Finite Group Databasebeta

← C3×#24334 #10642941

Subgroups — C3×#24334 #10642941

Order 768.

1042 conjugacy classes of subgroups.

The subgroup lattice has 672 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×C4×SD16C211yesmaximal, characteristic
4C3×#2580C211yesmaximal, characteristic
5C3×#2059C211yesmaximal, characteristic, complemented
6C3×#2058C211yesmaximal, characteristic, complemented
7C3×#2025C211yesmaximal, characteristic
8C3×#2023C211yesmaximal, characteristic
9C3×#1991C211yesmaximal, characteristic, complemented
10C3×#1984C211yesmaximal, characteristic, complemented
11C3×#1880C211yesmaximal, characteristic
12C3×#1880C211yesmaximal, characteristic
13C3×#1865C211yesmaximal, characteristic, complemented
14C3×#1863C211yesmaximal, characteristic, complemented
15C3×#1805C211yesmaximal, characteristic, complemented
16#24334C311yesmaximal, 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×C4×Q8—21no—
27C2×C3×C4×Q8C2211yescharacteristic
28C2×C3×C4×Q8C2211yescharacteristic
29C2×C3×C4×Q8C2211yescharacteristic
30C2×C3×C4×Q8C2211yescharacteristic
31C2×C3×C4×D4C2211yescharacteristic
32C3×#478—24no—
33C3×C4×SD16—24no—
34C2×C3×#107C2211yescharacteristic
35C2×C3×#106C2211yescharacteristic
36C2×C3×#106C2211yescharacteristic
37C2×C3×C4⋊C8C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#102C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×C4×C8C2211yescharacteristic
45C3×#399—21no—
46C3×#393—21no—
47C3×#390C2211yescharacteristic
48C3×#390C2211yescharacteristic
49C3×#389C2211yescharacteristic
50C3×#389C2211yescharacteristic
51C3×#385—21no—
52C3×#385—21no—
53C3×#382C2211yescharacteristic
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×C4×SD16C2×C311yescharacteristic
67#2580C2×C311yescharacteristic
68#2059C2×C311yescharacteristic, complemented
69#2058C2×C311yescharacteristic, complemented
70#2025C2×C311yescharacteristic
71#2023C2×C311yescharacteristic
72#1991C2×C311yescharacteristic, complemented
73#1984C2×C311yescharacteristic, complemented
74#1880C2×C311yescharacteristic
75#1880C2×C311yescharacteristic
76#1865C2×C311yescharacteristic, complemented
77#1863C2×C311yescharacteristic, complemented
78#1805C2×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×C4×Q8—28no—
101C3×C4×Q8—22no—
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×Q8D414yes—
109C3×C4×D4—22no—
110C3×C4×D4—22no—
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⋊C4—21no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4D411yescharacteristic
122C2×C3×C4⋊C4D411yescharacteristic
123C2×C3×C4⋊C4D411yescharacteristic
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C22⋊C4—21no—
131C2×C3×C22⋊C4—21no—
132C2×C3×C22⋊C4—21no—
133C2×C3×C22⋊C4—21no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C42—21no—
136C2×C3×C42—21no—
137C2×C3×C42—21no—
138C2×C3×C42C2311yescharacteristic
139C2×C3×C42C2311yescharacteristic
140C2×C3×C42C2311yescharacteristic
141C3×#107—22no—
142C3×#106—22no—
143C3×#106—22no—
144C3×C4⋊C8—22no—
145C3×#103—22no—
146C3×#103—22no—
147C3×#103—22no—
148C3×#102—22no—
149C3×#102—22no—
150C3×#102—22no—
151C3×C4×C8—22no—
152C3×#95—21no—
