Finite Group Databasebeta

← C3×#25505 #10644112

Subgroups — C3×#25505 #10644112

Order 768.

1140 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#529C211yesmaximal, characteristic
2C2×C3×#470C211yesmaximal, characteristic, complemented
3C2×C3×#468C211yesmaximal, characteristic
4C3×#2855C211yesmaximal, characteristic, complemented
5C3×#2059C211yesmaximal, characteristic, complemented
6C3×#2042C211yesmaximal, characteristic, complemented
7C3×#2026C211yesmaximal, characteristic, complemented
8C3×#2015C211yesmaximal, characteristic, complemented
9C3×#1895C211yesmaximal, characteristic
10C3×#1894C211yesmaximal, characteristic, complemented
11C3×#1878C211yesmaximal, characteristic, complemented
12C3×#1877C211yesmaximal, characteristic, complemented
13C3×#1864C211yesmaximal, characteristic, complemented
14C3×#1863C211yesmaximal, characteristic, complemented
15C3×#1728C211yesmaximal, characteristic, complemented
16#25505C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×Q16C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×M16C2211yescharacteristic
20C22×C3×M16C2211yescharacteristic
21C3×#529—24no—
22C3×#529—24no—
23C2×C3×#126—21no—
24C2×C3×#125C2211yescharacteristic
25C2×C3×#124C2211yescharacteristic
26C2×C3×#123—21no—
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×C22⋊Q8C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic
30C2×C3×C4×Q8C2211yescharacteristic
31C2×C3×C4×D4—21no—
32C2×C3×C4×D4C2211yescharacteristic
33C2×C3×#117—21no—
34C22×C3×C42C2211yescharacteristic
35C3×#470—24no—
36C3×#468—24no—
37C2×C3×#107C2211yescharacteristic
38C2×C3×#106C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#103C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
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×#529C2×C311yescharacteristic
65C2×#470C2×C311yescharacteristic, complemented
66C2×#468C2×C311yescharacteristic
67#2855C2×C311yescharacteristic, complemented
68#2059C2×C311yescharacteristic, complemented
69#2042C2×C311yescharacteristic, complemented
70#2026C2×C311yescharacteristic, complemented
71#2015C2×C311yescharacteristic, complemented
72#1895C2×C311yescharacteristic
73#1894C2×C311yescharacteristic, complemented
74#1878C2×C311yescharacteristic, complemented
75#1877C2×C311yescharacteristic, complemented
76#1864C2×C311yescharacteristic, complemented
77#1863C2×C311yescharacteristic, complemented
78#1728C2×C311yescharacteristic, complemented
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4—21no—
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4—21no—
84C23×C3×C4D411yescharacteristic
85C23×C3×C4D411yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C2×C3×Q16—22no—
88C2×C3×Q16—22no—
89C2×C3×Q16—41no—
90C2×C3×SD16—22no—
91C2×C3×SD16—22no—
92C2×C3×SD16—41no—
93C2×C3×M16—22no—
94C2×C3×M16—22no—
95C2×C3×M16—22no—
96C2×C3×M16—22no—
97C2×C3×M16—41no—
98C2×C3×M16—41no—
99C22×C3×C8C2311yescharacteristic
100C22×C3×C8C2311yescharacteristic
101C22×C3×C8C2311yescharacteristic
102C22×C3×C8C2311yescharacteristic
103C3×#126—28no—
104C3×#125—22no—
105C3×#125—22no—
106C3×#124—22no—
107C3×#124—22no—
108C3×#123—28no—
109C3×C22⋊Q8—22no—
110C3×C22⋊Q8—22no—
111C3×C22⋊Q8—22no—
112C3×C22⋊Q8D414yes—
113C3×#121—22no—
114C3×#121D414yes—
115C3×C4×Q8—22no—
116C3×C4×Q8—22no—
117C3×C4×D4—28no—
118C3×C4×D4—22no—
