Finite Group Databasebeta

← C3×#73659 #11807155

Subgroups — C3×#73659 #11807155

Order 1152.

1025 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#870C211yesmaximal, characteristic
2C32×C4×C4⋊C4C211yesmaximal, characteristic
3C3×#4978C212yesmaximal
4C3×#4976C212yesmaximal
5C3×C4×C4⋊Dic3C211yesmaximal, characteristic
6C3×C4×C4⋊Dic3C211yesmaximal, characteristic
7C3×C4×C4⋊Dic3C211yesmaximal, characteristic
8C3×#4928C211yesmaximal, characteristic
9C3×#4928C211yesmaximal, characteristic
10C3×#4652C212yesmaximal
11C3×#4649C212yesmaximal
12C3×#2370—31nomaximal
13#73659C311yesmaximal, characteristic, direct product factor
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C32×C42C2211yescharacteristic
17C2×C32×C42C2211yescharacteristic
18C2×C32×C42C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×Dic3⋊C4C2212yes—
26C2×C3×Dic3⋊C4C2212yes—
27C2×C3×C4×Dic3C2212yes—
28C2×C3×C4×Dic3C2212yes—
29C2×C3×C4×Dic3C2212yes—
30C3×#870C418yescomplemented
31C32×#95C2211yescharacteristic
32C32×#95C2211yescharacteristic
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38C2×C3×#125—31no—
39C2×#870C2×C311yescharacteristic
40C3×#389—32no—
41C3×#389—31no—
42C3×#389—31no—
43C3×#387—32no—
44C3×#387—32no—
45C3×C4×C4⋊C4—21no—
46C3×C4×C4⋊C4—31no—
47C3×C4×C4⋊C4—31no—
48C3×C4×C4⋊C4—31no—
49C3×C4×C4⋊C4—32no—
50C3×C4×C4⋊C4D311yescharacteristic
51C3×C4×C4⋊C4C2×C311yescharacteristic
52#4978C2×C312yes—
53#4976C2×C312yes—
54C4×C4⋊Dic3C2×C311yescharacteristic
55C4×C4⋊Dic3C2×C311yescharacteristic
56C4×C4⋊Dic3C2×C311yescharacteristic
57#4928C2×C311yescharacteristic
58#4928C2×C311yescharacteristic
59#4652C2×C312yes—
60#4649C2×C312yes—
61C22×C32×C4C2311yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C32×C4⋊C4—22no—
73C32×C4⋊C4—22no—
74C32×C42—22no—
75C32×C42—22no—
76C32×C42C2×C414yes—
77C3×C4⋊Dic3—22no—
78C3×C4⋊Dic3C2×C414yes—
79C3×C4⋊Dic3C2×C414yes—
80C3×C4⋊Dic3Q814yes—
81C3×Dic3⋊C4—24no—
82C3×Dic3⋊C4—42no—
83C3×Dic3⋊C4C2×C418yes—
84C3×Dic3⋊C4C2×C418yes—
85C3×C4×Dic3—24no—
86C3×C4×Dic3—42no—
87C3×C4×Dic3—42no—
88#2370—31noSylow
89C3×#125—38no—
90C2×C3×C4⋊C4—21no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4—32no—
93C2×C3×C4⋊C4—32no—
94C2×C3×C4⋊C4—31no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—32no—
98C2×C3×C4⋊C4—31no—
99C2×C3×C4⋊C4—32no—
100C2×C3×C4⋊C4C2×D311yescharacteristic
101C2×C3×C4⋊C4C2×D311yescharacteristic
102C2×C3×C4⋊C4C22×C311yescharacteristic
103C2×C3×C4⋊C4C22×C311yescharacteristic
104C2×C3×C42—21no—
105C2×C3×C42—21no—
106C2×C3×C42—21no—
107C2×C3×C42—32no—
108C2×C3×C42—32no—
109C2×C3×C42—32no—
110C2×C3×C42C2×D311yescharacteristic
111C2×C3×C42C2×D311yescharacteristic
112C2×C3×C42C2×D311yescharacteristic
113C2×C3×C42C22×C311yescharacteristic
114C2×C3×C42C22×C311yescharacteristic
115C2×C3×C42C22×C311yescharacteristic
116C2×C4⋊Dic3C22×C311yescharacteristic
117C2×C4⋊Dic3C22×C311yescharacteristic
