Finite Group Databasebeta

← C7×#13971 #13191187

Subgroups — C7×#13971 #13191187

Order 1792.

3526 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C7×C22⋊C4C211yesmaximal, characteristic
2C2×C7×#388C212yesmaximal, complemented
3C2×C7×#385C211yesmaximal, characteristic, complemented
4C2×C7×#379C211yesmaximal, characteristic
5C2×C7×#379C211yesmaximal, characteristic
6C2×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
7C7×#1440C212yesmaximal, complemented
8C7×#1439C212yesmaximal, complemented
9C7×#1437C212yesmaximal, complemented
10C7×C22⋊#95C211yesmaximal, characteristic, complemented
11C7×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C7C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C24×C4×C7C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic, complemented
16C22×C7×C4⋊C4C2211yescharacteristic, complemented
17C22×C7×C22⋊C4—24no—
18C22×C7×C22⋊C4—28no—
19C22×C7×C22⋊C4C2212yes—
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2212yes—
22C22×C7×C22⋊C4C2212yes—
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2212yes—
26C22×C7×C22⋊C4C2212yes—
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2212yes—
29C22×C42×C7C2212yescomplemented
30C7×#388—28no—
31C7×#385—24no—
32C7×#379—24no—
33C7×#379C418yescomplemented
34C4×C7×C22⋊C4—24no—
35C2×C7×#95C2212yescomplemented
36C2×C7×#95C2211yescharacteristic, complemented
37C2×C7×#95C2211yescharacteristic, complemented
38C2×C7×#95C2212yescomplemented
39C2×C7×#95C2212yescomplemented
40C2×C7×#95C2212yescomplemented
41C2×C7×#95C2212yescomplemented
42#13971C711yesmaximal, characteristic, direct product factor, Sylow
43C25×C7—24no—
44C25×C7—22no—
45C25×C7—24no—
46C25×C7—22no—
47C25×C7—22no—
48C25×C7—22no—
49C25×C7—22no—
50C25×C7—22no—
51C25×C7—42no—
52C25×C7—42no—
53C25×C7C2×C414yes—
54C25×C7C2312yes—
55C25×C7C2311yescharacteristic
56C23×C4×C7—22no—
57C23×C4×C7—22no—
58C23×C4×C7—22no—
59C23×C4×C7—24no—
60C23×C4×C7—24no—
61C23×C4×C7—22no—
62C23×C4×C7—22no—
63C23×C4×C7—42no—
64C23×C4×C7—42no—
65C23×C4×C7D414yes—
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2312yes—
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2312yes—
72C23×C4×C7C2312yes—
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C2×C7×C4⋊C4—22no—
76C2×C7×C4⋊C4—22no—
77C2×C7×C4⋊C4—24no—
78C2×C7×C4⋊C4—42no—
79C2×C7×C22⋊C4—232no—
80C2×C7×C22⋊C4—24no—
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—24no—
84C2×C7×C22⋊C4—22no—
85C2×C7×C22⋊C4—22no—
86C2×C7×C22⋊C4—24no—
87C2×C7×C22⋊C4—22no—
88C2×C7×C22⋊C4—22no—
89C2×C7×C22⋊C4—24no—
90C2×C7×C22⋊C4—24no—
91C2×C7×C22⋊C4—24no—
92C2×C7×C22⋊C4—24no—
93C2×C7×C22⋊C4—22no—
94C2×C7×C22⋊C4—22no—
95C2×C7×C22⋊C4—24no—
96C2×C7×C22⋊C4—24no—
97C2×C7×C22⋊C4—22no—
98C2×C7×C22⋊C4—24no—
99C2×C7×C22⋊C4—24no—
100C2×C7×C22⋊C4—42no—
101C2×C7×C22⋊C4—42no—
102C2×C7×C22⋊C4—42no—
103C2×C7×C22⋊C4—42no—
104C2×C7×C22⋊C4C2×C414yes—
105C2×C7×C22⋊C4C2×C414yes—
106C2×C7×C22⋊C4C2×C418yescomplemented
