Finite Group Databasebeta

← C2×C7×#2462 #13211902

Subgroups — C2×C7×#2462 #13211902

Order 1792.

2486 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#125C211yesmaximal, characteristic
2C22×C4×C7×Q8C211yesmaximal, characteristic
3C7×#2462C2116yesmaximal, direct product factor
4C2×C7×#398C211yesmaximal, characteristic
5C2×C7×#398C211yesmaximal, characteristic
6C2×C7×#395C211yesmaximal, characteristic
7C2×C7×#395C211yesmaximal, characteristic
8C2×C7×#389C211yesmaximal, characteristic
9C2×C7×#389C211yesmaximal, characteristic
10C2×C7×#387C211yesmaximal, characteristic
11C2×C7×#387C211yesmaximal, characteristic
12C2×C7×#387C211yesmaximal, characteristic
13C2×C7×#387C211yesmaximal, characteristic
14C2×C7×#387C211yesmaximal, characteristic
15C2×C7×#387C211yesmaximal, characteristic
16C2×C4×C7×C4⋊C4C211yesmaximal, characteristic
17C23×C7×Q8C2211yescharacteristic
18C2×C7×#125—28no—
19C2×C7×#125C2218yes—
20C2×C4×C7×Q8—28no—
21C2×C4×C7×Q8C2218yes—
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C4⋊C4C2211yescharacteristic
26C22×C7×C4⋊C4C2211yescharacteristic
27C22×C7×C4⋊C4C2211yescharacteristic
28C22×C7×C4⋊C4C2211yescharacteristic
29C22×C7×C4⋊C4C2211yescharacteristic
30C22×C7×C4⋊C4C2211yescharacteristic
31C22×C7×C4⋊C4C2211yescharacteristic
32C22×C7×C4⋊C4C2211yescharacteristic
33C22×C7×C4⋊C4C2211yescharacteristic
34C22×C7×C4⋊C4C2211yescharacteristic
35C22×C7×C4⋊C4C2211yescharacteristic
36C22×C7×C4⋊C4C2211yescharacteristic
37C22×C42×C7C2211yescharacteristic
38C22×C42×C7C2211yescharacteristic
39C22×C42×C7C2211yescharacteristic
40C22×C42×C7C2211yescharacteristic
41C22×C42×C7C2211yescharacteristic
42C7×#398C2218yes—
43C7×#398C2218yes—
44C7×#395C2218yes—
45C7×#395C2218yes—
46C7×#389C2218yes—
47C7×#389C2218yes—
48C7×#387C2218yes—
49C7×#387C2218yes—
50C7×#387C2218yes—
51C7×#387C2218yes—
52C7×#387C2218yes—
53C7×#387C2218yes—
54C4×C7×C4⋊C4C2218yes—
55C2×C7×#95C2211yescharacteristic
56C2×C7×#95C2211yescharacteristic
57C2×C7×#95C2211yescharacteristic
58C2×C7×#95C2211yescharacteristic
59C2×C7×#95C2211yescharacteristic
60C2×C7×#95C2211yescharacteristic
61C2×C7×#95C2211yescharacteristic
62C2×C7×#95C2211yescharacteristic
63C2×C7×#95C2211yescharacteristic
64C2×C7×#95C2211yescharacteristic
65C2×C7×#95C2211yescharacteristic
66C2×C7×#95C2211yescharacteristic
67C2×C7×#95C2211yescharacteristic
68C2×C7×#95C2211yescharacteristic
69C2×#2462C711yesmaximal, characteristic, direct product factor, Sylow
70C22×C7×Q8—24no—
71C22×C7×Q8—24no—
72C22×C7×Q8—24no—
73C22×C7×Q8C2314yes—
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2311yescharacteristic
85C23×C4×C7C2311yescharacteristic
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C23×C4×C7C2311yescharacteristic
89C7×#125—232no—
90C4×C7×Q8—232no—
91C2×C7×C4⋊C4—24no—
92C2×C7×C4⋊C4—24no—
93C2×C7×C4⋊C4—24no—
94C2×C7×C4⋊C4—24no—
95C2×C7×C4⋊C4—24no—
96C2×C7×C4⋊C4—24no—
97C2×C7×C4⋊C4—24no—
98C2×C7×C4⋊C4—24no—
