Finite Group Databasebeta

← #13360996

Subgroups — #13360996

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⋊C4×Dic7C211yesmaximal, characteristic, complemented
2C2×#89507C211yesmaximal, characteristic
3#11731310C211yesmaximal, characteristic
4C7×#1852C211yesmaximal, characteristic, complemented
5#11729314C211yesmaximal, characteristic
6#11728377C212yesmaximal, complemented
7#11728359C212yesmaximal, complemented
8#11727660C211yesmaximal, characteristic, complemented
9#11727256C211yesmaximal, characteristic, complemented
10#11726572C212yesmaximal, complemented
11#11726536C212yesmaximal, complemented
12C22×C7×C4⋊C4C2211yescharacteristic
13C2×#6493C2211yescharacteristic
14C22×C4⋊Dic7C2211yescharacteristic
15C22×C4×Dic7—21no—
16C22×C4×Dic7C2211yescharacteristic
17C2×#6456C2211yescharacteristic
18C2×(C22⋊D7)⋊C4—21no—
19C2×C7×#107C2212yes—
20C2×C7×C22⋊C8C2211yescharacteristic
21C7×#380C2211yescharacteristic
22C2×C7⋊#95—21no—
23C2×C22⋊(C7⋊C8)C2211yescharacteristic
24C2×#6395C2212yes—
25C2×#6391C2212yes—
26C2×#6389C2212yes—
27#89760C2211yescharacteristic
28C4⋊C4×Dic7—21no—
29C4⋊C4×Dic7—21no—
30C4⋊C4×Dic7C2211yescharacteristic
31C4⋊C4×Dic7C2212yes—
32C4⋊C4×Dic7C2212yes—
33#89745C2211yescharacteristic
34C2×#6383C2212yes—
35#89730—21no—
36#89507C418yescomplemented
37#89441—21no—
38#89438—21no—
39C7×#340C2212yes—
40#89345C2212yes—
41#89324C2212yes—
42#89324C2212yes—
43#89324C2212yes—
44#21580—71nomaximal, Sylow
45C23×C4×C7—21no—
46C23×C4×C7C2311yescharacteristic
47C22×C22⋊D7—21no—
48C23×Dic7—21no—
49C23×Dic7D411yescharacteristic
50C23×Dic7D411yescharacteristic
51C22×D28C2311yescharacteristic
52C22×C4×D7—21no—
53C22×C7×C8C2312yes—
54C2×C7×C4⋊C4—21no—
55C2×C7×C4⋊C4—24no—
56C2×C7×C4⋊C4C2311yescharacteristic
57C2×C7×C4⋊C4C2311yescharacteristic
58C2×C7×C4⋊C4C2312yes—
59C2×C7×C22⋊C4—21no—
60#6493—22no—
61#6493C2×C414yes—
62C2×(C2×D7)⋊C4—21no—
63C2×(C2×D7)⋊C4—21no—
64C2×(C2×D7)⋊C4—21no—
65C2×(C2×D7)⋊C4—21no—
66C2×C4⋊Dic7—21no—
67C2×C4⋊Dic7—22no—
68C2×C4⋊Dic7C2×C414yescomplemented
69C2×C4⋊Dic7C2311yescharacteristic
70C2×C4⋊Dic7C2312yes—
71C2×Dic7⋊C4—21no—
72C2×C4×Dic7—24no—
73C2×C4×Dic7—21no—
74C2×C4×Dic7—22no—
75C2×C4×Dic7—22no—
76C2×C4×Dic7—44no—
77C2×C4×Dic7D411yescharacteristic
78C2×C4×Dic7D411yescharacteristic
79C2×C4×Dic7C2311yescharacteristic
80C2×C4×Dic7C2311yescharacteristic
81C22×C7⋊C8C2312yes—
82#6456—24no—
83(C22⋊D7)⋊C4—44no—
84C7×#107—24no—
85C7×C22⋊C8C2×C414yescomplemented
86C7×#95—21no—
87C7⋊#95—21no—
88C7⋊#95—21no—
89C7⋊#95—22no—
90C7⋊#95—22no—
91C22⋊(C7⋊C8)—22no—
92#6395C2×C418yescomplemented
