Finite Group Databasebeta

← C2×C3×C42×C7×C32 #72199014

Subgroups — C2×C3×C42×C7×C32 #72199014

Order 21504.

7188 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C42×C7×C16C211yesmaximal, characteristic
2C22×C3×C4×C7×C32C216yesmaximal
3C3×C42×C7×C32C218yesmaximal, direct product factor
4C2×C42×C7×C32C311yesmaximal, characteristic, direct product factor, Hall
5C2×C3×C42×C7×C8C411yescharacteristic
6C22×C3×C4×C7×C16C413yes—
7C22×C3×C4×C7×C16C2213yes—
8C3×C42×C7×C16C414yes—
9C3×C42×C7×C16C2214yes—
10C23×C3×C7×C32C2214yes—
11C2×C3×C4×C7×C32C4148yesdirect product factor
12C2×C3×C4×C7×C32C22124yes—
13C2×C42×C7×C16C2×C311yescharacteristic
14C22×C4×C7×C32C2×C316yes—
15C42×C7×C32C2×C318yesdirect product factor
16C2×C3×C42×C32C711yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C43×C7C811yescharacteristic
18C22×C3×C4×C7×C8C813yes—
19C22×C3×C4×C7×C8C2×C413yes—
20C3×C42×C7×C8C814yes—
21C3×C42×C7×C8C2×C414yes—
22C23×C3×C7×C16C2×C413yes—
23C23×C3×C7×C16C2311yescharacteristic
24C2×C3×C4×C7×C16C8124yes—
25C2×C3×C4×C7×C16C2×C416yes—
26C2×C3×C4×C7×C16C2×C4112yes—
27C2×C3×C4×C7×C16C2×C4124yes—
28C2×C3×C4×C7×C16C2316yes—
29C22×C3×C7×C32C2×C4148yes—
30C22×C3×C7×C32C2318yes—
31C3×C4×C7×C32C2×C4196yesdirect product factor
32C2×C3×C42×C16C2×C711yescharacteristic
33C22×C3×C4×C32C2×C716yes—
34C3×C42×C32C2×C718yesdirect product factor
35C2×C42×C32C3×C711yescharacteristic, direct product factor, Sylow
36C23×C7×C32C22×C314yes—
37C22×C4×C7×C16C3×C413yes—
38C22×C4×C7×C16C22×C313yes—
39C2×C42×C7×C8C3×C411yescharacteristic
40C2×C4×C7×C32C3×C4148yesdirect product factor
41C2×C4×C7×C32C22×C3124yes—
42C42×C7×C16C3×C414yes—
43C42×C7×C16C22×C314yes—
44C23×C3×C7×C8C2×C813yes—
45C23×C3×C7×C8C22×C411yescharacteristic
46C22×C3×C42×C7C1614yes—
47C22×C3×C42×C7C2×C813yes—
48C22×C3×C7×C16C42112yes—
49C22×C3×C7×C16C2×C8124yes—
50C22×C3×C7×C16C22×C411yescharacteristic
51C22×C3×C7×C16C22×C416yes—
52C22×C3×C7×C16C22×C4112yes—
53C22×C3×C7×C16C2411yescharacteristic
54C2×C3×C4×C7×C8C16124yes—
55C2×C3×C4×C7×C8C42112yes—
56C2×C3×C4×C7×C8C2×C816yes—
57C2×C3×C4×C7×C8C2×C8112yes—
58C2×C3×C4×C7×C8C2×C8112yes—
59C2×C3×C4×C7×C8C22×C416yes—
60C3×C43×C7C1614yes—
61C3×C43×C7C2×C814yes—
62C2×C3×C7×C32C42164yesdirect product factor
