Finite Group Databasebeta

← C7×#13974 #13191190

Subgroups — C7×#13974 #13191190

Order 1792.

1802 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#389C211yesmaximal, characteristic, complemented
2C2×C7×#388C212yesmaximal
3C2×C7×#380C211yesmaximal, characteristic
4C2×C7×#380C211yesmaximal, characteristic
5C2×C4×C7×C4⋊C4C211yesmaximal, characteristic, complemented
6C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
7C7×#1443C212yesmaximal, complemented
8C7×#1440C212yesmaximal
9C7×#1436C212yesmaximal, complemented
10C7×C4⋊#95C211yesmaximal, characteristic, complemented
11C7×C4⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C7C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2212yes—
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2212yes—
20C22×C7×C22⋊C4C2212yes—
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C42×C7C2211yescharacteristic
23C22×C42×C7C2212yes—
24C22×C42×C7C2211yescharacteristic
25C7×#389—24no—
26C7×#388—28no—
27C7×#380—24no—
28C7×#380C418yescomplemented
29C4×C7×C4⋊C4—24no—
30C4×C7×C22⋊C4—24no—
31C2×C7×#95C2211yescharacteristic
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2212yes—
34C2×C7×#95C2212yes—
35C2×C7×#95C2212yes—
36C2×C7×#95C2212yes—
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39C2×C7×#95C2212yes—
40C2×C7×#95C2212yes—
41#13974C711yesmaximal, characteristic, direct product factor, Sylow
42C25×C7C2311yescharacteristic
43C23×C4×C7—22no—
44C23×C4×C7—22no—
45C23×C4×C7—22no—
46C23×C4×C7—22no—
47C23×C4×C7—22no—
48C23×C4×C7—22no—
49C23×C4×C7C2×C414yes—
50C23×C4×C7C2312yes—
51C23×C4×C7C2312yes—
52C23×C4×C7C2311yescharacteristic
53C23×C4×C7C2312yes—
54C23×C4×C7C2311yescharacteristic
55C23×C4×C7C2311yescharacteristic
56C23×C4×C7C2312yes—
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C2×C7×C4⋊C4—22no—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—22no—
64C2×C7×C4⋊C4—22no—
65C2×C7×C4⋊C4—22no—
66C2×C7×C4⋊C4—22no—
67C2×C7×C4⋊C4—24no—
68C2×C7×C4⋊C4—24no—
69C2×C7×C4⋊C4—22no—
70C2×C7×C4⋊C4—24no—
71C2×C7×C4⋊C4—22no—
72C2×C7×C4⋊C4C2×C414yes—
73C2×C7×C4⋊C4C2×C414yes—
74C2×C7×C4⋊C4D414yes—
75C2×C7×C22⋊C4—24no—
76C2×C7×C22⋊C4—22no—
77C2×C7×C22⋊C4—24no—
78C2×C7×C22⋊C4—22no—
79C2×C7×C22⋊C4—22no—
80C2×C7×C22⋊C4—22no—
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—24no—
83C2×C7×C22⋊C4—24no—
84C2×C7×C22⋊C4—42no—
85C2×C7×C22⋊C4C2×C418yes—
86C2×C7×C22⋊C4D414yes—
87C2×C42×C7—22no—
88C2×C42×C7—22no—
89C2×C42×C7—22no—
90C2×C42×C7—24no—
91C2×C42×C7—24no—
92C2×C42×C7—22no—
93C2×C42×C7—22no—
94C2×C42×C7—42no—
95C2×C42×C7D414yes—
96C7×#95—22no—
97C7×#95—22no—
98C7×#95—24no—
99C7×#95—24no—
100C7×#95—24no—
101C7×#95—24no—
102C7×#95—24no—
103C7×#95—24no—
104C7×#95—42no—
105C7×#95C2×C418yes—
106C2×#389C2×C711yescharacteristic, complemented
107C2×#388C2×C712yes—
108C2×#380C2×C711yescharacteristic
109C2×#380C2×C711yescharacteristic
110C2×C4×C4⋊C4C2×C711yescharacteristic, complemented
111C2×C4×C22⋊C4C2×C711yescharacteristic
112#1443C2×C712yescomplemented
113#1440C2×C712yes—
114#1436C2×C712yescomplemented
115C4⋊#95C2×C711yescharacteristic, complemented
116C4⋊#95C2×C711yescharacteristic, complemented
