Finite Group Databasebeta

← C7×#23947 #13201163

Subgroups — C7×#23947 #13201163

Order 1792.

1270 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#542C211yesmaximal, characteristic, complemented
2C2×C7×#452C211yesmaximal, characteristic, complemented
3C2×C7×#449C211yesmaximal, characteristic
4C7×#2311C211yesmaximal, characteristic, complemented
5C7×#2024C211yesmaximal, characteristic, complemented
6C7×#2023C211yesmaximal, characteristic, complemented
7C7×#2015C211yesmaximal, characteristic, complemented
8C7×#2012C211yesmaximal, characteristic, complemented
9C7×#1880C211yesmaximal, characteristic, complemented
10C7×#1879C211yesmaximal, characteristic, complemented
11C7×#1878C211yesmaximal, characteristic, complemented
12C7×#1877C211yesmaximal, characteristic, complemented
13C7×#1874C211yesmaximal, characteristic, complemented
14C7×#1872C211yesmaximal, characteristic, complemented
15C7×#1818C211yesmaximal, characteristic, complemented
16C22×C7×#41C2211yescharacteristic
17C22×C7×Q16C2211yescharacteristic
18C22×C7×SD16C2211yescharacteristic
19C22×C7×SD16C2211yescharacteristic
20C22×C7×D8C2211yescharacteristic
21C7×#542—24no—
22C7×#542—24no—
23C2×C7×C4⋊Q8C2211yescharacteristic
24C2×C7×#126—21no—
25C2×C7×#124—21no—
26C2×C7×#124C2211yescharacteristic
27C2×C7×#123—21no—
28C2×C7×C22⋊Q8—21no—
29C2×C7×C22⋊Q8C2211yescharacteristic
30C2×C7×#121C2211yescharacteristic
31C2×C4×C7×Q8C2211yescharacteristic
32C2×C4×C7×D4C2211yescharacteristic
33C2×C7×#117C2211yescharacteristic
34C22×C7×C4⋊C4C2211yescharacteristic
35C7×#452—24no—
36C7×#449—24no—
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
47C7×#391C2211yescharacteristic
48C7×#391C2211yescharacteristic
49C7×#390C2211yescharacteristic
50C7×#390C2211yescharacteristic
51C7×#386—21no—
52C7×#386—21no—
53C7×#380—21no—
54C7×#380—21no—
55C7×#340C2211yescharacteristic
56C7×#340C2211yescharacteristic
57C7×#340C2211yescharacteristic
58C7×#340C2211yescharacteristic
59C7×#336C2211yescharacteristic
60C7×#336C2211yescharacteristic
61C7×#336C2211yescharacteristic
62C7×#336C2211yescharacteristic
63#23947C711yesmaximal, 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×Q8—21no—
71C22×C7×Q8C2311yescharacteristic
72C22×C7×Q8C2311yescharacteristic
73C22×C7×D4—21no—
74C22×C7×D4—21no—
75C22×C7×D4C2311yescharacteristic
76C22×C7×D4C2311yescharacteristic
77C23×C4×C7—21no—
78C23×C4×C7—21no—
79C23×C4×C7—21no—
80C23×C4×C7C2311yescharacteristic
81C2×C7×Q16—22no—
82C2×C7×Q16—22no—
83C2×C7×Q16—41no—
84C2×C7×SD16—22no—
85C2×C7×SD16—22no—
86C2×C7×SD16—22no—
87C2×C7×SD16—22no—
88C2×C7×SD16—41no—
89C2×C7×SD16—41no—
90C2×C7×D8—22no—
91C2×C7×D8—22no—
92C2×C7×D8—41no—
93C22×C7×C8C2311yescharacteristic
94C22×C7×C8C2311yescharacteristic
95C22×C7×C8C2311yescharacteristic
96C22×C7×C8C2311yescharacteristic
