Finite Group Databasebeta

← C7×#14726 #13191942

Subgroups — C7×#14726 #13191942

Order 1792.

3494 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C7×C22⋊C4C211yesmaximal, characteristic
2C2×C7×#396C212yesmaximal, complemented
3C2×C7×#385C211yesmaximal, characteristic, complemented
4C2×C7×#385C211yesmaximal, characteristic, complemented
5C2×C7×#380C211yesmaximal, characteristic, complemented
6C2×C7×#379C211yesmaximal, characteristic
7C2×C7×#379C211yesmaximal, characteristic
8C7×#1439C212yesmaximal, complemented
9C7×#1439C212yesmaximal, complemented
10C7×#1439C212yesmaximal, complemented
11C7×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C7C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C24×C4×C7C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic, complemented
16C22×C7×C4⋊C4C2212yescomplemented
17C22×C7×C4⋊C4C2212yescomplemented
18C22×C7×C4⋊C4C2211yescharacteristic, complemented
19C22×C7×C22⋊C4—24no—
20C22×C7×C22⋊C4—28no—
21C22×C7×C22⋊C4C2212yes—
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2212yes—
25C22×C7×C22⋊C4C2212yes—
26C22×C7×C22⋊C4C2212yes—
27C22×C7×C22⋊C4C2212yes—
28C22×C7×C22⋊C4C2212yes—
29C22×C7×C22⋊C4C2211yescharacteristic
30C22×C7×C22⋊C4C2211yescharacteristic
31C7×#396—28no—
32C7×#385—24no—
33C7×#385—24no—
34C7×#380—24no—
35C7×#379—24no—
36C7×#379—24no—
37C2×C7×#95C2212yescomplemented
38C2×C7×#95C2212yescomplemented
39C2×C7×#95C2211yescharacteristic, complemented
40C2×C7×#95C2211yescharacteristic, complemented
41C2×C7×#95C2212yescomplemented
42C2×C7×#95C2212yescomplemented
43#14726C711yesmaximal, characteristic, direct product factor, Sylow
44C25×C7—24no—
45C25×C7—22no—
46C25×C7—24no—
47C25×C7—22no—
48C25×C7—22no—
49C25×C7—22no—
50C25×C7—22no—
51C25×C7—22no—
52C25×C7—42no—
53C25×C7—42no—
54C25×C7Q814yes—
55C25×C7C2312yes—
56C25×C7C2311yescharacteristic
57C23×C4×C7—22no—
58C23×C4×C7—22no—
59C23×C4×C7—22no—
60C23×C4×C7—24no—
61C23×C4×C7—24no—
62C23×C4×C7—22no—
63C23×C4×C7—22no—
64C23×C4×C7—42no—
65C23×C4×C7—42no—
66C23×C4×C7D414yes—
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2312yes—
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2312yes—
73C23×C4×C7C2312yes—
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C2×C7×C4⋊C4—24no—
77C2×C7×C4⋊C4—24no—
78C2×C7×C4⋊C4—22no—
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—24no—
81C2×C7×C4⋊C4—24no—
82C2×C7×C4⋊C4—24no—
83C2×C7×C4⋊C4—42no—
84C2×C7×C4⋊C4—42no—
85C2×C7×C4⋊C4—42no—
86C2×C7×C22⋊C4—232no—
87C2×C7×C22⋊C4—24no—
88C2×C7×C22⋊C4—22no—
89C2×C7×C22⋊C4—22no—
90C2×C7×C22⋊C4—22no—
91C2×C7×C22⋊C4—22no—
92C2×C7×C22⋊C4—24no—
93C2×C7×C22⋊C4—24no—
94C2×C7×C22⋊C4—24no—
95C2×C7×C22⋊C4—24no—
96C2×C7×C22⋊C4—22no—
97C2×C7×C22⋊C4—22no—
98C2×C7×C22⋊C4—22no—
99C2×C7×C22⋊C4—22no—
100C2×C7×C22⋊C4—24no—
