Finite Group Databasebeta

← C7×#14621 #13191837

Subgroups — C7×#14621 #13191837

Order 1792.

2018 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#392C211yesmaximal, characteristic
2C2×C7×#386C212yesmaximal, complemented
3C7×#1443C212yesmaximal, complemented
4C7×#1440C212yesmaximal, complemented
5C7×#1439C212yesmaximal, complemented
6C7×#1439C211yesmaximal, characteristic, complemented
7C7×#1438C212yesmaximal, complemented
8C7×#1438C212yesmaximal, complemented
9C7×C22⋊#95C211yesmaximal, characteristic, complemented
10C23×C7×D4C2212yes—
11C23×C7×D4C2211yescharacteristic
12C24×C4×C7C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C22⋊C4C2212yes—
15C22×C7×C22⋊C4C2212yes—
16C22×C7×C22⋊C4C2212yes—
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2212yes—
19C22×C7×C22⋊C4C2212yes—
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2212yes—
22C7×#392C418yescomplemented
23C7×#386—28no—
24C2×C7×#95C2212yes—
25C2×C7×#95C2212yes—
26C2×C7×#95C2212yes—
27C2×C7×#95C2212yes—
28C2×C7×#95C2212yes—
29C2×C7×#95C2212yes—
30C2×C7×#95C2212yes—
31C2×C7×#95C2211yescharacteristic
32C2×C7×#95C2211yescharacteristic
33#14621C711yesmaximal, characteristic, direct product factor, Sylow
34C25×C7C2312yes—
35C25×C7C2311yescharacteristic
36C22×C7×D4—24no—
37C22×C7×D4—24no—
38C22×C7×D4—42no—
39C22×C7×D4—42no—
40C22×C7×D4—42no—
41C22×C7×D4—42no—
42C22×C7×D4—42no—
43C22×C7×D4—42no—
44C22×C7×D4—41no—
45C22×C7×D4—41no—
46C22×C7×D4C2×C418yes—
47C22×C7×D4C2×C414yescomplemented
48C23×C4×C7—42no—
49C23×C4×C7—42no—
50C23×C4×C7—41no—
51C23×C4×C7—41no—
52C23×C4×C7D414yescomplemented
53C23×C4×C7C2312yes—
54C23×C4×C7C2312yes—
55C23×C4×C7C2312yes—
56C23×C4×C7C2312yes—
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2312yes—
60C2×C7×C4⋊C4—41no—
61C2×C7×C4⋊C4—42no—
62C2×C7×C22⋊C4—24no—
63C2×C7×C22⋊C4—22no—
64C2×C7×C22⋊C4—24no—
65C2×C7×C22⋊C4—24no—
66C2×C7×C22⋊C4—41no—
67C2×C7×C22⋊C4—41no—
68C2×C7×C22⋊C4—42no—
69C2×C7×C22⋊C4—42no—
70C2×C7×C22⋊C4—42no—
71C2×C7×C22⋊C4—42no—
72C2×C7×C22⋊C4—42no—
73C2×C7×C22⋊C4—42no—
74C2×C7×C22⋊C4—42no—
75C2×C7×C22⋊C4—41no—
76C2×C7×C22⋊C4—41no—
77C2×C7×C22⋊C4—42no—
78C2×C7×C22⋊C4—42no—
79C2×C7×C22⋊C4—42no—
80C2×C7×C22⋊C4—42no—
81C2×C7×C22⋊C4—42no—
82C2×C7×C22⋊C4—42no—
83C2×C7×C22⋊C4—42no—
84C2×C7×C22⋊C4C2×C414yes—
85C2×C7×C22⋊C4C2×C418yescomplemented
86C7×#95—24no—
87C7×#95—24no—
88C7×#95—42no—
89C7×#95—41no—
90C7×#95—42no—
91C7×#95—42no—
92C7×#95—42no—
93C7×#95—42no—
94C7×#95C2×C414yescomplemented
95C2×#392C2×C711yescharacteristic
96C2×#386C2×C712yescomplemented
97#1443C2×C712yescomplemented
98#1440C2×C712yescomplemented
99#1439C2×C711yescharacteristic, complemented
100#1439C2×C712yescomplemented
101#1438C2×C712yescomplemented
