Finite Group Databasebeta

← C3×#70144 #11793847

Subgroups — C3×#70144 #11793847

Order 1152.

607 conjugacy classes of subgroups.

The subgroup lattice has 549 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5822C211yesmaximal, characteristic
2C32×#413C211yesmaximal, characteristic, complemented
3C2×C3×#837C211yesmaximal, characteristic, complemented
4C2×C3×#825C211yesmaximal, characteristic, complemented
5C3×#5132C211yesmaximal, characteristic, complemented
6C3×#5118C211yesmaximal, characteristic, complemented
7C3×C3⋊#338C211yesmaximal, characteristic, complemented
8C3×#2050—31nomaximal
9#70144C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C3×#951—21no—
15C3×#950—22no—
16C3×#949—21no—
17C3×#942—21no—
18C3×#932—21no—
19C2×C3×C4×Dic3C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C32×#101—21no—
23C32×#100—21no—
24C3×#837—21no—
25C3×#837—21no—
26C3×#825—21no—
27C3×#825—21no—
28C3×#824—21no—
29C3×#823—21no—
30C3×Dic3⋊C8—22no—
31C3×#575—31no—
32#5822C2×C311yescharacteristic
33C3×#423—31no—
34C2×C3×#104—31no—
35C2×C3×#104—31no—
36C3×#413—21no—
37C3×#413—31no—
38C3×#413D311yescharacteristic, complemented
39C3×#413C2×C311yescharacteristic, complemented
40C2×#837C2×C311yescharacteristic, complemented
41C2×#825C2×C311yescharacteristic, complemented
42#5132C2×C311yescharacteristic, complemented
43#5118C2×C311yescharacteristic, complemented
44C3×#338—31no—
45C3⋊#338C2×C311yescharacteristic, complemented
46C32×#41—21no—
47C32×#41—21no—
48C32×#41—21no—
49C32×#41—21no—
50C2×C32×Q8D411yescharacteristic
51C2×C32×D4—21no—
52C2×C32×D4D411yescharacteristic
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C2×C3×#67—21no—
56C22×C3×Dic3—21no—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—21no—
61C2×C3×D12D411yescharacteristic
62C2×C3×C4×D3—21no—
63C2×C3×Dic6D411yescharacteristic
64C32×M16—21no—
65C32×M16—21no—
66C32×M16—21no—
67C32×M16—21no—
68C2×C32×C8—21no—
69C2×C32×C8—21no—
70C3×#216—22no—
71C3×#215—22no—
72C3×#214—22no—
73C3×#213—22no—
74C3×C4×Dic3—21no—
75C3×C4×Dic3D411yescharacteristic
76C3×C4×Dic3D411yescharacteristic
77C3×#208—21no—
78C3×#208—21no—
79C3×#208—21no—
80C3×#208—21no—
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8D412yes—
83#2050—31noSylow
84C2×C3×#41—21no—
85C2×C3×#41—31no—
86C2×C3×#41C2×D311yescharacteristic
87C2×C3×#41C22×C311yescharacteristic
88C2×#235C22×C311yescharacteristic
89C3×#137—61no—
90C3×#137—61no—
91C3×AGL(1,ℤ/8)—61no—
92C3×AGL(1,ℤ/8)—61no—
93C3×#135—62no—
94C2×C3×M16—21no—
95C2×C3×M16—21no—
96C2×C3×M16—31no—
97C2×C3×M16—31no—
98C2×C3×M16C2×D311yescharacteristic
99C2×C3×M16C2×D311yescharacteristic
100C2×C3×M16C22×C311yescharacteristic
101C2×C3×M16C22×C311yescharacteristic
102C2×C3×C42—31no—
103#951—21no—
104#950—22no—
105#949—21no—
106#942—21no—
107#932—21no—
108C2×C4×Dic3C22×C311yescharacteristic
109C2×#208C22×C311yescharacteristic
110C2×#208C22×C311yescharacteristic
111C3×C4⋊C8—62no—
112C3×#104—61no—
113C3×#104—61no—
114C3×#104—61no—
115C3×#104—61no—
