Finite Group Databasebeta

← C7×#13996 #13191212

Subgroups — C7×#13996 #13191212

Order 1792.

2474 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#123C211yesmaximal, characteristic
2C2×C7×#386C211yesmaximal, characteristic
3C2×C7×#386C211yesmaximal, characteristic
4C2×C7×#385C211yesmaximal, characteristic, complemented
5C2×C7×#381C211yesmaximal, characteristic, complemented
6C2×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
7C22×C7×#95C211yesmaximal, characteristic, complemented
8C7×#1445C212yesmaximal, complemented
9C7×#1439C212yesmaximal, complemented
10C7×#1437C212yesmaximal, complemented
11C7×C4⋊#95C212yesmaximal, complemented
12C23×C7×D4C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C24×C4×C7C2211yescharacteristic
15C24×C4×C7C2211yescharacteristic
16C2×C7×#123—24no—
17C2×C7×#123—24no—
18C2×C7×#123C418yescomplemented
19C22×C7×C4⋊C4C2212yes—
20C22×C7×C4⋊C4C2212yes—
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2212yes—
24C22×C7×C22⋊C4C2212yes—
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C42×C7C2212yes—
29C7×#386—24no—
30C7×#386—24no—
31C7×#385—24no—
32C7×#381—24no—
33C4×C7×C22⋊C4—24no—
34C2×C7×#95—24no—
35C2×C7×#95C2212yes—
36C2×C7×#95C2212yes—
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39C2×C7×#95C2212yes—
40C2×C7×#95C2212yes—
41C2×C7×#95C2211yescharacteristic
42C2×C7×#95C2212yes—
43C2×C7×#95C2211yescharacteristic
44#13996C711yesmaximal, characteristic, direct product factor, Sylow
45C25×C7C2311yescharacteristic
46C25×C7C2311yescharacteristic
47C22×C7×D4—22no—
48C22×C7×D4—22no—
49C22×C7×D4—22no—
50C22×C7×D4—22no—
51C22×C7×D4—22no—
52C22×C7×D4—22no—
53C22×C7×D4C2×C414yes—
54C23×C4×C7—22no—
55C23×C4×C7—22no—
56C23×C4×C7—22no—
57C23×C4×C7—22no—
58C23×C4×C7—22no—
59C23×C4×C7—22no—
60C23×C4×C7—22no—
61C23×C4×C7—22no—
62C23×C4×C7—22no—
63C23×C4×C7—24no—
64C23×C4×C7—24no—
65C23×C4×C7—22no—
66C23×C4×C7—22no—
67C23×C4×C7—42no—
68C23×C4×C7—42no—
69C23×C4×C7C2×C414yes—
70C23×C4×C7D414yes—
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2312yes—
75C23×C4×C7C2312yes—
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2312yes—
78C23×C4×C7C2312yes—
79C23×C4×C7C2311yescharacteristic
80C7×#123—232no—
81C2×C7×C4⋊C4—24no—
82C2×C7×C4⋊C4—24no—
83C2×C7×C4⋊C4—24no—
84C2×C7×C4⋊C4—24no—
85C2×C7×C4⋊C4—42no—
86C2×C7×C4⋊C4C2×C418yescomplemented
87C2×C7×C22⋊C4—22no—
88C2×C7×C22⋊C4—22no—
89C2×C7×C22⋊C4—24no—
90C2×C7×C22⋊C4—24no—
91C2×C7×C22⋊C4—22no—
92C2×C7×C22⋊C4—22no—
93C2×C7×C22⋊C4—22no—
94C2×C7×C22⋊C4—24no—
95C2×C7×C22⋊C4—22no—
96C2×C7×C22⋊C4—22no—
97C2×C7×C22⋊C4—24no—
98C2×C7×C22⋊C4—24no—
99C2×C7×C22⋊C4—42no—
100C2×C7×C22⋊C4—42no—
101C2×C7×C22⋊C4C2×C414yes—
102C2×C7×C22⋊C4C2×C418yescomplemented
103C2×C7×C22⋊C4D414yes—
104C2×C7×C22⋊C4D414yes—
105C2×C7×C22⋊C4D414yes—
106C2×C42×C7—24no—
107C2×C42×C7—24no—
108C2×C42×C7—42no—
109C7×#95—24no—
110C7×#95—24no—
111C7×#95—24no—
112C7×#95—24no—
113C7×#95—24no—
114C7×#95—24no—
115C7×#95—24no—
116C7×#95—22no—
117C7×#95—22no—
118C22×#123C2×C711yescharacteristic
119C2×#386C2×C711yescharacteristic
120C2×#386C2×C711yescharacteristic
121C2×#385C2×C711yescharacteristic, complemented
