Finite Group Databasebeta

← #13355429

Subgroups — #13355429

Order 1792.

2126 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#518C211yesmaximal, characteristic, complemented
2C2×#90495C211yesmaximal, characteristic
3C22×#6408C211yesmaximal, characteristic, complemented
4#11739566C212yesmaximal, complemented
5#11729409C214yesmaximal, complemented
6#11729408C214yesmaximal, complemented
7C2×#89321C212yesmaximal, complemented
8C23×C7×D4C2211yescharacteristic
9C23×C22⋊D7C2211yescharacteristic
10C7×#518—22no—
11C7×#518—24no—
12C7×#518C2214yes—
13C2×C4×C7×D4—24no—
14C2×C7×#117—21no—
15C22×C7×C22⋊C4—21no—
16C22×C7×C22⋊C4C2212yes—
17C2×#6516—21no—
18C22×C22⋊Dic7C2212yes—
19C22×C22⋊Dic7C2211yescharacteristic
20#90495—24no—
21#90495C418yescomplemented
22C2×#6502—22no—
23C2×#6500C2212yes—
24C2×#6498C2212yes—
25C2×#6492—21no—
26C2×#6408—24no—
27C2×#6408C2214yes—
28#89985—24no—
29#89730—24no—
30#89727C2214yescomplemented
31#89715C2214yescomplemented
32#89321C2218yescomplemented
33#20960—71nomaximal, Sylow
34C25×C7D411yescharacteristic
35C25×C7C2311yescharacteristic
36C24×D7C2311yescharacteristic
37C22×C7×D4—22no—
38C22×C7×D4—22no—
39C22×C7×D4—24no—
40C22×C7×D4C2×C414yes—
41C22×C7×D4D414yes—
42C22×C7×D4D412yes—
43C22×C7×D4C2312yes—
44C23×C4×C7—22no—
45C23×C4×C7D411yescharacteristic
46C23×C4×C7D414yescomplemented
47C22×C22⋊D7—21no—
48C22×C22⋊D7—21no—
49C22×C22⋊D7—22no—
50C22×C22⋊D7—22no—
51C22×C22⋊D7—22no—
52C22×C22⋊D7—24no—
53C22×C22⋊D7—22no—
54C22×C22⋊D7C2×C414yescomplemented
55C23×Dic7—21no—
56C23×Dic7—22no—
57C23×Dic7C2311yescharacteristic
58C4×C7×D4—216no—
59C4×C7×D4—216no—
60C7×#117—24no—
61C7×#117—24no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C22⋊C4—22no—
64C2×C7×C22⋊C4—24no—
65C2×C7×C22⋊C4—22no—
66C2×C7×C22⋊C4—24no—
67C2×C7×C22⋊C4—22no—
68C2×C7×C22⋊C4—22no—
69C2×C7×C22⋊C4—22no—
70C2×C7×C22⋊C4D414yescomplemented
71C2×C7×C22⋊C4C2314yes—
72C2×C42×C7—22no—
73#6516—28no—
74C2×C22⋊Dic7—21no—
75C2×C22⋊Dic7—22no—
76C2×C22⋊Dic7—22no—
77C2×C22⋊Dic7—24no—
78C2×C22⋊Dic7—24no—
79C2×C22⋊Dic7—22no—
80C2×C22⋊Dic7C2×C414yescomplemented
81C2×C22⋊Dic7C2314yes—
82C2×C22⋊Dic7C2312yes—
83#6502—216no—
84#6500—24no—
85#6500C2×C418yescomplemented
86#6498—24no—
87#6498C2×C418yescomplemented
88#6492—28no—
89C2×(C2×D7)⋊C4—22no—
90C2×(C2×D7)⋊C4—28no—
91C2×Dic7⋊C4—22no—
92#6408—28no—
93C7⋊#95—28no—
94C2×#534—71no—
95C2×#518D711yescharacteristic, complemented
96C22×#99—71no—
97#2308—72no—
98#1890—74no—
99#1889—74no—
100C2×#342—72no—
101C24×C7—21no—
102C24×C7—21no—
103C24×C7—22no—
104C24×C7—82no—
105C24×C7—82no—
