Finite Group Databasebeta

← C7×#25158 #13202374

Subgroups — C7×#25158 #13202374

Order 1792.

1140 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#463C211yesmaximal, characteristic, complemented
2C2×C7×#452C211yesmaximal, characteristic, complemented
3C2×C7×#449C211yesmaximal, characteristic
4C2×C4×C7×SD16C211yesmaximal, characteristic, complemented
5C7×#2426C211yesmaximal, characteristic, complemented
6C7×#2339C211yesmaximal, characteristic, complemented
7C7×#2066C211yesmaximal, characteristic, complemented
8C7×#2035C211yesmaximal, characteristic, complemented
9C7×#2034C211yesmaximal, characteristic, complemented
10C7×#2015C211yesmaximal, characteristic, complemented
11C7×#1968C211yesmaximal, characteristic, complemented
12C7×#1923C211yesmaximal, characteristic, complemented
13C7×#1879C211yesmaximal, characteristic, complemented
14C7×#1878C211yesmaximal, characteristic, complemented
15C7×#1864C211yesmaximal, characteristic, complemented
16C22×C7×#41C2211yescharacteristic
17C22×C7×Q16C2211yescharacteristic
18C22×C7×SD16C2211yescharacteristic
19C22×C7×SD16C2211yescharacteristic
20C22×C7×D8C2211yescharacteristic
21C2×C7×#124C2211yescharacteristic
22C2×C7×C22⋊Q8C2211yescharacteristic
23C2×C7×#121C2211yescharacteristic
24C2×C4×C7×Q8C2211yescharacteristic
25C2×C4×C7×D4C2211yescharacteristic
26C2×C4×C7×D4C2211yescharacteristic
27C7×#463—24no—
28C7×#452—24no—
29C7×#449—24no—
30C4×C7×SD16—24no—
31C2×C7×#106C2211yescharacteristic
32C2×C7×#106C2211yescharacteristic
33C2×C7×C4⋊C8C2211yescharacteristic
34C2×C7×#103C2211yescharacteristic
35C2×C7×#103C2211yescharacteristic
36C2×C7×#103C2211yescharacteristic
37C2×C7×#103C2211yescharacteristic
38C2×C7×#102C2211yescharacteristic
39C2×C7×#102C2211yescharacteristic
40C2×C7×#102C2211yescharacteristic
41C2×C7×#102C2211yescharacteristic
42C2×C7×C22⋊C8C2211yescharacteristic
43C2×C7×C22⋊C8C2211yescharacteristic
44C2×C4×C7×C8C2211yescharacteristic
45C7×#396—21no—
46C7×#394—21no—
47C7×#391C2211yescharacteristic
48C7×#391C2211yescharacteristic
49C7×#390—21no—
50C7×#390C2211yescharacteristic
51C7×#389C2211yescharacteristic
52C7×#388—21no—
53C7×#386—21no—
54C7×#386—21no—
55C7×#381—21no—
56C7×#380C2211yescharacteristic
57C4×C7×C22⋊C4C2211yescharacteristic
58C2×C7×#95—21no—
59C7×#340C2211yescharacteristic
60C7×#340C2211yescharacteristic
61C7×#336C2211yescharacteristic
62C7×#336C2211yescharacteristic
63#25158C711yesmaximal, characteristic, direct product factor, Sylow
64C2×C7×#41—22no—
65C2×C7×#41—22no—
66C2×C7×#41—22no—
67C2×C7×#41—22no—
68C2×C7×#41—41no—
69C2×C7×#41—41no—
70C22×C7×Q8C2311yescharacteristic
71C22×C7×Q8C2311yescharacteristic
72C22×C7×D4—21no—
73C22×C7×D4—21no—
74C22×C7×D4C2311yescharacteristic
75C22×C7×D4C2311yescharacteristic
76C23×C4×C7—21no—
