Finite Group Databasebeta

← C3×#24194 #10642801

Subgroups — C3×#24194 #10642801

Order 768.

1138 conjugacy classes of subgroups.

The subgroup lattice has 750 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×C4×SD16C211yesmaximal, characteristic, complemented
4C3×#2581C211yesmaximal, characteristic, complemented
5C3×#2042C211yesmaximal, characteristic, complemented
6C3×#2041C211yesmaximal, characteristic
7C3×#2015C211yesmaximal, characteristic, complemented
8C3×#2014C211yesmaximal, characteristic
9C3×#1984C211yesmaximal, characteristic, complemented
10C3×#1958C211yesmaximal, characteristic, complemented
11C3×#1878C211yesmaximal, characteristic, complemented
12C3×#1877C211yesmaximal, characteristic, complemented
13C3×#1865C211yesmaximal, characteristic, complemented
14C3×#1864C211yesmaximal, characteristic, complemented
15C3×#1804C211yesmaximal, characteristic, complemented
16#24194C311yesmaximal, 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×C4×SD16—24no—
36C2×C3×#106C2211yescharacteristic
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×C4×C8C2211yescharacteristic
49C3×#400—21no—
50C3×#395—21no—
51C3×#391C2211yescharacteristic
52C3×#391C2211yescharacteristic
53C3×#389C2211yescharacteristic
54C3×#389C2211yescharacteristic
55C3×#387—21no—
56C3×#387—21no—
57C3×#382C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#559C2×C311yescharacteristic
65C2×#464C2×C311yescharacteristic, complemented
66C2×C4×SD16C2×C311yescharacteristic, complemented
67#2581C2×C311yescharacteristic, complemented
68#2042C2×C311yescharacteristic, complemented
69#2041C2×C311yescharacteristic
70#2015C2×C311yescharacteristic, complemented
71#2014C2×C311yescharacteristic
72#1984C2×C311yescharacteristic, complemented
73#1958C2×C311yescharacteristic, complemented
74#1878C2×C311yescharacteristic, complemented
75#1877C2×C311yescharacteristic, complemented
76#1865C2×C311yescharacteristic, complemented
77#1864C2×C311yescharacteristic, complemented
78#1804C2×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⋊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×C42—21no—
139C2×C3×C42—21no—
140C2×C3×C42C2311yescharacteristic
141C2×C3×C42C2311yescharacteristic
142C2×C3×C42C2311yescharacteristic
143C3×#106—22no—
144C3×C4⋊C8—22no—
145C3×#103—22no—
146C3×#103—22no—
147C3×#103—22no—
148C3×#103—41no—
149C3×#102—22no—
150C3×#102—22no—
151C3×#102—22no—
152C3×#102—41no—
153C3×#102—41no—
154C3×#102—41no—
155C3×C4×C8—22no—
156C3×#95—21no—
157C3×#95—21no—
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—
182C4×SD16—24no—
183C2×#106C22×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×C4×C8C22×C311yescharacteristic
196#400—21no—
197#395—21no—
198#391C22×C311yescharacteristic
199#391C22×C311yescharacteristic
200#389C22×C311yescharacteristic
201#389C22×C311yescharacteristic
202#387—21no—
203#387—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—
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—42no—
294C3×C4⋊C4C2×D412yes—
295C3×C22⋊C4—24no—
296C3×C22⋊C4—24no—
297C3×C22⋊C4—24no—
298C3×C22⋊C4—24no—
299C3×C22⋊C4—24no—
300C3×C22⋊C4—24no—
301C3×C42—24no—
302C3×C42—21no—
303C3×C42—21no—
304C3×C42—21no—
305C3×C42—21no—
306C3×C42—42no—
307C3×C42C2×D412yes—
308C3×C42C2×D412yes—
309C22×Q8C3×D411yescharacteristic
310C22×Q8C23×C311yescharacteristic
311C22×Q8C23×C311yescharacteristic
312C22×D4—21no—
313C22×D4—21no—
314C22×D4C23×C311yescharacteristic
315C22×D4C23×C311yescharacteristic
316C23×C4—21no—
317C23×C4—21no—
318C2×Q16—22no—
319C2×Q16—22no—
320C2×Q16—41no—
321C2×SD16—22no—
322C2×SD16—22no—
323C2×SD16—22no—
