Finite Group Databasebeta

← C3×#78885 #11864190

Subgroups — C3×#78885 #11864190

Order 1152.

1589 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic, complemented
3C2×C3×#909C211yesmaximal, characteristic, complemented
4C2×C3×#897C211yesmaximal, characteristic, complemented
5C32×#417C211yesmaximal, characteristic, complemented
6C3×#5126C211yesmaximal, characteristic, complemented
7C3×#4966C211yesmaximal, characteristic, complemented
8C3×#4809C212yesmaximal, complemented
9C3×#4808C212yesmaximal, complemented
10C3×#4783C212yesmaximal, complemented
11C3×#4776C212yesmaximal, complemented
12C3×#3007—31nomaximal
13#78885C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2211yescharacteristic
15C3×D3×#41—24no—
16C3×D3×#41—24no—
17C2×C3×#239C2211yescharacteristic
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#237—21no—
20C2×C3×#237C2211yescharacteristic
21C2×C3×D3×D4—21no—
22C2×C3×D3×D4C2211yescharacteristic
23C2×C3×#235—21no—
24C2×C3×#235C2211yescharacteristic
25C22×C3×C4×D3—21no—
26C22×C3×C4×D3C2211yescharacteristic
27C22×C3×Dic6C2211yescharacteristic, complemented
28C2×C32×M16C2211yescharacteristic, complemented
29C2×C32×C4⋊C4C2211yescharacteristic, complemented
30C3×#951—24no—
31C2×C3×#216C2212yescomplemented
32C2×C3×#214C2212yescomplemented
33C2×C3×(C2×D3)⋊C4—21no—
34C2×C3×C4⋊Dic3—21no—
35C2×C3×#208C2211yescharacteristic, complemented
36C3×#909—24no—
37C2×C3×Dic12C2212yescomplemented
38C2×C3×#204C2212yescomplemented
39C3×#897—21no—
40C3×#897—21no—
41C3×#897C2212yes—
42C3×#897C2212yescomplemented
43C32×#103C2212yescomplemented
44C32×#102C2212yescomplemented
45C3×(C2×D3)⋊C8C2212yes—
46C3×(C2×D3)⋊C8C2212yescomplemented
47C3×#810C2212yescomplemented
48C3×#809C2212yescomplemented
49C22×C3×#41—31no—
50C2×D3×#41C2×C311yescharacteristic
51C2×C3×#137—31no—
52C2×C3×#137—31no—
53C2×C3×C22⋊Q8—31no—
54C2×#951C2×C311yescharacteristic, complemented
55C2×#909C2×C311yescharacteristic, complemented
56C2×#897C2×C311yescharacteristic, complemented
57C3×#452—32no—
58C3×#452—32no—
59C3×#451—32no—
60C3×#450—32no—
61C3×#417—21no—
62C3×#417—31no—
63C3×#417D311yescharacteristic, complemented
64C3×#417C2×C311yescharacteristic, complemented
65C3×#407—31no—
66#5126C2×C311yescharacteristic, complemented
67#4966C2×C311yescharacteristic, complemented
68#4809C2×C312yescomplemented
69#4808C2×C312yescomplemented
70#4783C2×C312yescomplemented
71#4776C2×C312yescomplemented
72C23×C3×D3—21no—
73C23×C3×D3D411yescharacteristic
74C32×#41—22no—
75C32×#41D414yes—
76C2×C32×Q8C2311yescharacteristic
77C2×C32×D4—21no—
78C2×C32×D4C2311yescharacteristic
79C22×C32×C4—21no—
80C22×C32×C4—21no—
81C22×C32×C4C2311yescharacteristic
82C2×C3×#67—21no—
83C2×C3×#67—21no—
84C2×C3×#67—21no—
85C22×C3×Dic3—21no—
86C22×C3×Dic3—21no—
87C22×C3×Dic3D411yescharacteristic
88C3×#239—22no—
