Finite Group Databasebeta

← C3×#24193 #10642800

Subgroups — C3×#24193 #10642800

Order 768.

1122 conjugacy classes of subgroups.

The subgroup lattice has 746 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×C4×SD16C211yesmaximal, characteristic, complemented
4C3×#2580C211yesmaximal, characteristic, complemented
5C3×#2043C211yesmaximal, characteristic, complemented
6C3×#2042C211yesmaximal, characteristic, complemented
7C3×#2013C211yesmaximal, characteristic, complemented
8C3×#2012C211yesmaximal, characteristic
9C3×#1984C211yesmaximal, characteristic, complemented
10C3×#1958C211yesmaximal, characteristic, complemented
11C3×#1880C211yesmaximal, characteristic, complemented
12C3×#1879C211yesmaximal, characteristic
13C3×#1865C211yesmaximal, characteristic, complemented
14C3×#1864C211yesmaximal, characteristic, complemented
15C3×#1805C211yesmaximal, characteristic, complemented
16#24193C311yesmaximal, 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×C4×Q8C2211yescharacteristic
29C2×C3×C4×Q8C2211yescharacteristic
30C2×C3×C4×Q8C2211yescharacteristic
31C2×C3×C4×D4C2211yescharacteristic
32C2×C3×C4×D4C2211yescharacteristic
33C2×C3×#117—21no—
34C3×#463—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×#103C2211yescharacteristic
43C2×C3×#103C2211yescharacteristic
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×#556C2×C311yescharacteristic, complemented
65C2×#463C2×C311yescharacteristic
66C2×C4×SD16C2×C311yescharacteristic, complemented
67#2580C2×C311yescharacteristic, complemented
68#2043C2×C311yescharacteristic, complemented
69#2042C2×C311yescharacteristic, complemented
70#2013C2×C311yescharacteristic, complemented
71#2012C2×C311yescharacteristic
72#1984C2×C311yescharacteristic, complemented
73#1958C2×C311yescharacteristic, complemented
74#1880C2×C311yescharacteristic, complemented
75#1879C2×C311yescharacteristic
76#1865C2×C311yescharacteristic, complemented
77#1864C2×C311yescharacteristic, complemented
78#1805C2×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×C4×Q8—22no—
109C3×C4×Q8—22no—
110C3×C4×Q8—22no—
111C3×C4×Q8—22no—
112C3×C4×Q8—22no—
113C3×C4×Q8D414yes—
114C3×C4×D4—22no—
115C3×C4×D4—22no—
116C3×C4×D4—22no—
117C3×C4×D4—22no—
118C3×#117—28no—
119C2×C3×C4⋊C4—21no—
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⋊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×C42—21no—
143C2×C3×C42—21no—
144C2×C3×C42C2311yescharacteristic
145C2×C3×C42C2311yescharacteristic
146C2×C3×C42C2311yescharacteristic
147C3×#106—22no—
148C3×C4⋊C8—22no—
149C3×#103—22no—
150C3×#103—22no—
151C3×#103—22no—
152C3×#103—41no—
153C3×#103—41no—
154C3×#103—41no—
155C3×#102—22no—
156C3×#102—22no—
157C3×#102—22no—
158C3×#102—41no—
159C3×C4×C8—22no—
160C3×#95—21no—
161C3×#95—21no—
162C3×#95—21no—
163C3×#95—21no—
164C22×SD16C22×C311yescharacteristic
165C22×SD16C22×C311yescharacteristic
166C22×D8C22×C311yescharacteristic
167#556—24no—
168#556—24no—
169C2×C4⋊Q8C22×C311yescharacteristic
170C2×#126—21no—
171C2×#126—21no—
172C2×#124C22×C311yescharacteristic
173C2×#124C22×C311yescharacteristic
174C2×C22⋊Q8—21no—
175C2×C4×Q8C22×C311yescharacteristic
176C2×C4×Q8C22×C311yescharacteristic
177C2×C4×Q8C22×C311yescharacteristic
178C2×C4×D4C22×C311yescharacteristic
179C2×C4×D4C22×C311yescharacteristic
180C2×#117—21no—
181#463—24no—
182C4×SD16—24no—
183C2×#106C22×C311yescharacteristic
184C2×C4⋊C8C22×C311yescharacteristic
185C2×#103C22×C311yescharacteristic
186C2×#103C22×C311yescharacteristic
187C2×#103C22×C311yescharacteristic
188C2×#103C22×C311yescharacteristic
189C2×#103C22×C311yescharacteristic
190C2×#103C22×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—
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×Q8C2×D412yes—
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×D4C2×D412yes—
239C2×C3×D4#4112yes—
