Finite Group Databasebeta

← C7×#26977 #13204193

Subgroups — C7×#26977 #13204193

Order 1792.

1028 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#466C211yesmaximal, characteristic, complemented
2C2×C7×#442C211yesmaximal, characteristic, complemented
3C7×#2428C211yesmaximal, characteristic, complemented
4C7×#2420C211yesmaximal, characteristic, complemented
5C7×#2085C211yesmaximal, characteristic, complemented
6C7×#2034C211yesmaximal, characteristic, complemented
7C7×#2011C211yesmaximal, characteristic, complemented
8C7×#1999C211yesmaximal, characteristic, complemented
9C7×#1961C211yesmaximal, characteristic, complemented
10C7×#1936C211yesmaximal, characteristic, complemented
11C7×#1936C211yesmaximal, characteristic, complemented
12C7×#1893C211yesmaximal, characteristic, complemented
13C7×#1879C211yesmaximal, characteristic, complemented
14C7×#1862C211yesmaximal, characteristic, complemented
15C7×#1752C211yesmaximal, characteristic, complemented
16C22×C7×D8C2211yescharacteristic
17C22×C7×D8C2211yescharacteristic
18C23×C7×C8C2211yescharacteristic
19C2×C7×#127C2211yescharacteristic
20C2×C7×#121—21no—
21C2×C7×#121C2211yescharacteristic
22C2×C7×#121C2211yescharacteristic
23C2×C7×#121C2211yescharacteristic
24C2×C4×C7×D4C2211yescharacteristic
25C2×C4×C7×D4C2211yescharacteristic
26C7×#466—24no—
27C7×#442—24no—
28C2×C7×#107C2211yescharacteristic
29C2×C7×#106C2211yescharacteristic
30C2×C7×#102C2211yescharacteristic
31C2×C7×#102C2211yescharacteristic
32C2×C7×#102C2211yescharacteristic
33C2×C7×#102C2211yescharacteristic
34C2×C7×#102C2211yescharacteristic
35C2×C7×#102C2211yescharacteristic
36C2×C7×#102C2211yescharacteristic
37C2×C7×#102C2211yescharacteristic
38C2×C7×C22⋊C8C2211yescharacteristic
39C2×C7×#97C2211yescharacteristic
40C2×C7×#97C2211yescharacteristic
41C7×#397—21no—
42C7×#394—21no—
43C7×#394—21no—
44C7×#392—21no—
45C7×#390C2211yescharacteristic
46C7×#390C2211yescharacteristic
47C7×#389C2211yescharacteristic
48C7×#389C2211yescharacteristic
49C7×#386—21no—
50C7×#386—21no—
51C7×#382C2211yescharacteristic
52C7×#381—21no—
53C7×#380C2211yescharacteristic
54C4×C7×C22⋊C4C2211yescharacteristic
55C7×#340C2211yescharacteristic
56C7×#340C2211yescharacteristic
57C7×#340C2211yescharacteristic
58C7×#340C2211yescharacteristic
59C7×#336C2211yescharacteristic
60C7×#336C2211yescharacteristic
61#26977C711yesmaximal, characteristic, direct product factor, Sylow
62C22×C7×D4—21no—
63C22×C7×D4—21no—
64C22×C7×D4—21no—
65C22×C7×D4—21no—
66C22×C7×D4—21no—
67C22×C7×D4C2311yescharacteristic
68C22×C7×D4C2311yescharacteristic
69C22×C7×D4C2311yescharacteristic
70C23×C4×C7—21no—
71C23×C4×C7—21no—
72C23×C4×C7C2311yescharacteristic
73C2×C7×D8—22no—
74C2×C7×D8—22no—
