Finite Group Databasebeta

← C7×#14722 #13191938

Subgroups — C7×#14722 #13191938

Order 1792.

3246 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#121C211yesmaximal, characteristic, complemented
2C22×C4×C7×D4C211yesmaximal, characteristic, complemented
3C2×C7×#394C211yesmaximal, characteristic, complemented
4C2×C7×#392C212yesmaximal, complemented
5C2×C7×#392C211yesmaximal, characteristic, complemented
6C2×C7×#386C212yesmaximal, complemented
7C7×#1441C211yesmaximal, characteristic, complemented
8C7×#1439C211yesmaximal, characteristic, complemented
9C7×#1438C212yesmaximal, complemented
10C7×#1437C212yesmaximal, complemented
11C7×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C7×D4C2211yescharacteristic
13C23×C7×D4C2212yes—
14C23×C7×D4C2211yescharacteristic
15C23×C7×D4C2212yes—
16C24×C4×C7C2211yescharacteristic
17C24×C4×C7C2211yescharacteristic
18C2×C7×#121—24no—
19C2×C7×#121—28no—
20C2×C4×C7×D4—24no—
21C2×C4×C7×D4—24no—
22C2×C4×C7×D4—24no—
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2212yes—
27C22×C7×C22⋊C4C2212yes—
28C22×C7×C22⋊C4C2212yes—
29C22×C7×C22⋊C4C2212yes—
30C22×C7×C22⋊C4C2212yes—
31C22×C7×C22⋊C4C2211yescharacteristic
32C22×C7×C22⋊C4C2212yes—
33C22×C42×C7C2211yescharacteristic
34C7×#394—24no—
35C7×#392—28no—
36C7×#392—24no—
37C7×#386—28no—
38C2×C7×#95C2212yes—
39C2×C7×#95C2212yes—
40C2×C7×#95C2211yescharacteristic
41C2×C7×#95C2211yescharacteristic
42C2×C7×#95C2212yes—
43C2×C7×#95C2212yes—
44#14722C711yesmaximal, characteristic, direct product factor, Sylow
45C25×C7C2312yes—
46C25×C7C2311yescharacteristic
47C25×C7C2311yescharacteristic
48C22×C7×D4—22no—
49C22×C7×D4—22no—
50C22×C7×D4—22no—
51C22×C7×D4—22no—
52C22×C7×D4—24no—
53C22×C7×D4—24no—
54C22×C7×D4—24no—
55C22×C7×D4—24no—
56C22×C7×D4—24no—
57C22×C7×D4—24no—
58C22×C7×D4—24no—
59C22×C7×D4—24no—
60C22×C7×D4—24no—
61C22×C7×D4—22no—
62C22×C7×D4—24no—
63C22×C7×D4—22no—
64C22×C7×D4—22no—
65C22×C7×D4—22no—
66C22×C7×D4—22no—
67C22×C7×D4—24no—
68C22×C7×D4—42no—
69C22×C7×D4—42no—
70C22×C7×D4—42no—
71C22×C7×D4—42no—
72C22×C7×D4—42no—
73C22×C7×D4D414yescomplemented
74C23×C4×C7—22no—
75C23×C4×C7—22no—
76C23×C4×C7—22no—
77C23×C4×C7—22no—
78C23×C4×C7—22no—
79C23×C4×C7—24no—
80C23×C4×C7—24no—
81C23×C4×C7—42no—
82C23×C4×C7—42no—
83C23×C4×C7D414yescomplemented
84C23×C4×C7C2312yes—
85C23×C4×C7C2312yes—
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C23×C4×C7C2312yes—
89C23×C4×C7C2311yescharacteristic
90C23×C4×C7C2311yescharacteristic
91C23×C4×C7C2311yescharacteristic
92C7×#121—232no—
93C4×C7×D4—232no—
94C2×C7×C4⋊C4—22no—
95C2×C7×C4⋊C4—22no—
96C2×C7×C4⋊C4—24no—
97C2×C7×C4⋊C4—22no—
98C2×C7×C4⋊C4D414yescomplemented
99C2×C7×C22⋊C4—22no—
100C2×C7×C22⋊C4—22no—
101C2×C7×C22⋊C4—22no—
102C2×C7×C22⋊C4—22no—
103C2×C7×C22⋊C4—22no—
104C2×C7×C22⋊C4—24no—
105C2×C7×C22⋊C4—24no—
106C2×C7×C22⋊C4—24no—
107C2×C7×C22⋊C4—24no—
108C2×C7×C22⋊C4—24no—
