Finite Group Databasebeta

← C3×#72050 #11791135

Subgroups — C3×#72050 #11791135

Order 1152.

829 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×SD16C211yesmaximal, characteristic
2C3×#5229C211yesmaximal, characteristic, complemented
3C2×C3×#835C211yesmaximal, characteristic, complemented
4C3×#5221C211yesmaximal, characteristic
5C2×C3×#832C211yesmaximal, characteristic
6C2×C3×#818C211yesmaximal, characteristic, complemented
7C2×C3×#815C211yesmaximal, characteristic, complemented
8C3×#1973—31nomaximal
9#72050C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C22×C32×D4C2211yescharacteristic
12C2×C32×SD16—22no—
13C2×C32×SD16—22no—
14C2×C32×SD16C414yescomplemented
15C22×C32×C8C2211yescharacteristic
16C2×C3×#217—22no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#835—22no—
22C3×#832—22no—
23C3×C3⋊#95—22no—
24C3×#818—22no—
25C3×#815—22no—
26C22×C3×SD16—21no—
27C22×C3×SD16D311yescharacteristic
28C22×C3×SD16C2×C311yescharacteristic
29C2×C3×#107—31no—
30C2×C3×#103—31no—
31C2×C3×#102—31no—
32C2×C3×#97—31no—
33C3×#391—31no—
34C3×#390—31no—
35#5229C2×C311yescharacteristic, complemented
36C2×#835C2×C311yescharacteristic, complemented
37#5221C2×C311yescharacteristic
38C2×#832C2×C311yescharacteristic
39C2×#818C2×C311yescharacteristic, complemented
40C2×#815C2×C311yescharacteristic, complemented
41C24×C32—21no—
42C2×C32×Q8—21no—
43C2×C32×Q8—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8C2×C412yes—
48C2×C32×D4—21no—
49C2×C32×D4—21no—
50C2×C32×D4—21no—
51C2×C32×D4—21no—
52C2×C32×D4—21no—
53C2×C32×D4C2×C412yes—
54C22×C32×C4—21no—
55C22×C32×C4C2311yescharacteristic
56C22×C3×Dic3—21no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3D412yes—
59C32×SD16—28no—
60C2×C32×C8C2×C412yes—
61C2×C32×C8D412yes—
62C2×C32×C8D412yes—
63C3×#217—44no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4×Dic3—21no—
69C3×C4×Dic3—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8D412yes—
73#1973—31noSylow
74C22×C3×Q8—21no—
75C22×C3×Q8C2×D311yescharacteristic
76C22×C3×Q8C22×C311yescharacteristic
77C22×C3×D4—21no—
78C22×C3×D4C2×D311yescharacteristic
79C22×C3×D4C22×C311yescharacteristic
80C2×C3×SD16—24no—
81C2×C3×SD16—24no—
82C2×C3×SD16—22no—
83C2×C3×SD16—22no—
84C2×C3×SD16—22no—
85C2×C3×SD16—22no—
86C2×C3×SD16—24no—
87C2×C3×SD16Dic314yescomplemented
88C2×C3×SD16C3×C414yescomplemented
89C22×C3×C8—21no—
90C22×C3×C8—31no—
91C22×C3×C8C2×D311yescharacteristic
92C22×C3×C8C22×C311yescharacteristic
93C2×C3×C4⋊C4—31no—
94C2×C3×C4⋊C4—31no—
95C2×C3×C22⋊C4—62no—
96C2×C3×C42—31no—
97C2×#217—22no—
98C2×C4⋊Dic3C22×C311yescharacteristic
99C2×C4⋊Dic3C22×C311yescharacteristic
100C2×C4×Dic3C22×C311yescharacteristic
101C22×C3⋊C8C22×C311yescharacteristic
102C3×#107—62no—
103C3×#103—62no—
104C3×#102—62no—
105C3×#97—62no—
106C3×#95—62no—
107#835—22no—
108#832—22no—
109C3⋊#95—22no—
110#818—22no—
111#815—22no—
112C23×C32—22no—
113C23×C32—41no—
114C23×C32—41no—
115C23×C32—42no—
116C23×C32—42no—
117C23×C32C2×D411yescharacteristic
118C32×Q8—22no—
119C32×Q8—22no—
120C32×Q8—41no—
