Finite Group Databasebeta

← C3×#24205 #10642812

Subgroups — C3×#24205 #10642812

Order 768.

1144 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#556C211yesmaximal, characteristic, complemented
2C2×C3×#463C211yesmaximal, characteristic
3C2×C3×#440C211yesmaximal, characteristic, complemented
4C3×#2538C211yesmaximal, characteristic, complemented
5C3×#2043C211yesmaximal, characteristic, complemented
6C3×#2042C211yesmaximal, characteristic, complemented
7C3×#2013C211yesmaximal, characteristic, complemented
8C3×#2012C211yesmaximal, characteristic
9C3×#1985C211yesmaximal, characteristic, complemented
10C3×#1959C211yesmaximal, characteristic, complemented
11C3×#1880C211yesmaximal, characteristic, complemented
12C3×#1879C211yesmaximal, characteristic
13C3×#1863C211yesmaximal, characteristic, complemented
14C3×#1862C211yesmaximal, characteristic, complemented
15C3×#1803C211yesmaximal, characteristic, complemented
16#24205C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×D8C2211yescharacteristic
20C3×#556—24no—
21C3×#556—24no—
22C2×C3×C4⋊Q8C2211yescharacteristic
23C2×C3×#126—21no—
24C2×C3×#126—21no—
25C2×C3×#124C2211yescharacteristic
26C2×C3×#124C2211yescharacteristic
27C2×C3×C22⋊Q8—21no—
28C2×C3×C22⋊Q8—21no—
29C2×C3×C4×Q8C2211yescharacteristic
30C2×C3×C4×Q8C2211yescharacteristic
31C2×C3×C4×Q8C2211yescharacteristic
32C2×C3×C4×D4C2211yescharacteristic
33C2×C3×C4×D4C2211yescharacteristic
34C2×C3×#117—21no—
35C3×#463—24no—
36C3×#440—24no—
37C2×C3×#107C2211yescharacteristic
38C2×C3×C4⋊C8C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#103C2211yescharacteristic
44C2×C3×#103C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×#102C2211yescharacteristic
48C2×C3×#102C2211yescharacteristic
49C2×C3×#97C2211yescharacteristic
50C3×#396—21no—
51C3×#396—21no—
52C3×#390C2211yescharacteristic
53C3×#390C2211yescharacteristic
54C3×#389C2211yescharacteristic
55C3×#389C2211yescharacteristic
56C3×#384C2211yescharacteristic
57C3×#380—21no—
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#556C2×C311yescharacteristic, complemented
65C2×#463C2×C311yescharacteristic
66C2×#440C2×C311yescharacteristic, complemented
67#2538C2×C311yescharacteristic, complemented
68#2043C2×C311yescharacteristic, complemented
69#2042C2×C311yescharacteristic, complemented
70#2013C2×C311yescharacteristic, complemented
71#2012C2×C311yescharacteristic
72#1985C2×C311yescharacteristic, complemented
73#1959C2×C311yescharacteristic, complemented
74#1880C2×C311yescharacteristic, complemented
75#1879C2×C311yescharacteristic
76#1863C2×C311yescharacteristic, complemented
77#1862C2×C311yescharacteristic, complemented
78#1803C2×C311yescharacteristic, complemented
79C22×C3×Q8D411yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×C3×Q8C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4—21no—
85C23×C3×C4—21no—
86C2×C3×SD16—22no—
87C2×C3×SD16—22no—
88C2×C3×SD16—22no—
89C2×C3×SD16—22no—
90C2×C3×SD16—22no—
91C2×C3×SD16—41no—
92C2×C3×D8—22no—
93C2×C3×D8—22no—
94C2×C3×D8—41no—
95C22×C3×C8C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C3×C4⋊Q8—22no—
100C3×C4⋊Q8—22no—
101C3×#126—28no—
102C3×#126—28no—
103C3×#124—22no—
104C3×#124—22no—
105C3×#124—22no—
106C3×#124D414yes—
107C3×C22⋊Q8—28no—
108C3×C22⋊Q8—44no—
109C3×C4×Q8—22no—
110C3×C4×Q8—22no—
111C3×C4×Q8—22no—
112C3×C4×Q8—22no—
113C3×C4×Q8—22no—
114C3×C4×Q8D414yes—
115C3×C4×D4—22no—
116C3×C4×D4—22no—
117C3×C4×D4—22no—
118C3×C4×D4—22no—
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⋊C4—21no—
126C2×C3×C4⋊C4—21no—
127C2×C3×C4⋊C4—21no—
128C2×C3×C4⋊C4D411yescharacteristic