101C2×C7×C22⋊C4—24no—
102C2×C7×C22⋊C4—24no—
103C2×C7×C22⋊C4—24no—
104C2×C7×C22⋊C4—22no—
105C2×C7×C22⋊C4—22no—
106C2×C7×C22⋊C4—24no—
107C2×C7×C22⋊C4—24no—
108C2×C7×C22⋊C4—24no—
109C2×C7×C22⋊C4—24no—
110C2×C7×C22⋊C4—42no—
111C2×C7×C22⋊C4—42no—
112C2×C7×C22⋊C4—42no—
113C2×C7×C22⋊C4—42no—
114C2×C7×C22⋊C4D418yes—
115C2×C7×C22⋊C4D414yes—
116C2×C7×C22⋊C4D414yes—
117C7×#95—24no—
118C7×#95—24no—
119C7×#95—22no—
120C7×#95—22no—
121C7×#95—24no—
122C7×#95—42no—
123C23×C22⋊C4C2×C711yescharacteristic
124C2×#396C2×C712yescomplemented
125C2×#385C2×C711yescharacteristic, complemented
126C2×#385C2×C711yescharacteristic, complemented
127C2×#380C2×C711yescharacteristic, complemented
128C2×#379C2×C711yescharacteristic
129C2×#379C2×C711yescharacteristic
130#1439C2×C712yescomplemented
131#1439C2×C712yescomplemented
132#1439C2×C712yescomplemented
133C22⋊#95C2×C711yescharacteristic, complemented
134C24×C7—22no—
135C24×C7—22no—
136C24×C7—22no—
137C24×C7—22no—
138C24×C7—28no—
139C24×C7—28no—
140C24×C7—216no—
141C24×C7—216no—
142C24×C7—28no—
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—22no—
153C24×C7—22no—
154C24×C7—22no—
155C24×C7—28no—
156C24×C7—28no—
157C24×C7—48no—
158C24×C7—48no—
159C24×C7—48no—
160C24×C7—48no—
161C24×C7—48no—
162C24×C7—48no—
163C24×C7—48no—
164C24×C7—48no—
165C24×C7—48no—
166C24×C7—44no—
167C24×C7—44no—
168C24×C7—48no—
169C24×C7—44no—
170C24×C7—44no—
171C24×C7—44no—
172C24×C7—44no—
173C24×C7C2×D414yes—
174C24×C7C2×D412yes—
175C24×C7C2×D412yes—
176C24×C7C2×D412yes—
177C24×C7C2×Q814yes—
178C24×C7C2×Q812yes—
179C24×C7#4114yes—
180C24×C7#4112yes—
181C24×C7#4112yes—
182C24×C7#4112yes—
183C24×C7C2411yescharacteristic
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—22no—
187C22×C4×C7—28no—
188C22×C4×C7—28no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—22no—
195C22×C4×C7—22no—
196C22×C4×C7—22no—
197C22×C4×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
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—28no—
214C22×C4×C7—21no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7—21no—
219C22×C4×C7—22no—
220C22×C4×C7—21no—
221C22×C4×C7—21no—
222C22×C4×C7—22no—
223C22×C4×C7—21no—
224C22×C4×C7—21no—
225C22×C4×C7—22no—
226C22×C4×C7—22no—
227C22×C4×C7—22no—
228C22×C4×C7—22no—
229C22×C4×C7—22no—
230C22×C4×C7—22no—
231C22×C4×C7—44no—
232C22×C4×C7—48no—
233C22×C4×C7—48no—
234C22×C4×C7—48no—
235C22×C4×C7—48no—
236C22×C4×C7—44no—
237C22×C4×C7—44no—
238C22×C4×C7C2×D412yes—
239C22×C4×C7C2×D414yes—
240C22×C4×C7C2×D412yes—
241C22×C4×C7C2×D414yes—
242C22×C4×C7C2×D412yes—
243C22×C4×C7C2×D412yes—
244C22×C4×C7C2×D414yes—
245C7×C4⋊C4—48no—
246C7×C4⋊C4—48no—
247C7×C4⋊C4—44no—
248C7×C4⋊C4—44no—
249C7×C22⋊C4—216no—
250C7×C22⋊C4—28no—
251C7×C22⋊C4—28no—
252C7×C22⋊C4—216no—
253C7×C22⋊C4—48no—
254C7×C22⋊C4—48no—