89C3×#239—22no—
90C3×D3×Q8—22no—
91C3×D3×Q8—22no—
92C3×#237—28no—
93C3×#237—22no—
94C3×#237—22no—
95C3×D3×D4—28no—
96C3×D3×D4—22no—
97C3×D3×D4—22no—
98C3×#235—28no—
99C3×#235—22no—
100C3×#235D414yes—
101C2×C3×D12—21no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—28no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—22no—
107C2×C3×C4×D3—22no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3D411yescharacteristic
110C2×C3×C4×D3D411yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×Dic6—21no—
114C2×C3×Dic6—22no—
115C2×C3×Dic6—22no—
116C2×C3×Dic6—21no—
117C2×C3×Dic6C2312yes—
118C2×C3×Dic6C2311yescharacteristic
119C32×M16—22no—
120C2×C32×C8C2312yes—
121C32×C4⋊C4—21no—
122C32×C4⋊C4C2312yes—
123C3×#216—24no—
124C3×#214—24no—
125C3×(C2×D3)⋊C4—22no—
126C3×(C2×D3)⋊C4—22no—
127C3×C4⋊Dic3—22no—
128C3×C4⋊Dic3—22no—
129C3×#208—22no—
130C2×C3×C3⋊C8C2312yes—
131C3×Dic12—24no—
132C3×#204—24no—
133#3007—31noSylow
134C2×C3×#41—21no—
135C2×C3×#41—31no—
136C2×C3×#41—31no—
137C2×C3×#41—31no—
138C2×C3×#41—61no—
139C2×C3×#41—61no—
140C2×C3×#41—64no—
141C2×C3×#41—64no—
142C2×C3×#41C2×D311yescharacteristic
143C2×C3×#41C22×C311yescharacteristic
144C22×C3×Q8—31no—
145C22×C3×Q8—31no—
146C22×C3×D4—31no—
147C22×C3×D4—61no—
148C23×C3×C4—31no—
149C23×C3×C4—61no—
150D3×#41—24no—
151D3×#41—24no—
152C2×#239C22×C311yescharacteristic
153C2×D3×Q8C22×C311yescharacteristic
154C2×#237—21no—
155C2×#237C22×C311yescharacteristic
156C2×D3×D4—21no—
157C2×D3×D4C22×C311yescharacteristic
158C2×#235—21no—
159C2×#235C22×C311yescharacteristic
160C22×C4×D3—21no—
161C22×C4×D3C22×C311yescharacteristic
162C22×Dic6C22×C311yescharacteristic, complemented
163C3×#137—64no—
164C3×#137—64no—
165C2×C3×Q16—32no—
166C2×C3×Q16—32no—
167C2×C3×SD16—32no—
168C2×C3×SD16—32no—
169C2×C3×M16—21no—
170C2×C3×M16—31no—
171C2×C3×M16C2×D311yescharacteristic, complemented
172C2×C3×M16C22×C311yescharacteristic, complemented
173C3×C22⋊Q8—32no—
174C3×C22⋊Q8—32no—
175C3×C22⋊Q8—61no—
176C3×C22⋊Q8—61no—
177C2×C3×C4⋊C4—21no—
178C2×C3×C4⋊C4—61no—
179C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
180C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
181C2×C3×C22⋊C4—61no—
182#951—24no—
183C2×#216C22×C312yescomplemented
184C2×#214C22×C312yescomplemented
185C2×(C2×D3)⋊C4—21no—
186C2×C4⋊Dic3—21no—
187C2×#208C22×C311yescharacteristic, complemented
188#909—24no—
189C2×Dic12C22×C312yescomplemented
190C2×#204C22×C312yescomplemented
191#897—21no—
192#897—21no—
193#897C22×C312yes—
194#897C22×C312yescomplemented
195C3×#103—22no—
196C3×#103—32no—
197C3×#103C2×D312yescomplemented
198C3×#103C22×C312yescomplemented
199C3×#102—22no—
200C3×#102—32no—
201C3×#102C2×D312yescomplemented
202C3×#102C22×C312yescomplemented
203C3×C22⋊C8—32no—
204C3×C22⋊C8—32no—
205(C2×D3)⋊C8C22×C312yes—
206(C2×D3)⋊C8C22×C312yescomplemented
