Finite Group Databasebeta

← C3×#82334 #11805479

Subgroups — C3×#82334 #11805479

Order 1152.

1621 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic
2C2×C3×D4×Dic3C211yesmaximal, characteristic
3C2×C3×D4×Dic3C211yesmaximal, characteristic
4C3×#5210C212yesmaximal, complemented
5C2×C3×C3⋊#95C212yesmaximal, complemented
6C3×#4977C211yesmaximal, characteristic, complemented
7C3×#4972C211yesmaximal, characteristic, complemented
8C3×#4946C212yesmaximal, complemented
9C3×#4942C212yesmaximal, complemented
10C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
11C3×#4928C211yesmaximal, characteristic, complemented
12C3×#2349—31nomaximal
13#82334C311yesmaximal, characteristic, direct product factor
14C22×C32×D4C2211yescharacteristic
15C23×C32×C4C2212yes—
16C23×C3×Dic3C2212yes—
17C23×C3×Dic3C2212yes—
18C32×C4×D4—24no—
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C32×C22⋊C4C2212yes—
21C2×C32×C42C2211yescharacteristic
22C2×C3×#217C2212yes—
23C2×C3×#217C2212yes—
24C3×D4×Dic3—24no—
25C3×D4×Dic3C418yescomplemented
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2212yes—
31C2×C3×Dic3⋊C4C2212yes—
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2211yescharacteristic
36C3×C3⋊#95C2211yescharacteristic
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2212yes—
39C3×C3⋊#95C2212yes—
40C2×C3×C4×D4—21no—
41C2×C3×C4×D4—31no—
42C2×C3×C4×D4—31no—
43C2×C3×C4×D4D311yescharacteristic
44C2×C3×C4×D4C2×C311yescharacteristic
45C2×D4×Dic3C2×C311yescharacteristic
46C2×D4×Dic3C2×C311yescharacteristic
47C3×#389—31no—
48C3×#389—31no—
49C3×#385—32no—
50C3×#385—32no—
51C3×#382—31no—
52C3×#380—32no—
53C3×C4×C4⋊C4—31no—
54C2×C3×#95—32no—
55#5210C2×C312yescomplemented
56C2×C3⋊#95C2×C312yescomplemented
57#4977C2×C311yescharacteristic, complemented
58#4972C2×C311yescharacteristic, complemented
59#4946C2×C312yescomplemented
60#4942C2×C312yescomplemented
61C4×Dic3⋊C4C2×C311yescharacteristic, complemented
62#4928C2×C311yescharacteristic, complemented
63C24×C32C2312yes—
64C2×C32×D4C2×C414yes—
65C2×C32×D4D414yes—
66C2×C32×D4Q814yes—
67C22×C32×C4—24no—
68C22×C32×C4—24no—
69C22×C32×C4—42no—
70C22×C32×C4C2311yescharacteristic
71C22×C32×C4C2312yes—
72C22×C32×C4C2311yescharacteristic
73C22×C32×C4C2311yescharacteristic
74C22×C3×Dic3—24no—
75C22×C3×Dic3—24no—
76C22×C3×Dic3—42no—
77C22×C3×Dic3—42no—
78C22×C3×Dic3—42no—
79C22×C3×Dic3C2×C418yescomplemented
80C22×C3×Dic3C2311yescharacteristic
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2311yescharacteristic
86C32×C4⋊C4—22no—
87C32×C22⋊C4—24no—
88C32×C42—22no—
89C3×#217—24no—
90C3×#217C2×C418yescomplemented
91C3×C4⋊Dic3—22no—
