Finite Group Databasebeta

← C3×#30473 #10649080

Subgroups — C3×#30473 #10649080

Order 768.

1078 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#497C211yesmaximal, characteristic, complemented
2C2×C3×#464C211yesmaximal, characteristic, complemented
3C2×C3×#451C211yesmaximal, characteristic, complemented
4C2×C3×#451C211yesmaximal, characteristic, complemented
5C3×#2436C211yesmaximal, characteristic
6C3×#2429C211yesmaximal, characteristic, complemented
7C3×#2056C211yesmaximal, characteristic, complemented
8C3×#2042C211yesmaximal, characteristic, complemented
9C3×#2016C211yesmaximal, characteristic, complemented
10C3×#2015C211yesmaximal, characteristic, complemented
11C3×#2000C211yesmaximal, characteristic
12C3×#2000C211yesmaximal, characteristic
13C3×#1935C211yesmaximal, characteristic, complemented
14C3×#1924C211yesmaximal, characteristic, complemented
15C3×#1878C211yesmaximal, characteristic, complemented
16#30473C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×Q8C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C22×C3×Q16C2211yescharacteristic
20C22×C3×Q16C2211yescharacteristic
21C22×C3×Q16C2211yescharacteristic
22C22×C3×SD16C2211yescharacteristic
23C22×C3×SD16C2211yescharacteristic
24C2×C3×C4⋊Q8C2211yescharacteristic
25C2×C3×#124C2211yescharacteristic
26C2×C3×#124C2211yescharacteristic
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×C22⋊Q8C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic
30C2×C3×C4×Q8C2211yescharacteristic
31C3×#497—24no—
32C3×#464—24no—
33C3×#451—24no—
34C3×#451—24no—
35C2×C3×C4⋊C8C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×C22⋊C8C2211yescharacteristic
45C2×C3×C22⋊C8C2211yescharacteristic
46C2×C3×#97C2211yescharacteristic
47C3×#398—21no—
48C3×#396—21no—
49C3×#393—21no—
50C3×#393—21no—
51C3×#391C2211yescharacteristic
52C3×#391C2211yescharacteristic
53C3×#391C2211yescharacteristic
54C3×#389—21no—
55C3×#389C2211yescharacteristic
56C3×#388—21no—
57C3×#386—21no—
58C3×#386—21no—
59C3×C4×C22⋊C4C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#497C2×C311yescharacteristic, complemented
65C2×#464C2×C311yescharacteristic, complemented
66C2×#451C2×C311yescharacteristic, complemented
67C2×#451C2×C311yescharacteristic, complemented
68#2436C2×C311yescharacteristic
69#2429C2×C311yescharacteristic, complemented
70#2056C2×C311yescharacteristic, complemented
71#2042C2×C311yescharacteristic, complemented
72#2016C2×C311yescharacteristic, complemented
73#2015C2×C311yescharacteristic, complemented
74#2000C2×C311yescharacteristic
75#2000C2×C311yescharacteristic
76#1935C2×C311yescharacteristic, complemented
77#1924C2×C311yescharacteristic, complemented
78#1878C2×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×Q8C2311yescharacteristic
90C22×C3×D4—21no—
91C22×C3×D4C2311yescharacteristic
92C23×C3×C4—21no—
93C23×C3×C4C2311yescharacteristic
94C2×C3×Q16—22no—
95C2×C3×Q16—22no—
96C2×C3×Q16—22no—
97C2×C3×Q16—22no—
98C2×C3×Q16—22no—
