Finite Group Databasebeta

← C7×#25947 #13203163

Subgroups — C7×#25947 #13203163

Order 1792.

1490 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×#3501C211yesmaximal, characteristic, complemented
2C7×#2435C212yesmaximal, complemented
3C7×#2408C211yesmaximal, characteristic
4C7×#2029C214yesmaximal, complemented
5C7×#1996C212yesmaximal, complemented
6C7×#1889C214yesmaximal, complemented
7C4×C7×#99C211yesmaximal, characteristic, complemented
8C23×C7×D4C2211yescharacteristic
9C7×#554—22no—
10C7×#554—24no—
11C7×D4×Q8—22no—
12C7×#544—21no—
13C7×#543—21no—
14C7×#543C2212yes—
15C7×#533—21no—
16C2×C7×#124—22no—
17C2×C7×C22⋊Q8—21no—
18C2×C7×C22⋊Q8C2212yes—
19C2×C7×#121—21no—
20C2×C7×#120C2212yes—
21C7×#518C2212yes—
22C2×C4×C7×D4C2211yescharacteristic
23C2×C7×#99C2212yes—
24C7×#394—21no—
25C7×#394—24no—
26C7×#392—21no—
27C7×#390—22no—
28C7×#390—21no—
29C7×#380C2211yescharacteristic
30C7×#379C2212yes—
31C7×#379C2218yes—
32C4×C7×C22⋊C4C2212yes—
33C7×#342C2218yes—
34C7×#342C2212yes—
35#25947C711yesmaximal, characteristic, direct product factor, Sylow
36C25×C7C2312yes—
37C22×C7×Q8—21no—
38C22×C7×Q8D412yescomplemented
39C22×C7×D4—22no—
40C22×C7×D4—21no—
41C22×C7×D4—22no—
42C22×C7×D4—21no—
43C22×C7×D4—22no—
44C22×C7×D4—44no—
45C22×C7×D4C2311yescharacteristic
46C23×C4×C7D411yescharacteristic
47C23×C4×C7C2311yescharacteristic
48C7×C4⋊Q8—21no—
49C7×C4⋊Q8—21no—
50C7×C4⋊Q8—24no—
51C7×#125—22no—
52C7×#125—24no—
53C7×#124—48no—
54C7×C22⋊Q8—22no—
55C7×C22⋊Q8—22no—
56C7×C22⋊Q8—24no—
57C7×C22⋊Q8—24no—
58C7×C22⋊Q8—22no—
59C7×C22⋊Q8—22no—
60C7×C22⋊Q8—22no—
61C7×C22⋊Q8—22no—
62C7×C22⋊Q8—22no—
63C7×C22⋊Q8—22no—
64C7×C22⋊Q8—24no—
65C7×C22⋊Q8—24no—
66C7×#121—44no—
67C7×#120—28no—
68C4×C7×Q8—22no—
69C4×C7×Q8—22no—
70C4×C7×D4—22no—
71C4×C7×D4—22no—
72C4×C7×D4—24no—
73C4×C7×D4—24no—
74C7×#117—22no—
75C2×C7×C4⋊C4—21no—
76C2×C7×C4⋊C4—22no—
77C2×C7×C4⋊C4—21no—
78C2×C7×C4⋊C4D411yescharacteristic
79C2×C7×C4⋊C4D412yescomplemented
80C2×C7×C4⋊C4D414yescomplemented
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—28no—
84C2×C7×C22⋊C4—22no—
85C2×C7×C22⋊C4—22no—
86C2×C7×C22⋊C4—28no—
87C2×C7×C22⋊C4D411yescharacteristic
88C2×C7×C22⋊C4C2312yes—
89C2×C7×C22⋊C4C2314yes—
90C2×C7×C22⋊C4C2311yescharacteristic
91C2×C7×C22⋊C4C2314yes—
92C2×C42×C7—22no—
93C2×C42×C7D411yescharacteristic
94C7×#99—24no—
95C7×#95—22no—
96C7×#95—21no—
97#3501C2×C711yescharacteristic, complemented
98#2435C2×C712yescomplemented
99#2408C2×C711yescharacteristic
100#2029C2×C714yescomplemented
101#1996C2×C712yescomplemented
102#1889C2×C714yescomplemented
103C4×#99C2×C711yescharacteristic, complemented
104C24×C7—24no—
105C24×C7—22no—
106C24×C7—24no—
107C24×C7—24no—
108C24×C7—44no—
109C24×C7—82no—
110C24×C7C2×D411yescharacteristic
111C24×C7C2411yescharacteristic
112C2×C7×Q8—22no—
113C2×C7×Q8—22no—
114C2×C7×Q8—22no—
115C2×C7×Q8—22no—
116C2×C7×Q8—44no—
117C2×C7×Q8—82no—
118C2×C7×D4—22no—
