Finite Group Databasebeta

← C3×#24192 #10642799

Subgroups — C3×#24192 #10642799

Order 768.

1186 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#559C211yesmaximal, characteristic, complemented
2C2×C3×#463C211yesmaximal, characteristic, complemented
3C2×C3×C4×D8C211yesmaximal, characteristic, complemented
4C3×#2580C211yesmaximal, characteristic, complemented
5C3×#2042C211yesmaximal, characteristic, complemented
6C3×#2041C211yesmaximal, characteristic, complemented
7C3×#2012C211yesmaximal, characteristic, complemented
8C3×#2011C211yesmaximal, characteristic
9C3×#1984C211yesmaximal, characteristic, complemented
10C3×#1958C211yesmaximal, characteristic, complemented
11C3×#1880C211yesmaximal, characteristic, complemented
12C3×#1879C211yesmaximal, characteristic, complemented
13C3×#1863C211yesmaximal, characteristic, complemented
14C3×#1862C211yesmaximal, characteristic, complemented
15C3×#1804C211yesmaximal, characteristic, complemented
16#24192C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×D8C2211yescharacteristic
19C22×C3×D8C2211yescharacteristic
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×D4—21no—
31C2×C3×C4×D4C2211yescharacteristic
32C2×C3×C4×D4C2211yescharacteristic
33C2×C3×C4×D4C2211yescharacteristic
34C3×#463—24no—
35C3×C4×D8—24no—
36C2×C3×#107C2211yescharacteristic
37C2×C3×C4⋊C8C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#102C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×#102C2211yescharacteristic
48C2×C3×C4×C8C2211yescharacteristic
49C3×#399—21no—
50C3×#393—21no—
51C3×#390C2211yescharacteristic
52C3×#390C2211yescharacteristic
53C3×#389C2211yescharacteristic
54C3×#389C2211yescharacteristic
55C3×#385—21no—
56C3×#385—21no—
57C3×#382C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#559C2×C311yescharacteristic, complemented
65C2×#463C2×C311yescharacteristic, complemented
66C2×C4×D8C2×C311yescharacteristic, complemented
67#2580C2×C311yescharacteristic, complemented
68#2042C2×C311yescharacteristic, complemented
69#2041C2×C311yescharacteristic, complemented
70#2012C2×C311yescharacteristic, complemented
71#2011C2×C311yescharacteristic
72#1984C2×C311yescharacteristic, complemented
73#1958C2×C311yescharacteristic, complemented
74#1880C2×C311yescharacteristic, complemented
75#1879C2×C311yescharacteristic, complemented
76#1863C2×C311yescharacteristic, complemented
77#1862C2×C311yescharacteristic, complemented
78#1804C2×C311yescharacteristic, complemented
79C22×C3×Q8D411yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4—21no—
82C22×C3×D4—21no—
83C22×C3×D4C2311yescharacteristic
84C22×C3×D4C2311yescharacteristic
85C22×C3×D4C2311yescharacteristic
86C23×C3×C4—21no—
87C23×C3×C4—21no—
88C23×C3×C4—21no—
89C2×C3×SD16—22no—
90C2×C3×SD16—22no—
91C2×C3×SD16—41no—
92C2×C3×D8—22no—
93C2×C3×D8—22no—
94C2×C3×D8—22no—
95C2×C3×D8—22no—
96C2×C3×D8—22no—
97C2×C3×D8—41no—
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C22×C3×C8C2311yescharacteristic
101C22×C3×C8C2311yescharacteristic
102C3×#127—22no—
103C3×#127—22no—
104C3×#124—28no—
105C3×#124—22no—
106C3×#124—22no—
107C3×#124—22no—
108C3×#124D414yes—
109C3×#123—28no—
110C3×#123—28no—
111C3×C4×Q8—22no—
112C3×C4×Q8—22no—
113C3×C4×Q8—22no—
114C3×C4×Q8—22no—
115C3×C4×D4—28no—
116C3×C4×D4—22no—
117C3×C4×D4—22no—
118C3×C4×D4—22no—
119C3×C4×D4—22no—
120C3×C4×D4—22no—
121C3×C4×D4D414yes—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4D411yescharacteristic