97C7×C4⋊Q8—22no—
98C7×C4⋊Q8—22no—
99C7×#126—28no—
100C7×#124—28no—
101C7×#124—22no—
102C7×#124—22no—
103C7×#123—28no—
104C7×C22⋊Q8—28no—
105C7×C22⋊Q8—22no—
106C7×C22⋊Q8D414yes—
107C7×#121—22no—
108C7×#121D414yes—
109C4×C7×Q8—22no—
110C4×C7×Q8—22no—
111C4×C7×D4—22no—
112C4×C7×D4—22no—
113C7×#117—22no—
114C7×#117—22no—
115C2×C7×C4⋊C4—21no—
116C2×C7×C4⋊C4—21no—
117C2×C7×C4⋊C4—21no—
118C2×C7×C4⋊C4—21no—
119C2×C7×C4⋊C4—41no—
120C2×C7×C4⋊C4—41no—
121C2×C7×C4⋊C4D411yescharacteristic
122C2×C7×C4⋊C4D411yescharacteristic
123C2×C7×C4⋊C4C2311yescharacteristic
124C2×C7×C4⋊C4C2311yescharacteristic
125C2×C7×C4⋊C4C2311yescharacteristic
126C2×C7×C4⋊C4C2311yescharacteristic
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×C7×C22⋊C4—21no—
133C2×C7×C22⋊C4—21no—
134C2×C7×C22⋊C4—21no—
135C2×C7×C22⋊C4—21no—
136C2×C7×C22⋊C4D411yescharacteristic
137C2×C7×C22⋊C4D411yescharacteristic
138C2×C42×C7—21no—
139C2×C42×C7C2311yescharacteristic
140C2×C42×C7C2311yescharacteristic
141C7×#103—22no—
142C7×#103—22no—
143C7×#103—41no—
144C7×#103—41no—
145C7×#102—22no—
146C7×#102—22no—
147C7×#102—41no—
148C7×#102—41no—
149C7×C22⋊C8—22no—
150C7×C22⋊C8—22no—
151C7×#95—21no—
152C7×#95—21no—
153C7×#95—21no—
154C7×#95—21no—
155C2×#542C2×C711yescharacteristic, complemented
156C2×#452C2×C711yescharacteristic, complemented
157C2×#449C2×C711yescharacteristic
158#2311C2×C711yescharacteristic, complemented
159#2024C2×C711yescharacteristic, complemented
160#2023C2×C711yescharacteristic, complemented
161#2015C2×C711yescharacteristic, complemented
162#2012C2×C711yescharacteristic, complemented
163#1880C2×C711yescharacteristic, complemented
164#1879C2×C711yescharacteristic, complemented
165#1878C2×C711yescharacteristic, complemented
166#1877C2×C711yescharacteristic, complemented
167#1874C2×C711yescharacteristic, complemented
168#1872C2×C711yescharacteristic, complemented
169#1818C2×C711yescharacteristic, complemented
170C24×C7—21no—
171C24×C7—21no—
172C24×C7C2×D411yescharacteristic
173C7×#41—44no—
174C7×#41—44no—
175C7×#41—44no—
176C7×#41—44no—
177C2×C7×Q8—24no—
178C2×C7×Q8—21no—
179C2×C7×Q8—21no—
180C2×C7×Q8—21no—
181C2×C7×Q8—21no—
182C2×C7×Q8—21no—
183C2×C7×Q8—21no—
184C2×C7×Q8—21no—
185C2×C7×Q8—21no—
186C2×C7×Q8—21no—
187C2×C7×Q8—21no—
188C2×C7×Q8—81no—
189C2×C7×Q8—81no—
190C2×C7×Q8C2×D412yes—
191C2×C7×Q8#4112yes—
192C2×C7×D4—24no—
193C2×C7×D4—24no—
194C2×C7×D4—21no—
195C2×C7×D4—21no—
196C2×C7×D4—21no—
197C2×C7×D4—21no—
198C2×C7×D4—21no—
199C2×C7×D4—21no—
200C2×C7×D4—21no—
201C2×C7×D4—21no—
202C2×C7×D4—21no—
203C2×C7×D4—21no—
204C2×C7×D4—42no—
205C2×C7×D4—42no—
206C2×C7×D4—81no—
207C2×C7×D4—81no—
208C2×C7×D4C2×D412yes—
209C2×C7×D4#4112yes—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—24no—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7—24no—
