Finite Group Databasebeta

← C3×#24346 #10642953

Subgroups — C3×#24346 #10642953

Order 768.

1064 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#557C211yesmaximal, characteristic, complemented
2C2×C3×#478C211yesmaximal, characteristic
3C2×C3×#440C211yesmaximal, characteristic
4C3×#2538C211yesmaximal, characteristic
5C3×#2059C211yesmaximal, characteristic, complemented
6C3×#2057C211yesmaximal, characteristic, complemented
7C3×#2025C211yesmaximal, characteristic
8C3×#2023C211yesmaximal, characteristic
9C3×#1992C211yesmaximal, characteristic, complemented
10C3×#1985C211yesmaximal, characteristic, complemented
11C3×#1880C211yesmaximal, characteristic
12C3×#1880C211yesmaximal, characteristic
13C3×#1865C211yesmaximal, characteristic, complemented
14C3×#1863C211yesmaximal, characteristic, complemented
15C3×#1803C211yesmaximal, characteristic, complemented
16#24346C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×SD16C2211yescharacteristic
18C3×#557—24no—
19C3×#557—24no—
20C2×C3×C4⋊Q8—21no—
21C2×C3×C4⋊Q8C2211yescharacteristic
22C2×C3×#125—21no—
23C2×C3×#125—21no—
24C2×C3×#125C2211yescharacteristic
25C2×C3×#125C2211yescharacteristic
26C2×C3×C22⋊Q8—21no—
27C2×C3×C4×Q8—21no—
28C2×C3×C4×Q8C2211yescharacteristic
29C2×C3×C4×Q8C2211yescharacteristic
30C2×C3×C4×Q8C2211yescharacteristic
31C2×C3×C4×Q8C2211yescharacteristic
32C2×C3×C4×D4C2211yescharacteristic
33C3×#478—24no—
34C3×#440—24no—
35C2×C3×#107C2211yescharacteristic
36C2×C3×#107C2211yescharacteristic
37C2×C3×#106C2211yescharacteristic
38C2×C3×C4⋊C8C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#97C2211yescharacteristic
46C3×#396—21no—
47C3×#396—21no—
48C3×#390C2211yescharacteristic
49C3×#390C2211yescharacteristic
50C3×#389C2211yescharacteristic
51C3×#389C2211yescharacteristic
52C3×#384C2211yescharacteristic
53C3×#380—21no—
54C3×#340C2211yescharacteristic
55C3×#340C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#557C2×C311yescharacteristic, complemented
65C2×#478C2×C311yescharacteristic
66C2×#440C2×C311yescharacteristic
67#2538C2×C311yescharacteristic
68#2059C2×C311yescharacteristic, complemented
69#2057C2×C311yescharacteristic, complemented
70#2025C2×C311yescharacteristic
71#2023C2×C311yescharacteristic
72#1992C2×C311yescharacteristic, complemented
73#1985C2×C311yescharacteristic, complemented
74#1880C2×C311yescharacteristic
75#1880C2×C311yescharacteristic
76#1865C2×C311yescharacteristic, complemented
77#1863C2×C311yescharacteristic, complemented
78#1803C2×C311yescharacteristic, complemented
79C22×C3×Q8—21no—
80C22×C3×Q8D411yescharacteristic
81C22×C3×Q8C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4—21no—
84C2×C3×SD16—22no—
85C2×C3×SD16—22no—
86C2×C3×SD16Q814yescomplemented
87C22×C3×C8C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C3×C4⋊Q8—28no—
92C3×C4⋊Q8—22no—
93C3×C4⋊Q8—22no—
94C3×#125—28no—
95C3×#125—28no—
96C3×#125—22no—
97C3×#125—22no—
98C3×#125—22no—
99C3×#125D414yes—
100C3×C22⋊Q8—44no—
101C3×C4×Q8—28no—
102C3×C4×Q8—22no—
103C3×C4×Q8—22no—
104C3×C4×Q8—22no—
105C3×C4×Q8—22no—
106C3×C4×Q8—22no—
107C3×C4×Q8—22no—
108C3×C4×Q8—22no—
109C3×C4×Q8D414yes—
110C3×C4×D4—22no—
111C3×C4×D4—22no—
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⋊C4—21no—
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⋊C4D411yescharacteristic
125C2×C3×C4⋊C4D411yescharacteristic
126C2×C3×C4⋊C4D411yescharacteristic
