Finite Group Databasebeta

← C3×#33011 #10651618

Subgroups — C3×#33011 #10651618

Order 768.

1346 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#41C211yesmaximal, characteristic
2C2×C3×#485C211yesmaximal, characteristic, complemented
3C2×C3×#452C211yesmaximal, characteristic
4C3×#2855C211yesmaximal, characteristic, complemented
5C3×#1878C211yesmaximal, characteristic, complemented
6C3×#1878C211yesmaximal, characteristic, complemented
7C3×#1877C211yesmaximal, characteristic, complemented
8C3×#1877C211yesmaximal, characteristic, complemented
9C3×#1865C211yesmaximal, characteristic, complemented
10C3×#1864C211yesmaximal, characteristic, complemented
11C3×#1863C211yesmaximal, characteristic, complemented
12C3×#1862C211yesmaximal, characteristic, complemented
13C3×#1825C211yesmaximal, characteristic, complemented
14C3×#1817C211yesmaximal, characteristic, complemented
15C3×#1788C211yesmaximal, characteristic
16#33011C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21C3×C4×#41—24no—
22C3×C4×#41—24no—
23C2×C3×C4×Q8C2211yescharacteristic
24C2×C3×C4×Q8C2211yescharacteristic
25C2×C3×C4×D4—21no—
26C2×C3×C4×D4—21no—
27C2×C3×C4×D4C2211yescharacteristic
28C2×C3×C4×D4C2211yescharacteristic
29C2×C3×#117—21no—
30C2×C3×#117C2211yescharacteristic
31C22×C3×C42—21no—
32C22×C3×C42C2211yescharacteristic
33C3×#485—24no—
34C3×#452—24no—
35C2×C3×#107C2211yescharacteristic
36C2×C3×#106C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×C22⋊C8C2211yescharacteristic
46C2×C3×C22⋊C8C2211yescharacteristic
47C3×#391C2211yescharacteristic
48C3×#391C2211yescharacteristic
49C3×#389C2211yescharacteristic
50C3×#389C2211yescharacteristic
51C3×#387—21no—
52C3×#387—21no—
53C3×#385—21no—
54C3×#381—21no—
55C3×#380C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×C4×#41C2×C311yescharacteristic
65C2×#485C2×C311yescharacteristic, complemented
66C2×#452C2×C311yescharacteristic
67#2855C2×C311yescharacteristic, complemented
68#1878C2×C311yescharacteristic, complemented
69#1878C2×C311yescharacteristic, complemented
70#1877C2×C311yescharacteristic, complemented
71#1877C2×C311yescharacteristic, complemented
72#1865C2×C311yescharacteristic, complemented
73#1864C2×C311yescharacteristic, complemented
74#1863C2×C311yescharacteristic, complemented
75#1862C2×C311yescharacteristic, complemented
76#1825C2×C311yescharacteristic, complemented
77#1817C2×C311yescharacteristic, complemented
78#1788C2×C311yescharacteristic
79C2×C3×#41—22no—
80C2×C3×#41—22no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41D414yes—
85C22×C3×Q8C2311yescharacteristic
86C22×C3×Q8C2311yescharacteristic
87C22×C3×D4—21no—
88C22×C3×D4C2311yescharacteristic
89C23×C3×C4—21no—
90C23×C3×C4—21no—
91C23×C3×C4—21no—
92C23×C3×C4D411yescharacteristic
93C23×C3×C4D411yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C2×C3×Q16—22no—
96C2×C3×Q16—22no—
97C2×C3×Q16—22no—
98C2×C3×SD16—22no—
99C2×C3×SD16—22no—
100C2×C3×SD16—22no—
101C22×C3×C8C2311yescharacteristic
102C22×C3×C8C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C22×C3×C8C2311yescharacteristic
105C3×C22⋊Q8—22no—
106C3×C22⋊Q8—22no—
107C3×C4×Q8—22no—
108C3×C4×Q8—22no—
109C3×C4×Q8—22no—
110C3×C4×Q8—22no—
111C3×C4×D4—28no—
112C3×C4×D4—28no—
113C3×C4×D4—22no—
114C3×C4×D4—22no—
115C3×C4×D4—22no—
116C3×C4×D4—22no—
117C3×#117—28no—
118C3×#117—22no—
119C3×#117D414yes—
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⋊C4C2311yescharacteristic
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C22⋊C4—21no—
131C2×C3×C22⋊C4—21no—
132C2×C3×C22⋊C4—21no—
133C2×C3×C22⋊C4—21no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C42—28no—
136C2×C3×C42—21no—
137C2×C3×C42—21no—
138C2×C3×C42—21no—
139C2×C3×C42—22no—
140C2×C3×C42—22no—
