Finite Group Databasebeta

← C4×C7×#394 #13191074

Subgroups — C4×C7×#394 #13191074

Order 1792.

2550 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C7×D4C211yesmaximal, characteristic
2C2×C7×#394C211yesmaximal, characteristic
3C2×C4×C7×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×C4×C7×C22⋊C4C212yesmaximal, complemented
5C2×C4×C7×C22⋊C4C212yesmaximal, complemented
6C7×#1442C211yesmaximal, characteristic, complemented
7C7×#1441C211yesmaximal, characteristic, complemented
8C7×#1440C212yesmaximal, complemented
9C7×#1439C212yesmaximal, complemented
10C7×#1438C211yesmaximal, characteristic
11C4×C7×#95C211yesmaximal, characteristic, complemented
12C23×C7×D4C2211yescharacteristic
13C24×C4×C7C2212yes—
14C2×C4×C7×D4—28no—
15C2×C4×C7×D4—24no—
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2212yes—
20C22×C7×C22⋊C4C2212yes—
21C22×C7×C22⋊C4C2212yes—
22C22×C7×C22⋊C4C2212yes—
23C22×C7×C22⋊C4C2212yes—
24C22×C42×C7C2211yescharacteristic
25C22×C42×C7C2212yes—
26C22×C42×C7C2211yescharacteristic
27C22×C42×C7C2211yescharacteristic
28C7×#394C418yesdirect product factor
29C4×C7×C4⋊C4—24no—
30C4×C7×C22⋊C4—28no—
31C4×C7×C22⋊C4—28no—
32C2×C7×#95C2212yes—
33C2×C7×#95C2212yes—
34C2×C7×#95C2212yes—
35C2×C7×#95C2212yes—
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2211yescharacteristic
38C2×C7×#95C2211yescharacteristic
39C2×C7×#95C2212yes—
40C2×C7×#95C2211yescharacteristic
41C4×#394C711yesmaximal, characteristic, direct product factor, Sylow
42C25×C7C2312yes—
43C22×C7×D4—24no—
44C22×C7×D4—24no—
45C22×C7×D4—22no—
46C22×C7×D4—22no—
47C22×C7×D4C2×C414yes—
48C23×C4×C7—24no—
49C23×C4×C7—24no—
50C23×C4×C7—24no—
51C23×C4×C7—24no—
52C23×C4×C7—24no—
53C23×C4×C7—24no—
54C23×C4×C7D418yes—
55C23×C4×C7C2312yes—
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2312yes—
60C23×C4×C7C2312yes—
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C4×C7×D4—232no—
66C2×C7×C4⋊C4—22no—
67C2×C7×C4⋊C4—22no—
68C2×C7×C4⋊C4—24no—
69C2×C7×C4⋊C4—22no—
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4—22no—
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4C2×C414yescomplemented
74C2×C7×C22⋊C4—24no—
75C2×C7×C22⋊C4—24no—
76C2×C7×C22⋊C4—24no—
77C2×C7×C22⋊C4—24no—
78C2×C7×C22⋊C4—24no—
79C2×C7×C22⋊C4—24no—
80C2×C7×C22⋊C4—24no—
81C2×C7×C22⋊C4—24no—
82C2×C7×C22⋊C4—24no—
83C2×C7×C22⋊C4—24no—
84C2×C7×C22⋊C4—24no—
85C2×C7×C22⋊C4—24no—
86C2×C7×C22⋊C4—24no—
87C2×C7×C22⋊C4C2×C418yescomplemented
88C2×C7×C22⋊C4C2×C418yescomplemented
89C2×C42×C7—22no—
90C2×C42×C7—24no—
91C2×C42×C7—22no—
92C2×C42×C7—24no—
93C2×C42×C7—24no—
94C2×C42×C7—24no—
95C2×C42×C7—22no—
96C2×C42×C7—24no—
97C2×C42×C7D414yes—
98C2×C42×C7D414yescomplemented
99C7×#95—24no—
100C7×#95—24no—
101C7×#95—24no—
102C7×#95—24no—
103C7×#95—22no—
104C7×#95—22no—
105C7×#95—24no—
106C7×#95—22no—
107C7×#95C2×C414yescomplemented
108C22×C4×D4C2×C711yescharacteristic
109C2×#394C2×C711yescharacteristic
110C2×C4×C4⋊C4C2×C711yescharacteristic, complemented
111C2×C4×C22⋊C4C2×C712yescomplemented
