Finite Group Databasebeta

← #13370016

Subgroups — #13370016

Order 1792.

1162 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90330C211yesmaximal, characteristic
2C2×C8×C22⋊D7C211yesmaximal, characteristic
3#11731457C211yesmaximal, characteristic
4C7×#1892C211yesmaximal, characteristic, complemented
5#11729723C211yesmaximal, characteristic, complemented
6#11729447C211yesmaximal, characteristic, complemented
7#11728024C211yesmaximal, characteristic, complemented
8#11728022C211yesmaximal, characteristic, complemented
9#11727976C211yesmaximal, characteristic, complemented
10Dic7×#103C211yesmaximal, characteristic, complemented
11#11727257C211yesmaximal, characteristic, complemented
12#11726625C211yesmaximal, characteristic, complemented
13D7×#340C211yesmaximal, characteristic, complemented
14#11726558C211yesmaximal, characteristic, complemented
15#11726556C211yesmaximal, characteristic, complemented
16C23×C7×C8C2211yescharacteristic
17C2×C7×C22⋊Q8C2211yescharacteristic
18C2×#6509C2211yescharacteristic
19C2×Q8×Dic7C2211yescharacteristic
20C2×C4×C22⋊D7C2211yescharacteristic
21C2×#6489C2211yescharacteristic
22C2×#6489C2211yescharacteristic
23C22×C8×D7C2211yescharacteristic
24#90330—24no—
25#90330C418yescomplemented
26C2×#6455—21no—
27C2×D7×C4⋊C4C2211yescharacteristic
28C2×D7×C4⋊C4C2211yescharacteristic
29C2×#6453C2211yescharacteristic
30C2×#6452—21no—
31C2×#6446—21no—
32C2×#6442—21no—
33C2×C7×#103C2211yescharacteristic
34C2×C7×#103C2211yescharacteristic
35C7×#380C2211yescharacteristic
36C2×#6409C2211yescharacteristic
37C2×#6409C2211yescharacteristic
38C2×C22⋊(C7⋊C8)C2211yescharacteristic
39C8×C22⋊D7—24no—
40C2×(C2×D7)⋊C8C2211yescharacteristic
41C2×Dic7⋊C8C2211yescharacteristic
42C2×C8×Dic7C2211yescharacteristic
43#89759C2211yescharacteristic
44#89749C2211yescharacteristic
45C4⋊C4×Dic7C2211yescharacteristic
46#89728—21no—
47#89716—21no—
48#89438—21no—
49#89424—21no—
50C7×#340C2211yescharacteristic
51C7×#340C2211yescharacteristic
52#89346C2211yescharacteristic
53#89346C2211yescharacteristic
54#89346C2211yescharacteristic
55#89346C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#22486—71nomaximal, Sylow
63C22×C7×Q8C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C22×C22⋊D7D411yescharacteristic
66C22×C4×D7—21no—
67C22×C4×D7—21no—
68C22×C4×D7C2311yescharacteristic
69C22×C7×C8—22no—
70C22×C7×C8—22no—
71C22×C7×C8—41no—
72C22×C7×C8C2311yescharacteristic
73C22×C7×C8C2311yescharacteristic
74C7×C22⋊Q8—22no—
75C7×C22⋊Q8C2×C414yescomplemented
76C2×C7×C4⋊C4—21no—