63C2×C3×C7×C32C22×C4148yes—
64C3×C4×C7×C16C42124yes—
65C3×C4×C7×C16C2×C8148yes—
66C3×C4×C7×C16C22×C4124yes—
67C23×C7×C16C2×C3×C413yes—
68C23×C7×C16C23×C311yescharacteristic
69C22×C4×C7×C8C3×C813yes—
70C22×C4×C7×C8C2×C3×C413yes—
71C2×C43×C7C3×C811yescharacteristic
72C22×C7×C32C2×C3×C4148yes—
73C22×C7×C32C23×C318yes—
74C2×C4×C7×C16C3×C8124yes—
75C2×C4×C7×C16C2×C3×C416yes—
76C2×C4×C7×C16C2×C3×C4112yes—
77C2×C4×C7×C16C2×C3×C4124yes—
78C2×C4×C7×C16C23×C316yes—
79C42×C7×C8C3×C814yes—
80C42×C7×C8C2×C3×C414yes—
81C4×C7×C32C2×C3×C4196yesdirect product factor
82C23×C3×C32C22×C714yes—
83C22×C3×C4×C16C4×C713yes—
84C22×C3×C4×C16C22×C713yes—
85C2×C3×C42×C8C4×C711yescharacteristic
86C2×C3×C4×C32C4×C7148yesdirect product factor
87C2×C3×C4×C32C22×C7124yes—
88C3×C42×C16C4×C714yes—
89C3×C42×C16C22×C714yes—
90C23×C3×C4×C7C2×C1616yes—
91C23×C3×C4×C7C22×C811yescharacteristic
92C22×C3×C7×C8C4×C8112yes—
93C22×C3×C7×C8C2×C16124yes—
94C22×C3×C7×C8C2×C4216yes—
95C22×C3×C7×C8C22×C811yescharacteristic
96C22×C3×C7×C8C22×C816yes—
97C22×C3×C7×C8C22×C816yes—
98C22×C3×C7×C8C23×C411yescharacteristic
99C2×C3×C42×C7C32132yesdirect product factor
100C2×C3×C42×C7C4×C8112yes—
101C2×C3×C42×C7C2×C1616yes—
102C2×C3×C42×C7C2×C16112yes—
103C2×C3×C42×C7C2×C16116yes—
104C2×C3×C42×C7C22×C816yes—
105C2×C3×C7×C16C4×C8148yes—
106C2×C3×C7×C16C2×C4216yes—
107C2×C3×C7×C16C2×C42112yes—
108C2×C3×C7×C16C2×C42116yes—
109C2×C3×C7×C16C22×C8124yes—
110C2×C3×C7×C16C23×C416yes—
111C3×C4×C7×C8C4×C8124yes—
112C3×C4×C7×C8C2×C16148yes—
113C3×C4×C7×C8C2×C42112yes—
114C3×C4×C7×C8C22×C8112yes—
115C3×C7×C32C2×C42132yesdirect product factor
116C22×C4×C32C2×C3×C716yes—
117C2×C42×C16C2×C3×C711yescharacteristic
118C42×C32C2×C3×C718yesdirect product factor
119C23×C7×C8C2×C3×C813yes—
120C23×C7×C8C22×C3×C411yescharacteristic
121C22×C42×C7C3×C1614yes—
122C22×C42×C7C2×C3×C813yes—
123C22×C7×C16C3×C42112yes—
124C22×C7×C16C2×C3×C8124yes—
125C22×C7×C16C22×C3×C411yescharacteristic
126C22×C7×C16C22×C3×C416yes—
127C22×C7×C16C22×C3×C4112yes—
128C22×C7×C16C24×C311yescharacteristic
129C2×C4×C7×C8C3×C16124yes—
130C2×C4×C7×C8C3×C42112yes—
131C2×C4×C7×C8C2×C3×C816yes—
132C2×C4×C7×C8C2×C3×C8112yes—
133C2×C4×C7×C8C2×C3×C8112yes—
134C2×C4×C7×C8C22×C3×C416yes—
135C43×C7C3×C1614yes—
