Finite Group Databasebeta

← C7×#24017 #13201233

Subgroups — C7×#24017 #13201233

Order 1792.

1340 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#537C211yesmaximal, characteristic
2C2×C7×#485C211yesmaximal, characteristic, complemented
3C2×C7×#482C211yesmaximal, characteristic, complemented
4C7×#2311C211yesmaximal, characteristic, complemented
5C7×#2036C211yesmaximal, characteristic, complemented
6C7×#2035C211yesmaximal, characteristic, complemented
7C7×#2034C211yesmaximal, characteristic, complemented
8C7×#2033C211yesmaximal, characteristic, complemented
9C7×#1874C211yesmaximal, characteristic, complemented
10C7×#1872C211yesmaximal, characteristic, complemented
11C7×#1853C211yesmaximal, characteristic, complemented
12C7×#1852C211yesmaximal, characteristic, complemented
13C7×#1788C211yesmaximal, characteristic, complemented
14C7×#1788C211yesmaximal, characteristic, complemented
15C7×#1780C211yesmaximal, characteristic, complemented
16C22×C7×#41C2211yescharacteristic
17C22×C7×#41C2211yescharacteristic
18C7×#537—24no—
19C7×#537—24no—
20C2×C7×C22⋊Q8—21no—
21C2×C7×C22⋊Q8C2211yescharacteristic
22C2×C7×C22⋊Q8C2211yescharacteristic
23C2×C7×#121—21no—
24C2×C7×#121—21no—
25C2×C7×#121—21no—
26C2×C7×#121C2211yescharacteristic
27C2×C7×#121C2211yescharacteristic
28C2×C7×#117C2211yescharacteristic
29C22×C7×C4⋊C4C2211yescharacteristic
30C22×C7×C4⋊C4C2211yescharacteristic
31C7×#485—24no—
32C7×#482—24no—
33C2×C7×#107C2211yescharacteristic
34C2×C7×#107C2211yescharacteristic
35C2×C7×#106C2211yescharacteristic
36C2×C7×#106C2211yescharacteristic
37C2×C7×#103C2211yescharacteristic
38C2×C7×#103C2211yescharacteristic
39C2×C7×#103C2211yescharacteristic
40C2×C7×#103C2211yescharacteristic
41C2×C7×#102C2211yescharacteristic
42C2×C7×#102C2211yescharacteristic
43C2×C7×#102C2211yescharacteristic
44C2×C7×#102C2211yescharacteristic
45C2×C7×C22⋊C8C2211yescharacteristic
46C2×C7×C22⋊C8C2211yescharacteristic
47C2×C7×C22⋊C8C2211yescharacteristic
48C2×C7×C22⋊C8C2211yescharacteristic
49C2×C7×C22⋊C8C2211yescharacteristic
50C2×C7×C22⋊C8C2211yescharacteristic
51C7×#391—21no—
52C7×#390—21no—
53C7×#386—21no—
54C7×#386—21no—
55C7×#380C2211yescharacteristic
56C7×#380C2211yescharacteristic
57C7×#380C2211yescharacteristic
58C7×#380C2211yescharacteristic
59C7×#340C2211yescharacteristic
60C7×#340C2211yescharacteristic
61C7×#340C2211yescharacteristic
62C7×#340C2211yescharacteristic
63#24017C711yesmaximal, characteristic, direct product factor, Sylow
64C2×C7×#41—22no—
65C2×C7×#41—22no—
66C2×C7×#41—22no—
67C2×C7×#41—22no—
68C2×C7×#41—22no—
69C2×C7×#41—22no—
70C2×C7×#41—22no—
71C2×C7×#41—22no—
72C2×C7×#41—41no—
73C2×C7×#41—41no—
74C2×C7×#41—41no—
75C2×C7×#41—41no—
76C22×C7×Q8D411yescharacteristic
77C22×C7×Q8C2311yescharacteristic
78C22×C7×D4—21no—
79C22×C7×D4—21no—
80C22×C7×D4—21no—
81C22×C7×D4D411yescharacteristic
82C22×C7×D4D411yescharacteristic
83C22×C7×D4D411yescharacteristic
84C22×C7×D4C2311yescharacteristic
85C23×C4×C7—21no—