106C24×C7C22⋊C414yescomplemented
107C24×C7C22×C412yes—
108C24×C7C2×D412yes—
109C24×C7C2×D411yescharacteristic
110C24×C7C2×D411yescharacteristic
111C24×C7C2×D412yes—
112C24×C7C2×D412yes—
113C24×C7C2×D412yes—
114C24×C7#4114yes—
115C24×C7C2411yescharacteristic
116C23×D7—22no—
117C23×D7—21no—
118C23×D7—21no—
119C23×D7—22no—
120C23×D7—82no—
121C23×D7C22×C412yescomplemented
122C2×C7×D4—28no—
123C2×C7×D4—28no—
124C2×C7×D4—24no—
125C2×C7×D4—28no—
126C2×C7×D4—28no—
127C2×C7×D4—24no—
128C2×C7×D4—24no—
129C2×C7×D4—24no—
130C2×C7×D4C22⋊C418yescomplemented
131C2×C7×D4C22×C414yes—
132C2×C7×D4C2×D414yes—
133C22×C4×C7—21no—
134C22×C4×C7—21no—
135C22×C4×C7—22no—
136C22×C4×C7—24no—
137C22×C4×C7—28no—
138C22×C4×C7—24no—
139C22×C4×C7—84no—
140C22×C4×C7—84no—
141C22×C4×C7C22⋊C414yescomplemented
142C22×C4×C7C2×D412yes—
143C22×C4×C7C2×D418yes—
144C2×C22⋊D7—24no—
145C2×C22⋊D7—24no—
146C2×C22⋊D7—28no—
147C2×C22⋊D7—28no—
148C2×C22⋊D7—28no—
149C2×C22⋊D7—41no—
150C2×C22⋊D7—42no—
151C2×C22⋊D7—41no—
152C2×C22⋊D7—44no—
153C2×C22⋊D7—44no—
154C2×C22⋊D7—42no—
155C2×C22⋊D7—42no—
156C2×C22⋊D7—84no—
157C22×Dic7—22no—
158C22×Dic7—21no—
159C22×Dic7—22no—
160C22×Dic7—21no—
161C22×Dic7—22no—
162C22×Dic7—24no—
163C22×Dic7—24no—
164C22×Dic7—44no—
165C22×Dic7—82no—
166C22×Dic7—84no—
167C22×Dic7C22×C412yescomplemented
168C7×C4⋊C4—28no—
169C7×C22⋊C4—28no—
170C7×C22⋊C4—24no—
171C7×C22⋊C4—24no—
172C7×C22⋊C4—24no—
173C7×C22⋊C4—24no—
174C42×C7—28no—
175C22⋊Dic7—24no—
176C22⋊Dic7—28no—
177C22⋊Dic7—22no—
178C22⋊Dic7—24no—
179C22⋊Dic7—24no—
180C22⋊Dic7—44no—
181C22⋊Dic7C22×C414yescomplemented
182(C2×D7)⋊C4—28no—
183(C2×D7)⋊C4—88no—
184Dic7⋊C4—28no—
185C23×D4—71no—
186C23×D4C2×D711yescharacteristic
187#534—78no—
188#534—144no—
189C2×#123—72no—
190C2×#123—141no—
191C2×#121—142no—
192C2×#120—72no—
193C2×#120—141no—
194#518—22no—
195#518—24no—
196#518C2×D714yes—
197C2×C4×D4—24no—
198C2×#117—21no—
199C22×C22⋊C4—21no—
200C22×C22⋊C4—71no—
201C22×C22⋊C4—72no—
202C22×C22⋊C4C2×D712yes—
203C2×#99—74no—
204C2×#99—144no—
205#386—144no—
206#386—144no—
207#381—74no—
208#379—74no—
209#342—78no—
210C23×C7—22no—
211C23×C7—24no—
212C23×C7—22no—
213C23×C7—24no—
214C23×C7—44no—
215C23×C7—42no—
216C23×C7—44no—
217C23×C7—42no—
218C23×C7—42no—
219C23×C7—44no—
220C23×C7—44no—
221C23×C7—82no—
222C23×C7—82no—
223C23×C7—82no—
224C23×C7—84no—
225C23×C7—84no—
226C23×C7—84no—
227C23×C7C2×C22⋊C414yes—
228C23×C7C2×C22⋊C412yes—
229C23×C7C2×C22⋊C412yes—
230C23×C7C4×D414yes—
231C23×C7C4×D414yes—
232C23×C7#12011yescharacteristic
233C23×C7#12012yes—
234C23×C7#12011yescharacteristic
235C23×C7#12114yes—
