Finite Group Databasebeta

← #13360999

Subgroups — #13360999

Order 1792.

1048 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#89740C211yesmaximal, characteristic
3C4×#6493C211yesmaximal, characteristic
4#11729314C211yesmaximal, characteristic
5#11729309C211yesmaximal, characteristic, complemented
6#11729308C211yesmaximal, characteristic, complemented
7#11729283C211yesmaximal, characteristic, complemented
8#11727235C212yesmaximal, complemented
9#11727228C212yesmaximal, complemented
10#11727216C212yesmaximal, complemented
11#11727214C212yesmaximal, complemented
12C22×C7×C4⋊C4C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C42×C7—21no—
15C22×C42×C7C2211yescharacteristic
16C2×#6493C2211yescharacteristic
17C2×C4×C22⋊D7—21no—
18C2×C4×D28C2211yescharacteristic
19C4×C7×C4⋊C4—21no—
20C4×C7×C4⋊C4—21no—
21C4×C7×C4⋊C4C2212yes—
22C4×C7×C4⋊C4C2212yes—
23C2×C7×#95—21no—
24#89985—21no—
25#89984C2211yescharacteristic
26C2×C22⋊(C7⋊C8)C2211yescharacteristic
27C2×C22⋊(C7⋊C8)C2211yescharacteristic
28#89740C418yescomplemented
29C2×#6383C2212yes—
30C2×#6383C2212yes—
31C2×#6382C2212yes—
32C2×#6381C2212yes—
33#89712—21no—
34#89711C2211yescharacteristic
35C4×(C2×D7)⋊C4—21no—
36C4×C4⋊Dic7C2211yescharacteristic
37#89700C2211yescharacteristic
38C2×#6377C2212yes—
39#89324C2212yes—
40#89324C2212yes—
41#89324C2212yes—
42#89324C2212yes—
43#89319C2212yes—
44#21580—71nomaximal, Sylow
45C23×C4×C7—21no—
46C23×C4×C7—21no—
47C23×C4×C7D411yescharacteristic
48C23×C4×C7D411yescharacteristic
49C23×C4×C7C2311yescharacteristic
50C22×C22⋊D7—21no—
51C22×D28C2311yescharacteristic
52C22×C4×D7—21no—
53C2×C7×C4⋊C4—21no—
54C2×C7×C4⋊C4—21no—
55C2×C7×C4⋊C4—22no—
56C2×C7×C4⋊C4—24no—
57C2×C7×C4⋊C4C2×C414yescomplemented
58C2×C7×C4⋊C4C2312yes—
59C2×C7×C4⋊C4C2312yes—
60C2×C42×C7—24no—
61C2×C42×C7—22no—
62C2×C42×C7—22no—
63C2×C42×C7—44no—
64C2×C42×C7D411yescharacteristic
65C2×C42×C7D411yescharacteristic
66C2×C42×C7C2311yescharacteristic
67C2×C42×C7C2311yescharacteristic
68C2×C22⋊Dic7—21no—
69#6493—22no—
70#6493C2×C414yes—
71C4×C22⋊D7—44no—
72C2×(C2×D7)⋊C4—21no—
73C2×(C2×D7)⋊C4—21no—
74C2×(C2×D7)⋊C4—21no—
75C2×(C2×D7)⋊C4—21no—
76C2×C4⋊Dic7C2311yescharacteristic
77C2×C4⋊Dic7C2311yescharacteristic
78C2×C4⋊Dic7C2311yescharacteristic
79C2×Dic7⋊C4—21no—
80C2×C4×Dic7—21no—
81C22×C7⋊C8C2312yes—
82C22×C7⋊C8C2312yes—
83C4×D28—24no—
84C7×#95—22no—
85C7×#95—22no—
86C7⋊#95—21no—
87C7⋊#95—21no—
88C7⋊#95—21no—
89C22⋊(C7⋊C8)—22no—
90C22⋊(C7⋊C8)C2×C414yescomplemented
91#6383—24no—
92#6383C2×C418yescomplemented
93#6382C2×C418yescomplemented
94#6381—24no—
95#6377—24no—
96C2×#481—71no—
97C4×#121—71no—
98C2×C4×C4⋊C4D711yescharacteristic, complemented
99#1925—72no—
100#1920—72no—
101#1874—71no—
102#1852—71no—
103#1824—71no—
104#1776—72no—
105#1762—72no—
106#1749—71no—
107C24×C7C2×D411yescharacteristic
108C23×D7—21no—
109C22×C4×C7—22no—
110C22×C4×C7—22no—
111C22×C4×C7—22no—
112C22×C4×C7—22no—
