Finite Group Databasebeta

← C7×#14587 #13191803

Subgroups — C7×#14587 #13191803

Order 1792.

1282 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#398C211yesmaximal, characteristic
2C2×C7×#389C212yesmaximal
3C7×#1444C212yesmaximal
4C7×#1441C212yesmaximal
5C7×#1441C211yesmaximal, characteristic
6C7×#1436C212yesmaximal
7C7×#1436C212yesmaximal
8C7×C4⋊#95C211yesmaximal, characteristic
9C7×#1434C212yesmaximal
10C22×C7×C4⋊C4C2212yes—
11C22×C7×C4⋊C4C2212yes—
12C22×C7×C4⋊C4C2212yes—
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C42×C7C2212yes—
18C22×C42×C7C2211yescharacteristic
19C7×#398C418yescomplemented
20C7×#389—28no—
21C2×C7×#95C2212yes—
22C2×C7×#95C2212yes—
23C2×C7×#95C2212yes—
24C2×C7×#95C2211yescharacteristic
25C2×C7×#95C2212yes—
26C2×C7×#95C2212yes—
27C2×C7×#95C2212yes—
28C2×C7×#95C2212yes—
29C2×C7×#95C2212yes—
30C2×C7×#95C2212yes—
31C2×C7×#95C2211yescharacteristic
32C2×C7×#95C2212yes—
33#14587C711yesmaximal, characteristic, direct product factor, Sylow
34C23×C4×C7C2312yes—
35C23×C4×C7C2311yescharacteristic
36C23×C4×C7C2311yescharacteristic
37C23×C4×C7C2312yes—
38C23×C4×C7C2312yes—
39C23×C4×C7C2312yes—
40C23×C4×C7C2312yes—
41C23×C4×C7C2311yescharacteristic
42C23×C4×C7C2312yes—
43C2×C7×C4⋊C4—24no—
44C2×C7×C4⋊C4—24no—
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—41no—
51C2×C7×C4⋊C4—41no—
52C2×C7×C4⋊C4—41no—
53C2×C7×C4⋊C4—41no—
54C2×C7×C4⋊C4—42no—
55C2×C7×C4⋊C4—42no—
56C2×C7×C4⋊C4—42no—
57C2×C7×C4⋊C4—42no—
58C2×C7×C4⋊C4—41no—
59C2×C7×C4⋊C4C2×C418yes—
60C2×C7×C4⋊C4C2×C414yes—
61C2×C7×C4⋊C4C2×C414yes—
62C2×C7×C4⋊C4D414yes—
63C2×C42×C7—24no—
64C2×C42×C7—24no—
65C2×C42×C7—22no—
66C2×C42×C7—42no—
67C2×C42×C7—41no—
68C2×C42×C7—41no—
69C7×#95—24no—
70C7×#95—24no—
71C7×#95—24no—
72C7×#95—41no—
73C7×#95—42no—
74C7×#95—42no—
75C7×#95—42no—
76C7×#95—42no—
77C7×#95—42no—
78C7×#95C2×C418yes—
79C7×#95C2×C414yes—
80C7×#95Q818yes—
81C2×#398C2×C711yescharacteristic
82C2×#389C2×C712yes—
83#1444C2×C712yes—
84#1441C2×C712yes—
85#1441C2×C711yescharacteristic
86#1436C2×C712yes—
87#1436C2×C712yes—
88C4⋊#95C2×C711yescharacteristic
89#1434C2×C712yes—
90C24×C7C2411yescharacteristic
91C22×C4×C7—22no—
92C22×C4×C7—22no—
93C22×C4×C7—21no—
94C22×C4×C7—21no—
95C22×C4×C7—22no—
96C22×C4×C7—21no—
97C22×C4×C7—21no—
98C22×C4×C7—22no—
99C22×C4×C7—22no—
100C22×C4×C7—22no—
101C22×C4×C7—22no—
102C22×C4×C7—22no—
103C22×C4×C7—22no—
104C22×C4×C7—22no—
105C22×C4×C7—22no—
106C22×C4×C7—22no—
107C22×C4×C7—22no—
108C22×C4×C7—22no—
109C22×C4×C7—22no—
110C22×C4×C7—22no—
111C22×C4×C7—22no—
112C22×C4×C7—22no—
113C22×C4×C7—22no—
114C22×C4×C7—22no—
115C22×C4×C7—21no—
116C22×C4×C7—22no—
117C22×C4×C7—22no—
118C22×C4×C7—22no—
119C22×C4×C7—21no—
120C22×C4×C7—21no—
121C22×C4×C7—22no—
122C22×C4×C7—21no—
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×C7—22no—
137C22×C4×C7—22no—
138C22×C4×C7C22×C412yes—
139C22×C4×C7C22×C414yes—
140C22×C4×C7C22×C412yes—
141C22×C4×C7C22×C412yes—
142C22×C4×C7C22×C414yes—
143C22×C4×C7C2×D414yes—
144C22×C4×C7C2×D412yes—
145C22×C4×C7C2×Q814yes—
146C22×C4×C7C2×Q814yes—
147C22×C4×C7C2×Q814yes—
148C22×C4×C7#4112yes—
149C22×C4×C7#4114yes—
150C7×C4⋊C4—216no—
151C7×C4⋊C4—44no—
152C7×C4⋊C4—44no—
153C7×C4⋊C4—44no—
154C7×C4⋊C4—48no—
