Finite Group Databasebeta

← C7×#16519 #13193735

Subgroups — C7×#16519 #13193735

Order 1792.

1690 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#396C212yesmaximal, complemented
2C2×C7×#394C211yesmaximal, characteristic
3C2×C7×#390C211yesmaximal, characteristic
4C2×C7×#387C211yesmaximal, characteristic, complemented
5C2×C7×#382C211yesmaximal, characteristic, complemented
6C7×#1444C211yesmaximal, characteristic, complemented
7C7×#1441C211yesmaximal, characteristic, complemented
8C7×#1440C212yesmaximal, complemented
9C7×#1439C212yesmaximal, complemented
10C7×#1439C212yesmaximal, complemented
11C7×#1438C211yesmaximal, characteristic
12C23×C7×D4C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2212yes—
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C7×C4⋊C4C2212yes—
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2212yes—
19C22×C7×C22⋊C4C2212yes—
20C22×C7×C22⋊C4C2212yes—
21C22×C7×C22⋊C4C2212yes—
22C22×C7×C22⋊C4C2212yes—
23C22×C7×C22⋊C4C2212yes—
24C22×C42×C7C2211yescharacteristic
25C7×#396—28no—
26C7×#394—24no—
27C7×#390—24no—
28C7×#387—24no—
29C7×#382—24no—
30C2×C7×#95C2212yes—
31C2×C7×#95C2211yescharacteristic
32C2×C7×#95C2212yes—
33C2×C7×#95C2211yescharacteristic
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2211yescharacteristic
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39C2×C7×#95C2211yescharacteristic
40#16519C711yesmaximal, characteristic, direct product factor, Sylow
41C25×C7C2312yes—
42C22×C7×D4—24no—
43C22×C7×D4—22no—
44C22×C7×D4—22no—
45C22×C7×D4—22no—
46C22×C7×D4—42no—
47C23×C4×C7C2311yescharacteristic
48C23×C4×C7C2312yes—
49C23×C4×C7C2311yescharacteristic
50C23×C4×C7C2312yes—
51C23×C4×C7C2311yescharacteristic
52C23×C4×C7C2311yescharacteristic
53C23×C4×C7C2312yes—
54C23×C4×C7C2311yescharacteristic
55C23×C4×C7C2311yescharacteristic
56C23×C4×C7C2311yescharacteristic
57C2×C7×C4⋊C4—22no—
58C2×C7×C4⋊C4—22no—
59C2×C7×C4⋊C4—24no—
60C2×C7×C4⋊C4—22no—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—24no—
64C2×C7×C4⋊C4—24no—
65C2×C7×C4⋊C4—22no—
66C2×C7×C4⋊C4—42no—
67C2×C7×C4⋊C4—42no—
68C2×C7×C4⋊C4—42no—
69C2×C7×C4⋊C4—42no—
70C2×C7×C4⋊C4D414yescomplemented
71C2×C7×C22⋊C4—24no—
72C2×C7×C22⋊C4—24no—
73C2×C7×C22⋊C4—24no—
74C2×C7×C22⋊C4—24no—
75C2×C7×C22⋊C4—24no—
76C2×C7×C22⋊C4—24no—
77C2×C7×C22⋊C4—24no—
78C2×C7×C22⋊C4—24no—
79C2×C7×C22⋊C4—24no—
80C2×C7×C22⋊C4—24no—
81C2×C7×C22⋊C4—42no—
82C2×C7×C22⋊C4—42no—
83C2×C7×C22⋊C4—42no—
84C2×C7×C22⋊C4—42no—
85C2×C7×C22⋊C4—42no—
86C2×C7×C22⋊C4—42no—
87C2×C7×C22⋊C4—42no—
88C2×C7×C22⋊C4—42no—
89C2×C42×C7—22no—
90C2×C42×C7—22no—
91C2×C42×C7D414yes—
92C7×#95—24no—
93C7×#95—22no—
94C7×#95—22no—
95C7×#95—22no—
96C7×#95—22no—