220C22×C4×C7—21no—
221C22×C4×C7—21no—
222C22×C4×C7—42no—
223C22×C4×C7—42no—
224C22×C4×C7—42no—
225C22×C4×C7—81no—
226C22×C4×C7—81no—
227C22×C4×C7—81no—
228C22×C4×C7—81no—
229C22×C4×C7C2×D411yescharacteristic
230C22×C4×C7C2×D411yescharacteristic
231C22×C4×C7C2×D411yescharacteristic
232C22×C4×C7C2×D411yescharacteristic
233C22×C4×C7C2×D411yescharacteristic
234C22×C4×C7C2×D412yes—
235C22×C4×C7C2×D412yes—
236C22×C4×C7C2411yescharacteristic
237C7×Q16—44no—
238C7×SD16—44no—
239C7×SD16—44no—
240C7×D8—44no—
241C2×C7×C8—21no—
242C2×C7×C8—21no—
243C2×C7×C8—21no—
244C2×C7×C8—21no—
245C2×C7×C8—21no—
246C2×C7×C8—21no—
247C2×C7×C8—21no—
248C2×C7×C8—21no—
249C2×C7×C8—21no—
250C2×C7×C8—21no—
251C2×C7×C8—21no—
252C2×C7×C8—21no—
253C7×C4⋊C4—24no—
254C7×C4⋊C4—24no—
255C7×C4⋊C4—24no—
256C7×C4⋊C4—22no—
257C7×C4⋊C4—22no—
258C7×C4⋊C4—21no—
259C7×C4⋊C4—21no—
260C7×C4⋊C4—21no—
261C7×C4⋊C4—21no—
262C7×C4⋊C4—21no—
263C7×C4⋊C4—21no—
264C7×C4⋊C4—42no—
265C7×C4⋊C4C2×D412yes—
266C7×C4⋊C4C2×D412yes—
267C7×C22⋊C4—24no—
268C7×C22⋊C4—24no—
269C7×C22⋊C4—24no—
270C7×C22⋊C4—24no—
271C7×C22⋊C4—22no—
272C7×C22⋊C4—22no—
273C7×C22⋊C4—24no—
274C7×C22⋊C4—81no—
275C7×C22⋊C4—81no—
276C7×C22⋊C4—81no—
277C7×C22⋊C4—81no—
278C42×C7—24no—
279C42×C7—21no—
280C42×C7—21no—
281C42×C7—21no—
282C42×C7—21no—
283C22×#41C22×C711yescharacteristic
284C22×Q16C22×C711yescharacteristic
285C22×SD16C22×C711yescharacteristic
286C22×SD16C22×C711yescharacteristic
287C22×D8C22×C711yescharacteristic
288#542—24no—
289#542—24no—
290C2×C4⋊Q8C22×C711yescharacteristic
291C2×#126—21no—
292C2×#124—21no—
293C2×#124C22×C711yescharacteristic
294C2×#123—21no—
295C2×C22⋊Q8—21no—
296C2×C22⋊Q8C22×C711yescharacteristic
297C2×#121C22×C711yescharacteristic
298C2×C4×Q8C22×C711yescharacteristic
299C2×C4×D4C22×C711yescharacteristic
300C2×#117C22×C711yescharacteristic
301C22×C4⋊C4C22×C711yescharacteristic
302#452—24no—
303#449—24no—
304C2×#103C22×C711yescharacteristic
305C2×#103C22×C711yescharacteristic
306C2×#103C22×C711yescharacteristic
307C2×#103C22×C711yescharacteristic
308C2×#102C22×C711yescharacteristic
309C2×#102C22×C711yescharacteristic
310C2×#102C22×C711yescharacteristic
311C2×#102C22×C711yescharacteristic
312C2×C22⋊C8C22×C711yescharacteristic
313C2×C22⋊C8C22×C711yescharacteristic
314#391C22×C711yescharacteristic
315#391C22×C711yescharacteristic
316#390C22×C711yescharacteristic
317#390C22×C711yescharacteristic
318#386—21no—
319#386—21no—
320#380—21no—
321#380—21no—
322#340C22×C711yescharacteristic
323#340C22×C711yescharacteristic
324#340C22×C711yescharacteristic
325#340C22×C711yescharacteristic
326#336C22×C711yescharacteristic
327#336C22×C711yescharacteristic
328#336C22×C711yescharacteristic
329#336C22×C711yescharacteristic
330C23×C7—21no—
331C23×C7—21no—
332C23×C7—21no—
333C23×C7—21no—
334C23×C7—21no—