141C2×C3×C42D411yescharacteristic
142C2×C3×C42D411yescharacteristic
143C2×C3×C42C2311yescharacteristic
144C2×C3×C42C2311yescharacteristic
145C3×#107—22no—
146C3×#106—22no—
147C3×#103—22no—
148C3×#103—22no—
149C3×#103—22no—
150C3×#103—22no—
151C3×#103—22no—
152C3×#102—22no—
153C3×#102—22no—
154C3×#102—22no—
155C3×C22⋊C8—22no—
156C3×C22⋊C8—22no—
157C3×#95—21no—
158C3×#95—21no—
159C3×#95—21no—
160C3×#95—21no—
161C3×#95—21no—
162C3×#95—21no—
163C3×#95—21no—
164C22×#41C22×C311yescharacteristic
165C22×Q16C22×C311yescharacteristic
166C22×SD16C22×C311yescharacteristic
167C2×C22⋊Q8C22×C311yescharacteristic
168C4×#41—24no—
169C4×#41—24no—
170C2×C4×Q8C22×C311yescharacteristic
171C2×C4×Q8C22×C311yescharacteristic
172C2×C4×D4—21no—
173C2×C4×D4—21no—
174C2×C4×D4C22×C311yescharacteristic
175C2×C4×D4C22×C311yescharacteristic
176C2×#117—21no—
177C2×#117C22×C311yescharacteristic
178C22×C42—21no—
179C22×C42C22×C311yescharacteristic
180#485—24no—
181#452—24no—
182C2×#107C22×C311yescharacteristic
183C2×#106C22×C311yescharacteristic
184C2×#103C22×C311yescharacteristic
185C2×#103C22×C311yescharacteristic
186C2×#103C22×C311yescharacteristic
187C2×#103C22×C311yescharacteristic
188C2×#103C22×C311yescharacteristic
189C2×#102C22×C311yescharacteristic
190C2×#102C22×C311yescharacteristic
191C2×#102C22×C311yescharacteristic
192C2×C22⋊C8C22×C311yescharacteristic
193C2×C22⋊C8C22×C311yescharacteristic
194#391C22×C311yescharacteristic
195#391C22×C311yescharacteristic
196#389C22×C311yescharacteristic
197#389C22×C311yescharacteristic
198#387—21no—
199#387—21no—
200#385—21no—
201#381—21no—
202#380C22×C311yescharacteristic
203#340C22×C311yescharacteristic
204#340C22×C311yescharacteristic
205#340C22×C311yescharacteristic
206#340C22×C311yescharacteristic
207#336C22×C311yescharacteristic
208#336C22×C311yescharacteristic
209#336C22×C311yescharacteristic
210#336C22×C311yescharacteristic
211C24×C3—21no—
212C24×C3C2×D411yescharacteristic
213C3×#41—28no—
214C3×#41—28no—
215C3×#41—28no—
216C3×#41—28no—
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—21no—
226C2×C3×Q8C2×D412yes—
227C2×C3×Q8#4112yes—
228C2×C3×Q8#4112yes—
229C2×C3×D4—24no—
230C2×C3×D4—24no—
231C2×C3×D4—24no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4C2×D412yes—
236C2×C3×D4#4112yes—
237C2×C3×D4#4112yes—
238C22×C3×C4—24no—
239C22×C3×C4—24no—
240C22×C3×C4—21no—
241C22×C3×C4—24no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—24no—
247C22×C3×C4—24no—
248C22×C3×C4—22no—
249C22×C3×C4—22no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—22no—
253C22×C3×C4—22no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—41no—
259C22×C3×C4—41no—
260C22×C3×C4—42no—
261C22×C3×C4—42no—
262C22×C3×C4—42no—
263C22×C3×C4—42no—
264C22×C3×C4C2×D411yescharacteristic
265C22×C3×C4C2×D411yescharacteristic
266C22×C3×C4C2×D411yescharacteristic
267C22×C3×C4C2×D412yes—
268C22×C3×C4C2×D412yes—
269C22×C3×C4C2×D411yescharacteristic
270C22×C3×C4C2×D411yescharacteristic
271C22×C3×C4C2411yescharacteristic
272C3×Q16—44no—
273C3×SD16—44no—
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—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C3×C4⋊C4—24no—
287C3×C4⋊C4—24no—
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—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4—42no—
297C3×C4⋊C4—42no—
298C3×C4⋊C4—42no—
299C3×C4⋊C4C2×D412yes—
300C3×C4⋊C4C2×D412yes—
301C3×C22⋊C4—24no—
302C3×C22⋊C4—24no—
303C3×C22⋊C4—24no—
304C3×C22⋊C4—42no—
305C3×C22⋊C4—42no—
306C3×C42—24no—
307C3×C42—24no—
308C3×C42—22no—
309C3×C42—24no—
310C3×C42—22no—
311C3×C42—21no—
312C3×C42—21no—
313C3×C42—21no—
314C3×C42—21no—
315C2×#41—22no—
316C2×#41—22no—
317C2×#41—22no—
318C2×#41—22no—
319C2×#41—22no—
320C2×#41C3×D414yes—