207#810C22×C312yescomplemented
208#809C22×C312yescomplemented
209C23×C32—21no—
210C23×C32C2×D411yescharacteristic
211C22×C3×D3—24no—
212C22×C3×D3—22no—
213C22×C3×D3—21no—
214C22×C3×D3—22no—
215C22×C3×D3—41no—
216C22×C3×D3—42no—
217C22×C3×D3—42no—
218C22×C3×D3C2×D411yescharacteristic
219C22×C3×D3C2×D411yescharacteristic
220C32×Q8—21no—
221C32×Q8C2×D412yes—
222C32×D4—24no—
223C32×D4—21no—
224C32×D4C2×D412yes—
225C2×C32×C4—21no—
226C2×C32×C4—24no—
227C2×C32×C4—22no—
228C2×C32×C4—42no—
229C2×C32×C4C2×D412yes—
230C2×C32×C4C2×D411yescharacteristic
231C2×C32×C4C2×D412yes—
232C2×C32×C4C2411yescharacteristic
233C3×#67—24no—
234C3×#67—24no—
235C3×#67—24no—
236C2×C3×Dic3—24no—
237C2×C3×Dic3—22no—
238C2×C3×Dic3—21no—
239C2×C3×Dic3—22no—
240C2×C3×Dic3—42no—
241C2×C3×Dic3C2×D411yescharacteristic
242C2×C3×Dic3C2×D411yescharacteristic
243C3×D12—24no—
244C3×D12—21no—
245C3×D12C2×D412yes—
246C3×C4×D3—24no—
247C3×C4×D3—24no—
248C3×C4×D3—22no—
249C3×C4×D3—24no—
250C3×C4×D3—22no—
251C3×C4×D3—21no—
252C3×C4×D3—21no—
253C3×C4×D3—21no—
254C3×C4×D3—21no—
255C3×Dic6—24no—
256C3×Dic6—21no—
257C3×Dic6—22no—
258C3×Dic6—22no—
259C3×Dic6—42no—
260C3×Dic6C2×D412yes—
261C32×C8—22no—
262C3×C3⋊C8—22no—
263C22×#41—31no—
264C2×#137—31no—
265C2×#137—31no—
266C2×C22⋊Q8—31no—
267#452—32no—
268#452—32no—
269#451—32no—
270#450—32no—
271#417—31no—
272#417C3×D311yescharacteristic, complemented
273#407—31no—
274C24×C3—31no—
275C24×C3—61no—
276C23×D3—21no—
277C23×D3C3×D411yescharacteristic
278C3×#41—22no—
279C3×#41—22no—
280C3×#41—24no—
281C3×#41—34no—
282C3×#41—42no—
283C3×#41—68no—
284C3×#41—62no—
285C3×#41—68no—
286C3×#41—62no—
287C3×#41—62no—
288C3×#41—62no—
289C3×#41—62no—
290C3×#41D1214yes—
291C3×#41C3×D414yes—
292C2×C3×Q8—21no—
293C2×C3×Q8—31no—
294C2×C3×Q8—32no—
295C2×C3×Q8—61no—
296C2×C3×Q8—62no—
297C2×C3×Q8—62no—
298C2×C3×Q8—61no—
299C2×C3×Q8—62no—
300C2×C3×Q8—62no—
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C23×C311yescharacteristic
303C2×C3×D4—21no—
304C2×C3×D4—21no—
305C2×C3×D4—21no—
306C2×C3×D4—31no—
307C2×C3×D4—41no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C2×C3×D4—62no—
311C2×C3×D4—68no—
312C2×C3×D4—61no—
313C2×C3×D4—61no—
314C2×C3×D4—62no—
315C2×C3×D4C22×D311yescharacteristic
316C2×C3×D4C23×C311yescharacteristic
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—41no—
328C22×C3×C4—41no—
329C22×C3×C4—61no—
330C22×C3×C4—61no—
331C22×C3×C4—68no—
332C22×C3×C4—61no—
333C22×C3×C4—62no—
334C22×C3×C4—62no—
335C22×C3×C4—61no—
336C22×C3×C4—61no—
337C22×C3×C4C22×D311yescharacteristic
338C22×C3×C4C23×C311yescharacteristic
339C2×#67—21no—
340C2×#67—21no—
341C2×#67—21no—
342C22×Dic3—21no—
343C22×Dic3—21no—
344C22×Dic3C3×D411yescharacteristic
345#239—22no—
346#239—22no—
347D3×Q8—22no—
348D3×Q8—22no—
349#237—28no—
350#237—22no—
351#237—22no—
352D3×D4—28no—