109C2×C7×C22⋊C4—24no—
110C2×C7×C22⋊C4—24no—
111C2×C7×C22⋊C4—24no—
112C2×C7×C22⋊C4—24no—
113C2×C7×C22⋊C4—24no—
114C2×C7×C22⋊C4—24no—
115C2×C7×C22⋊C4—24no—
116C2×C7×C22⋊C4—24no—
117C2×C7×C22⋊C4—42no—
118C2×C7×C22⋊C4—42no—
119C2×C7×C22⋊C4—42no—
120C2×C7×C22⋊C4—42no—
121C2×C7×C22⋊C4D414yescomplemented
122C2×C7×C22⋊C4D418yescomplemented
123C2×C42×C7—22no—
124C2×C42×C7—22no—
125C2×C42×C7—22no—
126C7×#95—24no—
127C7×#95—24no—
128C7×#95—22no—
129C7×#95—24no—
130C7×#95—22no—
131C7×#95—42no—
132C22×#121C2×C711yescharacteristic, complemented
133C22×C4×D4C2×C711yescharacteristic, complemented
134C2×#394C2×C711yescharacteristic, complemented
135C2×#392C2×C712yescomplemented
136C2×#392C2×C711yescharacteristic, complemented
137C2×#386C2×C712yescomplemented
138#1441C2×C711yescharacteristic, complemented
139#1439C2×C711yescharacteristic, complemented
140#1438C2×C712yescomplemented
141#1437C2×C712yescomplemented
142C22⋊#95C2×C711yescharacteristic, complemented
143C24×C7—21no—
144C24×C7—21no—
145C24×C7—21no—
146C24×C7—21no—
147C24×C7—22no—
148C24×C7—22no—
149C24×C7—22no—
150C24×C7—21no—
151C24×C7—21no—
152C24×C7—21no—
153C24×C7—21no—
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—22no—
167C24×C7—22no—
168C24×C7—22no—
169C24×C7—22no—
170C24×C7—22no—
171C24×C7—22no—
172C24×C7—22no—
173C24×C7C2×D414yes—
174C24×C7C2×D412yes—
175C24×C7C2×D412yes—
176C24×C7C2×D412yes—
177C24×C7C2×D412yes—
178C24×C7#4112yes—
179C24×C7#4112yes—
180C24×C7C2411yescharacteristic
181C2×C7×D4—28no—
182C2×C7×D4—28no—
183C2×C7×D4—28no—
184C2×C7×D4—28no—
185C2×C7×D4—28no—
186C2×C7×D4—28no—
187C2×C7×D4—28no—
188C2×C7×D4—216no—
189C2×C7×D4—216no—
190C2×C7×D4—28no—
191C2×C7×D4—48no—
192C2×C7×D4—48no—
193C2×C7×D4—48no—
194C2×C7×D4—48no—
195C2×C7×D4—48no—
196C2×C7×D4—48no—
197C2×C7×D4—44no—
198C2×C7×D4—48no—
199C2×C7×D4—48no—
200C2×C7×D4—48no—
201C2×C7×D4—48no—
202C2×C7×D4—48no—
203C2×C7×D4—48no—
204C2×C7×D4—48no—
205C2×C7×D4—48no—
206C2×C7×D4—44no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—22no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—28no—
217C22×C4×C7—22no—
218C22×C4×C7—22no—
219C22×C4×C7—22no—
220C22×C4×C7—22no—
221C22×C4×C7—22no—
222C22×C4×C7—21no—
223C22×C4×C7—21no—
224C22×C4×C7—21no—
225C22×C4×C7—21no—
226C22×C4×C7—22no—
227C22×C4×C7—22no—
228C22×C4×C7—22no—
229C22×C4×C7—22no—
230C22×C4×C7—22no—
231C22×C4×C7—22no—
232C22×C4×C7—22no—
233C22×C4×C7—22no—
234C22×C4×C7—22no—
235C22×C4×C7—22no—
236C22×C4×C7—22no—
237C22×C4×C7—28no—
238C22×C4×C7—28no—
239C22×C4×C7—22no—
240C22×C4×C7—22no—
241C22×C4×C7—22no—
242C22×C4×C7—22no—
243C22×C4×C7—22no—
244C22×C4×C7—22no—
245C22×C4×C7—22no—
246C22×C4×C7—44no—
247C22×C4×C7—48no—
248C22×C4×C7—48no—
249C22×C4×C7—48no—
250C22×C4×C7—48no—
251C22×C4×C7—44no—
252C22×C4×C7—44no—
253C22×C4×C7C2×D414yes—
254C22×C4×C7C2×D412yes—
255C22×C4×C7C2×D412yes—
256C22×C4×C7C2×D414yes—
257C22×C4×C7C2×D412yes—
258C22×C4×C7C2×D412yes—
