Finite Group Databasebeta

← C7×#23919 #13201135

Subgroups — C7×#23919 #13201135

Order 1792.

2252 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×C22⋊Q8C211yesmaximal, characteristic, complemented
2C22×C7×#121C211yesmaximal, characteristic
3C2×C7×#448C212yesmaximal, complemented
4C2×C7×#450C212yesmaximal, complemented
5C7×#2000C214yesmaximal, complemented
6C7×#1874C212yesmaximal, complemented
7C7×#1872C212yesmaximal, complemented
8C7×#1779C211yesmaximal, characteristic, complemented
9C23×C7×Q8C2211yescharacteristic, complemented
10C23×C7×D4—21no—
11C23×C7×D4C2211yescharacteristic
12C24×C4×C7C2211yescharacteristic
13C22×C7×SD16C2214yescomplemented
14C2×C7×C22⋊Q8—21no—
15C2×C7×C22⋊Q8—21no—
16C2×C7×C22⋊Q8—28no—
17C2×C7×C22⋊Q8C2212yes—
18C2×C7×C22⋊Q8C2212yescomplemented
19C2×C7×#121—21no—
20C2×C7×#121—21no—
21C2×C7×#121—28no—
22C2×C7×#121C2212yes—
23C2×C7×#121C2212yes—
24C22×C7×C4⋊C4—21no—
25C22×C7×C4⋊C4C2211yescharacteristic
26C22×C7×C4⋊C4C2211yescharacteristic, complemented
27C22×C7×C22⋊C4—21no—
28C22×C7×C22⋊C4—21no—
29C7×#450—28no—
30C7×#448—28no—
31C2×C7×#103C2214yescomplemented
32C2×C7×#102C2214yescomplemented
33C2×C7×C22⋊C8C2212yes—
34C2×C7×C22⋊C8C2212yescomplemented
35C2×C7×C22⋊C8C2212yescomplemented
36C7×#340C2214yescomplemented
37#23919C711yesmaximal, characteristic, direct product factor, Sylow
38C25×C7—21no—
39C25×C7D411yescharacteristic
40C22×C7×Q8—24no—
41C22×C7×Q8—21no—
42C22×C7×Q8—24no—
43C22×C7×Q8—42no—
44C22×C7×Q8C2312yes—
45C22×C7×D4—28no—
46C22×C7×D4—22no—
47C22×C7×D4—22no—
48C22×C7×D4—24no—
49C22×C7×D4—21no—
50C22×C7×D4—24no—
51C22×C7×D4—42no—
52C22×C7×D4—44no—
53C22×C7×D4—44no—
54C22×C7×D4C2312yes—
55C23×C4×C7—21no—
56C23×C4×C7—21no—
57C23×C4×C7—21no—
58C23×C4×C7—24no—
59C23×C4×C7—24no—
60C23×C4×C7—42no—
61C23×C4×C7D411yescharacteristic
62C23×C4×C7D411yescharacteristic
63C23×C4×C7D411yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C2×C7×SD16—28no—
68C2×C7×SD16—28no—
69C2×C7×SD16—44no—
70C22×C7×C8C2314yes—
71C7×C22⋊Q8—28no—
72C7×C22⋊Q8—28no—
73C7×C22⋊Q8—24no—
74C7×C22⋊Q8—24no—
75C7×C22⋊Q8—24no—
76C7×C22⋊Q8D418yescomplemented
77C7×#121—28no—
78C7×#121—28no—
79C7×#121—24no—
80C7×#121—24no—
81C7×#121—24no—
82C7×#121D418yes—
83C2×C7×C4⋊C4—28no—
84C2×C7×C4⋊C4—22no—
85C2×C7×C4⋊C4—22no—
86C2×C7×C4⋊C4—21no—
87C2×C7×C4⋊C4—21no—
88C2×C7×C4⋊C4—24no—
89C2×C7×C4⋊C4—24no—
90C2×C7×C4⋊C4C2312yes—
91C2×C7×C4⋊C4C2312yes—
92C2×C7×C22⋊C4—28no—
93C2×C7×C22⋊C4—28no—
94C2×C7×C22⋊C4—22no—
95C2×C7×C22⋊C4—22no—
96C2×C7×C22⋊C4—22no—
97C2×C7×C22⋊C4—22no—
98C7×#103—28no—
99C7×#102—28no—
100C7×C22⋊C8—24no—
101C7×C22⋊C8—24no—
102C7×C22⋊C8—42no—
103C22×C22⋊Q8C2×C711yescharacteristic, complemented
104C22×#121C2×C711yescharacteristic
105C2×#448C2×C712yescomplemented
106C2×#450C2×C712yescomplemented
107#2000C2×C714yescomplemented
108#1874C2×C712yescomplemented
