Finite Group Databasebeta

← C3×#83981 #11864175

Subgroups — C3×#83981 #11864175

Order 1152.

1637 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic
2C2×C32×#137C211yesmaximal, characteristic, complemented
3C2×C3×#946C211yesmaximal, characteristic, complemented
4C2×C3×#942C211yesmaximal, characteristic, complemented
5C3×#5232C211yesmaximal, characteristic, complemented
6C3×#5187C212yesmaximal, complemented
7C3×#5186C212yesmaximal, complemented
8C3×#5173C212yesmaximal, complemented
9C3×#5169C212yesmaximal, complemented
10C3×#5133C211yesmaximal, characteristic, complemented
11C3×#5126C211yesmaximal, characteristic, complemented
12C3×#3007—31nomaximal
13#83981C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2211yescharacteristic
15C22×C32×Q8C2211yescharacteristic, complemented
16C3×D3×#41—24no—
17C3×D3×#41—24no—
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C3×#237—21no—
21C2×C3×#237C2211yescharacteristic
22C2×C3×D3×D4—21no—
23C2×C3×D3×D4C2211yescharacteristic
24C2×C3×#235—21no—
25C2×C3×#235C2211yescharacteristic
26C22×C3×C4×D3—21no—
27C22×C3×C4×D3C2211yescharacteristic
28C32×#137—24no—
29C2×C32×Q16C2212yescomplemented
30C2×C32×SD16C2212yescomplemented
31C2×C32×M16C2211yescharacteristic, complemented
32C3×#946—21no—
33C3×#946—21no—
34C3×#946C2212yes—
35C3×#946C2212yescomplemented
36C2×C3×#216C2212yescomplemented
37C3×#942—24no—
38C2×C3×#215C2212yescomplemented
39C2×C3×(C2×D3)⋊C4—21no—
40C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
41C2×C3×Dic3⋊C4—21no—
42C2×C3×#208C2211yescharacteristic, complemented
43C3×#835C2212yescomplemented
44C3×#832C2212yescomplemented
45C3×#821C2212yescomplemented
46C3×(C2×D3)⋊C8C2212yes—
47C3×(C2×D3)⋊C8C2212yescomplemented
48C3×#816C2212yescomplemented
49C22×C3×#41—31no—
50C2×D3×#41C2×C311yescharacteristic
51C2×C3×#137—21no—
52C2×C3×#137—31no—
53C2×C3×#137D311yescharacteristic, complemented
54C2×C3×#137C2×C311yescharacteristic, complemented
55C2×C3×C22⋊Q8—31no—
56C2×#946C2×C311yescharacteristic, complemented
57C2×#942C2×C311yescharacteristic, complemented
58C3×#452—32no—
59C3×#452—32no—
60C3×#451—32no—
61C3×#450—32no—
62C3×#417—31no—
63C3×#417—31no—
64C3×#407—31no—
65#5232C2×C311yescharacteristic, complemented
66#5187C2×C312yescomplemented
67#5186C2×C312yescomplemented
68#5173C2×C312yescomplemented
69#5169C2×C312yescomplemented
70#5133C2×C311yescharacteristic, complemented
71#5126C2×C311yescharacteristic, complemented
72C23×C3×D3—21no—
73C23×C3×D3D411yescharacteristic
74C32×#41—22no—
75C32×#41D414yes—
76C2×C32×Q8—21no—
77C2×C32×Q8—22no—
78C2×C32×Q8—22no—
79C2×C32×Q8C2312yes—
80C2×C32×Q8C2311yescharacteristic
81C2×C32×D4—21no—
82C2×C32×D4C2311yescharacteristic
83C22×C32×C4—21no—
84C22×C32×C4—21no—
85C22×C32×C4C2311yescharacteristic
86C2×C3×#67—21no—
87C2×C3×#67—21no—
