Finite Group Databasebeta

← C7×#13875 #13191091

Subgroups — C7×#13875 #13191091

Order 1792.

1702 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#382C211yesmaximal, characteristic, complemented
2C2×C7×#380C211yesmaximal, characteristic
3C2×C7×#380C211yesmaximal, characteristic
4C2×C4×C7×C4⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
6C7×#1443C212yesmaximal, complemented
7C7×#1440C212yesmaximal
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×C22⋊C4C2212yes—
18C22×C7×C22⋊C4C2212yes—
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C42×C7C2212yes—
22C22×C42×C7C2211yescharacteristic
23C22×C42×C7C2211yescharacteristic
24C7×#382—24no—
25C7×#380—24no—
26C7×#380—24no—
27C4×C7×C4⋊C4—24no—
28C4×C7×C22⋊C4C418yescomplemented
29C2×C7×#95C2212yes—
30C2×C7×#95C2212yes—
31C2×C7×#95C2212yes—
32C2×C7×#95C2212yes—
33C2×C7×#95C2212yes—
34C2×C7×#95C2212yes—
35C2×C7×#95C2212yes—
36C2×C7×#95C2212yes—
37C2×C7×#95C2212yes—
38C2×C7×#95C2211yescharacteristic
39C2×C7×#95C2211yescharacteristic
40#13875C711yesmaximal, 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×C7C2311yescharacteristic
53C23×C4×C7C2311yescharacteristic
54C23×C4×C7C2311yescharacteristic
55C23×C4×C7C2312yes—
56C23×C4×C7C2312yes—
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—22no—
67C2×C7×C4⋊C4—22no—
68C2×C7×C4⋊C4—22no—
69C2×C7×C4⋊C4D414yes—
70C2×C7×C4⋊C4D414yes—
71C2×C7×C22⋊C4—22no—
72C2×C7×C22⋊C4—22no—
73C2×C7×C22⋊C4—22no—
74C2×C7×C22⋊C4—22no—
75C2×C7×C22⋊C4—24no—
76C2×C7×C22⋊C4—24no—
77C2×C7×C22⋊C4—24no—
78C2×C7×C22⋊C4—24no—
79C2×C7×C22⋊C4—42no—
80C2×C7×C22⋊C4—42no—
81C2×C7×C22⋊C4C2×C414yes—
82C2×C7×C22⋊C4C2×C414yes—
83C2×C42×C7—22no—
84C2×C42×C7—22no—
85C2×C42×C7—22no—
86C2×C42×C7—22no—
87C2×C42×C7—24no—
88C2×C42×C7—24no—
89C2×C42×C7—42no—
90C2×C42×C7C2×C414yes—
91C2×C42×C7C2×C414yes—
92C7×#95—24no—
93C7×#95—24no—
94C7×#95—24no—
95C7×#95—24no—
96C7×#95—24no—
97C7×#95—24no—
98C7×#95—42no—
99C7×#95—42no—
100C7×#95—42no—
101C7×#95C2×C414yes—
102C7×#95C2×C414yes—
103C2×#382C2×C711yescharacteristic, complemented
104C2×#380C2×C711yescharacteristic
105C2×#380C2×C711yescharacteristic
106C2×C4×C4⋊C4C2×C711yescharacteristic, complemented
107C2×C4×C22⋊C4C2×C711yescharacteristic
108#1443C2×C712yescomplemented
109#1440C2×C712yes—
110#1437C2×C712yes—
111C4⋊#95C2×C711yescharacteristic, complemented
112C4⋊#95C2×C711yescharacteristic, complemented
113#1434C2×C712yescomplemented
114C24×C7—21no—
115C24×C7—21no—
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×C7C22×C412yes—
127C24×C7#4112yes—
128C24×C7#4112yes—
129C24×C7C2411yescharacteristic
130C22×C4×C7—21no—
131C22×C4×C7—21no—
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—22no—
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
145C22×C4×C7—21no—
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—22no—
154C22×C4×C7—22no—
155C22×C4×C7—22no—