236C23×C7#12114yes—
237C23×C7#12312yes—
238C23×C7#12312yes—
239C23×C7C23×C411yescharacteristic
240C23×C7C22×D411yescharacteristic
241C23×C7C22×D411yescharacteristic
242C23×C7C22×D412yes—
243C23×C7C2×#4112yes—
244C22×D7—22no—
245C22×D7—24no—
246C22×D7—48no—
247C22×D7—44no—
248C22×D7—41no—
249C22×D7—42no—
250C22×D7—41no—
251C22×D7—82no—
252C22×D7—82no—
253C22×D7—84no—
254C7×D4—28no—
255C7×D4—28no—
256C7×D4—216no—
257C2×C4×C7—22no—
258C2×C4×C7—22no—
259C2×C4×C7—24no—
260C2×C4×C7—24no—
261C2×C4×C7—28no—
262C2×C4×C7—48no—
263C2×C4×C7—48no—
264C2×C4×C7—84no—
265C2×C4×C7—88no—
266C2×C4×C7C2×C22⋊C414yes—
267C22⋊D7—44no—
268C22⋊D7—44no—
269C22⋊D7—48no—
270C22⋊D7—88no—
271C2×Dic7—22no—
272C2×Dic7—24no—
273C2×Dic7—24no—
274C2×Dic7—44no—
275C2×Dic7—41no—
276C2×Dic7—42no—
277C2×Dic7—41no—
278C2×Dic7—48no—
279C2×Dic7—44no—
280C2×Dic7—84no—
281C2×Dic7—88no—
282C25—71no—
283C25C22⋊D711yescharacteristic
284C25C22×D711yescharacteristic
285C22×D4—24no—
286C22×D4—22no—
287C22×D4—22no—
288C22×D4—74no—
289C22×D4—142no—
290C22×D4—144no—
291C22×D4—141no—
292C22×D4—141no—
293C22×D4—142no—
294C22×D4—142no—
295C22×D4—142no—
296C22×D4C4×D714yes—
297C22×D4D2814yes—
298C22×D4C22⋊D712yes—
299C22×D4C22×D712yes—
300C23×C4—22no—
301C23×C4—71no—
302C23×C4—141no—
303C23×C4—142no—
304C23×C4C22⋊D711yescharacteristic
305C23×C4C22⋊D714yescomplemented
306#123—78no—
307#123—144no—
308#123—148no—
309#121—1416no—
310#120—78no—
311#120—148no—
312#120—144no—
313C4×D4—216no—
314C4×D4—216no—
315#117—24no—
316#117—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—142no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—74no—
327C2×C22⋊C4—72no—
328C2×C22⋊C4—74no—
329C2×C22⋊C4—142no—
330C2×C22⋊C4—141no—
331C2×C22⋊C4—142no—
332C2×C22⋊C4—142no—
333C2×C22⋊C4—144no—
334C2×C22⋊C4—144no—
335C2×C22⋊C4—142no—
336C2×C22⋊C4—148no—
337C2×C22⋊C4C22⋊D714yescomplemented
338C2×C22⋊C4C22×D714yes—
339C2×C42—22no—
340#99—148no—
341#95—148no—
342C22×C7—24no—
343C22×C7—22no—
344C22×C7—22no—
345C22×C7—24no—
346C22×C7—22no—
347C22×C7—24no—
348C22×C7—42no—
349C22×C7—44no—
350C22×C7—41no—
351C22×C7—41no—
352C22×C7—42no—
353C22×C7—42no—
354C22×C7—42no—
355C22×C7—44no—
356C22×C7—44no—
357C22×C7—44no—
358C22×C7—42no—
359C22×C7—44no—
360C22×C7—48no—
361C22×C7—44no—
362C22×C7—82no—
363C22×C7—84no—
364C22×C7#38612yes—
365C22×C7#38612yes—
366C22×C7#38614yes—
367C22×C7C22×C22⋊C411yescharacteristic
368C22×C7C2×C4×D412yes—
369C22×C7C2×#12011yescharacteristic
370C22×C7C2×#12112yes—
371C22×C7C2×#12311yescharacteristic
372C2×D7—44no—
373C2×D7—48no—
374C2×D7—42no—
375C2×D7—84no—
