Finite Group Databasebeta

← C3×#70478 #11786381

Subgroups — C3×#70478 #11786381

Order 1152.

717 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
1C22×C3×ΓL(1,𝔽25)C211yesmaximal, characteristic
2C2×C32×C4⋊C8C211yesmaximal, characteristic, complemented
3C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic
4C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
5C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
6C3×#4550C211yesmaximal, characteristic, complemented
7C3×#4524C211yesmaximal, characteristic, complemented
8C3×#1851—31nomaximal
9#70478C311yesmaximal, characteristic, direct product factor
10C22×C3×C4×D3C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4C411yescharacteristic
15C2×C3×(C2×D3)⋊C4C411yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×C3×ΓL(1,𝔽25)—22no—
20C2×C3×ΓL(1,𝔽25)—22no—
21C2×C3×ΓL(1,𝔽25)—22no—
22C32×C4⋊C8—22no—
23C3×C3⋊#95C411yescharacteristic
24C3×C3⋊#95C411yescharacteristic
25C3×(C2×D3)⋊C8—22no—
26C3×Dic3⋊C8—22no—
27C22×C3×M16—31no—
28C22×ΓL(1,𝔽25)C2×C311yescharacteristic
29C2×C3×C4⋊C8—21no—
30C2×C3×C4⋊C8—31no—
31C2×C3×C4⋊C8D311yescharacteristic, complemented
32C2×C3×C4⋊C8C2×C311yescharacteristic, complemented
33C2×C3×C22⋊C8—31no—
34C3×C4×C22⋊C4—31no—
35C2×(C2×D3)⋊C8C2×C311yescharacteristic
36C2×Dic3⋊C8C2×C311yescharacteristic, complemented
37C4×(C2×D3)⋊C4C2×C311yescharacteristic
38C3×#336—31no—
39C3×#336—31no—
40#4550C2×C311yescharacteristic, complemented
41#4524C2×C311yescharacteristic, complemented
42C23×C3×D3C2×C411yescharacteristic
43C22×C32×C4C2×C411yescharacteristic
44C22×C32×C4C2×C411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3×Dic3C2×C411yescharacteristic
47C22×C3×Dic3C2×C411yescharacteristic
48C22×C3×Dic3C2×C411yescharacteristic
49C2×C3×C4×D3—21no—
50C2×C3×C4×D3—21no—
51C2×C3×C4×D3—21no—
52C2×C3×C4×D3—21no—
53C2×C3×C4×D3D412yes—
54C2×C3×C4×D3Q812yes—
55C2×C32×C8—21no—
56C2×C32×C8—21no—
57C2×C32×C8—21no—
58C2×C32×C8—21no—
59C2×C32×C8—21no—
60C2×C32×C8D412yes—
61C32×C42—21no—
62C32×C42—21no—
63C3×(C2×D3)⋊C4—22no—
64C3×(C2×D3)⋊C4—22no—
65C3×C4×Dic3—21no—
66C3×C4×Dic3—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8D412yes—
73C3×ΓL(1,𝔽25)—28no—
74#1851—31noSylow
75C23×C3×C4—31no—
76C22×C4×D3C22×C311yescharacteristic
77C2×C3×M16—62no—
78C2×C3×M16—62no—
79C2×C3×M16—62no—
80C22×C3×C8—21no—
81C22×C3×C8—21no—
82C22×C3×C8—31no—
83C22×C3×C8—31no—
84C22×C3×C8C2×D311yescharacteristic
85C22×C3×C8C2×D311yescharacteristic
86C22×C3×C8C22×C311yescharacteristic
87C22×C3×C8C22×C311yescharacteristic
88C2×C3×C22⋊C4—31no—
89C2×C3×C22⋊C4—31no—
90C2×C3×C42—21no—
91C2×C3×C42—31no—
92C2×C3×C42C2×D311yescharacteristic
93C2×C3×C42C22×C311yescharacteristic
