Finite Group Databasebeta

← C7×#14054 #13191270

Subgroups — C7×#14054 #13191270

Order 1792.

1566 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#125C211yesmaximal, characteristic
2C2×C7×#389C211yesmaximal, characteristic
3C2×C4×C7×C4⋊C4C211yesmaximal, characteristic
4C7×#1445C212yesmaximal
5C7×#1441C212yesmaximal
6C7×#1436C212yesmaximal
7C7×C4⋊#95C211yesmaximal, characteristic
8C7×C4⋊#95C212yesmaximal
9C7×C4⋊#95C211yesmaximal, characteristic
10C7×C4⋊#95C211yesmaximal, characteristic
11C4×C7×#95C211yesmaximal, characteristic
12C2×C7×#125—24no—
13C2×C7×#125—24no—
14C2×C7×#125C418yescomplemented
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C7×C4⋊C4C2212yes—
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2212yes—
19C22×C7×C4⋊C4C2212yes—
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C42×C7C2211yescharacteristic
23C22×C42×C7C2212yes—
24C22×C42×C7C2211yescharacteristic
25C22×C42×C7C2211yescharacteristic
26C7×#389—24no—
27C4×C7×C4⋊C4—24no—
28C2×C7×#95C2212yes—
29C2×C7×#95C2212yes—
30C2×C7×#95C2211yescharacteristic
31C2×C7×#95C2211yescharacteristic
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2211yescharacteristic
34C2×C7×#95C2212yes—
35C2×C7×#95C2212yes—
36C2×C7×#95C2212yes—
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39C2×C7×#95C2212yes—
40#14054C711yesmaximal, characteristic, direct product factor, Sylow
41C23×C4×C7C2312yes—
42C23×C4×C7C2311yescharacteristic
43C23×C4×C7C2311yescharacteristic
44C23×C4×C7C2312yes—
45C23×C4×C7C2311yescharacteristic
46C23×C4×C7C2312yes—
47C23×C4×C7C2311yescharacteristic
48C23×C4×C7C2311yescharacteristic
49C23×C4×C7C2312yes—
50C23×C4×C7C2311yescharacteristic
51C23×C4×C7C2311yescharacteristic
52C7×#125—232no—
53C2×C7×C4⋊C4—22no—
54C2×C7×C4⋊C4—24no—
55C2×C7×C4⋊C4—24no—
56C2×C7×C4⋊C4—24no—
57C2×C7×C4⋊C4—24no—
58C2×C7×C4⋊C4—22no—
59C2×C7×C4⋊C4—22no—
60C2×C7×C4⋊C4—22no—
61C2×C7×C4⋊C4—24no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—24no—
64C2×C7×C4⋊C4—22no—
65C2×C7×C4⋊C4—22no—
66C2×C7×C4⋊C4—42no—
67C2×C7×C4⋊C4C2×C418yes—
68C2×C7×C4⋊C4C2×C418yes—
69C2×C7×C4⋊C4C2×C414yes—
70C2×C7×C4⋊C4C2×C414yes—
71C2×C7×C4⋊C4D414yes—
72C2×C7×C4⋊C4D414yes—
73C2×C7×C4⋊C4Q814yes—
74C2×C42×C7—22no—
75C2×C42×C7—22no—
76C2×C42×C7—22no—
77C2×C42×C7—22no—
78C2×C42×C7—24no—
79C2×C42×C7—22no—
80C2×C42×C7—24no—
81C2×C42×C7—22no—
82C2×C42×C7—22no—
83C2×C42×C7—42no—
84C2×C42×C7C2×C414yes—
85C2×C42×C7Q814yes—
86C7×#95—24no—
87C7×#95—24no—
88C7×#95—22no—
89C7×#95—24no—
90C7×#95—22no—
91C7×#95—22no—
92C7×#95—22no—
93C7×#95—24no—
94C7×#95—42no—
95C7×#95—42no—
96C7×#95—42no—
97C7×#95—42no—
98C22×#125C2×C711yescharacteristic
99C2×#389C2×C711yescharacteristic
100C2×C4×C4⋊C4C2×C711yescharacteristic
101#1445C2×C712yes—
102#1441C2×C712yes—
103#1436C2×C712yes—
104C4⋊#95C2×C711yescharacteristic
