Finite Group Databasebeta

← C7×#23922 #13201138

Subgroups — C7×#23922 #13201138

Order 1792.

1928 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#525C211yesmaximal, characteristic
2C22×C7×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×C7×#452C212yesmaximal, complemented
4C2×C7×#451C211yesmaximal, characteristic, complemented
5C2×C7×#448C211yesmaximal, characteristic, complemented
6C7×#2001C212yesmaximal, complemented
7C7×#2000C212yesmaximal, complemented
8C7×#1874C211yesmaximal, characteristic, complemented
9C7×#1873C212yesmaximal, complemented
10C7×#1872C211yesmaximal, characteristic, complemented
11C7×#1779C211yesmaximal, characteristic, complemented
12C22×C7×#41C2211yescharacteristic
13C23×C7×Q8C2211yescharacteristic
14C24×C4×C7C2211yescharacteristic
15C22×C7×Q16C2212yescomplemented
16C22×C7×SD16C2212yescomplemented
17C7×#525—24no—
18C7×#525—24no—
19C2×C7×#123—21no—
20C2×C7×C22⋊Q8—21no—
21C2×C7×C22⋊Q8—21no—
22C2×C7×C22⋊Q8—28no—
23C2×C7×C22⋊Q8C2212yes—
24C2×C7×C22⋊Q8C2211yescharacteristic
25C2×C7×C22⋊Q8C2211yescharacteristic
26C2×C7×C22⋊Q8C2212yes—
27C2×C7×#121C2211yescharacteristic
28C2×C7×#121C2211yescharacteristic
29C2×C7×#120—21no—
30C2×C4×C7×D4—21no—
31C2×C4×C7×D4—21no—
32C2×C7×#117C2211yescharacteristic
33C22×C7×C4⋊C4—21no—
34C22×C7×C4⋊C4C2211yescharacteristic
35C22×C7×C22⋊C4—21no—
36C7×#452—28no—
37C7×#451—24no—
38C7×#448—24no—
39C2×C7×#103C2212yescomplemented
40C2×C7×#103C2212yescomplemented
41C2×C7×#103C2212yescomplemented
42C2×C7×#102C2212yescomplemented
43C2×C7×C22⋊C8C2211yescharacteristic
44C2×C7×C22⋊C8C2211yescharacteristic
45C2×C7×C22⋊C8C2212yes—
46C2×C7×C22⋊C8C2212yes—
47C7×#340C2212yescomplemented
48C7×#340C2212yescomplemented
49#23922C711yesmaximal, characteristic, direct product factor, Sylow
50C25×C7D411yescharacteristic
51C2×C7×#41—22no—
52C2×C7×#41—22no—
53C2×C7×#41—24no—
54C2×C7×#41—42no—
55C22×C7×Q8—24no—
56C22×C7×Q8—21no—
57C22×C7×Q8—22no—
58C22×C7×Q8—22no—
59C22×C7×Q8—42no—
60C22×C7×Q8C2312yes—
61C22×C7×Q8C2311yescharacteristic
62C22×C7×D4—21no—
63C22×C7×D4—21no—
64C22×C7×D4—21no—
65C22×C7×D4C2311yescharacteristic
66C23×C4×C7—21no—
67C23×C4×C7—21no—
68C23×C4×C7—21no—
69C23×C4×C7—24no—
70C23×C4×C7—22no—
71C23×C4×C7—22no—
72C23×C4×C7—42no—
73C23×C4×C7D411yescharacteristic
74C23×C4×C7D411yescharacteristic
75C23×C4×C7D411yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C2×C7×Q16—24no—
80C2×C7×Q16—24no—
81C2×C7×Q16—42no—
82C2×C7×SD16—24no—
83C2×C7×SD16—24no—
84C2×C7×SD16—42no—
85C22×C7×C8C2312yes—
86C22×C7×C8C2312yes—
87C7×#123—28no—
88C7×C22⋊Q8—28no—
89C7×C22⋊Q8—28no—
90C7×C22⋊Q8—24no—