94C2×(C2×D3)⋊C4C3×C411yescharacteristic
95C2×(C2×D3)⋊C4C3×C411yescharacteristic
96C2×C4×Dic3C22×C311yescharacteristic
97C22×C3⋊C8C22×C311yescharacteristic
98C22×C3⋊C8C22×C311yescharacteristic
99C2×ΓL(1,𝔽25)—22no—
100C2×ΓL(1,𝔽25)—22no—
101C2×ΓL(1,𝔽25)—22no—
102C3×C4⋊C8—24no—
103C3×C4⋊C8—22no—
104C3×C4⋊C8—22no—
105C3×C4⋊C8—62no—
106C3×C22⋊C8—62no—
107C3×#95—31no—
108C3×#95—31no—
109C3⋊#95C3×C411yescharacteristic
110C3⋊#95C3×C411yescharacteristic
111(C2×D3)⋊C8—22no—
112Dic3⋊C8—22no—
113C23×C32C22×C411yescharacteristic
114C22×C3×D3—21no—
115C22×C3×D3—21no—
116C22×C3×D3—21no—
117C22×C3×D3—21no—
118C22×C3×D3—21no—
119C22×C3×D3—21no—
120C22×C3×D3C4⋊C412yes—
121C2×C32×C4—21no—
122C2×C32×C4—21no—
123C2×C32×C4—21no—
124C2×C32×C4—21no—
125C2×C32×C4—21no—
126C2×C32×C4M1612yescomplemented
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×Q811yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3C4⋊C412yes—
141C2×C3×Dic3M1612yescomplemented
142C3×C4×D3—22no—
143C3×C4×D3—22no—
144C3×C4×D3—22no—
145C3×C4×D3—22no—
146C32×C8—22no—
147C32×C8—41no—
148C3×C3⋊C8—22no—
149C3×C3⋊C8—41no—
150C22×M16—31no—
151C2×C4⋊C8—31no—
152C2×C4⋊C8C3×D311yescharacteristic, complemented
153C2×C22⋊C8—31no—
154C4×C22⋊C4—31no—
155#336—31no—
156#336—31no—
157C24×C3—31no—
158C23×D3C2×C3×C411yescharacteristic
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—31no—
163C22×C3×C4—31no—
164C22×C3×C4—32no—
165C22×C3×C4—32no—
166C22×C3×C4—31no—
167C22×C3×C4—61no—
168C22×C3×C4—61no—
169C22×C3×C4—61no—
170C22×C3×C4—61no—
171C22×C3×C4C4×D311yescharacteristic
172C22×C3×C4C4×D311yescharacteristic
173C22×C3×C4C2×C3×C411yescharacteristic
174C22×C3×C4C2×C3×C411yescharacteristic
175C22×C3×C4C22×D311yescharacteristic
176C22×C3×C4C23×C311yescharacteristic
177C22×Dic3C2×C3×C411yescharacteristic
178C22×Dic3C2×C3×C411yescharacteristic
179C22×Dic3C2×C3×C411yescharacteristic
180C2×C4×D3—21no—
181C2×C4×D3—21no—
182C2×C4×D3—21no—
183C2×C4×D3—21no—
184C2×C4×D3C3×D412yes—
185C2×C4×D3C3×Q812yes—
186C3×M16—68no—
187C2×C3×C8—21no—
188C2×C3×C8—21no—
189C2×C3×C8—21no—
190C2×C3×C8—21no—
191C2×C3×C8—22no—
192C2×C3×C8—21no—
193C2×C3×C8—21no—
194C2×C3×C8—21no—
195C2×C3×C8—21no—
196C2×C3×C8—21no—
197C2×C3×C8—21no—
198C2×C3×C8—22no—
199C2×C3×C8—32no—
200C2×C3×C8—41no—
201C2×C3×C8—41no—
202C2×C3×C8—41no—
203C2×C3×C8—41no—
204C2×C3×C8—61no—
205C2×C3×C8—61no—
206C2×C3×C8—61no—
207C2×C3×C8—61no—
208C2×C3×C8—61no—
209C2×C3×C8#6712yes—
210C2×C3×C8C3×D412yes—
211C3×C22⋊C4—62no—
212C3×C22⋊C4—62no—
213C3×C42—22no—
214C3×C42—22no—
215C3×C42—21no—
216C3×C42—21no—
217C3×C42—21no—
218C3×C42—21no—
219C3×C42—61no—
220C3×C42—61no—
221(C2×D3)⋊C4—22no—
222(C2×D3)⋊C4—22no—
223C4×Dic3—21no—
