Finite Group Databasebeta

← C7×#15881 #13193097

Subgroups — C7×#15881 #13193097

Order 1792.

1370 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#125C211yesmaximal, characteristic
2C2×C7×#400C211yesmaximal, characteristic
3C2×C7×#398C211yesmaximal, characteristic
4C2×C7×#382C211yesmaximal, characteristic
5C7×#1445C211yesmaximal, characteristic
6C7×#1442C212yesmaximal
7C7×#1442C212yesmaximal
8C7×#1441C212yesmaximal
9C7×#1436C212yesmaximal
10C7×#1436C211yesmaximal, characteristic
11C7×#1436C211yesmaximal, characteristic
12C2×C7×#125—24no—
13C2×C7×#125—24no—
14C2×C7×#125—24no—
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C7×C4⋊C4C2212yes—
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C42×C7C2211yescharacteristic
24C22×C42×C7C2211yescharacteristic
25C7×#400—24no—
26C7×#398—24no—
27C7×#382—24no—
28C2×C7×#95C2211yescharacteristic
29C2×C7×#95C2212yes—
30C2×C7×#95C2212yes—
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—
40C2×C7×#95C2212yes—
41#15881C711yesmaximal, characteristic, direct product factor, Sylow
42C23×C4×C7C2312yes—
43C23×C4×C7C2312yes—
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2311yescharacteristic
46C23×C4×C7C2311yescharacteristic
47C23×C4×C7C2311yescharacteristic
48C23×C4×C7C2311yescharacteristic
49C23×C4×C7C2312yes—
50C23×C4×C7C2312yes—
51C23×C4×C7C2311yescharacteristic
52C23×C4×C7C2311yescharacteristic
53C7×#125—232no—
54C2×C7×C4⋊C4—22no—
55C2×C7×C4⋊C4—22no—
56C2×C7×C4⋊C4—22no—
57C2×C7×C4⋊C4—22no—
58C2×C7×C4⋊C4—22no—
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⋊C4—22no—
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4—24no—
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4—24no—
74C2×C7×C4⋊C4—24no—
75C2×C7×C4⋊C4D414yes—
76C2×C7×C4⋊C4D414yes—
77C2×C7×C4⋊C4D414yes—
78C2×C42×C7—22no—
79C2×C42×C7—22no—
80C2×C42×C7—22no—
81C2×C42×C7—22no—
82C2×C42×C7—24no—
83C7×#95—24no—
84C7×#95—24no—
85C7×#95—22no—
86C7×#95—24no—
87C7×#95—22no—
88C7×#95—24no—
89C7×#95—24no—
90C7×#95—24no—
91C7×#95—24no—
92C7×#95—24no—
93C7×#95—24no—
94C7×#95—24no—
95C7×#95—24no—
96C22×#125C2×C711yescharacteristic
97C2×#400C2×C711yescharacteristic
98C2×#398C2×C711yescharacteristic
99C2×#382C2×C711yescharacteristic
100#1445C2×C711yescharacteristic
101#1442C2×C712yes—
102#1442C2×C712yes—
103#1441C2×C712yes—
104#1436C2×C712yes—
105#1436C2×C711yescharacteristic
106#1436C2×C711yescharacteristic
107C24×C7C2411yescharacteristic
108C22×C4×C7—21no—
109C22×C4×C7—21no—
110C22×C4×C7—22no—
111C22×C4×C7—22no—
112C22×C4×C7—22no—
113C22×C4×C7—22no—
114C22×C4×C7—22no—
115C22×C4×C7—21no—
116C22×C4×C7—21no—
117C22×C4×C7—21no—
118C22×C4×C7—21no—
119C22×C4×C7—21no—
120C22×C4×C7—21no—
121C22×C4×C7—21no—
122C22×C4×C7—21no—
123C22×C4×C7—21no—
124C22×C4×C7—21no—
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—22no—
132C22×C4×C7—22no—
133C22×C4×C7—22no—
134C22×C4×C7—22no—
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×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—22no—
159C22×C4×C7C2×D412yes—
160C22×C4×C7C2×D412yes—
161C22×C4×C7C2×D412yes—
162C22×C4×C7C2×D412yes—
163C22×C4×C7C2×D412yes—