77C2×C7×C4⋊C4C2311yescharacteristic
78C2×C7×C4⋊C4C2311yescharacteristic
79C2×C7×C4⋊C4C2311yescharacteristic
80C2×C7×C22⋊C4—21no—
81C2×C7×C22⋊C4—21no—
82C2×C22⋊Dic7—21no—
83C2×C22⋊Dic7—21no—
84C2×C22⋊Dic7D411yescharacteristic
85#6509—22no—
86#6509C2×C414yes—
87Q8×Dic7—22no—
88Q8×Dic7C2×C414yescomplemented
89C4×C22⋊D7C2×C414yes—
90C4×C22⋊D7D414yes—
91C2×(C2×D7)⋊C4—21no—
92C2×(C2×D7)⋊C4—21no—
93C2×(C2×D7)⋊C4D411yescharacteristic
94#6489—22no—
95#6489—22no—
96#6489—41no—
97#6489C2×C414yescomplemented
98C2×C4⋊Dic7—21no—
99C2×C4⋊Dic7—21no—
100C2×C4⋊Dic7C2311yescharacteristic
101C2×C4⋊Dic7C2311yescharacteristic
102C2×C4⋊Dic7C2311yescharacteristic
103C2×C4⋊Dic7C2311yescharacteristic
104C2×Dic7⋊C4—21no—
105C2×Dic7⋊C4—21no—
106C2×Dic7⋊C4—21no—
107C2×Dic7⋊C4—21no—
108C2×Dic7⋊C4D411yescharacteristic
109C2×C4×Dic7—21no—
110C2×C4×Dic7—21no—
111C2×C4×Dic7—21no—
112C2×C4×Dic7—21no—
113C2×C4×Dic7C2311yescharacteristic
114C22×C7⋊C8C2311yescharacteristic
115C22×C7⋊C8C2311yescharacteristic
116C2×C8×D7—22no—
117C2×C8×D7—22no—
118C2×C8×D7—41no—
119#6455—28no—
120D7×C4⋊C4—22no—
121D7×C4⋊C4—22no—
122D7×C4⋊C4—41no—
123D7×C4⋊C4C2×C414yes—
124#6453—22no—
125#6453C2×C414yescomplemented
126#6452—28no—
127#6446—28no—
128#6442—28no—
129C7×#103—22no—
130C7×#103—41no—
131C7×#95—21no—
132#6409—22no—
133#6409—41no—
134C7⋊#95—21no—
135C7⋊#95—21no—
136C7⋊#95—21no—
137C7⋊#95—21no—
138C22⋊(C7⋊C8)—22no—
139(C2×D7)⋊C8—22no—
140Dic7⋊C8—22no—
141C8×Dic7—22no—
142C2×#552—71no—
143C2×C8×D4—71no—
144#2352—71no—
145#1991—71no—
146#1989—71no—
147#1892—71no—
148#1892D711yescharacteristic, complemented
149#1873—71no—
150#1872—71no—
151#1825—71no—
152#1823—71no—
153#1805—71no—
154C4×#103—71no—
155#1735—71no—
156C2×#340—71no—
157C24×C7C2×D411yescharacteristic
158C23×D7C2×D411yescharacteristic
159C2×C7×Q8—21no—
160C2×C7×Q8—21no—
161C2×C7×Q8—21no—
162C2×C7×Q8—21no—
163C2×C7×Q8—21no—
164C2×C7×Q8C22×C412yes—
165C22×C4×C7—21no—
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×C7C22×C412yes—
174C22×C4×C7C2×D411yescharacteristic
175C22×C4×C7C2×D412yes—
176C22×C4×C7C2411yescharacteristic
177C2×C22⋊D7—22no—
178C2×C22⋊D7—22no—
179C2×C22⋊D7C22⋊C414yes—
180C22×Dic7—21no—
181C22×Dic7—21no—
182C22×Dic7—21no—
183C22×Dic7—21no—
184C22×Dic7C2×D411yescharacteristic
185C22×Dic7C2×D411yescharacteristic
186C22×Dic7C2×D411yescharacteristic
187C2×C4×D7—21no—
188C2×C4×D7—21no—
189C2×C4×D7—21no—
190C2×C4×D7—21no—
191C2×C4×D7—24no—
192C2×C4×D7—42no—
193C2×C4×D7—42no—
194C2×C4×D7—42no—
195C2×C4×D7—42no—
196C2×C4×D7—81no—