119C2×C7×D4—22no—
120C2×C7×D4—24no—
121C2×C7×D4—28no—
122C2×C7×D4—44no—
123C2×C7×D4—42no—
124C2×C7×D4—48no—
125C2×C7×D4—44no—
126C2×C7×D4—44no—
127C2×C7×D4—44no—
128C2×C7×D4—41no—
129C2×C7×D4—42no—
130C2×C7×D4—41no—
131C2×C7×D4—82no—
132C2×C7×D4#4114yes—
133C22×C4×C7—22no—
134C22×C4×C7—22no—
135C22×C4×C7—21no—
136C22×C4×C7—21no—
137C22×C4×C7—24no—
138C22×C4×C7—22no—
139C22×C4×C7—42no—
140C22×C4×C7—42no—
141C22×C4×C7C2×D412yes—
142C22×C4×C7C2×D411yescharacteristic
143C22×C4×C7C2×D411yescharacteristic
144C22×C4×C7C2×D411yescharacteristic
145C22×C4×C7C2×D411yescharacteristic
146C22×C4×C7C2×D414yes—
147C22×C4×C7C2×D414yes—
148C22×C4×C7C2×D411yescharacteristic
149C22×C4×C7C2×D412yes—
150C7×C4⋊C4—22no—
151C7×C4⋊C4—24no—
152C7×C4⋊C4—22no—
153C7×C4⋊C4—22no—
154C7×C4⋊C4—24no—
155C7×C4⋊C4—22no—
156C7×C4⋊C4—24no—
157C7×C4⋊C4—22no—
158C7×C4⋊C4—22no—
159C7×C4⋊C4—22no—
160C7×C4⋊C4—24no—
161C7×C4⋊C4—42no—
162C7×C22⋊C4—24no—
163C7×C22⋊C4—24no—
164C7×C22⋊C4—22no—
165C7×C22⋊C4—24no—
166C7×C22⋊C4—22no—
167C7×C22⋊C4—24no—
168C7×C22⋊C4—24no—
169C7×C22⋊C4—24no—
170C7×C22⋊C4—44no—
171C7×C22⋊C4—416no—
172C7×C22⋊C4—44no—
173C7×C22⋊C4—88no—
174C7×C22⋊C4—82no—
175C42×C7—24no—
176C42×C7—21no—
177C42×C7—21no—
178C42×C7—44no—
179C23×D4C22×C711yescharacteristic
180#554—22no—
181#554—24no—
182D4×Q8—22no—
183#544—21no—
184#543—21no—
185#543C22×C712yes—
186#533—21no—
187C2×#124—22no—
188C2×C22⋊Q8—21no—
189C2×C22⋊Q8C22×C712yes—
190C2×#121—21no—
191C2×#120C22×C712yes—
192#518C22×C712yes—
193C2×C4×D4C22×C711yescharacteristic
194C2×#99C22×C712yes—
195#394—21no—
196#394—24no—
197#392—21no—
198#390—22no—
199#390—21no—
200#380C22×C711yescharacteristic
201#379C22×C718yes—
202#379C22×C712yes—
203C4×C22⋊C4C22×C712yes—
204#342C22×C718yes—
205#342C22×C712yes—
206C23×C7—21no—
207C23×C7—21no—
208C23×C7—28no—
209C23×C7—24no—
210C23×C7—41no—
211C23×C7—41no—
212C23×C7—41no—
213C23×C7—41no—
214C23×C7—48no—
215C23×C7—42no—
216C23×C7—44no—
217C23×C7—42no—
218C23×C7—42no—
219C23×C7—42no—
220C23×C7—42no—
221C23×C7—42no—
222C23×C7—48no—
223C23×C7—88no—
224C23×C7—88no—
225C23×C7#12412yescomplemented
226C23×C7C22×D411yescharacteristic
227C23×C7C22×D412yes—
228C23×C7C2×#4112yes—
229C23×C72−1+412yes—
230C7×Q8—44no—
231C7×Q8—82no—
232C7×Q8—82no—
233C7×Q8—82no—
234C7×D4—28no—
235C7×D4—44no—
236C7×D4—48no—
237C7×D4—44no—
238C7×D4—88no—
239C2×C4×C7—21no—
240C2×C4×C7—21no—
241C2×C4×C7—24no—
242C2×C4×C7—22no—
243C2×C4×C7—21no—
244C2×C4×C7—24no—
245C2×C4×C7—24no—
246C2×C4×C7—21no—
247C2×C4×C7—42no—
248C2×C4×C7—41no—
249C2×C4×C7—42no—
250C2×C4×C7—41no—
251C2×C4×C7—44no—
252C2×C4×C7—44no—
253C2×C4×C7—41no—
254C2×C4×C7—44no—
255C2×C4×C7—42no—
256C2×C4×C7—44no—
257C2×C4×C7—42no—
258C2×C4×C7—42no—
259C2×C4×C7—44no—
260C2×C4×C7—81no—
261C2×C4×C7—82no—
262C2×C4×C7—82no—
263C2×C4×C7#12011yescharacteristic
264C2×C4×C7#12012yes—
265C2×C4×C7#12011yescharacteristic
266C2×C4×C7#12412yescomplemented
