Finite Group Databasebeta

← C3×#77740 #11808835

Subgroups — C3×#77740 #11808835

Order 1152.

1083 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#887C211yesmaximal, characteristic
2C2×C3×#887C211yesmaximal, characteristic
3C32×#398C211yesmaximal, characteristic
4C3×#4983C211yesmaximal, characteristic
5C3×#4979C211yesmaximal, characteristic
6C3×#4979C212yesmaximal
7C3×Dic3×C4⋊C4C212yesmaximal
8C3×#4657C212yesmaximal
9C3×#4656C211yesmaximal, characteristic
10C3×#4649C212yesmaximal
11C3×#4648C211yesmaximal, characteristic
12C3×#2399—31nomaximal
13#77740C311yesmaximal, characteristic, direct product factor
14C22×C3×Dic6C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×C32×C4⋊C4C2212yes—
19C2×C3×C4⋊Dic3C2212yes—
20C2×C3×Dic3⋊C4C2212yes—
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×Dic3⋊C4C2211yescharacteristic
23C2×C3×Dic3⋊C4C2211yescharacteristic
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2212yes—
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2212yes—
30C3×#887—24no—
31C3×#887—24no—
32C32×#95C2211yescharacteristic
33C32×#95C2212yes—
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2211yescharacteristic
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2212yes—
39C2×C3×C4×Q8—31no—
40C2×C3×C4×Q8—31no—
41C2×#887C2×C311yescharacteristic
42C2×#887C2×C311yescharacteristic
43C3×#398—21no—
44C3×#398—31no—
45C3×#398—32no—
46C3×#398D311yescharacteristic
47C3×#398C2×C311yescharacteristic
48C3×#395—31no—
49C3×#395—32no—
50C3×#395—31no—
51C3×C4×C4⋊C4—32no—
52C3×C4×C4⋊C4—32no—
53C3×#376—31no—
54#4983C2×C311yescharacteristic
55#4979C2×C312yes—
56#4979C2×C311yescharacteristic
57Dic3×C4⋊C4C2×C312yes—
58#4657C2×C312yes—
59#4656C2×C311yescharacteristic
60#4649C2×C312yes—
61#4648C2×C311yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C22×C32×C4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C3×Dic3C2311yescharacteristic
68C22×C3×Dic3C2311yescharacteristic
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2311yescharacteristic
73C2×C3×Dic6—22no—
74C2×C3×Dic6—22no—
75C2×C3×Dic6—22no—
76C2×C3×Dic6—22no—
77C2×C3×Dic6—24no—
78C32×C4⋊C4—22no—
79C32×C4⋊C4—22no—
80C32×C4⋊C4—24no—
81C3×C4⋊Dic3—24no—
82C3×Dic3⋊C4—22no—
83C3×Dic3⋊C4—24no—
84C3×Dic3⋊C4—22no—
85C3×Dic3⋊C4—24no—
86C3×Dic3⋊C4—24no—
87C3×C4×Dic3—22no—
88C3×C4×Dic3—24no—
89C3×C4×Dic3—22no—
90C3×C4×Dic3D414yes—
91C3×C4×Dic3Q818yescomplemented
92#2399—31noSylow
93C22×C3×Q8—31no—
94C22×C3×Q8—31no—
95C22×Dic6C22×C311yescharacteristic
96C22×Dic6C22×C311yescharacteristic
97C3×C4×Q8—64no—
98C3×C4×Q8—64no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4—22no—
102C2×C3×C4⋊C4—32no—
103C2×C3×C4⋊C4—32no—
104C2×C3×C4⋊C4—32no—
105C2×C3×C4⋊C4—31no—
106C2×C3×C4⋊C4—31no—
107C2×C3×C4⋊C4—32no—
108C2×C3×C4⋊C4C2×D312yes—
109C2×C3×C4⋊C4C2×D311yescharacteristic
110C2×C3×C4⋊C4C2×D311yescharacteristic
111C2×C3×C4⋊C4C22×C312yes—