92C3×C4⋊Dic3C2×C414yescomplemented
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4—22no—
95C3×Dic3⋊C4—42no—
96C3×Dic3⋊C4—42no—
97C3×C4×Dic3—22no—
98C3×C4×Dic3C2×C414yescomplemented
99#2349—31noSylow
100C22×C3×D4—21no—
101C22×C3×D4C2×D311yescharacteristic
102C22×C3×D4C22×C311yescharacteristic
103C23×C3×C4—22no—
104C23×C3×C4—32no—
105C23×C3×C4—32no—
106C23×C3×C4C2×D312yes—
107C23×C3×C4C22×C312yes—
108C23×Dic3C22×C312yes—
109C23×Dic3C22×C312yes—
110C3×C4×D4—28no—
111C3×C4×D4—24no—
112C3×C4×D4—24no—
113C3×C4×D4—38no—
114C3×C4×D4—64no—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4—31no—
117C2×C3×C4⋊C4—31no—
118C2×C3×C4⋊C4—31no—
119C2×C3×C4⋊C4—31no—
120C2×C3×C4⋊C4—32no—
121C2×C3×C4⋊C4—32no—
122C2×C3×C4⋊C4C2×D311yescharacteristic
123C2×C3×C4⋊C4C22×C311yescharacteristic
124C2×C3×C22⋊C4—22no—
125C2×C3×C22⋊C4—32no—
126C2×C3×C22⋊C4—32no—
127C2×C3×C22⋊C4C2×D312yes—
128C2×C3×C22⋊C4C22×C312yes—
129C2×C3×C42—21no—
130C2×C3×C42—31no—
131C2×C3×C42—31no—
132C2×C3×C42C2×D311yescharacteristic
133C2×C3×C42C22×C311yescharacteristic
134C2×#217C22×C312yes—
135C2×#217C22×C312yes—
136D4×Dic3—24no—
137D4×Dic3C3×C418yescomplemented
138C2×C4⋊Dic3C22×C311yescharacteristic
139C2×C4⋊Dic3C22×C311yescharacteristic
140C2×Dic3⋊C4C22×C311yescharacteristic
141C2×Dic3⋊C4C22×C311yescharacteristic
142C2×Dic3⋊C4C22×C312yes—
143C2×Dic3⋊C4C22×C312yes—
144C2×C4×Dic3C22×C311yescharacteristic
145C2×C4×Dic3C22×C311yescharacteristic
146C3×#95—31no—
147C3×#95—32no—
148C3×#95—32no—
149C3×#95—32no—
150C3×#95—31no—
151C3×#95—32no—
152C3⋊#95C22×C312yes—
153C3⋊#95C22×C311yescharacteristic
154C3⋊#95C22×C311yescharacteristic
155C3⋊#95C22×C312yes—
156C3⋊#95C22×C312yes—
157C3⋊#95C22×C312yes—
158C23×C32—22no—
159C23×C32—22no—
160C23×C32—22no—
161C23×C32—22no—
162C23×C32C22×C414yes—
163C23×C32C2×D414yes—
164C23×C32C2×Q814yes—
165C23×C32C2411yescharacteristic
166C32×D4C4⋊C4116yescomplemented
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—22no—
171C2×C32×C4—21no—
172C2×C32×C4—22no—
173C2×C32×C4—21no—
174C2×C32×C4—22no—
175C2×C32×C4—48no—
176C2×C32×C4C22×C412yes—
177C2×C32×C4C2×D412yes—
178C2×C32×C4C2×Q812yes—
179C2×C32×C4#4112yes—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—48no—
195C2×C3×Dic3—48no—
196C2×C3×Dic3C22×C412yes—
197C2×C3×Dic3C22×C412yes—
198C2×C3×Dic3C22×C414yes—
199C2×C3×Dic3#4112yes—
200C2×C4×D4—31no—
201C2×C4×D4—31no—
202C2×C4×D4C3×D311yescharacteristic
203#389—31no—
204#389—31no—
205#385—32no—
206#385—32no—
207#382—31no—
208#380—32no—
209C4×C4⋊C4—31no—
210C2×#95—32no—
211C24×C3—22no—
212C24×C3C22×D312yes—
213C24×C3C23×C312yes—
214C2×C3×D4—24no—