105C4⋊#95C2×C711yescharacteristic
106C4⋊#95C2×C712yes—
107C4⋊#95C2×C711yescharacteristic
108C4×#95C2×C711yescharacteristic
109C24×C7C2411yescharacteristic
110C22×C4×C7—21no—
111C22×C4×C7—22no—
112C22×C4×C7—21no—
113C22×C4×C7—22no—
114C22×C4×C7—21no—
115C22×C4×C7—22no—
116C22×C4×C7—22no—
117C22×C4×C7—21no—
118C22×C4×C7—21no—
119C22×C4×C7—21no—
120C22×C4×C7—22no—
121C22×C4×C7—21no—
122C22×C4×C7—21no—
123C22×C4×C7—21no—
124C22×C4×C7—21no—
125C22×C4×C7—21no—
126C22×C4×C7—22no—
127C22×C4×C7—22no—
128C22×C4×C7—21no—
129C22×C4×C7—21no—
130C22×C4×C7—21no—
131C22×C4×C7—22no—
132C22×C4×C7—21no—
133C22×C4×C7—22no—
134C22×C4×C7—21no—
135C22×C4×C7—21no—
136C22×C4×C7—21no—
137C22×C4×C7—21no—
138C22×C4×C7—22no—
139C22×C4×C7—21no—
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7—22no—
145C22×C4×C7—22no—
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7—22no—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—22no—
157C22×C4×C7—21no—
158C22×C4×C7—21no—
159C22×C4×C7—21no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7—22no—
163C22×C4×C7—22no—
164C22×C4×C7—22no—
165C22×C4×C7—22no—
166C22×C4×C7—22no—
167C22×C4×C7C22×C412yes—
168C22×C4×C7C22×C412yes—
169C22×C4×C7C22×C414yes—
170C22×C4×C7C22×C414yes—
171C22×C4×C7C22×C412yes—
172C22×C4×C7C2×D414yes—
173C22×C4×C7C2×D414yes—
174C22×C4×C7C2×D412yes—
175C22×C4×C7C2×D412yes—
176C22×C4×C7C2×Q812yes—
177C22×C4×C7C2×Q814yes—
178C22×C4×C7C2×Q812yes—
179C22×C4×C7C2×Q812yes—
180C22×C4×C7C2×Q812yes—
181C22×C4×C7#4112yes—
182C22×C4×C7#4112yes—
183C22×C4×C7#4112yes—
184C22×C4×C7#4112yes—
185C22×C4×C7#4112yes—
186C22×C4×C7#4112yes—
187C7×C4⋊C4—216no—
188C7×C4⋊C4—216no—
189C7×C4⋊C4—28no—
190C7×C4⋊C4—28no—
191C7×C4⋊C4—48no—
192C7×C4⋊C4—44no—
193C7×C4⋊C4C22⋊C4116yes—
194C42×C7—28no—
195C42×C7—28no—
196C42×C7—48no—
197C42×C7—44no—
198C2×#125—24no—
199C2×#125—24no—
200C2×#125C4×C718yescomplemented
201C22×C4⋊C4C22×C711yescharacteristic
202C22×C4⋊C4C22×C712yes—
203C22×C4⋊C4C22×C711yescharacteristic
204C22×C4⋊C4C22×C712yes—
205C22×C4⋊C4C22×C712yes—
206C22×C4⋊C4C22×C711yescharacteristic
207C22×C4⋊C4C22×C711yescharacteristic
208C22×C42C22×C711yescharacteristic
209C22×C42C22×C712yes—
210C22×C42C22×C711yescharacteristic
211C22×C42C22×C711yescharacteristic
212#389—24no—
213C4×C4⋊C4—24no—
214C2×#95C22×C711yescharacteristic
215C2×#95C22×C711yescharacteristic
216C2×#95C22×C711yescharacteristic
217C2×#95C22×C711yescharacteristic
218C2×#95C22×C712yes—
219C2×#95C22×C712yes—
220C2×#95C22×C712yes—
221C2×#95C22×C712yes—
222C2×#95C22×C712yes—
223C2×#95C22×C712yes—
224C2×#95C22×C712yes—
225C2×#95C22×C712yes—
226C23×C7C23×C411yescharacteristic
227C23×C7C22×D411yescharacteristic
228C23×C7C22×D411yescharacteristic
229C23×C7C22×Q811yescharacteristic
230C23×C7C22×Q811yescharacteristic
231C23×C7C2×#4111yescharacteristic
