Finite Group Databasebeta

← #13364940

Subgroups — #13364940

Order 1792.

1092 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#6493C211yesmaximal, characteristic
2C2×#89701C211yesmaximal, characteristic, complemented
3C2×#89510C211yesmaximal, characteristic
4C4×C7×C22⋊C8C211yesmaximal, characteristic, complemented
5#11727717C211yesmaximal, characteristic, complemented
6#11727686C211yesmaximal, characteristic
7#11727682C211yesmaximal, characteristic, complemented
8#11727528C212yesmaximal, complemented
9#11727521C212yesmaximal, complemented
10#11726426C212yesmaximal, complemented
11#11726381C212yesmaximal, complemented
12C23×Dic14C2211yescharacteristic
13C22×C42×C7C2211yescharacteristic
14C2×#6493C2211yescharacteristic
15C2×C4×C22⋊D7—21no—
16C22×C4⋊Dic7C2211yescharacteristic
17C22×#1132C2212yes—
18C2×C4×D28C2211yescharacteristic
19C2×C7×C22⋊C8C2211yescharacteristic
20C2×C7×C22⋊C8C2211yescharacteristic
21C2×C4×C7×C8C2212yes—
22#89985—21no—
23#89984C2211yescharacteristic
24C2×C7⋊#95—21no—
25C2×C7⋊#95—21no—
26C2×#6395C2212yes—
27C2×#6391C2212yes—
28C2×#6390C2212yes—
29C2×#6390C2212yes—
30C2×#6390C2212yes—
31#89712—21no—
32#89711C2211yescharacteristic
33C4×(C2×D7)⋊C4—21no—
34C4×C4⋊Dic7C2211yescharacteristic
35#89701—21no—
36#89701—21no—
37#89701C2212yes—
38#89701C2212yes—
39#89700C2211yescharacteristic
40#89510C418yescomplemented
41C7×#336C2212yes—
42#89346C2212yes—
43#89346C2212yes—
44#22041—71nomaximal, Sylow
45C23×C4×C7D411yescharacteristic
46C23×C4×C7D411yescharacteristic
47C23×C4×C7C2311yescharacteristic
48C22×C22⋊D7—21no—
49C23×Dic7—21no—
50C23×Dic7—21no—
51C22×D28C2311yescharacteristic
52C22×C4×D7—21no—
53C22×Dic14—21no—
54C22×Dic14—22no—
55C22×Dic14—42no—
56C22×Dic14—42no—
57C22×Dic14C2×C414yescomplemented
58C22×Dic14C2312yes—
59C22×C7×C8C2312yes—
60C22×C7×C8C2312yes—
61C2×C42×C7—42no—
62C2×C42×C7D411yescharacteristic
63C2×C42×C7D411yescharacteristic
64C2×C42×C7C2311yescharacteristic
65C2×C42×C7C2311yescharacteristic
66C2×C22⋊Dic7—21no—
67#6493—22no—
68#6493C2×C414yes—
69C4×C22⋊D7—44no—
70C2×(C2×D7)⋊C4—21no—
71C2×(C2×D7)⋊C4—21no—
72C2×(C2×D7)⋊C4—21no—
73C2×(C2×D7)⋊C4—21no—
74C2×C4⋊Dic7—21no—
75C2×C4⋊Dic7—42no—
76C2×C4⋊Dic7C2311yescharacteristic
77C2×C4⋊Dic7C2312yes—
78C2×C4⋊Dic7C2311yescharacteristic
79C2×C4⋊Dic7C2311yescharacteristic
80C2×Dic7⋊C4—21no—
81C2×C4×Dic7—21no—
82C2×#1132—42no—
83C2×#1132—42no—
84C2×#1132C2×C418yescomplemented
85C4×D28—42no—
86C7×C22⋊C8—22no—
87C7×C22⋊C8C2×C414yescomplemented