112C2×C3×C4⋊C4C22×C311yescharacteristic
113C2×C3×C4⋊C4C22×C311yescharacteristic
114C2×C3×C42—32no—
115C2×C3×C42—31no—
116C2×C3×C42—32no—
117C2×C3×C42—31no—
118C2×C3×C42—31no—
119C2×C4⋊Dic3C22×C312yes—
120C2×Dic3⋊C4C22×C312yes—
121C2×Dic3⋊C4C22×C312yes—
122C2×Dic3⋊C4C22×C311yescharacteristic
123C2×Dic3⋊C4C22×C311yescharacteristic
124C2×Dic3⋊C4C22×C312yes—
125C2×C4×Dic3C22×C311yescharacteristic
126C2×C4×Dic3C22×C312yes—
127C2×C4×Dic3C22×C311yescharacteristic
128C2×C4×Dic3C22×C311yescharacteristic
129C2×C4×Dic3C22×C312yes—
130#887—24no—
131#887—24no—
132C3×#95—21no—
133C3×#95—22no—
134C3×#95—31no—
135C3×#95—32no—
136C3×#95—32no—
137C3×#95—32no—
138C3×#95—32no—
139C3×#95C2×D311yescharacteristic
140C3×#95C2×D312yes—
141C3×#95C22×C311yescharacteristic
142C3×#95C22×C312yes—
143C3⋊#95C22×C312yes—
144C3⋊#95C22×C311yescharacteristic
145C3⋊#95C22×C312yes—
146C3⋊#95C22×C312yes—
147C3⋊#95C22×C312yes—
148C23×C32C2411yescharacteristic
149C2×C32×C4—21no—
150C2×C32×C4—22no—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4—22no—
156C2×C32×C4—22no—
157C2×C32×C4—22no—
158C2×C32×C4—22no—
159C2×C32×C4C2×D412yes—
160C2×C32×C4C2×Q814yes—
161C2×C32×C4#4112yes—
162C2×C3×Dic3—21no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—21no—
167C2×C3×Dic3—21no—
168C2×C3×Dic3—21no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3C2×D412yes—
173C2×C3×Dic3C2×D412yes—
174C2×C3×Dic3C2×Q814yes—
175C2×C3×Dic3C2×Q814yes—
176C2×C3×Dic3#4112yes—
177C2×C3×Dic3#4114yes—
178C3×Dic6—28no—
179C3×Dic6—28no—
180C2×C4×Q8—31no—
181C2×C4×Q8—31no—
182#398—31no—
183#398—32no—
184#398C3×D311yescharacteristic
185#395—32no—
186#395—31no—
187#395—31no—
188C4×C4⋊C4—32no—
189C4×C4⋊C4—32no—
190#376—31no—
191C2×C3×Q8—62no—
192C2×C3×Q8—64no—
193C2×C3×Q8—62no—
194C2×C3×Q8—62no—
195C2×C3×Q8—62no—
196C22×C3×C4—22no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—22no—
201C22×C3×C4—31no—
202C22×C3×C4—32no—
203C22×C3×C4—31no—
204C22×C3×C4—31no—
205C22×C3×C4—32no—
206C22×C3×C4—31no—
207C22×C3×C4C22×D312yes—
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D312yes—
212C22×C3×C4C23×C312yes—
213C22×C3×C4C23×C311yescharacteristic
214C22×C3×C4C23×C311yescharacteristic
215C22×C3×C4C23×C312yes—
216C22×C3×C4C23×C311yescharacteristic
217C22×Dic3C23×C311yescharacteristic
218C22×Dic3C23×C311yescharacteristic
219C22×Dic3C23×C312yes—
220C22×Dic3C23×C311yescharacteristic
221C22×Dic3C23×C312yes—
222C22×Dic3C23×C311yescharacteristic
223C2×Dic6—22no—
224C2×Dic6—22no—
225C2×Dic6—22no—
226C2×Dic6—22no—
227C2×Dic6—24no—
228C3×C4⋊C4—22no—
229C3×C4⋊C4—22no—
230C3×C4⋊C4—24no—
231C3×C4⋊C4—22no—
232C3×C4⋊C4—22no—
233C3×C4⋊C4—24no—
234C3×C4⋊C4—42no—
235C3×C4⋊C4—42no—
236C3×C4⋊C4—44no—
237C3×C4⋊C4—64no—
238C3×C4⋊C4—64no—
239C3×C4⋊C4—64no—
240C3×C4⋊C4—62no—
241C3×C4⋊C4—64no—
242C3×C4⋊C4—62no—
243C3×C42—34no—
244C3×C42—38no—
245C3×C42—62no—
246C3×C42—62no—
247C3×C42—64no—
