Finite Group Databasebeta

← C7×#13927 #13191143

Subgroups — C7×#13927 #13191143

Order 1792.

1650 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C7×Q8C211yesmaximal, characteristic
2C2×C7×#387C212yesmaximal
3C7×#1446C212yesmaximal
4C7×#1441C212yesmaximal
5C7×#1436C212yesmaximal
6C7×C4⋊#95C211yesmaximal, characteristic
7C7×#1434C211yesmaximal, characteristic
8C7×#1434C211yesmaximal, characteristic
9C7×#1434C211yesmaximal, characteristic
10C7×#1434C211yesmaximal, characteristic
11C4×C7×#95C211yesmaximal, characteristic
12C23×C7×Q8C2211yescharacteristic
13C2×C4×C7×Q8—28no—
14C2×C4×C7×Q8C418yescomplemented
15C22×C7×C4⋊C4C2212yes—
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C42×C7C2212yes—
20C22×C42×C7C2211yescharacteristic
21C22×C42×C7C2211yescharacteristic
22C22×C42×C7C2211yescharacteristic
23C7×#387—28no—
24C2×C7×#95C2212yes—
25C2×C7×#95C2212yes—
26C2×C7×#95C2212yes—
27C2×C7×#95C2212yes—
28C2×C7×#95C2211yescharacteristic
29C2×C7×#95C2212yes—
30C2×C7×#95C2211yescharacteristic
31C2×C7×#95C2211yescharacteristic
32C2×C7×#95C2212yes—
33C2×C7×#95C2212yes—
34C2×C7×#95C2212yes—
35C2×C7×#95C2212yes—
36C2×C7×#95C2212yes—
37C2×C7×#95C2211yescharacteristic
38#13927C711yesmaximal, characteristic, direct product factor, Sylow
39C22×C7×Q8—24no—
40C22×C7×Q8—24no—
41C22×C7×Q8—22no—
42C22×C7×Q8—22no—
43C22×C7×Q8C2×C414yes—
44C23×C4×C7C2312yes—
45C23×C4×C7C2312yes—
46C23×C4×C7C2311yescharacteristic
47C23×C4×C7C2312yes—
48C23×C4×C7C2312yes—
49C23×C4×C7C2311yescharacteristic
50C23×C4×C7C2311yescharacteristic
51C23×C4×C7C2311yescharacteristic
52C23×C4×C7C2311yescharacteristic
53C23×C4×C7C2311yescharacteristic
54C23×C4×C7C2311yescharacteristic
55C4×C7×Q8—232no—
56C2×C7×C4⋊C4—24no—
57C2×C7×C4⋊C4—24no—
58C2×C7×C4⋊C4—24no—
59C2×C7×C4⋊C4—24no—
60C2×C7×C4⋊C4—42no—
61C2×C7×C4⋊C4C2×C414yes—
62C2×C7×C4⋊C4C2×C414yes—
63C2×C7×C4⋊C4C2×C414yes—
64C2×C7×C4⋊C4D418yes—
65C2×C42×C7—24no—
66C2×C42×C7—24no—
67C2×C42×C7—24no—
68C2×C42×C7—24no—
69C2×C42×C7—24no—
70C2×C42×C7—42no—
71C2×C42×C7C2×C414yes—
72C2×C42×C7C2×C414yes—
73C2×C42×C7C2×C414yes—
74C7×#95—24no—
75C7×#95—24no—
76C7×#95—24no—
77C7×#95—24no—
78C7×#95—24no—
79C7×#95—22no—
80C7×#95—24no—
81C7×#95—24no—
82C7×#95—24no—
83C7×#95—24no—
84C7×#95—22no—
85C7×#95—22no—
86C7×#95—42no—
87C7×#95Q814yescomplemented
88C22×C4×Q8C2×C711yescharacteristic
89C2×#387C2×C712yes—
90#1446C2×C712yes—
91#1441C2×C712yes—
92#1436C2×C712yes—
93C4⋊#95C2×C711yescharacteristic
94#1434C2×C711yescharacteristic
95#1434C2×C711yescharacteristic
96#1434C2×C711yescharacteristic
97#1434C2×C711yescharacteristic
98C4×#95C2×C711yescharacteristic
99C24×C7C2411yescharacteristic
100C2×C7×Q8—216no—
101C2×C7×Q8—216no—
102C2×C7×Q8—28no—
103C2×C7×Q8—28no—
104C2×C7×Q8—28no—
105C22×C4×C7—22no—
106C22×C4×C7—22no—
107C22×C4×C7—22no—
108C22×C4×C7—22no—