259C22×C4×C7C2×D412yes—
260C22×C4×C7C2×D412yes—
261C22×C4×C7C2×D412yes—
262C22×C4×C7C2×D412yes—
263C22×C4×C7#4114yes—
264C22×C4×C7#4112yes—
265C7×C4⋊C4—28no—
266C7×C4⋊C4—28no—
267C7×C22⋊C4—28no—
268C7×C22⋊C4—28no—
269C7×C22⋊C4—216no—
270C7×C22⋊C4—48no—
271C7×C22⋊C4—48no—
272C7×C22⋊C4—48no—
273C7×C22⋊C4—48no—
274C7×C22⋊C4—48no—
275C42×C7—28no—
276C23×D4C22×C711yescharacteristic
277C23×D4C22×C712yes—
278C23×D4C22×C711yescharacteristic
279C23×D4C22×C712yes—
280C24×C4C22×C711yescharacteristic
281C24×C4C22×C711yescharacteristic
282C2×#121—24no—
283C2×#121—28no—
284C2×C4×D4—24no—
285C2×C4×D4—24no—
286C2×C4×D4—24no—
287C22×C4⋊C4C22×C711yescharacteristic
288C22×C4⋊C4C22×C711yescharacteristic
289C22×C22⋊C4C22×C712yes—
290C22×C22⋊C4C22×C711yescharacteristic
291C22×C22⋊C4C22×C712yes—
292C22×C22⋊C4C22×C712yes—
293C22×C22⋊C4C22×C712yes—
294C22×C22⋊C4C22×C712yes—
295C22×C22⋊C4C22×C711yescharacteristic
296C22×C22⋊C4C22×C712yes—
297C22×C42C22×C711yescharacteristic
298#394—24no—
299#392—28no—
300#392—24no—
301#386—28no—
302C2×#95C22×C711yescharacteristic
303C2×#95C22×C712yes—
304C2×#95C22×C711yescharacteristic
305C2×#95C22×C712yes—
306C2×#95C22×C712yes—
307C2×#95C22×C712yes—
308C23×C7—22no—
309C23×C7—22no—
310C23×C7—22no—
311C23×C7—22no—
312C23×C7—22no—
313C23×C7—22no—
314C23×C7—22no—
315C23×C7—22no—
316C23×C7—22no—
317C23×C7—22no—
318C23×C7—22no—
319C23×C7—22no—
320C23×C7—22no—
321C23×C7—24no—
322C23×C7—22no—
323C23×C7—22no—
324C23×C7—22no—
325C23×C7—24no—
326C23×C7—24no—
327C23×C7—24no—
328C23×C7—24no—
329C23×C7—24no—
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—24no—
340C23×C7—24no—
341C23×C7—41no—
342C23×C7—42no—
343C23×C7—42no—
344C23×C7—42no—
345C23×C7—41no—
346C23×C7—41no—
347C23×C7—41no—
348C23×C7—42no—
349C23×C7—42no—
350C23×C7—42no—
351C23×C7—42no—
352C23×C7—42no—
353C23×C7—42no—
354C23×C7—42no—
355C23×C7—42no—
356C23×C7—42no—
357C23×C7—42no—
358C23×C7—42no—
359C23×C7—42no—
360C23×C7—42no—
361C23×C7—42no—
362C23×C7—42no—
363C23×C7—42no—
364C23×C7—42no—
365C23×C7—42no—
366C23×C7—42no—
367C23×C7—42no—
368C23×C7—42no—
369C23×C7—42no—
370C23×C7—42no—
371C23×C7—42no—
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#12114yes—
388C23×C7#12114yescomplemented
389C23×C7C22×D411yescharacteristic
390C23×C7C22×D411yescharacteristic
391C23×C7C22×D411yescharacteristic
392C23×C7C22×D412yes—
393C23×C7C22×D411yescharacteristic
394C23×C7C2×#4111yescharacteristic
395C23×C7C2×#4111yescharacteristic
396C23×C7C2×#4111yescharacteristic
397C23×C7C2×#4112yes—
398C23×C7H(5,𝔽2)12yes—
399C23×C7H(5,𝔽2)12yes—
400C7×D4—232no—
401C7×D4—416no—
402C7×D4—432no—
403C7×D4—432no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—24no—
415C2×C4×C7—24no—
416C2×C4×C7—24no—
417C2×C4×C7—24no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—24no—
421C2×C4×C7—24no—
422C2×C4×C7—24no—
423C2×C4×C7—24no—
424C2×C4×C7—24no—
425C2×C4×C7—24no—