99C2×C7×C4⋊C4—24no—
100C2×C7×C4⋊C4—24no—
101C2×C7×C4⋊C4—24no—
102C2×C7×C4⋊C4—24no—
103C2×C7×C4⋊C4—24no—
104C2×C7×C4⋊C4D418yes—
105C2×C7×C4⋊C4Q818yescomplemented
106C2×C7×C4⋊C4C2314yes—
107C2×C7×C4⋊C4C2314yes—
108C2×C7×C4⋊C4C2314yes—
109C2×C7×C4⋊C4C2314yes—
110C2×C7×C4⋊C4C2314yes—
111C2×C7×C4⋊C4C2314yes—
112C2×C7×C4⋊C4C2314yes—
113C2×C7×C4⋊C4C2314yes—
114C2×C7×C4⋊C4C2314yes—
115C2×C7×C4⋊C4C2314yes—
116C2×C7×C4⋊C4C2314yes—
117C2×C7×C4⋊C4C2314yes—
118C2×C7×C4⋊C4C2314yes—
119C2×C7×C4⋊C4C2314yes—
120C2×C7×C4⋊C4C2314yes—
121C2×C42×C7—24no—
122C2×C42×C7—24no—
123C2×C42×C7—24no—
124C2×C42×C7—24no—
125C2×C42×C7—24no—
126C2×C42×C7C2314yes—
127C2×C42×C7C2314yes—
128C2×C42×C7C2314yes—
129C2×C42×C7C2314yes—
130C2×C42×C7C2314yes—
131C7×#95C2314yes—
132C7×#95C2314yes—
133C7×#95C2314yes—
134C7×#95C2314yes—
135C7×#95C2314yes—
136C7×#95C2314yes—
137C7×#95C2314yes—
138C7×#95C2314yes—
139C7×#95C2314yes—
140C7×#95C2314yes—
141C7×#95C2314yes—
142C7×#95C2314yes—
143C7×#95C2314yes—
144C7×#95C2314yes—
145C22×#125C2×C711yescharacteristic
146C22×C4×Q8C2×C711yescharacteristic
147#2462C2×C7116yesdirect product factor
148C2×#398C2×C711yescharacteristic
149C2×#398C2×C711yescharacteristic
150C2×#395C2×C711yescharacteristic
151C2×#395C2×C711yescharacteristic
152C2×#389C2×C711yescharacteristic
153C2×#389C2×C711yescharacteristic
154C2×#387C2×C711yescharacteristic
155C2×#387C2×C711yescharacteristic
156C2×#387C2×C711yescharacteristic
157C2×#387C2×C711yescharacteristic
158C2×#387C2×C711yescharacteristic
159C2×#387C2×C711yescharacteristic
160C2×C4×C4⋊C4C2×C711yescharacteristic
161C24×C7C2411yescharacteristic
162C2×C7×Q8—232no—
163C2×C7×Q8—28no—
164C2×C7×Q8—28no—
165C2×C7×Q8—28no—
166C22×C4×C7—22no—
167C22×C4×C7—22no—
168C22×C4×C7—22no—
169C22×C4×C7—22no—
170C22×C4×C7—22no—
171C22×C4×C7—22no—
172C22×C4×C7—22no—
173C22×C4×C7—22no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—22no—
184C22×C4×C7—22no—
185C22×C4×C7—22no—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—22no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—22no—
195C22×C4×C7—22no—
196C22×C4×C7—22no—
197C22×C4×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7C2×D414yes—
203C22×C4×C7C2×D414yes—
204C22×C4×C7C2×D414yes—
205C22×C4×C7C2×Q814yes—
206C22×C4×C7C2×Q814yes—
207C22×C4×C7C2×Q814yes—
208C22×C4×C7#4114yes—
209C22×C4×C7#4114yes—
210C22×C4×C7#4114yes—
211C22×C4×C7C2412yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2412yes—
214C22×C4×C7C2412yes—
215C22×C4×C7C2412yes—
216C22×C4×C7C2412yes—
217C22×C4×C7C2412yes—
218C22×C4×C7C2412yes—
219C22×C4×C7C2412yes—
220C22×C4×C7C2412yes—
221C22×C4×C7C2412yes—
222C22×C4×C7C2412yes—
223C22×C4×C7C2412yes—
224C22×C4×C7C2412yes—
225C22×C4×C7C2412yes—
226C7×C4⋊C4—28no—
227C7×C4⋊C4—28no—
228C7×C4⋊C4—28no—
229C7×C4⋊C4—28no—
230C7×C4⋊C4—28no—
231C7×C4⋊C4—28no—
232C7×C4⋊C4—28no—
233C7×C4⋊C4—28no—
234C7×C4⋊C4—28no—
235C7×C4⋊C4—28no—
236C7×C4⋊C4—28no—