255C7×C22⋊C4—48no—
256C7×C22⋊C4—48no—
257C7×C22⋊C4—44no—
258C7×C22⋊C4—44no—
259C26C22×C711yescharacteristic
260C24×C4C22×C711yescharacteristic
261C24×C4C22×C711yescharacteristic
262C22×C4⋊C4C22×C711yescharacteristic, complemented
263C22×C4⋊C4C22×C712yescomplemented
264C22×C4⋊C4C22×C712yescomplemented
265C22×C4⋊C4C22×C711yescharacteristic, complemented
266C22×C22⋊C4—24no—
267C22×C22⋊C4—28no—
268C22×C22⋊C4C22×C712yes—
269C22×C22⋊C4C22×C711yescharacteristic
270C22×C22⋊C4C22×C711yescharacteristic
271C22×C22⋊C4C22×C712yes—
272C22×C22⋊C4C22×C712yes—
273C22×C22⋊C4C22×C712yes—
274C22×C22⋊C4C22×C712yes—
275C22×C22⋊C4C22×C712yes—
276C22×C22⋊C4C22×C711yescharacteristic
277C22×C22⋊C4C22×C711yescharacteristic
278#396—28no—
279#385—24no—
280#385—24no—
281#380—24no—
282#379—24no—
283#379—24no—
284C2×#95C22×C712yescomplemented
285C2×#95C22×C712yescomplemented
286C2×#95C22×C711yescharacteristic, complemented
287C2×#95C22×C711yescharacteristic, complemented
288C2×#95C22×C712yescomplemented
289C2×#95C22×C712yescomplemented
290C23×C7—22no—
291C23×C7—24no—
292C23×C7—22no—
293C23×C7—24no—
294C23×C7—22no—
295C23×C7—22no—
296C23×C7—24no—
297C23×C7—24no—
298C23×C7—24no—
299C23×C7—24no—
300C23×C7—24no—
301C23×C7—24no—
302C23×C7—24no—
303C23×C7—24no—
304C23×C7—24no—
305C23×C7—24no—
306C23×C7—232no—
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—24no—
321C23×C7—24no—
322C23×C7—24no—
323C23×C7—24no—
324C23×C7—24no—
325C23×C7—432no—
326C23×C7—432no—
327C23×C7—416no—
328C23×C7—416no—
329C23×C7—416no—
330C23×C7—416no—
331C23×C7—432no—
332C23×C7—432no—
333C23×C7—416no—
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—42no—
346C23×C7—42no—
347C23×C7—42no—
348C23×C7—42no—
349C23×C7—42no—
350C23×C7—416no—
351C23×C7#12114yes—
352C23×C7#12114yes—
353C23×C7#12114yes—
354C23×C7C22⋊Q818yes—
355C23×C7C22⋊Q814yes—
356C23×C7C22⋊Q814yes—
357C23×C7C22⋊Q814yes—
358C23×C7#12614yes—
359C23×C7C22×D411yescharacteristic
360C23×C7C22×D412yes—
361C23×C7C22×D411yescharacteristic
362C23×C7C22×D411yescharacteristic
363C23×C7C22×Q811yescharacteristic
364C23×C7C2×#4111yescharacteristic
365C23×C7C2×#4111yescharacteristic
366C23×C7C2×#4111yescharacteristic
367C23×C7C2×#4112yes—
368C23×C7H(5,𝔽2)12yes—
369C23×C7H(5,𝔽2)12yes—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—24no—
373C2×C4×C7—24no—
374C2×C4×C7—24no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—24no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—24no—
382C2×C4×C7—24no—
383C2×C4×C7—24no—
384C2×C4×C7—24no—
385C2×C4×C7—24no—
386C2×C4×C7—24no—
387C2×C4×C7—416no—
388C2×C4×C7—416no—
389C2×C4×C7—41no—
390C2×C4×C7—42no—
391C2×C4×C7—42no—
392C2×C4×C7—41no—
393C2×C4×C7—41no—
394C2×C4×C7—41no—
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—41no—
406C2×C4×C7—41no—
