Finite Group Databasebeta

← C7×#13968 #13191184

Subgroups — C7×#13968 #13191184

Order 1792.

2742 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#123C211yesmaximal, characteristic
2C22×C4×C7×D4C211yesmaximal, characteristic
3C2×C7×#386C211yesmaximal, characteristic
4C2×C7×#381C211yesmaximal, characteristic, complemented
5C22×C7×#95C211yesmaximal, characteristic, complemented
6C7×#1441C212yesmaximal, complemented
7C7×#1440C212yesmaximal, complemented
8C7×#1436C212yesmaximal, complemented
9C7×C22⋊#95C212yesmaximal, complemented
10C7×C22⋊#95C211yesmaximal, characteristic, complemented
11C7×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C7×D4C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C24×C4×C7C2211yescharacteristic
15C24×C4×C7C2211yescharacteristic
16C24×C4×C7C2211yescharacteristic
17C2×C7×#123—24no—
18C2×C7×#123—24no—
19C2×C7×#123C418yescomplemented
20C2×C4×C7×D4—24no—
21C2×C4×C7×D4—24no—
22C2×C4×C7×D4—24no—
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C4⋊C4C2212yes—
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2212yes—
28C22×C7×C22⋊C4C2211yescharacteristic
29C22×C7×C22⋊C4C2212yes—
30C22×C7×C22⋊C4C2211yescharacteristic
31C22×C42×C7C2211yescharacteristic
32C7×#386—24no—
33C7×#381—24no—
34C2×C7×#95—24no—
35C2×C7×#95C2212yes—
36C2×C7×#95C2212yes—
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39C2×C7×#95C2212yes—
40C2×C7×#95C2212yes—
41C2×C7×#95C2212yes—
42C2×C7×#95C2212yes—
43C2×C7×#95C2212yes—
44#13968C711yesmaximal, characteristic, direct product factor, Sylow
45C25×C7C2311yescharacteristic
46C25×C7C2311yescharacteristic
47C22×C7×D4—22no—
48C22×C7×D4—22no—
49C22×C7×D4—22no—
50C22×C7×D4—22no—
51C22×C7×D4C2×C414yes—
52C22×C7×D4D414yes—
53C22×C7×D4D414yes—
54C23×C4×C7—22no—
55C23×C4×C7—22no—
56C23×C4×C7—22no—
57C23×C4×C7—22no—
58C23×C4×C7—22no—
59C23×C4×C7—22no—
60C23×C4×C7—22no—
61C23×C4×C7—22no—
62C23×C4×C7—22no—
63C23×C4×C7—22no—
64C23×C4×C7—22no—
65C23×C4×C7—22no—
66C23×C4×C7—24no—
67C23×C4×C7—24no—
68C23×C4×C7—22no—
69C23×C4×C7—22no—
70C23×C4×C7—24no—
71C23×C4×C7—42no—
72C23×C4×C7—42no—
73C23×C4×C7—42no—
74C23×C4×C7C2×C414yescomplemented
75C23×C4×C7D414yes—
76C23×C4×C7C2312yes—
77C23×C4×C7C2312yes—
78C23×C4×C7C2312yes—
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2312yes—
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2311yescharacteristic
85C7×#123—232no—
86C4×C7×D4—232no—
87C2×C7×C4⋊C4—22no—
88C2×C7×C4⋊C4—22no—
89C2×C7×C4⋊C4—22no—
90C2×C7×C4⋊C4—24no—
91C2×C7×C4⋊C4—24no—
92C2×C7×C4⋊C4C2×C418yescomplemented
93C2×C7×C22⋊C4—22no—
94C2×C7×C22⋊C4—22no—
95C2×C7×C22⋊C4—22no—
96C2×C7×C22⋊C4—22no—
97C2×C7×C22⋊C4—22no—
98C2×C7×C22⋊C4—24no—
99C2×C7×C22⋊C4—24no—
