Finite Group Databasebeta

← #13405998

Subgroups — #13405998

Order 1792.

1194 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#533C211yesmaximal, characteristic, complemented
2C2×#89820C212yesmaximal
3#11739525C211yesmaximal, characteristic
4#11729546C211yesmaximal, characteristic, complemented
5#11729545C211yesmaximal, characteristic, complemented
6#11729537C211yesmaximal, characteristic, complemented
7#11729535C211yesmaximal, characteristic, complemented
8#11729450C212yesmaximal, complemented
9#11729387C212yesmaximal, complemented
10#11729383C212yesmaximal, complemented
11C2×#89319C211yesmaximal, characteristic, complemented
12C7×#533—28no—
13C2×C7×C4⋊Q8C2211yescharacteristic
14C2×C7×C4⋊Q8C2211yescharacteristic
15C2×C7×#125—21no—
16C2×C7×C22⋊Q8—21no—
17C2×C7×C22⋊Q8C2212yes—
18C2×C4×C7×Q8—21no—
19C2×C4×C7×Q8C2212yes—
20C2×C7×#117—21no—
21C22×C42×C7C2211yescharacteristic
22C22×#1143C2212yes—
23C2×#6493C2211yescharacteristic
24C2×#6492—21no—
25C23×C7⋊C8C2212yes—
26C2×#6409C2212yes—
27C2×#6409C2212yes—
28C2×#6409C2212yes—
29#89985—21no—
30#89984C2211yescharacteristic
31#89820—28no—
32C2×#6383C2212yes—
33C2×#6382C2212yes—
34#89712—21no—
35#89712—21no—
36#89711C2211yescharacteristic
37#89711C2211yescharacteristic
38#89700C2211yescharacteristic
39#89700C2211yescharacteristic
40#89324C2212yes—
41#89324C2212yes—
42#89319C2211yescharacteristic
43#89319C2211yescharacteristic
44#89319C2212yes—
45#25497—71nomaximal, Sylow
46C22×C7×Q8—21no—
47C22×C7×Q8C2312yes—
48C23×C4×C7D411yescharacteristic
49C23×C4×C7D411yescharacteristic
50C23×C4×C7C2311yescharacteristic
51C22×C22⋊D7—21no—
52C22×D28C2311yescharacteristic
53C7×C4⋊Q8—24no—
54C7×C4⋊Q8—24no—
55C7×#125—28no—
56C7×C22⋊Q8—28no—
57C7×C22⋊Q8—24no—
58C7×C22⋊Q8D418yes—
59C4×C7×Q8—28no—
60C4×C7×Q8—24no—
61C4×C7×Q8—24no—
62C7×#117—28no—
63C2×C7×C4⋊C4—21no—
64C2×C7×C4⋊C4—21no—
65C2×C7×C4⋊C4—21no—
66C2×C7×C4⋊C4—22no—
67C2×C7×C4⋊C4—22no—
68C2×C7×C4⋊C4C2312yes—
69C2×C7×C22⋊C4—22no—
70C2×C42×C7—24no—
71C2×C42×C7—22no—
72C2×C42×C7D411yescharacteristic
73C2×C42×C7D411yescharacteristic
74C2×C42×C7C2311yescharacteristic
75C2×C42×C7C2311yescharacteristic
76C2×C22⋊Dic7—21no—
77C2×#1143—24no—
78C2×#1143—24no—
79C2×#1143—42no—
80#6493—24no—
81#6492—44no—
82C2×(C2×D7)⋊C4—21no—
83C2×(C2×D7)⋊C4—21no—
84C2×(C2×D7)⋊C4—21no—
85C2×(C2×D7)⋊C4—21no—
86C2×(C2×D7)⋊C4—21no—
87C2×C4⋊Dic7C2311yescharacteristic
88C2×C4⋊Dic7C2311yescharacteristic
89C2×C4⋊Dic7C2311yescharacteristic
90C2×Dic7⋊C4—21no—
91C2×Dic7⋊C4—21no—
92C22×C7⋊C8—24no—
93C22×C7⋊C8—24no—
94C22×C7⋊C8—42no—
95C22×C7⋊C8C2312yes—
96C22×C7⋊C8C2312yes—
97#6409—24no—
98#6409—24no—
99#6409—42no—
100C7⋊#95—21no—
101C7⋊#95—21no—
102C7⋊#95—21no—
103#6383—24no—
104#6382—24no—
105C2×#533D711yescharacteristic, complemented
106C2×#465—72no—
107#2854—71no—
108#2058—71no—
109#2043—71no—
110#2023—71no—
111#2013—71no—
112#1892—72no—
113#1880—72no—
114#1865—72no—
115C2×#336—71no—
116C24×C7C2×D411yescharacteristic
117C23×D7—21no—