248C4⋊Dic3—24no—
249Dic3⋊C4—22no—
250Dic3⋊C4—24no—
251Dic3⋊C4—22no—
252Dic3⋊C4—24no—
253Dic3⋊C4—24no—
254C4×Dic3—22no—
255C4×Dic3—24no—
256C4×Dic3—22no—
257C4×Dic3C3×D414yes—
258C4×Dic3C3×Q818yescomplemented
259C22×C32C22×D411yescharacteristic
260C22×C32C22×Q812yes—
261C22×C32C2×#4111yescharacteristic
262C22×C32C2×#4112yes—
263C22×C32C2×#4111yescharacteristic
264C32×C4—22no—
265C32×C4—22no—
266C32×C4—24no—
267C32×C4—41no—
268C32×C4—42no—
269C3×Dic3—22no—
270C3×Dic3—24no—
271C3×Dic3—22no—
272C3×Dic3—24no—
273C3×Dic3—41no—
274C3×Dic3C4⋊Q814yes—
275C22×Q8—31no—
276C22×Q8—31no—
277C4×Q8—64no—
278C4×Q8—64no—
279C2×C4⋊C4—32no—
280C2×C4⋊C4—31no—
281C2×C4⋊C4—31no—
282C2×C4⋊C4—32no—
283C2×C4⋊C4—32no—
284C2×C4⋊C4—32no—
285C2×C4⋊C4C2×C3×D311yescharacteristic
286C2×C4⋊C4C2×C3×D311yescharacteristic
287C2×C4⋊C4C2×C3×D312yes—
288C2×C42—31no—
289C2×C42—32no—
290C2×C42—32no—
291C2×C42—31no—
292C2×C42—31no—
293#95—31no—
294#95—32no—
295#95—32no—
296#95—32no—
297#95—32no—
298#95C2×C3×D311yescharacteristic
299#95C2×C3×D312yes—
300C23×C3—21no—
301C23×C3C23×D311yescharacteristic
302C23×C3C24×C311yescharacteristic
303C3×Q8—68no—
304C3×Q8—68no—
305C2×C3×C4—21no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—21no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—24no—
328C2×C3×C4—32no—
329C2×C3×C4—34no—
330C2×C3×C4—32no—
331C2×C3×C4—34no—
332C2×C3×C4—34no—
333C2×C3×C4—32no—
334C2×C3×C4—41no—
335C2×C3×C4—42no—
336C2×C3×C4—42no—
337C2×C3×C4—42no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—42no—
341C2×C3×C4—42no—
342C2×C3×C4—42no—
343C2×C3×C4—42no—
344C2×C3×C4—62no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—61no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—62no—
354C2×C3×C4D3×D412yes—
355C2×C3×C4#23712yes—
356C2×C3×C4D3×Q814yes—
357C2×C3×C4C2×C3×D412yes—
358C2×C3×C4C2×C3×Q814yes—
359C2×C3×C4C3×#4112yes—
360C2×Dic3—21no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—21no—
365C2×Dic3—21no—
366C2×Dic3—21no—
367C2×Dic3—22no—
368C2×Dic3—21no—
369C2×Dic3—22no—
370C2×Dic3C2×C3×D412yes—
371C2×Dic3C2×C3×D412yes—
372C2×Dic3C2×C3×Q814yes—
373C2×Dic3C2×C3×Q814yes—
374C2×Dic3C3×#4112yes—
375C2×Dic3C3×#4114yes—
376Dic6—28no—
377Dic6—28no—
378C2×C32#52511yescharacteristic
379C2×C32#52511yescharacteristic
380C2×C32C2×C4⋊Q811yescharacteristic
381C2×C32#53312yes—
382C2×C32#53312yes—
383C2×Q8—62no—
384C2×Q8—62no—
385C2×Q8—64no—
386C2×Q8—62no—
387C2×Q8—62no—
388C22×C4—31no—
389C22×C4—32no—
390C22×C4—31no—
391C22×C4—31no—
392C22×C4—32no—
393C22×C4—31no—
394C22×C4C22×C3×D312yes—
395C22×C4C22×C3×D311yescharacteristic
396C22×C4C22×C3×D311yescharacteristic
397C22×C4C22×C3×D311yescharacteristic
398C22×C4C22×C3×D312yes—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—24no—
402C4⋊C4—64no—
403C4⋊C4—62no—
404C4⋊C4—64no—
405C4⋊C4—64no—
406C4⋊C4—64no—
407C4⋊C4—62no—
408C42—34no—
409C42—38no—
410C42—62no—
411C42—64no—
