Finite Group Databasebeta

← C3×#24206 #10642813

Subgroups — C3×#24206 #10642813

Order 768.

1140 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#559C211yesmaximal, characteristic
2C2×C3×#464C211yesmaximal, characteristic, complemented
3C2×C3×#440C211yesmaximal, characteristic, complemented
4C3×#2582C211yesmaximal, characteristic, complemented
5C3×#2042C211yesmaximal, characteristic, complemented
6C3×#2041C211yesmaximal, characteristic
7C3×#2015C211yesmaximal, characteristic, complemented
8C3×#2014C211yesmaximal, characteristic
9C3×#1985C211yesmaximal, characteristic, complemented
10C3×#1959C211yesmaximal, characteristic, complemented
11C3×#1878C211yesmaximal, characteristic, complemented
12C3×#1877C211yesmaximal, characteristic, complemented
13C3×#1863C211yesmaximal, characteristic, complemented
14C3×#1862C211yesmaximal, characteristic, complemented
15C3×#1802C211yesmaximal, characteristic, complemented
16#24206C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×Q16C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C3×#559—24no—
21C3×#559—24no—
22C2×C3×#127C2211yescharacteristic
23C2×C3×#124—21no—
24C2×C3×#124C2211yescharacteristic
25C2×C3×#124C2211yescharacteristic
26C2×C3×#123—21no—
27C2×C3×#123—21no—
28C2×C3×C4×Q8C2211yescharacteristic
29C2×C3×C4×Q8C2211yescharacteristic
30C2×C3×C4×Q8C2211yescharacteristic
31C2×C3×C4×D4—21no—
32C2×C3×C4×D4C2211yescharacteristic
33C2×C3×C4×D4C2211yescharacteristic
34C3×#464—24no—
35C3×#440—24no—
36C2×C3×#107C2211yescharacteristic
37C2×C3×C4⋊C8C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×#102C2211yescharacteristic
48C2×C3×#97C2211yescharacteristic
49C3×#398—21no—
50C3×#398—21no—
51C3×#391—21no—
52C3×#391C2211yescharacteristic
53C3×#391C2211yescharacteristic
54C3×#389—21no—
55C3×#389C2211yescharacteristic
56C3×#389C2211yescharacteristic
57C3×#384C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#559C2×C311yescharacteristic
65C2×#464C2×C311yescharacteristic, complemented
66C2×#440C2×C311yescharacteristic, complemented
67#2582C2×C311yescharacteristic, complemented
68#2042C2×C311yescharacteristic, complemented
69#2041C2×C311yescharacteristic
70#2015C2×C311yescharacteristic, complemented
71#2014C2×C311yescharacteristic
72#1985C2×C311yescharacteristic, complemented
73#1959C2×C311yescharacteristic, complemented
74#1878C2×C311yescharacteristic, complemented
75#1877C2×C311yescharacteristic, complemented
76#1863C2×C311yescharacteristic, complemented
77#1862C2×C311yescharacteristic, complemented
78#1802C2×C311yescharacteristic, complemented
79C22×C3×Q8D411yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×C3×Q8C2311yescharacteristic
82C22×C3×D4—21no—
83C22×C3×D4—21no—
84C22×C3×D4C2311yescharacteristic
85C22×C3×D4C2311yescharacteristic
86C23×C3×C4—21no—
87C23×C3×C4—21no—
88C2×C3×Q16—22no—
89C2×C3×Q16—22no—
90C2×C3×Q16—41no—
91C2×C3×SD16—22no—
92C2×C3×SD16—22no—
93C2×C3×SD16—22no—
94C2×C3×SD16—22no—
95C2×C3×SD16—22no—
96C2×C3×SD16—41no—
97C22×C3×C8C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C22×C3×C8C2311yescharacteristic
101C3×#127—22no—
102C3×#127—22no—
103C3×#124—28no—
104C3×#124—22no—
105C3×#124—22no—
106C3×#124—22no—
107C3×#124D414yes—
108C3×#123—28no—
109C3×#123—28no—
110C3×C4×Q8—22no—
111C3×C4×Q8—22no—
112C3×C4×Q8—22no—
113C3×C4×Q8—22no—
114C3×C4×Q8—22no—
115C3×C4×Q8—22no—
116C3×C4×D4—28no—