102#1438C2×C712yescomplemented
103C22⋊#95C2×C711yescharacteristic, complemented
104C24×C7—21no—
105C24×C7—21no—
106C24×C7—21no—
107C24×C7—22no—
108C24×C7—22no—
109C24×C7—22no—
110C24×C7—22no—
111C24×C7—21no—
112C24×C7—22no—
113C24×C7—22no—
114C24×C7—22no—
115C24×C7—22no—
116C24×C7—22no—
117C24×C7—22no—
118C24×C7—22no—
119C24×C7—22no—
120C24×C7—22no—
121C24×C7—22no—
122C24×C7—22no—
123C24×C7—22no—
124C24×C7—22no—
125C24×C7—22no—
126C24×C7C22×C414yes—
127C24×C7C22×C412yes—
128C24×C7C2×D412yes—
129C24×C7#4112yes—
130C24×C7C2411yescharacteristic
131C2×C7×D4—216no—
132C2×C7×D4—48no—
133C2×C7×D4—48no—
134C2×C7×D4—44no—
135C2×C7×D4—48no—
136C2×C7×D4—48no—
137C2×C7×D4—48no—
138C2×C7×D4—48no—
139C2×C7×D4—48no—
140C2×C7×D4—48no—
141C2×C7×D4—44no—
142C2×C7×D4—44no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
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—21no—
154C22×C4×C7—22no—
155C22×C4×C7—22no—
156C22×C4×C7—22no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—22no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—22no—
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—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—44no—
185C22×C4×C7—48no—
186C22×C4×C7—48no—
187C22×C4×C7—44no—
188C22×C4×C7—44no—
189C22×C4×C7C22×C412yes—
190C22×C4×C7C22×C414yes—
191C22×C4×C7C22×C412yes—
192C22×C4×C7C2×D414yes—
193C7×C4⋊C4—44no—
194C7×C22⋊C4—44no—
195C7×C22⋊C4—48no—
196C7×C22⋊C4—48no—
197C7×C22⋊C4—48no—
198C7×C22⋊C4—48no—
199C7×C22⋊C4—44no—
200C7×C22⋊C4—48no—
201C7×C22⋊C4—48no—
202C23×D4C22×C712yes—
203C23×D4C22×C711yescharacteristic
204C24×C4C22×C711yescharacteristic
205C22×C4⋊C4C22×C711yescharacteristic
206C22×C22⋊C4C22×C711yescharacteristic
207C22×C22⋊C4C22×C712yes—
208C22×C22⋊C4C22×C712yes—
209C22×C22⋊C4C22×C712yes—
210C22×C22⋊C4C22×C712yes—
211C22×C22⋊C4C22×C712yes—
212C22×C22⋊C4C22×C711yescharacteristic
213C22×C22⋊C4C22×C712yes—
214#392C4×C718yescomplemented
215#386—28no—
216C2×#95C22×C712yes—
217C2×#95C22×C712yes—
218C2×#95C22×C712yes—
219C2×#95C22×C712yes—
220C2×#95C22×C712yes—
221C2×#95C22×C712yes—
222C2×#95C22×C712yes—
223C2×#95C22×C711yescharacteristic
224C2×#95C22×C711yescharacteristic
225C23×C7—22no—
226C23×C7—24no—
227C23×C7—24no—
228C23×C7—22no—
229C23×C7—24no—
230C23×C7—22no—
231C23×C7—24no—
232C23×C7—22no—
233C23×C7—22no—
234C23×C7—24no—
235C23×C7—24no—
236C23×C7—22no—
237C23×C7—24no—
238C23×C7—24no—
239C23×C7—24no—
240C23×C7—24no—
241C23×C7—24no—
242C23×C7—24no—
243C23×C7—24no—
244C23×C7—42no—
245C23×C7—41no—
246C23×C7—41no—
247C23×C7—42no—
248C23×C7—42no—
249C23×C7—42no—
250C23×C7—41no—
251C23×C7—41no—
252C23×C7—42no—
253C23×C7—42no—
254C23×C7—42no—
255C23×C7—42no—
256C23×C7—42no—
257C23×C7—42no—
