Finite Group Databasebeta

← C7×#14538 #13191754

Subgroups — C7×#14538 #13191754

Order 1792.

1402 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#395C211yesmaximal, characteristic
2C2×C7×#391C212yesmaximal
3C2×C7×#387C212yesmaximal
4C7×#1443C212yesmaximal
5C7×#1441C212yesmaximal
6C7×#1441C211yesmaximal, characteristic
7C7×#1436C212yesmaximal
8C7×#1436C212yesmaximal
9C7×C4⋊#95C211yesmaximal, characteristic
10C23×C7×Q8C2211yescharacteristic
11C22×C7×C4⋊C4C2211yescharacteristic
12C22×C7×C4⋊C4C2212yes—
13C22×C7×C4⋊C4C2212yes—
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C42×C7C2212yes—
17C22×C42×C7C2211yescharacteristic
18C7×#395C418yescomplemented
19C7×#391—28no—
20C7×#387—28no—
21C2×C7×#95C2212yes—
22C2×C7×#95C2212yes—
23C2×C7×#95C2212yes—
24C2×C7×#95C2212yes—
25C2×C7×#95C2212yes—
26C2×C7×#95C2212yes—
27C2×C7×#95C2212yes—
28C2×C7×#95C2212yes—
29C2×C7×#95C2212yes—
30C2×C7×#95C2211yescharacteristic
31C2×C7×#95C2212yes—
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2212yes—
34#14538C711yesmaximal, characteristic, direct product factor, Sylow
35C22×C7×Q8—24no—
36C22×C7×Q8—24no—
37C22×C7×Q8—41no—
38C22×C7×Q8—41no—
39C22×C7×Q8C2×C414yes—
40C23×C4×C7C2312yes—
41C23×C4×C7C2311yescharacteristic
42C23×C4×C7C2312yes—
43C23×C4×C7C2311yescharacteristic
44C23×C4×C7C2312yes—
45C23×C4×C7C2312yes—
46C23×C4×C7C2312yes—
47C23×C4×C7C2312yes—
48C23×C4×C7C2311yescharacteristic
49C2×C7×C4⋊C4—24no—
50C2×C7×C4⋊C4—24no—
51C2×C7×C4⋊C4—24no—
52C2×C7×C4⋊C4—24no—
53C2×C7×C4⋊C4—24no—
54C2×C7×C4⋊C4—41no—
55C2×C7×C4⋊C4—41no—
56C2×C7×C4⋊C4—41no—
57C2×C7×C4⋊C4—41no—
58C2×C7×C4⋊C4—42no—
59C2×C7×C4⋊C4—41no—
60C2×C7×C4⋊C4C2×C418yes—
61C2×C7×C4⋊C4C2×C414yes—
62C2×C7×C4⋊C4Q814yescomplemented
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—24no—
73C7×#95—24no—
74C7×#95—24no—
75C7×#95—24no—
76C7×#95—42no—
77C7×#95—42no—
78C7×#95—41no—
79C7×#95C2×C414yes—
80C7×#95C2×C418yes—
81C7×#95D418yes—
82C2×#395C2×C711yescharacteristic
83C2×#391C2×C712yes—
84C2×#387C2×C712yes—
85#1443C2×C712yes—
86#1441C2×C712yes—
87#1441C2×C711yescharacteristic
88#1436C2×C712yes—
89#1436C2×C712yes—
90C4⋊#95C2×C711yescharacteristic
91C24×C7C2411yescharacteristic
92C2×C7×Q8—216no—
93C2×C7×Q8—44no—
94C2×C7×Q8—44no—
95C2×C7×Q8—48no—
96C2×C7×Q8—44no—
97C22×C4×C7—22no—
98C22×C4×C7—22no—
99C22×C4×C7—21no—
100C22×C4×C7—21no—
101C22×C4×C7—22no—
102C22×C4×C7—21no—
103C22×C4×C7—22no—
104C22×C4×C7—21no—
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—22no—
116C22×C4×C7—22no—
117C22×C4×C7—22no—
118C22×C4×C7—22no—
119C22×C4×C7—21no—
120C22×C4×C7—22no—
121C22×C4×C7—22no—
122C22×C4×C7—22no—
123C22×C4×C7—22no—
124C22×C4×C7—21no—
125C22×C4×C7—21no—
126C22×C4×C7—21no—
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×C7—22no—
139C22×C4×C7—22no—
140C22×C4×C7—22no—
141C22×C4×C7—22no—
142C22×C4×C7—22no—
143C22×C4×C7—22no—
144C22×C4×C7C22×C414yes—
145C22×C4×C7C22×C412yes—
146C22×C4×C7C22×C412yes—
147C22×C4×C7C22×C414yes—
148C22×C4×C7C22×C412yes—
149C22×C4×C7C2×D414yes—
150C22×C4×C7C2×D414yes—
151C22×C4×C7C2×D414yes—
152C22×C4×C7C2×Q814yes—
153C22×C4×C7C2×Q812yes—
154C22×C4×C7#4114yes—
155C22×C4×C7#4112yes—
156C7×C4⋊C4—216no—
157C7×C4⋊C4—44no—
158C7×C4⋊C4—44no—
159C7×C4⋊C4—48no—
160C7×C4⋊C4—44no—