77C23×C4×C7—21no—
78C23×C4×C7—21no—
79C23×C4×C7C2311yescharacteristic
80C2×C7×Q16—22no—
81C2×C7×Q16—22no—
82C2×C7×Q16—41no—
83C2×C7×SD16—22no—
84C2×C7×SD16—22no—
85C2×C7×SD16—22no—
86C2×C7×SD16—22no—
87C2×C7×SD16—41no—
88C2×C7×SD16D414yescomplemented
89C2×C7×D8—22no—
90C2×C7×D8—22no—
91C2×C7×D8—22no—
92C22×C7×C8C2311yescharacteristic
93C22×C7×C8C2311yescharacteristic
94C22×C7×C8C2311yescharacteristic
95C22×C7×C8C2311yescharacteristic
96C7×#124—22no—
97C7×#124—41no—
98C7×C22⋊Q8—22no—
99C7×C22⋊Q8—41no—
100C7×#121—22no—
101C7×#121—41no—
102C4×C7×Q8—22no—
103C4×C7×Q8—41no—
104C4×C7×D4—22no—
105C4×C7×D4—22no—
106C4×C7×D4—41no—
107C4×C7×D4—41no—
108C2×C7×C4⋊C4—21no—
109C2×C7×C4⋊C4—21no—
110C2×C7×C4⋊C4—21no—
111C2×C7×C4⋊C4C2311yescharacteristic
112C2×C7×C4⋊C4C2311yescharacteristic
113C2×C7×C4⋊C4C2311yescharacteristic
114C2×C7×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
123C2×C7×C22⋊C4—21no—
124C2×C7×C22⋊C4D411yescharacteristic
125C2×C7×C22⋊C4D411yescharacteristic
126C2×C42×C7—21no—
127C2×C42×C7C2311yescharacteristic
128C2×C42×C7C2311yescharacteristic
129C7×#106—22no—
130C7×#106—41no—
131C7×C4⋊C8—22no—
132C7×#103—22no—
133C7×#103—22no—
134C7×#103—22no—
135C7×#103—22no—
136C7×#102—22no—
137C7×#102—22no—
138C7×#102—41no—
139C7×#102D414yes—
140C7×C22⋊C8—22no—
141C7×C22⋊C8—22no—
142C4×C7×C8—22no—
143C7×#95—21no—
144C7×#95—21no—
145C7×#95—21no—
146C7×#95—21no—
147C7×#95—21no—
148C7×#95—21no—
149C7×#95D411yescharacteristic
150C7×#95D411yescharacteristic
151C2×#463C2×C711yescharacteristic, complemented
152C2×#452C2×C711yescharacteristic, complemented
153C2×#449C2×C711yescharacteristic
154C2×C4×SD16C2×C711yescharacteristic, complemented
155#2426C2×C711yescharacteristic, complemented
156#2339C2×C711yescharacteristic, complemented
157#2066C2×C711yescharacteristic, complemented
158#2035C2×C711yescharacteristic, complemented
159#2034C2×C711yescharacteristic, complemented
160#2015C2×C711yescharacteristic, complemented
161#1968C2×C711yescharacteristic, complemented
162#1923C2×C711yescharacteristic, complemented
163#1879C2×C711yescharacteristic, complemented
164#1878C2×C711yescharacteristic, complemented
165#1864C2×C711yescharacteristic, complemented
166C24×C7—21no—
167C24×C7—21no—
168C24×C7C2×D411yescharacteristic
169C7×#41—44no—
170C7×#41—44no—
171C7×#41—44no—
172C7×#41—44no—
173C2×C7×Q8—21no—
174C2×C7×Q8—21no—
175C2×C7×Q8—21no—
176C2×C7×Q8—21no—
177C2×C7×Q8—21no—
178C2×C7×Q8—21no—
179C2×C7×Q8—21no—
180C2×C7×Q8—21no—
181C2×C7×Q8—21no—
182C2×C7×Q8—21no—
183C2×C7×Q8C2×D412yes—
184C2×C7×Q8#4112yes—
185C2×C7×D4—24no—
186C2×C7×D4—21no—
187C2×C7×D4—21no—
188C2×C7×D4—21no—
189C2×C7×D4—21no—
190C2×C7×D4—21no—
191C2×C7×D4—21no—
192C2×C7×D4—21no—
193C2×C7×D4—21no—
194C2×C7×D4—21no—
195C2×C7×D4—42no—
196C2×C7×D4—42no—
