Finite Group Databasebeta

← C7×#26975 #13204191

Subgroups — C7×#26975 #13204191

Order 1792.

956 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#466C211yesmaximal, characteristic
2C2×C7×#440C211yesmaximal, characteristic, complemented
3C7×#2426C211yesmaximal, characteristic, complemented
4C7×#2422C211yesmaximal, characteristic, complemented
5C7×#2083C211yesmaximal, characteristic, complemented
6C7×#2033C211yesmaximal, characteristic, complemented
7C7×#2012C211yesmaximal, characteristic, complemented
8C7×#2000C211yesmaximal, characteristic, complemented
9C7×#1959C211yesmaximal, characteristic, complemented
10C7×#1936C211yesmaximal, characteristic, complemented
11C7×#1936C211yesmaximal, characteristic, complemented
12C7×#1892C211yesmaximal, characteristic, complemented
13C7×#1879C211yesmaximal, characteristic, complemented
14C7×#1863C211yesmaximal, characteristic, complemented
15C7×#1752C211yesmaximal, characteristic, complemented
16C22×C7×SD16C2211yescharacteristic
17C22×C7×D8C2211yescharacteristic
18C23×C7×C8C2211yescharacteristic
19C2×C7×#124C2211yescharacteristic
20C2×C7×#123—21no—
21C2×C7×C22⋊Q8C2211yescharacteristic
22C2×C7×#121C2211yescharacteristic
23C2×C7×#121C2211yescharacteristic
24C2×C4×C7×Q8C2211yescharacteristic
25C2×C4×C7×D4C2211yescharacteristic
26C7×#466—24no—
27C7×#440—24no—
28C2×C7×#107C2211yescharacteristic
29C2×C7×#107C2211yescharacteristic
30C2×C7×#103C2211yescharacteristic
31C2×C7×#103C2211yescharacteristic
32C2×C7×#103C2211yescharacteristic
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×#396—21no—
43C7×#394—21no—
44C7×#394—21no—
45C7×#390—21no—
46C7×#390C2211yescharacteristic
47C7×#390C2211yescharacteristic
48C7×#389C2211yescharacteristic
49C7×#389C2211yescharacteristic
50C7×#388—21no—
51C7×#385—21no—
52C7×#384C2211yescharacteristic
53C7×#380C2211yescharacteristic
54C4×C7×C22⋊C4C2211yescharacteristic
55C7×#340C2211yescharacteristic
56C7×#340C2211yescharacteristic
57C7×#340C2211yescharacteristic
58C7×#340C2211yescharacteristic
59C7×#336C2211yescharacteristic
60C7×#336C2211yescharacteristic
61#26975C711yesmaximal, characteristic, direct product factor, Sylow
62C22×C7×Q8C2311yescharacteristic
63C22×C7×D4—21no—
64C22×C7×D4—21no—
65C22×C7×D4C2311yescharacteristic
66C22×C7×D4C2311yescharacteristic
67C23×C4×C7—21no—
68C23×C4×C7C2311yescharacteristic
69C2×C7×SD16—22no—
70C2×C7×SD16—22no—
71C2×C7×SD16—22no—
72C2×C7×D8—22no—
73C2×C7×D8—22no—
74C2×C7×D8—41no—
75C22×C7×C8—22no—
76C22×C7×C8—22no—
77C22×C7×C8—41no—
78C22×C7×C8C2311yescharacteristic
79C22×C7×C8C2311yescharacteristic
80C22×C7×C8C2311yescharacteristic
81C22×C7×C8C2311yescharacteristic
82C7×#124—22no—
83C7×#124—41no—
84C7×#123—44no—
85C7×C22⋊Q8—22no—
86C7×C22⋊Q8—41no—
87C7×#121—22no—
88C7×#121—22no—
89C7×#121—41no—
90C7×#121—41no—
91C4×C7×Q8—22no—
92C4×C7×Q8—41no—
93C4×C7×D4—22no—
94C4×C7×D4—41no—
95C2×C7×C4⋊C4—21no—
96C2×C7×C4⋊C4—21no—
97C2×C7×C4⋊C4—21no—
98C2×C7×C4⋊C4—21no—