156C22×C4×C7—21no—
157C22×C4×C7—21no—
158C22×C4×C7—21no—
159C22×C4×C7—21no—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—22no—
164C22×C4×C7—22no—
165C22×C4×C7—22no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—22no—
170C22×C4×C7—28no—
171C22×C4×C7—28no—
172C22×C4×C7—28no—
173C22×C4×C7—22no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
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—44no—
188C22×C4×C7—44no—
189C22×C4×C7—44no—
190C22×C4×C7—44no—
191C22×C4×C7C22×C412yes—
192C22×C4×C7C22×C412yes—
193C22×C4×C7C22×C412yes—
194C22×C4×C7C22×C412yes—
195C22×C4×C7C22×C412yes—
196C22×C4×C7C22×C412yes—
197C22×C4×C7C2×D414yes—
198C22×C4×C7C2×D414yes—
199C22×C4×C7C2×D412yes—
200C22×C4×C7C2×D412yes—
201C22×C4×C7#4112yes—
202C22×C4×C7#4112yes—
203C22×C4×C7#4112yes—
204C22×C4×C7#4112yes—
205C22×C4×C7#4112yes—
206C22×C4×C7#4112yes—
207C7×C4⋊C4—28no—
208C7×C4⋊C4—28no—
209C7×C4⋊C4—44no—
210C7×C4⋊C4—44no—
211C7×C22⋊C4—28no—
212C7×C22⋊C4—28no—
213C7×C22⋊C4—48no—
214C7×C22⋊C4—48no—
215C42×C7—28no—
216C42×C7—28no—
217C42×C7—48no—
218C24×C4C22×C711yescharacteristic
219C22×C4⋊C4C22×C711yescharacteristic
220C22×C4⋊C4C22×C711yescharacteristic
221C22×C4⋊C4C22×C711yescharacteristic
222C22×C4⋊C4C22×C711yescharacteristic
223C22×C22⋊C4C22×C712yes—
224C22×C22⋊C4C22×C712yes—
225C22×C22⋊C4C22×C711yescharacteristic
226C22×C22⋊C4C22×C711yescharacteristic
227C22×C42C22×C712yes—
228C22×C42C22×C711yescharacteristic
229C22×C42C22×C711yescharacteristic
230#382—24no—
231#380—24no—
232#380—24no—
233C4×C4⋊C4—24no—
234C4×C22⋊C4C4×C718yescomplemented
235C2×#95C22×C712yes—
236C2×#95C22×C712yes—
237C2×#95C22×C712yes—
238C2×#95C22×C712yes—
239C2×#95C22×C712yes—
240C2×#95C22×C712yes—
241C2×#95C22×C712yes—
242C2×#95C22×C712yes—
243C2×#95C22×C712yes—
244C2×#95C22×C711yescharacteristic
245C2×#95C22×C711yescharacteristic
246C23×C7—22no—
247C23×C7—22no—
248C23×C7—22no—
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—41no—
265C23×C7—41no—
266C23×C7—41no—
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#11714yes—
281C23×C7C23×C411yescharacteristic
282C23×C7C22×D411yescharacteristic
283C23×C7C22×D411yescharacteristic
284C23×C7C2×#4111yescharacteristic
285C23×C7C2×#4111yescharacteristic
286C23×C7C2×#4111yescharacteristic
287C23×C7C2×#4111yescharacteristic
288C23×C7C2×#4111yescharacteristic
289C23×C7C2×#4111yescharacteristic
290C23×C7C2×#4111yescharacteristic
291C23×C7C2×#4111yescharacteristic
292C23×C7H(5,𝔽2)11yescharacteristic
293C23×C7H(5,𝔽2)11yescharacteristic
294C23×C72−1+411yescharacteristic
295C23×C72−1+411yescharacteristic
296C2×C4×C7—22no—
297C2×C4×C7—22no—
298C2×C4×C7—22no—
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—22no—
307C2×C4×C7—22no—
308C2×C4×C7—22no—
309C2×C4×C7—22no—
310C2×C4×C7—22no—
311C2×C4×C7—22no—
312C2×C4×C7—22no—
313C2×C4×C7—22no—
314C2×C4×C7—24no—