407C2×C4×C7—41no—
408C2×C4×C7—42no—
409C2×C4×C7—41no—
410C2×C4×C7—42no—
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—42no—
418C2×C4×C7—42no—
419C2×C4×C7—42no—
420C2×C4×C7—42no—
421C2×C4×C7—42no—
422C2×C4×C7#12014yes—
423C25—24no—
424C25—22no—
425C25—24no—
426C25—22no—
427C25—22no—
428C25—22no—
429C25—22no—
430C25—22no—
431C25—42no—
432C25—42no—
433C25C7×Q814yes—
434C25C23×C712yes—
435C25C23×C711yescharacteristic
436C23×C4—22no—
437C23×C4—22no—
438C23×C4—22no—
439C23×C4—24no—
440C23×C4—24no—
441C23×C4—22no—
442C23×C4—22no—
443C23×C4—42no—
444C23×C4—42no—
445C23×C4C7×D414yes—
446C23×C4C23×C711yescharacteristic
447C23×C4C23×C712yes—
448C23×C4C23×C711yescharacteristic
449C23×C4C23×C711yescharacteristic
450C23×C4C23×C712yes—
451C23×C4C23×C711yescharacteristic
452C23×C4C23×C711yescharacteristic
453C23×C4C23×C712yes—
454C23×C4C23×C711yescharacteristic
455C2×C4⋊C4—24no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—42no—
465C2×C22⋊C4—232no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—42no—
493C2×C22⋊C4C7×D418yes—
494C2×C22⋊C4C7×D414yes—
495C2×C22⋊C4C7×D414yes—
496#95—24no—
497#95—24no—
498#95—22no—
499#95—22no—
500#95—24no—
501#95—42no—
502C22×C7—24no—
503C22×C7—24no—
504C22×C7—24no—
505C22×C7—24no—
506C22×C7—24no—
507C22×C7—28no—
508C22×C7—28no—
509C22×C7—28no—
510C22×C7—28no—
511C22×C7—24no—
512C22×C7—28no—
513C22×C7—28no—
514C22×C7—28no—
515C22×C7—464no—
516C22×C7—44no—
517C22×C7—44no—
518C22×C7—44no—
519C22×C7—44no—
520C22×C7—44no—
521C22×C7—44no—
522C22×C7—44no—
523C22×C7—44no—
524C22×C7—44no—
525C22×C7—44no—
526C22×C7—44no—
527C22×C7—44no—
528C22×C7#39618yescomplemented
529C22×C7C2×#12011yescharacteristic
530C22×C7C2×#12111yescharacteristic
531C22×C7C2×#12111yescharacteristic
532C22×C7C2×#12111yescharacteristic
533C22×C7C2×C22⋊Q811yescharacteristic
534C22×C7C2×C22⋊Q812yes—
535C22×C7C2×C22⋊Q811yescharacteristic
536C22×C7C2×C22⋊Q811yescharacteristic
537C22×C7#52511yescharacteristic
538C22×C7#52512yes—
539C22×C7C2×#12611yescharacteristic
540C22×C7#53411yescharacteristic
541C22×C7#53511yescharacteristic
542C22×C7#53812yes—
543C22×C7#54312yes—
544C22×C7D4212yes—
545C22×C7D4212yes—
546C22×C7#54612yes—
547C22×C7#54612yes—
548C22×C7#54612yes—
549C22×C7#54612yes—
550C22×C7#55112yes—
551C22×C7#55112yes—
552C4×C7—24no—
553C4×C7—42no—
554C4×C7—44no—
555C4×C7—42no—
556C4×C7—44no—
557C4×C7—42no—
558C4×C7—81no—
559C4×C7—81no—
560C4×C7—82no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24—28no—
566C24—28no—
567C24—216no—
568C24—216no—
569C24—28no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—28no—
583C24—28no—
584C24—48no—
585C24—48no—
586C24—48no—
587C24—48no—
588C24—48no—
589C24—48no—
590C24—48no—
591C24—48no—
592C24—48no—
593C24—44no—
594C24—44no—
595C24—48no—
596C24—44no—
597C24—44no—