153C3×#95—21no—
154C3×#95—21no—
155C3×#95—21no—
156C22×SD16C22×C311yescharacteristic
157#557—24no—
158#557—24no—
159C2×C4⋊Q8—21no—
160C2×C4⋊Q8C22×C311yescharacteristic
161C2×#125—21no—
162C2×#125—21no—
163C2×#125C22×C311yescharacteristic
164C2×#125C22×C311yescharacteristic
165C2×C4×Q8—21no—
166C2×C4×Q8C22×C311yescharacteristic
167C2×C4×Q8C22×C311yescharacteristic
168C2×C4×Q8C22×C311yescharacteristic
169C2×C4×Q8C22×C311yescharacteristic
170C2×C4×D4C22×C311yescharacteristic
171#478—24no—
172C4×SD16—24no—
173C2×#107C22×C311yescharacteristic
174C2×#106C22×C311yescharacteristic
175C2×#106C22×C311yescharacteristic
176C2×C4⋊C8C22×C311yescharacteristic
177C2×#103C22×C311yescharacteristic
178C2×#103C22×C311yescharacteristic
179C2×#103C22×C311yescharacteristic
180C2×#102C22×C311yescharacteristic
181C2×#102C22×C311yescharacteristic
182C2×#102C22×C311yescharacteristic
183C2×C4×C8C22×C311yescharacteristic
184#399—21no—
185#393—21no—
186#390C22×C311yescharacteristic
187#390C22×C311yescharacteristic
188#389C22×C311yescharacteristic
189#389C22×C311yescharacteristic
190#385—21no—
191#385—21no—
192#382C22×C311yescharacteristic
193#340C22×C311yescharacteristic
194#340C22×C311yescharacteristic
195#340C22×C311yescharacteristic
196#340C22×C311yescharacteristic
197#340C22×C311yescharacteristic
198#340C22×C311yescharacteristic
199#336C22×C311yescharacteristic
200#336C22×C311yescharacteristic
201#336C22×C311yescharacteristic
202#336C22×C311yescharacteristic
203C24×C3—21no—
204C2×C3×Q8—24no—
205C2×C3×Q8—22no—
206C2×C3×Q8—22no—
207C2×C3×Q8—21no—
208C2×C3×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—41no—
211C2×C3×Q8—42no—
212C2×C3×Q8—42no—
213C2×C3×Q8C2×D412yes—
214C2×C3×Q8C2×Q812yes—
215C2×C3×Q8#4112yes—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4C2×Q812yes—
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—42no—
230C22×C3×C4—81no—
231C22×C3×C4—81no—
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2411yescharacteristic
239C3×SD16—28no—
240C2×C3×C8—21no—
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×C8C2×Q812yes—
252C3×C4⋊C4—24no—
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—22no—
261C3×C4⋊C4—22no—
262C3×C4⋊C4—22no—
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—21no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—81no—
273C3×C4⋊C4—81no—
274C3×C4⋊C4C2×D412yes—
275C3×C4⋊C4C2×D412yes—
276C3×C4⋊C4C2×D412yes—
277C3×C22⋊C4—42no—
278C3×C22⋊C4—42no—
279C3×C22⋊C4—42no—
280C3×C22⋊C4—81no—
281C3×C22⋊C4—81no—
282C3×C42—24no—
283C3×C42—24no—
284C3×C42—24no—
285C3×C42—21no—
286C3×C42—21no—
287C3×C42—21no—
288C3×C42—21no—
289C3×C42C2×D412yes—
290C3×C42C2×D412yes—
291C22×Q8—21no—
292C22×Q8C3×D411yescharacteristic
293C22×Q8C23×C311yescharacteristic
294C22×D4C23×C311yescharacteristic
295C23×C4—21no—
296C2×SD16—22no—
297C2×SD16—22no—
298C2×SD16C3×Q814yescomplemented
299C22×C8C23×C311yescharacteristic
300C22×C8C23×C311yescharacteristic
301C22×C8C23×C311yescharacteristic
302C22×C8C23×C311yescharacteristic
303C4⋊Q8—28no—
304C4⋊Q8—22no—
305C4⋊Q8—22no—
306#125—28no—
307#125—28no—
308#125—22no—
309#125—22no—
310#125—22no—