127C2×C3×C4⋊C4C2311yescharacteristic
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×C42—21no—
139C2×C3×C42—21no—
140C2×C3×C42—21no—
141C2×C3×C42C2311yescharacteristic
142C2×C3×C42C2311yescharacteristic
143C2×C3×C42C2311yescharacteristic
144C3×#107—22no—
145C3×#107—22no—
146C3×#106—22no—
147C3×C4⋊C8—22no—
148C3×#103—22no—
149C3×#103—22no—
150C3×#103—22no—
151C3×#102—22no—
152C3×#102—22no—
153C3×#102—22no—
154C3×#97—22no—
155C3×#95—21no—
156C3×#95—21no—
157C22×SD16C22×C311yescharacteristic
158#557—24no—
159#557—24no—
160C2×C4⋊Q8—21no—
161C2×C4⋊Q8C22×C311yescharacteristic
162C2×#125—21no—
163C2×#125—21no—
164C2×#125C22×C311yescharacteristic
165C2×#125C22×C311yescharacteristic
166C2×C22⋊Q8—21no—
167C2×C4×Q8—21no—
168C2×C4×Q8C22×C311yescharacteristic
169C2×C4×Q8C22×C311yescharacteristic
170C2×C4×Q8C22×C311yescharacteristic
171C2×C4×Q8C22×C311yescharacteristic
172C2×C4×D4C22×C311yescharacteristic
173#478—24no—
174#440—24no—
175C2×#107C22×C311yescharacteristic
176C2×#107C22×C311yescharacteristic
177C2×#106C22×C311yescharacteristic
178C2×C4⋊C8C22×C311yescharacteristic
179C2×#103C22×C311yescharacteristic
180C2×#103C22×C311yescharacteristic
181C2×#103C22×C311yescharacteristic
182C2×#102C22×C311yescharacteristic
183C2×#102C22×C311yescharacteristic
184C2×#102C22×C311yescharacteristic
185C2×#97C22×C311yescharacteristic
186#396—21no—
187#396—21no—
188#390C22×C311yescharacteristic
189#390C22×C311yescharacteristic
190#389C22×C311yescharacteristic
191#389C22×C311yescharacteristic
192#384C22×C311yescharacteristic
193#380—21no—
194#340C22×C311yescharacteristic
195#340C22×C311yescharacteristic
196#340C22×C311yescharacteristic
197#340C22×C311yescharacteristic
198#340C22×C311yescharacteristic
199#340C22×C311yescharacteristic
200#336C22×C311yescharacteristic
201#336C22×C311yescharacteristic
202#336C22×C311yescharacteristic
203#336C22×C311yescharacteristic
204C24×C3—21no—
205C2×C3×Q8—24no—
206C2×C3×Q8—22no—
207C2×C3×Q8—22no—
208C2×C3×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—41no—
212C2×C3×Q8—42no—
213C2×C3×Q8—42no—
214C2×C3×Q8C2×D412yes—
215C2×C3×Q8C2×Q812yes—
216C2×C3×Q8#4112yes—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4C2×Q812yes—
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—42no—
231C22×C3×C4—42no—
232C22×C3×C4—42no—
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2411yescharacteristic
240C3×SD16—28no—
241C2×C3×C8—21no—
242C2×C3×C8—21no—
243C2×C3×C8—21no—
244C2×C3×C8—21no—
245C2×C3×C8—21no—
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×C8C2×Q812yes—
253C3×C4⋊C4—24no—
254C3×C4⋊C4—24no—
255C3×C4⋊C4—24no—
256C3×C4⋊C4—24no—
257C3×C4⋊C4—24no—
258C3×C4⋊C4—24no—
259C3×C4⋊C4—24no—
260C3×C4⋊C4—24no—
261C3×C4⋊C4—22no—
262C3×C4⋊C4—22no—
263C3×C4⋊C4—22no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—42no—
274C3×C4⋊C4—42no—
275C3×C4⋊C4—42no—
276C3×C4⋊C4—81no—
277C3×C4⋊C4C2×D412yes—
278C3×C4⋊C4C2×D412yes—
279C3×C4⋊C4C2×D412yes—
280C3×C22⋊C4—42no—
281C3×C22⋊C4—42no—
282C3×C22⋊C4—42no—
283C3×C22⋊C4—81no—
284C3×C22⋊C4—81no—
285C3×C42—24no—
286C3×C42—24no—
287C3×C42—24no—
288C3×C42—21no—
289C3×C42—21no—
290C3×C42—21no—
291C3×C42—21no—
292C3×C42C2×D412yes—
293C3×C42C2×D412yes—
294C22×Q8—21no—
295C22×Q8C3×D411yescharacteristic
296C22×Q8C23×C311yescharacteristic
297C22×D4C23×C311yescharacteristic
298C23×C4—21no—
299C2×SD16—22no—
300C2×SD16—22no—
301C2×SD16C3×Q814yescomplemented
