Finite Group Databasebeta

← C7×#13973 #13191189

Subgroups — C7×#13973 #13191189

Order 1792.

1746 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#389C211yesmaximal, characteristic, complemented
2C2×C7×#380C211yesmaximal, characteristic
3C2×C7×#380C211yesmaximal, characteristic
4C2×C4×C7×C4⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
6C7×#1442C212yesmaximal, complemented
7C7×#1439C212yesmaximal
8C7×#1437C212yesmaximal
9C7×C4⋊#95C211yesmaximal, characteristic, complemented
10C7×C4⋊#95C211yesmaximal, characteristic, complemented
11C7×#1434C212yesmaximal, complemented
12C24×C4×C7C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C4⋊C4C2212yes—
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2212yes—
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2212yes—
22C22×C42×C7C2211yescharacteristic
23C22×C42×C7C2212yes—
24C22×C42×C7C2211yescharacteristic
25C7×#389—24no—
26C7×#380—24no—
27C7×#380C418yescomplemented
28C4×C7×C4⋊C4—24no—
29C4×C7×C22⋊C4—24no—
30C2×C7×#95C2211yescharacteristic
31C2×C7×#95C2211yescharacteristic
32C2×C7×#95C2212yes—
33C2×C7×#95C2212yes—
34C2×C7×#95C2212yes—
35C2×C7×#95C2212yes—
36C2×C7×#95C2212yes—
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39C2×C7×#95C2212yes—
40#13973C711yesmaximal, characteristic, direct product factor, Sylow
41C25×C7C2311yescharacteristic
42C23×C4×C7—22no—
43C23×C4×C7—22no—
44C23×C4×C7—22no—
45C23×C4×C7—22no—
46C23×C4×C7—22no—
47C23×C4×C7—22no—
48C23×C4×C7C2×C414yes—
49C23×C4×C7C2312yes—
50C23×C4×C7C2312yes—
51C23×C4×C7C2311yescharacteristic
52C23×C4×C7C2312yes—
53C23×C4×C7C2312yes—
54C23×C4×C7C2311yescharacteristic
55C23×C4×C7C2311yescharacteristic
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C2×C7×C4⋊C4—22no—
60C2×C7×C4⋊C4—22no—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—22no—
64C2×C7×C4⋊C4—22no—
65C2×C7×C4⋊C4—22no—
66C2×C7×C4⋊C4—24no—
67C2×C7×C4⋊C4—22no—
68C2×C7×C4⋊C4—22no—
69C2×C7×C4⋊C4—42no—
70C2×C7×C4⋊C4—42no—
71C2×C7×C4⋊C4C2×C414yes—
72C2×C7×C4⋊C4C2×C414yes—
73C2×C7×C4⋊C4D414yes—
74C2×C7×C22⋊C4—22no—
75C2×C7×C22⋊C4—22no—
76C2×C7×C22⋊C4—22no—
77C2×C7×C22⋊C4—22no—
78C2×C7×C22⋊C4—22no—
79C2×C7×C22⋊C4—24no—
80C2×C7×C22⋊C4—24no—
81C2×C7×C22⋊C4—42no—
82C2×C7×C22⋊C4—42no—
83C2×C7×C22⋊C4—42no—
84C2×C7×C22⋊C4C2×C418yes—
85C2×C7×C22⋊C4Q814yes—
86C2×C42×C7—22no—
87C2×C42×C7—22no—
88C2×C42×C7—22no—
89C2×C42×C7—24no—
90C2×C42×C7—24no—
91C2×C42×C7—22no—
92C2×C42×C7—22no—
93C2×C42×C7—42no—
94C2×C42×C7D414yes—
95C7×#95—22no—
96C7×#95—22no—
97C7×#95—24no—
98C7×#95—24no—
99C7×#95—24no—
100C7×#95—24no—
101C7×#95—42no—
102C7×#95—42no—
103C7×#95—42no—
104C7×#95C2×C418yes—
105C2×#389C2×C711yescharacteristic, complemented
106C2×#380C2×C711yescharacteristic
107C2×#380C2×C711yescharacteristic
108C2×C4×C4⋊C4C2×C711yescharacteristic, complemented
109C2×C4×C22⋊C4C2×C711yescharacteristic
110#1442C2×C712yescomplemented
111#1439C2×C712yes—
112#1437C2×C712yes—
113C4⋊#95C2×C711yescharacteristic, complemented
114C4⋊#95C2×C711yescharacteristic, complemented
115#1434C2×C712yescomplemented
116C24×C7—21no—
117C24×C7—21no—
118C24×C7—21no—
119C24×C7—21no—
120C24×C7—21no—
121C24×C7—21no—
