Finite Group Databasebeta

← C7×#25949 #13203165

Subgroups — C7×#25949 #13203165

Order 1792.

1202 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3501C211yesmaximal, characteristic, complemented
2C7×#2561C212yesmaximal, complemented
3C7×#2534C211yesmaximal, characteristic
4C7×#2030C212yesmaximal, complemented
5C7×#2029C212yesmaximal, complemented
6C7×#1996C212yesmaximal, complemented
7C7×#1890C212yesmaximal, complemented
8C7×#1889C212yesmaximal
9C4×C7×#99C211yesmaximal, characteristic, complemented
10C7×#554—24no—
11C7×#554—22no—
12C7×D4×Q8—22no—
13C7×#544—21no—
14C7×#543—21no—
15C7×#543C2212yes—
16C7×#533—21no—
17C2×C7×#123C2211yescharacteristic
18C2×C7×C22⋊Q8—21no—
19C2×C7×C22⋊Q8C2212yes—
20C2×C7×#120C2211yescharacteristic
21C7×#518C2212yes—
22C2×C4×C7×D4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C2×C7×#99C2212yes—
25C7×#397—22no—
26C7×#396—21no—
27C7×#394—21no—
28C7×#393—22no—
29C7×#388—24no—
30C7×#388—21no—
31C7×#386—21no—
32C7×#381C2211yescharacteristic
33C7×#381C2214yes—
34C7×#380C2211yescharacteristic
35C7×#379C2211yescharacteristic
36C7×#379C2214yes—
37C4×C7×C22⋊C4C2212yes—
38C7×#342C2214yes—
39C7×#342C2214yes—
40C7×#342C2212yes—
41#25949C711yesmaximal, characteristic, direct product factor, Sylow
42C25×C7C2311yescharacteristic
43C22×C7×Q8—21no—
44C22×C7×Q8D412yescomplemented
45C22×C7×D4—21no—
46C22×C7×D4C2311yescharacteristic
47C23×C4×C7D411yescharacteristic
48C23×C4×C7C2311yescharacteristic
49C23×C4×C7C2311yescharacteristic
50C7×C4⋊Q8—21no—
51C7×C4⋊Q8—21no—
52C7×C4⋊Q8—24no—
53C7×#125—22no—
54C7×#125—24no—
55C7×#123—24no—
56C7×C22⋊Q8—22no—
57C7×C22⋊Q8—22no—
58C7×C22⋊Q8—24no—
59C7×C22⋊Q8—24no—
60C7×C22⋊Q8—22no—
61C7×C22⋊Q8—22no—
62C7×C22⋊Q8—22no—
63C7×C22⋊Q8—22no—
64C7×C22⋊Q8—22no—
65C7×C22⋊Q8—22no—
66C7×C22⋊Q8—24no—
67C7×C22⋊Q8—24no—
68C7×#120—24no—
69C4×C7×Q8—22no—
70C4×C7×Q8—22no—
71C4×C7×D4—22no—
72C4×C7×D4—22no—
73C4×C7×D4—24no—
74C4×C7×D4—24no—
75C7×#117—22no—
76C2×C7×C4⋊C4—21no—
77C2×C7×C4⋊C4—22no—
78C2×C7×C4⋊C4—21no—
79C2×C7×C4⋊C4—21no—
80C2×C7×C4⋊C4D411yescharacteristic
81C2×C7×C4⋊C4D414yescomplemented
82C2×C7×C4⋊C4D412yescomplemented
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4—21no—
85C2×C7×C22⋊C4—21no—
86C2×C7×C22⋊C4—22no—
87C2×C7×C22⋊C4—22no—
88C2×C7×C22⋊C4—21no—
89C2×C7×C22⋊C4—21no—
90C2×C7×C22⋊C4—24no—
91C2×C7×C22⋊C4—21no—
92C2×C7×C22⋊C4—21no—
93C2×C7×C22⋊C4—24no—
94C2×C7×C22⋊C4D411yescharacteristic
95C2×C7×C22⋊C4C2311yescharacteristic
96C2×C7×C22⋊C4C2311yescharacteristic
97C2×C7×C22⋊C4C2314yes—
98C2×C7×C22⋊C4C2311yescharacteristic
99C2×C7×C22⋊C4C2314yes—
100C2×C42×C7—22no—
101C2×C42×C7D411yescharacteristic
102C7×#99—24no—
103C7×#95—22no—
104C7×#95—21no—
105C7×#95—21no—
106C7×#95—24no—
107C7×#95—21no—
108C7×#95—24no—
109#3501C2×C711yescharacteristic, complemented
110#2561C2×C712yescomplemented
111#2534C2×C711yescharacteristic
112#2030C2×C712yescomplemented
113#2029C2×C712yescomplemented
114#1996C2×C712yescomplemented
115#1890C2×C712yescomplemented
116#1889C2×C712yes—
117C4×#99C2×C711yescharacteristic, complemented
