C2211yescharacteristic
27C2×C3×#121C2211yescharacteristic
28C2×C3×C4×Q8C2211yescharacteristic
29C2×C3×C4×D4—21no—
30C2×C3×C4×D4—21no—
31C2×C3×C4×D4C2211yescharacteristic
32C2×C3×C4×D4C2211yescharacteristic
33C2×C3×#117—21no—
34C22×C3×C42C2211yescharacteristic
35C3×#442—24no—
36C3×#440—24no—
37C2×C3×#107C2211yescharacteristic
38C2×C3×#106C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×C22⋊C8C2211yescharacteristic
48C2×C3×C22⋊C8C2211yescharacteristic
49C2×C3×#97C2211yescharacteristic
50C2×C3×#97C2211yescharacteristic
51C3×#390C2211yescharacteristic
52C3×#389C2211yescharacteristic
53C3×#388—21no—
54C3×#386—21no—
55C3×#380C2211yescharacteristic
56C3×C4×C4⋊C4C2211yescharacteristic
57C3×C4×C22⋊C4—21no—
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#529C2×C311yescharacteristic, complemented
65C2×#442C2×C311yescharacteristic, complemented
66C2×#440C2×C311yescharacteristic, complemented
67C4×#121C2×C311yescharacteristic, complemented
68#2059C2×C311yescharacteristic, complemented
69#2042C2×C311yescharacteristic, complemented
70#2035C2×C311yescharacteristic, complemented
71#2033C2×C311yescharacteristic, complemented
72#2025C2×C311yescharacteristic, complemented
73#2012C2×C311yescharacteristic, complemented
74#2000C2×C311yescharacteristic, complemented
75#1999C2×C311yescharacteristic
76#1763C2×C311yescharacteristic, complemented
77#1762C2×C311yescharacteristic, complemented
78#1749C2×C311yescharacteristic, complemented
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4—21no—
82C22×C3×D4C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4—21no—
85C23×C3×C4—21no—
86C23×C3×C4D411yescharacteristic
87C23×C3×C4D411yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C2×C3×SD16—22no—
90C2×C3×SD16—22no—
91C2×C3×SD16—22no—
92C2×C3×D8—22no—
93C2×C3×D8—22no—
94C2×C3×D8—22no—
95C22×C3×C8C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C3×#126—28no—
100C3×#125—22no—
101C3×#125—22no—
102C3×#124—22no—
103C3×#124—22no—
104C3×#123—28no—
105C3×C22⋊Q8—22no—
106C3×C22⋊Q8—22no—
107C3×#121—22no—
108C3×#121—22no—
109C3×#121—22no—
110C3×#121—22no—
111C3×C4×Q8—22no—
112C3×C4×Q8D414yescomplemented
113C3×C4×D4—28no—
114C3×C4×D4—22no—
115C3×C4×D4—22no—
116C3×C4×D4—22no—
117C3×C4×D4—44no—
118C3×C4×D4D414yescomplemented
119C3×#117—28no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—21no—
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×C42—21no—
141C2×C3×C42—22no—
142C2×C3×C42—22no—
143C2×C3×C42—21no—
144C2×C3×C42D411yescharacteristic
145C2×C3×C42D411yescharacteristic
146C2×C3×C42C2311yescharacteristic
147C2×C3×C42C2311yescharacteristic
148C3×#107—22no—
149C3×#106—22no—
150C3×#103—22no—
151C3×#103—22no—
152C3×#103—22no—
153C3×#102—22no—
154C3×#102—22no—
155C3×#102—22no—
156C3×#102—22no—
157C3×#102—22no—
158C3×C22⋊C8—22no—
159C3×C22⋊C8—22no—
160C3×#97—22no—
161C3×#97—22no—
162C3×#95—21no—
163C3×#95—21no—
164C3×#95—21no—
165C22×SD16C22×C311yescharacteristic
166C22×D8C22×C311yescharacteristic
167#529—24no—
168#529—24no—
169C2×#126—21no—
170C2×#125C22×C311yescharacteristic
171C2×#124C22×C311yescharacteristic
172C2×#123—21no—
173C2×C22⋊Q8C22×C311yescharacteristic
174C2×#121C22×C311yescharacteristic
175C2×#121C22×C311yescharacteristic
176C2×C4×Q8C22×C311yescharacteristic
177C2×C4×D4—21no—
178C2×C4×D4—21no—
179C2×C4×D4C22×C311yescharacteristic
180C2×C4×D4C22×C311yescharacteristic
181C2×#117—21no—