197C2×C7×D4—42no—
198C2×C7×D4—42no—
199C2×C7×D4—81no—
200C2×C7×D4C2×D412yes—
201C2×C7×D4C2×D412yes—
202C2×C7×D4#4112yes—
203C22×C4×C7—24no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7—42no—
217C22×C4×C7—42no—
218C22×C4×C7—42no—
219C22×C4×C7—42no—
220C22×C4×C7—42no—
221C22×C4×C7—42no—
222C22×C4×C7—81no—
223C22×C4×C7—81no—
224C22×C4×C7C2×D411yescharacteristic
225C22×C4×C7C2×D411yescharacteristic
226C22×C4×C7C2×D411yescharacteristic
227C22×C4×C7C2×D411yescharacteristic
228C22×C4×C7C2×D411yescharacteristic
229C22×C4×C7C2411yescharacteristic
230C7×Q16—44no—
231C7×SD16—28no—
232C7×SD16—44no—
233C7×D8—44no—
234C2×C7×C8—21no—
235C2×C7×C8—21no—
236C2×C7×C8—21no—
237C2×C7×C8—21no—
238C2×C7×C8—21no—
239C2×C7×C8—21no—
240C2×C7×C8—21no—
241C2×C7×C8—21no—
242C2×C7×C8—21no—
243C2×C7×C8—21no—
244C2×C7×C8C2×D412yes—
245C2×C7×C8C2×D412yes—
246C7×C4⋊C4—21no—
247C7×C4⋊C4—21no—
248C7×C4⋊C4—21no—
249C7×C4⋊C4—21no—
250C7×C4⋊C4—21no—
251C7×C4⋊C4—21no—
252C7×C4⋊C4—21no—
253C7×C4⋊C4—42no—
254C7×C4⋊C4—42no—
255C7×C4⋊C4—81no—
256C7×C4⋊C4C2×D412yes—
257C7×C22⋊C4—22no—
258C7×C22⋊C4—41no—
259C7×C22⋊C4—42no—
260C7×C22⋊C4—42no—
261C7×C22⋊C4—42no—
262C7×C22⋊C4—42no—
263C7×C22⋊C4—42no—
264C7×C22⋊C4—42no—
265C7×C22⋊C4—42no—
266C7×C22⋊C4—81no—
267C7×C22⋊C4—81no—
268C42×C7—21no—
269C42×C7—21no—
270C42×C7—21no—
271C42×C7—21no—
272C42×C7—42no—
273C22×#41C22×C711yescharacteristic
274C22×Q16C22×C711yescharacteristic
275C22×SD16C22×C711yescharacteristic
276C22×SD16C22×C711yescharacteristic
277C22×D8C22×C711yescharacteristic
278C2×#124C22×C711yescharacteristic
279C2×C22⋊Q8C22×C711yescharacteristic
280C2×#121C22×C711yescharacteristic
281C2×C4×Q8C22×C711yescharacteristic
282C2×C4×D4C22×C711yescharacteristic
283C2×C4×D4C22×C711yescharacteristic
284#463—24no—
285#452—24no—
286#449—24no—
287C4×SD16—24no—
288C2×#106C22×C711yescharacteristic
289C2×#106C22×C711yescharacteristic
290C2×C4⋊C8C22×C711yescharacteristic
291C2×#103C22×C711yescharacteristic
292C2×#103C22×C711yescharacteristic
293C2×#103C22×C711yescharacteristic
294C2×#103C22×C711yescharacteristic
295C2×#102C22×C711yescharacteristic
296C2×#102C22×C711yescharacteristic
297C2×#102C22×C711yescharacteristic
298C2×#102C22×C711yescharacteristic
299C2×C22⋊C8C22×C711yescharacteristic
300C2×C22⋊C8C22×C711yescharacteristic
301C2×C4×C8C22×C711yescharacteristic
302#396—21no—
303#394—21no—
304#391C22×C711yescharacteristic
305#391C22×C711yescharacteristic
306#390—21no—
307#390C22×C711yescharacteristic
308#389C22×C711yescharacteristic
309#388—21no—
310#386—21no—
311#386—21no—
312#381—21no—
313#380C22×C711yescharacteristic
314C4×C22⋊C4C22×C711yescharacteristic
315C2×#95—21no—
316#340C22×C711yescharacteristic
317#340C22×C711yescharacteristic
318#336C22×C711yescharacteristic
319#336C22×C711yescharacteristic