99C2×C3×Q16—41no—
100C2×C3×Q16—41no—
101C2×C3×Q16—41no—
102C2×C3×Q16—41no—
103C2×C3×Q16—41no—
104C2×C3×Q16—41no—
105C2×C3×Q16D414yescomplemented
106C2×C3×SD16—22no—
107C2×C3×SD16—22no—
108C2×C3×SD16—22no—
109C2×C3×SD16—41no—
110C2×C3×SD16—41no—
111C2×C3×SD16—41no—
112C22×C3×C8C2311yescharacteristic
113C22×C3×C8C2311yescharacteristic
114C22×C3×C8C2311yescharacteristic
115C22×C3×C8C2311yescharacteristic
116C3×C4⋊Q8—22no—
117C3×C4⋊Q8—41no—
118C3×#124—22no—
119C3×#124—22no—
120C3×#124—41no—
121C3×#124—41no—
122C3×C22⋊Q8—22no—
123C3×C22⋊Q8—22no—
124C3×C22⋊Q8—41no—
125C3×C22⋊Q8—41no—
126C3×#121—41no—
127C3×#121—41no—
128C3×C4×Q8—22no—
129C3×C4×Q8—41no—
130C2×C3×C4⋊C4—21no—
131C2×C3×C4⋊C4—21no—
132C2×C3×C4⋊C4—21no—
133C2×C3×C4⋊C4—21no—
134C2×C3×C4⋊C4—21no—
135C2×C3×C4⋊C4—21no—
136C2×C3×C4⋊C4C2311yescharacteristic
137C2×C3×C4⋊C4C2311yescharacteristic
138C2×C3×C4⋊C4C2311yescharacteristic
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4—21no—
141C2×C3×C22⋊C4—21no—
142C2×C3×C22⋊C4—21no—
143C2×C3×C22⋊C4—21no—
144C2×C3×C22⋊C4—21no—
145C2×C3×C22⋊C4—21no—
146C2×C3×C22⋊C4D411yescharacteristic
147C2×C3×C22⋊C4D411yescharacteristic
148C2×C3×C42—21no—
149C2×C3×C42C2311yescharacteristic
150C2×C3×C42C2311yescharacteristic
151C3×C4⋊C8—22no—
152C3×#103—22no—
153C3×#103—22no—
154C3×#103—22no—
155C3×#103—41no—
156C3×#103—41no—
157C3×#103D414yescomplemented
158C3×#102—22no—
159C3×#102—41no—
160C3×C22⋊C8—22no—
161C3×C22⋊C8—22no—
162C3×#97—22no—
163C3×#95—21no—
164C3×#95—21no—
165C3×#95—21no—
166C3×#95—21no—
167C3×#95—21no—
168C3×#95—21no—
169C3×#95—21no—
170C3×#95D411yescharacteristic
171C3×#95D411yescharacteristic
172C23×Q8C22×C311yescharacteristic
173C22×Q16C22×C311yescharacteristic
174C22×Q16C22×C311yescharacteristic
175C22×Q16C22×C311yescharacteristic
176C22×Q16C22×C311yescharacteristic
177C22×SD16C22×C311yescharacteristic
178C22×SD16C22×C311yescharacteristic
179C2×C4⋊Q8C22×C311yescharacteristic
180C2×#124C22×C311yescharacteristic
181C2×#124C22×C311yescharacteristic
182C2×C22⋊Q8C22×C311yescharacteristic
183C2×C22⋊Q8C22×C311yescharacteristic
184C2×#121C22×C311yescharacteristic
185C2×C4×Q8C22×C311yescharacteristic
186#497—24no—
187#464—24no—
188#451—24no—
189#451—24no—
190C2×C4⋊C8C22×C311yescharacteristic
191C2×#103C22×C311yescharacteristic
192C2×#103C22×C311yescharacteristic
193C2×#103C22×C311yescharacteristic
194C2×#103C22×C311yescharacteristic
195C2×#103C22×C311yescharacteristic
196C2×#103C22×C311yescharacteristic
197C2×#102C22×C311yescharacteristic
198C2×#102C22×C311yescharacteristic
199C2×C22⋊C8C22×C311yescharacteristic
200C2×C22⋊C8C22×C311yescharacteristic
201C2×#97C22×C311yescharacteristic
202#398—21no—
203#396—21no—
204#393—21no—
205#393—21no—
206#391C22×C311yescharacteristic
207#391C22×C311yescharacteristic
208#391C22×C311yescharacteristic
209#389—21no—
210#389C22×C311yescharacteristic
211#388—21no—
212#386—21no—
213#386—21no—
214C4×C22⋊C4C22×C311yescharacteristic
