Finite Group Databasebeta

← D7×#2043 #13381474

Subgroups — D7×#2043 #13381474

Order 1792.

1542 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D7×C4⋊Q8C211yesmaximal, characteristic
2C2×D7×#103C212yesmaximal
3C2×D7×#103C212yesmaximal
4D7×#389C211yesmaximal, characteristic
5C7×#2043C211yesmaximal, characteristic, complemented
6#11729535C211yesmaximal, characteristic, complemented
7#11728038C212yesmaximal, complemented
8#11728000C212yesmaximal, complemented
9#11727387C211yesmaximal, characteristic, complemented
10D7×#336C211yesmaximal, characteristic
11#11726385C211yesmaximal, characteristic, complemented
12C22×Q8×D7C2212yes—
13C2×C7×C4⋊Q8C2211yescharacteristic
14C2×#6507C2212yes—
15C22×C8×D7C2212yes—
16D7×C4⋊Q8—28no—
17C2×D7×C4⋊C4—21no—
18C2×D7×C4⋊C4—21no—
19C2×D7×C4⋊C4—21no—
20C2×D7×C4⋊C4C2211yescharacteristic
21C2×D7×C4⋊C4C2211yescharacteristic
22C2×#6451—21no—
23C2×#6451—21no—
24C2×C42×D7C2211yescharacteristic
25C2×#6432C2211yescharacteristic
26C2×C7×#103C2212yes—
27C2×C7×#103C2212yes—
28C7×#389C2211yescharacteristic
29C2×#6409C2212yes—
30C2×#6409C2212yes—
31C2×#6390C2212yes—
32C2×#6390C2212yes—
33#89757C2211yescharacteristic
34#89745C2211yescharacteristic
35#89744—21no—
36C2×#6384C2212yes—
37C2×#6384C2212yes—
38#89700C2211yescharacteristic
39D7×#103—28no—
40D7×#103—28no—
41D7×#95—21no—
42#89419—21no—
43C7×#336C2211yescharacteristic
44#89345C2212yes—
45#89319C2211yescharacteristic
46C2×#2043—71nomaximal, Sylow
47C22×C7×Q8C2312yes—
48C2×Q8×D7—24no—
49C2×Q8×D7—24no—
50C2×Q8×D7—24no—
51C2×Q8×D7—24no—
52C2×Q8×D7—24no—
53C2×Q8×D7D418yes—
54C22×C4×D7—22no—
55C22×C4×D7—21no—
56C22×C4×D7—21no—
57C22×C4×D7D411yescharacteristic
58C22×C4×D7D411yescharacteristic
59C22×C4×D7C2311yescharacteristic
60C22×Dic14—22no—
61C22×Dic14C2312yes—
62C22×C7×C8C2312yes—
63C7×C4⋊Q8—24no—
64C2×C7×C4⋊C4—21no—
65C2×C7×C4⋊C4—21no—
66C2×C7×C4⋊C4—21no—
67C2×C7×C4⋊C4C2311yescharacteristic
68C2×C7×C4⋊C4C2311yescharacteristic
69C2×C42×C7C2311yescharacteristic
70#6507—24no—
71#6507—24no—
72C2×C4⋊Dic7—21no—
73C2×C4⋊Dic7—21no—
74C2×C4⋊Dic7—21no—
75C2×C4⋊Dic7C2311yescharacteristic
76C2×C4⋊Dic7C2311yescharacteristic
77C2×Dic7⋊C4—21no—
78C2×Dic7⋊C4—22no—
79C2×Dic7⋊C4—22no—
80C2×Dic7⋊C4—21no—
81C2×Dic7⋊C4—21no—
82C2×Dic7⋊C4—21no—
83C2×C4×Dic7D411yescharacteristic
84C2×C4×Dic7D411yescharacteristic
85C2×C4×Dic7C2311yescharacteristic
86C22×C7⋊C8C2312yes—
87C2×C8×D7—24no—
88C2×C8×D7—24no—
89C2×C8×D7—24no—
90D7×C4⋊C4—28no—
