Finite Group Databasebeta

← C3×#30453 #10649060

Subgroups — C3×#30453 #10649060

Order 768.

1192 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#492C211yesmaximal, characteristic, complemented
2C2×C3×#461C211yesmaximal, characteristic, complemented
3C2×C3×#448C211yesmaximal, characteristic, complemented
4C2×C3×#448C211yesmaximal, characteristic, complemented
5C3×#2434C211yesmaximal, characteristic, complemented
6C3×#2428C211yesmaximal, characteristic
7C3×#2055C211yesmaximal, characteristic, complemented
8C3×#2043C211yesmaximal, characteristic, complemented
9C3×#2014C211yesmaximal, characteristic, complemented
10C3×#2013C211yesmaximal, characteristic, complemented
11C3×#2000C211yesmaximal, characteristic, complemented
12C3×#2000C211yesmaximal, characteristic, complemented
13C3×#1933C211yesmaximal, characteristic, complemented
14C3×#1923C211yesmaximal, characteristic, complemented
15C3×#1877C211yesmaximal, characteristic, complemented
16#30453C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×Q8C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×C3×SD16C2211yescharacteristic
21C22×C3×SD16C2211yescharacteristic
22C22×C3×SD16C2211yescharacteristic
23C22×C3×SD16C2211yescharacteristic
24C2×C3×C4⋊Q8C2211yescharacteristic
25C2×C3×C4⋊Q8C2211yescharacteristic
26C2×C3×#127C2211yescharacteristic
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×#121—21no—
29C2×C3×#121C2211yescharacteristic
30C2×C3×#121C2211yescharacteristic
31C2×C3×C4×D4C2211yescharacteristic
32C3×#492—24no—
33C3×#461—24no—
34C3×#448—24no—
35C3×#448—24no—
36C2×C3×C4⋊C8C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×C22⋊C8C2211yescharacteristic
46C2×C3×C22⋊C8C2211yescharacteristic
47C2×C3×C4×C8C2211yescharacteristic
48C3×#395—21no—
49C3×#395—21no—
50C3×#394—21no—
51C3×#392—21no—
52C3×#391C2211yescharacteristic
53C3×#391C2211yescharacteristic
54C3×#390C2211yescharacteristic
55C3×#389C2211yescharacteristic
56C3×#386—21no—
57C3×#385—21no—
58C3×#385—21no—
59C3×C4×C22⋊C4C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#492C2×C311yescharacteristic, complemented
65C2×#461C2×C311yescharacteristic, complemented
66C2×#448C2×C311yescharacteristic, complemented
67C2×#448C2×C311yescharacteristic, complemented
68#2434C2×C311yescharacteristic, complemented
69#2428C2×C311yescharacteristic
70#2055C2×C311yescharacteristic, complemented
71#2043C2×C311yescharacteristic, complemented
72#2014C2×C311yescharacteristic, complemented
73#2013C2×C311yescharacteristic, complemented
74#2000C2×C311yescharacteristic, complemented
75#2000C2×C311yescharacteristic, complemented
76#1933C2×C311yescharacteristic, complemented
77#1923C2×C311yescharacteristic, complemented
78#1877C2×C311yescharacteristic, complemented
79C22×C3×Q8—21no—
80C22×C3×Q8—22no—