215C2×C3×D4—24no—
216C2×C3×D4—24no—
217C2×C3×D4Dic614yes—
218C2×C3×D4C4×D314yes—
219C2×C3×D4#6714yes—
220C2×C3×D4C2×C3×C414yes—
221C2×C3×D4C3×D414yes—
222C2×C3×D4C3×Q814yes—
223C22×C3×C4—28no—
224C22×C3×C4—24no—
225C22×C3×C4—24no—
226C22×C3×C4—24no—
227C22×C3×C4—24no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—22no—
232C22×C3×C4—31no—
233C22×C3×C4—31no—
234C22×C3×C4—31no—
235C22×C3×C4—32no—
236C22×C3×C4—38no—
237C22×C3×C4—32no—
238C22×C3×C4—31no—
239C22×C3×C4—44no—
240C22×C3×C4—42no—
241C22×C3×C4—42no—
242C22×C3×C4—44no—
243C22×C3×C4—64no—
244C22×C3×C4—64no—
245C22×C3×C4—122no—
246C22×C3×C4—122no—
247C22×C3×C4—122no—
248C22×C3×C4C22×D312yes—
249C22×C3×C4C22×D311yescharacteristic
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C22×C3×C4C23×C312yes—
253C22×C3×C4C23×C311yescharacteristic
254C22×C3×C4C23×C311yescharacteristic
255C22×C3×C4C23×C311yescharacteristic
256C22×Dic3—24no—
257C22×Dic3—24no—
258C22×Dic3—42no—
259C22×Dic3—42no—
260C22×Dic3—42no—
261C22×Dic3C2×C3×C418yescomplemented
262C22×Dic3C23×C312yes—
263C22×Dic3C23×C311yescharacteristic
264C22×Dic3C23×C311yescharacteristic
265C22×Dic3C23×C311yescharacteristic
266C22×Dic3C23×C312yes—
267C22×Dic3C23×C311yescharacteristic
268C3×C4⋊C4—24no—
269C3×C4⋊C4—22no—
270C3×C4⋊C4—22no—
271C3×C4⋊C4—34no—
272C3×C4⋊C4—62no—
273C3×C4⋊C4—62no—
274C3×C4⋊C4—62no—
275C3×C4⋊C4—122no—
276C3×C4⋊C4—122no—
277C3×C22⋊C4—28no—
278C3×C22⋊C4—24no—
279C3×C22⋊C4—24no—
280C3×C22⋊C4—38no—
281C3×C22⋊C4—64no—
282C3×C42—24no—
283C3×C42—22no—
284C3×C42—22no—
285C3×C42—34no—
286C3×C42—62no—
287#217—24no—
288#217C2×C3×C418yescomplemented
289C4⋊Dic3—22no—
290C4⋊Dic3C2×C3×C414yescomplemented
291Dic3⋊C4—22no—
292Dic3⋊C4—22no—
293Dic3⋊C4—42no—
294Dic3⋊C4—42no—
295C4×Dic3—22no—
296C4×Dic3C2×C3×C414yescomplemented
297C22×C32—24no—
298C22×C32—24no—
299C22×C32—24no—
300C22×C32—24no—
301C22×C32—24no—
302C22×C32—24no—
303C22×C32C2×C4⋊C418yes—
304C22×C32C23×C411yescharacteristic
305C22×C32C22×D411yescharacteristic
306C22×C32C22×Q811yescharacteristic
307C22×C32C2×#4111yescharacteristic
308C22×C32C2×#4111yescharacteristic
309C22×C32H(5,𝔽2)11yescharacteristic
310C22×C32H(5,𝔽2)11yescharacteristic
311C32×C4—22no—
312C32×C4—41no—
313C32×C4—42no—
314C32×C4C2×C4⋊C414yes—
315C3×Dic3—22no—
316C3×Dic3—22no—
317C3×Dic3—24no—
318C3×Dic3—22no—
319C3×Dic3—41no—
320C3×Dic3—42no—
321C22×D4C2×C3×D311yescharacteristic
322C23×C4—32no—
323C23×C4—32no—
324C23×C4C2×C3×D312yes—
325C4×D4—24no—
326C4×D4—38no—
327C4×D4—64no—
328C2×C4⋊C4—31no—
329C2×C4⋊C4—31no—
330C2×C4⋊C4—31no—
331C2×C4⋊C4—31no—
332C2×C4⋊C4—32no—
333C2×C4⋊C4—32no—
334C2×C4⋊C4C2×C3×D311yescharacteristic
