Finite Group Databasebeta

← #13361010

Subgroups — #13361010

Order 1792.

964 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×C4×C7×C4⋊C4C211yesmaximal, characteristic
2C2×#89742C211yesmaximal, characteristic
3C4×#6487C211yesmaximal, characteristic
4#11729313C211yesmaximal, characteristic
5#11729310C211yesmaximal, characteristic
6#11729308C211yesmaximal, characteristic
7#11729283C211yesmaximal, characteristic
8#11727235C212yesmaximal, complemented
9#11727229C212yesmaximal, complemented
10#11727218C212yesmaximal, complemented
11#11727212C212yesmaximal, complemented
12C22×C7×C4⋊C4C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C42×C7—21no—
15C22×C42×C7C2211yescharacteristic
16C2×#6487C2211yescharacteristic
17C2×C4×Dic14C2211yescharacteristic
18C4×C7×C4⋊C4—21no—
19C4×C7×C4⋊C4—21no—
20C4×C7×C4⋊C4C2212yes—
21C4×C7×C4⋊C4C2212yes—
22C2×C7×#95—21no—
23#89984C2211yescharacteristic
24#89982—21no—
25C4×C22⋊Dic7—21no—
26C2×C22⋊(C7⋊C8)C2211yescharacteristic
27C2×C22⋊(C7⋊C8)C2211yescharacteristic
28#89742C418yescomplemented
29C2×#6384C2212yes—
30C2×#6384C2212yes—
31C2×#6382C2212yes—
32C2×#6381C2212yes—
33C4×C4⋊Dic7C2211yescharacteristic
34#89705—21no—
35C4×Dic7⋊C4—21no—
36#89701C2211yescharacteristic
37#89700C2211yescharacteristic
38C2×#6377C2212yes—
39#89324C2212yes—
40#89324C2212yes—
41#89324C2212yes—
42#89324C2212yes—
43#89319C2212yes—
44#21581—71nomaximal, Sylow
45C23×C4×C7—21no—
46C23×C4×C7—21no—
47C23×C4×C7D411yescharacteristic
48C23×C4×C7D411yescharacteristic
49C23×C4×C7C2311yescharacteristic
50C22×Dic14C2311yescharacteristic
51C2×C7×C4⋊C4—21no—
52C2×C7×C4⋊C4—21no—
53C2×C7×C4⋊C4—22no—
54C2×C7×C4⋊C4—24no—
55C2×C7×C4⋊C4C2×C414yes—
56C2×C7×C4⋊C4C2312yes—
57C2×C7×C4⋊C4C2312yes—
58C2×C42×C7—24no—
59C2×C42×C7—22no—
60C2×C42×C7—22no—
61C2×C42×C7—44no—
62C2×C42×C7D411yescharacteristic
63C2×C42×C7D411yescharacteristic
64C2×C42×C7C2311yescharacteristic
65C2×C42×C7C2311yescharacteristic
66C2×C22⋊Dic7—21no—
67C2×C22⋊Dic7—21no—
68C2×C4⋊Dic7C2311yescharacteristic
69C2×C4⋊Dic7C2311yescharacteristic
70C2×C4⋊Dic7C2311yescharacteristic
71#6487—22no—
72#6487C2×C414yes—
73C2×Dic7⋊C4—21no—
74C2×Dic7⋊C4—21no—
75C2×Dic7⋊C4—21no—
76C2×C4×Dic7—21no—
77C2×C4×Dic7—21no—
78C22×C7⋊C8C2312yes—
79C22×C7⋊C8C2312yes—
80C4×Dic14—24no—
81C7×#95—22no—
82C7×#95—22no—
83C7⋊#95—21no—
84C7⋊#95—21no—
85C7⋊#95—21no—
86C7⋊#95—21no—
87C7⋊#95—21no—
88C22⋊(C7⋊C8)—22no—
89C22⋊(C7⋊C8)C2×C414yes—
90#6384—24no—
91#6384C2×C418yescomplemented
92#6382—24no—
93#6381C2×C418yescomplemented
94#6377—24no—
95C2×#484—71no—
96C4×C22⋊Q8—71no—
97C2×C4×C4⋊C4D711yescharacteristic
98#1927—72no—
99#1918—72no—
100#1872—71no—
101#1853—71no—
102#1824—71no—
103#1776—72no—