81C22×C3×Q8—22no—
82C22×C3×Q8—41no—
83C22×C3×Q8—41no—
84C22×C3×Q8—41no—
85C22×C3×Q8—41no—
86C22×C3×Q8C2311yescharacteristic
87C22×C3×Q8C2311yescharacteristic
88C22×C3×Q8C2311yescharacteristic
89C22×C3×D4—21no—
90C22×C3×D4—21no—
91C22×C3×D4—21no—
92C22×C3×D4—21no—
93C22×C3×D4C2311yescharacteristic
94C22×C3×D4C2311yescharacteristic
95C23×C3×C4—21no—
96C23×C3×C4—21no—
97C23×C3×C4C2311yescharacteristic
98C2×C3×SD16—22no—
99C2×C3×SD16—22no—
100C2×C3×SD16—22no—
101C2×C3×SD16—22no—
102C2×C3×SD16—22no—
103C2×C3×SD16—22no—
104C2×C3×SD16—22no—
105C2×C3×SD16—22no—
106C2×C3×SD16—41no—
107C2×C3×SD16—41no—
108C2×C3×SD16—41no—
109C2×C3×SD16—41no—
110C2×C3×SD16—41no—
111C2×C3×SD16—41no—
112C2×C3×SD16—41no—
113C2×C3×SD16—41no—
114C2×C3×SD16—41no—
115C2×C3×SD16D414yescomplemented
116C22×C3×C8C2311yescharacteristic
117C22×C3×C8C2311yescharacteristic
118C22×C3×C8C2311yescharacteristic
119C22×C3×C8C2311yescharacteristic
120C3×C4⋊Q8—22no—
121C3×C4⋊Q8—22no—
122C3×C4⋊Q8—41no—
123C3×C4⋊Q8—41no—
124C3×#127—22no—
125C3×#127—41no—
126C3×C22⋊Q8—41no—
127C3×C22⋊Q8—41no—
128C3×#121—22no—
129C3×#121—22no—
130C3×#121—41no—
131C3×#121—41no—
132C3×#121—44no—
133C3×C4×D4—22no—
134C3×C4×D4—41no—
135C2×C3×C4⋊C4—21no—
136C2×C3×C4⋊C4—21no—
137C2×C3×C4⋊C4—21no—
138C2×C3×C4⋊C4—21no—
139C2×C3×C4⋊C4—21no—
140C2×C3×C4⋊C4—21no—
141C2×C3×C4⋊C4C2311yescharacteristic
142C2×C3×C4⋊C4C2311yescharacteristic
143C2×C3×C4⋊C4C2311yescharacteristic
144C2×C3×C22⋊C4—21no—
145C2×C3×C22⋊C4—21no—
146C2×C3×C22⋊C4—21no—
147C2×C3×C22⋊C4—21no—
148C2×C3×C22⋊C4—21no—
149C2×C3×C22⋊C4—21no—
150C2×C3×C22⋊C4D411yescharacteristic
151C2×C3×C22⋊C4D411yescharacteristic
152C2×C3×C42C2311yescharacteristic
153C2×C3×C42C2311yescharacteristic
154C3×C4⋊C8—22no—
155C3×#103—22no—
156C3×#103—22no—
157C3×#103—22no—
158C3×#103—22no—
159C3×#103—41no—
160C3×#103D414yescomplemented
161C3×#102—41no—
162C3×#102—41no—
163C3×C22⋊C8—22no—
164C3×C22⋊C8—22no—
165C3×C4×C8—22no—
166C3×#95—21no—
167C3×#95—21no—
168C3×#95—21no—
169C3×#95—21no—
170C3×#95—21no—
171C3×#95D411yescharacteristic
172C3×#95D411yescharacteristic
173C23×Q8C22×C311yescharacteristic
174C22×SD16C22×C311yescharacteristic
175C22×SD16C22×C311yescharacteristic
176C22×SD16C22×C311yescharacteristic
177C22×SD16C22×C311yescharacteristic
178C22×SD16C22×C311yescharacteristic
179C22×SD16C22×C311yescharacteristic
180C2×C4⋊Q8C22×C311yescharacteristic
181C2×C4⋊Q8C22×C311yescharacteristic
182C2×#127C22×C311yescharacteristic
183C2×C22⋊Q8C22×C311yescharacteristic
184C2×#121—21no—
185C2×#121C22×C311yescharacteristic
186C2×#121C22×C311yescharacteristic
187C2×C4×D4C22×C311yescharacteristic
188#492—24no—
189#461—24no—
190#448—24no—
191#448—24no—
192C2×C4⋊C8C22×C311yescharacteristic
193C2×#103C22×C311yescharacteristic