320C23×C7—22no—
321C23×C7—22no—
322C23×C7—22no—
323C23×C7—21no—
324C23×C7—21no—
325C23×C7—21no—
326C23×C7—21no—
327C23×C7—21no—
328C23×C7—21no—
329C23×C7—21no—
330C23×C7—41no—
331C23×C7—41no—
332C23×C7—41no—
333C23×C7—41no—
334C23×C7—41no—
335C23×C7—41no—
336C23×C7—41no—
337C23×C7—41no—
338C23×C7—41no—
339C23×C7—41no—
340C23×C7—41no—
341C23×C7C22×D411yescharacteristic
342C7×Q8—22no—
343C7×Q8—22no—
344C7×Q8—22no—
345C7×Q8—22no—
346C7×Q8—41no—
347C7×Q8—41no—
348C7×Q8—41no—
349C7×Q8—41no—
350C7×D4—22no—
351C7×D4—22no—
352C7×D4—22no—
353C7×D4—48no—
354C7×D4—41no—
355C7×D4—41no—
356C7×D4—41no—
357C7×D4—41no—
358C7×D4—84no—
359C7×D4#12114yes—
360C2×C4×C7—21no—
361C2×C4×C7—21no—
362C2×C4×C7—21no—
363C2×C4×C7—22no—
364C2×C4×C7—21no—
365C2×C4×C7—21no—
366C2×C4×C7—21no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—21no—
370C2×C4×C7—21no—
371C2×C4×C7—21no—
372C2×C4×C7—21no—
373C2×C4×C7—21no—
374C2×C4×C7—21no—
375C2×C4×C7—21no—
376C2×C4×C7—21no—
377C2×C4×C7—48no—
378C2×C4×C7—41no—
379C2×C4×C7—41no—
380C2×C4×C7—41no—
381C2×C4×C7—41no—
382C2×C4×C7—41no—
383C2×C4×C7—41no—
384C2×C4×C7—41no—
385C2×C4×C7—41no—
386C2×C4×C7—41no—
387C2×C4×C7—41no—
388C2×C4×C7—41no—
389C2×C4×C7—41no—
390C2×C4×C7—41no—
391C2×C4×C7—41no—
392C2×C4×C7—41no—
393C2×C4×C7—41no—
394C2×C4×C7—41no—
395C2×C4×C7—41no—
396C2×C4×C7—41no—
397C2×C4×C7—84no—
398C2×C4×C7—84no—
399C2×C4×C7#13512yes—
400C2×C4×C7C22×D411yescharacteristic
401C2×C4×C7C22×D411yescharacteristic
402C2×C4×C7C2×#4111yescharacteristic
403C2×C4×C7C2×#4111yescharacteristic
404C2×C4×C7H(5,𝔽2)11yescharacteristic
405C2×C4×C7H(5,𝔽2)11yescharacteristic
406C7×C8—22no—
407C7×C8—22no—
408C7×C8—41no—
409C7×C8—41no—
410C2×#41—22no—
411C2×#41—22no—
412C2×#41—22no—
413C2×#41—22no—
414C2×#41—41no—
415C2×#41—41no—
416C22×Q8C23×C711yescharacteristic
417C22×Q8C23×C711yescharacteristic
418C22×D4—21no—
419C22×D4—21no—
420C22×D4C23×C711yescharacteristic
421C22×D4C23×C711yescharacteristic
422C23×C4—21no—
423C23×C4—21no—
424C23×C4—21no—
425C23×C4C23×C711yescharacteristic
426C2×Q16—22no—
427C2×Q16—22no—
428C2×Q16—41no—
429C2×SD16—22no—
430C2×SD16—22no—
431C2×SD16—22no—
432C2×SD16—22no—
433C2×SD16—41no—
434C2×SD16C7×D414yescomplemented
435C2×D8—22no—
436C2×D8—22no—
437C2×D8—22no—
438C22×C8C23×C711yescharacteristic
439C22×C8C23×C711yescharacteristic
440C22×C8C23×C711yescharacteristic
441C22×C8C23×C711yescharacteristic
442#124—22no—
443#124—41no—
444C22⋊Q8—22no—
445C22⋊Q8—41no—
446#121—22no—
447#121—41no—
448C4×Q8—22no—
449C4×Q8—41no—
450C4×D4—22no—
451C4×D4—22no—
452C4×D4—41no—
453C4×D4—41no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4C23×C711yescharacteristic
458C2×C4⋊C4C23×C711yescharacteristic
459C2×C4⋊C4C23×C711yescharacteristic
460C2×C4⋊C4C23×C711yescharacteristic
