Finite Group Databasebeta

← C7×#14725 #13191941

Subgroups — C7×#14725 #13191941

Order 1792.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#120C211yesmaximal, characteristic
2C23×C7×C22⋊C4C211yesmaximal, characteristic, complemented
3C2×C7×#394C212yesmaximal, complemented
4C2×C7×#386C211yesmaximal, characteristic, complemented
5C2×C7×#386C211yesmaximal, characteristic, complemented
6C2×C7×#380C211yesmaximal, characteristic, complemented
7C2×C7×#379C211yesmaximal, characteristic, complemented
8C7×#1440C212yesmaximal, complemented
9C7×#1439C212yesmaximal, complemented
10C7×#1438C212yesmaximal, complemented
11C7×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C7C2211yescharacteristic
13C23×C7×D4C2211yescharacteristic
14C23×C7×D4C2212yes—
15C24×C4×C7C2211yescharacteristic
16C24×C4×C7C2211yescharacteristic
17C2×C7×#120—24no—
18C2×C7×#120—24no—
19C2×C7×#120—24no—
20C22×C7×C4⋊C4C2212yescomplemented
21C22×C7×C22⋊C4—24no—
22C22×C7×C22⋊C4—28no—
23C22×C7×C22⋊C4C2212yes—
24C22×C7×C22⋊C4C2212yes—
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2212yes—
28C22×C7×C22⋊C4C2211yescharacteristic
29C22×C7×C22⋊C4C2212yes—
30C22×C7×C22⋊C4C2212yes—
31C22×C7×C22⋊C4C2211yescharacteristic, complemented
32C22×C7×C22⋊C4C2212yescomplemented
33C22×C7×C22⋊C4C2211yescharacteristic, complemented
34C7×#394—28no—
35C7×#386—24no—
36C7×#386—24no—
37C7×#380—24no—
38C7×#379—24no—
39C2×C7×#95C2212yescomplemented
40C2×C7×#95C2211yescharacteristic, complemented
41C2×C7×#95C2212yescomplemented
42C2×C7×#95C2211yescharacteristic, complemented
43C2×C7×#95C2212yescomplemented
44C2×C7×#95C2212yescomplemented
45#14725C711yesmaximal, characteristic, direct product factor, Sylow
46C25×C7—24no—
47C25×C7—22no—
48C25×C7—24no—
49C25×C7—22no—
50C25×C7—22no—
51C25×C7—22no—
52C25×C7—22no—
53C25×C7—22no—
54C25×C7—42no—
55C25×C7—42no—
56C25×C7D414yes—
57C25×C7C2311yescharacteristic
58C25×C7C2312yes—
59C25×C7C2311yescharacteristic
60C22×C7×D4—24no—
61C22×C7×D4—24no—
62C22×C7×D4—22no—
63C22×C7×D4—22no—
64C22×C7×D4—22no—
65C22×C7×D4—22no—
66C22×C7×D4—22no—
67C22×C7×D4—22no—
68C22×C7×D4—24no—
69C22×C7×D4—24no—
70C22×C7×D4—24no—
71C22×C7×D4—42no—
72C22×C7×D4—42no—
73C22×C7×D4D414yes—
74C23×C4×C7—22no—
75C23×C4×C7—22no—
76C23×C4×C7—22no—
77C23×C4×C7—24no—
78C23×C4×C7—24no—
79C23×C4×C7—22no—
80C23×C4×C7—22no—
81C23×C4×C7—42no—
82C23×C4×C7—42no—
83C23×C4×C7D414yescomplemented
84C23×C4×C7C2311yescharacteristic
85C23×C4×C7C2311yescharacteristic
86C23×C4×C7C2312yes—
87C23×C4×C7C2311yescharacteristic
88C23×C4×C7C2312yes—
89C23×C4×C7C2311yescharacteristic
90C23×C4×C7C2312yes—
91C23×C4×C7C2311yescharacteristic
92C7×#120—232no—
93C2×C7×C4⋊C4—24no—
94C2×C7×C4⋊C4—24no—
95C2×C7×C4⋊C4—42no—
96C2×C7×C22⋊C4—232no—
97C2×C7×C22⋊C4—24no—
98C2×C7×C22⋊C4—24no—
99C2×C7×C22⋊C4—22no—
100C2×C7×C22⋊C4—22no—
101C2×C7×C22⋊C4—24no—
102C2×C7×C22⋊C4—24no—