237C7×C4⋊C4—28no—
238C7×C4⋊C4—28no—
239C7×C4⋊C4C2×D4116yes—
240C7×C4⋊C4C2×Q8116yescomplemented
241C42×C7—28no—
242C42×C7—28no—
243C42×C7—28no—
244C42×C7—28no—
245C42×C7—28no—
246C23×Q8C22×C711yescharacteristic
247C2×#125—28no—
248C2×#125C22×C718yes—
249C2×C4×Q8—28no—
250C2×C4×Q8C22×C718yes—
251C22×C4⋊C4C22×C711yescharacteristic
252C22×C4⋊C4C22×C711yescharacteristic
253C22×C4⋊C4C22×C711yescharacteristic
254C22×C4⋊C4C22×C711yescharacteristic
255C22×C4⋊C4C22×C711yescharacteristic
256C22×C4⋊C4C22×C711yescharacteristic
257C22×C4⋊C4C22×C711yescharacteristic
258C22×C4⋊C4C22×C711yescharacteristic
259C22×C4⋊C4C22×C711yescharacteristic
260C22×C4⋊C4C22×C711yescharacteristic
261C22×C4⋊C4C22×C711yescharacteristic
262C22×C4⋊C4C22×C711yescharacteristic
263C22×C4⋊C4C22×C711yescharacteristic
264C22×C4⋊C4C22×C711yescharacteristic
265C22×C4⋊C4C22×C711yescharacteristic
266C22×C42C22×C711yescharacteristic
267C22×C42C22×C711yescharacteristic
268C22×C42C22×C711yescharacteristic
269C22×C42C22×C711yescharacteristic
270C22×C42C22×C711yescharacteristic
271#398C22×C718yes—
272#398C22×C718yes—
273#395C22×C718yes—
274#395C22×C718yes—
275#389C22×C718yes—
276#389C22×C718yes—
277#387C22×C718yes—
278#387C22×C718yes—
279#387C22×C718yes—
280#387C22×C718yes—
281#387C22×C718yes—
282#387C22×C718yes—
283C4×C4⋊C4C22×C718yes—
284C2×#95C22×C711yescharacteristic
285C2×#95C22×C711yescharacteristic
286C2×#95C22×C711yescharacteristic
287C2×#95C22×C711yescharacteristic
288C2×#95C22×C711yescharacteristic
289C2×#95C22×C711yescharacteristic
290C2×#95C22×C711yescharacteristic
291C2×#95C22×C711yescharacteristic
292C2×#95C22×C711yescharacteristic
293C2×#95C22×C711yescharacteristic
294C2×#95C22×C711yescharacteristic
295C2×#95C22×C711yescharacteristic
296C2×#95C22×C711yescharacteristic
297C2×#95C22×C711yescharacteristic
298C23×C7C22×D412yes—
299C23×C7C22×Q812yes—
300C23×C7C2×#4112yes—
301C23×C7C2×#4112yes—
302C23×C7C2×#4112yes—
303C23×C72−1+412yes—
304C23×C72−1+412yes—
305C23×C7C2511yescharacteristic
306C7×Q8—232no—
307C2×C4×C7—28no—
308C2×C4×C7—28no—
309C2×C4×C7—28no—
310C2×C4×C7—28no—
311C2×C4×C7—28no—
312C2×C4×C7—28no—
313C2×C4×C7—28no—
314C2×C4×C7—28no—
315C2×C4×C7—28no—
316C2×C4×C7—22no—
317C2×C4×C7—22no—
318C2×C4×C7—22no—
319C2×C4×C7—22no—
320C2×C4×C7—22no—
321C2×C4×C7—22no—
322C2×C4×C7—22no—
323C2×C4×C7—22no—
324C2×C4×C7—22no—
325C2×C4×C7—22no—
326C2×C4×C7—22no—
327C2×C4×C7—22no—
328C2×C4×C7—22no—
329C2×C4×C7—22no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—22no—
342C2×C4×C7—22no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—22no—
348C2×C4×C7—22no—
349C2×C4×C7—22no—
350C2×C4×C7—22no—
351C2×C4×C7—22no—
352C2×C4×C7—44no—
353C2×C4×C7—44no—
354C2×C4×C7—44no—
355C2×C4×C7—44no—
356C2×C4×C7—44no—
357C2×C4×C7—44no—
358C2×C4×C7C22×D414yes—
359C2×C4×C7C22×D414yes—
360C2×C4×C7C22×D414yes—
361C2×C4×C7C22×Q814yes—
362C2×C4×C7C22×Q814yes—
363C2×C4×C7C22×Q814yes—
364C2×C4×C7C2×#4114yes—