107C2×C7×C22⋊C4C2×C418yescomplemented
108C2×C7×C22⋊C4D418yes—
109C2×C7×C22⋊C4D414yes—
110C2×C42×C7—24no—
111C2×C42×C7—24no—
112C2×C42×C7—42no—
113C7×#95—24no—
114C7×#95—22no—
115C7×#95—22no—
116C7×#95—24no—
117C7×#95—24no—
118C7×#95—42no—
119C7×#95—42no—
120C23×C22⋊C4C2×C711yescharacteristic
121C2×#388C2×C712yescomplemented
122C2×#385C2×C711yescharacteristic, complemented
123C2×#379C2×C711yescharacteristic
124C2×#379C2×C711yescharacteristic
125C2×C4×C22⋊C4C2×C711yescharacteristic, complemented
126#1440C2×C712yescomplemented
127#1439C2×C712yescomplemented
128#1437C2×C712yescomplemented
129C22⋊#95C2×C711yescharacteristic, complemented
130C22⋊#95C2×C711yescharacteristic, complemented
131C24×C7—22no—
132C24×C7—22no—
133C24×C7—22no—
134C24×C7—22no—
135C24×C7—28no—
136C24×C7—28no—
137C24×C7—216no—
138C24×C7—216no—
139C24×C7—28no—
140C24×C7—22no—
141C24×C7—22no—
142C24×C7—22no—
143C24×C7—22no—
144C24×C7—22no—
145C24×C7—22no—
146C24×C7—22no—
147C24×C7—22no—
148C24×C7—22no—
149C24×C7—22no—
150C24×C7—22no—
151C24×C7—22no—
152C24×C7—28no—
153C24×C7—28no—
154C24×C7—48no—
155C24×C7—48no—
156C24×C7—48no—
157C24×C7—48no—
158C24×C7—48no—
159C24×C7—48no—
160C24×C7—48no—
161C24×C7—48no—
162C24×C7—48no—
163C24×C7—44no—
164C24×C7—44no—
165C24×C7—48no—
166C24×C7—44no—
167C24×C7—44no—
168C24×C7—44no—
169C24×C7—44no—
170C24×C7C22×C414yes—
171C24×C7C22×C412yes—
172C24×C7C2×D414yes—
173C24×C7C2×D412yes—
174C24×C7C2×D412yes—
175C24×C7#4114yes—
176C24×C7#4112yes—
177C24×C7#4112yes—
178C24×C7#4112yes—
179C24×C7#4112yes—
180C24×C7C2411yescharacteristic
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—22no—
184C22×C4×C7—28no—
185C22×C4×C7—28no—
186C22×C4×C7—21no—
187C22×C4×C7—22no—
188C22×C4×C7—22no—
189C22×C4×C7—22no—
190C22×C4×C7—21no—
191C22×C4×C7—22no—
192C22×C4×C7—21no—
193C22×C4×C7—22no—
194C22×C4×C7—22no—
195C22×C4×C7—22no—
196C22×C4×C7—21no—
197C22×C4×C7—22no—
198C22×C4×C7—21no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—21no—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—28no—
217C22×C4×C7—21no—
218C22×C4×C7—22no—
219C22×C4×C7—21no—
220C22×C4×C7—21no—
221C22×C4×C7—21no—
222C22×C4×C7—21no—
223C22×C4×C7—21no—
224C22×C4×C7—22no—
225C22×C4×C7—22no—
226C22×C4×C7—22no—
227C22×C4×C7—44no—
228C22×C4×C7—48no—
229C22×C4×C7—48no—
230C22×C4×C7—48no—
231C22×C4×C7—48no—
232C22×C4×C7—44no—
233C22×C4×C7—44no—
234C22×C4×C7C22×C412yes—
235C22×C4×C7C22×C414yes—
236C22×C4×C7C22×C412yes—
237C22×C4×C7C2×D414yes—
238C22×C4×C7C2×D414yes—
239C22×C4×C7C2×D412yes—
240C22×C4×C7C2×D412yes—
241C22×C4×C7C2×D414yes—
242C7×C4⋊C4—44no—
243C7×C4⋊C4—44no—
244C7×C22⋊C4—216no—
245C7×C22⋊C4—28no—
246C7×C22⋊C4—28no—
247C7×C22⋊C4—216no—
248C7×C22⋊C4—28no—
249C7×C22⋊C4—216no—
250C7×C22⋊C4—48no—
251C7×C22⋊C4—48no—
252C7×C22⋊C4—48no—
253C7×C22⋊C4—44no—
254C42×C7—48no—
255C26C22×C711yescharacteristic
256C24×C4C22×C711yescharacteristic
257C24×C4C22×C711yescharacteristic
258C22×C4⋊C4C22×C711yescharacteristic, complemented