376C2×D7—82no—
377C2×D7—82no—
378C4×C7—24no—
379C4×C7—48no—
380Dic7—44no—
381Dic7—42no—
382Dic7—84no—
383C24—21no—
384C24—22no—
385C24—21no—
386C24—72no—
387C24—82no—
388C24—82no—
389C24—142no—
390C24—141no—
391C24—141no—
392C24—142no—
393C24—562no—
394C24(C2×D7)⋊C414yescomplemented
395C24C2×C4×D712yes—
396C24C2×D2812yes—
397C24#115714yes—
398C24C2×C22⋊D712yes—
399C24C2×C22⋊D711yescharacteristic
400C24C2×C22⋊D711yescharacteristic
401C24C2×C22⋊D712yes—
402C24C2×C22⋊D712yes—
403C24C23×D711yescharacteristic
404C2×D4—28no—
405C2×D4—28no—
406C2×D4—24no—
407C2×D4—28no—
408C2×D4—28no—
409C2×D4—24no—
410C2×D4—24no—
411C2×D4—24no—
412C2×D4—144no—
413C2×D4—144no—
414C2×D4—148no—
415C2×D4—148no—
416C2×D4—148no—
417C2×D4—282no—
418C2×D4—282no—
419C2×D4—284no—
420C2×D4—284no—
421C2×D4—281no—
422C2×D4—282no—
423C2×D4—281no—
424C2×D4—564no—
425C2×D4(C2×D7)⋊C418yescomplemented
426C2×D4C2×C4×D714yes—
427C2×D4C2×D2814yes—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—24no—
432C22×C4—28no—
433C22×C4—24no—
434C22×C4—72no—
435C22×C4—84no—
436C22×C4—84no—
437C22×C4—141no—
438C22×C4—142no—
439C22×C4—142no—
440C22×C4—142no—
441C22×C4—141no—
442C22×C4—144no—
443C22×C4—144no—
444C22×C4—284no—
445C22×C4—562no—
446C22×C4—564no—
447C22×C4(C2×D7)⋊C414yescomplemented
448C22×C4C2×C22⋊D712yes—
449C22×C4C2×C22⋊D718yes—
450C4⋊C4—28no—
451C4⋊C4—148no—
452C22⋊C4—28no—
453C22⋊C4—24no—
454C22⋊C4—24no—
455C22⋊C4—24no—
456C22⋊C4—24no—
457C22⋊C4—74no—
458C22⋊C4—144no—
459C22⋊C4—148no—
460C22⋊C4—142no—
461C22⋊C4—148no—
462C22⋊C4—144no—
463C22⋊C4—144no—
464C22⋊C4—284no—
465C22⋊C4—568no—
466C42—28no—
467C2×C7—21no—
468C2×C7—22no—
469C2×C7—22no—
470C2×C7—21no—
471C2×C7—22no—
472C2×C7—22no—
473C2×C7—24no—
474C2×C7—44no—
475C2×C7C2×#38611yescharacteristic
476C2×C7#302612yes—
477D7—82no—
478C23—24no—
479C23—22no—
480C23—22no—
481C23—24no—
482C23—44no—
483C23—44no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—44no—
488C23—44no—
489C23—82no—
490C23—82no—
491C23—82no—
492C23—84no—
493C23—84no—
494C23—84no—
495C23—142no—
496C23—144no—
497C23—288no—
498C23—284no—
499C23—281no—
500C23—282no—
501C23—281no—
502C23—562no—
503C23—562no—
504C23—564no—
505C23C2×(C2×D7)⋊C414yes—
506C23C2×(C2×D7)⋊C412yes—
507C23C2×(C2×D7)⋊C412yes—
508C23C4×C22⋊D714yes—
509C23C4×C22⋊D714yes—
510C23#649212yes—
511C23#649212yes—
512C23#649314yes—
513C23#649314yes—
514C23#651611yescharacteristic
515C23#651612yes—
516C23#651611yescharacteristic
517C23C22×C4×D711yescharacteristic
518C23C22×D2811yescharacteristic
519C23C2×#115712yes—
520C23C22×C22⋊D711yescharacteristic
521C23C22×C22⋊D712yes—