335C2×C22⋊C4—32no—
336C2×C22⋊C4—32no—
337C2×C22⋊C4C2×C3×D312yes—
338C2×C42—31no—
339C2×C42—31no—
340C2×C42C2×C3×D311yescharacteristic
341#95—31no—
342#95—32no—
343#95—32no—
344#95—32no—
345#95—31no—
346#95—32no—
347C23×C3—22no—
348C23×C3—22no—
349C23×C3—22no—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3—22no—
354C23×C3—22no—
355C23×C3—21no—
356C23×C3—24no—
357C23×C3—24no—
358C23×C3—24no—
359C23×C3—42no—
360C23×C3—42no—
361C23×C3—42no—
362C23×C3—42no—
363C23×C3C2×Dic614yes—
364C23×C3C2×C4×D314yes—
365C23×C3C2×#6714yes—
366C23×C3C22×C3×C414yes—
367C23×C3C2×C3×D414yes—
368C23×C3C2×C3×Q814yes—
369C23×C3C23×D311yescharacteristic
370C23×C3C24×C311yescharacteristic
371C3×D4—216no—
372C3×D4Dic3⋊C4116yescomplemented
373C3×D4C3×C4⋊C4116yescomplemented
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—22no—
381C2×C3×C4—24no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—21no—
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—22no—
392C2×C3×C4—21no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—32no—
399C2×C3×C4—32no—
400C2×C3×C4—34no—
401C2×C3×C4—32no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—42no—
405C2×C3×C4—42no—
406C2×C3×C4—48no—
407C2×C3×C4—48no—
408C2×C3×C4—416no—
409C2×C3×C4—61no—
410C2×C3×C4—62no—
411C2×C3×C4—61no—
412C2×C3×C4—61no—
413C2×C3×C4—62no—
414C2×C3×C4—61no—
415C2×C3×C4—61no—
416C2×C3×C4—61no—
417C2×C3×C4—61no—
418C2×C3×C4—61no—
419C2×C3×C4—62no—
420C2×C3×C4—62no—
421C2×C3×C4—61no—
422C2×C3×C4—62no—
423C2×C3×C4—128no—
424C2×C3×C4—128no—
425C2×C3×C4C2×Dic612yes—
426C2×C3×C4C2×C4×D312yes—
427C2×C3×C4#23712yes—
428C2×C3×C4C2×#6712yes—
429C2×C3×C4C22×C3×C412yes—
430C2×C3×C4C2×C3×D412yes—
431C2×C3×C4C2×C3×Q812yes—
432C2×C3×C4C3×#4112yes—
433C2×Dic3—21no—
434C2×Dic3—21no—
435C2×Dic3—21no—
436C2×Dic3—22no—
437C2×Dic3—22no—
438C2×Dic3—21no—
439C2×Dic3—21no—
440C2×Dic3—21no—
441C2×Dic3—21no—
442C2×Dic3—22no—
443C2×Dic3—21no—
444C2×Dic3—22no—
445C2×Dic3—21no—
446C2×Dic3—22no—
447C2×Dic3—48no—
448C2×Dic3—48no—
449C2×Dic3C22×C3×C412yes—
450C2×Dic3C22×C3×C412yes—
451C2×Dic3C22×C3×C414yes—
452C2×Dic3C3×#4112yes—
453C2×C32—28no—
454C2×C32C22×C4⋊C411yescharacteristic
455C2×C32C4×#4111yescharacteristic
456C2×C32#51811yescharacteristic
457C2×C32#54611yescharacteristic
458C2×C32#54611yescharacteristic
459C2×C32#55411yescharacteristic
460C2×C32#55411yescharacteristic
461C24C22×C3×D312yes—
462C2×D4C3×Dic614yes—
463C2×D4C3×C4×D314yes—
464C2×D4C3×#6714yes—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—31no—
468C22×C4—31no—
469C22×C4—31no—
470C22×C4—32no—
471C22×C4—38no—
472C22×C4—32no—
473C22×C4—31no—
