Finite Group Databasebeta

← C7×#14015 #13191231

Subgroups — C7×#14015 #13191231

Order 1792.

2950 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C7×D4C211yesmaximal, characteristic
2C23×C7×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C7×#386C211yesmaximal, characteristic
4C2×C7×#386C211yesmaximal, characteristic
5C2×C7×#385C212yesmaximal, complemented
6C2×C7×#385C211yesmaximal, characteristic, complemented
7C7×#1444C212yesmaximal, complemented
8C7×#1439C212yesmaximal, complemented
9C7×#1436C212yesmaximal, complemented
10C7×C22⋊#95C211yesmaximal, characteristic, complemented
11C7×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C7×D4C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C24×C4×C7C2211yescharacteristic
15C24×C4×C7C2211yescharacteristic
16C24×C4×C7C2211yescharacteristic
17C2×C4×C7×D4—24no—
18C2×C4×C7×D4—24no—
19C2×C4×C7×D4—24no—
20C22×C7×C4⋊C4—24no—
21C22×C7×C4⋊C4—28no—
22C22×C7×C4⋊C4C2212yes—
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C4⋊C4C2212yes—
25C22×C7×C4⋊C4C2212yes—
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2212yes—
29C22×C7×C22⋊C4C2211yescharacteristic
30C22×C7×C22⋊C4C2212yes—
31C22×C7×C22⋊C4C2211yescharacteristic
32C22×C42×C7C2211yescharacteristic
33C7×#386—24no—
34C7×#386C418yescomplemented
35C7×#385—28no—
36C7×#385—24no—
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39C2×C7×#95C2212yes—
40C2×C7×#95C2212yes—
41C2×C7×#95C2212yes—
42C2×C7×#95C2212yes—
43C2×C7×#95C2212yes—
44#14015C711yesmaximal, 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×D4C2×C414yes—
52C22×C7×D4D414yes—
53C22×C7×D4Q814yes—
54C23×C4×C7—22no—
55C23×C4×C7—22no—
56C23×C4×C7—24no—
57C23×C4×C7—24no—
58C23×C4×C7—22no—
59C23×C4×C7—22no—
60C23×C4×C7—22no—
61C23×C4×C7—22no—
62C23×C4×C7—24no—
63C23×C4×C7—24no—
64C23×C4×C7—22no—
65C23×C4×C7—22no—
66C23×C4×C7—22no—
67C23×C4×C7—22no—
68C23×C4×C7—24no—
69C23×C4×C7—42no—
70C23×C4×C7—42no—
71C23×C4×C7—42no—
72C23×C4×C7C2×C414yescomplemented
73C23×C4×C7D414yes—
74C23×C4×C7C2312yes—
75C23×C4×C7C2312yes—
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2312yes—
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2312yes—
82C23×C4×C7C2311yescharacteristic
83C4×C7×D4—232no—
84C2×C7×C4⋊C4—232no—
85C2×C7×C4⋊C4—24no—
86C2×C7×C4⋊C4—24no—
87C2×C7×C4⋊C4—24no—
88C2×C7×C4⋊C4—24no—
89C2×C7×C4⋊C4—24no—
90C2×C7×C4⋊C4—22no—
91C2×C7×C4⋊C4—22no—
92C2×C7×C4⋊C4—22no—
93C2×C7×C4⋊C4—24no—
94C2×C7×C4⋊C4—24no—
95C2×C7×C4⋊C4—42no—
96C2×C7×C4⋊C4D418yescomplemented
97C2×C7×C22⋊C4—22no—
98C2×C7×C22⋊C4—22no—
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—22no—
108C2×C7×C22⋊C4—22no—
109C2×C7×C22⋊C4—22no—
110C2×C7×C22⋊C4—24no—
111C2×C7×C22⋊C4—42no—
112C2×C7×C22⋊C4C2×C414yescomplemented