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4C7×D411yescharacteristic
471C2×C22⋊C4C7×D411yescharacteristic
472C2×C42—21no—
473C2×C42C23×C711yescharacteristic
474C2×C42C23×C711yescharacteristic
475#106—22no—
476#106—41no—
477C4⋊C8—22no—
478#103—22no—
479#103—22no—
480#103—22no—
481#103—22no—
482#102—22no—
483#102—22no—
484#102—41no—
485#102C7×D414yes—
486C22⋊C8—22no—
487C22⋊C8—22no—
488C4×C8—22no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95C7×D411yescharacteristic
496#95C7×D411yescharacteristic
497C22×C7—24no—
498C22×C7—42no—
499C22×C7—42no—
500C22×C7—42no—
501C22×C7—42no—
502C22×C7—42no—
503C22×C7—42no—
504C22×C7—41no—
505C22×C7—41no—
506C22×C7—41no—
507C22×C7—41no—
508C22×C7—41no—
509C22×C7—41no—
510C22×C7—41no—
511C22×C7—81no—
512C22×C7—81no—
513C22×C7—81no—
514C22×C7—81no—
515C22×C7—81no—
516C22×C7—81no—
517C22×C7—81no—
518C22×C7#52511yescharacteristic
519C22×C7D4211yescharacteristic
520C22×C7D4211yescharacteristic
521C22×C7C2×#13511yescharacteristic
522C22×C7#57511yescharacteristic
523C22×C7#57711yescharacteristic
524C22×C7#57711yescharacteristic
525C4×C7—22no—
526C4×C7—41no—
527C4×C7—42no—
528C4×C7—42no—
529C4×C7—41no—
530C4×C7—42no—
531C4×C7—41no—
532C4×C7—41no—
533C4×C7—81no—
534C4×C7—81no—
535C4×C7—81no—
536C4×C7C2×#12111yescharacteristic
537C4×C7#53811yescharacteristic
538C4×C7#54611yescharacteristic
539C4×C7#54611yescharacteristic
540C24—21no—
541C24—21no—
542C24C2×C7×D411yescharacteristic
543#41—44no—
544#41—44no—
545#41—44no—
546#41—44no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8C2×C7×D412yes—
558C2×Q8C7×#4112yes—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—81no—
574C2×D4C2×C7×D412yes—
575C2×D4C2×C7×D412yes—
576C2×D4C7×#4112yes—
577C22×C4—24no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—81no—
597C22×C4—81no—
598C22×C4C2×C7×D411yescharacteristic
599C22×C4C2×C7×D411yescharacteristic
600C22×C4C2×C7×D411yescharacteristic
601C22×C4C2×C7×D411yescharacteristic
602C22×C4C2×C7×D411yescharacteristic
603C22×C4C24×C711yescharacteristic
604Q16—44no—
605SD16—28no—
606SD16—44no—
607D8—44no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8C2×C7×D412yes—
619C2×C8C2×C7×D412yes—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—42no—
628C4⋊C4—42no—
629C4⋊C4—81no—
630C4⋊C4C2×C7×D412yes—
631C22⋊C4—22no—
632C22⋊C4—41no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—81no—
641C22⋊C4—81no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—42no—
647C2×C7—44no—
648C2×C7—81no—
649C2×C7—161no—
650C2×C7#242411yescharacteristic
651C2×C7#310211yescharacteristic
652C2×C7#312511yescharacteristic
653C2×C7#326711yescharacteristic
654C2×C7#327511yescharacteristic
655C2×C7#328211yescharacteristic
656C2×C7#328411yescharacteristic
657C23—22no—
658C23—22no—
