Finite Group Databasebeta

← C3×#25541 #10644148

Subgroups — C3×#25541 #10644148

Order 768.

1120 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#552C211yesmaximal, characteristic
2C2×C3×#483C211yesmaximal, characteristic, complemented
3C2×C3×#467C211yesmaximal, characteristic, complemented
4C3×#2417C211yesmaximal, characteristic
5C3×#2059C211yesmaximal, characteristic, complemented
6C3×#2035C211yesmaximal, characteristic, complemented
7C3×#2026C211yesmaximal, characteristic, complemented
8C3×#2001C211yesmaximal, characteristic, complemented
9C3×#1878C211yesmaximal, characteristic, complemented
10C3×#1873C211yesmaximal, characteristic, complemented
11C3×#1872C211yesmaximal, characteristic, complemented
12C3×#1869C211yesmaximal, characteristic
13C3×#1865C211yesmaximal, characteristic, complemented
14C3×#1854C211yesmaximal, characteristic, complemented
15C2×C3×#340C211yesmaximal, characteristic, complemented
16#25541C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×Q16C2211yescharacteristic
18C23×C3×C8C2211yescharacteristic
19C3×#552—24no—
20C3×#552—24no—
21C2×C3×#126—21no—
22C2×C3×#125—21no—
23C2×C3×#125C2211yescharacteristic
24C2×C3×#123—21no—
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×C3×C22⋊Q8C2211yescharacteristic
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×C22⋊Q8C2211yescharacteristic
29C2×C3×C4×Q8C2211yescharacteristic
30C2×C3×C4×D4C2211yescharacteristic
31C2×C3×#117—21no—
32C2×C3×#117C2211yescharacteristic
33C22×C3×C4⋊C4C2211yescharacteristic
34C22×C3×C4⋊C4C2211yescharacteristic
35C3×#483—24no—
36C3×#467—24no—
37C2×C3×#107C2211yescharacteristic
38C2×C3×#106C2211yescharacteristic
39C2×C3×#106C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#103C2211yescharacteristic
44C2×C3×#103C2211yescharacteristic
45C2×C3×#103C2211yescharacteristic
46C2×C3×C22⋊C8C2211yescharacteristic
47C2×C3×C22⋊C8C2211yescharacteristic
48C2×C3×C22⋊C8C2211yescharacteristic
49C3×#398—21no—
50C3×#396—21no—
51C3×#391C2211yescharacteristic
52C3×#389C2211yescharacteristic
53C3×#386—21no—
54C3×#380—21no—
55C3×#380C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#552C2×C311yescharacteristic
65C2×#483C2×C311yescharacteristic, complemented
66C2×#467C2×C311yescharacteristic, complemented
67#2417C2×C311yescharacteristic
68#2059C2×C311yescharacteristic, complemented
69#2035C2×C311yescharacteristic, complemented
70#2026C2×C311yescharacteristic, complemented
71#2001C2×C311yescharacteristic, complemented
72#1878C2×C311yescharacteristic, complemented
73#1873C2×C311yescharacteristic, complemented
74#1872C2×C311yescharacteristic, complemented
75#1869C2×C311yescharacteristic
76#1865C2×C311yescharacteristic, complemented
77#1854C2×C311yescharacteristic, complemented
78C2×#340C2×C311yescharacteristic, complemented
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4D411yescharacteristic
82C23×C3×C4—21no—
83C23×C3×C4—21no—
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C2×C3×Q16—22no—
87C2×C3×Q16—22no—
88C2×C3×Q16—41no—
89C22×C3×C8—22no—
90C22×C3×C8—22no—
91C22×C3×C8—41no—
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C3×#126—28no—
97C3×#125—28no—
98C3×#125—22no—
99C3×#125—22no—
100C3×#123—28no—
101C3×C22⋊Q8—22no—
102C3×C22⋊Q8—22no—
103C3×C22⋊Q8—22no—
104C3×C22⋊Q8—22no—
105C3×C22⋊Q8—22no—
106C3×C22⋊Q8—22no—
107C3×C22⋊Q8—41no—
108C3×C22⋊Q8D414yes—
109C3×C4×Q8—22no—
110C3×C4×Q8—22no—
111C3×C4×D4—22no—
112C3×C4×D4—22no—
113C3×#117—28no—
114C3×#117—22no—