88C2×C3×#67—21no—
89C22×C3×Dic3—21no—
90C22×C3×Dic3—21no—
91C22×C3×Dic3D411yescharacteristic
92C3×#239—22no—
93C3×#239—22no—
94C3×D3×Q8—22no—
95C3×D3×Q8—22no—
96C3×#237—28no—
97C3×#237—22no—
98C3×#237—22no—
99C3×D3×D4—28no—
100C3×D3×D4—22no—
101C3×D3×D4—22no—
102C3×#235—28no—
103C3×#235—22no—
104C3×#235D414yes—
105C2×C3×D12—21no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—28no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—22no—
111C2×C3×C4×D3—22no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3D411yescharacteristic
114C2×C3×C4×D3D411yescharacteristic
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×Dic6—21no—
118C2×C3×Dic6C2311yescharacteristic
119C32×Q16—24no—
120C32×SD16—24no—
121C32×M16—22no—
122C2×C32×C8C2312yes—
123C3×#216—24no—
124C3×#215—24no—
125C3×(C2×D3)⋊C4—22no—
126C3×(C2×D3)⋊C4—22no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2312yes—
129C3×Dic3⋊C4—22no—
130C3×Dic3⋊C4—22no—
131C3×#208—22no—
132C2×C3×C3⋊C8C2312yes—
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—21no—
145C22×C3×Q8—31no—
146C22×C3×Q8C2×D311yescharacteristic, complemented
147C22×C3×Q8C22×C311yescharacteristic, complemented
148C22×C3×D4—31no—
149C22×C3×D4—61no—
150C23×C3×C4—31no—
151C23×C3×C4—61no—
152D3×#41—24no—
153D3×#41—24no—
154C2×#239C22×C311yescharacteristic
155C2×D3×Q8C22×C311yescharacteristic
156C2×#237—21no—
157C2×#237C22×C311yescharacteristic
158C2×D3×D4—21no—
159C2×D3×D4C22×C311yescharacteristic
160C2×#235—21no—
161C2×#235C22×C311yescharacteristic
162C22×C4×D3—21no—
163C22×C4×D3C22×C311yescharacteristic
164C3×#137—28no—
165C3×#137—24no—
166C3×#137—24no—
167C3×#137—64no—
168C2×C3×Q16—22no—
169C2×C3×Q16—32no—
170C2×C3×Q16C2×D312yescomplemented
171C2×C3×Q16C22×C312yescomplemented
172C2×C3×SD16—22no—
173C2×C3×SD16—32no—
174C2×C3×SD16C2×D312yescomplemented
175C2×C3×SD16C22×C312yescomplemented
176C2×C3×M16—21no—
177C2×C3×M16—31no—
178C2×C3×M16C2×D311yescharacteristic, complemented
179C2×C3×M16C22×C311yescharacteristic, complemented
180C3×C22⋊Q8—32no—
181C3×C22⋊Q8—32no—
182C3×C22⋊Q8—61no—
183C3×C22⋊Q8—61no—
184C2×C3×C4⋊C4—31no—
185C2×C3×C4⋊C4—61no—
186C2×C3×C22⋊C4—61no—
187#946—21no—
188#946—21no—
189#946C22×C312yes—
190#946C22×C312yescomplemented
191C2×#216C22×C312yescomplemented
192#942—24no—
193C2×#215C22×C312yescomplemented
194C2×(C2×D3)⋊C4—21no—
195C2×C4⋊Dic3C22×C311yescharacteristic, complemented
196C2×Dic3⋊C4—21no—
197C2×#208C22×C311yescharacteristic, complemented
198C3×#103—32no—
199C3×#103—32no—
200C3×#102—32no—
201C3×#102—32no—
202C3×C22⋊C8—32no—
203C3×C22⋊C8—32no—
204#835C22×C312yescomplemented
205#832C22×C312yescomplemented
206#821C22×C312yescomplemented
207(C2×D3)⋊C8C22×C312yes—
208(C2×D3)⋊C8C22×C312yescomplemented
209#816C22×C312yescomplemented
210C23×C32—21no—
211C23×C32C2×D411yescharacteristic