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⋊C4—21no—
117C2×C7×C22⋊C4D411yescharacteristic
118C2×C7×C22⋊C4D411yescharacteristic
119C2×C42×C7—21no—
120C2×C42×C7C2311yescharacteristic
121C2×C42×C7C2311yescharacteristic
122C7×#107—22no—
123C7×#107—22no—
124C7×#103—22no—
125C7×#103—22no—
126C7×#103—41no—
127C7×#102—22no—
128C7×#102—22no—
129C7×#102—41no—
130C7×#102—41no—
131C7×#102D414yes—
132C7×C22⋊C8—22no—
133C7×#97—22no—
134C7×#97—41no—
135C7×#95—21no—
136C7×#95—21no—
137C7×#95—21no—
138C7×#95D411yescharacteristic
139C7×#95D411yescharacteristic
140C2×#466C2×C711yescharacteristic
141C2×#440C2×C711yescharacteristic, complemented
142#2426C2×C711yescharacteristic, complemented
143#2422C2×C711yescharacteristic, complemented
144#2083C2×C711yescharacteristic, complemented
145#2033C2×C711yescharacteristic, complemented
146#2012C2×C711yescharacteristic, complemented
147#2000C2×C711yescharacteristic, complemented
148#1959C2×C711yescharacteristic, complemented
149#1936C2×C711yescharacteristic, complemented
150#1936C2×C711yescharacteristic, complemented
151#1892C2×C711yescharacteristic, complemented
152#1879C2×C711yescharacteristic, complemented
153#1863C2×C711yescharacteristic, complemented
154#1752C2×C711yescharacteristic, complemented
155C24×C7—21no—
156C24×C7—21no—
157C24×C7C2×D411yescharacteristic
158C2×C7×Q8—21no—
159C2×C7×Q8—21no—
160C2×C7×Q8—21no—
161C2×C7×Q8—21no—
162C2×C7×Q8—21no—
163C2×C7×Q8#4112yes—
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—81no—
180C2×C7×D4—81no—
181C2×C7×D4C2×D412yes—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—42no—
195C22×C4×C7—42no—
196C22×C4×C7—81no—
197C22×C4×C7C2×D411yescharacteristic
198C22×C4×C7C2×D411yescharacteristic
199C22×C4×C7C2×D411yescharacteristic
200C22×C4×C7C2×D411yescharacteristic
201C22×C4×C7C2×D411yescharacteristic
202C22×C4×C7C2411yescharacteristic
203C7×SD16—28no—
204C7×D8—44no—
205C2×C7×C8—21no—
206C2×C7×C8—21no—
207C2×C7×C8—21no—
208C2×C7×C8—21no—
209C2×C7×C8—21no—
210C2×C7×C8—21no—
211C2×C7×C8—21no—
212C2×C7×C8—21no—
213C2×C7×C8—21no—
214C2×C7×C8—44no—
215C2×C7×C8C2×D412yes—
216C2×C7×C8#4112yes—
217C2×C7×C8#4112yes—
218C7×C4⋊C4—21no—
219C7×C4⋊C4—21no—
220C7×C4⋊C4—21no—
221C7×C4⋊C4—21no—
222C7×C4⋊C4—21no—
223C7×C4⋊C4—21no—
224C7×C4⋊C4—21no—
225C7×C4⋊C4—21no—
226C7×C4⋊C4—21no—
227C7×C4⋊C4—42no—
228C7×C4⋊C4—42no—
229C7×C4⋊C4—42no—
230C7×C4⋊C4—42no—
231C7×C4⋊C4—81no—
232C7×C4⋊C4—81no—
233C7×C4⋊C4C2×D412yes—
234C7×C22⋊C4—22no—
235C7×C22⋊C4—41no—
236C7×C22⋊C4—42no—
237C7×C22⋊C4—42no—
238C7×C22⋊C4—42no—
239C7×C22⋊C4—42no—
240C7×C22⋊C4—42no—
241C7×C22⋊C4—42no—
242C7×C22⋊C4—42no—
243C7×C22⋊C4—42no—
244C7×C22⋊C4—42no—
245C7×C22⋊C4—42no—
246C7×C22⋊C4—81no—
247C42×C7—21no—
248C42×C7—21no—
249C42×C7—21no—
250C42×C7—21no—
251C42×C7—42no—
252C22×SD16C22×C711yescharacteristic
253C22×D8C22×C711yescharacteristic
254C23×C8C22×C711yescharacteristic
255C2×#124C22×C711yescharacteristic
256C2×#123—21no—
257C2×C22⋊Q8C22×C711yescharacteristic