122C2×#381C2×C711yescharacteristic, complemented
123C2×C4×C22⋊C4C2×C711yescharacteristic, complemented
124C22×#95C2×C711yescharacteristic, complemented
125#1445C2×C712yescomplemented
126#1439C2×C712yescomplemented
127#1437C2×C712yescomplemented
128C4⋊#95C2×C712yescomplemented
129C24×C7—22no—
130C24×C7—22no—
131C24×C7—22no—
132C24×C7—22no—
133C24×C7—21no—
134C24×C7—21no—
135C24×C7—21no—
136C24×C7—21no—
137C24×C7—22no—
138C24×C7—22no—
139C24×C7—21no—
140C24×C7—21no—
141C24×C7—22no—
142C24×C7—22no—
143C24×C7C22×C412yes—
144C24×C7C22×C412yes—
145C24×C7C2×D412yes—
146C24×C7C2×D412yes—
147C24×C7C2×D412yes—
148C24×C7C2×D412yes—
149C24×C7#4112yes—
150C24×C7#4112yes—
151C24×C7C2411yescharacteristic
152C2×C7×D4—28no—
153C2×C7×D4—28no—
154C2×C7×D4—28no—
155C2×C7×D4—44no—
156C2×C7×D4—44no—
157C2×C7×D4—44no—
158C2×C7×D4—44no—
159C22×C4×C7—21no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7—21no—
163C22×C4×C7—22no—
164C22×C4×C7—22no—
165C22×C4×C7—22no—
166C22×C4×C7—28no—
167C22×C4×C7—28no—
168C22×C4×C7—28no—
169C22×C4×C7—28no—
170C22×C4×C7—28no—
171C22×C4×C7—22no—
172C22×C4×C7—22no—
173C22×C4×C7—21no—
174C22×C4×C7—22no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—22no—
185C22×C4×C7—22no—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—22no—
189C22×C4×C7—21no—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—22no—
195C22×C4×C7—22no—
196C22×C4×C7—22no—
197C22×C4×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7—28no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—44no—
211C22×C4×C7—48no—
212C22×C4×C7—48no—
213C22×C4×C7—48no—
214C22×C4×C7—48no—
215C22×C4×C7—44no—
216C22×C4×C7—44no—
217C22×C4×C7—44no—
218C22×C4×C7—44no—
219C22×C4×C7—44no—
220C22×C4×C7—44no—
221C22×C4×C7C22×C414yes—
222C22×C4×C7C22×C412yes—
223C22×C4×C7C22×C414yes—
224C22×C4×C7C2×D414yes—
225C22×C4×C7C2×D412yes—
226C22×C4×C7C2×D414yes—
227C22×C4×C7C2×D414yes—
228C22×C4×C7C2×D412yes—
229C22×C4×C7#4114yes—
230C22×C4×C7#4114yes—
231C7×C4⋊C4—216no—
232C7×C4⋊C4—48no—
233C7×C22⋊C4—28no—
234C7×C22⋊C4—216no—
235C7×C22⋊C4—48no—
236C7×C22⋊C4—44no—
237C7×C22⋊C4—44no—
238C7×C22⋊C4—44no—
239C7×C22⋊C4C22⋊C4116yescomplemented
240C42×C7—48no—
241C23×D4C22×C711yescharacteristic
242C24×C4C22×C711yescharacteristic
243C24×C4C22×C711yescharacteristic
244C24×C4C22×C711yescharacteristic
245C2×#123—24no—
246C2×#123—24no—
247C2×#123C4×C718yescomplemented
248C22×C4⋊C4C22×C712yes—
249C22×C4⋊C4C22×C712yes—
250C22×C22⋊C4C22×C711yescharacteristic
251C22×C22⋊C4C22×C711yescharacteristic
252C22×C22⋊C4C22×C712yes—
253C22×C22⋊C4C22×C712yes—
254C22×C22⋊C4C22×C711yescharacteristic
255C22×C22⋊C4C22×C711yescharacteristic
256C22×C22⋊C4C22×C711yescharacteristic
257C22×C42C22×C712yes—
258#386—24no—
259#386—24no—
260#385—24no—
261#381—24no—
262C4×C22⋊C4—24no—
263C2×#95—24no—
264C2×#95C22×C711yescharacteristic
265C2×#95C22×C712yes—
266C2×#95C22×C712yes—
267C2×#95C22×C712yes—
268C2×#95C22×C712yes—
269C2×#95C22×C712yes—
270C2×#95C22×C712yes—
271C2×#95C22×C712yes—
272C2×#95C22×C711yescharacteristic
273C23×C7—24no—
274C23×C7—24no—
275C23×C7—22no—
276C23×C7—22no—
277C23×C7—24no—
278C23×C7—22no—
279C23×C7—22no—
280C23×C7—24no—
281C23×C7—24no—