88C4×C7×C8—42no—
89C7⋊#95—21no—
90C7⋊#95—22no—
91C7⋊#95—22no—
92C7⋊#95—22no—
93C7⋊#95—22no—
94C7⋊#95—21no—
95C7⋊#95—21no—
96#6395—42no—
97#6391—42no—
98#6390—42no—
99#6390—42no—
100#6390C2×C418yescomplemented
101C2×#448—71no—
102C4×#121—71no—
103C2×#391—71no—
104#1968—72no—
105#1933—72no—
106#1927—72no—
107#1877—72no—
108#1874—71no—
109#1853—71no—
110#1787—71no—
111C4×C22⋊C8D711yescharacteristic, complemented
112C24×C7C2×D411yescharacteristic
113C23×D7—21no—
114C22×C4×C7—22no—
115C22×C4×C7—22no—
116C22×C4×C7—22no—
117C22×C4×C7—22no—
118C22×C4×C7—41no—
119C22×C4×C7—41no—
120C22×C4×C7—41no—
121C22×C4×C7SD1614yescomplemented
122C22×C4×C7C22×C412yes—
123C22×C4×C7C2×D411yescharacteristic
124C22×C4×C7C2×D411yescharacteristic
125C22×C4×C7C2×D411yescharacteristic
126C22×C4×C7C2×D411yescharacteristic
127C22×C4×C7C2×D411yescharacteristic
128C22×C4×C7#4112yes—
129C22×C4×C7C2411yescharacteristic
130C2×C22⋊D7—24no—
131C2×C22⋊D7—42no—
132C2×C22⋊D7—42no—
133C22×Dic7—24no—
134C22×Dic7—22no—
135C22×Dic7—21no—
136C22×Dic7—22no—
137C22×Dic7—21no—
138C22×Dic7—21no—
139C22×Dic7—42no—
140C22×Dic7—42no—
141C22×Dic7—42no—
142C22×Dic7—42no—
143C22×Dic7—42no—
144C2×D28—22no—
145C2×D28—22no—
146C2×D28—21no—
147C2×D28C22×C412yes—
148C2×C4×D7—42no—
149C2×C4×D7—42no—
150C2×C4×D7—42no—
151C2×Dic14—22no—
152C2×Dic14—22no—
153C2×Dic14—22no—
154C2×Dic14—22no—
155C2×Dic14—24no—
156C2×Dic14—22no—
157C2×Dic14—48no—
158C2×Dic14—42no—
159C2×Dic14—42no—
160C2×Dic14—48no—
161C2×Dic14C22×C414yes—
162C2×C7×C8—22no—
163C2×C7×C8—22no—
164C2×C7×C8—22no—
165C2×C7×C8—22no—
166C2×C7×C8—22no—
167C2×C7×C8C22×C414yes—
168C42×C7—22no—
169C42×C7—22no—
170C42×C7—41no—
171C42×C7—41no—
172C22⋊Dic7—42no—
173(C2×D7)⋊C4—24no—
174(C2×D7)⋊C4—42no—
175(C2×D7)⋊C4—42no—
176(C2×D7)⋊C4—42no—
177C4⋊Dic7—21no—
178C4⋊Dic7—22no—
179C4⋊Dic7—22no—
180C4⋊Dic7—22no—
181C4⋊Dic7—22no—
182C4⋊Dic7—42no—
183C4⋊Dic7C22×C412yes—
184Dic7⋊C4—42no—
185C4×Dic7—42no—
186#1132—48no—
187C23×Q8—71no—
188C22×SD16—72no—
189C2×#121—71no—
190C2×C4×D4—71no—
191C2×C4×D4—141no—
192C22×C4⋊C4—71no—
193C22×C42C2×D711yescharacteristic
194#448—78no—
195C2×#106—72no—
196C2×#103—72no—
197C2×#103—72no—
198C2×#103—72no—
199C2×#102—72no—
200C2×C22⋊C8C2×D711yescharacteristic
201C2×C22⋊C8C2×D711yescharacteristic
202C2×C4×C8C2×D712yes—
203#391—72no—
204#391—72no—
205#391—141no—
206#391—141no—
207#390—71no—
208#389—71no—
209#388—141no—
210#386—141no—
211#380—71no—
212C4×C4⋊C4—71no—
213C4×C22⋊C4—141no—