97C7×#95—22no—
98C7×#95—24no—
99C7×#95—42no—
100C7×#95—42no—
101C7×#95D414yes—
102C2×#396C2×C712yescomplemented
103C2×#394C2×C711yescharacteristic
104C2×#390C2×C711yescharacteristic
105C2×#387C2×C711yescharacteristic, complemented
106C2×#382C2×C711yescharacteristic, complemented
107#1444C2×C711yescharacteristic, complemented
108#1441C2×C711yescharacteristic, complemented
109#1440C2×C712yescomplemented
110#1439C2×C712yescomplemented
111#1439C2×C712yescomplemented
112#1438C2×C711yescharacteristic
113C24×C7—22no—
114C24×C7—22no—
115C24×C7—22no—
116C24×C7—22no—
117C24×C7—22no—
118C24×C7—22no—
119C24×C7—22no—
120C24×C7—22no—
121C24×C7—22no—
122C24×C7—22no—
123C24×C7—22no—
124C24×C7—22no—
125C24×C7—22no—
126C24×C7—22no—
127C24×C7#4114yes—
128C24×C7C2411yescharacteristic
129C2×C7×D4—28no—
130C2×C7×D4—48no—
131C2×C7×D4—48no—
132C2×C7×D4—44no—
133C2×C7×D4—44no—
134C22×C4×C7—21no—
135C22×C4×C7—21no—
136C22×C4×C7—22no—
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—21no—
146C22×C4×C7—22no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—22no—
151C22×C4×C7—22no—
152C22×C4×C7—21no—
153C22×C4×C7—22no—
154C22×C4×C7—22no—
155C22×C4×C7—22no—
156C22×C4×C7—22no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—21no—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—22no—
163C22×C4×C7—22no—
164C22×C4×C7—22no—
165C22×C4×C7—22no—
166C22×C4×C7—21no—
167C22×C4×C7—22no—
168C22×C4×C7—22no—
169C22×C4×C7—22no—
170C22×C4×C7—22no—
171C22×C4×C7—21no—
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—21no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7—21no—
183C22×C4×C7—22no—
184C22×C4×C7C2×D412yes—
185C22×C4×C7C2×D412yes—
186C22×C4×C7C2×D414yes—
187C22×C4×C7C2×D412yes—
188C22×C4×C7C2×D412yes—
189C22×C4×C7C2×D412yes—
190C22×C4×C7C2×D412yes—
191C22×C4×C7C2×D412yes—
192C22×C4×C7#4112yes—
193C22×C4×C7#4112yes—
194C7×C4⋊C4—28no—
195C7×C4⋊C4—48no—
196C7×C4⋊C4—44no—
197C7×C4⋊C4—48no—
198C7×C4⋊C4—44no—
199C7×C22⋊C4—48no—
200C7×C22⋊C4—48no—
201C7×C22⋊C4—48no—
202C7×C22⋊C4—48no—
203C7×C22⋊C4—48no—
204C7×C22⋊C4—48no—
205C42×C7—28no—
206C23×D4C22×C711yescharacteristic
207C22×C4⋊C4C22×C711yescharacteristic
208C22×C4⋊C4C22×C712yes—
209C22×C4⋊C4C22×C711yescharacteristic
210C22×C4⋊C4C22×C712yes—
211C22×C4⋊C4C22×C711yescharacteristic
212C22×C22⋊C4C22×C712yes—
213C22×C22⋊C4C22×C712yes—
214C22×C22⋊C4C22×C712yes—
215C22×C22⋊C4C22×C712yes—
216C22×C22⋊C4C22×C712yes—
217C22×C22⋊C4C22×C712yes—
218C22×C42C22×C711yescharacteristic
219#396—28no—
220#394—24no—
221#390—24no—
222#387—24no—
223#382—24no—
224C2×#95C22×C712yes—
225C2×#95C22×C711yescharacteristic
226C2×#95C22×C711yescharacteristic
227C2×#95C22×C711yescharacteristic