182C22×C42C22×C311yescharacteristic
183#442—24no—
184#440—24no—
185C2×#107C22×C311yescharacteristic
186C2×#106C22×C311yescharacteristic
187C2×#103C22×C311yescharacteristic
188C2×#103C22×C311yescharacteristic
189C2×#103C22×C311yescharacteristic
190C2×#102C22×C311yescharacteristic
191C2×#102C22×C311yescharacteristic
192C2×#102C22×C311yescharacteristic
193C2×#102C22×C311yescharacteristic
194C2×#102C22×C311yescharacteristic
195C2×C22⋊C8C22×C311yescharacteristic
196C2×C22⋊C8C22×C311yescharacteristic
197C2×#97C22×C311yescharacteristic
198C2×#97C22×C311yescharacteristic
199#390C22×C311yescharacteristic
200#389C22×C311yescharacteristic
201#388—21no—
202#386—21no—
203#380C22×C311yescharacteristic
204C4×C4⋊C4C22×C311yescharacteristic
205C4×C22⋊C4—21no—
206#340C22×C311yescharacteristic
207#340C22×C311yescharacteristic
208#340C22×C311yescharacteristic
209#340C22×C311yescharacteristic
210#336C22×C311yescharacteristic
211#336C22×C311yescharacteristic
212C24×C3—21no—
213C24×C3—21no—
214C24×C3C2×D411yescharacteristic
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8C2×D412yes—
221C2×C3×D4—24no—
222C2×C3×D4—24no—
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—42no—
234C2×C3×D4—42no—
235C2×C3×D4—42no—
236C2×C3×D4—42no—
237C2×C3×D4C2×D412yes—
238C2×C3×D4#4112yes—
239C22×C3×C4—22no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—22no—
245C22×C3×C4—22no—
246C22×C3×C4—24no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—41no—
256C22×C3×C4—41no—
257C22×C3×C4—41no—
258C22×C3×C4—42no—
259C22×C3×C4—42no—
260C22×C3×C4—42no—
261C22×C3×C4—42no—
262C22×C3×C4—42no—
263C22×C3×C4C2×D411yescharacteristic
264C22×C3×C4C2×D411yescharacteristic
265C22×C3×C4C2×D411yescharacteristic
266C22×C3×C4C2×D411yescharacteristic
267C22×C3×C4C2×D411yescharacteristic
268C22×C3×C4C2411yescharacteristic
269C3×SD16—28no—
270C3×D8—28no—
271C2×C3×C8—21no—
272C2×C3×C8—21no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8#4112yes—
282C2×C3×C8#4112yes—
283C3×C4⋊C4—24no—
284C3×C4⋊C4—24no—
285C3×C4⋊C4—24no—
286C3×C4⋊C4—24no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—21no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—42no—
295C3×C4⋊C4C2×D412yes—
296C3×C4⋊C4C2×D412yes—
297C3×C4⋊C4#4112yes—
298C3×C22⋊C4—24no—
299C3×C22⋊C4—24no—
300C3×C22⋊C4—24no—
301C3×C22⋊C4—24no—
302C3×C22⋊C4—24no—
303C3×C22⋊C4—24no—
304C3×C22⋊C4—42no—
305C3×C22⋊C4—42no—
306C3×C22⋊C4—42no—
307C3×C22⋊C4—42no—
308C3×C42—22no—
309C3×C42—22no—
310C3×C42—24no—
311C3×C42—21no—
312C3×C42—21no—
313C3×C42—42no—
314C3×C42C2×D412yes—
315C3×C42C2×D412yes—
316C22×Q8C23×C311yescharacteristic
317C22×D4—21no—
318C22×D4—21no—
319C22×D4C23×C311yescharacteristic
320C22×D4C23×C311yescharacteristic
321C23×C4—21no—
322C23×C4—21no—
323C23×C4C3×D411yescharacteristic
324C23×C4C3×D411yescharacteristic
325C23×C4C23×C311yescharacteristic
326C2×SD16—22no—
327C2×SD16—22no—
328C2×SD16—22no—
329C2×D8—22no—
330C2×D8—22no—
331C2×D8—22no—
332C22×C8C23×C311yescharacteristic
333C22×C8C23×C311yescharacteristic
334C22×C8C23×C311yescharacteristic
335C22×C8C23×C311yescharacteristic
336#126—28no—
337#125—22no—
338#125—22no—
339#124—22no—
340#124—22no—
341#123—28no—
342C22⋊Q8—22no—
343C22⋊Q8—22no—
344#121—22no—
345#121—22no—
346#121—22no—
347#121—22no—
348C4×Q8—22no—
349C4×Q8C3×D414yescomplemented
350C4×D4—28no—
351C4×D4—22no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4—44no—