86C23×C4×C7—21no—
87C23×C4×C7—21no—
88C23×C4×C7C2311yescharacteristic
89C23×C4×C7C2311yescharacteristic
90C23×C4×C7C2311yescharacteristic
91C22×C7×C8C2311yescharacteristic
92C22×C7×C8C2311yescharacteristic
93C22×C7×C8C2311yescharacteristic
94C22×C7×C8C2311yescharacteristic
95C7×C22⋊Q8—28no—
96C7×C22⋊Q8—22no—
97C7×C22⋊Q8—22no—
98C7×C22⋊Q8—22no—
99C7×C22⋊Q8D414yes—
100C7×#121—28no—
101C7×#121—28no—
102C7×#121—28no—
103C7×#121—22no—
104C7×#121—22no—
105C7×#121—22no—
106C7×#121D414yes—
107C7×#117—22no—
108C7×#117—22no—
109C2×C7×C4⋊C4—21no—
110C2×C7×C4⋊C4—21no—
111C2×C7×C4⋊C4—21no—
112C2×C7×C4⋊C4—22no—
113C2×C7×C4⋊C4—22no—
114C2×C7×C4⋊C4—21no—
115C2×C7×C4⋊C4—41no—
116C2×C7×C4⋊C4—41no—
117C2×C7×C4⋊C4C2311yescharacteristic
118C2×C7×C4⋊C4C2311yescharacteristic
119C2×C7×C4⋊C4C2311yescharacteristic
120C2×C7×C4⋊C4C2311yescharacteristic
121C2×C7×C4⋊C4C2311yescharacteristic
122C2×C7×C4⋊C4C2311yescharacteristic
123C2×C7×C22⋊C4—21no—
124C2×C7×C22⋊C4—21no—
125C2×C7×C22⋊C4—21no—
126C2×C7×C22⋊C4—21no—
127C2×C7×C22⋊C4—21no—
128C2×C7×C22⋊C4—21no—
129C2×C7×C22⋊C4—21no—
130C2×C7×C22⋊C4—21no—
131C2×C7×C22⋊C4—21no—
132C2×C42×C7—21no—
133C7×#107—22no—
134C7×#107—22no—
135C7×#106—22no—
136C7×#106—22no—
137C7×#103—22no—
138C7×#103—22no—
139C7×#103—41no—
140C7×#103—41no—
141C7×#102—22no—
142C7×#102—22no—
143C7×#102—41no—
144C7×#102—41no—
145C7×C22⋊C8—22no—
146C7×C22⋊C8—22no—
147C7×C22⋊C8—22no—
148C7×C22⋊C8—22no—
149C7×C22⋊C8—41no—
150C7×C22⋊C8—41no—
151C7×#95—21no—
152C7×#95—21no—
153C7×#95—21no—
154C7×#95—21no—
155C2×#537C2×C711yescharacteristic
156C2×#485C2×C711yescharacteristic, complemented
157C2×#482C2×C711yescharacteristic, complemented
158#2311C2×C711yescharacteristic, complemented
159#2036C2×C711yescharacteristic, complemented
160#2035C2×C711yescharacteristic, complemented
161#2034C2×C711yescharacteristic, complemented
162#2033C2×C711yescharacteristic, complemented
163#1874C2×C711yescharacteristic, complemented
164#1872C2×C711yescharacteristic, complemented
165#1853C2×C711yescharacteristic, complemented
166#1852C2×C711yescharacteristic, complemented
167#1788C2×C711yescharacteristic, complemented
168#1788C2×C711yescharacteristic, complemented
169#1780C2×C711yescharacteristic, complemented
170C24×C7—21no—
171C24×C7C2×D411yescharacteristic
172C24×C7C2×D411yescharacteristic
173C24×C7C2×D411yescharacteristic
174C7×#41—44no—
175C7×#41—44no—
176C7×#41—44no—
177C7×#41—44no—
178C7×#41—44no—
179C7×#41—44no—
180C7×#41—44no—
181C7×#41—44no—
182C2×C7×Q8—22no—
183C2×C7×Q8—22no—
184C2×C7×Q8—21no—
185C2×C7×Q8—21no—
186C2×C7×Q8—21no—
187C2×C7×Q8—21no—
188C2×C7×Q8—21no—
189C2×C7×Q8—41no—
190C2×C7×Q8C2×D412yes—
191C2×C7×D4—24no—
192C2×C7×D4—22no—
193C2×C7×D4—22no—
194C2×C7×D4—22no—
195C2×C7×D4—22no—
196C2×C7×D4—24no—
197C2×C7×D4—24no—
198C2×C7×D4—22no—
199C2×C7×D4—22no—
200C2×C7×D4—21no—
201C2×C7×D4—21no—
202C2×C7×D4—21no—
203C2×C7×D4—21no—
204C2×C7×D4—21no—
205C2×C7×D4—41no—
206C2×C7×D4—41no—
207C2×C7×D4—41no—
208C2×C7×D4—42no—
