Finite Group Databasebeta

← C7×#25948 #13203164

Subgroups — C7×#25948 #13203164

Order 1792.

1082 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3501C211yesmaximal, characteristic
2C7×#2503C212yesmaximal, complemented
3C7×#2486C211yesmaximal, characteristic
4C7×#2030C214yesmaximal, complemented
5C7×#1996C212yesmaximal, complemented
6C7×#1890C214yesmaximal
7C4×C7×#99C211yesmaximal, characteristic
8C7×#554—22no—
9C7×#554—24no—
10C7×D4×Q8—22no—
11C7×#544—21no—
12C7×#543—21no—
13C7×#543C2212yes—
14C7×#533—21no—
15C2×C7×#123C2212yes—
16C2×C7×C22⋊Q8—21no—
17C2×C7×C22⋊Q8C2212yes—
18C7×#518C2212yes—
19C2×C4×C7×D4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C2×C7×#99C2212yes—
22C7×#400—24no—
23C7×#398—21no—
24C7×#397—21no—
25C7×#391—22no—
26C7×#389—21no—
27C7×#382—22no—
28C7×#381C2212yes—
29C7×#381C2218yes—
30C7×#380—21no—
31C7×#380C2211yescharacteristic
32C4×C7×C22⋊C4C2212yes—
33C7×#342C2218yes—
34C7×#342C2212yes—
35#25948C711yesmaximal, characteristic, direct product factor, Sylow
36C22×C7×Q8—21no—
37C22×C7×Q8D412yes—
38C22×C7×D4C2311yescharacteristic
39C23×C4×C7D411yescharacteristic
40C23×C4×C7C2312yes—
41C23×C4×C7C2311yescharacteristic
42C7×C4⋊Q8—21no—
43C7×C4⋊Q8—21no—
44C7×C4⋊Q8—24no—
45C7×#125—22no—
46C7×#125—24no—
47C7×#123—28no—
48C7×C22⋊Q8—22no—
49C7×C22⋊Q8—22no—
50C7×C22⋊Q8—24no—
51C7×C22⋊Q8—24no—
52C7×C22⋊Q8—22no—
53C7×C22⋊Q8—22no—
54C7×C22⋊Q8—22no—
55C7×C22⋊Q8—22no—
56C7×C22⋊Q8—22no—
57C7×C22⋊Q8—22no—
58C7×C22⋊Q8—24no—
59C7×C22⋊Q8—24no—
60C4×C7×Q8—22no—
61C4×C7×Q8—22no—
62C4×C7×D4—22no—
63C4×C7×D4—22no—
64C4×C7×D4—24no—
65C4×C7×D4—24no—
66C7×#117—22no—
67C2×C7×C4⋊C4—21no—
68C2×C7×C4⋊C4—22no—
69C2×C7×C4⋊C4—21no—
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4—21no—
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4—21no—
74C2×C7×C4⋊C4—22no—
75C2×C7×C4⋊C4D411yescharacteristic
76C2×C7×C4⋊C4D412yes—
77C2×C7×C4⋊C4D414yes—
78C2×C7×C22⋊C4—22no—
79C2×C7×C22⋊C4—22no—
80C2×C7×C22⋊C4D411yescharacteristic
81C2×C7×C22⋊C4C2312yes—
82C2×C7×C22⋊C4C2314yes—
83C2×C7×C22⋊C4C2311yescharacteristic
84C2×C7×C22⋊C4C2314yes—
85C2×C42×C7—22no—
86C2×C42×C7D411yescharacteristic
87C7×#99—24no—
88C7×#95—22no—
89C7×#95—22no—
90C7×#95—21no—
91C7×#95—28no—
92C7×#95—22no—
93C7×#95—28no—
94#3501C2×C711yescharacteristic
95#2503C2×C712yescomplemented
96#2486C2×C711yescharacteristic
97#2030C2×C714yescomplemented
98#1996C2×C712yescomplemented
99#1890C2×C714yes—
100C4×#99C2×C711yescharacteristic
101C24×C7C2×D411yescharacteristic
102C24×C7C2411yescharacteristic
103C2×C7×Q8—22no—
104C2×C7×Q8—22no—
105C2×C7×Q8—22no—
106C2×C7×Q8—22no—
107C2×C7×Q8—44no—
108C2×C7×Q8—82no—
109C2×C7×D4—22no—
110C2×C7×D4—22no—
111C2×C7×D4#4114yes—
112C22×C4×C7—22no—
113C22×C4×C7—22no—
114C22×C4×C7—21no—
115C22×C4×C7—21no—
116C22×C4×C7—24no—
117C22×C4×C7—24no—
118C22×C4×C7—22no—
119C22×C4×C7—22no—
120C22×C4×C7—24no—
121C22×C4×C7—24no—
122C22×C4×C7—42no—
123C22×C4×C7—42no—
124C22×C4×C7C2×D412yes—
125C22×C4×C7C2×D411yescharacteristic
126C22×C4×C7C2×D411yescharacteristic
127C22×C4×C7C2×D411yescharacteristic
128C22×C4×C7C2×D414yes—
129C22×C4×C7C2×D414yes—
130C22×C4×C7C2×D411yescharacteristic
131C22×C4×C7C2×D411yescharacteristic
132C22×C4×C7C2×D412yes—
133C7×C4⋊C4—22no—
134C7×C4⋊C4—24no—
135C7×C4⋊C4—22no—