258C23×C7—42no—
259C23×C7—42no—
260C23×C7—42no—
261C23×C7—42no—
262C23×C7—42no—
263C23×C7—42no—
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×C7—42no—
281C23×C7—42no—
282C23×C7C4×D414yes—
283C23×C7C23×C411yescharacteristic
284C23×C7C22×D411yescharacteristic
285C23×C7C2×#4111yescharacteristic
286C23×C7H(5,𝔽2)12yes—
287C23×C7H(5,𝔽2)12yes—
288C23×C7H(5,𝔽2)11yescharacteristic
289C23×C7H(5,𝔽2)12yes—
290C23×C7H(5,𝔽2)12yes—
291C23×C7H(5,𝔽2)11yescharacteristic
292C23×C7H(5,𝔽2)11yescharacteristic
293C23×C72−1+411yescharacteristic
294C7×D4—432no—
295C7×D4—416no—
296C2×C4×C7—24no—
297C2×C4×C7—24no—
298C2×C4×C7—22no—
299C2×C4×C7—24no—
300C2×C4×C7—22no—
301C2×C4×C7—24no—
302C2×C4×C7—24no—
303C2×C4×C7—24no—
304C2×C4×C7—24no—
305C2×C4×C7—24no—
306C2×C4×C7—416no—
307C2×C4×C7—42no—
308C2×C4×C7—42no—
309C2×C4×C7—42no—
310C2×C4×C7—42no—
311C2×C4×C7—41no—
312C2×C4×C7—42no—
313C2×C4×C7—41no—
314C2×C4×C7—42no—
315C2×C4×C7—42no—
316C2×C4×C7—42no—
317C2×C4×C7—42no—
318C2×C4×C7—41no—
319C2×C4×C7—42no—
320C2×C4×C7—41no—
321C2×C4×C7—42no—
322C2×C4×C7—42no—
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—42no—
331C2×C4×C7—42no—
332C2×C4×C7—42no—
333C2×C4×C7—42no—
334C2×C4×C7—42no—
335C2×C4×C7—42no—
336C2×C4×C7—42no—
337C2×C4×C7—42no—
338C2×C4×C7—42no—
339C2×C4×C7—42no—
340C2×C4×C7—42no—
341C2×C4×C7—42no—
342C25C23×C712yes—
343C25C23×C711yescharacteristic
344C22×D4—24no—
345C22×D4—24no—
346C22×D4—42no—
347C22×D4—42no—
348C22×D4—42no—
349C22×D4—42no—
350C22×D4—42no—
351C22×D4—42no—
352C22×D4—41no—
353C22×D4—41no—
354C22×D4C2×C4×C718yes—
355C22×D4C2×C4×C714yescomplemented
356C23×C4—42no—
357C23×C4—42no—
358C23×C4—41no—
359C23×C4—41no—
360C23×C4C7×D414yescomplemented
361C23×C4C23×C712yes—
362C23×C4C23×C712yes—
363C23×C4C23×C712yes—
364C23×C4C23×C711yescharacteristic
365C23×C4C23×C712yes—
366C23×C4C23×C711yescharacteristic
367C23×C4C23×C712yes—
368C2×C4⋊C4—41no—
369C2×C4⋊C4—42no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—41no—
375C2×C22⋊C4—41no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—41no—
384C2×C22⋊C4—41no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4C2×C4×C714yes—
393C2×C22⋊C4C2×C4×C718yescomplemented
394#95—24no—
395#95—24no—
396#95—42no—
397#95—41no—
398#95—42no—
399#95—42no—
400#95—42no—
401#95—42no—
402#95C2×C4×C714yescomplemented
403C22×C7—28no—
404C22×C7—24no—
405C22×C7—42no—
406C22×C7—44no—
407C22×C7—42no—
408C22×C7—42no—
409C22×C7—44no—
410C22×C7—42no—
411C22×C7—42no—
412C22×C7—44no—
413C22×C7—42no—
414C22×C7—44no—
415C22×C7—44no—
416C22×C7—44no—
417C22×C7—44no—
418C22×C7—44no—
419C22×C7—44no—
420C22×C7—44no—
421C22×C7—82no—
422C22×C7—82no—
423C22×C7—82no—
424C22×C7—82no—
425C22×C7—82no—