302C22×C8C23×C311yescharacteristic
303C22×C8C23×C311yescharacteristic
304C22×C8C23×C311yescharacteristic
305C22×C8C23×C311yescharacteristic
306C4⋊Q8—28no—
307C4⋊Q8—22no—
308C4⋊Q8—22no—
309#125—28no—
310#125—28no—
311#125—22no—
312#125—22no—
313#125—22no—
314#125C3×D414yes—
315C22⋊Q8—44no—
316C4×Q8—28no—
317C4×Q8—22no—
318C4×Q8—22no—
319C4×Q8—22no—
320C4×Q8—22no—
321C4×Q8—22no—
322C4×Q8—22no—
323C4×Q8—22no—
324C4×Q8C3×D414yes—
325C4×D4—22no—
326C4×D4—22no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
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⋊C4—21no—
339C2×C4⋊C4C3×D411yescharacteristic
340C2×C4⋊C4C3×D411yescharacteristic
341C2×C4⋊C4C3×D411yescharacteristic
342C2×C4⋊C4C23×C311yescharacteristic
343C2×C4⋊C4C23×C311yescharacteristic
344C2×C4⋊C4C23×C311yescharacteristic
345C2×C4⋊C4C23×C311yescharacteristic
346C2×C4⋊C4C23×C311yescharacteristic
347C2×C4⋊C4C23×C311yescharacteristic
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—21no—
356C2×C42C23×C311yescharacteristic
357C2×C42C23×C311yescharacteristic
358C2×C42C23×C311yescharacteristic
359#107—22no—
360#107—22no—
361#106—22no—
362C4⋊C8—22no—
363#103—22no—
364#103—22no—
365#103—22no—
366#102—22no—
367#102—22no—
368#102—22no—
369#97—22no—
370#95—21no—
371#95—21no—
372C23×C3—22no—
373C23×C3—41no—
374C23×C3—41no—
375C23×C3—41no—
376C23×C3—41no—
377C23×C3—41no—
378C23×C3—41no—
379C23×C3C22×D411yescharacteristic
380C3×Q8—22no—
381C3×Q8—22no—
382C3×Q8—22no—
383C3×Q8—44no—
384C3×Q8—48no—
385C3×Q8C22⋊Q814yescomplemented
386C3×D4—22no—
387C3×D4—22no—
388C3×D4—41no—
389C3×D4—41no—
390C2×C3×C4—22no—
391C2×C3×C4—21no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
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—22no—
402C2×C3×C4—21no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
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—84no—
427C2×C3×C4#12012yes—
428C2×C3×C4#12012yes—
429C2×C3×C4AGL(1,ℤ/8)12yes—
430C2×C3×C4C22×D411yescharacteristic
431C2×C3×C4C22×D411yescharacteristic
432C2×C3×C4C22×Q811yescharacteristic
433C2×C3×C4C2×#4111yescharacteristic
434C2×C3×C42−1+411yescharacteristic
435C2×C3×C42−1+411yescharacteristic
436C3×C8—22no—
437C3×C8—41no—
438C3×C8—41no—
439C3×C8—41no—
440C24—21no—
441C2×Q8—24no—
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—41no—
448C2×Q8—42no—
449C2×Q8—42no—
450C2×Q8C2×C3×D412yes—
451C2×Q8C2×C3×Q812yes—
452C2×Q8C3×#4112yes—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4C2×C3×Q812yes—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4C2×C3×D411yescharacteristic
470C22×C4C2×C3×D411yescharacteristic
471C22×C4C2×C3×D411yescharacteristic
472C22×C4C2×C3×D411yescharacteristic
473C22×C4C2×C3×D411yescharacteristic
474C22×C4C2×C3×D411yescharacteristic
475C22×C4C24×C311yescharacteristic
476SD16—28no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8C2×C3×Q812yes—
489C4⋊C4—24no—
490C4⋊C4—24no—
491C4⋊C4—24no—
492C4⋊C4—24no—
493C4⋊C4—24no—
494C4⋊C4—24no—
495C4⋊C4—24no—
496C4⋊C4—24no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—42no—
510C4⋊C4—42no—
511C4⋊C4—42no—
512C4⋊C4—81no—
513C4⋊C4C2×C3×D412yes—
514C4⋊C4C2×C3×D412yes—
515C4⋊C4C2×C3×D412yes—
516C22⋊C4—42no—
517C22⋊C4—42no—
518C22⋊C4—42no—
519C22⋊C4—81no—
520C22⋊C4—81no—
521C42—24no—
522C42—24no—
523C42—24no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42C2×C3×D412yes—
529C42C2×C3×D412yes—
530C22×C3—42no—
