Finite Group Databasebeta

← C3×#25512 #10644119

Subgroups — C3×#25512 #10644119

Order 768.

1028 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#541C211yesmaximal, characteristic
2C2×C3×#470C211yesmaximal, characteristic
3C2×C3×#467C211yesmaximal, characteristic
4C3×#2625C211yesmaximal, characteristic
5C3×#2059C211yesmaximal, characteristic, complemented
6C3×#2043C211yesmaximal, characteristic, complemented
7C3×#2026C211yesmaximal, characteristic, complemented
8C3×#2016C211yesmaximal, characteristic, complemented
9C3×#1894C211yesmaximal, characteristic
10C3×#1892C211yesmaximal, characteristic
11C3×#1878C211yesmaximal, characteristic, complemented
12C3×#1878C211yesmaximal, characteristic, complemented
13C3×#1865C211yesmaximal, characteristic, complemented
14C3×#1863C211yesmaximal, characteristic, complemented
15C3×#1729C211yesmaximal, characteristic
16#25512C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×Q16C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C22×C3×M16C2211yescharacteristic
20C23×C3×C8C2211yescharacteristic
21C3×#541—24no—
22C3×#541—24no—
23C2×C3×C4⋊Q8C2211yescharacteristic
24C2×C3×#126—21no—
25C2×C3×#126—21no—
26C2×C3×#125—21no—
27C2×C3×#125—21no—
28C2×C3×#125C2211yescharacteristic
29C2×C3×C22⋊Q8C2211yescharacteristic
30C2×C3×C22⋊Q8C2211yescharacteristic
31C2×C3×C22⋊Q8C2211yescharacteristic
32C2×C3×C4×Q8C2211yescharacteristic
33C2×C3×C4×Q8C2211yescharacteristic
34C2×C3×#117C2211yescharacteristic
35C3×#470—24no—
36C3×#467—24no—
37C2×C3×#107C2211yescharacteristic
38C2×C3×#106C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#103C2211yescharacteristic
44C2×C3×#103C2211yescharacteristic
45C2×C3×#103C2211yescharacteristic
46C2×C3×#103C2211yescharacteristic
47C3×#400—21no—
48C3×#398—21no—
49C3×#397—21no—
50C3×#397—21no—
51C3×#391C2211yescharacteristic
52C3×#391C2211yescharacteristic
53C3×#389C2211yescharacteristic
54C3×#389C2211yescharacteristic
55C3×#380C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#541C2×C311yescharacteristic
65C2×#470C2×C311yescharacteristic
66C2×#467C2×C311yescharacteristic
67#2625C2×C311yescharacteristic
68#2059C2×C311yescharacteristic, complemented
69#2043C2×C311yescharacteristic, complemented
70#2026C2×C311yescharacteristic, complemented
71#2016C2×C311yescharacteristic, complemented
72#1894C2×C311yescharacteristic
73#1892C2×C311yescharacteristic
74#1878C2×C311yescharacteristic, complemented
75#1878C2×C311yescharacteristic, complemented
76#1865C2×C311yescharacteristic, complemented
77#1863C2×C311yescharacteristic, complemented
78#1729C2×C311yescharacteristic
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×C3×Q8C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C2×C3×Q16—22no—
84C2×C3×Q16—22no—
85C2×C3×Q16—22no—
86C2×C3×Q16—22no—
87C2×C3×Q16—41no—
88C2×C3×Q16—41no—
89C2×C3×M16—22no—
90C2×C3×M16—22no—
91C2×C3×M16—41no—
92C22×C3×C8—22no—
93C22×C3×C8—22no—
94C22×C3×C8—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×#125—28no—
104C3×#125—28no—
105C3×#125—22no—
106C3×#125—22no—
107C3×C22⋊Q8—22no—
108C3×C22⋊Q8—22no—
109C3×C22⋊Q8—22no—
110C3×C22⋊Q8—22no—
111C3×C22⋊Q8D414yes—
112C3×C22⋊Q8D414yes—
113C3×C4×Q8—22no—