91C7×C22⋊Q8—22no—
92C7×C22⋊Q8—24no—
93C7×C22⋊Q8—22no—
94C7×C22⋊Q8—24no—
95C7×C22⋊Q8—22no—
96C7×C22⋊Q8D414yes—
97C7×C22⋊Q8D418yescomplemented
98C7×#121—22no—
99C7×#121—22no—
100C7×#121—22no—
101C7×#121D414yes—
102C7×#120—28no—
103C4×C7×D4—28no—
104C4×C7×D4—28no—
105C7×#117—22no—
106C7×#117—22no—
107C2×C7×C4⋊C4—28no—
108C2×C7×C4⋊C4—22no—
109C2×C7×C4⋊C4—22no—
110C2×C7×C4⋊C4—21no—
111C2×C7×C4⋊C4—21no—
112C2×C7×C4⋊C4—21no—
113C2×C7×C4⋊C4—24no—
114C2×C7×C4⋊C4C2312yes—
115C2×C7×C4⋊C4C2311yescharacteristic
116C2×C7×C4⋊C4C2311yescharacteristic
117C2×C7×C22⋊C4—28no—
118C2×C7×C22⋊C4—22no—
119C2×C7×C22⋊C4—22no—
120C2×C7×C22⋊C4—21no—
121C2×C7×C22⋊C4—21no—
122C2×C7×C22⋊C4—21no—
123C2×C7×C22⋊C4—21no—
124C2×C7×C22⋊C4—21no—
125C2×C42×C7—21no—
126C7×#103—24no—
127C7×#103—24no—
128C7×#103—24no—
129C7×#102—24no—
130C7×C22⋊C8—22no—
131C7×C22⋊C8—22no—
132C7×C22⋊C8—24no—
133C7×C22⋊C8—42no—
134C2×#525C2×C711yescharacteristic
135C22×C22⋊Q8C2×C711yescharacteristic, complemented
136C2×#452C2×C712yescomplemented
137C2×#451C2×C711yescharacteristic, complemented
138C2×#448C2×C711yescharacteristic, complemented
139#2001C2×C712yescomplemented
140#2000C2×C712yescomplemented
141#1874C2×C711yescharacteristic, complemented
142#1873C2×C712yescomplemented
143#1872C2×C711yescharacteristic, complemented
144#1779C2×C711yescharacteristic, complemented
145C24×C7—22no—
146C24×C7—22no—
147C24×C7—22no—
148C24×C7—22no—
149C24×C7—22no—
150C24×C7—21no—
151C24×C7—41no—
152C24×C7—41no—
153C24×C7C2×D411yescharacteristic
154C24×C7C2×D411yescharacteristic
155C24×C7C2×D411yescharacteristic
156C7×#41—48no—
157C7×#41—48no—
158C2×C7×Q8—24no—
159C2×C7×Q8—22no—
160C2×C7×Q8—21no—
161C2×C7×Q8—22no—
162C2×C7×Q8—22no—
163C2×C7×Q8—22no—
164C2×C7×Q8—22no—
165C2×C7×Q8—22no—
166C2×C7×Q8—22no—
167C2×C7×Q8—48no—
168C2×C7×Q8—48no—
169C2×C7×Q8—42no—
170C2×C7×Q8—42no—
171C2×C7×Q8C2×D412yes—
172C2×C7×Q8C2×D414yes—
173C2×C7×D4—24no—
174C2×C7×D4—24no—
175C2×C7×D4—24no—
176C2×C7×D4—22no—
177C2×C7×D4—21no—
178C2×C7×D4—22no—
179C2×C7×D4—42no—
180C2×C7×D4—42no—
181C2×C7×D4—42no—
182C2×C7×D4—42no—
183C2×C7×D4—42no—
184C2×C7×D4—42no—
185C2×C7×D4C2×D412yes—
186C22×C4×C7—22no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7—24no—
192C22×C4×C7—24no—
193C22×C4×C7—24no—
194C22×C4×C7—22no—
195C22×C4×C7—22no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—22no—
199C22×C4×C7—21no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—41no—
210C22×C4×C7—41no—
211C22×C4×C7—41no—
212C22×C4×C7—48no—
213C22×C4×C7—48no—
214C22×C4×C7—42no—
215C22×C4×C7—42no—
216C22×C4×C7—42no—
217C22×C4×C7—42no—
218C22×C4×C7—42no—
