Finite Group Databasebeta

← C3×#26788 #10645395

Subgroups — C3×#26788 #10645395

Order 768.

882 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#481C211yesmaximal, characteristic
2C2×C3×#475C211yesmaximal, characteristic, complemented
3C3×#2491C211yesmaximal, characteristic
4C3×#2360C211yesmaximal, characteristic, complemented
5C3×#2065C211yesmaximal, characteristic, complemented
6C3×#2058C211yesmaximal, characteristic, complemented
7C3×#2035C211yesmaximal, characteristic, complemented
8C3×#2000C211yesmaximal, characteristic
9C3×#1968C211yesmaximal, characteristic, complemented
10C3×#1927C211yesmaximal, characteristic, complemented
11C3×#1926C211yesmaximal, characteristic, complemented
12C3×#1923C211yesmaximal, characteristic, complemented
13C3×#1880C211yesmaximal, characteristic, complemented
14C3×#1853C211yesmaximal, characteristic, complemented
15C3×C4×#106C211yesmaximal, characteristic, complemented
16#26788C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×SD16C2211yescharacteristic
18C2×C3×C4⋊Q8C2211yescharacteristic
19C2×C3×#124—21no—
20C2×C3×C22⋊Q8C2211yescharacteristic
21C2×C3×#121C2211yescharacteristic
22C2×C3×C4×Q8C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C3×#481—24no—
25C3×#475—24no—
26C2×C3×#106C2211yescharacteristic
27C2×C3×#106C2211yescharacteristic
28C2×C3×#106C2211yescharacteristic
29C2×C3×#106C2211yescharacteristic
30C2×C3×#106C2211yescharacteristic
31C2×C3×C4⋊C8C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×C22⋊C8C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40C2×C3×C4×C8C2211yescharacteristic
41C3×#394—21no—
42C3×#393—21no—
43C3×#391C2211yescharacteristic
44C3×#390C2211yescharacteristic
45C3×#390C2211yescharacteristic
46C3×#389—21no—
47C3×#389C2211yescharacteristic
48C3×#388—21no—
49C3×#387—21no—
50C3×#385—21no—
51C3×#380C2211yescharacteristic
52C3×C4×C4⋊C4C2211yescharacteristic
53C3×C4×C4⋊C4C2211yescharacteristic
54C3×C4×C22⋊C4—21no—
55C3×C4×C22⋊C4C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C2×#481C2×C311yescharacteristic
63C2×#475C2×C311yescharacteristic, complemented
64#2491C2×C311yescharacteristic
65#2360C2×C311yescharacteristic, complemented
66#2065C2×C311yescharacteristic, complemented
67#2058C2×C311yescharacteristic, complemented
68#2035C2×C311yescharacteristic, complemented
69#2000C2×C311yescharacteristic
70#1968C2×C311yescharacteristic, complemented
71#1927C2×C311yescharacteristic, complemented
72#1926C2×C311yescharacteristic, complemented
73#1923C2×C311yescharacteristic, complemented
74#1880C2×C311yescharacteristic, complemented
75#1853C2×C311yescharacteristic, complemented
76C4×#106C2×C311yescharacteristic, complemented
77C22×C3×Q8—21no—
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—41no—
86C22×C3×C8C2311yescharacteristic
87C22×C3×C8C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C3×C4⋊Q8—22no—
91C3×C4⋊Q8—41no—
92C3×#124—44no—
93C3×C22⋊Q8—22no—
94C3×C22⋊Q8—22no—
95C3×#121—22no—
96C3×#121—41no—
97C3×C4×Q8—22no—
98C3×C4×Q8—41no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4—22no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4—41no—
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C22⋊C4—21no—
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4D411yescharacteristic
120C2×C3×C22⋊C4D411yescharacteristic
121C2×C3×C42—21no—
122C2×C3×C42—21no—
123C2×C3×C42—21no—
124C2×C3×C42C2311yescharacteristic
125C2×C3×C42C2311yescharacteristic
126C3×#106—22no—
127C3×#106—22no—