474C22×C4—42no—
475C22×C4—64no—
476C22×C4—64no—
477C22×C4—122no—
478C22×C4—122no—
479C22×C4—122no—
480C22×C4C22×C3×D312yes—
481C22×C4C22×C3×D311yescharacteristic
482C22×C4C22×C3×D311yescharacteristic
483C22×C4C22×C3×D311yescharacteristic
484C4⋊C4—22no—
485C4⋊C4—34no—
486C4⋊C4—62no—
487C4⋊C4—62no—
488C4⋊C4—62no—
489C4⋊C4—122no—
490C4⋊C4—122no—
491C22⋊C4—24no—
492C22⋊C4—38no—
493C22⋊C4—64no—
494C42—22no—
495C42—34no—
496C42—62no—
497C22×C3—24no—
498C22×C3—24no—
499C22×C3—24no—
500C22×C3—24no—
501C22×C3—24no—
502C22×C3—24no—
503C22×C3—24no—
504C22×C3—24no—
505C22×C3—24no—
506C22×C3—24no—
507C22×C3—24no—
508C22×C3—24no—
509C22×C3—28no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—21no—
517C22×C3—44no—
518C22×C3—44no—
519C22×C3—44no—
520C22×C3—44no—
521C22×C3—44no—
522C22×C3—44no—
523C22×C3C2×Dic3⋊C418yes—
524C22×C3C2×C3×C4⋊C418yes—
525C22×C3C22×Dic611yescharacteristic
526C22×C3C22×C4×D311yescharacteristic
527C22×C3C2×#23711yescharacteristic
528C22×C3#100411yescharacteristic
529C22×C3D3×#4111yescharacteristic
530C22×C3#100911yescharacteristic
531C22×C3C22×#6711yescharacteristic
532C22×C3C23×C3×C411yescharacteristic
533C22×C3C22×C3×D411yescharacteristic
534C22×C3C22×C3×Q811yescharacteristic
535C22×C3C2×C3×#4111yescharacteristic
536C22×C3C2×C3×#4111yescharacteristic
537C22×C3C3×H(5,𝔽2)11yescharacteristic
538C22×C3C3×H(5,𝔽2)11yescharacteristic
539C3×C4—24no—
540C3×C4—22no—
541C3×C4—22no—
542C3×C4—24no—
543C3×C4—44no—
544C3×C4—42no—
545C3×C4—42no—
546C3×C4—41no—
547C3×C4—42no—
548C3×C4—41no—
549C3×C4—62no—
550C3×C4—62no—
551C3×C4—64no—
552C3×C4—62no—
553C3×C4—121no—
554C3×C4—122no—
555C3×C4C2×Dic3⋊C414yes—
556C3×C4C2×C3×C4⋊C414yes—
557Dic3—22no—
558Dic3—22no—
559Dic3—24no—
560Dic3—22no—
561Dic3—42no—
562Dic3—41no—
563C32#234911yescharacteristic, complemented, Sylow
564C23—22no—
565C23—22no—
566C23—22no—
567C23—22no—
568C23C2×C3×Dic614yes—
569C23C2×C3×C4×D314yes—
570C23C2×C3×#6714yes—
571C23C23×C3×D311yescharacteristic
572D4C3×Dic3⋊C4116yescomplemented
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—32no—
582C2×C4—32no—
583C2×C4—34no—
584C2×C4—32no—
585C2×C4—48no—
586C2×C4—61no—
587C2×C4—62no—
588C2×C4—61no—
589C2×C4—61no—
590C2×C4—62no—
591C2×C4—61no—
592C2×C4—61no—
593C2×C4—61no—
594C2×C4—61no—
595C2×C4—61no—
596C2×C4—62no—
597C2×C4—62no—
598C2×C4—61no—
599C2×C4—62no—
600C2×C4—128no—
601C2×C4—128no—
602C2×C4C2×C3×Dic612yes—
603C2×C4C2×C3×C4×D312yes—
604C2×C4C3×#23712yes—
605C2×C4C2×C3×#6712yes—
606C2×C3—28no—
607C2×C3—28no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—48no—
616C2×C3C4×#23711yescharacteristic
617C2×C3#553911yescharacteristic
