Finite Group Databasebeta

← #13403955

Subgroups — #13403955

Order 1792.

914 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2535C211yesmaximal, characteristic
2#11739828C211yesmaximal, characteristic, complemented
3C2×D4×C7⋊C8C211yesmaximal, characteristic, complemented
4C2×#89781C211yesmaximal, characteristic, complemented
5#11729435C211yesmaximal, characteristic, complemented
6#11729435C211yesmaximal, characteristic, complemented
7#11729434C211yesmaximal, characteristic, complemented
8#11729433C211yesmaximal, characteristic, complemented
9C4×#6406C211yesmaximal, characteristic, complemented
10#11727308C211yesmaximal, characteristic, complemented
11#11727294C211yesmaximal, characteristic, complemented
12#11727273C211yesmaximal, characteristic, complemented
13#11727266C211yesmaximal, characteristic, complemented
14#11727265C211yesmaximal, characteristic, complemented
15#11727261C211yesmaximal, characteristic, complemented
16C2×C7×#121C2211yescharacteristic
17C2×C7×#121C2211yescharacteristic
18C2×C4×C7×D4C2211yescharacteristic
19C2×C4×C7×D4C2211yescharacteristic
20C23×C7⋊C8C2211yescharacteristic
21C23×C7⋊C8C2211yescharacteristic
22C2×#6433C2211yescharacteristic
23C7×#397—21no—
24C7×#392—21no—
25C7×#386—21no—
26C7×#386—21no—
27C7×#382C2211yescharacteristic
28C7×#380C2211yescharacteristic
29C7×#380C2211yescharacteristic
30#89994—21no—
31C2×#6406C2211yescharacteristic
32C2×#6406C2211yescharacteristic
33C2×#6406C2211yescharacteristic
34C2×#6406C2211yescharacteristic
35#89984C2211yescharacteristic
36#89984C2211yescharacteristic
37#89984C2211yescharacteristic
38#89984C2211yescharacteristic
39C2×C22⋊(C7⋊C8)C2211yescharacteristic
40C2×C22⋊(C7⋊C8)C2211yescharacteristic
41D4×C7⋊C8—24no—
42#89781—24no—
43#89754—21no—
44C2×#6382C2211yescharacteristic
45C2×#6382C2211yescharacteristic
46C2×#6381C2211yescharacteristic
47C2×#6381C2211yescharacteristic
48#89717—21no—
49#89717—21no—
50C4×C4⋊Dic7C2211yescharacteristic
51C2×C4⋊(C7⋊C8)C2211yescharacteristic
52C2×C4×C7⋊C8C2211yescharacteristic
53#89324C2211yescharacteristic
54#89324C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89324C2211yescharacteristic
61#25342—71nomaximal, Sylow
62C22×C7×D4—21no—
63C22×C7×D4—21no—
64C22×C7×D4D411yescharacteristic
65C22×C7×D4C2311yescharacteristic
66C23×C4×C7—21no—
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C7×#121—22no—
70C7×#121—22no—
71C7×#121—41no—
72C7×#121—41no—
73C4×C7×D4—22no—
74C4×C7×D4—22no—
75C4×C7×D4—22no—
76C4×C7×D4—22no—
77C2×C7×C4⋊C4D411yescharacteristic
78C2×C7×C4⋊C4C2311yescharacteristic
79C2×C7×C4⋊C4C2311yescharacteristic
80C2×C7×C4⋊C4C2311yescharacteristic
81C2×C7×C22⋊C4—21no—
82C2×C7×C22⋊C4—21no—
83C2×C7×C22⋊C4—21no—
84C2×C7×C22⋊C4—21no—
85C2×C7×C22⋊C4—21no—
86C2×C7×C22⋊C4D411yescharacteristic
87C2×C7×C22⋊C4D411yescharacteristic
88C2×C42×C7C2311yescharacteristic