194C2×#103C22×C311yescharacteristic
195C2×#103C22×C311yescharacteristic
196C2×#103C22×C311yescharacteristic
197C2×#103C22×C311yescharacteristic
198C2×#103C22×C311yescharacteristic
199C2×#102C22×C311yescharacteristic
200C2×#102C22×C311yescharacteristic
201C2×C22⋊C8C22×C311yescharacteristic
202C2×C22⋊C8C22×C311yescharacteristic
203C2×C4×C8C22×C311yescharacteristic
204#395—21no—
205#395—21no—
206#394—21no—
207#392—21no—
208#391C22×C311yescharacteristic
209#391C22×C311yescharacteristic
210#390C22×C311yescharacteristic
211#389C22×C311yescharacteristic
212#386—21no—
213#385—21no—
214#385—21no—
215C4×C22⋊C4C22×C311yescharacteristic
216#340C22×C311yescharacteristic
217#340C22×C311yescharacteristic
218#336C22×C311yescharacteristic
219#336C22×C311yescharacteristic
220C24×C3—21no—
221C24×C3—21no—
222C24×C3C2×D411yescharacteristic
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8—21no—
231C2×C3×Q8—21no—
232C2×C3×Q8—21no—
233C2×C3×Q8—21no—
234C2×C3×Q8—21no—
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×Q8—21no—
239C2×C3×Q8—42no—
240C2×C3×Q8—42no—
241C2×C3×Q8—42no—
242C2×C3×Q8—44no—
243C2×C3×Q8—44no—
244C2×C3×Q8—44no—
245C2×C3×Q8—44no—
246C2×C3×Q8C2×D412yes—
247C2×C3×Q8C2×D412yes—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4—21no—
252C2×C3×D4—21no—
253C2×C3×D4—21no—
254C2×C3×D4—21no—
255C2×C3×D4—21no—
256C2×C3×D4—21no—
257C2×C3×D4—21no—
258C2×C3×D4—21no—
259C2×C3×D4—42no—
260C2×C3×D4—42no—
261C2×C3×D4—42no—
262C2×C3×D4—42no—
263C2×C3×D4—42no—
264C2×C3×D4—42no—
265C2×C3×D4—42no—
266C2×C3×D4—42no—
267C2×C3×D4—81no—
268C2×C3×D4—81no—
269C2×C3×D4—81no—
270C2×C3×D4—81no—
271C2×C3×D4C2×D412yes—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—42no—
285C22×C3×C4—42no—
286C22×C3×C4—42no—
287C22×C3×C4—42no—
288C22×C3×C4—42no—
289C22×C3×C4—81no—
290C22×C3×C4C2×D411yescharacteristic
291C22×C3×C4C2×D411yescharacteristic
292C22×C3×C4C2×D411yescharacteristic
293C22×C3×C4C2×D411yescharacteristic
294C22×C3×C4C2×D411yescharacteristic
295C22×C3×C4C2411yescharacteristic
296C3×SD16—44no—
297C3×SD16—44no—
298C3×SD16—44no—
299C3×SD16—44no—
300C3×SD16—44no—
301C3×SD16—44no—
302C2×C3×C8—21no—
303C2×C3×C8—21no—
304C2×C3×C8—21no—
305C2×C3×C8—21no—
306C2×C3×C8—21no—
307C2×C3×C8—21no—
308C2×C3×C8—21no—
309C2×C3×C8—21no—
310C2×C3×C8—21no—
311C2×C3×C8—21no—
312C2×C3×C8C2×D412yes—
313C2×C3×C8C2×D412yes—
314C3×C4⋊C4—21no—
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—42no—
320C3×C4⋊C4—42no—
321C3×C4⋊C4—42no—
322C3×C4⋊C4—42no—
323C3×C4⋊C4—42no—
324C3×C4⋊C4—42no—
325C3×C4⋊C4C2×D412yes—
326C3×C22⋊C4—22no—
327C3×C22⋊C4—42no—
328C3×C22⋊C4—42no—
329C3×C22⋊C4—42no—
330C3×C22⋊C4—42no—
331C3×C22⋊C4—42no—
332C3×C22⋊C4—81no—
333C3×C22⋊C4SD1614yescomplemented
334C3×C42—21no—
335C3×C42—21no—
336C3×C42—21no—
337C3×C42—21no—
338C22×Q8—21no—