136C43×C7C2×C3×C814yes—
137C2×C7×C32C3×C42164yesdirect product factor
138C2×C7×C32C22×C3×C4148yes—
139C4×C7×C16C3×C42124yes—
140C4×C7×C16C2×C3×C8148yes—
141C4×C7×C16C22×C3×C4124yes—
142C23×C3×C16C2×C4×C713yes—
143C23×C3×C16C23×C711yescharacteristic
144C22×C3×C4×C8C7×C813yes—
145C22×C3×C4×C8C2×C4×C713yes—
146C2×C3×C43C7×C811yescharacteristic
147C22×C3×C32C2×C4×C7148yes—
148C22×C3×C32C23×C718yes—
149C2×C3×C4×C16C7×C8124yes—
150C2×C3×C4×C16C2×C4×C716yes—
151C2×C3×C4×C16C2×C4×C7112yes—
152C2×C3×C4×C16C2×C4×C7124yes—
153C2×C3×C4×C16C23×C716yes—
154C3×C42×C8C7×C814yes—
155C3×C42×C8C2×C4×C714yes—
156C3×C4×C32C2×C4×C7196yesdirect product factor
157C24×C3×C7C22×C1611yescharacteristic
158C22×C3×C4×C7C4×C16124yes—
159C22×C3×C4×C7C2×C32148yes—
160C22×C3×C4×C7C2×C4×C816yes—
161C22×C3×C4×C7C22×C1611yescharacteristic
162C22×C3×C4×C7C22×C1616yes—
163C22×C3×C4×C7C22×C16112yes—
164C22×C3×C4×C7C23×C811yescharacteristic
165C2×C3×C7×C8C4×C16148yes—
166C2×C3×C7×C8C4314yes—
167C2×C3×C7×C8C2×C4×C816yes—
168C2×C3×C7×C8C2×C4×C8112yes—
169C2×C3×C7×C8C2×C4×C8112yes—
170C2×C3×C7×C8C22×C16124yes—
171C2×C3×C7×C8C22×C4213yes—
172C2×C3×C7×C8C23×C813yes—
173C3×C42×C7C4×C16124yes—
174C3×C42×C7C2×C32164yesdirect product factor
175C3×C42×C7C2×C4×C8112yes—
176C3×C42×C7C22×C16112yes—
177C3×C7×C16C4314yes—
178C3×C7×C16C2×C4×C8124yes—
179C3×C7×C16C22×C4214yes—
180C23×C32C22×C3×C714yes—
181C22×C4×C16C3×C4×C713yes—
182C22×C4×C16C22×C3×C713yes—
183C2×C42×C8C3×C4×C711yescharacteristic
184C2×C4×C32C3×C4×C7148yesdirect product factor
185C2×C4×C32C22×C3×C7124yes—
186C42×C16C3×C4×C714yes—
187C42×C16C22×C3×C714yes—
188C23×C4×C7C2×C3×C1616yes—
189C23×C4×C7C22×C3×C811yescharacteristic
190C22×C7×C8C3×C4×C8112yes—
191C22×C7×C8C2×C3×C16124yes—
192C22×C7×C8C2×C3×C4216yes—
193C22×C7×C8C22×C3×C811yescharacteristic
194C22×C7×C8C22×C3×C816yes—
195C22×C7×C8C22×C3×C816yes—
196C22×C7×C8C23×C3×C411yescharacteristic
197C2×C42×C7C3×C32132yesdirect product factor
198C2×C42×C7C3×C4×C8112yes—
199C2×C42×C7C2×C3×C1616yes—
200C2×C42×C7C2×C3×C16112yes—
201C2×C42×C7C2×C3×C16116yes—
202C2×C42×C7C22×C3×C816yes—
203C2×C7×C16C3×C4×C8148yes—
204C2×C7×C16C2×C3×C4216yes—
205C2×C7×C16C2×C3×C42112yes—
206C2×C7×C16C2×C3×C42116yes—
207C2×C7×C16C22×C3×C8124yes—
208C2×C7×C16C23×C3×C416yes—