258C2×#121C22×C711yescharacteristic
259C2×#121C22×C711yescharacteristic
260C2×C4×Q8C22×C711yescharacteristic
261C2×C4×D4C22×C711yescharacteristic
262#466—24no—
263#440—24no—
264C2×#107C22×C711yescharacteristic
265C2×#107C22×C711yescharacteristic
266C2×#103C22×C711yescharacteristic
267C2×#103C22×C711yescharacteristic
268C2×#103C22×C711yescharacteristic
269C2×#102C22×C711yescharacteristic
270C2×#102C22×C711yescharacteristic
271C2×#102C22×C711yescharacteristic
272C2×#102C22×C711yescharacteristic
273C2×#102C22×C711yescharacteristic
274C2×C22⋊C8C22×C711yescharacteristic
275C2×#97C22×C711yescharacteristic
276C2×#97C22×C711yescharacteristic
277#397—21no—
278#396—21no—
279#394—21no—
280#394—21no—
281#390—21no—
282#390C22×C711yescharacteristic
283#390C22×C711yescharacteristic
284#389C22×C711yescharacteristic
285#389C22×C711yescharacteristic
286#388—21no—
287#385—21no—
288#384C22×C711yescharacteristic
289#380C22×C711yescharacteristic
290C4×C22⋊C4C22×C711yescharacteristic
291#340C22×C711yescharacteristic
292#340C22×C711yescharacteristic
293#340C22×C711yescharacteristic
294#340C22×C711yescharacteristic
295#336C22×C711yescharacteristic
296#336C22×C711yescharacteristic
297C23×C7—21no—
298C23×C7—21no—
299C23×C7—21no—
300C23×C7—21no—
301C23×C7—21no—
302C23×C7—21no—
303C23×C7—22no—
304C23×C7—41no—
305C23×C7—41no—
306C23×C7—41no—
307C23×C7—41no—
308C23×C7—41no—
309C23×C7—41no—
310C23×C7—41no—
311C23×C7—41no—
312C23×C7—41no—
313C23×C7—41no—
314C23×C7—41no—
315C23×C7—41no—
316C23×C7—41no—
317C23×C7AGL(1,ℤ/8)12yes—
318C23×C7C22×D411yescharacteristic
319C7×Q8—22no—
320C7×Q8—22no—
321C7×Q8—41no—
322C7×Q8—41no—
323C7×D4—22no—
324C7×D4—22no—
325C7×D4—41no—
326C7×D4—41no—
327C7×D4—41no—
328C7×D4—41no—
329C7×D4—41no—
330C7×D4—41no—
331C7×D4—84no—
332C7×D4—84no—
333C2×C4×C7—21no—
334C2×C4×C7—21no—
335C2×C4×C7—21no—
336C2×C4×C7—22no—
337C2×C4×C7—21no—
338C2×C4×C7—21no—
339C2×C4×C7—21no—
340C2×C4×C7—22no—
341C2×C4×C7—21no—
342C2×C4×C7—21no—
343C2×C4×C7—21no—
344C2×C4×C7—21no—
345C2×C4×C7—21no—
346C2×C4×C7—21no—
347C2×C4×C7—21no—
348C2×C4×C7—21no—
349C2×C4×C7—21no—
350C2×C4×C7—41no—
351C2×C4×C7—41no—
352C2×C4×C7—41no—
353C2×C4×C7—41no—
354C2×C4×C7—41no—
355C2×C4×C7—41no—
356C2×C4×C7—41no—
357C2×C4×C7—41no—
358C2×C4×C7—41no—
359C2×C4×C7—41no—
360C2×C4×C7—41no—
361C2×C4×C7—41no—
362C2×C4×C7—41no—
363C2×C4×C7—41no—
364C2×C4×C7—41no—
365C2×C4×C7—41no—
366C2×C4×C7—41no—
367C2×C4×C7—41no—
368C2×C4×C7—41no—
369C2×C4×C7—41no—
370C2×C4×C7—84no—
371C2×C4×C7C22×D411yescharacteristic
372C2×C4×C7C2×#4111yescharacteristic
373C2×C4×C7C2×#4111yescharacteristic
374C2×C4×C7C2×#4111yescharacteristic
375C2×C4×C7H(5,𝔽2)11yescharacteristic
376C2×C4×C7H(5,𝔽2)11yescharacteristic
377C7×C8—22no—
378C7×C8—22no—
379C7×C8—22no—
380C7×C8—41no—
381C22×Q8C23×C711yescharacteristic
382C22×D4—21no—
383C22×D4—21no—
384C22×D4C23×C711yescharacteristic
385C22×D4C23×C711yescharacteristic
386C23×C4—21no—
387C23×C4C23×C711yescharacteristic
388C2×SD16—22no—
389C2×SD16—22no—
