Finite Group Databasebeta

← C3×#25653 #10644260

Subgroups — C3×#25653 #10644260

Order 768.

1082 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#559C211yesmaximal, characteristic
2C2×C3×#488C211yesmaximal, characteristic, complemented
3C2×C3×#478C211yesmaximal, characteristic, complemented
4C3×#2584C211yesmaximal, characteristic, complemented
5C3×#2042C211yesmaximal, characteristic, complemented
6C3×#2042C211yesmaximal, characteristic, complemented
7C3×#2041C211yesmaximal, characteristic
8C3×#2041C211yesmaximal, characteristic
9C3×#1984C211yesmaximal, characteristic, complemented
10C3×#1983C211yesmaximal, characteristic, complemented
11C3×#1865C211yesmaximal, characteristic, complemented
12C3×#1864C211yesmaximal, characteristic, complemented
13C3×#1863C211yesmaximal, characteristic, complemented
14C3×#1862C211yesmaximal, characteristic, complemented
15C3×C4×#102C211yesmaximal, characteristic, complemented
16#25653C311yesmaximal, characteristic, direct product factor, Sylow
17C3×#559—24no—
18C3×#559—24no—
19C2×C3×#127C2211yescharacteristic
20C2×C3×#125C2211yescharacteristic
21C2×C3×#124—21no—
22C2×C3×#124C2211yescharacteristic
23C2×C3×#124C2211yescharacteristic
24C2×C3×#123—21no—
25C2×C3×#123—21no—
26C2×C3×C4×Q8C2211yescharacteristic
27C2×C3×C4×Q8C2211yescharacteristic
28C2×C3×C4×D4—21no—
29C2×C3×C4×D4C2211yescharacteristic
30C2×C3×C4×D4C2211yescharacteristic
31C3×#488—24no—
32C3×#478—24no—
33C2×C3×#107C2211yescharacteristic
34C2×C3×#106C2211yescharacteristic
35C2×C3×C4⋊C8C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#102C2211yescharacteristic
41C2×C3×#102C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×#102C2211yescharacteristic
48C2×C3×C4×C8C2211yescharacteristic
49C3×#398—21no—
50C3×#395—21no—
51C3×#389—21no—
52C3×#389—21no—
53C3×#389C2211yescharacteristic
54C3×#389C2211yescharacteristic
55C3×#389C2211yescharacteristic
56C3×#389C2211yescharacteristic
57C3×C4×C4⋊C4C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#559C2×C311yescharacteristic
65C2×#488C2×C311yescharacteristic, complemented
66C2×#478C2×C311yescharacteristic, complemented
67#2584C2×C311yescharacteristic, complemented
68#2042C2×C311yescharacteristic, complemented
69#2042C2×C311yescharacteristic, complemented
70#2041C2×C311yescharacteristic
71#2041C2×C311yescharacteristic
72#1984C2×C311yescharacteristic, complemented
73#1983C2×C311yescharacteristic, complemented
74#1865C2×C311yescharacteristic, complemented
75#1864C2×C311yescharacteristic, complemented
76#1863C2×C311yescharacteristic, complemented
77#1862C2×C311yescharacteristic, complemented
78C4×#102C2×C311yescharacteristic, complemented
79C22×C3×Q8D411yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4—21no—
82C22×C3×D4—21no—
83C22×C3×D4C2311yescharacteristic
84C22×C3×D4C2311yescharacteristic
85C23×C3×C4—21no—
86C23×C3×C4—21no—
87C22×C3×C8C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C3×#127—22no—
92C3×#127—22no—
93C3×#125—22no—
94C3×#125—22no—
95C3×#124—28no—
96C3×#124—22no—
97C3×#124—22no—
98C3×#124—22no—
99C3×#124D414yes—
100C3×#123—28no—
101C3×#123—28no—
102C3×C4×Q8—22no—
103C3×C4×Q8—22no—
104C3×C4×Q8—22no—
105C3×C4×Q8—22no—
106C3×C4×D4—28no—
107C3×C4×D4—22no—
108C3×C4×D4—22no—
109C3×C4×D4—22no—
110C3×C4×D4D414yes—
111C2×C3×C4⋊C4—21no—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4—21no—
114C2×C3×C4⋊C4—21no—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4—21no—
117C2×C3×C4⋊C4—21no—
118C2×C3×C4⋊C4D411yescharacteristic
119C2×C3×C4⋊C4D411yescharacteristic
120C2×C3×C4⋊C4D411yescharacteristic
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C22⋊C4—21no—
