Finite Group Databasebeta

← C7×#25899 #13203115

Subgroups — C7×#25899 #13203115

Order 1792.

1574 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3496C211yesmaximal, characteristic
2C7×#2436C212yesmaximal, complemented
3C7×#2409C211yesmaximal, characteristic, complemented
4C7×#2044C214yesmaximal, complemented
5C7×#1964C212yesmaximal, complemented
6C7×#1790C214yesmaximal, complemented
7C4×C7×#99C211yesmaximal, characteristic, complemented
8C2×C7×H(5,𝔽2)C2212yes—
9C23×C7×Q8C2211yescharacteristic, complemented
10C7×#547—22no—
11C7×#546—24no—
12C7×D42—22no—
13C7×#537—21no—
14C7×#534—21no—
15C7×#534C2212yes—
16C7×#532—21no—
17C2×C7×#124—22no—
18C2×C7×C22⋊Q8—21no—
19C2×C7×#121—21no—
20C2×C7×#121C2212yes—
21C2×C4×C7×D4C2211yescharacteristic
22C2×C7×#99C2212yes—
23C2×C7×#99C2218yescomplemented
24C7×#395—21no—
25C7×#393—21no—
26C7×#393—24no—
27C7×#391—22no—
28C7×#391—21no—
29C7×#386C2212yes—
30C7×#386C2218yescomplemented
31C7×#385C2212yescomplemented
32C7×#380C2211yescharacteristic, complemented
33C4×C7×C22⋊C4C2212yescomplemented
34C7×#342C2212yescomplemented
35#25899C711yesmaximal, characteristic, direct product factor, Sylow
36C7×H(5,𝔽2)—28no—
37C7×H(5,𝔽2)—44no—
38C2×C7×#41—22no—
39C2×C7×#41—24no—
40C22×C7×Q8—21no—
41C22×C7×Q8—22no—
42C22×C7×Q8—22no—
43C22×C7×Q8—21no—
44C22×C7×Q8—44no—
45C22×C7×D4—22no—
46C22×C7×D4—24no—
47C22×C7×D4—21no—
48C22×C7×D4D412yes—
49C22×C7×D4C2314yes—
50C22×C7×D4C2311yescharacteristic
51C23×C4×C7D411yescharacteristic
52C23×C4×C7C2312yes—
53C23×C4×C7C2311yescharacteristic
54C7×C4⋊Q8—21no—
55C7×#127—21no—
56C7×#124—22no—
57C7×#124—48no—
58C7×#123—24no—
59C7×#123—24no—
60C7×C22⋊Q8—24no—
61C7×C22⋊Q8—44no—
62C7×#121—22no—
63C7×#121—22no—
64C7×#121—24no—
65C7×#121—22no—
66C7×#121—22no—
67C7×#121—22no—
68C7×#121—22no—
69C7×#121—22no—
70C7×#121—22no—
71C7×#120—24no—
72C7×#120—24no—
73C4×C7×D4—22no—
74C4×C7×D4—22no—
75C4×C7×D4—22no—
76C4×C7×D4—22no—
77C2×C7×C4⋊C4—21no—
78C2×C7×C4⋊C4—21no—
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4D411yescharacteristic
81C2×C7×C4⋊C4D412yes—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4—28no—
85C2×C7×C22⋊C4D411yescharacteristic
86C2×C7×C22⋊C4D414yes—
87C2×C7×C22⋊C4C2314yes—
88C2×C7×C22⋊C4C2312yes—
89C2×C7×C22⋊C4C2311yescharacteristic
90C2×C42×C7—22no—
91C2×C42×C7D411yescharacteristic
92C7×#99—24no—
93C7×#99—48no—
94C7×#95—22no—
95C7×#95—21no—
96C7×#95—22no—
97C7×#95—22no—
98C7×#95—28no—
99#3496C2×C711yescharacteristic
100#2436C2×C712yescomplemented
101#2409C2×C711yescharacteristic, complemented
102#2044C2×C714yescomplemented
103#1964C2×C712yescomplemented
104#1790C2×C714yescomplemented
105C4×#99C2×C711yescharacteristic, complemented
106C24×C7—22no—
107C24×C7C2×D414yes—
108C24×C7C2×D411yescharacteristic
109C24×C7C2411yescharacteristic
110C7×#41—416no—
111C7×#41—44no—
112C7×#41—44no—
113C2×C7×Q8—22no—
114C2×C7×Q8—24no—
115C2×C7×Q8—28no—
116C2×C7×Q8—44no—
117C2×C7×Q8—42no—
118C2×C7×Q8—48no—
119C2×C7×Q8—44no—
120C2×C7×Q8—41no—