109#1872C2×C712yescomplemented
110#1779C2×C711yescharacteristic, complemented
111C24×C7—22no—
112C24×C7—22no—
113C24×C7—22no—
114C24×C7—22no—
115C24×C7—24no—
116C24×C7—22no—
117C24×C7—41no—
118C24×C7—41no—
119C24×C7—42no—
120C24×C7—42no—
121C24×C7—42no—
122C24×C7—42no—
123C24×C7—42no—
124C24×C7—42no—
125C24×C7SD1614yescomplemented
126C24×C7C2×D411yescharacteristic
127C24×C7C2×D411yescharacteristic
128C24×C7C2×D411yescharacteristic
129C2×C7×Q8—24no—
130C2×C7×Q8—22no—
131C2×C7×Q8—24no—
132C2×C7×Q8—24no—
133C2×C7×Q8—416no—
134C2×C7×Q8—42no—
135C2×C7×Q8—42no—
136C2×C7×Q8C2×D414yescomplemented
137C2×C7×D4—24no—
138C2×C7×D4—28no—
139C2×C7×D4—28no—
140C2×C7×D4—24no—
141C2×C7×D4—22no—
142C2×C7×D4—24no—
143C2×C7×D4—416no—
144C2×C7×D4—42no—
145C2×C7×D4—432no—
146C2×C7×D4—44no—
147C2×C7×D4—44no—
148C2×C7×D4—44no—
149C2×C7×D4—44no—
150C2×C7×D4—42no—
151C2×C7×D4C2×D414yes—
152C22×C4×C7—22no—
153C22×C4×C7—22no—
154C22×C4×C7—22no—
155C22×C4×C7—22no—
156C22×C4×C7—24no—
157C22×C4×C7—24no—
158C22×C4×C7—24no—
159C22×C4×C7—22no—
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×C7—22no—
168C22×C4×C7—22no—
169C22×C4×C7—22no—
170C22×C4×C7—22no—
171C22×C4×C7—41no—
172C22×C4×C7—41no—
173C22×C4×C7—41no—
174C22×C4×C7—416no—
175C22×C4×C7—42no—
176C22×C4×C7—42no—
177C22×C4×C7—42no—
178C22×C4×C7—42no—
179C22×C4×C7—42no—
180C22×C4×C7—42no—
181C22×C4×C7C2×D411yescharacteristic
182C22×C4×C7C2×D411yescharacteristic
183C22×C4×C7C2×D411yescharacteristic
184C22×C4×C7C2×D414yes—
185C22×C4×C7C2×D414yes—
186C22×C4×C7C2411yescharacteristic
187C7×SD16—416no—
188C2×C7×C8—24no—
189C2×C7×C8—24no—
190C2×C7×C8—24no—
191C7×C4⋊C4—24no—
192C7×C4⋊C4—24no—
193C7×C4⋊C4—28no—
194C7×C4⋊C4—28no—
195C7×C4⋊C4—22no—
196C7×C4⋊C4—22no—
197C7×C4⋊C4C2×D414yes—
198C7×C4⋊C4C2×D414yescomplemented
199C7×C22⋊C4—28no—
200C7×C22⋊C4—28no—
201C7×C22⋊C4—28no—
202C7×C22⋊C4—28no—
203C23×Q8C22×C711yescharacteristic, complemented
204C23×D4—21no—
205C23×D4C22×C711yescharacteristic
206C24×C4C22×C711yescharacteristic
207C22×SD16C22×C714yescomplemented
208C2×C22⋊Q8—21no—
209C2×C22⋊Q8—21no—
210C2×C22⋊Q8—28no—
211C2×C22⋊Q8C22×C712yes—
212C2×C22⋊Q8C22×C712yescomplemented
213C2×#121—21no—
214C2×#121—21no—
215C2×#121—28no—
216C2×#121C22×C712yes—
217C2×#121C22×C712yes—
218C22×C4⋊C4—21no—
219C22×C4⋊C4C22×C711yescharacteristic
220C22×C4⋊C4C22×C711yescharacteristic, complemented
221C22×C22⋊C4—21no—
222C22×C22⋊C4—21no—
223#450—28no—
224#448—28no—
225C2×#103C22×C714yescomplemented
226C2×#102C22×C714yescomplemented
227C2×C22⋊C8C22×C712yes—
228C2×C22⋊C8C22×C712yescomplemented
229C2×C22⋊C8C22×C712yescomplemented
230#340C22×C714yescomplemented
231C23×C7—21no—
232C23×C7—21no—
233C23×C7—21no—
234C23×C7—21no—
235C23×C7—21no—
236C23×C7—21no—
237C23×C7—21no—
238C23×C7—21no—
239C23×C7—21no—
240C23×C7—21no—
241C23×C7—21no—
242C23×C7—21no—