324C2×SD16—22no—
325C2×SD16—22no—
326C2×SD16—41no—
327C22×C8C23×C311yescharacteristic
328C22×C8C23×C311yescharacteristic
329C22×C8C23×C311yescharacteristic
330C22×C8C23×C311yescharacteristic
331#127—22no—
332#127—22no—
333#124—28no—
334#124—22no—
335#124—22no—
336#124—22no—
337#124C3×D414yes—
338#123—28no—
339#123—28no—
340C4×Q8—22no—
341C4×Q8—22no—
342C4×Q8—22no—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×Q8—22no—
346C4×D4—28no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—22no—
350C4×D4C3×D414yes—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4C3×D411yescharacteristic
356C2×C4⋊C4C3×D411yescharacteristic
357C2×C4⋊C4C3×D411yescharacteristic
358C2×C4⋊C4C23×C311yescharacteristic
359C2×C4⋊C4C23×C311yescharacteristic
360C2×C4⋊C4C23×C311yescharacteristic
361C2×C4⋊C4C23×C311yescharacteristic
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42C23×C311yescharacteristic
371C2×C42C23×C311yescharacteristic
372C2×C42C23×C311yescharacteristic
373#106—22no—
374C4⋊C8—22no—
375#103—22no—
376#103—22no—
377#103—22no—
378#103—41no—
379#102—22no—
380#102—22no—
381#102—22no—
382#102—41no—
383#102—41no—
384#102—41no—
385C4×C8—22no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—41no—
397C23×C3—41no—
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×C3C22×D411yescharacteristic
409C3×Q8—22no—
410C3×Q8—22no—
411C3×Q8—22no—
412C3×Q8—22no—
413C3×Q8—44no—
414C3×Q8—41no—
415C3×Q8—41no—
416C3×Q8—41no—
417C3×Q8—41no—
418C3×D4—22no—
419C3×D4—22no—
420C3×D4—22no—
421C3×D4—22no—
422C3×D4—48no—
423C3×D4—41no—
424C3×D4—41no—
425C3×D4—41no—
426C3×D4—41no—
427C3×D4—84no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—22no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—22no—
438C2×C3×C4—21no—
439C2×C3×C4—22no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
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—84no—
463C2×C3×C4#12012yes—
464C2×C3×C4#12012yes—
465C2×C3×C4#13512yes—
466C2×C3×C4C22×D411yescharacteristic
467C2×C3×C4C22×D411yescharacteristic
468C2×C3×C4C2×#4111yescharacteristic
469C2×C3×C4C2×#4111yescharacteristic
470C2×C3×C4H(5,𝔽2)11yescharacteristic
471C2×C3×C42−1+411yescharacteristic
472C3×C8—22no—
473C3×C8—41no—
474C3×C8—41no—
475C3×C8—41no—
476C24—21no—
477C24—21no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—21no—
481C2×Q8—21no—
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—41no—
491C2×Q8C2×C3×D412yes—
492C2×Q8C3×#4112yes—
493C2×D4—24no—
494C2×D4—24no—
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×D4—42no—
506C2×D4—42no—
507C2×D4—81no—
508C2×D4—81no—
509C2×D4C2×C3×D412yes—
510C2×D4C2×C3×D412yes—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—81no—
520C22×C4—81no—
521C22×C4—81no—
522C22×C4—81no—
523C22×C4C2×C3×D411yescharacteristic
524C22×C4C2×C3×D411yescharacteristic
525C22×C4C2×C3×D411yescharacteristic
526C22×C4C2×C3×D411yescharacteristic
527C22×C4C2×C3×D411yescharacteristic
528C22×C4C2×C3×D411yescharacteristic
529C22×C4C24×C311yescharacteristic
530Q16—44no—
531SD16—28no—
532SD16—44no—
533C2×C8—21no—
534C2×C8—21no—
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×C8C3×#4112yes—
545C4⋊C4—24no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4C2×C3×D412yes—
560C22⋊C4—24no—
561C22⋊C4—24no—
562C22⋊C4—24no—
563C22⋊C4—24no—
564C22⋊C4—24no—
565C22⋊C4—24no—
566C42—24no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—42no—
572C42C2×C3×D412yes—
573C42C2×C3×D412yes—
574C22×C3—42no—
575C22×C3—42no—
576C22×C3—42no—
577C22×C3—42no—
578C22×C3—42no—
579C22×C3—42no—
580C22×C3—81no—
581C22×C3—81no—
582C22×C3—81no—
583C22×C3—81no—
584C22×C3—81no—
