Finite Group Databasebeta

← C7×#24787 #13202003

Subgroups — C7×#24787 #13202003

Order 1792.

1054 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#468C211yesmaximal, characteristic, complemented
2C2×C7×#465C211yesmaximal, characteristic, complemented
3C2×C7×#435C211yesmaximal, characteristic, complemented
4C22×C7×#107C211yesmaximal, characteristic, complemented
5C7×#2417C211yesmaximal, characteristic, complemented
6C7×#2416C211yesmaximal, characteristic
7C7×#2068C211yesmaximal, characteristic, complemented
8C7×#2067C211yesmaximal, characteristic, complemented
9C7×#2036C211yesmaximal, characteristic, complemented
10C7×#2033C211yesmaximal, characteristic, complemented
11C7×#1973C211yesmaximal, characteristic, complemented
12C7×#1943C211yesmaximal, characteristic, complemented
13C7×#1874C211yesmaximal, characteristic, complemented
14C7×#1872C211yesmaximal, characteristic, complemented
15C7×#1809C211yesmaximal, characteristic, complemented
16C22×C7×SD16C2211yescharacteristic
17C22×C7×M16C2211yescharacteristic
18C23×C7×C8C2211yescharacteristic
19C2×C7×C22⋊Q8C2211yescharacteristic
20C2×C7×C22⋊Q8C2211yescharacteristic
21C2×C7×#121—21no—
22C2×C7×#121C2211yescharacteristic
23C2×C7×#121C2211yescharacteristic
24C2×C4×C7×D4C2211yescharacteristic
25C22×C7×C4⋊C4C2211yescharacteristic
26C22×C7×C4⋊C4C2211yescharacteristic
27C7×#468—24no—
28C7×#465—24no—
29C7×#435—24no—
30C2×C7×#107—24no—
31C2×C7×#107C2211yescharacteristic
32C2×C7×#107C2211yescharacteristic
33C2×C7×#107C2211yescharacteristic
34C2×C7×#107C2211yescharacteristic
35C2×C7×#106C2211yescharacteristic
36C2×C7×C4⋊C8C2211yescharacteristic
37C2×C7×#103C2211yescharacteristic
38C2×C7×#103C2211yescharacteristic
39C2×C7×#103C2211yescharacteristic
40C2×C7×#102C2211yescharacteristic
41C2×C7×#102C2211yescharacteristic
42C2×C7×#102C2211yescharacteristic
43C2×C7×C22⋊C8C2211yescharacteristic
44C2×C7×C22⋊C8C2211yescharacteristic
45C2×C7×#97C2211yescharacteristic
46C7×#398—21no—
47C7×#396—21no—
48C7×#396—21no—
49C7×#394—21no—
50C7×#391C2211yescharacteristic
51C7×#390C2211yescharacteristic
52C7×#389C2211yescharacteristic
53C7×#389C2211yescharacteristic
54C7×#386—21no—
55C7×#386—21no—
56C7×#380—21no—
57C7×#380C2211yescharacteristic
58C7×#380C2211yescharacteristic
59C7×#340C2211yescharacteristic
60C7×#340C2211yescharacteristic
61C7×#340C2211yescharacteristic
62C7×#340C2211yescharacteristic
63#24787C711yesmaximal, characteristic, direct product factor, Sylow
64C22×C7×Q8C2311yescharacteristic
65C22×C7×D4—21no—
66C22×C7×D4—21no—
67C22×C7×D4D411yescharacteristic
68C22×C7×D4C2311yescharacteristic
69C23×C4×C7—21no—
70C23×C4×C7—21no—
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C2×C7×SD16—22no—
74C2×C7×SD16—22no—
75C2×C7×SD16—22no—
76C2×C7×M16—22no—
77C2×C7×M16—22no—
78C2×C7×M16—22no—
79C22×C7×C8—22no—
80C22×C7×C8—22no—
81C22×C7×C8D414yescomplemented
82C22×C7×C8C2311yescharacteristic
83C22×C7×C8C2311yescharacteristic
84C22×C7×C8C2311yescharacteristic
85C22×C7×C8C2311yescharacteristic
86C7×C22⋊Q8—22no—
87C7×C22⋊Q8—22no—
88C7×C22⋊Q8—22no—
89C7×C22⋊Q8—41no—
90C7×#121—22no—
91C7×#121—22no—
92C7×#121—22no—
93C7×#121—41no—
94C7×#121—44no—
95C4×C7×D4—22no—