355C4×D4C3×D414yescomplemented
356#117—28no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4C23×C311yescharacteristic
363C2×C4⋊C4C23×C311yescharacteristic
364C2×C4⋊C4C23×C311yescharacteristic
365C2×C4⋊C4C23×C311yescharacteristic
366C2×C4⋊C4C23×C311yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C42—21no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—21no—
381C2×C42C3×D411yescharacteristic
382C2×C42C3×D411yescharacteristic
383C2×C42C23×C311yescharacteristic
384C2×C42C23×C311yescharacteristic
385#107—22no—
386#106—22no—
387#103—22no—
388#103—22no—
389#103—22no—
390#102—22no—
391#102—22no—
392#102—22no—
393#102—22no—
394#102—22no—
395C22⋊C8—22no—
396C22⋊C8—22no—
397#97—22no—
398#97—22no—
399#95—21no—
400#95—21no—
401#95—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—22no—
409C23×C3—22no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3AGL(1,ℤ/8)12yes—
423C23×C3C22×D411yescharacteristic
424C3×Q8—22no—
425C3×Q8—22no—
426C3×Q8—41no—
427C3×Q8—41no—
428C3×D4—22no—
429C3×D4—22no—
430C3×D4—22no—
431C3×D4—22no—
432C3×D4—48no—
433C3×D4—48no—
434C3×D4—41no—
435C3×D4—41no—
436C3×D4—41no—
437C3×D4—41no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—21no—
449C2×C3×C4—22no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—44no—
456C2×C3×C4—44no—
457C2×C3×C4—48no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
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—84no—
477C2×C3×C4#12012yes—
478C2×C3×C4#12012yes—
479C2×C3×C4C22×D411yescharacteristic
480C2×C3×C4C22×D411yescharacteristic
481C2×C3×C4C2×#4111yescharacteristic
482C2×C3×C4C2×#4111yescharacteristic
483C2×C3×C4C2×#4111yescharacteristic
484C2×C3×C4C2×#4111yescharacteristic
485C3×C8—22no—
486C3×C8—22no—
487C3×C8—41no—
488C3×C8—41no—
489C24—21no—
490C24—21no—
491C24C2×C3×D411yescharacteristic
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8C2×C3×D412yes—
498C2×D4—24no—
499C2×D4—24no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4C2×C3×D412yes—
515C2×D4C3×#4112yes—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4C2×C3×D411yescharacteristic
541C22×C4C2×C3×D411yescharacteristic
542C22×C4C2×C3×D411yescharacteristic
543C22×C4C2×C3×D411yescharacteristic
544C22×C4C2×C3×D411yescharacteristic
545C22×C4C24×C311yescharacteristic
546SD16—28no—
547D8—28no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8C3×#4112yes—
559C2×C8C3×#4112yes—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—42no—
572C4⋊C4C2×C3×D412yes—
573C4⋊C4C2×C3×D412yes—
574C4⋊C4C3×#4112yes—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—24no—
580C22⋊C4—24no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C42—22no—
586C42—22no—
587C42—24no—
588C42—21no—
589C42—21no—
590C42—42no—
591C42C2×C3×D412yes—
592C42C2×C3×D412yes—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—41no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—42no—
601C22×C3—42no—
602C22×C3—42no—
603C22×C3—42no—
604C22×C3—42no—
605C22×C3—42no—
606C22×C3—81no—
607C22×C3—81no—
608C22×C3—81no—
609C22×C3—81no—
610C22×C3—81no—
611C22×C3—81no—
612C22×C3—81no—
613C22×C3—81no—
614C22×C3C2×#12011yescharacteristic
615C22×C3#52511yescharacteristic
616C22×C3#53211yescharacteristic
617C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
618C22×C3#57511yescharacteristic
619C22×C3#57511yescharacteristic
620C22×C3#57511yescharacteristic
621C3×C4—22no—
622C3×C4—22no—
