Finite Group Databasebeta

← C7×#15946 #13193162

Subgroups — C7×#15946 #13193162

Order 1792.

1170 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#400C211yesmaximal, characteristic
2C2×C7×#382C211yesmaximal, characteristic
3C7×#1444C212yesmaximal
4C7×#1444C212yesmaximal
5C7×#1442C212yesmaximal
6C7×#1442C212yesmaximal
7C7×#1436C212yesmaximal
8C7×#1436C211yesmaximal, characteristic
9C7×C4⋊#95C212yesmaximal
10C22×C7×C4⋊C4C2212yes—
11C22×C7×C4⋊C4C2211yescharacteristic
12C22×C7×C4⋊C4C2211yescharacteristic
13C22×C7×C4⋊C4C2212yes—
14C22×C7×C4⋊C4C2212yes—
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C42×C7C2211yescharacteristic
17C22×C42×C7C2211yescharacteristic
18C7×#400—24no—
19C7×#382—24no—
20C2×C7×#95C2212yes—
21C2×C7×#95C2212yes—
22C2×C7×#95C2211yescharacteristic
23C2×C7×#95C2212yes—
24C2×C7×#95C2212yes—
25C2×C7×#95C2212yes—
26C2×C7×#95C2212yes—
27C2×C7×#95C2212yes—
28C2×C7×#95C2212yes—
29C2×C7×#95C2211yescharacteristic
30C2×C7×#95C2212yes—
31C2×C7×#95C2212yes—
32C2×C7×#95C2212yes—
33#15946C711yesmaximal, characteristic, direct product factor, Sylow
34C23×C4×C7C2312yes—
35C23×C4×C7C2312yes—
36C23×C4×C7C2312yes—
37C23×C4×C7C2311yescharacteristic
38C23×C4×C7C2311yescharacteristic
39C23×C4×C7C2312yes—
40C23×C4×C7C2312yes—
41C23×C4×C7C2311yescharacteristic
42C23×C4×C7C2312yes—
43C2×C7×C4⋊C4—22no—
44C2×C7×C4⋊C4—22no—
45C2×C7×C4⋊C4—24no—
46C2×C7×C4⋊C4—24no—
47C2×C7×C4⋊C4—24no—
48C2×C7×C4⋊C4—41no—
49C2×C7×C4⋊C4—41no—
50C2×C7×C4⋊C4—42no—
51C2×C7×C4⋊C4—42no—
52C2×C7×C4⋊C4—41no—
53C2×C7×C4⋊C4—41no—
54C2×C7×C4⋊C4—42no—
55C2×C7×C4⋊C4—41no—
56C2×C7×C4⋊C4—41no—
57C2×C7×C4⋊C4—42no—
58C2×C7×C4⋊C4—42no—
59C2×C7×C4⋊C4—42no—
60C2×C7×C4⋊C4D414yes—
61C2×C42×C7—22no—
62C2×C42×C7—24no—
63C2×C42×C7—24no—
64C2×C42×C7—41no—
65C7×#95—24no—
66C7×#95—24no—
67C7×#95—22no—
68C7×#95—24no—
69C7×#95—24no—
70C7×#95—24no—
71C7×#95—24no—
72C7×#95—24no—
73C7×#95—24no—
74C7×#95—41no—
75C7×#95—42no—
76C7×#95—42no—
77C7×#95Q818yes—
78C2×#400C2×C711yescharacteristic
79C2×#382C2×C711yescharacteristic
80#1444C2×C712yes—
81#1444C2×C712yes—
82#1442C2×C712yes—
83#1442C2×C712yes—
84#1436C2×C712yes—
85#1436C2×C711yescharacteristic
86C4⋊#95C2×C712yes—
87C24×C7C2411yescharacteristic
88C22×C4×C7—22no—
89C22×C4×C7—22no—
90C22×C4×C7—22no—
91C22×C4×C7—22no—
92C22×C4×C7—21no—
93C22×C4×C7—21no—
94C22×C4×C7—22no—
95C22×C4×C7—22no—
96C22×C4×C7—22no—
97C22×C4×C7—22no—
98C22×C4×C7—22no—
99C22×C4×C7—22no—
100C22×C4×C7—22no—
101C22×C4×C7—22no—
102C22×C4×C7—22no—
103C22×C4×C7—21no—
104C22×C4×C7—22no—
105C22×C4×C7—22no—
106C22×C4×C7—22no—
107C22×C4×C7—22no—
108C22×C4×C7—21no—
109C22×C4×C7—21no—
110C22×C4×C7—21no—
111C22×C4×C7—22no—
112C22×C4×C7—22no—
113C22×C4×C7—22no—
114C22×C4×C7—22no—
115C22×C4×C7—22no—
116C22×C4×C7—22no—
117C22×C4×C7—22no—
118C22×C4×C7—22no—
119C22×C4×C7—22no—
120C22×C4×C7—22no—
121C22×C4×C7—22no—
122C22×C4×C7—22no—
123C22×C4×C7—22no—
124C22×C4×C7—22no—
125C22×C4×C7—22no—
126C22×C4×C7—22no—
127C22×C4×C7—22no—
128C22×C4×C7—22no—
129C22×C4×C7—22no—
130C22×C4×C7—22no—
131C22×C4×C7—22no—
132C22×C4×C7—22no—