214C2×#95—141no—
215C2×#95—141no—
216#340—72no—
217#340—72no—
218#336C2×D712yes—
219C23×C7—21no—
220C23×C7—21no—
221C23×C7—21no—
222C23×C7—21no—
223C23×C7C4×D412yes—
224C23×C7C2×SD1612yes—
225C23×C7#13512yes—
226C23×C7C22×D411yescharacteristic
227C22×D7—22no—
228C22×D7—41no—
229C22×D7—41no—
230C22×D7—41no—
231C22×D7—41no—
232C22×D7—41no—
233C22×D7—41no—
234C2×C4×C7—21no—
235C2×C4×C7—21no—
236C2×C4×C7—21no—
237C2×C4×C7—21no—
238C2×C4×C7—21no—
239C2×C4×C7—21no—
240C2×C4×C7—21no—
241C2×C4×C7—21no—
242C2×C4×C7—24no—
243C2×C4×C7—24no—
244C2×C4×C7—21no—
245C2×C4×C7—21no—
246C2×C4×C7—21no—
247C2×C4×C7—44no—
248C2×C4×C7—44no—
249C2×C4×C7C4×D412yes—
250C2×C4×C7C2×SD1612yes—
251C2×C4×C7C2×SD1612yes—
252C2×C4×C7#13712yes—
253C2×C4×C7C23×C411yescharacteristic
254C2×C4×C7C2×#4111yescharacteristic
255C2×C4×C7H(5,𝔽2)12yes—
256C2×C4×C7H(5,𝔽2)12yes—
257C22⋊D7—48no—
258C2×Dic7—22no—
259C2×Dic7—24no—
260C2×Dic7—48no—
261C2×Dic7—42no—
262C2×Dic7—42no—
263C2×Dic7—41no—
264C2×Dic7—41no—
265C2×Dic7—41no—
266C2×Dic7—42no—
267C2×Dic7—41no—
268C2×Dic7—41no—
269C2×Dic7—41no—
270C2×Dic7—42no—
271C2×Dic7—41no—
272C2×Dic7—41no—
273C2×Dic7—42no—
274C2×Dic7—84no—
275D28—24no—
276D28—42no—
277C4×D7—84no—
278Dic14—24no—
279Dic14—24no—
280Dic14—48no—
281Dic14—42no—
282Dic14—42no—
283C7×C8—24no—
284C7×C8—42no—
285C22×Q8—74no—
286C22×Q8—72no—
287C22×Q8—141no—
288C22×Q8—142no—
289C22×Q8—282no—
290C22×Q8—282no—
291C22×D4—71no—
292C22×D4—141no—
293C23×C4—141no—
294C23×C4—141no—
295C23×C4—141no—
296C23×C4D2811yescharacteristic
297C23×C4D2811yescharacteristic
298C23×C4C22×D711yescharacteristic
299C2×SD16—78no—
300C2×SD16—282no—
301C2×SD16—282no—
302C22×C8C22×D712yes—
303C22×C8C22×D712yes—
304#121—74no—
305#121—142no—
306C4×D4—282no—
307C4×D4—284no—
308C2×C4⋊C4—71no—
309C2×C4⋊C4—72no—
310C2×C4⋊C4—71no—
311C2×C4⋊C4—71no—
312C2×C4⋊C4—141no—
313C2×C4⋊C4—141no—
314C2×C4⋊C4—282no—
315C2×C22⋊C4—141no—
316C2×C22⋊C4—141no—
317C2×C22⋊C4—141no—
318C2×C22⋊C4—141no—
319C2×C22⋊C4—141no—
320C2×C42—42no—
321C2×C42—141no—
322C2×C42D2811yescharacteristic
323C2×C42D2811yescharacteristic
324C2×C42C22×D711yescharacteristic
325C2×C42C22×D711yescharacteristic
326#106—282no—
327#103—78no—
328#103—282no—
329#103—282no—
330#102—282no—
331C22⋊C8—22no—
332C22⋊C8C4×D714yescomplemented
333C4×C8—42no—
334#95—142no—
335#95—142no—
336#95—142no—
337#95—142no—
338#95—141no—
339#95—141no—
340#95—141no—
341C22×C7—22no—
342C22×C7—22no—
343C22×C7—22no—
344C22×C7—22no—
345C22×C7—22no—