129C2×C3×C4⋊C4D411yescharacteristic
130C2×C3×C4⋊C4D411yescharacteristic
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⋊C4—21no—
144C2×C3×C22⋊C4—21no—
145C2×C3×C42—21no—
146C2×C3×C42—21no—
147C2×C3×C42C2311yescharacteristic
148C2×C3×C42C2311yescharacteristic
149C2×C3×C42C2311yescharacteristic
150C3×#107—22no—
151C3×C4⋊C8—22no—
152C3×#103—22no—
153C3×#103—22no—
154C3×#103—22no—
155C3×#103—41no—
156C3×#103—41no—
157C3×#103—41no—
158C3×#102—22no—
159C3×#102—22no—
160C3×#102—22no—
161C3×#102—41no—
162C3×#97—22no—
163C3×#95—21no—
164C3×#95—21no—
165C22×SD16C22×C311yescharacteristic
166C22×SD16C22×C311yescharacteristic
167C22×D8C22×C311yescharacteristic
168#556—24no—
169#556—24no—
170C2×C4⋊Q8C22×C311yescharacteristic
171C2×#126—21no—
172C2×#126—21no—
173C2×#124C22×C311yescharacteristic
174C2×#124C22×C311yescharacteristic
175C2×C22⋊Q8—21no—
176C2×C22⋊Q8—21no—
177C2×C4×Q8C22×C311yescharacteristic
178C2×C4×Q8C22×C311yescharacteristic
179C2×C4×Q8C22×C311yescharacteristic
180C2×C4×D4C22×C311yescharacteristic
181C2×C4×D4C22×C311yescharacteristic
182C2×#117—21no—
183#463—24no—
184#440—24no—
185C2×#107C22×C311yescharacteristic
186C2×C4⋊C8C22×C311yescharacteristic
187C2×#103C22×C311yescharacteristic
188C2×#103C22×C311yescharacteristic
189C2×#103C22×C311yescharacteristic
190C2×#103C22×C311yescharacteristic
191C2×#103C22×C311yescharacteristic
192C2×#103C22×C311yescharacteristic
193C2×#102C22×C311yescharacteristic
194C2×#102C22×C311yescharacteristic
195C2×#102C22×C311yescharacteristic
196C2×#102C22×C311yescharacteristic
197C2×#97C22×C311yescharacteristic
198#396—21no—
199#396—21no—
200#390C22×C311yescharacteristic
201#390C22×C311yescharacteristic
202#389C22×C311yescharacteristic
203#389C22×C311yescharacteristic
204#384C22×C311yescharacteristic
205#380—21no—
206#340C22×C311yescharacteristic
207#340C22×C311yescharacteristic
208#336C22×C311yescharacteristic
209#336C22×C311yescharacteristic
210#336C22×C311yescharacteristic
211#336C22×C311yescharacteristic
212C24×C3—21no—
213C24×C3—21no—
214C2×C3×Q8—22no—
215C2×C3×Q8—22no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
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—41no—
227C2×C3×Q8C2×D412yes—
228C2×C3×Q8C2×D412yes—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4C2×D412yes—
240C2×C3×D4#4112yes—
241C22×C3×C4—24no—
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—42no—
249C22×C3×C4—42no—
250C22×C3×C4—42no—
251C22×C3×C4—42no—
252C22×C3×C4—42no—
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2411yescharacteristic
260C3×SD16—28no—
261C3×SD16—44no—
262C3×D8—44no—
263C2×C3×C8—21no—
264C2×C3×C8—21no—
265C2×C3×C8—21no—
266C2×C3×C8—21no—
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#4112yes—
275C3×C4⋊C4—24no—
276C3×C4⋊C4—24no—
277C3×C4⋊C4—24no—
278C3×C4⋊C4—24no—
279C3×C4⋊C4—22no—
280C3×C4⋊C4—22no—
281C3×C4⋊C4—22no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—42no—
290C3×C4⋊C4—42no—
291C3×C4⋊C4—42no—
292C3×C4⋊C4—81no—
293C3×C4⋊C4C2×D412yes—
294C3×C22⋊C4—24no—
295C3×C22⋊C4—24no—
296C3×C22⋊C4—24no—
297C3×C22⋊C4—24no—
298C3×C22⋊C4—24no—
299C3×C22⋊C4—42no—
300C3×C22⋊C4—42no—
301C3×C22⋊C4—42no—
302C3×C22⋊C4—81no—
303C3×C22⋊C4—81no—
304C3×C42—24no—
305C3×C42—24no—
306C3×C42—21no—
307C3×C42—21no—
308C3×C42—21no—
309C3×C42—21no—
310C3×C42C2×D412yes—
311C3×C42C2×D412yes—
312C22×Q8C3×D411yescharacteristic
313C22×Q8C23×C311yescharacteristic
314C22×Q8C23×C311yescharacteristic
315C22×D4C23×C311yescharacteristic
316C22×D4C23×C311yescharacteristic
317C23×C4—21no—
318C23×C4—21no—
319C2×SD16—22no—
320C2×SD16—22no—
321C2×SD16—22no—
