Finite Group Databasebeta

← #13336109

Subgroups — #13336109

Order 1792.

716 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3101C211yesmaximal, characteristic, complemented
2#11740779C211yesmaximal, characteristic, complemented
3#11739753C211yesmaximal, characteristic
4C2×D4×C7⋊C8C211yesmaximal, characteristic, complemented
5#11729582C211yesmaximal, characteristic, complemented
6#11728889C212yesmaximal, complemented
7#11728888C212yesmaximal, complemented
8#11728793C212yesmaximal, complemented
9#11728792C212yesmaximal, complemented
10#11728526C211yesmaximal, characteristic, complemented
11#11728499C211yesmaximal, characteristic, complemented
12C7×#533C2211yescharacteristic
13C2×C4×C7×D4C2211yescharacteristic
14C23×C7⋊C8—21no—
15#90168C2211yescharacteristic
16C7×#483—21no—
17C7×#476C2212yes—
18C7×#461C2212yes—
19C7×#450—21no—
20C4×C7×SD16—22no—
21C7×#431C2211yescharacteristic
22#89989—21no—
23C2×C22⋊(C7⋊C8)—21no—
24#89865C2211yescharacteristic, complemented
25#89865C2211yescharacteristic, complemented
26#89860C2211yescharacteristic, complemented
27#89860C2211yescharacteristic, complemented
28#89840—21no—
29#89840—21no—
30#89787C2212yes—
31C4×#1141—22no—
32D4×C7⋊C8—21no—
33D4×C7⋊C8—21no—
34D4×C7⋊C8C2212yes—
35D4×C7⋊C8C2212yes—
36#89779C2212yes—
37#89774—21no—
38#89774—21no—
39#89739—21no—
40#89697C2211yescharacteristic
41C2×C4⋊(C7⋊C8)C2211yescharacteristic
42C2×C4×C7⋊C8C2211yescharacteristic
43#89342C2212yescomplemented
44#89341C2212yescomplemented
45#89281C2212yescomplemented
46#89280C2212yescomplemented
47#89275C2212yescomplemented
48#89274C2212yescomplemented
49#19110—71nomaximal, Sylow
50C22×C7×D4D411yescharacteristic
51C23×C4×C7—21no—
52C2×#1157—21no—
53C2×C7×SD16—22no—
54C7×C4⋊Q8C2311yescharacteristic
55C7×C4⋊Q8C2311yescharacteristic
56C7×#125—21no—
57C7×C22⋊Q8—21no—
58C7×C22⋊Q8—21no—
59C4×C7×Q8—21no—
60C4×C7×Q8—21no—
61C4×C7×D4—21no—
62C4×C7×D4—21no—
63C4×C7×D4D412yes—
64C4×C7×D4C2312yes—
65C7×#117—21no—
66C2×C7×C4⋊C4D411yescharacteristic
67C2×C7×C22⋊C4—21no—
68C2×C42×C7C2311yescharacteristic
69C2×#1141—22no—
70#6493—21no—
71#6493—21no—
72C22×C7⋊C8—21no—
73C22×C7⋊C8—22no—
74C22×C7⋊C8—22no—
75C22×C7⋊C8—44no—
76C22×C7⋊C8D411yescharacteristic
77C22×C7⋊C8D411yescharacteristic
78#6438—21no—
79#6437C2311yescharacteristic
80C4×D28—21no—
81C4×D28—21no—
82#6432C2311yescharacteristic
83C7×#106—22no—
84C7×C4⋊C8C2312yes—
85C7×#103—22no—
86C7×#102—22no—
87C7×C22⋊C8—21no—
88C4×C7×C8—21no—
89#6406—22no—
90C22⋊(C7⋊C8)—21no—
91C22⋊(C7⋊C8)—22no—
92C22⋊(C7⋊C8)—22no—
93#6384—21no—
94#6384—21no—
95#6384—21no—
96#6384—21no—
97#6383—22no—
98#6383—21no—
99#6383—21no—
100#6383—21no—
101#6383—21no—
102#6381—22no—
103C4⋊(C7⋊C8)—21no—
