Finite Group Databasebeta

← C3×#72073 #11792622

Subgroups — C3×#72073 #11792622

Order 1152.

869 conjugacy classes of subgroups.

The subgroup lattice has 541 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×Q16C211yesmaximal, characteristic
2C2×C3×#944C211yesmaximal, characteristic
3C22×C3×#216C211yesmaximal, characteristic
4C3×#5229C211yesmaximal, characteristic
5C2×C3×#835C211yesmaximal, characteristic
6C2×C3×#816C211yesmaximal, characteristic
7C3×#4550C211yesmaximal, characteristic
8C3×#2016—31nomaximal
9#72073C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C22×C32×Q8C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C32×Q16—22no—
14C2×C32×Q16—22no—
15C2×C32×Q16—22no—
16C22×C32×C8C2211yescharacteristic
17C3×#944—22no—
18C3×#944—22no—
19C2×C3×#216—22no—
20C2×C3×#216—22no—
21C2×C3×#216—22no—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×Dic3⋊C4—22no—
24C2×C3×C4×Dic3C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C3×#835—22no—
27C3×C3⋊#95—22no—
28C3×#816—22no—
29C22×C3×Q16—21no—
30C22×C3×Q16—31no—
31C22×C3×Q16D311yescharacteristic
32C22×C3×Q16C2×C311yescharacteristic
33C2×C3×C4⋊Q8—31no—
34C2×#944C2×C311yescharacteristic
35C22×#216C2×C311yescharacteristic
36C2×C3×#103—31no—
37C2×C3×#103—31no—
38C3×#391—31no—
39#5229C2×C311yescharacteristic
40C2×#835C2×C311yescharacteristic
41C2×#816C2×C311yescharacteristic
42C3×#336—31no—
43#4550C2×C311yescharacteristic
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8—21no—
48C2×C32×Q8—21no—
49C2×C32×Q8—21no—
50C2×C32×Q8—21no—
51C2×C32×Q8—21no—
52C2×C32×Q8—21no—
53C2×C32×Q8—21no—
54C2×C32×Q8D412yes—
55C2×C32×Q8D412yes—
56C22×C32×C4—21no—
57C22×C32×C4—21no—
58C22×C32×C4C2311yescharacteristic
59C22×C3×Dic3—21no—
60C22×C3×Dic3—21no—
61C22×C3×Dic3D412yes—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6D412yes—
68C32×Q16—28no—
69C2×C32×C8—21no—
70C2×C32×C8—21no—
71C2×C32×C8D412yes—
72C3×#216—28no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C3×Dic3⋊C4—28no—
76C3×C4×Dic3—21no—
77C3×C4×Dic3—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8D412yes—
81#2016—31noSylow
82C22×C3×Q8—21no—
83C22×C3×Q8—21no—
84C22×C3×Q8—31no—
85C22×C3×Q8C2×D311yescharacteristic
86C22×C3×Q8C2×D311yescharacteristic
87C22×C3×Q8C22×C311yescharacteristic
88C22×C3×Q8C22×C311yescharacteristic
89C22×Dic6C22×C311yescharacteristic
90C2×C3×Q16—24no—
91C2×C3×Q16—24no—
92C2×C3×Q16—24no—
93C2×C3×Q16—22no—
94C2×C3×Q16—22no—
95C2×C3×Q16—22no—
96C2×C3×Q16—22no—
97C2×C3×Q16—22no—
98C2×C3×Q16—22no—
99C2×C3×Q16—62no—
100C2×C3×Q16—62no—
101C2×C3×Q16—62no—
102C22×C3×C8—21no—
103C22×C3×C8—31no—
104C22×C3×C8C2×D311yescharacteristic
105C22×C3×C8C22×C311yescharacteristic
106C3×C4⋊Q8—62no—
107C3×C4⋊Q8—62no—
108C2×C3×C4⋊C4—31no—
109C2×C3×C4⋊C4—62no—
110C2×C3×C42—31no—
111#944—22no—
112#944—22no—
113C2×#216—22no—
114C2×#216—22no—
115C2×#216—22no—
116C2×C4⋊Dic3C22×C311yescharacteristic