212C22×C3×D3—24no—
213C22×C3×D3—22no—
214C22×C3×D3—21no—
215C22×C3×D3—22no—
216C22×C3×D3—41no—
217C22×C3×D3—42no—
218C22×C3×D3—42no—
219C22×C3×D3C2×D411yescharacteristic
220C22×C3×D3C2×D411yescharacteristic
221C32×Q8—22no—
222C32×Q8—21no—
223C32×Q8—22no—
224C32×Q8—42no—
225C32×Q8C2×D412yes—
226C32×D4—24no—
227C32×D4—21no—
228C32×D4C2×D412yes—
229C2×C32×C4—21no—
230C2×C32×C4—24no—
231C2×C32×C4—22no—
232C2×C32×C4—42no—
233C2×C32×C4C2×D411yescharacteristic
234C2×C32×C4C2×D412yes—
235C2×C32×C4C2×D412yes—
236C2×C32×C4C2411yescharacteristic
237C3×#67—24no—
238C3×#67—24no—
239C3×#67—24no—
240C2×C3×Dic3—24no—
241C2×C3×Dic3—22no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—22no—
244C2×C3×Dic3—42no—
245C2×C3×Dic3C2×D411yescharacteristic
246C2×C3×Dic3C2×D411yescharacteristic
247C3×D12—24no—
248C3×D12—21no—
249C3×D12C2×D412yes—
250C3×C4×D3—24no—
251C3×C4×D3—24no—
252C3×C4×D3—22no—
253C3×C4×D3—24no—
254C3×C4×D3—22no—
255C3×C4×D3—21no—
256C3×C4×D3—21no—
257C3×C4×D3—21no—
258C3×C4×D3—21no—
259C3×Dic6—24no—
260C3×Dic6—21no—
261C3×Dic6C2×D412yes—
262C32×C8—22no—
263C3×C3⋊C8—22no—
264C22×#41—31no—
265C2×#137—31no—
266C2×#137C3×D311yescharacteristic, complemented
267C2×C22⋊Q8—31no—
268#452—32no—
269#452—32no—
270#451—32no—
271#450—32no—
272#417—31no—
273#417—31no—
274#407—31no—
275C24×C3—31no—
276C24×C3—61no—
277C23×D3—21no—
278C23×D3C3×D411yescharacteristic
279C3×#41—22no—
280C3×#41—22no—
281C3×#41—24no—
282C3×#41—34no—
283C3×#41—42no—
284C3×#41—68no—
285C3×#41—62no—
286C3×#41—68no—
287C3×#41—62no—
288C3×#41—62no—
289C3×#41—62no—
290C3×#41—62no—
291C3×#41#6714yes—
292C3×#41C3×D414yes—
293C2×C3×Q8—21no—
294C2×C3×Q8—21no—
295C2×C3×Q8—24no—
296C2×C3×Q8—22no—
297C2×C3×Q8—22no—
298C2×C3×Q8—22no—
299C2×C3×Q8—22no—
300C2×C3×Q8—22no—
301C2×C3×Q8—21no—
302C2×C3×Q8—31no—
303C2×C3×Q8—41no—
304C2×C3×Q8—42no—
305C2×C3×Q8—61no—
306C2×C3×Q8—62no—
307C2×C3×Q8—62no—
308C2×C3×Q8C22×D312yes—
309C2×C3×Q8C22×D311yescharacteristic
310C2×C3×Q8C23×C312yes—
311C2×C3×Q8C23×C311yescharacteristic
312C2×C3×D4—21no—
313C2×C3×D4—21no—
314C2×C3×D4—21no—
315C2×C3×D4—31no—
316C2×C3×D4—41no—
317C2×C3×D4—61no—
318C2×C3×D4—61no—
319C2×C3×D4—62no—
320C2×C3×D4—68no—
321C2×C3×D4—61no—
322C2×C3×D4—61no—
323C2×C3×D4—62no—
324C2×C3×D4C22×D311yescharacteristic
325C2×C3×D4C23×C311yescharacteristic
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—41no—
337C22×C3×C4—41no—
338C22×C3×C4—61no—
339C22×C3×C4—61no—
340C22×C3×C4—68no—
341C22×C3×C4—61no—
342C22×C3×C4—62no—
343C22×C3×C4—61no—
344C22×C3×C4—62no—
345C22×C3×C4—61no—
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C23×C311yescharacteristic
348C2×#67—21no—
349C2×#67—21no—
350C2×#67—21no—
351C22×Dic3—21no—
352C22×Dic3—21no—
353C22×Dic3C3×D411yescharacteristic
354#239—22no—
355#239—22no—
356D3×Q8—22no—
357D3×Q8—22no—