531C22×C3—42no—
532C22×C3—42no—
533C22×C3—81no—
534C22×C3—81no—
535C22×C3—81no—
536C22×C3—81no—
537C22×C3C2×#12011yescharacteristic
538C22×C3#54811yescharacteristic
539C22×C3D4×Q811yescharacteristic
540C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
541C22×C3#57511yescharacteristic
542C22×C3#57711yescharacteristic
543C22×C3#57811yescharacteristic
544C3×C4—24no—
545C3×C4—22no—
546C3×C4—22no—
547C3×C4—22no—
548C3×C4—41no—
549C3×C4—42no—
550C3×C4—42no—
551C3×C4—41no—
552C3×C4—41no—
553C3×C4—42no—
554C3×C4—81no—
555C3×C4—81no—
556C3×C4—81no—
557C3×C4C2×C22⋊Q811yescharacteristic
558C3×C4#53611yescharacteristic
559C3×C4#54811yescharacteristic
560C3×C4D4×Q811yescharacteristic
561C23—22no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23C22×C3×D411yescharacteristic
569Q8—22no—
570Q8—22no—
571Q8—22no—
572Q8—44no—
573Q8—48no—
574Q8C3×C22⋊Q814yescomplemented
575D4—22no—
576D4—22no—
577D4—41no—
578D4—41no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—84no—
616C2×C4C3×#12012yes—
617C2×C4C3×#12012yes—
618C2×C4C3×AGL(1,ℤ/8)12yes—
619C2×C4C22×C3×D411yescharacteristic
620C2×C4C22×C3×D411yescharacteristic
621C2×C4C22×C3×Q811yescharacteristic
622C2×C4C2×C3×#4111yescharacteristic
623C2×C4C3×2−1+411yescharacteristic
624C2×C4C3×2−1+411yescharacteristic
625C8—22no—
626C8—41no—
627C8—41no—
628C8—41no—
629C2×C3—82no—
630C2×C3#240911yescharacteristic
631C2×C3#300611yescharacteristic
632C2×C3#301311yescharacteristic
633C2×C3#336811yescharacteristic
634C2×C3#337711yescharacteristic
635C2×C3#338611yescharacteristic
636C2×C3#338811yescharacteristic
637C22—42no—
638C22—42no—
639C22—42no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22C2×C3×#12011yescharacteristic
645C22C3×#54811yescharacteristic
646C22C3×D4×Q811yescharacteristic
647C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
648C22C3×#57511yescharacteristic
649C22C3×#57711yescharacteristic
650C22C3×#57811yescharacteristic
651C4—24no—
652C4—22no—
653C4—22no—
654C4—22no—
655C4—41no—
656C4—42no—
657C4—42no—
658C4—41no—
659C4—41no—
660C4—42no—
661C4—81no—
662C4—81no—
663C4—81no—
664C4C2×C3×C22⋊Q811yescharacteristic
665C4C3×#53611yescharacteristic
666C4C3×#54811yescharacteristic
667C4C3×D4×Q811yescharacteristic
668C3#2434611yescharacteristic, direct product factor, Sylow
669C2—82no—
670C2C3×#240911yescharacteristic
671C2C3×#300611yescharacteristic
672C2C3×#301311yescharacteristic
673C2C3×#336811yescharacteristic
674C2C3×#337711yescharacteristic
675C2C3×#338611yescharacteristic
676C2C3×#338811yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×D4C23
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
1. C2×C3×#557C2semidirect
5. C3×#2059C2semidirect
6. C3×#2057C2semidirect
9. C3×#1992C2semidirect
10. C3×#1985C2semidirect
13. C3×#1865C2semidirect
14. C3×#1863C2semidirect
15. C3×#1803C2semidirect
16. #24346C3direct (N × H)
64. C2×#557C2×C3semidirect
68. #2059C2×C3semidirect
69. #2057C2×C3semidirect
72. #1992C2×C3semidirect
73. #1985C2×C3semidirect
76. #1865C2×C3semidirect
77. #1863C2×C3semidirect
78. #1803C2×C3semidirect
86. C2×C3×SD16Q8semidirect
301. C2×SD16C3×Q8semidirect
385. C3×Q8C22⋊Q8semidirect
574. Q8C3×C22⋊Q8semidirect
668. C3#24346direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5572
C2×C3×#4782
C2×C3×#4402
C3×#25382
C3×#20592
C3×#20572
C3×#20252
C3×#20232
C3×#19922
C3×#19852
C3×#18802
C3×#18652
C3×#18632
C3×#18032
#243463