282C23×C7—24no—
283C23×C7—24no—
284C23×C7—24no—
285C23×C7—24no—
286C23×C7—24no—
287C23×C7—24no—
288C23×C7—24no—
289C23×C7—22no—
290C23×C7—22no—
291C23×C7—22no—
292C23×C7—24no—
293C23×C7—24no—
294C23×C7—41no—
295C23×C7—41no—
296C23×C7—41no—
297C23×C7—41no—
298C23×C7—41no—
299C23×C7—42no—
300C23×C7—41no—
301C23×C7—41no—
302C23×C7—41no—
303C23×C7—42no—
304C23×C7—42no—
305C23×C7—42no—
306C23×C7—42no—
307C23×C7—42no—
308C23×C7—42no—
309C23×C7—42no—
310C23×C7—42no—
311C23×C7—42no—
312C23×C7C2×C22⋊C414yes—
313C23×C7C4×D414yes—
314C23×C7C4×D414yes—
315C23×C7#12114yes—
316C23×C7#12114yes—
317C23×C7#12414yes—
318C23×C7#12714yes—
319C23×C7C23×C411yescharacteristic
320C23×C7C22×D411yescharacteristic
321C23×C7C22×D411yescharacteristic
322C23×C7C22×D411yescharacteristic
323C23×C7C22×D411yescharacteristic
324C23×C7C2×#4111yescharacteristic
325C23×C7C2×#4111yescharacteristic
326C23×C7C2×#4112yes—
327C23×C7C2×#4112yes—
328C23×C7H(5,𝔽2)12yes—
329C23×C72−1+412yes—
330C7×D4—416no—
331C2×C4×C7—24no—
332C2×C4×C7—24no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—24no—
336C2×C4×C7—24no—
337C2×C4×C7—24no—
338C2×C4×C7—24no—
339C2×C4×C7—24no—
340C2×C4×C7—24no—
341C2×C4×C7—24no—
342C2×C4×C7—22no—
343C2×C4×C7—24no—
344C2×C4×C7—24no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—24no—
348C2×C4×C7—22no—
349C2×C4×C7—22no—
350C2×C4×C7—24no—
351C2×C4×C7—22no—
352C2×C4×C7—24no—
353C2×C4×C7—24no—
354C2×C4×C7—24no—
355C2×C4×C7—24no—
356C2×C4×C7—416no—
357C2×C4×C7—416no—
358C2×C4×C7—42no—
359C2×C4×C7—42no—
360C2×C4×C7—41no—
361C2×C4×C7—41no—
362C2×C4×C7—42no—
363C2×C4×C7—41no—
364C2×C4×C7—42no—
365C2×C4×C7—42no—
366C2×C4×C7—42no—
367C2×C4×C7—41no—
368C2×C4×C7—42no—
369C2×C4×C7—42no—
370C2×C4×C7—42no—
371C2×C4×C7—42no—
372C2×C4×C7—42no—
373C2×C4×C7—42no—
374C2×C4×C7—42no—
375C2×C4×C7—42no—
376C2×C4×C7—416no—
377C2×C4×C7—41no—
378C2×C4×C7—41no—
379C2×C4×C7—41no—
380C2×C4×C7—41no—
381C2×C4×C7—41no—
382C2×C4×C7—41no—
383C2×C4×C7—42no—
384C2×C4×C7—42no—
385C2×C4×C7—42no—
386C2×C4×C7—42no—
387C2×C4×C7C2×C22⋊C418yes—
388C2×C4×C7#12314yescomplemented
389C25C23×C711yescharacteristic
390C25C23×C711yescharacteristic
391C22×D4—22no—
392C22×D4—22no—
393C22×D4—22no—
394C22×D4—22no—
395C22×D4—22no—
396C22×D4—22no—
397C22×D4C2×C4×C714yes—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—24no—
408C23×C4—24no—
409C23×C4—22no—
410C23×C4—22no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4C2×C4×C714yes—
414C23×C4C7×D414yes—
415C23×C4C23×C711yescharacteristic
416C23×C4C23×C711yescharacteristic
417C23×C4C23×C712yes—
418C23×C4C23×C711yescharacteristic
419C23×C4C23×C712yes—
420C23×C4C23×C711yescharacteristic
421C23×C4C23×C712yes—
422C23×C4C23×C712yes—
423C23×C4C23×C711yescharacteristic
424#123—232no—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—42no—
430C2×C4⋊C4C2×C4×C718yescomplemented
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—24no—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—42no—
444C2×C22⋊C4—42no—
445C2×C22⋊C4C2×C4×C714yes—
446C2×C22⋊C4C2×C4×C718yescomplemented
447C2×C22⋊C4C7×D414yes—
448C2×C22⋊C4C7×D414yes—
449C2×C22⋊C4C7×D414yes—
450C2×C42—24no—
451C2×C42—24no—
