Finite Group Databasebeta

← C7×#13889 #13191105

Subgroups — C7×#13889 #13191105

Order 1792.

1442 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#387C212yesmaximal
2C2×C7×#382C211yesmaximal, characteristic
3C2×C4×C7×C4⋊C4C211yesmaximal, characteristic
4C2×C4×C7×C4⋊C4C211yesmaximal, characteristic
5C7×#1444C212yesmaximal
6C7×#1441C212yesmaximal
7C7×#1436C212yesmaximal
8C7×C4⋊#95C211yesmaximal, characteristic
9C7×#1434C211yesmaximal, characteristic
10C7×#1434C211yesmaximal, characteristic
11C7×#1434C211yesmaximal, characteristic
12C22×C7×C4⋊C4C2212yes—
13C22×C7×C4⋊C4C2212yes—
14C22×C7×C4⋊C4C2212yes—
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C42×C7C2212yes—
18C22×C42×C7C2211yescharacteristic
19C22×C42×C7C2211yescharacteristic
20C22×C42×C7C2211yescharacteristic
21C7×#387—28no—
22C7×#382—24no—
23C4×C7×C4⋊C4—24no—
24C4×C7×C4⋊C4C418yescomplemented
25C2×C7×#95C2211yescharacteristic
26C2×C7×#95C2211yescharacteristic
27C2×C7×#95C2212yes—
28C2×C7×#95C2212yes—
29C2×C7×#95C2212yes—
30C2×C7×#95C2212yes—
31C2×C7×#95C2212yes—
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2212yes—
34C2×C7×#95C2212yes—
35C2×C7×#95C2212yes—
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2211yescharacteristic
38C2×C7×#95C2211yescharacteristic
39#13889C711yesmaximal, characteristic, direct product factor, Sylow
40C23×C4×C7C2312yes—
41C23×C4×C7C2312yes—
42C23×C4×C7C2311yescharacteristic
43C23×C4×C7C2312yes—
44C23×C4×C7C2312yes—
45C23×C4×C7C2311yescharacteristic
46C23×C4×C7C2311yescharacteristic
47C23×C4×C7C2311yescharacteristic
48C23×C4×C7C2311yescharacteristic
49C23×C4×C7C2311yescharacteristic
50C23×C4×C7C2311yescharacteristic
51C2×C7×C4⋊C4—24no—
52C2×C7×C4⋊C4—24no—
53C2×C7×C4⋊C4—24no—
54C2×C7×C4⋊C4—24no—
55C2×C7×C4⋊C4—24no—
56C2×C7×C4⋊C4—24no—
57C2×C7×C4⋊C4—24no—
58C2×C7×C4⋊C4—24no—
59C2×C7×C4⋊C4—42no—
60C2×C7×C4⋊C4—42no—
61C2×C7×C4⋊C4C2×C414yes—
62C2×C7×C4⋊C4C2×C414yes—
63C2×C7×C4⋊C4D414yes—
64C2×C7×C4⋊C4Q814yes—
65C2×C42×C7—22no—
66C2×C42×C7—22no—
67C2×C42×C7—24no—
68C2×C42×C7—22no—
69C2×C42×C7—22no—
70C2×C42×C7—24no—
71C2×C42×C7—24no—
72C2×C42×C7—42no—
73C2×C42×C7C2×C414yes—
74C2×C42×C7C2×C414yes—
75C2×C42×C7C2×C414yes—
76C7×#95—22no—
77C7×#95—24no—
78C7×#95—22no—
79C7×#95—24no—
80C7×#95—24no—
81C7×#95—24no—
82C7×#95—24no—
83C7×#95—24no—
84C7×#95—24no—
85C7×#95—24no—
86C7×#95—22no—
87C7×#95C2×C414yes—
88C7×#95C2×C414yes—
89C7×#95D414yes—
90C2×#387C2×C712yes—
91C2×#382C2×C711yescharacteristic
92C2×C4×C4⋊C4C2×C711yescharacteristic
93C2×C4×C4⋊C4C2×C711yescharacteristic
94#1444C2×C712yes—
95#1441C2×C712yes—
96#1436C2×C712yes—
97C4⋊#95C2×C711yescharacteristic