197C2×C4×D7C22×C412yes—
198C2×C4×D7C2×D412yes—
199C2×C7×C8—21no—
200C2×C7×C8—21no—
201C2×C7×C8—21no—
202C2×C7×C8—21no—
203C2×C7×C8—21no—
204C2×C7×C8—44no—
205C2×C7×C8#4112yes—
206C7×C4⋊C4—24no—
207C7×C4⋊C4—21no—
208C7×C4⋊C4—21no—
209C7×C4⋊C4—21no—
210C7×C4⋊C4—21no—
211C7×C4⋊C4—21no—
212C7×C4⋊C4C22×C412yes—
213C7×C22⋊C4—24no—
214C7×C22⋊C4—81no—
215C22⋊Dic7—24no—
216C22⋊Dic7—42no—
217C22⋊Dic7C22⋊C414yes—
218(C2×D7)⋊C4—24no—
219(C2×D7)⋊C4—42no—
220(C2×D7)⋊C4C22⋊C414yes—
221C4⋊Dic7—21no—
222C4⋊Dic7—21no—
223C4⋊Dic7—21no—
224C4⋊Dic7—24no—
225C4⋊Dic7—24no—
226C4⋊Dic7—21no—
227C4⋊Dic7—21no—
228C4⋊Dic7C22×C412yes—
229C4⋊Dic7C22×C412yes—
230C4⋊Dic7#4112yes—
231Dic7⋊C4—24no—
232Dic7⋊C4—24no—
233Dic7⋊C4—24no—
234Dic7⋊C4—42no—
235Dic7⋊C4C22⋊C414yes—
236C4×Dic7—24no—
237C4×Dic7—24no—
238C4×Dic7—42no—
239C4×Dic7—81no—
240C4×Dic7C22×C412yes—
241C4×Dic7C2×D412yes—
242C2×C7⋊C8—21no—
243C2×C7⋊C8—21no—
244C2×C7⋊C8—21no—
245C2×C7⋊C8—21no—
246C2×C7⋊C8—21no—
247C2×C7⋊C8—21no—
248C8×D7—44no—
249C23×C8—71no—
250C23×C8C2×D711yescharacteristic
251#552—78no—
252#552—144no—
253C2×#126—141no—
254C2×#125—71no—
255C2×#125—141no—
256C2×#123—141no—
257C2×C22⋊Q8—71no—
258C2×C22⋊Q8C2×D711yescharacteristic
259C2×C4×Q8—71no—
260C2×C4×D4—71no—
261C2×#117—71no—
262C2×#117—71no—
263C2×#117—141no—
264C22×C4⋊C4—71no—
265C22×C4⋊C4—71no—
266C8×D4—144no—
267C2×C4⋊C8—71no—
268C2×#103—71no—
269C2×#103—71no—
270C2×#103C2×D711yescharacteristic
271C2×#103C2×D711yescharacteristic
272C2×C22⋊C8—71no—
273C2×C22⋊C8—71no—
274C2×C4×C8—71no—
275#388—141no—
276#387—141no—
277#386—141no—
278#382—71no—
279#380—71no—
280#380C2×D711yescharacteristic
281C4×C4⋊C4—71no—
282C4×C22⋊C4—141no—
283#340—71no—
284#340—71no—
285#340—71no—
286#340—71no—
287#340—71no—
288#340—71no—
289#340—71no—
290#340—71no—
291#340—71no—
292#340—71no—
293#340C2×D711yescharacteristic
294#340C2×D711yescharacteristic
295C23×C7—21no—
296C23×C7—21no—
297C23×C7—21no—
298C23×C7—21no—
299C23×C7—21no—
300C23×C7—21no—
301C23×C7C2×C22⋊C412yes—
302C23×C7C22×D411yescharacteristic
303C22×D7—21no—
304C22×D7—21no—
305C22×D7—21no—
306C22×D7—21no—
307C22×D7C2×C22⋊C412yes—
308C22×D7#13512yes—
309C22×D7#13512yes—
310C7×Q8—22no—
311C7×Q8—22no—
312C7×Q8—41no—
313C7×Q8—41no—
314C2×C4×C7—21no—
315C2×C4×C7—21no—
316C2×C4×C7—22no—
317C2×C4×C7—22no—
318C2×C4×C7—22no—
319C2×C4×C7—22no—
320C2×C4×C7—22no—
321C2×C4×C7—22no—
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×C7C2×C22⋊C412yes—
333C2×C4×C7C23×C411yescharacteristic
334C2×C4×C7C22×D411yescharacteristic