133C22×C4×C7—22no—
134C22×C4×C7—22no—
135C22×C4×C7—22no—
136C22×C4×C7C2×D412yes—
137C22×C4×C7C2×D412yes—
138C22×C4×C7C2×D412yes—
139C22×C4×C7C2×Q814yes—
140C22×C4×C7C2×Q814yes—
141C22×C4×C7C2×Q814yes—
142C22×C4×C7#4114yes—
143C22×C4×C7#4114yes—
144C22×C4×C7#4114yes—
145C7×C4⋊C4—44no—
146C7×C4⋊C4—48no—
147C7×C4⋊C4—44no—
148C7×C4⋊C4—48no—
149C7×C4⋊C4—44no—
150C7×C4⋊C4—48no—
151C42×C7—28no—
152C42×C7—44no—
153C22×C4⋊C4C22×C712yes—
154C22×C4⋊C4C22×C711yescharacteristic
155C22×C4⋊C4C22×C712yes—
156C22×C4⋊C4C22×C711yescharacteristic
157C22×C4⋊C4C22×C712yes—
158C22×C4⋊C4C22×C711yescharacteristic
159C22×C42C22×C711yescharacteristic
160C22×C42C22×C711yescharacteristic
161#400—24no—
162#382—24no—
163C2×#95C22×C712yes—
164C2×#95C22×C712yes—
165C2×#95C22×C711yescharacteristic
166C2×#95C22×C712yes—
167C2×#95C22×C712yes—
168C2×#95C22×C712yes—
169C2×#95C22×C712yes—
170C2×#95C22×C712yes—
171C2×#95C22×C712yes—
172C2×#95C22×C711yescharacteristic
173C2×#95C22×C712yes—
174C2×#95C22×C712yes—
175C2×#95C22×C712yes—
176C23×C7C22×D411yescharacteristic
177C23×C7C22×Q812yes—
178C23×C7C2×#4112yes—
179C23×C7C2×#4112yes—
180C23×C7C2×#4112yes—
181C23×C7H(5,𝔽2)11yescharacteristic
182C23×C7H(5,𝔽2)11yescharacteristic
183C23×C7H(5,𝔽2)12yes—
184C23×C72−1+412yes—
185C2×C4×C7—22no—
186C2×C4×C7—24no—
187C2×C4×C7—22no—
188C2×C4×C7—24no—
189C2×C4×C7—24no—
190C2×C4×C7—24no—
191C2×C4×C7—24no—
192C2×C4×C7—24no—
193C2×C4×C7—24no—
194C2×C4×C7—24no—
195C2×C4×C7—24no—
196C2×C4×C7—22no—
197C2×C4×C7—22no—
198C2×C4×C7—24no—
199C2×C4×C7—24no—
200C2×C4×C7—24no—
201C2×C4×C7—24no—
202C2×C4×C7—24no—
203C2×C4×C7—24no—
204C2×C4×C7—24no—
205C2×C4×C7—42no—
206C2×C4×C7—42no—
207C2×C4×C7—42no—
208C2×C4×C7—42no—
209C2×C4×C7—42no—
210C2×C4×C7—42no—
211C2×C4×C7—42no—
212C2×C4×C7—42no—
213C2×C4×C7—41no—
214C2×C4×C7—41no—
215C2×C4×C7—42no—
216C2×C4×C7—42no—
217C2×C4×C7—41no—
218C2×C4×C7—41no—
219C2×C4×C7—42no—
220C2×C4×C7—42no—
221C2×C4×C7—42no—
222C2×C4×C7—42no—
223C2×C4×C7—42no—
224C2×C4×C7—42no—
225C2×C4×C7—42no—
226C2×C4×C7—42no—
227C2×C4×C7—42no—
228C2×C4×C7—42no—
229C2×C4×C7—42no—
230C2×C4×C7—42no—
231C2×C4×C7—42no—
232C2×C4×C7—42no—
233C2×C4×C7—42no—
234C2×C4×C7—42no—
235C2×C4×C7—42no—
236C2×C4×C7—42no—
237C2×C4×C7—42no—
238C2×C4×C7—42no—
239C2×C4×C7—42no—
240C2×C4×C7#12518yes—
241C2×C4×C7C4⋊Q814yes—
242C23×C4C23×C712yes—
243C23×C4C23×C712yes—
244C23×C4C23×C712yes—
245C23×C4C23×C711yescharacteristic
246C23×C4C23×C711yescharacteristic
247C23×C4C23×C712yes—
248C23×C4C23×C712yes—
249C23×C4C23×C711yescharacteristic
250C23×C4C23×C712yes—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—24no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4—24no—
256C2×C4⋊C4—41no—
257C2×C4⋊C4—41no—
258C2×C4⋊C4—42no—
259C2×C4⋊C4—42no—
260C2×C4⋊C4—42no—
261C2×C4⋊C4—41no—
262C2×C4⋊C4—41no—
263C2×C4⋊C4—41no—
264C2×C4⋊C4—41no—
265C2×C4⋊C4—42no—
266C2×C4⋊C4—42no—
267C2×C4⋊C4—42no—
268C2×C4⋊C4C7×D414yes—
269C2×C42—22no—
270C2×C42—24no—
271C2×C42—24no—
272C2×C42—41no—
273#95—24no—
274#95—24no—
275#95—22no—
276#95—24no—
277#95—24no—
278#95—24no—