104#1763—72no—
105#1749—71no—
106C24×C7C2×D411yescharacteristic
107C22×C4×C7—22no—
108C22×C4×C7—22no—
109C22×C4×C7—22no—
110C22×C4×C7—22no—
111C22×C4×C7—22no—
112C22×C4×C7—24no—
113C22×C4×C7—24no—
114C22×C4×C7—22no—
115C22×C4×C7—22no—
116C22×C4×C7—22no—
117C22×C4×C7—22no—
118C22×C4×C7—41no—
119C22×C4×C7—42no—
120C22×C4×C7—42no—
121C22×C4×C7—42no—
122C22×C4×C7—42no—
123C22×C4×C7C22×C412yes—
124C22×C4×C7C2×D411yescharacteristic
125C22×C4×C7C2×D411yescharacteristic
126C22×C4×C7C2×D411yescharacteristic
127C22×C4×C7C2×D411yescharacteristic
128C22×C4×C7C2×D411yescharacteristic
129C22×C4×C7#4112yes—
130C22×C4×C7C2411yescharacteristic
131C22×Dic7—21no—
132C22×Dic7—21no—
133C22×Dic7—21no—
134C22×Dic7—21no—
135C2×Dic14—22no—
136C2×Dic14—22no—
137C2×Dic14—21no—
138C2×Dic14C22×C412yes—
139C7×C4⋊C4—24no—
140C7×C4⋊C4—24no—
141C7×C4⋊C4—22no—
142C7×C4⋊C4—22no—
143C7×C4⋊C4C22×C414yes—
144C7×C4⋊C4#4114yes—
145C42×C7—22no—
146C42×C7—22no—
147C42×C7—22no—
148C42×C7—44no—
149C42×C7—44no—
150C42×C7#4114yes—
151C22⋊Dic7—24no—
152C22⋊Dic7—42no—
153C4⋊Dic7—21no—
154C4⋊Dic7—22no—
155C4⋊Dic7—22no—
156C4⋊Dic7C22×C412yes—
157Dic7⋊C4—24no—
158Dic7⋊C4—42no—
159Dic7⋊C4—42no—
160C4×Dic7—42no—
161C4×Dic7—42no—
162C2×C7⋊C8—22no—
163C2×C7⋊C8—22no—
164C2×C7⋊C8—22no—
165C2×C7⋊C8—22no—
166C2×C7⋊C8—22no—
167C2×C7⋊C8C22×C414yes—
168C2×C22⋊Q8—71no—
169C2×C4×Q8—71no—
170C22×C4⋊C4C2×D711yescharacteristic
171C22×C4⋊C4C2×D711yescharacteristic
172C22×C42—21no—
173C22×C42C2×D711yescharacteristic
174#484—78no—
175C2×#107—72no—
176C2×#106—72no—
177C2×#103—72no—
178C2×#103—72no—
179C2×C22⋊C8—71no—
180C2×C22⋊C8—71no—
181C2×#97—72no—
182#391—71no—
183#389—71no—
184#387—141no—
185#385—141no—
186#380—71no—
187C4×C4⋊C4—21no—
188C4×C4⋊C4—21no—
189C4×C4⋊C4—71no—
190C4×C4⋊C4—141no—
191C4×C4⋊C4C2×D712yes—
192C4×C4⋊C4C2×D712yes—
193C4×C22⋊C4—141no—
194C2×#95—21no—
195#340—72no—
196#340—72no—
197#340—72no—
198#340—72no—
199#336—72no—
200C23×C7—21no—
201C23×C7—21no—
202C23×C7—21no—
203C23×C7—21no—
204C23×C7C4×D412yes—
205C23×C7#13712yes—
206C23×C7#13712yes—
207C23×C7C22×D411yescharacteristic
208C2×C4×C7—28no—
209C2×C4×C7—21no—
210C2×C4×C7—21no—
211C2×C4×C7—21no—
212C2×C4×C7—21no—
213C2×C4×C7—21no—
214C2×C4×C7—21no—
215C2×C4×C7—21no—
216C2×C4×C7—21no—
217C2×C4×C7—24no—
218C2×C4×C7—24no—
219C2×C4×C7—24no—
220C2×C4×C7—21no—
221C2×C4×C7—24no—
222C2×C4×C7—21no—
223C2×C4×C7—21no—
224C2×C4×C7—44no—
225C2×C4×C7—48no—
226C2×C4×C7—48no—
227C2×C4×C7—42no—
228C2×C4×C7—42no—
229C2×C4×C7—42no—
230C2×C4×C7—42no—
231C2×C4×C7C4×D412yes—
232C2×C4×C7#12312yes—
233C2×C4×C7#12312yes—
234C2×C4×C7AGL(1,ℤ/8)12yes—
235C2×C4×C7C23×C411yescharacteristic
236C2×C4×C7C2×#4112yes—
237C2×C4×C7C2×#4112yes—