321C22×Q8C23×C311yescharacteristic
322C22×Q8C23×C311yescharacteristic
323C22×D4—21no—
324C22×D4C23×C311yescharacteristic
325C23×C4—21no—
326C23×C4—21no—
327C23×C4—21no—
328C23×C4C3×D411yescharacteristic
329C23×C4C3×D411yescharacteristic
330C23×C4C23×C311yescharacteristic
331C2×Q16—22no—
332C2×Q16—22no—
333C2×Q16—22no—
334C2×SD16—22no—
335C2×SD16—22no—
336C2×SD16—22no—
337C22×C8C23×C311yescharacteristic
338C22×C8C23×C311yescharacteristic
339C22×C8C23×C311yescharacteristic
340C22×C8C23×C311yescharacteristic
341C22⋊Q8—22no—
342C22⋊Q8—22no—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×Q8—22no—
346C4×Q8—22no—
347C4×D4—28no—
348C4×D4—28no—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4—22no—
352C4×D4—22no—
353#117—28no—
354#117—22no—
355#117C3×D414yes—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
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×C42—28no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42C3×D411yescharacteristic
378C2×C42C3×D411yescharacteristic
379C2×C42C23×C311yescharacteristic
380C2×C42C23×C311yescharacteristic
381#107—22no—
382#106—22no—
383#103—22no—
384#103—22no—
385#103—22no—
386#103—22no—
387#103—22no—
388#102—22no—
389#102—22no—
390#102—22no—
391C22⋊C8—22no—
392C22⋊C8—22no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400C23×C3—22no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—22no—
404C23×C3—22no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3#12012yes—
414C23×C3C22×D411yescharacteristic
415C3×Q8—22no—
416C3×Q8—22no—
417C3×Q8—22no—
418C3×Q8—41no—
419C3×Q8—41no—
420C3×Q8—41no—
421C3×Q8—41no—
422C3×Q8#12314yes—
423C3×D4—216no—
424C3×D4—22no—
425C3×D4—22no—
426C3×D4—22no—
427C3×D4#12314yes—
428C2×C3×C4—216no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—22no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—44no—
451C2×C3×C4—44no—
452C2×C3×C4—48no—
453C2×C3×C4—48no—
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—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#12012yes—
471C2×C3×C4#13512yes—
472C2×C3×C4#13712yes—
473C2×C3×C4C22×D411yescharacteristic
474C2×C3×C4C22×D411yescharacteristic
475C2×C3×C4C2×#4111yescharacteristic
476C2×C3×C4C2×#4111yescharacteristic
477C2×C3×C4C2×#4111yescharacteristic
478C2×C3×C4C2×#4111yescharacteristic
479C3×C8—41no—
480C3×C8—41no—
481C3×C8—41no—
482C3×C8—41no—
483C24—21no—
484C24C2×C3×D411yescharacteristic
485#41—28no—
486#41—28no—
487#41—28no—
488#41—28no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8C2×C3×D412yes—
499C2×Q8C3×#4112yes—
500C2×Q8C3×#4112yes—
501C2×D4—24no—
502C2×D4—24no—
503C2×D4—24no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4C2×C3×D412yes—
508C2×D4C3×#4112yes—
509C2×D4C3×#4112yes—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—21no—
513C22×C4—24no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4C2×C3×D411yescharacteristic
537C22×C4C2×C3×D411yescharacteristic
538C22×C4C2×C3×D411yescharacteristic
539C22×C4C2×C3×D412yes—
540C22×C4C2×C3×D412yes—
541C22×C4C2×C3×D411yescharacteristic
542C22×C4C2×C3×D411yescharacteristic
543C22×C4C24×C311yescharacteristic
544Q16—44no—
545SD16—44no—
546C2×C8—21no—
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—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4C2×C3×D412yes—
572C4⋊C4C2×C3×D412yes—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C42—24no—
579C42—24no—
580C42—22no—
581C42—24no—
582C42—22no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—21no—
587C22×C3—22no—
588C22×C3—24no—
589C22×C3—22no—
590C22×C3—22no—
591C22×C3—41no—
592C22×C3—42no—
593C22×C3—41no—
594C22×C3—42no—
595C22×C3—41no—
596C22×C3—42no—
597C22×C3—41no—
598C22×C3—42no—
599C22×C3—42no—
600C22×C3—42no—
601C22×C3C2×#12011yescharacteristic