209C2×C7×D4—42no—
210C2×C7×D4—81no—
211C2×C7×D4—81no—
212C2×C7×D4—81no—
213C2×C7×D4—81no—
214C2×C7×D4C2×D412yes—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7—21no—
220C22×C4×C7—21no—
221C22×C4×C7—21no—
222C22×C4×C7—21no—
223C22×C4×C7—24no—
224C22×C4×C7—21no—
225C22×C4×C7—21no—
226C22×C4×C7—21no—
227C22×C4×C7—24no—
228C22×C4×C7—21no—
229C22×C4×C7—21no—
230C22×C4×C7—21no—
231C22×C4×C7—21no—
232C22×C4×C7—21no—
233C22×C4×C7—21no—
234C22×C4×C7—21no—
235C22×C4×C7—21no—
236C22×C4×C7—21no—
237C22×C4×C7—21no—
238C22×C4×C7—42no—
239C22×C4×C7—42no—
240C22×C4×C7—42no—
241C22×C4×C7—81no—
242C22×C4×C7—81no—
243C22×C4×C7—81no—
244C22×C4×C7—81no—
245C22×C4×C7C2×D411yescharacteristic
246C22×C4×C7C2×D411yescharacteristic
247C22×C4×C7C2×D412yes—
248C22×C4×C7C2×D412yes—
249C22×C4×C7C2×D411yescharacteristic
250C22×C4×C7#4112yes—
251C22×C4×C7#4112yes—
252C22×C4×C7C2411yescharacteristic
253C2×C7×C8—21no—
254C2×C7×C8—21no—
255C2×C7×C8—21no—
256C2×C7×C8—21no—
257C2×C7×C8—21no—
258C2×C7×C8—21no—
259C2×C7×C8—21no—
260C2×C7×C8—21no—
261C2×C7×C8—21no—
262C2×C7×C8—21no—
263C2×C7×C8—21no—
264C2×C7×C8—21no—
265C7×C4⋊C4—24no—
266C7×C4⋊C4—24no—
267C7×C4⋊C4—24no—
268C7×C4⋊C4—21no—
269C7×C4⋊C4—21no—
270C7×C4⋊C4—21no—
271C7×C4⋊C4—21no—
272C7×C4⋊C4—21no—
273C7×C4⋊C4—21no—
274C7×C4⋊C4—21no—
275C7×C4⋊C4—21no—
276C7×C4⋊C4—21no—
277C7×C4⋊C4—21no—
278C7×C4⋊C4—42no—
279C7×C4⋊C4C2×D412yes—
280C7×C4⋊C4C2×D412yes—
281C7×C22⋊C4—24no—
282C7×C22⋊C4—24no—
283C7×C22⋊C4—24no—
284C7×C22⋊C4—24no—
285C7×C22⋊C4—42no—
286C7×C22⋊C4—81no—
287C7×C22⋊C4—81no—
288C7×C22⋊C4—81no—
289C7×C22⋊C4—81no—
290C42×C7—42no—
291C22×#41C22×C711yescharacteristic
292C22×#41C22×C711yescharacteristic
293#537—24no—
294#537—24no—
295C2×C22⋊Q8—21no—
296C2×C22⋊Q8C22×C711yescharacteristic
297C2×C22⋊Q8C22×C711yescharacteristic
298C2×#121—21no—
299C2×#121—21no—
300C2×#121—21no—
301C2×#121C22×C711yescharacteristic
302C2×#121C22×C711yescharacteristic
303C2×#117C22×C711yescharacteristic
304C22×C4⋊C4C22×C711yescharacteristic
305C22×C4⋊C4C22×C711yescharacteristic
306#485—24no—
307#482—24no—
308C2×#107C22×C711yescharacteristic
309C2×#107C22×C711yescharacteristic
310C2×#106C22×C711yescharacteristic
311C2×#106C22×C711yescharacteristic
312C2×#103C22×C711yescharacteristic
313C2×#103C22×C711yescharacteristic
314C2×#103C22×C711yescharacteristic
315C2×#103C22×C711yescharacteristic
316C2×#102C22×C711yescharacteristic
317C2×#102C22×C711yescharacteristic
318C2×#102C22×C711yescharacteristic
319C2×#102C22×C711yescharacteristic
320C2×C22⋊C8C22×C711yescharacteristic
321C2×C22⋊C8C22×C711yescharacteristic
322C2×C22⋊C8C22×C711yescharacteristic
323C2×C22⋊C8C22×C711yescharacteristic
324C2×C22⋊C8C22×C711yescharacteristic
325C2×C22⋊C8C22×C711yescharacteristic
326#391—21no—
327#390—21no—
328#386—21no—
329#386—21no—
330#380C22×C711yescharacteristic
331#380C22×C711yescharacteristic
332#380C22×C711yescharacteristic
333#380C22×C711yescharacteristic
334#340C22×C711yescharacteristic