161C42×C7—48no—
162C42×C7—44no—
163C23×Q8C22×C711yescharacteristic
164C22×C4⋊C4C22×C712yes—
165C22×C4⋊C4C22×C711yescharacteristic
166C22×C4⋊C4C22×C712yes—
167C22×C4⋊C4C22×C711yescharacteristic
168C22×C4⋊C4C22×C711yescharacteristic
169C22×C42C22×C712yes—
170C22×C42C22×C711yescharacteristic
171#395C4×C718yescomplemented
172#391—28no—
173#387—28no—
174C2×#95C22×C712yes—
175C2×#95C22×C712yes—
176C2×#95C22×C712yes—
177C2×#95C22×C712yes—
178C2×#95C22×C712yes—
179C2×#95C22×C712yes—
180C2×#95C22×C712yes—
181C2×#95C22×C712yes—
182C2×#95C22×C712yes—
183C2×#95C22×C711yescharacteristic
184C2×#95C22×C712yes—
185C2×#95C22×C711yescharacteristic
186C2×#95C22×C712yes—
187C23×C7C23×C411yescharacteristic
188C23×C7C22×D412yes—
189C23×C7C22×Q811yescharacteristic
190C23×C7C2×#4112yes—
191C23×C7C2×#4111yescharacteristic
192C23×C7H(5,𝔽2)11yescharacteristic
193C23×C7H(5,𝔽2)11yescharacteristic
194C23×C7H(5,𝔽2)11yescharacteristic
195C23×C72−1+412yes—
196C23×C72−1+412yes—
197C23×C72−1+411yescharacteristic
198C7×Q8—416no—
199C2×C4×C7—24no—
200C2×C4×C7—22no—
201C2×C4×C7—24no—
202C2×C4×C7—22no—
203C2×C4×C7—22no—
204C2×C4×C7—22no—
205C2×C4×C7—22no—
206C2×C4×C7—22no—
207C2×C4×C7—24no—
208C2×C4×C7—24no—
209C2×C4×C7—24no—
210C2×C4×C7—24no—
211C2×C4×C7—24no—
212C2×C4×C7—24no—
213C2×C4×C7—24no—
214C2×C4×C7—22no—
215C2×C4×C7—22no—
216C2×C4×C7—24no—
217C2×C4×C7—24no—
218C2×C4×C7—24no—
219C2×C4×C7—24no—
220C2×C4×C7—24no—
221C2×C4×C7—24no—
222C2×C4×C7—24no—
223C2×C4×C7—24no—
224C2×C4×C7—24no—
225C2×C4×C7—24no—
226C2×C4×C7—24no—
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—41no—
239C2×C4×C7—41no—
240C2×C4×C7—42no—
241C2×C4×C7—42no—
242C2×C4×C7—42no—
243C2×C4×C7—41no—
244C2×C4×C7—41no—
245C2×C4×C7—42no—
246C2×C4×C7—42no—
247C2×C4×C7—42no—
248C2×C4×C7—42no—
249C2×C4×C7—42no—
250C2×C4×C7—42no—
251C2×C4×C7—42no—
252C2×C4×C7—42no—
253C2×C4×C7—42no—
254C2×C4×C7—42no—
255C2×C4×C7—42no—
256C2×C4×C7C4×D418yes—
257C2×C4×C7C4×Q814yes—
258C22×Q8—24no—
259C22×Q8—24no—
260C22×Q8—41no—
261C22×Q8—41no—
262C22×Q8C2×C4×C714yes—
263C23×C4C23×C712yes—
264C23×C4C23×C711yescharacteristic
265C23×C4C23×C711yescharacteristic
266C23×C4C23×C712yes—
267C23×C4C23×C712yes—
268C23×C4C23×C712yes—
269C23×C4C23×C712yes—
270C23×C4C23×C712yes—
271C23×C4C23×C711yescharacteristic
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—41no—
278C2×C4⋊C4—41no—
279C2×C4⋊C4—41no—
280C2×C4⋊C4—41no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—41no—
283C2×C4⋊C4C2×C4×C718yes—
284C2×C4⋊C4C2×C4×C714yes—
285C2×C4⋊C4C7×Q814yescomplemented
286C2×C42—24no—
287C2×C42—24no—
288C2×C42—22no—
289C2×C42—42no—
290C2×C42—41no—
291C2×C42—41no—
292#95—24no—
293#95—24no—
294#95—24no—
295#95—24no—
296#95—24no—
297#95—24no—
298#95—24no—
299#95—42no—
300#95—42no—
301#95—41no—
302#95C2×C4×C714yes—
303#95C2×C4×C718yes—
304#95C7×D418yes—
305C22×C7C2×C4×D412yes—
306C22×C7C2×C4×Q811yescharacteristic
307C22×C7#51811yescharacteristic
308C22×C7#51912yes—
309C22×C7#52011yescharacteristic
310C22×C7#53612yes—
311C22×C7#53712yes—
312C22×C7#53811yescharacteristic
313C22×C7#53911yescharacteristic
314C22×C7#54112yes—
315C22×C7#54212yes—
316C22×C7#54311yescharacteristic
317C22×C7#54411yescharacteristic
318C22×C7D4211yescharacteristic
319C22×C7#54612yes—