121C2×C7×Q8—42no—
122C2×C7×Q8—41no—
123C2×C7×D4—22no—
124C2×C7×D4—22no—
125C2×C7×D4—24no—
126C2×C7×D4—22no—
127C2×C7×D4—24no—
128C2×C7×D4—24no—
129C2×C7×D4—28no—
130C2×C7×D4—28no—
131C2×C7×D4—22no—
132C2×C7×D4—22no—
133C2×C7×D4—22no—
134C2×C7×D4—22no—
135C2×C7×D4—44no—
136C2×C7×D4—416no—
137C2×C7×D4—44no—
138C2×C7×D4—44no—
139C2×C7×D4—82no—
140C2×C7×D4#4114yes—
141C22×C4×C7—22no—
142C22×C4×C7—24no—
143C22×C4×C7—24no—
144C22×C4×C7—22no—
145C22×C4×C7—21no—
146C22×C4×C7—21no—
147C22×C4×C7—24no—
148C22×C4×C7—22no—
149C22×C4×C7—44no—
150C22×C4×C7—42no—
151C22×C4×C7—42no—
152C22×C4×C7C2×D414yes—
153C22×C4×C7C2×D412yes—
154C22×C4×C7C2×D411yescharacteristic
155C22×C4×C7C2×D411yescharacteristic
156C22×C4×C7C2×D411yescharacteristic
157C22×C4×C7C2×D411yescharacteristic
158C22×C4×C7C2×D412yes—
159C22×C4×C7C2×D411yescharacteristic
160C7×C4⋊C4—22no—
161C7×C4⋊C4—22no—
162C7×C4⋊C4—22no—
163C7×C4⋊C4—22no—
164C7×C4⋊C4—22no—
165C7×C4⋊C4—42no—
166C7×C4⋊C4—44no—
167C7×C22⋊C4—24no—
168C7×C22⋊C4—24no—
169C7×C22⋊C4—22no—
170C7×C22⋊C4—24no—
171C7×C22⋊C4—22no—
172C7×C22⋊C4—24no—
173C7×C22⋊C4—24no—
174C7×C22⋊C4—24no—
175C7×C22⋊C4—24no—
176C7×C22⋊C4—44no—
177C7×C22⋊C4—416no—
178C42×C7—21no—
179C42×C7—21no—
180C42×C7—44no—
181C2×H(5,𝔽2)C22×C712yes—
182C23×Q8C22×C711yescharacteristic, complemented
183#547—22no—
184#546—24no—
185D42—22no—
186#537—21no—
187#534—21no—
188#534C22×C712yes—
189#532—21no—
190C2×#124—22no—
191C2×C22⋊Q8—21no—
192C2×#121—21no—
193C2×#121C22×C712yes—
194C2×C4×D4C22×C711yescharacteristic
195C2×#99C22×C712yes—
196C2×#99C22×C718yescomplemented
197#395—21no—
198#393—21no—
199#393—24no—
200#391—22no—
201#391—21no—
202#386C22×C712yes—
203#386C22×C718yescomplemented
204#385C22×C712yescomplemented
205#380C22×C711yescharacteristic, complemented
206C4×C22⋊C4C22×C712yescomplemented
207#342C22×C712yescomplemented
208C23×C7—21no—
209C23×C7—21no—
210C23×C7—24no—
211C23×C7—28no—
212C23×C7—41no—
213C23×C7—41no—
214C23×C7—41no—
215C23×C7—41no—
216C23×C7—44no—
217C23×C7—44no—
218C23×C7—44no—
219C23×C7—82no—
220C23×C7—82no—
221C23×C7#12412yescomplemented
222C23×C7C22×D411yescharacteristic
223C23×C7C22×D412yes—
224C23×C7C2×#4112yes—
225C23×C7H(5,𝔽2)12yes—
226C7×Q8—44no—
227C7×Q8—48no—
228C7×Q8—44no—
229C7×Q8—44no—
230C7×D4—28no—
231C7×D4—44no—
232C7×D4—48no—
233C7×D4—44no—
234C7×D4—44no—
235C7×D4—48no—
236C7×D4—44no—
237C7×D4—82no—
238C7×D4—82no—
239C7×D4—82no—
240C2×C4×C7—21no—
241C2×C4×C7—21no—
242C2×C4×C7—24no—
243C2×C4×C7—22no—
244C2×C4×C7—28no—
245C2×C4×C7—24no—
246C2×C4×C7—21no—
247C2×C4×C7—21no—
248C2×C4×C7—24no—
249C2×C4×C7—28no—
250C2×C4×C7—42no—
251C2×C4×C7—41no—
252C2×C4×C7—48no—
253C2×C4×C7—42no—
254C2×C4×C7—44no—
255C2×C4×C7—44no—
256C2×C4×C7—42no—
257C2×C4×C7—42no—
258C2×C4×C7—41no—
259C2×C4×C7—41no—
260C2×C4×C7—44no—
261C2×C4×C7—42no—
262C2×C4×C7—42no—
263C2×C4×C7—44no—
264C2×C4×C7—42no—
265C2×C4×C7—44no—
266C2×C4×C7—81no—
267C2×C4×C7#12011yescharacteristic
268C2×C4×C7#12012yes—
269C2×C4×C7#12011yescharacteristic
