Finite Group Databasebeta

← C7×#24114 #13201330

Subgroups — C7×#24114 #13201330

Order 1792.

1254 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3490C211yesmaximal, characteristic
2C7×#2622C212yesmaximal, complemented
3C7×#2315C211yesmaximal, characteristic, complemented
4C7×#2062C212yesmaximal, complemented
5C7×#2044C212yesmaximal, complemented
6C7×#1898C212yesmaximal, complemented
7C7×#1867C214yesmaximal, complemented
8C7×#1819C211yesmaximal, characteristic, complemented
9C7×#551—24no—
10C7×#546—24no—
11C7×#543C2211yescharacteristic
12C7×#538—22no—
13C7×#534C2211yescharacteristic
14C7×#525—22no—
15C2×C7×#120C2212yes—
16C7×#518C2212yes—
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C2×C7×#99C2214yes—
21C7×#397—24no—
22C7×#394—24no—
23C7×#386C2214yes—
24C7×#385—22no—
25C7×#385C2212yes—
26C7×#385C2214yes—
27C7×#385C2212yes—
28C7×#380—22no—
29C7×#379C2212yes—
30C7×#342C2212yes—
31C7×#342C2214yes—
32C7×#342C2212yes—
33#24114C711yesmaximal, characteristic, direct product factor, Sylow
34C25×C7C2311yescharacteristic
35C2×C7×#41—22no—
36C22×C7×D4D414yes—
37C22×C7×D4C2312yes—
38C23×C4×C7—21no—
39C23×C4×C7D412yes—
40C23×C4×C7C2312yes—
41C7×#126—24no—
42C7×#124—24no—
43C7×#123—24no—
44C7×#123—24no—
45C7×#123—22no—
46C7×C22⋊Q8—22no—
47C7×C22⋊Q8—22no—
48C7×C22⋊Q8—24no—
49C7×#121—22no—
50C7×#121—24no—
51C7×#121—22no—
52C7×#120—22no—
53C7×#120—22no—
54C7×#120—24no—
55C7×#120—22no—
56C4×C7×D4—24no—
57C4×C7×D4—24no—
58C4×C7×D4—24no—
59C7×#117—22no—
60C7×#117—22no—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—24no—
64C2×C7×C22⋊C4—21no—
65C2×C7×C22⋊C4—24no—
66C2×C7×C22⋊C4—22no—
67C2×C7×C22⋊C4—24no—
68C2×C7×C22⋊C4—21no—
69C2×C7×C22⋊C4—21no—
70C2×C7×C22⋊C4—24no—
71C2×C7×C22⋊C4—24no—
72C2×C7×C22⋊C4—24no—
73C2×C7×C22⋊C4D412yes—
74C2×C7×C22⋊C4D414yes—
75C2×C7×C22⋊C4C2314yes—
76C2×C7×C22⋊C4C2311yescharacteristic
77C2×C7×C22⋊C4C2311yescharacteristic
78C2×C7×C22⋊C4C2312yes—
79C2×C7×C22⋊C4C2312yes—
80C7×#99—28no—
81C7×#95—22no—
82C7×#95—22no—
83C7×#95—24no—
84C7×#95—24no—
85#3490C2×C711yescharacteristic
86#2622C2×C712yescomplemented
87#2315C2×C711yescharacteristic, complemented
88#2062C2×C712yescomplemented
89#2044C2×C712yescomplemented
90#1898C2×C712yescomplemented
91#1867C2×C714yescomplemented
92#1819C2×C711yescharacteristic, complemented
93C24×C7—22no—
94C24×C7—22no—
95C24×C7—82no—
96C24×C7C2×D412yes—
97C24×C7C2×D414yes—
98C24×C7C2×D411yescharacteristic
99C24×C7C2×D411yescharacteristic
100C24×C7C2411yescharacteristic
101C7×#41—84no—
102C2×C7×Q8—22no—
103C2×C7×D4—24no—
104C2×C7×D4—22no—
105C2×C7×D4—22no—
106C2×C7×D4—24no—
107C2×C7×D4—24no—
108C2×C7×D4—22no—
109C2×C7×D4—24no—
110C2×C7×D4—84no—
111C22×C4×C7—22no—
112C22×C4×C7—22no—
113C22×C4×C7—24no—
114C22×C4×C7—24no—
115C22×C4×C7—22no—
116C22×C4×C7—24no—
117C22×C4×C7—24no—
118C22×C4×C7—22no—
119C22×C4×C7—82no—
120C22×C4×C7—82no—
121C22×C4×C7—82no—
122C22×C4×C7C2×D412yes—
123C22×C4×C7C2×D412yes—
124C22×C4×C7C2×D414yes—
125C22×C4×C7C2×D412yes—
126C7×C4⋊C4—24no—
127C7×C4⋊C4—22no—
128C7×C4⋊C4—22no—
129C7×C4⋊C4—24no—
130C7×C4⋊C4—82no—
131C7×C4⋊C4—82no—
132C7×C4⋊C4—84no—
133C7×C22⋊C4—24no—
134C7×C22⋊C4—24no—
135C7×C22⋊C4—24no—
136C7×C22⋊C4—24no—
137C7×C22⋊C4—24no—
138C7×C22⋊C4—24no—
139C7×C22⋊C4—22no—
