Finite Group Databasebeta

← #13329943

Subgroups — #13329943

Order 1792.

1168 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×D4×Q8C211yesmaximal, characteristic, complemented
2#11740644C211yesmaximal, characteristic, complemented
3#11739889C211yesmaximal, characteristic, complemented
4#11739755C211yesmaximal, characteristic
5#11729669C214yesmaximal, complemented
6#11729668C214yesmaximal, complemented
7#11729530C211yesmaximal, characteristic, complemented
8#11729377C211yesmaximal, characteristic, complemented
9#11729353C211yesmaximal, characteristic, complemented
10C23×C7×Q8—21no—
11C7×D4×Q8—22no—
12C7×D4×Q8—22no—
13C7×D4×Q8—22no—
14C7×D4×Q8C2214yes—
15C2×C7×C4⋊Q8—21no—
16C2×C7×C4⋊Q8C2211yescharacteristic
17C2×C7×C22⋊Q8—21no—
18C2×C7×C22⋊Q8—22no—
19C2×C4×C7×Q8C2211yescharacteristic
20C2×C4×C7×D4—21no—
21C2×C4×C7×D4C2211yescharacteristic
22#90168C2211yescharacteristic
23#89999—21no—
24#89989—21no—
25#89865C2212yescomplemented
26#89861—22no—
27#89860C2212yescomplemented
28#89799C2212yescomplemented
29#89798—22no—
30#89793C2212yescomplemented
31#89787C2212yes—
32#89786—22no—
33#89780C2212yes—
34#89740—21no—
35#89739—21no—
36#89738—22no—
37#89698C2211yescharacteristic
38#89698C2211yescharacteristic
39C4×#1136C2211yescharacteristic
40#89342C2214yescomplemented
41Q8⋊(C7⋊C8)C2214yescomplemented
42D4⋊(C7⋊C8)C2214yes—
43#18534—71nomaximal, Sylow
44C22×C7×Q8—22no—
45C22×C7×Q8—24no—
46C22×C7×Q8—24no—
47C22×C7×Q8—21no—
48C22×C7×Q8—48no—
49C22×C7×Q8D411yescharacteristic
50C22×C7×D4D411yescharacteristic
51C23×C4×C7—22no—
52C23×C4×C7—21no—
53C2×#1157—21no—
54C7×C4⋊Q8—24no—
55C7×C4⋊Q8—24no—
56C7×C4⋊Q8—21no—
57C7×C4⋊Q8—21no—
58C7×C4⋊Q8D412yes—
59C7×C4⋊Q8C2312yes—
60C7×C22⋊Q8—24no—
61C7×C22⋊Q8—28no—
62C7×C22⋊Q8—24no—
63C7×C22⋊Q8—28no—
64C4×C7×Q8—21no—
65C4×C7×Q8—21no—
66C4×C7×Q8D412yes—
67C4×C7×Q8C2312yes—
68C4×C7×D4—24no—
69C4×C7×D4—24no—
70C4×C7×D4—21no—
71C4×C7×D4—21no—
72C4×C7×D4D412yes—
73C4×C7×D4C2312yes—
74C2×C7×C4⋊C4—22no—
75C2×C7×C4⋊C4—21no—
76C2×C7×C4⋊C4—21no—
77C2×C7×C4⋊C4D412yes—
78C2×C7×C4⋊C4D411yescharacteristic
79C2×C7×C4⋊C4D411yescharacteristic
80C2×C7×C22⋊C4—22no—
81C2×C7×C22⋊C4—21no—
82C2×C42×C7—21no—
83C2×C42×C7C2311yescharacteristic
84C2×#1143—22no—
85C2×#1141—22no—
86#6493—21no—
87#6493—21no—
88C2×#1136—21no—
89#6438—21no—
90#6437C2311yescharacteristic
91C4×D28—21no—
92C4×D28—21no—
93#6432C2311yescharacteristic
94#6409—22no—
95#6406—22no—
96C22⋊(C7⋊C8)—21no—
97C22⋊(C7⋊C8)—21no—
98#6384—24no—
99#6383—24no—
100#6383—22no—
101#6383—22no—
102#6382—22no—
103#6381—22no—
104C4⋊(C7⋊C8)C2312yes—
105C4⋊(C7⋊C8)C2312yes—
106#6377—21no—
107#6377—21no—
108#6377—21no—