75C2×C7×D8—22no—
76C2×C7×D8—22no—
77C2×C7×D8—22no—
78C2×C7×D8—41no—
79C22×C7×C8—22no—
80C22×C7×C8—22no—
81C22×C7×C8—41no—
82C22×C7×C8C2311yescharacteristic
83C22×C7×C8C2311yescharacteristic
84C22×C7×C8C2311yescharacteristic
85C22×C7×C8C2311yescharacteristic
86C7×#127—22no—
87C7×#127—41no—
88C7×#121—22no—
89C7×#121—22no—
90C7×#121—22no—
91C7×#121—44no—
92C7×#121—41no—
93C7×#121—41no—
94C7×#121—41no—
95C4×C7×D4—22no—
96C4×C7×D4—22no—
97C4×C7×D4—41no—
98C4×C7×D4—41no—
99C2×C7×C4⋊C4—21no—
100C2×C7×C4⋊C4—21no—
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C4⋊C4C2311yescharacteristic
104C2×C7×C4⋊C4C2311yescharacteristic
105C2×C7×C4⋊C4C2311yescharacteristic
106C2×C7×C22⋊C4—21no—
107C2×C7×C22⋊C4—21no—
108C2×C7×C22⋊C4—21no—
109C2×C7×C22⋊C4—21no—
110C2×C7×C22⋊C4—21no—
111C2×C7×C22⋊C4—21no—
112C2×C7×C22⋊C4—21no—
113C2×C7×C22⋊C4—21no—
114C2×C7×C22⋊C4—21no—
115C2×C7×C22⋊C4—21no—
116C2×C7×C22⋊C4D411yescharacteristic
117C2×C7×C22⋊C4D411yescharacteristic
118C2×C42×C7C2311yescharacteristic
119C2×C42×C7C2311yescharacteristic
120C7×#107—22no—
121C7×#106—22no—
122C7×#102—22no—
123C7×#102—22no—
124C7×#102—22no—
125C7×#102—22no—
126C7×#102—41no—
127C7×#102—41no—
128C7×#102—41no—
129C7×#102D414yescomplemented
130C7×C22⋊C8—22no—
131C7×#97—22no—
132C7×#97—41no—
133C7×#95—21no—
134C7×#95—21no—
135C7×#95—21no—
136C7×#95—21no—
137C7×#95—21no—
138C7×#95D411yescharacteristic
139C7×#95D411yescharacteristic
140C2×#466C2×C711yescharacteristic, complemented
141C2×#442C2×C711yescharacteristic, complemented
142#2428C2×C711yescharacteristic, complemented
143#2420C2×C711yescharacteristic, complemented
144#2085C2×C711yescharacteristic, complemented
145#2034C2×C711yescharacteristic, complemented
146#2011C2×C711yescharacteristic, complemented
147#1999C2×C711yescharacteristic, complemented
148#1961C2×C711yescharacteristic, complemented
149#1936C2×C711yescharacteristic, complemented
150#1936C2×C711yescharacteristic, complemented
151#1893C2×C711yescharacteristic, complemented
152#1879C2×C711yescharacteristic, complemented
153#1862C2×C711yescharacteristic, complemented
154#1752C2×C711yescharacteristic, complemented
155C24×C7—21no—
156C24×C7—21no—
157C24×C7—21no—
158C24×C7C2×D411yescharacteristic
159C2×C7×D4—21no—
160C2×C7×D4—21no—
161C2×C7×D4—21no—
162C2×C7×D4—21no—
163C2×C7×D4—21no—
164C2×C7×D4—21no—
165C2×C7×D4—21no—
166C2×C7×D4—21no—
167C2×C7×D4—21no—
168C2×C7×D4—21no—
169C2×C7×D4—21no—
170C2×C7×D4—21no—
171C2×C7×D4—21no—
172C2×C7×D4—21no—
173C2×C7×D4—21no—
174C2×C7×D4—21no—
175C2×C7×D4—42no—
176C2×C7×D4—42no—
177C2×C7×D4—42no—
178C2×C7×D4—42no—
179C2×C7×D4—42no—
180C2×C7×D4—42no—
181C2×C7×D4—42no—
182C2×C7×D4—42no—
183C2×C7×D4—42no—
184C2×C7×D4—42no—
185C2×C7×D4—81no—