117C24×C7—21no—
118C24×C7—21no—
119C24×C7—21no—
120C24×C7—21no—
121C24×C7—21no—
122C24×C7—21no—
123C24×C7—21no—
124C24×C7—21no—
125C24×C7—21no—
126C24×C7—21no—
127C24×C7—21no—
128C24×C7—21no—
129C24×C7C22×C412yes—
130C24×C7C2×D412yes—
131C24×C7#4112yes—
132C24×C7C2411yescharacteristic
133C22×C4×C7—21no—
134C22×C4×C7—21no—
135C22×C4×C7—21no—
136C22×C4×C7—21no—
137C22×C4×C7—21no—
138C22×C4×C7—21no—
139C22×C4×C7—21no—
140C22×C4×C7—22no—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
145C22×C4×C7—22no—
146C22×C4×C7—22no—
147C22×C4×C7—22no—
148C22×C4×C7—22no—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—22no—
155C22×C4×C7—22no—
156C22×C4×C7—21no—
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—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—22no—
171C22×C4×C7—22no—
172C22×C4×C7—22no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—22no—
178C22×C4×C7—21no—
179C22×C4×C7—28no—
180C22×C4×C7—28no—
181C22×C4×C7—28no—
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—44no—
190C22×C4×C7—44no—
191C22×C4×C7—44no—
192C22×C4×C7—44no—
193C22×C4×C7C22×C412yes—
194C22×C4×C7C22×C414yes—
195C22×C4×C7C22×C414yes—
196C22×C4×C7C22×C412yes—
197C22×C4×C7C2×D412yes—
198C22×C4×C7C2×D412yes—
199C22×C4×C7C2×D414yes—
200C22×C4×C7C2×D412yes—
201C22×C4×C7C2×D412yes—
202C22×C4×C7C2×D412yes—
203C22×C4×C7C2×D412yes—
204C22×C4×C7#4112yes—
205C22×C4×C7#4112yes—
206C22×C4×C7#4112yes—
207C22×C4×C7#4112yes—
208C22×C4×C7#4112yes—
209C22×C4×C7#4112yes—
210C7×C4⋊C4—28no—
211C7×C4⋊C4—28no—
212C7×C4⋊C4—28no—
213C7×C4⋊C4—48no—
214C7×C4⋊C4—44no—
215C7×C22⋊C4—28no—
216C7×C22⋊C4—216no—
217C7×C22⋊C4—28no—
218C7×C22⋊C4—48no—
219C42×C7—28no—
220C42×C7—48no—
221C42×C7—44no—
222C24×C4C22×C711yescharacteristic
223C22×C4⋊C4C22×C711yescharacteristic
224C22×C4⋊C4C22×C712yes—
225C22×C4⋊C4C22×C711yescharacteristic
226C22×C4⋊C4C22×C711yescharacteristic
227C22×C4⋊C4C22×C711yescharacteristic
228C22×C22⋊C4C22×C711yescharacteristic
229C22×C22⋊C4C22×C712yes—
230C22×C22⋊C4C22×C712yes—
231C22×C22⋊C4C22×C711yescharacteristic
232C22×C42C22×C711yescharacteristic
233C22×C42C22×C712yes—
234C22×C42C22×C711yescharacteristic
235#389—24no—
236#388—28no—
237#380—24no—
238#380C4×C718yescomplemented
239C4×C4⋊C4—24no—
240C4×C22⋊C4—24no—
241C2×#95C22×C712yes—
242C2×#95C22×C712yes—
243C2×#95C22×C712yes—
244C2×#95C22×C711yescharacteristic
245C2×#95C22×C712yes—
246C2×#95C22×C712yes—
247C2×#95C22×C712yes—
248C2×#95C22×C711yescharacteristic
249C2×#95C22×C712yes—
250C2×#95C22×C712yes—
251C23×C7—22no—
252C23×C7—22no—
253C23×C7—22no—
254C23×C7—22no—
255C23×C7—22no—
256C23×C7—22no—
257C23×C7—22no—
258C23×C7—22no—
259C23×C7—22no—
260C23×C7—22no—
261C23×C7—22no—
262C23×C7—22no—
263C23×C7—22no—
264C23×C7—22no—
265C23×C7—22no—
266C23×C7—22no—
267C23×C7—22no—
268C23×C7—22no—
269C23×C7—41no—
270C23×C7—41no—
271C23×C7—41no—
272C23×C7—41no—
273C23×C7—41no—
274C23×C7—41no—
275C23×C7—41no—
276C23×C7—41no—
277C23×C7—41no—
278C23×C7—41no—
279C23×C7—41no—
280C23×C7—41no—
281C23×C7—41no—
282C23×C7—41no—
283C23×C7—41no—
284C23×C7—41no—
285C23×C7C4×D414yes—
286C23×C7C23×C411yescharacteristic
287C23×C7C22×D411yescharacteristic