164C22×C4×C7C2×D412yes—
165C22×C4×C7C2×D412yes—
166C22×C4×C7C2×D412yes—
167C22×C4×C7C2×D412yes—
168C22×C4×C7#4114yes—
169C22×C4×C7#4114yes—
170C22×C4×C7#4114yes—
171C7×C4⋊C4—28no—
172C7×C4⋊C4—28no—
173C7×C4⋊C4—28no—
174C7×C4⋊C4—28no—
175C7×C4⋊C4—28no—
176C7×C4⋊C4—28no—
177C7×C4⋊C4—44no—
178C7×C4⋊C4—48no—
179C42×C7—28no—
180C42×C7—28no—
181C2×#125—24no—
182C2×#125—24no—
183C2×#125—24no—
184C22×C4⋊C4C22×C711yescharacteristic
185C22×C4⋊C4C22×C712yes—
186C22×C4⋊C4C22×C711yescharacteristic
187C22×C4⋊C4C22×C711yescharacteristic
188C22×C4⋊C4C22×C711yescharacteristic
189C22×C4⋊C4C22×C711yescharacteristic
190C22×C4⋊C4C22×C711yescharacteristic
191C22×C4⋊C4C22×C711yescharacteristic
192C22×C42C22×C711yescharacteristic
193C22×C42C22×C711yescharacteristic
194#400—24no—
195#398—24no—
196#382—24no—
197C2×#95C22×C711yescharacteristic
198C2×#95C22×C712yes—
199C2×#95C22×C712yes—
200C2×#95C22×C711yescharacteristic
201C2×#95C22×C712yes—
202C2×#95C22×C712yes—
203C2×#95C22×C712yes—
204C2×#95C22×C712yes—
205C2×#95C22×C712yes—
206C2×#95C22×C712yes—
207C2×#95C22×C712yes—
208C2×#95C22×C712yes—
209C2×#95C22×C712yes—
210C23×C7C22×D411yescharacteristic
211C23×C7C22×D411yescharacteristic
212C23×C7C22×D411yescharacteristic
213C23×C7C2×#4112yes—
214C23×C7C2×#4112yes—
215C23×C7C2×#4112yes—
216C23×C72−1+412yes—
217C23×C72−1+412yes—
218C23×C72−1+412yes—
219C2×C4×C7—22no—
220C2×C4×C7—22no—
221C2×C4×C7—22no—
222C2×C4×C7—22no—
223C2×C4×C7—24no—
224C2×C4×C7—24no—
225C2×C4×C7—24no—
226C2×C4×C7—24no—
227C2×C4×C7—22no—
228C2×C4×C7—22no—
229C2×C4×C7—22no—
230C2×C4×C7—22no—
231C2×C4×C7—22no—
232C2×C4×C7—24no—
233C2×C4×C7—24no—
234C2×C4×C7—22no—
235C2×C4×C7—22no—
236C2×C4×C7—24no—
237C2×C4×C7—24no—
238C2×C4×C7—24no—
239C2×C4×C7—24no—
240C2×C4×C7—24no—
241C2×C4×C7—24no—
242C2×C4×C7—24no—
243C2×C4×C7—24no—
244C2×C4×C7—41no—
245C2×C4×C7—41no—
246C2×C4×C7—42no—
247C2×C4×C7—42no—
248C2×C4×C7—41no—
249C2×C4×C7—41no—
250C2×C4×C7—41no—
251C2×C4×C7—41no—
252C2×C4×C7—41no—
253C2×C4×C7—41no—
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×C7—42no—
272C2×C4×C7—42no—
273C2×C4×C7—42no—
274C2×C4×C7—42no—
275C2×C4×C7—42no—
276C2×C4×C7—42no—
277C2×C4×C7—42no—
278C2×C4×C7—42no—
279C2×C4×C7—42no—
280C2×C4×C7#12014yes—
281C2×C4×C7#12414yes—
282C23×C4C23×C712yes—
283C23×C4C23×C712yes—
284C23×C4C23×C711yescharacteristic
285C23×C4C23×C711yescharacteristic
286C23×C4C23×C711yescharacteristic
287C23×C4C23×C711yescharacteristic
288C23×C4C23×C711yescharacteristic
289C23×C4C23×C712yes—
290C23×C4C23×C712yes—
291C23×C4C23×C711yescharacteristic
292C23×C4C23×C711yescharacteristic
293#125—232no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4C7×D414yes—
316C2×C4⋊C4C7×D414yes—
317C2×C4⋊C4C7×D414yes—
318C2×C42—22no—
319C2×C42—22no—
320C2×C42—22no—
321C2×C42—22no—
322C2×C42—24no—
323#95—24no—
324#95—24no—
325#95—22no—
326#95—24no—
327#95—22no—
328#95—24no—
329#95—24no—
330#95—24no—
331#95—24no—
332#95—24no—
333#95—24no—
334#95—24no—
335#95—24no—
336C22×C7C2×#12011yescharacteristic
337C22×C7#52511yescharacteristic
338C22×C7C2×#12411yescharacteristic
339C22×C7#52912yes—