91D7×C4⋊C4—28no—
92D7×C4⋊C4—22no—
93D7×C4⋊C4—24no—
94D7×C4⋊C4—44no—
95D7×C4⋊C4D414yes—
96#6451—28no—
97#6451—28no—
98C42×D7—24no—
99#6432—24no—
100C7×#103—24no—
101C7×#103—24no—
102C7×#95—21no—
103#6409—24no—
104#6409—24no—
105C7⋊#95—21no—
106C7⋊#95—21no—
107C7⋊#95—21no—
108#6390—24no—
109#6390—24no—
110#6384—24no—
111#6384—24no—
112C22×C4⋊Q8—71no—
113C22×#103—72no—
114C22×#103—72no—
115C2×#389—71no—
116#2043—72no—
117#2043—72no—
118#2043—71no—
119#2043—71no—
120#2043—71no—
121#2043D711yescharacteristic, direct product factor
122C2×#336—71no—
123C23×D7C2×D411yescharacteristic
124C2×C7×Q8—22no—
125C2×C7×Q8—22no—
126C2×C7×Q8—22no—
127C2×C7×Q8—22no—
128C2×C7×Q8—22no—
129C2×C7×Q8C2×D414yes—
130C22×C4×C7—21no—
131C22×C4×C7—22no—
132C22×C4×C7—21no—
133C22×C4×C7C2×D411yescharacteristic
134C22×C4×C7C2×D411yescharacteristic
135C22×C4×C7C2411yescharacteristic
136C22×Dic7—21no—
137C22×Dic7—22no—
138C22×Dic7—21no—
139C22×Dic7C2×D411yescharacteristic
140C22×Dic7C2×D411yescharacteristic
141C22×Dic7C2×D411yescharacteristic
142Q8×D7—216no—
143Q8×D7—216no—
144Q8×D7—48no—
145Q8×D7—48no—
146C2×C4×D7—22no—
147C2×C4×D7—22no—
148C2×C4×D7—22no—
149C2×C4×D7—22no—
150C2×C4×D7—28no—
151C2×C4×D7—24no—
152C2×C4×D7—44no—
153C2×C4×D7—44no—
154C2×C4×D7—42no—
155C2×C4×D7—42no—
156C2×C4×D7—42no—
157C2×C4×D7—42no—
158C2×C4×D7—42no—
159C2×C4×D7SD1614yes—
160C2×C4×D7Q1614yes—
161C2×C4×D7C2×D412yes—
162C2×C4×D7C2×D414yes—
163C2×C4×D7#4114yes—
164C2×C4×D7#4112yes—
165C2×Dic14—22no—
166C2×Dic14—22no—
167C2×Dic14—22no—
168C2×Dic14—22no—
169C2×Dic14—22no—
170C2×Dic14—28no—
171C2×Dic14—44no—
172C2×Dic14—44no—
173C2×Dic14C2×D414yes—
174C2×C7×C8—22no—
175C2×C7×C8—22no—
176C2×C7×C8—22no—
177C7×C4⋊C4—24no—
178C7×C4⋊C4—24no—
179C7×C4⋊C4—21no—
180C7×C4⋊C4—22no—
181C7×C4⋊C4—42no—
182C7×C4⋊C4C2×D412yes—
183C42×C7—22no—
184C4⋊Dic7—24no—
185C4⋊Dic7—24no—
186C4⋊Dic7—21no—
187C4⋊Dic7—22no—
188C4⋊Dic7—42no—
189C4⋊Dic7C2×D412yes—
190Dic7⋊C4—28no—
191Dic7⋊C4—28no—
192Dic7⋊C4—24no—
193Dic7⋊C4—42no—
194Dic7⋊C4—42no—
195Dic7⋊C4—42no—
196C4×Dic7—22no—
197C4×Dic7—22no—
198C4×Dic7—22no—
199C2×C7⋊C8—22no—
200C2×C7⋊C8—22no—
201C2×C7⋊C8—22no—
202C8×D7—48no—
203C23×Q8—72no—
204C23×C8—72no—
205C2×C4⋊Q8—72no—
206C2×C4⋊Q8—71no—
207C2×C4⋊Q8—141no—
208C2×C4⋊Q8—141no—
209C2×C4⋊Q8—148no—
210C2×C4⋊Q8C2×D711yescharacteristic
211C22×C4⋊C4—71no—
212C22×C4⋊C4—71no—
213C22×C4⋊C4—141no—
214C22×C4⋊C4—141no—
215C22×C4⋊C4—141no—
216C22×C42—71no—
217C2×#103—72no—
218C2×#103—72no—