598C24—44no—
599C24—44no—
600C24C2×C7×D414yes—
601C24C2×C7×D412yes—
602C24C2×C7×D412yes—
603C24C2×C7×D412yes—
604C24C2×C7×Q814yes—
605C24C2×C7×Q812yes—
606C24C7×#4114yes—
607C24C7×#4112yes—
608C24C7×#4112yes—
609C24C7×#4112yes—
610C24C24×C711yescharacteristic
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—28no—
615C22×C4—28no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—21no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—28no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—21no—
646C22×C4—22no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—44no—
659C22×C4—48no—
660C22×C4—48no—
661C22×C4—48no—
662C22×C4—48no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4C2×C7×D412yes—
666C22×C4C2×C7×D414yes—
667C22×C4C2×C7×D412yes—
668C22×C4C2×C7×D414yes—
669C22×C4C2×C7×D412yes—
670C22×C4C2×C7×D412yes—
671C22×C4C2×C7×D414yes—
672C4⋊C4—48no—
673C4⋊C4—48no—
674C4⋊C4—44no—
675C4⋊C4—44no—
676C22⋊C4—216no—
677C22⋊C4—28no—
678C22⋊C4—28no—
679C22⋊C4—216no—
680C22⋊C4—48no—
681C22⋊C4—48no—
682C22⋊C4—48no—
683C22⋊C4—48no—
684C22⋊C4—44no—
685C22⋊C4—44no—
686C2×C7—28no—
687C2×C7—48no—
688C2×C7C2×#39611yescharacteristic
689C2×C7#240811yescharacteristic
690C2×C7#241011yescharacteristic
691C2×C7#241111yescharacteristic
692C2×C7#242412yes—
693C2×C7#243712yes—
694C2×C7#243712yes—
695C2×C7#248012yes—
696C2×C7#253411yescharacteristic
697C2×C7#262611yescharacteristic
698C2×C7#284811yescharacteristic
699C23—22no—
700C23—24no—
701C23—22no—
702C23—24no—
703C23—22no—
704C23—22no—
705C23—24no—
706C23—24no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—232no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—24no—
734C23—432no—
735C23—432no—
736C23—416no—
737C23—416no—
738C23—416no—
739C23—432no—
740C23—432no—
741C23—416no—
742C23—416no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—416no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23C7×#12114yes—
761C23C7×#12114yes—
762C23C7×#12114yes—
763C23C7×C22⋊Q818yes—
764C23C7×C22⋊Q814yes—
765C23C7×C22⋊Q814yes—
766C23C7×C22⋊Q814yes—
767C23C7×#12614yes—
768C23C22×C7×D411yescharacteristic
769C23C22×C7×D412yes—
770C23C22×C7×D411yescharacteristic
771C23C22×C7×D411yescharacteristic
772C23C22×C7×Q811yescharacteristic
773C23C2×C7×#4111yescharacteristic
774C23C2×C7×#4111yescharacteristic
775C23C2×C7×#4111yescharacteristic
776C23C2×C7×#4112yes—
777C23C7×H(5,𝔽2)12yes—
778C23C7×H(5,𝔽2)12yes—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—416no—
797C2×C4—416no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
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—42no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—41no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4C7×#12014yes—
832C7#1472611yescharacteristic, direct product factor, Sylow