335#340C22×C711yescharacteristic
336#340C22×C711yescharacteristic
337#340C22×C711yescharacteristic
338C23×C7—21no—
339C23×C7—21no—
340C23×C7—21no—
341C23×C7—21no—
342C23×C7—21no—
343C23×C7—21no—
344C23×C7—21no—
345C23×C7—21no—
346C23×C7—21no—
347C23×C7—21no—
348C23×C7—21no—
349C23×C7—21no—
350C23×C7—21no—
351C23×C7—22no—
352C23×C7—21no—
353C23×C7—21no—
354C23×C7—21no—
355C23×C7—21no—
356C23×C7—21no—
357C23×C7—21no—
358C23×C7—41no—
359C23×C7—41no—
360C23×C7—41no—
361C23×C7—41no—
362C23×C7—41no—
363C23×C7—41no—
364C23×C7#12012yes—
365C23×C7#12312yes—
366C23×C7C22×D411yescharacteristic
367C7×Q8—22no—
368C7×Q8—22no—
369C7×Q8—44no—
370C7×Q8—41no—
371C7×Q8—41no—
372C7×D4—22no—
373C7×D4—22no—
374C7×D4—44no—
375C7×D4—44no—
376C7×D4—44no—
377C7×D4—48no—
378C7×D4—41no—
379C7×D4—41no—
380C7×D4—84no—
381C7×D4—84no—
382C2×C4×C7—21no—
383C2×C4×C7—21no—
384C2×C4×C7—21no—
385C2×C4×C7—21no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—21no—
398C2×C4×C7—21no—
399C2×C4×C7—21no—
400C2×C4×C7—48no—
401C2×C4×C7—41no—
402C2×C4×C7—41no—
403C2×C4×C7—41no—
404C2×C4×C7—41no—
405C2×C4×C7—41no—
406C2×C4×C7—41no—
407C2×C4×C7—41no—
408C2×C4×C7—41no—
409C2×C4×C7—41no—
410C2×C4×C7—41no—
411C2×C4×C7—41no—
412C2×C4×C7—41no—
413C2×C4×C7—41no—
414C2×C4×C7—41no—
415C2×C4×C7—41no—
416C2×C4×C7—41no—
417C2×C4×C7—41no—
418C2×C4×C7—41no—
419C2×C4×C7—41no—
420C2×C4×C7—41no—
421C2×C4×C7—41no—
422C2×C4×C7—41no—
423C2×C4×C7—84no—
424C2×C4×C7—84no—
425C2×C4×C7#12012yes—
426C2×C4×C7#12312yes—
427C2×C4×C7C22×D411yescharacteristic
428C2×C4×C7C22×D411yescharacteristic
429C2×C4×C7C2×#4111yescharacteristic
430C2×C4×C7C2×#4111yescharacteristic
431C2×C4×C7H(5,𝔽2)11yescharacteristic
432C2×C4×C7H(5,𝔽2)11yescharacteristic
433C7×C8—41no—
434C7×C8—41no—
435C7×C8—41no—
436C7×C8—41no—
437C2×#41—22no—
438C2×#41—22no—
439C2×#41—22no—
440C2×#41—22no—
441C2×#41—22no—
442C2×#41—22no—
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—41no—
446C2×#41—41no—
447C2×#41—41no—
448C2×#41—41no—
449C22×Q8C7×D411yescharacteristic
450C22×Q8C23×C711yescharacteristic
451C22×D4—21no—
452C22×D4—21no—
453C22×D4—21no—
454C22×D4C7×D411yescharacteristic
455C22×D4C7×D411yescharacteristic
456C22×D4C7×D411yescharacteristic
457C22×D4C23×C711yescharacteristic
458C23×C4—21no—
459C23×C4—21no—
460C23×C4—21no—
461C23×C4C23×C711yescharacteristic
462C23×C4C23×C711yescharacteristic
463C23×C4C23×C711yescharacteristic
464C22×C8C23×C711yescharacteristic
465C22×C8C23×C711yescharacteristic
466C22×C8C23×C711yescharacteristic
467C22×C8C23×C711yescharacteristic
468C22⋊Q8—28no—
469C22⋊Q8—22no—
470C22⋊Q8—22no—
471C22⋊Q8—22no—
472C22⋊Q8C7×D414yes—
473#121—28no—
474#121—28no—
475#121—28no—
476#121—22no—
477#121—22no—
478#121—22no—
479#121C7×D414yes—
480#117—22no—
481#117—22no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—41no—
489C2×C4⋊C4—41no—
490C2×C4⋊C4C23×C711yescharacteristic
491C2×C4⋊C4C23×C711yescharacteristic
492C2×C4⋊C4C23×C711yescharacteristic
493C2×C4⋊C4C23×C711yescharacteristic