112C2×C4×C22⋊C4C2×C712yescomplemented
113#1442C2×C711yescharacteristic, complemented
114#1441C2×C711yescharacteristic, complemented
115#1440C2×C712yescomplemented
116#1439C2×C712yescomplemented
117#1438C2×C711yescharacteristic
118C4×#95C2×C711yescharacteristic, complemented
119C24×C7—22no—
120C24×C7—22no—
121C24×C7—22no—
122C24×C7—22no—
123C24×C7—22no—
124C24×C7—22no—
125C24×C7—22no—
126C24×C7—22no—
127C24×C7—22no—
128C24×C7—22no—
129C24×C7—22no—
130C24×C7—22no—
131C24×C7C22×C414yes—
132C24×C7C2×D414yes—
133C24×C7#4114yes—
134C24×C7C2411yescharacteristic
135C2×C7×D4—28no—
136C2×C7×D4—28no—
137C2×C7×D4—216no—
138C2×C7×D4—216no—
139C2×C7×D4—28no—
140C22×C4×C7—21no—
141C22×C4×C7—22no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7—21no—
145C22×C4×C7—22no—
146C22×C4×C7—21no—
147C22×C4×C7—22no—
148C22×C4×C7—22no—
149C22×C4×C7—22no—
150C22×C4×C7—22no—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—22no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—22no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7—22no—
163C22×C4×C7—21no—
164C22×C4×C7—22no—
165C22×C4×C7—22no—
166C22×C4×C7—22no—
167C22×C4×C7—22no—
168C22×C4×C7—22no—
169C22×C4×C7—22no—
170C22×C4×C7—22no—
171C22×C4×C7—22no—
172C22×C4×C7—22no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7—216no—
181C22×C4×C7—216no—
182C22×C4×C7—216no—
183C22×C4×C7—48no—
184C22×C4×C7—48no—
185C22×C4×C7—48no—
186C22×C4×C7—48no—
187C22×C4×C7C22×C414yes—
188C22×C4×C7C22×C412yes—
189C22×C4×C7C22×C412yes—
190C22×C4×C7C22×C412yes—
191C22×C4×C7C2×D412yes—
192C22×C4×C7C2×D414yes—
193C22×C4×C7C2×D412yes—
194C22×C4×C7C2×D412yes—
195C22×C4×C7C2×D412yes—
196C22×C4×C7C2×D414yes—
197C22×C4×C7C2×D412yes—
198C22×C4×C7C2×D412yes—
199C22×C4×C7#4114yes—
200C22×C4×C7#4112yes—
201C22×C4×C7#4112yes—
202C22×C4×C7#4112yes—
203C22×C4×C7#4112yes—
204C22×C4×C7#4114yes—
205C7×C4⋊C4—28no—
206C7×C4⋊C4—28no—
207C7×C4⋊C4—28no—
208C7×C22⋊C4—216no—
209C7×C22⋊C4—216no—
210C7×C22⋊C4—216no—
211C7×C22⋊C4—216no—
212C7×C22⋊C4—216no—
213C42×C7—28no—
214C42×C7—28no—
215C42×C7—44no—
216C42×C7—48no—
217C23×D4C22×C711yescharacteristic
218C24×C4C22×C712yes—
219C2×C4×D4—28no—
220C2×C4×D4—24no—
221C22×C4⋊C4C22×C711yescharacteristic
222C22×C4⋊C4C22×C711yescharacteristic
223C22×C4⋊C4C22×C711yescharacteristic
224C22×C22⋊C4C22×C712yes—
225C22×C22⋊C4C22×C712yes—
226C22×C22⋊C4C22×C712yes—
227C22×C22⋊C4C22×C712yes—
228C22×C22⋊C4C22×C712yes—
229C22×C42C22×C712yes—
230C22×C42C22×C711yescharacteristic
231C22×C42C22×C711yescharacteristic
232C22×C42C22×C711yescharacteristic
233#394C4×C718yesdirect product factor
234C4×C4⋊C4—24no—
235C4×C22⋊C4—28no—
236C4×C22⋊C4—28no—
237C2×#95C22×C711yescharacteristic
238C2×#95C22×C712yes—
239C2×#95C22×C711yescharacteristic
240C2×#95C22×C712yes—
241C2×#95C22×C712yes—
242C2×#95C22×C711yescharacteristic
243C2×#95C22×C712yes—
244C2×#95C22×C712yes—
245C2×#95C22×C711yescharacteristic
246C23×C7—24no—
247C23×C7—24no—
248C23×C7—24no—
249C23×C7—24no—
250C23×C7—24no—