121C32×Q8—41no—
122C32×D4—22no—
123C32×D4—22no—
124C32×D4—41no—
125C32×D4—41no—
126C2×C32×C4—22no—
127C2×C32×C4—41no—
128C2×C32×C4—41no—
129C2×C32×C4C22×C411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C32×C4#4111yescharacteristic
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—42no—
141C2×C3×Dic3—42no—
142C32×C8C22⋊C414yescomplemented
143C3×C3⋊C8—22no—
144C22×SD16C3×D311yescharacteristic
145C2×#107—31no—
146C2×#103—31no—
147C2×#102—31no—
148C2×#97—31no—
149#391—31no—
150#390—31no—
151C24×C3—21no—
152C24×C3—21no—
153C24×C3—41no—
154C2×C3×Q8—21no—
155C2×C3×Q8—21no—
156C2×C3×Q8—22no—
157C2×C3×Q8—22no—
158C2×C3×Q8—21no—
159C2×C3×Q8—21no—
160C2×C3×Q8—21no—
161C2×C3×Q8—21no—
162C2×C3×Q8—21no—
163C2×C3×Q8—21no—
164C2×C3×Q8—21no—
165C2×C3×Q8—21no—
166C2×C3×Q8—22no—
167C2×C3×Q8—41no—
168C2×C3×Q8—41no—
169C2×C3×Q8—41no—
170C2×C3×Q8C2×Dic312yes—
171C2×C3×Q8C2×C3×C412yes—
172C2×C3×D4—22no—
173C2×C3×D4—22no—
174C2×C3×D4—21no—
175C2×C3×D4—21no—
176C2×C3×D4—21no—
177C2×C3×D4—21no—
178C2×C3×D4—21no—
179C2×C3×D4—21no—
180C2×C3×D4—21no—
181C2×C3×D4—21no—
182C2×C3×D4—21no—
183C2×C3×D4—21no—
184C2×C3×D4—22no—
185C2×C3×D4—41no—
186C2×C3×D4—41no—
187C2×C3×D4—41no—
188C2×C3×D4C2×Dic312yes—
189C2×C3×D4C2×C3×C412yes—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—32no—
194C22×C3×C4—41no—
195C22×C3×C4—61no—
196C22×C3×C4—61no—
197C22×C3×C4C22×D311yescharacteristic
198C22×C3×C4C23×C311yescharacteristic
199C22×Dic3—21no—
200C22×Dic3—21no—
201C22×Dic3C3×D412yes—
202C3×SD16—216no—
203C3×SD16—28no—
204C3×SD16—28no—
205C2×C3×C8—22no—
206C2×C3×C8—22no—
207C2×C3×C8—22no—
208C2×C3×C8—32no—
209C2×C3×C8—61no—
210C2×C3×C8—61no—
211C2×C3×C8C2×Dic312yes—
212C2×C3×C8#6712yes—
213C2×C3×C8#6712yes—
214C2×C3×C8C2×C3×C412yes—
215C2×C3×C8C3×D412yes—
216C2×C3×C8C3×D412yes—
217C3×C4⋊C4—61no—
218C3×C4⋊C4—61no—
219C3×C4⋊C4—61no—
220C3×C4⋊C4—61no—
221C3×C22⋊C4—124no—
222C3×C42—61no—
223C3×C42—61no—
224#217—44no—
225C4⋊Dic3—21no—
226C4⋊Dic3—21no—
227C4⋊Dic3—21no—
228C4⋊Dic3—21no—
229C4×Dic3—21no—
230C4×Dic3—21no—
231C2×C3⋊C8—21no—
232C2×C3⋊C8—21no—
233C2×C3⋊C8C3×D412yes—
234C22×C32—42no—
235C22×C32—44no—
236C22×C32—82no—
237C22×C32—81no—
238C22×C32—81no—
239C22×C32C4×D411yescharacteristic
240C22×C32#12111yescharacteristic
241C22×C32#12711yescharacteristic
242C22×C32AGL(1,ℤ/8)12yes—
243C22×C32#13712yes—
244C32×C4—42no—
245C32×C4C2×C22⋊C411yescharacteristic
246C32×C4C4×D411yescharacteristic
247C32×C4#12111yescharacteristic
248C32×C4#12411yescharacteristic
249C3×Dic3—42no—
250C3×Dic3—81no—
251C3×Dic3—81no—
252C22×Q8C2×C3×D311yescharacteristic
253C22×D4C2×C3×D311yescharacteristic
254C2×SD16—22no—
255C2×SD16—22no—
256C2×SD16C3×Dic314yescomplemented
257C22×C8—31no—
258C22×C8C2×C3×D311yescharacteristic
259C2×C4⋊C4—31no—
260C2×C4⋊C4—31no—
261C2×C22⋊C4—62no—
262C2×C42—31no—
263#107—62no—
264#103—62no—
265#102—62no—
266#97—62no—
267#95—62no—
268C23×C3—22no—
269C23×C3—22no—
270C23×C3—21no—
271C23×C3—42no—
272C23×C3—42no—
273C23×C3—42no—
274C23×C3—42no—
275C23×C3—42no—
276C23×C3—41no—