118C2×C7×Q8—24no—
119C2×C7×Q8—22no—
120C2×C7×Q8—22no—
121C2×C7×Q8—22no—
122C2×C7×Q8—22no—
123C2×C7×Q8—22no—
124C2×C7×Q8—42no—
125C2×C7×Q8—42no—
126C2×C7×Q8C2×D414yes—
127C22×C4×C7—22no—
128C22×C4×C7—22no—
129C22×C4×C7—22no—
130C22×C4×C7—21no—
131C22×C4×C7—21no—
132C22×C4×C7—22no—
133C22×C4×C7—22no—
134C22×C4×C7—22no—
135C22×C4×C7—22no—
136C22×C4×C7—41no—
137C22×C4×C7SD1614yescomplemented
138C22×C4×C7C2×D411yescharacteristic
139C22×C4×C7C2×D411yescharacteristic
140C22×C4×C7C2×D414yes—
141C22×C4×C7C2×D411yescharacteristic
142C22×C4×C7C2×D411yescharacteristic
143C22×C4×C7C2×D411yescharacteristic
144C22×C4×C7C2411yescharacteristic
145C2×C22⋊D7—42no—
146C2×C22⋊D7—42no—
147C2×C22⋊D7—42no—
148C22×Dic7—21no—
149C22×Dic7—21no—
150C22×Dic7—21no—
151C2×D28—22no—
152C2×D28—22no—
153C2×D28—21no—
154C2×D28—21no—
155C7×C4⋊C4—24no—
156C7×C4⋊C4—24no—
157C7×C4⋊C4—28no—
158C7×C4⋊C4—24no—
159C7×C4⋊C4—28no—
160C7×C4⋊C4—22no—
161C7×C4⋊C4C2×D414yes—
162C7×C22⋊C4—28no—
163C42×C7—28no—
164C42×C7—22no—
165C42×C7—22no—
166C42×C7—22no—
167C42×C7—22no—
168C22⋊Dic7—42no—
169#1143—48no—
170(C2×D7)⋊C4—42no—
171(C2×D7)⋊C4—42no—
172(C2×D7)⋊C4—42no—
173(C2×D7)⋊C4—42no—
174(C2×D7)⋊C4—42no—
175C4⋊Dic7—22no—
176C4⋊Dic7—22no—
177C4⋊Dic7—21no—
178C4⋊Dic7—21no—
179Dic7⋊C4—42no—
180Dic7⋊C4—42no—
181C2×C7⋊C8—22no—
182C2×C7⋊C8—22no—
183C2×C7⋊C8—22no—
184C2×C7⋊C8—22no—
185C2×C7⋊C8—22no—
186C2×C7⋊C8—48no—
187C2×C7⋊C8#4114yes—
188C22×SD16—72no—
189C23×C8—72no—
190#533—28no—
191C2×C4⋊Q8C2×D711yescharacteristic
192C2×C4⋊Q8C2×D711yescharacteristic
193C2×#125—21no—
194C2×#123—141no—
195C2×C22⋊Q8—21no—
196C2×C22⋊Q8C2×D712yes—
197C2×#121—71no—
198C2×C4×Q8—21no—
199C2×C4×Q8C2×D712yes—
200C2×#117—21no—
201C22×C42C2×D711yescharacteristic
202#465—148no—
203C2×#106—72no—
204C2×#103—72no—
205C2×#103—72no—
206C2×#103—72no—
207C2×#102—72no—
208#390—71no—
209#390—71no—
210#389—71no—
211#389—71no—
212#388—141no—
213#388—141no—
214#386—141no—
215#380—71no—
216#340—72no—
217#340—72no—
218#336—71no—
219#336—72no—
220#336—71no—
221C23×C7—21no—
222C23×C7—21no—
223C23×C7—21no—
224C23×C7—21no—
225C23×C7#12012yes—
226C23×C7C2×SD1612yes—
227C23×C7#13712yes—
228C23×C7C22×D411yescharacteristic
229C22×D7—41no—
230C22×D7—41no—
231C22×D7—41no—
232C22×D7—41no—
233C22×D7—41no—
234C22×D7—41no—
235C22×D7—41no—
236C7×Q8—24no—
237C7×Q8—24no—
238C7×Q8—48no—
239C7×Q8—42no—
240C7×Q8—42no—
241C2×C4×C7—21no—
242C2×C4×C7—21no—
243C2×C4×C7—21no—
244C2×C4×C7—21no—
245C2×C4×C7—21no—
246C2×C4×C7—21no—
247C2×C4×C7—21no—
248C2×C4×C7—21no—
249C2×C4×C7—28no—
250C2×C4×C7—24no—
251C2×C4×C7—24no—
252C2×C4×C7—21no—
253C2×C4×C7—24no—
254C2×C4×C7—24no—
255C2×C4×C7—21no—
256C2×C4×C7—21no—
257C2×C4×C7—44no—
258C2×C4×C7—42no—
259C2×C4×C7—42no—
260C2×C4×C7—42no—
261C2×C4×C7—42no—
262C2×C4×C7#12012yes—
263C2×C4×C7C2×SD1612yes—
264C2×C4×C7C2×SD1612yes—
265C2×C4×C7#13512yes—
266C2×C4×C7C22×D412yes—
267C2×C4×C7C2×#4112yes—
268C2×C4×C7H(5,𝔽2)11yescharacteristic
269C2×C4×C72−1+411yescharacteristic
270C22⋊D7—84no—