100C2×C7×C22⋊C4—22no—
101C2×C7×C22⋊C4—22no—
102C2×C7×C22⋊C4—22no—
103C2×C7×C22⋊C4—24no—
104C2×C7×C22⋊C4—22no—
105C2×C7×C22⋊C4—22no—
106C2×C7×C22⋊C4—24no—
107C2×C7×C22⋊C4—42no—
108C2×C7×C22⋊C4C2×C414yescomplemented
109C2×C7×C22⋊C4C2×C418yescomplemented
110C2×C7×C22⋊C4D414yes—
111C2×C42×C7—22no—
112C2×C42×C7—22no—
113C2×C42×C7—22no—
114C7×#95—24no—
115C7×#95—24no—
116C7×#95—24no—
117C7×#95—24no—
118C7×#95—24no—
119C7×#95—24no—
120C7×#95—24no—
121C7×#95—42no—
122C7×#95—42no—
123C22×#123C2×C711yescharacteristic
124C22×C4×D4C2×C711yescharacteristic
125C2×#386C2×C711yescharacteristic
126C2×#381C2×C711yescharacteristic, complemented
127C22×#95C2×C711yescharacteristic, complemented
128#1441C2×C712yescomplemented
129#1440C2×C712yescomplemented
130#1436C2×C712yescomplemented
131C22⋊#95C2×C711yescharacteristic, complemented
132C22⋊#95C2×C712yescomplemented
133C22⋊#95C2×C711yescharacteristic, complemented
134C24×C7—22no—
135C24×C7—22no—
136C24×C7—22no—
137C24×C7—22no—
138C24×C7—21no—
139C24×C7—21no—
140C24×C7—22no—
141C24×C7—22no—
142C24×C7—21no—
143C24×C7—21no—
144C24×C7—22no—
145C24×C7—22no—
146C24×C7C22×C412yes—
147C24×C7C22×C412yes—
148C24×C7C2×D412yes—
149C24×C7C2×D412yes—
150C24×C7C2×D412yes—
151C24×C7C2×D412yes—
152C24×C7C2×D412yes—
153C24×C7C2×D412yes—
154C24×C7#4112yes—
155C24×C7#4112yes—
156C24×C7C2411yescharacteristic
157C2×C7×D4—28no—
158C2×C7×D4—28no—
159C2×C7×D4—28no—
160C2×C7×D4—28no—
161C2×C7×D4—28no—
162C2×C7×D4—28no—
163C2×C7×D4C22⋊C4116yes—
164C22×C4×C7—21no—
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—28no—
172C22×C4×C7—28no—
173C22×C4×C7—28no—
174C22×C4×C7—28no—
175C22×C4×C7—28no—
176C22×C4×C7—28no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—22no—
184C22×C4×C7—22no—
185C22×C4×C7—22no—
186C22×C4×C7—22no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
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×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—28no—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—44no—
216C22×C4×C7—48no—
217C22×C4×C7—48no—
218C22×C4×C7—48no—
219C22×C4×C7—48no—
220C22×C4×C7—48no—
221C22×C4×C7—48no—
222C22×C4×C7—44no—
223C22×C4×C7—44no—
224C22×C4×C7—44no—
225C22×C4×C7—44no—
226C22×C4×C7—44no—
227C22×C4×C7—44no—
228C22×C4×C7—44no—
229C22×C4×C7—44no—
230C22×C4×C7C22×C414yes—
231C22×C4×C7C22×C414yes—
232C22×C4×C7C22×C412yes—
233C22×C4×C7C2×D412yes—
234C22×C4×C7C2×D412yes—
235C22×C4×C7C2×D412yes—
236C22×C4×C7C2×D412yes—
237C22×C4×C7C2×D412yes—
238C22×C4×C7C2×D412yes—
239C22×C4×C7#4114yes—
240C22×C4×C7#4114yes—
241C7×C4⋊C4—28no—
242C7×C4⋊C4—216no—
243C7×C22⋊C4—28no—
244C7×C22⋊C4—28no—
245C7×C22⋊C4—216no—
246C7×C22⋊C4—28no—
247C7×C22⋊C4—48no—
248C7×C22⋊C4—44no—