104C4⋊(C7⋊C8)C2312yes—
105C4⋊(C7⋊C8)C2312yes—
106C4×C7⋊C8—21no—
107C4×C7⋊C8D411yescharacteristic
108C4×C7⋊C8D411yescharacteristic
109C4×C7⋊C8C2311yescharacteristic
110C4×C7⋊C8C2311yescharacteristic
111#3131—71no—
112#3101D711yescharacteristic, complemented
113#3100—71no—
114C2×C8×D4—71no—
115#1683—72no—
116#1681—72no—
117#1679—72no—
118#1677—72no—
119#1564—71no—
120#1542—71no—
121#1540—71no—
122C24×C7—21no—
123C2×C7×Q8—21no—
124C2×C7×Q8—21no—
125C2×C7×D4—24no—
126C2×C7×D4—21no—
127C2×C7×D4C2×D412yes—
128C22×C4×C7—21no—
129C22×C4×C7—22no—
130C22×C4×C7—22no—
131C22×C4×C7—42no—
132C22×C4×C7—42no—
133C22×C4×C7C2×D411yescharacteristic
134C22×C4×C7C2×D411yescharacteristic
135C22×C4×C7#4111yescharacteristic
136C2×C22⋊D7—41no—
137#1157—42no—
138#1157—42no—
139C2×D28—21no—
140C2×D28—21no—
141C2×D28—21no—
142C2×C4×D7—41no—
143C2×Dic14—21no—
144C7×SD16—44no—
145C2×C7×C8—22no—
146C7×C4⋊C4—21no—
147C7×C4⋊C4—21no—
148C7×C4⋊C4—21no—
149C7×C4⋊C4—21no—
150C7×C4⋊C4—21no—
151C7×C4⋊C4—41no—
152C7×C4⋊C4—41no—
153C7×C4⋊C4C2×D412yes—
154C7×C22⋊C4—22no—
155C7×C22⋊C4—22no—
156C7×C22⋊C4—41no—
157C42×C7—41no—
158C42×C7C2×D411yescharacteristic
159C42×C7C2×D411yescharacteristic
160C42×C7#4111yescharacteristic
161C42×C7C2411yescharacteristic
162#1141—44no—
163(C2×D7)⋊C4—41no—
164(C2×D7)⋊C4—41no—
165C4⋊Dic7—21no—
166C4⋊Dic7—21no—
167C2×C7⋊C8—22no—
168C2×C7⋊C8—22no—
169C2×C7⋊C8—22no—
170C2×C7⋊C8—22no—
171C2×C7⋊C8—44no—
172C2×C7⋊C8—44no—
173C2×C7⋊C8—42no—
174C2×C7⋊C8C2×D411yescharacteristic
175C2×C7⋊C8C2×D411yescharacteristic
176C2×C7⋊C8C2×D411yescharacteristic
177C2×C7⋊C8C2×D411yescharacteristic
178C23×C8—141no—
179#533C2×D711yescharacteristic
180#532—71no—
181C2×C4×D4C2×D711yescharacteristic
182#488—141no—
183#488—141no—
184#487—71no—
185#487—71no—
186#486—71no—
187#486—71no—
188#483—21no—
189#480—141no—
190#476C2×D712yes—
191#474—72no—
192#461C2×D712yes—
193#459—72no—
194#450—21no—
195#447—141no—
196C4×SD16—22no—
197C4×D8—142no—
198C8×D4—72no—
199C8×D4—72no—
200C8×D4—141no—
201C8×D4—141no—
202#431—71no—
203#431C2×D711yescharacteristic
204C2×C4⋊C8—71no—
205#416—141no—
206#416—141no—
207C2×C22⋊C8—141no—
208C2×C4×C8—71no—
209#335—72no—
210#334—72no—
211#333—72no—
212#332—72no—
213#332—72no—
214#331—72no—
215C23×C7—24no—
216C23×C7—22no—
217C23×C7—42no—
218C23×C7—42no—
219C23×C7#12111yescharacteristic
220C22×D7—41no—
221C7×Q8—42no—
222C7×Q8—81no—
223C7×D4—24no—
224C7×D4—22no—
225C7×D4#13514yes—
226C2×C4×C7—22no—
227C2×C4×C7—22no—
228C2×C4×C7—41no—
229C2×C4×C7—42no—
230C2×C4×C7—42no—
231C2×C4×C7—42no—
232C2×C4×C7—44no—
233C2×C4×C7—41no—
234C2×C4×C7—41no—
235C2×C4×C7#12111yescharacteristic
236C2×C4×C7#12111yescharacteristic