353D3×D4—22no—
354D3×D4—22no—
355#235—28no—
356#235—22no—
357#235C3×D414yes—
358C2×D12—21no—
359C2×D12C23×C311yescharacteristic
360C2×C4×D3—28no—
361C2×C4×D3—21no—
362C2×C4×D3—21no—
363C2×C4×D3—22no—
364C2×C4×D3—22no—
365C2×C4×D3—21no—
366C2×C4×D3C3×D411yescharacteristic
367C2×C4×D3C3×D411yescharacteristic
368C2×C4×D3C23×C311yescharacteristic
369C2×C4×D3C23×C311yescharacteristic
370C2×Dic6—21no—
371C2×Dic6—22no—
372C2×Dic6—22no—
373C2×Dic6—21no—
374C2×Dic6C23×C312yes—
375C2×Dic6C23×C311yescharacteristic
376C3×Q16—64no—
377C3×Q16—64no—
378C3×SD16—64no—
379C3×SD16—64no—
380C3×M16—22no—
381C3×M16—22no—
382C3×M16—42no—
383C3×M16—62no—
384C2×C3×C8—22no—
385C2×C3×C8—32no—
386C2×C3×C8C22×D312yes—
387C2×C3×C8C23×C312yes—
388C3×C4⋊C4—21no—
389C3×C4⋊C4—21no—
390C3×C4⋊C4—22no—
391C3×C4⋊C4—41no—
392C3×C4⋊C4—62no—
393C3×C4⋊C4—62no—
394C3×C4⋊C4C22×D312yes—
395C3×C4⋊C4C23×C312yes—
396C3×C22⋊C4—62no—
397C3×C22⋊C4—62no—
398#216—24no—
399#214—24no—
400(C2×D3)⋊C4—22no—
401(C2×D3)⋊C4—22no—
402C4⋊Dic3—22no—
403C4⋊Dic3—22no—
404#208—22no—
405C2×C3⋊C8C23×C312yes—
406Dic12—24no—
407#204—24no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—22no—
411C22×C32—41no—
412C22×C32—41no—
413C22×C32#12012yes—
414C22×C32C22×D411yescharacteristic
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—22no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—44no—
422C2×C3×D3—48no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3#13712yescomplemented
426C32×C4—22no—
427C32×C4—42no—
428C32×C4#12012yes—
429C32×C4C22×D411yescharacteristic
430C32×C4C22×D411yescharacteristic
431C3×Dic3—21no—
432C3×Dic3—22no—
433C3×Dic3—21no—
434C3×Dic3—42no—
435C2×#41—31no—
436C2×#41—31no—
437C2×#41—31no—
438C2×#41—61no—
439C2×#41—61no—
440C2×#41—64no—
441C2×#41—64no—
442C2×#41C2×C3×D311yescharacteristic
443C22×Q8—31no—
444C22×Q8—31no—
445C22×D4—31no—
446C22×D4—61no—
447C23×C4—31no—
448C23×C4—61no—
449#137—64no—
450#137—64no—
451C2×Q16—32no—
452C2×Q16—32no—
453C2×SD16—32no—
454C2×SD16—32no—
455C2×M16—31no—
456C2×M16C2×C3×D311yescharacteristic, complemented
457C22⋊Q8—32no—
458C22⋊Q8—32no—
459C22⋊Q8—61no—
460C22⋊Q8—61no—
461C2×C4⋊C4—61no—
462C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
463C2×C22⋊C4—61no—
464#103—32no—
465#103C2×C3×D312yescomplemented
466#102—32no—
467#102C2×C3×D312yescomplemented
468C22⋊C8—32no—
469C22⋊C8—32no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—31no—
474C23×C3—31no—
475C23×C3—41no—
476C23×C3—62no—
477C23×C3—64no—
478C23×C3—62no—
479C23×C3—61no—
480C23×C3—121no—
481C23×C3—122no—
482C23×C3—122no—
483C23×C3D3×D411yescharacteristic
484C23×C3C2×C3×D411yescharacteristic
485C22×D3—24no—
486C22×D3—22no—
487C22×D3—21no—
488C22×D3—22no—
489C22×D3—41no—
490C22×D3—42no—
491C22×D3—42no—
492C22×D3C2×C3×D411yescharacteristic
493C22×D3C2×C3×D411yescharacteristic
