Finite Group Databasebeta

← C3×#70191 #11791087

Subgroups — C3×#70191 #11791087

Order 1152.

853 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#213C211yesmaximal, characteristic
2C2×C32×#102C211yesmaximal, characteristic, complemented
3C3×#5221C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic, complemented
5C2×C3×#815C211yesmaximal, characteristic, complemented
6C3×#4988C211yesmaximal, characteristic, complemented
7C2×C3×#808C211yesmaximal, characteristic, complemented
8C3×#1972—31nomaximal
9#70191C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C3×#217—22no—
15C2×C3×#213—22no—
16C2×C3×#213—22no—
17C2×C3×#213C414yescomplemented
18C2×C3×(C2×D3)⋊C4—22no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C32×#102—22no—
23C3×#821—22no—
24C3×#815—22no—
25C3×#808—22no—
26C22×C3×D8—31no—
27C22×#213C2×C311yescharacteristic
28C2×C3×#106—31no—
29C2×C3×#102—21no—
30C2×C3×#102—31no—
31C2×C3×#102D311yescharacteristic, complemented
32C2×C3×#102C2×C311yescharacteristic, complemented
33C2×C3×#97—31no—
34C3×#390—31no—
35C3×#390—31no—
36#5221C2×C311yescharacteristic, complemented
37C2×#821C2×C311yescharacteristic, complemented
38C2×#815C2×C311yescharacteristic, complemented
39#4988C2×C311yescharacteristic, complemented
40C2×#808C2×C311yescharacteristic, complemented
41C24×C32—21no—
42C23×C3×D3—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4C2×C412yes—
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3×Dic3—21no—
52C22×C3×Dic3D412yes—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12C2×C412yes—
59C2×C32×C8—21no—
60C2×C32×C8—21no—
61C2×C32×C8D412yes—
62C32×C4⋊C4—21no—
63C32×C4⋊C4—21no—
64C3×#217—44no—
65C3×#213—28no—
66C3×(C2×D3)⋊C4—44no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4×Dic3—21no—
70C3×C4×Dic3—21no—
71C2×C3×C3⋊C8C2×C412yes—
72C2×C3×C3⋊C8D412yes—
73C2×C3×C3⋊C8D412yes—
74#1972—31noSylow
75C22×C3×D4—21no—
76C22×C3×D4—31no—
77C22×C3×D4C2×D311yescharacteristic
78C22×C3×D4C22×C311yescharacteristic
79C22×D12C22×C311yescharacteristic
80C2×C3×D8—34no—
81C2×C3×D8—62no—
82C2×C3×D8—62no—
83C22×C3×C8—21no—
84C22×C3×C8—31no—
85C22×C3×C8C2×D311yescharacteristic
86C22×C3×C8C22×C311yescharacteristic
87C2×C3×C4⋊C4—21no—
88C2×C3×C4⋊C4—31no—
89C2×C3×C4⋊C4C2×D311yescharacteristic
90C2×C3×C4⋊C4C22×C311yescharacteristic
91C2×C3×C22⋊C4—62no—
92C2×C3×C22⋊C4—62no—
93C2×C3×C42—31no—
94C2×#217—22no—
95C2×#213—22no—
96C2×#213—22no—
97C2×#213C3×C414yescomplemented
98C2×(C2×D3)⋊C4—22no—
99C2×C4⋊Dic3C22×C311yescharacteristic
100C2×C4×Dic3C22×C311yescharacteristic
101C22×C3⋊C8C22×C311yescharacteristic
102C3×#106—62no—
103C3×#102—24no—
104C3×#102—22no—
105C3×#102—22no—
106C3×#102—62no—
107C3×#97—62no—
108#821—22no—
109#815—22no—
110#808—22no—
111C23×C32—22no—
112C23×C32—41no—
113C23×C32—41no—
114C23×C32—42no—
115C23×C32—42no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3—22no—
118C22×C3×D3—41no—
119C22×C3×D3—41no—
120C22×C3×D3—42no—
121C22×C3×D3—42no—
122C32×D4—22no—
123C32×D4—22no—
124C32×D4—41no—
125C32×D4—41no—
126C2×C32×C4—41no—