103C2×C7×C22⋊C4—24no—
104C2×C7×C22⋊C4—24no—
105C2×C7×C22⋊C4—24no—
106C2×C7×C22⋊C4—24no—
107C2×C7×C22⋊C4—24no—
108C2×C7×C22⋊C4—22no—
109C2×C7×C22⋊C4—24no—
110C2×C7×C22⋊C4—22no—
111C2×C7×C22⋊C4—22no—
112C2×C7×C22⋊C4—22no—
113C2×C7×C22⋊C4—22no—
114C2×C7×C22⋊C4—24no—
115C2×C7×C22⋊C4—24no—
116C2×C7×C22⋊C4—24no—
117C2×C7×C22⋊C4—22no—
118C2×C7×C22⋊C4—22no—
119C2×C7×C22⋊C4—22no—
120C2×C7×C22⋊C4—24no—
121C2×C7×C22⋊C4—24no—
122C2×C7×C22⋊C4—42no—
123C2×C7×C22⋊C4—42no—
124C2×C7×C22⋊C4—42no—
125C2×C7×C22⋊C4—42no—
126C2×C7×C22⋊C4D414yes—
127C2×C7×C22⋊C4D418yescomplemented
128C7×#95—24no—
129C7×#95—22no—
130C7×#95—22no—
131C7×#95—24no—
132C7×#95—24no—
133C7×#95—42no—
134C22×#120C2×C711yescharacteristic
135C23×C22⋊C4C2×C711yescharacteristic, complemented
136C2×#394C2×C712yescomplemented
137C2×#386C2×C711yescharacteristic, complemented
138C2×#386C2×C711yescharacteristic, complemented
139C2×#380C2×C711yescharacteristic, complemented
140C2×#379C2×C711yescharacteristic, complemented
141#1440C2×C712yescomplemented
142#1439C2×C712yescomplemented
143#1438C2×C712yescomplemented
144C22⋊#95C2×C711yescharacteristic, complemented
145C24×C7—22no—
146C24×C7—22no—
147C24×C7—22no—
148C24×C7—22no—
149C24×C7—28no—
150C24×C7—28no—
151C24×C7—216no—
152C24×C7—216no—
153C24×C7—28no—
154C24×C7—22no—
155C24×C7—22no—
156C24×C7—22no—
157C24×C7—22no—
158C24×C7—22no—
159C24×C7—22no—
160C24×C7—22no—
161C24×C7—22no—
162C24×C7—22no—
163C24×C7—22no—
164C24×C7—22no—
165C24×C7—22no—
166C24×C7—28no—
167C24×C7—28no—
168C24×C7—21no—
169C24×C7—22no—
170C24×C7—21no—
171C24×C7—21no—
172C24×C7—21no—
173C24×C7—21no—
174C24×C7—21no—
175C24×C7—22no—
176C24×C7—22no—
177C24×C7—22no—
178C24×C7—48no—
179C24×C7—48no—
180C24×C7—48no—
181C24×C7—48no—
182C24×C7—48no—
183C24×C7—48no—
184C24×C7—48no—
185C24×C7—48no—
186C24×C7—48no—
187C24×C7—44no—
188C24×C7—44no—
189C24×C7—48no—
190C24×C7—44no—
191C24×C7—44no—
192C24×C7—44no—
193C24×C7—44no—
194C24×C7C2×D412yes—
195C24×C7C2×D414yes—
196C24×C7C2×D414yes—
197C24×C7C2×D412yes—
198C24×C7C2×D412yes—
199C24×C7C2×D412yes—
200C24×C7C2×D412yes—
201C24×C7#4114yes—
202C24×C7#4112yes—
203C24×C7#4112yes—
204C24×C7#4112yes—
205C24×C7C2411yescharacteristic
206C2×C7×D4—216no—
207C2×C7×D4—28no—
208C2×C7×D4—28no—
209C2×C7×D4—28no—
210C2×C7×D4—48no—
211C2×C7×D4—48no—
212C2×C7×D4—48no—
213C2×C7×D4—48no—
214C2×C7×D4—48no—
215C2×C7×D4—48no—
216C2×C7×D4—44no—
217C2×C7×D4—44no—
218C2×C7×D4—44no—
219C2×C7×D4—44no—
220C22×C4×C7—21no—
221C22×C4×C7—21no—
222C22×C4×C7—22no—
223C22×C4×C7—28no—
224C22×C4×C7—28no—
225C22×C4×C7—21no—
226C22×C4×C7—21no—
227C22×C4×C7—22no—
228C22×C4×C7—22no—
229C22×C4×C7—22no—
230C22×C4×C7—22no—
231C22×C4×C7—22no—
232C22×C4×C7—21no—
233C22×C4×C7—21no—
234C22×C4×C7—22no—
235C22×C4×C7—22no—
236C22×C4×C7—21no—
237C22×C4×C7—22no—
238C22×C4×C7—21no—
239C22×C4×C7—21no—
240C22×C4×C7—21no—