277C23×C3—41no—
278C23×C3—41no—
279C23×C3—41no—
280C23×C3—42no—
281C23×C3—42no—
282C23×C3—82no—
283C23×C3—82no—
284C23×C3D3×D411yescharacteristic
285C23×C3C2×C3×D411yescharacteristic
286C3×Q8—24no—
287C3×Q8—22no—
288C3×Q8—22no—
289C3×Q8—22no—
290C3×Q8—22no—
291C3×Q8—42no—
292C3×Q8—42no—
293C3×Q8—42no—
294C3×Q8—41no—
295C3×Q8—41no—
296C3×Q8—41no—
297C3×Q8—41no—
298C3×D4—24no—
299C3×D4—22no—
300C3×D4—22no—
301C3×D4—22no—
302C3×D4—22no—
303C3×D4—42no—
304C3×D4—42no—
305C3×D4—42no—
306C3×D4—41no—
307C3×D4—41no—
308C3×D4—41no—
309C3×D4—41no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—42no—
319C2×C3×C4—42no—
320C2×C3×C4—42no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—41no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—122no—
329C2×C3×C4—122no—
330C2×C3×C4—121no—
331C2×C3×C4—121no—
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4#23711yescharacteristic
334C2×C3×C4#23711yescharacteristic
335C2×C3×C4C22×Dic311yescharacteristic
336C2×C3×C4C2×#6711yescharacteristic
337C2×C3×C4C2×#6711yescharacteristic
338C2×C3×C4C22×C3×C411yescharacteristic
339C2×C3×C4C2×C3×D411yescharacteristic
340C2×C3×C4C2×C3×D411yescharacteristic
341C2×C3×C4C2×C3×D411yescharacteristic
342C2×C3×C4C3×#4111yescharacteristic
343C2×C3×C4C3×#4111yescharacteristic
344C2×Dic3—22no—
345C2×Dic3—22no—
346C2×Dic3—22no—
347C2×Dic3—41no—
348C2×Dic3—41no—
349C2×Dic3—42no—
350C2×Dic3—42no—
351C3×C8—24no—
352C3×C8—62no—
353C3×C8#21714yescomplemented
354C3×C8C3×C22⋊C414yescomplemented
355C3⋊C8—22no—
356C2×C32—82no—
357C2×C32#39011yescharacteristic
358C2×C32#44012yes—
359C2×C32#46812yes—
360C2×C32#49611yescharacteristic
361C2×C32#49711yescharacteristic
362C24—21no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8C2×C3×Dic312yes—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4C2×C3×Dic312yes—
375C22×C4—21no—
376C22×C4—32no—
377C22×C4—61no—
378C22×C4—61no—
379C22×C4C22×C3×D311yescharacteristic
380SD16—28no—
381C2×C8—32no—
382C2×C8—61no—
383C2×C8—61no—
384C2×C8C2×C3×Dic312yes—
385C2×C8C3×#6712yes—
386C2×C8C3×#6712yes—
387C4⋊C4—61no—
388C4⋊C4—61no—
389C4⋊C4—61no—
390C4⋊C4—61no—
391C22⋊C4—124no—
392C42—61no—
393C42—61no—
394C22×C3—22no—
395C22×C3—22no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—44no—
400C22×C3—44no—
401C22×C3—42no—
402C22×C3—42no—
403C22×C3—44no—
404C22×C3—84no—
405C22×C3—82no—
406C22×C3—84no—
407C22×C3—82no—
408C22×C3—81no—
409C22×C3—82no—
410C22×C3—81no—
411C22×C3—82no—
412C22×C3—81no—
413C22×C3—81no—
414C22×C3#91412yes—
415C22×C3#91512yes—
416C22×C3D4×Dic311yescharacteristic
417C22×C3#93811yescharacteristic
418C22×C3#94011yescharacteristic
419C22×C3C3×C4×D411yescharacteristic
420C22×C3C3×#12111yescharacteristic
421C22×C3C3×#12711yescharacteristic
422C22×C3C3×AGL(1,ℤ/8)12yes—
423C22×C3C3×#13712yes—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—44no—
429C3×C4—42no—
430C3×C4—42no—
431C3×C4—122no—
432C3×C4—241no—
433C3×C4—241no—
434C3×C4D4×Dic311yescharacteristic
435C3×C4#93611yescharacteristic
436C3×C4#93811yescharacteristic