116C3×#101—22no—
117C3×#101—21no—
118C3×#101—21no—
119C3×#101—61no—
120C3×#100—22no—
121C3×#100—21no—
122C3×#100—21no—
123C3×#100—61no—
124#837—21no—
125#837—21no—
126#825—21no—
127#825—21no—
128#824—21no—
129#823—21no—
130Dic3⋊C8—22no—
131C23×C32—21no—
132C23×C32#4111yescharacteristic
133C22×C3×D3—21no—
134C32×Q8—21no—
135C32×Q8—21no—
136C32×D4—21no—
137C32×D4—21no—
138C32×D4—41no—
139C32×D4—41no—
140C2×C32×C4—21no—
141C2×C32×C4—41no—
142C2×C32×C4—41no—
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4#4111yescharacteristic
148C2×C32×C4#4111yescharacteristic
149C3×#67—41no—
150C3×#67—41no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—21no—
153C2×C3×Dic3—21no—
154C2×C3×Dic3—42no—
155C3×D12—21no—
156C3×D12—21no—
157C3×C4×D3—41no—
158C3×C4×D3—41no—
159C3×Dic6—21no—
160C3×Dic6—21no—
161C32×C8—41no—
162C32×C8—41no—
163C3×C3⋊C8—22no—
164C3×C3⋊C8—41no—
165#575—31no—
166#423—31no—
167C2×#104—31no—
168C2×#104—31no—
169#413—31no—
170#413C3×D311yescharacteristic, complemented
171#338—31no—
172C3×#41—21no—
173C3×#41—21no—
174C3×#41—21no—
175C3×#41—21no—
176C3×#41—21no—
177C3×#41—21no—
178C3×#41—21no—
179C3×#41—21no—
180C3×#41—41no—
181C3×#41—41no—
182C3×#41—41no—
183C3×#41—41no—
184C3×#41—61no—
185C3×#41—61no—
186C3×#41—61no—
187C3×#41—61no—
188C2×C3×Q8—21no—
189C2×C3×Q8—31no—
190C2×C3×Q8#6711yescharacteristic
191C2×C3×Q8C3×D411yescharacteristic
192C2×C3×D4—22no—
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—31no—
197C2×C3×D4—61no—
198C2×C3×D4#6711yescharacteristic
199C2×C3×D4C3×D411yescharacteristic
200C22×C3×C4—22no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—61no—
205C22×C3×C4—61no—
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C23×C311yescharacteristic
208C2×#67—21no—
209C22×Dic3—21no—
210#235—21no—
211#235—21no—
212#235—21no—
213#235—21no—
214C2×D12C3×D411yescharacteristic
215C2×C4×D3—21no—
216C2×Dic6C3×D411yescharacteristic
217C3×Q16—62no—
218C3×SD16—62no—
219C3×SD16—62no—
220C3×D8—62no—
221C3×M16—22no—
222C3×M16—22no—
223C3×M16—21no—
224C3×M16—21no—
225C3×M16—21no—
226C3×M16—21no—
227C3×M16—21no—
228C3×M16—21no—
229C3×M16—21no—
230C3×M16—21no—
231C3×M16—41no—
232C3×M16—41no—
233C3×M16—61no—
234C3×M16—61no—
235C3×M16—61no—
236C3×M16—61no—
237C2×C3×C8—21no—
238C2×C3×C8—21no—
239C2×C3×C8—21no—
240C2×C3×C8—21no—
241C2×C3×C8—32no—
242C2×C3×C8—41no—
243C2×C3×C8—41no—
244C2×C3×C8—61no—
245C3×C42—31no—
246C3×C42—31no—
247C3×C42—61no—
248#216—22no—
249#215—22no—
250#214—22no—
251#213—22no—
252C4×Dic3—21no—
253C4×Dic3C3×D411yescharacteristic
254C4×Dic3C3×D411yescharacteristic
255#208—21no—
256#208—21no—
257#208—21no—
258#208—21no—
259C2×C3⋊C8—21no—
260C2×C3⋊C8C3×D412yes—
261C22×C32—41no—
262C22×C32—41no—
263C22×C32—81no—
264C22×C32#12111yescharacteristic
265C22×C32#12311yescharacteristic
266C22×C32#12311yescharacteristic
267C2×C3×D3—41no—
268C2×C3×D3—81no—
269C32×C4—41no—
270C32×C4#12011yescharacteristic
271C32×C4#12111yescharacteristic
272C32×C4#12111yescharacteristic
273C32×C4#12411yescharacteristic