186C2×C7×D4—81no—
187C2×C7×D4—81no—
188C2×C7×D4—81no—
189C2×C7×D4—81no—
190C2×C7×D4C2×D412yes—
191C2×C7×D4#4112yes—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—42no—
204C22×C4×C7—42no—
205C22×C4×C7—42no—
206C22×C4×C7—42no—
207C22×C4×C7—81no—
208C22×C4×C7—81no—
209C22×C4×C7C2×D411yescharacteristic
210C22×C4×C7C2×D411yescharacteristic
211C22×C4×C7C2×D411yescharacteristic
212C22×C4×C7C2×D411yescharacteristic
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2411yescharacteristic
215C7×D8—28no—
216C7×D8—44no—
217C2×C7×C8—21no—
218C2×C7×C8—21no—
219C2×C7×C8—21no—
220C2×C7×C8—21no—
221C2×C7×C8—21no—
222C2×C7×C8—21no—
223C2×C7×C8—21no—
224C2×C7×C8—21no—
225C2×C7×C8—21no—
226C2×C7×C8—44no—
227C2×C7×C8C2×D412yes—
228C2×C7×C8#4112yes—
229C2×C7×C8#4112yes—
230C7×C4⋊C4—21no—
231C7×C4⋊C4—21no—
232C7×C4⋊C4—21no—
233C7×C4⋊C4—21no—
234C7×C4⋊C4—21no—
235C7×C4⋊C4—21no—
236C7×C4⋊C4—21no—
237C7×C4⋊C4—21no—
238C7×C4⋊C4—21no—
239C7×C4⋊C4—42no—
240C7×C4⋊C4—81no—
241C7×C4⋊C4C2×D412yes—
242C7×C22⋊C4—22no—
243C7×C22⋊C4—41no—
244C7×C22⋊C4—42no—
245C7×C22⋊C4—42no—
246C7×C22⋊C4—42no—
247C7×C22⋊C4—42no—
248C7×C22⋊C4—42no—
249C7×C22⋊C4—42no—
250C7×C22⋊C4—81no—
251C7×C22⋊C4—81no—
252C7×C22⋊C4—81no—
253C7×C22⋊C4—81no—
254C42×C7—21no—
255C42×C7—21no—
256C42×C7—21no—
257C42×C7—21no—
258C22×D8C22×C711yescharacteristic
259C22×D8C22×C711yescharacteristic
260C23×C8C22×C711yescharacteristic
261C2×#127C22×C711yescharacteristic
262C2×#121—21no—
263C2×#121C22×C711yescharacteristic
264C2×#121C22×C711yescharacteristic
265C2×#121C22×C711yescharacteristic
266C2×C4×D4C22×C711yescharacteristic
267C2×C4×D4C22×C711yescharacteristic
268#466—24no—
269#442—24no—
270C2×#107C22×C711yescharacteristic
271C2×#106C22×C711yescharacteristic
272C2×#102C22×C711yescharacteristic
273C2×#102C22×C711yescharacteristic
274C2×#102C22×C711yescharacteristic
275C2×#102C22×C711yescharacteristic
276C2×#102C22×C711yescharacteristic
277C2×#102C22×C711yescharacteristic
278C2×#102C22×C711yescharacteristic
279C2×#102C22×C711yescharacteristic
280C2×C22⋊C8C22×C711yescharacteristic
281C2×#97C22×C711yescharacteristic
282C2×#97C22×C711yescharacteristic
283#397—21no—
284#394—21no—
285#394—21no—
286#392—21no—
287#390C22×C711yescharacteristic
288#390C22×C711yescharacteristic
289#389C22×C711yescharacteristic
290#389C22×C711yescharacteristic
291#386—21no—
292#386—21no—
293#382C22×C711yescharacteristic
294#381—21no—
295#380C22×C711yescharacteristic
296C4×C22⋊C4C22×C711yescharacteristic
297#340C22×C711yescharacteristic
298#340C22×C711yescharacteristic
299#340C22×C711yescharacteristic
300#340C22×C711yescharacteristic
301#336C22×C711yescharacteristic
302#336C22×C711yescharacteristic
303C23×C7—21no—
304C23×C7—21no—