113C2×C7×C22⋊C4C2×C418yescomplemented
114C2×C7×C22⋊C4D414yes—
115C2×C42×C7—22no—
116C2×C42×C7—22no—
117C2×C42×C7—22no—
118C7×#95—24no—
119C7×#95—24no—
120C7×#95—24no—
121C7×#95—24no—
122C7×#95—24no—
123C7×#95—42no—
124C7×#95C2×C418yescomplemented
125C22×C4×D4C2×C711yescharacteristic
126C23×C4⋊C4C2×C711yescharacteristic, complemented
127C2×#386C2×C711yescharacteristic
128C2×#386C2×C711yescharacteristic
129C2×#385C2×C712yescomplemented
130C2×#385C2×C711yescharacteristic, complemented
131#1444C2×C712yescomplemented
132#1439C2×C712yescomplemented
133#1436C2×C712yescomplemented
134C22⋊#95C2×C711yescharacteristic, complemented
135C22⋊#95C2×C711yescharacteristic, complemented
136C24×C7—22no—
137C24×C7—22no—
138C24×C7—22no—
139C24×C7—22no—
140C24×C7—22no—
141C24×C7—21no—
142C24×C7—21no—
143C24×C7—22no—
144C24×C7—21no—
145C24×C7—21no—
146C24×C7—22no—
147C24×C7—22no—
148C24×C7C22×C412yes—
149C24×C7C22×C412yes—
150C24×C7C2×D412yes—
151C24×C7C2×D412yes—
152C24×C7C2×D412yes—
153C24×C7C2×D412yes—
154C24×C7C2×Q812yes—
155C24×C7C2×Q812yes—
156C24×C7#4112yes—
157C24×C7#4112yes—
158C24×C7C2411yescharacteristic
159C2×C7×D4—28no—
160C2×C7×D4—28no—
161C2×C7×D4—28no—
162C2×C7×D4—28no—
163C2×C7×D4—28no—
164C2×C7×D4—28no—
165C2×C7×D4C4⋊C4116yescomplemented
166C22×C4×C7—28no—
167C22×C4×C7—216no—
168C22×C4×C7—28no—
169C22×C4×C7—28no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—22no—
181C22×C4×C7—216no—
182C22×C4×C7—28no—
183C22×C4×C7—28no—
184C22×C4×C7—28no—
185C22×C4×C7—22no—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—22no—
189C22×C4×C7—22no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—22no—
197C22×C4×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—28no—
210C22×C4×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—44no—
218C22×C4×C7—48no—
219C22×C4×C7—48no—
220C22×C4×C7—48no—
221C22×C4×C7—48no—
222C22×C4×C7—48no—
223C22×C4×C7—48no—
224C22×C4×C7—44no—
225C22×C4×C7—44no—
226C22×C4×C7—44no—
227C22×C4×C7—44no—
228C22×C4×C7C22×C414yes—
229C22×C4×C7C22×C412yes—
230C22×C4×C7C22×C414yes—
231C22×C4×C7C2×D412yes—
232C22×C4×C7C2×D412yes—
233C22×C4×C7C2×D414yes—
234C22×C4×C7C2×D412yes—
235C22×C4×C7C2×D412yes—
236C22×C4×C7C2×D414yes—
237C22×C4×C7C2×D414yes—
238C22×C4×C7C2×D412yes—
239C22×C4×C7C2×Q812yes—
240C22×C4×C7#4114yes—
241C7×C4⋊C4—216no—
242C7×C4⋊C4—28no—
243C7×C4⋊C4—216no—
244C7×C4⋊C4—48no—
245C7×C22⋊C4—28no—
246C7×C22⋊C4—28no—
247C7×C22⋊C4—28no—
248C7×C22⋊C4—216no—
249C7×C22⋊C4—48no—
250C7×C22⋊C4—44no—
251C42×C7—28no—
252C23×D4C22×C711yescharacteristic
253C24×C4C22×C711yescharacteristic
254C24×C4C22×C711yescharacteristic
255C24×C4C22×C711yescharacteristic
256C24×C4C22×C711yescharacteristic
257C2×C4×D4—24no—
258C2×C4×D4—24no—
259C2×C4×D4—24no—
260C22×C4⋊C4—24no—