127C2×C32×C4—42no—
128C2×C32×C4C22×C411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C3×Dic3—22no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—42no—
139C3×D12—22no—
140C3×D12—22no—
141C3×D12—41no—
142C3×D12—41no—
143C32×C8—22no—
144C3×C3⋊C8C22⋊C414yescomplemented
145C22×D8—31no—
146C2×#106—31no—
147C2×#102—31no—
148C2×#102C3×D311yescharacteristic, complemented
149C2×#97—31no—
150#390—31no—
151#390—31no—
152C24×C3—21no—
153C24×C3—21no—
154C24×C3—41no—
155C24×C3—61no—
156C23×D3—21no—
157C2×C3×D4—22no—
158C2×C3×D4—22no—
159C2×C3×D4—21no—
160C2×C3×D4—21no—
161C2×C3×D4—21no—
162C2×C3×D4—21no—
163C2×C3×D4—21no—
164C2×C3×D4—21no—
165C2×C3×D4—21no—
166C2×C3×D4—21no—
167C2×C3×D4—21no—
168C2×C3×D4—21no—
169C2×C3×D4—22no—
170C2×C3×D4—32no—
171C2×C3×D4—41no—
172C2×C3×D4—41no—
173C2×C3×D4—41no—
174C2×C3×D4—61no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C2×C3×D4C4×D312yes—
180C2×C3×D4C2×C3×C412yes—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—32no—
185C22×C3×C4—41no—
186C22×C3×C4—61no—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C23×C311yescharacteristic
189C22×Dic3—21no—
190C22×Dic3C3×D412yes—
191C2×D12—21no—
192C2×D12—21no—
193C2×D12—21no—
194C2×D12—21no—
195C2×D12—21no—
196C2×D12C2×C3×C412yes—
197C3×D8—68no—
198C2×C3×C8—21no—
199C2×C3×C8—21no—
200C2×C3×C8—21no—
201C2×C3×C8—21no—
202C2×C3×C8—22no—
203C2×C3×C8—32no—
204C2×C3×C8—32no—
205C2×C3×C8—32no—
206C2×C3×C8—41no—
207C2×C3×C8—41no—
208C2×C3×C8#6712yes—
209C2×C3×C8C3×D412yes—
210C3×C4⋊C4—22no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—41no—
216C3×C4⋊C4—61no—
217C3×C4⋊C4—61no—
218C3×C22⋊C4—124no—
219C3×C22⋊C4—124no—
220C3×C42—61no—
221C3×C42—61no—
222#217—44no—
223#213—28no—
224(C2×D3)⋊C4—44no—
225C4⋊Dic3—21no—
226C4⋊Dic3—21no—
227C4×Dic3—21no—
228C4×Dic3—21no—
229C2×C3⋊C8C2×C3×C412yes—
230C2×C3⋊C8C3×D412yes—
231C2×C3⋊C8C3×D412yes—
232C22×C32—42no—
233C22×C32—44no—
234C22×C32—82no—
235C22×C32—81no—
236C22×C32—81no—
237C22×C32C4×D411yescharacteristic
238C22×C32#12111yescharacteristic
239C22×C32#12711yescharacteristic
240C22×C32AGL(1,ℤ/8)12yes—
241C22×C32AGL(1,ℤ/8)12yes—
242C2×C3×D3—42no—
243C2×C3×D3—44no—
244C2×C3×D3—82no—
245C2×C3×D3—81no—
246C2×C3×D3—81no—
247C32×C4—81no—
248C32×C4C2×C22⋊C411yescharacteristic
249C32×C4C4×D411yescharacteristic
250C32×C4#12111yescharacteristic
251C32×C4#12411yescharacteristic
252C3×Dic3—42no—
253C3×Dic3—81no—
254C22×D4—31no—
255C22×D4C2×C3×D311yescharacteristic
256C2×D8—34no—
257C2×D8—62no—
258C2×D8—62no—
259C22×C8—31no—
260C22×C8C2×C3×D311yescharacteristic
261C2×C4⋊C4—31no—
262C2×C4⋊C4C2×C3×D311yescharacteristic
263C2×C22⋊C4—62no—
264C2×C22⋊C4—62no—
265C2×C42—31no—
266#106—62no—
267#102—22no—
268#102—62no—
269#97—62no—
270C23×C3—22no—
271C23×C3—22no—
272C23×C3—21no—
273C23×C3—42no—
274C23×C3—42no—
275C23×C3—42no—
276C23×C3—41no—
277C23×C3—42no—
278C23×C3—42no—
279C23×C3—41no—
280C23×C3—41no—
281C23×C3—41no—
282C23×C3—42no—
283C23×C3—42no—
284C23×C3—62no—
285C23×C3—82no—
286C23×C3—82no—
287C23×C3—121no—