155C7×C4⋊C4—48no—
156C7×C4⋊C4—44no—
157C42×C7—48no—
158C42×C7—44no—
159C22×C4⋊C4C22×C712yes—
160C22×C4⋊C4C22×C712yes—
161C22×C4⋊C4C22×C712yes—
162C22×C4⋊C4C22×C711yescharacteristic
163C22×C4⋊C4C22×C711yescharacteristic
164C22×C4⋊C4C22×C711yescharacteristic
165C22×C4⋊C4C22×C711yescharacteristic
166C22×C42C22×C712yes—
167C22×C42C22×C711yescharacteristic
168#398C4×C718yescomplemented
169#389—28no—
170C2×#95C22×C712yes—
171C2×#95C22×C712yes—
172C2×#95C22×C712yes—
173C2×#95C22×C711yescharacteristic
174C2×#95C22×C712yes—
175C2×#95C22×C712yes—
176C2×#95C22×C712yes—
177C2×#95C22×C712yes—
178C2×#95C22×C712yes—
179C2×#95C22×C712yes—
180C2×#95C22×C711yescharacteristic
181C2×#95C22×C712yes—
182C23×C7C23×C411yescharacteristic
183C23×C7C22×D411yescharacteristic
184C23×C7C22×Q812yes—
185C23×C7C2×#4111yescharacteristic
186C23×C7C2×#4112yes—
187C23×C7H(5,𝔽2)11yescharacteristic
188C23×C7H(5,𝔽2)11yescharacteristic
189C23×C7H(5,𝔽2)11yescharacteristic
190C23×C7H(5,𝔽2)12yes—
191C23×C72−1+411yescharacteristic
192C23×C72−1+412yes—
193C2×C4×C7—24no—
194C2×C4×C7—22no—
195C2×C4×C7—22no—
196C2×C4×C7—24no—
197C2×C4×C7—22no—
198C2×C4×C7—22no—
199C2×C4×C7—22no—
200C2×C4×C7—22no—
201C2×C4×C7—24no—
202C2×C4×C7—24no—
203C2×C4×C7—24no—
204C2×C4×C7—24no—
205C2×C4×C7—24no—
206C2×C4×C7—22no—
207C2×C4×C7—24no—
208C2×C4×C7—22no—
209C2×C4×C7—24no—
210C2×C4×C7—24no—
211C2×C4×C7—24no—
212C2×C4×C7—24no—
213C2×C4×C7—24no—
214C2×C4×C7—24no—
215C2×C4×C7—24no—
216C2×C4×C7—24no—
217C2×C4×C7—24no—
218C2×C4×C7—24no—
219C2×C4×C7—24no—
220C2×C4×C7—24no—
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—41no—
235C2×C4×C7—41no—
236C2×C4×C7—42no—
237C2×C4×C7—42no—
238C2×C4×C7—42no—
239C2×C4×C7—42no—
240C2×C4×C7—42no—
241C2×C4×C7—41no—
242C2×C4×C7—41no—
243C2×C4×C7—42no—
244C2×C4×C7—42no—
245C2×C4×C7—42no—
246C2×C4×C7—42no—
247C2×C4×C7—42no—
248C2×C4×C7—42no—
249C2×C4×C7—42no—
250C2×C4×C7C4×D414yes—
251C2×C4×C7C4×Q818yes—
252C23×C4C23×C712yes—
253C23×C4C23×C712yes—
254C23×C4C23×C711yescharacteristic
255C23×C4C23×C711yescharacteristic
256C23×C4C23×C712yes—
257C23×C4C23×C712yes—
258C23×C4C23×C712yes—
259C23×C4C23×C711yescharacteristic
260C23×C4C23×C712yes—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—41no—
267C2×C4⋊C4—41no—
268C2×C4⋊C4—41no—
269C2×C4⋊C4—41no—
270C2×C4⋊C4—41no—
271C2×C4⋊C4—41no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—41no—
277C2×C4⋊C4C2×C4×C718yes—
278C2×C4⋊C4C2×C4×C714yes—
279C2×C4⋊C4C2×C4×C714yes—
280C2×C4⋊C4C7×D414yes—
281C2×C42—24no—
282C2×C42—24no—
283C2×C42—22no—
284C2×C42—42no—
285C2×C42—41no—
286C2×C42—41no—
287#95—24no—
288#95—24no—
289#95—24no—
290#95—41no—
291#95—42no—
292#95—42no—
293#95—42no—
294#95—42no—
295#95—42no—
296#95C2×C4×C718yes—
297#95C2×C4×C714yes—
298#95C7×Q818yes—
299C22×C7C2×C4×D411yescharacteristic
300C22×C7C2×C4×Q812yes—
301C22×C7#51811yescharacteristic
302C22×C7#52011yescharacteristic
303C22×C7#52012yes—
304C22×C7#53411yescharacteristic
305C22×C7#53711yescharacteristic
306C22×C7#53811yescharacteristic
307C22×C7#53911yescharacteristic
308C22×C7#54012yes—
309C22×C7#54112yes—
310C22×C7#54412yes—
311C22×C7#54412yes—
312C22×C7#54612yes—
313C22×C7D4×Q812yes—
314C22×C7#55212yes—
315C22×C7#55412yes—
316C22×C7#55412yes—