494C3×Q8—21no—
495C3×Q8—21no—
496C3×Q8—22no—
497C3×Q8—32no—
498C3×Q8—41no—
499C3×Q8—64no—
500C3×Q8—61no—
501C3×Q8—62no—
502C3×Q8—62no—
503C3×Q8—122no—
504C3×Q8C2×D1212yes—
505C3×Q8C2×C3×D412yes—
506C3×D4—24no—
507C3×D4—24no—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—22no—
511C3×D4—32no—
512C3×D4—41no—
513C3×D4—44no—
514C3×D4—64no—
515C3×D4—64no—
516C3×D4—64no—
517C3×D4—64no—
518C3×D4—61no—
519C3×D4C2×D1212yes—
520C3×D4C2×C3×D412yes—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—24no—
524C2×C3×C4—24no—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—21no—
528C2×C3×C4—22no—
529C2×C3×C4—21no—
530C2×C3×C4—22no—
531C2×C3×C4—31no—
532C2×C3×C4—31no—
533C2×C3×C4—44no—
534C2×C3×C4—41no—
535C2×C3×C4—42no—
536C2×C3×C4—42no—
537C2×C3×C4—42no—
538C2×C3×C4—64no—
539C2×C3×C4—64no—
540C2×C3×C4—64no—
541C2×C3×C4—62no—
542C2×C3×C4—61no—
543C2×C3×C4—62no—
544C2×C3×C4—62no—
545C2×C3×C4—64no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—62no—
551C2×C3×C4—82no—
552C2×C3×C4—122no—
553C2×C3×C4C2×D1212yes—
554C2×C3×C4D3×D411yescharacteristic
555C2×C3×C4D3×D412yes—
556C2×C3×C4C2×C3×D412yes—
557C2×C3×C4C2×C3×D411yescharacteristic
558C2×C3×C4C2×C3×D412yes—
559C2×C3×C4C23×D311yescharacteristic
560C2×C3×C4C24×C311yescharacteristic
561#67—24no—
562#67—24no—
563#67—24no—
564C2×Dic3—24no—
565C2×Dic3—22no—
566C2×Dic3—21no—
567C2×Dic3—22no—
568C2×Dic3—42no—
569C2×Dic3C2×C3×D411yescharacteristic
570C2×Dic3C2×C3×D411yescharacteristic
571D12—24no—
572D12—21no—
573D12C2×C3×D412yes—
574C4×D3—24no—
575C4×D3—24no—
576C4×D3—22no—
577C4×D3—24no—
578C4×D3—22no—
579C4×D3—21no—
580C4×D3—21no—
581C4×D3—21no—
582C4×D3—21no—
583Dic6—24no—
584Dic6—21no—
585Dic6—22no—
586Dic6—22no—
587Dic6—42no—
588Dic6C2×C3×D412yes—
589C3×C8—22no—
590C3×C8—22no—
591C3×C8—42no—
592C3×C8—62no—
593C3⋊C8—22no—
594C2×C32—22no—
595C2×C32—42no—
596C2×C32C2×#12011yescharacteristic
597C2×C32C2×#13711yescharacteristic
598C2×C32#57511yescharacteristic
599C3×D3—22no—
600C3×D3—41no—
601C3×D3—42no—
602C24—31no—
603C24—61no—
604#41—22no—
605#41—34no—
606#41—68no—
607#41—62no—
608#41—68no—
609#41—62no—
610#41—62no—
611#41—62no—
612#41—62no—
613#41C3×D1214yes—
614C2×Q8—31no—
615C2×Q8—32no—
616C2×Q8—61no—
617C2×Q8—62no—
618C2×Q8—62no—
619C2×Q8—61no—
620C2×Q8—62no—
621C2×Q8—62no—
622C2×Q8C22×C3×D311yescharacteristic
623C2×D4—21no—
624C2×D4—31no—
625C2×D4—61no—
626C2×D4—61no—
627C2×D4—62no—
628C2×D4—68no—
629C2×D4—61no—
630C2×D4—61no—
631C2×D4—62no—
632C2×D4C22×C3×D311yescharacteristic
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—31no—
636C22×C4—31no—
637C22×C4—31no—
638C22×C4—31no—
639C22×C4—31no—
640C22×C4—61no—
641C22×C4—61no—
642C22×C4—68no—
643C22×C4—61no—
644C22×C4—62no—
645C22×C4—62no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4C22×C3×D311yescharacteristic