238C2×C4×C7C2×#4111yescharacteristic
239C2×Dic7—22no—
240C2×Dic7—22no—
241C2×Dic7—41no—
242C2×Dic7—41no—
243C2×Dic7—41no—
244C2×Dic7—41no—
245C2×Dic7—41no—
246C2×Dic7—41no—
247C2×Dic7—41no—
248C2×Dic7—41no—
249C2×Dic7—41no—
250C2×Dic7—41no—
251Dic14—24no—
252Dic14—42no—
253C7⋊C8—24no—
254C7⋊C8—42no—
255C22×Q8—71no—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4C22⋊D711yescharacteristic
259C23×C4C22⋊D711yescharacteristic
260C23×C4C22×D711yescharacteristic
261C22×C8—72no—
262C22×C8—72no—
263C22⋊Q8—74no—
264C22⋊Q8—142no—
265C4×Q8—144no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—71no—
271C2×C4⋊C4—71no—
272C2×C4⋊C4—71no—
273C2×C4⋊C4—141no—
274C2×C4⋊C4—141no—
275C2×C4⋊C4—141no—
276C2×C4⋊C4C4×D714yes—
277C2×C4⋊C4C22×D712yes—
278C2×C4⋊C4C22×D712yes—
279C2×C22⋊C4—141no—
280C2×C22⋊C4—141no—
281C2×C42—24no—
282C2×C42—22no—
283C2×C42—22no—
284C2×C42—44no—
285C2×C42—141no—
286C2×C42—141no—
287C2×C42C22⋊D711yescharacteristic
288C2×C42C22⋊D711yescharacteristic
289C2×C42C22×D711yescharacteristic
290C2×C42C22×D711yescharacteristic
291#107—78no—
292#106—144no—
293#103—78no—
294#103—144no—
295C22⋊C8—74no—
296C22⋊C8—142no—
297#97—144no—
298#95—22no—
299#95—22no—
300#95—141no—
301#95—141no—
302#95—141no—
303#95—141no—
304#95—141no—
305C22×C7—22no—
306C22×C7—22no—
307C22×C7—22no—
308C22×C7—22no—
309C22×C7—22no—
310C22×C7—22no—
311C22×C7#44114yes—
312C22×C7C2×C4×D411yescharacteristic
313C22×C7C2×#12311yescharacteristic
314C22×C7#52511yescharacteristic
315C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
316C22×C7C2×#13711yescharacteristic
317C22×C7C2×#13711yescharacteristic
318C22×C7#57511yescharacteristic
319C4×C7—22no—
320C4×C7—22no—
321C4×C7—22no—
322C4×C7—22no—
323C4×C7—41no—
324C4×C7—44no—
325C4×C7—44no—
326C4×C7C4×#4112yes—
327C4×C7#52912yes—
328Dic7—42no—
329Dic7—42no—
330Dic7—81no—
331Dic7—81no—
332C24C2×C22⋊D711yescharacteristic
333C2×Q8—72no—
334C2×Q8—141no—
335C2×Q8—142no—
336C2×Q8—142no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—24no—
343C22×C4—24no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—41no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—141no—
354C22×C4—141no—
355C22×C4—141no—
356C22×C4—141no—
357C22×C4C2×C4×D712yes—
358C22×C4#115712yes—
359C22×C4C2×C22⋊D711yescharacteristic
360C22×C4C2×C22⋊D711yescharacteristic
361C22×C4C2×C22⋊D711yescharacteristic
362C22×C4C2×C22⋊D711yescharacteristic
363C22×C4C2×C22⋊D711yescharacteristic
364C22×C4C23×D711yescharacteristic
365C2×C8—74no—
366C2×C8—142no—
367C2×C8—142no—
368C2×C8—142no—
369C2×C8—142no—
370C2×C8—142no—
371C4⋊C4—24no—
372C4⋊C4—24no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—72no—
376C4⋊C4—144no—
377C4⋊C4—141no—
378C4⋊C4—142no—