241C22×C4×C7—22no—
242C22×C4×C7—22no—
243C22×C4×C7—22no—
244C22×C4×C7—22no—
245C22×C4×C7—22no—
246C22×C4×C7—22no—
247C22×C4×C7—28no—
248C22×C4×C7—21no—
249C22×C4×C7—22no—
250C22×C4×C7—22no—
251C22×C4×C7—21no—
252C22×C4×C7—22no—
253C22×C4×C7—22no—
254C22×C4×C7—21no—
255C22×C4×C7—21no—
256C22×C4×C7—22no—
257C22×C4×C7—21no—
258C22×C4×C7—22no—
259C22×C4×C7—21no—
260C22×C4×C7—22no—
261C22×C4×C7—22no—
262C22×C4×C7—22no—
263C22×C4×C7—22no—
264C22×C4×C7—22no—
265C22×C4×C7—44no—
266C22×C4×C7—48no—
267C22×C4×C7—48no—
268C22×C4×C7—48no—
269C22×C4×C7—48no—
270C22×C4×C7—44no—
271C22×C4×C7—44no—
272C22×C4×C7C2×D412yes—
273C22×C4×C7C2×D412yes—
274C22×C4×C7C2×D414yes—
275C22×C4×C7C2×D414yes—
276C22×C4×C7C2×D412yes—
277C22×C4×C7C2×D414yes—
278C7×C4⋊C4—48no—
279C7×C22⋊C4—216no—
280C7×C22⋊C4—216no—
281C7×C22⋊C4—28no—
282C7×C22⋊C4—216no—
283C7×C22⋊C4—48no—
284C7×C22⋊C4—44no—
285C7×C22⋊C4—48no—
286C7×C22⋊C4—44no—
287C7×C22⋊C4—48no—
288C7×C22⋊C4—44no—
289C7×C22⋊C4—44no—
290C26C22×C711yescharacteristic
291C23×D4C22×C711yescharacteristic
292C23×D4C22×C712yes—
293C24×C4C22×C711yescharacteristic
294C24×C4C22×C711yescharacteristic
295C2×#120—24no—
296C2×#120—24no—
297C2×#120—24no—
298C22×C4⋊C4C22×C712yescomplemented
299C22×C22⋊C4—24no—
300C22×C22⋊C4—28no—
301C22×C22⋊C4C22×C712yes—
302C22×C22⋊C4C22×C712yes—
303C22×C22⋊C4C22×C712yes—
304C22×C22⋊C4C22×C711yescharacteristic
305C22×C22⋊C4C22×C711yescharacteristic
306C22×C22⋊C4C22×C711yescharacteristic
307C22×C22⋊C4C22×C712yes—
308C22×C22⋊C4C22×C712yes—
309C22×C22⋊C4C22×C711yescharacteristic, complemented
310C22×C22⋊C4C22×C712yescomplemented
311C22×C22⋊C4C22×C711yescharacteristic, complemented
312#394—28no—
313#386—24no—
314#386—24no—
315#380—24no—
316#379—24no—
317C2×#95C22×C712yescomplemented
318C2×#95C22×C712yescomplemented
319C2×#95C22×C711yescharacteristic, complemented
320C2×#95C22×C712yescomplemented
321C2×#95C22×C711yescharacteristic, complemented
322C2×#95C22×C712yescomplemented
323C23×C7—22no—
324C23×C7—24no—
325C23×C7—22no—
326C23×C7—24no—
327C23×C7—22no—
328C23×C7—24no—
329C23×C7—22no—
330C23×C7—24no—
331C23×C7—24no—
332C23×C7—24no—
333C23×C7—24no—
334C23×C7—24no—
335C23×C7—24no—
336C23×C7—24no—
337C23×C7—24no—
338C23×C7—24no—
339C23×C7—232no—
340C23×C7—24no—
341C23×C7—24no—
342C23×C7—24no—
343C23×C7—24no—
344C23×C7—24no—
345C23×C7—24no—
346C23×C7—24no—
347C23×C7—24no—
348C23×C7—24no—
349C23×C7—24no—
350C23×C7—24no—
351C23×C7—24no—
352C23×C7—24no—
353C23×C7—24no—
354C23×C7—24no—
355C23×C7—24no—
356C23×C7—24no—
357C23×C7—24no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—24no—
362C23×C7—24no—
363C23×C7—432no—
364C23×C7—432no—
365C23×C7—416no—
366C23×C7—416no—
367C23×C7—416no—
368C23×C7—416no—
369C23×C7—432no—
370C23×C7—432no—
371C23×C7—416no—
372C23×C7—42no—
373C23×C7—42no—
374C23×C7—42no—
375C23×C7—42no—
376C23×C7—42no—
377C23×C7—42no—