339C22×Q8—22no—
340C22×Q8—22no—
341C22×Q8—41no—
342C22×Q8—41no—
343C22×Q8—41no—
344C22×Q8—41no—
345C22×Q8C23×C311yescharacteristic
346C22×Q8C23×C311yescharacteristic
347C22×Q8C23×C311yescharacteristic
348C22×D4—21no—
349C22×D4—21no—
350C22×D4—21no—
351C22×D4—21no—
352C22×D4C23×C311yescharacteristic
353C22×D4C23×C311yescharacteristic
354C23×C4—21no—
355C23×C4—21no—
356C23×C4C23×C311yescharacteristic
357C2×SD16—22no—
358C2×SD16—22no—
359C2×SD16—22no—
360C2×SD16—22no—
361C2×SD16—22no—
362C2×SD16—22no—
363C2×SD16—22no—
364C2×SD16—22no—
365C2×SD16—41no—
366C2×SD16—41no—
367C2×SD16—41no—
368C2×SD16—41no—
369C2×SD16—41no—
370C2×SD16—41no—
371C2×SD16—41no—
372C2×SD16—41no—
373C2×SD16—41no—
374C2×SD16C3×D414yescomplemented
375C22×C8C23×C311yescharacteristic
376C22×C8C23×C311yescharacteristic
377C22×C8C23×C311yescharacteristic
378C22×C8C23×C311yescharacteristic
379C4⋊Q8—22no—
380C4⋊Q8—22no—
381C4⋊Q8—41no—
382C4⋊Q8—41no—
383#127—22no—
384#127—41no—
385C22⋊Q8—41no—
386C22⋊Q8—41no—
387#121—22no—
388#121—22no—
389#121—41no—
390#121—41no—
391#121—44no—
392C4×D4—22no—
393C4×D4—41no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4C23×C311yescharacteristic
401C2×C4⋊C4C23×C311yescharacteristic
402C2×C4⋊C4C23×C311yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4C3×D411yescharacteristic
410C2×C22⋊C4C3×D411yescharacteristic
411C2×C42C23×C311yescharacteristic
412C2×C42C23×C311yescharacteristic
413C4⋊C8—22no—
414#103—22no—
415#103—22no—
416#103—22no—
417#103—22no—
418#103—41no—
419#103C3×D414yescomplemented
420#102—41no—
421#102—41no—
422C22⋊C8—22no—
423C22⋊C8—22no—
424C4×C8—22no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95C3×D411yescharacteristic
431#95C3×D411yescharacteristic
432C23×C3—21no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—21no—
438C23×C3—22no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3—41no—
443C23×C3—41no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3—41no—
449C23×C3—41no—
450C23×C3—41no—
451C23×C3—41no—
452C23×C3C2×SD1612yes—
453C23×C3C22×D411yescharacteristic
454C3×Q8—22no—
455C3×Q8—22no—
456C3×Q8—22no—
457C3×Q8—22no—
458C3×Q8—48no—
459C3×Q8—41no—
460C3×Q8—41no—
461C3×Q8—41no—
462C3×Q8—41no—
463C3×Q8—41no—
464C3×Q8—41no—
465C3×Q8—41no—
466C3×Q8—41no—
467C3×D4—22no—
468C3×D4—22no—
469C3×D4—41no—
470C3×D4—41no—
471C3×D4—41no—
472C3×D4—41no—
473C3×D4—41no—
474C3×D4—41no—
475C3×D4—84no—
476C3×D4—84no—
477C3×D4—84no—
478C3×D4—84no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—22no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—48no—
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—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—84no—
515C2×C3×C4C2×SD1612yes—
516C2×C3×C4C2×SD1612yes—
517C2×C3×C4#13712yes—
518C2×C3×C4C22×D411yescharacteristic