96C4×C7×D4—22no—
97C2×C7×C4⋊C4—22no—
98C2×C7×C4⋊C4—22no—
99C2×C7×C4⋊C4—21no—
100C2×C7×C4⋊C4—21no—
101C2×C7×C4⋊C4—21no—
102C2×C7×C4⋊C4—21no—
103C2×C7×C4⋊C4—21no—
104C2×C7×C4⋊C4—21no—
105C2×C7×C4⋊C4—41no—
106C2×C7×C4⋊C4—41no—
107C2×C7×C4⋊C4D411yescharacteristic
108C2×C7×C4⋊C4C2311yescharacteristic
109C2×C7×C4⋊C4C2311yescharacteristic
110C2×C7×C4⋊C4C2311yescharacteristic
111C2×C7×C4⋊C4C2311yescharacteristic
112C2×C7×C4⋊C4C2311yescharacteristic
113C2×C7×C4⋊C4C2311yescharacteristic
114C2×C7×C22⋊C4—21no—
115C2×C7×C22⋊C4—21no—
116C2×C7×C22⋊C4—21no—
117C2×C7×C22⋊C4—21no—
118C2×C7×C22⋊C4—21no—
119C2×C7×C22⋊C4—21no—
120C2×C7×C22⋊C4—21no—
121C2×C7×C22⋊C4—21no—
122C2×C7×C22⋊C4D411yescharacteristic
123C2×C7×C22⋊C4D411yescharacteristic
124C2×C42×C7C2311yescharacteristic
125C7×#107—22no—
126C7×#107—22no—
127C7×#107—22no—
128C7×#107D414yescomplemented
129C7×#106—22no—
130C7×C4⋊C8—22no—
131C7×#103—22no—
132C7×#103—22no—
133C7×#103—41no—
134C7×#102—22no—
135C7×#102—22no—
136C7×#102—41no—
137C7×C22⋊C8—22no—
138C7×C22⋊C8—22no—
139C7×#97—22no—
140C7×#95—21no—
141C7×#95—21no—
142C7×#95—21no—
143C7×#95—21no—
144C7×#95—21no—
145C7×#95—21no—
146C2×#468C2×C711yescharacteristic, complemented
147C2×#465C2×C711yescharacteristic, complemented
148C2×#435C2×C711yescharacteristic, complemented
149C22×#107C2×C711yescharacteristic, complemented
150#2417C2×C711yescharacteristic, complemented
151#2416C2×C711yescharacteristic
152#2068C2×C711yescharacteristic, complemented
153#2067C2×C711yescharacteristic, complemented
154#2036C2×C711yescharacteristic, complemented
155#2033C2×C711yescharacteristic, complemented
156#1973C2×C711yescharacteristic, complemented
157#1943C2×C711yescharacteristic, complemented
158#1874C2×C711yescharacteristic, complemented
159#1872C2×C711yescharacteristic, complemented
160#1809C2×C711yescharacteristic, complemented
161C24×C7—21no—
162C24×C7C2×D411yescharacteristic
163C24×C7C2×D411yescharacteristic
164C2×C7×Q8—21no—
165C2×C7×Q8—21no—
166C2×C7×Q8—21no—
167C2×C7×Q8—21no—
168C2×C7×Q8—21no—
169C2×C7×Q8—21no—
170C2×C7×D4—22no—
171C2×C7×D4—22no—
172C2×C7×D4—22no—
173C2×C7×D4—21no—
174C2×C7×D4—21no—
175C2×C7×D4—21no—
176C2×C7×D4—21no—
177C2×C7×D4—21no—
178C2×C7×D4—21no—
179C2×C7×D4—42no—
180C2×C7×D4—42no—
181C2×C7×D4—42no—
182C2×C7×D4—42no—
183C2×C7×D4—42no—
184C2×C7×D4—81no—
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—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—42no—
203C22×C4×C7—42no—
204C22×C4×C7—42no—
205C22×C4×C7—42no—
206C22×C4×C7—81no—
207C22×C4×C7—81no—
208C22×C4×C7C2×D411yescharacteristic
209C22×C4×C7C2×D411yescharacteristic
210C22×C4×C7C2×D411yescharacteristic
211C22×C4×C7C2×D411yescharacteristic
212C22×C4×C7C2×D412yes—
213C22×C4×C7#4112yes—
214C22×C4×C7C2411yescharacteristic
215C7×SD16—44no—
216C7×M16—44no—
217C2×C7×C8—21no—
218C2×C7×C8—21no—
219C2×C7×C8—28no—
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×C8C2×D412yes—
227C2×C7×C8C2×D412yes—
228C2×C7×C8C2×D412yes—
229C2×C7×C8#4112yes—
230C7×C4⋊C4—22no—
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—21no—
240C7×C4⋊C4—21no—
241C7×C4⋊C4—42no—
242C7×C4⋊C4—42no—
243C7×C4⋊C4—42no—
244C7×C4⋊C4—42no—
245C7×C4⋊C4—42no—
246C7×C4⋊C4—81no—