378C23×C7—42no—
379C23×C7—42no—
380C23×C7—42no—
381C23×C7—42no—
382C23×C7—42no—
383C23×C7—42no—
384C23×C7—42no—
385C23×C7—42no—
386C23×C7—42no—
387C23×C7—42no—
388C23×C7—416no—
389C23×C7—41no—
390C23×C7—41no—
391C23×C7—41no—
392C23×C7—42no—
393C23×C7—41no—
394C23×C7—42no—
395C23×C7—41no—
396C23×C7—41no—
397C23×C7—41no—
398C23×C7—42no—
399C23×C7—41no—
400C23×C7—42no—
401C23×C7—42no—
402C23×C7—42no—
403C23×C7—42no—
404C23×C7—42no—
405C23×C7—42no—
406C23×C7—42no—
407C23×C7#12014yes—
408C23×C7#12118yes—
409C23×C7#12114yes—
410C23×C7#12114yes—
411C23×C7#12114yes—
412C23×C7#12314yes—
413C23×C7#12314yes—
414C23×C7#12414yes—
415C23×C7C22×D411yescharacteristic
416C23×C7C22×D411yescharacteristic
417C23×C7C22×D411yescharacteristic
418C23×C7C22×D412yes—
419C23×C7C22×D411yescharacteristic
420C23×C7C2×#4111yescharacteristic
421C23×C7C2×#4111yescharacteristic
422C23×C7C2×#4111yescharacteristic
423C23×C7C2×#4112yes—
424C23×C7H(5,𝔽2)12yes—
425C23×C7H(5,𝔽2)12yes—
426C7×D4—432no—
427C7×D4—416no—
428C2×C4×C7—22no—
429C2×C4×C7—22no—
430C2×C4×C7—24no—
431C2×C4×C7—24no—
432C2×C4×C7—24no—
433C2×C4×C7—22no—
434C2×C4×C7—22no—
435C2×C4×C7—24no—
436C2×C4×C7—22no—
437C2×C4×C7—22no—
438C2×C4×C7—22no—
439C2×C4×C7—22no—
440C2×C4×C7—24no—
441C2×C4×C7—24no—
442C2×C4×C7—24no—
443C2×C4×C7—24no—
444C2×C4×C7—416no—
445C2×C4×C7—416no—
446C2×C4×C7—42no—
447C2×C4×C7—41no—
448C2×C4×C7—41no—
449C2×C4×C7—42no—
450C2×C4×C7—41no—
451C2×C4×C7—41no—
452C2×C4×C7—42no—
453C2×C4×C7—42no—
454C2×C4×C7—42no—
455C2×C4×C7—42no—
456C2×C4×C7—42no—
457C2×C4×C7—42no—
458C2×C4×C7—42no—
459C2×C4×C7—42no—
460C2×C4×C7—41no—
461C2×C4×C7—42no—
462C2×C4×C7—41no—
463C2×C4×C7—42no—
464C2×C4×C7—41no—
465C2×C4×C7—42no—
466C2×C4×C7—41no—
467C2×C4×C7—42no—
468C2×C4×C7—42no—
469C2×C4×C7—41no—
470C2×C4×C7—42no—
471C2×C4×C7—41no—
472C2×C4×C7—42no—
473C2×C4×C7—42no—
474C2×C4×C7—42no—
475C2×C4×C7—42no—
476C2×C4×C7—42no—
477C2×C4×C7#12014yescomplemented
478C25—24no—
479C25—22no—
480C25—24no—
481C25—22no—
482C25—22no—
483C25—22no—
484C25—22no—
485C25—22no—
486C25—42no—
487C25—42no—
488C25C7×D414yes—
489C25C23×C711yescharacteristic
490C25C23×C712yes—
491C25C23×C711yescharacteristic
492C22×D4—24no—
493C22×D4—24no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—22no—
500C22×D4—24no—
501C22×D4—24no—
502C22×D4—24no—
503C22×D4—42no—
504C22×D4—42no—
505C22×D4C7×D414yes—
506C23×C4—22no—
507C23×C4—22no—
508C23×C4—22no—
509C23×C4—24no—
510C23×C4—24no—
511C23×C4—22no—
512C23×C4—22no—
513C23×C4—42no—
514C23×C4—42no—
515C23×C4C7×D414yescomplemented
516C23×C4C23×C712yes—
517C23×C4C23×C711yescharacteristic
518C23×C4C23×C711yescharacteristic
519C23×C4C23×C711yescharacteristic
520C23×C4C23×C712yes—
521C23×C4C23×C712yes—
522C23×C4C23×C711yescharacteristic
523C23×C4C23×C711yescharacteristic
524#120—232no—
525C2×C4⋊C4—24no—
526C2×C4⋊C4—24no—
527C2×C4⋊C4—42no—