122C24×C7—21no—
123C24×C7—21no—
124C24×C7—21no—
125C24×C7—21no—
126C24×C7—21no—
127C24×C7—21no—
128C24×C7C22×C412yes—
129C24×C7C2×Q812yes—
130C24×C7#4112yes—
131C24×C7C2411yescharacteristic
132C22×C4×C7—21no—
133C22×C4×C7—21no—
134C22×C4×C7—21no—
135C22×C4×C7—21no—
136C22×C4×C7—21no—
137C22×C4×C7—21no—
138C22×C4×C7—21no—
139C22×C4×C7—21no—
140C22×C4×C7—21no—
141C22×C4×C7—22no—
142C22×C4×C7—22no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
145C22×C4×C7—21no—
146C22×C4×C7—22no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—22no—
156C22×C4×C7—22no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
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—22no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—22no—
177C22×C4×C7—21no—
178C22×C4×C7—28no—
179C22×C4×C7—28no—
180C22×C4×C7—28no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—22no—
184C22×C4×C7—22no—
185C22×C4×C7—22no—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—44no—
189C22×C4×C7—44no—
190C22×C4×C7—44no—
191C22×C4×C7—44no—
192C22×C4×C7C22×C412yes—
193C22×C4×C7C22×C414yes—
194C22×C4×C7C22×C414yes—
195C22×C4×C7C22×C412yes—
196C22×C4×C7C2×D414yes—
197C22×C4×C7C2×D412yes—
198C22×C4×C7C2×D412yes—
199C22×C4×C7C2×D412yes—
200C22×C4×C7C2×D412yes—
201C22×C4×C7C2×Q812yes—
202C22×C4×C7C2×Q812yes—
203C22×C4×C7#4112yes—
204C22×C4×C7#4112yes—
205C22×C4×C7#4112yes—
206C22×C4×C7#4112yes—
207C22×C4×C7#4112yes—
208C22×C4×C7#4112yes—
209C7×C4⋊C4—28no—
210C7×C4⋊C4—28no—
211C7×C4⋊C4—28no—
212C7×C4⋊C4—48no—
213C7×C4⋊C4—44no—
214C7×C22⋊C4—28no—
215C7×C22⋊C4—28no—
216C7×C22⋊C4—48no—
217C7×C22⋊C4—48no—
218C42×C7—28no—
219C42×C7—48no—
220C42×C7—44no—
221C24×C4C22×C711yescharacteristic
222C22×C4⋊C4C22×C711yescharacteristic
223C22×C4⋊C4C22×C711yescharacteristic
224C22×C4⋊C4C22×C711yescharacteristic
225C22×C4⋊C4C22×C711yescharacteristic
226C22×C4⋊C4C22×C712yes—
227C22×C22⋊C4C22×C711yescharacteristic
228C22×C22⋊C4C22×C712yes—
229C22×C22⋊C4C22×C711yescharacteristic
230C22×C22⋊C4C22×C712yes—
231C22×C42C22×C711yescharacteristic
232C22×C42C22×C712yes—
233C22×C42C22×C711yescharacteristic
234#389—24no—
235#380—24no—
236#380C4×C718yescomplemented
237C4×C4⋊C4—24no—
238C4×C22⋊C4—24no—
239C2×#95C22×C711yescharacteristic
240C2×#95C22×C712yes—
241C2×#95C22×C712yes—
242C2×#95C22×C712yes—
243C2×#95C22×C712yes—
244C2×#95C22×C711yescharacteristic
245C2×#95C22×C712yes—
246C2×#95C22×C712yes—
247C2×#95C22×C712yes—
248C2×#95C22×C712yes—
249C23×C7—22no—
250C23×C7—22no—
251C23×C7—22no—
252C23×C7—22no—
253C23×C7—22no—
254C23×C7—22no—
255C23×C7—22no—
256C23×C7—22no—
257C23×C7—22no—
258C23×C7—22no—
259C23×C7—22no—
260C23×C7—22no—
261C23×C7—22no—
262C23×C7—22no—
263C23×C7—22no—
264C23×C7—22no—
265C23×C7—22no—
266C23×C7—22no—
267C23×C7—41no—
268C23×C7—41no—
269C23×C7—41no—
270C23×C7—41no—
271C23×C7—41no—
272C23×C7—41no—
273C23×C7—41no—
274C23×C7—41no—
275C23×C7—41no—
276C23×C7—41no—
277C23×C7—41no—
278C23×C7—41no—
279C23×C7—41no—
280C23×C7—41no—
281C23×C7—41no—
282C23×C7—41no—
283C23×C7C4×Q814yes—
284C23×C7C23×C411yescharacteristic
285C23×C7C22×D411yescharacteristic
286C23×C7C22×D411yescharacteristic
