Finite Group Databasebeta

← #13388697

Subgroups — #13388697

Order 1792.

1180 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#559C211yesmaximal, characteristic, complemented
2C2×#89844C211yesmaximal, characteristic
3#11739946C211yesmaximal, characteristic, complemented
4C2×#89798C211yesmaximal, characteristic, complemented
5#11729519C211yesmaximal, characteristic, complemented
6#11729482C212yesmaximal, complemented
7#11729476C212yesmaximal, complemented
8#11729389C211yesmaximal, characteristic, complemented
9#11729381C211yesmaximal, characteristic, complemented
10#11729367C212yesmaximal, complemented
11#11729360C212yesmaximal, complemented
12C7×#559—24no—
13C7×#559—24no—
14C2×C7×#127C2211yescharacteristic
15C2×C7×#124—21no—
16C2×C7×#124C2212yes—
17C2×C7×#123—22no—
18C2×C4×C7×Q8C2211yescharacteristic
19C2×C4×C7×Q8C2211yescharacteristic
20C2×C4×C7×D4—21no—
21C2×C4×C7×D4C2212yes—
22C22×#1143C2211yescharacteristic
23C22×#1141C2212yes—
24C2×C4×D28C2211yescharacteristic
25#90003—21no—
26C2×#6409C2211yescharacteristic
27C2×#6409C2212yes—
28C2×#6406C2212yes—
29C2×#6406C2212yes—
30C2×#6406C2212yes—
31#89844—24no—
32#89798—24no—
33#89764—21no—
34#89761—22no—
35C2×#6383C2211yescharacteristic
36C2×#6381C2211yescharacteristic
37#89711C2212yes—
38#89708C2211yescharacteristic
39#89700C2212yes—
40C2×C4⋊(C7⋊C8)C2211yescharacteristic
41C2×#6377C2211yescharacteristic
42#89324C2212yes—
43#89319C2212yes—
44#89319C2212yes—
45#24198—71nomaximal, Sylow
46C22×C7×Q8D411yescharacteristic
47C22×C7×Q8C2311yescharacteristic
48C22×C7×D4—21no—
49C22×C7×D4—21no—
50C22×C7×D4C2312yes—
51C23×C4×C7—22no—
52C22×D28C2311yescharacteristic
53C22×C4×D7—21no—
54C7×#127—22no—
55C7×#127D414yes—
56C7×#124—28no—
57C7×#124—24no—
58C7×#124—24no—
59C7×#123—216no—
60C4×C7×Q8—22no—
61C4×C7×Q8—22no—
62C4×C7×Q8—22no—
63C4×C7×Q8D414yes—
64C4×C7×D4—28no—
65C4×C7×D4—24no—
66C4×C7×D4—24no—
67C2×C7×C4⋊C4—21no—
68C2×C7×C4⋊C4D412yes—
69C2×C7×C4⋊C4D411yescharacteristic
70C2×C7×C4⋊C4C2311yescharacteristic
71C2×C7×C22⋊C4—22no—
72C2×C7×C22⋊C4—22no—
73C2×C7×C22⋊C4—22no—
74C2×C42×C7—21no—
75C2×C42×C7C2312yes—
76C2×C42×C7C2311yescharacteristic
77C2×#1143—22no—
78C2×#1143—22no—
79C2×#1143—22no—
80C2×#1141—24no—
81C2×#1141—24no—
82C2×#1141—42no—
83C2×(C2×D7)⋊C4—21no—
84C2×(C2×D7)⋊C4—22no—
85C2×(C2×D7)⋊C4—22no—
86C2×C4⋊Dic7C2311yescharacteristic
87C2×C4⋊Dic7C2312yes—
88C2×Dic7⋊C4—22no—
89C22×C7⋊C8C2311yescharacteristic