232C23×C7C2×#4111yescharacteristic
233C23×C7C2×#4111yescharacteristic
234C23×C7C2×#4111yescharacteristic
235C23×C7C2×#4111yescharacteristic
236C23×C7C2×#4111yescharacteristic
237C23×C7H(5,𝔽2)11yescharacteristic
238C23×C7H(5,𝔽2)11yescharacteristic
239C23×C72−1+411yescharacteristic
240C23×C72−1+411yescharacteristic
241C2×C4×C7—24no—
242C2×C4×C7—24no—
243C2×C4×C7—22no—
244C2×C4×C7—22no—
245C2×C4×C7—22no—
246C2×C4×C7—24no—
247C2×C4×C7—24no—
248C2×C4×C7—24no—
249C2×C4×C7—24no—
250C2×C4×C7—22no—
251C2×C4×C7—22no—
252C2×C4×C7—22no—
253C2×C4×C7—22no—
254C2×C4×C7—22no—
255C2×C4×C7—24no—
256C2×C4×C7—22no—
257C2×C4×C7—22no—
258C2×C4×C7—24no—
259C2×C4×C7—22no—
260C2×C4×C7—22no—
261C2×C4×C7—24no—
262C2×C4×C7—22no—
263C2×C4×C7—24no—
264C2×C4×C7—22no—
265C2×C4×C7—22no—
266C2×C4×C7—22no—
267C2×C4×C7—22no—
268C2×C4×C7—22no—
269C2×C4×C7—22no—
270C2×C4×C7—22no—
271C2×C4×C7—22no—
272C2×C4×C7—24no—
273C2×C4×C7—24no—
274C2×C4×C7—41no—
275C2×C4×C7—41no—
276C2×C4×C7—42no—
277C2×C4×C7—42no—
278C2×C4×C7—41no—
279C2×C4×C7—41no—
280C2×C4×C7—42no—
281C2×C4×C7—41no—
282C2×C4×C7—41no—
283C2×C4×C7—41no—
284C2×C4×C7—41no—
285C2×C4×C7—41no—
286C2×C4×C7—41no—
287C2×C4×C7—41no—
288C2×C4×C7—42no—
289C2×C4×C7—41no—
290C2×C4×C7—42no—
291C2×C4×C7—41no—
292C2×C4×C7—42no—
293C2×C4×C7—41no—
294C2×C4×C7—42no—
295C2×C4×C7—41no—
296C2×C4×C7—42no—
297C2×C4×C7—41no—
298C2×C4×C7—41no—
299C2×C4×C7—41no—
300C2×C4×C7—41no—
301C2×C4×C7—41no—
302C2×C4×C7—42no—
303C2×C4×C7—42no—
304C2×C4×C7—42no—
305C2×C4×C7—42no—
306C2×C4×C7—42no—
307C2×C4×C7—42no—
308C2×C4×C7—42no—
309C2×C4×C7C2×C22⋊C418yes—
310C2×C4×C7C2×C22⋊C414yes—
311C2×C4×C7C4×Q814yes—
312C2×C4×C7C4×Q814yes—
313C2×C4×C7C22⋊Q814yes—
314C2×C4×C7C22⋊Q814yes—
315C2×C4×C7#12414yes—
316C2×C4×C7#12514yescomplemented
317C2×C4×C7C4⋊Q814yes—
318C23×C4C23×C712yes—
319C23×C4C23×C712yes—
320C23×C4C23×C711yescharacteristic
321C23×C4C23×C711yescharacteristic
322C23×C4C23×C712yes—
323C23×C4C23×C711yescharacteristic
324C23×C4C23×C711yescharacteristic
325C23×C4C23×C711yescharacteristic
326C23×C4C23×C712yes—
327C23×C4C23×C711yescharacteristic
328C23×C4C23×C711yescharacteristic
329#125—232no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4C2×C4×C718yes—
345C2×C4⋊C4C2×C4×C718yes—
346C2×C4⋊C4C2×C4×C714yes—
347C2×C4⋊C4C2×C4×C714yes—
348C2×C4⋊C4C7×D414yes—
349C2×C4⋊C4C7×D414yes—
350C2×C4⋊C4C7×Q814yes—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—24no—
356C2×C42—22no—
357C2×C42—24no—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—42no—
361C2×C42C2×C4×C714yes—
362C2×C42C7×Q814yes—
363#95—24no—
364#95—24no—
365#95—22no—
366#95—24no—
367#95—22no—
368#95—22no—
369#95—22no—
370#95—24no—
371#95—42no—
372#95—42no—
373#95—42no—
374#95—42no—
375C22×C7C22×C22⋊C411yescharacteristic
376C22×C7C2×C4×Q811yescharacteristic