287C23×C7C22×Q811yescharacteristic
288C23×C7C2×#4111yescharacteristic
289C23×C7C2×#4111yescharacteristic
290C23×C7C2×#4111yescharacteristic
291C23×C7C2×#4111yescharacteristic
292C23×C7C2×#4111yescharacteristic
293C23×C7C2×#4111yescharacteristic
294C23×C7C2×#4111yescharacteristic
295C23×C7H(5,𝔽2)11yescharacteristic
296C23×C7H(5,𝔽2)11yescharacteristic
297C23×C7H(5,𝔽2)11yescharacteristic
298C23×C72−1+411yescharacteristic
299C2×C4×C7—22no—
300C2×C4×C7—22no—
301C2×C4×C7—22no—
302C2×C4×C7—22no—
303C2×C4×C7—22no—
304C2×C4×C7—22no—
305C2×C4×C7—22no—
306C2×C4×C7—24no—
307C2×C4×C7—24no—
308C2×C4×C7—22no—
309C2×C4×C7—22no—
310C2×C4×C7—24no—
311C2×C4×C7—24no—
312C2×C4×C7—24no—
313C2×C4×C7—24no—
314C2×C4×C7—22no—
315C2×C4×C7—22no—
316C2×C4×C7—24no—
317C2×C4×C7—22no—
318C2×C4×C7—22no—
319C2×C4×C7—22no—
320C2×C4×C7—24no—
321C2×C4×C7—24no—
322C2×C4×C7—22no—
323C2×C4×C7—22no—
324C2×C4×C7—22no—
325C2×C4×C7—22no—
326C2×C4×C7—41no—
327C2×C4×C7—41no—
328C2×C4×C7—41no—
329C2×C4×C7—41no—
330C2×C4×C7—41no—
331C2×C4×C7—41no—
332C2×C4×C7—42no—
333C2×C4×C7—42no—
334C2×C4×C7—41no—
335C2×C4×C7—41no—
336C2×C4×C7—42no—
337C2×C4×C7—42no—
338C2×C4×C7—42no—
339C2×C4×C7—42no—
340C2×C4×C7—42no—
341C2×C4×C7—41no—
342C2×C4×C7—42no—
343C2×C4×C7—41no—
344C2×C4×C7—41no—
345C2×C4×C7—41no—
346C2×C4×C7—42no—
347C2×C4×C7—41no—
348C2×C4×C7—42no—
349C2×C4×C7—41no—
350C2×C4×C7—41no—
351C2×C4×C7—42no—
352C2×C4×C7—41no—
353C2×C4×C7—42no—
354C2×C4×C7—416no—
355C2×C4×C7—42no—
356C2×C4×C7—42no—
357C2×C4×C7—42no—
358C2×C4×C7—42no—
359C2×C4×C7—42no—
360C2×C4×C7—42no—
361C2×C4×C7—42no—
362C2×C4×C7#11714yes—
363C2×C4×C7C4×D414yes—
364C2×C4×C7C4×D414yes—
365C2×C4×C7#12114yes—
366C2×C4×C7C22⋊Q814yes—
367C2×C4×C7#12314yes—
368C2×C4×C7#12414yes—
369C2×C4×C7#12614yes—
370C25C23×C711yescharacteristic
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4C2×C4×C714yes—
378C23×C4C23×C712yes—
379C23×C4C23×C712yes—
380C23×C4C23×C712yes—
381C23×C4C23×C711yescharacteristic
382C23×C4C23×C711yescharacteristic
383C23×C4C23×C712yes—
384C23×C4C23×C711yescharacteristic
385C23×C4C23×C711yescharacteristic
386C23×C4C23×C711yescharacteristic
387C23×C4C23×C711yescharacteristic
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—42no—
399C2×C4⋊C4—42no—
400C2×C4⋊C4C2×C4×C714yes—
401C2×C4⋊C4C2×C4×C714yes—
402C2×C4⋊C4C7×D414yes—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—42no—
411C2×C22⋊C4—42no—
412C2×C22⋊C4—42no—
413C2×C22⋊C4C2×C4×C718yes—
414C2×C22⋊C4C7×Q814yes—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—24no—
419C2×C42—24no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—42no—
423C2×C42C7×D414yes—
424#95—22no—
425#95—22no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—42no—
431#95—42no—
432#95—42no—
433#95C2×C4×C718yes—
434C22×C7—24no—
435C22×C7—24no—
436C22×C7—24no—
437C22×C7—42no—
438C22×C7—42no—
439C22×C7—42no—
440C22×C7—42no—
441C22×C7—42no—
442C22×C7—42no—
443C22×C7—42no—
444C22×C7—42no—
445C22×C7—42no—
446C22×C7—42no—
447C22×C7—42no—
448C22×C7—42no—
449C22×C7C2×#11711yescharacteristic
450C22×C7C2×C4×D411yescharacteristic
451C22×C7C2×C4×D411yescharacteristic
452C22×C7C2×C4×Q811yescharacteristic