274C3×Dic3—22no—
275C3×Dic3—41no—
276C3×Dic3—41no—
277C2×#41—31no—
278C2×#41C2×C3×D311yescharacteristic
279#137—61no—
280#137—61no—
281AGL(1,ℤ/8)—61no—
282AGL(1,ℤ/8)—61no—
283#135—62no—
284C2×M16—31no—
285C2×M16—31no—
286C2×M16C2×C3×D311yescharacteristic
287C2×M16C2×C3×D311yescharacteristic
288C2×C42—31no—
289C4⋊C8—62no—
290#104—61no—
291#104—61no—
292#104—61no—
293#104—61no—
294#101—21no—
295#101—61no—
296#100—21no—
297#100—61no—
298C23×C3—22no—
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—21no—
302C23×C3—61no—
303C23×C3#23511yescharacteristic
304C23×C3C3×#4111yescharacteristic
305C22×D3—21no—
306C3×Q8—21no—
307C3×Q8—21no—
308C3×Q8—21no—
309C3×Q8—21no—
310C3×Q8—41no—
311C3×Q8—41no—
312C3×Q8—61no—
313C3×Q8—61no—
314C3×D4—21no—
315C3×D4—21no—
316C3×D4—21no—
317C3×D4—21no—
318C3×D4—41no—
319C3×D4—41no—
320C3×D4—42no—
321C3×D4—42no—
322C3×D4—41no—
323C3×D4—41no—
324C3×D4—41no—
325C3×D4—41no—
326C3×D4—61no—
327C3×D4—61no—
328C3×D4—121no—
329C3×D4—121no—
330C2×C3×C4—22no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—42no—
340C2×C3×C4—42no—
341C2×C3×C4—41no—
342C2×C3×C4—41no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—61no—
348C2×C3×C4—122no—
349C2×C3×C4—121no—
350C2×C3×C4—121no—
351C2×C3×C4#23511yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4#23711yescharacteristic
356C2×C3×C4C2×#6711yescharacteristic
357C2×C3×C4C2×C3×D411yescharacteristic
358C2×C3×C4C2×C3×D411yescharacteristic
359C2×C3×C4C2×C3×D411yescharacteristic
360C2×C3×C4C2×C3×D411yescharacteristic
361C2×C3×C4C3×#4111yescharacteristic
362C2×C3×C4C3×#4111yescharacteristic
363#67—41no—
364#67—41no—
365C2×Dic3—21no—
366C2×Dic3—21no—
367C2×Dic3—21no—
368C2×Dic3—42no—
369D12—21no—
370D12—21no—
371C4×D3—41no—
372C4×D3—41no—
373Dic6—21no—
374Dic6—21no—
375C3×C8—42no—
376C3×C8—42no—
377C3×C8—41no—
378C3×C8—41no—
379C3×C8—41no—
380C3×C8—41no—
381C3×C8—62no—
382C3×C8—121no—
383C3⋊C8—22no—
384C3⋊C8—41no—
385C2×C32—21no—
386C2×C32—21no—
387C2×C32—21no—
388C2×C32—81no—
389C2×C32#39411yescharacteristic
390C3×D3—81no—
391#41—21no—
392#41—21no—
393#41—21no—
394#41—21no—
395#41—61no—
396#41—61no—
397#41—61no—
398#41—61no—
399C2×Q8—31no—
400C2×Q8C3×#6711yescharacteristic
401C2×D4—21no—
402C2×D4—31no—
403C2×D4—61no—
404C2×D4C3×#6711yescharacteristic
405C22×C4—21no—
406C22×C4—61no—
407C22×C4—61no—
408C22×C4C22×C3×D311yescharacteristic
409Q16—62no—
410SD16—62no—
411SD16—62no—
412D8—62no—
413M16—21no—
414M16—21no—
415M16—21no—
416M16—21no—
417M16—61no—
418M16—61no—
419M16—61no—
420M16—61no—
421C2×C8—21no—
422C2×C8—21no—
423C2×C8—32no—
424C2×C8—61no—
425C42—31no—
426C42—31no—
427C42—61no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—41no—
432C22×C3—41no—
433C22×C3—42no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—81no—
437C22×C3—81no—
438C22×C3—81no—
439C22×C3—82no—
440C22×C3—121no—
441C22×C3—241no—
442C22×C3#88311yescharacteristic
443C22×C3#88411yescharacteristic
444C22×C3#92911yescharacteristic
445C22×C3C3×#12111yescharacteristic