261C22×C4⋊C4—28no—
262C22×C4⋊C4C22×C712yes—
263C22×C4⋊C4C22×C711yescharacteristic
264C22×C4⋊C4C22×C712yes—
265C22×C4⋊C4C22×C712yes—
266C22×C22⋊C4C22×C711yescharacteristic
267C22×C22⋊C4C22×C711yescharacteristic
268C22×C22⋊C4C22×C712yes—
269C22×C22⋊C4C22×C711yescharacteristic
270C22×C22⋊C4C22×C712yes—
271C22×C22⋊C4C22×C711yescharacteristic
272C22×C42C22×C711yescharacteristic
273#386—24no—
274#386C4×C718yescomplemented
275#385—28no—
276#385—24no—
277C2×#95C22×C712yes—
278C2×#95C22×C712yes—
279C2×#95C22×C712yes—
280C2×#95C22×C712yes—
281C2×#95C22×C712yes—
282C2×#95C22×C712yes—
283C2×#95C22×C712yes—
284C23×C7—24no—
285C23×C7—24no—
286C23×C7—22no—
287C23×C7—22no—
288C23×C7—24no—
289C23×C7—22no—
290C23×C7—22no—
291C23×C7—24no—
292C23×C7—24no—
293C23×C7—24no—
294C23×C7—24no—
295C23×C7—24no—
296C23×C7—24no—
297C23×C7—24no—
298C23×C7—24no—
299C23×C7—24no—
300C23×C7—24no—
301C23×C7—22no—
302C23×C7—22no—
303C23×C7—24no—
304C23×C7—22no—
305C23×C7—22no—
306C23×C7—22no—
307C23×C7—22no—
308C23×C7—24no—
309C23×C7—24no—
310C23×C7—24no—
311C23×C7—24no—
312C23×C7—41no—
313C23×C7—41no—
314C23×C7—42no—
315C23×C7—41no—
316C23×C7—41no—
317C23×C7—42no—
318C23×C7—42no—
319C23×C7—42no—
320C23×C7—42no—
321C23×C7—42no—
322C23×C7C2×C4⋊C414yes—
323C23×C7C2×C4⋊C414yescomplemented
324C23×C7C4×D414yes—
325C23×C7C4×D414yes—
326C23×C7#12014yes—
327C23×C7C22⋊Q814yes—
328C23×C7C22⋊Q814yes—
329C23×C7#12314yes—
330C23×C7C23×C411yescharacteristic
331C23×C7C22×D411yescharacteristic
332C23×C7C22×D411yescharacteristic
333C23×C7C22×D411yescharacteristic
334C23×C7C22×D412yes—
335C23×C7C22×Q811yescharacteristic
336C23×C7C2×#4111yescharacteristic
337C23×C7C2×#4111yescharacteristic
338C23×C7C2×#4112yes—
339C23×C7H(5,𝔽2)12yes—
340C23×C72−1+412yes—
341C7×D4—232no—
342C2×C4×C7—232no—
343C2×C4×C7—24no—
344C2×C4×C7—24no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—22no—
348C2×C4×C7—22no—
349C2×C4×C7—24no—
350C2×C4×C7—22no—
351C2×C4×C7—22no—
352C2×C4×C7—22no—
353C2×C4×C7—24no—
354C2×C4×C7—24no—
355C2×C4×C7—24no—
356C2×C4×C7—22no—
357C2×C4×C7—24no—
358C2×C4×C7—24no—
359C2×C4×C7—24no—
360C2×C4×C7—24no—
361C2×C4×C7—24no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—24no—
367C2×C4×C7—22no—
368C2×C4×C7—24no—
369C2×C4×C7—24no—
370C2×C4×C7—24no—
371C2×C4×C7—24no—
372C2×C4×C7—416no—
373C2×C4×C7—416no—
374C2×C4×C7—416no—
375C2×C4×C7—42no—
376C2×C4×C7—41no—
377C2×C4×C7—41no—
378C2×C4×C7—41no—
379C2×C4×C7—42no—
380C2×C4×C7—41no—
381C2×C4×C7—42no—
382C2×C4×C7—42no—
383C2×C4×C7—42no—
384C2×C4×C7—42no—
385C2×C4×C7—42no—
386C2×C4×C7—42no—
387C2×C4×C7—42no—
388C2×C4×C7—42no—
389C2×C4×C7—42no—
390C2×C4×C7—42no—
391C2×C4×C7—42no—
392C2×C4×C7—42no—
393C2×C4×C7—42no—
394C2×C4×C7—42no—
395C2×C4×C7—42no—
396C2×C4×C7—42no—