119C3×C4×D4—22no—
120C3×#117—28no—
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⋊C4—21no—
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C4⋊C4C2311yescharacteristic
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×C42—22no—
141C2×C3×C42—22no—
142C2×C3×C42—21no—
143C2×C3×C42D411yescharacteristic
144C2×C3×C42D411yescharacteristic
145C2×C3×C42C2311yescharacteristic
146C2×C3×C42C2311yescharacteristic
147C3×#107—22no—
148C3×#106—22no—
149C3×#103—22no—
150C3×#103—22no—
151C3×#103—22no—
152C3×#103—22no—
153C3×#103—41no—
154C3×#102—22no—
155C3×#102—22no—
156C3×#102—41no—
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×M16C22×C311yescharacteristic
167C22×M16C22×C311yescharacteristic
168#529—24no—
169#529—24no—
170C2×#126—21no—
171C2×#125C22×C311yescharacteristic
172C2×#124C22×C311yescharacteristic
173C2×#123—21no—
174C2×C22⋊Q8C22×C311yescharacteristic
175C2×C22⋊Q8C22×C311yescharacteristic
176C2×#121C22×C311yescharacteristic
177C2×C4×Q8C22×C311yescharacteristic
178C2×C4×D4—21no—
179C2×C4×D4C22×C311yescharacteristic
180C2×#117—21no—
181C22×C42C22×C311yescharacteristic
182#470—24no—
183#468—24no—
184C2×#107C22×C311yescharacteristic
185C2×#106C22×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
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
213C2×C3×Q8—21no—
214C2×C3×Q8—21no—
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×Q8C2×D412yes—
225C2×C3×D4—24no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—42no—
232C2×C3×D4—42no—
233C2×C3×D4C2×D412yes—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—24no—
239C22×C3×C4—22no—
240C22×C3×C4—22no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—22no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—41no—
250C22×C3×C4—41no—
251C22×C3×C4—41no—
252C22×C3×C4—42no—
253C22×C3×C4—42no—
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2×D412yes—
259C22×C3×C4C2×D412yes—
260C22×C3×C4C2×D411yescharacteristic
261C22×C3×C4C2411yescharacteristic
262C3×Q16—44no—
263C3×SD16—44no—
264C3×M16—44no—
265C3×M16—44no—
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—21no—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8#4112yes—
277C2×C3×C8#4112yes—
278C3×C4⋊C4—24no—
279C3×C4⋊C4—24no—
280C3×C4⋊C4—24no—
281C3×C4⋊C4—24no—
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—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—42no—
291C3×C4⋊C4—42no—
292C3×C4⋊C4—42no—
293C3×C4⋊C4C2×D412yes—
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—42no—
301C3×C22⋊C4—42no—
302C3×C42—24no—
303C3×C42—22no—
304C3×C42—22no—
305C3×C42—21no—
306C3×C42—21no—
307C3×C42—21no—
308C3×C42—21no—
309C22×Q8C23×C311yescharacteristic
310C22×Q8C23×C311yescharacteristic
311C22×D4—21no—
312C22×D4C23×C311yescharacteristic
313C23×C4—21no—
314C23×C4C3×D411yescharacteristic
315C23×C4C3×D411yescharacteristic
316C23×C4C23×C311yescharacteristic
317C2×Q16—22no—
318C2×Q16—22no—
319C2×Q16—41no—
320C2×SD16—22no—
321C2×SD16—22no—
322C2×SD16—41no—
323C2×M16—22no—
324C2×M16—22no—
325C2×M16—22no—
326C2×M16—22no—
327C2×M16—41no—
328C2×M16—41no—
329C22×C8C23×C311yescharacteristic
330C22×C8C23×C311yescharacteristic
331C22×C8C23×C311yescharacteristic
332C22×C8C23×C311yescharacteristic
333#126—28no—
334#125—22no—
335#125—22no—
336#124—22no—
337#124—22no—
338#123—28no—
339C22⋊Q8—22no—