118C2×C4⋊Dic3C22×C311yescharacteristic
119C2×C4⋊Dic3C22×C311yescharacteristic
120C2×Dic3⋊C4C22×C312yes—
121C2×Dic3⋊C4C22×C312yes—
122C2×Dic3⋊C4C22×C312yes—
123C2×Dic3⋊C4C22×C312yes—
124C2×C4×Dic3C22×C312yes—
125C2×C4×Dic3C22×C312yes—
126C2×C4×Dic3C22×C312yes—
127#870C3×C418yescomplemented
128C3×#95—21no—
129C3×#95—21no—
130C3×#95—32no—
131C3×#95—32no—
132C3×#95—32no—
133C3×#95—32no—
134C3×#95—32no—
135C3×#95C2×D311yescharacteristic
136C3×#95C2×D311yescharacteristic
137C3×#95C22×C311yescharacteristic
138C3×#95C22×C311yescharacteristic
139C3⋊#95C22×C312yes—
140C3⋊#95C22×C312yes—
141C3⋊#95C22×C312yes—
142C3⋊#95C22×C312yes—
143C3⋊#95C22×C312yes—
144C23×C32C2411yescharacteristic
145C2×C32×C4—21no—
146C2×C32×C4—21no—
147C2×C32×C4—21no—
148C2×C32×C4—21no—
149C2×C32×C4—21no—
150C2×C32×C4—21no—
151C2×C32×C4—21no—
152C2×C32×C4—21no—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4C22×C412yes—
160C2×C32×C4C22×C412yes—
161C2×C32×C4C22×C412yes—
162C2×C32×C4C2×Q812yes—
163C2×C32×C4#4112yes—
164C2×C32×C4#4112yes—
165C2×C32×C4#4112yes—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3C22×C414yes—
176C2×C3×Dic3C22×C414yes—
177C2×C3×Dic3C2×Q814yes—
178C2×#125—31no—
179#389—32no—
180#389—31no—
181#389—31no—
182#387—32no—
183#387—32no—
184C4×C4⋊C4—31no—
185C4×C4⋊C4—31no—
186C4×C4⋊C4—31no—
187C4×C4⋊C4—32no—
188C4×C4⋊C4C3×D311yescharacteristic
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—32no—
197C22×C3×C4—32no—
198C22×C3×C4—32no—
199C22×C3×C4—32no—
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D311yescharacteristic
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C23×C311yescharacteristic
208C22×C3×C4C23×C311yescharacteristic
209C22×C3×C4C23×C311yescharacteristic
210C22×C3×C4C23×C311yescharacteristic
211C22×C3×C4C23×C311yescharacteristic
212C22×C3×C4C23×C311yescharacteristic
213C22×C3×C4C23×C311yescharacteristic
214C22×Dic3C23×C312yes—
215C22×Dic3C23×C312yes—
216C22×Dic3C23×C312yes—
217C22×Dic3C23×C312yes—
218C3×C4⋊C4—24no—
219C3×C4⋊C4—24no—
220C3×C4⋊C4—22no—
221C3×C4⋊C4—22no—
222C3×C4⋊C4—22no—
223C3×C4⋊C4—22no—
224C3×C4⋊C4—38no—
225C3×C4⋊C4—38no—
226C3×C4⋊C4—34no—
227C3×C4⋊C4—34no—
228C3×C4⋊C4—34no—
229C3×C4⋊C4—64no—
230C3×C4⋊C4—62no—
231C3×C4⋊C4—122no—
232C3×C42—22no—
233C3×C42—22no—
234C3×C42—22no—
235C3×C42—22no—
236C3×C42—24no—
237C3×C42—42no—
238C3×C42—42no—
239C3×C42—64no—
240C3×C42—122no—
241C3×C42—122no—
242C3×C42C4×D314yes—
243C3×C42C2×C3×C414yes—
244C4⋊Dic3—22no—
245C4⋊Dic3C2×C3×C414yes—
246C4⋊Dic3C2×C3×C414yes—
247C4⋊Dic3C3×Q814yes—
248Dic3⋊C4—24no—
249Dic3⋊C4—42no—
250Dic3⋊C4C2×C3×C418yes—
251Dic3⋊C4C2×C3×C418yes—
252C4×Dic3—24no—
253C4×Dic3—42no—
254C4×Dic3—42no—
255C22×C32C23×C411yescharacteristic
256C22×C32C22×Q811yescharacteristic
257C22×C32C2×#4111yescharacteristic
258C22×C32C2×#4111yescharacteristic
259C22×C32C2×#4111yescharacteristic
260C22×C32H(5,𝔽2)11yescharacteristic
261C22×C322−1+411yescharacteristic