249C42×C7—28no—
250C23×D4C22×C711yescharacteristic
251C24×C4C22×C711yescharacteristic
252C24×C4C22×C711yescharacteristic
253C24×C4C22×C711yescharacteristic
254C24×C4C22×C711yescharacteristic
255C2×#123—24no—
256C2×#123—24no—
257C2×#123C4×C718yescomplemented
258C2×C4×D4—24no—
259C2×C4×D4—24no—
260C2×C4×D4—24no—
261C22×C4⋊C4C22×C711yescharacteristic
262C22×C4⋊C4C22×C712yes—
263C22×C22⋊C4C22×C711yescharacteristic
264C22×C22⋊C4C22×C711yescharacteristic
265C22×C22⋊C4C22×C712yes—
266C22×C22⋊C4C22×C711yescharacteristic
267C22×C22⋊C4C22×C712yes—
268C22×C22⋊C4C22×C711yescharacteristic
269C22×C42C22×C711yescharacteristic
270#386—24no—
271#381—24no—
272C2×#95—24no—
273C2×#95C22×C712yes—
274C2×#95C22×C712yes—
275C2×#95C22×C712yes—
276C2×#95C22×C712yes—
277C2×#95C22×C712yes—
278C2×#95C22×C712yes—
279C2×#95C22×C712yes—
280C2×#95C22×C712yes—
281C2×#95C22×C712yes—
282C23×C7—24no—
283C23×C7—24no—
284C23×C7—22no—
285C23×C7—22no—
286C23×C7—24no—
287C23×C7—22no—
288C23×C7—22no—
289C23×C7—24no—
290C23×C7—24no—
291C23×C7—24no—
292C23×C7—24no—
293C23×C7—24no—
294C23×C7—24no—
295C23×C7—24no—
296C23×C7—24no—
297C23×C7—24no—
298C23×C7—22no—
299C23×C7—22no—
300C23×C7—24no—
301C23×C7—24no—
302C23×C7—22no—
303C23×C7—22no—
304C23×C7—22no—
305C23×C7—22no—
306C23×C7—24no—
307C23×C7—24no—
308C23×C7—24no—
309C23×C7—24no—
310C23×C7—41no—
311C23×C7—41no—
312C23×C7—42no—
313C23×C7—41no—
314C23×C7—41no—
315C23×C7—42no—
316C23×C7—42no—
317C23×C7—42no—
318C23×C7—42no—
319C23×C7—42no—
320C23×C7C2×C22⋊C414yes—
321C23×C7C2×C22⋊C414yes—
322C23×C7C4×D414yes—
323C23×C7C4×D414yes—
324C23×C7#12014yes—
325C23×C7#12114yes—
326C23×C7#12114yes—
327C23×C7#12314yes—
328C23×C7C23×C411yescharacteristic
329C23×C7C22×D411yescharacteristic
330C23×C7C22×D411yescharacteristic
331C23×C7C22×D411yescharacteristic
332C23×C7C22×D411yescharacteristic
333C23×C7C2×#4111yescharacteristic
334C23×C7C2×#4111yescharacteristic
335C23×C7C2×#4112yes—
336C23×C7C2×#4112yes—
337C23×C7H(5,𝔽2)12yes—
338C23×C72−1+412yes—
339C7×D4—232no—
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—24no—
349C2×C4×C7—24no—
350C2×C4×C7—24no—
351C2×C4×C7—24no—
352C2×C4×C7—24no—
353C2×C4×C7—24no—
354C2×C4×C7—24no—
355C2×C4×C7—24no—
356C2×C4×C7—22no—
357C2×C4×C7—22no—
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—24no—
361C2×C4×C7—22no—
362C2×C4×C7—24no—
363C2×C4×C7—24no—
364C2×C4×C7—24no—
365C2×C4×C7—24no—
366C2×C4×C7—416no—
367C2×C4×C7—416no—
368C2×C4×C7—416no—
369C2×C4×C7—42no—
370C2×C4×C7—42no—
371C2×C4×C7—42no—
372C2×C4×C7—42no—
373C2×C4×C7—41no—
374C2×C4×C7—42no—
375C2×C4×C7—41no—
376C2×C4×C7—41no—
377C2×C4×C7—42no—
378C2×C4×C7—41no—
379C2×C4×C7—42no—
380C2×C4×C7—42no—
381C2×C4×C7—42no—