215#340C22×C311yescharacteristic
216#340C22×C311yescharacteristic
217#336C22×C311yescharacteristic
218#336C22×C311yescharacteristic
219C24×C3—21no—
220C24×C3C2×D411yescharacteristic
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
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—21no—
240C2×C3×Q8—21no—
241C2×C3×Q8—21no—
242C2×C3×Q8—42no—
243C2×C3×Q8—42no—
244C2×C3×Q8—42no—
245C2×C3×Q8—44no—
246C2×C3×Q8—44no—
247C2×C3×Q8—44no—
248C2×C3×Q8—44no—
249C2×C3×Q8C2×D412yes—
250C2×C3×Q8C2×D412yes—
251C2×C3×Q8C2×D412yes—
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—42no—
259C2×C3×D4—42no—
260C2×C3×D4—42no—
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—42no—
275C22×C3×C4—42no—
276C22×C3×C4—42no—
277C22×C3×C4C2×D411yescharacteristic
278C22×C3×C4C2×D411yescharacteristic
279C22×C3×C4C2×D411yescharacteristic
280C22×C3×C4C2×D411yescharacteristic
281C22×C3×C4C2×D411yescharacteristic
282C22×C3×C4C2411yescharacteristic
283C3×Q16—44no—
284C3×Q16—44no—
285C3×Q16—44no—
286C3×Q16—44no—
287C3×SD16—44no—
288C3×SD16—44no—
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×C8—21no—
298C2×C3×C8—21no—
299C2×C3×C8C2×D412yes—
300C2×C3×C8C2×D412yes—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—42no—
307C3×C4⋊C4—42no—
308C3×C4⋊C4—42no—
309C3×C4⋊C4—42no—
310C3×C4⋊C4—42no—
311C3×C4⋊C4—42no—
312C3×C4⋊C4C2×D412yes—
313C3×C22⋊C4—22no—
314C3×C22⋊C4—41no—
315C3×C22⋊C4—42no—
316C3×C22⋊C4—42no—
317C3×C22⋊C4—42no—
318C3×C22⋊C4—42no—
319C3×C22⋊C4—42no—
320C3×C22⋊C4—42no—
321C3×C22⋊C4—42no—
322C3×C42—21no—
323C3×C42—21no—
324C3×C42—21no—
325C3×C42—21no—
326C3×C42—42no—
327C22×Q8—21no—
328C22×Q8—22no—
329C22×Q8—22no—
330C22×Q8—41no—
331C22×Q8—41no—
332C22×Q8—41no—
333C22×Q8—41no—
334C22×Q8C23×C311yescharacteristic
335C22×Q8C23×C311yescharacteristic
336C22×Q8C23×C311yescharacteristic
337C22×Q8C23×C311yescharacteristic
338C22×D4—21no—
339C22×D4C23×C311yescharacteristic
340C23×C4—21no—
341C23×C4C23×C311yescharacteristic
342C2×Q16—22no—
343C2×Q16—22no—
344C2×Q16—22no—
345C2×Q16—22no—
346C2×Q16—22no—
347C2×Q16—41no—
348C2×Q16—41no—
349C2×Q16—41no—
350C2×Q16—41no—
351C2×Q16—41no—
352C2×Q16—41no—
353C2×Q16C3×D414yescomplemented
354C2×SD16—22no—
355C2×SD16—22no—
356C2×SD16—22no—
357C2×SD16—41no—
358C2×SD16—41no—
359C2×SD16—41no—
360C22×C8C23×C311yescharacteristic
361C22×C8C23×C311yescharacteristic
362C22×C8C23×C311yescharacteristic
363C22×C8C23×C311yescharacteristic
364C4⋊Q8—22no—
365C4⋊Q8—41no—
366#124—22no—
367#124—22no—
368#124—41no—
369#124—41no—
370C22⋊Q8—22no—
371C22⋊Q8—22no—
372C22⋊Q8—41no—
373C22⋊Q8—41no—
374#121—41no—
375#121—41no—
376C4×Q8—22no—
377C4×Q8—41no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4C23×C311yescharacteristic
385C2×C4⋊C4C23×C311yescharacteristic
386C2×C4⋊C4C23×C311yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4C3×D411yescharacteristic
395C2×C22⋊C4C3×D411yescharacteristic
396C2×C42—21no—
397C2×C42C23×C311yescharacteristic
398C2×C42C23×C311yescharacteristic