128C3×#106—22no—
129C3×#106—41no—
130C3×#106D414yes—
131C3×C4⋊C8—22no—
132C3×#103—22no—
133C3×#103—22no—
134C3×#103—22no—
135C3×#102—22no—
136C3×#102—22no—
137C3×#102—22no—
138C3×C22⋊C8—22no—
139C3×C22⋊C8—22no—
140C3×C4×C8—22no—
141C3×#95—21no—
142C3×#95—21no—
143C3×#95—21no—
144C3×#95—21no—
145C3×#95—21no—
146C3×#95—21no—
147C3×#95D411yescharacteristic
148C3×#95D411yescharacteristic
149C22×SD16C22×C311yescharacteristic
150C2×C4⋊Q8C22×C311yescharacteristic
151C2×#124—21no—
152C2×C22⋊Q8C22×C311yescharacteristic
153C2×#121C22×C311yescharacteristic
154C2×C4×Q8C22×C311yescharacteristic
155C22×C4⋊C4C22×C311yescharacteristic
156#481—24no—
157#475—24no—
158C2×#106C22×C311yescharacteristic
159C2×#106C22×C311yescharacteristic
160C2×#106C22×C311yescharacteristic
161C2×#106C22×C311yescharacteristic
162C2×#106C22×C311yescharacteristic
163C2×C4⋊C8C22×C311yescharacteristic
164C2×#103C22×C311yescharacteristic
165C2×#103C22×C311yescharacteristic
166C2×#103C22×C311yescharacteristic
167C2×#102C22×C311yescharacteristic
168C2×#102C22×C311yescharacteristic
169C2×#102C22×C311yescharacteristic
170C2×C22⋊C8C22×C311yescharacteristic
171C2×C22⋊C8C22×C311yescharacteristic
172C2×C4×C8C22×C311yescharacteristic
173#394—21no—
174#393—21no—
175#391C22×C311yescharacteristic
176#390C22×C311yescharacteristic
177#390C22×C311yescharacteristic
178#389—21no—
179#389C22×C311yescharacteristic
180#388—21no—
181#387—21no—
182#385—21no—
183#380C22×C311yescharacteristic
184C4×C4⋊C4C22×C311yescharacteristic
185C4×C4⋊C4C22×C311yescharacteristic
186C4×C22⋊C4—21no—
187C4×C22⋊C4C22×C311yescharacteristic
188#340C22×C311yescharacteristic
189#340C22×C311yescharacteristic
190#340C22×C311yescharacteristic
191#340C22×C311yescharacteristic
192#336C22×C311yescharacteristic
193#336C22×C311yescharacteristic
194C24×C3—21no—
195C24×C3C2×D411yescharacteristic
196C2×C3×Q8—21no—
197C2×C3×Q8—21no—
198C2×C3×Q8—21no—
199C2×C3×Q8—21no—
200C2×C3×Q8—21no—
201C2×C3×Q8—42no—
202C2×C3×Q8—42no—
203C2×C3×Q8—81no—
204C2×C3×Q8#4112yes—
205C2×C3×D4—21no—
206C2×C3×D4—21no—
207C2×C3×D4—21no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—42no—
212C2×C3×D4—42no—
213C2×C3×D4—81no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—42no—
228C22×C3×C4—42no—
229C22×C3×C4—81no—
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2×D411yescharacteristic
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2411yescharacteristic
236C3×SD16—44no—
237C2×C3×C8—21no—
238C2×C3×C8—21no—
239C2×C3×C8—21no—
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×C8C2×D412yes—
248C2×C3×C8#4112yes—
249C3×C4⋊C4—24no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—21no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—21no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—42no—
260C3×C4⋊C4—42no—
261C3×C4⋊C4—42no—
262C3×C4⋊C4—81no—
263C3×C4⋊C4C2×D412yes—
264C3×C4⋊C4C2×D412yes—
265C3×C4⋊C4#4112yes—
266C3×C22⋊C4—24no—
267C3×C22⋊C4—41no—
268C3×C22⋊C4—42no—
269C3×C22⋊C4—42no—
270C3×C22⋊C4—42no—
271C3×C22⋊C4—42no—
272C3×C22⋊C4—42no—
273C3×C22⋊C4—81no—
274C3×C22⋊C4SD1614yescomplemented
275C3×C42—21no—
276C3×C42—21no—
277C3×C42—21no—
278C3×C42—21no—
279C3×C42—42no—
280C3×C42—42no—
281C3×C42—81no—
282C22×Q8—21no—
283C22×Q8C23×C311yescharacteristic
284C22×D4—21no—
285C22×D4C23×C311yescharacteristic
286C23×C4—21no—
287C23×C4C23×C311yescharacteristic
288C2×SD16—22no—
289C2×SD16—22no—
290C2×SD16—41no—
291C22×C8C23×C311yescharacteristic
292C22×C8C23×C311yescharacteristic