315C2×C4×C7—24no—
316C2×C4×C7—24no—
317C2×C4×C7—24no—
318C2×C4×C7—24no—
319C2×C4×C7—24no—
320C2×C4×C7—41no—
321C2×C4×C7—41no—
322C2×C4×C7—41no—
323C2×C4×C7—41no—
324C2×C4×C7—42no—
325C2×C4×C7—42no—
326C2×C4×C7—42no—
327C2×C4×C7—42no—
328C2×C4×C7—42no—
329C2×C4×C7—41no—
330C2×C4×C7—41no—
331C2×C4×C7—41no—
332C2×C4×C7—41no—
333C2×C4×C7—41no—
334C2×C4×C7—42no—
335C2×C4×C7—41no—
336C2×C4×C7—41no—
337C2×C4×C7—41no—
338C2×C4×C7—41no—
339C2×C4×C7—41no—
340C2×C4×C7—42no—
341C2×C4×C7—41no—
342C2×C4×C7—42no—
343C2×C4×C7—41no—
344C2×C4×C7—416no—
345C2×C4×C7—42no—
346C2×C4×C7—42no—
347C2×C4×C7—42no—
348C2×C4×C7—42no—
349C2×C4×C7—42no—
350C2×C4×C7—42no—
351C2×C4×C7—42no—
352C2×C4×C7—42no—
353C2×C4×C7—42no—
354C2×C4×C7—42no—
355C2×C4×C7—42no—
356C2×C4×C7—42no—
357C2×C4×C7—42no—
358C2×C4×C7—42no—
359C2×C4×C7#11714yes—
360C2×C4×C7#11714yes—
361C2×C4×C7C4×D414yes—
362C2×C4×C7C4×D414yes—
363C2×C4×C7#12114yes—
364C2×C4×C7#12314yes—
365C2×C4×C7#12414yes—
366C2×C4×C7#12614yes—
367C25C23×C711yescharacteristic
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4C2×C4×C714yes—
375C23×C4C23×C712yes—
376C23×C4C23×C712yes—
377C23×C4C23×C711yescharacteristic
378C23×C4C23×C711yescharacteristic
379C23×C4C23×C711yescharacteristic
380C23×C4C23×C711yescharacteristic
381C23×C4C23×C712yes—
382C23×C4C23×C712yes—
383C23×C4C23×C711yescharacteristic
384C23×C4C23×C711yescharacteristic
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
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⋊C4C7×D414yes—
396C2×C4⋊C4C7×D414yes—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4C2×C4×C714yes—
408C2×C22⋊C4C2×C4×C714yes—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—24no—
414C2×C42—24no—
415C2×C42—42no—
416C2×C42C2×C4×C714yes—
417C2×C42C2×C4×C714yes—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—42no—
425#95—42no—
426#95—42no—
427#95C2×C4×C714yes—
428#95C2×C4×C714yes—
429C22×C7—24no—
430C22×C7—24no—
431C22×C7—24no—
432C22×C7—42no—
433C22×C7—42no—
434C22×C7—42no—
435C22×C7—42no—
436C22×C7—42no—
437C22×C7—42no—
438C22×C7—42no—
439C22×C7—42no—
440C22×C7—42no—
441C22×C7—42no—
442C22×C7—42no—
443C22×C7—42no—
444C22×C7C2×#11711yescharacteristic
445C22×C7C2×#11711yescharacteristic
446C22×C7C2×#11711yescharacteristic
447C22×C7C2×C4×D411yescharacteristic
448C22×C7C2×C4×D411yescharacteristic
449C22×C7#52011yescharacteristic
450C22×C7#52011yescharacteristic
451C22×C7C2×#12111yescharacteristic
452C22×C7C2×#12311yescharacteristic
453C22×C7C2×#12411yescharacteristic
454C22×C7C2×#12611yescharacteristic
455C22×C7#52911yescharacteristic
456C22×C7#52911yescharacteristic
457C22×C7#52911yescharacteristic
458C22×C7#52911yescharacteristic
459C22×C7#54011yescharacteristic
460C22×C7#54111yescharacteristic
461C22×C7#54211yescharacteristic
462C22×C7#54211yescharacteristic
463C22×C7#54611yescharacteristic
464C22×C7#54611yescharacteristic