437C3×C4C2×#21711yescharacteristic
438C3×C4C2×C3×C22⋊C411yescharacteristic
439C3×C4C3×C4×D411yescharacteristic
440C3×C4C3×#12111yescharacteristic
441C3×C4C3×#12411yescharacteristic
442Dic3—42no—
443Dic3—81no—
444Dic3—81no—
445C32#197311yescharacteristic, complemented, Sylow
446C23—22no—
447C23—42no—
448C23—42no—
449C23—41no—
450C23—41no—
451C23C3×D3×D411yescharacteristic
452Q8—22no—
453Q8—22no—
454Q8—41no—
455Q8—41no—
456D4—22no—
457D4—22no—
458D4—41no—
459D4—41no—
460C2×C4—22no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—62no—
464C2×C4—62no—
465C2×C4—62no—
466C2×C4—122no—
467C2×C4—122no—
468C2×C4—121no—
469C2×C4—121no—
470C2×C4C3×D3×D411yescharacteristic
471C2×C4C3×#23711yescharacteristic
472C2×C4C3×#23711yescharacteristic
473C2×C4C22×C3×Dic311yescharacteristic
474C2×C4C2×C3×#6711yescharacteristic
475C2×C4C2×C3×#6711yescharacteristic
476C8—62no—
477C8C3×#21714yescomplemented
478C2×C3—22no—
479C2×C3—21no—
480C2×C3—22no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—84no—
484C2×C3—82no—
485C2×C3—82no—
486C2×C3#516412yes—
487C2×C3#516711yescharacteristic
488C2×C3#517412yes—
489C2×C3#517611yescharacteristic
490C2×C3#522111yescharacteristic
491C2×C3C3×#39011yescharacteristic
492C2×C3C3×#44012yes—
493C2×C3C3×#46812yes—
494C2×C3C3×#49611yescharacteristic
495C2×C3C3×#49711yescharacteristic
496C22—44no—
497C22—42no—
498C22—81no—
499C22—82no—
500C22—81no—
501C22C3×#91412yes—
502C22C3×#91512yes—
503C22C3×D4×Dic311yescharacteristic
504C22C3×#93811yescharacteristic
505C22C3×#94011yescharacteristic
506C4—42no—
507C4—122no—
508C4—241no—
509C4—241no—
510C4C3×D4×Dic311yescharacteristic
511C4C3×#93611yescharacteristic
512C4C3×#93811yescharacteristic
513C4C2×C3×#21711yescharacteristic
514C3—21no—
515C3#7205011yescharacteristic, direct product factor
516C3C3×#197311yescharacteristic, complemented
517C2—82no—
518C2C3×#516412yes—
519C2C3×#516711yescharacteristic
520C2C3×#517412yes—
521C2C3×#517611yescharacteristic
522C2C3×#522111yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC22×C32×SD16C2
socleC23×C32C2×D4
prime radicalC22×C32×D4C22
cosocleC22×C3×C4C23×C3
hypercenterC22×C3×SD16D3
hypocenterC3C3×#1973
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C22×C3×SD16

Complements

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

NH ≅ G/Ntype
2. C3×#5229C2semidirect
3. C2×C3×#835C2semidirect
6. C2×C3×#818C2semidirect
7. C2×C3×#815C2semidirect
9. #72050C3direct (N × H)
14. C2×C32×SD16C4semidirect
35. #5229C2×C3semidirect
36. C2×#835C2×C3semidirect
39. C2×#818C2×C3semidirect
40. C2×#815C2×C3semidirect
87. C2×C3×SD16Dic3semidirect
88. C2×C3×SD16C3×C4semidirect
142. C32×C8C22⋊C4semidirect
256. C2×SD16C3×Dic3semidirect
353. C3×C8#217semidirect
354. C3×C8C3×C22⋊C4semidirect
445. C32#1973semidirect
477. C8C3×#217semidirect
515. C3#72050direct (N × H)
516. C3C3×#1973semidirect

Maximal subgroups

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

subgroupindex
C22×C32×SD162
C3×#52292
C2×C3×#8352
C3×#52212
C2×C3×#8322
C2×C3×#8182
C2×C3×#8152
C3×#19733
#720503