262C32×C4—22no—
263C32×C4—22no—
264C32×C4—22no—
265C32×C4—22no—
266C32×C4—41no—
267C32×C4—41no—
268C32×C4C4×Q814yes—
269C3×Dic3—24no—
270C3×Dic3—24no—
271C3×Dic3—24no—
272C3×Dic3—42no—
273#125—38no—
274C2×C4⋊C4—32no—
275C2×C4⋊C4—31no—
276C2×C4⋊C4—31no—
277C2×C4⋊C4—32no—
278C2×C4⋊C4—31no—
279C2×C4⋊C4—32no—
280C2×C4⋊C4—31no—
281C2×C4⋊C4—32no—
282C2×C4⋊C4C2×C3×D311yescharacteristic
283C2×C4⋊C4C2×C3×D311yescharacteristic
284C2×C42—32no—
285C2×C42—32no—
286C2×C42—32no—
287C2×C42C2×C3×D311yescharacteristic
288C2×C42C2×C3×D311yescharacteristic
289C2×C42C2×C3×D311yescharacteristic
290#95—32no—
291#95—32no—
292#95—32no—
293#95—32no—
294#95—32no—
295#95C2×C3×D311yescharacteristic
296#95C2×C3×D311yescharacteristic
297C23×C3—21no—
298C23×C3C23×D311yescharacteristic
299C23×C3C24×C311yescharacteristic
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
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—22no—
319C2×C3×C4—22no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—34no—
340C2×C3×C4—34no—
341C2×C3×C4—34no—
342C2×C3×C4—41no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—41no—
351C2×C3×C4—41no—
352C2×C3×C4—62no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4C2×C4×D312yes—
362C2×C3×C4C2×C4×D312yes—
363C2×C3×C4C2×C4×D312yes—
364C2×C3×C4#23512yes—
365C2×C3×C4#23512yes—
366C2×C3×C4#23712yes—
367C2×C3×C4D3×Q812yes—
368C2×C3×C4C22×C3×C412yes—
369C2×C3×C4C22×C3×C412yes—
370C2×C3×C4C22×C3×C412yes—
371C2×C3×C4C2×C3×Q812yes—
372C2×C3×C4C3×#4112yes—
373C2×C3×C4C3×#4112yes—
374C2×C3×C4C3×#4112yes—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—22no—
383C2×Dic3—22no—
384C2×Dic3C22×C3×C414yes—
385C2×Dic3C22×C3×C414yes—
386C2×Dic3C2×C3×Q814yes—
387C2×C32C2×C4×Q811yescharacteristic
388C2×C32C4×#4111yescharacteristic
389C2×C32#52011yescharacteristic
390C2×C32#55211yescharacteristic
391C2×C32#55311yescharacteristic
392C2×C32#55411yescharacteristic
393C2×C32#55711yescharacteristic
394C22×C4—32no—
395C22×C4—32no—
396C22×C4—32no—
397C22×C4—32no—
398C22×C4C22×C3×D311yescharacteristic
399C22×C4C22×C3×D311yescharacteristic
400C22×C4C22×C3×D311yescharacteristic
401C22×C4C22×C3×D311yescharacteristic
402C22×C4C22×C3×D311yescharacteristic
403C22×C4C22×C3×D311yescharacteristic
404C22×C4C22×C3×D311yescharacteristic
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—38no—
408C4⋊C4—38no—
409C4⋊C4—34no—
410C4⋊C4—34no—
411C4⋊C4—34no—
412C4⋊C4—64no—
413C4⋊C4—62no—
414C4⋊C4—122no—
415C42—22no—
416C42—22no—
417C42—64no—
418C42—122no—
419C42—122no—
420C42C3×C4×D314yes—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3C22×C4×D311yescharacteristic
429C22×C3C2×#23511yescharacteristic
430C22×C3C2×#23511yescharacteristic
431C22×C3C2×#23711yescharacteristic
432C22×C3C2×D3×Q811yescharacteristic
433C22×C3#100911yescharacteristic
434C22×C3#101011yescharacteristic
435C22×C3C23×C3×C411yescharacteristic
436C22×C3C22×C3×Q811yescharacteristic