224C4×Dic3—21no—
225C2×C3⋊C8—21no—
226C2×C3⋊C8—21no—
227C2×C3⋊C8—21no—
228C2×C3⋊C8—21no—
229C2×C3⋊C8—21no—
230C2×C3⋊C8C3×D412yes—
231ΓL(1,𝔽25)—28no—
232C22×C32C2×C4⋊C411yescharacteristic
233C22×C32C4×D411yescharacteristic
234C22×C32C4×D411yescharacteristic
235C22×C32C2×M1611yescharacteristic
236C22×C32C2×M1611yescharacteristic
237C22×C32#13111yescharacteristic
238C22×C32#13111yescharacteristic
239C2×C3×D3—22no—
240C2×C3×D3—22no—
241C2×C3×D3—22no—
242C2×C3×D3—41no—
243C2×C3×D3—41no—
244C2×C3×D3—41no—
245C2×C3×D3—41no—
246C32×C4—22no—
247C32×C4—41no—
248C32×C4#12011yescharacteristic
249C32×C4C22⋊Q811yescharacteristic
250C32×C4C22⋊Q811yescharacteristic
251C32×C4#12311yescharacteristic
252C3×Dic3—22no—
253C3×Dic3—22no—
254C3×Dic3—41no—
255C23×C4—31no—
256C2×M16—62no—
257C2×M16—62no—
258C2×M16—62no—
259C22×C8—31no—
260C22×C8—31no—
261C22×C8C2×C3×D311yescharacteristic
262C22×C8C2×C3×D311yescharacteristic
263C2×C22⋊C4—31no—
264C2×C22⋊C4—31no—
265C2×C42—31no—
266C2×C42C2×C3×D311yescharacteristic
267C4⋊C8—22no—
268C4⋊C8—62no—
269C22⋊C8—62no—
270#95—31no—
271#95—31no—
272C23×C3—21no—
273C23×C3—32no—
274C23×C3—61no—
275C23×C3—61no—
276C23×C3—61no—
277C23×C3—61no—
278C23×C3—61no—
279C23×C3—61no—
280C23×C3C2×C4×D311yescharacteristic
281C23×C3C22×C3×C411yescharacteristic
282C22×D3—21no—
283C22×D3—21no—
284C22×D3—21no—
285C22×D3—21no—
286C22×D3—21no—
287C22×D3—21no—
288C22×D3C3×C4⋊C412yes—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—22no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—22no—
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—32no—
310C2×C3×C4—32no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4—61no—
314C2×C3×C4—61no—
315C2×C3×C4—61no—
316C2×C3×C4—61no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4—61no—
322C2×C3×C4—61no—
323C2×C3×C4—61no—
324C2×C3×C4ΓL(1,𝔽25)12yescomplemented
325C2×C3×C4C3×M1612yescomplemented
326C2×C3×C4#23511yescharacteristic
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4D3×Q811yescharacteristic
330C2×C3×C4#23911yescharacteristic
331C2×C3×C4C2×#6711yescharacteristic
332C2×C3×C4C2×C3×D411yescharacteristic
333C2×C3×C4C2×C3×D411yescharacteristic
334C2×C3×C4C2×C3×D411yescharacteristic
335C2×C3×C4C2×C3×Q811yescharacteristic
336C2×C3×C4C3×#4111yescharacteristic
337C2×C3×C4C3×#4111yescharacteristic
338C2×Dic3—21no—
339C2×Dic3—21no—
340C2×Dic3—21no—
341C2×Dic3—21no—
342C2×Dic3—21no—
343C2×Dic3—21no—
344C2×Dic3—21no—
345C2×Dic3C3×C4⋊C412yes—
346C2×Dic3C3×M1612yescomplemented
347C4×D3—22no—
348C4×D3—22no—
349C4×D3—22no—
350C4×D3—22no—
351C3×C8—22no—
352C3×C8—22no—
353C3×C8—42no—
354C3×C8—42no—
355C3×C8—41no—
356C3×C8—41no—
357C3×C8—62no—
358C3×C8—121no—