117C3×C4×D4—22no—
118C3×C4×D4—22no—
119C3×C4×D4—22no—
120C3×C4×D4D414yes—
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⋊C4D411yescharacteristic
128C2×C3×C4⋊C4D411yescharacteristic
129C2×C3×C4⋊C4D411yescharacteristic
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C22⋊C4—21no—
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×C42—21no—
141C2×C3×C42—21no—
142C2×C3×C42C2311yescharacteristic
143C2×C3×C42C2311yescharacteristic
144C2×C3×C42C2311yescharacteristic
145C3×#107—22no—
146C3×C4⋊C8—22no—
147C3×#103—22no—
148C3×#103—22no—
149C3×#103—22no—
150C3×#103—41no—
151C3×#102—22no—
152C3×#102—22no—
153C3×#102—22no—
154C3×#102—41no—
155C3×#102—41no—
156C3×#102—41no—
157C3×#97—22no—
158C3×#95—21no—
159C3×#95—21no—
160C3×#95—21no—
161C3×#95—21no—
162C3×#95—21no—
163C3×#95—21no—
164C22×Q16C22×C311yescharacteristic
165C22×SD16C22×C311yescharacteristic
166C22×SD16C22×C311yescharacteristic
167#559—24no—
168#559—24no—
169C2×#127C22×C311yescharacteristic
170C2×#124—21no—
171C2×#124C22×C311yescharacteristic
172C2×#124C22×C311yescharacteristic
173C2×#123—21no—
174C2×#123—21no—
175C2×C4×Q8C22×C311yescharacteristic
176C2×C4×Q8C22×C311yescharacteristic
177C2×C4×Q8C22×C311yescharacteristic
178C2×C4×D4—21no—
179C2×C4×D4C22×C311yescharacteristic
180C2×C4×D4C22×C311yescharacteristic
181#464—24no—
182#440—24no—
183C2×#107C22×C311yescharacteristic
184C2×C4⋊C8C22×C311yescharacteristic
185C2×#103C22×C311yescharacteristic
186C2×#103C22×C311yescharacteristic
187C2×#103C22×C311yescharacteristic
188C2×#103C22×C311yescharacteristic
189C2×#102C22×C311yescharacteristic
190C2×#102C22×C311yescharacteristic
191C2×#102C22×C311yescharacteristic
192C2×#102C22×C311yescharacteristic
193C2×#102C22×C311yescharacteristic
194C2×#102C22×C311yescharacteristic
195C2×#97C22×C311yescharacteristic
196#398—21no—
197#398—21no—
198#391—21no—
199#391C22×C311yescharacteristic
200#391C22×C311yescharacteristic
201#389—21no—
202#389C22×C311yescharacteristic
203#389C22×C311yescharacteristic
204#384C22×C311yescharacteristic
205#340C22×C311yescharacteristic
206#340C22×C311yescharacteristic
207#336C22×C311yescharacteristic
208#336C22×C311yescharacteristic
209#336C22×C311yescharacteristic
210#336C22×C311yescharacteristic
211C24×C3—21no—
212C24×C3—21no—
213C2×C3×Q8—22no—
214C2×C3×Q8—22no—
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×Q8—21no—
225C2×C3×Q8—41no—
226C2×C3×Q8C2×D412yes—
227C2×C3×Q8#4112yes—
228C2×C3×D4—24no—
229C2×C3×D4—24no—
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×D4—21no—
240C2×C3×D4—42no—
241C2×C3×D4—42no—
242C2×C3×D4—81no—
243C2×C3×D4—81no—
244C2×C3×D4C2×D412yes—
245C2×C3×D4C2×D412yes—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—24no—
250C22×C3×C4—24no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—81no—
255C22×C3×C4—81no—
256C22×C3×C4—81no—
257C22×C3×C4—81no—
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2×D411yescharacteristic
261C22×C3×C4C2×D411yescharacteristic
262C22×C3×C4C2×D411yescharacteristic
263C22×C3×C4C2×D411yescharacteristic
264C22×C3×C4C2411yescharacteristic
265C3×Q16—44no—
266C3×SD16—28no—
267C3×SD16—44no—
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—21no—
279C2×C3×C8#4112yes—
280C3×C4⋊C4—24no—
281C3×C4⋊C4—22no—
282C3×C4⋊C4—22no—
283C3×C4⋊C4—22no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—42no—
292C3×C4⋊C4—42no—
293C3×C4⋊C4—81no—