322C2×SD16—22no—
323C2×SD16—22no—
324C2×SD16—41no—
325C2×D8—22no—
326C2×D8—22no—
327C2×D8—41no—
328C22×C8C23×C311yescharacteristic
329C22×C8C23×C311yescharacteristic
330C22×C8C23×C311yescharacteristic
331C22×C8C23×C311yescharacteristic
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334#126—28no—
335#126—28no—
336#124—22no—
337#124—22no—
338#124—22no—
339#124C3×D414yes—
340C22⋊Q8—28no—
341C22⋊Q8—44no—
342C4×Q8—22no—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×Q8—22no—
346C4×Q8—22no—
347C4×Q8C3×D414yes—
348C4×D4—22no—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4—22no—
352#117—28no—
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—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4C3×D411yescharacteristic
362C2×C4⋊C4C3×D411yescharacteristic
363C2×C4⋊C4C3×D411yescharacteristic
364C2×C4⋊C4C23×C311yescharacteristic
365C2×C4⋊C4C23×C311yescharacteristic
366C2×C4⋊C4C23×C311yescharacteristic
367C2×C4⋊C4C23×C311yescharacteristic
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×C22⋊C4—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42C23×C311yescharacteristic
381C2×C42C23×C311yescharacteristic
382C2×C42C23×C311yescharacteristic
383#107—22no—
384C4⋊C8—22no—
385#103—22no—
386#103—22no—
387#103—22no—
388#103—41no—
389#103—41no—
390#103—41no—
391#102—22no—
392#102—22no—
393#102—22no—
394#102—41no—
395#97—22no—
396#95—21no—
397#95—21no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—41no—
401C23×C3—41no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3C22×D411yescharacteristic
413C3×Q8—22no—
414C3×Q8—22no—
415C3×Q8—22no—
416C3×Q8—22no—
417C3×Q8—44no—
418C3×Q8—41no—
419C3×Q8—41no—
420C3×Q8—41no—
421C3×Q8—41no—
422C3×D4—22no—
423C3×D4—22no—
424C3×D4—22no—
425C3×D4—22no—
426C3×D4—41no—
427C3×D4—41no—
428C3×D4—41no—
429C3×D4—41no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—22no—
438C2×C3×C4—21no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—48no—
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—84no—
465C2×C3×C4#12012yes—
466C2×C3×C4#12012yes—
467C2×C3×C4AGL(1,ℤ/8)12yes—
468C2×C3×C4C22×D411yescharacteristic
469C2×C3×C4C22×D411yescharacteristic
470C2×C3×C4C2×#4111yescharacteristic
471C2×C3×C4C2×#4111yescharacteristic
472C2×C3×C4H(5,𝔽2)11yescharacteristic
473C2×C3×C42−1+411yescharacteristic
474C3×C8—22no—
475C3×C8—41no—
476C3×C8—41no—
477C3×C8—41no—
478C24—21no—
479C24—21no—
480C2×Q8—22no—
481C2×Q8—22no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—41no—
493C2×Q8C2×C3×D412yes—
494C2×Q8C2×C3×D412yes—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4C2×C3×D412yes—
506C2×D4C3×#4112yes—
507C22×C4—24no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4C2×C3×D411yescharacteristic
520C22×C4C2×C3×D411yescharacteristic
521C22×C4C2×C3×D411yescharacteristic
522C22×C4C2×C3×D411yescharacteristic
523C22×C4C2×C3×D411yescharacteristic
524C22×C4C2×C3×D411yescharacteristic
525C22×C4C24×C311yescharacteristic
526SD16—28no—
527SD16—44no—
528D8—44no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8C3×#4112yes—
541C4⋊C4—24no—
542C4⋊C4—24no—
543C4⋊C4—24no—
544C4⋊C4—24no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—42no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—81no—
559C4⋊C4C2×C3×D412yes—
560C22⋊C4—24no—
561C22⋊C4—24no—
562C22⋊C4—24no—
563C22⋊C4—24no—
564C22⋊C4—24no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—81no—
569C22⋊C4—81no—
570C42—24no—
571C42—24no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42C2×C3×D412yes—
577C42C2×C3×D412yes—
578C22×C3—42no—
579C22×C3—42no—
580C22×C3—42no—
581C22×C3—42no—