426C2×C4×C7—24no—
427C2×C4×C7—24no—
428C2×C4×C7—416no—
429C2×C4×C7—416no—
430C2×C4×C7—41no—
431C2×C4×C7—42no—
432C2×C4×C7—42no—
433C2×C4×C7—41no—
434C2×C4×C7—41no—
435C2×C4×C7—41no—
436C2×C4×C7—42no—
437C2×C4×C7—42no—
438C2×C4×C7—42no—
439C2×C4×C7—42no—
440C2×C4×C7—42no—
441C2×C4×C7—42no—
442C2×C4×C7—42no—
443C2×C4×C7—42no—
444C2×C4×C7—42no—
445C2×C4×C7—42no—
446C2×C4×C7—42no—
447C2×C4×C7—42no—
448C2×C4×C7—42no—
449C2×C4×C7—42no—
450C2×C4×C7—42no—
451C2×C4×C7#12014yes—
452C2×C4×C7#12014yes—
453C2×C4×C7#12114yescomplemented
454C25C23×C712yes—
455C25C23×C711yescharacteristic
456C25C23×C711yescharacteristic
457C22×D4—22no—
458C22×D4—22no—
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—24no—
462C22×D4—24no—
463C22×D4—24no—
464C22×D4—24no—
465C22×D4—24no—
466C22×D4—24no—
467C22×D4—24no—
468C22×D4—24no—
469C22×D4—24no—
470C22×D4—22no—
471C22×D4—24no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—22no—
475C22×D4—22no—
476C22×D4—24no—
477C22×D4—42no—
478C22×D4—42no—
479C22×D4—42no—
480C22×D4—42no—
481C22×D4—42no—
482C22×D4C7×D414yescomplemented
483C23×C4—22no—
484C23×C4—22no—
485C23×C4—22no—
486C23×C4—22no—
487C23×C4—22no—
488C23×C4—24no—
489C23×C4—24no—
490C23×C4—42no—
491C23×C4—42no—
492C23×C4C7×D414yescomplemented
493C23×C4C23×C712yes—
494C23×C4C23×C711yescharacteristic
495C23×C4C23×C711yescharacteristic
496C23×C4C23×C712yes—
497C23×C4C23×C712yes—
498C23×C4C23×C711yescharacteristic
499C23×C4C23×C711yescharacteristic
500C23×C4C23×C711yescharacteristic
501#121—232no—
502C4×D4—232no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—24no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4C7×D414yescomplemented
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4C7×D414yescomplemented
531C2×C22⋊C4C7×D418yescomplemented
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—22no—
535#95—24no—
536#95—24no—
537#95—22no—
538#95—24no—
539#95—22no—
540#95—42no—
541C22×C7—24no—
542C22×C7—24no—
543C22×C7—24no—
544C22×C7—28no—
545C22×C7—24no—
546C22×C7—42no—
547C22×C7—42no—
548C22×C7—42no—
549C22×C7—42no—
550C22×C7—42no—
551C22×C7—42no—
552C22×C7—42no—
553C22×C7—44no—
554C22×C7—44no—
555C22×C7—44no—
556C22×C7—42no—
557C22×C7—42no—
558C22×C7—44no—
559C22×C7—44no—
560C22×C7—44no—
561C22×C7—44no—
562C22×C7—42no—
563C22×C7—44no—
564C22×C7—44no—
565C22×C7—44no—
566C22×C7—44no—
567C22×C7—44no—
568C22×C7—44no—
569C22×C7—44no—
570C22×C7—82no—
571C22×C7—82no—
572C22×C7—82no—
573C22×C7—82no—
574C22×C7—82no—
575C22×C7—82no—
576C22×C7—82no—
577C22×C7—82no—
578C22×C7C2×#12011yescharacteristic
579C22×C7C2×#12011yescharacteristic
580C22×C7C2×#12111yescharacteristic
581C22×C7C2×#12111yescharacteristic
582C22×C7C2×#12111yescharacteristic
583C22×C7#52511yescharacteristic
584C22×C7#52511yescharacteristic
585C22×C7#52511yescharacteristic
586C22×C7#52512yes—
587C22×C7#53212yes—
588C22×C7#53211yescharacteristic
