Finite Group Databasebeta

← C7×#13882 #13191098

Subgroups — C7×#13882 #13191098

Order 1792.

2222 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C7×C4⋊C4C211yesmaximal, characteristic
2C2×C7×#387C212yesmaximal, complemented
3C2×C7×#380C211yesmaximal, characteristic
4C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
5C7×#1445C212yesmaximal, complemented
6C7×#1441C212yesmaximal, complemented
7C7×#1436C212yesmaximal, complemented
8C7×C22⋊#95C211yesmaximal, characteristic
9C7×C22⋊#95C211yesmaximal, characteristic
10C7×C22⋊#95C211yesmaximal, characteristic
11C7×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C7C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C24×C4×C7C2211yescharacteristic
15C22×C7×C4⋊C4—28no—
16C22×C7×C4⋊C4C418yescomplemented
17C22×C7×C4⋊C4C2212yes—
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C42×C7C2212yes—
27C7×#387—28no—
28C7×#380—24no—
29C4×C7×C22⋊C4—24no—
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×#95C2212yes—
39C2×C7×#95C2212yes—
40#13882C711yesmaximal, characteristic, direct product factor, Sylow
41C25×C7C2311yescharacteristic
42C23×C4×C7—22no—
43C23×C4×C7—22no—
44C23×C4×C7—24no—
45C23×C4×C7—24no—
46C23×C4×C7—22no—
47C23×C4×C7—22no—
48C23×C4×C7—22no—
49C23×C4×C7—22no—
50C23×C4×C7—24no—
51C23×C4×C7—24no—
52C23×C4×C7—42no—
53C23×C4×C7—42no—
54C23×C4×C7C2×C414yes—
55C23×C4×C7C2×C414yes—
56C23×C4×C7C2×C414yes—
57C23×C4×C7C2312yes—
58C23×C4×C7C2312yes—
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2312yes—
62C23×C4×C7C2312yes—
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C2×C7×C4⋊C4—24no—
68C2×C7×C4⋊C4—24no—
69C2×C7×C4⋊C4—24no—
70C2×C7×C4⋊C4—232no—
71C2×C7×C4⋊C4—24no—
72C2×C7×C4⋊C4—24no—
73C2×C7×C4⋊C4—42no—
74C2×C7×C4⋊C4C2×C414yes—
75C2×C7×C4⋊C4C2×C414yes—
76C2×C7×C4⋊C4C2×C414yes—
77C2×C7×C4⋊C4C2×C414yes—
78C2×C7×C4⋊C4D418yes—
79C2×C7×C22⋊C4—22no—
80C2×C7×C22⋊C4—22no—
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4—22no—
85C2×C7×C22⋊C4—22no—
86C2×C7×C22⋊C4—22no—
87C2×C7×C22⋊C4—22no—
88C2×C7×C22⋊C4—22no—
89C2×C7×C22⋊C4D414yes—
90C2×C7×C22⋊C4Q814yes—
91C2×C42×C7—24no—
92C2×C42×C7—24no—
93C2×C42×C7—42no—
94C7×#95—24no—
95C7×#95—24no—
96C7×#95—24no—
97C7×#95—24no—
98C7×#95—24no—
99C7×#95—24no—
100C7×#95—24no—
101C7×#95—24no—
102C7×#95—42no—
103C7×#95—42no—
104C23×C4⋊C4C2×C711yescharacteristic
105C2×#387C2×C712yescomplemented
106C2×#380C2×C711yescharacteristic
107C2×C4×C22⋊C4C2×C711yescharacteristic
108#1445C2×C712yescomplemented
109#1441C2×C712yescomplemented
110#1436C2×C712yescomplemented
111C22⋊#95C2×C711yescharacteristic
112C22⋊#95C2×C711yescharacteristic