358#237—28no—
359#237—22no—
360#237—22no—
361D3×D4—28no—
362D3×D4—22no—
363D3×D4—22no—
364#235—28no—
365#235—22no—
366#235C3×D414yes—
367C2×D12—21no—
368C2×D12C23×C311yescharacteristic
369C2×C4×D3—28no—
370C2×C4×D3—21no—
371C2×C4×D3—21no—
372C2×C4×D3—22no—
373C2×C4×D3—22no—
374C2×C4×D3—21no—
375C2×C4×D3C3×D411yescharacteristic
376C2×C4×D3C3×D411yescharacteristic
377C2×C4×D3C23×C311yescharacteristic
378C2×C4×D3C23×C311yescharacteristic
379C2×Dic6—21no—
380C2×Dic6C23×C311yescharacteristic
381C3×Q16—28no—
382C3×Q16—24no—
383C3×Q16—24no—
384C3×Q16—64no—
385C3×SD16—28no—
386C3×SD16—24no—
387C3×SD16—24no—
388C3×SD16—64no—
389C3×M16—24no—
390C3×M16—22no—
391C3×M16—22no—
392C3×M16—62no—
393C2×C3×C8—22no—
394C2×C3×C8—32no—
395C2×C3×C8C22×D312yes—
396C2×C3×C8C23×C312yes—
397C3×C4⋊C4—32no—
398C3×C4⋊C4—62no—
399C3×C4⋊C4—62no—
400C3×C4⋊C4—61no—
401C3×C22⋊C4—62no—
402C3×C22⋊C4—62no—
403#216—24no—
404#215—24no—
405(C2×D3)⋊C4—22no—
406(C2×D3)⋊C4—22no—
407C4⋊Dic3—21no—
408C4⋊Dic3C23×C312yes—
409Dic3⋊C4—22no—
410Dic3⋊C4—22no—
411#208—22no—
412C2×C3⋊C8C23×C312yes—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—22no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32#12012yes—
419C22×C32C22×D411yescharacteristic
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—22no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—44no—
427C2×C3×D3—48no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3#13712yescomplemented
431C32×C4—22no—
432C32×C4—42no—
433C32×C4#12012yes—
434C32×C4C22×D411yescharacteristic
435C32×C4C22×D411yescharacteristic
436C3×Dic3—21no—
437C3×Dic3—22no—
438C3×Dic3—21no—
439C3×Dic3—42no—
440C2×#41—31no—
441C2×#41—31no—
442C2×#41—31no—
443C2×#41—61no—
444C2×#41—61no—
445C2×#41—64no—
446C2×#41—64no—
447C2×#41C2×C3×D311yescharacteristic
448C22×Q8—31no—
449C22×Q8C2×C3×D311yescharacteristic, complemented
450C22×D4—31no—
451C22×D4—61no—
452C23×C4—31no—
453C23×C4—61no—
454#137—24no—
455#137—64no—
456C2×Q16—32no—
457C2×Q16C2×C3×D312yescomplemented
458C2×SD16—32no—
459C2×SD16C2×C3×D312yescomplemented
460C2×M16—31no—
461C2×M16C2×C3×D311yescharacteristic, complemented
462C22⋊Q8—32no—
463C22⋊Q8—32no—
464C22⋊Q8—61no—
465C22⋊Q8—61no—
466C2×C4⋊C4—31no—
467C2×C4⋊C4—61no—
468C2×C22⋊C4—61no—
469#103—32no—
470#103—32no—
471#102—32no—
472#102—32no—
473C22⋊C8—32no—
474C22⋊C8—32no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—31no—
479C23×C3—31no—
480C23×C3—41no—
481C23×C3—62no—
482C23×C3—64no—
483C23×C3—62no—
484C23×C3—61no—
485C23×C3—121no—
486C23×C3—122no—
487C23×C3—122no—
488C23×C3D3×D411yescharacteristic
489C23×C3C2×C3×D411yescharacteristic
490C22×D3—24no—
491C22×D3—22no—
492C22×D3—21no—
493C22×D3—22no—
494C22×D3—41no—
495C22×D3—42no—
496C22×D3—42no—
497C22×D3C2×C3×D411yescharacteristic
498C22×D3C2×C3×D411yescharacteristic