251C23×C7—24no—
252C23×C7—24no—
253C23×C7—24no—
254C23×C7—24no—
255C23×C7—24no—
256C23×C7—24no—
257C23×C7—24no—
258C23×C7—24no—
259C23×C7—24no—
260C23×C7—24no—
261C23×C7—24no—
262C23×C7—24no—
263C23×C7—24no—
264C23×C7—42no—
265C23×C7—42no—
266C23×C7—42no—
267C23×C7—42no—
268C23×C7—42no—
269C23×C7—42no—
270C23×C7—42no—
271C23×C7—42no—
272C23×C7—42no—
273C23×C7—42no—
274C23×C7—42no—
275C23×C7—42no—
276C23×C7—42no—
277C23×C7—42no—
278C23×C7—42no—
279C23×C7—42no—
280C23×C7C4×D418yes—
281C23×C7C23×C411yescharacteristic
282C23×C7C22×D412yes—
283C23×C7C22×D411yescharacteristic
284C23×C7C22×D411yescharacteristic
285C23×C7C2×#4112yes—
286C23×C7C2×#4111yescharacteristic
287C23×C7C2×#4111yescharacteristic
288C23×C7C2×#4111yescharacteristic
289C23×C7C2×#4112yes—
290C23×C7C2×#4111yescharacteristic
291C23×C7C2×#4112yes—
292C7×D4—232no—
293C2×C4×C7—22no—
294C2×C4×C7—24no—
295C2×C4×C7—22no—
296C2×C4×C7—22no—
297C2×C4×C7—22no—
298C2×C4×C7—22no—
299C2×C4×C7—22no—
300C2×C4×C7—24no—
301C2×C4×C7—22no—
302C2×C4×C7—22no—
303C2×C4×C7—24no—
304C2×C4×C7—24no—
305C2×C4×C7—24no—
306C2×C4×C7—22no—
307C2×C4×C7—24no—
308C2×C4×C7—22no—
309C2×C4×C7—24no—
310C2×C4×C7—22no—
311C2×C4×C7—24no—
312C2×C4×C7—24no—
313C2×C4×C7—24no—
314C2×C4×C7—24no—
315C2×C4×C7—24no—
316C2×C4×C7—24no—
317C2×C4×C7—22no—
318C2×C4×C7—22no—
319C2×C4×C7—24no—
320C2×C4×C7—22no—
321C2×C4×C7—41no—
322C2×C4×C7—41no—
323C2×C4×C7—42no—
324C2×C4×C7—42no—
325C2×C4×C7—42no—
326C2×C4×C7—42no—
327C2×C4×C7—42no—
328C2×C4×C7—42no—
329C2×C4×C7—42no—
330C2×C4×C7—41no—
331C2×C4×C7—42no—
332C2×C4×C7—41no—
333C2×C4×C7—42no—
334C2×C4×C7—42no—
335C2×C4×C7—42no—
336C2×C4×C7—42no—
337C2×C4×C7—42no—
338C2×C4×C7—41no—
339C2×C4×C7—42no—
340C2×C4×C7—42no—
341C2×C4×C7—41no—
342C2×C4×C7—42no—
343C2×C4×C7—42no—
344C2×C4×C7—432no—
345C2×C4×C7C4×D414yes—
346C2×C4×C7C4×D414yescomplemented
347C2×C4×C7#12014yes—
348C2×C4×C7#12114yes—
349C2×C4×C7#12118yes—
350C2×C4×C7#12318yes—
351C2×C4×C7#12414yes—
352C25C23×C712yes—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4C2×C4×C714yes—
358C23×C4—24no—
359C23×C4—24no—
360C23×C4—24no—
361C23×C4—24no—
362C23×C4—24no—
363C23×C4—24no—
364C23×C4C7×D418yes—
365C23×C4C23×C711yescharacteristic
366C23×C4C23×C712yes—
367C23×C4C23×C711yescharacteristic
368C23×C4C23×C711yescharacteristic
369C23×C4C23×C712yes—
370C23×C4C23×C711yescharacteristic
371C23×C4C23×C712yes—
372C23×C4C23×C711yescharacteristic
373C23×C4C23×C711yescharacteristic
374C23×C4C23×C711yescharacteristic
375C4×D4—232no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4C2×C4×C714yescomplemented
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4C2×C4×C718yescomplemented
398C2×C22⋊C4C2×C4×C718yescomplemented
399C2×C42—24no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—24no—
405C2×C42—22no—
406C2×C42—24no—
407C2×C42C7×D414yes—
408C2×C42C7×D414yescomplemented
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—22no—
414#95—22no—
415#95—24no—
416#95—22no—
417#95C2×C4×C714yescomplemented