382C2×C4×C7—42no—
383C2×C4×C7—42no—
384C2×C4×C7—42no—
385C2×C4×C7—42no—
386C2×C4×C7—42no—
387C2×C4×C7—42no—
388C2×C4×C7—42no—
389C2×C4×C7—416no—
390C2×C4×C7—42no—
391C2×C4×C7—42no—
392C2×C4×C7—42no—
393C2×C4×C7—42no—
394C2×C4×C7—42no—
395C2×C4×C7—42no—
396C2×C4×C7—42no—
397C2×C4×C7C2×C22⋊C414yes—
398C2×C4×C7#12314yescomplemented
399C25C23×C711yescharacteristic
400C25C23×C711yescharacteristic
401C22×D4—22no—
402C22×D4—22no—
403C22×D4—22no—
404C22×D4—22no—
405C22×D4C2×C4×C714yes—
406C22×D4C7×D414yes—
407C22×D4C7×D414yes—
408C23×C4—22no—
409C23×C4—22no—
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—22no—
413C23×C4—22no—
414C23×C4—22no—
415C23×C4—22no—
416C23×C4—22no—
417C23×C4—22no—
418C23×C4—22no—
419C23×C4—22no—
420C23×C4—24no—
421C23×C4—24no—
422C23×C4—22no—
423C23×C4—22no—
424C23×C4—24no—
425C23×C4—42no—
426C23×C4—42no—
427C23×C4—42no—
428C23×C4C2×C4×C714yescomplemented
429C23×C4C7×D414yes—
430C23×C4C23×C712yes—
431C23×C4C23×C712yes—
432C23×C4C23×C712yes—
433C23×C4C23×C711yescharacteristic
434C23×C4C23×C711yescharacteristic
435C23×C4C23×C711yescharacteristic
436C23×C4C23×C712yes—
437C23×C4C23×C711yescharacteristic
438C23×C4C23×C711yescharacteristic
439#123—232no—
440C4×D4—232no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4C2×C4×C718yescomplemented
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—42no—
462C2×C22⋊C4C2×C4×C714yescomplemented
463C2×C22⋊C4C2×C4×C718yescomplemented
464C2×C22⋊C4C7×D414yes—
465C2×C42—22no—
466C2×C42—22no—
467C2×C42—22no—
468#95—24no—
469#95—24no—
470#95—24no—
471#95—24no—
472#95—24no—
473#95—24no—
474#95—24no—
475#95—42no—
476#95—42no—
477C22×C7—24no—
478C22×C7—28no—
479C22×C7—28no—
480C22×C7—24no—
481C22×C7—24no—
482C22×C7—28no—
483C22×C7—28no—
484C22×C7—24no—
485C22×C7—24no—
486C22×C7—24no—
487C22×C7—28no—
488C22×C7—24no—
489C22×C7—42no—
490C22×C7—44no—
491C22×C7—42no—
492C22×C7—42no—
493C22×C7—44no—
494C22×C7—44no—
495C22×C7—42no—
496C22×C7—42no—
497C22×C7—42no—
498C22×C7#38618yes—
499C22×C7C22×C22⋊C411yescharacteristic
500C22×C7C2×C4×D411yescharacteristic
501C22×C7C2×C4×D411yescharacteristic
502C22×C7C4×#4112yes—
503C22×C7#52012yes—
504C22×C7C2×#12011yescharacteristic
505C22×C7C2×#12111yescharacteristic
506C22×C7C2×#12111yescharacteristic
507C22×C7C2×#12311yescharacteristic
508C22×C7C2×#12311yescharacteristic
509C22×C7#52511yescharacteristic
510C22×C7#52912yes—
511C22×C7#53411yescharacteristic
512C22×C7#53611yescharacteristic
513C22×C7#53912yes—
514C22×C7#54612yes—
515C22×C7#54612yes—
516C22×C7#54612yes—
517C22×C7#54712yes—
518C22×C7#54712yes—
519C22×C7#54712yes—
520C22×C7#55112yes—
521C22×C7#55212yes—
522C4×C7—24no—
523C4×C7—24no—
524C4×C7—44no—
525C4×C7—42no—