127C2×C3×C22⋊C4—21no—
128C2×C3×C22⋊C4—21no—
129C2×C3×C22⋊C4—21no—
130C2×C3×C22⋊C4—21no—
131C2×C3×C22⋊C4—21no—
132C2×C3×C42—21no—
133C2×C3×C42—21no—
134C2×C3×C42C2311yescharacteristic
135C2×C3×C42C2311yescharacteristic
136C2×C3×C42C2311yescharacteristic
137C3×#107—22no—
138C3×#106—22no—
139C3×C4⋊C8—22no—
140C3×#103—22no—
141C3×#103—22no—
142C3×#103—22no—
143C3×#103—22no—
144C3×#102—22no—
145C3×#102—22no—
146C3×#102—22no—
147C3×#102—22no—
148C3×#102—22no—
149C3×#102—22no—
150C3×#102—22no—
151C3×#102—22no—
152C3×C4×C8—22no—
153C3×#95—21no—
154C3×#95—21no—
155C3×#95—21no—
156C3×#95—21no—
157C3×#95—21no—
158#559—24no—
159#559—24no—
160C2×#127C22×C311yescharacteristic
161C2×#125C22×C311yescharacteristic
162C2×#124—21no—
163C2×#124C22×C311yescharacteristic
164C2×#124C22×C311yescharacteristic
165C2×#123—21no—
166C2×#123—21no—
167C2×C4×Q8C22×C311yescharacteristic
168C2×C4×Q8C22×C311yescharacteristic
169C2×C4×D4—21no—
170C2×C4×D4C22×C311yescharacteristic
171C2×C4×D4C22×C311yescharacteristic
172#488—24no—
173#478—24no—
174C2×#107C22×C311yescharacteristic
175C2×#106C22×C311yescharacteristic
176C2×C4⋊C8C22×C311yescharacteristic
177C2×#103C22×C311yescharacteristic
178C2×#103C22×C311yescharacteristic
179C2×#103C22×C311yescharacteristic
180C2×#103C22×C311yescharacteristic
181C2×#102C22×C311yescharacteristic
182C2×#102C22×C311yescharacteristic
183C2×#102C22×C311yescharacteristic
184C2×#102C22×C311yescharacteristic
185C2×#102C22×C311yescharacteristic
186C2×#102C22×C311yescharacteristic
187C2×#102C22×C311yescharacteristic
188C2×#102C22×C311yescharacteristic
189C2×C4×C8C22×C311yescharacteristic
190#398—21no—
191#395—21no—
192#389—21no—
193#389—21no—
194#389C22×C311yescharacteristic
195#389C22×C311yescharacteristic
196#389C22×C311yescharacteristic
197#389C22×C311yescharacteristic
198C4×C4⋊C4C22×C311yescharacteristic
199#340C22×C311yescharacteristic
200#340C22×C311yescharacteristic
201#336C22×C311yescharacteristic
202#336C22×C311yescharacteristic
203#336C22×C311yescharacteristic
204#336C22×C311yescharacteristic
205C24×C3—21no—
206C24×C3—21no—
207C2×C3×Q8—22no—
208C2×C3×Q8—22no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—21no—
212C2×C3×Q8—21no—
213C2×C3×Q8—21no—
214C2×C3×Q8—41no—
215C2×C3×Q8C2×D412yes—
216C2×C3×D4—24no—
217C2×C3×D4—24no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—42no—
229C2×C3×D4—42no—
230C2×C3×D4—81no—
231C2×C3×D4—81no—
232C2×C3×D4C2×D412yes—
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—24no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—81no—
243C22×C3×C4—81no—
244C22×C3×C4—81no—
245C22×C3×C4—81no—
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2×D411yescharacteristic
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2×D411yescharacteristic
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2411yescharacteristic
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—21no—
264C2×C3×C8—21no—
265C3×C4⋊C4—24no—
266C3×C4⋊C4—22no—
267C3×C4⋊C4—22no—
268C3×C4⋊C4—22no—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—42no—
277C3×C4⋊C4—42no—
278C3×C4⋊C4—42no—
279C3×C4⋊C4—42no—
280C3×C4⋊C4—81no—
281C3×C4⋊C4—81no—
282C3×C4⋊C4C2×D412yes—
283C3×C4⋊C4#4112yes—
284C3×C4⋊C4#4112yes—
285C3×C22⋊C4—24no—
286C3×C22⋊C4—24no—
287C3×C22⋊C4—24no—
288C3×C22⋊C4—24no—
289C3×C22⋊C4—24no—
290C3×C22⋊C4—24no—
291C3×C42—24no—
292C3×C42—21no—
293C3×C42—21no—
294C3×C42—21no—
295C3×C42—21no—
296C3×C42—81no—
297C3×C42C2×D412yes—
298C3×C42C2×D412yes—
299C22×Q8C3×D411yescharacteristic
300C22×Q8C23×C311yescharacteristic
301C22×D4—21no—
302C22×D4—21no—