340C22⋊Q8—22no—
341C22⋊Q8—22no—
342C22⋊Q8C3×D414yes—
343#121—22no—
344#121C3×D414yes—
345C4×Q8—22no—
346C4×Q8—22no—
347C4×D4—28no—
348C4×D4—22no—
349C4×D4—22no—
350#117—28no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4C23×C311yescharacteristic
359C2×C4⋊C4C23×C311yescharacteristic
360C2×C4⋊C4C23×C311yescharacteristic
361C2×C4⋊C4C23×C311yescharacteristic
362C2×C4⋊C4C23×C311yescharacteristic
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×C42—21no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42C3×D411yescharacteristic
374C2×C42C3×D411yescharacteristic
375C2×C42C23×C311yescharacteristic
376C2×C42C23×C311yescharacteristic
377#107—22no—
378#106—22no—
379#103—22no—
380#103—22no—
381#103—22no—
382#103—22no—
383#103—41no—
384#102—22no—
385#102—22no—
386#102—41no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—22no—
401C23×C3—41no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3#12012yes—
408C23×C3C22×D411yescharacteristic
409C3×Q8—22no—
410C3×Q8—22no—
411C3×Q8—41no—
412C3×Q8—41no—
413C3×Q8—41no—
414C3×Q8—41no—
415C3×Q8—41no—
416C3×Q8—41no—
417C3×D4—22no—
418C3×D4—22no—
419C3×D4—48no—
420C3×D4—41no—
421C3×D4—41no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—44no—
443C2×C3×C4—48no—
444C2×C3×C4—44no—
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—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4#12012yes—
464C2×C3×C4#13712yes—
465C2×C3×C4C22×D411yescharacteristic
466C2×C3×C4C22×D411yescharacteristic
467C2×C3×C4C2×#4111yescharacteristic
468C2×C3×C4C2×#4111yescharacteristic
469C2×C3×C4H(5,𝔽2)11yescharacteristic
470C2×C3×C42−1+411yescharacteristic
471C3×C8—22no—
472C3×C8—22no—
473C3×C8—41no—
474C3×C8—41no—
475C24—21no—
476C24C2×C3×D411yescharacteristic
477C2×Q8—21no—
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×Q8C2×C3×D412yes—
489C2×D4—24no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4C2×C3×D412yes—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4C2×C3×D411yescharacteristic
519C22×C4C2×C3×D411yescharacteristic
520C22×C4C2×C3×D411yescharacteristic
521C22×C4C2×C3×D411yescharacteristic
522C22×C4C2×C3×D412yes—
523C22×C4C2×C3×D412yes—
524C22×C4C2×C3×D411yescharacteristic
525C22×C4C24×C311yescharacteristic
526Q16—44no—
527SD16—44no—
528M16—44no—
529M16—44no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8C3×#4112yes—
541C2×C8C3×#4112yes—
542C4⋊C4—24no—
543C4⋊C4—24no—
544C4⋊C4—24no—
545C4⋊C4—24no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—42no—
557C4⋊C4C2×C3×D412yes—
558C4⋊C4C2×C3×D412yes—
559C22⋊C4—24no—
560C22⋊C4—24no—
561C22⋊C4—24no—
562C22⋊C4—24no—
563C22⋊C4—24no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C42—24no—
567C42—22no—
568C42—22no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—21no—
573C22×C3—22no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—41no—
577C22×C3—41no—
578C22×C3—41no—
579C22×C3—41no—
580C22×C3—42no—
581C22×C3—42no—
582C22×C3—42no—
583C22×C3—81no—
584C22×C3—81no—
585C22×C3—81no—
586C22×C3—81no—
587C22×C3C2×#12011yescharacteristic
588C22×C3#53211yescharacteristic
589C22×C3#53711yescharacteristic
590C22×C3C2×#13711yescharacteristic
591C22×C3#57511yescharacteristic
592C22×C3#57511yescharacteristic
593C22×C3#57511yescharacteristic
594C3×C4—22no—
595C3×C4—22no—
596C3×C4—42no—
597C3×C4—41no—
598C3×C4—41no—