649Q16—64no—
650Q16—64no—
651SD16—64no—
652SD16—64no—
653M16—22no—
654M16—62no—
655C2×C8—32no—
656C2×C8C22×C3×D312yes—
657C4⋊C4—21no—
658C4⋊C4—62no—
659C4⋊C4—62no—
660C4⋊C4C22×C3×D312yes—
661C22⋊C4—62no—
662C22⋊C4—62no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—22no—
668C22×C3—22no—
669C22×C3—22no—
670C22×C3—21no—
671C22×C3—32no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—42no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—61no—
680C22×C3—61no—
681C22×C3—62no—
682C22×C3—61no—
683C22×C3—61no—
684C22×C3—61no—
685C22×C3—81no—
686C22×C3—81no—
687C22×C3—124no—
688C22×C3—128no—
689C22×C3—121no—
690C22×C3—121no—
691C22×C3#88212yes—
692C22×C3C3×#12012yes—
693C22×C3C2×D3×D411yescharacteristic
694C22×C3C22×C3×D411yescharacteristic
695C2×D3—21no—
696C2×D3—21no—
697C2×D3—21no—
698C2×D3—21no—
699C2×D3—21no—
700C2×D3—22no—
701C2×D3—44no—
702C2×D3—48no—
703C2×D3—41no—
704C2×D3—41no—
705C2×D3C3×#13712yescomplemented
706C3×C4—22no—
707C3×C4—22no—
708C3×C4—22no—
709C3×C4—21no—
710C3×C4—21no—
711C3×C4—42no—
712C3×C4—42no—
713C3×C4—42no—
714C3×C4—61no—
715C3×C4—61no—
716C3×C4—62no—
717C3×C4—82no—
718C3×C4—122no—
719C3×C4#88212yes—
720C3×C4C3×#12012yes—
721C3×C4C22×D1211yescharacteristic
722C3×C4C2×D3×D411yescharacteristic
723C3×C4C22×C3×D411yescharacteristic
724C3×C4C22×C3×D411yescharacteristic
725Dic3—21no—
726Dic3—22no—
727Dic3—21no—
728Dic3—42no—
729C32#300711yescharacteristic, complemented, Sylow
730C23—21no—
731C23—31no—
732C23—31no—
733C23—62no—
734C23—64no—
735C23—62no—
736C23—61no—
737C23—121no—
738C23—122no—
739C23—122no—
740C23C3×D3×D411yescharacteristic
741Q8—21no—
742Q8—32no—
743Q8—64no—
744Q8—61no—
745Q8—62no—
746Q8—62no—
747Q8—122no—
748Q8C2×C3×D1212yes—
749D4—24no—
750D4—21no—
751D4—32no—
752D4—64no—
753D4—64no—
754D4—64no—
755D4—64no—
756D4—61no—
757D4C2×C3×D1212yes—
758C2×C4—21no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—31no—
762C2×C4—31no—
763C2×C4—42no—
764C2×C4—64no—
765C2×C4—64no—
766C2×C4—64no—
767C2×C4—62no—
768C2×C4—61no—
769C2×C4—62no—
770C2×C4—62no—
771C2×C4—64no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—62no—
777C2×C4—122no—
778C2×C4C2×C3×D1212yes—
779C2×C4C3×D3×D411yescharacteristic
780C2×C4C3×D3×D412yes—
781C2×C4C23×C3×D311yescharacteristic
782C8—22no—
783C8—62no—
784C2×C3—22no—
785C2×C3—22no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—42no—
790C2×C3—42no—
791C2×C3—42no—
792C2×C3—62no—
793C2×C3—82no—
794C2×C3—121no—
795C2×C3—122no—
796C2×C3C2×#88211yescharacteristic
797C2×C3#577311yescharacteristic
798C2×C3D3×#13711yescharacteristic
799C2×C3C2×C3×#12011yescharacteristic
800C2×C3C2×C3×#13711yescharacteristic
801C2×C3C3×#57511yescharacteristic
802D3—22no—
803D3—41no—
804D3—42no—
805C22—21no—
806C22—21no—
807C22—22no—
808C22—32no—
809C22—41no—
810C22—41no—
811C22—61no—
812C22—61no—