109C4×C7⋊C8C2312yes—
110C2×D4×Q8D711yescharacteristic, complemented
111#3141—71no—
112#3112—71no—
113#3109—71no—
114#1637—74no—
115#1627—74no—
116#1556—71no—
117#1491—71no—
118#1490—71no—
119C24×C7—21no—
120C2×C7×Q8—24no—
121C2×C7×Q8—28no—
122C2×C7×Q8—21no—
123C2×C7×Q8—22no—
124C2×C7×Q8—22no—
125C2×C7×Q8—48no—
126C2×C7×Q8—44no—
127C2×C7×Q8—416no—
128C2×C7×Q8—48no—
129C2×C7×Q8—48no—
130C2×C7×Q8C2×D412yes—
131C2×C7×D4—24no—
132C2×C7×D4—21no—
133C2×C7×D4C2×D412yes—
134C22×C4×C7—21no—
135C22×C4×C7—28no—
136C22×C4×C7—21no—
137C22×C4×C7—22no—
138C22×C4×C7—21no—
139C22×C4×C7—22no—
140C22×C4×C7—22no—
141C22×C4×C7—48no—
142C22×C4×C7—44no—
143C22×C4×C7C2×D411yescharacteristic
144C22×C4×C7C2×D411yescharacteristic
145C22×C4×C7C2×D411yescharacteristic
146C2×C22⋊D7—41no—
147#1157—44no—
148C2×D28—21no—
149C2×D28—21no—
150C2×D28—21no—
151C2×C4×D7—41no—
152C2×Dic14—21no—
153C7×C4⋊C4—28no—
154C7×C4⋊C4—22no—
155C7×C4⋊C4—22no—
156C7×C4⋊C4—21no—
157C7×C4⋊C4—21no—
158C7×C4⋊C4—22no—
159C7×C4⋊C4—22no—
160C7×C4⋊C4—22no—
161C7×C4⋊C4C2×D412yes—
162C7×C4⋊C4C2×D412yes—
163C7×C4⋊C4C2×D414yes—
164C7×C22⋊C4—28no—
165C7×C22⋊C4—22no—
166C7×C22⋊C4—22no—
167C42×C7—22no—
168C42×C7—22no—
169C42×C7C2×D411yescharacteristic
170C42×C7C2×D411yescharacteristic
171C42×C7C2×D411yescharacteristic
172C42×C7C2411yescharacteristic
173#1143—44no—
174#1141—44no—
175(C2×D7)⋊C4—41no—
176(C2×D7)⋊C4—41no—
177C4⋊Dic7—21no—
178C4⋊Dic7—21no—
179#1136—42no—
180C2×C7⋊C8—22no—
181C2×C7⋊C8—22no—
182C2×C7⋊C8—22no—
183C23×Q8—21no—
184D4×Q8—22no—
185D4×Q8—22no—
186D4×Q8—22no—
187D4×Q8C2×D714yes—
188#532—71no—
189C2×C4⋊Q8—21no—
190C2×C4⋊Q8C2×D711yescharacteristic
191C2×C22⋊Q8—21no—
192C2×C22⋊Q8—22no—
193C2×C4×Q8C2×D711yescharacteristic
194C2×C4×D4—21no—
195C2×C4×D4C2×D711yescharacteristic
196#489—142no—
197#487—72no—
198#486—72no—
199#481—141no—
200#480—141no—
201#477—72no—
202#476—72no—
203#460—72no—
204#459—72no—
205#448—141no—
206#447—141no—
207#442—142no—
208#440—142no—
209#432—71no—
210#432—71no—
211#417—142no—
212C4×M16—71no—
213#332—74no—
214Q8⋊C8—74no—
215D4⋊C8—74no—
216C23×C7—24no—
217C23×C7—22no—
218C23×C7—42no—
219C23×C7—42no—
220C23×C7#12011yescharacteristic
221C22×D7—41no—
222C7×Q8—24no—
223C7×Q8—22no—
224C7×Q8—416no—
225C7×Q8—44no—
226C7×Q8—44no—
227C7×Q8AGL(1,ℤ/8)14yes—
228C7×D4—24no—
229C7×D4—22no—
230C7×D4#13714yes—
231C2×C4×C7—24no—
232C2×C4×C7—22no—
233C2×C4×C7—22no—
234C2×C4×C7—22no—
235C2×C4×C7—22no—
236C2×C4×C7—22no—
237C2×C4×C7—24no—
238C2×C4×C7—22no—
239C2×C4×C7—416no—
240C2×C4×C7—44no—
241C2×C4×C7—44no—
242C2×C4×C7—42no—
243C2×C4×C7—42no—
244C2×C4×C7—44no—
245C2×C4×C7#12011yescharacteristic