115C3×#117—22no—
116C2×C3×C4⋊C4—21no—
117C2×C3×C4⋊C4—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—22no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4—21no—
127C2×C3×C4⋊C4—21no—
128C2×C3×C4⋊C4—41no—
129C2×C3×C4⋊C4D411yescharacteristic
130C2×C3×C4⋊C4D414yes—
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C4⋊C4C2311yescharacteristic
136C2×C3×C4⋊C4C2311yescharacteristic
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×#106—22no—
150C3×#106—22no—
151C3×#103—22no—
152C3×#103—22no—
153C3×#103—22no—
154C3×#103—22no—
155C3×#103—22no—
156C3×#103—41no—
157C3×C22⋊C8—22no—
158C3×C22⋊C8—22no—
159C3×C22⋊C8—41no—
160C3×#95—21no—
161C3×#95—21no—
162C3×#95—21no—
163C3×#95—21no—
164C22×Q16C22×C311yescharacteristic
165C23×C8C22×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×C22⋊Q8C22×C311yescharacteristic
175C2×C22⋊Q8C22×C311yescharacteristic
176C2×C4×Q8C22×C311yescharacteristic
177C2×C4×D4C22×C311yescharacteristic
178C2×#117—21no—
179C2×#117C22×C311yescharacteristic
180C22×C4⋊C4C22×C311yescharacteristic
181C22×C4⋊C4C22×C311yescharacteristic
182#483—24no—
183#467—24no—
184C2×#107C22×C311yescharacteristic
185C2×#106C22×C311yescharacteristic
186C2×#106C22×C311yescharacteristic
187C2×#103C22×C311yescharacteristic
188C2×#103C22×C311yescharacteristic
189C2×#103C22×C311yescharacteristic
190C2×#103C22×C311yescharacteristic
191C2×#103C22×C311yescharacteristic
192C2×#103C22×C311yescharacteristic
193C2×C22⋊C8C22×C311yescharacteristic
194C2×C22⋊C8C22×C311yescharacteristic
195C2×C22⋊C8C22×C311yescharacteristic
196#398—21no—
197#396—21no—
198#391C22×C311yescharacteristic
199#389C22×C311yescharacteristic
200#386—21no—
201#380—21no—
202#380C22×C311yescharacteristic
203#340C22×C311yescharacteristic
204#340C22×C311yescharacteristic
205#340C22×C311yescharacteristic
206#340C22×C311yescharacteristic
207#340C22×C311yescharacteristic
208#340C22×C311yescharacteristic
209#336C22×C311yescharacteristic
210#336C22×C311yescharacteristic
211C24×C3C2×D411yescharacteristic
212C24×C3C2×D411yescharacteristic
213C2×C3×Q8—21no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
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×Q8C2×D412yes—
225C2×C3×D4—22no—
226C2×C3×D4—22no—
227C2×C3×D4—22no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—24no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
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—42no—
248C22×C3×C4—42no—
249C22×C3×C4—42no—
250C22×C3×C4—42no—
251C22×C3×C4—81no—
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D412yes—
257C22×C3×C4C2×D412yes—
258C22×C3×C4C2411yescharacteristic
259C3×Q16—44no—
260C2×C3×C8—21no—
261C2×C3×C8—21no—
262C2×C3×C8—21no—
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—44no—
272C2×C3×C8#4112yes—
273C3×C4⋊C4—24no—
274C3×C4⋊C4—24no—
275C3×C4⋊C4—24no—
276C3×C4⋊C4—24no—
277C3×C4⋊C4—24no—
278C3×C4⋊C4—24no—
279C3×C4⋊C4—22no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
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—42no—
289C3×C4⋊C4—42no—
290C3×C4⋊C4—42no—
291C3×C4⋊C4—81no—
292C3×C4⋊C4C2×D412yes—
293C3×C4⋊C4C2×D412yes—
294C3×C4⋊C4C2×D412yes—
295C3×C4⋊C4#4112yes—
296C3×C22⋊C4—24no—
297C3×C22⋊C4—24no—
298C3×C22⋊C4—24no—
299C3×C22⋊C4—22no—
300C3×C22⋊C4—22no—
301C3×C22⋊C4—42no—
302C3×C22⋊C4—42no—
303C3×C22⋊C4—81no—
304C3×C42—24no—
305C3×C42—24no—
306C3×C42—21no—
307C3×C42—21no—
308C22×Q8C23×C311yescharacteristic
309C22×Q8C23×C311yescharacteristic