346C22×C7—22no—
347C22×C7C4×SD1614yes—
348C22×C7C2×C4×D411yescharacteristic
349C22×C7#53411yescharacteristic
350C22×C7#53511yescharacteristic
351C22×C7C22×SD1611yescharacteristic
352C22×C7C2×#13511yescharacteristic
353C22×C7C2×#13711yescharacteristic
354C22×C7#57511yescharacteristic
355C2×D7—42no—
356C2×D7—42no—
357C2×D7—42no—
358C2×D7—81no—
359C2×D7—81no—
360C2×D7—81no—
361C2×D7—81no—
362C4×C7—22no—
363C4×C7—22no—
364C4×C7—22no—
365C4×C7—22no—
366C4×C7—41no—
367C4×C7#51812yes—
368C4×C7#53812yes—
369Dic7—44no—
370Dic7—42no—
371Dic7—81no—
372Dic7—81no—
373Dic7—82no—
374C24—141no—
375C24C2×D2811yescharacteristic
376C2×Q8—74no—
377C2×Q8—144no—
378C2×Q8—142no—
379C2×Q8—142no—
380C2×Q8—142no—
381C2×Q8—142no—
382C2×Q8—142no—
383C2×Q8—288no—
384C2×Q8—282no—
385C2×Q8—282no—
386C2×Q8—288no—
387C2×D4—72no—
388C2×D4—144no—
389C2×D4—141no—
390C2×D4—142no—
391C2×D4—142no—
392C2×D4—282no—
393C2×D4—282no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—144no—
402C22×C4—142no—
403C22×C4—141no—
404C22×C4—142no—
405C22×C4—141no—
406C22×C4—141no—
407C22×C4—282no—
408C22×C4—282no—
409C22×C4—282no—
410C22×C4—282no—
411C22×C4—282no—
412C22×C4—282no—
413C22×C4—282no—
414C22×C4—282no—
415C22×C4#113214yescomplemented
416C22×C4C2×C4×D712yes—
417C22×C4C2×D2811yescharacteristic
418C22×C4C2×D2811yescharacteristic
419C22×C4C2×D2811yescharacteristic
420C22×C4C2×D2811yescharacteristic
421C22×C4C2×D2811yescharacteristic
422C22×C4#115712yes—
423C22×C4C23×D711yescharacteristic
424SD16—288no—
425C2×C8—22no—
426C2×C8—22no—
427C2×C8—22no—
428C2×C8—22no—
429C2×C8—22no—
430C2×C8C2×C4×D714yes—
431C4⋊C4—72no—
432C4⋊C4—141no—
433C4⋊C4—142no—
434C4⋊C4—142no—
435C4⋊C4—142no—
436C4⋊C4—142no—
437C4⋊C4—282no—
438C4⋊C4—282no—
439C22⋊C4—144no—
440C22⋊C4—282no—
441C22⋊C4—282no—
442C22⋊C4—282no—
443C22⋊C4—282no—
444C42—22no—
445C42—22no—
446C42—41no—
447C42—41no—
448C42—282no—
449C2×C7—24no—
450C2×C7#232111yescharacteristic
451C2×C7C2×C4×SD1611yescharacteristic
452C2×C7C4×#13711yescharacteristic
453C2×C7#318711yescharacteristic
454C2×C7#319011yescharacteristic
455C2×C7#320611yescharacteristic
456C2×C7#321111yescharacteristic
457D7—82no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—142no—
463C23—281no—
464C23—281no—
465C23—281no—
466C23—281no—
467C23—281no—
468C23—281no—
469C23C4×D2812yes—
470C23C2×#113212yes—
471C23#646712yes—
472C23C22×D2811yescharacteristic
473Q8—144no—
474Q8—144no—
475Q8—288no—
476Q8—282no—
477Q8—282no—
478D4—144no—
479D4—288no—