602C22×C3#52511yescharacteristic
603C22×C3#52511yescharacteristic
604C22×C3C2×#13511yescharacteristic
605C22×C3C2×#13711yescharacteristic
606C22×C3#57511yescharacteristic
607C22×C3#57511yescharacteristic
608C3×C4—22no—
609C3×C4—24no—
610C3×C4—22no—
611C3×C4—22no—
612C3×C4—41no—
613C3×C4—42no—
614C3×C4—41no—
615C3×C4—42no—
616C3×C4—81no—
617C3×C4—81no—
618C3×C4—81no—
619C3×C4—81no—
620C3×C4C2×#12311yescharacteristic
621C3×C4C2×#12311yescharacteristic
622C3×C4#52511yescharacteristic
623C3×C4#52511yescharacteristic
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—22no—
629C23—21no—
630C23—21no—
631C23—22no—
632C23—22no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23C3×#12012yes—
638C23C22×C3×D411yescharacteristic
639Q8—22no—
640Q8—22no—
641Q8—22no—
642Q8—41no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8C3×#12314yes—
647D4—216no—
648D4—22no—
649D4—22no—
650D4—22no—
651D4C3×#12314yes—
652C2×C4—216no—
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—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—44no—
675C2×C4—44no—
676C2×C4—48no—
677C2×C4—48no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4C3×#12012yes—
695C2×C4C3×#13512yes—
696C2×C4C3×#13712yes—
697C2×C4C22×C3×D411yescharacteristic
698C2×C4C22×C3×D411yescharacteristic
699C2×C4C2×C3×#4111yescharacteristic
700C2×C4C2×C3×#4111yescharacteristic
701C2×C4C2×C3×#4111yescharacteristic
702C2×C4C2×C3×#4111yescharacteristic
703C8—41no—
704C8—41no—
705C8—41no—
706C8—41no—
707C2×C3—42no—
708C2×C3—44no—
709C2×C3#284911yescharacteristic
710C2×C3#300211yescharacteristic
711C2×C3#300711yescharacteristic
712C2×C3#310211yescharacteristic
713C2×C3#310711yescharacteristic
714C2×C3#311111yescharacteristic
715C2×C3#311611yescharacteristic
716C22—22no—
717C22—22no—
718C22—22no—
719C22—24no—
720C22—42no—
721C22—42no—
722C22—41no—
723C22—42no—
724C22—41no—
725C22—42no—
726C22—41no—
727C22—42no—
728C22—41no—
729C22—42no—
730C22C2×C3×#12011yescharacteristic
731C22C3×#52511yescharacteristic
732C22C3×#52511yescharacteristic
733C22C2×C3×#13511yescharacteristic
734C22C2×C3×#13711yescharacteristic
735C22C3×#57511yescharacteristic
736C22C3×#57511yescharacteristic
737C4—22no—
738C4—22no—
739C4—22no—
740C4—24no—
741C4—41no—
742C4—42no—
743C4—41no—
744C4—42no—
745C4—81no—
746C4—81no—
747C4—81no—
748C4—81no—
749C4C2×C3×#12311yescharacteristic
750C4C2×C3×#12311yescharacteristic
751C4C3×#52511yescharacteristic
752C4C3×#52511yescharacteristic
753C3#3301111yescharacteristic, direct product factor, Sylow
754C2—42no—
755C2—44no—
756C2C3×#284911yescharacteristic
757C2C3×#300211yescharacteristic
758C2C3×#300711yescharacteristic
759C2C3×#310211yescharacteristic
760C2C3×#310711yescharacteristic
761C2C3×#311111yescharacteristic
762C2C3×#311611yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C22×C3×C42 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C3×#485C2semidirect
4. C3×#2855C2semidirect
5. C3×#1878C2semidirect
6. C3×#1878C2semidirect
7. C3×#1877C2semidirect
8. C3×#1877C2semidirect
9. C3×#1865C2semidirect
10. C3×#1864C2semidirect
11. C3×#1863C2semidirect
12. C3×#1862C2semidirect
13. C3×#1825C2semidirect
14. C3×#1817C2semidirect
16. #33011C3direct (N × H)
65. C2×#485C2×C3semidirect
67. #2855C2×C3semidirect
68. #1878C2×C3semidirect
69. #1878C2×C3semidirect
70. #1877C2×C3semidirect
71. #1877C2×C3semidirect
72. #1865C2×C3semidirect
73. #1864C2×C3semidirect
74. #1863C2×C3semidirect
75. #1862C2×C3semidirect
76. #1825C2×C3semidirect
77. #1817C2×C3semidirect
753. C3#33011direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×#412
C2×C3×#4852
C2×C3×#4522
C3×#28552
C3×#18782
C3×#18772
C3×#18652
C3×#18642
C3×#18632
C3×#18622
C3×#18252
C3×#18172
C3×#17882
#330113