240C22×C3×C4—24no—
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—81no—
251C22×C3×C4—81no—
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2411yescharacteristic
259C3×SD16—28no—
260C3×SD16—44no—
261C3×D8—44no—
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—21no—
272C2×C3×C8—21no—
273C2×C3×C8#4112yes—
274C3×C4⋊C4—24no—
275C3×C4⋊C4—24no—
276C3×C4⋊C4—24no—
277C3×C4⋊C4—24no—
278C3×C4⋊C4—22no—
279C3×C4⋊C4—22no—
280C3×C4⋊C4—22no—
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—81no—
289C3×C4⋊C4—81no—
290C3×C4⋊C4C2×D412yes—
291C3×C22⋊C4—24no—
292C3×C22⋊C4—24no—
293C3×C22⋊C4—24no—
294C3×C22⋊C4—24no—
295C3×C22⋊C4—24no—
296C3×C22⋊C4—42no—
297C3×C22⋊C4—42no—
298C3×C22⋊C4—42no—
299C3×C22⋊C4—81no—
300C3×C22⋊C4—81no—
301C3×C42—24no—
302C3×C42—24no—
303C3×C42—21no—
304C3×C42—21no—
305C3×C42—21no—
306C3×C42—21no—
307C3×C42C2×D412yes—
308C3×C42C2×D412yes—
309C22×Q8C3×D411yescharacteristic
310C22×Q8C23×C311yescharacteristic
311C22×Q8C23×C311yescharacteristic
312C22×D4C23×C311yescharacteristic
313C22×D4C23×C311yescharacteristic
314C23×C4—21no—
315C23×C4—21no—
316C2×SD16—22no—
317C2×SD16—22no—
318C2×SD16—22no—
319C2×SD16—22no—
320C2×SD16—22no—
321C2×SD16—41no—
322C2×D8—22no—
323C2×D8—22no—
324C2×D8—41no—
325C22×C8C23×C311yescharacteristic
326C22×C8C23×C311yescharacteristic
327C22×C8C23×C311yescharacteristic
328C22×C8C23×C311yescharacteristic
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331#126—28no—
332#126—28no—
333#124—22no—
334#124—22no—
335#124—22no—
336#124C3×D414yes—
337C22⋊Q8—28no—
338C4×Q8—22no—
339C4×Q8—22no—
340C4×Q8—22no—
341C4×Q8—22no—
342C4×Q8—22no—
343C4×Q8C3×D414yes—
344C4×D4—22no—
345C4×D4—22no—
346C4×D4—22no—
347C4×D4—22no—
348#117—28no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
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×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#106—22no—
378C4⋊C8—22no—
379#103—22no—
380#103—22no—
381#103—22no—
382#103—41no—
383#103—41no—
384#103—41no—
385#102—22no—
386#102—22no—
387#102—22no—
388#102—41no—
389C4×C8—22no—
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—41no—
423C3×D4—41no—
424C3×D4—41no—
425C3×D4—41no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—22no—
434C2×C3×C4—21no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—48no—
445C2×C3×C4—41no—
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—84no—
461C2×C3×C4#12012yes—
462C2×C3×C4#12012yes—
463C2×C3×C4#13512yes—
464C2×C3×C4C22×D411yescharacteristic
465C2×C3×C4C22×D411yescharacteristic
466C2×C3×C4C2×#4111yescharacteristic
467C2×C3×C4C2×#4111yescharacteristic
468C2×C3×C4H(5,𝔽2)11yescharacteristic
469C2×C3×C42−1+411yescharacteristic
470C3×C8—22no—
471C3×C8—41no—
472C3×C8—41no—
473C3×C8—41no—
474C24—21no—
475C24—21no—
476C2×Q8—22no—
477C2×Q8—22no—
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×Q8—21no—
487C2×Q8—21no—
488C2×Q8—41no—
489C2×Q8C2×C3×D412yes—
490C2×Q8C2×C3×D412yes—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4C2×C3×D412yes—
502C2×D4C3×#4112yes—
503C22×C4—24no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—81no—
514C22×C4—81no—
515C22×C4C2×C3×D411yescharacteristic
516C22×C4C2×C3×D411yescharacteristic
517C22×C4C2×C3×D411yescharacteristic
518C22×C4C2×C3×D411yescharacteristic
519C22×C4C2×C3×D411yescharacteristic
520C22×C4C2×C3×D411yescharacteristic
521C22×C4C24×C311yescharacteristic
522SD16—28no—
523SD16—44no—
524D8—44no—
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—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8C3×#4112yes—
537C4⋊C4—24no—
538C4⋊C4—24no—
539C4⋊C4—24no—
540C4⋊C4—24no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—81no—
552C4⋊C4—81no—
553C4⋊C4C2×C3×D412yes—
554C22⋊C4—24no—
555C22⋊C4—24no—
556C22⋊C4—24no—
557C22⋊C4—24no—
558C22⋊C4—24no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—81no—