93#6391C2×C418yescomplemented
94#6389—24no—
95#6383—24no—
96C2×#481—71no—
97C4×#121—71no—
98C2×C4×C4⋊C4—71no—
99#1925—72no—
100#1920—72no—
101#1874—71no—
102#1852D711yescharacteristic, complemented
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—24no—
112C22×C4×C7—22no—
113C22×C4×C7—21no—
114C22×C4×C7—21no—
115C22×C4×C7—42no—
116C22×C4×C7—42no—
117C22×C4×C7C22×C412yes—
118C22×C4×C7C2×D411yescharacteristic
119C22×C4×C7#4112yes—
120C22×C4×C7C2411yescharacteristic
121C2×C22⋊D7—24no—
122C2×C22⋊D7—42no—
123C2×C22⋊D7—42no—
124C22×Dic7—22no—
125C22×Dic7—22no—
126C22×Dic7—22no—
127C22×Dic7—24no—
128C22×Dic7—22no—
129C22×Dic7—22no—
130C22×Dic7—21no—
131C22×Dic7—22no—
132C22×Dic7—41no—
133C22×Dic7—42no—
134C22×Dic7—42no—
135C22×Dic7C2×D411yescharacteristic
136C22×Dic7C2×D411yescharacteristic
137C22×Dic7C2×D411yescharacteristic
138C22×Dic7C2×D411yescharacteristic
139C2×D28—22no—
140C2×D28—22no—
141C2×D28—21no—
142C2×D28C22×C412yes—
143C2×C4×D7—42no—
144C2×C4×D7—42no—
145C2×C4×D7—42no—
146C2×C7×C8—22no—
147C2×C7×C8—22no—
148C2×C7×C8C22×C414yes—
149C7×C4⋊C4—24no—
150C7×C4⋊C4—22no—
151C7×C4⋊C4—22no—
152C7×C4⋊C4—22no—
153C7×C4⋊C4#4114yes—
154C7×C22⋊C4—42no—
155(C2×D7)⋊C4—24no—
156(C2×D7)⋊C4—42no—
157(C2×D7)⋊C4—42no—
158(C2×D7)⋊C4—42no—
159C4⋊Dic7—24no—
160C4⋊Dic7—22no—
161C4⋊Dic7—21no—
162C4⋊Dic7C22×C414yes—
163C4⋊Dic7C22×C412yes—
164Dic7⋊C4—42no—
165C4×Dic7—22no—
166C4×Dic7—22no—
167C4×Dic7—22no—
168C4×Dic7—42no—
169C4×Dic7—44no—
170C4×Dic7—44no—
171C4×Dic7#4114yes—
172C2×C7⋊C8—22no—
173C2×C7⋊C8—22no—
174C2×C7⋊C8—22no—
175C2×#121—71no—
176C2×C4×D4—71no—
177C2×C4×D4—141no—
178C22×C4⋊C4—71no—
179C22×C4⋊C4C2×D711yescharacteristic
180C22×C42—71no—
181C22×C42—141no—
182#481—78no—
183C2×#107C2×D712yes—
184C2×#106—72no—
185C2×#102—72no—
186C2×#102—72no—
187C2×C22⋊C8—71no—
188C2×C22⋊C8C2×D711yescharacteristic
189C2×#97—72no—
190#390—71no—
191#389—71no—
192#388—141no—
193#386—141no—
194#380C2×D711yescharacteristic
195C4×C4⋊C4—72no—
196C4×C4⋊C4—72no—
197C4×C4⋊C4—71no—
198C4×C4⋊C4—141no—
199C4×C4⋊C4—141no—
200C4×C22⋊C4—141no—
201C2×#95—141no—
202#340—72no—
203#340—72no—
204#340—72no—
205#340C2×D712yes—
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—21no—
223C2×C4×C7—21no—
224C2×C4×C7—24no—
225C2×C4×C7—24no—
226C2×C4×C7—24no—
227C2×C4×C7—48no—
228C2×C4×C7—42no—
229C2×C4×C7—42no—
230C2×C4×C7—41no—
231C2×C4×C7—41no—
232C2×C4×C7—41no—
233C2×C4×C7—41no—
234C2×C4×C7—41no—
235C2×C4×C7—41no—
236C2×C4×C7C4×D412yes—
237C2×C4×C7C23×C411yescharacteristic
238C2×C4×C7C2×#4112yes—