114C3×C4×Q8—22no—
115C3×C4×Q8—22no—
116C3×C4×Q8—22no—
117C3×#117—22no—
118C3×#117—22no—
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⋊C4—21no—
126C2×C3×C4⋊C4—21no—
127C2×C3×C4⋊C4—21no—
128C2×C3×C4⋊C4—21no—
129C2×C3×C4⋊C4—21no—
130C2×C3×C4⋊C4D411yescharacteristic
131C2×C3×C4⋊C4D411yescharacteristic
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C4⋊C4C2311yescharacteristic
136C2×C3×C4⋊C4C2311yescharacteristic
137C2×C3×C22⋊C4—21no—
138C2×C3×C22⋊C4—21no—
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4—21no—
141C2×C3×C22⋊C4D411yescharacteristic
142C2×C3×C22⋊C4D411yescharacteristic
143C2×C3×C42—21no—
144C2×C3×C42—21no—
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—22no—
154C3×#103—22no—
155C3×#103—41no—
156C3×#103—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×Q16C22×C311yescharacteristic
166C22×M16C22×C311yescharacteristic
167C23×C8C22×C311yescharacteristic
168#541—24no—
169#541—24no—
170C2×C4⋊Q8C22×C311yescharacteristic
171C2×#126—21no—
172C2×#126—21no—
173C2×#125—21no—
174C2×#125—21no—
175C2×#125C22×C311yescharacteristic
176C2×C22⋊Q8C22×C311yescharacteristic
177C2×C22⋊Q8C22×C311yescharacteristic
178C2×C22⋊Q8C22×C311yescharacteristic
179C2×C4×Q8C22×C311yescharacteristic
180C2×C4×Q8C22×C311yescharacteristic
181C2×#117C22×C311yescharacteristic
182#470—24no—
183#467—24no—
184C2×#107C22×C311yescharacteristic
185C2×#106C22×C311yescharacteristic
186C2×#103C22×C311yescharacteristic
187C2×#103C22×C311yescharacteristic
188C2×#103C22×C311yescharacteristic
189C2×#103C22×C311yescharacteristic
190C2×#103C22×C311yescharacteristic
191C2×#103C22×C311yescharacteristic
192C2×#103C22×C311yescharacteristic
193C2×#103C22×C311yescharacteristic
194#400—21no—
195#398—21no—
196#397—21no—
197#397—21no—
198#391C22×C311yescharacteristic
199#391C22×C311yescharacteristic
200#389C22×C311yescharacteristic
201#389C22×C311yescharacteristic
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×C3C2×D411yescharacteristic
212C2×C3×Q8—21no—
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×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8C2×D412yes—
229C2×C3×Q8C2×D412yes—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2×D412yes—
248C22×C3×C4C2×D412yes—
249C22×C3×C4C2411yescharacteristic
250C3×Q16—44no—
251C3×Q16—44no—
252C3×M16—44no—
253C2×C3×C8—21no—
254C2×C3×C8—21no—
255C2×C3×C8—21no—
256C2×C3×C8—21no—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8—21no—
261C2×C3×C8—21no—
262C2×C3×C8—21no—
263C2×C3×C8—44no—
264C2×C3×C8#4112yes—
265C2×C3×C8#4112yes—
266C3×C4⋊C4—24no—
267C3×C4⋊C4—24no—
268C3×C4⋊C4—24no—
269C3×C4⋊C4—24no—
270C3×C4⋊C4—24no—
271C3×C4⋊C4—24no—
272C3×C4⋊C4—24no—
273C3×C4⋊C4—24no—
274C3×C4⋊C4—22no—
275C3×C4⋊C4—22no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—42no—
285C3×C4⋊C4—81no—
286C3×C4⋊C4—81no—
287C3×C4⋊C4C2×D412yes—
288C3×C4⋊C4C2×D412yes—
289C3×C22⋊C4—24no—
290C3×C22⋊C4—24no—
291C3×C22⋊C4—22no—
292C3×C22⋊C4—22no—
293C3×C22⋊C4—42no—
294C3×C22⋊C4—81no—
295C3×C42—24no—
296C3×C42—24no—
297C3×C42—21no—
298C3×C42—21no—
299C3×C42—21no—
300C3×C42—21no—
301C22×Q8C23×C311yescharacteristic
302C22×Q8C23×C311yescharacteristic
303C22×Q8C23×C311yescharacteristic