377C22×C7C2×C4×Q811yescharacteristic
378C22×C7C4×#4111yescharacteristic
379C22×C7C4×#4111yescharacteristic
380C22×C7#52011yescharacteristic
381C22×C7#52011yescharacteristic
382C22×C7C2×C22⋊Q811yescharacteristic
383C22×C7C2×C22⋊Q811yescharacteristic
384C22×C7C2×#12411yescharacteristic
385C22×C7C2×#12511yescharacteristic
386C22×C7#52911yescharacteristic
387C22×C7#52911yescharacteristic
388C22×C7C2×C4⋊Q811yescharacteristic
389C22×C7#53311yescharacteristic
390C22×C7#54011yescharacteristic
391C22×C7#54111yescharacteristic
392C22×C7#54411yescharacteristic
393C22×C7#54411yescharacteristic
394C22×C7#54611yescharacteristic
395C22×C7#54611yescharacteristic
396C22×C7#54711yescharacteristic
397C22×C7#54711yescharacteristic
398C22×C7#54811yescharacteristic
399C22×C7#54811yescharacteristic
400C22×C7#55011yescharacteristic
401C22×C7#55011yescharacteristic
402C22×C7#55211yescharacteristic
403C22×C7#55211yescharacteristic
404C22×C7#55311yescharacteristic
405C22×C7#55311yescharacteristic
406C22×C7#55411yescharacteristic
407C22×C7#55411yescharacteristic
408C22×C7#55711yescharacteristic
409C22×C7#55711yescharacteristic
410C4×C7—28no—
411C4×C7—24no—
412C4×C7—42no—
413C4×C7—42no—
414C4×C7—44no—
415C4×C7—42no—
416C4×C7—44no—
417C4×C7—42no—
418C4×C7—42no—
419C4×C7—82no—
420C4×C7#39118yes—
421C24C24×C711yescharacteristic
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4C22×C4×C712yes—
480C22×C4C22×C4×C712yes—
481C22×C4C22×C4×C714yes—
482C22×C4C22×C4×C714yes—
483C22×C4C22×C4×C712yes—
484C22×C4C2×C7×D414yes—
485C22×C4C2×C7×D414yes—
486C22×C4C2×C7×D412yes—
487C22×C4C2×C7×D412yes—
488C22×C4C2×C7×Q812yes—
489C22×C4C2×C7×Q814yes—
490C22×C4C2×C7×Q812yes—
491C22×C4C2×C7×Q812yes—
492C22×C4C2×C7×Q812yes—
493C22×C4C7×#4112yes—
494C22×C4C7×#4112yes—
495C22×C4C7×#4112yes—
496C22×C4C7×#4112yes—
497C22×C4C7×#4112yes—
498C22×C4C7×#4112yes—
499C4⋊C4—216no—
500C4⋊C4—216no—
501C4⋊C4—28no—
502C4⋊C4—28no—
503C4⋊C4—48no—
504C4⋊C4—44no—
505C4⋊C4C7×C22⋊C4116yes—
506C42—28no—
507C42—28no—
508C42—48no—
509C42—44no—
510C2×C7C2×#39111yescharacteristic
511C2×C7C4×#12511yescharacteristic
512C2×C7#233011yescharacteristic
513C2×C7#233911yescharacteristic
514C2×C7#234111yescharacteristic
515C2×C7#237011yescharacteristic
516C2×C7#237011yescharacteristic
517C2×C7#244111yescharacteristic
518C2×C7#244211yescharacteristic
519C2×C7#245311yescharacteristic
520C2×C7#245411yescharacteristic
521C2×C7#248911yescharacteristic
522C2×C7#249011yescharacteristic
523C2×C7#255011yescharacteristic
524C2×C7#255211yescharacteristic
525C23C23×C4×C711yescharacteristic
526C23C22×C7×D411yescharacteristic
527C23C22×C7×D411yescharacteristic
528C23C22×C7×Q811yescharacteristic
529C23C22×C7×Q811yescharacteristic
530C23C2×C7×#4111yescharacteristic
531C23C2×C7×#4111yescharacteristic