589C22×C7#53411yescharacteristic
590C22×C7#53511yescharacteristic
591C22×C7#53812yes—
592C22×C7#54012yes—
593C22×C7D4212yes—
594C22×C7D4212yes—
595C22×C7D4212yes—
596C22×C7#54612yes—
597C22×C7#54612yes—
598C22×C7#54612yes—
599C22×C7#55012yes—
600C22×C7#55312yes—
601C4×C7—24no—
602C4×C7—24no—
603C4×C7—24no—
604C4×C7—42no—
605C4×C7—44no—
606C4×C7—44no—
607C4×C7—42no—
608C4×C7—82no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24C2×C7×D414yes—
640C24C2×C7×D412yes—
641C24C2×C7×D412yes—
642C24C2×C7×D412yes—
643C24C2×C7×D412yes—
644C24C7×#4112yes—
645C24C7×#4112yes—
646C24C24×C711yescharacteristic
647C2×D4—28no—
648C2×D4—28no—
649C2×D4—28no—
650C2×D4—28no—
651C2×D4—28no—
652C2×D4—28no—
653C2×D4—28no—
654C2×D4—216no—
655C2×D4—216no—
656C2×D4—28no—
657C2×D4—48no—
658C2×D4—48no—
659C2×D4—48no—
660C2×D4—48no—
661C2×D4—48no—
662C2×D4—48no—
663C2×D4—44no—
664C2×D4—48no—
665C2×D4—48no—
666C2×D4—48no—
667C2×D4—48no—
668C2×D4—48no—
669C2×D4—48no—
670C2×D4—48no—
671C2×D4—48no—
672C2×D4—44no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—22no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—28no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—28no—
704C22×C4—28no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—44no—
713C22×C4—48no—
714C22×C4—48no—
715C22×C4—48no—
716C22×C4—48no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4C2×C7×D414yes—
720C22×C4C2×C7×D412yes—
721C22×C4C2×C7×D412yes—
722C22×C4C2×C7×D414yes—
723C22×C4C2×C7×D412yes—
724C22×C4C2×C7×D412yes—
725C22×C4C2×C7×D412yes—
726C22×C4C2×C7×D412yes—
727C22×C4C2×C7×D412yes—
728C22×C4C2×C7×D412yes—
729C22×C4C7×#4114yes—
730C22×C4C7×#4112yes—
731C4⋊C4—28no—
732C4⋊C4—28no—
733C22⋊C4—28no—
734C22⋊C4—28no—
735C22⋊C4—216no—
736C22⋊C4—48no—
737C22⋊C4—48no—
738C22⋊C4—48no—
739C22⋊C4—48no—
740C22⋊C4—48no—
741C42—28no—
742C2×C7—44no—
743C2×C7—44no—
744C2×C7—84no—
745C2×C7#238811yescharacteristic
746C2×C7#240311yescharacteristic
747C2×C7#240811yescharacteristic
748C2×C7#242412yes—
749C2×C7#242812yes—
750C2×C7#243111yescharacteristic
751C2×C7#245612yes—
752C2×C7#246412yes—
753C2×C7#254311yescharacteristic
754C2×C7#263511yescharacteristic
755C2×C7#284711yescharacteristic
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—24no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—24no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—24no—
789C23—41no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23C7×#12114yes—
836C23C7×#12114yescomplemented
837C23C22×C7×D411yescharacteristic
838C23C22×C7×D411yescharacteristic
839C23C22×C7×D411yescharacteristic
840C23C22×C7×D412yes—
841C23C22×C7×D411yescharacteristic
842C23C2×C7×#4111yescharacteristic
843C23C2×C7×#4111yescharacteristic
844C23C2×C7×#4111yescharacteristic
845C23C2×C7×#4112yes—
846C23C7×H(5,𝔽2)12yes—
847C23C7×H(5,𝔽2)12yes—
848D4—232no—
849D4—416no—
850D4—432no—
851D4—432no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—416no—