209C4×C7×C8C3×C4×C8124yes—
210C4×C7×C8C2×C3×C16148yes—
211C4×C7×C8C2×C3×C42112yes—
212C4×C7×C8C22×C3×C8112yes—
213C7×C32C2×C3×C42132yesdirect product factor
214C23×C3×C8C2×C7×C813yes—
215C23×C3×C8C22×C4×C711yescharacteristic
216C22×C3×C42C7×C1614yes—
217C22×C3×C42C2×C7×C813yes—
218C22×C3×C16C42×C7112yes—
219C22×C3×C16C2×C7×C8124yes—
220C22×C3×C16C22×C4×C711yescharacteristic
221C22×C3×C16C22×C4×C716yes—
222C22×C3×C16C22×C4×C7112yes—
223C22×C3×C16C24×C711yescharacteristic
224C2×C3×C4×C8C7×C16124yes—
225C2×C3×C4×C8C42×C7112yes—
226C2×C3×C4×C8C2×C7×C816yes—
227C2×C3×C4×C8C2×C7×C8112yes—
228C2×C3×C4×C8C2×C7×C8112yes—
229C2×C3×C4×C8C22×C4×C716yes—
230C3×C43C7×C1614yes—
231C3×C43C2×C7×C814yes—
232C2×C3×C32C42×C7164yesdirect product factor
233C2×C3×C32C22×C4×C7148yes—
234C3×C4×C16C42×C7124yes—
235C3×C4×C16C2×C7×C8148yes—
236C3×C4×C16C22×C4×C7124yes—
237C23×C3×C7C2×C4×C1616yes—
238C23×C3×C7C22×C3218yes—
239C23×C3×C7C23×C1611yescharacteristic
240C2×C3×C4×C7C4×C32196yesdirect product factor
241C2×C3×C4×C7C42×C814yes—
242C2×C3×C4×C7C2×C4×C1616yes—
243C2×C3×C4×C7C2×C4×C16112yes—
244C2×C3×C4×C7C2×C4×C16124yes—
245C2×C3×C4×C7C22×C32148yes—
246C2×C3×C4×C7C22×C4×C813yes—
247C2×C3×C4×C7C23×C1613yes—
248C3×C7×C8C42×C814yes—
249C3×C7×C8C2×C4×C16124yes—
250C3×C7×C8C2×C4311yescharacteristic
251C3×C7×C8C22×C4×C813yes—
252C23×C16C2×C3×C4×C713yes—
253C23×C16C23×C3×C711yescharacteristic
254C22×C4×C8C3×C7×C813yes—
255C22×C4×C8C2×C3×C4×C713yes—
256C2×C43C3×C7×C811yescharacteristic
257C22×C32C2×C3×C4×C7148yes—
258C22×C32C23×C3×C718yes—
259C2×C4×C16C3×C7×C8124yes—
260C2×C4×C16C2×C3×C4×C716yes—
261C2×C4×C16C2×C3×C4×C7112yes—
262C2×C4×C16C2×C3×C4×C7124yes—
263C2×C4×C16C23×C3×C716yes—
264C42×C8C3×C7×C814yes—
265C42×C8C2×C3×C4×C714yes—
266C4×C32C2×C3×C4×C7196yesdirect product factor
267C24×C7C22×C3×C1611yescharacteristic
268C22×C4×C7C3×C4×C16124yes—
269C22×C4×C7C2×C3×C32148yes—
270C22×C4×C7C2×C3×C4×C816yes—
271C22×C4×C7C22×C3×C1611yescharacteristic
272C22×C4×C7C22×C3×C1616yes—
273C22×C4×C7C22×C3×C16112yes—
274C22×C4×C7C23×C3×C811yescharacteristic
275C2×C7×C8C3×C4×C16148yes—
276C2×C7×C8C3×C4314yes—
277C2×C7×C8C2×C3×C4×C816yes—
278C2×C7×C8C2×C3×C4×C8112yes—
279C2×C7×C8C2×C3×C4×C8112yes—
280C2×C7×C8C22×C3×C16124yes—