113C22⋊#95C2×C711yescharacteristic
114C22⋊#95C2×C711yescharacteristic
115C24×C7—22no—
116C24×C7—22no—
117C24×C7—22no—
118C24×C7—22no—
119C24×C7C22×C412yes—
120C24×C7C2×D412yes—
121C24×C7C2×Q812yes—
122C24×C7#4112yes—
123C24×C7#4112yes—
124C24×C7#4112yes—
125C24×C7#4112yes—
126C24×C7C2411yescharacteristic
127C22×C4×C7—216no—
128C22×C4×C7—216no—
129C22×C4×C7—28no—
130C22×C4×C7—21no—
131C22×C4×C7—22no—
132C22×C4×C7—21no—
133C22×C4×C7—21no—
134C22×C4×C7—21no—
135C22×C4×C7—22no—
136C22×C4×C7—21no—
137C22×C4×C7—21no—
138C22×C4×C7—21no—
139C22×C4×C7—21no—
140C22×C4×C7—22no—
141C22×C4×C7—22no—
142C22×C4×C7—28no—
143C22×C4×C7—28no—
144C22×C4×C7—28no—
145C22×C4×C7—28no—
146C22×C4×C7—22no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—22no—
150C22×C4×C7—22no—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—22no—
154C22×C4×C7—22no—
155C22×C4×C7—22no—
156C22×C4×C7—22no—
157C22×C4×C7—22no—
158C22×C4×C7—21no—
159C22×C4×C7—21no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7—22no—
163C22×C4×C7—22no—
164C22×C4×C7—22no—
165C22×C4×C7—22no—
166C22×C4×C7—28no—
167C22×C4×C7—28no—
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—44no—
183C22×C4×C7—44no—
184C22×C4×C7—48no—
185C22×C4×C7—48no—
186C22×C4×C7—48no—
187C22×C4×C7—48no—
188C22×C4×C7C22×C412yes—
189C22×C4×C7C22×C412yes—
190C22×C4×C7C22×C412yes—
191C22×C4×C7C22×C412yes—
192C22×C4×C7C22×C412yes—
193C22×C4×C7C22×C412yes—
194C22×C4×C7C2×D414yes—
195C22×C4×C7C2×D414yes—
196C22×C4×C7C2×D414yes—
197C22×C4×C7C2×D414yes—
198C22×C4×C7C2×Q814yes—
199C22×C4×C7#4114yes—
200C7×C4⋊C4—28no—
201C7×C4⋊C4—28no—
202C7×C4⋊C4—28no—
203C7×C4⋊C4—48no—
204C7×C4⋊C4C22⋊C4116yescomplemented
205C7×C22⋊C4—28no—
206C7×C22⋊C4—28no—
207C7×C22⋊C4—44no—
208C7×C22⋊C4—44no—
209C42×C7—48no—
210C24×C4C22×C711yescharacteristic
211C24×C4C22×C711yescharacteristic
212C24×C4C22×C711yescharacteristic
213C22×C4⋊C4—28no—
214C22×C4⋊C4C4×C718yescomplemented
215C22×C4⋊C4C22×C712yes—
216C22×C4⋊C4C22×C711yescharacteristic
217C22×C4⋊C4C22×C711yescharacteristic
218C22×C4⋊C4C22×C711yescharacteristic
219C22×C4⋊C4C22×C711yescharacteristic
220C22×C22⋊C4C22×C711yescharacteristic
221C22×C22⋊C4C22×C711yescharacteristic
222C22×C22⋊C4C22×C711yescharacteristic
223C22×C22⋊C4C22×C711yescharacteristic
224C22×C42C22×C712yes—
225#387—28no—
226#380—24no—
227C4×C22⋊C4—24no—
228C2×#95C22×C712yes—
229C2×#95C22×C712yes—
230C2×#95C22×C712yes—
231C2×#95C22×C712yes—
232C2×#95C22×C712yes—
233C2×#95C22×C712yes—
234C2×#95C22×C712yes—
235C2×#95C22×C712yes—
236C2×#95C22×C712yes—
237C2×#95C22×C712yes—
238C23×C7—22no—
239C23×C7—22no—
240C23×C7—22no—
241C23×C7—22no—
242C23×C7—24no—