412C42—62no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—22no—
416C22×C3—21no—
417C22×C3—22no—
418C22×C3C2×D3×D411yescharacteristic
419C22×C3C2×#23711yescharacteristic
420C22×C3C2×D3×Q812yes—
421C22×C3D3×#4112yes—
422C22×C3D3×#4111yescharacteristic
423C22×C3C22×C3×D411yescharacteristic
424C22×C3C22×C3×Q812yes—
425C22×C3C2×C3×#4111yescharacteristic
426C22×C3C2×C3×#4111yescharacteristic
427C22×C3C2×C3×#4112yes—
428C3×C4—22no—
429C3×C4—22no—
430C3×C4—22no—
431C3×C4—22no—
432C3×C4—24no—
433C3×C4—24no—
434C3×C4—34no—
435C3×C4—42no—
436C3×C4—44no—
437C3×C4—42no—
438C3×C4—41no—
439C3×C4—42no—
440C3×C4—41no—
441C3×C4—42no—
442C3×C4—64no—
443C3×C4—64no—
444C3×C4—62no—
445C3×C4—62no—
446C3×C4—82no—
447C3×C4—81no—
448C3×C4—121no—
449Dic3—22no—
450Dic3—22no—
451Dic3—24no—
452Dic3—24no—
453Dic3—41no—
454Dic3C3×C4⋊Q814yes—
455C32#239911yescharacteristic, complemented, Sylow
456C23C23×C3×D311yescharacteristic
457Q8—68no—
458Q8—68no—
459C2×C4—21no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—21no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—32no—
470C2×C4—34no—
471C2×C4—32no—
472C2×C4—34no—
473C2×C4—32no—
474C2×C4—34no—
475C2×C4—61no—
476C2×C4—62no—
477C2×C4—61no—
478C2×C4—61no—
479C2×C4—62no—
480C2×C4—62no—
481C2×C4—61no—
482C2×C4—62no—
483C2×C4—61no—
484C2×C4—62no—
485C2×C4C3×D3×D412yes—
486C2×C4C3×#23712yes—
487C2×C4C3×D3×Q814yes—
488C2×C3—21no—
489C2×C3—22no—
490C2×C3—21no—
491C2×C3—22no—
492C2×C3—21no—
493C2×C3#560611yescharacteristic
494C2×C3#562212yes—
495C2×C3#565611yescharacteristic
496C2×C3#568812yes—
497C2×C3D3×C4⋊Q811yescharacteristic
498C2×C3C3×#52511yescharacteristic
499C2×C3C3×#52511yescharacteristic
500C2×C3C2×C3×C4⋊Q811yescharacteristic
501C2×C3C3×#53312yes—
502C2×C3C3×#53312yes—
503C22C2×C3×D3×D411yescharacteristic
504C22C2×C3×#23711yescharacteristic
505C22C2×C3×D3×Q812yes—
506C22C3×D3×#4111yescharacteristic
507C22C3×D3×#4112yes—
508C4—22no—
509C4—24no—
510C4—22no—
511C4—34no—
512C4—42no—
513C4—41no—
514C4—62no—
515C4—62no—
516C4—64no—
517C4—64no—
518C4—121no—
519C3—21no—
520C3#7774011yescharacteristic, direct product factor
521C3C3×#239911yescharacteristic, complemented
522C2C3×#560611yescharacteristic
523C2C3×#562212yes—
524C2C3×#565611yescharacteristic
525C2C3×#568812yes—
526C2C3×D3×C4⋊Q811yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#398C2
socle, prime radicalC23×C32C24
hypercenterC3×#398D3
hypocenterC3C3×#2399
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#398

Complements

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

NH ≅ G/Ntype
13. #77740C3direct (N × H)
91. C3×C4×Dic3Q8semidirect
258. C4×Dic3C3×Q8semidirect
455. C32#2399semidirect
520. C3#77740direct (N × H)
521. C3C3×#2399semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8872
C32×#3982
C3×#49832
C3×#49792
C3×Dic3×C4⋊C42
C3×#46572
C3×#46562
C3×#46492
C3×#46482
C3×#23993
#777403