118C24×C7—22no—
119C24×C7—21no—
120C24×C7—22no—
121C24×C7—22no—
122C24×C7—42no—
123C24×C7—81no—
124C24×C7C2×D411yescharacteristic
125C24×C7C2411yescharacteristic
126C2×C7×Q8—22no—
127C2×C7×Q8—22no—
128C2×C7×Q8—22no—
129C2×C7×Q8—22no—
130C2×C7×Q8—82no—
131C2×C7×Q8—82no—
132C2×C7×D4—22no—
133C2×C7×D4—22no—
134C2×C7×D4—42no—
135C2×C7×D4—42no—
136C2×C7×D4—81no—
137C2×C7×D4#4114yes—
138C22×C4×C7—22no—
139C22×C4×C7—22no—
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—22no—
143C22×C4×C7—24no—
144C22×C4×C7—21no—
145C22×C4×C7—21no—
146C22×C4×C7—21no—
147C22×C4×C7—22no—
148C22×C4×C7—22no—
149C22×C4×C7—81no—
150C22×C4×C7—81no—
151C22×C4×C7C2×D411yescharacteristic
152C22×C4×C7C2×D411yescharacteristic
153C22×C4×C7C2×D411yescharacteristic
154C22×C4×C7C2×D414yes—
155C22×C4×C7C2×D414yes—
156C22×C4×C7C2×D411yescharacteristic
157C22×C4×C7C2×D412yes—
158C22×C4×C7C2×D412yes—
159C22×C4×C7C2×D411yescharacteristic
160C7×C4⋊C4—22no—
161C7×C4⋊C4—24no—
162C7×C4⋊C4—22no—
163C7×C4⋊C4—22no—
164C7×C4⋊C4—24no—
165C7×C4⋊C4—22no—
166C7×C4⋊C4—24no—
167C7×C4⋊C4—22no—
168C7×C4⋊C4—22no—
169C7×C4⋊C4—22no—
170C7×C4⋊C4—24no—
171C7×C4⋊C4—42no—
172C7×C4⋊C4—81no—
173C7×C22⋊C4—24no—
174C7×C22⋊C4—24no—
175C7×C22⋊C4—22no—
176C7×C22⋊C4—24no—
177C7×C22⋊C4—22no—
178C7×C22⋊C4—24no—
179C7×C22⋊C4—22no—
180C7×C22⋊C4—22no—
181C7×C22⋊C4—24no—
182C7×C22⋊C4—48no—
183C7×C22⋊C4—42no—
184C7×C22⋊C4—42no—
185C7×C22⋊C4—41no—
186C7×C22⋊C4—41no—
187C7×C22⋊C4—42no—
188C7×C22⋊C4—42no—
189C7×C22⋊C4—81no—
190C7×C22⋊C4—84no—
191C42×C7—24no—
192C42×C7—21no—
193C42×C7—21no—
194C42×C7—82no—
195#554—24no—
196#554—22no—
197D4×Q8—22no—
198#544—21no—
199#543—21no—
200#543C22×C712yes—
201#533—21no—
202C2×#123C22×C711yescharacteristic
203C2×C22⋊Q8—21no—
204C2×C22⋊Q8C22×C712yes—
205C2×#120C22×C711yescharacteristic
206#518C22×C712yes—
207C2×C4×D4C22×C711yescharacteristic
208C22×C22⋊C4C22×C711yescharacteristic
209C2×#99C22×C712yes—
210#397—22no—
211#396—21no—
212#394—21no—
213#393—22no—
214#388—24no—
215#388—21no—
216#386—21no—
217#381C22×C714yes—
218#381C22×C711yescharacteristic
219#380C22×C711yescharacteristic
220#379C22×C714yes—
221#379C22×C711yescharacteristic
222C4×C22⋊C4C22×C712yes—
223#342C22×C714yes—
224#342C22×C714yes—
225#342C22×C712yes—
226C23×C7—21no—
227C23×C7—21no—
228C23×C7—24no—
229C23×C7—22no—
230C23×C7—41no—
231C23×C7—41no—
232C23×C7—41no—
233C23×C7—41no—
234C23×C7—44no—
235C23×C7—41no—
236C23×C7—41no—
237C23×C7—42no—
238C23×C7—41no—
239C23×C7—41no—
240C23×C7—41no—
241C23×C7—41no—
242C23×C7—44no—
243C23×C7—84no—
244C23×C7—84no—
245C23×C7#12412yes—
246C23×C7C22×D411yescharacteristic
247C23×C7C22×D412yes—
248C23×C7C2×#4112yes—
249C23×C72−1+412yes—
250C7×Q8—44no—
251C7×Q8—82no—
252C7×Q8—82no—
253C7×Q8—82no—
254C7×D4—28no—
255C7×D4—84no—
256C2×C4×C7—21no—
257C2×C4×C7—21no—
258C2×C4×C7—21no—
259C2×C4×C7—24no—
260C2×C4×C7—24no—
261C2×C4×C7—21no—
262C2×C4×C7—42no—
263C2×C4×C7—41no—
264C2×C4×C7—41no—
265C2×C4×C7—42no—
266C2×C4×C7—42no—
267C2×C4×C7—44no—
268C2×C4×C7—41no—
269C2×C4×C7—41no—
270C2×C4×C7—44no—
271C2×C4×C7—44no—