237C2×C4×C7#12111yescharacteristic
238C2×C4×C7#13512yes—
239C2×C4×C7AGL(1,ℤ/8)12yes—
240C2×C4×C7C22×D411yescharacteristic
241C2×C4×C7C22×D411yescharacteristic
242C2×C4×C7C2×#4111yescharacteristic
243C22⋊D7—82no—
244C2×Dic7—41no—
245D28—42no—
246D28—41no—
247D28—41no—
248D28—81no—
249C4×D7—82no—
250Dic14—41no—
251Dic14—41no—
252C7×C8—42no—
253C7⋊C8—21no—
254C7⋊C8—21no—
255C7⋊C8—21no—
256C7⋊C8—21no—
257C7⋊C8—42no—
258C7⋊C8—42no—
259C2×#41—141no—
260C22×D4C22⋊D711yescharacteristic
261C23×C4—21no—
262C2×SD16—22no—
263C2×D8—142no—
264C22×C8—71no—
265C22×C8—71no—
266C22×C8—142no—
267C22×C8—142no—
268C22×C8—141no—
269C22×C8—284no—
270C4⋊Q8—71no—
271C4⋊Q8C22×D711yescharacteristic
272C4⋊Q8C22×D711yescharacteristic
273#127—71no—
274#125—21no—
275#124—141no—
276C22⋊Q8—21no—
277C22⋊Q8—21no—
278#121—141no—
279#121—141no—
280C4×Q8—21no—
281C4×Q8—21no—
282C4×D4—21no—
283C4×D4—21no—
284C4×D4—141no—
285C4×D4—141no—
286C4×D4C22⋊D712yes—
287C4×D4C22×D712yes—
288#117—21no—
289C2×C4⋊C4C22⋊D711yescharacteristic
290C2×C22⋊C4—21no—
291C2×C42C22×D711yescharacteristic
292#107—142no—
293#106—22no—
294C4⋊C8—72no—
295C4⋊C8—72no—
296C4⋊C8—141no—
297C4⋊C8C22×D712yes—
298#103—22no—
299#103—141no—
300#103—141no—
301#103—141no—
302#103—141no—
303#102—22no—
304#102—141no—
305#102—141no—
306#102—141no—
307#102—141no—
308#102—142no—
309#102—142no—
310C22⋊C8—21no—
311C22⋊C8—142no—
312C22⋊C8—142no—
313C22⋊C8—141no—
314C4×C8—21no—
315C4×C8—71no—
316C4×C8—71no—
317C4×C8—71no—
318C4×C8—71no—
319C4×C8—141no—
320C22×C7—21no—
321C22×C7—21no—
322C22×C7—24no—
323C22×C7—48no—
324C22×C7—42no—
325C22×C7—42no—
326C22×C7#46312yes—
327C22×C7C2×#12111yescharacteristic
328C2×D7—81no—
329C2×D7—81no—
330C2×D7—81no—
331C4×C7—21no—
332C4×C7—21no—
333C4×C7—21no—
334C4×C7—42no—
335C4×C7—81no—
336C4×C7—81no—
337C4×C7#46312yes—
338C4×C7C2×#13511yescharacteristic
339C4×C7C2×#13512yes—
340C4×C7C2×AGL(1,ℤ/8)11yescharacteristic
341Dic7—81no—
342C24—21no—
343#41—282no—
344#41—282no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—141no—
348C2×D4—24no—
349C2×D4—21no—
350C2×D4—141no—
351C2×D4—141no—
352C2×D4—141no—
353C2×D4—281no—
354C2×D4C2×C22⋊D712yes—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—281no—
361C22×C4D4×D711yescharacteristic
362C22×C4#115911yescharacteristic
363C22×C4C2×C22⋊D711yescharacteristic
364SD16—44no—
365D8—284no—
366C2×C8—22no—
367C2×C8—71no—
368C2×C8—71no—
369C2×C8—71no—
370C2×C8—71no—
371C2×C8—142no—
372C2×C8—142no—
373C2×C8—142no—
374C2×C8—142no—
375C2×C8—284no—
376C2×C8—284no—
377C2×C8—282no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—141no—
386C4⋊C4—141no—
387C4⋊C4C2×C22⋊D712yes—
388C22⋊C4—22no—
389C22⋊C4—22no—
390C22⋊C4—41no—
391C22⋊C4—281no—