310C22×D4C3×D411yescharacteristic
311C23×C4—21no—
312C23×C4—21no—
313C23×C4C23×C311yescharacteristic
314C23×C4C23×C311yescharacteristic
315C2×Q16—22no—
316C2×Q16—22no—
317C2×Q16—41no—
318C22×C8—22no—
319C22×C8—22no—
320C22×C8—41no—
321C22×C8C23×C311yescharacteristic
322C22×C8C23×C311yescharacteristic
323C22×C8C23×C311yescharacteristic
324C22×C8C23×C311yescharacteristic
325#126—28no—
326#125—28no—
327#125—22no—
328#125—22no—
329#123—28no—
330C22⋊Q8—22no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335C22⋊Q8—22no—
336C22⋊Q8—41no—
337C22⋊Q8C3×D414yes—
338C4×Q8—22no—
339C4×Q8—22no—
340C4×D4—22no—
341C4×D4—22no—
342#117—28no—
343#117—22no—
344#117—22no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—41no—
358C2×C4⋊C4C3×D411yescharacteristic
359C2×C4⋊C4C3×D414yes—
360C2×C4⋊C4C23×C311yescharacteristic
361C2×C4⋊C4C23×C311yescharacteristic
362C2×C4⋊C4C23×C311yescharacteristic
363C2×C4⋊C4C23×C311yescharacteristic
364C2×C4⋊C4C23×C311yescharacteristic
365C2×C4⋊C4C23×C311yescharacteristic
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4C3×D411yescharacteristic
373C2×C22⋊C4C3×D411yescharacteristic
374C2×C42—21no—
375C2×C42—21no—
376C2×C42C23×C311yescharacteristic
377#107—22no—
378#106—22no—
379#106—22no—
380#103—22no—
381#103—22no—
382#103—22no—
383#103—22no—
384#103—22no—
385#103—41no—
386C22⋊C8—22no—
387C22⋊C8—22no—
388C22⋊C8—41no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3#12012yes—
405C23×C3#13512yes—
406C23×C3#13712yes—
407C23×C3C22×D411yescharacteristic
408C3×Q8—22no—
409C3×Q8—22no—
410C3×Q8—41no—
411C3×Q8—41no—
412C3×Q8—41no—
413C3×Q8—41no—
414C3×Q8—41no—
415C3×Q8—41no—
416C3×D4—44no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—21no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
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—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
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—84no—
462C2×C3×C4#12012yes—
463C2×C3×C4C22×D411yescharacteristic
464C2×C3×C4C22×D411yescharacteristic
465C2×C3×C4C2×#4111yescharacteristic
466C2×C3×C4C2×#4111yescharacteristic
467C2×C3×C4H(5,𝔽2)11yescharacteristic
468C2×C3×C42−1+411yescharacteristic
469C3×C8—22no—
470C3×C8—41no—
471C3×C8—41no—
472C3×C8—41no—
473C24C2×C3×D411yescharacteristic
474C24C2×C3×D411yescharacteristic
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8C2×C3×D412yes—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—24no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—81no—
514C22×C4C2×C3×D411yescharacteristic
515C22×C4C2×C3×D411yescharacteristic
516C22×C4C2×C3×D411yescharacteristic
517C22×C4C2×C3×D411yescharacteristic
518C22×C4C2×C3×D412yes—
519C22×C4C2×C3×D412yes—
520C22×C4C24×C311yescharacteristic
521Q16—44no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—44no—
534C2×C8C3×#4112yes—
535C4⋊C4—24no—
536C4⋊C4—24no—
537C4⋊C4—24no—
538C4⋊C4—24no—
539C4⋊C4—24no—
540C4⋊C4—24no—
541C4⋊C4—22no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4—81no—
554C4⋊C4C2×C3×D412yes—
555C4⋊C4C2×C3×D412yes—
556C4⋊C4C2×C3×D412yes—
557C4⋊C4C3×#4112yes—
558C22⋊C4—24no—
559C22⋊C4—24no—
560C22⋊C4—24no—
561C22⋊C4—22no—
562C22⋊C4—22no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—81no—
566C42—24no—
567C42—24no—
568C42—21no—
569C42—21no—
570C22×C3—22no—
571C22×C3—22no—
572C22×C3—22no—
573C22×C3—22no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—41no—
577C22×C3—41no—
578C22×C3—41no—
579C22×C3—41no—
580C22×C3—41no—