390C2×SD16—22no—
391C2×D8—22no—
392C2×D8—22no—
393C2×D8—41no—
394C22×C8—22no—
395C22×C8—22no—
396C22×C8—41no—
397C22×C8C23×C711yescharacteristic
398C22×C8C23×C711yescharacteristic
399C22×C8C23×C711yescharacteristic
400C22×C8C23×C711yescharacteristic
401#124—22no—
402#124—41no—
403#123—44no—
404C22⋊Q8—22no—
405C22⋊Q8—41no—
406#121—22no—
407#121—22no—
408#121—41no—
409#121—41no—
410C4×Q8—22no—
411C4×Q8—41no—
412C4×D4—22no—
413C4×D4—41no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4C23×C711yescharacteristic
421C2×C4⋊C4C23×C711yescharacteristic
422C2×C4⋊C4C23×C711yescharacteristic
423C2×C4⋊C4C23×C711yescharacteristic
424C2×C4⋊C4C23×C711yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4C7×D411yescharacteristic
437C2×C22⋊C4C7×D411yescharacteristic
438C2×C42—21no—
439C2×C42C23×C711yescharacteristic
440C2×C42C23×C711yescharacteristic
441#107—22no—
442#107—22no—
443#103—22no—
444#103—22no—
445#103—41no—
446#102—22no—
447#102—22no—
448#102—41no—
449#102—41no—
450#102C7×D414yes—
451C22⋊C8—22no—
452#97—22no—
453#97—41no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95C7×D411yescharacteristic
458#95C7×D411yescharacteristic
459C22×C7—22no—
460C22×C7—22no—
461C22×C7—22no—
462C22×C7—41no—
463C22×C7—41no—
464C22×C7—41no—
465C22×C7—41no—
466C22×C7—42no—
467C22×C7—42no—
468C22×C7—42no—
469C22×C7—81no—
470C22×C7—81no—
471C22×C7—81no—
472C22×C7—81no—
473C22×C7—81no—
474C22×C7—81no—
475C22×C7—81no—
476C22×C7—81no—
477C22×C7—81no—
478C22×C7—81no—
479C22×C7—81no—
480C22×C7#53211yescharacteristic
481C22×C7D4211yescharacteristic
482C22×C7#54611yescharacteristic
483C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
484C22×C7#57511yescharacteristic
485C22×C7#57611yescharacteristic
486C22×C7#57811yescharacteristic
487C4×C7—41no—
488C4×C7—42no—
489C4×C7—41no—
490C4×C7—42no—
491C4×C7—41no—
492C4×C7—41no—
493C4×C7—41no—
494C4×C7—81no—
495C4×C7—81no—
496C4×C7—81no—
497C4×C7—81no—
498C4×C7#52511yescharacteristic
499C4×C7#54011yescharacteristic
500C4×C7#54611yescharacteristic
501C4×C7#55311yescharacteristic
502C24—21no—
503C24—21no—
504C24C2×C7×D411yescharacteristic
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8C7×#4112yes—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—81no—
527C2×D4—81no—
528C2×D4C2×C7×D412yes—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—81no—
544C22×C4C2×C7×D411yescharacteristic
545C22×C4C2×C7×D411yescharacteristic
546C22×C4C2×C7×D411yescharacteristic
547C22×C4C2×C7×D411yescharacteristic
548C22×C4C2×C7×D411yescharacteristic
549C22×C4C24×C711yescharacteristic
550SD16—28no—
551D8—44no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—44no—
562C2×C8C2×C7×D412yes—
563C2×C8C7×#4112yes—
564C2×C8C7×#4112yes—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—81no—
579C4⋊C4—81no—
580C4⋊C4C2×C7×D412yes—
581C22⋊C4—22no—
582C22⋊C4—41no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—81no—
594C42—21no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—42no—