126C2×C3×C4⋊C4D411yescharacteristic
127C2×C3×C4⋊C4D411yescharacteristic
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C22⋊C4—21no—
133C2×C3×C22⋊C4—21no—
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×C22⋊C4—21no—
141C2×C3×C22⋊C4—21no—
142C2×C3×C22⋊C4—21no—
143C2×C3×C42—21no—
144C2×C3×C42C2311yescharacteristic
145C2×C3×C42C2311yescharacteristic
146C2×C3×C42C2311yescharacteristic
147C3×#107—22no—
148C3×C4⋊C8—22no—
149C3×#103—22no—
150C3×#103—22no—
151C3×#103—41no—
152C3×#102—22no—
153C3×#102—22no—
154C3×#102—22no—
155C3×#102—22no—
156C3×#102—41no—
157C3×#102—41no—
158C3×#102—41no—
159C3×C4×C8—22no—
160C3×#95—21no—
161C3×#95—21no—
162C3×#95—21no—
163C3×#95—21no—
164C22×SD16C22×C311yescharacteristic
165C22×D8C22×C311yescharacteristic
166C22×D8C22×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×D4—21no—
178C2×C4×D4C22×C311yescharacteristic
179C2×C4×D4C22×C311yescharacteristic
180C2×C4×D4C22×C311yescharacteristic
181#463—24no—
182C4×D8—24no—
183C2×#107C22×C311yescharacteristic
184C2×C4⋊C8C22×C311yescharacteristic
185C2×#103C22×C311yescharacteristic
186C2×#103C22×C311yescharacteristic
187C2×#103C22×C311yescharacteristic
188C2×#102C22×C311yescharacteristic
189C2×#102C22×C311yescharacteristic
190C2×#102C22×C311yescharacteristic
191C2×#102C22×C311yescharacteristic
192C2×#102C22×C311yescharacteristic
193C2×#102C22×C311yescharacteristic
194C2×#102C22×C311yescharacteristic
195C2×C4×C8C22×C311yescharacteristic
196#399—21no—
197#393—21no—
198#390C22×C311yescharacteristic
199#390C22×C311yescharacteristic
200#389C22×C311yescharacteristic
201#389C22×C311yescharacteristic
202#385—21no—
203#385—21no—
204#382C22×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—
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—41no—
222C2×C3×Q8C2×D412yes—
223C2×C3×D4—24no—
224C2×C3×D4—24no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
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×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—
246C2×C3×D4#4112yes—
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—42no—
255C22×C3×C4—81no—
256C22×C3×C4—81no—
257C22×C3×C4—81no—
258C22×C3×C4—81no—
259C22×C3×C4—81no—
260C22×C3×C4—81no—
261C22×C3×C4C2×D411yescharacteristic
262C22×C3×C4C2×D411yescharacteristic
263C22×C3×C4C2×D411yescharacteristic
264C22×C3×C4C2×D411yescharacteristic
265C22×C3×C4C2×D411yescharacteristic
266C22×C3×C4C2×D411yescharacteristic
267C22×C3×C4C2411yescharacteristic
268C3×SD16—44no—
269C3×D8—28no—
270C3×D8—44no—
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—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8#4112yes—
283C3×C4⋊C4—24no—
284C3×C4⋊C4—22no—
285C3×C4⋊C4—22no—
286C3×C4⋊C4—22no—
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—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×C22⋊C4—42no—
304C3×C22⋊C4—42no—
305C3×C22⋊C4—42no—
306C3×C22⋊C4—81no—
307C3×C22⋊C4—81no—
308C3×C42—24no—
309C3×C42—21no—
310C3×C42—21no—
311C3×C42—21no—
312C3×C42—21no—
313C3×C42C2×D412yes—
314C3×C42C2×D412yes—
315C22×Q8C3×D411yescharacteristic
316C22×Q8C23×C311yescharacteristic
317C22×D4—21no—
318C22×D4—21no—
319C22×D4C23×C311yescharacteristic
320C22×D4C23×C311yescharacteristic
321C22×D4C23×C311yescharacteristic
322C23×C4—21no—
323C23×C4—21no—
324C23×C4—21no—
325C2×SD16—22no—
326C2×SD16—22no—
327C2×SD16—41no—
328C2×D8—22no—
329C2×D8—22no—
330C2×D8—22no—
331C2×D8—22no—
332C2×D8—22no—
333C2×D8—41no—
