Finite Group Databasebeta

← C3×#24666 #10643273

Subgroups — C3×#24666 #10643273

Order 768.

870 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#461C211yesmaximal, characteristic, complemented
2C2×C3×#433C211yesmaximal, characteristic, complemented
3C3×#2621C211yesmaximal, characteristic, complemented
4C3×#2324C211yesmaximal, characteristic
5C3×#2036C211yesmaximal, characteristic, complemented
6C3×#2035C211yesmaximal, characteristic, complemented
7C3×#2000C211yesmaximal, characteristic
8C3×#2000C211yesmaximal, characteristic
9C3×#1981C211yesmaximal, characteristic, complemented
10C3×#1973C211yesmaximal, characteristic, complemented
11C3×#1968C211yesmaximal, characteristic, complemented
12C3×#1949C211yesmaximal, characteristic, complemented
13C3×#1935C211yesmaximal, characteristic, complemented
14C3×#1933C211yesmaximal, characteristic, complemented
15C3×#1804C211yesmaximal, characteristic, complemented
16#24666C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C2×C3×C4⋊Q8C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21C2×C3×C22⋊Q8C2211yescharacteristic
22C2×C3×#121C2211yescharacteristic
23C2×C3×C4×D4C2211yescharacteristic
24C2×C3×#117C2211yescharacteristic
25C3×#461—24no—
26C3×#433—24no—
27C2×C3×#107C2211yescharacteristic
28C2×C3×#106C2211yescharacteristic
29C2×C3×C4⋊C8C2211yescharacteristic
30C2×C3×C4⋊C8C2211yescharacteristic
31C2×C3×#103C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic
41C2×C3×#97C2211yescharacteristic
42C2×C3×C4×C8C2211yescharacteristic
43C3×#398—21no—
44C3×#398—21no—
45C3×#397—21no—
46C3×#397—21no—
47C3×#391C2211yescharacteristic
48C3×#391C2211yescharacteristic
49C3×#390—21no—
50C3×#390C2211yescharacteristic
51C3×#389C2211yescharacteristic
52C3×#388—21no—
53C3×#386—21no—
54C3×#385—21no—
55C3×#382C2211yescharacteristic
56C3×#380C2211yescharacteristic
57C3×C4×C4⋊C4C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C2×#461C2×C311yescharacteristic, complemented
63C2×#433C2×C311yescharacteristic, complemented
64#2621C2×C311yescharacteristic, complemented
65#2324C2×C311yescharacteristic
66#2036C2×C311yescharacteristic, complemented
67#2035C2×C311yescharacteristic, complemented
68#2000C2×C311yescharacteristic
69#2000C2×C311yescharacteristic
70#1981C2×C311yescharacteristic, complemented
71#1973C2×C311yescharacteristic, complemented
72#1968C2×C311yescharacteristic, complemented
73#1949C2×C311yescharacteristic, complemented
74#1935C2×C311yescharacteristic, complemented
75#1933C2×C311yescharacteristic, complemented
76#1804C2×C311yescharacteristic, complemented
77C22×C3×Q8C2311yescharacteristic
78C22×C3×Q8C2311yescharacteristic
79C22×C3×D4—21no—
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4—21no—
82C23×C3×C4C2311yescharacteristic
83C2×C3×SD16—22no—
84C2×C3×SD16—22no—
85C2×C3×SD16—22no—
86C2×C3×SD16—22no—
87C2×C3×SD16—41no—
88C2×C3×SD16—41no—
89C22×C3×C8C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C3×C4⋊Q8—22no—
94C3×C4⋊Q8—22no—
95C3×C22⋊Q8—41no—
96C3×C22⋊Q8—41no—
97C3×C22⋊Q8—41no—
98C3×C22⋊Q8—41no—
99C3×#121—22no—
100C3×#121—22no—
101C3×C4×D4—22no—
102C3×C4×D4—22no—
103C3×#117—22no—
104C3×#117—22no—
105C2×C3×C4⋊C4—21no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4—21no—
110C2×C3×C4⋊C4D411yescharacteristic
111C2×C3×C4⋊C4D411yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C4⋊C4C2311yescharacteristic
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4—21no—
121C2×C3×C22⋊C4—21no—
122C2×C3×C22⋊C4—21no—
123C2×C3×C22⋊C4—21no—
124C2×C3×C22⋊C4D411yescharacteristic