279#95—24no—
280#95—24no—
281#95—24no—
282#95—41no—
283#95—42no—
284#95—42no—
285#95C7×Q818yes—
286C22×C7#52511yescharacteristic
287C22×C7C2×#12512yes—
288C22×C7#52912yes—
289C22×C7C2×C4⋊Q811yescharacteristic
290C22×C7#53411yescharacteristic
291C22×C7#53812yes—
292C22×C7#54212yes—
293C22×C7#54212yes—
294C22×C7#54412yes—
295C22×C7#54712yes—
296C22×C7#55012yes—
297C22×C7#55111yescharacteristic
298C22×C7#55112yes—
299C22×C7#55212yes—
300C22×C7#55412yes—
301C22×C7#55412yes—
302C22×C7#55412yes—
303C22×C7#55511yescharacteristic
304C22×C7#55712yes—
305C22×C7H(3,𝔽4)11yescharacteristic
306C22×C7#56311yescharacteristic
307C4×C7—24no—
308C4×C7—28no—
309C4×C7—42no—
310C4×C7—42no—
311C4×C7—44no—
312C4×C7—44no—
313C4×C7—82no—
314C4×C7—82no—
315C4×C7—82no—
316C24C24×C711yescharacteristic
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—21no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4C2×C7×D412yes—
366C22×C4C2×C7×D412yes—
367C22×C4C2×C7×D412yes—
368C22×C4C2×C7×Q814yes—
369C22×C4C2×C7×Q814yes—
370C22×C4C2×C7×Q814yes—
371C22×C4C7×#4114yes—
372C22×C4C7×#4114yes—
373C22×C4C7×#4114yes—
374C4⋊C4—44no—
375C4⋊C4—48no—
376C4⋊C4—44no—
377C4⋊C4—48no—
378C4⋊C4—44no—
379C4⋊C4—48no—
380C42—28no—
381C42—44no—
382C2×C7#247912yes—
383C2×C7#250512yes—
384C2×C7#250812yes—
385C2×C7#255212yes—
386C2×C7#258311yescharacteristic
387C2×C7#271711yescharacteristic
388C2×C7#273311yescharacteristic
389C2×C7#276312yes—
390C2×C7#277412yes—
391C23C22×C7×D411yescharacteristic
392C23C22×C7×Q812yes—
393C23C2×C7×#4112yes—
394C23C2×C7×#4112yes—
395C23C2×C7×#4112yes—
396C23C7×H(5,𝔽2)11yescharacteristic
397C23C7×H(5,𝔽2)11yescharacteristic
398C23C7×H(5,𝔽2)12yes—
399C23C7×2−1+412yes—
400C2×C4—22no—
401C2×C4—24no—
402C2×C4—22no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4C7×#12518yes—
456C2×C4C7×C4⋊Q814yes—
457C7#1594611yescharacteristic, direct product factor, Sylow
458C22C7×#52511yescharacteristic
459C22C2×C7×#12512yes—
460C22C7×#52912yes—
461C22C2×C7×C4⋊Q811yescharacteristic
462C22C7×#53411yescharacteristic
463C22C7×#53812yes—
464C22C7×#54212yes—
465C22C7×#54212yes—
466C22C7×#54412yes—
467C22C7×#54712yes—
468C22C7×#55012yes—
469C22C7×#55111yescharacteristic
470C22C7×#55112yes—
471C22C7×#55212yes—
472C22C7×#55412yes—
473C22C7×#55412yes—
474C22C7×#55412yes—
475C22C7×#55511yescharacteristic
476C22C7×#55712yes—
477C22C7×H(3,𝔽4)11yescharacteristic
478C22C7×#56311yescharacteristic
479C4—28no—
480C4—24no—
481C4—42no—
482C4—42no—
483C4—44no—
484C4—44no—
485C4—82no—
486C4—82no—
487C4—82no—
488C2C7×#247912yes—
489C2C7×#250512yes—
490C2C7×#250812yes—
491C2C7×#255212yes—
492C2C7×#258311yescharacteristic
493C2C7×#271711yescharacteristic
494C2C7×#273311yescharacteristic
495C2C7×#276312yes—
496C2C7×#277412yes—
subgroupG/H
center, socle, prime radicalC24×C7C24
commutator, Frattini, cosocleC24C24×C7
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
33. #15946C7direct (N × H)
457. C7#15946direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#4002
C2×C7×#3822
C7×#14442
C7×#14422
C7×#14362
C7×C4⋊#952
#159467