219C2×#103—72no—
220C2×#103—72no—
221C2×#103—72no—
222C2×#103—72no—
223C2×#103—148no—
224C2×#103—148no—
225C2×#103C2×D712yes—
226C2×#103C2×D712yes—
227#389—71no—
228#389—71no—
229#389—71no—
230#389—141no—
231#389—141no—
232#389C2×D711yescharacteristic
233C2×#95—141no—
234#336—72no—
235#336—71no—
236#336C2×D711yescharacteristic
237C23×C7C22×D411yescharacteristic
238C22×D7#12012yes—
239C22×D7#12112yes—
240C22×D7#12412yes—
241C22×D7C2×SD1612yes—
242C22×D7C2×Q1612yes—
243C22×D7#13712yes—
244C22×D7#13712yes—
245C7×Q8—24no—
246C7×Q8—24no—
247C7×Q8—42no—
248C7×Q8—42no—
249C2×C4×C7—21no—
250C2×C4×C7—21no—
251C2×C4×C7—21no—
252C2×C4×C7—21no—
253C2×C4×C7—24no—
254C2×C4×C7—22no—
255C2×C4×C7—42no—
256C2×C4×C7—42no—
257C2×C4×C7—41no—
258C2×C4×C7—41no—
259C2×C4×C7—41no—
260C2×C4×C7—41no—
261C2×C4×C7—41no—
262C2×C4×C7C2×SD1612yes—
263C2×C4×C7C2×Q1612yes—
264C2×C4×C7C22×D411yescharacteristic
265C2×C4×C7C22×D412yes—
266C2×C4×C7C2×#4112yes—
267C2×C4×C7C2×#4111yescharacteristic
268C2×Dic7—21no—
269C2×Dic7—21no—
270C2×Dic7—21no—
271C2×Dic7—21no—
272C2×Dic7—24no—
273C2×Dic7—22no—
274C2×Dic7—42no—
275C2×Dic7—42no—
276C2×Dic7—41no—
277C2×Dic7—41no—
278C2×Dic7—41no—
279C2×Dic7—41no—
280C2×Dic7—41no—
281C2×Dic7#12012yes—
282C2×Dic7#12112yes—
283C2×Dic7#12412yes—
284C2×Dic7C2×SD1612yes—
285C2×Dic7C2×Q1612yes—
286C4×D7—28no—
287C4×D7—28no—
288C4×D7—416no—
289C4×D7—48no—
290C4×D7—84no—
291C4×D7#12118yes—
292C4×D7#12318yes—
293Dic14—24no—
294Dic14—24no—
295Dic14—42no—
296Dic14—42no—
297Dic14—416no—
298C7×C8—42no—
299C7⋊C8—42no—
300C22×Q8—78no—
301C22×Q8—72no—
302C22×Q8—142no—
303C22×Q8—144no—
304C22×Q8—144no—
305C22×Q8—144no—
306C22×Q8—144no—
307C22×Q8—144no—
308C22×Q8C22×D712yes—
309C23×C4—71no—
310C23×C4—71no—
311C23×C4—71no—
312C23×C4—141no—
313C23×C4—142no—
314C23×C4—141no—
315C22×C8—72no—
316C22×C8—144no—
317C22×C8—144no—
318C22×C8—144no—
319C22×C8C22×D712yes—
320C4⋊Q8—24no—
321C4⋊Q8—144no—
322C4⋊Q8—148no—
323C4⋊Q8—148no—
324C4⋊Q8—144no—
325C4⋊Q8—144no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—71no—
330C2×C4⋊C4—74no—
331C2×C4⋊C4—71no—
332C2×C4⋊C4—142no—
333C2×C4⋊C4—148no—
334C2×C4⋊C4—148no—
335C2×C4⋊C4—144no—
336C2×C4⋊C4—141no—
337C2×C4⋊C4—142no—
338C2×C4⋊C4—142no—
339C2×C4⋊C4—141no—
340C2×C4⋊C4—141no—
341C2×C4⋊C4—141no—
342C2×C4⋊C4—141no—
343C2×C4⋊C4—141no—
344C2×C4⋊C4—141no—
345C2×C4⋊C4—284no—
346C2×C4⋊C4C22×D711yescharacteristic
347C2×C4⋊C4C22×D711yescharacteristic
348C2×C42—71no—
349C2×C42—71no—
