Finite Group Databasebeta

← C3×#30449 #10649056

Subgroups — C3×#30449 #10649056

Order 768.

1058 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#494C211yesmaximal, characteristic, complemented
2C2×C3×#462C211yesmaximal, characteristic, complemented
3C2×C3×#451C211yesmaximal, characteristic
4C2×C3×#451C211yesmaximal, characteristic
5C3×#2434C211yesmaximal, characteristic
6C3×#2429C211yesmaximal, characteristic
7C3×#2056C211yesmaximal, characteristic, complemented
8C3×#2043C211yesmaximal, characteristic, complemented
9C3×#2016C211yesmaximal, characteristic, complemented
10C3×#2016C211yesmaximal, characteristic, complemented
11C3×#2001C211yesmaximal, characteristic
12C3×#2001C211yesmaximal, characteristic
13C3×#1933C211yesmaximal, characteristic, complemented
14C3×#1923C211yesmaximal, characteristic
15C3×#1878C211yesmaximal, characteristic, complemented
16#30449C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×Q8C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C22×C3×Q16C2211yescharacteristic
20C22×C3×Q16C2211yescharacteristic
21C22×C3×Q16C2211yescharacteristic
22C22×C3×Q16C2211yescharacteristic
23C22×C3×Q16C2211yescharacteristic
24C2×C3×C4⋊Q8C2211yescharacteristic
25C2×C3×C4⋊Q8C2211yescharacteristic
26C2×C3×C4⋊Q8C2211yescharacteristic
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×C22⋊Q8C2211yescharacteristic
29C2×C3×C22⋊Q8C2211yescharacteristic
30C2×C3×C4×Q8C2211yescharacteristic
31C3×#494—24no—
32C3×#462—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×#103C2211yescharacteristic
43C2×C3×#103C2211yescharacteristic
44C2×C3×C22⋊C8C2211yescharacteristic
45C2×C3×C22⋊C8C2211yescharacteristic
46C2×C3×C4×C8C2211yescharacteristic
47C3×#398—21no—
48C3×#396—21no—
49C3×#395—21no—
50C3×#395—21no—
51C3×#391C2211yescharacteristic
52C3×#391C2211yescharacteristic
53C3×#391C2211yescharacteristic
54C3×#389—21no—
55C3×#389C2211yescharacteristic
56C3×#388—21no—
57C3×#385—21no—
58C3×#385—21no—
59C3×C4×C22⋊C4C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#494C2×C311yescharacteristic, complemented
65C2×#462C2×C311yescharacteristic, complemented
66C2×#451C2×C311yescharacteristic
67C2×#451C2×C311yescharacteristic
68#2434C2×C311yescharacteristic
69#2429C2×C311yescharacteristic
70#2056C2×C311yescharacteristic, complemented
71#2043C2×C311yescharacteristic, complemented
72#2016C2×C311yescharacteristic, complemented
73#2016C2×C311yescharacteristic, complemented
74#2001C2×C311yescharacteristic
75#2001C2×C311yescharacteristic
76#1933C2×C311yescharacteristic, complemented
77#1923C2×C311yescharacteristic
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×Q8C2311yescharacteristic
91C23×C3×C4—21no—
92C23×C3×C4C2311yescharacteristic
93C2×C3×Q16—22no—
94C2×C3×Q16—22no—
95C2×C3×Q16—22no—
96C2×C3×Q16—22no—
97C2×C3×Q16—22no—
98C2×C3×Q16—22no—
99C2×C3×Q16—22no—
100C2×C3×Q16—22no—
101C2×C3×Q16—41no—
102C2×C3×Q16—41no—
103C2×C3×Q16—41no—
104C2×C3×Q16—41no—
105C2×C3×Q16—41no—
106C2×C3×Q16—41no—
107C2×C3×Q16—41no—
108C2×C3×Q16—41no—
109C2×C3×Q16—41no—
110C2×C3×Q16D414yes—
111C22×C3×C8C2311yescharacteristic
112C22×C3×C8C2311yescharacteristic
113C22×C3×C8C2311yescharacteristic
114C22×C3×C8C2311yescharacteristic
115C3×C4⋊Q8—22no—
116C3×C4⋊Q8—22no—
117C3×C4⋊Q8—22no—
118C3×C4⋊Q8—41no—
119C3×C4⋊Q8—41no—
120C3×C4⋊Q8—41no—
121C3×C22⋊Q8—22no—
122C3×C22⋊Q8—22no—