219C22×C4×C7—42no—
220C22×C4×C7C2×D411yescharacteristic
221C22×C4×C7C2×D411yescharacteristic
222C22×C4×C7C2×D411yescharacteristic
223C22×C4×C7C2×D412yes—
224C22×C4×C7C2×D412yes—
225C22×C4×C7C2×D414yes—
226C22×C4×C7C2411yescharacteristic
227C7×Q16—48no—
228C7×SD16—48no—
229C2×C7×C8—22no—
230C2×C7×C8—22no—
231C2×C7×C8—22no—
232C2×C7×C8—22no—
233C2×C7×C8—22no—
234C2×C7×C8—22no—
235C7×C4⋊C4—24no—
236C7×C4⋊C4—28no—
237C7×C4⋊C4—24no—
238C7×C4⋊C4—28no—
239C7×C4⋊C4—24no—
240C7×C4⋊C4—22no—
241C7×C4⋊C4—21no—
242C7×C4⋊C4—21no—
243C7×C4⋊C4C2×D414yes—
244C7×C4⋊C4C2×D412yes—
245C7×C4⋊C4C2×D412yes—
246C7×C22⋊C4—28no—
247C7×C22⋊C4—24no—
248C7×C22⋊C4—24no—
249C7×C22⋊C4—24no—
250C7×C22⋊C4—28no—
251C7×C22⋊C4—24no—
252C7×C22⋊C4—24no—
253C42×C7—24no—
254C22×#41C22×C711yescharacteristic
255C23×Q8C22×C711yescharacteristic
256C24×C4C22×C711yescharacteristic
257C22×Q16C22×C712yescomplemented
258C22×SD16C22×C712yescomplemented
259#525—24no—
260#525—24no—
261C2×#123—21no—
262C2×C22⋊Q8—21no—
263C2×C22⋊Q8—21no—
264C2×C22⋊Q8—28no—
265C2×C22⋊Q8C22×C712yes—
266C2×C22⋊Q8C22×C711yescharacteristic
267C2×C22⋊Q8C22×C711yescharacteristic
268C2×C22⋊Q8C22×C712yes—
269C2×#121C22×C711yescharacteristic
270C2×#121C22×C711yescharacteristic
271C2×#120—21no—
272C2×C4×D4—21no—
273C2×C4×D4—21no—
274C2×#117C22×C711yescharacteristic
275C22×C4⋊C4—21no—
276C22×C4⋊C4C22×C711yescharacteristic
277C22×C22⋊C4—21no—
278#452—28no—
279#451—24no—
280#448—24no—
281C2×#103C22×C712yescomplemented
282C2×#103C22×C712yescomplemented
283C2×#103C22×C712yescomplemented
284C2×#102C22×C712yescomplemented
285C2×C22⋊C8C22×C711yescharacteristic
286C2×C22⋊C8C22×C712yes—
287C2×C22⋊C8C22×C711yescharacteristic
288C2×C22⋊C8C22×C712yes—
289#340C22×C712yescomplemented
290#340C22×C712yescomplemented
291C23×C7—21no—
292C23×C7—21no—
293C23×C7—21no—
294C23×C7—21no—
295C23×C7—28no—
296C23×C7—21no—
297C23×C7—21no—
298C23×C7—21no—
299C23×C7—21no—
300C23×C7—21no—
301C23×C7—21no—
302C23×C7—21no—
303C23×C7—21no—
304C23×C7—21no—
305C23×C7—21no—
306C23×C7—21no—
307C23×C7—21no—
308C23×C7—22no—
309C23×C7—44no—
310C23×C7—44no—
311C23×C7—44no—
312C23×C7—44no—
313C23×C7—44no—
314C23×C7—44no—
315C23×C7—41no—
316C23×C7—41no—
317C23×C7—41no—
318C23×C7—41no—
319C23×C7—41no—
320C23×C7—41no—
321C23×C7#12012yes—
322C23×C7#12012yes—
323C23×C7#13512yes—
324C23×C7#13712yes—
325C23×C7#13712yes—
326C23×C7C22×D411yescharacteristic
327C7×Q8—24no—
328C7×Q8—24no—
329C7×Q8—24no—
330C7×Q8—48no—
331C7×Q8—42no—
332C7×Q8—42no—
333C7×Q8—42no—
334C7×D4—24no—
335C7×D4—48no—
336C7×D4—48no—
337C7×D4—48no—
338C7×D4—42no—
339C2×C4×C7—21no—
340C2×C4×C7—21no—