272C2×C4×C7—44no—
273C2×C4×C7—41no—
274C2×C4×C7—41no—
275C2×C4×C7—41no—
276C2×C4×C7—41no—
277C2×C4×C7—41no—
278C2×C4×C7—41no—
279C2×C4×C7—41no—
280C2×C4×C7—41no—
281C2×C4×C7—41no—
282C2×C4×C7—44no—
283C2×C4×C7—44no—
284C2×C4×C7—81no—
285C2×C4×C7—82no—
286C2×C4×C7—82no—
287C2×C4×C7#12011yescharacteristic
288C2×C4×C7#12011yescharacteristic
289C2×C4×C7#12012yes—
290C2×C4×C7#12412yes—
291C25C23×C711yescharacteristic
292C22×Q8—21no—
293C22×Q8C7×D412yescomplemented
294C22×D4—21no—
295C22×D4C23×C711yescharacteristic
296C23×C4C7×D411yescharacteristic
297C23×C4C23×C711yescharacteristic
298C23×C4C23×C711yescharacteristic
299C4⋊Q8—21no—
300C4⋊Q8—21no—
301C4⋊Q8—24no—
302#125—22no—
303#125—24no—
304#123—24no—
305C22⋊Q8—22no—
306C22⋊Q8—22no—
307C22⋊Q8—24no—
308C22⋊Q8—24no—
309C22⋊Q8—22no—
310C22⋊Q8—22no—
311C22⋊Q8—22no—
312C22⋊Q8—22no—
313C22⋊Q8—22no—
314C22⋊Q8—22no—
315C22⋊Q8—24no—
316C22⋊Q8—24no—
317#120—24no—
318C4×Q8—22no—
319C4×Q8—22no—
320C4×D4—22no—
321C4×D4—22no—
322C4×D4—24no—
323C4×D4—24no—
324#117—22no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4C7×D411yescharacteristic
330C2×C4⋊C4C7×D414yescomplemented
331C2×C4⋊C4C7×D412yescomplemented
332C2×C22⋊C4—22no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4C7×D411yescharacteristic
344C2×C22⋊C4C23×C711yescharacteristic
345C2×C22⋊C4C23×C711yescharacteristic
346C2×C22⋊C4C23×C714yes—
347C2×C22⋊C4C23×C711yescharacteristic
348C2×C22⋊C4C23×C714yes—
349C2×C42—22no—
350C2×C42C7×D411yescharacteristic
351#99—24no—
352#95—22no—
353#95—21no—
354#95—21no—
355#95—24no—
356#95—21no—
357#95—24no—
358C22×C7—22no—
359C22×C7—21no—
360C22×C7—22no—
361C22×C7—21no—
362C22×C7—22no—
363C22×C7—42no—
364C22×C7—42no—
365C22×C7—42no—
366C22×C7—42no—
367C22×C7—48no—
368C22×C7—42no—
369C22×C7—41no—
370C22×C7—41no—
371C22×C7—42no—
372C22×C7—81no—
373C22×C7—81no—
374C22×C7—84no—
375C22×C7—81no—
376C22×C7—81no—
377C22×C7—81no—
378C22×C7C2×#12011yescharacteristic
379C22×C7C2×#12411yescharacteristic
380C22×C7#53611yescharacteristic
381C22×C7#54814yes—
382C4×C7—22no—
383C4×C7—21no—
384C4×C7—21no—
385C4×C7—22no—
386C4×C7—44no—
387C4×C7—41no—
388C4×C7—41no—
389C4×C7—44no—
390C4×C7—81no—
391C4×C7—84no—
392C4×C7—81no—
393C4×C7—81no—
394C24—22no—
395C24—21no—
396C24—22no—
397C24—22no—
398C24—42no—
399C24—81no—
400C24C2×C7×D411yescharacteristic
401C24C24×C711yescharacteristic
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—82no—
407C2×Q8—82no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—42no—
411C2×D4—42no—
412C2×D4—81no—
413C2×D4C7×#4114yes—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—81no—
426C22×C4—81no—
427C22×C4C2×C7×D411yescharacteristic
428C22×C4C2×C7×D411yescharacteristic
429C22×C4C2×C7×D411yescharacteristic
430C22×C4C2×C7×D414yes—
431C22×C4C2×C7×D414yes—
432C22×C4C2×C7×D411yescharacteristic
433C22×C4C2×C7×D412yes—
434C22×C4C2×C7×D412yes—
435C22×C4C2×C7×D411yescharacteristic
436C4⋊C4—22no—
437C4⋊C4—24no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—24no—
441C4⋊C4—22no—
442C4⋊C4—24no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—24no—