437C22×C3C2×C3×#4111yescharacteristic
438C22×C3C2×C3×#4111yescharacteristic
439C22×C3C2×C3×#4111yescharacteristic
440C22×C3C3×H(5,𝔽2)11yescharacteristic
441C22×C3C3×2−1+411yescharacteristic
442C3×C4—24no—
443C3×C4—22no—
444C3×C4—22no—
445C3×C4—22no—
446C3×C4—22no—
447C3×C4—22no—
448C3×C4—22no—
449C3×C4—22no—
450C3×C4—22no—
451C3×C4—24no—
452C3×C4—42no—
453C3×C4—42no—
454C3×C4—42no—
455C3×C4—42no—
456C3×C4—42no—
457C3×C4—41no—
458C3×C4—41no—
459C3×C4—41no—
460C3×C4—41no—
461C3×C4—64no—
462C3×C4—64no—
463C3×C4—64no—
464C3×C4—122no—
465C3×C4#88714yes—
466C3×C4C3×C4×Q814yes—
467Dic3—24no—
468Dic3—24no—
469Dic3—24no—
470Dic3—42no—
471C32#237011yescharacteristic, complemented, Sylow
472C23C23×C3×D311yescharacteristic
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—34no—
488C2×C4—34no—
489C2×C4—34no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—62no—
493C2×C4—62no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4C2×C3×C4×D312yes—
500C2×C4C2×C3×C4×D312yes—
501C2×C4C2×C3×C4×D312yes—
502C2×C4C3×#23512yes—
503C2×C4C3×#23512yes—
504C2×C4C3×#23712yes—
505C2×C4C3×D3×Q812yes—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3C4×#23511yescharacteristic
514C2×C3C2×#88711yescharacteristic
515C2×C3#552311yescharacteristic
516C2×C3#554111yescharacteristic
517C2×C3#556511yescharacteristic
518C2×C3#556711yescharacteristic
519C2×C3#557911yescharacteristic
520C2×C3C2×C3×C4×Q811yescharacteristic
521C2×C3C3×C4×#4111yescharacteristic
522C2×C3C3×#52011yescharacteristic
523C2×C3C3×#55211yescharacteristic
524C2×C3C3×#55311yescharacteristic
525C2×C3C3×#55411yescharacteristic
526C2×C3C3×#55711yescharacteristic
527C22C22×C3×C4×D311yescharacteristic
528C22C2×C3×#23511yescharacteristic
529C22C2×C3×#23511yescharacteristic
530C22C2×C3×#23711yescharacteristic
531C22C2×C3×D3×Q811yescharacteristic
532C22C3×#100911yescharacteristic
533C22C3×#101011yescharacteristic
534C4—22no—
535C4—22no—
536C4—22no—
537C4—22no—
538C4—41no—
539C4—41no—
540C4—64no—
541C4—64no—
542C4—64no—
543C4—122no—
544C4C3×#88714yes—
545C3—21no—
546C3#7365911yescharacteristic, direct product factor
547C3C3×#237011yescharacteristic, complemented
548C2C3×C4×#23511yescharacteristic
549C2C2×C3×#88711yescharacteristic
550C2C3×#552311yescharacteristic
551C2C3×#554111yescharacteristic
552C2C3×#556511yescharacteristic
553C2C3×#556711yescharacteristic
554C2C3×#557911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×C4×C4⋊C4C2
socle, prime radicalC23×C32C24
cosocleC23×C3C24×C3
hypercenterC3×C4×C4⋊C4D3
hypocenterC3C3×#2370
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
13. #73659C3direct (N × H)
30. C3×#870C4semidirect
127. #870C3×C4semidirect
471. C32#2370semidirect
546. C3#73659direct (N × H)
547. C3C3×#2370semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8702
C32×C4×C4⋊C42
C3×#49782
C3×#49762
C3×C4×C4⋊Dic32
C3×#49282
C3×#46522
C3×#46492
C3×#23703
#736593