341C2×C4×C7—21no—
342C2×C4×C7—21no—
343C2×C4×C7—24no—
344C2×C4×C7—24no—
345C2×C4×C7—24no—
346C2×C4×C7—24no—
347C2×C4×C7—22no—
348C2×C4×C7—22no—
349C2×C4×C7—24no—
350C2×C4×C7—21no—
351C2×C4×C7—22no—
352C2×C4×C7—24no—
353C2×C4×C7—21no—
354C2×C4×C7—21no—
355C2×C4×C7—44no—
356C2×C4×C7—44no—
357C2×C4×C7—44no—
358C2×C4×C7—48no—
359C2×C4×C7—48no—
360C2×C4×C7—48no—
361C2×C4×C7—41no—
362C2×C4×C7—42no—
363C2×C4×C7—41no—
364C2×C4×C7—42no—
365C2×C4×C7—42no—
366C2×C4×C7—41no—
367C2×C4×C7—41no—
368C2×C4×C7—41no—
369C2×C4×C7—42no—
370C2×C4×C7—41no—
371C2×C4×C7—42no—
372C2×C4×C7—42no—
373C2×C4×C7#12012yes—
374C2×C4×C7#12012yes—
375C2×C4×C7C22×D412yes—
376C2×C4×C7C22×D411yescharacteristic
377C2×C4×C7C22×D411yescharacteristic
378C2×C4×C7H(5,𝔽2)12yes—
379C7×C8—42no—
380C7×C8—42no—
381C25C7×D411yescharacteristic
382C2×#41—22no—
383C2×#41—22no—
384C2×#41—24no—
385C2×#41—42no—
386C22×Q8—24no—
387C22×Q8—21no—
388C22×Q8—22no—
389C22×Q8—22no—
390C22×Q8—42no—
391C22×Q8C23×C712yes—
392C22×Q8C23×C711yescharacteristic
393C22×D4—21no—
394C22×D4—21no—
395C22×D4—21no—
396C22×D4C23×C711yescharacteristic
397C23×C4—21no—
398C23×C4—21no—
399C23×C4—21no—
400C23×C4—24no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—42no—
404C23×C4C7×D411yescharacteristic
405C23×C4C7×D411yescharacteristic
406C23×C4C7×D411yescharacteristic
407C23×C4C23×C711yescharacteristic
408C23×C4C23×C711yescharacteristic
409C23×C4C23×C711yescharacteristic
410C2×Q16—24no—
411C2×Q16—24no—
412C2×Q16—42no—
413C2×SD16—24no—
414C2×SD16—24no—
415C2×SD16—42no—
416C22×C8C23×C712yes—
417C22×C8C23×C712yes—
418#123—28no—
419C22⋊Q8—28no—
420C22⋊Q8—28no—
421C22⋊Q8—24no—
422C22⋊Q8—22no—
423C22⋊Q8—24no—
424C22⋊Q8—22no—
425C22⋊Q8—24no—
426C22⋊Q8—22no—
427C22⋊Q8C7×D414yes—
428C22⋊Q8C7×D418yescomplemented
429#121—22no—
430#121—22no—
431#121—22no—
432#121C7×D414yes—
433#120—28no—
434C4×D4—28no—
435C4×D4—28no—
436#117—22no—
437#117—22no—
438C2×C4⋊C4—28no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4C23×C712yes—
446C2×C4⋊C4C23×C711yescharacteristic
447C2×C4⋊C4C23×C711yescharacteristic
448C2×C22⋊C4—28no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C42—21no—
457#103—24no—
458#103—24no—
459#103—24no—
460#102—24no—
461C22⋊C8—22no—
462C22⋊C8—22no—
463C22⋊C8—24no—
464C22⋊C8—42no—
465C22×C7—22no—
466C22×C7—22no—
467C22×C7—22no—
468C22×C7—22no—
469C22×C7—22no—
470C22×C7—22no—
471C22×C7—22no—
472C22×C7—22no—
473C22×C7—22no—
474C22×C7—22no—
475C22×C7—22no—
476C22×C7—22no—
477C22×C7—416no—
478C22×C7—41no—
479C22×C7—41no—
480C22×C7—41no—
481C22×C7—41no—
482C22×C7—41no—
483C22×C7—41no—
484C22×C7—41no—