243C23×C7—21no—
244C23×C7—21no—
245C23×C7—28no—
246C23×C7—28no—
247C23×C7—24no—
248C23×C7—44no—
249C23×C7—44no—
250C23×C7—44no—
251C23×C7—44no—
252C23×C7—44no—
253C23×C7—48no—
254C23×C7—48no—
255C23×C7—48no—
256C23×C7—42no—
257C23×C7—42no—
258C23×C7—42no—
259C23×C7—42no—
260C23×C7—42no—
261C23×C7—42no—
262C23×C7—84no—
263C23×C7—84no—
264C23×C7—84no—
265C23×C7—84no—
266C23×C7#12012yes—
267C23×C7#12012yes—
268C23×C7C2×SD1612yes—
269C23×C7C2×SD1612yes—
270C23×C7C2×SD1612yes—
271C23×C7AGL(1,ℤ/8)12yes—
272C23×C7#13712yes—
273C23×C7C22×D411yescharacteristic
274C7×Q8—28no—
275C7×Q8—48no—
276C7×Q8—44no—
277C7×D4—28no—
278C7×D4—48no—
279C7×D4—416no—
280C7×D4—416no—
281C7×D4—44no—
282C2×C4×C7—21no—
283C2×C4×C7—21no—
284C2×C4×C7—21no—
285C2×C4×C7—21no—
286C2×C4×C7—28no—
287C2×C4×C7—28no—
288C2×C4×C7—21no—
289C2×C4×C7—24no—
290C2×C4×C7—24no—
291C2×C4×C7—24no—
292C2×C4×C7—21no—
293C2×C4×C7—21no—
294C2×C4×C7—44no—
295C2×C4×C7—44no—
296C2×C4×C7—44no—
297C2×C4×C7—48no—
298C2×C4×C7—48no—
299C2×C4×C7—48no—
300C2×C4×C7—42no—
301C2×C4×C7—42no—
302C2×C4×C7—42no—
303C2×C4×C7—42no—
304C2×C4×C7—42no—
305C2×C4×C7—42no—
306C2×C4×C7—44no—
307C2×C4×C7#12012yes—
308C2×C4×C7#12012yes—
309C2×C4×C7C22×D412yes—
310C2×C4×C7C22×D412yes—
311C2×C4×C7H(5,𝔽2)12yes—
312C7×C8—44no—
313C25—21no—
314C25C7×D411yescharacteristic
315C22×Q8—24no—
316C22×Q8—21no—
317C22×Q8—24no—
318C22×Q8—42no—
319C22×Q8C23×C712yes—
320C22×D4—28no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—24no—
324C22×D4—21no—
325C22×D4—24no—
326C22×D4—42no—
327C22×D4—44no—
328C22×D4—44no—
329C22×D4C23×C712yes—
330C23×C4—21no—
331C23×C4—21no—
332C23×C4—21no—
333C23×C4—24no—
334C23×C4—24no—
335C23×C4—42no—
336C23×C4C7×D411yescharacteristic
337C23×C4C7×D411yescharacteristic
338C23×C4C7×D411yescharacteristic
339C23×C4C23×C711yescharacteristic
340C23×C4C23×C711yescharacteristic
341C23×C4C23×C711yescharacteristic
342C2×SD16—28no—
343C2×SD16—28no—
344C2×SD16—44no—
345C22×C8C23×C714yes—
346C22⋊Q8—28no—
347C22⋊Q8—28no—
348C22⋊Q8—24no—
349C22⋊Q8—24no—
350C22⋊Q8—24no—
351C22⋊Q8C7×D418yescomplemented
352#121—28no—
353#121—28no—
354#121—24no—
355#121—24no—
356#121—24no—
357#121C7×D418yes—
358C2×C4⋊C4—28no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4C23×C712yes—
366C2×C4⋊C4C23×C712yes—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373#103—28no—
374#102—28no—
375C22⋊C8—24no—
376C22⋊C8—24no—
377C22⋊C8—42no—
378C22×C7—22no—
379C22×C7—22no—
380C22×C7—22no—
381C22×C7—22no—
382C22×C7—22no—
383C22×C7—22no—
384C22×C7—22no—
385C22×C7—22no—
386C22×C7—22no—
387C22×C7—22no—
388C22×C7—22no—
389C22×C7—22no—
390C22×C7—22no—
391C22×C7—22no—
392C22×C7—22no—
393C22×C7—416no—
394C22×C7—41no—
395C22×C7—41no—
396C22×C7—41no—
397C22×C7—41no—
398C22×C7—44no—
399C22×C7—44no—
400C22×C7—44no—
401C22×C7—816no—
402C22×C7—82no—
403C22×C7—82no—
404C22×C7—82no—