136C7×C4⋊C4—22no—
137C7×C4⋊C4—24no—
138C7×C4⋊C4—22no—
139C7×C4⋊C4—24no—
140C7×C4⋊C4—22no—
141C7×C4⋊C4—22no—
142C7×C4⋊C4—22no—
143C7×C4⋊C4—24no—
144C7×C4⋊C4—42no—
145C7×C4⋊C4—41no—
146C7×C4⋊C4—42no—
147C7×C4⋊C4—41no—
148C7×C4⋊C4—44no—
149C7×C22⋊C4—24no—
150C7×C22⋊C4—24no—
151C7×C22⋊C4—22no—
152C7×C22⋊C4—24no—
153C7×C22⋊C4—22no—
154C7×C22⋊C4—24no—
155C7×C22⋊C4—24no—
156C7×C22⋊C4—24no—
157C7×C22⋊C4—44no—
158C42×C7—24no—
159C42×C7—21no—
160C42×C7—21no—
161C42×C7—44no—
162#554—22no—
163#554—24no—
164D4×Q8—22no—
165#544—21no—
166#543—21no—
167#543C22×C712yes—
168#533—21no—
169C2×#123C22×C712yes—
170C2×C22⋊Q8—21no—
171C2×C22⋊Q8C22×C712yes—
172#518C22×C712yes—
173C2×C4×D4C22×C711yescharacteristic
174C22×C4⋊C4C22×C711yescharacteristic
175C2×#99C22×C712yes—
176#400—24no—
177#398—21no—
178#397—21no—
179#391—22no—
180#389—21no—
181#382—22no—
182#381C22×C718yes—
183#381C22×C712yes—
184#380—21no—
185#380C22×C711yescharacteristic
186C4×C22⋊C4C22×C712yes—
187#342C22×C718yes—
188#342C22×C712yes—
189C23×C7—21no—
190C23×C7—21no—
191C23×C7—41no—
192C23×C7—41no—
193C23×C7—41no—
194C23×C7—41no—
195C23×C7#12412yes—
196C23×C7C22×D411yescharacteristic
197C23×C7C22×D412yes—
198C23×C7C2×#4112yes—
199C23×C72−1+412yes—
200C7×Q8—44no—
201C7×Q8—82no—
202C7×Q8—82no—
203C7×Q8—82no—
204C7×D4—28no—
205C2×C4×C7—21no—
206C2×C4×C7—21no—
207C2×C4×C7—24no—
208C2×C4×C7—22no—
209C2×C4×C7—21no—
210C2×C4×C7—24no—
211C2×C4×C7—24no—
212C2×C4×C7—21no—
213C2×C4×C7—42no—
214C2×C4×C7—41no—
215C2×C4×C7—42no—
216C2×C4×C7—41no—
217C2×C4×C7—44no—
218C2×C4×C7—41no—
219C2×C4×C7—44no—
220C2×C4×C7—44no—
221C2×C4×C7—42no—
222C2×C4×C7—44no—
223C2×C4×C7—42no—
224C2×C4×C7—42no—
225C2×C4×C7—42no—
226C2×C4×C7—42no—
227C2×C4×C7—42no—
228C2×C4×C7—44no—
229C2×C4×C7—48no—
230C2×C4×C7—81no—
231C2×C4×C7—82no—
232C2×C4×C7—82no—
233C2×C4×C7#12011yescharacteristic
234C2×C4×C7#12012yes—
235C2×C4×C7#12011yescharacteristic
236C2×C4×C7#12412yes—
237C22×Q8—21no—
238C22×Q8C7×D412yes—
239C22×D4C23×C711yescharacteristic
240C23×C4C7×D411yescharacteristic
241C23×C4C23×C712yes—
242C23×C4C23×C711yescharacteristic
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—24no—
246#125—22no—
247#125—24no—
248#123—28no—
249C22⋊Q8—22no—
250C22⋊Q8—22no—
251C22⋊Q8—24no—
252C22⋊Q8—24no—
253C22⋊Q8—22no—
254C22⋊Q8—22no—
255C22⋊Q8—22no—
256C22⋊Q8—22no—
257C22⋊Q8—22no—
258C22⋊Q8—22no—
259C22⋊Q8—24no—
260C22⋊Q8—24no—
261C4×Q8—22no—
262C4×Q8—22no—
263C4×D4—22no—
264C4×D4—22no—
265C4×D4—24no—
266C4×D4—24no—
267#117—22no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4C7×D411yescharacteristic
277C2×C4⋊C4C7×D412yes—
278C2×C4⋊C4C7×D414yes—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4C7×D411yescharacteristic
282C2×C22⋊C4C23×C712yes—
283C2×C22⋊C4C23×C714yes—
284C2×C22⋊C4C23×C711yescharacteristic
285C2×C22⋊C4C23×C714yes—
286C2×C42—22no—
287C2×C42C7×D411yescharacteristic
288#99—24no—
289#95—22no—
290#95—22no—
291#95—21no—
292#95—28no—
293#95—22no—
294#95—28no—
295C22×C7—22no—
296C22×C7—21no—
297C22×C7—22no—
298C22×C7—21no—
299C22×C7—22no—
300C22×C7—42no—
301C22×C7—42no—
302C22×C7—42no—
303C22×C7—41no—
304C22×C7—41no—
305C22×C7—81no—
306C22×C7C2×#12011yescharacteristic
307C22×C7C2×#12411yescharacteristic
308C22×C7#53611yescharacteristic
309C22×C7#54814yes—
