Finite Group Databasebeta

← C3×#83025 #11807173

Subgroups — C3×#83025 #11807173

Order 1152.

1041 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#125C211yesmaximal, characteristic
2C3×#4984C211yesmaximal, characteristic
3C3×#4984C211yesmaximal, characteristic
4C3×#4984C212yesmaximal
5C3×#4980C212yesmaximal
6C3×#4980C212yesmaximal
7C3×Dic3×C4⋊C4C211yesmaximal, characteristic
8C3×Dic3×C4⋊C4C211yesmaximal, characteristic
9C3×Dic3×C4⋊C4C212yesmaximal
10C3×C4×C4⋊Dic3C211yesmaximal, characteristic
11C3×C4×C4⋊Dic3C211yesmaximal, characteristic
12C3×#2370—31nomaximal
13#83025C311yesmaximal, characteristic, direct product factor
14C32×#125C418yescomplemented
15C2×C32×C4⋊C4C2212yes—
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×C32×C4⋊C4C2212yes—
19C2×C32×C42C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2212yes—
24C2×C3×C4⋊Dic3C2212yes—
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2212yes—
29C2×C3×C4×Dic3C2212yes—
30C2×C3×C4×Dic3C2212yes—
31C3×C3⋊#95C2211yescharacteristic
32C3×C3⋊#95C2211yescharacteristic
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38C2×C3×#125—21no—
39C2×C3×#125D311yescharacteristic
40C2×C3×#125C2×C311yescharacteristic
41C3×#389—31no—
42C3×#389—32no—
43C3×#389—31no—
44C3×#387—32no—
45C3×#387—32no—
46C3×C4×C4⋊C4—32no—
47C3×C4×C4⋊C4—31no—
48C3×C4×C4⋊C4—31no—
49C3×C4×C4⋊C4—31no—
50C3×C4×C4⋊C4—31no—
51#4984C2×C312yes—
52#4984C2×C311yescharacteristic
53#4984C2×C311yescharacteristic
54#4980C2×C312yes—
55#4980C2×C312yes—
56Dic3×C4⋊C4C2×C312yes—
57Dic3×C4⋊C4C2×C311yescharacteristic
58Dic3×C4⋊C4C2×C311yescharacteristic
59C4×C4⋊Dic3C2×C311yescharacteristic
60C4×C4⋊Dic3C2×C311yescharacteristic
61C22×C32×C4C2311yescharacteristic
62C22×C32×C4C2312yes—
63C22×C32×C4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3×Dic3C2311yescharacteristic
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2311yescharacteristic
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C32×C4⋊C4C2×C418yes—
73C32×C4⋊C4C2×C418yes—
74C32×C4⋊C4C2×C414yes—
75C32×C4⋊C4C2×C414yes—
76C32×C42C2×C414yes—
77C3×C4⋊Dic3—22no—
78C3×C4⋊Dic3—22no—
79C3×C4⋊Dic3—22no—
80C3×C4⋊Dic3—24no—
81C3×C4⋊Dic3—42no—
82C3×C4⋊Dic3Q814yes—
83C3×C4×Dic3—22no—
84C3×C4×Dic3—22no—
85C3×C4×Dic3—24no—
86C3×C4×Dic3—42no—
87C3×C4×Dic3—42no—
88#2370—31noSylow
89C3×#125—28no—
90C3×#125Dic318yescomplemented
91C3×#125C3×C418yescomplemented
92C2×C3×C4⋊C4—22no—
93C2×C3×C4⋊C4—21no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4—22no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—31no—
98C2×C3×C4⋊C4—32no—
99C2×C3×C4⋊C4—31no—
100C2×C3×C4⋊C4—31no—
101C2×C3×C4⋊C4—32no—
102C2×C3×C4⋊C4C2×D312yes—
103C2×C3×C4⋊C4C2×D311yescharacteristic
104C2×C3×C4⋊C4C2×D311yescharacteristic
105C2×C3×C4⋊C4C2×D312yes—
106C2×C3×C4⋊C4C22×C312yes—
107C2×C3×C4⋊C4C22×C311yescharacteristic
108C2×C3×C4⋊C4C22×C311yescharacteristic
109C2×C3×C4⋊C4C22×C312yes—
110C2×C3×C42—21no—
111C2×C3×C42—32no—
112C2×C3×C42—31no—
113C2×C3×C42—31no—
114C2×C3×C42—32no—
115C2×C3×C42—32no—
116C2×C3×C42C2×D311yescharacteristic
117C2×C3×C42C22×C311yescharacteristic
118C2×C4⋊Dic3C22×C311yescharacteristic
119C2×C4⋊Dic3C22×C311yescharacteristic
120C2×C4⋊Dic3C22×C311yescharacteristic
121C2×C4⋊Dic3C22×C312yes—