392C22⋊C4—281no—
393C42—41no—
394C42D4×D711yescharacteristic
395C42#115911yescharacteristic
396C42C2×C22⋊D711yescharacteristic
397C42C23×D711yescharacteristic
398C2×C7—22no—
399C2×C7—44no—
400C2×C7C2×#46311yescharacteristic
401C2×C7#305011yescharacteristic
402C2×C7#306711yescharacteristic
403D7—161no—
404C23—24no—
405C23—22no—
406C23—42no—
407C23—42no—
408C23—281no—
409C23#650211yescharacteristic
410Q8—42no—
411Q8—81no—
412Q8—281no—
413Q8—281no—
414D4—24no—
415D4—22no—
416D4—281no—
417D4—281no—
418D4—282no—
419D4—561no—
420D4—562no—
421D4#651314yes—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—44no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—281no—
432C2×C4—562no—
433C2×C4#647712yes—
434C2×C4#647912yes—
435C2×C4#650211yescharacteristic
436C2×C4#650211yescharacteristic
437C2×C4#650211yescharacteristic
438C2×C4C2×D4×D711yescharacteristic
439C2×C4C2×#115911yescharacteristic
440C2×C4C22×C22⋊D711yescharacteristic
441C8—42no—
442C8—141no—
443C8—141no—
444C8—141no—
445C8—141no—
446C8—282no—
447C8—282no—
448C7#1911011yescharacteristic, complemented, Sylow
449C22—21no—
450C22—21no—
451C22—24no—
452C22—48no—
453C22—42no—
454C22—42no—
455C22—561no—
456C22—561no—
457C22—561no—
458C22#8993712yes—
459C22C2×#650211yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—42no—
464C4—81no—
465C4—81no—
466C4—561no—
467C4#8993712yes—
468C4C2×#647711yescharacteristic
469C4C2×#647911yescharacteristic
470C4C2×#651312yes—
471C2—22no—
472C2—44no—
473C2—1121no—
474C2#1174036711yescharacteristic
475C2C2×#8993711yescharacteristic
476C2#1174144611yescharacteristic
subgroupG/H
centerC2×C4#6502
commutator, cosocleC42×C7C24
FrattiniC42C23×D7
FittingC7×#3101C2
socleC22×C7C2×#121
prime radical#11739753C2
hypercenter#3101D7
hypocenterC7#19110
LCSG ▷ C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3101

Complements

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

NH ≅ G/Ntype
1. C7×#3101C2semidirect
2. #11740779C2semidirect
4. C2×D4×C7⋊C8C2semidirect
5. #11729582C2semidirect
6. #11728889C2semidirect
7. #11728888C2semidirect
8. #11728793C2semidirect
9. #11728792C2semidirect
10. #11728526C2semidirect
11. #11728499C2semidirect
24. #89865C22semidirect
25. #89865C22semidirect
26. #89860C22semidirect
27. #89860C22semidirect
43. #89342C22semidirect
44. #89341C22semidirect
45. #89281C22semidirect
46. #89280C22semidirect
47. #89275C22semidirect
48. #89274C22semidirect
112. #3101D7semidirect
448. C7#19110semidirect

Maximal subgroups

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

subgroupindex
C7×#31012
#117407792
#117397532
C2×D4×C7⋊C82
#117295822
#117288892
#117288882
#117287932
#117287922
#117285262
#117284992
#191107