125C2×C3×C22⋊C4D411yescharacteristic
126C2×C3×C42—21no—
127C2×C3×C42C2311yescharacteristic
128C2×C3×C42C2311yescharacteristic
129C3×#107—41no—
130C3×#106—41no—
131C3×C4⋊C8—22no—
132C3×C4⋊C8D414yescomplemented
133C3×#103—22no—
134C3×#103—22no—
135C3×#103—22no—
136C3×#103—22no—
137C3×#103—41no—
138C3×#103—41no—
139C3×#102—41no—
140C3×#102—41no—
141C3×C22⋊C8—22no—
142C3×C22⋊C8—22no—
143C3×#97—22no—
144C3×C4×C8—22no—
145C3×#95—21no—
146C3×#95—21no—
147C3×#95—21no—
148C3×#95—21no—
149C3×#95—21no—
150C3×#95—21no—
151C3×#95—21no—
152C3×#95—21no—
153C3×#95—21no—
154C22×SD16C22×C311yescharacteristic
155C22×SD16C22×C311yescharacteristic
156C2×C4⋊Q8C22×C311yescharacteristic
157C2×C22⋊Q8C22×C311yescharacteristic
158C2×C22⋊Q8C22×C311yescharacteristic
159C2×#121C22×C311yescharacteristic
160C2×C4×D4C22×C311yescharacteristic
161C2×#117C22×C311yescharacteristic
162#461—24no—
163#433—24no—
164C2×#107C22×C311yescharacteristic
165C2×#106C22×C311yescharacteristic
166C2×C4⋊C8C22×C311yescharacteristic
167C2×C4⋊C8C22×C311yescharacteristic
168C2×#103C22×C311yescharacteristic
169C2×#103C22×C311yescharacteristic
170C2×#103C22×C311yescharacteristic
171C2×#103C22×C311yescharacteristic
172C2×#103C22×C311yescharacteristic
173C2×#103C22×C311yescharacteristic
174C2×#102C22×C311yescharacteristic
175C2×#102C22×C311yescharacteristic
176C2×C22⋊C8C22×C311yescharacteristic
177C2×C22⋊C8C22×C311yescharacteristic
178C2×#97C22×C311yescharacteristic
179C2×C4×C8C22×C311yescharacteristic
180#398—21no—
181#398—21no—
182#397—21no—
183#397—21no—
184#391C22×C311yescharacteristic
185#391C22×C311yescharacteristic
186#390—21no—
187#390C22×C311yescharacteristic
188#389C22×C311yescharacteristic
189#388—21no—
190#386—21no—
191#385—21no—
192#382C22×C311yescharacteristic
193#380C22×C311yescharacteristic
194C4×C4⋊C4C22×C311yescharacteristic
195#340C22×C311yescharacteristic
196#340C22×C311yescharacteristic
197#340C22×C311yescharacteristic
198#340C22×C311yescharacteristic
199C24×C3—21no—
200C24×C3C2×D411yescharacteristic
201C2×C3×Q8—21no—
202C2×C3×Q8—21no—
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—21no—
206C2×C3×Q8—21no—
207C2×C3×Q8—21no—
208C2×C3×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—21no—
212C2×C3×Q8—21no—
213C2×C3×D4—24no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—81no—
220C2×C3×D4—81no—
221C2×C3×D4#4112yes—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—42no—
236C22×C3×C4—81no—
237C22×C3×C4—81no—
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2411yescharacteristic
244C3×SD16—44no—
245C3×SD16—44no—
246C2×C3×C8—21no—
247C2×C3×C8—21no—
248C2×C3×C8—21no—
249C2×C3×C8—21no—
250C2×C3×C8—21no—
251C2×C3×C8—21no—
252C2×C3×C8—21no—
253C2×C3×C8—21no—
254C2×C3×C8—21no—
255C2×C3×C8—21no—
256C2×C3×C8C2×D412yes—
257C2×C3×C8C2×D412yes—
258C3×C4⋊C4—22no—
259C3×C4⋊C4—22no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—42no—
270C3×C4⋊C4—42no—
271C3×C4⋊C4—42no—
272C3×C4⋊C4—42no—
273C3×C4⋊C4—81no—
274C3×C4⋊C4#4112yes—
275C3×C22⋊C4—24no—
276C3×C22⋊C4—22no—
277C3×C22⋊C4—22no—
278C3×C22⋊C4—42no—
279C3×C22⋊C4—42no—
280C3×C22⋊C4—42no—
281C3×C22⋊C4—81no—
282C3×C22⋊C4—81no—
283C3×C22⋊C4—81no—
284C3×C42—21no—
285C3×C42—21no—
286C3×C42—81no—
287C3×C42C2×D412yes—
288C3×C42#4112yes—
289C22×Q8C23×C311yescharacteristic
290C22×Q8C23×C311yescharacteristic
291C22×D4—21no—
292C22×D4C23×C311yescharacteristic
293C23×C4—21no—
294C23×C4C23×C311yescharacteristic
295C2×SD16—22no—
296C2×SD16—22no—
297C2×SD16—22no—
298C2×SD16—22no—
299C2×SD16—41no—
300C2×SD16—41no—
301C22×C8C23×C311yescharacteristic