293C22×C8C23×C311yescharacteristic
294C22×C8C23×C311yescharacteristic
295C4⋊Q8—22no—
296C4⋊Q8—41no—
297#124—44no—
298C22⋊Q8—22no—
299C22⋊Q8—22no—
300#121—22no—
301#121—41no—
302C4×Q8—22no—
303C4×Q8—41no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—41no—
311C2×C4⋊C4C23×C311yescharacteristic
312C2×C4⋊C4C23×C311yescharacteristic
313C2×C4⋊C4C23×C311yescharacteristic
314C2×C4⋊C4C23×C311yescharacteristic
315C2×C4⋊C4C23×C311yescharacteristic
316C2×C4⋊C4C23×C311yescharacteristic
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4C3×D411yescharacteristic
325C2×C22⋊C4C3×D411yescharacteristic
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42C23×C311yescharacteristic
330C2×C42C23×C311yescharacteristic
331#106—22no—
332#106—22no—
333#106—22no—
334#106—41no—
335#106C3×D414yes—
336C4⋊C8—22no—
337#103—22no—
338#103—22no—
339#103—22no—
340#102—22no—
341#102—22no—
342#102—22no—
343C22⋊C8—22no—
344C22⋊C8—22no—
345C4×C8—22no—
346#95—21no—
347#95—21no—
348#95—21no—
349#95—21no—
350#95—21no—
351#95—21no—
352#95C3×D411yescharacteristic
353#95C3×D411yescharacteristic
354C23×C3—21no—
355C23×C3—21no—
356C23×C3—21no—
357C23×C3—21no—
358C23×C3—21no—
359C23×C3—21no—
360C23×C3—41no—
361C23×C3—41no—
362C23×C3—41no—
363C23×C3—41no—
364C23×C3—41no—
365C23×C3—41no—
366C23×C3—41no—
367C23×C3C2×SD1612yes—
368C23×C3C22×D411yescharacteristic
369C3×Q8—22no—
370C3×Q8—22no—
371C3×Q8—41no—
372C3×Q8—41no—
373C3×Q8—84no—
374C3×D4—41no—
375C3×D4—41no—
376C3×D4—41no—
377C3×D4—41no—
378C3×D4—84no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
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—41no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—41no—
400C2×C3×C4—41no—
401C2×C3×C4—41no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—41no—
405C2×C3×C4—41no—
406C2×C3×C4—41no—
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—84no—
418C2×C3×C4C2×SD1612yes—
419C2×C3×C4C2×SD1612yes—
420C2×C3×C4C22×D411yescharacteristic
421C2×C3×C4C2×#4111yescharacteristic
422C2×C3×C4C2×#4111yescharacteristic
423C2×C3×C4C2×#4111yescharacteristic
424C2×C3×C4H(5,𝔽2)11yescharacteristic
425C2×C3×C42−1+411yescharacteristic
426C3×C8—22no—
427C3×C8—22no—
428C3×C8—41no—
429C3×C8—41no—
430C24—21no—
431C24C2×C3×D411yescharacteristic
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—42no—
438C2×Q8—42no—
439C2×Q8—81no—
440C2×Q8C3×#4112yes—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—81no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—81no—
466C22×C4C2×C3×D411yescharacteristic
467C22×C4C2×C3×D411yescharacteristic
468C22×C4C2×C3×D411yescharacteristic
469C22×C4C2×C3×D411yescharacteristic
470C22×C4C2×C3×D411yescharacteristic
471C22×C4C24×C311yescharacteristic
472SD16—44no—
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×C8C2×C3×D412yes—
484C2×C8C3×#4112yes—
485C4⋊C4—24no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—42no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4—81no—
499C4⋊C4C2×C3×D412yes—
500C4⋊C4C2×C3×D412yes—
501C4⋊C4C3×#4112yes—
502C22⋊C4—24no—
503C22⋊C4—41no—
504C22⋊C4—42no—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—42no—
508C22⋊C4—42no—
509C22⋊C4—81no—
510C22⋊C4C3×SD1614yescomplemented
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—42no—
516C42—42no—
517C42—81no—
518C22×C3—22no—
519C22×C3—22no—
520C22×C3—22no—
521C22×C3—41no—
522C22×C3—41no—
523C22×C3—41no—
524C22×C3—41no—
525C22×C3—81no—
526C22×C3—81no—
527C22×C3—81no—
528C22×C3—81no—