239C2×C4×C7C2×#4111yescharacteristic
240C2×C4×C7C2×#4112yes—
241C22⋊D7—48no—
242C2×Dic7—28no—
243C2×Dic7—21no—
244C2×Dic7—21no—
245C2×Dic7—21no—
246C2×Dic7—21no—
247C2×Dic7—21no—
248C2×Dic7—21no—
249C2×Dic7—24no—
250C2×Dic7—22no—
251C2×Dic7—21no—
252C2×Dic7—21no—
253C2×Dic7—21no—
254C2×Dic7—44no—
255C2×Dic7—48no—
256C2×Dic7—42no—
257C2×Dic7—41no—
258C2×Dic7—41no—
259C2×Dic7—42no—
260C2×Dic7#12312yes—
261C2×Dic7#12312yes—
262C2×Dic7AGL(1,ℤ/8)12yes—
263D28—24no—
264D28—42no—
265C4×D7—84no—
266C7×C8—24no—
267C7⋊C8—42no—
268C22×D4—71no—
269C22×D4—141no—
270C23×C4—21no—
271C23×C4—71no—
272C23×C4—71no—
273C23×C4—141no—
274C23×C4—141no—
275C23×C4C22×D711yescharacteristic
276C22×C8—72no—
277C22×C8C22×D712yes—
278#121—74no—
279#121—142no—
280C4×D4—144no—
281C4×D4—284no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—74no—
285C2×C4⋊C4—72no—
286C2×C4⋊C4—71no—
287C2×C4⋊C4—141no—
288C2×C4⋊C4—142no—
289C2×C4⋊C4—141no—
290C2×C4⋊C4C22×D711yescharacteristic
291C2×C4⋊C4C22×D711yescharacteristic
292C2×C4⋊C4C22×D712yes—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—141no—
295C2×C22⋊C4—141no—
296C2×C22⋊C4—141no—
297C2×C22⋊C4—141no—
298C2×C42—71no—
299C2×C42—71no—
300C2×C42—71no—
301C2×C42—71no—
302C2×C42—144no—
303C2×C42—141no—
304C2×C42—142no—
305C2×C42—142no—
306C2×C42—284no—
307#107—24no—
308#106—78no—
309#102—78no—
310#102—144no—
311C22⋊C8—142no—
312C22⋊C8C4×D714yescomplemented
313#97—144no—
314#95—21no—
315#95—142no—
316#95—142no—
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—44no—
342C4×C7—81no—
343C4×C7—81no—
344C4×C7C4×#4112yes—
345C4×C7#52912yes—
346Dic7—22no—
347Dic7—22no—
348Dic7—22no—
349Dic7—41no—
350Dic7—42no—
351Dic7—44no—
352C24—141no—
353C24D4×D711yescharacteristic
354C2×D4—72no—
355C2×D4—144no—
356C2×D4—142no—
357C2×D4—141no—
358C2×D4—142no—
359C2×D4—282no—
360C2×D4—282no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—24no—
364C22×C4—22no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—71no—
370C22×C4—71no—
371C22×C4—71no—
372C22×C4—71no—
373C22×C4—142no—
374C22×C4—142no—
375C22×C4—142no—
376C22×C4—142no—
377C22×C4—144no—
378C22×C4—142no—
379C22×C4—142no—
380C22×C4—141no—
381C22×C4—282no—
382C22×C4—282no—
383C22×C4—282no—
384C22×C4—281no—
385C22×C4—282no—
386C22×C4—282no—
387C22×C4C2×C4×D712yes—
388C22×C4D4×D711yescharacteristic
389C22×C4#116112yes—
390C22×C4C23×D711yescharacteristic
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—142no—
394C2×C8—142no—
395C2×C8—142no—
396C2×C8C2×C4×D714yes—
397C4⋊C4—24no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—74no—