117C2×Dic3⋊C4—22no—
118C2×C4×Dic3C22×C311yescharacteristic
119C22×C3⋊C8C22×C311yescharacteristic
120C3×#103—62no—
121C3×#103—62no—
122C3×#95—62no—
123#835—22no—
124C3⋊#95—22no—
125#816—22no—
126C23×C32C2×D411yescharacteristic
127C32×Q8—22no—
128C32×Q8—22no—
129C32×Q8—22no—
130C32×Q8—22no—
131C32×Q8—41no—
132C32×Q8—41no—
133C32×Q8—41no—
134C32×Q8—41no—
135C2×C32×C4—22no—
136C2×C32×C4—22no—
137C2×C32×C4—41no—
138C2×C32×C4—41no—
139C2×C32×C4—41no—
140C2×C32×C4—41no—
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4#4111yescharacteristic
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—42no—
154C2×C3×Dic3Q1614yescomplemented
155C3×Dic6—22no—
156C3×Dic6—22no—
157C3×Dic6—41no—
158C3×Dic6—41no—
159C32×C8—22no—
160C3×C3⋊C8—22no—
161C22×Q16—31no—
162C22×Q16C3×D311yescharacteristic
163C2×C4⋊Q8—31no—
164C2×#103—31no—
165C2×#103—31no—
166#391—31no—
167#336—31no—
168C2×C3×Q8—21no—
169C2×C3×Q8—21no—
170C2×C3×Q8—21no—
171C2×C3×Q8—21no—
172C2×C3×Q8—22no—
173C2×C3×Q8—22no—
174C2×C3×Q8—22no—
175C2×C3×Q8—22no—
176C2×C3×Q8—21no—
177C2×C3×Q8—21no—
178C2×C3×Q8—21no—
179C2×C3×Q8—21no—
180C2×C3×Q8—21no—
181C2×C3×Q8—21no—
182C2×C3×Q8—21no—
183C2×C3×Q8—21no—
184C2×C3×Q8—21no—
185C2×C3×Q8—21no—
186C2×C3×Q8—21no—
187C2×C3×Q8—21no—
188C2×C3×Q8—21no—
189C2×C3×Q8—21no—
190C2×C3×Q8—21no—
191C2×C3×Q8—21no—
192C2×C3×Q8—22no—
193C2×C3×Q8—22no—
194C2×C3×Q8—32no—
195C2×C3×Q8—41no—
196C2×C3×Q8—41no—
197C2×C3×Q8—41no—
198C2×C3×Q8—41no—
199C2×C3×Q8—41no—
200C2×C3×Q8—41no—
201C2×C3×Q8—61no—
202C2×C3×Q8—61no—
203C2×C3×Q8—61no—
204C2×C3×Q8—61no—
205C2×C3×Q8—61no—
206C2×C3×Q8#6712yes—
207C2×C3×Q8#6712yes—
208C2×C3×Q8C3×D412yes—
209C2×C3×Q8C3×D412yes—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—32no—
216C22×C3×C4—41no—
217C22×C3×C4—41no—
218C22×C3×C4—61no—
219C22×C3×C4—61no—
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C23×C311yescharacteristic
222C22×Dic3—21no—
223C22×Dic3—21no—
224C22×Dic3C3×D412yes—
225C2×Dic6—21no—
226C2×Dic6—21no—
227C2×Dic6—21no—
228C2×Dic6—21no—
229C2×Dic6—21no—
230C2×Dic6C3×D412yes—
231C3×Q16—216no—
232C3×Q16—28no—
233C3×Q16—28no—
234C3×Q16—68no—
235C2×C3×C8—22no—
236C2×C3×C8—22no—
237C2×C3×C8—21no—
238C2×C3×C8—21no—
239C2×C3×C8—21no—
240C2×C3×C8—21no—
241C2×C3×C8—22no—
242C2×C3×C8—32no—
243C2×C3×C8—61no—
244C2×C3×C8—61no—
245C2×C3×C8#6712yes—
246C2×C3×C8C3×D412yes—
247C3×C4⋊C4—68no—
248C3×C4⋊C4—61no—
249C3×C4⋊C4—61no—
250C3×C42—61no—
251C3×C42—61no—
252#216—28no—
253C4⋊Dic3—21no—
254C4⋊Dic3—21no—
255Dic3⋊C4—28no—
256C4×Dic3—21no—
257C4×Dic3—21no—
258C2×C3⋊C8—21no—
259C2×C3⋊C8—21no—
260C2×C3⋊C8C3×D412yes—
261C22×C32#12011yescharacteristic
262C22×C32#12111yescharacteristic
263C22×C32#12711yescharacteristic
264C22×C32C2×Q1612yes—
265C22×C32#13712yes—
266C32×C4—42no—
267C32×C4—42no—
268C32×C4#12011yescharacteristic
269C32×C4#12011yescharacteristic
270C32×C4#12111yescharacteristic