529C22×C3—81no—
530C22×C3—81no—
531C22×C3—81no—
532C22×C3#52511yescharacteristic
533C22×C3D4211yescharacteristic
534C22×C3#54711yescharacteristic
535C22×C3C22×SD1611yescharacteristic
536C22×C3#57511yescharacteristic
537C22×C3#57711yescharacteristic
538C22×C3#57711yescharacteristic
539C3×C4—22no—
540C3×C4—22no—
541C3×C4—41no—
542C3×C4—42no—
543C3×C4—41no—
544C3×C4—42no—
545C3×C4—41no—
546C3×C4—42no—
547C3×C4—42no—
548C3×C4—81no—
549C3×C4—81no—
550C3×C4—81no—
551C3×C4#53211yescharacteristic
552C3×C4#54211yescharacteristic
553C3×C4#54811yescharacteristic
554C3×C4#55111yescharacteristic
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23C2×C3×SD1612yes—
569C23C22×C3×D411yescharacteristic
570Q8—22no—
571Q8—22no—
572Q8—41no—
573Q8—41no—
574Q8—84no—
575D4—41no—
576D4—41no—
577D4—41no—
578D4—41no—
579D4—84no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—21no—
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—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—84no—
619C2×C4C2×C3×SD1612yes—
620C2×C4C2×C3×SD1612yes—
621C2×C4C22×C3×D411yescharacteristic
622C2×C4C2×C3×#4111yescharacteristic
623C2×C4C2×C3×#4111yescharacteristic
624C2×C4C2×C3×#4111yescharacteristic
625C2×C4C3×H(5,𝔽2)11yescharacteristic
626C2×C4C3×2−1+411yescharacteristic
627C8—22no—
628C8—22no—
629C8—41no—
630C8—41no—
631C2×C3—42no—
632C2×C3—161no—
633C2×C3#246111yescharacteristic
634C2×C3#310311yescharacteristic
635C2×C3#312511yescharacteristic
636C2×C3#327511yescharacteristic
637C2×C3D4×SD1611yescharacteristic
638C2×C3#333511yescharacteristic
639C2×C3#334811yescharacteristic
640C22—22no—
641C22—22no—
642C22—22no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22C3×#52511yescharacteristic
655C22C3×D4211yescharacteristic
656C22C3×#54711yescharacteristic
657C22C22×C3×SD1611yescharacteristic
658C22C3×#57511yescharacteristic
659C22C3×#57711yescharacteristic
660C22C3×#57711yescharacteristic
661C4—22no—
662C4—22no—
663C4—41no—
664C4—42no—
665C4—41no—
666C4—42no—
667C4—42no—
668C4—41no—
669C4—42no—
670C4—81no—
671C4—81no—
672C4—81no—
673C4C3×#53211yescharacteristic
674C4C3×#54211yescharacteristic
675C4C3×#54811yescharacteristic
676C4C3×#55111yescharacteristic
677C3#2678811yescharacteristic, direct product factor, Sylow
678C2—42no—
679C2—161no—
680C2C3×#246111yescharacteristic
681C2C3×#310311yescharacteristic
682C2C3×#312511yescharacteristic
683C2C3×#327511yescharacteristic
684C2C3×D4×SD1611yescharacteristic
685C2C3×#333511yescharacteristic
686C2C3×#334811yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#475C2semidirect
4. C3×#2360C2semidirect
5. C3×#2065C2semidirect
6. C3×#2058C2semidirect
7. C3×#2035C2semidirect
9. C3×#1968C2semidirect
10. C3×#1927C2semidirect
11. C3×#1926C2semidirect
12. C3×#1923C2semidirect
13. C3×#1880C2semidirect
14. C3×#1853C2semidirect
15. C3×C4×#106C2semidirect
16. #26788C3direct (N × H)
63. C2×#475C2×C3semidirect
65. #2360C2×C3semidirect
66. #2065C2×C3semidirect
67. #2058C2×C3semidirect
68. #2035C2×C3semidirect
70. #1968C2×C3semidirect
71. #1927C2×C3semidirect
72. #1926C2×C3semidirect
73. #1923C2×C3semidirect
74. #1880C2×C3semidirect
75. #1853C2×C3semidirect
76. C4×#106C2×C3semidirect
274. C3×C22⋊C4SD16semidirect
510. C22⋊C4C3×SD16semidirect
677. C3#26788direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4812
C2×C3×#4752
C3×#24912
C3×#23602
C3×#20652
C3×#20582
C3×#20352
C3×#20002
C3×#19682
C3×#19272
C3×#19262
C3×#19232
C3×#18802
C3×#18532
C3×C4×#1062
#267883