303C22×D4C23×C311yescharacteristic
304C22×D4C23×C311yescharacteristic
305C23×C4—21no—
306C23×C4—21no—
307C22×C8C23×C311yescharacteristic
308C22×C8C23×C311yescharacteristic
309C22×C8C23×C311yescharacteristic
310C22×C8C23×C311yescharacteristic
311#127—22no—
312#127—22no—
313#125—22no—
314#125—22no—
315#124—28no—
316#124—22no—
317#124—22no—
318#124—22no—
319#124C3×D414yes—
320#123—28no—
321#123—28no—
322C4×Q8—22no—
323C4×Q8—22no—
324C4×Q8—22no—
325C4×Q8—22no—
326C4×D4—28no—
327C4×D4—22no—
328C4×D4—22no—
329C4×D4—22no—
330C4×D4C3×D414yes—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4C3×D411yescharacteristic
339C2×C4⋊C4C3×D411yescharacteristic
340C2×C4⋊C4C3×D411yescharacteristic
341C2×C4⋊C4C23×C311yescharacteristic
342C2×C4⋊C4C23×C311yescharacteristic
343C2×C4⋊C4C23×C311yescharacteristic
344C2×C4⋊C4C23×C311yescharacteristic
345C2×C4⋊C4C23×C311yescharacteristic
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42C23×C311yescharacteristic
355C2×C42C23×C311yescharacteristic
356C2×C42C23×C311yescharacteristic
357#107—22no—
358#106—22no—
359C4⋊C8—22no—
360#103—22no—
361#103—22no—
362#103—22no—
363#103—22no—
364#102—22no—
365#102—22no—
366#102—22no—
367#102—22no—
368#102—22no—
369#102—22no—
370#102—22no—
371#102—22no—
372C4×C8—22no—
373#95—21no—
374#95—21no—
375#95—21no—
376#95—21no—
377#95—21no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—41no—
381C23×C3—41no—
382C23×C3—41no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—41no—
387C23×C3—41no—
388C23×C3—41no—
389C23×C3—41no—
390C23×C3—41no—
391C23×C3—41no—
392C23×C3C22×D411yescharacteristic
393C3×Q8—22no—
394C3×Q8—22no—
395C3×Q8—44no—
396C3×Q8—41no—
397C3×Q8—41no—
398C3×D4—22no—
399C3×D4—22no—
400C3×D4—22no—
401C3×D4—22no—
402C3×D4—48no—
403C3×D4—41no—
404C3×D4—41no—
405C3×D4—41no—
406C3×D4—41no—
407C3×D4—84no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—22no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—22no—
418C2×C3×C4—21no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
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—41no—
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—84no—
442C2×C3×C4—84no—
443C2×C3×C4#12012yes—
444C2×C3×C4#12012yes—
445C2×C3×C4#13512yes—
446C2×C3×C4C22×D411yescharacteristic
447C2×C3×C4C22×D411yescharacteristic
448C2×C3×C4C2×#4111yescharacteristic
449C2×C3×C4C2×#4111yescharacteristic
450C2×C3×C42−1+411yescharacteristic
451C2×C3×C42−1+411yescharacteristic
452C3×C8—41no—
453C3×C8—41no—
454C3×C8—41no—
455C3×C8—41no—
456C24—21no—
457C24—21no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—41no—
466C2×Q8C2×C3×D412yes—
467C2×D4—24no—
468C2×D4—24no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—81no—
482C2×D4—81no—
483C2×D4C2×C3×D412yes—
484C2×D4C2×C3×D412yes—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—81no—
494C22×C4—81no—
495C22×C4—81no—
496C22×C4—81no—
497C22×C4C2×C3×D411yescharacteristic
498C22×C4C2×C3×D411yescharacteristic
499C22×C4C2×C3×D411yescharacteristic
500C22×C4C2×C3×D411yescharacteristic
501C22×C4C2×C3×D411yescharacteristic
502C22×C4C2×C3×D411yescharacteristic
503C22×C4C24×C311yescharacteristic
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C4⋊C4—24no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—42no—
528C4⋊C4—42no—
529C4⋊C4—42no—
530C4⋊C4—42no—
531C4⋊C4—81no—
532C4⋊C4—81no—
533C4⋊C4C2×C3×D412yes—
534C4⋊C4C3×#4112yes—
535C4⋊C4C3×#4112yes—
536C22⋊C4—24no—
537C22⋊C4—24no—
538C22⋊C4—24no—
539C22⋊C4—24no—
540C22⋊C4—24no—
541C22⋊C4—24no—
542C42—24no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—81no—
548C42C2×C3×D412yes—
549C42C2×C3×D412yes—