89C2×C22⋊Dic7—21no—
90C2×C22⋊Dic7—21no—
91C2×C22⋊Dic7—21no—
92C2×C22⋊Dic7—21no—
93C2×C4⋊Dic7C2311yescharacteristic
94C2×C4⋊Dic7C2311yescharacteristic
95C2×C4⋊Dic7C2311yescharacteristic
96C2×C4⋊Dic7C2311yescharacteristic
97C2×Dic7⋊C4—21no—
98C2×Dic7⋊C4—21no—
99C2×C4×Dic7—21no—
100C22×C7⋊C8—22no—
101C22×C7⋊C8—22no—
102C22×C7⋊C8—22no—
103C22×C7⋊C8—22no—
104C22×C7⋊C8—41no—
105C22×C7⋊C8—41no—
106C22×C7⋊C8C2311yescharacteristic
107C22×C7⋊C8C2311yescharacteristic
108C22×C7⋊C8C2311yescharacteristic
109C22×C7⋊C8C2311yescharacteristic
110#6433—22no—
111#6433—22no—
112C7×#95—21no—
113C7×#95—21no—
114C7×#95—21no—
115C7×#95—21no—
116#6406—22no—
117#6406—22no—
118#6406—22no—
119#6406—22no—
120C7⋊#95—21no—
121C7⋊#95—21no—
122C7⋊#95—21no—
123C7⋊#95—21no—
124C7⋊#95—21no—
125C22⋊(C7⋊C8)—22no—
126C22⋊(C7⋊C8)—22no—
127#6382—22no—
128#6382—41no—
129#6381—22no—
130#6381—41no—
131C4⋊(C7⋊C8)D414yescomplemented
132C4×C7⋊C8—22no—
133C2×#478—71no—
134C2×C8×D4—71no—
135#2562—71no—
136#2535D711yescharacteristic
137#2077—71no—
138#2076—71no—
139#2034—71no—
140#2033—71no—
141#1991—71no—
142#1949—71no—
143#1893—71no—
144#1893—71no—
145#1808—71no—
146#1807—71no—
147C4×#102—71no—
148C24×C7—21no—
149C24×C7C2×D411yescharacteristic
150C24×C7C2×D411yescharacteristic
151C2×C7×D4—22no—
152C2×C7×D4—22no—
153C2×C7×D4—22no—
154C2×C7×D4—21no—
155C2×C7×D4—21no—
156C2×C7×D4—21no—
157C2×C7×D4—21no—
158C2×C7×D4—21no—
159C2×C7×D4—42no—
160C2×C7×D4—42no—
161C2×C7×D4—42no—
162C2×C7×D4—42no—
163C2×C7×D4—81no—
164C2×C7×D4—81no—
165C2×C7×D4#4112yes—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—42no—
182C22×C4×C7—81no—
183C22×C4×C7—81no—
184C22×C4×C7C2×D411yescharacteristic
185C22×C4×C7C2×D411yescharacteristic
186C22×C4×C7C2×D411yescharacteristic
187C22×C4×C7C2×D411yescharacteristic
188C22×C4×C7C2411yescharacteristic
189C22×Dic7—21no—
190C22×Dic7—21no—
191C22×Dic7—21no—
192C22×Dic7—21no—
193C7×C4⋊C4—22no—
194C7×C4⋊C4—21no—
195C7×C4⋊C4—21no—
196C7×C4⋊C4—21no—
197C7×C4⋊C4—21no—
198C7×C4⋊C4—21no—
199C7×C4⋊C4—21no—
200C7×C22⋊C4—22no—
201C7×C22⋊C4—22no—
202C7×C22⋊C4—42no—
203C7×C22⋊C4—42no—
204C7×C22⋊C4—42no—
205C7×C22⋊C4—81no—
206C7×C22⋊C4—81no—
207C42×C7C2×D412yes—
208C42×C7#4112yes—
209C22⋊Dic7—42no—
210C22⋊Dic7—42no—
211C22⋊Dic7—81no—
212C22⋊Dic7—81no—
213C4⋊Dic7—21no—
214C4⋊Dic7—21no—
215C4⋊Dic7—21no—
216C4⋊Dic7—21no—
217C4⋊Dic7—21no—
218C4⋊Dic7—21no—
219C4⋊Dic7—21no—
220C4⋊Dic7—21no—
221Dic7⋊C4—42no—
222Dic7⋊C4—42no—
223C4×Dic7—81no—
224C2×C7⋊C8—21no—
225C2×C7⋊C8—21no—
226C2×C7⋊C8—21no—
227C2×C7⋊C8—21no—
228C2×C7⋊C8—21no—
229C2×C7⋊C8—21no—
230C2×C7⋊C8—21no—
231C2×C7⋊C8—21no—
232C2×C7⋊C8—21no—
233C2×C7⋊C8—44no—
234C2×C7⋊C8—44no—
235C2×C7⋊C8C2×D412yes—
236C2×C7⋊C8C2×D412yes—
237C2×C7⋊C8#4112yes—
238C23×C8—71no—
239C23×C8—71no—
240C2×#125—71no—
241C2×#121C2×D711yescharacteristic
242C2×#121C2×D711yescharacteristic