522D4—28no—
523D4—28no—
524D4—216no—
525D4—284no—
526D4—284no—
527D4—288no—
528D4—568no—
529C2×C4—22no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—28no—
534C2×C4—48no—
535C2×C4—48no—
536C2×C4—84no—
537C2×C4—88no—
538C2×C4—144no—
539C2×C4—142no—
540C2×C4—144no—
541C2×C4—284no—
542C2×C4—281no—
543C2×C4—282no—
544C2×C4—281no—
545C2×C4—288no—
546C2×C4—284no—
547C2×C4—564no—
548C2×C4—568no—
549C2×C4C2×(C2×D7)⋊C414yes—
550C7#2096011yescharacteristic, complemented, Sylow
551C22—22no—
552C22—24no—
553C22—24no—
554C22—22no—
555C22—22no—
556C22—24no—
557C22—42no—
558C22—44no—
559C22—42no—
560C22—42no—
561C22—41no—
562C22—41no—
563C22—42no—
564C22—44no—
565C22—44no—
566C22—42no—
567C22—44no—
568C22—44no—
569C22—48no—
570C22—44no—
571C22—82no—
572C22—84no—
573C22—284no—
574C22—288no—
575C22—282no—
576C22—564no—
577C22—562no—
578C22—562no—
579C22#8998512yes—
580C22#8998512yes—
581C22#8998514yes—
582C22C22×(C2×D7)⋊C411yescharacteristic
583C22C2×C4×C22⋊D712yes—
584C22C2×#649211yescharacteristic
585C22C2×#649312yes—
586C22C2×#651611yescharacteristic
587C4—24no—
588C4—48no—
589C4—284no—
590C4—282no—
591C4—564no—
592C2—21no—
593C2—22no—
594C2—22no—
595C2—21no—
596C2—22no—
597C2—22no—
598C2—24no—
599C2—44no—
600C2—562no—
601C2C2×#8998511yescharacteristic
602C2#1174155512yes—
subgroupG/H
centerC22C2×#6516
commutatorC23×C7C23×C4
FrattiniC24C23×D7
FittingC2×C7×#518C2
socleC22×C7C2×#120
prime radicalC2×#90495C2
cosocleC24×C7C24
hypercenterC2×#518D7
hypocenterC7#20960
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C25 ◁ C2×#518

Complements

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

NH ≅ G/Ntype
1. C2×C7×#518C2semidirect
3. C22×#6408C2semidirect
4. #11739566C2semidirect
5. #11729409C2semidirect
6. #11729408C2semidirect
7. C2×#89321C2semidirect
21. #90495C4semidirect
30. #89727C22semidirect
31. #89715C22semidirect
32. #89321C22semidirect
46. C23×C4×C7D4semidirect
54. C22×C22⋊D7C2×C4semidirect
70. C2×C7×C22⋊C4D4semidirect
80. C2×C22⋊Dic7C2×C4semidirect
85. #6500C2×C4semidirect
87. #6498C2×C4semidirect
95. C2×#518D7semidirect
106. C24×C7C22⋊C4semidirect
121. C23×D7C22×C4semidirect
130. C2×C7×D4C22⋊C4semidirect
141. C22×C4×C7C22⋊C4semidirect
167. C22×Dic7C22×C4semidirect
181. C22⋊Dic7C22×C4semidirect
305. C23×C4C22⋊D7semidirect
337. C2×C22⋊C4C22⋊D7semidirect
394. C24(C2×D7)⋊C4semidirect
425. C2×D4(C2×D7)⋊C4semidirect
447. C22×C4(C2×D7)⋊C4semidirect
550. C7#20960semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5182
C2×#904952
C22×#64082
#117395662
#117294092
#117294082
C2×#893212
#209607