526C4×C7—42no—
527C4×C7—42no—
528C4×C7—44no—
529C4×C7—44no—
530C4×C7—82no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—21no—
536C24—21no—
537C24—22no—
538C24—22no—
539C24—21no—
540C24—21no—
541C24—22no—
542C24—22no—
543C24C22×C4×C712yes—
544C24C22×C4×C712yes—
545C24C2×C7×D412yes—
546C24C2×C7×D412yes—
547C24C2×C7×D412yes—
548C24C2×C7×D412yes—
549C24C2×C7×D412yes—
550C24C2×C7×D412yes—
551C24C7×#4112yes—
552C24C7×#4112yes—
553C24C24×C711yescharacteristic
554C2×D4—28no—
555C2×D4—28no—
556C2×D4—28no—
557C2×D4—28no—
558C2×D4—28no—
559C2×D4—28no—
560C2×D4C7×C22⋊C4116yes—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—28no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—28no—
573C22×C4—28no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—28no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—44no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—48no—
618C22×C4—48no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4C22×C4×C714yes—
628C22×C4C22×C4×C714yes—
629C22×C4C22×C4×C712yes—
630C22×C4C2×C7×D412yes—
631C22×C4C2×C7×D412yes—
632C22×C4C2×C7×D412yes—
633C22×C4C2×C7×D412yes—
634C22×C4C2×C7×D412yes—
635C22×C4C2×C7×D412yes—
636C22×C4C7×#4114yes—
637C22×C4C7×#4114yes—
638C4⋊C4—28no—
639C4⋊C4—216no—
640C22⋊C4—28no—
641C22⋊C4—28no—
642C22⋊C4—216no—
643C22⋊C4—28no—
644C22⋊C4—48no—
645C22⋊C4—44no—
646C42—28no—
647C2×C7—28no—
648C2×C7—44no—
649C2×C7C2×#38611yescharacteristic
650C2×C7C4×#12311yescharacteristic
651C2×C7#232211yescharacteristic
652C2×C7#233912yes—
653C2×C7#235912yes—
654C2×C7#240511yescharacteristic
655C2×C7#240611yescharacteristic
656C2×C7#241912yes—
657C2×C7#242512yes—
658C2×C7#248611yescharacteristic
659C2×C7#253411yescharacteristic
660C23—24no—
661C23—24no—
662C23—22no—
663C23—22no—
664C23—24no—
665C23—22no—
666C23—22no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—22no—
677C23—22no—
678C23—24no—
679C23—24no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—41no—
689C23—41no—
690C23—42no—
691C23—41no—
692C23—41no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23C2×C7×C22⋊C414yes—
699C23C2×C7×C22⋊C414yes—
700C23C4×C7×D414yes—
701C23C4×C7×D414yes—
702C23C7×#12014yes—
703C23C7×#12114yes—
704C23C7×#12114yes—
705C23C7×#12314yes—
706C23C23×C4×C711yescharacteristic
707C23C22×C7×D411yescharacteristic
708C23C22×C7×D411yescharacteristic
709C23C22×C7×D411yescharacteristic
710C23C22×C7×D411yescharacteristic
711C23C2×C7×#4111yescharacteristic
712C23C2×C7×#4111yescharacteristic
713C23C2×C7×#4112yes—
714C23C2×C7×#4112yes—
715C23C7×H(5,𝔽2)12yes—
716C23C7×2−1+412yes—
717D4—232no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—416no—
745C2×C4—416no—