402C4⋊C4—72no—
403C4⋊C4—144no—
404C4⋊C4—142no—
405C4⋊C4—141no—
406C4⋊C4—282no—
407C4⋊C4#115914yes—
408C22⋊C4—42no—
409C22⋊C4—144no—
410C22⋊C4—282no—
411C22⋊C4—282no—
412C22⋊C4—282no—
413C42—74no—
414C42—142no—
415C42—142no—
416C42—142no—
417C42—284no—
418C42—284no—
419C42—282no—
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—
440C23#645612yes—
441C23#647412yes—
442C23#648112yes—
443C23C2×D4×D711yescharacteristic
444D4—144no—
445D4—288no—
446D4—282no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—48no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—72no—
462C2×C4—72no—
463C2×C4—72no—
464C2×C4—148no—
465C2×C4—141no—
466C2×C4—141no—
467C2×C4—141no—
468C2×C4—141no—
469C2×C4—141no—
470C2×C4—141no—
471C2×C4—141no—
472C2×C4—142no—
473C2×C4—144no—
474C2×C4—141no—
475C2×C4—141no—
476C2×C4—284no—
477C2×C4—288no—
478C2×C4—281no—
479C2×C4—281no—
480C2×C4—282no—
481C2×C4—282no—
482C2×C4—564no—
483C2×C4#645612yes—
484C2×C4C22×C4×D711yescharacteristic
485C2×C4C2×#115912yes—
486C2×C4C2×#116111yescharacteristic
487C2×C4D7×#4112yes—
488C8—24no—
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#8966114yes—
505C22C2×#645611yescharacteristic
506C22#9027711yescharacteristic
507C22D7×#12311yescharacteristic
508C22C2×#647411yescharacteristic
509C22C2×#648111yescharacteristic
510C22D7×AGL(1,ℤ/8)11yescharacteristic
511C22#9046811yescharacteristic
512C4—22no—
513C4—44no—
514C4—81no—
515C4—81no—
516C4—142no—
517C4—142no—
518C4—142no—
519C4—282no—
520C4—284no—
521C4—281no—
522C4C4×#115912yes—
523C4#9031512yes—
524C2—24no—
525C2—562no—
526C2#1173182511yescharacteristic
527C2C2×#8966111yescharacteristic
528C2#1173664411yescharacteristic
529C2#1173743511yescharacteristic
530C2#1173762011yescharacteristic
531C2#1173872811yescharacteristic
532C2#1173891311yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1852C2
socleC23×C7C22×D4
prime radicalC2×#6493C22
cosocleC22×C4×C7C24
hypercenter#1852D7
hypocenterC7#21580
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×Dic7C2semidirect
4. C7×#1852C2semidirect
6. #11728377C2semidirect
7. #11728359C2semidirect
8. #11727660C2semidirect
9. #11727256C2semidirect
10. #11726572C2semidirect
11. #11726536C2semidirect
36. #89507C4semidirect
68. C2×C4⋊Dic7C2×C4semidirect
85. C7×C22⋊C8C2×C4semidirect
92. #6395C2×C4semidirect
93. #6391C2×C4semidirect
102. #1852D7semidirect
312. C22⋊C8C4×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⋊C4×Dic72
C2×#895072
#117313102
C7×#18522
#117293142
#117283772
#117283592
#117276602
#117272562
#117265722
#117265362
#215807