519C2×C3×C4C22×D411yescharacteristic
520C2×C3×C4H(5,𝔽2)11yescharacteristic
521C2×C3×C4H(5,𝔽2)11yescharacteristic
522C2×C3×C4H(5,𝔽2)11yescharacteristic
523C2×C3×C4H(5,𝔽2)11yescharacteristic
524C3×C8—22no—
525C3×C8—22no—
526C3×C8—41no—
527C3×C8—41no—
528C24—21no—
529C24—21no—
530C24C2×C3×D411yescharacteristic
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—42no—
548C2×Q8—42no—
549C2×Q8—42no—
550C2×Q8—44no—
551C2×Q8—44no—
552C2×Q8—44no—
553C2×Q8—44no—
554C2×Q8C2×C3×D412yes—
555C2×Q8C2×C3×D412yes—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—81no—
576C2×D4—81no—
577C2×D4—81no—
578C2×D4—81no—
579C2×D4C2×C3×D412yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—81no—
598C22×C4C2×C3×D411yescharacteristic
599C22×C4C2×C3×D411yescharacteristic
600C22×C4C2×C3×D411yescharacteristic
601C22×C4C2×C3×D411yescharacteristic
602C22×C4C2×C3×D411yescharacteristic
603C22×C4C24×C311yescharacteristic
604SD16—44no—
605SD16—44no—
606SD16—44no—
607SD16—44no—
608SD16—44no—
609SD16—44no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8C2×C3×D412yes—
621C2×C8C2×C3×D412yes—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—42no—
628C4⋊C4—42no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4—42no—
632C4⋊C4—42no—
633C4⋊C4C2×C3×D412yes—
634C22⋊C4—22no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—81no—
641C22⋊C4C3×SD1614yescomplemented
642C42—21no—
643C42—21no—
644C42—21no—
645C42—21no—
646C22×C3—22no—
647C22×C3—22no—
648C22×C3—22no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—42no—
654C22×C3—42no—
655C22×C3—42no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3—81no—
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#53511yescharacteristic
668C22×C3D4211yescharacteristic
669C22×C3D4211yescharacteristic
670C22×C3C22×SD1611yescharacteristic
671C22×C3C2×#13711yescharacteristic
672C22×C3#57711yescharacteristic
673C22×C3#57711yescharacteristic
674C3×C4—22no—
675C3×C4—22no—
676C3×C4—22no—
677C3×C4—41no—
678C3×C4—42no—
679C3×C4—42no—
680C3×C4—41no—
681C3×C4—42no—
682C3×C4—81no—
683C3×C4—81no—
684C3×C4—81no—
685C3×C4#53411yescharacteristic
686C3×C4#53511yescharacteristic
687C3×C4D4211yescharacteristic
688C3×C4#56011yescharacteristic
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—22no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23C2×C3×SD1612yes—
710C23C22×C3×D411yescharacteristic
711Q8—22no—
712Q8—22no—
713Q8—22no—
714Q8—22no—
715Q8—48no—
716Q8—41no—
717Q8—41no—
718Q8—41no—
719Q8—41no—
720Q8—41no—
721Q8—41no—
722Q8—41no—
723Q8—41no—
724D4—22no—
725D4—22no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—84no—
733D4—84no—
734D4—84no—
735D4—84no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—48no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—84no—