98#1434C2×C711yescharacteristic
99#1434C2×C711yescharacteristic
100#1434C2×C711yescharacteristic
101C24×C7C2411yescharacteristic
102C22×C4×C7—21no—
103C22×C4×C7—21no—
104C22×C4×C7—21no—
105C22×C4×C7—22no—
106C22×C4×C7—22no—
107C22×C4×C7—21no—
108C22×C4×C7—21no—
109C22×C4×C7—21no—
110C22×C4×C7—22no—
111C22×C4×C7—22no—
112C22×C4×C7—22no—
113C22×C4×C7—21no—
114C22×C4×C7—21no—
115C22×C4×C7—21no—
116C22×C4×C7—22no—
117C22×C4×C7—21no—
118C22×C4×C7—21no—
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—21no—
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×C7C22×C412yes—
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×C7C2×D414yes—
158C22×C4×C7C2×D412yes—
159C22×C4×C7C2×D412yes—
160C22×C4×C7C2×D412yes—
161C22×C4×C7C2×D412yes—
162C22×C4×C7C2×Q812yes—
163C22×C4×C7C2×Q812yes—
164C22×C4×C7C2×Q812yes—
165C22×C4×C7#4114yes—
166C22×C4×C7#4114yes—
167C22×C4×C7#4114yes—
168C22×C4×C7#4112yes—
169C7×C4⋊C4—216no—
170C7×C4⋊C4—28no—
171C7×C4⋊C4—48no—
172C7×C4⋊C4—48no—
173C7×C4⋊C4C4⋊C4116yescomplemented
174C42×C7—28no—
175C42×C7—28no—
176C42×C7—28no—
177C42×C7—48no—
178C22×C4⋊C4C22×C712yes—
179C22×C4⋊C4C22×C712yes—
180C22×C4⋊C4C22×C712yes—
181C22×C4⋊C4C22×C711yescharacteristic
182C22×C4⋊C4C22×C711yescharacteristic
183C22×C42C22×C712yes—
184C22×C42C22×C711yescharacteristic
185C22×C42C22×C711yescharacteristic
186C22×C42C22×C711yescharacteristic
187#387—28no—
188#382—24no—
189C4×C4⋊C4—24no—
190C4×C4⋊C4C4×C718yescomplemented
191C2×#95C22×C711yescharacteristic
192C2×#95C22×C711yescharacteristic
193C2×#95C22×C711yescharacteristic
194C2×#95C22×C712yes—
195C2×#95C22×C712yes—
196C2×#95C22×C712yes—
197C2×#95C22×C712yes—
198C2×#95C22×C712yes—
199C2×#95C22×C712yes—
200C2×#95C22×C712yes—
201C2×#95C22×C712yes—
202C2×#95C22×C711yescharacteristic
203C2×#95C22×C711yescharacteristic
204C2×#95C22×C711yescharacteristic
205C23×C7C23×C411yescharacteristic
206C23×C7C22×D411yescharacteristic
207C23×C7C22×D411yescharacteristic
208C23×C7C22×Q811yescharacteristic
209C23×C7C2×#4112yes—
210C23×C7C2×#4112yes—
211C23×C7C2×#4111yescharacteristic
212C23×C7C2×#4112yes—
213C23×C7H(5,𝔽2)11yescharacteristic
214C23×C72−1+412yes—
215C23×C72−1+411yescharacteristic
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—22no—
227C2×C4×C7—22no—
228C2×C4×C7—24no—
229C2×C4×C7—24no—
230C2×C4×C7—24no—
231C2×C4×C7—24no—
232C2×C4×C7—22no—
233C2×C4×C7—22no—
234C2×C4×C7—24no—
235C2×C4×C7—22no—
236C2×C4×C7—22no—
237C2×C4×C7—22no—
238C2×C4×C7—22no—
239C2×C4×C7—24no—
240C2×C4×C7—24no—
241C2×C4×C7—24no—
242C2×C4×C7—22no—
243C2×C4×C7—22no—
244C2×C4×C7—22no—
245C2×C4×C7—22no—
246C2×C4×C7—22no—
247C2×C4×C7—24no—
248C2×C4×C7—24no—
249C2×C4×C7—24no—