305C23×C7—21no—
306C23×C7—21no—
307C23×C7—21no—
308C23×C7—21no—
309C23×C7—22no—
310C23×C7—22no—
311C23×C7—41no—
312C23×C7—41no—
313C23×C7—41no—
314C23×C7—41no—
315C23×C7—41no—
316C23×C7—41no—
317C23×C7—41no—
318C23×C7—41no—
319C23×C7—41no—
320C23×C7—41no—
321C23×C7—41no—
322C23×C7—41no—
323C23×C7—41no—
324C23×C7—41no—
325C23×C7—41no—
326C23×C7—41no—
327C23×C7—41no—
328C23×C7—41no—
329C23×C7—41no—
330C23×C7AGL(1,ℤ/8)12yes—
331C23×C7C22×D411yescharacteristic
332C7×D4—22no—
333C7×D4—22no—
334C7×D4—22no—
335C7×D4—22no—
336C7×D4—41no—
337C7×D4—41no—
338C7×D4—41no—
339C7×D4—41no—
340C7×D4—41no—
341C7×D4—41no—
342C7×D4—41no—
343C7×D4—41no—
344C7×D4—84no—
345C7×D4—84no—
346C7×D4—84no—
347C7×D4—84no—
348C7×D4—84no—
349C2×C4×C7—21no—
350C2×C4×C7—21no—
351C2×C4×C7—21no—
352C2×C4×C7—21no—
353C2×C4×C7—22no—
354C2×C4×C7—21no—
355C2×C4×C7—21no—
356C2×C4×C7—21no—
357C2×C4×C7—21no—
358C2×C4×C7—21no—
359C2×C4×C7—21no—
360C2×C4×C7—21no—
361C2×C4×C7—21no—
362C2×C4×C7—21no—
363C2×C4×C7—21no—
364C2×C4×C7—21no—
365C2×C4×C7—41no—
366C2×C4×C7—41no—
367C2×C4×C7—41no—
368C2×C4×C7—41no—
369C2×C4×C7—41no—
370C2×C4×C7—41no—
371C2×C4×C7—41no—
372C2×C4×C7—41no—
373C2×C4×C7—41no—
374C2×C4×C7—41no—
375C2×C4×C7—41no—
376C2×C4×C7—41no—
377C2×C4×C7—41no—
378C2×C4×C7—41no—
379C2×C4×C7—41no—
380C2×C4×C7—41no—
381C2×C4×C7—41no—
382C2×C4×C7—41no—
383C2×C4×C7—84no—
384C2×C4×C7—84no—
385C2×C4×C7C22×D411yescharacteristic
386C2×C4×C7C2×#4111yescharacteristic
387C2×C4×C7C2×#4111yescharacteristic
388C2×C4×C7C2×#4111yescharacteristic
389C2×C4×C7H(5,𝔽2)11yescharacteristic
390C2×C4×C7H(5,𝔽2)11yescharacteristic
391C7×C8—22no—
392C7×C8—22no—
393C7×C8—22no—
394C7×C8—41no—
395C22×D4—21no—
396C22×D4—21no—
397C22×D4—21no—
398C22×D4—21no—
399C22×D4—21no—
400C22×D4C23×C711yescharacteristic
401C22×D4C23×C711yescharacteristic
402C22×D4C23×C711yescharacteristic
403C23×C4—21no—
404C23×C4—21no—
405C23×C4C23×C711yescharacteristic
406C2×D8—22no—
407C2×D8—22no—
408C2×D8—22no—
409C2×D8—22no—
410C2×D8—22no—
411C2×D8—41no—
412C22×C8—22no—
413C22×C8—22no—
414C22×C8—41no—
415C22×C8C23×C711yescharacteristic
416C22×C8C23×C711yescharacteristic
417C22×C8C23×C711yescharacteristic
418C22×C8C23×C711yescharacteristic
419#127—22no—
420#127—41no—
421#121—22no—
422#121—22no—
423#121—22no—
424#121—44no—
425#121—41no—
426#121—41no—
427#121—41no—
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—41no—
431C4×D4—41no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4C23×C711yescharacteristic
435C2×C4⋊C4C23×C711yescharacteristic
436C2×C4⋊C4C23×C711yescharacteristic
437C2×C4⋊C4C23×C711yescharacteristic
438C2×C4⋊C4C23×C711yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4C7×D411yescharacteristic