359C3⋊C8—22no—
360C3⋊C8—41no—
361C2×C32#38511yescharacteristic
362C2×C32#42311yescharacteristic
363C2×C32#42411yescharacteristic
364C2×C32#43511yescharacteristic
365C2×C32#43511yescharacteristic
366C2×C32#43611yescharacteristic
367C2×C32#43611yescharacteristic
368C3×D3—42no—
369C24—31no—
370C22×C4—31no—
371C22×C4—31no—
372C22×C4—32no—
373C22×C4—32no—
374C22×C4—31no—
375C22×C4—61no—
376C22×C4—61no—
377C22×C4—61no—
378C22×C4—61no—
379C22×C4C3×C4×D311yescharacteristic
380C22×C4C3×C4×D311yescharacteristic
381C22×C4C22×C3×D311yescharacteristic
382M16—68no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—21no—
387C2×C8—21no—
388C2×C8—32no—
389C2×C8—61no—
390C2×C8—61no—
391C2×C8—61no—
392C2×C8—61no—
393C2×C8—61no—
394C2×C8C3×#6712yes—
395C22⋊C4—62no—
396C22⋊C4—62no—
397C42—21no—
398C42—21no—
399C42—61no—
400C42—61no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—62no—
409C22×C3—62no—
410C22×C3—62no—
411C22×C3—121no—
412C22×C3—121no—
413C22×C3—121no—
414C22×C3—121no—
415C22×C3D3×C4⋊C411yescharacteristic
416C22×C3#89311yescharacteristic
417C22×C3C2×ΓL(1,𝔽25)11yescharacteristic
418C22×C3#90111yescharacteristic
419C22×C3D3×M1611yescharacteristic
420C22×C3#90711yescharacteristic
421C22×C3C4×#6711yescharacteristic
422C22×C3C2×C3×C4⋊C411yescharacteristic
423C22×C3C3×C4×D411yescharacteristic
424C22×C3C3×C4×D411yescharacteristic
425C22×C3C2×C3×M1611yescharacteristic
426C22×C3C2×C3×M1611yescharacteristic
427C22×C3C3×#13111yescharacteristic
428C22×C3C3×#13111yescharacteristic
429C2×D3—22no—
430C2×D3—22no—
431C2×D3—22no—
432C2×D3—41no—
433C2×D3—41no—
434C2×D3—41no—
435C2×D3—41no—
436C3×C4—24no—
437C3×C4—22no—
438C3×C4—22no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—42no—
444C3×C4—41no—
445C3×C4—41no—
446C3×C4—62no—
447C3×C4—62no—
448C3×C4—121no—
449C3×C4#89411yescharacteristic
450C3×C4#89611yescharacteristic
451C3×C4#93711yescharacteristic
452C3×C4#94611yescharacteristic
453C3×C4C3×#12011yescharacteristic
454C3×C4C3×C22⋊Q811yescharacteristic
455C3×C4C3×C22⋊Q811yescharacteristic
456C3×C4C3×#12311yescharacteristic
457Dic3—22no—
458Dic3—22no—
459Dic3—41no—
460C32#185111yescharacteristic, complemented, Sylow
461C23—32no—
462C23—61no—
463C23—61no—
464C23—61no—
465C23—61no—
466C23—61no—
467C23—61no—
468C23C2×C3×C4×D311yescharacteristic
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—32no—
475C2×C4—32no—
476C2×C4—61no—
477C2×C4—61no—
478C2×C4—61no—
479C2×C4—61no—
480C2×C4—62no—
481C2×C4—62no—
482C2×C4—62no—
483C2×C4—62no—
484C2×C4—61no—
485C2×C4—61no—
486C2×C4—61no—
487C2×C4C3×ΓL(1,𝔽25)12yescomplemented
488C2×C4C3×#23511yescharacteristic
489C2×C4C3×D3×D411yescharacteristic
490C2×C4C3×D3×D411yescharacteristic