335C23×C7—21no—
336C23×C7—22no—
337C23×C7—22no—
338C23×C7—41no—
339C23×C7—41no—
340C23×C7—41no—
341C23×C7—41no—
342C23×C7—41no—
343C23×C7—41no—
344C23×C7—41no—
345C23×C7—41no—
346C23×C7—41no—
347C23×C7—41no—
348C23×C7—41no—
349C23×C7—41no—
350C23×C7#12012yes—
351C23×C7C22×D411yescharacteristic
352C7×Q8—22no—
353C7×Q8—22no—
354C7×Q8—22no—
355C7×Q8—22no—
356C7×Q8—41no—
357C7×Q8—41no—
358C7×Q8—41no—
359C7×Q8—41no—
360C7×Q8—84no—
361C7×D4—22no—
362C7×D4—22no—
363C7×D4—22no—
364C7×D4—22no—
365C7×D4—48no—
366C7×D4—41no—
367C7×D4—41no—
368C7×D4—41no—
369C7×D4—41no—
370C7×D4—84no—
371C2×C4×C7—21no—
372C2×C4×C7—21no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—21no—
378C2×C4×C7—21no—
379C2×C4×C7—22no—
380C2×C4×C7—21no—
381C2×C4×C7—21no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—21no—
386C2×C4×C7—21no—
387C2×C4×C7—21no—
388C2×C4×C7—21no—
389C2×C4×C7—21no—
390C2×C4×C7—21no—
391C2×C4×C7—21no—
392C2×C4×C7—21no—
393C2×C4×C7—48no—
394C2×C4×C7—41no—
395C2×C4×C7—41no—
396C2×C4×C7—41no—
397C2×C4×C7—41no—
398C2×C4×C7—41no—
399C2×C4×C7—41no—
400C2×C4×C7—41no—
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—84no—
409C2×C4×C7—84no—
410C2×C4×C7#12012yes—
411C2×C4×C7C22×D411yescharacteristic
412C2×C4×C7C22×D411yescharacteristic
413C2×C4×C7C2×#4111yescharacteristic
414C2×C4×C7C2×#4111yescharacteristic
415C2×C4×C7H(5,𝔽2)11yescharacteristic
416C2×C4×C7H(5,𝔽2)11yescharacteristic
417C7×C8—41no—
418C7×C8—41no—
419C7×C8—41no—
420C7×C8—41no—
421C2×#41—22no—
422C2×#41—22no—
423C2×#41—22no—
424C2×#41—22no—
425C2×#41—41no—
426C2×#41—41no—
427C22×Q8—21no—
428C22×Q8C23×C711yescharacteristic
429C22×Q8C23×C711yescharacteristic
430C22×D4—21no—
431C22×D4—21no—
432C22×D4C23×C711yescharacteristic
433C22×D4C23×C711yescharacteristic
434C23×C4—21no—
435C23×C4—21no—
436C23×C4—21no—
437C23×C4C23×C711yescharacteristic
438C2×Q16—22no—
439C2×Q16—22no—
440C2×Q16—41no—
441C2×SD16—22no—
442C2×SD16—22no—
443C2×SD16—22no—
444C2×SD16—22no—
445C2×SD16—41no—
446C2×SD16—41no—
447C2×D8—22no—
448C2×D8—22no—
449C2×D8—41no—
450C22×C8C23×C711yescharacteristic
451C22×C8C23×C711yescharacteristic
452C22×C8C23×C711yescharacteristic
453C22×C8C23×C711yescharacteristic
454C4⋊Q8—22no—
455C4⋊Q8—22no—
456#126—28no—
457#124—28no—
458#124—22no—
459#124—22no—
460#123—28no—
461C22⋊Q8—28no—
462C22⋊Q8—22no—
463C22⋊Q8C7×D414yes—
464#121—22no—
465#121C7×D414yes—
466C4×Q8—22no—
467C4×Q8—22no—
468C4×D4—22no—
469C4×D4—22no—
470#117—22no—
471#117—22no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—41no—
477C2×C4⋊C4—41no—
478C2×C4⋊C4C7×D411yescharacteristic
479C2×C4⋊C4C7×D411yescharacteristic
480C2×C4⋊C4C23×C711yescharacteristic
481C2×C4⋊C4C23×C711yescharacteristic
482C2×C4⋊C4C23×C711yescharacteristic
483C2×C4⋊C4C23×C711yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4C7×D411yescharacteristic