281C2×C7×C8C22×C3×C4213yes—
282C2×C7×C8C23×C3×C813yes—
283C42×C7C3×C4×C16124yes—
284C42×C7C2×C3×C32164yesdirect product factor
285C42×C7C2×C3×C4×C8112yes—
286C42×C7C22×C3×C16112yes—
287C7×C16C3×C4314yes—
288C7×C16C2×C3×C4×C8124yes—
289C7×C16C22×C3×C4214yes—
290C23×C3×C4C2×C7×C1616yes—
291C23×C3×C4C22×C7×C811yescharacteristic
292C22×C3×C8C4×C7×C8112yes—
293C22×C3×C8C2×C7×C16124yes—
294C22×C3×C8C2×C42×C716yes—
295C22×C3×C8C22×C7×C811yescharacteristic
296C22×C3×C8C22×C7×C816yes—
297C22×C3×C8C22×C7×C816yes—
298C22×C3×C8C23×C4×C711yescharacteristic
299C2×C3×C42C7×C32132yesdirect product factor
300C2×C3×C42C4×C7×C8112yes—
301C2×C3×C42C2×C7×C1616yes—
302C2×C3×C42C2×C7×C16112yes—
303C2×C3×C42C2×C7×C16116yes—
304C2×C3×C42C22×C7×C816yes—
305C2×C3×C16C4×C7×C8148yes—
306C2×C3×C16C2×C42×C716yes—
307C2×C3×C16C2×C42×C7112yes—
308C2×C3×C16C2×C42×C7116yes—
309C2×C3×C16C22×C7×C8124yes—
310C2×C3×C16C23×C4×C716yes—
311C3×C4×C8C4×C7×C8124yes—
312C3×C4×C8C2×C7×C16148yes—
313C3×C4×C8C2×C42×C7112yes—
314C3×C4×C8C22×C7×C8112yes—
315C3×C32C2×C42×C7132yesdirect product factor
316C22×C3×C7C42×C1614yes—
317C22×C3×C7C2×C4×C32124yes—
318C22×C3×C7C22×C4×C1613yes—
319C22×C3×C7C23×C3214yes—
320C3×C4×C7C42×C1614yes—
321C3×C4×C7C2×C4×C32148yesdirect product factor
322C3×C4×C7C2×C42×C811yescharacteristic
323C3×C4×C7C22×C4×C1613yes—
324C23×C8C2×C3×C7×C813yes—
325C23×C8C22×C3×C4×C711yescharacteristic
326C22×C42C3×C7×C1614yes—
327C22×C42C2×C3×C7×C813yes—
328C22×C16C3×C42×C7112yes—
329C22×C16C2×C3×C7×C8124yes—
330C22×C16C22×C3×C4×C711yescharacteristic
331C22×C16C22×C3×C4×C716yes—
332C22×C16C22×C3×C4×C7112yes—
333C22×C16C24×C3×C711yescharacteristic
334C2×C4×C8C3×C7×C16124yes—
335C2×C4×C8C3×C42×C7112yes—
336C2×C4×C8C2×C3×C7×C816yes—
337C2×C4×C8C2×C3×C7×C8112yes—
338C2×C4×C8C2×C3×C7×C8112yes—
339C2×C4×C8C22×C3×C4×C716yes—
340C43C3×C7×C1614yes—
341C43C2×C3×C7×C814yes—
342C2×C32C3×C42×C7164yesdirect product factor
343C2×C32C22×C3×C4×C7148yes—
344C4×C16C3×C42×C7124yes—
345C4×C16C2×C3×C7×C8148yes—
346C4×C16C22×C3×C4×C7124yes—
347C23×C7C2×C3×C4×C1616yes—
348C23×C7C22×C3×C3218yes—
349C23×C7C23×C3×C1611yescharacteristic
350C2×C4×C7C3×C4×C32196yesdirect product factor
351C2×C4×C7C3×C42×C814yes—
352C2×C4×C7C2×C3×C4×C1616yes—