270C2×C4×C7#12412yescomplemented
271H(5,𝔽2)—28no—
272H(5,𝔽2)—44no—
273C2×#41—22no—
274C2×#41—24no—
275C22×Q8—21no—
276C22×Q8—22no—
277C22×Q8—22no—
278C22×Q8—21no—
279C22×Q8—44no—
280C22×D4—22no—
281C22×D4—24no—
282C22×D4—21no—
283C22×D4C7×D412yes—
284C22×D4C23×C714yes—
285C22×D4C23×C711yescharacteristic
286C23×C4C7×D411yescharacteristic
287C23×C4C23×C712yes—
288C23×C4C23×C711yescharacteristic
289C4⋊Q8—21no—
290#127—21no—
291#124—22no—
292#124—48no—
293#123—24no—
294#123—24no—
295C22⋊Q8—24no—
296C22⋊Q8—44no—
297#121—22no—
298#121—22no—
299#121—24no—
300#121—22no—
301#121—22no—
302#121—22no—
303#121—22no—
304#121—22no—
305#121—22no—
306#120—24no—
307#120—24no—
308C4×D4—22no—
309C4×D4—22no—
310C4×D4—22no—
311C4×D4—22no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4C7×D411yescharacteristic
316C2×C4⋊C4C7×D412yes—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4C7×D411yescharacteristic
321C2×C22⋊C4C7×D414yes—
322C2×C22⋊C4C23×C714yes—
323C2×C22⋊C4C23×C712yes—
324C2×C22⋊C4C23×C711yescharacteristic
325C2×C42—22no—
326C2×C42C7×D411yescharacteristic
327#99—24no—
328#99—48no—
329#95—22no—
330#95—21no—
331#95—22no—
332#95—22no—
333#95—28no—
334C22×C7—21no—
335C22×C7—22no—
336C22×C7—21no—
337C22×C7—22no—
338C22×C7—22no—
339C22×C7—42no—
340C22×C7—42no—
341C22×C7—42no—
342C22×C7—41no—
343C22×C7—41no—
344C22×C7—44no—
345C22×C7—44no—
346C22×C7—44no—
347C22×C7—81no—
348C22×C7—88no—
349C22×C7—164no—
350C22×C7C2×#12011yescharacteristic
351C22×C7C2×#12411yescharacteristic
352C22×C7#53511yescharacteristic
353C22×C7#54614yes—
354C4×C7—22no—
355C4×C7—21no—
356C4×C7—22no—
357C4×C7—44no—
358C4×C7—44no—
359C4×C7—41no—
360C4×C7—41no—
361C4×C7—82no—
362C4×C7—84no—
363C4×C7B(4,𝔽2)12yes—
364C24—22no—
365C24C2×C7×D414yes—
366C24C2×C7×D411yescharacteristic
367C24C24×C711yescharacteristic
368#41—416no—
369#41—44no—
370#41—44no—
371C2×Q8—22no—
372C2×Q8—24no—
373C2×Q8—28no—
374C2×Q8—44no—
375C2×Q8—42no—
376C2×Q8—48no—
377C2×Q8—44no—
378C2×Q8—41no—
379C2×Q8—42no—
380C2×Q8—41no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—24no—
384C2×D4—22no—
385C2×D4—24no—
386C2×D4—24no—
387C2×D4—28no—
388C2×D4—28no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—44no—
394C2×D4—416no—
395C2×D4—44no—
396C2×D4—44no—
397C2×D4—82no—
398C2×D4C7×#4114yes—
399C22×C4—22no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—24no—
406C22×C4—22no—
407C22×C4—42no—
408C22×C4—44no—
409C22×C4—42no—
410C22×C4C2×C7×D414yes—
411C22×C4C2×C7×D412yes—
412C22×C4C2×C7×D411yescharacteristic
413C22×C4C2×C7×D411yescharacteristic
414C22×C4C2×C7×D411yescharacteristic
415C22×C4C2×C7×D411yescharacteristic
416C22×C4C2×C7×D412yes—
417C22×C4C2×C7×D411yescharacteristic
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—42no—
424C4⋊C4—44no—
425C22⋊C4—24no—
426C22⋊C4—24no—
427C22⋊C4—22no—
428C22⋊C4—24no—
429C22⋊C4—22no—
430C22⋊C4—24no—
431C22⋊C4—24no—
432C22⋊C4—24no—
433C22⋊C4—24no—
434C22⋊C4—44no—
435C22⋊C4—416no—
436C42—21no—
437C42—21no—
438C42—44no—