659C23—22no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23C22×C7×D411yescharacteristic
679Q8—22no—
680Q8—22no—
681Q8—22no—
682Q8—22no—
683Q8—41no—
684Q8—41no—
685Q8—41no—
686Q8—41no—
687D4—22no—
688D4—22no—
689D4—22no—
690D4—48no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—84no—
696D4C7×#12114yes—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—48no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—84no—
735C2×C4—84no—
736C2×C4C7×#13512yes—
737C2×C4C22×C7×D411yescharacteristic
738C2×C4C22×C7×D411yescharacteristic
739C2×C4C2×C7×#4111yescharacteristic
740C2×C4C2×C7×#4111yescharacteristic
741C2×C4C7×H(5,𝔽2)11yescharacteristic
742C2×C4C7×H(5,𝔽2)11yescharacteristic
743C8—22no—
744C8—22no—
745C8—41no—
746C8—41no—
747C7#2515811yescharacteristic, direct product factor, Sylow
748C22—24no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22C7×#52511yescharacteristic
770C22C7×D4211yescharacteristic
771C22C7×D4211yescharacteristic
772C22C2×C7×#13511yescharacteristic
773C22C7×#57511yescharacteristic
774C22C7×#57711yescharacteristic
775C22C7×#57711yescharacteristic
776C4—22no—
777C4—41no—
778C4—42no—
779C4—42no—
780C4—41no—
781C4—42no—
782C4—41no—
783C4—41no—
784C4—81no—
785C4—81no—
786C4—81no—
787C4C2×C7×#12111yescharacteristic
788C4C7×#53811yescharacteristic
789C4C7×#54611yescharacteristic
790C4C7×#54611yescharacteristic
791C2—44no—
792C2—81no—
793C2—161no—
794C2C7×#242411yescharacteristic
795C2C7×#310211yescharacteristic
796C2C7×#312511yescharacteristic
797C2C7×#326711yescharacteristic
798C2C7×#327511yescharacteristic
799C2C7×#328211yescharacteristic
800C2C7×#328411yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC2×C7×#449C2
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×#463C2semidirect
2. C2×C7×#452C2semidirect
4. C2×C4×C7×SD16C2semidirect
5. C7×#2426C2semidirect
6. C7×#2339C2semidirect
7. C7×#2066C2semidirect
8. C7×#2035C2semidirect
9. C7×#2034C2semidirect
10. C7×#2015C2semidirect
11. C7×#1968C2semidirect
12. C7×#1923C2semidirect
13. C7×#1879C2semidirect
14. C7×#1878C2semidirect
15. C7×#1864C2semidirect
63. #25158C7direct (N × H)
88. C2×C7×SD16D4semidirect
151. C2×#463C2×C7semidirect
152. C2×#452C2×C7semidirect
154. C2×C4×SD16C2×C7semidirect
155. #2426C2×C7semidirect
156. #2339C2×C7semidirect
157. #2066C2×C7semidirect
158. #2035C2×C7semidirect
159. #2034C2×C7semidirect
160. #2015C2×C7semidirect
161. #1968C2×C7semidirect
162. #1923C2×C7semidirect
163. #1879C2×C7semidirect
164. #1878C2×C7semidirect
165. #1864C2×C7semidirect
434. C2×SD16C7×D4semidirect
747. C7#25158direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#4632
C2×C7×#4522
C2×C7×#4492
C2×C4×C7×SD162
C7×#24262
C7×#23392
C7×#20662
C7×#20352
C7×#20342
C7×#20152
C7×#19682
C7×#19232
C7×#18792
C7×#18782
C7×#18642
#251587