90C22×C7⋊C8C2312yes—
91C22×C7⋊C8C2311yescharacteristic
92C4×D28—22no—
93C4×D28—22no—
94#6409—22no—
95#6409—42no—
96#6406—24no—
97#6406—24no—
98#6406—42no—
99C7⋊#95—22no—
100C7⋊#95—21no—
101C7⋊#95—21no—
102#6383—22no—
103#6381—22no—
104C4⋊(C7⋊C8)—22no—
105#6377—22no—
106C2×#559D711yescharacteristic, complemented
107C2×#459—71no—
108C2×#440—71no—
109#2580—71no—
110#2042—72no—
111#2012—72no—
112#1985—71no—
113#1961—71no—
114#1879—72no—
115#1862—72no—
116#1805—71no—
117C24×C7—22no—
118C23×D7—21no—
119C2×C7×Q8—22no—
120C2×C7×Q8—21no—
121C2×C7×Q8—21no—
122C2×C7×Q8—21no—
123C2×C7×Q8—21no—
124C2×C7×Q8—21no—
125C2×C7×Q8—42no—
126C2×C7×Q8C2×D412yes—
127C2×C7×D4—24no—
128C2×C7×D4—24no—
129C2×C7×D4—22no—
130C2×C7×D4—22no—
131C2×C7×D4—22no—
132C2×C7×D4—22no—
133C2×C7×D4—22no—
134C2×C7×D4—44no—
135C2×C7×D4—82no—
136C2×C7×D4C2×D414yes—
137C22×C4×C7—21no—
138C22×C4×C7—21no—
139C22×C4×C7—28no—
140C22×C4×C7—82no—
141C22×C4×C7—82no—
142C22×C4×C7C2×D412yes—
143C22×C4×C7C2×D412yes—
144C22×C4×C7C2×D411yescharacteristic
145C22×C4×C7C2×D411yescharacteristic
146C22×C4×C7C2411yescharacteristic
147C22×Dic7—22no—
148C22×Dic7—21no—
149C2×D28—21no—
150C2×D28—21no—
151C2×D28—21no—
152C2×D28—21no—
153C2×D28—21no—
154C2×D28#4112yes—
155C2×C4×D7—42no—
156C2×C4×D7—82no—
157C7×C4⋊C4—24no—
158C7×C4⋊C4—22no—
159C7×C4⋊C4—24no—
160C7×C4⋊C4—21no—
161C7×C4⋊C4C2×D412yes—
162C7×C22⋊C4—28no—
163C7×C22⋊C4—28no—
164C7×C22⋊C4—28no—
165C42×C7—24no—
166C42×C7—22no—
167C42×C7—22no—
168C42×C7C2×D412yes—
169C42×C7C2×D412yes—
170#1143—28no—
171#1141—48no—
172(C2×D7)⋊C4—44no—
173(C2×D7)⋊C4—42no—
174(C2×D7)⋊C4—82no—
175C4⋊Dic7—21no—
176C4⋊Dic7—21no—
177C4⋊Dic7—22no—
178C4⋊Dic7—22no—
179Dic7⋊C4—82no—
180C2×C7⋊C8—21no—
181C2×C7⋊C8—21no—
182C2×C7⋊C8—22no—
183C2×C7⋊C8—21no—
184C2×C7⋊C8—22no—
185C2×C7⋊C8—21no—
186C2×C7⋊C8—22no—
187C2×C7⋊C8—21no—
188C2×C7⋊C8#4112yes—
189C22×SD16—71no—
190C22×D8—72no—
191#559—24no—
192#559—24no—
193C2×#127C2×D711yescharacteristic
194C2×#124—21no—
195C2×#124C2×D712yes—
196C2×#123—22no—
197C2×C4×Q8C2×D711yescharacteristic
198C2×C4×Q8C2×D711yescharacteristic
199C2×C4×D4—21no—
200C2×C4×D4—71no—
201C2×C4×D4C2×D712yes—
202#459—144no—
203#440—144no—
204C2×#107—71no—
205C2×C4⋊C8—71no—
206C2×#103—71no—
207C2×#103—72no—
208C2×#102—72no—
209C2×#102—72no—
210C2×#102—71no—
211C2×#102—72no—
212C2×#97—71no—
213#399—141no—
214#393—141no—
215#390—72no—
216#389—72no—
217#385—142no—
218#382—71no—
219#340—72no—