772C2×C4C2×C3×SD1612yes—
773C2×C4C2×C3×SD1612yes—
774C2×C4C3×#13712yes—
775C2×C4C22×C3×D411yescharacteristic
776C2×C4C22×C3×D411yescharacteristic
777C2×C4C3×H(5,𝔽2)11yescharacteristic
778C2×C4C3×H(5,𝔽2)11yescharacteristic
779C2×C4C3×H(5,𝔽2)11yescharacteristic
780C2×C4C3×H(5,𝔽2)11yescharacteristic
781C8—22no—
782C8—22no—
783C8—41no—
784C8—41no—
785C2×C3—42no—
786C2×C3—82no—
787C2×C3—161no—
788C2×C3#266911yescharacteristic
789C2×C3#320611yescharacteristic
790C2×C3#322111yescharacteristic
791C2×C3#326611yescharacteristic
792C2×C3#327811yescharacteristic
793C2×C3D4×SD1611yescharacteristic
794C2×C3D4×SD1611yescharacteristic
795C22—22no—
796C22—22no—
797C22—22no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22C3×#53511yescharacteristic
817C22C3×D4211yescharacteristic
818C22C3×D4211yescharacteristic
819C22C22×C3×SD1611yescharacteristic
820C22C2×C3×#13711yescharacteristic
821C22C3×#57711yescharacteristic
822C22C3×#57711yescharacteristic
823C4—22no—
824C4—22no—
825C4—22no—
826C4—41no—
827C4—42no—
828C4—42no—
829C4—41no—
830C4—42no—
831C4—81no—
832C4—81no—
833C4—81no—
834C4C3×#53411yescharacteristic
835C4C3×#53511yescharacteristic
836C4C3×D4211yescharacteristic
837C4C3×#56011yescharacteristic
838C3#3045311yescharacteristic, direct product factor, Sylow
839C2—42no—
840C2—82no—
841C2—161no—
842C2C3×#266911yescharacteristic
843C2C3×#320611yescharacteristic
844C2C3×#322111yescharacteristic
845C2C3×#326611yescharacteristic
846C2C3×#327811yescharacteristic
847C2C3×D4×SD1611yescharacteristic
848C2C3×D4×SD1611yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#2428C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#492C2semidirect
2. C2×C3×#461C2semidirect
3. C2×C3×#448C2semidirect
4. C2×C3×#448C2semidirect
5. C3×#2434C2semidirect
7. C3×#2055C2semidirect
8. C3×#2043C2semidirect
9. C3×#2014C2semidirect
10. C3×#2013C2semidirect
11. C3×#2000C2semidirect
12. C3×#2000C2semidirect
13. C3×#1933C2semidirect
14. C3×#1923C2semidirect
15. C3×#1877C2semidirect
16. #30453C3direct (N × H)
64. C2×#492C2×C3semidirect
65. C2×#461C2×C3semidirect
66. C2×#448C2×C3semidirect
67. C2×#448C2×C3semidirect
68. #2434C2×C3semidirect
70. #2055C2×C3semidirect
71. #2043C2×C3semidirect
72. #2014C2×C3semidirect
73. #2013C2×C3semidirect
74. #2000C2×C3semidirect
75. #2000C2×C3semidirect
76. #1933C2×C3semidirect
77. #1923C2×C3semidirect
78. #1877C2×C3semidirect
115. C2×C3×SD16D4semidirect
160. C3×#103D4semidirect
333. C3×C22⋊C4SD16semidirect
374. C2×SD16C3×D4semidirect
419. #103C3×D4semidirect
641. C22⋊C4C3×SD16semidirect
838. C3#30453direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4922
C2×C3×#4612
C2×C3×#4482
C3×#24342
C3×#24282
C3×#20552
C3×#20432
C3×#20142
C3×#20132
C3×#20002
C3×#19332
C3×#19232
C3×#18772
#304533