247C7×C4⋊C4C2×D412yes—
248C7×C4⋊C4C2×D412yes—
249C7×C22⋊C4—22no—
250C7×C22⋊C4—22no—
251C7×C22⋊C4—42no—
252C7×C22⋊C4—42no—
253C7×C22⋊C4—42no—
254C7×C22⋊C4—42no—
255C7×C22⋊C4—42no—
256C7×C22⋊C4—42no—
257C7×C22⋊C4—81no—
258C7×C22⋊C4—81no—
259C42×C7—21no—
260C42×C7—21no—
261C22×SD16C22×C711yescharacteristic
262C22×M16C22×C711yescharacteristic
263C23×C8C22×C711yescharacteristic
264C2×C22⋊Q8C22×C711yescharacteristic
265C2×C22⋊Q8C22×C711yescharacteristic
266C2×#121—21no—
267C2×#121C22×C711yescharacteristic
268C2×#121C22×C711yescharacteristic
269C2×C4×D4C22×C711yescharacteristic
270C22×C4⋊C4C22×C711yescharacteristic
271C22×C4⋊C4C22×C711yescharacteristic
272#468—24no—
273#465—24no—
274#435—24no—
275C2×#107—24no—
276C2×#107C22×C711yescharacteristic
277C2×#107C22×C711yescharacteristic
278C2×#107C22×C711yescharacteristic
279C2×#107C22×C711yescharacteristic
280C2×#106C22×C711yescharacteristic
281C2×C4⋊C8C22×C711yescharacteristic
282C2×#103C22×C711yescharacteristic
283C2×#103C22×C711yescharacteristic
284C2×#103C22×C711yescharacteristic
285C2×#102C22×C711yescharacteristic
286C2×#102C22×C711yescharacteristic
287C2×#102C22×C711yescharacteristic
288C2×C22⋊C8C22×C711yescharacteristic
289C2×C22⋊C8C22×C711yescharacteristic
290C2×#97C22×C711yescharacteristic
291#398—21no—
292#396—21no—
293#396—21no—
294#394—21no—
295#391C22×C711yescharacteristic
296#390C22×C711yescharacteristic
297#389C22×C711yescharacteristic
298#389C22×C711yescharacteristic
299#386—21no—
300#386—21no—
301#380—21no—
302#380C22×C711yescharacteristic
303#380C22×C711yescharacteristic
304#340C22×C711yescharacteristic
305#340C22×C711yescharacteristic
306#340C22×C711yescharacteristic
307#340C22×C711yescharacteristic
308C23×C7—21no—
309C23×C7—21no—
310C23×C7—21no—
311C23×C7—21no—
312C23×C7—21no—
313C23×C7—21no—
314C23×C7—21no—
315C23×C7—21no—
316C23×C7—21no—
317C23×C7—21no—
318C23×C7—21no—
319C23×C7—41no—
320C23×C7—41no—
321C23×C7—41no—
322C23×C7—41no—
323C23×C7—41no—
324C23×C7—41no—
325C23×C7—41no—
326C23×C7#12112yes—
327C23×C7AGL(1,ℤ/8)12yes—
328C23×C7#13712yes—
329C23×C7C22×D411yescharacteristic
330C7×Q8—41no—
331C7×Q8—41no—
332C7×Q8—41no—
333C7×Q8—41no—
334C7×D4—44no—
335C7×D4—41no—
336C7×D4—41no—
337C7×D4—41no—
338C7×D4—41no—
339C7×D4—84no—
340C7×D4—84no—
341C2×C4×C7—21no—
342C2×C4×C7—21no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—21no—
348C2×C4×C7—21no—
349C2×C4×C7—21no—
350C2×C4×C7—21no—
351C2×C4×C7—22no—
352C2×C4×C7—22no—
353C2×C4×C7—21no—
354C2×C4×C7—21no—
355C2×C4×C7—21no—
356C2×C4×C7—21no—
357C2×C4×C7—21no—
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—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—84no—
382C2×C4×C7—84no—
383C2×C4×C7#12112yes—
384C2×C4×C7C22×D411yescharacteristic
385C2×C4×C7C22×D411yescharacteristic
386C2×C4×C7C2×#4111yescharacteristic
387C2×C4×C7C2×#4111yescharacteristic
388C2×C4×C7H(5,𝔽2)11yescharacteristic
389C2×C4×C72−1+411yescharacteristic
390C7×C8—22no—
391C7×C8—41no—
392C7×C8—41no—
393C7×C8#12114yescomplemented
394C22×Q8C23×C711yescharacteristic
395C22×D4—21no—
396C22×D4—21no—
397C22×D4C7×D411yescharacteristic
398C22×D4C23×C711yescharacteristic
399C23×C4—21no—
400C23×C4—21no—