288C23×C7C22×D411yescharacteristic
289C23×C7C22×D411yescharacteristic
290C23×C7C2×#4111yescharacteristic
291C23×C7C2×#4111yescharacteristic
292C23×C7C2×#4111yescharacteristic
293C23×C7C2×#4111yescharacteristic
294C23×C7C2×#4111yescharacteristic
295C23×C7C2×#4111yescharacteristic
296C23×C7C2×#4111yescharacteristic
297C23×C7H(5,𝔽2)11yescharacteristic
298C23×C72−1+411yescharacteristic
299C23×C72−1+411yescharacteristic
300C23×C72−1+411yescharacteristic
301C2×C4×C7—22no—
302C2×C4×C7—22no—
303C2×C4×C7—22no—
304C2×C4×C7—22no—
305C2×C4×C7—22no—
306C2×C4×C7—22no—
307C2×C4×C7—22no—
308C2×C4×C7—24no—
309C2×C4×C7—24no—
310C2×C4×C7—24no—
311C2×C4×C7—24no—
312C2×C4×C7—22no—
313C2×C4×C7—22no—
314C2×C4×C7—24no—
315C2×C4×C7—24no—
316C2×C4×C7—22no—
317C2×C4×C7—22no—
318C2×C4×C7—24no—
319C2×C4×C7—22no—
320C2×C4×C7—22no—
321C2×C4×C7—22no—
322C2×C4×C7—24no—
323C2×C4×C7—24no—
324C2×C4×C7—22no—
325C2×C4×C7—22no—
326C2×C4×C7—22no—
327C2×C4×C7—22no—
328C2×C4×C7—42no—
329C2×C4×C7—41no—
330C2×C4×C7—41no—
331C2×C4×C7—42no—
332C2×C4×C7—41no—
333C2×C4×C7—41no—
334C2×C4×C7—41no—
335C2×C4×C7—41no—
336C2×C4×C7—42no—
337C2×C4×C7—42no—
338C2×C4×C7—42no—
339C2×C4×C7—41no—
340C2×C4×C7—41no—
341C2×C4×C7—42no—
342C2×C4×C7—42no—
343C2×C4×C7—42no—
344C2×C4×C7—41no—
345C2×C4×C7—42no—
346C2×C4×C7—42no—
347C2×C4×C7—41no—
348C2×C4×C7—41no—
349C2×C4×C7—41no—
350C2×C4×C7—41no—
351C2×C4×C7—42no—
352C2×C4×C7—42no—
353C2×C4×C7—41no—
354C2×C4×C7—41no—
355C2×C4×C7—41no—
356C2×C4×C7—416no—
357C2×C4×C7—42no—
358C2×C4×C7—42no—
359C2×C4×C7—42no—
360C2×C4×C7—42no—
361C2×C4×C7—42no—
362C2×C4×C7—42no—
363C2×C4×C7—42no—
364C2×C4×C7#11714yes—
365C2×C4×C7C4×D414yes—
366C2×C4×C7C4×D414yes—
367C2×C4×C7#12114yes—
368C2×C4×C7#12114yes—
369C2×C4×C7#12314yes—
370C2×C4×C7#12414yes—
371C2×C4×C7#12614yes—
372C25C23×C711yescharacteristic
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4C2×C4×C714yes—
380C23×C4C23×C712yes—
381C23×C4C23×C712yes—
382C23×C4C23×C712yes—
383C23×C4C23×C711yescharacteristic
384C23×C4C23×C712yes—
385C23×C4C23×C711yescharacteristic
386C23×C4C23×C711yescharacteristic
387C23×C4C23×C711yescharacteristic
388C23×C4C23×C711yescharacteristic
389C23×C4C23×C711yescharacteristic
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4C2×C4×C714yes—
403C2×C4⋊C4C2×C4×C714yes—
404C2×C4⋊C4C7×D414yes—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—24no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—42no—
415C2×C22⋊C4C2×C4×C718yes—
416C2×C22⋊C4C7×D414yes—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—24no—
421C2×C42—24no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—42no—
425C2×C42C7×D414yes—
426#95—22no—
427#95—22no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—42no—
435#95C2×C4×C718yes—
436C22×C7—24no—
437C22×C7—24no—
438C22×C7—24no—
439C22×C7—42no—
440C22×C7—42no—
441C22×C7—42no—
442C22×C7—42no—
443C22×C7—42no—
444C22×C7—42no—
445C22×C7—42no—
446C22×C7—42no—
447C22×C7—42no—
448C22×C7—42no—
449C22×C7—42no—
450C22×C7—42no—
451C22×C7C2×#11711yescharacteristic
452C22×C7C2×C4×D411yescharacteristic
453C22×C7C2×C4×D411yescharacteristic
454C22×C7C2×C4×D411yescharacteristic