335C2×C4×C7C2×#4111yescharacteristic
336C2×C4×C7C2×#4111yescharacteristic
337C2×C4×C7H(5,𝔽2)11yescharacteristic
338C2×C4×C72−1+411yescharacteristic
339C22⋊D7—28no—
340C2×Dic7—21no—
341C2×Dic7—21no—
342C2×Dic7—21no—
343C2×Dic7—21no—
344C2×Dic7—21no—
345C2×Dic7—21no—
346C2×Dic7—22no—
347C2×Dic7—22no—
348C2×Dic7—22no—
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×Dic7C2×C22⋊C412yes—
359C2×Dic7C2×C22⋊C412yes—
360C2×Dic7C2×C22⋊C412yes—
361C4×D7—22no—
362C4×D7—22no—
363C4×D7—22no—
364C4×D7—22no—
365C4×D7—48no—
366C4×D7—84no—
367C7×C8—22no—
368C7×C8—41no—
369C7⋊C8—41no—
370C7⋊C8—41no—
371C22×Q8C22×D711yescharacteristic
372C22×D4—71no—
373C23×C4—71no—
374C23×C4—141no—
375C23×C4—141no—
376C23×C4C22×D711yescharacteristic
377C22×C8—22no—
378C22×C8—22no—
379C22×C8—41no—
380C22×C8—71no—
381C22×C8—71no—
382C22×C8—142no—
383C22×C8—142no—
384C22×C8—281no—
385C22×C8C22×D711yescharacteristic
386C22×C8C22×D711yescharacteristic
387#126—148no—
388#125—74no—
389#125—142no—
390#125—148no—
391#123—148no—
392C22⋊Q8—22no—
393C22⋊Q8—74no—
394C22⋊Q8—142no—
395C22⋊Q8C4×D714yescomplemented
396C4×Q8—74no—
397C4×Q8—142no—
398C4×D4—74no—
399C4×D4—74no—
400#117—74no—
401#117—148no—
402#117—142no—
403#117—142no—
404#117—281no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—71no—
407C2×C4⋊C4—71no—
408C2×C4⋊C4—71no—
409C2×C4⋊C4—71no—
410C2×C4⋊C4—74no—
411C2×C4⋊C4—71no—
412C2×C4⋊C4—142no—
413C2×C4⋊C4—142no—
414C2×C4⋊C4—141no—
415C2×C4⋊C4—141no—
416C2×C4⋊C4—141no—
417C2×C4⋊C4—141no—
418C2×C4⋊C4—141no—
419C2×C4⋊C4—141no—
420C2×C4⋊C4—281no—
421C2×C4⋊C4C22×D711yescharacteristic
422C2×C4⋊C4C22×D711yescharacteristic
423C2×C4⋊C4C22×D711yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—71no—
427C2×C22⋊C4—71no—
428C2×C22⋊C4—141no—
429C2×C22⋊C4—141no—
430C2×C22⋊C4—141no—
431C2×C22⋊C4—141no—
432C2×C42—71no—
433C2×C42—141no—
434C2×C42—141no—
435C2×C42—141no—
436C2×C42—141no—
437C4⋊C8—142no—
438#103—22no—
439#103—41no—
440#103—142no—
441#103—281no—
442C22⋊C8—142no—
443C22⋊C8—142no—
444C4×C8—142no—
445#95—21no—
446#95—141no—
447#95—141no—
448#95—141no—
449#95—141no—
450C22×C7—22no—
451C22×C7—22no—
452C22×C7—22no—
453C22×C7—41no—
454C22×C7—41no—
455C22×C7—41no—
456C22×C7—41no—
457C22×C7C22×C22⋊C411yescharacteristic
458C22×C7#54611yescharacteristic
459C22×C7#54711yescharacteristic
460C22×C7C2×#13511yescharacteristic
461C22×C7C2×#13511yescharacteristic
462C22×C7#57711yescharacteristic
463C22×C7#57811yescharacteristic
464C2×D7—22no—
465C2×D7—22no—
466C2×D7—22no—
467C2×D7—22no—
468C2×D7—22no—