532C23C2×C7×#4111yescharacteristic
533C23C2×C7×#4111yescharacteristic
534C23C2×C7×#4111yescharacteristic
535C23C2×C7×#4111yescharacteristic
536C23C7×H(5,𝔽2)11yescharacteristic
537C23C7×H(5,𝔽2)11yescharacteristic
538C23C7×2−1+411yescharacteristic
539C23C7×2−1+411yescharacteristic
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4C2×C7×C22⋊C418yes—
609C2×C4C2×C7×C22⋊C414yes—
610C2×C4C4×C7×Q814yes—
611C2×C4C4×C7×Q814yes—
612C2×C4C7×C22⋊Q814yes—
613C2×C4C7×C22⋊Q814yes—
614C2×C4C7×#12414yes—
615C2×C4C7×#12514yescomplemented
616C2×C4C7×C4⋊Q814yes—
617C7#1405411yescharacteristic, direct product factor, Sylow
618C22C22×C7×C22⋊C411yescharacteristic
619C22C2×C4×C7×Q811yescharacteristic
620C22C2×C4×C7×Q811yescharacteristic
621C22C4×C7×#4111yescharacteristic
622C22C4×C7×#4111yescharacteristic
623C22C7×#52011yescharacteristic
624C22C7×#52011yescharacteristic
625C22C2×C7×C22⋊Q811yescharacteristic
626C22C2×C7×C22⋊Q811yescharacteristic
627C22C2×C7×#12411yescharacteristic
628C22C2×C7×#12511yescharacteristic
629C22C7×#52911yescharacteristic
630C22C7×#52911yescharacteristic
631C22C2×C7×C4⋊Q811yescharacteristic
632C22C7×#53311yescharacteristic
633C22C7×#54011yescharacteristic
634C22C7×#54111yescharacteristic
635C22C7×#54411yescharacteristic
636C22C7×#54411yescharacteristic
637C22C7×#54611yescharacteristic
638C22C7×#54611yescharacteristic
639C22C7×#54711yescharacteristic
640C22C7×#54711yescharacteristic
641C22C7×#54811yescharacteristic
642C22C7×#54811yescharacteristic
643C22C7×#55011yescharacteristic
644C22C7×#55011yescharacteristic
645C22C7×#55211yescharacteristic
646C22C7×#55211yescharacteristic
647C22C7×#55311yescharacteristic
648C22C7×#55311yescharacteristic
649C22C7×#55411yescharacteristic
650C22C7×#55411yescharacteristic
651C22C7×#55711yescharacteristic
652C22C7×#55711yescharacteristic
653C4—24no—
654C4—28no—
655C4—42no—
656C4—44no—
657C4—42no—
658C4—42no—
659C4—42no—
660C4—42no—
661C4—44no—
662C4—82no—
663C4C7×#39118yes—
664C2C2×C7×#39111yescharacteristic
665C2C4×C7×#12511yescharacteristic
666C2C7×#233011yescharacteristic
667C2C7×#233911yescharacteristic
668C2C7×#234111yescharacteristic
669C2C7×#237011yescharacteristic
670C2C7×#237011yescharacteristic
671C2C7×#244111yescharacteristic
672C2C7×#244211yescharacteristic
673C2C7×#245311yescharacteristic
674C2C7×#245411yescharacteristic
675C2C7×#248911yescharacteristic
676C2C7×#249011yescharacteristic
677C2C7×#255011yescharacteristic
678C2C7×#255211yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
14. C2×C7×#125C4semidirect
40. #14054C7direct (N × H)
200. C2×#125C4×C7semidirect
316. C2×C4×C7#125semidirect
615. C2×C4C7×#125semidirect
617. C7#14054direct (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
C2×C7×#3892
C2×C4×C7×C4⋊C42
C7×#14452
C7×#14412
C7×#14362
C7×C4⋊#952
C4×C7×#952
#140547