439C2×C7—21no—
440C2×C7—24no—
441C2×C7—21no—
442C2×C7—42no—
443C2×C7—84no—
444C2×C7#243511yescharacteristic
445C2×C7C2×B(4,𝔽2)11yescharacteristic
446C2×C7#302811yescharacteristic
447C23—21no—
448C23—21no—
449C23—24no—
450C23—28no—
451C23—41no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—44no—
456C23—44no—
457C23—44no—
458C23—82no—
459C23—82no—
460C23C7×#12412yescomplemented
461C23C22×C7×D411yescharacteristic
462C23C22×C7×D412yes—
463C23C2×C7×#4112yes—
464C23C7×H(5,𝔽2)12yes—
465Q8—44no—
466Q8—48no—
467Q8—44no—
468Q8—44no—
469D4—28no—
470D4—44no—
471D4—48no—
472D4—44no—
473D4—44no—
474D4—48no—
475D4—44no—
476D4—82no—
477D4—82no—
478D4—82no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—28no—
484C2×C4—24no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—24no—
488C2×C4—28no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—48no—
492C2×C4—42no—
493C2×C4—44no—
494C2×C4—44no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—44no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—44no—
503C2×C4—42no—
504C2×C4—44no—
505C2×C4—81no—
506C2×C4C7×#12011yescharacteristic
507C2×C4C7×#12012yes—
508C2×C4C7×#12011yescharacteristic
509C2×C4C7×#12412yescomplemented
510C7#2589911yescharacteristic, direct product factor, Sylow
511C22—21no—
512C22—22no—
513C22—21no—
514C22—22no—
515C22—22no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—41no—
520C22—41no—
521C22—44no—
522C22—44no—
523C22—44no—
524C22—81no—
525C22—88no—
526C22—164no—
527C22C2×C7×#12011yescharacteristic
528C22C2×C7×#12411yescharacteristic
529C22C7×#53511yescharacteristic
530C22C7×#54614yes—
531C4—22no—
532C4—21no—
533C4—22no—
534C4—44no—
535C4—44no—
536C4—41no—
537C4—41no—
538C4—82no—
539C4—84no—
540C4C7×B(4,𝔽2)12yes—
541C2—21no—
542C2—24no—
543C2—21no—
544C2—42no—
545C2—84no—
546C2C7×#243511yescharacteristic
547C2C2×C7×B(4,𝔽2)11yescharacteristic
548C2C7×#302811yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC24C24×C7
prime radicalC7×#3496C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C7×#2436C2semidirect
3. C7×#2409C2semidirect
4. C7×#2044C2semidirect
5. C7×#1964C2semidirect
6. C7×#1790C2semidirect
7. C4×C7×#99C2semidirect
9. C23×C7×Q8C22semidirect
23. C2×C7×#99C22semidirect
30. C7×#386C22semidirect
31. C7×#385C22semidirect
32. C7×#380C22semidirect
33. C4×C7×C22⋊C4C22semidirect
34. C7×#342C22semidirect
35. #25899C7direct (N × H)
100. #2436C2×C7semidirect
101. #2409C2×C7semidirect
102. #2044C2×C7semidirect
103. #1964C2×C7semidirect
104. #1790C2×C7semidirect
105. C4×#99C2×C7semidirect
182. C23×Q8C22×C7semidirect
196. C2×#99C22×C7semidirect
203. #386C22×C7semidirect
204. #385C22×C7semidirect
205. #380C22×C7semidirect
206. C4×C22⋊C4C22×C7semidirect
207. #342C22×C7semidirect
221. C23×C7#124semidirect
270. C2×C4×C7#124semidirect
460. C23C7×#124semidirect
509. C2×C4C7×#124semidirect
510. C7#25899direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#34962
C7×#24362
C7×#24092
C7×#20442
C7×#19642
C7×#17902
C4×C7×#992
#258997