465C22×C7#54611yescharacteristic
466C22×C7#54711yescharacteristic
467C22×C7#54811yescharacteristic
468C22×C7#54811yescharacteristic
469C22×C7#54811yescharacteristic
470C22×C7#55011yescharacteristic
471C22×C7#55211yescharacteristic
472C22×C7#55211yescharacteristic
473C22×C7#55211yescharacteristic
474C22×C7#55311yescharacteristic
475C22×C7#55311yescharacteristic
476C22×C7#55311yescharacteristic
477C22×C7#55511yescharacteristic
478C22×C7#55611yescharacteristic
479C4×C7—24no—
480C4×C7—42no—
481C4×C7—42no—
482C4×C7—42no—
483C4×C7—44no—
484C4×C7—44no—
485C4×C7—42no—
486C4×C7—82no—
487C4×C7—82no—
488C4×C7#38818yes—
489C24—21no—
490C24—21no—
491C24—21no—
492C24—21no—
493C24—21no—
494C24—21no—
495C24—21no—
496C24—21no—
497C24—21no—
498C24—21no—
499C24—21no—
500C24—21no—
501C24C22×C4×C712yes—
502C24C7×#4112yes—
503C24C7×#4112yes—
504C24C24×C711yescharacteristic
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—28no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4C22×C4×C712yes—
567C22×C4C22×C4×C712yes—
568C22×C4C22×C4×C712yes—
569C22×C4C22×C4×C712yes—
570C22×C4C22×C4×C712yes—
571C22×C4C22×C4×C712yes—
572C22×C4C2×C7×D414yes—
573C22×C4C2×C7×D414yes—
574C22×C4C2×C7×D412yes—
575C22×C4C2×C7×D412yes—
576C22×C4C7×#4112yes—
577C22×C4C7×#4112yes—
578C22×C4C7×#4112yes—
579C22×C4C7×#4112yes—
580C22×C4C7×#4112yes—
581C22×C4C7×#4112yes—
582C4⋊C4—28no—
583C4⋊C4—28no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C22⋊C4—28no—
587C22⋊C4—28no—
588C22⋊C4—48no—
589C22⋊C4—48no—
590C42—28no—
591C42—28no—
592C42—48no—
593C2×C7—44no—
594C2×C7#228311yescharacteristic
595C2×C7C2×#38811yescharacteristic
596C2×C7#231411yescharacteristic
597C2×C7#235211yescharacteristic
598C2×C7#235211yescharacteristic
599C2×C7#235211yescharacteristic
600C2×C7#235411yescharacteristic
601C2×C7#242011yescharacteristic
602C2×C7#242111yescharacteristic
603C2×C7#242611yescharacteristic
604C2×C7#242711yescharacteristic
605C2×C7#248911yescharacteristic
606C2×C7#249011yescharacteristic
607C2×C7#249411yescharacteristic
608C2×C7#249511yescharacteristic
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
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—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23C7×#11714yes—
644C23C23×C4×C711yescharacteristic
645C23C22×C7×D411yescharacteristic
646C23C22×C7×D411yescharacteristic
647C23C2×C7×#4111yescharacteristic
648C23C2×C7×#4111yescharacteristic
649C23C2×C7×#4111yescharacteristic
650C23C2×C7×#4111yescharacteristic
651C23C2×C7×#4111yescharacteristic
652C23C2×C7×#4111yescharacteristic
653C23C2×C7×#4111yescharacteristic
654C23C2×C7×#4111yescharacteristic
655C23C7×H(5,𝔽2)11yescharacteristic
656C23C7×H(5,𝔽2)11yescharacteristic
657C23C7×2−1+411yescharacteristic
658C23C7×2−1+411yescharacteristic
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—416no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4C7×#11714yes—