491C2×C4C3×D3×Q811yescharacteristic
492C2×C4C3×#23911yescharacteristic
493C2×C4C2×C3×#6711yescharacteristic
494C8—22no—
495C8—41no—
496C8—62no—
497C8—121no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—122no—
506C2×C3#483611yescharacteristic
507C2×C3#483711yescharacteristic
508C2×C3#483811yescharacteristic
509C2×C3#483911yescharacteristic
510C2×C3#498911yescharacteristic
511C2×C3#511111yescharacteristic
512C2×C3#512811yescharacteristic
513C2×C3C3×#38511yescharacteristic
514C2×C3C3×#42311yescharacteristic
515C2×C3C3×#42411yescharacteristic
516C2×C3C3×#43511yescharacteristic
517C2×C3C3×#43511yescharacteristic
518C2×C3C3×#43611yescharacteristic
519C2×C3C3×#43611yescharacteristic
520D3—42no—
521C22—62no—
522C22—62no—
523C22—62no—
524C22—121no—
525C22—121no—
526C22—121no—
527C22—121no—
528C22C3×D3×C4⋊C411yescharacteristic
529C22C3×#89311yescharacteristic
530C22C2×C3×ΓL(1,𝔽25)11yescharacteristic
531C22C3×#90111yescharacteristic
532C22C3×D3×M1611yescharacteristic
533C22C3×#90711yescharacteristic
534C22C3×C4×#6711yescharacteristic
535C4—22no—
536C4—41no—
537C4—62no—
538C4—62no—
539C4—121no—
540C4C3×#89411yescharacteristic
541C4C3×#89611yescharacteristic
542C4C3×#93711yescharacteristic
543C4C3×#94611yescharacteristic
544C3—21no—
545C3#7047811yescharacteristic, direct product factor
546C3C3×#185111yescharacteristic, complemented
547C2—122no—
548C2C3×#483611yescharacteristic
549C2C3×#483711yescharacteristic
550C2C3×#483811yescharacteristic
551C2C3×#483911yescharacteristic
552C2C3×#498911yescharacteristic
553C2C3×#511111yescharacteristic
554C2C3×#512811yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D3
commutatorC23×C3C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C4⋊C8C2
socleC23×C32C22×C4
prime radicalC23×C3×D3C2×C4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×C4⋊C8D3
hypocenterC3C3×#1851
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C32×C4⋊C8C2semidirect
4. C2×C3×Dic3⋊C8C2semidirect
6. C3×#4550C2semidirect
7. C3×#4524C2semidirect
9. #70478C3direct (N × H)
31. C2×C3×C4⋊C8D3semidirect
32. C2×C3×C4⋊C8C2×C3semidirect
36. C2×Dic3⋊C8C2×C3semidirect
40. #4550C2×C3semidirect
41. #4524C2×C3semidirect
126. C2×C32×C4M16semidirect
141. C2×C3×Dic3M16semidirect
152. C2×C4⋊C8C3×D3semidirect
324. C2×C3×C4ΓL(1,𝔽25)semidirect
325. C2×C3×C4C3×M16semidirect
346. C2×Dic3C3×M16semidirect
460. C32#1851semidirect
487. C2×C4C3×ΓL(1,𝔽25)semidirect
545. C3#70478direct (N × H)
546. C3C3×#1851semidirect

Maximal subgroups

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

subgroupindex
C22×C3×ΓL(1,𝔽25)2
C2×C32×C4⋊C82
C2×C3×(C2×D3)⋊C82
C2×C3×Dic3⋊C82
C3×C4×(C2×D3)⋊C42
C3×#45502
C3×#45242
C3×#18513
#704783