581C22×C3—41no—
582C22×C3—41no—
583C22×C3#45214yes—
584C22×C3C2×#12011yescharacteristic
585C22×C3#54611yescharacteristic
586C22×C3#54711yescharacteristic
587C22×C3C2×#13511yescharacteristic
588C22×C3C2×#13711yescharacteristic
589C22×C3#57711yescharacteristic
590C22×C3#57811yescharacteristic
591C3×C4—22no—
592C3×C4—41no—
593C3×C4—42no—
594C3×C4—41no—
595C3×C4—42no—
596C3×C4—42no—
597C3×C4—41no—
598C3×C4—42no—
599C3×C4—42no—
600C3×C4—81no—
601C3×C4—81no—
602C3×C4—81no—
603C3×C4#53211yescharacteristic
604C3×C4#53711yescharacteristic
605C3×C4#54611yescharacteristic
606C3×C4#54711yescharacteristic
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23C3×#12012yes—
619C23C3×#13512yes—
620C23C3×#13712yes—
621C23C22×C3×D411yescharacteristic
622Q8—22no—
623Q8—22no—
624Q8—41no—
625Q8—41no—
626Q8—41no—
627Q8—41no—
628Q8—41no—
629Q8—41no—
630D4—44no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—48no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
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—84no—
676C2×C4C3×#12012yes—
677C2×C4C22×C3×D411yescharacteristic
678C2×C4C22×C3×D411yescharacteristic
679C2×C4C2×C3×#4111yescharacteristic
680C2×C4C2×C3×#4111yescharacteristic
681C2×C4C3×H(5,𝔽2)11yescharacteristic
682C2×C4C3×2−1+411yescharacteristic
683C8—22no—
684C8—41no—
685C8—41no—
686C8—41no—
687C2×C3—24no—
688C2×C3—81no—
689C2×C3#243011yescharacteristic
690C2×C3C2×#45211yescharacteristic
691C2×C3#301311yescharacteristic
692C2×C3#329611yescharacteristic
693C2×C3#331211yescharacteristic
694C2×C3#333611yescharacteristic
695C2×C3#334411yescharacteristic
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22C3×#45214yes—
710C22C2×C3×#12011yescharacteristic
711C22C3×#54611yescharacteristic
712C22C3×#54711yescharacteristic
713C22C2×C3×#13511yescharacteristic
714C22C2×C3×#13711yescharacteristic
715C22C3×#57711yescharacteristic
716C22C3×#57811yescharacteristic
717C4—22no—
718C4—41no—
719C4—42no—
720C4—41no—
721C4—42no—
722C4—42no—
723C4—41no—
724C4—42no—
725C4—42no—
726C4—81no—
727C4—81no—
728C4—81no—
729C4C3×#53211yescharacteristic
730C4C3×#53711yescharacteristic
731C4C3×#54611yescharacteristic
732C4C3×#54711yescharacteristic
733C3#2554111yescharacteristic, direct product factor, Sylow
734C2—24no—
735C2—81no—
736C2C3×#243011yescharacteristic
737C2C2×C3×#45211yescharacteristic
738C2C3×#301311yescharacteristic
739C2C3×#329611yescharacteristic
740C2C3×#331211yescharacteristic
741C2C3×#333611yescharacteristic
742C2C3×#334411yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×D4D4
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
2. C2×C3×#483C2semidirect
3. C2×C3×#467C2semidirect
5. C3×#2059C2semidirect
6. C3×#2035C2semidirect
7. C3×#2026C2semidirect
8. C3×#2001C2semidirect
9. C3×#1878C2semidirect
10. C3×#1873C2semidirect
11. C3×#1872C2semidirect
13. C3×#1865C2semidirect
14. C3×#1854C2semidirect
15. C2×C3×#340C2semidirect
16. #25541C3direct (N × H)
65. C2×#483C2×C3semidirect
66. C2×#467C2×C3semidirect
68. #2059C2×C3semidirect
69. #2035C2×C3semidirect
70. #2026C2×C3semidirect
71. #2001C2×C3semidirect
72. #1878C2×C3semidirect
73. #1873C2×C3semidirect
74. #1872C2×C3semidirect
76. #1865C2×C3semidirect
77. #1854C2×C3semidirect
78. C2×#340C2×C3semidirect
733. C3#25541direct (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×#4832
C2×C3×#4672
C3×#24172
C3×#20592
C3×#20352
C3×#20262
C3×#20012
C3×#18782
C3×#18732
C3×#18722
C3×#18692
C3×#18652
C3×#18542
C2×C3×#3402
#255413