877C2×C4—416no—
878C2×C4—41no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4C7×#12014yes—
900C2×C4C7×#12014yes—
901C2×C4C7×#12114yescomplemented
902C7#1472211yescharacteristic, direct product factor, Sylow
903C22—24no—
904C22—28no—
905C22—24no—
906C22—24no—
907C22—24no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—44no—
914C22—44no—
915C22—44no—
916C22—42no—
917C22—42no—
918C22—44no—
919C22—44no—
920C22—44no—
921C22—44no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22—82no—
936C22—82no—
937C22—82no—
938C22—82no—
939C22—82no—
940C22C2×C7×#12011yescharacteristic
941C22C2×C7×#12011yescharacteristic
942C22C2×C7×#12111yescharacteristic
943C22C2×C7×#12111yescharacteristic
944C22C2×C7×#12111yescharacteristic
945C22C7×#52512yes—
946C22C7×#52511yescharacteristic
947C22C7×#52511yescharacteristic
948C22C7×#52511yescharacteristic
949C22C7×#53212yes—
950C22C7×#53211yescharacteristic
951C22C7×#53411yescharacteristic
952C22C7×#53511yescharacteristic
953C22C7×#53812yes—
954C22C7×#54012yes—
955C22C7×D4212yes—
956C22C7×D4212yes—
957C22C7×D4212yes—
958C22C7×#54612yes—
959C22C7×#54612yes—
960C22C7×#54612yes—
961C22C7×#55012yes—
962C22C7×#55312yes—
963C4—24no—
964C4—24no—
965C4—24no—
966C4—42no—
967C4—44no—
968C4—44no—
969C4—42no—
970C4—82no—
971C2—44no—
972C2—44no—
973C2—84no—
974C2C7×#238811yescharacteristic
975C2C7×#240311yescharacteristic
976C2C7×#240811yescharacteristic
977C2C7×#242412yes—
978C2C7×#242812yes—
979C2C7×#243111yescharacteristic
980C2C7×#245612yes—
981C2C7×#246412yes—
982C2C7×#254311yescharacteristic
983C2C7×#263511yescharacteristic
984C2C7×#284711yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C7×#121C2semidirect
2. C22×C4×C7×D4C2semidirect
3. C2×C7×#394C2semidirect
4. C2×C7×#392C2semidirect
5. C2×C7×#392C2semidirect
6. C2×C7×#386C2semidirect
7. C7×#1441C2semidirect
8. C7×#1439C2semidirect
9. C7×#1438C2semidirect
10. C7×#1437C2semidirect
11. C7×C22⋊#95C2semidirect
44. #14722C7direct (N × H)
73. C22×C7×D4D4semidirect
83. C23×C4×C7D4semidirect
98. C2×C7×C4⋊C4D4semidirect
121. C2×C7×C22⋊C4D4semidirect
122. C2×C7×C22⋊C4D4semidirect
132. C22×#121C2×C7semidirect
133. C22×C4×D4C2×C7semidirect
134. C2×#394C2×C7semidirect
135. C2×#392C2×C7semidirect
136. C2×#392C2×C7semidirect
137. C2×#386C2×C7semidirect
138. #1441C2×C7semidirect
139. #1439C2×C7semidirect
140. #1438C2×C7semidirect
141. #1437C2×C7semidirect
142. C22⋊#95C2×C7semidirect
388. C23×C7#121semidirect
453. C2×C4×C7#121semidirect
482. C22×D4C7×D4semidirect
492. C23×C4C7×D4semidirect
507. C2×C4⋊C4C7×D4semidirect
530. C2×C22⋊C4C7×D4semidirect
531. C2×C22⋊C4C7×D4semidirect
836. C23C7×#121semidirect
901. C2×C4C7×#121semidirect
902. C7#14722direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1212
C22×C4×C7×D42
C2×C7×#3942
C2×C7×#3922
C2×C7×#3862
C7×#14412
C7×#14392
C7×#14382
C7×#14372
C7×C22⋊#952
#147227