485C22×C7—41no—
486C22×C7—42no—
487C22×C7—42no—
488C22×C7—42no—
489C22×C7—81no—
490C22×C7—81no—
491C22×C7—81no—
492C22×C7—81no—
493C22×C7#45214yescomplemented
494C22×C7C2×#12011yescharacteristic
495C22×C7C2×#12011yescharacteristic
496C22×C7#53411yescharacteristic
497C22×C7C2×#13511yescharacteristic
498C22×C7C2×#13711yescharacteristic
499C22×C7C2×#13711yescharacteristic
500C22×C7#57511yescharacteristic
501C4×C7—22no—
502C4×C7—22no—
503C4×C7—41no—
504C4×C7—42no—
505C4×C7—44no—
506C4×C7—42no—
507C4×C7—44no—
508C4×C7—42no—
509C4×C7D4212yes—
510C4×C7D4212yes—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—21no—
517C24—41no—
518C24—41no—
519C24C2×C7×D411yescharacteristic
520C24C2×C7×D411yescharacteristic
521C24C2×C7×D411yescharacteristic
522#41—48no—
523#41—48no—
524C2×Q8—24no—
525C2×Q8—22no—
526C2×Q8—21no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—48no—
534C2×Q8—48no—
535C2×Q8—42no—
536C2×Q8—42no—
537C2×Q8C2×C7×D412yes—
538C2×Q8C2×C7×D414yes—
539C2×D4—24no—
540C2×D4—24no—
541C2×D4—24no—
542C2×D4—22no—
543C2×D4—21no—
544C2×D4—22no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4C2×C7×D412yes—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4C2×C7×D411yescharacteristic
587C22×C4C2×C7×D411yescharacteristic
588C22×C4C2×C7×D411yescharacteristic
589C22×C4C2×C7×D412yes—
590C22×C4C2×C7×D412yes—
591C22×C4C2×C7×D414yes—
592C22×C4C24×C711yescharacteristic
593Q16—48no—
594SD16—48no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C4⋊C4—24no—
602C4⋊C4—28no—
603C4⋊C4—24no—
604C4⋊C4—28no—
605C4⋊C4—24no—
606C4⋊C4—22no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4C2×C7×D414yes—
610C4⋊C4C2×C7×D412yes—
611C4⋊C4C2×C7×D412yes—
612C22⋊C4—28no—
613C22⋊C4—24no—
614C22⋊C4—24no—
615C22⋊C4—24no—
616C22⋊C4—28no—
617C22⋊C4—24no—
618C22⋊C4—24no—
619C42—24no—
620C2×C7—24no—
621C2×C7—42no—
622C2×C7—42no—
623C2×C7—82no—
624C2×C7#240311yescharacteristic
625C2×C7C2×#45211yescharacteristic
626C2×C7#300211yescharacteristic
627C2×C7#300411yescharacteristic
628C2×C7#300711yescharacteristic
629C2×C7#319011yescharacteristic
630C2×C7#319611yescharacteristic
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—28no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—22no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23C7×#12012yes—
662C23C7×#12012yes—
663C23C7×#13512yes—
664C23C7×#13712yes—
665C23C7×#13712yes—
666C23C22×C7×D411yescharacteristic
667Q8—24no—
668Q8—24no—
669Q8—24no—
670Q8—48no—
671Q8—42no—
672Q8—42no—
673Q8—42no—
674D4—24no—
675D4—48no—
676D4—48no—
677D4—48no—
678D4—42no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—48no—