271C32×C4#12111yescharacteristic
272C3×Dic3—24no—
273C3×Dic3—42no—
274C3×Dic3—81no—
275C22×Q8—31no—
276C22×Q8C2×C3×D311yescharacteristic
277C22×Q8C2×C3×D311yescharacteristic
278C2×Q16—22no—
279C2×Q16—22no—
280C2×Q16—22no—
281C2×Q16—62no—
282C2×Q16—62no—
283C2×Q16—62no—
284C22×C8—31no—
285C22×C8C2×C3×D311yescharacteristic
286C4⋊Q8—62no—
287C4⋊Q8—62no—
288C2×C4⋊C4—31no—
289C2×C4⋊C4—62no—
290C2×C42—31no—
291#103—62no—
292#103—62no—
293#95—62no—
294C23×C3—21no—
295C23×C3D3×D411yescharacteristic
296C23×C3C2×C3×D411yescharacteristic
297C3×Q8—24no—
298C3×Q8—24no—
299C3×Q8—22no—
300C3×Q8—22no—
301C3×Q8—22no—
302C3×Q8—22no—
303C3×Q8—22no—
304C3×Q8—22no—
305C3×Q8—22no—
306C3×Q8—22no—
307C3×Q8—42no—
308C3×Q8—42no—
309C3×Q8—42no—
310C3×Q8—42no—
311C3×Q8—42no—
312C3×Q8—42no—
313C3×Q8—41no—
314C3×Q8—41no—
315C3×Q8—41no—
316C3×Q8—41no—
317C3×Q8—41no—
318C3×Q8—41no—
319C3×Q8—41no—
320C3×Q8—41no—
321C3×Q8—62no—
322C3×Q8—62no—
323C3×Q8—121no—
324C3×Q8—121no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—34no—
336C2×C3×C4—42no—
337C2×C3×C4—42no—
338C2×C3×C4—42no—
339C2×C3×C4—42no—
340C2×C3×C4—42no—
341C2×C3×C4—42no—
342C2×C3×C4—41no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4—121no—
354C2×C3×C4—121no—
355C2×C3×C4—122no—
356C2×C3×C4—121no—
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4#23711yescharacteristic
360C2×C3×C4C2×#6711yescharacteristic
361C2×C3×C4C2×#6711yescharacteristic
362C2×C3×C4C2×#6711yescharacteristic
363C2×C3×C4C2×C3×D411yescharacteristic
364C2×C3×C4C2×C3×D411yescharacteristic
365C2×C3×C4C2×C3×D411yescharacteristic
366C2×C3×C4C2×C3×D411yescharacteristic
367C2×C3×C4C2×C3×D411yescharacteristic
368C2×C3×C4C3×#4111yescharacteristic
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—41no—
373C2×Dic3—41no—
374C2×Dic3—41no—
375C2×Dic3—42no—
376C2×Dic3C3×Q1614yescomplemented
377Dic6—22no—
378Dic6—22no—
379Dic6—41no—
380Dic6—41no—
381C3×C8—24no—
382C3×C8—22no—
383C3×C8—22no—
384C3×C8—62no—
385C3⋊C8—22no—
386C2×C32#39211yescharacteristic
387C2×C32#45112yes—
388C2×C32#46212yes—
389C2×C32#49411yescharacteristic
390C2×C32#49711yescharacteristic
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—32no—
402C2×Q8—61no—
403C2×Q8—61no—
404C2×Q8—61no—
405C2×Q8—61no—
406C2×Q8—61no—
407C2×Q8C3×#6712yes—
408C2×Q8C3×#6712yes—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—32no—
412C22×C4—61no—
413C22×C4—61no—
414C22×C4C22×C3×D311yescharacteristic
415Q16—28no—
416Q16—68no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—32no—
420C2×C8—61no—
421C2×C8—61no—
422C2×C8C3×#6712yes—
423C4⋊C4—68no—
424C4⋊C4—61no—
425C4⋊C4—61no—
426C42—61no—
427C42—61no—
428C22×C3—22no—
429C22×C3—22no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3D3×Q1612yes—
434C22×C3#91812yes—
435C22×C3#93711yescharacteristic
436C22×C3#93911yescharacteristic
437C22×C3#94011yescharacteristic
438C22×C3C3×#12011yescharacteristic
