Finite Group Databasebeta

← C3×#24137 #10642744

Subgroups — C3×#24137 #10642744

Order 768.

1174 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#552C211yesmaximal, characteristic, complemented
2C2×C3×#478C211yesmaximal, characteristic, complemented
3C2×C3×#440C211yesmaximal, characteristic, complemented
4C3×#2537C211yesmaximal, characteristic
5C3×#2036C211yesmaximal, characteristic, complemented
6C3×#2035C211yesmaximal, characteristic, complemented
7C3×#2000C211yesmaximal, characteristic, complemented
8C3×#2000C211yesmaximal, characteristic, complemented
9C3×#1992C211yesmaximal, characteristic, complemented
10C3×#1955C211yesmaximal, characteristic, complemented
11C3×#1875C211yesmaximal, characteristic, complemented
12C3×#1874C211yesmaximal, characteristic, complemented
13C3×#1854C211yesmaximal, characteristic, complemented
14C3×#1852C211yesmaximal, characteristic, complemented
15C3×#1803C211yesmaximal, characteristic, complemented
16#24137C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×SD16C2211yescharacteristic
18C3×#552—24no—
19C3×#552—24no—
20C2×C3×#126—21no—
21C2×C3×#125—21no—
22C2×C3×#125C2211yescharacteristic
23C2×C3×#123—21no—
24C2×C3×C22⋊Q8C2211yescharacteristic
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×C3×#121—21no—
27C2×C3×#121C2211yescharacteristic
28C2×C3×#121C2211yescharacteristic
29C2×C3×C4×Q8C2211yescharacteristic
30C2×C3×C4×D4C2211yescharacteristic
31C2×C3×C4×D4C2211yescharacteristic
32C2×C3×#117—21no—
33C2×C3×#117C2211yescharacteristic
34C22×C3×C4⋊C4C2211yescharacteristic
35C3×#478—24no—
36C3×#440—24no—
37C2×C3×#107C2211yescharacteristic
38C2×C3×#107C2211yescharacteristic
39C2×C3×#106C2211yescharacteristic
40C2×C3×C4⋊C8C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#103C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×C22⋊C8C2211yescharacteristic
48C2×C3×C22⋊C8C2211yescharacteristic
49C2×C3×C22⋊C8C2211yescharacteristic
50C2×C3×C22⋊C8C2211yescharacteristic
51C2×C3×#97C2211yescharacteristic
52C3×#394—21no—
53C3×#394—21no—
54C3×#384C2211yescharacteristic
55C3×#380—21no—
56C3×#380C2211yescharacteristic
57C3×#380C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#340C2211yescharacteristic
63C3×#340C2211yescharacteristic
64C2×#552C2×C311yescharacteristic, complemented
65C2×#478C2×C311yescharacteristic, complemented
66C2×#440C2×C311yescharacteristic, complemented
67#2537C2×C311yescharacteristic
68#2036C2×C311yescharacteristic, complemented
69#2035C2×C311yescharacteristic, complemented
70#2000C2×C311yescharacteristic, complemented
71#2000C2×C311yescharacteristic, complemented
72#1992C2×C311yescharacteristic, complemented
73#1955C2×C311yescharacteristic, complemented
74#1875C2×C311yescharacteristic, complemented
75#1874C2×C311yescharacteristic, complemented
76#1854C2×C311yescharacteristic, complemented
77#1852C2×C311yescharacteristic, complemented
78#1803C2×C311yescharacteristic, complemented
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4—21no—
82C22×C3×D4D411yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4—21no—
85C23×C3×C4—21no—
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C2×C3×SD16—22no—
89C2×C3×SD16—22no—
90C2×C3×SD16—22no—
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C3×#126—28no—
96C3×#125—28no—
97C3×#125—22no—
98C3×#125D414yescomplemented
99C3×#123—28no—
100C3×C22⋊Q8—22no—
101C3×C22⋊Q8—22no—
102C3×C22⋊Q8—22no—
103C3×C22⋊Q8—22no—
104C3×#121—22no—
105C3×#121—22no—
106C3×#121—41no—
107C3×#121—41no—
108C3×#121—44no—
109C3×C4×Q8—22no—
110C3×C4×Q8D414yescomplemented
111C3×C4×D4—22no—
112C3×C4×D4—22no—
113C3×C4×D4—22no—
114C3×C4×D4—22no—
115C3×#117—28no—
116C3×#117—22no—
117C3×#117—22no—
118C2×C3×C4⋊C4—21no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—22no—
125C2×C3×C4⋊C4—22no—