397C2×C4×C7—42no—
398C2×C4×C7C2×C4⋊C414yescomplemented
399C2×C4×C7C4×D418yescomplemented
400C2×C4×C7#12014yes—
401C25C23×C711yescharacteristic
402C25C23×C711yescharacteristic
403C22×D4—22no—
404C22×D4—22no—
405C22×D4—22no—
406C22×D4—22no—
407C22×D4C2×C4×C714yes—
408C22×D4C7×D414yes—
409C22×D4C7×Q814yes—
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—24no—
413C23×C4—24no—
414C23×C4—22no—
415C23×C4—22no—
416C23×C4—22no—
417C23×C4—22no—
418C23×C4—24no—
419C23×C4—24no—
420C23×C4—22no—
421C23×C4—22no—
422C23×C4—22no—
423C23×C4—22no—
424C23×C4—24no—
425C23×C4—42no—
426C23×C4—42no—
427C23×C4—42no—
428C23×C4C2×C4×C714yescomplemented
429C23×C4C7×D414yes—
430C23×C4C23×C712yes—
431C23×C4C23×C712yes—
432C23×C4C23×C711yescharacteristic
433C23×C4C23×C712yes—
434C23×C4C23×C711yescharacteristic
435C23×C4C23×C711yescharacteristic
436C23×C4C23×C711yescharacteristic
437C23×C4C23×C712yes—
438C23×C4C23×C711yescharacteristic
439C4×D4—232no—
440C2×C4⋊C4—232no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4C7×D418yescomplemented
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—42no—
468C2×C22⋊C4C2×C4×C714yescomplemented
469C2×C22⋊C4C2×C4×C718yescomplemented
470C2×C22⋊C4C7×D414yes—
471C2×C42—22no—
472C2×C42—22no—
473C2×C42—22no—
474#95—24no—
475#95—24no—
476#95—24no—
477#95—24no—
478#95—24no—
479#95—42no—
480#95C2×C4×C718yescomplemented
481C22×C7—24no—
482C22×C7—24no—
483C22×C7—28no—
484C22×C7—28no—
485C22×C7—24no—
486C22×C7—24no—
487C22×C7—24no—
488C22×C7—28no—
489C22×C7—28no—
490C22×C7—24no—
491C22×C7—28no—
492C22×C7—24no—
493C22×C7—42no—
494C22×C7—42no—
495C22×C7—44no—
496C22×C7—42no—
497C22×C7—42no—
498C22×C7—42no—
499C22×C7—44no—
500C22×C7—44no—
501C22×C7—42no—
502C22×C7#38518yescomplemented
503C22×C7C22×C4⋊C411yescharacteristic
504C22×C7C2×C4×D411yescharacteristic
505C22×C7C2×C4×D412yes—
506C22×C7C2×C4×D411yescharacteristic
507C22×C7#52012yes—
508C22×C7C2×#12011yescharacteristic
509C22×C7C2×#12011yescharacteristic
510C22×C7C2×C22⋊Q811yescharacteristic
511C22×C7C2×C22⋊Q811yescharacteristic
512C22×C7C2×#12311yescharacteristic
513C22×C7#52511yescharacteristic
514C22×C7#52512yes—
515C22×C7#53411yescharacteristic
516C22×C7#53611yescharacteristic
517C22×C7#53912yes—
518C22×C7D4212yes—
519C22×C7D4212yes—
520C22×C7#54712yes—
521C22×C7#54712yes—
522C22×C7#54812yes—
523C22×C7D4×Q812yes—
524C22×C7#55312yes—
525C22×C7#55412yes—
526C4×C7—24no—
527C4×C7—24no—
528C4×C7—28no—
529C4×C7—44no—
530C4×C7—42no—
531C4×C7—42no—
532C4×C7—44no—
533C4×C7—42no—
534C4×C7—82no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—21no—
541C24—21no—
542C24—22no—
543C24—21no—
544C24—21no—
545C24—22no—
546C24—22no—
547C24C22×C4×C712yes—
548C24C22×C4×C712yes—
549C24C2×C7×D412yes—