452C2×C42—42no—
453#95—24no—
454#95—24no—
455#95—24no—
456#95—24no—
457#95—24no—
458#95—24no—
459#95—24no—
460#95—22no—
461#95—22no—
462C22×C7—24no—
463C22×C7—28no—
464C22×C7—28no—
465C22×C7—24no—
466C22×C7—24no—
467C22×C7—28no—
468C22×C7—28no—
469C22×C7—24no—
470C22×C7—24no—
471C22×C7—24no—
472C22×C7—42no—
473C22×C7—44no—
474C22×C7—44no—
475C22×C7—42no—
476C22×C7—42no—
477C22×C7—81no—
478C22×C7—81no—
479C22×C7—82no—
480C22×C7—82no—
481C22×C7—81no—
482C22×C7—81no—
483C22×C7#39018yes—
484C22×C7C22×C22⋊C411yescharacteristic
485C22×C7C2×C4×D411yescharacteristic
486C22×C7C2×C4×D411yescharacteristic
487C22×C7C4×#4112yes—
488C22×C7#52012yes—
489C22×C7C2×#12111yescharacteristic
490C22×C7C2×#12111yescharacteristic
491C22×C7C2×#12311yescharacteristic
492C22×C7#52511yescharacteristic
493C22×C7C2×#12411yescharacteristic
494C22×C7#52912yes—
495C22×C7C2×#12711yescharacteristic
496C22×C7#53411yescharacteristic
497C22×C7#53611yescharacteristic
498C22×C7#53912yes—
499C22×C7#54612yes—
500C22×C7#54612yes—
501C22×C7#54612yes—
502C22×C7#54712yes—
503C22×C7#54712yes—
504C22×C7#54712yes—
505C22×C7#55112yes—
506C22×C7#55212yes—
507C4×C7—28no—
508C4×C7—24no—
509C4×C7—42no—
510C4×C7—44no—
511C4×C7—44no—
512C4×C7—44no—
513C4×C7—42no—
514C4×C7—81no—
515C4×C7—81no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—22no—
525C24—22no—
526C24—21no—
527C24—21no—
528C24—22no—
529C24—22no—
530C24C22×C4×C712yes—
531C24C22×C4×C712yes—
532C24C2×C7×D412yes—
533C24C2×C7×D412yes—
534C24C2×C7×D412yes—
535C24C2×C7×D412yes—
536C24C7×#4112yes—
537C24C7×#4112yes—
538C24C24×C711yescharacteristic
539C2×D4—28no—
540C2×D4—28no—
541C2×D4—28no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—44no—
545C2×D4—44no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—28no—
554C22×C4—28no—
555C22×C4—28no—
556C22×C4—28no—
557C22×C4—28no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—28no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—44no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4C22×C4×C714yes—
609C22×C4C22×C4×C712yes—
610C22×C4C22×C4×C714yes—
611C22×C4C2×C7×D414yes—
612C22×C4C2×C7×D412yes—
613C22×C4C2×C7×D414yes—
614C22×C4C2×C7×D414yes—
615C22×C4C2×C7×D412yes—
616C22×C4C7×#4114yes—
617C22×C4C7×#4114yes—
618C4⋊C4—216no—
619C4⋊C4—48no—
620C22⋊C4—28no—
621C22⋊C4—216no—
622C22⋊C4—48no—
623C22⋊C4—44no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C22⋊C4C7×C22⋊C4116yescomplemented
627C42—48no—
628C2×C7—28no—
629C2×C7—82no—
630C2×C7C2×#39011yescharacteristic
631C2×C7C4×#12311yescharacteristic
632C2×C7#232211yescharacteristic
633C2×C7#233912yes—
634C2×C7#235912yes—
635C2×C7#241211yescharacteristic
636C2×C7#241311yescharacteristic
637C2×C7#242512yes—
638C2×C7#248812yes—
639C2×C7#250111yescharacteristic
640C2×C7#253911yescharacteristic
641C23—24no—
642C23—24no—
643C23—22no—
644C23—22no—
645C23—24no—
646C23—22no—
647C23—22no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—24no—
661C23—24no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—42no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23C2×C7×C22⋊C414yes—
681C23C4×C7×D414yes—
682C23C4×C7×D414yes—
683C23C7×#12114yes—