340C22×C7#53211yescharacteristic
341C22×C7#53611yescharacteristic
342C22×C7#53611yescharacteristic
343C22×C7#53611yescharacteristic
344C22×C7#54112yes—
345C22×C7#54112yes—
346C22×C7#54112yes—
347C22×C7#54712yes—
348C22×C7#54712yes—
349C22×C7#54712yes—
350C22×C7#54812yes—
351C22×C7#54812yes—
352C22×C7#54812yes—
353C22×C7#55212yes—
354C22×C7#55212yes—
355C22×C7#55212yes—
356C22×C7#56412yes—
357C4×C7—24no—
358C4×C7—24no—
359C4×C7—42no—
360C4×C7—42no—
361C4×C7—42no—
362C4×C7—42no—
363C4×C7—42no—
364C4×C7—44no—
365C4×C7—44no—
366C4×C7—82no—
367C4×C7—82no—
368C24C24×C711yescharacteristic
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
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×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4C2×C7×D412yes—
421C22×C4C2×C7×D412yes—
422C22×C4C2×C7×D412yes—
423C22×C4C2×C7×D412yes—
424C22×C4C2×C7×D412yes—
425C22×C4C2×C7×D412yes—
426C22×C4C2×C7×D412yes—
427C22×C4C2×C7×D412yes—
428C22×C4C2×C7×D412yes—
429C22×C4C7×#4114yes—
430C22×C4C7×#4114yes—
431C22×C4C7×#4114yes—
432C4⋊C4—28no—
433C4⋊C4—28no—
434C4⋊C4—28no—
435C4⋊C4—28no—
436C4⋊C4—28no—
437C4⋊C4—28no—
438C4⋊C4—44no—
439C4⋊C4—48no—
440C42—28no—
441C42—28no—
442C2×C7#240611yescharacteristic
443C2×C7#243211yescharacteristic
444C2×C7#243611yescharacteristic
445C2×C7#247512yes—
446C2×C7#248912yes—
447C2×C7#251912yes—
448C2×C7#271912yes—
449C2×C7#271912yes—
450C2×C7#271912yes—
451C23C22×C7×D411yescharacteristic
452C23C22×C7×D411yescharacteristic
453C23C22×C7×D411yescharacteristic
454C23C2×C7×#4112yes—
455C23C2×C7×#4112yes—
456C23C2×C7×#4112yes—
457C23C7×2−1+412yes—
458C23C7×2−1+412yes—
459C23C7×2−1+412yes—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
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×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4C7×#12014yes—
522C2×C4C7×#12414yes—
523C7#1588111yescharacteristic, direct product factor, Sylow
524C22C2×C7×#12011yescharacteristic
525C22C7×#52511yescharacteristic
526C22C2×C7×#12411yescharacteristic
527C22C7×#52912yes—
528C22C7×#53211yescharacteristic
529C22C7×#53611yescharacteristic
530C22C7×#53611yescharacteristic
531C22C7×#53611yescharacteristic
532C22C7×#54112yes—
533C22C7×#54112yes—
534C22C7×#54112yes—
535C22C7×#54712yes—
536C22C7×#54712yes—
537C22C7×#54712yes—
538C22C7×#54812yes—
539C22C7×#54812yes—
540C22C7×#54812yes—
541C22C7×#55212yes—
542C22C7×#55212yes—
543C22C7×#55212yes—
544C22C7×#56412yes—
545C4—24no—
546C4—24no—
547C4—42no—
548C4—42no—
549C4—42no—
550C4—42no—
551C4—42no—
552C4—44no—
553C4—44no—
554C4—82no—
555C4—82no—
556C2C7×#240611yescharacteristic
557C2C7×#243211yescharacteristic
558C2C7×#243611yescharacteristic
559C2C7×#247512yes—
560C2C7×#248912yes—
561C2C7×#251912yes—
562C2C7×#271912yes—
563C2C7×#271912yes—
564C2C7×#271912yes—
subgroupG/H
center, socle, prime radicalC24×C7C24
commutator, Frattini, cosocleC24C24×C7
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
41. #15881C7direct (N × H)
523. C7#15881direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1252
C2×C7×#4002
C2×C7×#3982
C2×C7×#3822
C7×#14452
C7×#14422
C7×#14412
C7×#14362
#158817