494C2×C22⋊C4C7×D411yescharacteristic
495C2×C42—21no—
496C2×C42C23×C711yescharacteristic
497C2×C42C23×C711yescharacteristic
498#103—22no—
499#103—22no—
500#103—41no—
501#103—41no—
502#102—22no—
503#102—22no—
504#102—41no—
505#102—41no—
506C22⋊C8—22no—
507C22⋊C8—22no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—21no—
512C22×C7—22no—
513C22×C7—22no—
514C22×C7—22no—
515C22×C7—41no—
516C22×C7—41no—
517C22×C7—41no—
518C22×C7—41no—
519C22×C7—42no—
520C22×C7—42no—
521C22×C7—42no—
522C22×C7—42no—
523C22×C7—42no—
524C22×C7—42no—
525C22×C7—81no—
526C22×C7—81no—
527C22×C7—81no—
528C22×C7—81no—
529C22×C7—81no—
530C22×C7—81no—
531C22×C7—81no—
532C22×C7—81no—
533C22×C7C2×#12011yescharacteristic
534C22×C7#52511yescharacteristic
535C22×C7#53511yescharacteristic
536C22×C7#57611yescharacteristic
537C22×C7#57711yescharacteristic
538C22×C7#57711yescharacteristic
539C22×C7#57811yescharacteristic
540C4×C7—22no—
541C4×C7—42no—
542C4×C7—42no—
543C4×C7—41no—
544C4×C7—41no—
545C4×C7—42no—
546C4×C7—42no—
547C4×C7—41no—
548C4×C7—41no—
549C4×C7—81no—
550C4×C7—81no—
551C4×C7#54611yescharacteristic
552C4×C7#54611yescharacteristic
553C4×C7#54611yescharacteristic
554C4×C7#54611yescharacteristic
555C24—21no—
556C24—21no—
557C24C2×C7×D411yescharacteristic
558#41—44no—
559#41—44no—
560#41—44no—
561#41—44no—
562C2×Q8—24no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—81no—
574C2×Q8—81no—
575C2×Q8C2×C7×D412yes—
576C2×Q8C7×#4112yes—
577C2×D4—24no—
578C2×D4—24no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4C2×C7×D412yes—
594C2×D4C7×#4112yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—24no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4C2×C7×D411yescharacteristic
615C22×C4C2×C7×D411yescharacteristic
616C22×C4C2×C7×D411yescharacteristic
617C22×C4C2×C7×D411yescharacteristic
618C22×C4C2×C7×D411yescharacteristic
619C22×C4C2×C7×D412yes—
620C22×C4C2×C7×D412yes—
621C22×C4C24×C711yescharacteristic
622Q16—44no—
623SD16—44no—
624SD16—44no—
625D8—44no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C4⋊C4—24no—
639C4⋊C4—24no—
640C4⋊C4—24no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—42no—
650C4⋊C4C2×C7×D412yes—
651C4⋊C4C2×C7×D412yes—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—24no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C22⋊C4—81no—
662C22⋊C4—81no—
663C42—24no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C2×C7—42no—
669C2×C7—82no—
670C2×C7—82no—
671C2×C7#240411yescharacteristic
672C2×C7#301211yescharacteristic
673C2×C7#301311yescharacteristic
674C2×C7#312411yescharacteristic
675C2×C7#312511yescharacteristic
676C2×C7#322411yescharacteristic
677C2×C7#322511yescharacteristic
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—22no—