563C22⋊C4—81no—
564C42—24no—
565C42—24no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42C2×C3×D412yes—
571C42C2×C3×D412yes—
572C22×C3—42no—
573C22×C3—42no—
574C22×C3—42no—
575C22×C3—42no—
576C22×C3—42no—
577C22×C3—42no—
578C22×C3—81no—
579C22×C3—81no—
580C22×C3—81no—
581C22×C3—81no—
582C22×C3—81no—
583C22×C3—81no—
584C22×C3—81no—
585C22×C3—81no—
586C22×C3C2×#12011yescharacteristic
587C22×C3#54811yescharacteristic
588C22×C3#55011yescharacteristic
589C22×C3C2×#13511yescharacteristic
590C22×C3#57511yescharacteristic
591C22×C3#57711yescharacteristic
592C22×C3#57711yescharacteristic
593C3×C4—22no—
594C3×C4—22no—
595C3×C4—22no—
596C3×C4—42no—
597C3×C4—42no—
598C3×C4—41no—
599C3×C4—42no—
600C3×C4—41no—
601C3×C4—41no—
602C3×C4—81no—
603C3×C4—81no—
604C3×C4—81no—
605C3×C4#52511yescharacteristic
606C3×C4#53711yescharacteristic
607C3×C4#54611yescharacteristic
608C3×C4#54711yescharacteristic
609C23—22no—
610C23—22no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23C22×C3×D411yescharacteristic
624Q8—22no—
625Q8—22no—
626Q8—22no—
627Q8—22no—
628Q8—44no—
629Q8—41no—
630Q8—41no—
631Q8—41no—
632Q8—41no—
633D4—22no—
634D4—22no—
635D4—22no—
636D4—22no—
637D4—41no—
638D4—41no—
639D4—41no—
640D4—41no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
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—22no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—21no—
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×C4C3×#12012yes—
678C2×C4C3×#13512yes—
679C2×C4C22×C3×D411yescharacteristic
680C2×C4C22×C3×D411yescharacteristic
681C2×C4C2×C3×#4111yescharacteristic
682C2×C4C2×C3×#4111yescharacteristic
683C2×C4C3×H(5,𝔽2)11yescharacteristic
684C2×C4C3×2−1+411yescharacteristic
685C8—22no—
686C8—41no—
687C8—41no—
688C8—41no—
689C2×C3—82no—
690C2×C3—82no—
691C2×C3#240711yescharacteristic
692C2×C3#300211yescharacteristic
693C2×C3#301011yescharacteristic
694C2×C3#336011yescharacteristic
695C2×C3#337611yescharacteristic
696C2×C3#339411yescharacteristic
697C2×C3#340111yescharacteristic
698C22—42no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22C2×C3×#12011yescharacteristic
713C22C3×#54811yescharacteristic
714C22C3×#55011yescharacteristic
715C22C2×C3×#13511yescharacteristic
716C22C3×#57511yescharacteristic
717C22C3×#57711yescharacteristic
718C22C3×#57711yescharacteristic
719C4—22no—
720C4—22no—
721C4—22no—
722C4—42no—
723C4—42no—
724C4—41no—
725C4—42no—
726C4—41no—
727C4—41no—
728C4—81no—
729C4—81no—
730C4—81no—
731C4C3×#52511yescharacteristic
732C4C3×#53711yescharacteristic
733C4C3×#54611yescharacteristic
734C4C3×#54711yescharacteristic
735C3#2419311yescharacteristic, direct product factor, Sylow
736C2—82no—
737C2—82no—
738C2C3×#240711yescharacteristic
739C2C3×#300211yescharacteristic
740C2C3×#301011yescharacteristic
741C2C3×#336011yescharacteristic
742C2C3×#337611yescharacteristic
743C2C3×#339411yescharacteristic
744C2C3×#340111yescharacteristic
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×C4×SD16C2semidirect
4. C3×#2580C2semidirect
5. C3×#2043C2semidirect
6. C3×#2042C2semidirect
7. C3×#2013C2semidirect
9. C3×#1984C2semidirect
10. C3×#1958C2semidirect
11. C3×#1880C2semidirect
13. C3×#1865C2semidirect
14. C3×#1864C2semidirect
15. C3×#1805C2semidirect
16. #24193C3direct (N × H)
64. C2×#556C2×C3semidirect
66. C2×C4×SD16C2×C3semidirect
67. #2580C2×C3semidirect
68. #2043C2×C3semidirect
69. #2042C2×C3semidirect
70. #2013C2×C3semidirect
72. #1984C2×C3semidirect
73. #1958C2×C3semidirect
74. #1880C2×C3semidirect
76. #1865C2×C3semidirect
77. #1864C2×C3semidirect
78. #1805C2×C3semidirect
735. C3#24193direct (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×C4×SD162
C3×#25802
C3×#20432
C3×#20422
C3×#20132
C3×#20122
C3×#19842
C3×#19582
C3×#18802
C3×#18792
C3×#18652
C3×#18642
C3×#18052
#241933