353C2×C4×C7C2×C3×C4×C16112yes—
354C2×C4×C7C2×C3×C4×C16124yes—
355C2×C4×C7C22×C3×C32148yes—
356C2×C4×C7C22×C3×C4×C813yes—
357C2×C4×C7C23×C3×C1613yes—
358C7×C8C3×C42×C814yes—
359C7×C8C2×C3×C4×C16124yes—
360C7×C8C2×C3×C4311yescharacteristic
361C7×C8C22×C3×C4×C813yes—
362C24×C3C22×C7×C1611yescharacteristic
363C22×C3×C4C4×C7×C16124yes—
364C22×C3×C4C2×C7×C32148yes—
365C22×C3×C4C2×C4×C7×C816yes—
366C22×C3×C4C22×C7×C1611yescharacteristic
367C22×C3×C4C22×C7×C1616yes—
368C22×C3×C4C22×C7×C16112yes—
369C22×C3×C4C23×C7×C811yescharacteristic
370C2×C3×C8C4×C7×C16148yes—
371C2×C3×C8C43×C714yes—
372C2×C3×C8C2×C4×C7×C816yes—
373C2×C3×C8C2×C4×C7×C8112yes—
374C2×C3×C8C2×C4×C7×C8112yes—
375C2×C3×C8C22×C7×C16124yes—
376C2×C3×C8C22×C42×C713yes—
377C2×C3×C8C23×C7×C813yes—
378C3×C42C4×C7×C16124yes—
379C3×C42C2×C7×C32164yesdirect product factor
380C3×C42C2×C4×C7×C8112yes—
381C3×C42C22×C7×C16112yes—
382C3×C16C43×C714yes—
383C3×C16C2×C4×C7×C8124yes—
384C3×C16C22×C42×C714yes—
385C2×C3×C7C42×C3218yesdirect product factor
386C2×C3×C7C2×C42×C1611yescharacteristic
387C2×C3×C7C22×C4×C3216yes—
388C23×C4C2×C3×C7×C1616yes—
389C23×C4C22×C3×C7×C811yescharacteristic
390C22×C8C3×C4×C7×C8112yes—
391C22×C8C2×C3×C7×C16124yes—
392C22×C8C2×C3×C42×C716yes—
393C22×C8C22×C3×C7×C811yescharacteristic
394C22×C8C22×C3×C7×C816yes—
395C22×C8C22×C3×C7×C816yes—
396C22×C8C23×C3×C4×C711yescharacteristic
397C2×C42C3×C7×C32132yesdirect product factor
398C2×C42C3×C4×C7×C8112yes—
399C2×C42C2×C3×C7×C1616yes—
400C2×C42C2×C3×C7×C16112yes—
401C2×C42C2×C3×C7×C16116yes—
402C2×C42C22×C3×C7×C816yes—
403C2×C16C3×C4×C7×C8148yes—
404C2×C16C2×C3×C42×C716yes—
405C2×C16C2×C3×C42×C7112yes—
406C2×C16C2×C3×C42×C7116yes—
407C2×C16C22×C3×C7×C8124yes—
408C2×C16C23×C3×C4×C716yes—
409C4×C8C3×C4×C7×C8124yes—
410C4×C8C2×C3×C7×C16148yes—
411C4×C8C2×C3×C42×C7112yes—
412C4×C8C22×C3×C7×C8112yes—
413C32C2×C3×C42×C7132yesdirect product factor
414C22×C7C3×C42×C1614yes—
415C22×C7C2×C3×C4×C32124yes—
416C22×C7C22×C3×C4×C1613yes—
417C22×C7C23×C3×C3214yes—
418C4×C7C3×C42×C1614yes—
419C4×C7C2×C3×C4×C32148yesdirect product factor
420C4×C7C2×C3×C42×C811yescharacteristic
421C4×C7C22×C3×C4×C1613yes—
422C23×C3C2×C4×C7×C1616yes—
423C23×C3C22×C7×C3218yes—
424C23×C3C23×C7×C1611yescharacteristic