453C22×C7C4×#4111yescharacteristic
454C22×C7#51811yescharacteristic
455C22×C7#52011yescharacteristic
456C22×C7C2×#12111yescharacteristic
457C22×C7C2×C22⋊Q811yescharacteristic
458C22×C7C2×#12311yescharacteristic
459C22×C7#52511yescharacteristic
460C22×C7C2×#12411yescharacteristic
461C22×C7C2×#12611yescharacteristic
462C22×C7#52911yescharacteristic
463C22×C7#53311yescharacteristic
464C22×C7#53511yescharacteristic
465C22×C7#53711yescharacteristic
466C22×C7#54011yescharacteristic
467C22×C7#54211yescharacteristic
468C22×C7#54611yescharacteristic
469C22×C7#54611yescharacteristic
470C22×C7D4×Q811yescharacteristic
471C22×C7#55011yescharacteristic
472C22×C7#55211yescharacteristic
473C22×C7#55211yescharacteristic
474C22×C7#55211yescharacteristic
475C22×C7#55311yescharacteristic
476C22×C7#55311yescharacteristic
477C22×C7#55311yescharacteristic
478C22×C7#55411yescharacteristic
479C22×C7#55411yescharacteristic
480C22×C7#55411yescharacteristic
481C22×C7#55511yescharacteristic
482C22×C7#55511yescharacteristic
483C22×C7#55511yescharacteristic
484C4×C7—24no—
485C4×C7—42no—
486C4×C7—42no—
487C4×C7—44no—
488C4×C7—44no—
489C4×C7—42no—
490C4×C7—44no—
491C4×C7—42no—
492C4×C7—82no—
493C4×C7#38818yes—
494C24—21no—
495C24—21no—
496C24—21no—
497C24—21no—
498C24—21no—
499C24—21no—
500C24—21no—
501C24—21no—
502C24—21no—
503C24—21no—
504C24—21no—
505C24—21no—
506C24C22×C4×C712yes—
507C24C2×C7×Q812yes—
508C24C7×#4112yes—
509C24C24×C711yescharacteristic
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—28no—
557C22×C4—28no—
558C22×C4—28no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4C22×C4×C712yes—
571C22×C4C22×C4×C714yes—
572C22×C4C22×C4×C714yes—
573C22×C4C22×C4×C712yes—
574C22×C4C2×C7×D414yes—
575C22×C4C2×C7×D412yes—
576C22×C4C2×C7×D412yes—
577C22×C4C2×C7×D412yes—
578C22×C4C2×C7×D412yes—
579C22×C4C2×C7×Q812yes—
580C22×C4C2×C7×Q812yes—
581C22×C4C7×#4112yes—
582C22×C4C7×#4112yes—
583C22×C4C7×#4112yes—
584C22×C4C7×#4112yes—
585C22×C4C7×#4112yes—
586C22×C4C7×#4112yes—
587C4⋊C4—28no—
588C4⋊C4—28no—
589C4⋊C4—28no—
590C4⋊C4—48no—
591C4⋊C4—44no—
592C22⋊C4—28no—
593C22⋊C4—28no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C42—28no—
597C42—48no—
598C42—44no—
599C2×C7—44no—
600C2×C7C2×#38811yescharacteristic
601C2×C7C4×C22⋊Q811yescharacteristic
602C2×C7#232411yescharacteristic
603C2×C7#234511yescharacteristic
604C2×C7#234611yescharacteristic
605C2×C7#236011yescharacteristic
606C2×C7#236311yescharacteristic
607C2×C7#241411yescharacteristic
608C2×C7#241711yescharacteristic
609C2×C7#242011yescharacteristic
610C2×C7#242311yescharacteristic
611C2×C7#249511yescharacteristic
612C2×C7#249711yescharacteristic
613C2×C7#256211yescharacteristic
614C2×C7#256311yescharacteristic
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23C4×C7×Q814yes—
650C23C23×C4×C711yescharacteristic
651C23C22×C7×D411yescharacteristic
652C23C22×C7×D411yescharacteristic
653C23C22×C7×Q811yescharacteristic
654C23C2×C7×#4111yescharacteristic
655C23C2×C7×#4111yescharacteristic
656C23C2×C7×#4111yescharacteristic
657C23C2×C7×#4111yescharacteristic
658C23C2×C7×#4111yescharacteristic
659C23C2×C7×#4111yescharacteristic