126C2×C3×C4⋊C4—21no—
127C2×C3×C4⋊C4—21no—
128C2×C3×C4⋊C4D411yescharacteristic
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C4⋊C4C2311yescharacteristic
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×C22⋊C4—21no—
141C2×C3×C22⋊C4—21no—
142C2×C3×C22⋊C4—21no—
143C2×C3×C22⋊C4D411yescharacteristic
144C2×C3×C22⋊C4D411yescharacteristic
145C2×C3×C42—21no—
146C2×C3×C42—21no—
147C2×C3×C42C2311yescharacteristic
148C3×#107—22no—
149C3×#107—22no—
150C3×#106—22no—
151C3×C4⋊C8—22no—
152C3×#103—22no—
153C3×#103—41no—
154C3×#103—41no—
155C3×#102—22no—
156C3×#102—22no—
157C3×#102—22no—
158C3×C22⋊C8—22no—
159C3×C22⋊C8—22no—
160C3×C22⋊C8—41no—
161C3×C22⋊C8—41no—
162C3×#97—22no—
163C3×#95—21no—
164C3×#95—21no—
165C22×SD16C22×C311yescharacteristic
166#552—24no—
167#552—24no—
168C2×#126—21no—
169C2×#125—21no—
170C2×#125C22×C311yescharacteristic
171C2×#123—21no—
172C2×C22⋊Q8C22×C311yescharacteristic
173C2×C22⋊Q8C22×C311yescharacteristic
174C2×#121—21no—
175C2×#121C22×C311yescharacteristic
176C2×#121C22×C311yescharacteristic
177C2×C4×Q8C22×C311yescharacteristic
178C2×C4×D4C22×C311yescharacteristic
179C2×C4×D4C22×C311yescharacteristic
180C2×#117—21no—
181C2×#117C22×C311yescharacteristic
182C22×C4⋊C4C22×C311yescharacteristic
183#478—24no—
184#440—24no—
185C2×#107C22×C311yescharacteristic
186C2×#107C22×C311yescharacteristic
187C2×#106C22×C311yescharacteristic
188C2×C4⋊C8C22×C311yescharacteristic
189C2×#103C22×C311yescharacteristic
190C2×#103C22×C311yescharacteristic
191C2×#103C22×C311yescharacteristic
192C2×#102C22×C311yescharacteristic
193C2×#102C22×C311yescharacteristic
194C2×#102C22×C311yescharacteristic
195C2×C22⋊C8C22×C311yescharacteristic
196C2×C22⋊C8C22×C311yescharacteristic
197C2×C22⋊C8C22×C311yescharacteristic
198C2×C22⋊C8C22×C311yescharacteristic
199C2×#97C22×C311yescharacteristic
200#394—21no—
201#394—21no—
202#384C22×C311yescharacteristic
203#380—21no—
204#380C22×C311yescharacteristic
205#380C22×C311yescharacteristic
206#340C22×C311yescharacteristic
207#340C22×C311yescharacteristic
208#340C22×C311yescharacteristic
209#340C22×C311yescharacteristic
210#340C22×C311yescharacteristic
211#340C22×C311yescharacteristic
212C24×C3—21no—
213C24×C3C2×D411yescharacteristic
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—22no—
222C2×C3×D4—22no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—41no—
229C2×C3×D4—42no—
230C2×C3×D4—42no—
231C2×C3×D4—42no—
232C2×C3×D4—42no—
233C2×C3×D4—81no—
234C2×C3×D4—81no—
235C2×C3×D4#4112yes—
236C22×C3×C4—24no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
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—21no—
256C22×C3×C4—42no—
257C22×C3×C4—42no—
258C22×C3×C4—42no—
259C22×C3×C4—42no—
260C22×C3×C4—42no—
261C22×C3×C4C2×D411yescharacteristic
262C22×C3×C4C2×D411yescharacteristic
263C22×C3×C4C2×D411yescharacteristic
264C22×C3×C4C2×D411yescharacteristic
265C22×C3×C4C2411yescharacteristic
266C3×SD16—28no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
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#4112yes—
279C3×C4⋊C4—24no—
280C3×C4⋊C4—24no—
281C3×C4⋊C4—24no—
282C3×C4⋊C4—24no—
283C3×C4⋊C4—24no—
284C3×C4⋊C4—24no—
285C3×C4⋊C4—22no—
286C3×C4⋊C4—21no—
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—21no—
295C3×C4⋊C4—42no—
296C3×C4⋊C4—81no—
297C3×C4⋊C4C2×D412yes—
298C3×C4⋊C4C2×D412yes—
299C3×C4⋊C4C2×D412yes—
300C3×C22⋊C4—24no—
301C3×C22⋊C4—24no—
302C3×C22⋊C4—24no—
303C3×C22⋊C4—22no—
304C3×C22⋊C4—22no—
305C3×C22⋊C4—42no—
306C3×C22⋊C4—42no—
307C3×C22⋊C4—42no—
308C3×C22⋊C4—42no—
309C3×C22⋊C4—42no—
310C3×C42—24no—
311C3×C42—24no—
312C3×C42C2×D412yes—
313C3×C42C2×D412yes—
314C22×Q8C23×C311yescharacteristic
315C22×D4—21no—
316C22×D4—21no—
317C22×D4C3×D411yescharacteristic
318C22×D4C23×C311yescharacteristic
319C23×C4—21no—
320C23×C4—21no—