450C2×C22⋊C4C7×D411yescharacteristic
451C2×C42C23×C711yescharacteristic
452C2×C42C23×C711yescharacteristic
453#107—22no—
454#106—22no—
455#102—22no—
456#102—22no—
457#102—22no—
458#102—22no—
459#102—41no—
460#102—41no—
461#102—41no—
462#102C7×D414yescomplemented
463C22⋊C8—22no—
464#97—22no—
465#97—41no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95C7×D411yescharacteristic
472#95C7×D411yescharacteristic
473C22×C7—22no—
474C22×C7—22no—
475C22×C7—22no—
476C22×C7—41no—
477C22×C7—41no—
478C22×C7—41no—
479C22×C7—41no—
480C22×C7—42no—
481C22×C7—42no—
482C22×C7—42no—
483C22×C7—42no—
484C22×C7—42no—
485C22×C7—42no—
486C22×C7—81no—
487C22×C7—81no—
488C22×C7—81no—
489C22×C7—81no—
490C22×C7—81no—
491C22×C7—81no—
492C22×C7—81no—
493C22×C7—81no—
494C22×C7—81no—
495C22×C7—81no—
496C22×C7—81no—
497C22×C7—81no—
498C22×C7—81no—
499C22×C7—81no—
500C22×C7—81no—
501C22×C7#53211yescharacteristic
502C22×C7D4211yescharacteristic
503C22×C7#54611yescharacteristic
504C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
505C22×C7#57511yescharacteristic
506C22×C7#57611yescharacteristic
507C22×C7#57611yescharacteristic
508C4×C7—41no—
509C4×C7—41no—
510C4×C7—42no—
511C4×C7—41no—
512C4×C7—41no—
513C4×C7—41no—
514C4×C7—81no—
515C4×C7—81no—
516C4×C7—81no—
517C4×C7—81no—
518C4×C7#52511yescharacteristic
519C4×C7#54011yescharacteristic
520C4×C7#54611yescharacteristic
521C4×C7#55311yescharacteristic
522C24—21no—
523C24—21no—
524C24—21no—
525C24C2×C7×D411yescharacteristic
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4—81no—
553C2×D4—81no—
554C2×D4—81no—
555C2×D4—81no—
556C2×D4—81no—
557C2×D4C2×C7×D412yes—
558C2×D4C7×#4112yes—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—81no—
575C22×C4—81no—
576C22×C4C2×C7×D411yescharacteristic
577C22×C4C2×C7×D411yescharacteristic
578C22×C4C2×C7×D411yescharacteristic
579C22×C4C2×C7×D411yescharacteristic
580C22×C4C2×C7×D411yescharacteristic
581C22×C4C24×C711yescharacteristic
582D8—28no—
583D8—44no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—44no—
594C2×C8C2×C7×D412yes—
595C2×C8C7×#4112yes—
596C2×C8C7×#4112yes—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—42no—
607C4⋊C4—81no—
608C4⋊C4C2×C7×D412yes—
609C22⋊C4—22no—
610C22⋊C4—41no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—81no—
618C22⋊C4—81no—
619C22⋊C4—81no—
620C22⋊C4—81no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—21no—
625C2×C7—42no—
626C2×C7—82no—
627C2×C7—82no—
628C2×C7—161no—
629C2×C7#246411yescharacteristic
630C2×C7#317611yescharacteristic
631C2×C7#318011yescharacteristic
632C2×C7#326411yescharacteristic
633C2×C7#326811yescharacteristic
634C2×C7#331811yescharacteristic
635C2×C7#331911yescharacteristic