246C2×C4×C7#12011yescharacteristic
247C2×C4×C7#12011yescharacteristic
248C2×C4×C7C22×D411yescharacteristic
249C2×C4×C7C22×D411yescharacteristic
250C2×C4×C7C22×D411yescharacteristic
251C22⋊D7—82no—
252C2×Dic7—41no—
253D28—42no—
254D28—42no—
255D28—42no—
256C4×D7—82no—
257Dic14—42no—
258C7⋊C8—42no—
259C7⋊C8—42no—
260C7⋊C8—42no—
261C2×#41—141no—
262C22×Q8—22no—
263C22×Q8—24no—
264C22×Q8—24no—
265C22×Q8—21no—
266C22×Q8—48no—
267C22×Q8C22⋊D711yescharacteristic
268C22×D4C22⋊D711yescharacteristic
269C23×C4—22no—
270C23×C4—21no—
271C2×SD16—142no—
272C2×D8—142no—
273C2×M16—141no—
274C4⋊Q8—24no—
275C4⋊Q8—24no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8—71no—
279C4⋊Q8C22⋊D712yes—
280C4⋊Q8C22×D712yes—
281#127—71no—
282#124—141no—
283C22⋊Q8—24no—
284C22⋊Q8—28no—
285C22⋊Q8—24no—
286C22⋊Q8—28no—
287#121—141no—
288#121—141no—
289C4×Q8—21no—
290C4×Q8—21no—
291C4×Q8C22⋊D712yes—
292C4×Q8C22×D712yes—
293C4×D4—24no—
294C4×D4—24no—
295C4×D4—21no—
296C4×D4—21no—
297C4×D4—141no—
298C4×D4—141no—
299C4×D4C22⋊D712yes—
300C4×D4C22×D712yes—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4C22⋊D711yescharacteristic
305C2×C4⋊C4C22⋊D711yescharacteristic
306C2×C4⋊C4C22⋊D712yes—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—21no—
309C2×C42—21no—
310C2×C42C22×D711yescharacteristic
311#107—142no—
312#106—142no—
313C4⋊C8—72no—
314C4⋊C8—72no—
315#103—142no—
316#103—144no—
317#102—142no—
318#102—144no—
319#102—142no—
320#102—142no—
321C22⋊C8—141no—
322C22⋊C8—141no—
323#97—141no—
324#97—141no—
325#97—141no—
326C4×C8—72no—
327C22×C7—21no—
328C22×C7—21no—
329C22×C7—24no—
330C22×C7—48no—
331C22×C7—42no—
332C22×C7—42no—
333C22×C7#45412yes—
334C22×C7C2×#12011yescharacteristic
335C2×D7—81no—
336C2×D7—81no—
337C2×D7—81no—
338C4×C7—24no—
339C4×C7—21no—
340C4×C7—21no—
341C4×C7—21no—
342C4×C7—21no—
343C4×C7—44no—
344C4×C7—42no—
345C4×C7—42no—
346C4×C7C2×AGL(1,ℤ/8)12yes—
347C4×C7C2×#13712yes—
348Dic7—81no—
349C24—21no—
350#41—284no—
351C2×Q8—24no—
352C2×Q8—28no—
353C2×Q8—21no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8—48no—
357C2×Q8—44no—
358C2×Q8—416no—
359C2×Q8—48no—
360C2×Q8—48no—
361C2×Q8—141no—
362C2×Q8C2×C22⋊D712yes—
363C2×D4—24no—
364C2×D4—21no—
365C2×D4—141no—
366C2×D4—141no—
367C2×D4—141no—
368C2×D4—281no—
369C2×D4C2×C22⋊D712yes—
370C22×C4—21no—
371C22×C4—28no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—48no—
378C22×C4—44no—
379C22×C4—281no—
380C22×C4C2×C22⋊D711yescharacteristic
381C22×C4C2×C22⋊D711yescharacteristic
382C22×C4C2×C22⋊D711yescharacteristic
383SD16—284no—
384D8—284no—
385M16—282no—
386C2×C8—142no—
387C2×C8—142no—
388C2×C8—142no—
389C4⋊C4—28no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—141no—