122C2×C4⋊Dic3C22×C312yes—
123C2×C4⋊Dic3C22×C311yescharacteristic
124C2×C4×Dic3C22×C311yescharacteristic
125C2×C4×Dic3C22×C311yescharacteristic
126C2×C4×Dic3C22×C312yes—
127C2×C4×Dic3C22×C312yes—
128C2×C4×Dic3C22×C312yes—
129C3×#95—31no—
130C3×#95—32no—
131C3×#95—31no—
132C3×#95—32no—
133C3×#95—32no—
134C3×#95—32no—
135C3×#95—32no—
136C3⋊#95C22×C311yescharacteristic
137C3⋊#95C22×C311yescharacteristic
138C3⋊#95C22×C312yes—
139C3⋊#95C22×C312yes—
140C3⋊#95C22×C312yes—
141C3⋊#95C22×C312yes—
142C3⋊#95C22×C312yes—
143C23×C32C2411yescharacteristic
144C2×C32×C4—22no—
145C2×C32×C4—21no—
146C2×C32×C4—22no—
147C2×C32×C4—21no—
148C2×C32×C4—21no—
149C2×C32×C4—22no—
150C2×C32×C4—21no—
151C2×C32×C4—22no—
152C2×C32×C4C22×C412yes—
153C2×C32×C4C22×C412yes—
154C2×C32×C4C22×C414yes—
155C2×C32×C4C22×C414yes—
156C2×C32×C4C22×C412yes—
157C2×C32×C4C2×Q812yes—
158C2×C32×C4#4112yes—
159C2×C3×Dic3—21no—
160C2×C3×Dic3—21no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—21no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3—21no—
166C2×C3×Dic3—21no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—21no—
169C2×C3×Dic3—21no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3C2×Q814yes—
175C2×C3×Dic3#4112yes—
176C2×C3×Dic3#4112yes—
177C2×#125C3×D311yescharacteristic
178#389—31no—
179#389—32no—
180#389—31no—
181#387—32no—
182#387—32no—
183C4×C4⋊C4—32no—
184C4×C4⋊C4—31no—
185C4×C4⋊C4—31no—
186C4×C4⋊C4—31no—
187C4×C4⋊C4—31no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—32no—
194C22×C3×C4—31no—
195C22×C3×C4—31no—
196C22×C3×C4—31no—
197C22×C3×C4—31no—
198C22×C3×C4—32no—
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D312yes—
201C22×C3×C4C22×D312yes—
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C23×C311yescharacteristic
205C22×C3×C4C23×C312yes—
206C22×C3×C4C23×C312yes—
207C22×C3×C4C23×C311yescharacteristic
208C22×C3×C4C23×C311yescharacteristic
209C22×Dic3C23×C311yescharacteristic
210C22×Dic3C23×C311yescharacteristic
211C22×Dic3C23×C312yes—
212C22×Dic3C23×C312yes—
213C22×Dic3C23×C311yescharacteristic
214C22×Dic3C23×C311yescharacteristic
215C3×C4⋊C4—24no—
216C3×C4⋊C4—24no—
217C3×C4⋊C4—28no—
218C3×C4⋊C4—28no—
219C3×C4⋊C4—34no—
220C3×C4⋊C4—62no—
221C3×C4⋊C4—64no—
222C3×C4⋊C4—62no—
223C3×C4⋊C4—62no—
224C3×C4⋊C4—122no—
225C3×C4⋊C4C2×Dic318yes—
226C3×C4⋊C4C2×Dic318yes—
227C3×C4⋊C4C2×Dic314yes—
228C3×C4⋊C4C2×Dic314yes—
229C3×C4⋊C4C2×C3×C418yes—
230C3×C4⋊C4C2×C3×C418yes—
231C3×C4⋊C4C2×C3×C414yes—
232C3×C4⋊C4C2×C3×C414yes—
233C3×C42—24no—
234C3×C42—64no—
235C3×C42—62no—
236C3×C42—62no—
237C3×C42—122no—
238C3×C42—122no—
239C3×C42C2×Dic314yes—
240C3×C42C2×C3×C414yes—
241C4⋊Dic3—22no—
242C4⋊Dic3—22no—
243C4⋊Dic3—22no—
244C4⋊Dic3—24no—
245C4⋊Dic3—42no—
246C4⋊Dic3C3×Q814yes—
247C4×Dic3—22no—
248C4×Dic3—22no—
249C4×Dic3—24no—
250C4×Dic3—42no—
251C4×Dic3—42no—
252C22×C32C23×C411yescharacteristic
253C22×C32C22×Q811yescharacteristic
254C22×C32C2×#4111yescharacteristic
255C22×C32C2×#4111yescharacteristic
256C22×C32C2×#4111yescharacteristic
257C22×C32H(5,𝔽2)11yescharacteristic
258C22×C322−1+411yescharacteristic
259C32×C4—24no—
260C32×C4—22no—
261C32×C4—22no—
262C32×C4—24no—
263C32×C4C4×Q814yes—
264C3×Dic3—22no—
265C3×Dic3—22no—
266C3×Dic3—24no—
267C3×Dic3—41no—