321C23×C4C23×C311yescharacteristic
322C23×C4C23×C311yescharacteristic
323C2×SD16—22no—
324C2×SD16—22no—
325C2×SD16—22no—
326C22×C8C23×C311yescharacteristic
327C22×C8C23×C311yescharacteristic
328C22×C8C23×C311yescharacteristic
329C22×C8C23×C311yescharacteristic
330#126—28no—
331#125—28no—
332#125—22no—
333#125C3×D414yescomplemented
334#123—28no—
335C22⋊Q8—22no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338C22⋊Q8—22no—
339#121—22no—
340#121—22no—
341#121—41no—
342#121—41no—
343#121—44no—
344C4×Q8—22no—
345C4×Q8C3×D414yescomplemented
346C4×D4—22no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—22no—
350#117—28no—
351#117—22no—
352#117—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4C3×D411yescharacteristic
364C2×C4⋊C4C23×C311yescharacteristic
365C2×C4⋊C4C23×C311yescharacteristic
366C2×C4⋊C4C23×C311yescharacteristic
367C2×C4⋊C4C23×C311yescharacteristic
368C2×C4⋊C4C23×C311yescharacteristic
369C2×C4⋊C4C23×C311yescharacteristic
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×C22⋊C4—21no—
378C2×C22⋊C4C3×D411yescharacteristic
379C2×C22⋊C4C3×D411yescharacteristic
380C2×C42—21no—
381C2×C42—21no—
382C2×C42C23×C311yescharacteristic
383#107—22no—
384#107—22no—
385#106—22no—
386C4⋊C8—22no—
387#103—22no—
388#103—41no—
389#103—41no—
390#102—22no—
391#102—22no—
392#102—22no—
393C22⋊C8—22no—
394C22⋊C8—22no—
395C22⋊C8—41no—
396C22⋊C8—41no—
397#97—22no—
398#95—21no—
399#95—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—22no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3AGL(1,ℤ/8)12yes—
421C23×C3C22×D411yescharacteristic
422C3×Q8—22no—
423C3×Q8—22no—
424C3×Q8—41no—
425C3×Q8—41no—
426C3×D4—22no—
427C3×D4—22no—
428C3×D4—44no—
429C3×D4—41no—
430C3×D4—41no—
431C3×D4—84no—
432C3×D4—84no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—21no—
442C2×C3×C4—22no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—48no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
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—84no—
474C2×C3×C4#12012yes—
475C2×C3×C4#12012yes—
476C2×C3×C4C22×D411yescharacteristic
477C2×C3×C4C22×D411yescharacteristic
478C2×C3×C4C2×#4111yescharacteristic
479C2×C3×C4C2×#4111yescharacteristic
480C2×C3×C4H(5,𝔽2)11yescharacteristic
481C2×C3×C42−1+411yescharacteristic
482C3×C8—22no—
483C3×C8—41no—
484C3×C8—41no—
485C3×C8—41no—
486C24—21no—
487C24C2×C3×D411yescharacteristic
488C24C2×C3×D411yescharacteristic
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8C2×C3×D412yes—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—41no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—81no—
508C2×D4—81no—
509C2×D4C3×#4112yes—
510C22×C4—24no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4C2×C3×D411yescharacteristic
536C22×C4C2×C3×D411yescharacteristic
537C22×C4C2×C3×D411yescharacteristic
538C22×C4C2×C3×D411yescharacteristic
539C22×C4C24×C311yescharacteristic
540SD16—28no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8C3×#4112yes—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—22no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—42no—
570C4⋊C4—81no—
571C4⋊C4C2×C3×D412yes—
572C4⋊C4C2×C3×D412yes—
573C4⋊C4C2×C3×D412yes—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—22no—
578C22⋊C4—22no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C42—24no—
585C42—24no—
586C42C2×C3×D412yes—
587C42C2×C3×D412yes—
588C22×C3—22no—
589C22×C3—22no—
590C22×C3—22no—
591C22×C3—41no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3—41no—
597C22×C3—41no—
598C22×C3—42no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—42no—
603C22×C3—41no—
604C22×C3—42no—
605C22×C3—81no—
606C22×C3—81no—
607C22×C3—81no—
608C22×C3—81no—
609C22×C3C2×#12011yescharacteristic
610C22×C3#54611yescharacteristic
611C22×C3#54711yescharacteristic