267C25C23×C712yes—
268C22×Q8—21no—
269C22×Q8C7×D412yescomplemented
270C22×D4—22no—
271C22×D4—21no—
272C22×D4—22no—
273C22×D4—21no—
274C22×D4—22no—
275C22×D4—44no—
276C22×D4C23×C711yescharacteristic
277C23×C4C7×D411yescharacteristic
278C23×C4C23×C711yescharacteristic
279C4⋊Q8—21no—
280C4⋊Q8—21no—
281C4⋊Q8—24no—
282#125—22no—
283#125—24no—
284#124—48no—
285C22⋊Q8—22no—
286C22⋊Q8—22no—
287C22⋊Q8—24no—
288C22⋊Q8—24no—
289C22⋊Q8—22no—
290C22⋊Q8—22no—
291C22⋊Q8—22no—
292C22⋊Q8—22no—
293C22⋊Q8—22no—
294C22⋊Q8—22no—
295C22⋊Q8—24no—
296C22⋊Q8—24no—
297#121—44no—
298#120—28no—
299C4×Q8—22no—
300C4×Q8—22no—
301C4×D4—22no—
302C4×D4—22no—
303C4×D4—24no—
304C4×D4—24no—
305#117—22no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4C7×D411yescharacteristic
310C2×C4⋊C4C7×D412yescomplemented
311C2×C4⋊C4C7×D414yescomplemented
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4C7×D411yescharacteristic
319C2×C22⋊C4C23×C712yes—
320C2×C22⋊C4C23×C714yes—
321C2×C22⋊C4C23×C711yescharacteristic
322C2×C22⋊C4C23×C714yes—
323C2×C42—22no—
324C2×C42C7×D411yescharacteristic
325#99—24no—
326#95—22no—
327#95—21no—
328C22×C7—22no—
329C22×C7—21no—
330C22×C7—22no—
331C22×C7—21no—
332C22×C7—22no—
333C22×C7—42no—
334C22×C7—42no—
335C22×C7—42no—
336C22×C7—44no—
337C22×C7—416no—
338C22×C7—44no—
339C22×C7—41no—
340C22×C7—41no—
341C22×C7—44no—
342C22×C7—81no—
343C22×C7—82no—
344C22×C7—88no—
345C22×C7—82no—
346C22×C7—82no—
347C22×C7—82no—
348C22×C7C2×#12011yescharacteristic
349C22×C7C2×#12411yescharacteristic
350C22×C7#53611yescharacteristic
351C22×C7#54814yes—
352C4×C7—22no—
353C4×C7—21no—
354C4×C7—22no—
355C4×C7—41no—
356C4×C7—44no—
357C4×C7—44no—
358C4×C7—41no—
359C4×C7—84no—
360C4×C7—82no—
361C4×C7B(4,𝔽2)12yes—
362C24—24no—
363C24—22no—
364C24—24no—
365C24—24no—
366C24—44no—
367C24—82no—
368C24C2×C7×D411yescharacteristic
369C24C24×C711yescharacteristic
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8—44no—
375C2×Q8—82no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—24no—
379C2×D4—28no—
380C2×D4—44no—
381C2×D4—42no—
382C2×D4—48no—
383C2×D4—44no—
384C2×D4—44no—
385C2×D4—44no—
386C2×D4—41no—
387C2×D4—42no—
388C2×D4—41no—
389C2×D4—82no—
390C2×D4C7×#4114yes—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—24no—
396C22×C4—22no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4C2×C7×D412yes—
400C22×C4C2×C7×D411yescharacteristic
401C22×C4C2×C7×D411yescharacteristic
402C22×C4C2×C7×D411yescharacteristic
403C22×C4C2×C7×D411yescharacteristic
404C22×C4C2×C7×D414yes—
405C22×C4C2×C7×D414yes—
406C22×C4C2×C7×D411yescharacteristic
407C22×C4C2×C7×D412yes—
408C4⋊C4—22no—
409C4⋊C4—24no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—24no—
413C4⋊C4—22no—
414C4⋊C4—24no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—24no—
419C4⋊C4—42no—
420C22⋊C4—24no—
421C22⋊C4—24no—
422C22⋊C4—22no—
423C22⋊C4—24no—
424C22⋊C4—22no—
425C22⋊C4—24no—
426C22⋊C4—24no—