268C3×Dic3—41no—
269C3×Dic3—42no—
270#125C3×Dic318yescomplemented
271C2×C4⋊C4—31no—
272C2×C4⋊C4—31no—
273C2×C4⋊C4—32no—
274C2×C4⋊C4—31no—
275C2×C4⋊C4—31no—
276C2×C4⋊C4—32no—
277C2×C4⋊C4C2×C3×D312yes—
278C2×C4⋊C4C2×C3×D311yescharacteristic
279C2×C4⋊C4C2×C3×D311yescharacteristic
280C2×C4⋊C4C2×C3×D312yes—
281C2×C42—32no—
282C2×C42—31no—
283C2×C42—31no—
284C2×C42—32no—
285C2×C42—32no—
286C2×C42C2×C3×D311yescharacteristic
287#95—31no—
288#95—32no—
289#95—31no—
290#95—32no—
291#95—32no—
292#95—32no—
293#95—32no—
294C23×C3—21no—
295C23×C3C23×D311yescharacteristic
296C23×C3C24×C311yescharacteristic
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—22no—
303C2×C3×C4—21no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—21no—
307C2×C3×C4—22no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—22no—
311C2×C3×C4—21no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—24no—
319C2×C3×C4—24no—
320C2×C3×C4—34no—
321C2×C3×C4—32no—
322C2×C3×C4—32no—
323C2×C3×C4—42no—
324C2×C3×C4—41no—
325C2×C3×C4—41no—
326C2×C3×C4—42no—
327C2×C3×C4—41no—
328C2×C3×C4—42no—
329C2×C3×C4—41no—
330C2×C3×C4—42no—
331C2×C3×C4—61no—
332C2×C3×C4—61no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—61no—
336C2×C3×C4—61no—
337C2×C3×C4—61no—
338C2×C3×C4—61no—
339C2×C3×C4—62no—
340C2×C3×C4—61no—
341C2×C3×C4—61no—
342C2×C3×C4—62no—
343C2×C3×C4—62no—
344C2×C3×C4—61no—
345C2×C3×C4—61no—
346C2×C3×C4D3×Q812yes—
347C2×C3×C4#23912yes—
348C2×C3×C4C22×Dic312yes—
349C2×C3×C4C22×Dic312yes—
350C2×C3×C4C22×Dic314yes—
351C2×C3×C4C22×Dic314yes—
352C2×C3×C4C22×Dic312yes—
353C2×C3×C4C22×C3×C412yes—
354C2×C3×C4C22×C3×C412yes—
355C2×C3×C4C22×C3×C414yes—
356C2×C3×C4C22×C3×C414yes—
357C2×C3×C4C22×C3×C412yes—
358C2×C3×C4C2×C3×Q812yes—
359C2×C3×C4C3×#4112yes—
360C2×Dic3—21no—
361C2×Dic3—21no—
362C2×Dic3—22no—
363C2×Dic3—21no—
364C2×Dic3—22no—
365C2×Dic3—21no—
366C2×Dic3—21no—
367C2×Dic3—21no—
368C2×Dic3—22no—
369C2×Dic3—21no—
370C2×Dic3—21no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—21no—
374C2×Dic3—21no—
375C2×Dic3C2×C3×Q814yes—
376C2×Dic3C3×#4112yes—
377C2×Dic3C3×#4112yes—
378C2×C32C2×C4×Q811yescharacteristic
379C2×C32C4×#4111yescharacteristic
380C2×C32#52011yescharacteristic
381C2×C32#55211yescharacteristic
382C2×C32#55311yescharacteristic
383C2×C32#55411yescharacteristic
384C2×C32#55711yescharacteristic
385C22×C4—32no—
386C22×C4—31no—
387C22×C4—31no—
388C22×C4—31no—
389C22×C4—31no—
390C22×C4—32no—
391C22×C4C22×C3×D311yescharacteristic
392C22×C4C22×C3×D312yes—
393C22×C4C22×C3×D312yes—
394C22×C4C22×C3×D311yescharacteristic
395C22×C4C22×C3×D311yescharacteristic
396C4⋊C4—34no—
397C4⋊C4—62no—
398C4⋊C4—64no—
399C4⋊C4—62no—
400C4⋊C4—62no—
401C4⋊C4—122no—
402C4⋊C4C2×C3×Dic318yes—
403C4⋊C4C2×C3×Dic318yes—
404C4⋊C4C2×C3×Dic314yes—
405C4⋊C4C2×C3×Dic314yes—
406C42—64no—
407C42—62no—
408C42—62no—
409C42—122no—
410C42—122no—
411C42C2×C3×Dic314yes—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3C2×D3×Q811yescharacteristic
420C22×C3C2×#23911yescharacteristic
421C22×C3D3×#4111yescharacteristic
422C22×C3D3×#4111yescharacteristic
423C22×C3#100911yescharacteristic
424C22×C3#101011yescharacteristic
425C22×C3C23×Dic311yescharacteristic
426C22×C3C23×C3×C411yescharacteristic