447C4⋊C4—42no—
448C4⋊C4—81no—
449C22⋊C4—24no—
450C22⋊C4—24no—
451C22⋊C4—22no—
452C22⋊C4—24no—
453C22⋊C4—22no—
454C22⋊C4—24no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—24no—
458C22⋊C4—48no—
459C22⋊C4—42no—
460C22⋊C4—42no—
461C22⋊C4—41no—
462C22⋊C4—41no—
463C22⋊C4—42no—
464C22⋊C4—42no—
465C22⋊C4—81no—
466C22⋊C4—84no—
467C42—24no—
468C42—21no—
469C42—21no—
470C42—82no—
471C2×C7—21no—
472C2×C7—24no—
473C2×C7—21no—
474C2×C7—42no—
475C2×C7—82no—
476C2×C7#243611yescharacteristic
477C2×C7#302511yescharacteristic
478C2×C7#302611yescharacteristic
479C23—21no—
480C23—21no—
481C23—24no—
482C23—22no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—44no—
488C23—41no—
489C23—41no—
490C23—42no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—44no—
496C23—84no—
497C23—84no—
498C23C7×#12412yes—
499C23C22×C7×D411yescharacteristic
500C23C22×C7×D412yes—
501C23C2×C7×#4112yes—
502C23C7×2−1+412yes—
503Q8—44no—
504Q8—82no—
505Q8—82no—
506Q8—82no—
507D4—28no—
508D4—84no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—21no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—44no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—44no—
524C2×C4—44no—
525C2×C4—44no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4—81no—
538C2×C4—82no—
539C2×C4—82no—
540C2×C4C7×#12011yescharacteristic
541C2×C4C7×#12011yescharacteristic
542C2×C4C7×#12012yes—
543C2×C4C7×#12412yes—
544C7#2594911yescharacteristic, direct product factor, Sylow
545C22—22no—
546C22—21no—
547C22—22no—
548C22—21no—
549C22—22no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—48no—
555C22—42no—
556C22—41no—
557C22—41no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—84no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22C2×C7×#12011yescharacteristic
566C22C2×C7×#12411yescharacteristic
567C22C7×#53611yescharacteristic
568C22C7×#54814yes—
569C4—22no—
570C4—21no—
571C4—21no—
572C4—22no—
573C4—44no—
574C4—41no—
575C4—41no—
576C4—44no—
577C4—81no—
578C4—81no—
579C4—84no—
580C4—81no—
581C2—21no—
582C2—24no—
583C2—21no—
584C2—42no—
585C2—82no—
586C2C7×#243611yescharacteristic
587C2C7×#302511yescharacteristic
588C2C7×#302611yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC24C24×C7
prime radicalC2×C7×#120C22
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
1. C7×#3501C2semidirect
2. C7×#2561C2semidirect
4. C7×#2030C2semidirect
5. C7×#2029C2semidirect
6. C7×#1996C2semidirect
7. C7×#1890C2semidirect
9. C4×C7×#99C2semidirect
41. #25949C7direct (N × H)
44. C22×C7×Q8D4semidirect
81. C2×C7×C4⋊C4D4semidirect
82. C2×C7×C4⋊C4D4semidirect
109. #3501C2×C7semidirect
110. #2561C2×C7semidirect
112. #2030C2×C7semidirect
113. #2029C2×C7semidirect
114. #1996C2×C7semidirect
115. #1890C2×C7semidirect
117. C4×#99C2×C7semidirect
293. C22×Q8C7×D4semidirect
330. C2×C4⋊C4C7×D4semidirect
331. C2×C4⋊C4C7×D4semidirect
544. C7#25949direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#35012
C7×#25612
C7×#25342
C7×#20302
C7×#20292
C7×#19962
C7×#18902
C7×#18892
C4×C7×#992
#259497