599C2×C7—42no—
600C2×C7—82no—
601C2×C7—161no—
602C2×C7#246411yescharacteristic
603C2×C7#317511yescharacteristic
604C2×C7#318011yescharacteristic
605C2×C7#326411yescharacteristic
606C2×C7#326911yescharacteristic
607C2×C7#330811yescharacteristic
608C2×C7#330911yescharacteristic
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—22no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23C7×AGL(1,ℤ/8)12yes—
630C23C22×C7×D411yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—41no—
634Q8—41no—
635D4—22no—
636D4—22no—
637D4—41no—
638D4—41no—
639D4—41no—
640D4—41no—
641D4—41no—
642D4—41no—
643D4—84no—
644D4—84no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—84no—
683C2×C4C22×C7×D411yescharacteristic
684C2×C4C2×C7×#4111yescharacteristic
685C2×C4C2×C7×#4111yescharacteristic
686C2×C4C2×C7×#4111yescharacteristic
687C2×C4C7×H(5,𝔽2)11yescharacteristic
688C2×C4C7×H(5,𝔽2)11yescharacteristic
689C8—22no—
690C8—22no—
691C8—22no—
692C8—41no—
693C7#2697511yescharacteristic, direct product factor, Sylow
694C22—22no—
695C22—22no—
696C22—22no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22C7×#53211yescharacteristic
716C22C7×D4211yescharacteristic
717C22C7×#54611yescharacteristic
718C22C2×C7×AGL(1,ℤ/8)11yescharacteristic
719C22C7×#57511yescharacteristic
720C22C7×#57611yescharacteristic
721C22C7×#57811yescharacteristic
722C4—41no—
723C4—42no—
724C4—41no—
725C4—42no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4—81no—
730C4—81no—
731C4—81no—
732C4—81no—
733C4C7×#52511yescharacteristic
734C4C7×#54011yescharacteristic
735C4C7×#54611yescharacteristic
736C4C7×#55311yescharacteristic
737C2—42no—
738C2—82no—
739C2—161no—
740C2C7×#246411yescharacteristic
741C2C7×#317511yescharacteristic
742C2C7×#318011yescharacteristic
743C2C7×#326411yescharacteristic
744C2C7×#326911yescharacteristic
745C2C7×#330811yescharacteristic
746C2C7×#330911yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC2×C7×#466C2
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
2. C2×C7×#440C2semidirect
3. C7×#2426C2semidirect
4. C7×#2422C2semidirect
5. C7×#2083C2semidirect
6. C7×#2033C2semidirect
7. C7×#2012C2semidirect
8. C7×#2000C2semidirect
9. C7×#1959C2semidirect
10. C7×#1936C2semidirect
11. C7×#1936C2semidirect
12. C7×#1892C2semidirect
13. C7×#1879C2semidirect
14. C7×#1863C2semidirect
15. C7×#1752C2semidirect
61. #26975C7direct (N × H)
141. C2×#440C2×C7semidirect
142. #2426C2×C7semidirect
143. #2422C2×C7semidirect
144. #2083C2×C7semidirect
145. #2033C2×C7semidirect
146. #2012C2×C7semidirect
147. #2000C2×C7semidirect
148. #1959C2×C7semidirect
149. #1936C2×C7semidirect
150. #1936C2×C7semidirect
151. #1892C2×C7semidirect
152. #1879C2×C7semidirect
153. #1863C2×C7semidirect
154. #1752C2×C7semidirect
693. C7#26975direct (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×#4402
C7×#24262
C7×#24222
C7×#20832
C7×#20332
C7×#20122
C7×#20002
C7×#19592
C7×#19362
C7×#18922
C7×#18792
C7×#18632
C7×#17522
#269757