259C22×C4⋊C4C22×C711yescharacteristic, complemented
260C22×C22⋊C4—24no—
261C22×C22⋊C4—28no—
262C22×C22⋊C4C22×C712yes—
263C22×C22⋊C4C22×C711yescharacteristic
264C22×C22⋊C4C22×C712yes—
265C22×C22⋊C4C22×C712yes—
266C22×C22⋊C4C22×C711yescharacteristic
267C22×C22⋊C4C22×C711yescharacteristic
268C22×C22⋊C4C22×C712yes—
269C22×C22⋊C4C22×C712yes—
270C22×C22⋊C4C22×C711yescharacteristic
271C22×C22⋊C4C22×C712yes—
272C22×C42C22×C712yescomplemented
273#388—28no—
274#385—24no—
275#379—24no—
276#379C4×C718yescomplemented
277C4×C22⋊C4—24no—
278C2×#95C22×C712yescomplemented
279C2×#95C22×C712yescomplemented
280C2×#95C22×C711yescharacteristic, complemented
281C2×#95C22×C712yescomplemented
282C2×#95C22×C711yescharacteristic, complemented
283C2×#95C22×C712yescomplemented
284C2×#95C22×C712yescomplemented
285C23×C7—24no—
286C23×C7—24no—
287C23×C7—22no—
288C23×C7—22no—
289C23×C7—24no—
290C23×C7—22no—
291C23×C7—22no—
292C23×C7—24no—
293C23×C7—24no—
294C23×C7—24no—
295C23×C7—24no—
296C23×C7—24no—
297C23×C7—24no—
298C23×C7—24no—
299C23×C7—24no—
300C23×C7—24no—
301C23×C7—232no—
302C23×C7—24no—
303C23×C7—24no—
304C23×C7—24no—
305C23×C7—24no—
306C23×C7—24no—
307C23×C7—24no—
308C23×C7—24no—
309C23×C7—24no—
310C23×C7—24no—
311C23×C7—24no—
312C23×C7—24no—
313C23×C7—24no—
314C23×C7—24no—
315C23×C7—24no—
316C23×C7—24no—
317C23×C7—24no—
318C23×C7—24no—
319C23×C7—24no—
320C23×C7—432no—
321C23×C7—432no—
322C23×C7—416no—
323C23×C7—416no—
324C23×C7—416no—
325C23×C7—416no—
326C23×C7—432no—
327C23×C7—416no—
328C23×C7—432no—
329C23×C7—42no—
330C23×C7—42no—
331C23×C7—42no—
332C23×C7—42no—
333C23×C7—42no—
334C23×C7—42no—
335C23×C7—42no—
336C23×C7—42no—
337C23×C7—42no—
338C23×C7—42no—
339C23×C7—42no—
340C23×C7—42no—
341C23×C7—42no—
342C23×C7—42no—
343C23×C7—42no—
344C23×C7—42no—
345C23×C7—416no—
346C23×C7#11714yes—
347C23×C7C4×D418yes—
348C23×C7C4×D414yes—
349C23×C7C4×D414yes—
350C23×C7#12114yes—
351C23×C7#12314yes—
352C23×C7#12414yes—
353C23×C7#12614yes—
354C23×C7C23×C411yescharacteristic
355C23×C7C22×D411yescharacteristic
356C23×C7C22×D412yes—
357C23×C7C22×D411yescharacteristic
358C23×C7C2×#4111yescharacteristic
359C23×C7C2×#4111yescharacteristic
360C23×C7C2×#4111yescharacteristic
361C23×C7C2×#4112yes—
362C23×C7C2×#4111yescharacteristic
363C23×C7H(5,𝔽2)12yes—
364C23×C7H(5,𝔽2)12yes—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—24no—
368C2×C4×C7—24no—
369C2×C4×C7—22no—
370C2×C4×C7—24no—
371C2×C4×C7—24no—
372C2×C4×C7—22no—
373C2×C4×C7—24no—
374C2×C4×C7—24no—
375C2×C4×C7—24no—
376C2×C4×C7—22no—
377C2×C4×C7—24no—
378C2×C4×C7—22no—
379C2×C4×C7—24no—
380C2×C4×C7—22no—
381C2×C4×C7—24no—
382C2×C4×C7—24no—
383C2×C4×C7—24no—
384C2×C4×C7—24no—
385C2×C4×C7—416no—
386C2×C4×C7—416no—
387C2×C4×C7—41no—
388C2×C4×C7—42no—
389C2×C4×C7—41no—
390C2×C4×C7—42no—
391C2×C4×C7—42no—
392C2×C4×C7—41no—
393C2×C4×C7—41no—
394C2×C4×C7—42no—
395C2×C4×C7—42no—
396C2×C4×C7—42no—
397C2×C4×C7—42no—
398C2×C4×C7—42no—
399C2×C4×C7—42no—
400C2×C4×C7—42no—