723C2×C4C7×#11714yes—
724C2×C4C4×C7×D414yes—
725C2×C4C4×C7×D414yes—
726C2×C4C7×#12114yes—
727C2×C4C7×#12314yes—
728C2×C4C7×#12414yes—
729C2×C4C7×#12614yes—
730C7#1387511yescharacteristic, direct product factor, Sylow
731C22—24no—
732C22—24no—
733C22—24no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22C2×C7×#11711yescharacteristic
747C22C2×C7×#11711yescharacteristic
748C22C2×C7×#11711yescharacteristic
749C22C2×C4×C7×D411yescharacteristic
750C22C2×C4×C7×D411yescharacteristic
751C22C7×#52011yescharacteristic
752C22C7×#52011yescharacteristic
753C22C2×C7×#12111yescharacteristic
754C22C2×C7×#12311yescharacteristic
755C22C2×C7×#12411yescharacteristic
756C22C2×C7×#12611yescharacteristic
757C22C7×#52911yescharacteristic
758C22C7×#52911yescharacteristic
759C22C7×#52911yescharacteristic
760C22C7×#52911yescharacteristic
761C22C7×#54011yescharacteristic
762C22C7×#54111yescharacteristic
763C22C7×#54211yescharacteristic
764C22C7×#54211yescharacteristic
765C22C7×#54611yescharacteristic
766C22C7×#54611yescharacteristic
767C22C7×#54611yescharacteristic
768C22C7×#54711yescharacteristic
769C22C7×#54811yescharacteristic
770C22C7×#54811yescharacteristic
771C22C7×#54811yescharacteristic
772C22C7×#55011yescharacteristic
773C22C7×#55211yescharacteristic
774C22C7×#55211yescharacteristic
775C22C7×#55211yescharacteristic
776C22C7×#55311yescharacteristic
777C22C7×#55311yescharacteristic
778C22C7×#55311yescharacteristic
779C22C7×#55511yescharacteristic
780C22C7×#55611yescharacteristic
781C4—24no—
782C4—44no—
783C4—44no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—42no—
788C4—82no—
789C4—82no—
790C4C7×#38818yes—
791C2—44no—
792C2C7×#228311yescharacteristic
793C2C2×C7×#38811yescharacteristic
794C2C7×#231411yescharacteristic
795C2C7×#235211yescharacteristic
796C2C7×#235211yescharacteristic
797C2C7×#235211yescharacteristic
798C2C7×#235411yescharacteristic
799C2C7×#242011yescharacteristic
800C2C7×#242111yescharacteristic
801C2C7×#242611yescharacteristic
802C2C7×#242711yescharacteristic
803C2C7×#248911yescharacteristic
804C2C7×#249011yescharacteristic
805C2C7×#249411yescharacteristic
806C2C7×#249511yescharacteristic
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×#382C2semidirect
4. C2×C4×C7×C4⋊C4C2semidirect
6. C7×#1443C2semidirect
9. C7×C4⋊#95C2semidirect
10. C7×C4⋊#95C2semidirect
11. C7×#1434C2semidirect
28. C4×C7×C22⋊C4C4semidirect
40. #13875C7direct (N × H)
103. C2×#382C2×C7semidirect
106. C2×C4×C4⋊C4C2×C7semidirect
108. #1443C2×C7semidirect
111. C4⋊#95C2×C7semidirect
112. C4⋊#95C2×C7semidirect
113. #1434C2×C7semidirect
234. C4×C22⋊C4C4×C7semidirect
730. C7#13875direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3822
C2×C7×#3802
C2×C4×C7×C4⋊C42
C2×C4×C7×C22⋊C42
C7×#14432
C7×#14402
C7×#14372
C7×C4⋊#952
C7×#14342
#138757