469C2×D7—22no—
470C2×D7#41614yes—
471C4×C7—22no—
472C4×C7—42no—
473C4×C7—42no—
474C4×C7—81no—
475C4×C7—81no—
476C4×C7C4×#4111yescharacteristic
477C4×C7#52011yescharacteristic
478C4×C7#54611yescharacteristic
479C4×C7#54711yescharacteristic
480Dic7—22no—
481Dic7—22no—
482Dic7—22no—
483Dic7—42no—
484Dic7—42no—
485Dic7—42no—
486Dic7—81no—
487C24—71no—
488C24D4×D711yescharacteristic
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8C2×C4×D712yes—
495C2×D4—74no—
496C2×D4—142no—
497C2×D4—142no—
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—71no—
507C22×C4—71no—
508C22×C4—71no—
509C22×C4—72no—
510C22×C4—72no—
511C22×C4—144no—
512C22×C4—141no—
513C22×C4—141no—
514C22×C4—141no—
515C22×C4—141no—
516C22×C4—141no—
517C22×C4—141no—
518C22×C4—141no—
519C22×C4—141no—
520C22×C4—282no—
521C22×C4—282no—
522C22×C4—282no—
523C22×C4—282no—
524C22×C4—561no—
525C22×C4C2×C4×D712yes—
526C22×C4D4×D711yescharacteristic
527C22×C4D4×D712yes—
528C22×C4C23×D711yescharacteristic
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—44no—
535C2×C8—141no—
536C2×C8—141no—
537C2×C8—141no—
538C2×C8—141no—
539C2×C8—141no—
540C2×C8—141no—
541C2×C8—284no—
542C2×C8#115912yes—
543C4⋊C4—24no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—74no—
550C4⋊C4—72no—
551C4⋊C4—72no—
552C4⋊C4—72no—
553C4⋊C4—144no—
554C4⋊C4—144no—
555C4⋊C4—144no—
556C4⋊C4—144no—
557C4⋊C4—144no—
558C4⋊C4—141no—
559C4⋊C4—141no—
560C4⋊C4—141no—
561C4⋊C4—141no—
562C4⋊C4—141no—
563C4⋊C4—282no—
564C4⋊C4C2×C4×D712yes—
565C22⋊C4—24no—
566C22⋊C4—74no—
567C22⋊C4—74no—
568C22⋊C4—81no—
569C22⋊C4—144no—
570C22⋊C4—144no—
571C22⋊C4—282no—
572C22⋊C4—282no—
573C42—72no—
574C42—72no—
575C42—144no—
576C42—144no—
577C42—282no—
578C42—561no—
579C2×C7—42no—
580C2×C7#233911yescharacteristic
581C2×C7C2×#41611yescharacteristic
582C2×C7#289811yescharacteristic
583C2×C7#329611yescharacteristic
584C2×C7#330011yescharacteristic
585C2×C7#333611yescharacteristic
586C2×C7#333711yescharacteristic
587D7—24no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—72no—
595C23—72no—
596C23—72no—
597C23—141no—
598C23—141no—
599C23—141no—
600C23—141no—
601C23D7×C22⋊C412yes—
602C23C2×D4×D711yescharacteristic
603Q8—22no—
604Q8—22no—
605Q8—41no—
606Q8—41no—
607D4—148no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—41no—
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—72no—
627C2×C4—72no—
628C2×C4—72no—
629C2×C4—141no—
630C2×C4—141no—
631C2×C4—141no—
632C2×C4—141no—
633C2×C4—141no—
634C2×C4—141no—
635C2×C4—142no—
636C2×C4—142no—
637C2×C4—142no—