401C2×C4×C7—42no—
402C2×C4×C7—42no—
403C2×C4×C7—42no—
404C2×C4×C7—42no—
405C2×C4×C7—42no—
406C2×C4×C7—42no—
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—42no—
414C2×C4×C7—42no—
415C2×C4×C7—42no—
416C2×C4×C7—42no—
417C2×C4×C7#12014yes—
418C25—24no—
419C25—22no—
420C25—24no—
421C25—22no—
422C25—22no—
423C25—22no—
424C25—22no—
425C25—22no—
426C25—42no—
427C25—42no—
428C25C2×C4×C714yes—
429C25C23×C712yes—
430C25C23×C711yescharacteristic
431C23×C4—22no—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—24no—
435C23×C4—24no—
436C23×C4—22no—
437C23×C4—22no—
438C23×C4—42no—
439C23×C4—42no—
440C23×C4C7×D414yes—
441C23×C4C23×C711yescharacteristic
442C23×C4C23×C711yescharacteristic
443C23×C4C23×C711yescharacteristic
444C23×C4C23×C711yescharacteristic
445C23×C4C23×C712yes—
446C23×C4C23×C712yes—
447C23×C4C23×C711yescharacteristic
448C23×C4C23×C712yes—
449C23×C4C23×C711yescharacteristic
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—42no—
454C2×C22⋊C4—232no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—42no—
476C2×C22⋊C4—42no—
477C2×C22⋊C4—42no—
478C2×C22⋊C4—42no—
479C2×C22⋊C4C2×C4×C714yes—
480C2×C22⋊C4C2×C4×C714yes—
481C2×C22⋊C4C2×C4×C718yescomplemented
482C2×C22⋊C4C2×C4×C718yescomplemented
483C2×C22⋊C4C7×D418yes—
484C2×C22⋊C4C7×D414yes—
485C2×C42—24no—
486C2×C42—24no—
487C2×C42—42no—
488#95—24no—
489#95—22no—
490#95—22no—
491#95—24no—
492#95—24no—
493#95—42no—
494#95—42no—
495C22×C7—24no—
496C22×C7—24no—
497C22×C7—28no—
498C22×C7—28no—
499C22×C7—24no—
500C22×C7—24no—
501C22×C7—28no—
502C22×C7—24no—
503C22×C7—28no—
504C22×C7—24no—
505C22×C7—28no—
506C22×C7—28no—
507C22×C7—28no—
508C22×C7—464no—
509C22×C7—44no—
510C22×C7—44no—
511C22×C7—44no—
512C22×C7—44no—
513C22×C7—44no—
514C22×C7—44no—
515C22×C7—44no—
516C22×C7—44no—
517C22×C7—44no—
518C22×C7—44no—
519C22×C7—44no—
520C22×C7—44no—
521C22×C7#38818yescomplemented
522C22×C7C2×#11711yescharacteristic
523C22×C7C2×C4×D411yescharacteristic
524C22×C7C2×C4×D412yes—
525C22×C7C2×C4×D411yescharacteristic
526C22×C7#51812yes—
527C22×C7C2×#12011yescharacteristic
528C22×C7C2×#12111yescharacteristic
529C22×C7C2×#12311yescharacteristic
530C22×C7#52511yescharacteristic
531C22×C7#52512yes—
532C22×C7C2×#12411yescharacteristic
533C22×C7C2×#12611yescharacteristic
534C22×C7#53411yescharacteristic
535C22×C7#53511yescharacteristic
536C22×C7#53812yes—
537C22×C7D4212yes—
538C22×C7#54612yes—
539C22×C7#54612yes—
540C22×C7#54612yes—
541C22×C7#54612yes—
542C22×C7#55112yes—
543C22×C7#55112yes—
544C22×C7#55112yes—
545C4×C7—24no—
546C4×C7—42no—
547C4×C7—44no—
548C4×C7—42no—
549C4×C7—44no—
550C4×C7—44no—
551C4×C7—42no—
552C4×C7—81no—
553C4×C7—81no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—28no—
559C24—28no—
560C24—216no—
561C24—216no—
562C24—28no—
563C24—22no—
564C24—22no—
565C24—22no—
566C24—22no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—28no—
576C24—28no—
577C24—48no—
578C24—48no—
579C24—48no—
580C24—48no—
581C24—48no—