334C22×C8C23×C311yescharacteristic
335C22×C8C23×C311yescharacteristic
336C22×C8C23×C311yescharacteristic
337C22×C8C23×C311yescharacteristic
338#127—22no—
339#127—22no—
340#124—28no—
341#124—22no—
342#124—22no—
343#124—22no—
344#124C3×D414yes—
345#123—28no—
346#123—28no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×Q8—22no—
350C4×Q8—22no—
351C4×D4—28no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4—22no—
355C4×D4—22no—
356C4×D4—22no—
357C4×D4C3×D414yes—
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×C22⋊C4—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—41no—
388#102—22no—
389#102—22no—
390#102—22no—
391#102—22no—
392#102—41no—
393#102—41no—
394#102—41no—
395C4×C8—22no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—22no—
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×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3C22×D411yescharacteristic
422C3×Q8—22no—
423C3×Q8—22no—
424C3×Q8—44no—
425C3×Q8—41no—
426C3×Q8—41no—
427C3×D4—22no—
428C3×D4—22no—
429C3×D4—22no—
430C3×D4—22no—
431C3×D4—22no—
432C3×D4—22no—
433C3×D4—48no—
434C3×D4—41no—
435C3×D4—41no—
436C3×D4—41no—
437C3×D4—41no—
438C3×D4—41no—
439C3×D4—41no—
440C3×D4—84no—
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—22no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—22no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
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—84no—
472C2×C3×C4—84no—
473C2×C3×C4—84no—
474C2×C3×C4#12012yes—
475C2×C3×C4#12012yes—
476C2×C3×C4#13512yes—
477C2×C3×C4C22×D411yescharacteristic
478C2×C3×C4C22×D411yescharacteristic
479C2×C3×C4C2×#4111yescharacteristic
480C2×C3×C4C2×#4111yescharacteristic
481C2×C3×C4H(5,𝔽2)11yescharacteristic
482C2×C3×C42−1+411yescharacteristic
483C3×C8—22no—
484C3×C8—41no—
485C3×C8—41no—
486C3×C8—41no—
487C24—21no—
488C24—21no—
489C24—21no—
490C2×Q8—22no—
491C2×Q8—22no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—41no—
498C2×Q8C2×C3×D412yes—
499C2×D4—24no—
500C2×D4—24no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—81no—
519C2×D4—81no—
520C2×D4C2×C3×D412yes—
521C2×D4C2×C3×D412yes—
522C2×D4C3×#4112yes—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—42no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—81no—
535C22×C4—81no—
536C22×C4—81no—
537C22×C4C2×C3×D411yescharacteristic
538C22×C4C2×C3×D411yescharacteristic
539C22×C4C2×C3×D411yescharacteristic
540C22×C4C2×C3×D411yescharacteristic
541C22×C4C2×C3×D411yescharacteristic
542C22×C4C2×C3×D411yescharacteristic
543C22×C4C24×C311yescharacteristic
544SD16—44no—
545D8—28no—
546D8—44no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8C3×#4112yes—
559C4⋊C4—24no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—81no—
571C4⋊C4—81no—
572C4⋊C4C2×C3×D412yes—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—81no—
583C22⋊C4—81no—
584C42—24no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42C2×C3×D412yes—
590C42C2×C3×D412yes—
591C22×C3—42no—
592C22×C3—42no—
593C22×C3—42no—
594C22×C3—42no—
595C22×C3—42no—
596C22×C3—42no—
597C22×C3—42no—
598C22×C3—42no—
599C22×C3—42no—
600C22×C3—81no—
601C22×C3—81no—
602C22×C3—81no—
603C22×C3—81no—
604C22×C3—81no—
605C22×C3—81no—
606C22×C3—81no—
607C22×C3—81no—
608C22×C3—81no—
609C22×C3—81no—
610C22×C3—81no—
611C22×C3—81no—
612C22×C3C2×#12011yescharacteristic
613C22×C3#54811yescharacteristic
614C22×C3#55011yescharacteristic
615C22×C3C2×#13511yescharacteristic
616C22×C3#57511yescharacteristic