109C22×C4×C7—22no—
110C22×C4×C7—22no—
111C22×C4×C7—21no—
112C22×C4×C7—21no—
113C22×C4×C7—22no—
114C22×C4×C7—21no—
115C22×C4×C7—21no—
116C22×C4×C7—21no—
117C22×C4×C7—21no—
118C22×C4×C7—22no—
119C22×C4×C7—21no—
120C22×C4×C7—21no—
121C22×C4×C7—22no—
122C22×C4×C7—22no—
123C22×C4×C7—22no—
124C22×C4×C7—22no—
125C22×C4×C7—22no—
126C22×C4×C7—22no—
127C22×C4×C7—22no—
128C22×C4×C7—22no—
129C22×C4×C7—22no—
130C22×C4×C7—22no—
131C22×C4×C7—21no—
132C22×C4×C7—22no—
133C22×C4×C7—22no—
134C22×C4×C7—21no—
135C22×C4×C7—22no—
136C22×C4×C7—22no—
137C22×C4×C7—22no—
138C22×C4×C7—22no—
139C22×C4×C7—22no—
140C22×C4×C7—22no—
141C22×C4×C7—22no—
142C22×C4×C7—22no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
145C22×C4×C7—22no—
146C22×C4×C7—22no—
147C22×C4×C7—22no—
148C22×C4×C7—22no—
149C22×C4×C7—22no—
150C22×C4×C7—22no—
151C22×C4×C7C22×C412yes—
152C22×C4×C7C22×C412yes—
153C22×C4×C7C22×C412yes—
154C22×C4×C7C22×C412yes—
155C22×C4×C7C22×C412yes—
156C22×C4×C7C22×C412yes—
157C22×C4×C7C22×C412yes—
158C22×C4×C7C2×D414yes—
159C22×C4×C7C2×D414yes—
160C22×C4×C7C2×D414yes—
161C22×C4×C7C2×Q814yes—
162C22×C4×C7C2×Q812yes—
163C22×C4×C7#4114yes—
164C22×C4×C7#4114yes—
165C22×C4×C7#4112yes—
166C22×C4×C7#4112yes—
167C22×C4×C7#4112yes—
168C7×C4⋊C4—28no—
169C7×C4⋊C4—28no—
170C7×C4⋊C4—48no—
171C7×C4⋊C4C22⋊C4116yes—
172C42×C7—28no—
173C42×C7—28no—
174C42×C7—28no—
175C42×C7—48no—
176C23×Q8C22×C711yescharacteristic
177C2×C4×Q8—28no—
178C2×C4×Q8C4×C718yescomplemented
179C22×C4⋊C4C22×C712yes—
180C22×C4⋊C4C22×C711yescharacteristic
181C22×C4⋊C4C22×C711yescharacteristic
182C22×C4⋊C4C22×C711yescharacteristic
183C22×C42C22×C712yes—
184C22×C42C22×C711yescharacteristic
185C22×C42C22×C711yescharacteristic
186C22×C42C22×C711yescharacteristic
187#387—28no—
188C2×#95C22×C711yescharacteristic
189C2×#95C22×C712yes—
190C2×#95C22×C711yescharacteristic
191C2×#95C22×C711yescharacteristic
192C2×#95C22×C712yes—
193C2×#95C22×C712yes—
194C2×#95C22×C712yes—
195C2×#95C22×C712yes—
196C2×#95C22×C712yes—
197C2×#95C22×C712yes—
198C2×#95C22×C712yes—
199C2×#95C22×C712yes—
200C2×#95C22×C712yes—
201C2×#95C22×C711yescharacteristic
202C23×C7C23×C411yescharacteristic
203C23×C7C22×D412yes—
204C23×C7C22×Q811yescharacteristic
205C23×C7C2×#4112yes—
206C23×C7C2×#4111yescharacteristic
207C23×C7C2×#4111yescharacteristic
208C23×C7C2×#4111yescharacteristic
209C23×C7C2×#4112yes—
210C23×C7H(5,𝔽2)11yescharacteristic
211C23×C72−1+412yes—
212C23×C72−1+411yescharacteristic
213C7×Q8—232no—
214C2×C4×C7—22no—
215C2×C4×C7—22no—
216C2×C4×C7—22no—
217C2×C4×C7—22no—
218C2×C4×C7—22no—
219C2×C4×C7—22no—
220C2×C4×C7—22no—
221C2×C4×C7—22no—
222C2×C4×C7—22no—
223C2×C4×C7—22no—
224C2×C4×C7—22no—
225C2×C4×C7—22no—
226C2×C4×C7—24no—
227C2×C4×C7—24no—
228C2×C4×C7—24no—
229C2×C4×C7—24no—
230C2×C4×C7—24no—
231C2×C4×C7—24no—
232C2×C4×C7—24no—
233C2×C4×C7—24no—