550C22×C3—42no—
551C22×C3—42no—
552C22×C3—42no—
553C22×C3—42no—
554C22×C3—42no—
555C22×C3—42no—
556C22×C3—81no—
557C22×C3—81no—
558C22×C3—81no—
559C22×C3—81no—
560C22×C3—81no—
561C22×C3—81no—
562C22×C3—81no—
563C22×C3—81no—
564C22×C3C2×#12011yescharacteristic
565C22×C3#54811yescharacteristic
566C22×C3#54811yescharacteristic
567C22×C3C2×#13511yescharacteristic
568C22×C3#57511yescharacteristic
569C22×C3#57611yescharacteristic
570C22×C3#57711yescharacteristic
571C3×C4—22no—
572C3×C4—22no—
573C3×C4—22no—
574C3×C4—42no—
575C3×C4—42no—
576C3×C4—42no—
577C3×C4—41no—
578C3×C4—41no—
579C3×C4—41no—
580C3×C4—42no—
581C3×C4—81no—
582C3×C4—81no—
583C3×C4#53211yescharacteristic
584C3×C4#53611yescharacteristic
585C3×C4#54711yescharacteristic
586C3×C4#54711yescharacteristic
587C23—22no—
588C23—22no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23C22×C3×D411yescharacteristic
602Q8—22no—
603Q8—22no—
604Q8—44no—
605Q8—41no—
606Q8—41no—
607D4—22no—
608D4—22no—
609D4—22no—
610D4—22no—
611D4—48no—
612D4—41no—
613D4—41no—
614D4—41no—
615D4—41no—
616D4—84no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—21no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—84no—
651C2×C4—84no—
652C2×C4C3×#12012yes—
653C2×C4C3×#12012yes—
654C2×C4C3×#13512yes—
655C2×C4C22×C3×D411yescharacteristic
656C2×C4C22×C3×D411yescharacteristic
657C2×C4C2×C3×#4111yescharacteristic
658C2×C4C2×C3×#4111yescharacteristic
659C2×C4C3×2−1+411yescharacteristic
660C2×C4C3×2−1+411yescharacteristic
661C8—41no—
662C8—41no—
663C8—41no—
664C8—41no—
665C2×C3—82no—
666C2×C3—82no—
667C2×C3#243211yescharacteristic
668C2×C3#300211yescharacteristic
669C2×C3#301211yescharacteristic
670C2×C3#336111yescharacteristic
671C2×C3#336511yescharacteristic
672C2×C3#337011yescharacteristic
673C2×C3#337111yescharacteristic
674C22—42no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22C2×C3×#12011yescharacteristic
689C22C3×#54811yescharacteristic
690C22C3×#54811yescharacteristic
691C22C2×C3×#13511yescharacteristic
692C22C3×#57511yescharacteristic
693C22C3×#57611yescharacteristic
694C22C3×#57711yescharacteristic
695C4—22no—
696C4—22no—
697C4—22no—
698C4—42no—
699C4—41no—
700C4—41no—
701C4—41no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—81no—
706C4—81no—
707C4C3×#53211yescharacteristic
708C4C3×#53611yescharacteristic
709C4C3×#54711yescharacteristic
710C4C3×#54711yescharacteristic
711C3#2565311yescharacteristic, direct product factor, Sylow
712C2—82no—
713C2—82no—
714C2C3×#243211yescharacteristic
715C2C3×#300211yescharacteristic
716C2C3×#301211yescharacteristic
717C2C3×#336111yescharacteristic
718C2C3×#336511yescharacteristic
719C2C3×#337011yescharacteristic
720C2C3×#337111yescharacteristic
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×#488C2semidirect
3. C2×C3×#478C2semidirect
4. C3×#2584C2semidirect
5. C3×#2042C2semidirect
6. C3×#2042C2semidirect
9. C3×#1984C2semidirect
10. C3×#1983C2semidirect
11. C3×#1865C2semidirect
12. C3×#1864C2semidirect
13. C3×#1863C2semidirect
14. C3×#1862C2semidirect
15. C3×C4×#102C2semidirect
16. #25653C3direct (N × H)
65. C2×#488C2×C3semidirect
66. C2×#478C2×C3semidirect
67. #2584C2×C3semidirect
68. #2042C2×C3semidirect
69. #2042C2×C3semidirect
72. #1984C2×C3semidirect
73. #1983C2×C3semidirect
74. #1865C2×C3semidirect
75. #1864C2×C3semidirect
76. #1863C2×C3semidirect
77. #1862C2×C3semidirect
78. C4×#102C2×C3semidirect
711. C3#25653direct (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×#4882
C2×C3×#4782
C3×#25842
C3×#20422
C3×#20412
C3×#19842
C3×#19832
C3×#18652
C3×#18642
C3×#18632
C3×#18622
C3×C4×#1022
#256533