304C23×C4C23×C311yescharacteristic
305C2×Q16—22no—
306C2×Q16—22no—
307C2×Q16—22no—
308C2×Q16—22no—
309C2×Q16—41no—
310C2×Q16—41no—
311C2×M16—22no—
312C2×M16—22no—
313C2×M16—41no—
314C22×C8—22no—
315C22×C8—22no—
316C22×C8—41no—
317C22×C8C23×C311yescharacteristic
318C22×C8C23×C311yescharacteristic
319C22×C8C23×C311yescharacteristic
320C22×C8C23×C311yescharacteristic
321C4⋊Q8—22no—
322C4⋊Q8—22no—
323#126—28no—
324#126—28no—
325#125—28no—
326#125—28no—
327#125—22no—
328#125—22no—
329C22⋊Q8—22no—
330C22⋊Q8—22no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8C3×D414yes—
334C22⋊Q8C3×D414yes—
335C4×Q8—22no—
336C4×Q8—22no—
337C4×Q8—22no—
338C4×Q8—22no—
339#117—22no—
340#117—22no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4C3×D411yescharacteristic
353C2×C4⋊C4C3×D411yescharacteristic
354C2×C4⋊C4C23×C311yescharacteristic
355C2×C4⋊C4C23×C311yescharacteristic
356C2×C4⋊C4C23×C311yescharacteristic
357C2×C4⋊C4C23×C311yescharacteristic
358C2×C4⋊C4C23×C311yescharacteristic
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4C3×D411yescharacteristic
364C2×C22⋊C4C3×D411yescharacteristic
365C2×C42—21no—
366C2×C42—21no—
367C2×C42C23×C311yescharacteristic
368C2×C42C23×C311yescharacteristic
369#107—22no—
370#106—22no—
371#103—22no—
372#103—22no—
373#103—22no—
374#103—22no—
375#103—22no—
376#103—22no—
377#103—41no—
378#103—41no—
379#95—21no—
380#95—21no—
381#95—21no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—21no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3#12012yes—
393C23×C3C22×D411yescharacteristic
394C3×Q8—22no—
395C3×Q8—22no—
396C3×Q8—22no—
397C3×Q8—22no—
398C3×Q8—41no—
399C3×Q8—41no—
400C3×Q8—41no—
401C3×Q8—41no—
402C3×Q8—41no—
403C3×Q8—41no—
404C3×Q8—41no—
405C3×Q8—41no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4#12012yes—
449C2×C3×C4C22×D411yescharacteristic
450C2×C3×C4C22×D411yescharacteristic
451C2×C3×C4C2×#4111yescharacteristic
452C2×C3×C4C2×#4111yescharacteristic
453C2×C3×C4H(5,𝔽2)11yescharacteristic
454C2×C3×C42−1+411yescharacteristic
455C3×C8—22no—
456C3×C8—22no—
457C3×C8—41no—
458C3×C8—41no—
459C24C2×C3×D411yescharacteristic
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8C2×C3×D412yes—
477C2×Q8C2×C3×D412yes—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4C2×C3×D411yescharacteristic
491C22×C4C2×C3×D411yescharacteristic
492C22×C4C2×C3×D411yescharacteristic
493C22×C4C2×C3×D411yescharacteristic
494C22×C4C2×C3×D411yescharacteristic
495C22×C4C2×C3×D412yes—
496C22×C4C2×C3×D412yes—
497C22×C4C24×C311yescharacteristic
498Q16—44no—
499Q16—44no—
500M16—44no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—44no—
512C2×C8C3×#4112yes—
513C2×C8C3×#4112yes—
514C4⋊C4—24no—
515C4⋊C4—24no—
516C4⋊C4—24no—
517C4⋊C4—24no—
518C4⋊C4—24no—
519C4⋊C4—24no—
520C4⋊C4—24no—
521C4⋊C4—24no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—42no—
533C4⋊C4—81no—
534C4⋊C4—81no—
535C4⋊C4C2×C3×D412yes—
536C4⋊C4C2×C3×D412yes—
537C22⋊C4—24no—
538C22⋊C4—24no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—42no—
542C22⋊C4—81no—
543C42—24no—
544C42—24no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C22×C3—22no—
550C22×C3—22no—
551C22×C3—22no—
552C22×C3—41no—
553C22×C3—41no—