234C2×C4×C7—24no—
235C2×C4×C7—24no—
236C2×C4×C7—24no—
237C2×C4×C7—24no—
238C2×C4×C7—22no—
239C2×C4×C7—22no—
240C2×C4×C7—22no—
241C2×C4×C7—24no—
242C2×C4×C7—24no—
243C2×C4×C7—24no—
244C2×C4×C7—24no—
245C2×C4×C7—24no—
246C2×C4×C7—24no—
247C2×C4×C7—42no—
248C2×C4×C7—42no—
249C2×C4×C7—42no—
250C2×C4×C7—42no—
251C2×C4×C7—42no—
252C2×C4×C7—42no—
253C2×C4×C7—42no—
254C2×C4×C7—42no—
255C2×C4×C7—42no—
256C2×C4×C7—42no—
257C2×C4×C7—42no—
258C2×C4×C7—42no—
259C2×C4×C7—42no—
260C2×C4×C7—42no—
261C2×C4×C7—42no—
262C2×C4×C7—42no—
263C2×C4×C7—42no—
264C2×C4×C7—42no—
265C2×C4×C7—42no—
266C2×C4×C7—42no—
267C2×C4×C7—42no—
268C2×C4×C7—42no—
269C2×C4×C7—42no—
270C2×C4×C7—42no—
271C2×C4×C7C2×C22⋊C414yes—
272C2×C4×C7C2×C22⋊C414yes—
273C2×C4×C7C2×C22⋊C414yes—
274C2×C4×C7#11714yes—
275C2×C4×C7#11714yes—
276C2×C4×C7C4×Q814yes—
277C22×Q8—24no—
278C22×Q8—24no—
279C22×Q8—22no—
280C22×Q8—22no—
281C22×Q8C2×C4×C714yes—
282C23×C4C23×C712yes—
283C23×C4C23×C712yes—
284C23×C4C23×C711yescharacteristic
285C23×C4C23×C712yes—
286C23×C4C23×C712yes—
287C23×C4C23×C711yescharacteristic
288C23×C4C23×C711yescharacteristic
289C23×C4C23×C711yescharacteristic
290C23×C4C23×C711yescharacteristic
291C23×C4C23×C711yescharacteristic
292C23×C4C23×C711yescharacteristic
293C4×Q8—232no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4C2×C4×C714yes—
300C2×C4⋊C4C2×C4×C714yes—
301C2×C4⋊C4C2×C4×C714yes—
302C2×C4⋊C4C7×D418yes—
303C2×C42—24no—
304C2×C42—24no—
305C2×C42—24no—
306C2×C42—24no—
307C2×C42—24no—
308C2×C42—42no—
309C2×C42C2×C4×C714yes—
310C2×C42C2×C4×C714yes—
311C2×C42C2×C4×C714yes—
312#95—24no—
313#95—24no—
314#95—24no—
315#95—24no—
316#95—24no—
317#95—22no—
318#95—24no—
319#95—24no—
320#95—24no—
321#95—24no—
322#95—22no—
323#95—22no—
324#95—42no—
325#95C7×Q814yescomplemented
326C22×C7C22×C22⋊C411yescharacteristic
327C22×C7C2×#11711yescharacteristic
328C22×C7C2×#11711yescharacteristic
329C22×C7C2×C4×Q811yescharacteristic
330C22×C7C4×#4111yescharacteristic
331C22×C7#51911yescharacteristic
332C22×C7#52011yescharacteristic
333C22×C7#52512yes—
334C22×C7#52512yes—
335C22×C7#52912yes—
336C22×C7#53312yes—
337C22×C7#54112yes—
338C22×C7#54212yes—
339C22×C7#54612yes—
340C22×C7#54712yes—
341C22×C7#54812yes—
342C22×C7D4×Q812yes—
343C22×C7#55212yes—
344C22×C7#55411yescharacteristic
345C22×C7#55611yescharacteristic
346C22×C7#55612yes—
347C22×C7#55711yescharacteristic
348C22×C7#55911yescharacteristic
349C4×C7—24no—
350C4×C7—24no—
351C4×C7—24no—
352C4×C7—24no—
353C4×C7—24no—
354C4×C7—24no—
355C4×C7—42no—
356C4×C7—44no—
357C4×C7—44no—
358C4×C7—82no—
359C4×C7—82no—
360C24C24×C711yescharacteristic
361C2×Q8—216no—
362C2×Q8—216no—
363C2×Q8—28no—
364C2×Q8—28no—
365C2×Q8—28no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4C22×C4×C712yes—
413C22×C4C22×C4×C712yes—
414C22×C4C22×C4×C712yes—
415C22×C4C22×C4×C712yes—