612C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
613C22×C3#57511yescharacteristic
614C22×C3#57711yescharacteristic
615C22×C3#57811yescharacteristic
616C3×C4—22no—
617C3×C4—22no—
618C3×C4—41no—
619C3×C4—41no—
620C3×C4—42no—
621C3×C4—42no—
622C3×C4—42no—
623C3×C4—42no—
624C3×C4—81no—
625C3×C4—81no—
626C3×C4—81no—
627C3×C4#52511yescharacteristic
628C3×C4#53711yescharacteristic
629C3×C4#54811yescharacteristic
630C3×C4#55011yescharacteristic
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—21no—
644C23—21no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23C3×AGL(1,ℤ/8)12yes—
652C23C22×C3×D411yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—41no—
656Q8—41no—
657D4—22no—
658D4—22no—
659D4—44no—
660D4—41no—
661D4—41no—
662D4—84no—
663D4—84no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—48no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
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—84no—
705C2×C4C3×#12012yes—
706C2×C4C3×#12012yes—
707C2×C4C22×C3×D411yescharacteristic
708C2×C4C22×C3×D411yescharacteristic
709C2×C4C2×C3×#4111yescharacteristic
710C2×C4C2×C3×#4111yescharacteristic
711C2×C4C3×H(5,𝔽2)11yescharacteristic
712C2×C4C3×2−1+411yescharacteristic
713C8—22no—
714C8—41no—
715C8—41no—
716C8—41no—
717C2×C3—42no—
718C2×C3—81no—
719C2×C3—82no—
720C2×C3#240711yescharacteristic
721C2×C3#300611yescharacteristic
722C2×C3#301311yescharacteristic
723C2×C3#331011yescharacteristic
724C2×C3#331511yescharacteristic
725C2×C3#334311yescharacteristic
726C2×C3#334811yescharacteristic
727C22—22no—
728C22—22no—
729C22—22no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—42no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—42no—
740C22—41no—
741C22—42no—
742C22—41no—
743C22—41no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22C2×C3×#12011yescharacteristic
749C22C3×#54611yescharacteristic
750C22C3×#54711yescharacteristic
751C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
752C22C3×#57511yescharacteristic
753C22C3×#57711yescharacteristic
754C22C3×#57811yescharacteristic
755C4—22no—
756C4—22no—
757C4—41no—
758C4—41no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—42no—
763C4—81no—
764C4—81no—
765C4—81no—
766C4C3×#52511yescharacteristic
767C4C3×#53711yescharacteristic
768C4C3×#54811yescharacteristic
769C4C3×#55011yescharacteristic
770C3#2413711yescharacteristic, direct product factor, Sylow
771C2—42no—
772C2—81no—
773C2—82no—
774C2C3×#240711yescharacteristic
775C2C3×#300611yescharacteristic
776C2C3×#301311yescharacteristic
777C2C3×#331011yescharacteristic
778C2C3×#331511yescharacteristic
779C2C3×#334311yescharacteristic
780C2C3×#334811yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#2537C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#552C2semidirect
2. C2×C3×#478C2semidirect
3. C2×C3×#440C2semidirect
5. C3×#2036C2semidirect
6. C3×#2035C2semidirect
7. C3×#2000C2semidirect
8. C3×#2000C2semidirect
9. C3×#1992C2semidirect
10. C3×#1955C2semidirect
11. C3×#1875C2semidirect
12. C3×#1874C2semidirect
13. C3×#1854C2semidirect
14. C3×#1852C2semidirect
15. C3×#1803C2semidirect
16. #24137C3direct (N × H)
64. C2×#552C2×C3semidirect
65. C2×#478C2×C3semidirect
66. C2×#440C2×C3semidirect
68. #2036C2×C3semidirect
69. #2035C2×C3semidirect
70. #2000C2×C3semidirect
71. #2000C2×C3semidirect
72. #1992C2×C3semidirect
73. #1955C2×C3semidirect
74. #1875C2×C3semidirect
75. #1874C2×C3semidirect
76. #1854C2×C3semidirect
77. #1852C2×C3semidirect
78. #1803C2×C3semidirect
98. C3×#125D4semidirect
110. C3×C4×Q8D4semidirect
333. #125C3×D4semidirect
345. C4×Q8C3×D4semidirect
770. C3#24137direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5522
C2×C3×#4782
C2×C3×#4402
C3×#25372
C3×#20362
C3×#20352
C3×#20002
C3×#19922
C3×#19552
C3×#18752
C3×#18742
C3×#18542
C3×#18522
C3×#18032
#241373