243C2×C4×D4C2×D711yescharacteristic
244C2×C4×D4C2×D711yescharacteristic
245#478—144no—
246C8×D4—144no—
247C2×#107—71no—
248C2×#107—71no—
249C2×#106—71no—
250C2×#106—71no—
251C2×C4⋊C8—71no—
252C2×#102—71no—
253C2×#102—71no—
254C2×#102—71no—
255C2×#102—71no—
256C2×C22⋊C8—71no—
257C2×C22⋊C8—71no—
258C2×C4×C8—71no—
259#400—141no—
260#397—21no—
261#394—141no—
262#392—21no—
263#388—141no—
264#388—141no—
265#386—21no—
266#386—21no—
267#382C2×D711yescharacteristic
268#380—71no—
269#380—71no—
270#380—71no—
271#380—71no—
272#380C2×D711yescharacteristic
273#380C2×D711yescharacteristic
274C4×C4⋊C4—71no—
275#340—71no—
276#340—71no—
277#340—71no—
278#340—71no—
279#340—71no—
280#340—71no—
281#340—71no—
282#340—71no—
283C23×C7—21no—
284C23×C7—21no—
285C23×C7—21no—
286C23×C7—21no—
287C23×C7—21no—
288C23×C7—21no—
289C23×C7—21no—
290C23×C7—21no—
291C23×C7—21no—
292C23×C7—21no—
293C23×C7—21no—
294C23×C7—21no—
295C23×C7—22no—
296C23×C7—41no—
297C23×C7—41no—
298C23×C7—41no—
299C23×C7—41no—
300C23×C7—41no—
301C23×C7—41no—
302C23×C7#13512yes—
303C23×C7#13512yes—
304C23×C7C22×D411yescharacteristic
305C7×D4—28no—
306C7×D4—22no—
307C7×D4—22no—
308C7×D4—41no—
309C7×D4—41no—
310C7×D4—84no—
311C7×D4—84no—
312C2×C4×C7—21no—
313C2×C4×C7—21no—
314C2×C4×C7—21no—
315C2×C4×C7—21no—
316C2×C4×C7—21no—
317C2×C4×C7—21no—
318C2×C4×C7—21no—
319C2×C4×C7—21no—
320C2×C4×C7—21no—
321C2×C4×C7—21no—
322C2×C4×C7—41no—
323C2×C4×C7—41no—
324C2×C4×C7—41no—
325C2×C4×C7—41no—
326C2×C4×C7—41no—
327C2×C4×C7—41no—
328C2×C4×C7—41no—
329C2×C4×C7—41no—
330C2×C4×C7—41no—
331C2×C4×C7—41no—
332C2×C4×C7—41no—
333C2×C4×C7—41no—
334C2×C4×C7—41no—
335C2×C4×C7—41no—
336C2×C4×C7—41no—
337C2×C4×C7—41no—
338C2×C4×C7—41no—
339C2×C4×C7—84no—
340C2×C4×C7#12112yes—
341C2×C4×C7#12112yes—
342C2×C4×C7C22×D411yescharacteristic
343C2×C4×C7C2×#4111yescharacteristic
344C2×C4×C7C2×#4111yescharacteristic
345C2×C4×C7C2×#4111yescharacteristic
346C2×C4×C7H(5,𝔽2)11yescharacteristic
347C2×C4×C72−1+411yescharacteristic
348C2×Dic7—41no—
349C2×Dic7—41no—
350C2×Dic7—41no—
351C2×Dic7—41no—
352C2×Dic7—41no—
353C2×Dic7—41no—
354C2×Dic7—41no—
355C2×Dic7—41no—
356C2×Dic7—41no—
357C2×Dic7—41no—
358C2×Dic7—41no—
359C2×Dic7—41no—
360C7⋊C8—22no—
361C7⋊C8—22no—
362C7⋊C8—22no—
363C7⋊C8—41no—
364C22×D4—21no—
365C22×D4—21no—
366C22×D4C22⋊D711yescharacteristic
367C22×D4C22×D711yescharacteristic
368C23×C4—21no—
369C23×C4C22×D711yescharacteristic
370C23×C4C22×D711yescharacteristic
371C22×C8—71no—
372C22×C8—71no—
373C22×C8—71no—
374C22×C8—71no—
375C22×C8—142no—
376C22×C8—142no—
377C22×C8—142no—
378C22×C8—142no—
379C22×C8—281no—
380C22×C8—281no—
381#125—142no—
382#125—142no—
383#121—22no—
384#121—22no—
385#121—41no—
386#121—41no—
387C4×D4—22no—
388C4×D4—22no—
389C4×D4—22no—
390C4×D4—22no—
391C2×C4⋊C4—71no—
392C2×C4⋊C4—71no—
393C2×C4⋊C4—71no—
394C2×C4⋊C4—71no—