418C22×C7—28no—
419C22×C7—28no—
420C22×C7—28no—
421C22×C7—44no—
422C22×C7—44no—
423C22×C7—44no—
424C22×C7—44no—
425C22×C7—44no—
426C22×C7—44no—
427C22×C7—44no—
428C22×C7—44no—
429C22×C7—44no—
430C22×C7—44no—
431C22×C7—44no—
432C22×C7—44no—
433C22×C7C2×C4×D412yes—
434C22×C7C2×C4×D411yescharacteristic
435C22×C7C2×C4×D411yescharacteristic
436C22×C7C4×#4111yescharacteristic
437C22×C7C4×#4112yes—
438C22×C7C2×#12011yescharacteristic
439C22×C7C2×#12111yescharacteristic
440C22×C7C2×#12112yes—
441C22×C7C2×#12312yes—
442C22×C7#52512yes—
443C22×C7#52511yescharacteristic
444C22×C7#52512yes—
445C22×C7#52512yes—
446C22×C7#52511yescharacteristic
447C22×C7C2×#12411yescharacteristic
448C22×C7#52912yes—
449C22×C7#52912yes—
450C22×C7#52912yes—
451C22×C7#52911yescharacteristic
452C22×C7#52912yes—
453C22×C7#53211yescharacteristic
454C22×C7#53212yes—
455C22×C7#53211yescharacteristic
456C4×C7—24no—
457C4×C7—24no—
458C4×C7—44no—
459C4×C7—42no—
460C4×C7—42no—
461C4×C7—42no—
462C4×C7—44no—
463C4×C7—42no—
464C4×C7—44no—
465C4×C7#39418yesdirect product factor
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24C22×C4×C714yes—
479C24C2×C7×D414yes—
480C24C7×#4114yes—
481C24C24×C711yescharacteristic
482C2×D4—28no—
483C2×D4—28no—
484C2×D4—216no—
485C2×D4—216no—
486C2×D4—28no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—216no—
528C22×C4—216no—
529C22×C4—216no—
530C22×C4—48no—
531C22×C4—48no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4C22×C4×C714yes—
535C22×C4C22×C4×C712yes—
536C22×C4C22×C4×C712yes—
537C22×C4C22×C4×C712yes—
538C22×C4C2×C7×D412yes—
539C22×C4C2×C7×D414yes—
540C22×C4C2×C7×D412yes—
541C22×C4C2×C7×D412yes—
542C22×C4C2×C7×D412yes—
543C22×C4C2×C7×D414yes—
544C22×C4C2×C7×D412yes—
545C22×C4C2×C7×D412yes—
546C22×C4C7×#4114yes—
547C22×C4C7×#4112yes—
548C22×C4C7×#4112yes—
549C22×C4C7×#4112yes—
550C22×C4C7×#4112yes—
551C22×C4C7×#4114yes—
552C4⋊C4—28no—
553C4⋊C4—28no—
554C4⋊C4—28no—
555C22⋊C4—216no—
556C22⋊C4—216no—
557C22⋊C4—216no—
558C22⋊C4—216no—
559C22⋊C4—216no—
560C42—28no—
561C42—28no—
562C42—44no—
563C42—48no—
564C2×C7—48no—
565C2×C7C4×#12011yescharacteristic
566C2×C7C4×#12111yescharacteristic
567C2×C7C4×#12112yes—
568C2×C7C4×#12312yes—
569C2×C7C4×#12411yescharacteristic
570C2×C7C2×#39411yescharacteristic
571C2×C7#238811yescharacteristic
572C2×C7#239211yescharacteristic
573C2×C7#239212yes—
574C2×C7#239512yes—
575C2×C7#239811yescharacteristic
576C23—24no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23C4×C7×D418yes—
611C23C23×C4×C711yescharacteristic
612C23C22×C7×D412yes—
613C23C22×C7×D411yescharacteristic
614C23C22×C7×D411yescharacteristic
615C23C2×C7×#4112yes—
616C23C2×C7×#4111yescharacteristic
617C23C2×C7×#4111yescharacteristic
618C23C2×C7×#4111yescharacteristic
619C23C2×C7×#4112yes—
620C23C2×C7×#4111yescharacteristic
621C23C2×C7×#4112yes—
622D4—232no—
623C2×C4—22no—
624C2×C4—24no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—24no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—24no—