302C22×C8C23×C311yescharacteristic
303C22×C8C23×C311yescharacteristic
304C22×C8C23×C311yescharacteristic
305C4⋊Q8—22no—
306C4⋊Q8—22no—
307C22⋊Q8—41no—
308C22⋊Q8—41no—
309C22⋊Q8—41no—
310C22⋊Q8—41no—
311#121—22no—
312#121—22no—
313C4×D4—22no—
314C4×D4—22no—
315#117—22no—
316#117—22no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4C3×D411yescharacteristic
323C2×C4⋊C4C3×D411yescharacteristic
324C2×C4⋊C4C23×C311yescharacteristic
325C2×C4⋊C4C23×C311yescharacteristic
326C2×C4⋊C4C23×C311yescharacteristic
327C2×C4⋊C4C23×C311yescharacteristic
328C2×C4⋊C4C23×C311yescharacteristic
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4C3×D411yescharacteristic
337C2×C22⋊C4C3×D411yescharacteristic
338C2×C42—21no—
339C2×C42C23×C311yescharacteristic
340C2×C42C23×C311yescharacteristic
341#107—41no—
342#106—41no—
343C4⋊C8—22no—
344C4⋊C8C3×D414yescomplemented
345#103—22no—
346#103—22no—
347#103—22no—
348#103—22no—
349#103—41no—
350#103—41no—
351#102—41no—
352#102—41no—
353C22⋊C8—22no—
354C22⋊C8—22no—
355#97—22no—
356C4×C8—22no—
357#95—21no—
358#95—21no—
359#95—21no—
360#95—21no—
361#95—21no—
362#95—21no—
363#95—21no—
364#95—21no—
365#95—21no—
366C23×C3—21no—
367C23×C3—22no—
368C23×C3—21no—
369C23×C3—21no—
370C23×C3—21no—
371C23×C3—21no—
372C23×C3—21no—
373C23×C3—21no—
374C23×C3—41no—
375C23×C3—41no—
376C23×C3—41no—
377C23×C3—41no—
378C23×C3—41no—
379C23×C3—41no—
380C23×C3C22×D411yescharacteristic
381C3×Q8—41no—
382C3×Q8—41no—
383C3×Q8—41no—
384C3×Q8—41no—
385C3×Q8—41no—
386C3×Q8—41no—
387C3×Q8—41no—
388C3×Q8—41no—
389C3×D4—22no—
390C3×D4—22no—
391C3×D4—41no—
392C3×D4—41no—
393C3×D4—84no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—22no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4—41no—
414C2×C3×C4—41no—
415C2×C3×C4—41no—
416C2×C3×C4—41no—
417C2×C3×C4—41no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—84no—
433C2×C3×C4#12112yes—
434C2×C3×C4#12112yes—
435C2×C3×C4C22×D411yescharacteristic
436C2×C3×C4C2×#4111yescharacteristic
437C2×C3×C4C2×#4111yescharacteristic
438C2×C3×C4C2×#4111yescharacteristic
439C2×C3×C4H(5,𝔽2)11yescharacteristic
440C2×C3×C4H(5,𝔽2)11yescharacteristic
441C3×C8—22no—
442C3×C8—22no—
443C3×C8—41no—
444C3×C8—41no—
445C24—21no—
446C24C2×C3×D411yescharacteristic
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×D4—24no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—81no—
466C2×D4—81no—
467C2×D4C3×#4112yes—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—42no—
482C22×C4—81no—
483C22×C4—81no—
484C22×C4C2×C3×D411yescharacteristic
485C22×C4C2×C3×D411yescharacteristic
486C22×C4C2×C3×D411yescharacteristic
487C22×C4C2×C3×D411yescharacteristic
488C22×C4C2×C3×D411yescharacteristic
489C22×C4C24×C311yescharacteristic
490SD16—44no—
491SD16—44no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8C2×C3×D412yes—
503C2×C8C2×C3×D412yes—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—42no—
516C4⋊C4—42no—
517C4⋊C4—42no—
518C4⋊C4—42no—
519C4⋊C4—81no—
520C4⋊C4C3×#4112yes—
521C22⋊C4—24no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—42no—
525C22⋊C4—42no—
526C22⋊C4—42no—
527C22⋊C4—81no—
528C22⋊C4—81no—
529C22⋊C4—81no—
530C42—21no—
531C42—21no—
532C42—81no—
533C42C2×C3×D412yes—
534C42C3×#4112yes—
535C22×C3—41no—
536C22×C3—42no—
537C22×C3—41no—
538C22×C3—42no—
539C22×C3—41no—
540C22×C3—42no—
541C22×C3—41no—
542C22×C3—41no—
543C22×C3—41no—
544C22×C3—41no—
545C22×C3—81no—
546C22×C3—81no—
547C22×C3—81no—
548C22×C3—81no—
549C22×C3C2×#12111yescharacteristic
550C22×C3#52511yescharacteristic
551C22×C3#53511yescharacteristic