243C23×C7—24no—
244C23×C7—24no—
245C23×C7—24no—
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#11714yes—
255C23×C7C4×D414yes—
256C23×C7C4×Q814yes—
257C23×C7C22⋊Q814yes—
258C23×C7#12314yes—
259C23×C7#12514yes—
260C23×C7#12614yes—
261C23×C7C23×C411yescharacteristic
262C23×C7C22×D412yes—
263C23×C7C22×D411yescharacteristic
264C23×C7C22×Q811yescharacteristic
265C23×C7C2×#4111yescharacteristic
266C23×C7C2×#4111yescharacteristic
267C23×C7C2×#4112yes—
268C23×C7C2×#4111yescharacteristic
269C23×C7C2×#4111yescharacteristic
270C23×C7H(5,𝔽2)12yes—
271C23×C72−1+412yes—
272C2×C4×C7—232no—
273C2×C4×C7—22no—
274C2×C4×C7—22no—
275C2×C4×C7—22no—
276C2×C4×C7—22no—
277C2×C4×C7—22no—
278C2×C4×C7—22no—
279C2×C4×C7—22no—
280C2×C4×C7—22no—
281C2×C4×C7—24no—
282C2×C4×C7—24no—
283C2×C4×C7—24no—
284C2×C4×C7—24no—
285C2×C4×C7—24no—
286C2×C4×C7—24no—
287C2×C4×C7—24no—
288C2×C4×C7—24no—
289C2×C4×C7—22no—
290C2×C4×C7—22no—
291C2×C4×C7—22no—
292C2×C4×C7—22no—
293C2×C4×C7—22no—
294C2×C4×C7—22no—
295C2×C4×C7—24no—
296C2×C4×C7—24no—
297C2×C4×C7—24no—
298C2×C4×C7—24no—
299C2×C4×C7—24no—
300C2×C4×C7—24no—
301C2×C4×C7—416no—
302C2×C4×C7—416no—
303C2×C4×C7—42no—
304C2×C4×C7—42no—
305C2×C4×C7—42no—
306C2×C4×C7—42no—
307C2×C4×C7—42no—
308C2×C4×C7—42no—
309C2×C4×C7—42no—
310C2×C4×C7—42no—
311C2×C4×C7—42no—
312C2×C4×C7—42no—
313C2×C4×C7—42no—
314C2×C4×C7—42no—
315C2×C4×C7—42no—
316C2×C4×C7—42no—
317C2×C4×C7—42no—
318C2×C4×C7—42no—
319C2×C4×C7—42no—
320C2×C4×C7—42no—
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×C7C2×C22⋊C414yes—
330C2×C4×C7C2×C22⋊C414yes—
331C2×C4×C7C2×C22⋊C414yes—
332C2×C4×C7#11714yes—
333C25C23×C711yescharacteristic
334C23×C4—22no—
335C23×C4—22no—
336C23×C4—24no—
337C23×C4—24no—
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—24no—
343C23×C4—24no—
344C23×C4—42no—
345C23×C4—42no—
346C23×C4C2×C4×C714yes—
347C23×C4C2×C4×C714yes—
348C23×C4C2×C4×C714yes—
349C23×C4C23×C712yes—
350C23×C4C23×C712yes—
351C23×C4C23×C711yescharacteristic
352C23×C4C23×C711yescharacteristic
353C23×C4C23×C712yes—
354C23×C4C23×C712yes—
355C23×C4C23×C711yescharacteristic
356C23×C4C23×C711yescharacteristic
357C23×C4C23×C711yescharacteristic
358C23×C4C23×C711yescharacteristic
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—232no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4C2×C4×C714yes—
367C2×C4⋊C4C2×C4×C714yes—
368C2×C4⋊C4C2×C4×C714yes—
369C2×C4⋊C4C2×C4×C714yes—
370C2×C4⋊C4C7×D418yes—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4C7×D414yes—
382C2×C22⋊C4C7×Q814yes—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—42no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—42no—