416C22×C4C22×C4×C712yes—
417C22×C4C22×C4×C712yes—
418C22×C4C22×C4×C712yes—
419C22×C4C2×C7×D414yes—
420C22×C4C2×C7×D414yes—
421C22×C4C2×C7×D414yes—
422C22×C4C2×C7×Q814yes—
423C22×C4C2×C7×Q812yes—
424C22×C4C7×#4114yes—
425C22×C4C7×#4114yes—
426C22×C4C7×#4112yes—
427C22×C4C7×#4112yes—
428C22×C4C7×#4112yes—
429C4⋊C4—28no—
430C4⋊C4—28no—
431C4⋊C4—48no—
432C4⋊C4C7×C22⋊C4116yes—
433C42—28no—
434C42—28no—
435C42—28no—
436C42—48no—
437C2×C7#228011yescharacteristic
438C2×C7#229511yescharacteristic
439C2×C7#232011yescharacteristic
440C2×C7#233911yescharacteristic
441C2×C7Q8×C22⋊C411yescharacteristic
442C2×C7#235511yescharacteristic
443C2×C7#235611yescharacteristic
444C2×C7#245812yes—
445C2×C7#246212yes—
446C2×C7#246512yes—
447C2×C7#246912yes—
448C23C23×C4×C711yescharacteristic
449C23C22×C7×D412yes—
450C23C22×C7×Q811yescharacteristic
451C23C2×C7×#4112yes—
452C23C2×C7×#4111yescharacteristic
453C23C2×C7×#4111yescharacteristic
454C23C2×C7×#4111yescharacteristic
455C23C2×C7×#4112yes—
456C23C7×H(5,𝔽2)11yescharacteristic
457C23C7×2−1+412yes—
458C23C7×2−1+411yescharacteristic
459Q8—232no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4C2×C7×C22⋊C414yes—
518C2×C4C2×C7×C22⋊C414yes—
519C2×C4C2×C7×C22⋊C414yes—
520C2×C4C7×#11714yes—
521C2×C4C7×#11714yes—
522C2×C4C4×C7×Q814yes—
523C7#1392711yescharacteristic, direct product factor, Sylow
524C22C22×C7×C22⋊C411yescharacteristic
525C22C2×C7×#11711yescharacteristic
526C22C2×C7×#11711yescharacteristic
527C22C2×C4×C7×Q811yescharacteristic
528C22C4×C7×#4111yescharacteristic
529C22C7×#51911yescharacteristic
530C22C7×#52011yescharacteristic
531C22C7×#52512yes—
532C22C7×#52512yes—
533C22C7×#52912yes—
534C22C7×#53312yes—
535C22C7×#54112yes—
536C22C7×#54212yes—
537C22C7×#54612yes—
538C22C7×#54712yes—
539C22C7×#54812yes—
540C22C7×D4×Q812yes—
541C22C7×#55212yes—
542C22C7×#55411yescharacteristic
543C22C7×#55612yes—
544C22C7×#55611yescharacteristic
545C22C7×#55711yescharacteristic
546C22C7×#55911yescharacteristic
547C4—24no—
548C4—24no—
549C4—24no—
550C4—24no—
551C4—24no—
552C4—24no—
553C4—44no—
554C4—44no—
555C4—42no—
556C4—82no—
557C4—82no—
558C2C7×#228011yescharacteristic
559C2C7×#229511yescharacteristic
560C2C7×#232011yescharacteristic
561C2C7×#233911yescharacteristic
562C2C7×Q8×C22⋊C411yescharacteristic
563C2C7×#235511yescharacteristic
564C2C7×#235611yescharacteristic
565C2C7×#245812yes—
566C2C7×#246212yes—
567C2C7×#246512yes—
568C2C7×#246912yes—
subgroupG/H
center, socle, prime radicalC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
14. C2×C4×C7×Q8C4semidirect
38. #13927C7direct (N × H)
87. C7×#95Q8semidirect
178. C2×C4×Q8C4×C7semidirect
325. #95C7×Q8semidirect
523. C7#13927direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C7×Q82
C2×C7×#3872
C7×#14462
C7×#14412
C7×#14362
C7×C4⋊#952
C7×#14342
C4×C7×#952
#139277