638C2×C4—22no—
639C2×C4—24no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—432no—
675C2×C4C4×C7×D414yes—
676C2×C4C4×C7×D414yescomplemented
677C2×C4C7×#12014yes—
678C2×C4C7×#12114yes—
679C2×C4C7×#12118yes—
680C2×C4C7×#12318yes—
681C2×C4C7×#12414yes—
682C7C4×#39411yescharacteristic, direct product factor, Sylow
683C22—28no—
684C22—28no—
685C22—28no—
686C22—44no—
687C22—44no—
688C22—44no—
689C22—44no—
690C22—44no—
691C22—44no—
692C22—44no—
693C22—44no—
694C22—44no—
695C22—44no—
696C22—44no—
697C22—44no—
698C22C2×C4×C7×D412yes—
699C22C2×C4×C7×D411yescharacteristic
700C22C2×C4×C7×D411yescharacteristic
701C22C4×C7×#4111yescharacteristic
702C22C4×C7×#4112yes—
703C22C2×C7×#12011yescharacteristic
704C22C2×C7×#12111yescharacteristic
705C22C2×C7×#12112yes—
706C22C2×C7×#12312yes—
707C22C7×#52512yes—
708C22C7×#52511yescharacteristic
709C22C7×#52512yes—
710C22C7×#52512yes—
711C22C7×#52511yescharacteristic
712C22C2×C7×#12411yescharacteristic
713C22C7×#52912yes—
714C22C7×#52912yes—
715C22C7×#52912yes—
716C22C7×#52911yescharacteristic
717C22C7×#52912yes—
718C22C7×#53211yescharacteristic
719C22C7×#53212yes—
720C22C7×#53211yescharacteristic
721C4—24no—
722C4—24no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—44no—
727C4—42no—
728C4—44no—
729C4—44no—
730C4C7×#39418yesdirect product factor
731C2—48no—
732C2C4×C7×#12011yescharacteristic
733C2C4×C7×#12111yescharacteristic
734C2C4×C7×#12112yes—
735C2C4×C7×#12312yes—
736C2C4×C7×#12411yescharacteristic
737C2C2×C7×#39411yescharacteristic
738C2C7×#238811yescharacteristic
739C2C7×#239211yescharacteristic
740C2C7×#239212yes—
741C2C7×#239512yes—
742C2C7×#239811yescharacteristic
subgroupG/H
centerC23×C4×C7C23
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
socleC24×C7C24
prime radicalC23×C7×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×C7×C4⋊C4C2semidirect
4. C2×C4×C7×C22⋊C4C2semidirect
5. C2×C4×C7×C22⋊C4C2semidirect
6. C7×#1442C2semidirect
7. C7×#1441C2semidirect
8. C7×#1440C2semidirect
9. C7×#1439C2semidirect
11. C4×C7×#95C2semidirect
28. C7×#394C4direct (N × H)
41. C4×#394C7direct (N × H)
73. C2×C7×C4⋊C4C2×C4semidirect
87. C2×C7×C22⋊C4C2×C4semidirect
88. C2×C7×C22⋊C4C2×C4semidirect
98. C2×C42×C7D4semidirect
107. C7×#95C2×C4semidirect
110. C2×C4×C4⋊C4C2×C7semidirect
111. C2×C4×C22⋊C4C2×C7semidirect
112. C2×C4×C22⋊C4C2×C7semidirect
113. #1442C2×C7semidirect
114. #1441C2×C7semidirect
115. #1440C2×C7semidirect
116. #1439C2×C7semidirect
118. C4×#95C2×C7semidirect
233. #394C4×C7direct (N × H)
346. C2×C4×C7C4×D4semidirect
383. C2×C4⋊C4C2×C4×C7semidirect
397. C2×C22⋊C4C2×C4×C7semidirect
398. C2×C22⋊C4C2×C4×C7semidirect
408. C2×C42C7×D4semidirect
417. #95C2×C4×C7semidirect
465. C4×C7#394direct (N × H)
676. C2×C4C4×C7×D4semidirect
682. C7C4×#394direct (N × H)
730. C4C7×#394direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C7×D42
C2×C7×#3942
C2×C4×C7×C4⋊C42
C2×C4×C7×C22⋊C42
C7×#14422
C7×#14412
C7×#14402
C7×#14392
C7×#14382
C4×C7×#952
C4×#3947