446C22×C3C3×#12311yescharacteristic
447C22×C3C3×#12311yescharacteristic
448C2×D3—41no—
449C2×D3—81no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—42no—
455C3×C4—41no—
456C3×C4—41no—
457C3×C4—62no—
458C3×C4—121no—
459C3×C4—121no—
460C3×C4#88411yescharacteristic
461C3×C4#88511yescharacteristic
462C3×C4#93711yescharacteristic
463C3×C4#93911yescharacteristic
464C3×C4C3×#12011yescharacteristic
465C3×C4C3×#12111yescharacteristic
466C3×C4C3×#12111yescharacteristic
467C3×C4C3×#12411yescharacteristic
468Dic3—22no—
469Dic3—41no—
470Dic3—41no—
471C32#205011yescharacteristic, complemented, Sylow
472C23—21no—
473C23—61no—
474C23C3×#23511yescharacteristic
475Q8—21no—
476Q8—21no—
477Q8—61no—
478Q8—61no—
479D4—21no—
480D4—21no—
481D4—41no—
482D4—41no—
483D4—61no—
484D4—61no—
485D4—121no—
486D4—121no—
487C2×C4—21no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—61no—
491C2×C4—61no—
492C2×C4—61no—
493C2×C4—122no—
494C2×C4—121no—
495C2×C4—121no—
496C2×C4C3×#23511yescharacteristic
497C2×C4C3×D3×D411yescharacteristic
498C2×C4C3×D3×D411yescharacteristic
499C2×C4C3×D3×D411yescharacteristic
500C2×C4C3×#23711yescharacteristic
501C2×C4C2×C3×#6711yescharacteristic
502C8—41no—
503C8—41no—
504C8—62no—
505C8—121no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—41no—
514C2×C3—41no—
515C2×C3—41no—
516C2×C3—82no—
517C2×C3—81no—
518C2×C3—81no—
519C2×C3—241no—
520C2×C3#495911yescharacteristic
521C2×C3C3×#39411yescharacteristic
522D3—81no—
523C22—41no—
524C22—41no—
525C22—81no—
526C22—121no—
527C22—241no—
528C22C3×#88311yescharacteristic
529C22C3×#88411yescharacteristic
530C22C3×#92911yescharacteristic
531C4—41no—
532C4—62no—
533C4—121no—
534C4—121no—
535C4C3×#88411yescharacteristic
536C4C3×#88511yescharacteristic
537C4C3×#93711yescharacteristic
538C4C3×#93911yescharacteristic
539C3—21no—
540C3#7014411yescharacteristic, direct product factor
541C3C3×#205011yescharacteristic, complemented
542C2—21no—
543C2—21no—
544C2—21no—
545C2—81no—
546C2—241no—
547C2C3×#495911yescharacteristic
subgroupG/H
centerC3×C4#885
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#413C2
socleC2×C32#394
prime radicalC3×#5822C2
hypercenterC3×#413D3
hypocenterC3C3×#2050
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#413

Complements

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

NH ≅ G/Ntype
2. C32×#413C2semidirect
3. C2×C3×#837C2semidirect
4. C2×C3×#825C2semidirect
5. C3×#5132C2semidirect
6. C3×#5118C2semidirect
7. C3×C3⋊#338C2semidirect
9. #70144C3direct (N × H)
38. C3×#413D3semidirect
39. C3×#413C2×C3semidirect
40. C2×#837C2×C3semidirect
41. C2×#825C2×C3semidirect
42. #5132C2×C3semidirect
43. #5118C2×C3semidirect
45. C3⋊#338C2×C3semidirect
170. #413C3×D3semidirect
471. C32#2050semidirect
540. C3#70144direct (N × H)
541. C3C3×#2050semidirect

Maximal subgroups

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

subgroupindex
C3×#58222
C32×#4132
C2×C3×#8372
C2×C3×#8252
C3×#51322
C3×#51182
C3×C3⋊#3382
C3×#20503
#701443