427C22⋊C4—24no—
428C22⋊C4—44no—
429C22⋊C4—416no—
430C22⋊C4—44no—
431C22⋊C4—88no—
432C22⋊C4—82no—
433C42—24no—
434C42—21no—
435C42—21no—
436C42—44no—
437C2×C7—21no—
438C2×C7—24no—
439C2×C7—21no—
440C2×C7—42no—
441C2×C7—84no—
442C2×C7#243611yescharacteristic
443C2×C7C2×B(4,𝔽2)11yescharacteristic
444C2×C7#302711yescharacteristic
445C23—21no—
446C23—21no—
447C23—28no—
448C23—24no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23—48no—
454C23—42no—
455C23—44no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23—48no—
462C23—88no—
463C23—88no—
464C23C7×#12412yescomplemented
465C23C22×C7×D411yescharacteristic
466C23C22×C7×D412yes—
467C23C2×C7×#4112yes—
468C23C7×2−1+412yes—
469Q8—44no—
470Q8—82no—
471Q8—82no—
472Q8—82no—
473D4—28no—
474D4—44no—
475D4—48no—
476D4—44no—
477D4—88no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—24no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—21no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—41no—
490C2×C4—44no—
491C2×C4—44no—
492C2×C4—41no—
493C2×C4—44no—
494C2×C4—42no—
495C2×C4—44no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—44no—
499C2×C4—81no—
500C2×C4—82no—
501C2×C4—82no—
502C2×C4C7×#12011yescharacteristic
503C2×C4C7×#12012yes—
504C2×C4C7×#12011yescharacteristic
505C2×C4C7×#12412yescomplemented
506C7#2594711yescharacteristic, direct product factor, Sylow
507C22—22no—
508C22—21no—
509C22—22no—
510C22—21no—
511C22—22no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—44no—
516C22—416no—
517C22—44no—
518C22—41no—
519C22—41no—
520C22—44no—
521C22—81no—
522C22—82no—
523C22—88no—
524C22—82no—
525C22—82no—
526C22—82no—
527C22C2×C7×#12011yescharacteristic
528C22C2×C7×#12411yescharacteristic
529C22C7×#53611yescharacteristic
530C22C7×#54814yes—
531C4—22no—
532C4—21no—
533C4—22no—
534C4—41no—
535C4—44no—
536C4—44no—
537C4—41no—
538C4—82no—
539C4—84no—
540C4C7×B(4,𝔽2)12yes—
541C2—21no—
542C2—24no—
543C2—21no—
544C2—42no—
545C2—84no—
546C2C7×#243611yescharacteristic
547C2C2×C7×B(4,𝔽2)11yescharacteristic
548C2C7×#302711yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC24C24×C7
prime radicalC7×#2408C2
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×#2435C2semidirect
4. C7×#2029C2semidirect
5. C7×#1996C2semidirect
6. C7×#1889C2semidirect
7. C4×C7×#99C2semidirect
35. #25947C7direct (N × H)
38. C22×C7×Q8D4semidirect
79. C2×C7×C4⋊C4D4semidirect
80. C2×C7×C4⋊C4D4semidirect
97. #3501C2×C7semidirect
98. #2435C2×C7semidirect
100. #2029C2×C7semidirect
101. #1996C2×C7semidirect
102. #1889C2×C7semidirect
103. C4×#99C2×C7semidirect
225. C23×C7#124semidirect
266. C2×C4×C7#124semidirect
269. C22×Q8C7×D4semidirect
310. C2×C4⋊C4C7×D4semidirect
311. C2×C4⋊C4C7×D4semidirect
464. C23C7×#124semidirect
505. C2×C4C7×#124semidirect
506. C7#25947direct (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×#24352
C7×#24082
C7×#20292
C7×#19962
C7×#18892
C4×C7×#992
#259477