528C2×C22⋊C4—232no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4C7×D414yes—
559C2×C22⋊C4C7×D418yescomplemented
560#95—24no—
561#95—22no—
562#95—22no—
563#95—24no—
564#95—24no—
565#95—42no—
566C22×C7—24no—
567C22×C7—24no—
568C22×C7—24no—
569C22×C7—24no—
570C22×C7—28no—
571C22×C7—24no—
572C22×C7—28no—
573C22×C7—28no—
574C22×C7—28no—
575C22×C7—24no—
576C22×C7—28no—
577C22×C7—28no—
578C22×C7—28no—
579C22×C7—464no—
580C22×C7—44no—
581C22×C7—44no—
582C22×C7—44no—
583C22×C7—44no—
584C22×C7—44no—
585C22×C7—44no—
586C22×C7—44no—
587C22×C7—44no—
588C22×C7—44no—
589C22×C7—44no—
590C22×C7—44no—
591C22×C7—44no—
592C22×C7—42no—
593C22×C7—42no—
594C22×C7—44no—
595C22×C7—44no—
596C22×C7—42no—
597C22×C7—81no—
598C22×C7—81no—
599C22×C7—81no—
600C22×C7—81no—
601C22×C7—82no—
602C22×C7—82no—
603C22×C7#39418yescomplemented
604C22×C7C2×#12011yescharacteristic
605C22×C7C2×#12011yescharacteristic
606C22×C7C2×#12111yescharacteristic
607C22×C7C2×#12112yes—
608C22×C7C2×#12111yescharacteristic
609C22×C7C2×#12111yescharacteristic
610C22×C7C2×#12311yescharacteristic
611C22×C7C2×#12311yescharacteristic
612C22×C7#52511yescharacteristic
613C22×C7#52512yes—
614C22×C7C2×#12411yescharacteristic
615C22×C7#53412yes—
616C22×C7#53411yescharacteristic
617C22×C7#53511yescharacteristic
618C22×C7#53812yes—
619C22×C7D4212yes—
620C22×C7D4212yes—
621C22×C7#54612yes—
622C22×C7#54612yes—
623C22×C7#54612yes—
624C22×C7#54612yes—
625C22×C7#55112yes—
626C22×C7#55112yes—
627C4×C7—24no—
628C4×C7—42no—
629C4×C7—44no—
630C4×C7—42no—
631C4×C7—44no—
632C4×C7—81no—
633C4×C7—81no—
634C4×C7—82no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—28no—
640C24—28no—
641C24—216no—
642C24—216no—
643C24—28no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—28no—
657C24—28no—
658C24—21no—
659C24—22no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—48no—
669C24—48no—
670C24—48no—
671C24—48no—
672C24—48no—
673C24—48no—
674C24—48no—
675C24—48no—
676C24—48no—
677C24—44no—
678C24—44no—
679C24—48no—
680C24—44no—
681C24—44no—
682C24—44no—
683C24—44no—
684C24C2×C7×D412yes—
685C24C2×C7×D414yes—
686C24C2×C7×D414yes—
687C24C2×C7×D412yes—
688C24C2×C7×D412yes—
689C24C2×C7×D412yes—
690C24C2×C7×D412yes—
691C24C7×#4114yes—
692C24C7×#4112yes—
693C24C7×#4112yes—
694C24C7×#4112yes—
695C24C24×C711yescharacteristic
696C2×D4—216no—
697C2×D4—28no—
698C2×D4—28no—
699C2×D4—28no—
700C2×D4—48no—
701C2×D4—48no—
702C2×D4—48no—
703C2×D4—48no—
704C2×D4—48no—
705C2×D4—48no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—44no—
709C2×D4—44no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—22no—
713C22×C4—28no—
714C22×C4—28no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—28no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—21no—
748C22×C4—22no—
749C22×C4—21no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—44no—
756C22×C4—48no—