405C22×C7—82no—
406C22×C7#44814yescomplemented
407C22×C7#45014yescomplemented
408C22×C7C2×#12011yescharacteristic
409C22×C7C2×#12011yescharacteristic
410C22×C7#53411yescharacteristic
411C22×C7C22×SD1611yescharacteristic
412C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
413C22×C7C2×#13711yescharacteristic
414C22×C7#57511yescharacteristic
415C4×C7—22no—
416C4×C7—22no—
417C4×C7—41no—
418C4×C7—44no—
419C4×C7—44no—
420C4×C7—44no—
421C4×C7D4214yes—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—24no—
427C24—22no—
428C24—41no—
429C24—41no—
430C24—42no—
431C24—42no—
432C24—42no—
433C24—42no—
434C24—42no—
435C24—42no—
436C24C7×SD1614yescomplemented
437C24C2×C7×D411yescharacteristic
438C24C2×C7×D411yescharacteristic
439C24C2×C7×D411yescharacteristic
440C2×Q8—24no—
441C2×Q8—22no—
442C2×Q8—24no—
443C2×Q8—24no—
444C2×Q8—416no—
445C2×Q8—42no—
446C2×Q8—42no—
447C2×Q8C2×C7×D414yescomplemented
448C2×D4—24no—
449C2×D4—28no—
450C2×D4—28no—
451C2×D4—24no—
452C2×D4—22no—
453C2×D4—24no—
454C2×D4—416no—
455C2×D4—42no—
456C2×D4—432no—
457C2×D4—44no—
458C2×D4—44no—
459C2×D4—44no—
460C2×D4—44no—
461C2×D4—42no—
462C2×D4C2×C7×D414yes—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—416no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4C2×C7×D411yescharacteristic
493C22×C4C2×C7×D411yescharacteristic
494C22×C4C2×C7×D411yescharacteristic
495C22×C4C2×C7×D414yes—
496C22×C4C2×C7×D414yes—
497C22×C4C24×C711yescharacteristic
498SD16—416no—
499C2×C8—24no—
500C2×C8—24no—
501C2×C8—24no—
502C4⋊C4—24no—
503C4⋊C4—24no—
504C4⋊C4—28no—
505C4⋊C4—28no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4C2×C7×D414yes—
509C4⋊C4C2×C7×D414yescomplemented
510C22⋊C4—28no—
511C22⋊C4—28no—
512C22⋊C4—28no—
513C22⋊C4—28no—
514C2×C7—24no—
515C2×C7—24no—
516C2×C7—42no—
517C2×C7—84no—
518C2×C7#240311yescharacteristic
519C2×C7C2×#45011yescharacteristic
520C2×C7C2×#44811yescharacteristic
521C2×C7#300611yescharacteristic
522C2×C7#300711yescharacteristic
523C2×C7#318711yescharacteristic
524C2×C7#319311yescharacteristic
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—28no—
540C23—28no—
541C23—24no—
542C23—44no—
543C23—44no—
544C23—44no—
545C23—44no—
546C23—44no—
547C23—48no—
548C23—48no—
549C23—48no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—42no—
554C23—42no—
555C23—42no—
556C23—84no—
557C23—84no—
558C23—84no—
559C23—84no—
560C23C7×#12012yes—
561C23C7×#12012yes—
562C23C2×C7×SD1612yes—
563C23C2×C7×SD1612yes—
564C23C2×C7×SD1612yes—
565C23C7×AGL(1,ℤ/8)12yes—
566C23C7×#13712yes—
567C23C22×C7×D411yescharacteristic
568Q8—28no—
569Q8—48no—
570Q8—44no—
571D4—28no—
572D4—48no—
573D4—416no—
574D4—416no—
575D4—44no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—28no—
581C2×C4—28no—
582C2×C4—21no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4—44no—
591C2×C4—48no—