228C2×#95C22×C711yescharacteristic
229C2×#95C22×C712yes—
230C2×#95C22×C711yescharacteristic
231C2×#95C22×C712yes—
232C2×#95C22×C712yes—
233C2×#95C22×C711yescharacteristic
234C23×C7—24no—
235C23×C7—24no—
236C23×C7—24no—
237C23×C7—24no—
238C23×C7—24no—
239C23×C7—24no—
240C23×C7—24no—
241C23×C7—42no—
242C23×C7—42no—
243C23×C7—42no—
244C23×C7—42no—
245C23×C7—42no—
246C23×C7—42no—
247C23×C7—42no—
248C23×C7—42no—
249C23×C7—42no—
250C23×C7—42no—
251C23×C7—42no—
252C23×C7—42no—
253C23×C7—42no—
254C23×C7—42no—
255C23×C7—42no—
256C23×C7—42no—
257C23×C7—42no—
258C23×C7—42no—
259C23×C7—42no—
260C23×C7—42no—
261C23×C7—42no—
262C23×C7—42no—
263C23×C7—42no—
264C23×C7—42no—
265C23×C7—42no—
266C23×C7—42no—
267C23×C7—42no—
268C23×C7—42no—
269C23×C7C22×D411yescharacteristic
270C23×C7C22×D411yescharacteristic
271C23×C7C22×D411yescharacteristic
272C23×C7C2×#4111yescharacteristic
273C23×C7C2×#4111yescharacteristic
274C23×C7C2×#4112yes—
275C23×C7H(5,𝔽2)12yes—
276C23×C7H(5,𝔽2)12yes—
277C23×C7H(5,𝔽2)11yescharacteristic
278C23×C72−1+412yes—
279C23×C72−1+411yescharacteristic
280C7×D4—416no—
281C2×C4×C7—22no—
282C2×C4×C7—22no—
283C2×C4×C7—22no—
284C2×C4×C7—22no—
285C2×C4×C7—22no—
286C2×C4×C7—24no—
287C2×C4×C7—22no—
288C2×C4×C7—22no—
289C2×C4×C7—24no—
290C2×C4×C7—22no—
291C2×C4×C7—22no—
292C2×C4×C7—22no—
293C2×C4×C7—22no—
294C2×C4×C7—22no—
295C2×C4×C7—24no—
296C2×C4×C7—22no—
297C2×C4×C7—24no—
298C2×C4×C7—22no—
299C2×C4×C7—24no—
300C2×C4×C7—24no—
301C2×C4×C7—22no—
302C2×C4×C7—41no—
303C2×C4×C7—42no—
304C2×C4×C7—41no—
305C2×C4×C7—41no—
306C2×C4×C7—42no—
307C2×C4×C7—41no—
308C2×C4×C7—42no—
309C2×C4×C7—42no—
310C2×C4×C7—42no—
311C2×C4×C7—41no—
312C2×C4×C7—42no—
313C2×C4×C7—41no—
314C2×C4×C7—42no—
315C2×C4×C7—42no—
316C2×C4×C7—41no—
317C2×C4×C7—41no—
318C2×C4×C7—41no—
319C2×C4×C7—42no—
320C2×C4×C7—42no—
321C2×C4×C7—42no—
322C2×C4×C7—42no—
323C2×C4×C7—42no—
324C2×C4×C7—41no—
325C2×C4×C7—41no—
326C2×C4×C7—41no—
327C2×C4×C7—42no—
328C2×C4×C7—42no—
329C2×C4×C7—42no—
330C2×C4×C7—42no—
331C2×C4×C7—42no—
332C2×C4×C7—42no—
333C2×C4×C7—42no—
334C2×C4×C7—42no—
335C2×C4×C7—42no—
336C2×C4×C7—42no—
337C2×C4×C7—42no—
338C2×C4×C7—42no—
339C2×C4×C7#12114yes—
340C2×C4×C7#12114yes—
341C25C23×C712yes—
342C22×D4—24no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—42no—
347C23×C4C23×C712yes—
348C23×C4C23×C712yes—
349C23×C4C23×C711yescharacteristic
350C23×C4C23×C711yescharacteristic
351C23×C4C23×C711yescharacteristic
352C23×C4C23×C711yescharacteristic
353C23×C4C23×C712yes—
354C23×C4C23×C711yescharacteristic
355C23×C4C23×C711yescharacteristic
356C23×C4C23×C711yescharacteristic
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4C7×D414yescomplemented