113C22×C4×C7—22no—
114C22×C4×C7—24no—
115C22×C4×C7—24no—
116C22×C4×C7—22no—
117C22×C4×C7—22no—
118C22×C4×C7—22no—
119C22×C4×C7—22no—
120C22×C4×C7—41no—
121C22×C4×C7—42no—
122C22×C4×C7—42no—
123C22×C4×C7—42no—
124C22×C4×C7—42no—
125C22×C4×C7C22×C412yes—
126C22×C4×C7C2×D411yescharacteristic
127C22×C4×C7C2×D411yescharacteristic
128C22×C4×C7C2×D411yescharacteristic
129C22×C4×C7C2×D411yescharacteristic
130C22×C4×C7C2×D411yescharacteristic
131C22×C4×C7#4112yes—
132C22×C4×C7C2411yescharacteristic
133C2×C22⋊D7—24no—
134C2×C22⋊D7—42no—
135C2×C22⋊D7—42no—
136C22×Dic7—21no—
137C22×Dic7—21no—
138C22×Dic7—21no—
139C2×D28—22no—
140C2×D28—22no—
141C2×D28—21no—
142C2×D28C22×C412yes—
143C2×C4×D7—42no—
144C2×C4×D7—42no—
145C2×C4×D7—42no—
146C7×C4⋊C4—24no—
147C7×C4⋊C4—24no—
148C7×C4⋊C4—22no—
149C7×C4⋊C4—22no—
150C7×C4⋊C4C22×C414yes—
151C7×C4⋊C4#4114yes—
152C42×C7—22no—
153C42×C7—22no—
154C42×C7—22no—
155C42×C7—44no—
156C42×C7—44no—
157C42×C7#4114yes—
158C22⋊Dic7—42no—
159(C2×D7)⋊C4—24no—
160(C2×D7)⋊C4—42no—
161(C2×D7)⋊C4—42no—
162(C2×D7)⋊C4—42no—
163C4⋊Dic7—21no—
164C4⋊Dic7—22no—
165C4⋊Dic7—22no—
166C4⋊Dic7C22×C412yes—
167Dic7⋊C4—42no—
168C4×Dic7—42no—
169C2×C7⋊C8—22no—
170C2×C7⋊C8—22no—
171C2×C7⋊C8—22no—
172C2×C7⋊C8—22no—
173C2×C7⋊C8—22no—
174C2×C7⋊C8C22×C414yes—
175C2×#121—71no—
176C2×C4×D4—71no—
177C2×C4×D4—141no—
178C22×C4⋊C4C2×D711yescharacteristic
179C22×C4⋊C4C2×D711yescharacteristic
180C22×C42—21no—
181C22×C42C2×D711yescharacteristic
182#481—78no—
183C2×#107—72no—
184C2×#106—72no—
185C2×#102—72no—
186C2×#102—72no—
187C2×C22⋊C8—71no—
188C2×C22⋊C8—71no—
189C2×#97—72no—
190#390—71no—
191#389—71no—
192#388—141no—
193#386—141no—
194#380—71no—
195C4×C4⋊C4—21no—
196C4×C4⋊C4—21no—
197C4×C4⋊C4—71no—
198C4×C4⋊C4C2×D712yes—
199C4×C4⋊C4C2×D712yes—
200C4×C22⋊C4—141no—
201C2×#95—21no—
202#340—72no—
203#340—72no—
204#340—72no—
205#340—72no—
206#336—72no—
207C23×C7—21no—
208C23×C7—21no—
209C23×C7—21no—
210C23×C7—21no—
211C23×C7C4×D412yes—
212C23×C7AGL(1,ℤ/8)12yes—
213C23×C7#13712yes—
214C23×C7C22×D411yescharacteristic
215C22×D7—22no—
216C22×D7—41no—
217C22×D7—41no—
218C22×D7—41no—
219C22×D7—41no—
220C22×D7—41no—
221C22×D7—41no—
222C2×C4×C7—28no—
223C2×C4×C7—21no—
224C2×C4×C7—21no—
225C2×C4×C7—21no—
226C2×C4×C7—21no—
227C2×C4×C7—21no—
228C2×C4×C7—21no—
229C2×C4×C7—21no—
230C2×C4×C7—21no—
231C2×C4×C7—24no—
232C2×C4×C7—24no—
233C2×C4×C7—24no—
234C2×C4×C7—21no—
235C2×C4×C7—24no—
236C2×C4×C7—21no—
237C2×C4×C7—21no—
238C2×C4×C7—44no—
239C2×C4×C7—48no—
240C2×C4×C7—48no—
241C2×C4×C7—42no—
242C2×C4×C7—42no—
243C2×C4×C7—42no—
244C2×C4×C7—42no—
245C2×C4×C7C4×D412yes—
246C2×C4×C7#12312yes—
247C2×C4×C7#12312yes—
248C2×C4×C7AGL(1,ℤ/8)12yes—
249C2×C4×C7C23×C411yescharacteristic
250C2×C4×C7C2×#4112yes—
251C2×C4×C7C2×#4112yes—
252C2×C4×C7C2×#4111yescharacteristic
253C22⋊D7—48no—
254C2×Dic7—22no—
255C2×Dic7—41no—
256C2×Dic7—41no—
257C2×Dic7—41no—
258C2×Dic7—41no—