398C4⋊C4—141no—
399C4⋊C4C2×C22⋊D714yes—
400C4⋊C4C2×C22⋊D712yes—
401C4⋊C4C2×C22⋊D712yes—
402C22⋊C4—28no—
403C22⋊C4—22no—
404C22⋊C4—22no—
405C22⋊C4—281no—
406C22⋊C4—281no—
407C42—22no—
408C42—22no—
409C42C2×C22⋊D711yescharacteristic
410C42C2×C22⋊D711yescharacteristic
411C42C2×C22⋊D711yescharacteristic
412C42C23×D711yescharacteristic
413C2×C7—22no—
414C2×C7—44no—
415C2×C7#300311yescharacteristic
416C2×C7#300411yescharacteristic
417C2×C7C2×#45411yescharacteristic
418D7—161no—
419C23—24no—
420C23—22no—
421C23—42no—
422C23—42no—
423C23—281no—
424C23#651611yescharacteristic
425Q8—24no—
426Q8—22no—
427Q8—416no—
428Q8—44no—
429Q8—44no—
430Q8—282no—
431Q8#649514yes—
432D4—24no—
433D4—22no—
434D4—282no—
435D4—282no—
436D4—282no—
437D4—562no—
438D4#650514yes—
439C2×C4—24no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—24no—
446C2×C4—22no—
447C2×C4—416no—
448C2×C4—44no—
449C2×C4—44no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—44no—
453C2×C4—281no—
454C2×C4—562no—
455C2×C4#651611yescharacteristic
456C2×C4#651611yescharacteristic
457C2×C4#651611yescharacteristic
458C2×C4C22×C22⋊D711yescharacteristic
459C2×C4C22×C22⋊D711yescharacteristic
460C2×C4C22×C22⋊D711yescharacteristic
461C8—282no—
462C8—282no—
463C8—282no—
464C7#1853411yescharacteristic, complemented, Sylow
465C22—21no—
466C22—21no—
467C22—24no—
468C22—48no—
469C22—42no—
470C22—42no—
471C22—561no—
472C22—561no—
473C22—561no—
474C22#9001712yes—
475C22C2×#651611yescharacteristic
476C4—24no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—44no—
482C4—42no—
483C4—42no—
484C4—561no—
485C4C2×#649512yes—
486C4C2×#650512yes—
487C2—22no—
488C2—44no—
489C2—1121no—
490C2#1174148311yescharacteristic
491C2#1174150411yescharacteristic
492C2C2×#9001711yescharacteristic
subgroupG/H
centerC22C2×#6516
commutator, cosocleC42×C7C24
FrattiniC42C23×D7
FittingC2×C7×D4×Q8C2
socleC22×C7C2×#120
prime radical#11739755C2
hypercenterC2×D4×Q8D7
hypocenterC7#18534
LCSG ▷ C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C7×D4×Q8C2semidirect
2. #11740644C2semidirect
3. #11739889C2semidirect
5. #11729669C2semidirect
6. #11729668C2semidirect
7. #11729530C2semidirect
8. #11729377C2semidirect
9. #11729353C2semidirect
25. #89865C22semidirect
27. #89860C22semidirect
28. #89799C22semidirect
30. #89793C22semidirect
40. #89342C22semidirect
41. Q8⋊(C7⋊C8)C22semidirect
110. C2×D4×Q8D7semidirect
464. C7#18534semidirect

Maximal subgroups

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

subgroupindex
C2×C7×D4×Q82
#117406442
#117398892
#117397552
#117296692
#117296682
#117295302
#117293772
#117293532
#185347