426C22×C7—82no—
427C22×C7—82no—
428C22×C7—82no—
429C22×C7C2×C4×D411yescharacteristic
430C22×C7#51812yes—
431C22×C7#51812yes—
432C22×C7#51811yescharacteristic
433C22×C7#52011yescharacteristic
434C22×C7#53412yes—
435C22×C7#53411yescharacteristic
436C22×C7#53512yes—
437C22×C7#53711yescharacteristic
438C22×C7#53812yes—
439C22×C7#53811yescharacteristic
440C22×C7#53812yes—
441C22×C7#53911yescharacteristic
442C22×C7#56011yescharacteristic
443C22×C7#56012yes—
444C22×C7#56012yes—
445C22×C7#56012yes—
446C22×C7#56012yes—
447C22×C7#56011yescharacteristic
448C22×C7#56011yescharacteristic
449C22×C7H(3,𝔽4)11yescharacteristic
450C22×C7#56212yes—
451C22×C7#56212yes—
452C4×C7—44no—
453C4×C7—42no—
454C4×C7—42no—
455C4×C7—44no—
456C4×C7—82no—
457C4×C7—82no—
458C4×C7—82no—
459C24—21no—
460C24—21no—
461C24—21no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—21no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24C22×C4×C714yes—
482C24C22×C4×C712yes—
483C24C2×C7×D412yes—
484C24C7×#4112yes—
485C24C24×C711yescharacteristic
486C2×D4—216no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—44no—
490C2×D4—48no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4—48no—
494C2×D4—48no—
495C2×D4—48no—
496C2×D4—44no—
497C2×D4—44no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—44no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4C22×C4×C712yes—
545C22×C4C22×C4×C714yes—
546C22×C4C22×C4×C712yes—
547C22×C4C2×C7×D414yes—
548C4⋊C4—44no—
549C22⋊C4—44no—
550C22⋊C4—48no—
551C22⋊C4—48no—
552C22⋊C4—48no—
553C22⋊C4—48no—
554C22⋊C4—44no—
555C22⋊C4—48no—
556C22⋊C4—48no—
557C2×C7—44no—
558C2×C7—84no—
559C2×C7#232112yes—
560C2×C7#232511yescharacteristic
561C2×C7#237511yescharacteristic
562C2×C7#237712yes—
563C2×C7#238011yescharacteristic
564C2×C7#281211yescharacteristic
565C2×C7#281312yes—
566C2×C7#281511yescharacteristic
567C2×C7#282411yescharacteristic
568C2×C7#282512yes—
569C2×C7#282611yescharacteristic
570C23—22no—
571C23—24no—
572C23—24no—
573C23—22no—
574C23—24no—
575C23—22no—
576C23—24no—
577C23—22no—
578C23—22no—
579C23—24no—
580C23—24no—
581C23—22no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—42no—
590C23—41no—
591C23—42no—
592C23—42no—
593C23—41no—
594C23—42no—
595C23—41no—
596C23—41no—
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—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23C4×C7×D414yes—
628C23C23×C4×C711yescharacteristic
629C23C22×C7×D411yescharacteristic
630C23C2×C7×#4111yescharacteristic
631C23C7×H(5,𝔽2)12yes—
632C23C7×H(5,𝔽2)12yes—
633C23C7×H(5,𝔽2)11yescharacteristic
634C23C7×H(5,𝔽2)12yes—
635C23C7×H(5,𝔽2)12yes—
636C23C7×H(5,𝔽2)11yescharacteristic
637C23C7×H(5,𝔽2)11yescharacteristic
638C23C7×2−1+411yescharacteristic