271C2×Dic7—41no—
272C2×Dic7—41no—
273C2×Dic7—41no—
274C2×Dic7—41no—
275C2×Dic7—41no—
276C2×Dic7—41no—
277C2×Dic7—41no—
278C2×Dic7—41no—
279C2×Dic7—41no—
280D28—42no—
281D28—42no—
282C7⋊C8—24no—
283C7⋊C8—42no—
284C22×Q8—21no—
285C22×Q8C22×D712yes—
286C22×D4—71no—
287C22×D4—141no—
288C23×C4C22⋊D711yescharacteristic
289C23×C4C22⋊D711yescharacteristic
290C23×C4C22×D711yescharacteristic
291C2×SD16—144no—
292C2×SD16—144no—
293C2×SD16—282no—
294C22×C8—72no—
295C22×C8—72no—
296C22×C8—144no—
297C22×C8—144no—
298C22×C8—282no—
299C4⋊Q8—24no—
300C4⋊Q8—24no—
301#125—28no—
302#123—284no—
303C22⋊Q8—28no—
304C22⋊Q8—24no—
305C22⋊Q8C22⋊D718yes—
306#121—144no—
307C4×Q8—28no—
308C4×Q8—24no—
309C4×Q8—24no—
310#117—28no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—71no—
317C2×C4⋊C4—71no—
318C2×C4⋊C4—71no—
319C2×C4⋊C4—141no—
320C2×C4⋊C4—141no—
321C2×C4⋊C4C22×D712yes—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—141no—
324C2×C22⋊C4—141no—
325C2×C22⋊C4—141no—
326C2×C22⋊C4—141no—
327C2×C22⋊C4—141no—
328C2×C22⋊C4—141no—
329C2×C42—22no—
330C2×C42—24no—
331C2×C42C22⋊D711yescharacteristic
332C2×C42C22⋊D711yescharacteristic
333C2×C42C22×D711yescharacteristic
334C2×C42C22×D711yescharacteristic
335#106—144no—
336#103—144no—
337#103—144no—
338#103—282no—
339#102—144no—
340#95—141no—
341#95—141no—
342#95—141no—
343C22×C7—22no—
344C22×C7—22no—
345C22×C7—22no—
346C22×C7—22no—
347C22×C7—22no—
348C22×C7—22no—
349C22×C7#44814yes—
350C22×C7C2×#12011yescharacteristic
351C22×C7#53211yescharacteristic
352C22×C7#53711yescharacteristic
353C22×C7C22×SD1611yescharacteristic
354C22×C7C2×#13511yescharacteristic
355C22×C7C2×#13711yescharacteristic
356C22×C7#57511yescharacteristic
357C2×D7—81no—
358C2×D7—81no—
359C2×D7—81no—
360C2×D7—81no—
361C2×D7—81no—
362C2×D7—81no—
363C2×D7—81no—
364C4×C7—22no—
365C4×C7—22no—
366C4×C7—22no—
367C4×C7—22no—
368C4×C7—44no—
369C4×C7—41no—
370C4×C7—44no—
371C4×C7#54612yes—
372C4×C7#54712yes—
373Dic7—81no—
374Dic7—81no—
375Dic7—81no—
376C24—141no—
377C24C2×C22⋊D711yescharacteristic
378C2×Q8—24no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—42no—
385C2×Q8—42no—
386C2×Q8C2×C22⋊D714yes—
387C2×D4—142no—
388C2×D4—141no—
389C2×D4—141no—
390C2×D4—142no—
391C2×D4—282no—
392C2×D4—282no—
393C2×D4—282no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—41no—
404C22×C4—141no—
405C22×C4—141no—
406C22×C4—141no—
407C22×C4#114314yescomplemented
408C22×C4C2×C22⋊D711yescharacteristic
409C22×C4C2×C22⋊D711yescharacteristic
410C22×C4C2×C22⋊D711yescharacteristic
411C22×C4C2×C22⋊D711yescharacteristic
412C22×C4C2×C22⋊D711yescharacteristic
413C22×C4C2×C22⋊D714yes—
414C22×C4C23×D711yescharacteristic
415SD16—288no—
416C2×C8—74no—
417C2×C8—142no—
418C2×C8—142no—
419C2×C8—142no—
420C2×C8—142no—
421C2×C8—142no—
422C2×C8—288no—
423C4⋊C4—24no—
424C4⋊C4—24no—
425C4⋊C4—28no—
426C4⋊C4—24no—
427C4⋊C4—28no—
428C4⋊C4—22no—
429C4⋊C4—142no—
430C4⋊C4—141no—
431C4⋊C4—141no—
432C4⋊C4—142no—
433C4⋊C4—282no—
434C4⋊C4—282no—