623C3×C4—42no—
624C3×C4—41no—
625C3×C4—42no—
626C3×C4—41no—
627C3×C4—42no—
628C3×C4—41no—
629C3×C4—42no—
630C3×C4—81no—
631C3×C4—81no—
632C3×C4#52511yescharacteristic
633C3×C4#52511yescharacteristic
634C3×C4#53211yescharacteristic
635C3×C4#53211yescharacteristic
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—22no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23C3×AGL(1,ℤ/8)12yes—
657C23C22×C3×D411yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—41no—
661Q8—41no—
662D4—22no—
663D4—22no—
664D4—22no—
665D4—22no—
666D4—48no—
667D4—48no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—48no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—84no—
711C2×C4C3×#12012yes—
712C2×C4C3×#12012yes—
713C2×C4C22×C3×D411yescharacteristic
714C2×C4C22×C3×D411yescharacteristic
715C2×C4C2×C3×#4111yescharacteristic
716C2×C4C2×C3×#4111yescharacteristic
717C2×C4C2×C3×#4111yescharacteristic
718C2×C4C2×C3×#4111yescharacteristic
719C8—22no—
720C8—22no—
721C8—41no—
722C8—41no—
723C2×C3—42no—
724C2×C3—82no—
725C2×C3—82no—
726C2×C3#238811yescharacteristic
727C2×C3#300511yescharacteristic
728C2×C3#300611yescharacteristic
729C2×C3#311111yescharacteristic
730C2×C3#311411yescharacteristic
731C2×C3#318011yescharacteristic
732C2×C3#318311yescharacteristic
733C22—22no—
734C22—22no—
735C22—22no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22C2×C3×#12011yescharacteristic
755C22C3×#52511yescharacteristic
756C22C3×#53211yescharacteristic
757C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
758C22C3×#57511yescharacteristic
759C22C3×#57511yescharacteristic
760C22C3×#57511yescharacteristic
761C4—22no—
762C4—22no—
763C4—41no—
764C4—42no—
765C4—41no—
766C4—42no—
767C4—41no—
768C4—42no—
769C4—42no—
770C4—81no—
771C4—81no—
772C4C3×#52511yescharacteristic
773C4C3×#52511yescharacteristic
774C4C3×#53211yescharacteristic
775C4C3×#53211yescharacteristic
776C3#2357511yescharacteristic, direct product factor, Sylow
777C2—42no—
778C2—82no—
779C2—82no—
780C2C3×#238811yescharacteristic
781C2C3×#300511yescharacteristic
782C2C3×#300611yescharacteristic
783C2C3×#311111yescharacteristic
784C2C3×#311411yescharacteristic
785C2C3×#318011yescharacteristic
786C2C3×#318311yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#1999C2
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×#529C2semidirect
2. C2×C3×#442C2semidirect
3. C2×C3×#440C2semidirect
4. C3×C4×#121C2semidirect
5. C3×#2059C2semidirect
6. C3×#2042C2semidirect
7. C3×#2035C2semidirect
8. C3×#2033C2semidirect
9. C3×#2025C2semidirect
10. C3×#2012C2semidirect
11. C3×#2000C2semidirect
13. C3×#1763C2semidirect
14. C3×#1762C2semidirect
15. C3×#1749C2semidirect
16. #23575C3direct (N × H)
64. C2×#529C2×C3semidirect
65. C2×#442C2×C3semidirect
66. C2×#440C2×C3semidirect
67. C4×#121C2×C3semidirect
68. #2059C2×C3semidirect
69. #2042C2×C3semidirect
70. #2035C2×C3semidirect
71. #2033C2×C3semidirect
72. #2025C2×C3semidirect
73. #2012C2×C3semidirect
74. #2000C2×C3semidirect
76. #1763C2×C3semidirect
77. #1762C2×C3semidirect
78. #1749C2×C3semidirect
112. C3×C4×Q8D4semidirect
118. C3×C4×D4D4semidirect
349. C4×Q8C3×D4semidirect
355. C4×D4C3×D4semidirect
776. C3#23575direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5292
C2×C3×#4422
C2×C3×#4402
C3×C4×#1212
C3×#20592
C3×#20422
C3×#20352
C3×#20332
C3×#20252
C3×#20122
C3×#20002
C3×#19992
C3×#17632
C3×#17622
C3×#17492
#235753