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42C7×D414yes—
392#95—24no—
393#95—22no—
394#95—22no—
395#95—22no—
396#95—22no—
397#95—22no—
398#95—24no—
399#95—42no—
400#95—42no—
401#95C7×D414yes—
402C22×C7—44no—
403C22×C7—44no—
404C22×C7—44no—
405C22×C7—44no—
406C22×C7—44no—
407C22×C7—44no—
408C22×C7—44no—
409C22×C7—82no—
410C22×C7—82no—
411C22×C7—82no—
412C22×C7—82no—
413C22×C7—82no—
414C22×C7—82no—
415C22×C7—82no—
416C22×C7—82no—
417C22×C7C2×#12111yescharacteristic
418C22×C7C2×#12111yescharacteristic
419C22×C7#52511yescharacteristic
420C22×C7#53511yescharacteristic
421C22×C7#53511yescharacteristic
422C22×C7#53512yes—
423C22×C7#53611yescharacteristic
424C22×C7#53711yescharacteristic
425C22×C7#53712yes—
426C22×C7#53812yes—
427C22×C7#53912yes—
428C22×C7#54012yes—
429C22×C7#54212yes—
430C22×C7D4211yescharacteristic
431C22×C7#54612yes—
432C22×C7#54711yescharacteristic
433C22×C7#54811yescharacteristic
434C22×C7#54812yes—
435C22×C7#55112yes—
436C22×C7#55212yes—
437C22×C7#55311yescharacteristic
438C22×C7#56212yes—
439C22×C7#56312yes—
440C4×C7—24no—
441C4×C7—24no—
442C4×C7—42no—
443C4×C7—42no—
444C4×C7—42no—
445C4×C7—44no—
446C4×C7—82no—
447C4×C7—81no—
448C4×C7—81no—
449C4×C7—82no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24C7×#4114yes—
465C24C24×C711yescharacteristic
466C2×D4—28no—
467C2×D4—48no—
468C2×D4—48no—
469C2×D4—44no—
470C2×D4—44no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4C2×C7×D412yes—
522C22×C4C2×C7×D412yes—
523C22×C4C2×C7×D414yes—
524C22×C4C2×C7×D412yes—
525C22×C4C2×C7×D412yes—
526C22×C4C2×C7×D412yes—
527C22×C4C2×C7×D412yes—
528C22×C4C2×C7×D412yes—
529C22×C4C7×#4112yes—
530C22×C4C7×#4112yes—
531C4⋊C4—28no—
532C4⋊C4—48no—
533C4⋊C4—44no—
534C4⋊C4—48no—
535C4⋊C4—44no—
536C22⋊C4—48no—
537C22⋊C4—48no—
538C22⋊C4—48no—
539C22⋊C4—48no—
540C22⋊C4—48no—
541C22⋊C4—48no—
542C42—28no—
543C2×C7—84no—
544C2×C7#241111yescharacteristic
545C2×C7#241611yescharacteristic
546C2×C7#253611yescharacteristic
547C2×C7#261911yescharacteristic
548C2×C7#262011yescharacteristic
549C2×C7#263611yescharacteristic
550C2×C7#267612yes—
551C2×C7#270712yes—
552C2×C7#272312yes—
553C2×C7#276112yes—
554C2×C7#282011yescharacteristic
555C23—24no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23—24no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23C22×C7×D411yescharacteristic
591C23C22×C7×D411yescharacteristic
592C23C22×C7×D411yescharacteristic
593C23C2×C7×#4111yescharacteristic
594C23C2×C7×#4111yescharacteristic
595C23C2×C7×#4112yes—
596C23C7×H(5,𝔽2)12yes—
597C23C7×H(5,𝔽2)12yes—
598C23C7×H(5,𝔽2)11yescharacteristic
599C23C7×2−1+412yes—
600C23C7×2−1+411yescharacteristic