480D4—282no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—44no—
495C2×C4—44no—
496C2×C4—142no—
497C2×C4—144no—
498C2×C4—288no—
499C2×C4—281no—
500C2×C4—281no—
501C2×C4—282no—
502C2×C4—282no—
503C2×C4—281no—
504C2×C4—281no—
505C2×C4—282no—
506C2×C4—281no—
507C2×C4—282no—
508C2×C4—281no—
509C2×C4—281no—
510C2×C4—282no—
511C2×C4—281no—
512C2×C4—564no—
513C2×C4—564no—
514C2×C4C4×D2812yes—
515C2×C4C2×#113212yes—
516C2×C4C2×#113212yes—
517C2×C4#647212yes—
518C2×C4C22×C4×D711yescharacteristic
519C2×C4C2×#115711yescharacteristic
520C2×C4#654812yes—
521C2×C4#655312yes—
522C8—24no—
523C8—42no—
524C7#2204111yescharacteristic, complemented, Sylow
525C22—22no—
526C22—22no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—282no—
532C22—282no—
533C22—282no—
534C22—561no—
535C22—561no—
536C22—561no—
537C22—561no—
538C22C4×#113214yes—
539C22C2×C4×D2811yescharacteristic
540C22#9018411yescharacteristic
541C22#9021611yescharacteristic
542C22C22×#113211yescharacteristic
543C22C2×#646711yescharacteristic
544C22C2×#647211yescharacteristic
545C22#9043911yescharacteristic
546C4—22no—
547C4—22no—
548C4—22no—
549C4—22no—
550C4—41no—
551C4—284no—
552C4—282no—
553C4—562no—
554C4—561no—
555C4—561no—
556C4#9023612yes—
557C4#9025112yes—
558C2—24no—
559C2—562no—
560C2#1173101411yescharacteristic
561C2C2×C4×#113211yescharacteristic
562C2C4×#647211yescharacteristic
563C2#1173605711yescharacteristic
564C2#1173606311yescharacteristic
565C2#1173675211yescharacteristic
566C2#1173675711yescharacteristic
subgroupG/H
centerC23C22×D28
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC4×C7×C22⋊C8C2
socleC23×C7C22×D4
prime radicalC2×#6493C22
cosocleC22×C4×C7C24
hypercenterC4×C22⋊C8D7
hypocenterC7#22041
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#89701C2semidirect
4. C4×C7×C22⋊C8C2semidirect
5. #11727717C2semidirect
7. #11727682C2semidirect
8. #11727528C2semidirect
9. #11727521C2semidirect
10. #11726426C2semidirect
11. #11726381C2semidirect
40. #89510C4semidirect
57. C22×Dic14C2×C4semidirect
84. C2×#1132C2×C4semidirect
87. C7×C22⋊C8C2×C4semidirect
100. #6390C2×C4semidirect
111. C4×C22⋊C8D7semidirect
121. C22×C4×C7SD16semidirect
332. C22⋊C8C4×D7semidirect
415. C22×C4#1132semidirect
524. C7#22041semidirect

Maximal subgroups

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

subgroupindex
C4×#64932
C2×#897012
C2×#895102
C4×C7×C22⋊C82
#117277172
#117276862
#117276822
#117275282
#117275212
#117264262
#117263812
#220417