699C2×C4—48no—
700C2×C4—48no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4C7×#12012yes—
714C2×C4C7×#12012yes—
715C2×C4C22×C7×D412yes—
716C2×C4C22×C7×D411yescharacteristic
717C2×C4C22×C7×D411yescharacteristic
718C2×C4C7×H(5,𝔽2)12yes—
719C8—42no—
720C8—42no—
721C7#2392211yescharacteristic, direct product factor, Sylow
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—416no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22C7×#45214yescomplemented
751C22C2×C7×#12011yescharacteristic
752C22C2×C7×#12011yescharacteristic
753C22C7×#53411yescharacteristic
754C22C2×C7×#13511yescharacteristic
755C22C2×C7×#13711yescharacteristic
756C22C2×C7×#13711yescharacteristic
757C22C7×#57511yescharacteristic
758C4—22no—
759C4—22no—
760C4—41no—
761C4—42no—
762C4—44no—
763C4—42no—
764C4—44no—
765C4—42no—
766C4C7×D4212yes—
767C4C7×D4212yes—
768C2—24no—
769C2—42no—
770C2—42no—
771C2—82no—
772C2C7×#240311yescharacteristic
773C2C2×C7×#45211yescharacteristic
774C2C7×#300211yescharacteristic
775C2C7×#300411yescharacteristic
776C2C7×#300711yescharacteristic
777C2C7×#319011yescharacteristic
778C2C7×#319611yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC2×C7×#525C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C24×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C7×C22⋊Q8C2semidirect
3. C2×C7×#452C2semidirect
4. C2×C7×#451C2semidirect
5. C2×C7×#448C2semidirect
6. C7×#2001C2semidirect
7. C7×#2000C2semidirect
8. C7×#1874C2semidirect
9. C7×#1873C2semidirect
10. C7×#1872C2semidirect
11. C7×#1779C2semidirect
15. C22×C7×Q16C22semidirect
16. C22×C7×SD16C22semidirect
39. C2×C7×#103C22semidirect
40. C2×C7×#103C22semidirect
41. C2×C7×#103C22semidirect
42. C2×C7×#102C22semidirect
47. C7×#340C22semidirect
48. C7×#340C22semidirect
49. #23922C7direct (N × H)
97. C7×C22⋊Q8D4semidirect
135. C22×C22⋊Q8C2×C7semidirect
136. C2×#452C2×C7semidirect
137. C2×#451C2×C7semidirect
138. C2×#448C2×C7semidirect
139. #2001C2×C7semidirect
140. #2000C2×C7semidirect
141. #1874C2×C7semidirect
142. #1873C2×C7semidirect
143. #1872C2×C7semidirect
144. #1779C2×C7semidirect
257. C22×Q16C22×C7semidirect
258. C22×SD16C22×C7semidirect
281. C2×#103C22×C7semidirect
282. C2×#103C22×C7semidirect
283. C2×#103C22×C7semidirect
284. C2×#102C22×C7semidirect
289. #340C22×C7semidirect
290. #340C22×C7semidirect
428. C22⋊Q8C7×D4semidirect
493. C22×C7#452semidirect
721. C7#23922direct (N × H)
750. C22C7×#452semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5252
C22×C7×C22⋊Q82
C2×C7×#4522
C2×C7×#4512
C2×C7×#4482
C7×#20012
C7×#20002
C7×#18742
C7×#18732
C7×#18722
C7×#17792
#239227