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—22no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23C7×AGL(1,ℤ/8)12yes—
664C23C22×C7×D411yescharacteristic
665D4—22no—
666D4—22no—
667D4—22no—
668D4—22no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—84no—
678D4—84no—
679D4—84no—
680D4—84no—
681D4—84no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—84no—
717C2×C4—84no—
718C2×C4C22×C7×D411yescharacteristic
719C2×C4C2×C7×#4111yescharacteristic
720C2×C4C2×C7×#4111yescharacteristic
721C2×C4C2×C7×#4111yescharacteristic
722C2×C4C7×H(5,𝔽2)11yescharacteristic
723C2×C4C7×H(5,𝔽2)11yescharacteristic
724C8—22no—
725C8—22no—
726C8—22no—
727C8—41no—
728C7#2697711yescharacteristic, direct product factor, Sylow
729C22—22no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22C7×#53211yescharacteristic
758C22C7×D4211yescharacteristic
759C22C7×#54611yescharacteristic
760C22C2×C7×AGL(1,ℤ/8)11yescharacteristic
761C22C7×#57511yescharacteristic
762C22C7×#57611yescharacteristic
763C22C7×#57611yescharacteristic
764C4—41no—
765C4—41no—
766C4—42no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—81no—
771C4—81no—
772C4—81no—
773C4—81no—
774C4C7×#52511yescharacteristic
775C4C7×#54011yescharacteristic
776C4C7×#54611yescharacteristic
777C4C7×#55311yescharacteristic
778C2—42no—
779C2—82no—
780C2—82no—
781C2—161no—
782C2C7×#246411yescharacteristic
783C2C7×#317611yescharacteristic
784C2C7×#318011yescharacteristic
785C2C7×#326411yescharacteristic
786C2C7×#326811yescharacteristic
787C2C7×#331811yescharacteristic
788C2C7×#331911yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C4×C7×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C7×#466C2semidirect
2. C2×C7×#442C2semidirect
3. C7×#2428C2semidirect
4. C7×#2420C2semidirect
5. C7×#2085C2semidirect
6. C7×#2034C2semidirect
7. C7×#2011C2semidirect
8. C7×#1999C2semidirect
9. C7×#1961C2semidirect
10. C7×#1936C2semidirect
11. C7×#1936C2semidirect
12. C7×#1893C2semidirect
13. C7×#1879C2semidirect
14. C7×#1862C2semidirect
15. C7×#1752C2semidirect
61. #26977C7direct (N × H)
129. C7×#102D4semidirect
140. C2×#466C2×C7semidirect
141. C2×#442C2×C7semidirect
142. #2428C2×C7semidirect
143. #2420C2×C7semidirect
144. #2085C2×C7semidirect
145. #2034C2×C7semidirect
146. #2011C2×C7semidirect
147. #1999C2×C7semidirect
148. #1961C2×C7semidirect
149. #1936C2×C7semidirect
150. #1936C2×C7semidirect
151. #1893C2×C7semidirect
152. #1879C2×C7semidirect
153. #1862C2×C7semidirect
154. #1752C2×C7semidirect
462. #102C7×D4semidirect
728. C7#26977direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#4662
C2×C7×#4422
C7×#24282
C7×#24202
C7×#20852
C7×#20342
C7×#20112
C7×#19992
C7×#19612
C7×#19362
C7×#18932
C7×#18792
C7×#18622
C7×#17522
#269777