617C22×C3#57611yescharacteristic
618C22×C3#57611yescharacteristic
619C3×C4—22no—
620C3×C4—22no—
621C3×C4—22no—
622C3×C4—42no—
623C3×C4—41no—
624C3×C4—41no—
625C3×C4—41no—
626C3×C4—42no—
627C3×C4—81no—
628C3×C4—81no—
629C3×C4—81no—
630C3×C4#52511yescharacteristic
631C3×C4#53711yescharacteristic
632C3×C4#54611yescharacteristic
633C3×C4#54711yescharacteristic
634C23—22no—
635C23—22no—
636C23—22no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23C22×C3×D411yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—44no—
659Q8—41no—
660Q8—41no—
661D4—22no—
662D4—22no—
663D4—22no—
664D4—22no—
665D4—22no—
666D4—22no—
667D4—48no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—84no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—21no—
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—84no—
706C2×C4—84no—
707C2×C4—84no—
708C2×C4C3×#12012yes—
709C2×C4C3×#12012yes—
710C2×C4C3×#13512yes—
711C2×C4C22×C3×D411yescharacteristic
712C2×C4C22×C3×D411yescharacteristic
713C2×C4C2×C3×#4111yescharacteristic
714C2×C4C2×C3×#4111yescharacteristic
715C2×C4C3×H(5,𝔽2)11yescharacteristic
716C2×C4C3×2−1+411yescharacteristic
717C8—22no—
718C8—41no—
719C8—41no—
720C8—41no—
721C2×C3—82no—
722C2×C3—82no—
723C2×C3—82no—
724C2×C3#240711yescharacteristic
725C2×C3#300211yescharacteristic
726C2×C3#300811yescharacteristic
727C2×C3#336111yescharacteristic
728C2×C3#337011yescharacteristic
729C2×C3#339611yescharacteristic
730C2×C3#340311yescharacteristic
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22C2×C3×#12011yescharacteristic
753C22C3×#54811yescharacteristic
754C22C3×#55011yescharacteristic
755C22C2×C3×#13511yescharacteristic
756C22C3×#57511yescharacteristic
757C22C3×#57611yescharacteristic
758C22C3×#57611yescharacteristic
759C4—22no—
760C4—22no—
761C4—22no—
762C4—42no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4—42no—
767C4—81no—
768C4—81no—
769C4—81no—
770C4C3×#52511yescharacteristic
771C4C3×#53711yescharacteristic
772C4C3×#54611yescharacteristic
773C4C3×#54711yescharacteristic
774C3#2419211yescharacteristic, direct product factor, Sylow
775C2—82no—
776C2—82no—
777C2—82no—
778C2C3×#240711yescharacteristic
779C2C3×#300211yescharacteristic
780C2C3×#300811yescharacteristic
781C2C3×#336111yescharacteristic
782C2C3×#337011yescharacteristic
783C2C3×#339611yescharacteristic
784C2C3×#340311yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#2011C2
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×#559C2semidirect
2. C2×C3×#463C2semidirect
3. C2×C3×C4×D8C2semidirect
4. C3×#2580C2semidirect
5. C3×#2042C2semidirect
6. C3×#2041C2semidirect
7. C3×#2012C2semidirect
9. C3×#1984C2semidirect
10. C3×#1958C2semidirect
11. C3×#1880C2semidirect
12. C3×#1879C2semidirect
13. C3×#1863C2semidirect
14. C3×#1862C2semidirect
15. C3×#1804C2semidirect
16. #24192C3direct (N × H)
64. C2×#559C2×C3semidirect
65. C2×#463C2×C3semidirect
66. C2×C4×D8C2×C3semidirect
67. #2580C2×C3semidirect
68. #2042C2×C3semidirect
69. #2041C2×C3semidirect
70. #2012C2×C3semidirect
72. #1984C2×C3semidirect
73. #1958C2×C3semidirect
74. #1880C2×C3semidirect
75. #1879C2×C3semidirect
76. #1863C2×C3semidirect
77. #1862C2×C3semidirect
78. #1804C2×C3semidirect
774. C3#24192direct (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×#4632
C2×C3×C4×D82
C3×#25802
C3×#20422
C3×#20412
C3×#20122
C3×#20112
C3×#19842
C3×#19582
C3×#18802
C3×#18792
C3×#18632
C3×#18622
C3×#18042
#241923