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—24no—
502C3×Q8—22no—
503C3×Q8—22no—
504C3×Q8—22no—
505C3×Q8—22no—
506C3×Q8—22no—
507C3×Q8—32no—
508C3×Q8—42no—
509C3×Q8—41no—
510C3×Q8—44no—
511C3×Q8—42no—
512C3×Q8—42no—
513C3×Q8—64no—
514C3×Q8—61no—
515C3×Q8C2×#6712yes—
516C3×Q8C2×C3×D412yes—
517C3×D4—24no—
518C3×D4—24no—
519C3×D4—21no—
520C3×D4—21no—
521C3×D4—22no—
522C3×D4—32no—
523C3×D4—41no—
524C3×D4—44no—
525C3×D4—64no—
526C3×D4—64no—
527C3×D4—64no—
528C3×D4—64no—
529C3×D4—61no—
530C3×D4C2×#6712yes—
531C3×D4C2×C3×D412yes—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—24no—
535C2×C3×C4—24no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—22no—
541C2×C3×C4—22no—
542C2×C3×C4—31no—
543C2×C3×C4—31no—
544C2×C3×C4—44no—
545C2×C3×C4—41no—
546C2×C3×C4—42no—
547C2×C3×C4—44no—
548C2×C3×C4—42no—
549C2×C3×C4—42no—
550C2×C3×C4—64no—
551C2×C3×C4—64no—
552C2×C3×C4—64no—
553C2×C3×C4—62no—
554C2×C3×C4—61no—
555C2×C3×C4—62no—
556C2×C3×C4—62no—
557C2×C3×C4—64no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—62no—
563C2×C3×C4—122no—
564C2×C3×C4D3×D411yescharacteristic
565C2×C3×C4D3×D412yes—
566C2×C3×C4C2×#6712yes—
567C2×C3×C4C2×C3×D411yescharacteristic
568C2×C3×C4C2×C3×D412yes—
569C2×C3×C4C2×C3×D412yes—
570C2×C3×C4C23×D311yescharacteristic
571C2×C3×C4C24×C311yescharacteristic
572#67—24no—
573#67—24no—
574#67—24no—
575C2×Dic3—24no—
576C2×Dic3—22no—
577C2×Dic3—21no—
578C2×Dic3—22no—
579C2×Dic3—42no—
580C2×Dic3C2×C3×D411yescharacteristic
581C2×Dic3C2×C3×D411yescharacteristic
582D12—24no—
583D12—21no—
584D12C2×C3×D412yes—
585C4×D3—24no—
586C4×D3—24no—
587C4×D3—22no—
588C4×D3—24no—
589C4×D3—22no—
590C4×D3—21no—
591C4×D3—21no—
592C4×D3—21no—
593C4×D3—21no—
594Dic6—24no—
595Dic6—21no—
596Dic6C2×C3×D412yes—
597C3×C8—24no—
598C3×C8—22no—
599C3×C8—22no—
600C3×C8—62no—
601C3⋊C8—22no—
602C2×C32—22no—
603C2×C32—42no—
604C2×C32C2×#12011yescharacteristic
605C2×C32C2×#13711yescharacteristic
606C2×C32#57511yescharacteristic
607C3×D3—22no—
608C3×D3—41no—
609C3×D3—42no—
610C24—31no—
611C24—61no—
612#41—22no—
613#41—34no—
614#41—68no—
615#41—62no—
616#41—68no—
617#41—62no—
618#41—62no—
619#41—62no—
620#41—62no—
621#41C3×#6714yes—
622C2×Q8—21no—
623C2×Q8—22no—
624C2×Q8—22no—
625C2×Q8—31no—
626C2×Q8—61no—
627C2×Q8—62no—
628C2×Q8—62no—
629C2×Q8C22×C3×D312yes—
630C2×Q8C22×C3×D311yescharacteristic
631C2×D4—21no—
632C2×D4—31no—
633C2×D4—61no—
634C2×D4—61no—
635C2×D4—62no—
636C2×D4—68no—
637C2×D4—61no—
638C2×D4—61no—
639C2×D4—62no—
640C2×D4C22×C3×D311yescharacteristic
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—31no—
647C22×C4—31no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—68no—
651C22×C4—61no—
652C22×C4—62no—
653C22×C4—61no—
654C22×C4—62no—
655C22×C4—61no—
656C22×C4C22×C3×D311yescharacteristic
657Q16—24no—
658Q16—64no—