601D4—416no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—24no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—24no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—24no—
617C2×C4—22no—
618C2×C4—24no—
619C2×C4—22no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—22no—
623C2×C4—41no—
624C2×C4—42no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—41no—
633C2×C4—42no—
634C2×C4—41no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—41no—
645C2×C4—42no—
646C2×C4—41no—
647C2×C4—42no—
648C2×C4—41no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4C7×#12114yes—
661C2×C4C7×#12114yes—
662C7#1651911yescharacteristic, direct product factor, Sylow
663C22—44no—
664C22—44no—
665C22—44no—
666C22—44no—
667C22—44no—
668C22—44no—
669C22—44no—
670C22—82no—
671C22—82no—
672C22—82no—
673C22—82no—
674C22—82no—
675C22—82no—
676C22—82no—
677C22—82no—
678C22C2×C7×#12111yescharacteristic
679C22C2×C7×#12111yescharacteristic
680C22C7×#52511yescharacteristic
681C22C7×#53511yescharacteristic
682C22C7×#53512yes—
683C22C7×#53511yescharacteristic
684C22C7×#53611yescharacteristic
685C22C7×#53711yescharacteristic
686C22C7×#53712yes—
687C22C7×#53812yes—
688C22C7×#53912yes—
689C22C7×#54012yes—
690C22C7×#54212yes—
691C22C7×D4211yescharacteristic
692C22C7×#54612yes—
693C22C7×#54711yescharacteristic
694C22C7×#54811yescharacteristic
695C22C7×#54812yes—
696C22C7×#55112yes—
697C22C7×#55212yes—
698C22C7×#55311yescharacteristic
699C22C7×#56212yes—
700C22C7×#56312yes—
701C4—24no—
702C4—24no—
703C4—42no—
704C4—44no—
705C4—42no—
706C4—42no—
707C4—81no—
708C4—82no—
709C4—82no—
710C4—81no—
711C2—84no—
712C2C7×#241111yescharacteristic
713C2C7×#241611yescharacteristic
714C2C7×#253611yescharacteristic
715C2C7×#261911yescharacteristic
716C2C7×#262011yescharacteristic
717C2C7×#263611yescharacteristic
718C2C7×#267612yes—
719C2C7×#270712yes—
720C2C7×#272312yes—
721C2C7×#276112yes—
722C2C7×#282011yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC23×C7×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C7×#396C2semidirect
4. C2×C7×#387C2semidirect
5. C2×C7×#382C2semidirect
6. C7×#1444C2semidirect
7. C7×#1441C2semidirect
8. C7×#1440C2semidirect
9. C7×#1439C2semidirect
10. C7×#1439C2semidirect
40. #16519C7direct (N × H)
70. C2×C7×C4⋊C4D4semidirect
102. C2×#396C2×C7semidirect
105. C2×#387C2×C7semidirect
106. C2×#382C2×C7semidirect
107. #1444C2×C7semidirect
108. #1441C2×C7semidirect
109. #1440C2×C7semidirect
110. #1439C2×C7semidirect
111. #1439C2×C7semidirect
370. C2×C4⋊C4C7×D4semidirect
662. C7#16519direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3962
C2×C7×#3942
C2×C7×#3902
C2×C7×#3872
C2×C7×#3822
C7×#14442
C7×#14412
C7×#14402
C7×#14392
C7×#14382
#165197