435C4⋊C4C2×C22⋊D714yes—
436C22⋊C4—28no—
437C22⋊C4—282no—
438C22⋊C4—282no—
439C22⋊C4—282no—
440C22⋊C4—282no—
441C22⋊C4—282no—
442C22⋊C4—282no—
443C42—28no—
444C42—22no—
445C42—22no—
446C42—22no—
447C42—22no—
448C2×C7—24no—
449C2×C7#243011yescharacteristic
450C2×C7C2×#44811yescharacteristic
451C2×C7#300211yescharacteristic
452C2×C7#316711yescharacteristic
453C2×C7#318111yescharacteristic
454C2×C7#324611yescharacteristic
455C2×C7#324811yescharacteristic
456D7—161no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—281no—
462C23—281no—
463C23—281no—
464C23—281no—
465C23—281no—
466C23—281no—
467C23—281no—
468C23C2×#114312yes—
469C23#650512yes—
470C23#651612yes—
471C23C22×C22⋊D711yescharacteristic
472Q8—24no—
473Q8—24no—
474Q8—48no—
475Q8—42no—
476Q8—42no—
477D4—282no—
478D4—282no—
479D4—564no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—28no—
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—24no—
495C2×C4—24no—
496C2×C4—44no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—281no—
502C2×C4—281no—
503C2×C4—281no—
504C2×C4—281no—
505C2×C4—281no—
506C2×C4—281no—
507C2×C4—281no—
508C2×C4—281no—
509C2×C4—281no—
510C2×C4C2×#114312yes—
511C2×C4C2×#114312yes—
512C2×C4#651312yes—
513C2×C4#651612yes—
514C2×C4D7×#4112yes—
515C2×C4#655311yescharacteristic
516C2×C4#655411yescharacteristic
517C2×C4C22×C22⋊D712yes—
518C8—144no—
519C8—282no—
520C7#2549711yescharacteristic, complemented, Sylow
521C22—22no—
522C22—22no—
523C22—22no—
524C22—22no—
525C22—22no—
526C22—22no—
527C22—561no—
528C22—561no—
529C22—561no—
530C22—561no—
531C22—561no—
532C22—561no—
533C22—561no—
534C22#8999914yes—
535C22C22×#114311yescharacteristic
536C22C2×#650511yescharacteristic
537C22C2×#651311yescharacteristic
538C22#9051311yescharacteristic
539C22#9052311yescharacteristic
540C22#9052411yescharacteristic
541C22C2×#651611yescharacteristic
542C4—22no—
543C4—22no—
544C4—22no—
545C4—22no—
546C4—41no—
547C4—44no—
548C4—44no—
549C4—561no—
550C4—561no—
551C4—561no—
552C4#9051512yes—
553C4#9052012yes—
554C2—24no—
555C2—1121no—
556C2#1174078811yescharacteristic
557C2#1174079111yescharacteristic
558C2#1174080811yescharacteristic
559C2#1174080911yescharacteristic
560C2C2×#8999911yescharacteristic
561C2#1174152511yescharacteristic
562C2#1174153611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC2×C7×#533C2
socleC23×C7C22×D4
prime radicalC2×#6493C22
hypercenterC2×#533D7
hypocenterC7#25497
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. C2×C7×#533C2semidirect
4. #11729546C2semidirect
5. #11729545C2semidirect
6. #11729537C2semidirect
7. #11729535C2semidirect
8. #11729450C2semidirect
9. #11729387C2semidirect
10. #11729383C2semidirect
11. C2×#89319C2semidirect
105. C2×#533D7semidirect
137. C22×C4×C7SD16semidirect
407. C22×C4#1143semidirect
520. C7#25497semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5332
C2×#898202
#117395252
#117295462
#117295452
#117295372
#117295352
#117294502
#117293872
#117293832
C2×#893192
#254977