395#95—42no—
396C22×C7—24no—
397C22×C7—24no—
398C22×C7—24no—
399C22×C7—24no—
400C22×C7—24no—
401C22×C7—28no—
402C22×C7—28no—
403C22×C7—28no—
404C22×C7—28no—
405C22×C7—24no—
406C22×C7#38718yescomplemented
407C22×C7C22×C22⋊C411yescharacteristic
408C22×C7C2×#11711yescharacteristic
409C22×C7C2×#11711yescharacteristic
410C22×C7C2×C4×D411yescharacteristic
411C22×C7C2×C4×Q811yescharacteristic
412C22×C7#51811yescharacteristic
413C22×C7#51911yescharacteristic
414C22×C7C2×C22⋊Q811yescharacteristic
415C22×C7C2×#12311yescharacteristic
416C22×C7#52512yes—
417C22×C7#52512yes—
418C22×C7C2×#12511yescharacteristic
419C22×C7C2×#12611yescharacteristic
420C22×C7#53912yes—
421C22×C7#53912yes—
422C22×C7D4212yes—
423C22×C7#54612yes—
424C22×C7#54712yes—
425C22×C7#54812yes—
426C22×C7D4×Q812yes—
427C22×C7#55212yes—
428C22×C7#55312yes—
429C22×C7#55412yes—
430C4×C7—24no—
431C4×C7—24no—
432C4×C7—24no—
433C4×C7—24no—
434C4×C7—42no—
435C4×C7—42no—
436C4×C7—44no—
437C4×C7—44no—
438C4×C7—82no—
439C4×C7—82no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24C22×C4×C712yes—
445C24C2×C7×D412yes—
446C24C2×C7×Q812yes—
447C24C7×#4112yes—
448C24C7×#4112yes—
449C24C7×#4112yes—
450C24C7×#4112yes—
451C24C24×C711yescharacteristic
452C22×C4—216no—
453C22×C4—216no—
454C22×C4—28no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—28no—
468C22×C4—28no—
469C22×C4—28no—
470C22×C4—28no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—28no—
492C22×C4—28no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—48no—
510C22×C4—48no—
511C22×C4—48no—
512C22×C4—48no—
513C22×C4C22×C4×C712yes—
514C22×C4C22×C4×C712yes—
515C22×C4C22×C4×C712yes—
516C22×C4C22×C4×C712yes—
517C22×C4C22×C4×C712yes—
518C22×C4C22×C4×C712yes—
519C22×C4C2×C7×D414yes—
520C22×C4C2×C7×D414yes—
521C22×C4C2×C7×D414yes—
522C22×C4C2×C7×D414yes—
523C22×C4C2×C7×Q814yes—
524C22×C4C7×#4114yes—
525C4⋊C4—28no—
526C4⋊C4—28no—
527C4⋊C4—28no—
528C4⋊C4—48no—
529C4⋊C4C7×C22⋊C4116yescomplemented
530C22⋊C4—28no—
531C22⋊C4—28no—
532C22⋊C4—44no—
533C22⋊C4—44no—
534C42—48no—
535C2×C7—28no—
536C2×C7#228011yescharacteristic
537C2×C7C2×#38711yescharacteristic
538C2×C7#231311yescharacteristic
539C2×C7D4×C22⋊C411yescharacteristic
540C2×C7Q8×C22⋊C411yescharacteristic
541C2×C7#234411yescharacteristic
542C2×C7#234511yescharacteristic
543C2×C7#244312yes—
544C2×C7#244912yes—
545C2×C7#247312yes—
546C2×C7#248112yes—
547C23—22no—
548C23—22no—
549C23—22no—
550C23—22no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23—24no—
562C23—24no—
563C23C7×#11714yes—
564C23C4×C7×D414yes—
565C23C4×C7×Q814yes—
566C23C7×C22⋊Q814yes—
567C23C7×#12314yes—