294C3×C4⋊C4—81no—
295C3×C4⋊C4—81no—
296C3×C4⋊C4C2×D412yes—
297C3×C22⋊C4—24no—
298C3×C22⋊C4—24no—
299C3×C22⋊C4—24no—
300C3×C22⋊C4—24no—
301C3×C22⋊C4—24no—
302C3×C22⋊C4—24no—
303C3×C42—24no—
304C3×C42—21no—
305C3×C42—21no—
306C3×C42—21no—
307C3×C42—21no—
308C3×C42—42no—
309C3×C42C2×D412yes—
310C3×C42C2×D412yes—
311C22×Q8C3×D411yescharacteristic
312C22×Q8C23×C311yescharacteristic
313C22×Q8C23×C311yescharacteristic
314C22×D4—21no—
315C22×D4—21no—
316C22×D4C23×C311yescharacteristic
317C22×D4C23×C311yescharacteristic
318C23×C4—21no—
319C23×C4—21no—
320C2×Q16—22no—
321C2×Q16—22no—
322C2×Q16—41no—
323C2×SD16—22no—
324C2×SD16—22no—
325C2×SD16—22no—
326C2×SD16—22no—
327C2×SD16—22no—
328C2×SD16—41no—
329C22×C8C23×C311yescharacteristic
330C22×C8C23×C311yescharacteristic
331C22×C8C23×C311yescharacteristic
332C22×C8C23×C311yescharacteristic
333#127—22no—
334#127—22no—
335#124—28no—
336#124—22no—
337#124—22no—
338#124—22no—
339#124C3×D414yes—
340#123—28no—
341#123—28no—
342C4×Q8—22no—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×Q8—22no—
346C4×Q8—22no—
347C4×Q8—22no—
348C4×D4—28no—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4—22no—
352C4×D4C3×D414yes—
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⋊C4C3×D411yescharacteristic
360C2×C4⋊C4C3×D411yescharacteristic
361C2×C4⋊C4C3×D411yescharacteristic
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×C42—21no—
373C2×C42—21no—
374C2×C42C23×C311yescharacteristic
375C2×C42C23×C311yescharacteristic
376C2×C42C23×C311yescharacteristic
377#107—22no—
378C4⋊C8—22no—
379#103—22no—
380#103—22no—
381#103—22no—
382#103—41no—
383#102—22no—
384#102—22no—
385#102—22no—
386#102—41no—
387#102—41no—
388#102—41no—
389#97—22no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—41no—
399C23×C3—41no—
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×C3C22×D411yescharacteristic
411C3×Q8—22no—
412C3×Q8—22no—
413C3×Q8—22no—
414C3×Q8—22no—
415C3×Q8—44no—
416C3×Q8—41no—
417C3×Q8—41no—
418C3×Q8—41no—
419C3×Q8—41no—
420C3×D4—22no—
421C3×D4—22no—
422C3×D4—22no—
423C3×D4—22no—
424C3×D4—48no—
425C3×D4—41no—
426C3×D4—41no—
427C3×D4—41no—
428C3×D4—41no—
429C3×D4—84no—
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—22no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—22no—
440C2×C3×C4—21no—
441C2×C3×C4—22no—
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—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—84no—
464C2×C3×C4—84no—
465C2×C3×C4#12012yes—
466C2×C3×C4#12012yes—
467C2×C3×C4#13712yes—
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×Q8C3×#4112yes—
495C2×D4—24no—
496C2×D4—24no—
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×D4—21no—
506C2×D4—21no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—81no—
510C2×D4—81no—
511C2×D4C2×C3×D412yes—
512C2×D4C2×C3×D412yes—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—81no—
522C22×C4—81no—
523C22×C4—81no—
524C22×C4—81no—
525C22×C4C2×C3×D411yescharacteristic
526C22×C4C2×C3×D411yescharacteristic
527C22×C4C2×C3×D411yescharacteristic
528C22×C4C2×C3×D411yescharacteristic
529C22×C4C2×C3×D411yescharacteristic
530C22×C4C2×C3×D411yescharacteristic
531C22×C4C24×C311yescharacteristic
532Q16—44no—
533SD16—28no—
534SD16—44no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8C3×#4112yes—
547C4⋊C4—24no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—42no—