439C22×C3C3×#12111yescharacteristic
440C22×C3C3×#12711yescharacteristic
441C22×C3C2×C3×Q1612yes—
442C22×C3C3×#13712yes—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—44no—
448C3×C4—44no—
449C3×C4—42no—
450C3×C4—42no—
451C3×C4—42no—
452C3×C4—42no—
453C3×C4—64no—
454C3×C4—122no—
455C3×C4—241no—
456C3×C4#93711yescharacteristic
457C3×C4#93811yescharacteristic
458C3×C4#93911yescharacteristic
459C3×C4#95311yescharacteristic
460C3×C4C3×#12011yescharacteristic
461C3×C4C3×#12011yescharacteristic
462C3×C4C3×#12111yescharacteristic
463C3×C4C3×#12111yescharacteristic
464Dic3—24no—
465Dic3—42no—
466Dic3—81no—
467C32#201611yescharacteristic, complemented, Sylow
468C23C3×D3×D411yescharacteristic
469Q8—22no—
470Q8—22no—
471Q8—22no—
472Q8—22no—
473Q8—41no—
474Q8—41no—
475Q8—41no—
476Q8—41no—
477Q8—62no—
478Q8—62no—
479Q8—121no—
480Q8—121no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—34no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—121no—
492C2×C4—121no—
493C2×C4—122no—
494C2×C4—121no—
495C2×C4C3×D3×D411yescharacteristic
496C2×C4C3×D3×D411yescharacteristic
497C2×C4C3×#23711yescharacteristic
498C2×C4C2×C3×#6711yescharacteristic
499C2×C4C2×C3×#6711yescharacteristic
500C2×C4C2×C3×#6711yescharacteristic
501C8—22no—
502C8—62no—
503C2×C3—22no—
504C2×C3—21no—
505C2×C3—22no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3#518212yes—
509C2×C3#518311yescharacteristic
510C2×C3#518612yes—
511C2×C3#519011yescharacteristic
512C2×C3#522311yescharacteristic
513C2×C3C3×#39211yescharacteristic
514C2×C3C3×#45112yes—
515C2×C3C3×#46212yes—
516C2×C3C3×#49411yescharacteristic
517C2×C3C3×#49711yescharacteristic
518C22C3×D3×Q1612yes—
519C22C3×#91812yes—
520C22C3×#93711yescharacteristic
521C22C3×#93911yescharacteristic
522C22C3×#94011yescharacteristic
523C4—42no—
524C4—42no—
525C4—64no—
526C4—122no—
527C4—241no—
528C4C3×#93711yescharacteristic
529C4C3×#93811yescharacteristic
530C4C3×#93911yescharacteristic
531C4C3×#95311yescharacteristic
532C3—21no—
533C3#7207311yescharacteristic, direct product factor
534C3C3×#201611yescharacteristic, complemented
535C2C3×#518212yes—
536C2C3×#518311yescharacteristic
537C2C3×#518612yes—
538C2C3×#519011yescharacteristic
539C2C3×#522311yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC22×C32×Q16C2
socle, prime radicalC23×C32C2×D4
hypercenterC22×C3×Q16D3
hypocenterC3C3×#2016
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C22×C3×Q16

Complements

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

NH ≅ G/Ntype
9. #72073C3direct (N × H)
154. C2×C3×Dic3Q16semidirect
376. C2×Dic3C3×Q16semidirect
467. C32#2016semidirect
533. C3#72073direct (N × H)
534. C3C3×#2016semidirect

Maximal subgroups

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

subgroupindex
C22×C32×Q162
C2×C3×#9442
C22×C3×#2162
C3×#52292
C2×C3×#8352
C2×C3×#8162
C3×#45502
C3×#20163
#720733