813C22—62no—
814C22—61no—
815C22—61no—
816C22—61no—
817C22—124no—
818C22—128no—
819C22—121no—
820C22—121no—
821C22C3×#88212yes—
822C22C2×C3×D3×D411yescharacteristic
823C4—22no—
824C4—42no—
825C4—61no—
826C4—61no—
827C4—62no—
828C4—122no—
829C4C3×#88212yes—
830C4C22×C3×D1211yescharacteristic
831C4C2×C3×D3×D411yescharacteristic
832C3—21no—
833C3#7888511yescharacteristic, direct product factor
834C3C3×#300711yescharacteristic, complemented
835C2—22no—
836C2—42no—
837C2—62no—
838C2—121no—
839C2—122no—
840C2C2×C3×#88211yescharacteristic
841C2C3×#577311yescharacteristic
842C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#417C2
socleC22×C32C22×D4
prime radicalC2×C3×D3×#41C2
hypercenterC3×#417D3
hypocenterC3C3×#3007
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#417

Complements

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

NH ≅ G/Ntype
2. C2×C3×#951C2semidirect
3. C2×C3×#909C2semidirect
4. C2×C3×#897C2semidirect
5. C32×#417C2semidirect
6. C3×#5126C2semidirect
7. C3×#4966C2semidirect
8. C3×#4809C2semidirect
9. C3×#4808C2semidirect
10. C3×#4783C2semidirect
11. C3×#4776C2semidirect
13. #78885C3direct (N × H)
27. C22×C3×Dic6C22semidirect
28. C2×C32×M16C22semidirect
29. C2×C32×C4⋊C4C22semidirect
31. C2×C3×#216C22semidirect
32. C2×C3×#214C22semidirect
35. C2×C3×#208C22semidirect
37. C2×C3×Dic12C22semidirect
38. C2×C3×#204C22semidirect
42. C3×#897C22semidirect
43. C32×#103C22semidirect
44. C32×#102C22semidirect
46. C3×(C2×D3)⋊C8C22semidirect
47. C3×#810C22semidirect
48. C3×#809C22semidirect
54. C2×#951C2×C3semidirect
55. C2×#909C2×C3semidirect
56. C2×#897C2×C3semidirect
63. C3×#417D3semidirect
64. C3×#417C2×C3semidirect
66. #5126C2×C3semidirect
67. #4966C2×C3semidirect
68. #4809C2×C3semidirect
69. #4808C2×C3semidirect
70. #4783C2×C3semidirect
71. #4776C2×C3semidirect
162. C22×Dic6C22×C3semidirect
171. C2×C3×M16C2×D3semidirect
172. C2×C3×M16C22×C3semidirect
179. C2×C3×C4⋊C4C2×D3semidirect
180. C2×C3×C4⋊C4C22×C3semidirect
183. C2×#216C22×C3semidirect
184. C2×#214C22×C3semidirect
187. C2×#208C22×C3semidirect
189. C2×Dic12C22×C3semidirect
190. C2×#204C22×C3semidirect
194. #897C22×C3semidirect
197. C3×#103C2×D3semidirect
198. C3×#103C22×C3semidirect
201. C3×#102C2×D3semidirect
202. C3×#102C22×C3semidirect
206. (C2×D3)⋊C8C22×C3semidirect
207. #810C22×C3semidirect
208. #809C22×C3semidirect
272. #417C3×D3semidirect
425. C2×C3×D3#137semidirect
456. C2×M16C2×C3×D3semidirect
462. C2×C4⋊C4C2×C3×D3semidirect
465. #103C2×C3×D3semidirect
467. #102C2×C3×D3semidirect
705. C2×D3C3×#137semidirect
729. C32#3007semidirect
833. C3#78885direct (N × H)
834. C3C3×#3007semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×#412
C2×C3×#9512
C2×C3×#9092
C2×C3×#8972
C32×#4172
C3×#51262
C3×#49662
C3×#48092
C3×#48082
C3×#47832
C3×#47762
C3×#30073
#788853