559C4⋊C4—42no—
560C4⋊C4—81no—
561C4⋊C4—81no—
562C4⋊C4—81no—
563C4⋊C4C2×C3×D412yes—
564C22⋊C4—24no—
565C22⋊C4—24no—
566C22⋊C4—24no—
567C22⋊C4—24no—
568C22⋊C4—24no—
569C22⋊C4—24no—
570C42—24no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—42no—
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×#13711yescharacteristic
596C22×C3#57511yescharacteristic
597C22×C3#57611yescharacteristic
598C22×C3#57711yescharacteristic
599C3×C4—22no—
600C3×C4—22no—
601C3×C4—22no—
602C3×C4—42no—
603C3×C4—42no—
604C3×C4—41no—
605C3×C4—41no—
606C3×C4—41no—
607C3×C4—42no—
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—48no—
644D4—41no—
645D4—41no—
646D4—41no—
647D4—41no—
648D4—84no—
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—21no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—22no—
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—41no—
682C2×C4—84no—
683C2×C4—84no—
684C2×C4C3×#12012yes—
685C2×C4C3×#12012yes—
686C2×C4C3×#13712yes—
687C2×C4C22×C3×D411yescharacteristic
688C2×C4C22×C3×D411yescharacteristic
689C2×C4C2×C3×#4111yescharacteristic
690C2×C4C2×C3×#4111yescharacteristic
691C2×C4C3×H(5,𝔽2)11yescharacteristic
692C2×C4C3×2−1+411yescharacteristic
693C8—22no—
694C8—41no—
695C8—41no—
696C8—41no—
697C2×C3—82no—
698C2×C3—82no—
699C2×C3#240711yescharacteristic
700C2×C3#300711yescharacteristic
701C2×C3#301211yescharacteristic
702C2×C3#337111yescharacteristic
703C2×C3#337511yescharacteristic
704C2×C3#340011yescharacteristic
705C2×C3#340311yescharacteristic
706C22—42no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22C2×C3×#12011yescharacteristic
721C22C3×#54811yescharacteristic
722C22C3×#55011yescharacteristic
723C22C2×C3×#13711yescharacteristic
724C22C3×#57511yescharacteristic
725C22C3×#57611yescharacteristic
726C22C3×#57711yescharacteristic
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—42no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—42no—
736C4—81no—
737C4—81no—
738C4—81no—
739C4C3×#52511yescharacteristic
740C4C3×#53711yescharacteristic
741C4C3×#54611yescharacteristic
742C4C3×#54711yescharacteristic
743C3#2420611yescharacteristic, direct product factor, Sylow
744C2—82no—
745C2—82no—
746C2C3×#240711yescharacteristic
747C2C3×#300711yescharacteristic
748C2C3×#301211yescharacteristic
749C2C3×#337111yescharacteristic
750C2C3×#337511yescharacteristic
751C2C3×#340011yescharacteristic
752C2C3×#340311yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#127C22
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
2. C2×C3×#464C2semidirect
3. C2×C3×#440C2semidirect
4. C3×#2582C2semidirect
5. C3×#2042C2semidirect
7. C3×#2015C2semidirect
9. C3×#1985C2semidirect
10. C3×#1959C2semidirect
11. C3×#1878C2semidirect
12. C3×#1877C2semidirect
13. C3×#1863C2semidirect
14. C3×#1862C2semidirect
15. C3×#1802C2semidirect
16. #24206C3direct (N × H)
65. C2×#464C2×C3semidirect
66. C2×#440C2×C3semidirect
67. #2582C2×C3semidirect
68. #2042C2×C3semidirect
70. #2015C2×C3semidirect
72. #1985C2×C3semidirect
73. #1959C2×C3semidirect
74. #1878C2×C3semidirect
75. #1877C2×C3semidirect
76. #1863C2×C3semidirect
77. #1862C2×C3semidirect
78. #1802C2×C3semidirect
743. C3#24206direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5592
C2×C3×#4642
C2×C3×#4402
C3×#25822
C3×#20422
C3×#20412
C3×#20152
C3×#20142
C3×#19852
C3×#19592
C3×#18782
C3×#18772
C3×#18632
C3×#18622
C3×#18022
#242063