250C2×C4×C7—24no—
251C2×C4×C7—24no—
252C2×C4×C7—24no—
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×C7—42no—
272C2×C4×C7—42no—
273C2×C4×C7—42no—
274C2×C4×C7—42no—
275C2×C4×C7—42no—
276C2×C4×C7—42no—
277C2×C4×C7C2×C4⋊C414yes—
278C2×C4×C7C2×C4⋊C414yes—
279C2×C4×C7C2×C4⋊C414yes—
280C2×C4×C7#11714yes—
281C2×C4×C7#11714yes—
282C2×C4×C7C4×D414yes—
283C23×C4C23×C712yes—
284C23×C4C23×C712yes—
285C23×C4C23×C711yescharacteristic
286C23×C4C23×C712yes—
287C23×C4C23×C712yes—
288C23×C4C23×C711yescharacteristic
289C23×C4C23×C711yescharacteristic
290C23×C4C23×C711yescharacteristic
291C23×C4C23×C711yescharacteristic
292C23×C4C23×C711yescharacteristic
293C23×C4C23×C711yescharacteristic
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4C2×C4×C714yes—
305C2×C4⋊C4C2×C4×C714yes—
306C2×C4⋊C4C7×D414yes—
307C2×C4⋊C4C7×Q814yes—
308C2×C42—22no—
309C2×C42—22no—
310C2×C42—24no—
311C2×C42—22no—
312C2×C42—22no—
313C2×C42—24no—
314C2×C42—24no—
315C2×C42—42no—
316C2×C42C2×C4×C714yes—
317C2×C42C2×C4×C714yes—
318C2×C42C2×C4×C714yes—
319#95—22no—
320#95—24no—
321#95—22no—
322#95—24no—
323#95—24no—
324#95—24no—
325#95—24no—
326#95—24no—
327#95—24no—
328#95—24no—
329#95—22no—
330#95C2×C4×C714yes—
331#95C2×C4×C714yes—
332#95C7×D414yes—
333C22×C7C22×C4⋊C411yescharacteristic
334C22×C7C2×#11711yescharacteristic
335C22×C7C2×#11711yescharacteristic
336C22×C7C2×C4×D411yescharacteristic
337C22×C7C4×#4111yescharacteristic
338C22×C7#51911yescharacteristic
339C22×C7#52011yescharacteristic
340C22×C7#52512yes—
341C22×C7#52912yes—
342C22×C7#53212yes—
343C22×C7#53312yes—
344C22×C7#54112yes—
345C22×C7#54212yes—
346C22×C7D4211yescharacteristic
347C22×C7#54712yes—
348C22×C7#54711yescharacteristic
349C22×C7#54812yes—
350C22×C7D4×Q811yescharacteristic
351C22×C7#55112yes—
352C22×C7#55212yes—
353C22×C7#55212yes—
354C22×C7#55411yescharacteristic
355C22×C7#55712yes—
356C4×C7—24no—
357C4×C7—24no—
358C4×C7—24no—
359C4×C7—24no—
360C4×C7—24no—
361C4×C7—24no—
362C4×C7—44no—
363C4×C7—44no—
364C4×C7—42no—
365C4×C7—82no—
366C4×C7—82no—
367C24C24×C711yescharacteristic
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
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—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×C4C22×C4×C712yes—
417C22×C4C22×C4×C712yes—
418C22×C4C22×C4×C712yes—
419C22×C4C22×C4×C712yes—
420C22×C4C22×C4×C712yes—
421C22×C4C22×C4×C712yes—
422C22×C4C22×C4×C712yes—
423C22×C4C2×C7×D414yes—
424C22×C4C2×C7×D412yes—
425C22×C4C2×C7×D412yes—
426C22×C4C2×C7×D412yes—
427C22×C4C2×C7×D412yes—
428C22×C4C2×C7×Q812yes—
429C22×C4C2×C7×Q812yes—
430C22×C4C2×C7×Q812yes—
431C22×C4C7×#4114yes—
432C22×C4C7×#4114yes—