401C23×C4C23×C711yescharacteristic
402C23×C4C23×C711yescharacteristic
403C2×SD16—22no—
404C2×SD16—22no—
405C2×SD16—22no—
406C2×M16—22no—
407C2×M16—22no—
408C2×M16—22no—
409C22×C8—22no—
410C22×C8—22no—
411C22×C8C7×D414yescomplemented
412C22×C8C23×C711yescharacteristic
413C22×C8C23×C711yescharacteristic
414C22×C8C23×C711yescharacteristic
415C22×C8C23×C711yescharacteristic
416C22⋊Q8—22no—
417C22⋊Q8—22no—
418C22⋊Q8—22no—
419C22⋊Q8—41no—
420#121—22no—
421#121—22no—
422#121—22no—
423#121—41no—
424#121—44no—
425C4×D4—22no—
426C4×D4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—41no—
436C2×C4⋊C4—41no—
437C2×C4⋊C4C7×D411yescharacteristic
438C2×C4⋊C4C23×C711yescharacteristic
439C2×C4⋊C4C23×C711yescharacteristic
440C2×C4⋊C4C23×C711yescharacteristic
441C2×C4⋊C4C23×C711yescharacteristic
442C2×C4⋊C4C23×C711yescharacteristic
443C2×C4⋊C4C23×C711yescharacteristic
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4C7×D411yescharacteristic
453C2×C22⋊C4C7×D411yescharacteristic
454C2×C42C23×C711yescharacteristic
455#107—22no—
456#107—22no—
457#107—22no—
458#107C7×D414yescomplemented
459#106—22no—
460C4⋊C8—22no—
461#103—22no—
462#103—22no—
463#103—41no—
464#102—22no—
465#102—22no—
466#102—41no—
467C22⋊C8—22no—
468C22⋊C8—22no—
469#97—22no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476C22×C7—22no—
477C22×C7—22no—
478C22×C7—22no—
479C22×C7—22no—
480C22×C7—22no—
481C22×C7—22no—
482C22×C7—41no—
483C22×C7—41no—
484C22×C7—41no—
485C22×C7—41no—
486C22×C7—41no—
487C22×C7—41no—
488C22×C7—41no—
489C22×C7—81no—
490C22×C7—81no—
491C22×C7—81no—
492C22×C7—81no—
493C22×C7—81no—
494C22×C7—81no—
495C22×C7—81no—
496C22×C7#46814yescomplemented
497C22×C7C2×#12111yescharacteristic
498C22×C7D4211yescharacteristic
499C22×C7#54711yescharacteristic
500C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
501C22×C7C2×#13711yescharacteristic
502C22×C7#57611yescharacteristic
503C22×C7#57811yescharacteristic
504C4×C7—22no—
505C4×C7—41no—
506C4×C7—42no—
507C4×C7—42no—
508C4×C7—41no—
509C4×C7—41no—
510C4×C7—81no—
511C4×C7—81no—
512C4×C7—81no—
513C4×C7—81no—
514C4×C7—81no—
515C4×C7C2×#12111yescharacteristic
516C4×C7#53711yescharacteristic
517C4×C7#54811yescharacteristic
518C4×C7#55311yescharacteristic
519C24—21no—
520C24C2×C7×D411yescharacteristic
521C24C2×C7×D411yescharacteristic
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—81no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—81no—
565C22×C4—81no—
566C22×C4C2×C7×D411yescharacteristic
567C22×C4C2×C7×D411yescharacteristic
568C22×C4C2×C7×D411yescharacteristic
569C22×C4C2×C7×D411yescharacteristic
570C22×C4C2×C7×D412yes—
571C22×C4C7×#4112yes—
572C22×C4C24×C711yescharacteristic
573SD16—44no—
574M16—44no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—28no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8C2×C7×D412yes—
585C2×C8C2×C7×D412yes—
586C2×C8C2×C7×D412yes—
587C2×C8C7×#4112yes—
588C4⋊C4—22no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—81no—
605C4⋊C4C2×C7×D412yes—
606C4⋊C4C2×C7×D412yes—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—81no—
616C22⋊C4—81no—
617C42—21no—
618C42—21no—
619C2×C7—24no—
620C2×C7—81no—
621C2×C7—161no—
622C2×C7#241611yescharacteristic