379C4⋊C4—142no—
380C4⋊C4—282no—
381C4⋊C4—282no—
382C4⋊C4C2×C4×D714yes—
383C4⋊C4#115714yes—
384C22⋊C4—144no—
385C22⋊C4—282no—
386C42—22no—
387C42—22no—
388C42—22no—
389C42—44no—
390C42—44no—
391C42—282no—
392C42—282no—
393C42#115714yes—
394C2×C7—24no—
395C2×C7C4×#12311yescharacteristic
396C2×C7C2×#44111yescharacteristic
397C2×C7C4×AGL(1,ℤ/8)11yescharacteristic
398C2×C7#309211yescharacteristic
399C2×C7#309511yescharacteristic
400C2×C7#311011yescharacteristic
401C2×C7#311711yescharacteristic
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23C4×C22⋊D712yes—
407C23#650512yes—
408C23#651412yes—
409C23C22×C22⋊D711yescharacteristic
410Q8—144no—
411Q8—282no—
412C2×C4—28no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—21no—
425C2×C4—24no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—44no—
429C2×C4—48no—
430C2×C4—48no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—142no—
436C2×C4—142no—
437C2×C4—281no—
438C2×C4—281no—
439C2×C4—281no—
440C2×C4—281no—
441C2×C4—281no—
442C2×C4—281no—
443C2×C4—281no—
444C2×C4—281no—
445C2×C4—281no—
446C2×C4—281no—
447C2×C4C4×C22⋊D712yes—
448C2×C4#649212yes—
449C2×C4#649212yes—
450C2×C4#649512yes—
451C2×C4C22×C4×D711yescharacteristic
452C2×C4C2×#115712yes—
453C2×C4C2×#115712yes—
454C2×C4C2×#115711yescharacteristic
455C8—144no—
456C8—282no—
457C7#2158111yescharacteristic, complemented, Sylow
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22#8980214yes—
465C22C2×C4×C22⋊D711yescharacteristic
466C22C2×#649211yescharacteristic
467C22#9048211yescharacteristic
468C22C2×#649511yescharacteristic
469C22C2×#650511yescharacteristic
470C22#9051311yescharacteristic
471C22C2×#651411yescharacteristic
472C4—22no—
473C4—22no—
474C4—22no—
475C4—22no—
476C4—41no—
477C4—44no—
478C4—44no—
479C4—282no—
480C4—282no—
481C4—561no—
482C4—561no—
483C4C4×#115712yes—
484C4#9017012yes—
485C2—24no—
486C2C4×#649211yescharacteristic
487C2#1173958411yescharacteristic
488C2#1173966511yescharacteristic
489C2C4×#649511yescharacteristic
490C2#1173976011yescharacteristic
491C2C2×#8980211yescharacteristic
492C2#1173989011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C4×C7×C4⋊C4C2
socleC23×C7C22×D4
prime radicalC24×C7C2×D4
cosocleC22×C4×C7C24
hypercenterC2×C4×C4⋊C4D7
hypocenterC7#21581
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
8. #11727235C2semidirect
9. #11727229C2semidirect
10. #11727218C2semidirect
11. #11727212C2semidirect
28. #89742C4semidirect
91. #6384C2×C4semidirect
93. #6381C2×C4semidirect
457. C7#21581semidirect

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×#897422
C4×#64872
#117293132
#117293102
#117293082
#117292832
#117272352
#117272292
#117272182
#117272122
#215817