140C7×C22⋊C4—22no—
141C7×C22⋊C4—22no—
142C7×C22⋊C4—22no—
143C7×C22⋊C4—22no—
144C7×C22⋊C4—24no—
145C7×C22⋊C4—24no—
146C7×C22⋊C4—42no—
147C7×C22⋊C4—42no—
148C7×C22⋊C4—84no—
149C7×C22⋊C4—84no—
150C7×C22⋊C4#4114yescomplemented
151C42×C7—24no—
152#551—24no—
153#546—24no—
154#543C22×C711yescharacteristic
155#538—22no—
156#534C22×C711yescharacteristic
157#525—22no—
158C2×#120C22×C712yes—
159#518C22×C712yes—
160C22×C22⋊C4C22×C711yescharacteristic
161C22×C22⋊C4C22×C711yescharacteristic
162C22×C22⋊C4C22×C711yescharacteristic
163C2×#99C22×C714yes—
164#397—24no—
165#394—24no—
166#386C22×C714yes—
167#385—22no—
168#385C22×C712yes—
169#385C22×C712yes—
170#385C22×C714yes—
171#380—22no—
172#379C22×C712yes—
173#342C22×C712yes—
174#342C22×C714yes—
175#342C22×C712yes—
176C23×C7—21no—
177C23×C7—21no—
178C23×C7—21no—
179C23×C7—21no—
180C23×C7—28no—
181C23×C7—22no—
182C23×C7—24no—
183C23×C7—42no—
184C23×C7—42no—
185C23×C7—42no—
186C23×C7—44no—
187C23×C7—44no—
188C23×C7—44no—
189C23×C7—84no—
190C23×C7—84no—
191C23×C7#12012yes—
192C23×C7#12012yes—
193C23×C7C22×D411yescharacteristic
194C23×C7C22×D412yes—
195C23×C7C2×#4112yes—
196C23×C72−1+412yes—
197C7×Q8—82no—
198C7×D4—48no—
199C7×D4—42no—
200C7×D4—42no—
201C7×D4—44no—
202C7×D4—84no—
203C7×D4—82no—
204C2×C4×C7—22no—
205C2×C4×C7—22no—
206C2×C4×C7—24no—
207C2×C4×C7—22no—
208C2×C4×C7—24no—
209C2×C4×C7—24no—
210C2×C4×C7—42no—
211C2×C4×C7—42no—
212C2×C4×C7—44no—
213C2×C4×C7—42no—
214C2×C4×C7—42no—
215C2×C4×C7—44no—
216C2×C4×C7—44no—
217C2×C4×C7—44no—
218C2×C4×C7—44no—
219C2×C4×C7—42no—
220C2×C4×C7—42no—
221C2×C4×C7—44no—
222C2×C4×C7—42no—
223C2×C4×C7—44no—
224C2×C4×C7—82no—
225C2×C4×C7—84no—
226C2×C4×C7—84no—
227C25C23×C711yescharacteristic
228C2×#41—22no—
229C22×D4C7×D414yes—
230C22×D4C23×C712yes—
231C23×C4—21no—
232C23×C4C7×D412yes—
233C23×C4C23×C712yes—
234#126—24no—
235#124—24no—
236#123—24no—
237#123—24no—
238#123—22no—
239C22⋊Q8—22no—
240C22⋊Q8—22no—
241C22⋊Q8—24no—
242#121—22no—
243#121—24no—
244#121—22no—
245#120—22no—
246#120—22no—
247#120—24no—
248#120—22no—
249C4×D4—24no—
250C4×D4—24no—
251C4×D4—24no—
252#117—22no—
253#117—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—24no—
257C2×C22⋊C4—24no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—22no—
260C2×C22⋊C4—24no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—24no—
264C2×C22⋊C4—24no—
265C2×C22⋊C4—24no—
266C2×C22⋊C4C7×D412yes—
267C2×C22⋊C4C7×D414yes—
268C2×C22⋊C4C23×C714yes—
269C2×C22⋊C4C23×C711yescharacteristic
270C2×C22⋊C4C23×C711yescharacteristic
271C2×C22⋊C4C23×C712yes—
272C2×C22⋊C4C23×C712yes—
273#99—28no—
274#95—22no—
275#95—22no—
276#95—24no—
277#95—24no—
278C22×C7—22no—
279C22×C7—24no—
280C22×C7—22no—
281C22×C7—22no—
282C22×C7—22no—
283C22×C7—22no—
284C22×C7—24no—
285C22×C7—42no—
286C22×C7—42no—
287C22×C7—42no—
288C22×C7—42no—
289C22×C7—42no—
290C22×C7—42no—
291C22×C7—42no—
292C22×C7—44no—
293C22×C7—88no—
294C22×C7—84no—
295C22×C7C2×#12011yescharacteristic
296C22×C7#52511yescharacteristic
297C22×C7#53611yescharacteristic
298C22×C7#54714yes—
299C4×C7—44no—
300C4×C7—42no—
301C4×C7—42no—
302C4×C7—42no—
303C4×C7—44no—
304C4×C7—84no—
305C4×C7—82no—
306C24—22no—
307C24—22no—
308C24—82no—
309C24C2×C7×D412yes—
310C24C2×C7×D414yes—
311C24C2×C7×D411yescharacteristic