425C2×C3×C4C4×C7×C32196yesdirect product factor
426C2×C3×C4C42×C7×C814yes—
427C2×C3×C4C2×C4×C7×C1616yes—
428C2×C3×C4C2×C4×C7×C16112yes—
429C2×C3×C4C2×C4×C7×C16124yes—
430C2×C3×C4C22×C7×C32148yes—
431C2×C3×C4C22×C4×C7×C813yes—
432C2×C3×C4C23×C7×C1613yes—
433C3×C8C42×C7×C814yes—
434C3×C8C2×C4×C7×C16124yes—
435C3×C8C2×C43×C711yescharacteristic
436C3×C8C22×C4×C7×C813yes—
437C3×C7C2×C42×C3211yescharacteristic, direct product factor, Hall
438C24C22×C3×C7×C1611yescharacteristic
439C22×C4C3×C4×C7×C16124yes—
440C22×C4C2×C3×C7×C32148yes—
441C22×C4C2×C3×C4×C7×C816yes—
442C22×C4C22×C3×C7×C1611yescharacteristic
443C22×C4C22×C3×C7×C1616yes—
444C22×C4C22×C3×C7×C16112yes—
445C22×C4C23×C3×C7×C811yescharacteristic
446C2×C8C3×C4×C7×C16148yes—
447C2×C8C3×C43×C714yes—
448C2×C8C2×C3×C4×C7×C816yes—
449C2×C8C2×C3×C4×C7×C8112yes—
450C2×C8C2×C3×C4×C7×C8112yes—
451C2×C8C22×C3×C7×C16124yes—
452C2×C8C22×C3×C42×C713yes—
453C2×C8C23×C3×C7×C813yes—
454C42C3×C4×C7×C16124yes—
455C42C2×C3×C7×C32164yesdirect product factor
456C42C2×C3×C4×C7×C8112yes—
457C42C22×C3×C7×C16112yes—
458C16C3×C43×C714yes—
459C16C2×C3×C4×C7×C8124yes—
460C16C22×C3×C42×C714yes—
461C2×C7C3×C42×C3218yesdirect product factor
462C2×C7C22×C3×C4×C3216yes—
463C2×C7C2×C3×C42×C1611yescharacteristic
464C22×C3C42×C7×C1614yes—
465C22×C3C2×C4×C7×C32124yes—
466C22×C3C22×C4×C7×C1613yes—
467C22×C3C23×C7×C3214yes—
468C3×C4C42×C7×C1614yes—
469C3×C4C2×C4×C7×C32148yesdirect product factor
470C3×C4C2×C42×C7×C811yescharacteristic
471C3×C4C22×C4×C7×C1613yes—
472C23C22×C3×C7×C3218yes—
473C23C2×C3×C4×C7×C1616yes—
474C23C23×C3×C7×C1611yescharacteristic
475C2×C4C3×C4×C7×C32196yesdirect product factor
476C2×C4C22×C3×C7×C32148yes—
477C2×C4C2×C3×C4×C7×C1616yes—
478C2×C4C2×C3×C4×C7×C16112yes—
479C2×C4C2×C3×C4×C7×C16124yes—
480C2×C4C23×C3×C7×C1613yes—
481C2×C4C3×C42×C7×C814yes—
482C2×C4C22×C3×C4×C7×C813yes—
483C8C2×C3×C4×C7×C16124yes—
484C8C3×C42×C7×C814yes—
485C8C22×C3×C4×C7×C813yes—
486C8C2×C3×C43×C711yescharacteristic
487C7C2×C3×C42×C3211yescharacteristic, direct product factor, Sylow
488C2×C3C42×C7×C3218yesdirect product factor
489C2×C3C22×C4×C7×C3216yes—
490C2×C3C2×C42×C7×C1611yescharacteristic
491C22C2×C3×C4×C7×C32124yes—
492C22C23×C3×C7×C3214yes—
493C22C3×C42×C7×C1614yes—