399C4⋊C8—22no—
400#103—22no—
401#103—22no—
402#103—22no—
403#103—41no—
404#103—41no—
405#103C3×D414yescomplemented
406#102—22no—
407#102—41no—
408C22⋊C8—22no—
409C22⋊C8—22no—
410#97—22no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95C3×D411yescharacteristic
419#95C3×D411yescharacteristic
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—21no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3#13712yes—
434C23×C3C22×D411yescharacteristic
435C3×Q8—22no—
436C3×Q8—22no—
437C3×Q8—22no—
438C3×Q8—22no—
439C3×Q8—22no—
440C3×Q8—22no—
441C3×Q8—48no—
442C3×Q8—41no—
443C3×Q8—41no—
444C3×Q8—41no—
445C3×Q8—41no—
446C3×Q8—41no—
447C3×Q8—41no—
448C3×Q8—41no—
449C3×Q8—41no—
450C3×Q8—41no—
451C3×Q8—41no—
452C3×D4—41no—
453C3×D4—41no—
454C3×D4—41no—
455C3×D4—41no—
456C3×D4—84no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
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—48no—
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—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×C4C22×D411yescharacteristic
499C2×C3×C4C22×D411yescharacteristic
500C2×C3×C4H(5,𝔽2)11yescharacteristic
501C2×C3×C4H(5,𝔽2)11yescharacteristic
502C2×C3×C4H(5,𝔽2)11yescharacteristic
503C2×C3×C4H(5,𝔽2)11yescharacteristic
504C3×C8—22no—
505C3×C8—22no—
506C3×C8—41no—
507C3×C8—41no—
508C24—21no—
509C24C2×C3×D411yescharacteristic
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—42no—
532C2×Q8—42no—
533C2×Q8—42no—
534C2×Q8—44no—
535C2×Q8—44no—
536C2×Q8—44no—
537C2×Q8—44no—
538C2×Q8C2×C3×D412yes—
539C2×Q8C2×C3×D412yes—
540C2×Q8C2×C3×D412yes—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4C2×C3×D411yescharacteristic
567C22×C4C2×C3×D411yescharacteristic
568C22×C4C2×C3×D411yescharacteristic
569C22×C4C2×C3×D411yescharacteristic
570C22×C4C2×C3×D411yescharacteristic
571C22×C4C24×C311yescharacteristic
572Q16—44no—
573Q16—44no—
574Q16—44no—
575Q16—44no—
576SD16—44no—
577SD16—44no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8C2×C3×D412yes—
589C2×C8C2×C3×D412yes—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4C2×C3×D412yes—
602C22⋊C4—22no—
603C22⋊C4—41no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—42no—
616C22×C3—22no—
617C22×C3—22no—
618C22×C3—22no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—81no—
624C22×C3—81no—
625C22×C3—81no—
626C22×C3—81no—
627C22×C3—81no—
628C22×C3—81no—
629C22×C3—81no—
630C22×C3#53511yescharacteristic
631C22×C3D4211yescharacteristic
632C22×C3D4211yescharacteristic
633C22×C3C2×#13711yescharacteristic
634C22×C3#57511yescharacteristic
635C22×C3#57811yescharacteristic
636C22×C3#57811yescharacteristic
637C3×C4—41no—
638C3×C4—42no—
639C3×C4—42no—
640C3×C4—42no—
641C3×C4—41no—
642C3×C4—42no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—81no—
647C3×C4—81no—
648C3×C4—81no—
649C3×C4#53411yescharacteristic
650C3×C4#53511yescharacteristic
651C3×C4D4211yescharacteristic
652C3×C4#56011yescharacteristic
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23C3×#13712yes—