552C22×C3#57711yescharacteristic
553C22×C3#57711yescharacteristic
554C22×C3#57711yescharacteristic
555C22×C3#57811yescharacteristic
556C3×C4—22no—
557C3×C4—22no—
558C3×C4—42no—
559C3×C4—41no—
560C3×C4—41no—
561C3×C4—41no—
562C3×C4—81no—
563C3×C4—81no—
564C3×C4—81no—
565C3×C4—81no—
566C3×C4—81no—
567C3×C4—81no—
568C3×C4#54611yescharacteristic
569C3×C4#55011yescharacteristic
570C3×C4#55311yescharacteristic
571C3×C4#55511yescharacteristic
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—22no—
578C23—21no—
579C23—21no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23C22×C3×D411yescharacteristic
587Q8—41no—
588Q8—41no—
589Q8—41no—
590Q8—41no—
591Q8—41no—
592Q8—41no—
593Q8—41no—
594Q8—41no—
595D4—22no—
596D4—22no—
597D4—41no—
598D4—41no—
599D4—84no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—21no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
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—84no—
639C2×C4C3×#12112yes—
640C2×C4C3×#12112yes—
641C2×C4C22×C3×D411yescharacteristic
642C2×C4C2×C3×#4111yescharacteristic
643C2×C4C2×C3×#4111yescharacteristic
644C2×C4C2×C3×#4111yescharacteristic
645C2×C4C3×H(5,𝔽2)11yescharacteristic
646C2×C4C3×H(5,𝔽2)11yescharacteristic
647C8—22no—
648C8—22no—
649C8—41no—
650C8—41no—
651C2×C3—81no—
652C2×C3—82no—
653C2×C3#241411yescharacteristic
654C2×C3#305711yescharacteristic
655C2×C3#306311yescharacteristic
656C2×C3#312011yescharacteristic
657C2×C3#312311yescharacteristic
658C2×C3#322111yescharacteristic
659C2×C3#322511yescharacteristic
660C22—41no—
661C22—42no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—42no—
668C22—41no—
669C22—42no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22C2×C3×#12111yescharacteristic
675C22C3×#52511yescharacteristic
676C22C3×#53511yescharacteristic
677C22C3×#57711yescharacteristic
678C22C3×#57711yescharacteristic
679C22C3×#57711yescharacteristic
680C22C3×#57811yescharacteristic
681C4—22no—
682C4—22no—
683C4—41no—
684C4—41no—
685C4—41no—
686C4—42no—
687C4—81no—
688C4—81no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4—81no—
693C4C3×#54611yescharacteristic
694C4C3×#55011yescharacteristic
695C4C3×#55311yescharacteristic
696C4C3×#55511yescharacteristic
697C3#2466611yescharacteristic, direct product factor, Sylow
698C2—81no—
699C2—82no—
700C2C3×#241411yescharacteristic
701C2C3×#305711yescharacteristic
702C2C3×#306311yescharacteristic
703C2C3×#312011yescharacteristic
704C2C3×#312311yescharacteristic
705C2C3×#322111yescharacteristic
706C2C3×#322511yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#121C22
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
1. C2×C3×#461C2semidirect
2. C2×C3×#433C2semidirect
3. C3×#2621C2semidirect
5. C3×#2036C2semidirect
6. C3×#2035C2semidirect
9. C3×#1981C2semidirect
10. C3×#1973C2semidirect
11. C3×#1968C2semidirect
12. C3×#1949C2semidirect
13. C3×#1935C2semidirect
14. C3×#1933C2semidirect
15. C3×#1804C2semidirect
16. #24666C3direct (N × H)
62. C2×#461C2×C3semidirect
63. C2×#433C2×C3semidirect
64. #2621C2×C3semidirect
66. #2036C2×C3semidirect
67. #2035C2×C3semidirect
70. #1981C2×C3semidirect
71. #1973C2×C3semidirect
72. #1968C2×C3semidirect
73. #1949C2×C3semidirect
74. #1935C2×C3semidirect
75. #1933C2×C3semidirect
76. #1804C2×C3semidirect
132. C3×C4⋊C8D4semidirect
344. C4⋊C8C3×D4semidirect
697. C3#24666direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4612
C2×C3×#4332
C3×#26212
C3×#23242
C3×#20362
C3×#20352
C3×#20002
C3×#19812
C3×#19732
C3×#19682
C3×#19492
C3×#19352
C3×#19332
C3×#18042
#246663