623C2×C7C2×#46811yescharacteristic
624C2×C7#306111yescharacteristic
625C2×C7#326411yescharacteristic
626C2×C7#327011yescharacteristic
627C2×C7#334311yescharacteristic
628C2×C7#334611yescharacteristic
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23C7×#12112yes—
648C23C7×AGL(1,ℤ/8)12yes—
649C23C7×#13712yes—
650C23C22×C7×D411yescharacteristic
651Q8—41no—
652Q8—41no—
653Q8—41no—
654Q8—41no—
655D4—44no—
656D4—41no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—84no—
661D4—84no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—84no—
703C2×C4—84no—
704C2×C4C7×#12112yes—
705C2×C4C22×C7×D411yescharacteristic
706C2×C4C22×C7×D411yescharacteristic
707C2×C4C2×C7×#4111yescharacteristic
708C2×C4C2×C7×#4111yescharacteristic
709C2×C4C7×H(5,𝔽2)11yescharacteristic
710C2×C4C7×2−1+411yescharacteristic
711C8—22no—
712C8—41no—
713C8—41no—
714C8C7×#12114yescomplemented
715C7#2478711yescharacteristic, direct product factor, Sylow
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22C7×#46814yescomplemented
737C22C2×C7×#12111yescharacteristic
738C22C7×D4211yescharacteristic
739C22C7×#54711yescharacteristic
740C22C2×C7×AGL(1,ℤ/8)11yescharacteristic
741C22C2×C7×#13711yescharacteristic
742C22C7×#57611yescharacteristic
743C22C7×#57811yescharacteristic
744C4—22no—
745C4—41no—
746C4—42no—
747C4—42no—
748C4—41no—
749C4—41no—
750C4—81no—
751C4—81no—
752C4—81no—
753C4—81no—
754C4—81no—
755C4C2×C7×#12111yescharacteristic
756C4C7×#53711yescharacteristic
757C4C7×#54811yescharacteristic
758C4C7×#55311yescharacteristic
759C2—24no—
760C2—81no—
761C2—161no—
762C2C7×#241611yescharacteristic
763C2C2×C7×#46811yescharacteristic
764C2C7×#306111yescharacteristic
765C2C7×#326411yescharacteristic
766C2C7×#327011yescharacteristic
767C2C7×#334311yescharacteristic
768C2C7×#334611yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC7×#2416C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C2×C4×C7×D4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C7×#468C2semidirect
2. C2×C7×#465C2semidirect
3. C2×C7×#435C2semidirect
4. C22×C7×#107C2semidirect
5. C7×#2417C2semidirect
7. C7×#2068C2semidirect
8. C7×#2067C2semidirect
9. C7×#2036C2semidirect
10. C7×#2033C2semidirect
11. C7×#1973C2semidirect
12. C7×#1943C2semidirect
13. C7×#1874C2semidirect
14. C7×#1872C2semidirect
15. C7×#1809C2semidirect
63. #24787C7direct (N × H)
81. C22×C7×C8D4semidirect
128. C7×#107D4semidirect
146. C2×#468C2×C7semidirect
147. C2×#465C2×C7semidirect
148. C2×#435C2×C7semidirect
149. C22×#107C2×C7semidirect
150. #2417C2×C7semidirect
152. #2068C2×C7semidirect
153. #2067C2×C7semidirect
154. #2036C2×C7semidirect
155. #2033C2×C7semidirect
156. #1973C2×C7semidirect
157. #1943C2×C7semidirect
158. #1874C2×C7semidirect
159. #1872C2×C7semidirect
160. #1809C2×C7semidirect
393. C7×C8#121semidirect
411. C22×C8C7×D4semidirect
458. #107C7×D4semidirect
496. C22×C7#468semidirect
714. C8C7×#121semidirect
715. C7#24787direct (N × H)
736. C22C7×#468semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4682
C2×C7×#4652
C2×C7×#4352
C22×C7×#1072
C7×#24172
C7×#24162
C7×#20682
C7×#20672
C7×#20362
C7×#20332
C7×#19732
C7×#19432
C7×#18742
C7×#18722
C7×#18092
#247877