833C22—24no—
834C22—24no—
835C22—24no—
836C22—28no—
837C22—28no—
838C22—28no—
839C22—28no—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—28no—
844C22—28no—
845C22—28no—
846C22—464no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—44no—
854C22—44no—
855C22—44no—
856C22—44no—
857C22—44no—
858C22—44no—
859C22C7×#39618yescomplemented
860C22C2×C7×#12011yescharacteristic
861C22C2×C7×#12111yescharacteristic
862C22C2×C7×#12111yescharacteristic
863C22C2×C7×#12111yescharacteristic
864C22C2×C7×C22⋊Q811yescharacteristic
865C22C2×C7×C22⋊Q811yescharacteristic
866C22C2×C7×C22⋊Q811yescharacteristic
867C22C2×C7×C22⋊Q812yes—
868C22C7×#52511yescharacteristic
869C22C7×#52512yes—
870C22C2×C7×#12611yescharacteristic
871C22C7×#53411yescharacteristic
872C22C7×#53511yescharacteristic
873C22C7×#53812yes—
874C22C7×#54312yes—
875C22C7×D4212yes—
876C22C7×D4212yes—
877C22C7×#54612yes—
878C22C7×#54612yes—
879C22C7×#54612yes—
880C22C7×#54612yes—
881C22C7×#55112yes—
882C22C7×#55112yes—
883C4—24no—
884C4—44no—
885C4—42no—
886C4—42no—
887C4—44no—
888C4—42no—
889C4—81no—
890C4—81no—
891C4—82no—
892C2—28no—
893C2—48no—
894C2C2×C7×#39611yescharacteristic
895C2C7×#240811yescharacteristic
896C2C7×#241011yescharacteristic
897C2C7×#241111yescharacteristic
898C2C7×#242412yes—
899C2C7×#243712yes—
900C2C7×#243712yes—
901C2C7×#248012yes—
902C2C7×#253411yescharacteristic
903C2C7×#262611yescharacteristic
904C2C7×#284811yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC26×C7C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#396C2semidirect
3. C2×C7×#385C2semidirect
4. C2×C7×#385C2semidirect
5. C2×C7×#380C2semidirect
8. C7×#1439C2semidirect
9. C7×#1439C2semidirect
10. C7×#1439C2semidirect
11. C7×C22⋊#95C2semidirect
15. C22×C7×C4⋊C4C22semidirect
16. C22×C7×C4⋊C4C22semidirect
17. C22×C7×C4⋊C4C22semidirect
18. C22×C7×C4⋊C4C22semidirect
37. C2×C7×#95C22semidirect
38. C2×C7×#95C22semidirect
39. C2×C7×#95C22semidirect
40. C2×C7×#95C22semidirect
41. C2×C7×#95C22semidirect
42. C2×C7×#95C22semidirect
43. #14726C7direct (N × H)
124. C2×#396C2×C7semidirect
125. C2×#385C2×C7semidirect
126. C2×#385C2×C7semidirect
127. C2×#380C2×C7semidirect
130. #1439C2×C7semidirect
131. #1439C2×C7semidirect
132. #1439C2×C7semidirect
133. C22⋊#95C2×C7semidirect
262. C22×C4⋊C4C22×C7semidirect
263. C22×C4⋊C4C22×C7semidirect
264. C22×C4⋊C4C22×C7semidirect
265. C22×C4⋊C4C22×C7semidirect
284. C2×#95C22×C7semidirect
285. C2×#95C22×C7semidirect
286. C2×#95C22×C7semidirect
287. C2×#95C22×C7semidirect
288. C2×#95C22×C7semidirect
289. C2×#95C22×C7semidirect
528. C22×C7#396semidirect
832. C7#14726direct (N × H)
859. C22C7×#396semidirect

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×#3962
C2×C7×#3852
C2×C7×#3802
C2×C7×#3792
C7×#14392
C7×C22⋊#952
#147267