554C22×C3—41no—
555C22×C3—41no—
556C22×C3C2×#12011yescharacteristic
557C22×C3#53211yescharacteristic
558C22×C3#53711yescharacteristic
559C22×C3#57711yescharacteristic
560C22×C3#57811yescharacteristic
561C22×C3#57811yescharacteristic
562C22×C3#57811yescharacteristic
563C3×C4—22no—
564C3×C4—42no—
565C3×C4—42no—
566C3×C4—41no—
567C3×C4—41no—
568C3×C4—42no—
569C3×C4—41no—
570C3×C4—41no—
571C3×C4—42no—
572C3×C4—81no—
573C3×C4—81no—
574C3×C4—81no—
575C3×C4—81no—
576C3×C4#54611yescharacteristic
577C3×C4#54611yescharacteristic
578C3×C4#54711yescharacteristic
579C3×C4#54711yescharacteristic
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23C3×#12012yes—
587C23C22×C3×D411yescharacteristic
588Q8—22no—
589Q8—22no—
590Q8—22no—
591Q8—22no—
592Q8—41no—
593Q8—41no—
594Q8—41no—
595Q8—41no—
596Q8—41no—
597Q8—41no—
598Q8—41no—
599Q8—41no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4C3×#12012yes—
643C2×C4C22×C3×D411yescharacteristic
644C2×C4C22×C3×D411yescharacteristic
645C2×C4C2×C3×#4111yescharacteristic
646C2×C4C2×C3×#4111yescharacteristic
647C2×C4C3×H(5,𝔽2)11yescharacteristic
648C2×C4C3×2−1+411yescharacteristic
649C8—22no—
650C8—22no—
651C8—41no—
652C8—41no—
653C2×C3—42no—
654C2×C3#243011yescharacteristic
655C2×C3#301111yescharacteristic
656C2×C3#301311yescharacteristic
657C2×C3#317711yescharacteristic
658C2×C3#317811yescharacteristic
659C2×C3#325811yescharacteristic
660C2×C3#326111yescharacteristic
661C22—22no—
662C22—22no—
663C22—22no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22C2×C3×#12011yescharacteristic
669C22C3×#53211yescharacteristic
670C22C3×#53711yescharacteristic
671C22C3×#57711yescharacteristic
672C22C3×#57811yescharacteristic
673C22C3×#57811yescharacteristic
674C22C3×#57811yescharacteristic
675C4—22no—
676C4—42no—
677C4—42no—
678C4—41no—
679C4—41no—
680C4—42no—
681C4—41no—
682C4—41no—
683C4—42no—
684C4—81no—
685C4—81no—
686C4—81no—
687C4—81no—
688C4C3×#54611yescharacteristic
689C4C3×#54611yescharacteristic
690C4C3×#54711yescharacteristic
691C4C3×#54711yescharacteristic
692C3#2551211yescharacteristic, direct product factor, Sylow
693C2—42no—
694C2C3×#243011yescharacteristic
695C2C3×#301111yescharacteristic
696C2C3×#301311yescharacteristic
697C2C3×#317711yescharacteristic
698C2C3×#317811yescharacteristic
699C2C3×#325811yescharacteristic
700C2C3×#326111yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC24×C3C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×#117 ◁ G

Complements

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

NH ≅ G/Ntype
5. C3×#2059C2semidirect
6. C3×#2043C2semidirect
7. C3×#2026C2semidirect
8. C3×#2016C2semidirect
11. C3×#1878C2semidirect
12. C3×#1878C2semidirect
13. C3×#1865C2semidirect
14. C3×#1863C2semidirect
16. #25512C3direct (N × H)
68. #2059C2×C3semidirect
69. #2043C2×C3semidirect
70. #2026C2×C3semidirect
71. #2016C2×C3semidirect
74. #1878C2×C3semidirect
75. #1878C2×C3semidirect
76. #1865C2×C3semidirect
77. #1863C2×C3semidirect
692. C3#25512direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5412
C2×C3×#4702
C2×C3×#4672
C3×#26252
C3×#20592
C3×#20432
C3×#20262
C3×#20162
C3×#18942
C3×#18922
C3×#18782
C3×#18652
C3×#18632
C3×#17292
#255123