288C23×C3—122no—
289C23×C3—122no—
290C23×C3—121no—
291C23×C3D3×D411yescharacteristic
292C23×C3C2×C3×D411yescharacteristic
293C22×D3—22no—
294C22×D3—41no—
295C22×D3—41no—
296C22×D3—42no—
297C22×D3—42no—
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—
310C3×D4—62no—
311C3×D4—62no—
312C3×D4—121no—
313C3×D4—121no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—42no—
321C2×C3×C4—42no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—42no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—82no—
329C2×C3×C4—122no—
330C2×C3×C4—121no—
331C2×C3×C4C2×C4×D311yescharacteristic
332C2×C3×C4#23511yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4#23711yescharacteristic
336C2×C3×C4C2×#6711yescharacteristic
337C2×C3×C4C22×C3×C411yescharacteristic
338C2×C3×C4C2×C3×D411yescharacteristic
339C2×C3×C4C2×C3×D411yescharacteristic
340C2×C3×C4C2×C3×D411yescharacteristic
341C2×C3×C4C3×#4111yescharacteristic
342C2×C3×C4C3×#4111yescharacteristic
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—22no—
346C2×Dic3—41no—
347C2×Dic3—42no—
348D12—22no—
349D12—22no—
350D12—41no—
351D12—41no—
352C3×C8—22no—
353C3×C8—22no—
354C3×C8—34no—
355C3×C8—42no—
356C3⋊C8C3×C22⋊C414yescomplemented
357C2×C32—82no—
358C2×C32#39011yescharacteristic
359C2×C32#44212yes—
360C2×C32#46912yes—
361C2×C32#49611yescharacteristic
362C2×C32#49611yescharacteristic
363C3×D3—82no—
364C24—21no—
365C24—61no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—32no—
372C2×D4—61no—
373C2×D4—61no—
374C2×D4—61no—
375C2×D4—61no—
376C2×D4—61no—
377C2×D4C3×C4×D312yes—
378C22×C4—21no—
379C22×C4—32no—
380C22×C4—61no—
381C22×C4C22×C3×D311yescharacteristic
382D8—68no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—32no—
386C2×C8—32no—
387C2×C8—32no—
388C2×C8C3×#6712yes—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—61no—
392C4⋊C4—61no—
393C22⋊C4—124no—
394C22⋊C4—124no—
395C42—61no—
396C42—61no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—22no—
400C22×C3—22no—
401C22×C3—21no—
402C22×C3—44no—
403C22×C3—42no—
404C22×C3—42no—
405C22×C3—44no—
406C22×C3—44no—
407C22×C3—84no—
408C22×C3—82no—
409C22×C3—84no—
410C22×C3—82no—
411C22×C3—81no—
412C22×C3—81no—
413C22×C3—82no—
414C22×C3—82no—
415C22×C3—81no—
416C22×C3—81no—
417C22×C3—122no—
418C22×C3—124no—
419C22×C3—241no—
420C22×C3—241no—
421C22×C3—242no—
422C22×C3#67⋊C411yescharacteristic
423C22×C3#88411yescharacteristic
424C22×C3#91112yes—
425C22×C3#91412yes—
426C22×C3#94011yescharacteristic
427C22×C3C3×C4×D411yescharacteristic
428C22×C3C3×#12111yescharacteristic
429C22×C3C3×#12711yescharacteristic
430C22×C3C3×AGL(1,ℤ/8)12yes—
431C22×C3C3×AGL(1,ℤ/8)12yes—
432C2×D3—42no—
433C2×D3—44no—
434C2×D3—82no—
435C2×D3—81no—
436C2×D3—81no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—82no—
442C3×C4—81no—
443C3×C4—81no—
444C3×C4—122no—
445C3×C4—241no—
446C3×C4D3×C22⋊C411yescharacteristic
447C3×C4#88511yescharacteristic
448C3×C4C4×#6711yescharacteristic
449C3×C4#93911yescharacteristic
450C3×C4C2×C3×C22⋊C411yescharacteristic