660C23C2×C7×#4111yescharacteristic
661C23C7×H(5,𝔽2)11yescharacteristic
662C23C7×H(5,𝔽2)11yescharacteristic
663C23C7×H(5,𝔽2)11yescharacteristic
664C23C7×2−1+411yescharacteristic
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—416no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4C7×#11714yes—
729C2×C4C4×C7×D414yes—
730C2×C4C4×C7×D414yes—
731C2×C4C7×#12114yes—
732C2×C4C7×C22⋊Q814yes—
733C2×C4C7×#12314yes—
734C2×C4C7×#12414yes—
735C2×C4C7×#12614yes—
736C7#1397311yescharacteristic, direct product factor, Sylow
737C22—24no—
738C22—24no—
739C22—24no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22C2×C7×#11711yescharacteristic
753C22C2×C4×C7×D411yescharacteristic
754C22C2×C4×C7×D411yescharacteristic
755C22C2×C4×C7×Q811yescharacteristic
756C22C4×C7×#4111yescharacteristic
757C22C7×#51811yescharacteristic
758C22C7×#52011yescharacteristic
759C22C2×C7×#12111yescharacteristic
760C22C2×C7×C22⋊Q811yescharacteristic
761C22C2×C7×#12311yescharacteristic
762C22C7×#52511yescharacteristic
763C22C2×C7×#12411yescharacteristic
764C22C2×C7×#12611yescharacteristic
765C22C7×#52911yescharacteristic
766C22C7×#53311yescharacteristic
767C22C7×#53511yescharacteristic
768C22C7×#53711yescharacteristic
769C22C7×#54011yescharacteristic
770C22C7×#54211yescharacteristic
771C22C7×#54611yescharacteristic
772C22C7×#54611yescharacteristic
773C22C7×D4×Q811yescharacteristic
774C22C7×#55011yescharacteristic
775C22C7×#55211yescharacteristic
776C22C7×#55211yescharacteristic
777C22C7×#55211yescharacteristic
778C22C7×#55311yescharacteristic
779C22C7×#55311yescharacteristic
780C22C7×#55311yescharacteristic
781C22C7×#55411yescharacteristic
782C22C7×#55411yescharacteristic
783C22C7×#55411yescharacteristic
784C22C7×#55511yescharacteristic
785C22C7×#55511yescharacteristic
786C22C7×#55511yescharacteristic
787C4—24no—
788C4—42no—
789C4—44no—
790C4—42no—
791C4—42no—
792C4—42no—
793C4—44no—
794C4—44no—
795C4—82no—
796C4C7×#38818yes—
797C2—44no—
798C2C2×C7×#38811yescharacteristic
799C2C4×C7×C22⋊Q811yescharacteristic
800C2C7×#232411yescharacteristic
801C2C7×#234511yescharacteristic
802C2C7×#234611yescharacteristic
803C2C7×#236011yescharacteristic
804C2C7×#236311yescharacteristic
805C2C7×#241411yescharacteristic
806C2C7×#241711yescharacteristic
807C2C7×#242011yescharacteristic
808C2C7×#242311yescharacteristic
809C2C7×#249511yescharacteristic
810C2C7×#249711yescharacteristic
811C2C7×#256211yescharacteristic
812C2C7×#256311yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC25×C7C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C7×#389C2semidirect
4. C2×C4×C7×C4⋊C4C2semidirect
6. C7×#1442C2semidirect
9. C7×C4⋊#95C2semidirect
10. C7×C4⋊#95C2semidirect
11. C7×#1434C2semidirect
27. C7×#380C4semidirect
40. #13973C7direct (N × H)
105. C2×#389C2×C7semidirect
108. C2×C4×C4⋊C4C2×C7semidirect
110. #1442C2×C7semidirect
113. C4⋊#95C2×C7semidirect
114. C4⋊#95C2×C7semidirect
115. #1434C2×C7semidirect
236. #380C4×C7semidirect
736. C7#13973direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3892
C2×C7×#3802
C2×C4×C7×C4⋊C42
C2×C4×C7×C22⋊C42
C7×#14422
C7×#14392
C7×#14372
C7×C4⋊#952
C7×#14342
#139737