494C2×C4⋊C4C23×C711yescharacteristic
495C2×C4⋊C4C23×C711yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C42—21no—
506#107—22no—
507#107—22no—
508#106—22no—
509#106—22no—
510#103—22no—
511#103—22no—
512#103—41no—
513#103—41no—
514#102—22no—
515#102—22no—
516#102—41no—
517#102—41no—
518C22⋊C8—22no—
519C22⋊C8—22no—
520C22⋊C8—22no—
521C22⋊C8—22no—
522C22⋊C8—41no—
523C22⋊C8—41no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528C22×C7—22no—
529C22×C7—22no—
530C22×C7—22no—
531C22×C7—22no—
532C22×C7—22no—
533C22×C7—22no—
534C22×C7—41no—
535C22×C7—41no—
536C22×C7—41no—
537C22×C7—41no—
538C22×C7—41no—
539C22×C7—41no—
540C22×C7—41no—
541C22×C7—41no—
542C22×C7—41no—
543C22×C7—41no—
544C22×C7—42no—
545C22×C7—41no—
546C22×C7—41no—
547C22×C7—41no—
548C22×C7—41no—
549C22×C7—42no—
550C22×C7—41no—
551C22×C7—42no—
552C22×C7—81no—
553C22×C7—81no—
554C22×C7—81no—
555C22×C7—81no—
556C22×C7C2×#12011yescharacteristic
557C22×C7C2×#12311yescharacteristic
558C22×C7#53411yescharacteristic
559C22×C7#57611yescharacteristic
560C22×C7#57711yescharacteristic
561C22×C7#57711yescharacteristic
562C22×C7#57811yescharacteristic
563C4×C7—22no—
564C4×C7—22no—
565C4×C7—41no—
566C4×C7—42no—
567C4×C7—42no—
568C4×C7—42no—
569C4×C7—81no—
570C4×C7—81no—
571C4×C7—81no—
572C4×C7—81no—
573C4×C7#54611yescharacteristic
574C4×C7#54611yescharacteristic
575C4×C7#54611yescharacteristic
576C4×C7#54611yescharacteristic
577C24—21no—
578C24C2×C7×D411yescharacteristic
579C24C2×C7×D411yescharacteristic
580C24C2×C7×D411yescharacteristic
581#41—44no—
582#41—44no—
583#41—44no—
584#41—44no—
585#41—44no—
586#41—44no—
587#41—44no—
588#41—44no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—41no—
597C2×Q8C2×C7×D412yes—
598C2×D4—24no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—24no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—41no—
613C2×D4—41no—
614C2×D4—41no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4C2×C7×D412yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—24no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—24no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4—81no—
649C22×C4—81no—
650C22×C4—81no—
651C22×C4—81no—
652C22×C4C2×C7×D411yescharacteristic
653C22×C4C2×C7×D411yescharacteristic
654C22×C4C2×C7×D412yes—
655C22×C4C2×C7×D412yes—
656C22×C4C2×C7×D411yescharacteristic
657C22×C4C7×#4112yes—
658C22×C4C7×#4112yes—
659C22×C4C24×C711yescharacteristic
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—42no—
686C4⋊C4C2×C7×D412yes—
687C4⋊C4C2×C7×D412yes—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—24no—
691C22⋊C4—24no—
692C22⋊C4—42no—
693C22⋊C4—81no—
694C22⋊C4—81no—
695C22⋊C4—81no—
696C22⋊C4—81no—
697C42—42no—
698C2×C7—42no—
699C2×C7—42no—
700C2×C7—81no—
701C2×C7—82no—
702C2×C7#240511yescharacteristic
703C2×C7#301211yescharacteristic
704C2×C7#301311yescharacteristic
705C2×C7#309811yescharacteristic
706C2×C7#309911yescharacteristic
707C2×C7#319811yescharacteristic
708C2×C7#320111yescharacteristic