746C2×C4—416no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—416no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4C2×C7×C22⋊C414yes—
776C2×C4C7×#12314yescomplemented
777C7#1396811yescharacteristic, direct product factor, Sylow
778C22—24no—
779C22—24no—
780C22—28no—
781C22—28no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—28no—
787C22—28no—
788C22—24no—
789C22—28no—
790C22—42no—
791C22—42no—
792C22—44no—
793C22—44no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—44no—
799C22C7×#38618yes—
800C22C22×C7×C22⋊C411yescharacteristic
801C22C2×C4×C7×D411yescharacteristic
802C22C2×C4×C7×D411yescharacteristic
803C22C4×C7×#4112yes—
804C22C7×#52012yes—
805C22C2×C7×#12011yescharacteristic
806C22C2×C7×#12111yescharacteristic
807C22C2×C7×#12111yescharacteristic
808C22C2×C7×#12311yescharacteristic
809C22C2×C7×#12311yescharacteristic
810C22C7×#52511yescharacteristic
811C22C7×#52912yes—
812C22C7×#53411yescharacteristic
813C22C7×#53611yescharacteristic
814C22C7×#53912yes—
815C22C7×#54612yes—
816C22C7×#54612yes—
817C22C7×#54612yes—
818C22C7×#54712yes—
819C22C7×#54712yes—
820C22C7×#54712yes—
821C22C7×#55112yes—
822C22C7×#55212yes—
823C4—24no—
824C4—24no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—44no—
829C4—44no—
830C4—44no—
831C4—82no—
832C2—28no—
833C2—44no—
834C2C2×C7×#38611yescharacteristic
835C2C4×C7×#12311yescharacteristic
836C2C7×#232211yescharacteristic
837C2C7×#233912yes—
838C2C7×#235912yes—
839C2C7×#240511yescharacteristic
840C2C7×#240611yescharacteristic
841C2C7×#241912yes—
842C2C7×#242512yes—
843C2C7×#248611yescharacteristic
844C2C7×#253411yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC23×C7×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C7×#381C2semidirect
5. C22×C7×#95C2semidirect
6. C7×#1441C2semidirect
7. C7×#1440C2semidirect
8. C7×#1436C2semidirect
9. C7×C22⋊#95C2semidirect
10. C7×C22⋊#95C2semidirect
11. C7×C22⋊#95C2semidirect
19. C2×C7×#123C4semidirect
44. #13968C7direct (N × H)
74. C23×C4×C7C2×C4semidirect
92. C2×C7×C4⋊C4C2×C4semidirect
108. C2×C7×C22⋊C4C2×C4semidirect
109. C2×C7×C22⋊C4C2×C4semidirect
126. C2×#381C2×C7semidirect
127. C22×#95C2×C7semidirect
128. #1441C2×C7semidirect
129. #1440C2×C7semidirect
130. #1436C2×C7semidirect
131. C22⋊#95C2×C7semidirect
132. C22⋊#95C2×C7semidirect
133. C22⋊#95C2×C7semidirect
257. C2×#123C4×C7semidirect
398. C2×C4×C7#123semidirect
428. C23×C4C2×C4×C7semidirect
446. C2×C4⋊C4C2×C4×C7semidirect
462. C2×C22⋊C4C2×C4×C7semidirect
463. C2×C22⋊C4C2×C4×C7semidirect
776. C2×C4C7×#123semidirect
777. C7#13968direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1232
C22×C4×C7×D42
C2×C7×#3862
C2×C7×#3812
C22×C7×#952
C7×#14412
C7×#14402
C7×#14362
C7×C22⋊#952
#139687