639D4—432no—
640D4—416no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—22no—
644C2×C4—24no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—416no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—41no—
664C2×C4—42no—
665C2×C4—41no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C7#1462111yescharacteristic, direct product factor, Sylow
688C22—28no—
689C22—24no—
690C22—42no—
691C22—44no—
692C22—42no—
693C22—42no—
694C22—44no—
695C22—42no—
696C22—42no—
697C22—44no—
698C22—42no—
699C22—44no—
700C22—44no—
701C22—44no—
702C22—44no—
703C22—44no—
704C22—44no—
705C22—44no—
706C22—82no—
707C22—82no—
708C22—82no—
709C22—82no—
710C22—82no—
711C22—82no—
712C22—82no—
713C22—82no—
714C22C2×C4×C7×D411yescharacteristic
715C22C7×#51812yes—
716C22C7×#51812yes—
717C22C7×#51811yescharacteristic
718C22C7×#52011yescharacteristic
719C22C7×#53412yes—
720C22C7×#53411yescharacteristic
721C22C7×#53512yes—
722C22C7×#53711yescharacteristic
723C22C7×#53812yes—
724C22C7×#53811yescharacteristic
725C22C7×#53812yes—
726C22C7×#53911yescharacteristic
727C22C7×#56012yes—
728C22C7×#56011yescharacteristic
729C22C7×#56012yes—
730C22C7×#56012yes—
731C22C7×#56011yescharacteristic
732C22C7×#56012yes—
733C22C7×#56011yescharacteristic
734C22C7×H(3,𝔽4)11yescharacteristic
735C22C7×#56212yes—
736C22C7×#56212yes—
737C4—44no—
738C4—44no—
739C4—42no—
740C4—42no—
741C4—82no—
742C4—82no—
743C4—82no—
744C2—44no—
745C2—84no—
746C2C7×#232112yes—
747C2C7×#232511yescharacteristic
748C2C7×#237511yescharacteristic
749C2C7×#237712yes—
750C2C7×#238011yescharacteristic
751C2C7×#281211yescharacteristic
752C2C7×#281312yes—
753C2C7×#281511yescharacteristic
754C2C7×#282411yescharacteristic
755C2C7×#282512yes—
756C2C7×#282611yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC2×C7×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#386C2semidirect
3. C7×#1443C2semidirect
4. C7×#1440C2semidirect
5. C7×#1439C2semidirect
6. C7×#1439C2semidirect
7. C7×#1438C2semidirect
8. C7×#1438C2semidirect
9. C7×C22⋊#95C2semidirect
22. C7×#392C4semidirect
33. #14621C7direct (N × H)
47. C22×C7×D4C2×C4semidirect
52. C23×C4×C7D4semidirect
85. C2×C7×C22⋊C4C2×C4semidirect
94. C7×#95C2×C4semidirect
96. C2×#386C2×C7semidirect
97. #1443C2×C7semidirect
98. #1440C2×C7semidirect
99. #1439C2×C7semidirect
100. #1439C2×C7semidirect
101. #1438C2×C7semidirect
102. #1438C2×C7semidirect
103. C22⋊#95C2×C7semidirect
214. #392C4×C7semidirect
355. C22×D4C2×C4×C7semidirect
360. C23×C4C7×D4semidirect
393. C2×C22⋊C4C2×C4×C7semidirect
402. #95C2×C4×C7semidirect
687. C7#14621direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3922
C2×C7×#3862
C7×#14432
C7×#14402
C7×#14392
C7×#14382
C7×C22⋊#952
#146217