585C22×C3—81no—
586C22×C3—81no—
587C22×C3—81no—
588C22×C3C2×#12011yescharacteristic
589C22×C3#54811yescharacteristic
590C22×C3#55011yescharacteristic
591C22×C3C2×#13511yescharacteristic
592C22×C3#57511yescharacteristic
593C22×C3#57711yescharacteristic
594C22×C3#57711yescharacteristic
595C3×C4—22no—
596C3×C4—22no—
597C3×C4—22no—
598C3×C4—42no—
599C3×C4—42no—
600C3×C4—41no—
601C3×C4—41no—
602C3×C4—41no—
603C3×C4—42no—
604C3×C4—81no—
605C3×C4—81no—
606C3×C4—81no—
607C3×C4#52511yescharacteristic
608C3×C4#53711yescharacteristic
609C3×C4#54611yescharacteristic
610C3×C4#54711yescharacteristic
611C23—22no—
612C23—22no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23C22×C3×D411yescharacteristic
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—44no—
631Q8—41no—
632Q8—41no—
633Q8—41no—
634Q8—41no—
635D4—22no—
636D4—22no—
637D4—22no—
638D4—22no—
639D4—48no—
640D4—41no—
641D4—41no—
642D4—41no—
643D4—41no—
644D4—84no—
645C2×C4—21no—
646C2×C4—21no—
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—22no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—22no—
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—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—84no—
679C2×C4—84no—
680C2×C4C3×#12012yes—
681C2×C4C3×#12012yes—
682C2×C4C3×#13512yes—
683C2×C4C22×C3×D411yescharacteristic
684C2×C4C22×C3×D411yescharacteristic
685C2×C4C2×C3×#4111yescharacteristic
686C2×C4C2×C3×#4111yescharacteristic
687C2×C4C3×H(5,𝔽2)11yescharacteristic
688C2×C4C3×2−1+411yescharacteristic
689C8—22no—
690C8—41no—
691C8—41no—
692C8—41no—
693C2×C3—82no—
694C2×C3—82no—
695C2×C3#240711yescharacteristic
696C2×C3#300211yescharacteristic
697C2×C3#300911yescharacteristic
698C2×C3#336511yescharacteristic
699C2×C3#337111yescharacteristic
700C2×C3#339411yescharacteristic
701C2×C3#340111yescharacteristic
702C22—42no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22C2×C3×#12011yescharacteristic
717C22C3×#54811yescharacteristic
718C22C3×#55011yescharacteristic
719C22C2×C3×#13511yescharacteristic
720C22C3×#57511yescharacteristic
721C22C3×#57711yescharacteristic
722C22C3×#57711yescharacteristic
723C4—22no—
724C4—22no—
725C4—22no—
726C4—42no—
727C4—42no—
728C4—41no—
729C4—41no—
730C4—41no—
731C4—42no—
732C4—81no—
733C4—81no—
734C4—81no—
735C4C3×#52511yescharacteristic
736C4C3×#53711yescharacteristic
737C4C3×#54611yescharacteristic
738C4C3×#54711yescharacteristic
739C3#2419411yescharacteristic, direct product factor, Sylow
740C2—82no—
741C2—82no—
742C2C3×#240711yescharacteristic
743C2C3×#300211yescharacteristic
744C2C3×#300911yescharacteristic
745C2C3×#336511yescharacteristic
746C2C3×#337111yescharacteristic
747C2C3×#339411yescharacteristic
748C2C3×#340111yescharacteristic
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×C4×SD16C2semidirect
4. C3×#2581C2semidirect
5. C3×#2042C2semidirect
7. C3×#2015C2semidirect
9. C3×#1984C2semidirect
10. C3×#1958C2semidirect
11. C3×#1878C2semidirect
12. C3×#1877C2semidirect
13. C3×#1865C2semidirect
14. C3×#1864C2semidirect
15. C3×#1804C2semidirect
16. #24194C3direct (N × H)
65. C2×#464C2×C3semidirect
66. C2×C4×SD16C2×C3semidirect
67. #2581C2×C3semidirect
68. #2042C2×C3semidirect
70. #2015C2×C3semidirect
72. #1984C2×C3semidirect
73. #1958C2×C3semidirect
74. #1878C2×C3semidirect
75. #1877C2×C3semidirect
76. #1865C2×C3semidirect
77. #1864C2×C3semidirect
78. #1804C2×C3semidirect
739. C3#24194direct (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×C4×SD162
C3×#25812
C3×#20422
C3×#20412
C3×#20152
C3×#20142
C3×#19842
C3×#19582
C3×#18782
C3×#18772
C3×#18652
C3×#18642
C3×#18042
#241943