350C2×C42—71no—
351C2×C42—144no—
352C2×C42C22×D711yescharacteristic
353#103—24no—
354#103—24no—
355#103—144no—
356#103—144no—
357#103—144no—
358#103—144no—
359#103—144no—
360#103—144no—
361#95—21no—
362#95—141no—
363#95—141no—
364#95—141no—
365C22×C7C2×#12011yescharacteristic
366C22×C7C2×#12111yescharacteristic
367C22×C7C2×#12411yescharacteristic
368C22×C7C22×SD1611yescharacteristic
369C22×C7C22×Q1611yescharacteristic
370C22×C7C2×#13711yescharacteristic
371C22×C7C2×#13711yescharacteristic
372C2×D7#39414yes—
373C2×D7#44814yes—
374C2×D7#45114yes—
375C2×D7#46114yes—
376C2×D7#46214yes—
377C2×D7#48714yes—
378C2×D7#49114yes—
379C4×C7—22no—
380C4×C7—22no—
381C4×C7—44no—
382C4×C7—42no—
383C4×C7—81no—
384C4×C7C2×#12112yes—
385C4×C7C2×#12312yes—
386Dic7—22no—
387Dic7—22no—
388Dic7—44no—
389Dic7—42no—
390Dic7—81no—
391Dic7#39414yes—
392C24—71no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—74no—
399C2×Q8—148no—
400C2×Q8—1416no—
401C2×Q8—1416no—
402C2×Q8—142no—
403C2×Q8—142no—
404C2×Q8—142no—
405C2×Q8—142no—
406C2×Q8—142no—
407C2×Q8—284no—
408C2×Q8—284no—
409C2×Q8—288no—
410C2×Q8—288no—
411C2×Q8D4×D714yes—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—71no—
416C22×C4—74no—
417C22×C4—72no—
418C22×C4—72no—
419C22×C4—74no—
420C22×C4—71no—
421C22×C4—71no—
422C22×C4—74no—
423C22×C4—74no—
424C22×C4—142no—
425C22×C4—142no—
426C22×C4—142no—
427C22×C4—142no—
428C22×C4—144no—
429C22×C4—148no—
430C22×C4—141no—
431C22×C4—142no—
432C22×C4—141no—
433C22×C4—282no—
434C22×C4—282no—
435C22×C4—284no—
436C22×C4—284no—
437C22×C4—282no—
438C22×C4—282no—
439C22×C4—282no—
440C22×C4D4×D711yescharacteristic
441C22×C4D4×D711yescharacteristic
442C22×C4C23×D711yescharacteristic
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—22no—
446C2×C8—142no—
447C2×C8—142no—
448C2×C8—142no—
449C2×C8—288no—
450C4⋊C4—24no—
451C4⋊C4—24no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—42no—
455C4⋊C4—72no—
456C4⋊C4—144no—
457C4⋊C4—148no—
458C4⋊C4—148no—
459C4⋊C4—144no—
460C4⋊C4—144no—
461C4⋊C4—141no—
462C4⋊C4—142no—
463C4⋊C4—282no—
464C4⋊C4—282no—
465C4⋊C4—282no—
466C4⋊C4—282no—
467C4⋊C4D4×D712yes—
468C42—22no—
469C42—142no—
470C42—142no—
471C42—142no—
472C2×C7C2×#39411yescharacteristic
473C2×C7C2×#44811yescharacteristic
474C2×C7C2×#45111yescharacteristic
475C2×C7C2×#46111yescharacteristic
476C2×C7C2×#46211yescharacteristic
477C2×C7C2×#48711yescharacteristic
478C2×C7C2×#49111yescharacteristic
479D7#204318yesdirect product factor