123C3×C22⋊Q8—41no—
124C3×C22⋊Q8—41no—
125C3×C22⋊Q8—41no—
126C3×C22⋊Q8—41no—
127C3×C4×Q8—22no—
128C3×C4×Q8—41no—
129C2×C3×C4⋊C4—21no—
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⋊C4—21no—
137C2×C3×C4⋊C4—21no—
138C2×C3×C4⋊C4—21no—
139C2×C3×C4⋊C4—21no—
140C2×C3×C4⋊C4C2311yescharacteristic
141C2×C3×C4⋊C4C2311yescharacteristic
142C2×C3×C4⋊C4C2311yescharacteristic
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—22no—
156C3×#103—41no—
157C3×#103—41no—
158C3×#103—41no—
159C3×#103D414yes—
160C3×C22⋊C8—22no—
161C3×C22⋊C8—22no—
162C3×C4×C8—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×Q16C22×C311yescharacteristic
178C22×Q16C22×C311yescharacteristic
179C2×C4⋊Q8C22×C311yescharacteristic
180C2×C4⋊Q8C22×C311yescharacteristic
181C2×C4⋊Q8C22×C311yescharacteristic
182C2×C22⋊Q8C22×C311yescharacteristic
183C2×C22⋊Q8C22×C311yescharacteristic
184C2×C22⋊Q8C22×C311yescharacteristic
185C2×C4×Q8C22×C311yescharacteristic
186#494—24no—
187#462—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×#103C22×C311yescharacteristic
198C2×#103C22×C311yescharacteristic
199C2×C22⋊C8C22×C311yescharacteristic
200C2×C22⋊C8C22×C311yescharacteristic
201C2×C4×C8C22×C311yescharacteristic
202#398—21no—
203#396—21no—
204#395—21no—
205#395—21no—
206#391C22×C311yescharacteristic
207#391C22×C311yescharacteristic
208#391C22×C311yescharacteristic
209#389—21no—
210#389C22×C311yescharacteristic
211#388—21no—
212#385—21no—
213#385—21no—
214C4×C22⋊C4C22×C311yescharacteristic
215#340C22×C311yescharacteristic
216#340C22×C311yescharacteristic
217#336C22×C311yescharacteristic
218#336C22×C311yescharacteristic
219C24×C3C2×D411yescharacteristic
220C2×C3×Q8—21no—
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—21no—
243C2×C3×Q8—21no—
244C2×C3×Q8—21no—
245C2×C3×Q8—21no—
246C2×C3×Q8—21no—
247C2×C3×Q8—42no—
248C2×C3×Q8—42no—
249C2×C3×Q8—42no—
250C2×C3×Q8—44no—
251C2×C3×Q8—44no—
252C2×C3×Q8—44no—
253C2×C3×Q8—44no—
254C2×C3×Q8C2×D412yes—
255C2×C3×Q8C2×D412yes—
256C2×C3×Q8C2×D412yes—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
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—42no—
272C22×C3×C4—42no—
273C22×C3×C4—42no—
274C22×C3×C4C2×D411yescharacteristic
275C22×C3×C4C2×D411yescharacteristic
276C22×C3×C4C2×D411yescharacteristic
277C22×C3×C4C2×D411yescharacteristic
278C22×C3×C4C2×D411yescharacteristic
279C22×C3×C4C2411yescharacteristic
280C3×Q16—44no—
281C3×Q16—44no—
282C3×Q16—44no—
283C3×Q16—44no—
284C3×Q16—44no—
285C3×Q16—44no—
286C2×C3×C8—21no—
287C2×C3×C8—21no—
288C2×C3×C8—21no—
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×C8C2×D412yes—
297C2×C3×C8C2×D412yes—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—42no—
304C3×C4⋊C4—42no—
305C3×C4⋊C4—42no—
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⋊C4—42no—
313C3×C4⋊C4—42no—
314C3×C4⋊C4C2×D412yes—
315C3×C22⋊C4—22no—
316C3×C22⋊C4—42no—
317C3×C22⋊C4—42no—
318C3×C22⋊C4—42no—
319C3×C22⋊C4Q1614yescomplemented
320C3×C42—21no—
321C3×C42—21no—
322C3×C42—21no—
323C3×C42—21no—
324C3×C42—42no—
325C22×Q8—21no—
326C22×Q8—22no—
327C22×Q8—22no—
328C22×Q8—41no—
329C22×Q8—41no—
330C22×Q8—41no—
331C22×Q8—41no—
332C22×Q8C23×C311yescharacteristic
333C22×Q8C23×C311yescharacteristic
334C22×Q8C23×C311yescharacteristic
335C22×Q8C23×C311yescharacteristic
336C22×Q8C23×C311yescharacteristic
337C23×C4—21no—
338C23×C4C23×C311yescharacteristic