568C23C7×#12514yes—
569C23C7×#12614yes—
570C23C23×C4×C711yescharacteristic
571C23C22×C7×D412yes—
572C23C22×C7×D411yescharacteristic
573C23C22×C7×Q811yescharacteristic
574C23C2×C7×#4111yescharacteristic
575C23C2×C7×#4111yescharacteristic
576C23C2×C7×#4112yes—
577C23C2×C7×#4111yescharacteristic
578C23C2×C7×#4111yescharacteristic
579C23C7×H(5,𝔽2)12yes—
580C23C7×2−1+412yes—
581C2×C4—232no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—416no—
611C2×C4—416no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4C2×C7×C22⋊C414yes—
639C2×C4C2×C7×C22⋊C414yes—
640C2×C4C2×C7×C22⋊C414yes—
641C2×C4C7×#11714yes—
642C7#1388211yescharacteristic, direct product factor, Sylow
643C22—28no—
644C22—28no—
645C22—28no—
646C22—28no—
647C22—24no—
648C22—24no—
649C22—24no—
650C22—24no—
651C22—24no—
652C22—24no—
653C22C7×#38718yescomplemented
654C22C22×C7×C22⋊C411yescharacteristic
655C22C2×C7×#11711yescharacteristic
656C22C2×C7×#11711yescharacteristic
657C22C2×C4×C7×D411yescharacteristic
658C22C2×C4×C7×Q811yescharacteristic
659C22C7×#51811yescharacteristic
660C22C7×#51911yescharacteristic
661C22C2×C7×C22⋊Q811yescharacteristic
662C22C2×C7×#12311yescharacteristic
663C22C7×#52512yes—
664C22C7×#52512yes—
665C22C2×C7×#12511yescharacteristic
666C22C2×C7×#12611yescharacteristic
667C22C7×#53912yes—
668C22C7×#53912yes—
669C22C7×D4212yes—
670C22C7×#54612yes—
671C22C7×#54712yes—
672C22C7×#54812yes—
673C22C7×D4×Q812yes—
674C22C7×#55212yes—
675C22C7×#55312yes—
676C22C7×#55412yes—
677C4—24no—
678C4—24no—
679C4—24no—
680C4—24no—
681C4—44no—
682C4—44no—
683C4—42no—
684C4—42no—
685C4—82no—
686C4—82no—
687C2—28no—
688C2C7×#228011yescharacteristic
689C2C2×C7×#38711yescharacteristic
690C2C7×#231311yescharacteristic
691C2C7×D4×C22⋊C411yescharacteristic
692C2C7×Q8×C22⋊C411yescharacteristic
693C2C7×#234411yescharacteristic
694C2C7×#234511yescharacteristic
695C2C7×#244312yes—
696C2C7×#244912yes—
697C2C7×#247312yes—
698C2C7×#248112yes—
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
2. C2×C7×#387C2semidirect
5. C7×#1445C2semidirect
6. C7×#1441C2semidirect
7. C7×#1436C2semidirect
16. C22×C7×C4⋊C4C4semidirect
40. #13882C7direct (N × H)
105. C2×#387C2×C7semidirect
108. #1445C2×C7semidirect
109. #1441C2×C7semidirect
110. #1436C2×C7semidirect
204. C7×C4⋊C4C22⋊C4semidirect
214. C22×C4⋊C4C4×C7semidirect
406. C22×C7#387semidirect
529. C4⋊C4C7×C22⋊C4semidirect
642. C7#13882direct (N × H)
653. C22C7×#387semidirect

Maximal subgroups

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

subgroupindex
C23×C7×C4⋊C42
C2×C7×#3872
C2×C7×#3802
C2×C4×C7×C22⋊C42
C7×#14452
C7×#14412
C7×#14362
C7×C22⋊#952
#138827