451C3×C4C3×C4×D411yescharacteristic
452C3×C4C3×#12111yescharacteristic
453C3×C4C3×#12411yescharacteristic
454Dic3—42no—
455Dic3—81no—
456C32#197211yescharacteristic, complemented, Sylow
457C23—22no—
458C23—41no—
459C23—42no—
460C23—42no—
461C23—41no—
462C23—62no—
463C23—121no—
464C23—122no—
465C23—122no—
466C23—121no—
467C23C3×D3×D411yescharacteristic
468D4—22no—
469D4—22no—
470D4—41no—
471D4—41no—
472D4—62no—
473D4—62no—
474D4—121no—
475D4—121no—
476C2×C4—42no—
477C2×C4—41no—
478C2×C4—62no—
479C2×C4—62no—
480C2×C4—62no—
481C2×C4—122no—
482C2×C4—121no—
483C2×C4C2×C3×C4×D311yescharacteristic
484C2×C4C3×#23511yescharacteristic
485C2×C4C3×D3×D411yescharacteristic
486C2×C4C3×D3×D411yescharacteristic
487C2×C4C3×#23711yescharacteristic
488C2×C4C2×C3×#6711yescharacteristic
489C8—22no—
490C8—34no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—22no—
494C2×C3—22no—
495C2×C3—21no—
496C2×C3—84no—
497C2×C3—82no—
498C2×C3—82no—
499C2×C3—242no—
500C2×C3#478212yes—
501C2×C3#478512yes—
502C2×C3#495711yescharacteristic
503C2×C3#515411yescharacteristic
504C2×C3#517611yescharacteristic
505C2×C3C3×#39011yescharacteristic
506C2×C3C3×#44212yes—
507C2×C3C3×#46912yes—
508C2×C3C3×#49611yescharacteristic
509C2×C3C3×#49611yescharacteristic
510D3—82no—
511C22—42no—
512C22—44no—
513C22—81no—
514C22—82no—
515C22—81no—
516C22—122no—
517C22—124no—
518C22—241no—
519C22—242no—
520C22—241no—
521C22C3×#67⋊C411yescharacteristic
522C22C3×#88411yescharacteristic
523C22C3×#91112yes—
524C22C3×#91412yes—
525C22C3×#94011yescharacteristic
526C4—81no—
527C4—122no—
528C4—241no—
529C4C3×D3×C22⋊C411yescharacteristic
530C4C3×#88511yescharacteristic
531C4C3×C4×#6711yescharacteristic
532C4C3×#93911yescharacteristic
533C3—21no—
534C3#7019111yescharacteristic, direct product factor
535C3C3×#197211yescharacteristic, complemented
536C2—82no—
537C2—242no—
538C2C3×#478212yes—
539C2C3×#478512yes—
540C2C3×#495711yescharacteristic
541C2C3×#515411yescharacteristic
542C2C3×#517611yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#102C2
socleC23×C32C2×D4
prime radicalC22×C3×#213C2
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#102D3
hypocenterC3C3×#1972
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#102

Complements

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

NH ≅ G/Ntype
2. C2×C32×#102C2semidirect
3. C3×#5221C2semidirect
4. C2×C3×#821C2semidirect
5. C2×C3×#815C2semidirect
6. C3×#4988C2semidirect
7. C2×C3×#808C2semidirect
9. #70191C3direct (N × H)
17. C2×C3×#213C4semidirect
31. C2×C3×#102D3semidirect
32. C2×C3×#102C2×C3semidirect
36. #5221C2×C3semidirect
37. C2×#821C2×C3semidirect
38. C2×#815C2×C3semidirect
39. #4988C2×C3semidirect
40. C2×#808C2×C3semidirect
97. C2×#213C3×C4semidirect
144. C3×C3⋊C8C22⋊C4semidirect
148. C2×#102C3×D3semidirect
356. C3⋊C8C3×C22⋊C4semidirect
456. C32#1972semidirect
534. C3#70191direct (N × H)
535. C3C3×#1972semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2132
C2×C32×#1022
C3×#52212
C2×C3×#8212
C2×C3×#8152
C3×#49882
C2×C3×#8082
C3×#19723
#701913