310C4×C7—22no—
311C4×C7—21no—
312C4×C7—22no—
313C4×C7—41no—
314C4×C7—44no—
315C4×C7—44no—
316C4×C7—41no—
317C4×C7—82no—
318C4×C7—84no—
319C4×C7—82no—
320C4×C7#45812yes—
321C24C2×C7×D411yescharacteristic
322C24C24×C711yescharacteristic
323C2×Q8—22no—
324C2×Q8—22no—
325C2×Q8—22no—
326C2×Q8—22no—
327C2×Q8—44no—
328C2×Q8—82no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4C7×#4114yes—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—24no—
341C22×C4—24no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4C2×C7×D412yes—
345C22×C4C2×C7×D411yescharacteristic
346C22×C4C2×C7×D411yescharacteristic
347C22×C4C2×C7×D411yescharacteristic
348C22×C4C2×C7×D414yes—
349C22×C4C2×C7×D414yes—
350C22×C4C2×C7×D411yescharacteristic
351C22×C4C2×C7×D411yescharacteristic
352C22×C4C2×C7×D412yes—
353C4⋊C4—22no—
354C4⋊C4—24no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—24no—
358C4⋊C4—22no—
359C4⋊C4—24no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—24no—
364C4⋊C4—42no—
365C4⋊C4—41no—
366C4⋊C4—42no—
367C4⋊C4—41no—
368C4⋊C4—44no—
369C22⋊C4—24no—
370C22⋊C4—24no—
371C22⋊C4—22no—
372C22⋊C4—24no—
373C22⋊C4—22no—
374C22⋊C4—24no—
375C22⋊C4—24no—
376C22⋊C4—24no—
377C22⋊C4—44no—
378C42—24no—
379C42—21no—
380C42—21no—
381C42—44no—
382C2×C7—21no—
383C2×C7—24no—
384C2×C7—21no—
385C2×C7—42no—
386C2×C7#243611yescharacteristic
387C2×C7C2×#45811yescharacteristic
388C2×C7#302811yescharacteristic
389C23—21no—
390C23—21no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23C7×#12412yes—
396C23C22×C7×D411yescharacteristic
397C23C22×C7×D412yes—
398C23C2×C7×#4112yes—
399C23C7×2−1+412yes—
400Q8—44no—
401Q8—82no—
402Q8—82no—
403Q8—82no—
404D4—28no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—24no—
408C2×C4—22no—
409C2×C4—21no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—21no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—44no—
418C2×C4—41no—
419C2×C4—44no—
420C2×C4—44no—
421C2×C4—42no—
422C2×C4—44no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—44no—
429C2×C4—48no—
430C2×C4—81no—
431C2×C4—82no—
432C2×C4—82no—
433C2×C4C7×#12011yescharacteristic
434C2×C4C7×#12012yes—
435C2×C4C7×#12011yescharacteristic
436C2×C4C7×#12412yes—
437C7#2594811yescharacteristic, direct product factor, Sylow
438C22—22no—
439C22—21no—
440C22—22no—
441C22—21no—
442C22—22no—
443C22—42no—
444C22—42no—
445C22—42no—
446C22—41no—
447C22—41no—
448C22—81no—
449C22C2×C7×#12011yescharacteristic
450C22C2×C7×#12411yescharacteristic
451C22C7×#53611yescharacteristic
452C22C7×#54814yes—
453C4—22no—
454C4—21no—
455C4—22no—
456C4—41no—
457C4—44no—
458C4—44no—
459C4—41no—
460C4—82no—
461C4—84no—
462C4—82no—
463C4C7×#45812yes—
464C2—21no—
465C2—24no—
466C2—21no—
467C2—42no—
468C2C7×#243611yescharacteristic
469C2C2×C7×#45811yescharacteristic
470C2C7×#302811yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC24C24×C7
prime radicalC22×C7×D4C23
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×#2503C2semidirect
4. C7×#2030C2semidirect
5. C7×#1996C2semidirect
35. #25948C7direct (N × H)
95. #2503C2×C7semidirect
97. #2030C2×C7semidirect
98. #1996C2×C7semidirect
437. C7#25948direct (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×#25032
C7×#24862
C7×#20302
C7×#19962
C7×#18902
C4×C7×#992
#259487