365C2×C4×C7C2×#4114yes—
366C2×C4×C7C2×#4114yes—
367C22×Q8—24no—
368C22×Q8—24no—
369C22×Q8—24no—
370C22×Q8C23×C714yes—
371C23×C4C23×C711yescharacteristic
372C23×C4C23×C711yescharacteristic
373C23×C4C23×C711yescharacteristic
374C23×C4C23×C711yescharacteristic
375C23×C4C23×C711yescharacteristic
376C23×C4C23×C711yescharacteristic
377C23×C4C23×C711yescharacteristic
378C23×C4C23×C711yescharacteristic
379C23×C4C23×C711yescharacteristic
380C23×C4C23×C711yescharacteristic
381C23×C4C23×C711yescharacteristic
382C23×C4C23×C711yescharacteristic
383C23×C4C23×C711yescharacteristic
384C23×C4C23×C711yescharacteristic
385C23×C4C23×C711yescharacteristic
386#125—232no—
387C4×Q8—232no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—24no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4C7×D418yes—
402C2×C4⋊C4C7×Q818yescomplemented
403C2×C4⋊C4C23×C714yes—
404C2×C4⋊C4C23×C714yes—
405C2×C4⋊C4C23×C714yes—
406C2×C4⋊C4C23×C714yes—
407C2×C4⋊C4C23×C714yes—
408C2×C4⋊C4C23×C714yes—
409C2×C4⋊C4C23×C714yes—
410C2×C4⋊C4C23×C714yes—
411C2×C4⋊C4C23×C714yes—
412C2×C4⋊C4C23×C714yes—
413C2×C4⋊C4C23×C714yes—
414C2×C4⋊C4C23×C714yes—
415C2×C4⋊C4C23×C714yes—
416C2×C4⋊C4C23×C714yes—
417C2×C4⋊C4C23×C714yes—
418C2×C42—24no—
419C2×C42—24no—
420C2×C42—24no—
421C2×C42—24no—
422C2×C42—24no—
423C2×C42C23×C714yes—
424C2×C42C23×C714yes—
425C2×C42C23×C714yes—
426C2×C42C23×C714yes—
427C2×C42C23×C714yes—
428#95C23×C714yes—
429#95C23×C714yes—
430#95C23×C714yes—
431#95C23×C714yes—
432#95C23×C714yes—
433#95C23×C714yes—
434#95C23×C714yes—
435#95C23×C714yes—
436#95C23×C714yes—
437#95C23×C714yes—
438#95C23×C714yes—
439#95C23×C714yes—
440#95C23×C714yes—
441#95C23×C714yes—
442C22×C7#52514yes—
443C22×C7#53314yes—
444C22×C7#54114yes—
445C22×C7#54714yes—
446C22×C7D4×Q814yes—
447C22×C7#55214yes—
448C22×C7#55714yes—
449C22×C7C23×D411yescharacteristic
450C22×C7C23×Q811yescharacteristic
451C22×C7C22×#4111yescharacteristic
452C22×C7C22×#4111yescharacteristic
453C22×C7C22×#4111yescharacteristic
454C22×C7C2×2−1+411yescharacteristic
455C22×C7C2×2−1+411yescharacteristic
456C4×C7—24no—
457C4×C7—24no—
458C4×C7—24no—
459C4×C7—24no—
460C4×C7—24no—
461C4×C7—24no—
462C4×C7—24no—
463C4×C7—24no—
464C4×C7—24no—
465C4×C7—42no—
466C4×C7—42no—
467C4×C7—42no—
468C4×C7—42no—
469C4×C7—42no—
470C4×C7—42no—
471C24C24×C711yescharacteristic
472C2×Q8—232no—
473C2×Q8—28no—
474C2×Q8—28no—
475C2×Q8—28no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4C2×C7×D414yes—
513C22×C4C2×C7×D414yes—
514C22×C4C2×C7×D414yes—
515C22×C4C2×C7×Q814yes—
516C22×C4C2×C7×Q814yes—
517C22×C4C2×C7×Q814yes—
518C22×C4C7×#4114yes—
519C22×C4C7×#4114yes—
520C22×C4C7×#4114yes—
521C22×C4C24×C712yes—
522C22×C4C24×C712yes—
523C22×C4C24×C712yes—
524C22×C4C24×C712yes—
525C22×C4C24×C712yes—
526C22×C4C24×C712yes—
527C22×C4C24×C712yes—
528C22×C4C24×C712yes—
529C22×C4C24×C712yes—
530C22×C4C24×C712yes—
531C22×C4C24×C712yes—
532C22×C4C24×C712yes—