480C23—72no—
481C23—72no—
482C23—72no—
483C23—72no—
484C23—72no—
485C23—72no—
486C23—72no—
487C23C2×D4×D711yescharacteristic
488Q8—24no—
489Q8—24no—
490Q8—42no—
491Q8—42no—
492Q8—144no—
493Q8—144no—
494Q8—2816no—
495Q8—282no—
496Q8—282no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—24no—
502C2×C4—22no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—72no—
511C2×C4—72no—
512C2×C4—72no—
513C2×C4—78no—
514C2×C4—78no—
515C2×C4—72no—
516C2×C4—72no—
517C2×C4—148no—
518C2×C4—148no—
519C2×C4—141no—
520C2×C4—141no—
521C2×C4—141no—
522C2×C4—141no—
523C2×C4—144no—
524C2×C4—142no—
525C2×C4—288no—
526C2×C4—2816no—
527C2×C4—281no—
528C2×C4—281no—
529C2×C4—282no—
530C2×C4—282no—
531C2×C4—281no—
532C2×C4—281no—
533C2×C4—281no—
534C2×C4—564no—
535C2×C4D7×SD1612yes—
536C2×C4D7×Q1612yes—
537C2×C4C2×D4×D711yescharacteristic
538C2×C4C2×D4×D712yes—
539C2×C4D7×#4112yes—
540C2×C4D7×#4111yescharacteristic
541C8—42no—
542C8—282no—
543C7C2×#204311yescharacteristic, complemented, Sylow
544C22—74no—
545C22—74no—
546C22—74no—
547C22—74no—
548C22—74no—
549C22—74no—
550C22—74no—
551C22D7×#12011yescharacteristic
552C22D7×#12111yescharacteristic
553C22D7×#12411yescharacteristic
554C22C2×D7×SD1611yescharacteristic
555C22C2×D7×Q1611yescharacteristic
556C22D7×#13711yescharacteristic
557C22D7×#13711yescharacteristic
558C4—22no—
559C4—22no—
560C4—42no—
561C4—44no—
562C4—74no—
563C4—81no—
564C4—142no—
565C4—142no—
566C4—282no—
567C4—284no—
568C4—561no—
569C4D7×#12112yes—
570C4D7×#12312yes—
571C2—78no—
572C2D7×#39411yescharacteristic
573C2D7×#44811yescharacteristic
574C2D7×#45111yescharacteristic
575C2D7×#46111yescharacteristic
576C2D7×#46211yescharacteristic
577C2D7×#48711yescharacteristic
578C2D7×#49111yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC7×#2043C2
socleC23×C7C22×D4
prime radicalC23×D7C2×D4
hypercenter#2043D7
hypocenterC7C2×#2043
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2043

Complements

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

NH ≅ G/Ntype
5. C7×#2043C2semidirect
6. #11729535C2semidirect
7. #11728038C2semidirect
8. #11728000C2semidirect
9. #11727387C2semidirect
11. #11726385C2semidirect
121. #2043D7direct (N × H)
479. D7#2043direct (N × H)
543. C7C2×#2043semidirect

Maximal subgroups

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

subgroupindex
C2×D7×C4⋊Q82
C2×D7×#1032
D7×#3892
C7×#20432
#117295352
#117280382
#117280002
#117273872
D7×#3362
#117263852
C2×#20437