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—22no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23C7×#12012yes—
736C23C7×#12312yes—
737C23C22×C7×D411yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—44no—
741Q8—41no—
742Q8—41no—
743D4—22no—
744D4—22no—
745D4—44no—
746D4—44no—
747D4—44no—
748D4—48no—
749D4—41no—
750D4—41no—
751D4—84no—
752D4—84no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—48no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—84no—
795C2×C4—84no—
796C2×C4C7×#12012yes—
797C2×C4C7×#12312yes—
798C2×C4C22×C7×D411yescharacteristic
799C2×C4C22×C7×D411yescharacteristic
800C2×C4C2×C7×#4111yescharacteristic
801C2×C4C2×C7×#4111yescharacteristic
802C2×C4C7×H(5,𝔽2)11yescharacteristic
803C2×C4C7×H(5,𝔽2)11yescharacteristic
804C8—41no—
805C8—41no—
806C8—41no—
807C8—41no—
808C7#2401711yescharacteristic, direct product factor, Sylow
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—42no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—42no—
829C22—41no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22C2×C7×#12011yescharacteristic
838C22C2×C7×#12311yescharacteristic
839C22C7×#53411yescharacteristic
840C22C7×#57611yescharacteristic
841C22C7×#57711yescharacteristic
842C22C7×#57711yescharacteristic
843C22C7×#57811yescharacteristic
844C4—22no—
845C4—22no—
846C4—41no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—81no—
851C4—81no—
852C4—81no—
853C4—81no—
854C4C7×#54611yescharacteristic
855C4C7×#54611yescharacteristic
856C4C7×#54611yescharacteristic
857C4C7×#54611yescharacteristic
858C2—42no—
859C2—42no—
860C2—81no—
861C2—82no—
862C2C7×#240511yescharacteristic
863C2C7×#301211yescharacteristic
864C2C7×#301311yescharacteristic
865C2C7×#309811yescharacteristic
866C2C7×#309911yescharacteristic
867C2C7×#319811yescharacteristic
868C2C7×#320111yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC2×C7×#537C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C22×C7×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#485C2semidirect
3. C2×C7×#482C2semidirect
4. C7×#2311C2semidirect
5. C7×#2036C2semidirect
6. C7×#2035C2semidirect
7. C7×#2034C2semidirect
8. C7×#2033C2semidirect
9. C7×#1874C2semidirect
10. C7×#1872C2semidirect
11. C7×#1853C2semidirect
12. C7×#1852C2semidirect
13. C7×#1788C2semidirect
14. C7×#1788C2semidirect
15. C7×#1780C2semidirect
63. #24017C7direct (N × H)
156. C2×#485C2×C7semidirect
157. C2×#482C2×C7semidirect
158. #2311C2×C7semidirect
159. #2036C2×C7semidirect
160. #2035C2×C7semidirect
161. #2034C2×C7semidirect
162. #2033C2×C7semidirect
163. #1874C2×C7semidirect
164. #1872C2×C7semidirect
165. #1853C2×C7semidirect
166. #1852C2×C7semidirect
167. #1788C2×C7semidirect
168. #1788C2×C7semidirect
169. #1780C2×C7semidirect
808. C7#24017direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5372
C2×C7×#4852
C2×C7×#4822
C7×#23112
C7×#20362
C7×#20352
C7×#20342
C7×#20332
C7×#18742
C7×#18722
C7×#18532
C7×#18522
C7×#17882
C7×#17802
#240177