395C2×C4⋊C4—141no—
396C2×C4⋊C4—141no—
397C2×C4⋊C4C22⋊D711yescharacteristic
398C2×C4⋊C4C22×D711yescharacteristic
399C2×C4⋊C4C22×D711yescharacteristic
400C2×C4⋊C4C22×D711yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—141no—
407C2×C22⋊C4—141no—
408C2×C22⋊C4—141no—
409C2×C22⋊C4—141no—
410C2×C22⋊C4C22⋊D711yescharacteristic
411C2×C22⋊C4C22⋊D711yescharacteristic
412C2×C42—141no—
413C2×C42C22×D711yescharacteristic
414#107—142no—
415#107—281no—
416#106—142no—
417#106—281no—
418C4⋊C8—74no—
419#102—142no—
420#102—142no—
421#102—142no—
422#102—142no—
423C22⋊C8—142no—
424C22⋊C8—142no—
425C4×C8—142no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—141no—
431#95—141no—
432#95—141no—
433#95—141no—
434#95—141no—
435C22×C7—22no—
436C22×C7—22no—
437C22×C7—22no—
438C22×C7—22no—
439C22×C7—22no—
440C22×C7—22no—
441C22×C7—41no—
442C22×C7—41no—
443C22×C7—41no—
444C22×C7—41no—
445C22×C7—41no—
446C22×C7—41no—
447C22×C7—41no—
448C22×C7—41no—
449C22×C7—42no—
450C22×C7—42no—
451C22×C7—42no—
452C22×C7—81no—
453C22×C7—81no—
454C22×C7—81no—
455C22×C7—81no—
456C22×C7C2×#12111yescharacteristic
457C22×C7#54611yescharacteristic
458C22×C7#54711yescharacteristic
459C22×C7C2×#13511yescharacteristic
460C22×C7C2×#13511yescharacteristic
461C22×C7#57611yescharacteristic
462C22×C7#57711yescharacteristic
463C4×C7—22no—
464C4×C7—22no—
465C4×C7—41no—
466C4×C7—41no—
467C4×C7—81no—
468C4×C7—81no—
469C4×C7—81no—
470C4×C7#52911yescharacteristic
471C4×C7#54211yescharacteristic
472C4×C7#54611yescharacteristic
473C4×C7#54811yescharacteristic
474Dic7—81no—
475Dic7—81no—
476Dic7—81no—
477Dic7—81no—
478C24—21no—
479C24C2×C22⋊D711yescharacteristic
480C24C2×C22⋊D711yescharacteristic
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—81no—
494C2×D4—81no—
495C2×D4#115912yes—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—42no—
512C22×C4—81no—
513C22×C4—81no—
514C22×C4—141no—
515C22×C4—141no—
516C22×C4—141no—
517C22×C4—141no—
518C22×C4C2×C22⋊D711yescharacteristic
519C22×C4C2×C22⋊D711yescharacteristic
520C22×C4C2×C22⋊D711yescharacteristic
521C22×C4C2×C22⋊D711yescharacteristic
522C22×C4C23×D711yescharacteristic
523C2×C8—72no—
524C2×C8—72no—
525C2×C8—72no—
526C2×C8—141no—
527C2×C8—141no—
528C2×C8—141no—
529C2×C8—141no—
530C2×C8—141no—
531C2×C8—141no—
532C2×C8—141no—
533C2×C8—141no—
534C2×C8—141no—
535C2×C8—284no—
536C2×C8—284no—
537C4⋊C4—22no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—141no—
545C4⋊C4—141no—
546C4⋊C4—141no—
547C4⋊C4—141no—
548C4⋊C4—141no—
549C4⋊C4—141no—
550C4⋊C4—141no—
551C4⋊C4—141no—
552C4⋊C4—282no—
553C4⋊C4—282no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—81no—
560C22⋊C4—81no—
561C22⋊C4—282no—
562C22⋊C4—282no—
563C22⋊C4—561no—
564C22⋊C4—561no—
565C42—561no—
566C42D4×D712yes—
567C42#115912yes—
568C2×C7—42no—
569C2×C7—42no—
570C2×C7—82no—
571C2×C7#242711yescharacteristic