320C22×C7#54712yes—
321C22×C7D4×Q812yes—
322C22×C7#55111yescharacteristic
323C22×C7#55612yes—
324C22×C7#55712yes—
325C22×C7#56311yescharacteristic
326C22×C7#56311yescharacteristic
327C22×C7#56312yes—
328C4×C7—24no—
329C4×C7—28no—
330C4×C7—44no—
331C4×C7—42no—
332C4×C7—42no—
333C4×C7—44no—
334C4×C7—44no—
335C4×C7—44no—
336C4×C7—82no—
337C24C24×C711yescharacteristic
338C2×Q8—216no—
339C2×Q8—44no—
340C2×Q8—44no—
341C2×Q8—48no—
342C2×Q8—44no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—21no—
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×C4—21no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4C22×C4×C714yes—
391C22×C4C22×C4×C712yes—
392C22×C4C22×C4×C712yes—
393C22×C4C22×C4×C714yes—
394C22×C4C22×C4×C712yes—
395C22×C4C2×C7×D414yes—
396C22×C4C2×C7×D414yes—
397C22×C4C2×C7×D414yes—
398C22×C4C2×C7×Q814yes—
399C22×C4C2×C7×Q812yes—
400C22×C4C7×#4114yes—
401C22×C4C7×#4112yes—
402C4⋊C4—216no—
403C4⋊C4—44no—
404C4⋊C4—44no—
405C4⋊C4—48no—
406C4⋊C4—44no—
407C42—48no—
408C42—44no—
409C2×C7#232312yes—
410C2×C7#232911yescharacteristic
411C2×C7#235811yescharacteristic
412C2×C7#236512yes—
413C2×C7#238111yescharacteristic
414C2×C7#268011yescharacteristic
415C2×C7#268311yescharacteristic
416C2×C7#271312yes—
417C2×C7#271512yes—
418C2×C7#278911yescharacteristic
419C2×C7#279911yescharacteristic
420C23C23×C4×C711yescharacteristic
421C23C22×C7×D412yes—
422C23C22×C7×Q811yescharacteristic
423C23C2×C7×#4112yes—
424C23C2×C7×#4111yescharacteristic
425C23C7×H(5,𝔽2)11yescharacteristic
426C23C7×H(5,𝔽2)11yescharacteristic
427C23C7×H(5,𝔽2)11yescharacteristic
428C23C7×2−1+412yes—
429C23C7×2−1+412yes—
430C23C7×2−1+411yescharacteristic
431Q8—416no—
432C2×C4—24no—
433C2×C4—22no—
434C2×C4—24no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4C4×C7×D418yes—
490C2×C4C4×C7×Q814yes—
491C7#1453811yescharacteristic, direct product factor, Sylow
492C22C2×C4×C7×D412yes—
493C22C2×C4×C7×Q811yescharacteristic
494C22C7×#51811yescharacteristic
495C22C7×#51912yes—
496C22C7×#52011yescharacteristic
497C22C7×#53612yes—
498C22C7×#53712yes—
499C22C7×#53811yescharacteristic
500C22C7×#53911yescharacteristic
501C22C7×#54112yes—
502C22C7×#54212yes—
503C22C7×#54311yescharacteristic
504C22C7×#54411yescharacteristic
505C22C7×D4211yescharacteristic
506C22C7×#54612yes—
507C22C7×#54712yes—
508C22C7×D4×Q812yes—
509C22C7×#55111yescharacteristic
510C22C7×#55612yes—
511C22C7×#55712yes—
512C22C7×#56311yescharacteristic
513C22C7×#56311yescharacteristic
514C22C7×#56312yes—
515C4—24no—
516C4—28no—
517C4—44no—
518C4—44no—
519C4—44no—
520C4—44no—
521C4—42no—
522C4—42no—
523C4—82no—
524C2C7×#232312yes—
525C2C7×#232911yescharacteristic
526C2C7×#235811yescharacteristic
527C2C7×#236512yes—
528C2C7×#238111yescharacteristic
529C2C7×#268011yescharacteristic
530C2C7×#268311yescharacteristic
531C2C7×#271312yes—
532C2C7×#271512yes—
533C2C7×#278911yescharacteristic
534C2C7×#279911yescharacteristic
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
18. C7×#395C4semidirect
34. #14538C7direct (N × H)
62. C2×C7×C4⋊C4Q8semidirect
171. #395C4×C7semidirect
285. C2×C4⋊C4C7×Q8semidirect
491. C7#14538direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3952
C2×C7×#3912
C2×C7×#3872
C7×#14432
C7×#14412
C7×#14362
C7×C4⋊#952
#145387