638C2×C4—142no—
639C2×C4—142no—
640C2×C4—142no—
641C2×C4—142no—
642C2×C4—288no—
643C2×C4—281no—
644C2×C4—281no—
645C2×C4—281no—
646C2×C4—281no—
647C2×C4—281no—
648C2×C4—281no—
649C2×C4—281no—
650C2×C4—281no—
651C2×C4—281no—
652C2×C4—564no—
653C2×C4D7×C22⋊C412yes—
654C2×C4C22×C4×D711yescharacteristic
655C2×C4C2×D4×D711yescharacteristic
656C2×C4C2×#115911yescharacteristic
657C2×C4#654811yescharacteristic
658C2×C4D7×#4111yescharacteristic
659C2×C4#655411yescharacteristic
660C8—22no—
661C8—41no—
662C8—281no—
663C8—281no—
664C7#2248611yescharacteristic, complemented, Sylow
665C22—22no—
666C22—22no—
667C22—22no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—74no—
673C22—142no—
674C22—142no—
675C22—142no—
676C22—142no—
677C22—142no—
678C22—142no—
679C22C2×D7×C22⋊C411yescharacteristic
680C22#9030111yescharacteristic
681C22#9030211yescharacteristic
682C22#9045311yescharacteristic
683C22#9045711yescharacteristic
684C22D7×#13511yescharacteristic
685C22D7×#13511yescharacteristic
686C4—22no—
687C4—42no—
688C4—42no—
689C4—81no—
690C4—81no—
691C4—142no—
692C4—142no—
693C4—142no—
694C4—282no—
695C4—282no—
696C4—282no—
697C4—561no—
698C4C4×#115911yescharacteristic
699C4#9023711yescharacteristic
700C4#9028211yescharacteristic
701C4#9034611yescharacteristic
702C2—42no—
703C2—144no—
704C2#1173211711yescharacteristic
705C2#1173623511yescharacteristic
706C2D7×#41611yescharacteristic
707C2#1173811611yescharacteristic
708C2#1173811811yescharacteristic
709C2#1173821411yescharacteristic
710C2#1173821511yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1892C2
socleC23×C7C22×D4
prime radicalC22×C22⋊D7D4
cosocleC22×C4×C7C24
hypercenter#1892D7
hypocenterC7#22486
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
4. C7×#1892C2semidirect
5. #11729723C2semidirect
6. #11729447C2semidirect
7. #11728024C2semidirect
8. #11728022C2semidirect
9. #11727976C2semidirect
10. Dic7×#103C2semidirect
11. #11727257C2semidirect
12. #11726625C2semidirect
13. D7×#340C2semidirect
14. #11726558C2semidirect
15. #11726556C2semidirect
25. #90330C4semidirect
75. C7×C22⋊Q8C2×C4semidirect
88. Q8×Dic7C2×C4semidirect
97. #6489C2×C4semidirect
125. #6453C2×C4semidirect
148. #1892D7semidirect
395. C22⋊Q8C4×D7semidirect
664. C7#22486semidirect

Maximal subgroups

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

subgroupindex
C2×#903302
C2×C8×C22⋊D72
#117314572
C7×#18922
#117297232
#117294472
#117280242
#117280222
#117279762
Dic7×#1032
#117272572
#117266252
D7×#3402
#117265582
#117265562
#224867