311#125C3×D414yes—
312C4×Q8—28no—
313C4×Q8—22no—
314C4×Q8—22no—
315C4×Q8—22no—
316C4×Q8—22no—
317C4×Q8—22no—
318C4×Q8—22no—
319C4×Q8—22no—
320C4×Q8C3×D414yes—
321C4×D4—22no—
322C4×D4—22no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
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⋊C4C3×D411yescharacteristic
334C2×C4⋊C4C3×D411yescharacteristic
335C2×C4⋊C4C3×D411yescharacteristic
336C2×C4⋊C4C23×C311yescharacteristic
337C2×C4⋊C4C23×C311yescharacteristic
338C2×C4⋊C4C23×C311yescharacteristic
339C2×C4⋊C4C23×C311yescharacteristic
340C2×C4⋊C4C23×C311yescharacteristic
341C2×C4⋊C4C23×C311yescharacteristic
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42C23×C311yescharacteristic
351C2×C42C23×C311yescharacteristic
352C2×C42C23×C311yescharacteristic
353#107—22no—
354#106—22no—
355#106—22no—
356C4⋊C8—22no—
357#103—22no—
358#103—22no—
359#103—22no—
360#102—22no—
361#102—22no—
362#102—22no—
363C4×C8—22no—
364#95—21no—
365#95—21no—
366#95—21no—
367#95—21no—
368C23×C3—22no—
369C23×C3—41no—
370C23×C3—41no—
371C23×C3—41no—
372C23×C3—41no—
373C23×C3—41no—
374C23×C3—41no—
375C23×C3C22×D411yescharacteristic
376C3×Q8—22no—
377C3×Q8—22no—
378C3×Q8—22no—
379C3×Q8—44no—
380C3×Q8—48no—
381C3×Q8C22⋊Q814yes—
382C3×D4—22no—
383C3×D4—22no—
384C3×D4—41no—
385C3×D4—41no—
386C2×C3×C4—22no—
387C2×C3×C4—21no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—22no—
398C2×C3×C4—21no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—41no—
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—84no—
423C2×C3×C4#12012yes—
424C2×C3×C4#12012yes—
425C2×C3×C4#13512yes—
426C2×C3×C4C22×D411yescharacteristic
427C2×C3×C4C22×D411yescharacteristic
428C2×C3×C4C22×Q811yescharacteristic
429C2×C3×C4C2×#4111yescharacteristic
430C2×C3×C42−1+411yescharacteristic
431C2×C3×C42−1+411yescharacteristic
432C3×C8—22no—
433C3×C8—41no—
434C3×C8—41no—
435C3×C8—41no—
436C24—21no—
437C2×Q8—24no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—41no—
444C2×Q8—42no—
445C2×Q8—42no—
446C2×Q8C2×C3×D412yes—
447C2×Q8C2×C3×Q812yes—
448C2×Q8C3×#4112yes—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4C2×C3×Q812yes—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—42no—
463C22×C4—81no—
464C22×C4—81no—
465C22×C4C2×C3×D411yescharacteristic
466C22×C4C2×C3×D411yescharacteristic
467C22×C4C2×C3×D411yescharacteristic
468C22×C4C2×C3×D411yescharacteristic
469C22×C4C2×C3×D411yescharacteristic
470C22×C4C2×C3×D411yescharacteristic
471C22×C4C24×C311yescharacteristic
472SD16—28no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8C2×C3×Q812yes—
485C4⋊C4—24no—
486C4⋊C4—24no—
487C4⋊C4—24no—
488C4⋊C4—24no—
489C4⋊C4—24no—
490C4⋊C4—24no—
491C4⋊C4—24no—
492C4⋊C4—24no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—81no—
506C4⋊C4—81no—
507C4⋊C4C2×C3×D412yes—
508C4⋊C4C2×C3×D412yes—
509C4⋊C4C2×C3×D412yes—
510C22⋊C4—42no—
511C22⋊C4—42no—
512C22⋊C4—42no—
513C22⋊C4—81no—
514C22⋊C4—81no—
515C42—24no—
516C42—24no—
517C42—24no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42C2×C3×D412yes—
523C42C2×C3×D412yes—
524C22×C3—42no—
525C22×C3—42no—
526C22×C3—42no—
527C22×C3—81no—
528C22×C3—81no—
529C22×C3—81no—