339C2×Q16—22no—
340C2×Q16—22no—
341C2×Q16—22no—
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×Q16—41no—
354C2×Q16—41no—
355C2×Q16—41no—
356C2×Q16C3×D414yes—
357C22×C8C23×C311yescharacteristic
358C22×C8C23×C311yescharacteristic
359C22×C8C23×C311yescharacteristic
360C22×C8C23×C311yescharacteristic
361C4⋊Q8—22no—
362C4⋊Q8—22no—
363C4⋊Q8—22no—
364C4⋊Q8—41no—
365C4⋊Q8—41no—
366C4⋊Q8—41no—
367C22⋊Q8—22no—
368C22⋊Q8—22no—
369C22⋊Q8—41no—
370C22⋊Q8—41no—
371C22⋊Q8—41no—
372C22⋊Q8—41no—
373C4×Q8—22no—
374C4×Q8—41no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
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⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4C23×C311yescharacteristic
387C2×C4⋊C4C23×C311yescharacteristic
388C2×C4⋊C4C23×C311yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4C3×D411yescharacteristic
393C2×C22⋊C4C3×D411yescharacteristic
394C2×C42—21no—
395C2×C42C23×C311yescharacteristic
396C2×C42C23×C311yescharacteristic
397C4⋊C8—22no—
398#103—22no—
399#103—22no—
400#103—22no—
401#103—22no—
402#103—41no—
403#103—41no—
404#103—41no—
405#103C3×D414yes—
406C22⋊C8—22no—
407C22⋊C8—22no—
408C4×C8—22no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95C3×D411yescharacteristic
417#95C3×D411yescharacteristic
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3C2×Q1612yes—
425C23×C3C22×D411yescharacteristic
426C3×Q8—22no—
427C3×Q8—22no—
428C3×Q8—22no—
429C3×Q8—22no—
430C3×Q8—22no—
431C3×Q8—22no—
432C3×Q8—48no—
433C3×Q8—41no—
434C3×Q8—41no—
435C3×Q8—41no—
436C3×Q8—41no—
437C3×Q8—41no—
438C3×Q8—41no—
439C3×Q8—41no—
440C3×Q8—41no—
441C3×Q8—41no—
442C3×Q8—41no—
443C3×Q8—41no—
444C3×Q8—41no—
445C3×Q8—41no—
446C3×Q8—41no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—48no—
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—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—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4C2×Q1612yes—
489C2×C3×C4C2×Q1612yes—
490C2×C3×C4#13712yes—
491C2×C3×C4C22×D411yescharacteristic
492C2×C3×C4C22×D411yescharacteristic
493C2×C3×C4H(5,𝔽2)11yescharacteristic
494C2×C3×C4H(5,𝔽2)11yescharacteristic
495C2×C3×C4H(5,𝔽2)11yescharacteristic
496C2×C3×C4H(5,𝔽2)11yescharacteristic
497C3×C8—22no—
498C3×C8—22no—
499C3×C8—41no—
500C3×C8—41no—
501C24C2×C3×D411yescharacteristic
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
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—42no—
530C2×Q8—42no—
531C2×Q8—42no—
532C2×Q8—44no—
533C2×Q8—44no—
534C2×Q8—44no—
535C2×Q8—44no—
536C2×Q8C2×C3×D412yes—
537C2×Q8C2×C3×D412yes—
538C2×Q8C2×C3×D412yes—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4C2×C3×D411yescharacteristic
557C22×C4C2×C3×D411yescharacteristic
558C22×C4C2×C3×D411yescharacteristic
559C22×C4C2×C3×D411yescharacteristic
560C22×C4C2×C3×D411yescharacteristic
561C22×C4C24×C311yescharacteristic
562Q16—44no—
563Q16—44no—
564Q16—44no—
565Q16—44no—
566Q16—44no—
567Q16—44no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8C2×C3×D412yes—
579C2×C8C2×C3×D412yes—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4C2×C3×D412yes—
597C22⋊C4—22no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4C3×Q1614yescomplemented
602C42—21no—
603C42—21no—
604C42—21no—
605C42—21no—
606C42—42no—
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3#53511yescharacteristic