427C22×C3C22×C3×Q811yescharacteristic
428C22×C3C2×C3×#4111yescharacteristic
429C22×C3C2×C3×#4111yescharacteristic
430C22×C3C2×C3×#4111yescharacteristic
431C22×C3C3×H(5,𝔽2)11yescharacteristic
432C22×C3C3×2−1+411yescharacteristic
433C3×C4—24no—
434C3×C4—22no—
435C3×C4—22no—
436C3×C4—24no—
437C3×C4—24no—
438C3×C4—22no—
439C3×C4—22no—
440C3×C4—24no—
441C3×C4—24no—
442C3×C4—42no—
443C3×C4—44no—
444C3×C4—42no—
445C3×C4—44no—
446C3×C4—64no—
447C3×C4—62no—
448C3×C4—62no—
449C3×C4—121no—
450C3×C4—121no—
451C3×C4—122no—
452C3×C4Q8×Dic314yes—
453C3×C4C3×C4×Q814yes—
454Dic3—22no—
455Dic3—22no—
456Dic3—24no—
457Dic3—41no—
458Dic3—41no—
459Dic3—42no—
460C32#237011yescharacteristic, complemented, Sylow
461C23C23×C3×D311yescharacteristic
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—22no—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—34no—
471C2×C4—32no—
472C2×C4—32no—
473C2×C4—61no—
474C2×C4—61no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4—61no—
478C2×C4—61no—
479C2×C4—61no—
480C2×C4—61no—
481C2×C4—62no—
482C2×C4—61no—
483C2×C4—61no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—61no—
487C2×C4—61no—
488C2×C4C3×D3×Q812yes—
489C2×C4C3×#23912yes—
490C2×C4C22×C3×Dic312yes—
491C2×C4C22×C3×Dic312yes—
492C2×C4C22×C3×Dic314yes—
493C2×C4C22×C3×Dic314yes—
494C2×C4C22×C3×Dic312yes—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3#568511yescharacteristic
503C2×C3#569011yescharacteristic
504C2×C3#569411yescharacteristic
505C2×C3#569511yescharacteristic
506C2×C3C2×Q8×Dic311yescharacteristic
507C2×C3Dic3×#4111yescharacteristic
508C2×C3#582711yescharacteristic
509C2×C3C2×C3×C4×Q811yescharacteristic
510C2×C3C3×C4×#4111yescharacteristic
511C2×C3C3×#52011yescharacteristic
512C2×C3C3×#55211yescharacteristic
513C2×C3C3×#55311yescharacteristic
514C2×C3C3×#55411yescharacteristic
515C2×C3C3×#55711yescharacteristic
516C22C2×C3×D3×Q811yescharacteristic
517C22C2×C3×#23911yescharacteristic
518C22C3×D3×#4111yescharacteristic
519C22C3×D3×#4111yescharacteristic
520C22C3×#100911yescharacteristic
521C22C3×#101011yescharacteristic
522C22C23×C3×Dic311yescharacteristic
523C4—24no—
524C4—22no—
525C4—22no—
526C4—24no—
527C4—64no—
528C4—62no—
529C4—62no—
530C4—121no—
531C4—121no—
532C4—122no—
533C4C3×Q8×Dic314yes—
534C3—21no—
535C3#8302511yescharacteristic, direct product factor
536C3C3×#237011yescharacteristic, complemented
537C2C3×#568511yescharacteristic
538C2C3×#569011yescharacteristic
539C2C3×#569411yescharacteristic
540C2C3×#569511yescharacteristic
541C2C2×C3×Q8×Dic311yescharacteristic
542C2C3×Dic3×#4111yescharacteristic
543C2C3×#582711yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC2×C32×#125C2
socle, prime radicalC23×C32C24
cosocleC23×C3C24×C3
hypercenterC2×C3×#125D3
hypocenterC3C3×#2370
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#125

Complements

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

NH ≅ G/Ntype
13. #83025C3direct (N × H)
14. C32×#125C4semidirect
90. C3×#125Dic3semidirect
91. C3×#125C3×C4semidirect
270. #125C3×Dic3semidirect
460. C32#2370semidirect
535. C3#83025direct (N × H)
536. C3C3×#2370semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1252
C3×#49842
C3×#49802
C3×Dic3×C4⋊C42
C3×C4×C4⋊Dic32
C3×#23703
#830253