592C2×C4—48no—
593C2×C4—48no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—44no—
601C2×C4C7×#12012yes—
602C2×C4C7×#12012yes—
603C2×C4C22×C7×D412yes—
604C2×C4C22×C7×D412yes—
605C2×C4C7×H(5,𝔽2)12yes—
606C8—44no—
607C7#2391911yescharacteristic, direct product factor, Sylow
608C22—22no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—22no—
623C22—416no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—44no—
629C22—44no—
630C22—44no—
631C22—816no—
632C22—82no—
633C22—82no—
634C22—82no—
635C22—82no—
636C22C7×#44814yescomplemented
637C22C7×#45014yescomplemented
638C22C2×C7×#12011yescharacteristic
639C22C2×C7×#12011yescharacteristic
640C22C7×#53411yescharacteristic
641C22C22×C7×SD1611yescharacteristic
642C22C2×C7×AGL(1,ℤ/8)11yescharacteristic
643C22C2×C7×#13711yescharacteristic
644C22C7×#57511yescharacteristic
645C4—22no—
646C4—22no—
647C4—41no—
648C4—44no—
649C4—44no—
650C4—44no—
651C4C7×D4214yes—
652C2—24no—
653C2—24no—
654C2—42no—
655C2—84no—
656C2C7×#240311yescharacteristic
657C2C2×C7×#45011yescharacteristic
658C2C2×C7×#44811yescharacteristic
659C2C7×#300611yescharacteristic
660C2C7×#300711yescharacteristic
661C2C7×#318711yescharacteristic
662C2C7×#319311yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC22×C7×#121C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C24×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C7×C22⋊Q8C2semidirect
3. C2×C7×#448C2semidirect
4. C2×C7×#450C2semidirect
5. C7×#2000C2semidirect
6. C7×#1874C2semidirect
7. C7×#1872C2semidirect
8. C7×#1779C2semidirect
9. C23×C7×Q8C22semidirect
13. C22×C7×SD16C22semidirect
18. C2×C7×C22⋊Q8C22semidirect
26. C22×C7×C4⋊C4C22semidirect
31. C2×C7×#103C22semidirect
32. C2×C7×#102C22semidirect
34. C2×C7×C22⋊C8C22semidirect
35. C2×C7×C22⋊C8C22semidirect
36. C7×#340C22semidirect
37. #23919C7direct (N × H)
76. C7×C22⋊Q8D4semidirect
103. C22×C22⋊Q8C2×C7semidirect
105. C2×#448C2×C7semidirect
106. C2×#450C2×C7semidirect
107. #2000C2×C7semidirect
108. #1874C2×C7semidirect
109. #1872C2×C7semidirect
110. #1779C2×C7semidirect
125. C24×C7SD16semidirect
136. C2×C7×Q8C2×D4semidirect
198. C7×C4⋊C4C2×D4semidirect
203. C23×Q8C22×C7semidirect
207. C22×SD16C22×C7semidirect
212. C2×C22⋊Q8C22×C7semidirect
220. C22×C4⋊C4C22×C7semidirect
225. C2×#103C22×C7semidirect
226. C2×#102C22×C7semidirect
228. C2×C22⋊C8C22×C7semidirect
229. C2×C22⋊C8C22×C7semidirect
230. #340C22×C7semidirect
351. C22⋊Q8C7×D4semidirect
406. C22×C7#448semidirect
407. C22×C7#450semidirect
436. C24C7×SD16semidirect
447. C2×Q8C2×C7×D4semidirect
509. C4⋊C4C2×C7×D4semidirect
607. C7#23919direct (N × H)
636. C22C7×#448semidirect
637. C22C7×#450semidirect

Maximal subgroups

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

subgroupindex
C22×C7×C22⋊Q82
C22×C7×#1212
C2×C7×#4482
C2×C7×#4502
C7×#20002
C7×#18742
C7×#18722
C7×#17792
#239197