599C3×C4—42no—
600C3×C4—41no—
601C3×C4—42no—
602C3×C4—81no—
603C3×C4—81no—
604C3×C4—81no—
605C3×C4—81no—
606C3×C4#54611yescharacteristic
607C3×C4#54611yescharacteristic
608C3×C4#54711yescharacteristic
609C3×C4#54711yescharacteristic
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—22no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23C3×#12012yes—
624C23C22×C3×D411yescharacteristic
625Q8—22no—
626Q8—22no—
627Q8—41no—
628Q8—41no—
629Q8—41no—
630Q8—41no—
631Q8—41no—
632Q8—41no—
633D4—22no—
634D4—22no—
635D4—48no—
636D4—41no—
637D4—41no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
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—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—44no—
659C2×C4—48no—
660C2×C4—44no—
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—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4C3×#12012yes—
680C2×C4C3×#13712yes—
681C2×C4C22×C3×D411yescharacteristic
682C2×C4C22×C3×D411yescharacteristic
683C2×C4C2×C3×#4111yescharacteristic
684C2×C4C2×C3×#4111yescharacteristic
685C2×C4C3×H(5,𝔽2)11yescharacteristic
686C2×C4C3×2−1+411yescharacteristic
687C8—22no—
688C8—22no—
689C8—41no—
690C8—41no—
691C2×C3—42no—
692C2×C3—82no—
693C2×C3#243011yescharacteristic
694C2×C3#300511yescharacteristic
695C2×C3#300711yescharacteristic
696C2×C3#317211yescharacteristic
697C2×C3#318311yescharacteristic
698C2×C3#325211yescharacteristic
699C2×C3#325611yescharacteristic
700C22—22no—
701C22—22no—
702C22—22no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22C2×C3×#12011yescharacteristic
715C22C3×#53211yescharacteristic
716C22C3×#53711yescharacteristic
717C22C2×C3×#13711yescharacteristic
718C22C3×#57511yescharacteristic
719C22C3×#57511yescharacteristic
720C22C3×#57511yescharacteristic
721C4—22no—
722C4—22no—
723C4—42no—
724C4—41no—
725C4—41no—
726C4—42no—
727C4—41no—
728C4—42no—
729C4—81no—
730C4—81no—
731C4—81no—
732C4—81no—
733C4C3×#54611yescharacteristic
734C4C3×#54611yescharacteristic
735C4C3×#54711yescharacteristic
736C4C3×#54711yescharacteristic
737C3#2550511yescharacteristic, direct product factor, Sylow
738C2—42no—
739C2—82no—
740C2C3×#243011yescharacteristic
741C2C3×#300511yescharacteristic
742C2C3×#300711yescharacteristic
743C2C3×#317211yescharacteristic
744C2C3×#318311yescharacteristic
745C2C3×#325211yescharacteristic
746C2C3×#325611yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#121C22
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×#470C2semidirect
4. C3×#2855C2semidirect
5. C3×#2059C2semidirect
6. C3×#2042C2semidirect
7. C3×#2026C2semidirect
8. C3×#2015C2semidirect
10. C3×#1894C2semidirect
11. C3×#1878C2semidirect
12. C3×#1877C2semidirect
13. C3×#1864C2semidirect
14. C3×#1863C2semidirect
15. C3×#1728C2semidirect
16. #25505C3direct (N × H)
65. C2×#470C2×C3semidirect
67. #2855C2×C3semidirect
68. #2059C2×C3semidirect
69. #2042C2×C3semidirect
70. #2026C2×C3semidirect
71. #2015C2×C3semidirect
73. #1894C2×C3semidirect
74. #1878C2×C3semidirect
75. #1877C2×C3semidirect
76. #1864C2×C3semidirect
77. #1863C2×C3semidirect
78. #1728C2×C3semidirect
737. C3#25505direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5292
C2×C3×#4702
C2×C3×#4682
C3×#28552
C3×#20592
C3×#20422
C3×#20262
C3×#20152
C3×#18952
C3×#18942
C3×#18782
C3×#18772
C3×#18642
C3×#18632
C3×#17282
#255053