582C24—48no—
583C24—48no—
584C24—48no—
585C24—48no—
586C24—44no—
587C24—44no—
588C24—48no—
589C24—44no—
590C24—44no—
591C24—44no—
592C24—44no—
593C24C22×C4×C714yes—
594C24C22×C4×C712yes—
595C24C2×C7×D414yes—
596C24C2×C7×D412yes—
597C24C2×C7×D412yes—
598C24C7×#4114yes—
599C24C7×#4112yes—
600C24C7×#4112yes—
601C24C7×#4112yes—
602C24C7×#4112yes—
603C24C24×C711yescharacteristic
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—28no—
608C22×C4—28no—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—21no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—21no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—28no—
640C22×C4—21no—
641C22×C4—22no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—44no—
651C22×C4—48no—
652C22×C4—48no—
653C22×C4—48no—
654C22×C4—48no—
655C22×C4—44no—
656C22×C4—44no—
657C22×C4C22×C4×C712yes—
658C22×C4C22×C4×C714yes—
659C22×C4C22×C4×C712yes—
660C22×C4C2×C7×D414yes—
661C22×C4C2×C7×D414yes—
662C22×C4C2×C7×D412yes—
663C22×C4C2×C7×D412yes—
664C22×C4C2×C7×D414yes—
665C4⋊C4—44no—
666C4⋊C4—44no—
667C22⋊C4—216no—
668C22⋊C4—28no—
669C22⋊C4—28no—
670C22⋊C4—216no—
671C22⋊C4—28no—
672C22⋊C4—216no—
673C22⋊C4—48no—
674C22⋊C4—48no—
675C22⋊C4—48no—
676C22⋊C4—44no—
677C42—48no—
678C2×C7—28no—
679C2×C7—48no—
680C2×C7C2×#38811yescharacteristic
681C2×C7C4×#12011yescharacteristic
682C2×C7#232111yescharacteristic
683C2×C7#234212yes—
684C2×C7#235812yes—
685C2×C7#241011yescharacteristic
686C2×C7#241111yescharacteristic
687C2×C7#241812yes—
688C2×C7#243511yescharacteristic
689C2×C7#248012yes—
690C2×C7#256111yescharacteristic
691C23—24no—
692C23—24no—
693C23—22no—
694C23—22no—
695C23—24no—
696C23—22no—
697C23—22no—
698C23—24no—
699C23—24no—
700C23—24no—
701C23—24no—
702C23—24no—
703C23—24no—
704C23—24no—
705C23—24no—
706C23—24no—
707C23—232no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—432no—
727C23—432no—
728C23—416no—
729C23—416no—
730C23—432no—
731C23—416no—
732C23—432no—
733C23—416no—
734C23—416no—
735C23—42no—
736C23—42no—
737C23—416no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23C7×#11714yes—
753C23C4×C7×D418yes—
754C23C4×C7×D414yes—
755C23C4×C7×D414yes—
756C23C7×#12114yes—
757C23C7×#12314yes—
758C23C7×#12414yes—
759C23C7×#12614yes—
760C23C23×C4×C711yescharacteristic
761C23C22×C7×D411yescharacteristic
762C23C22×C7×D412yes—
763C23C22×C7×D411yescharacteristic
764C23C2×C7×#4111yescharacteristic
765C23C2×C7×#4111yescharacteristic
766C23C2×C7×#4111yescharacteristic
767C23C2×C7×#4112yes—
768C23C2×C7×#4111yescharacteristic
769C23C7×H(5,𝔽2)12yes—
770C23C7×H(5,𝔽2)12yes—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—22no—
785C2×C4—24no—
786C2×C4—22no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—416no—
792C2×C4—416no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4C7×#12014yes—
824C7#1397111yescharacteristic, direct product factor, Sylow
825C22—24no—
826C22—24no—
827C22—28no—
828C22—24no—
829C22—28no—
830C22—24no—
831C22—24no—