312C24C2×C7×D411yescharacteristic
313C24C24×C711yescharacteristic
314#41—84no—
315C2×Q8—22no—
316C2×D4—24no—
317C2×D4—22no—
318C2×D4—22no—
319C2×D4—24no—
320C2×D4—24no—
321C2×D4—22no—
322C2×D4—24no—
323C2×D4—84no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—24no—
327C22×C4—24no—
328C22×C4—22no—
329C22×C4—24no—
330C22×C4—24no—
331C22×C4—22no—
332C22×C4—82no—
333C22×C4—82no—
334C22×C4—82no—
335C22×C4C2×C7×D412yes—
336C22×C4C2×C7×D412yes—
337C22×C4C2×C7×D414yes—
338C22×C4C2×C7×D412yes—
339C4⋊C4—24no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—24no—
343C4⋊C4—82no—
344C4⋊C4—82no—
345C4⋊C4—84no—
346C22⋊C4—24no—
347C22⋊C4—24no—
348C22⋊C4—24no—
349C22⋊C4—24no—
350C22⋊C4—24no—
351C22⋊C4—24no—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—22no—
355C22⋊C4—22no—
356C22⋊C4—22no—
357C22⋊C4—24no—
358C22⋊C4—24no—
359C22⋊C4—42no—
360C22⋊C4—42no—
361C22⋊C4—84no—
362C22⋊C4—84no—
363C22⋊C4C7×#4114yescomplemented
364C42—24no—
365C2×C7—21no—
366C2×C7—24no—
367C2×C7—21no—
368C2×C7—42no—
369C2×C7—42no—
370C2×C7—82no—
371C2×C7#240611yescharacteristic
372C2×C7#302612yes—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—28no—
378C23—22no—
379C23—24no—
380C23—42no—
381C23—42no—
382C23—42no—
383C23—44no—
384C23—44no—
385C23—44no—
386C23—84no—
387C23—84no—
388C23C7×#12012yes—
389C23C7×#12012yes—
390C23C22×C7×D411yescharacteristic
391C23C22×C7×D412yes—
392C23C2×C7×#4112yes—
393C23C7×2−1+412yes—
394Q8—82no—
395D4—48no—
396D4—42no—
397D4—42no—
398D4—44no—
399D4—84no—
400D4—82no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—24no—
404C2×C4—22no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—44no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—44no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—44no—
419C2×C4—42no—
420C2×C4—44no—
421C2×C4—82no—
422C2×C4—84no—
423C2×C4—84no—
424C7#2411411yescharacteristic, direct product factor, Sylow
425C22—22no—
426C22—24no—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—24no—
432C22—42no—
433C22—42no—
434C22—42no—
435C22—42no—
436C22—42no—
437C22—42no—
438C22—42no—
439C22—44no—
440C22—88no—
441C22—84no—
442C22C2×C7×#12011yescharacteristic
443C22C7×#52511yescharacteristic
444C22C7×#53611yescharacteristic
445C22C7×#54714yes—
446C4—44no—
447C4—42no—
448C4—42no—
449C4—42no—
450C4—44no—
451C4—84no—
452C4—82no—
453C2—21no—
454C2—24no—
455C2—21no—
456C2—42no—
457C2—42no—
458C2—82no—
459C2C7×#240611yescharacteristic
460C2C7×#302612yes—
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC24C24×C7
prime radicalC7×#3490C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C25×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C7×#2622C2semidirect
3. C7×#2315C2semidirect
4. C7×#2062C2semidirect
5. C7×#2044C2semidirect
6. C7×#1898C2semidirect
7. C7×#1867C2semidirect
8. C7×#1819C2semidirect
33. #24114C7direct (N × H)
86. #2622C2×C7semidirect
87. #2315C2×C7semidirect
88. #2062C2×C7semidirect
89. #2044C2×C7semidirect
90. #1898C2×C7semidirect
91. #1867C2×C7semidirect
92. #1819C2×C7semidirect
150. C7×C22⋊C4#41semidirect
363. C22⋊C4C7×#41semidirect
424. C7#24114direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#34902
C7×#26222
C7×#23152
C7×#20622
C7×#20442
C7×#18982
C7×#18672
C7×#18192
#241147