667C23C22×C3×D411yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—22no—
673Q8—22no—
674Q8—48no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681Q8—41no—
682Q8—41no—
683Q8—41no—
684Q8—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—84no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—48no—
710C2×C4—41no—
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×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4C22×C3×D411yescharacteristic
732C2×C4C22×C3×D411yescharacteristic
733C2×C4C3×H(5,𝔽2)11yescharacteristic
734C2×C4C3×H(5,𝔽2)11yescharacteristic
735C2×C4C3×H(5,𝔽2)11yescharacteristic
736C2×C4C3×H(5,𝔽2)11yescharacteristic
737C8—22no—
738C8—22no—
739C8—41no—
740C8—41no—
741C2×C3—42no—
742C2×C3—161no—
743C2×C3#266911yescharacteristic
744C2×C3#321511yescharacteristic
745C2×C3#322311yescharacteristic
746C2×C3#326911yescharacteristic
747C2×C3#327011yescharacteristic
748C2×C3#327011yescharacteristic
749C2×C3#327711yescharacteristic
750C22—22no—
751C22—22no—
752C22—22no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22C3×#53511yescharacteristic
765C22C3×D4211yescharacteristic
766C22C3×D4211yescharacteristic
767C22C2×C3×#13711yescharacteristic
768C22C3×#57511yescharacteristic
769C22C3×#57811yescharacteristic
770C22C3×#57811yescharacteristic
771C4—41no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—41no—
776C4—42no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4C3×#53411yescharacteristic
784C4C3×#53511yescharacteristic
785C4C3×D4211yescharacteristic
786C4C3×#56011yescharacteristic
787C3#3047311yescharacteristic, direct product factor, Sylow
788C2—42no—
789C2—161no—
790C2C3×#266911yescharacteristic
791C2C3×#321511yescharacteristic
792C2C3×#322311yescharacteristic
793C2C3×#326911yescharacteristic
794C2C3×#327011yescharacteristic
795C2C3×#327011yescharacteristic
796C2C3×#327711yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#121C22
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×#497C2semidirect
2. C2×C3×#464C2semidirect
3. C2×C3×#451C2semidirect
4. C2×C3×#451C2semidirect
6. C3×#2429C2semidirect
7. C3×#2056C2semidirect
8. C3×#2042C2semidirect
9. C3×#2016C2semidirect
10. C3×#2015C2semidirect
13. C3×#1935C2semidirect
14. C3×#1924C2semidirect
15. C3×#1878C2semidirect
16. #30473C3direct (N × H)
64. C2×#497C2×C3semidirect
65. C2×#464C2×C3semidirect
66. C2×#451C2×C3semidirect
67. C2×#451C2×C3semidirect
69. #2429C2×C3semidirect
70. #2056C2×C3semidirect
71. #2042C2×C3semidirect
72. #2016C2×C3semidirect
73. #2015C2×C3semidirect
76. #1935C2×C3semidirect
77. #1924C2×C3semidirect
78. #1878C2×C3semidirect
105. C2×C3×Q16D4semidirect
157. C3×#103D4semidirect
353. C2×Q16C3×D4semidirect
405. #103C3×D4semidirect
787. C3#30473direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4972
C2×C3×#4642
C2×C3×#4512
C3×#24362
C3×#24292
C3×#20562
C3×#20422
C3×#20162
C3×#20152
C3×#20002
C3×#19352
C3×#19242
C3×#18782
#304733