533C22×C4C24×C712yes—
534C22×C4C24×C712yes—
535C22×C4C24×C712yes—
536C4⋊C4—28no—
537C4⋊C4—28no—
538C4⋊C4—28no—
539C4⋊C4—28no—
540C4⋊C4—28no—
541C4⋊C4—28no—
542C4⋊C4—28no—
543C4⋊C4—28no—
544C4⋊C4—28no—
545C4⋊C4—28no—
546C4⋊C4—28no—
547C4⋊C4—28no—
548C4⋊C4—28no—
549C4⋊C4C2×C7×D4116yes—
550C4⋊C4C2×C7×Q8116yescomplemented
551C42—28no—
552C42—28no—
553C42—28no—
554C42—28no—
555C42—28no—
556C2×C7#246218yesdirect product factor
557C2×C7C2×#52511yescharacteristic
558C2×C7C2×#53311yescharacteristic
559C2×C7C2×#54111yescharacteristic
560C2×C7C2×#54711yescharacteristic
561C2×C7C2×D4×Q811yescharacteristic
562C2×C7C2×#55211yescharacteristic
563C2×C7C2×#55711yescharacteristic
564C23C22×C7×D412yes—
565C23C22×C7×Q812yes—
566C23C2×C7×#4112yes—
567C23C2×C7×#4112yes—
568C23C2×C7×#4112yes—
569C23C7×2−1+412yes—
570C23C7×2−1+412yes—
571C23C25×C711yescharacteristic
572Q8—232no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—28no—
592C2×C4—28no—
593C2×C4—28no—
594C2×C4—28no—
595C2×C4—28no—
596C2×C4—28no—
597C2×C4—28no—
598C2×C4—28no—
599C2×C4—28no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—44no—
619C2×C4—44no—
620C2×C4—44no—
621C2×C4—44no—
622C2×C4—44no—
623C2×C4—44no—
624C2×C4C22×C7×D414yes—
625C2×C4C22×C7×D414yes—
626C2×C4C22×C7×D414yes—
627C2×C4C22×C7×Q814yes—
628C2×C4C22×C7×Q814yes—
629C2×C4C22×C7×Q814yes—
630C2×C4C2×C7×#4114yes—
631C2×C4C2×C7×#4114yes—
632C2×C4C2×C7×#4114yes—
633C7C2×#246211yescharacteristic, direct product factor, Sylow
634C22C7×#52514yes—
635C22C7×#53314yes—
636C22C7×#54114yes—
637C22C7×#54714yes—
638C22C7×D4×Q814yes—
639C22C7×#55214yes—
640C22C7×#55714yes—
641C22C23×C7×D411yescharacteristic
642C22C23×C7×Q811yescharacteristic
643C22C22×C7×#4111yescharacteristic
644C22C22×C7×#4111yescharacteristic
645C22C22×C7×#4111yescharacteristic
646C22C2×C7×2−1+411yescharacteristic
647C22C2×C7×2−1+411yescharacteristic
648C4—24no—
649C4—24no—
650C4—24no—
651C4—24no—
652C4—24no—
653C4—24no—
654C4—24no—
655C4—24no—
656C4—24no—
657C4—42no—
658C4—42no—
659C4—42no—
660C4—42no—
661C4—42no—
662C4—42no—
663C2C7×#246218yesdirect product factor
664C2C2×C7×#52511yescharacteristic
665C2C2×C7×#53311yescharacteristic
666C2C2×C7×#54111yescharacteristic
667C2C2×C7×#54711yescharacteristic
668C2C2×C7×D4×Q811yescharacteristic
669C2C2×C7×#55211yescharacteristic
670C2C2×C7×#55711yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C7C24
commutator, Frattini, cosocleC23C25×C7
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
3. C7×#2462C2direct (N × H)
69. C2×#2462C7direct (N × H)
105. C2×C7×C4⋊C4Q8semidirect
147. #2462C2×C7direct (N × H)
240. C7×C4⋊C4C2×Q8semidirect
402. C2×C4⋊C4C7×Q8semidirect
550. C4⋊C4C2×C7×Q8semidirect
556. C2×C7#2462direct (N × H)
633. C7C2×#2462direct (N × H)
663. C2C7×#2462direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1252
C22×C4×C7×Q82
C7×#24622
C2×C7×#3982
C2×C7×#3952
C2×C7×#3892
C2×C7×#3872
C2×C4×C7×C4⋊C42
C2×#24627