550C24C2×C7×D412yes—
551C24C2×C7×D412yes—
552C24C2×C7×D412yes—
553C24C2×C7×Q812yes—
554C24C2×C7×Q812yes—
555C24C7×#4112yes—
556C24C7×#4112yes—
557C24C24×C711yescharacteristic
558C2×D4—28no—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4—28no—
562C2×D4—28no—
563C2×D4—28no—
564C2×D4C7×C4⋊C4116yescomplemented
565C22×C4—28no—
566C22×C4—216no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—216no—
581C22×C4—28no—
582C22×C4—28no—
583C22×C4—28no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—28no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—44no—
617C22×C4—48no—
618C22×C4—48no—
619C22×C4—48no—
620C22×C4—48no—
621C22×C4—48no—
622C22×C4—48no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4C22×C4×C714yes—
628C22×C4C22×C4×C712yes—
629C22×C4C22×C4×C714yes—
630C22×C4C2×C7×D412yes—
631C22×C4C2×C7×D412yes—
632C22×C4C2×C7×D414yes—
633C22×C4C2×C7×D412yes—
634C22×C4C2×C7×D412yes—
635C22×C4C2×C7×D414yes—
636C22×C4C2×C7×D414yes—
637C22×C4C2×C7×D412yes—
638C22×C4C2×C7×Q812yes—
639C22×C4C7×#4114yes—
640C4⋊C4—216no—
641C4⋊C4—28no—
642C4⋊C4—216no—
643C4⋊C4—48no—
644C22⋊C4—28no—
645C22⋊C4—28no—
646C22⋊C4—28no—
647C22⋊C4—216no—
648C22⋊C4—48no—
649C22⋊C4—44no—
650C42—28no—
651C2×C7—28no—
652C2×C7—44no—
653C2×C7C2×#38511yescharacteristic
654C2×C7C4×#12011yescharacteristic
655C2×C7#232211yescharacteristic
656C2×C7D4×C4⋊C412yes—
657C2×C7#236112yes—
658C2×C7#240311yescharacteristic
659C2×C7#240611yescharacteristic
660C2×C7#240911yescharacteristic
661C2×C7#244312yes—
662C2×C7#244912yes—
663C2×C7#257911yescharacteristic
664C23—24no—
665C23—24no—
666C23—22no—
667C23—22no—
668C23—24no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—22no—
682C23—22no—
683C23—24no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—41no—
693C23—41no—
694C23—42no—
695C23—41no—
696C23—41no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23C2×C7×C4⋊C414yes—
703C23C2×C7×C4⋊C414yescomplemented
704C23C4×C7×D414yes—
705C23C4×C7×D414yes—
706C23C7×#12014yes—
707C23C7×C22⋊Q814yes—
708C23C7×C22⋊Q814yes—
709C23C7×#12314yes—
710C23C23×C4×C711yescharacteristic
711C23C22×C7×D411yescharacteristic
712C23C22×C7×D411yescharacteristic
713C23C22×C7×D411yescharacteristic
714C23C22×C7×D412yes—
715C23C22×C7×Q811yescharacteristic
716C23C2×C7×#4111yescharacteristic
717C23C2×C7×#4111yescharacteristic
718C23C2×C7×#4112yes—
719C23C7×H(5,𝔽2)12yes—
720C23C7×2−1+412yes—
721D4—232no—
722C2×C4—232no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—416no—
753C2×C4—416no—
754C2×C4—416no—
755C2×C4—42no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4C2×C7×C4⋊C414yescomplemented
779C2×C4C4×C7×D418yescomplemented
780C2×C4C7×#12014yes—
781C7#1401511yescharacteristic, direct product factor, Sylow
782C22—24no—