615C22×C3D4211yescharacteristic
616C22×C3D4211yescharacteristic
617C22×C3C22×Q1611yescharacteristic
618C22×C3C2×#13711yescharacteristic
619C22×C3#57811yescharacteristic
620C22×C3#57811yescharacteristic
621C3×C4—22no—
622C3×C4—22no—
623C3×C4—22no—
624C3×C4—41no—
625C3×C4—42no—
626C3×C4—42no—
627C3×C4—42no—
628C3×C4—41no—
629C3×C4—42no—
630C3×C4—81no—
631C3×C4—81no—
632C3×C4—81no—
633C3×C4—81no—
634C3×C4#53411yescharacteristic
635C3×C4#53511yescharacteristic
636C3×C4D4211yescharacteristic
637C3×C4#56011yescharacteristic
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23C2×C3×Q1612yes—
645C23C22×C3×D411yescharacteristic
646Q8—22no—
647Q8—22no—
648Q8—22no—
649Q8—22no—
650Q8—22no—
651Q8—22no—
652Q8—48no—
653Q8—41no—
654Q8—41no—
655Q8—41no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659Q8—41no—
660Q8—41no—
661Q8—41no—
662Q8—41no—
663Q8—41no—
664Q8—41no—
665Q8—41no—
666Q8—41no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—48no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
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×C4C2×C3×Q1612yes—
709C2×C4C2×C3×Q1612yes—
710C2×C4C3×#13712yes—
711C2×C4C22×C3×D411yescharacteristic
712C2×C4C22×C3×D411yescharacteristic
713C2×C4C3×H(5,𝔽2)11yescharacteristic
714C2×C4C3×H(5,𝔽2)11yescharacteristic
715C2×C4C3×H(5,𝔽2)11yescharacteristic
716C2×C4C3×H(5,𝔽2)11yescharacteristic
717C8—22no—
718C8—22no—
719C8—41no—
720C8—41no—
721C2×C3—42no—
722C2×C3#266911yescharacteristic
723C2×C3#320911yescharacteristic
724C2×C3#322311yescharacteristic
725C2×C3#327011yescharacteristic
726C2×C3#327611yescharacteristic
727C2×C3D4×Q1611yescharacteristic
728C2×C3D4×Q1611yescharacteristic
729C22—22no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22C3×#53511yescharacteristic
737C22C3×D4211yescharacteristic
738C22C3×D4211yescharacteristic
739C22C22×C3×Q1611yescharacteristic
740C22C2×C3×#13711yescharacteristic
741C22C3×#57811yescharacteristic
742C22C3×#57811yescharacteristic
743C4—22no—
744C4—22no—
745C4—22no—
746C4—41no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—41no—
751C4—42no—
752C4—81no—
753C4—81no—
754C4—81no—
755C4—81no—
756C4C3×#53411yescharacteristic
757C4C3×#53511yescharacteristic
758C4C3×D4211yescharacteristic
759C4C3×#56011yescharacteristic
760C3#3044911yescharacteristic, direct product factor, Sylow
761C2—42no—
762C2C3×#266911yescharacteristic
763C2C3×#320911yescharacteristic
764C2C3×#322311yescharacteristic
765C2C3×#327011yescharacteristic
766C2C3×#327611yescharacteristic
767C2C3×D4×Q1611yescharacteristic
768C2C3×D4×Q1611yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC24×C3C2×D4
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×#494C2semidirect
2. C2×C3×#462C2semidirect
7. C3×#2056C2semidirect
8. C3×#2043C2semidirect
9. C3×#2016C2semidirect
10. C3×#2016C2semidirect
13. C3×#1933C2semidirect
15. C3×#1878C2semidirect
16. #30449C3direct (N × H)
64. C2×#494C2×C3semidirect
65. C2×#462C2×C3semidirect
70. #2056C2×C3semidirect
71. #2043C2×C3semidirect
72. #2016C2×C3semidirect
73. #2016C2×C3semidirect
76. #1933C2×C3semidirect
78. #1878C2×C3semidirect
319. C3×C22⋊C4Q16semidirect
601. C22⋊C4C3×Q16semidirect
760. C3#30449direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4942
C2×C3×#4622
C2×C3×#4512
C3×#24342
C3×#24292
C3×#20562
C3×#20432
C3×#20162
C3×#20012
C3×#19332
C3×#19232
C3×#18782
#304493