455C22×C7C4×#4111yescharacteristic
456C22×C7#51911yescharacteristic
457C22×C7#52011yescharacteristic
458C22×C7C2×#12111yescharacteristic
459C22×C7C2×#12111yescharacteristic
460C22×C7C2×#12311yescharacteristic
461C22×C7#52511yescharacteristic
462C22×C7C2×#12411yescharacteristic
463C22×C7C2×#12611yescharacteristic
464C22×C7#52911yescharacteristic
465C22×C7#53211yescharacteristic
466C22×C7#53611yescharacteristic
467C22×C7#53711yescharacteristic
468C22×C7#54111yescharacteristic
469C22×C7#54211yescharacteristic
470C22×C7D4211yescharacteristic
471C22×C7#54711yescharacteristic
472C22×C7#54711yescharacteristic
473C22×C7#54711yescharacteristic
474C22×C7#54711yescharacteristic
475C22×C7#54811yescharacteristic
476C22×C7#54811yescharacteristic
477C22×C7#55211yescharacteristic
478C22×C7#55211yescharacteristic
479C22×C7#55211yescharacteristic
480C22×C7#55311yescharacteristic
481C22×C7#55311yescharacteristic
482C22×C7#55311yescharacteristic
483C22×C7#55611yescharacteristic
484C22×C7#55611yescharacteristic
485C22×C7#55611yescharacteristic
486C4×C7—24no—
487C4×C7—42no—
488C4×C7—44no—
489C4×C7—42no—
490C4×C7—44no—
491C4×C7—42no—
492C4×C7—42no—
493C4×C7—44no—
494C4×C7—82no—
495C4×C7#38818yescomplemented
496C24—21no—
497C24—21no—
498C24—21no—
499C24—21no—
500C24—21no—
501C24—21no—
502C24—21no—
503C24—21no—
504C24—21no—
505C24—21no—
506C24—21no—
507C24—21no—
508C24C22×C4×C712yes—
509C24C2×C7×D412yes—
510C24C7×#4112yes—
511C24C24×C711yescharacteristic
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—28no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4C22×C4×C712yes—
573C22×C4C22×C4×C714yes—
574C22×C4C22×C4×C714yes—
575C22×C4C22×C4×C712yes—
576C22×C4C2×C7×D412yes—
577C22×C4C2×C7×D412yes—
578C22×C4C2×C7×D414yes—
579C22×C4C2×C7×D412yes—
580C22×C4C2×C7×D412yes—
581C22×C4C2×C7×D412yes—
582C22×C4C2×C7×D412yes—
583C22×C4C7×#4112yes—
584C22×C4C7×#4112yes—
585C22×C4C7×#4112yes—
586C22×C4C7×#4112yes—
587C22×C4C7×#4112yes—
588C22×C4C7×#4112yes—
589C4⋊C4—28no—
590C4⋊C4—28no—
591C4⋊C4—28no—
592C4⋊C4—48no—
593C4⋊C4—44no—
594C22⋊C4—28no—
595C22⋊C4—216no—
596C22⋊C4—28no—
597C22⋊C4—48no—
598C42—28no—
599C42—48no—
600C42—44no—
601C2×C7—44no—
602C2×C7C2×#38811yescharacteristic
603C2×C7C4×#12111yescharacteristic
604C2×C7#232311yescharacteristic
605C2×C7#234411yescharacteristic
606C2×C7#234711yescharacteristic
607C2×C7#236111yescharacteristic
608C2×C7#236211yescharacteristic
609C2×C7#241511yescharacteristic
610C2×C7#241611yescharacteristic
611C2×C7#242111yescharacteristic
612C2×C7#242211yescharacteristic
613C2×C7#249411yescharacteristic
614C2×C7#249611yescharacteristic
615C2×C7#254711yescharacteristic
616C2×C7#256211yescharacteristic
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23C4×C7×D414yes—
652C23C23×C4×C711yescharacteristic
653C23C22×C7×D411yescharacteristic
654C23C22×C7×D411yescharacteristic
655C23C22×C7×D411yescharacteristic
656C23C2×C7×#4111yescharacteristic
657C23C2×C7×#4111yescharacteristic
658C23C2×C7×#4111yescharacteristic
659C23C2×C7×#4111yescharacteristic
660C23C2×C7×#4111yescharacteristic
661C23C2×C7×#4111yescharacteristic
662C23C2×C7×#4111yescharacteristic