582C22×C3—42no—
583C22×C3—42no—
584C22×C3—81no—
585C22×C3—81no—
586C22×C3—81no—
587C22×C3—81no—
588C22×C3—81no—
589C22×C3—81no—
590C22×C3—81no—
591C22×C3—81no—
592C22×C3C2×#12011yescharacteristic
593C22×C3#54811yescharacteristic
594C22×C3#55011yescharacteristic
595C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
596C22×C3#57511yescharacteristic
597C22×C3#57711yescharacteristic
598C22×C3#57811yescharacteristic
599C3×C4—22no—
600C3×C4—22no—
601C3×C4—22no—
602C3×C4—42no—
603C3×C4—42no—
604C3×C4—41no—
605C3×C4—42no—
606C3×C4—41no—
607C3×C4—41no—
608C3×C4—81no—
609C3×C4—81no—
610C3×C4—81no—
611C3×C4#52511yescharacteristic
612C3×C4#53711yescharacteristic
613C3×C4#54611yescharacteristic
614C3×C4#54711yescharacteristic
615C23—22no—
616C23—22no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23C22×C3×D411yescharacteristic
630Q8—22no—
631Q8—22no—
632Q8—22no—
633Q8—22no—
634Q8—44no—
635Q8—41no—
636Q8—41no—
637Q8—41no—
638Q8—41no—
639D4—22no—
640D4—22no—
641D4—22no—
642D4—22no—
643D4—41no—
644D4—41no—
645D4—41no—
646D4—41no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—48no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—84no—
682C2×C4C3×#12012yes—
683C2×C4C3×#12012yes—
684C2×C4C3×AGL(1,ℤ/8)12yes—
685C2×C4C22×C3×D411yescharacteristic
686C2×C4C22×C3×D411yescharacteristic
687C2×C4C2×C3×#4111yescharacteristic
688C2×C4C2×C3×#4111yescharacteristic
689C2×C4C3×H(5,𝔽2)11yescharacteristic
690C2×C4C3×2−1+411yescharacteristic
691C8—22no—
692C8—41no—
693C8—41no—
694C8—41no—
695C2×C3—82no—
696C2×C3—82no—
697C2×C3#240711yescharacteristic
698C2×C3#300611yescharacteristic
699C2×C3#301311yescharacteristic
700C2×C3#336711yescharacteristic
701C2×C3#337611yescharacteristic
702C2×C3#339711yescharacteristic
703C2×C3#340211yescharacteristic
704C22—42no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22C2×C3×#12011yescharacteristic
719C22C3×#54811yescharacteristic
720C22C3×#55011yescharacteristic
721C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
722C22C3×#57511yescharacteristic
723C22C3×#57711yescharacteristic
724C22C3×#57811yescharacteristic
725C4—22no—
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—41no—
731C4—42no—
732C4—41no—
733C4—41no—
734C4—81no—
735C4—81no—
736C4—81no—
737C4C3×#52511yescharacteristic
738C4C3×#53711yescharacteristic
739C4C3×#54611yescharacteristic
740C4C3×#54711yescharacteristic
741C3#2420511yescharacteristic, direct product factor, Sylow
742C2—82no—
743C2—82no—
744C2C3×#240711yescharacteristic
745C2C3×#300611yescharacteristic
746C2C3×#301311yescharacteristic
747C2C3×#336711yescharacteristic
748C2C3×#337611yescharacteristic
749C2C3×#339711yescharacteristic
750C2C3×#340211yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#556C2semidirect
3. C2×C3×#440C2semidirect
4. C3×#2538C2semidirect
5. C3×#2043C2semidirect
6. C3×#2042C2semidirect
7. C3×#2013C2semidirect
9. C3×#1985C2semidirect
10. C3×#1959C2semidirect
11. C3×#1880C2semidirect
13. C3×#1863C2semidirect
14. C3×#1862C2semidirect
15. C3×#1803C2semidirect
16. #24205C3direct (N × H)
64. C2×#556C2×C3semidirect
66. C2×#440C2×C3semidirect
67. #2538C2×C3semidirect
68. #2043C2×C3semidirect
69. #2042C2×C3semidirect
70. #2013C2×C3semidirect
72. #1985C2×C3semidirect
73. #1959C2×C3semidirect
74. #1880C2×C3semidirect
76. #1863C2×C3semidirect
77. #1862C2×C3semidirect
78. #1803C2×C3semidirect
741. C3#24205direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5562
C2×C3×#4632
C2×C3×#4402
C3×#25382
C3×#20432
C3×#20422
C3×#20132
C3×#20122
C3×#19852
C3×#19592
C3×#18802
C3×#18792
C3×#18632
C3×#18622
C3×#18032
#242053