757C22×C4—48no—
758C22×C4—48no—
759C22×C4—48no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4C2×C7×D412yes—
763C22×C4C2×C7×D412yes—
764C22×C4C2×C7×D414yes—
765C22×C4C2×C7×D414yes—
766C22×C4C2×C7×D412yes—
767C22×C4C2×C7×D414yes—
768C4⋊C4—48no—
769C22⋊C4—216no—
770C22⋊C4—216no—
771C22⋊C4—28no—
772C22⋊C4—216no—
773C22⋊C4—48no—
774C22⋊C4—44no—
775C22⋊C4—48no—
776C22⋊C4—44no—
777C22⋊C4—48no—
778C22⋊C4—44no—
779C22⋊C4—44no—
780C2×C7—28no—
781C2×C7—48no—
782C2×C7—82no—
783C2×C7C2×#39411yescharacteristic
784C2×C7#240811yescharacteristic
785C2×C7#241011yescharacteristic
786C2×C7#241012yes—
787C2×C7#241111yescharacteristic
788C2×C7#241212yes—
789C2×C7#241812yes—
790C2×C7#247212yes—
791C2×C7#253411yescharacteristic
792C2×C7#261711yescharacteristic
793C2×C7#284711yescharacteristic
794C23—22no—
795C23—24no—
796C23—22no—
797C23—24no—
798C23—22no—
799C23—24no—
800C23—22no—
801C23—24no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—232no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—24no—
833C23—24no—
834C23—432no—
835C23—432no—
836C23—416no—
837C23—416no—
838C23—416no—
839C23—432no—
840C23—432no—
841C23—416no—
842C23—416no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—416no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—41no—
861C23—42no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—42no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—42no—
870C23—41no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23C7×#12014yes—
879C23C7×#12118yes—
880C23C7×#12114yes—
881C23C7×#12114yes—
882C23C7×#12114yes—
883C23C7×#12314yes—
884C23C7×#12314yes—
885C23C7×#12414yes—
886C23C22×C7×D411yescharacteristic
887C23C22×C7×D411yescharacteristic
888C23C22×C7×D411yescharacteristic
889C23C22×C7×D412yes—
890C23C22×C7×D411yescharacteristic
891C23C2×C7×#4111yescharacteristic
892C23C2×C7×#4111yescharacteristic
893C23C2×C7×#4111yescharacteristic
894C23C2×C7×#4112yes—
895C23C7×H(5,𝔽2)12yes—
896C23C7×H(5,𝔽2)12yes—
897D4—432no—
898D4—416no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—24no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—22no—
905C2×C4—24no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—416no—
916C2×C4—416no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—42no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—41no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4C7×#12014yescomplemented
949C7#1472511yescharacteristic, direct product factor, Sylow
950C22—24no—
951C22—24no—
952C22—28no—
953C22—24no—
954C22—28no—
955C22—28no—
956C22—28no—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—28no—
961C22—28no—
962C22—28no—
963C22—464no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—42no—
977C22—44no—
978C22—44no—
979C22—42no—
980C22—42no—
981C22—81no—
982C22—81no—
983C22—82no—
984C22—82no—
985C22—81no—
986C22—81no—