832C22—24no—
833C22—28no—
834C22—28no—
835C22—28no—
836C22—28no—
837C22—28no—
838C22—464no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—44no—
843C22—44no—
844C22—44no—
845C22—44no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22C7×#38818yescomplemented
852C22C2×C7×#11711yescharacteristic
853C22C2×C4×C7×D411yescharacteristic
854C22C2×C4×C7×D411yescharacteristic
855C22C2×C4×C7×D412yes—
856C22C7×#51812yes—
857C22C2×C7×#12011yescharacteristic
858C22C2×C7×#12111yescharacteristic
859C22C2×C7×#12311yescharacteristic
860C22C7×#52511yescharacteristic
861C22C7×#52512yes—
862C22C2×C7×#12411yescharacteristic
863C22C2×C7×#12611yescharacteristic
864C22C7×#53411yescharacteristic
865C22C7×#53511yescharacteristic
866C22C7×#53812yes—
867C22C7×D4212yes—
868C22C7×#54612yes—
869C22C7×#54612yes—
870C22C7×#54612yes—
871C22C7×#54612yes—
872C22C7×#55112yes—
873C22C7×#55112yes—
874C22C7×#55112yes—
875C4—24no—
876C4—42no—
877C4—44no—
878C4—44no—
879C4—42no—
880C4—42no—
881C4—44no—
882C4—81no—
883C4—81no—
884C2—28no—
885C2—48no—
886C2C2×C7×#38811yescharacteristic
887C2C4×C7×#12011yescharacteristic
888C2C7×#232111yescharacteristic
889C2C7×#234212yes—
890C2C7×#235812yes—
891C2C7×#241011yescharacteristic
892C2C7×#241111yescharacteristic
893C2C7×#241812yes—
894C2C7×#243511yescharacteristic
895C2C7×#248012yes—
896C2C7×#256111yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC26×C7C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#388C2semidirect
3. C2×C7×#385C2semidirect
6. C2×C4×C7×C22⋊C4C2semidirect
7. C7×#1440C2semidirect
8. C7×#1439C2semidirect
9. C7×#1437C2semidirect
10. C7×C22⋊#95C2semidirect
11. C7×C22⋊#95C2semidirect
15. C22×C7×C4⋊C4C22semidirect
16. C22×C7×C4⋊C4C22semidirect
29. C22×C42×C7C22semidirect
33. C7×#379C4semidirect
35. C2×C7×#95C22semidirect
36. C2×C7×#95C22semidirect
37. C2×C7×#95C22semidirect
38. C2×C7×#95C22semidirect
39. C2×C7×#95C22semidirect
40. C2×C7×#95C22semidirect
41. C2×C7×#95C22semidirect
42. #13971C7direct (N × H)
106. C2×C7×C22⋊C4C2×C4semidirect
107. C2×C7×C22⋊C4C2×C4semidirect
121. C2×#388C2×C7semidirect
122. C2×#385C2×C7semidirect
125. C2×C4×C22⋊C4C2×C7semidirect
126. #1440C2×C7semidirect
127. #1439C2×C7semidirect
128. #1437C2×C7semidirect
129. C22⋊#95C2×C7semidirect
130. C22⋊#95C2×C7semidirect
258. C22×C4⋊C4C22×C7semidirect
259. C22×C4⋊C4C22×C7semidirect
272. C22×C42C22×C7semidirect
276. #379C4×C7semidirect
278. C2×#95C22×C7semidirect
279. C2×#95C22×C7semidirect
280. C2×#95C22×C7semidirect
281. C2×#95C22×C7semidirect
282. C2×#95C22×C7semidirect
283. C2×#95C22×C7semidirect
284. C2×#95C22×C7semidirect
481. C2×C22⋊C4C2×C4×C7semidirect
482. C2×C22⋊C4C2×C4×C7semidirect
521. C22×C7#388semidirect
824. C7#13971direct (N × H)
851. C22C7×#388semidirect

Maximal subgroups

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

subgroupindex
C23×C7×C22⋊C42
C2×C7×#3882
C2×C7×#3852
C2×C7×#3792
C2×C4×C7×C22⋊C42
C7×#14402
C7×#14392
C7×#14372
C7×C22⋊#952
#139717