494C22C22×C3×C4×C7×C1613yes—
495C4C2×C3×C4×C7×C32148yesdirect product factor
496C4C3×C42×C7×C1614yes—
497C4C22×C3×C4×C7×C1613yes—
498C4C2×C3×C42×C7×C811yescharacteristic
499C3C2×C42×C7×C3211yescharacteristic, direct product factor, Sylow
500C2C3×C42×C7×C3218yesdirect product factor
501C2C22×C3×C4×C7×C3216yes—
502C2C2×C3×C42×C7×C1611yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C16C24×C3×C7
socle, prime radicalC24×C3×C7C22×C16
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
3. C3×C42×C7×C32C2direct (N × H)
4. C2×C42×C7×C32C3direct (N × H)
11. C2×C3×C4×C7×C32C4direct (N × H)
15. C42×C7×C32C2×C3direct (N × H)
16. C2×C3×C42×C32C7direct (N × H)
31. C3×C4×C7×C32C2×C4direct (N × H)
34. C3×C42×C32C2×C7direct (N × H)
35. C2×C42×C32C3×C7direct (N × H)
40. C2×C4×C7×C32C3×C4direct (N × H)
62. C2×C3×C7×C32C42direct (N × H)
81. C4×C7×C32C2×C3×C4direct (N × H)
86. C2×C3×C4×C32C4×C7direct (N × H)
99. C2×C3×C42×C7C32direct (N × H)
115. C3×C7×C32C2×C42direct (N × H)
118. C42×C32C2×C3×C7direct (N × H)
137. C2×C7×C32C3×C42direct (N × H)
156. C3×C4×C32C2×C4×C7direct (N × H)
174. C3×C42×C7C2×C32direct (N × H)
184. C2×C4×C32C3×C4×C7direct (N × H)
197. C2×C42×C7C3×C32direct (N × H)
213. C7×C32C2×C3×C42direct (N × H)
232. C2×C3×C32C42×C7direct (N × H)
240. C2×C3×C4×C7C4×C32direct (N × H)
266. C4×C32C2×C3×C4×C7direct (N × H)
284. C42×C7C2×C3×C32direct (N × H)
299. C2×C3×C42C7×C32direct (N × H)
315. C3×C32C2×C42×C7direct (N × H)
321. C3×C4×C7C2×C4×C32direct (N × H)
342. C2×C32C3×C42×C7direct (N × H)
350. C2×C4×C7C3×C4×C32direct (N × H)
379. C3×C42C2×C7×C32direct (N × H)
385. C2×C3×C7C42×C32direct (N × H)
397. C2×C42C3×C7×C32direct (N × H)
413. C32C2×C3×C42×C7direct (N × H)
419. C4×C7C2×C3×C4×C32direct (N × H)
425. C2×C3×C4C4×C7×C32direct (N × H)
437. C3×C7C2×C42×C32direct (N × H)
455. C42C2×C3×C7×C32direct (N × H)
461. C2×C7C3×C42×C32direct (N × H)
469. C3×C4C2×C4×C7×C32direct (N × H)
475. C2×C4C3×C4×C7×C32direct (N × H)
487. C7C2×C3×C42×C32direct (N × H)
488. C2×C3C42×C7×C32direct (N × H)
495. C4C2×C3×C4×C7×C32direct (N × H)
499. C3C2×C42×C7×C32direct (N × H)
500. C2C3×C42×C7×C32direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C42×C7×C162
C22×C3×C4×C7×C322
C3×C42×C7×C322
C2×C42×C7×C323
C2×C3×C42×C327