684C23C7×#12114yes—
685C23C7×#12414yes—
686C23C7×#12714yes—
687C23C23×C4×C711yescharacteristic
688C23C22×C7×D411yescharacteristic
689C23C22×C7×D411yescharacteristic
690C23C22×C7×D411yescharacteristic
691C23C22×C7×D411yescharacteristic
692C23C2×C7×#4111yescharacteristic
693C23C2×C7×#4111yescharacteristic
694C23C2×C7×#4112yes—
695C23C2×C7×#4112yes—
696C23C7×H(5,𝔽2)12yes—
697C23C7×2−1+412yes—
698D4—416no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—416no—
725C2×C4—416no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—416no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4C2×C7×C22⋊C418yes—
756C2×C4C7×#12314yescomplemented
757C7#1399611yescharacteristic, direct product factor, Sylow
758C22—24no—
759C22—24no—
760C22—28no—
761C22—28no—
762C22—24no—
763C22—24no—
764C22—24no—
765C22—24no—
766C22—28no—
767C22—28no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—44no—
772C22—44no—
773C22—81no—
774C22—81no—
775C22—82no—
776C22—82no—
777C22—81no—
778C22—81no—
779C22C7×#39018yes—
780C22C22×C7×C22⋊C411yescharacteristic
781C22C2×C4×C7×D411yescharacteristic
782C22C2×C4×C7×D411yescharacteristic
783C22C4×C7×#4112yes—
784C22C7×#52012yes—
785C22C2×C7×#12111yescharacteristic
786C22C2×C7×#12111yescharacteristic
787C22C2×C7×#12311yescharacteristic
788C22C7×#52511yescharacteristic
789C22C2×C7×#12411yescharacteristic
790C22C7×#52912yes—
791C22C2×C7×#12711yescharacteristic
792C22C7×#53411yescharacteristic
793C22C7×#53611yescharacteristic
794C22C7×#53912yes—
795C22C7×#54612yes—
796C22C7×#54612yes—
797C22C7×#54612yes—
798C22C7×#54712yes—
799C22C7×#54712yes—
800C22C7×#54712yes—
801C22C7×#55112yes—
802C22C7×#55212yes—
803C4—24no—
804C4—28no—
805C4—42no—
806C4—44no—
807C4—44no—
808C4—44no—
809C4—42no—
810C4—81no—
811C4—81no—
812C2—28no—
813C2—82no—
814C2C2×C7×#39011yescharacteristic
815C2C4×C7×#12311yescharacteristic
816C2C7×#232211yescharacteristic
817C2C7×#233912yes—
818C2C7×#235912yes—
819C2C7×#241211yescharacteristic
820C2C7×#241311yescharacteristic
821C2C7×#242512yes—
822C2C7×#248812yes—
823C2C7×#250111yescharacteristic
824C2C7×#253911yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC23×C7×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C7×#385C2semidirect
5. C2×C7×#381C2semidirect
6. C2×C4×C7×C22⋊C4C2semidirect
7. C22×C7×#95C2semidirect
8. C7×#1445C2semidirect
9. C7×#1439C2semidirect
10. C7×#1437C2semidirect
11. C7×C4⋊#95C2semidirect
18. C2×C7×#123C4semidirect
44. #13996C7direct (N × H)
86. C2×C7×C4⋊C4C2×C4semidirect
102. C2×C7×C22⋊C4C2×C4semidirect
121. C2×#385C2×C7semidirect
122. C2×#381C2×C7semidirect
123. C2×C4×C22⋊C4C2×C7semidirect
124. C22×#95C2×C7semidirect
125. #1445C2×C7semidirect
126. #1439C2×C7semidirect
127. #1437C2×C7semidirect
128. C4⋊#95C2×C7semidirect
239. C7×C22⋊C4C22⋊C4semidirect
247. C2×#123C4×C7semidirect
388. C2×C4×C7#123semidirect
430. C2×C4⋊C4C2×C4×C7semidirect
446. C2×C22⋊C4C2×C4×C7semidirect
626. C22⋊C4C7×C22⋊C4semidirect
756. C2×C4C7×#123semidirect
757. C7#13996direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1232
C2×C7×#3862
C2×C7×#3852
C2×C7×#3812
C2×C4×C7×C22⋊C42
C22×C7×#952
C7×#14452
C7×#14392
C7×#14372
C7×C4⋊#952
#139967