663C23C7×H(5,𝔽2)11yescharacteristic
664C23C7×2−1+411yescharacteristic
665C23C7×2−1+411yescharacteristic
666C23C7×2−1+411yescharacteristic
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—416no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4C7×#11714yes—
731C2×C4C4×C7×D414yes—
732C2×C4C4×C7×D414yes—
733C2×C4C7×#12114yes—
734C2×C4C7×#12114yes—
735C2×C4C7×#12314yes—
736C2×C4C7×#12414yes—
737C2×C4C7×#12614yes—
738C7#1397411yescharacteristic, direct product factor, Sylow
739C22—24no—
740C22—24no—
741C22—24no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22C2×C7×#11711yescharacteristic
755C22C2×C4×C7×D411yescharacteristic
756C22C2×C4×C7×D411yescharacteristic
757C22C2×C4×C7×D411yescharacteristic
758C22C4×C7×#4111yescharacteristic
759C22C7×#51911yescharacteristic
760C22C7×#52011yescharacteristic
761C22C2×C7×#12111yescharacteristic
762C22C2×C7×#12111yescharacteristic
763C22C2×C7×#12311yescharacteristic
764C22C7×#52511yescharacteristic
765C22C2×C7×#12411yescharacteristic
766C22C2×C7×#12611yescharacteristic
767C22C7×#52911yescharacteristic
768C22C7×#53211yescharacteristic
769C22C7×#53611yescharacteristic
770C22C7×#53711yescharacteristic
771C22C7×#54111yescharacteristic
772C22C7×#54211yescharacteristic
773C22C7×D4211yescharacteristic
774C22C7×#54711yescharacteristic
775C22C7×#54711yescharacteristic
776C22C7×#54711yescharacteristic
777C22C7×#54711yescharacteristic
778C22C7×#54811yescharacteristic
779C22C7×#54811yescharacteristic
780C22C7×#55211yescharacteristic
781C22C7×#55211yescharacteristic
782C22C7×#55211yescharacteristic
783C22C7×#55311yescharacteristic
784C22C7×#55311yescharacteristic
785C22C7×#55311yescharacteristic
786C22C7×#55611yescharacteristic
787C22C7×#55611yescharacteristic
788C22C7×#55611yescharacteristic
789C4—24no—
790C4—42no—
791C4—44no—
792C4—42no—
793C4—42no—
794C4—44no—
795C4—42no—
796C4—44no—
797C4—82no—
798C4C7×#38818yescomplemented
799C2—44no—
800C2C2×C7×#38811yescharacteristic
801C2C4×C7×#12111yescharacteristic
802C2C7×#232311yescharacteristic
803C2C7×#234411yescharacteristic
804C2C7×#234711yescharacteristic
805C2C7×#236111yescharacteristic
806C2C7×#236211yescharacteristic
807C2C7×#241511yescharacteristic
808C2C7×#241611yescharacteristic
809C2C7×#242111yescharacteristic
810C2C7×#242211yescharacteristic
811C2C7×#249411yescharacteristic
812C2C7×#249611yescharacteristic
813C2C7×#254711yescharacteristic
814C2C7×#256211yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC25×C7C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C7×#389C2semidirect
5. C2×C4×C7×C4⋊C4C2semidirect
7. C7×#1443C2semidirect
9. C7×#1436C2semidirect
10. C7×C4⋊#95C2semidirect
11. C7×C4⋊#95C2semidirect
28. C7×#380C4semidirect
41. #13974C7direct (N × H)
106. C2×#389C2×C7semidirect
110. C2×C4×C4⋊C4C2×C7semidirect
112. #1443C2×C7semidirect
114. #1436C2×C7semidirect
115. C4⋊#95C2×C7semidirect
116. C4⋊#95C2×C7semidirect
238. #380C4×C7semidirect
495. C4×C7#388semidirect
738. C7#13974direct (N × H)
798. C4C7×#388semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3892
C2×C7×#3882
C2×C7×#3802
C2×C4×C7×C4⋊C42
C2×C4×C7×C22⋊C42
C7×#14432
C7×#14402
C7×#14362
C7×C4⋊#952
#139747