987C22C7×#39418yescomplemented
988C22C2×C7×#12011yescharacteristic
989C22C2×C7×#12011yescharacteristic
990C22C2×C7×#12111yescharacteristic
991C22C2×C7×#12111yescharacteristic
992C22C2×C7×#12112yes—
993C22C2×C7×#12111yescharacteristic
994C22C2×C7×#12311yescharacteristic
995C22C2×C7×#12311yescharacteristic
996C22C7×#52511yescharacteristic
997C22C7×#52512yes—
998C22C2×C7×#12411yescharacteristic
999C22C7×#53412yes—
1000C22C7×#53411yescharacteristic
1001C22C7×#53511yescharacteristic
1002C22C7×#53812yes—
1003C22C7×D4212yes—
1004C22C7×D4212yes—
1005C22C7×#54612yes—
1006C22C7×#54612yes—
1007C22C7×#54612yes—
1008C22C7×#54612yes—
1009C22C7×#55112yes—
1010C22C7×#55112yes—
1011C4—24no—
1012C4—44no—
1013C4—42no—
1014C4—44no—
1015C4—42no—
1016C4—82no—
1017C4—81no—
1018C4—81no—
1019C2—28no—
1020C2—48no—
1021C2—82no—
1022C2C2×C7×#39411yescharacteristic
1023C2C7×#240811yescharacteristic
1024C2C7×#241011yescharacteristic
1025C2C7×#241012yes—
1026C2C7×#241111yescharacteristic
1027C2C7×#241212yes—
1028C2C7×#241812yes—
1029C2C7×#247212yes—
1030C2C7×#253411yescharacteristic
1031C2C7×#261711yescharacteristic
1032C2C7×#284711yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC22×C7×#120C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C7×C22⋊C4C2semidirect
3. C2×C7×#394C2semidirect
4. C2×C7×#386C2semidirect
5. C2×C7×#386C2semidirect
6. C2×C7×#380C2semidirect
7. C2×C7×#379C2semidirect
8. C7×#1440C2semidirect
9. C7×#1439C2semidirect
10. C7×#1438C2semidirect
11. C7×C22⋊#95C2semidirect
20. C22×C7×C4⋊C4C22semidirect
31. C22×C7×C22⋊C4C22semidirect
32. C22×C7×C22⋊C4C22semidirect
33. C22×C7×C22⋊C4C22semidirect
39. C2×C7×#95C22semidirect
40. C2×C7×#95C22semidirect
41. C2×C7×#95C22semidirect
42. C2×C7×#95C22semidirect
43. C2×C7×#95C22semidirect
44. C2×C7×#95C22semidirect
45. #14725C7direct (N × H)
83. C23×C4×C7D4semidirect
127. C2×C7×C22⋊C4D4semidirect
135. C23×C22⋊C4C2×C7semidirect
136. C2×#394C2×C7semidirect
137. C2×#386C2×C7semidirect
138. C2×#386C2×C7semidirect
139. C2×#380C2×C7semidirect
140. C2×#379C2×C7semidirect
141. #1440C2×C7semidirect
142. #1439C2×C7semidirect
143. #1438C2×C7semidirect
144. C22⋊#95C2×C7semidirect
298. C22×C4⋊C4C22×C7semidirect
309. C22×C22⋊C4C22×C7semidirect
310. C22×C22⋊C4C22×C7semidirect
311. C22×C22⋊C4C22×C7semidirect
317. C2×#95C22×C7semidirect
318. C2×#95C22×C7semidirect
319. C2×#95C22×C7semidirect
320. C2×#95C22×C7semidirect
321. C2×#95C22×C7semidirect
322. C2×#95C22×C7semidirect
477. C2×C4×C7#120semidirect
515. C23×C4C7×D4semidirect
559. C2×C22⋊C4C7×D4semidirect
603. C22×C7#394semidirect
948. C2×C4C7×#120semidirect
949. C7#14725direct (N × H)
987. C22C7×#394semidirect

Maximal subgroups

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

subgroupindex
C22×C7×#1202
C23×C7×C22⋊C42
C2×C7×#3942
C2×C7×#3862
C2×C7×#3802
C2×C7×#3792
C7×#14402
C7×#14392
C7×#14382
C7×C22⋊#952
#147257