659SD16—24no—
660SD16—64no—
661M16—22no—
662M16—62no—
663C2×C8—32no—
664C2×C8C22×C3×D312yes—
665C4⋊C4—32no—
666C4⋊C4—62no—
667C4⋊C4—62no—
668C4⋊C4—61no—
669C22⋊C4—62no—
670C22⋊C4—62no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—22no—
676C22×C3—22no—
677C22×C3—22no—
678C22×C3—21no—
679C22×C3—32no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—42no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—61no—
688C22×C3—61no—
689C22×C3—61no—
690C22×C3—61no—
691C22×C3—62no—
692C22×C3—61no—
693C22×C3—81no—
694C22×C3—81no—
695C22×C3—124no—
696C22×C3—128no—
697C22×C3—121no—
698C22×C3—121no—
699C22×C3#93712yes—
700C22×C3C3×#12012yes—
701C22×C3C2×D3×D411yescharacteristic
702C22×C3C22×C3×D411yescharacteristic
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—22no—
709C2×D3—44no—
710C2×D3—48no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3C3×#13712yescomplemented
714C3×C4—22no—
715C3×C4—22no—
716C3×C4—22no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—42no—
720C3×C4—44no—
721C3×C4—42no—
722C3×C4—42no—
723C3×C4—61no—
724C3×C4—61no—
725C3×C4—62no—
726C3×C4—122no—
727C3×C4#93712yes—
728C3×C4C3×#12012yes—
729C3×C4C2×D3×D411yescharacteristic
730C3×C4C22×#6711yescharacteristic
731C3×C4C22×C3×D411yescharacteristic
732C3×C4C22×C3×D411yescharacteristic
733Dic3—21no—
734Dic3—22no—
735Dic3—21no—
736Dic3—42no—
737C32#300711yescharacteristic, complemented, Sylow
738C23—21no—
739C23—31no—
740C23—31no—
741C23—62no—
742C23—64no—
743C23—62no—
744C23—61no—
745C23—121no—
746C23—122no—
747C23—122no—
748C23C3×D3×D411yescharacteristic
749Q8—21no—
750Q8—22no—
751Q8—22no—
752Q8—32no—
753Q8—42no—
754Q8—64no—
755Q8—61no—
756Q8C2×C3×#6712yes—
757D4—24no—
758D4—21no—
759D4—32no—
760D4—64no—
761D4—64no—
762D4—64no—
763D4—64no—
764D4—61no—
765D4C2×C3×#6712yes—
766C2×C4—21no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—31no—
770C2×C4—31no—
771C2×C4—42no—
772C2×C4—64no—
773C2×C4—64no—
774C2×C4—64no—
775C2×C4—62no—
776C2×C4—61no—
777C2×C4—62no—
778C2×C4—62no—
779C2×C4—64no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—62no—
785C2×C4—122no—
786C2×C4C3×D3×D411yescharacteristic
787C2×C4C3×D3×D412yes—
788C2×C4C2×C3×#6712yes—
789C2×C4C23×C3×D311yescharacteristic
790C8—22no—
791C8—62no—
792C2×C3—22no—
793C2×C3—22no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—42no—
798C2×C3—42no—
799C2×C3—42no—
800C2×C3—62no—
801C2×C3—82no—
802C2×C3—121no—
803C2×C3—122no—
804C2×C3D3×#13711yescharacteristic
805C2×C3#577711yescharacteristic
806C2×C3C2×#93711yescharacteristic
807C2×C3C2×C3×#12011yescharacteristic
808C2×C3C2×C3×#13711yescharacteristic
809C2×C3C3×#57511yescharacteristic
810D3—22no—
811D3—41no—
812D3—42no—
813C22—21no—
814C22—21no—
815C22—22no—
816C22—32no—
817C22—41no—
818C22—41no—
819C22—61no—
820C22—61no—
821C22—61no—