618C2×C3#554311yescharacteristic
619C2×C3#554511yescharacteristic
620C2×C3C22×Dic3⋊C411yescharacteristic
621C2×C3#580611yescharacteristic
622C2×C3#582911yescharacteristic
623C2×C3C22×C3×C4⋊C411yescharacteristic
624C2×C3C3×C4×#4111yescharacteristic
625C2×C3C3×#51811yescharacteristic
626C2×C3C3×#54611yescharacteristic
627C2×C3C3×#54611yescharacteristic
628C2×C3C3×#55411yescharacteristic
629C2×C3C3×#55411yescharacteristic
630C22—24no—
631C22—24no—
632C22—24no—
633C22—24no—
634C22—24no—
635C22—24no—
636C22C2×C3×Dic3⋊C418yes—
637C22C22×C3×Dic611yescharacteristic
638C22C22×C3×C4×D311yescharacteristic
639C22C2×C3×#23711yescharacteristic
640C22C3×#100411yescharacteristic
641C22C3×D3×#4111yescharacteristic
642C22C3×#100911yescharacteristic
643C22C22×C3×#6711yescharacteristic
644C4—22no—
645C4—42no—
646C4—41no—
647C4—62no—
648C4—62no—
649C4—64no—
650C4—62no—
651C4—121no—
652C4—122no—
653C4C2×C3×Dic3⋊C414yes—
654C3—21no—
655C3#8233411yescharacteristic, direct product factor
656C3C3×#234911yescharacteristic, complemented
657C2—28no—
658C2C3×C4×#23711yescharacteristic
659C2C3×#553911yescharacteristic
660C2C3×#554311yescharacteristic
661C2C3×#554511yescharacteristic
662C2C22×C3×Dic3⋊C411yescharacteristic
663C2C3×#580611yescharacteristic
664C2C3×#582911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC2×C32×C4×D4C2
socleC23×C32C24
prime radicalC22×C32×D4C22
cosocleC23×C3C24×C3
hypercenterC2×C3×C4×D4D3
hypocenterC3C3×#2349
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
4. C3×#5210C2semidirect
5. C2×C3×C3⋊#95C2semidirect
6. C3×#4977C2semidirect
7. C3×#4972C2semidirect
8. C3×#4946C2semidirect
9. C3×#4942C2semidirect
10. C3×C4×Dic3⋊C4C2semidirect
11. C3×#4928C2semidirect
13. #82334C3direct (N × H)
25. C3×D4×Dic3C4semidirect
55. #5210C2×C3semidirect
56. C2×C3⋊#95C2×C3semidirect
57. #4977C2×C3semidirect
58. #4972C2×C3semidirect
59. #4946C2×C3semidirect
60. #4942C2×C3semidirect
61. C4×Dic3⋊C4C2×C3semidirect
62. #4928C2×C3semidirect
79. C22×C3×Dic3C2×C4semidirect
90. C3×#217C2×C4semidirect
92. C3×C4⋊Dic3C2×C4semidirect
98. C3×C4×Dic3C2×C4semidirect
137. D4×Dic3C3×C4semidirect
166. C32×D4C4⋊C4semidirect
261. C22×Dic3C2×C3×C4semidirect
288. #217C2×C3×C4semidirect
290. C4⋊Dic3C2×C3×C4semidirect
296. C4×Dic3C2×C3×C4semidirect
372. C3×D4Dic3⋊C4semidirect
373. C3×D4C3×C4⋊C4semidirect
563. C32#2349semidirect
572. D4C3×Dic3⋊C4semidirect
655. C3#82334direct (N × H)
656. C3C3×#2349semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×C3×D4×Dic32
C3×#52102
C2×C3×C3⋊#952
C3×#49772
C3×#49722
C3×#49462
C3×#49422
C3×C4×Dic3⋊C42
C3×#49282
C3×#23493
#823343