783C22—24no—
784C22—24no—
785C22—28no—
786C22—28no—
787C22—24no—
788C22—24no—
789C22—24no—
790C22—28no—
791C22—28no—
792C22—24no—
793C22—28no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—44no—
798C22—44no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—44no—
803C22C7×#38518yescomplemented
804C22C22×C7×C4⋊C411yescharacteristic
805C22C2×C4×C7×D411yescharacteristic
806C22C2×C4×C7×D411yescharacteristic
807C22C2×C4×C7×D412yes—
808C22C7×#52012yes—
809C22C2×C7×#12011yescharacteristic
810C22C2×C7×#12011yescharacteristic
811C22C2×C7×C22⋊Q811yescharacteristic
812C22C2×C7×C22⋊Q811yescharacteristic
813C22C2×C7×#12311yescharacteristic
814C22C7×#52511yescharacteristic
815C22C7×#52512yes—
816C22C7×#53411yescharacteristic
817C22C7×#53611yescharacteristic
818C22C7×#53912yes—
819C22C7×D4212yes—
820C22C7×D4212yes—
821C22C7×#54712yes—
822C22C7×#54712yes—
823C22C7×#54812yes—
824C22C7×D4×Q812yes—
825C22C7×#55312yes—
826C22C7×#55412yes—
827C4—24no—
828C4—24no—
829C4—28no—
830C4—42no—
831C4—42no—
832C4—44no—
833C4—42no—
834C4—44no—
835C4—82no—
836C2—28no—
837C2—44no—
838C2C2×C7×#38511yescharacteristic
839C2C4×C7×#12011yescharacteristic
840C2C7×#232211yescharacteristic
841C2C7×D4×C4⋊C412yes—
842C2C7×#236112yes—
843C2C7×#240311yescharacteristic
844C2C7×#240611yescharacteristic
845C2C7×#240911yescharacteristic
846C2C7×#244312yes—
847C2C7×#244912yes—
848C2C7×#257911yescharacteristic
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
2. C23×C7×C4⋊C4C2semidirect
5. C2×C7×#385C2semidirect
6. C2×C7×#385C2semidirect
7. C7×#1444C2semidirect
8. C7×#1439C2semidirect
9. C7×#1436C2semidirect
10. C7×C22⋊#95C2semidirect
11. C7×C22⋊#95C2semidirect
34. C7×#386C4semidirect
44. #14015C7direct (N × H)
72. C23×C4×C7C2×C4semidirect
96. C2×C7×C4⋊C4D4semidirect
112. C2×C7×C22⋊C4C2×C4semidirect
113. C2×C7×C22⋊C4C2×C4semidirect
124. C7×#95C2×C4semidirect
126. C23×C4⋊C4C2×C7semidirect
129. C2×#385C2×C7semidirect
130. C2×#385C2×C7semidirect
131. #1444C2×C7semidirect
132. #1439C2×C7semidirect
133. #1436C2×C7semidirect
134. C22⋊#95C2×C7semidirect
135. C22⋊#95C2×C7semidirect
165. C2×C7×D4C4⋊C4semidirect
274. #386C4×C7semidirect
323. C23×C7C2×C4⋊C4semidirect
398. C2×C4×C7C2×C4⋊C4semidirect
399. C2×C4×C7C4×D4semidirect
428. C23×C4C2×C4×C7semidirect
452. C2×C4⋊C4C7×D4semidirect
468. C2×C22⋊C4C2×C4×C7semidirect
469. C2×C22⋊C4C2×C4×C7semidirect
480. #95C2×C4×C7semidirect
502. C22×C7#385semidirect
564. C2×D4C7×C4⋊C4semidirect
703. C23C2×C7×C4⋊C4semidirect
778. C2×C4C2×C7×C4⋊C4semidirect
779. C2×C4C4×C7×D4semidirect
781. C7#14015direct (N × H)
803. C22C7×#385semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C7×D42
C23×C7×C4⋊C42
C2×C7×#3862
C2×C7×#3852
C7×#14442
C7×#14392
C7×#14362
C7×C22⋊#952
#140157