572C2×C7#305011yescharacteristic
573C2×C7#306211yescharacteristic
574C2×C7#329611yescharacteristic
575C2×C7#329711yescharacteristic
576C2×C7#333711yescharacteristic
577C2×C7#333911yescharacteristic
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—22no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23#651312yes—
598C23#651312yes—
599C23C22×C22⋊D711yescharacteristic
600D4—28no—
601D4—22no—
602D4—22no—
603D4—41no—
604D4—41no—
605D4—84no—
606D4—84no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—84no—
635C2×C4—281no—
636C2×C4—281no—
637C2×C4—281no—
638C2×C4—281no—
639C2×C4—281no—
640C2×C4—281no—
641C2×C4—281no—
642C2×C4—281no—
643C2×C4—281no—
644C2×C4—281no—
645C2×C4—281no—
646C2×C4—281no—
647C2×C4#650212yes—
648C2×C4#650212yes—
649C2×C4C2×D4×D711yescharacteristic
650C2×C4C2×#115911yescharacteristic
651C2×C4C2×#115911yescharacteristic
652C2×C4#654811yescharacteristic
653C2×C4D7×#4111yescharacteristic
654C2×C4#655411yescharacteristic
655C8—142no—
656C8—142no—
657C8—142no—
658C8—281no—
659C7#2534211yescharacteristic, complemented, Sylow
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22C2×#650211yescharacteristic
682C22#9049711yescharacteristic
683C22C2×#651311yescharacteristic
684C22C2×#651311yescharacteristic
685C22#9051511yescharacteristic
686C22#9052611yescharacteristic
687C22#9052711yescharacteristic
688C4—22no—
689C4—22no—
690C4—41no—
691C4—41no—
692C4—81no—
693C4—81no—
694C4—81no—
695C4—561no—
696C4—561no—
697C4—561no—
698C4—561no—
699C4#9028911yescharacteristic
700C4#9029111yescharacteristic
701C4#9029411yescharacteristic
702C4#9030311yescharacteristic
703C2—42no—
704C2—42no—
705C2—82no—
706C2#1174009211yescharacteristic
707C2#1174036711yescharacteristic
708C2#1174082411yescharacteristic
709C2#1174093911yescharacteristic
710C2#1174094011yescharacteristic
711C2#1174105111yescharacteristic
712C2#1174105211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
Fitting, prime radicalC7×#2535C2
socleC23×C7C22×D4
hypercenter#2535D7
hypocenterC7#25342
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2535

Complements

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

NH ≅ G/Ntype
2. #11739828C2semidirect
3. C2×D4×C7⋊C8C2semidirect
4. C2×#89781C2semidirect
5. #11729435C2semidirect
6. #11729435C2semidirect
7. #11729434C2semidirect
8. #11729433C2semidirect
9. C4×#6406C2semidirect
10. #11727308C2semidirect
11. #11727294C2semidirect
12. #11727273C2semidirect
13. #11727266C2semidirect
14. #11727265C2semidirect
15. #11727261C2semidirect
131. C4⋊(C7⋊C8)D4semidirect
659. C7#25342semidirect

Maximal subgroups

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

subgroupindex
C7×#25352
#117398282
C2×D4×C7⋊C82
C2×#897812
#117294352
#117294342
#117294332
C4×#64062
#117273082
#117272942
#117272732
#117272662
#117272652
#117272612
#253427