317C22×C7#55511yescharacteristic
318C22×C7Q8211yescharacteristic
319C22×C7#56011yescharacteristic
320C22×C7#56212yes—
321C22×C7#56311yescharacteristic
322C4×C7—24no—
323C4×C7—28no—
324C4×C7—44no—
325C4×C7—42no—
326C4×C7—42no—
327C4×C7—44no—
328C4×C7—44no—
329C4×C7—44no—
330C4×C7—82no—
331C24C24×C711yescharacteristic
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—22no—
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—21no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4C22×C4×C712yes—
380C22×C4C22×C4×C714yes—
381C22×C4C22×C4×C712yes—
382C22×C4C22×C4×C712yes—
383C22×C4C22×C4×C714yes—
384C22×C4C2×C7×D414yes—
385C22×C4C2×C7×D412yes—
386C22×C4C2×C7×Q814yes—
387C22×C4C2×C7×Q814yes—
388C22×C4C2×C7×Q814yes—
389C22×C4C7×#4112yes—
390C22×C4C7×#4114yes—
391C4⋊C4—216no—
392C4⋊C4—44no—
393C4⋊C4—44no—
394C4⋊C4—44no—
395C4⋊C4—48no—
396C4⋊C4—48no—
397C4⋊C4—44no—
398C42—48no—
399C42—44no—
400C2×C7#232511yescharacteristic
401C2×C7#233012yes—
402C2×C7#236012yes—
403C2×C7#236911yescharacteristic
404C2×C7#237611yescharacteristic
405C2×C7#269911yescharacteristic
406C2×C7#270412yes—
407C2×C7#273411yescharacteristic
408C2×C7#276812yes—
409C2×C7#276911yescharacteristic
410C2×C7#279211yescharacteristic
411C23C23×C4×C711yescharacteristic
412C23C22×C7×D411yescharacteristic
413C23C22×C7×Q812yes—
414C23C2×C7×#4111yescharacteristic
415C23C2×C7×#4112yes—
416C23C7×H(5,𝔽2)11yescharacteristic
417C23C7×H(5,𝔽2)11yescharacteristic
418C23C7×H(5,𝔽2)11yescharacteristic
419C23C7×H(5,𝔽2)12yes—
420C23C7×2−1+411yescharacteristic
421C23C7×2−1+412yes—
422C2×C4—24no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—22no—
436C2×C4—24no—
437C2×C4—22no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—41no—
464C2×C4—42no—
465C2×C4—41no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4C4×C7×D414yes—
480C2×C4C4×C7×Q818yes—
481C7#1458711yescharacteristic, direct product factor, Sylow
482C22C2×C4×C7×D411yescharacteristic
483C22C2×C4×C7×Q812yes—
484C22C7×#51811yescharacteristic
485C22C7×#52011yescharacteristic
486C22C7×#52012yes—
487C22C7×#53411yescharacteristic
488C22C7×#53711yescharacteristic
489C22C7×#53811yescharacteristic
490C22C7×#53911yescharacteristic
491C22C7×#54012yes—
492C22C7×#54112yes—
493C22C7×#54412yes—
494C22C7×#54412yes—
495C22C7×#54612yes—
496C22C7×D4×Q812yes—
497C22C7×#55212yes—
498C22C7×#55412yes—
499C22C7×#55412yes—
500C22C7×#55511yescharacteristic
501C22C7×Q8211yescharacteristic
502C22C7×#56011yescharacteristic
503C22C7×#56212yes—
504C22C7×#56311yescharacteristic
505C4—24no—
506C4—28no—
507C4—44no—
508C4—44no—
509C4—44no—
510C4—44no—
511C4—42no—
512C4—42no—
513C4—82no—
514C2C7×#232511yescharacteristic
515C2C7×#233012yes—
516C2C7×#236012yes—
517C2C7×#236911yescharacteristic
518C2C7×#237611yescharacteristic
519C2C7×#269911yescharacteristic
520C2C7×#270412yes—
521C2C7×#273411yescharacteristic
522C2C7×#276812yes—
523C2C7×#276911yescharacteristic
524C2C7×#279211yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
19. C7×#398C4semidirect
33. #14587C7direct (N × H)
168. #398C4×C7semidirect
481. C7#14587direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3982
C2×C7×#3892
C7×#14442
C7×#14412
C7×#14362
C7×C4⋊#952
C7×#14342
#145877