259C2×Dic7—41no—
260C2×Dic7—41no—
261C2×Dic7—41no—
262C2×Dic7—41no—
263D28—24no—
264D28—42no—
265C4×D7—84no—
266C7⋊C8—24no—
267C7⋊C8—42no—
268C22×D4—71no—
269C22×D4—141no—
270C23×C4—21no—
271C23×C4—21no—
272C23×C4—141no—
273C23×C4C22⋊D711yescharacteristic
274C23×C4C22⋊D711yescharacteristic
275C23×C4C22×D711yescharacteristic
276C22×C8—72no—
277C22×C8—72no—
278#121—74no—
279#121—142no—
280C4×D4—144no—
281C4×D4—284no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—71no—
287C2×C4⋊C4—71no—
288C2×C4⋊C4—71no—
289C2×C4⋊C4—141no—
290C2×C4⋊C4C4×D714yescomplemented
291C2×C4⋊C4C22×D712yes—
292C2×C4⋊C4C22×D712yes—
293C2×C22⋊C4—141no—
294C2×C22⋊C4—141no—
295C2×C22⋊C4—141no—
296C2×C22⋊C4—141no—
297C2×C22⋊C4—141no—
298C2×C42—24no—
299C2×C42—22no—
300C2×C42—22no—
301C2×C42—44no—
302C2×C42—141no—
303C2×C42C22⋊D711yescharacteristic
304C2×C42C22⋊D711yescharacteristic
305C2×C42C22×D711yescharacteristic
306C2×C42C22×D711yescharacteristic
307#107—144no—
308#106—78no—
309#102—78no—
310#102—144no—
311C22⋊C8—74no—
312C22⋊C8—142no—
313#97—144no—
314#95—22no—
315#95—22no—
316#95—141no—
317#95—141no—
318#95—141no—
319C22×C7—22no—
320C22×C7—22no—
321C22×C7—22no—
322C22×C7—22no—
323C22×C7—22no—
324C22×C7—22no—
325C22×C7#44014yes—
326C22×C7C2×C4×D411yescharacteristic
327C22×C7C2×#12311yescharacteristic
328C22×C7#52511yescharacteristic
329C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
330C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
331C22×C7C2×#13711yescharacteristic
332C22×C7#57511yescharacteristic
333C2×D7—42no—
334C2×D7—42no—
335C2×D7—42no—
336C2×D7—81no—
337C2×D7—81no—
338C2×D7—81no—
339C2×D7—81no—
340C4×C7—22no—
341C4×C7—22no—
342C4×C7—22no—
343C4×C7—22no—
344C4×C7—41no—
345C4×C7—44no—
346C4×C7—44no—
347C4×C7C4×#4112yes—
348C4×C7#52912yes—
349Dic7—42no—
350Dic7—81no—
351Dic7—81no—
352C24—141no—
353C24C2×C22⋊D711yescharacteristic
354C2×D4—72no—
355C2×D4—144no—
356C2×D4—142no—
357C2×D4—142no—
358C2×D4—141no—
359C2×D4—282no—
360C2×D4—282no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—41no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—141no—
378C22×C4—141no—
379C22×C4—141no—
380C22×C4—282no—
381C22×C4—282no—
382C22×C4—282no—
383C22×C4C2×C4×D712yes—
384C22×C4#115712yes—
385C22×C4C2×C22⋊D711yescharacteristic
386C22×C4C2×C22⋊D711yescharacteristic
387C22×C4C2×C22⋊D711yescharacteristic
388C22×C4C2×C22⋊D711yescharacteristic
389C22×C4C2×C22⋊D711yescharacteristic
390C22×C4C23×D711yescharacteristic
391C2×C8—74no—
392C2×C8—142no—
393C2×C8—142no—
394C2×C8—142no—
395C2×C8—142no—
396C2×C8—142no—
397C4⋊C4—24no—
398C4⋊C4—24no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—72no—
402C4⋊C4—141no—
403C4⋊C4—142no—
404C4⋊C4—142no—
405C4⋊C4—282no—
406C4⋊C4C2×C4×D714yes—
407C4⋊C4#115714yes—
408C22⋊C4—144no—
409C22⋊C4—282no—
410C22⋊C4—282no—
411C22⋊C4—282no—
412C22⋊C4—282no—
413C42—22no—
414C42—22no—
415C42—22no—
416C42—44no—