822C22—61no—
823C22—62no—
824C22—61no—
825C22—124no—
826C22—128no—
827C22—121no—
828C22—121no—
829C22C3×#93712yes—
830C22C2×C3×D3×D411yescharacteristic
831C4—22no—
832C4—42no—
833C4—61no—
834C4—61no—
835C4—62no—
836C4—122no—
837C4C3×#93712yes—
838C4C2×C3×D3×D411yescharacteristic
839C4C22×C3×#6711yescharacteristic
840C3—21no—
841C3#8398111yescharacteristic, direct product factor
842C3C3×#300711yescharacteristic, complemented
843C2—22no—
844C2—42no—
845C2—62no—
846C2—121no—
847C2—122no—
848C2C3×D3×#13711yescharacteristic
849C2C3×#577711yescharacteristic
850C2C2×C3×#93711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#137C2
socleC22×C32C22×D4
prime radicalC2×C3×D3×#41C2
hypercenterC2×C3×#137D3
hypocenterC3C3×#3007
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#137

Complements

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

NH ≅ G/Ntype
2. C2×C32×#137C2semidirect
3. C2×C3×#946C2semidirect
4. C2×C3×#942C2semidirect
5. C3×#5232C2semidirect
6. C3×#5187C2semidirect
7. C3×#5186C2semidirect
8. C3×#5173C2semidirect
9. C3×#5169C2semidirect
10. C3×#5133C2semidirect
11. C3×#5126C2semidirect
13. #83981C3direct (N × H)
15. C22×C32×Q8C22semidirect
29. C2×C32×Q16C22semidirect
30. C2×C32×SD16C22semidirect
31. C2×C32×M16C22semidirect
35. C3×#946C22semidirect
36. C2×C3×#216C22semidirect
38. C2×C3×#215C22semidirect
40. C2×C3×C4⋊Dic3C22semidirect
42. C2×C3×#208C22semidirect
43. C3×#835C22semidirect
44. C3×#832C22semidirect
45. C3×#821C22semidirect
47. C3×(C2×D3)⋊C8C22semidirect
48. C3×#816C22semidirect
53. C2×C3×#137D3semidirect
54. C2×C3×#137C2×C3semidirect
56. C2×#946C2×C3semidirect
57. C2×#942C2×C3semidirect
65. #5232C2×C3semidirect
66. #5187C2×C3semidirect
67. #5186C2×C3semidirect
68. #5173C2×C3semidirect
69. #5169C2×C3semidirect
70. #5133C2×C3semidirect
71. #5126C2×C3semidirect
146. C22×C3×Q8C2×D3semidirect
147. C22×C3×Q8C22×C3semidirect
170. C2×C3×Q16C2×D3semidirect
171. C2×C3×Q16C22×C3semidirect
174. C2×C3×SD16C2×D3semidirect
175. C2×C3×SD16C22×C3semidirect
178. C2×C3×M16C2×D3semidirect
179. C2×C3×M16C22×C3semidirect
190. #946C22×C3semidirect
191. C2×#216C22×C3semidirect
193. C2×#215C22×C3semidirect
195. C2×C4⋊Dic3C22×C3semidirect
197. C2×#208C22×C3semidirect
204. #835C22×C3semidirect
205. #832C22×C3semidirect
206. #821C22×C3semidirect
208. (C2×D3)⋊C8C22×C3semidirect
209. #816C22×C3semidirect
266. C2×#137C3×D3semidirect
430. C2×C3×D3#137semidirect
449. C22×Q8C2×C3×D3semidirect
457. C2×Q16C2×C3×D3semidirect
459. C2×SD16C2×C3×D3semidirect
461. C2×M16C2×C3×D3semidirect
713. C2×D3C3×#137semidirect
737. C32#3007semidirect
841. C3#83981direct (N × H)
842. 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×C32×#1372
C2×C3×#9462
C2×C3×#9422
C3×#52322
C3×#51872
C3×#51862
C3×#51732
C3×#51692
C3×#51332
C3×#51262
C3×#30073
#839813