530C22×C3—81no—
531C22×C3C2×#12011yescharacteristic
532C22×C3#54811yescharacteristic
533C22×C3D4×Q811yescharacteristic
534C22×C3C2×#13511yescharacteristic
535C22×C3#57511yescharacteristic
536C22×C3#57711yescharacteristic
537C22×C3#57711yescharacteristic
538C3×C4—24no—
539C3×C4—22no—
540C3×C4—22no—
541C3×C4—22no—
542C3×C4—41no—
543C3×C4—42no—
544C3×C4—42no—
545C3×C4—41no—
546C3×C4—41no—
547C3×C4—42no—
548C3×C4—81no—
549C3×C4—81no—
550C3×C4—81no—
551C3×C4C2×C22⋊Q811yescharacteristic
552C3×C4#53611yescharacteristic
553C3×C4#54811yescharacteristic
554C3×C4D4×Q811yescharacteristic
555C23—22no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23C22×C3×D411yescharacteristic
563Q8—22no—
564Q8—22no—
565Q8—22no—
566Q8—44no—
567Q8—48no—
568Q8C3×C22⋊Q814yes—
569D4—22no—
570D4—22no—
571D4—41no—
572D4—41no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
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—84no—
610C2×C4C3×#12012yes—
611C2×C4C3×#12012yes—
612C2×C4C3×#13512yes—
613C2×C4C22×C3×D411yescharacteristic
614C2×C4C22×C3×D411yescharacteristic
615C2×C4C22×C3×Q811yescharacteristic
616C2×C4C2×C3×#4111yescharacteristic
617C2×C4C3×2−1+411yescharacteristic
618C2×C4C3×2−1+411yescharacteristic
619C8—22no—
620C8—41no—
621C8—41no—
622C8—41no—
623C2×C3—82no—
624C2×C3#240911yescharacteristic
625C2×C3#300211yescharacteristic
626C2×C3#301011yescharacteristic
627C2×C3#336511yescharacteristic
628C2×C3#337111yescharacteristic
629C2×C3#338111yescharacteristic
630C2×C3#338811yescharacteristic
631C22—42no—
632C22—42no—
633C22—42no—
634C22—81no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22C2×C3×#12011yescharacteristic
639C22C3×#54811yescharacteristic
640C22C3×D4×Q811yescharacteristic
641C22C2×C3×#13511yescharacteristic
642C22C3×#57511yescharacteristic
643C22C3×#57711yescharacteristic
644C22C3×#57711yescharacteristic
645C4—24no—
646C4—22no—
647C4—22no—
648C4—22no—
649C4—41no—
650C4—42no—
651C4—42no—
652C4—41no—
653C4—41no—
654C4—42no—
655C4—81no—
656C4—81no—
657C4—81no—
658C4C2×C3×C22⋊Q811yescharacteristic
659C4C3×#53611yescharacteristic
660C4C3×#54811yescharacteristic
661C4C3×D4×Q811yescharacteristic
662C3#2433411yescharacteristic, direct product factor, Sylow
663C2—82no—
664C2C3×#240911yescharacteristic
665C2C3×#300211yescharacteristic
666C2C3×#301011yescharacteristic
667C2C3×#336511yescharacteristic
668C2C3×#337111yescharacteristic
669C2C3×#338111yescharacteristic
670C2C3×#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×#2058C2semidirect
9. C3×#1991C2semidirect
10. C3×#1984C2semidirect
13. C3×#1865C2semidirect
14. C3×#1863C2semidirect
15. C3×#1805C2semidirect
16. #24334C3direct (N × H)
64. C2×#557C2×C3semidirect
68. #2059C2×C3semidirect
69. #2058C2×C3semidirect
72. #1991C2×C3semidirect
73. #1984C2×C3semidirect
76. #1865C2×C3semidirect
77. #1863C2×C3semidirect
78. #1805C2×C3semidirect
86. C2×C3×SD16Q8semidirect
298. C2×SD16C3×Q8semidirect
662. C3#24334direct (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×C4×SD162
C3×#25802
C3×#20592
C3×#20582
C3×#20252
C3×#20232
C3×#19912
C3×#19842
C3×#18802
C3×#18652
C3×#18632
C3×#18052
#243343