685C23—22no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23C7×#12012yes—
699C23C22×C7×D411yescharacteristic
700Q8—22no—
701Q8—22no—
702Q8—22no—
703Q8—22no—
704Q8—41no—
705Q8—41no—
706Q8—41no—
707Q8—41no—
708Q8—84no—
709D4—22no—
710D4—22no—
711D4—22no—
712D4—22no—
713D4—48no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—84no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—48no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—84no—
757C2×C4—84no—
758C2×C4C7×#12012yes—
759C2×C4C22×C7×D411yescharacteristic
760C2×C4C22×C7×D411yescharacteristic
761C2×C4C2×C7×#4111yescharacteristic
762C2×C4C2×C7×#4111yescharacteristic
763C2×C4C7×H(5,𝔽2)11yescharacteristic
764C2×C4C7×H(5,𝔽2)11yescharacteristic
765C8—41no—
766C8—41no—
767C8—41no—
768C8—41no—
769C7#2394711yescharacteristic, direct product factor, Sylow
770C22—22no—
771C22—22no—
772C22—22no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22C2×C7×#12011yescharacteristic
792C22C7×#52511yescharacteristic
793C22C7×#53511yescharacteristic
794C22C7×#57611yescharacteristic
795C22C7×#57711yescharacteristic
796C22C7×#57711yescharacteristic
797C22C7×#57811yescharacteristic
798C4—22no—
799C4—42no—
800C4—42no—
801C4—41no—
802C4—41no—
803C4—42no—
804C4—42no—
805C4—41no—
806C4—41no—
807C4—81no—
808C4—81no—
809C4C7×#54611yescharacteristic
810C4C7×#54611yescharacteristic
811C4C7×#54611yescharacteristic
812C4C7×#54611yescharacteristic
813C2—42no—
814C2—82no—
815C2—82no—
816C2C7×#240411yescharacteristic
817C2C7×#301211yescharacteristic
818C2C7×#301311yescharacteristic
819C2C7×#312411yescharacteristic
820C2C7×#312511yescharacteristic
821C2C7×#322411yescharacteristic
822C2C7×#322511yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC2×C7×#449C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C2×C7×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C7×#542C2semidirect
2. C2×C7×#452C2semidirect
4. C7×#2311C2semidirect
5. C7×#2024C2semidirect
6. C7×#2023C2semidirect
7. C7×#2015C2semidirect
8. C7×#2012C2semidirect
9. C7×#1880C2semidirect
10. C7×#1879C2semidirect
11. C7×#1878C2semidirect
12. C7×#1877C2semidirect
13. C7×#1874C2semidirect
14. C7×#1872C2semidirect
15. C7×#1818C2semidirect
63. #23947C7direct (N × H)
155. C2×#542C2×C7semidirect
156. C2×#452C2×C7semidirect
158. #2311C2×C7semidirect
159. #2024C2×C7semidirect
160. #2023C2×C7semidirect
161. #2015C2×C7semidirect
162. #2012C2×C7semidirect
163. #1880C2×C7semidirect
164. #1879C2×C7semidirect
165. #1878C2×C7semidirect
166. #1877C2×C7semidirect
167. #1874C2×C7semidirect
168. #1872C2×C7semidirect
169. #1818C2×C7semidirect
769. C7#23947direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5422
C2×C7×#4522
C2×C7×#4492
C7×#23112
C7×#20242
C7×#20232
C7×#20152
C7×#20122
C7×#18802
C7×#18792
C7×#18782
C7×#18772
C7×#18742
C7×#18722
C7×#18182
#239477