417C42—44no—
418C42—282no—
419C42#115714yes—
420C2×C7—24no—
421C2×C7C4×#12311yescharacteristic
422C2×C7C2×#44011yescharacteristic
423C2×C7C4×AGL(1,ℤ/8)11yescharacteristic
424C2×C7#309211yescharacteristic
425C2×C7#309411yescharacteristic
426C2×C7#310911yescharacteristic
427C2×C7#311711yescharacteristic
428D7—82no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—142no—
434C23—281no—
435C23—281no—
436C23—281no—
437C23—281no—
438C23—281no—
439C23—281no—
440C23C4×C22⋊D712yes—
441C23#650512yes—
442C23#651212yes—
443C23C22×C22⋊D711yescharacteristic
444D4—144no—
445D4—288no—
446D4—282no—
447C2×C4—28no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—21no—
460C2×C4—24no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—44no—
464C2×C4—48no—
465C2×C4—48no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—142no—
471C2×C4—281no—
472C2×C4—281no—
473C2×C4—281no—
474C2×C4—281no—
475C2×C4—281no—
476C2×C4—281no—
477C2×C4—281no—
478C2×C4—281no—
479C2×C4—564no—
480C2×C4C4×C22⋊D712yes—
481C2×C4#649212yes—
482C2×C4#649212yes—
483C2×C4#649512yes—
484C2×C4C22×C4×D711yescharacteristic
485C2×C4C2×#115712yes—
486C2×C4C2×#115712yes—
487C2×C4C2×#115711yescharacteristic
488C8—144no—
489C8—282no—
490C7#2158011yescharacteristic, complemented, Sylow
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—282no—
498C22—282no—
499C22—282no—
500C22—561no—
501C22—561no—
502C22—561no—
503C22—561no—
504C22#8979814yes—
505C22C2×C4×C22⋊D711yescharacteristic
506C22C2×#649211yescharacteristic
507C22#9048211yescharacteristic
508C22C2×#649511yescharacteristic
509C22C2×#650511yescharacteristic
510C22C2×#651211yescharacteristic
511C22#9051311yescharacteristic
512C4—22no—
513C4—22no—
514C4—22no—
515C4—22no—
516C4—41no—
517C4—44no—
518C4—44no—
519C4—282no—
520C4—561no—
521C4—561no—
522C4C4×#115712yes—
523C4#9017012yes—
524C2—24no—
525C2—562no—
526C2C4×#649211yescharacteristic
527C2#1173958411yescharacteristic
528C2#1173966211yescharacteristic
529C2C4×#649511yescharacteristic
530C2#1173975511yescharacteristic
531C2C2×#8979811yescharacteristic
532C2#1173989011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C4×C7×C4⋊C4C2
socleC23×C7C22×D4
prime radicalC2×#6493C22
cosocleC22×C4×C7C24
hypercenterC2×C4×C4⋊C4D7
hypocenterC7#21580
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×C7×C4⋊C4C2semidirect
5. #11729309C2semidirect
6. #11729308C2semidirect
7. #11729283C2semidirect
8. #11727235C2semidirect
9. #11727228C2semidirect
10. #11727216C2semidirect
11. #11727214C2semidirect
28. #89740C4semidirect
57. C2×C7×C4⋊C4C2×C4semidirect
90. C22⋊(C7⋊C8)C2×C4semidirect
92. #6383C2×C4semidirect
93. #6382C2×C4semidirect
98. C2×C4×C4⋊C4D7semidirect
290. C2×C4⋊C4C4×D7semidirect
490. C7#21580semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C7×C4⋊C42
C2×#897402
C4×#64932
#117293142
#117293092
#117293082
#117292832
#117272352
#117272282
#117272162
#117272142
#215807