433C22×C4C7×#4114yes—
434C22×C4C7×#4112yes—
435C4⋊C4—216no—
436C4⋊C4—28no—
437C4⋊C4—48no—
438C4⋊C4—48no—
439C4⋊C4C7×C4⋊C4116yescomplemented
440C42—28no—
441C42—28no—
442C42—28no—
443C42—48no—
444C2×C7#228511yescharacteristic
445C2×C7#229011yescharacteristic
446C2×C7#232011yescharacteristic
447C2×C7#234311yescharacteristic
448C2×C7#234411yescharacteristic
449C2×C7D4×C4⋊C411yescharacteristic
450C2×C7#235111yescharacteristic
451C2×C7#246112yes—
452C2×C7#246212yes—
453C2×C7#251912yes—
454C2×C7#252012yes—
455C23C23×C4×C711yescharacteristic
456C23C22×C7×D411yescharacteristic
457C23C22×C7×D411yescharacteristic
458C23C22×C7×Q811yescharacteristic
459C23C2×C7×#4112yes—
460C23C2×C7×#4112yes—
461C23C2×C7×#4111yescharacteristic
462C23C2×C7×#4112yes—
463C23C7×H(5,𝔽2)11yescharacteristic
464C23C7×2−1+412yes—
465C23C7×2−1+411yescharacteristic
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
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×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4C2×C7×C4⋊C414yes—
528C2×C4C2×C7×C4⋊C414yes—
529C2×C4C2×C7×C4⋊C414yes—
530C2×C4C7×#11714yes—
531C2×C4C7×#11714yes—
532C2×C4C4×C7×D414yes—
533C7#1388911yescharacteristic, direct product factor, Sylow
534C22C22×C7×C4⋊C411yescharacteristic
535C22C2×C7×#11711yescharacteristic
536C22C2×C7×#11711yescharacteristic
537C22C2×C4×C7×D411yescharacteristic
538C22C4×C7×#4111yescharacteristic
539C22C7×#51911yescharacteristic
540C22C7×#52011yescharacteristic
541C22C7×#52512yes—
542C22C7×#52912yes—
543C22C7×#53212yes—
544C22C7×#53312yes—
545C22C7×#54112yes—
546C22C7×#54212yes—
547C22C7×D4211yescharacteristic
548C22C7×#54712yes—
549C22C7×#54711yescharacteristic
550C22C7×#54812yes—
551C22C7×D4×Q811yescharacteristic
552C22C7×#55112yes—
553C22C7×#55212yes—
554C22C7×#55212yes—
555C22C7×#55411yescharacteristic
556C22C7×#55712yes—
557C4—24no—
558C4—24no—
559C4—24no—
560C4—24no—
561C4—24no—
562C4—24no—
563C4—44no—
564C4—44no—
565C4—42no—
566C4—82no—
567C4—82no—
568C2C7×#228511yescharacteristic
569C2C7×#229011yescharacteristic
570C2C7×#232011yescharacteristic
571C2C7×#234311yescharacteristic
572C2C7×#234411yescharacteristic
573C2C7×D4×C4⋊C411yescharacteristic
574C2C7×#235111yescharacteristic
575C2C7×#246112yes—
576C2C7×#246212yes—
577C2C7×#251912yes—
578C2C7×#252012yes—
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
24. C4×C7×C4⋊C4C4semidirect
39. #13889C7direct (N × H)
173. C7×C4⋊C4C4⋊C4semidirect
190. C4×C4⋊C4C4×C7semidirect
439. C4⋊C4C7×C4⋊C4semidirect
533. C7#13889direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3872
C2×C7×#3822
C2×C4×C7×C4⋊C42
C7×#14442
C7×#14412
C7×#14362
C7×C4⋊#952
C7×#14342
#138897