220#336—72no—
221#336—72no—
222C23×C7—24no—
223C23×C7—42no—
224C23×C7—42no—
225C23×C7—42no—
226C23×C7—42no—
227C23×C7—42no—
228C23×C7—42no—
229C23×C7C22×D411yescharacteristic
230C22×D7—22no—
231C22×D7—41no—
232C22×D7—41no—
233C22×D7—42no—
234C22×D7—42no—
235C7×Q8—22no—
236C7×Q8—22no—
237C7×Q8—44no—
238C7×Q8—41no—
239C7×Q8—41no—
240C7×D4—24no—
241C7×D4—24no—
242C7×D4—48no—
243C7×D4—42no—
244C7×D4—42no—
245C7×D4—84no—
246C2×C4×C7—22no—
247C2×C4×C7—22no—
248C2×C4×C7—22no—
249C2×C4×C7—22no—
250C2×C4×C7—22no—
251C2×C4×C7—22no—
252C2×C4×C7—22no—
253C2×C4×C7—22no—
254C2×C4×C7—22no—
255C2×C4×C7—22no—
256C2×C4×C7—41no—
257C2×C4×C7—41no—
258C2×C4×C7—42no—
259C2×C4×C7—88no—
260C2×C4×C7#12012yes—
261C2×C4×C7#12012yes—
262C2×C4×C7C22×D411yescharacteristic
263C2×C4×C7C22×D411yescharacteristic
264C2×C4×C7C2×#4111yescharacteristic
265C2×C4×C7C2×#4111yescharacteristic
266C2×C4×C7H(5,𝔽2)11yescharacteristic
267C2×C4×C72−1+411yescharacteristic
268C2×Dic7—41no—
269C2×Dic7—42no—
270C2×Dic7—42no—
271C2×Dic7—42no—
272C2×Dic7—42no—
273D28—22no—
274D28—22no—
275D28—41no—
276D28—41no—
277C4×D7—84no—
278C7⋊C8—22no—
279C7⋊C8—41no—
280C7⋊C8—42no—
281C22×Q8C22⋊D711yescharacteristic
282C22×Q8C22×D711yescharacteristic
283C22×D4—21no—
284C22×D4—21no—
285C22×D4—71no—
286C22×D4C22×D712yes—
287C23×C4—22no—
288C23×C4—141no—
289C2×SD16—142no—
290C2×SD16—142no—
291C2×SD16—142no—
292C2×D8—144no—
293C2×D8—144no—
294C2×D8—282no—
295C22×C8—71no—
296C22×C8—72no—
297C22×C8—71no—
298#127—22no—
299#127C22⋊D714yes—
300#124—28no—
301#124—24no—
302#124—24no—
303#123—216no—
304C4×Q8—22no—
305C4×Q8—22no—
306C4×Q8—22no—
307C4×Q8C22⋊D714yes—
308C4×D4—28no—
309C4×D4—24no—
310C4×D4—24no—
311C4×D4—142no—
312C4×D4—142no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—71no—
315C2×C4⋊C4—72no—
316C2×C4⋊C4—142no—
317C2×C4⋊C4C22⋊D711yescharacteristic
318C2×C4⋊C4C22⋊D712yes—
319C2×C4⋊C4C22×D711yescharacteristic
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—141no—
324C2×C22⋊C4—142no—
325C2×C22⋊C4—142no—
326C2×C42—21no—
327C2×C42C22×D712yes—
328C2×C42C22×D711yescharacteristic
329#107—142no—
330C4⋊C8—142no—
331#103—142no—
332#103—282no—
333#102—144no—
334#102—144no—
335#102—142no—
336#102—282no—
337#97—142no—
338#95—141no—
339#95—141no—
340#95—142no—
341C22×C7—44no—
342C22×C7—44no—
343C22×C7—44no—
344C22×C7—82no—
345C22×C7—82no—
346C22×C7—82no—
347C22×C7—82no—
348C22×C7C2×#12011yescharacteristic
349C22×C7#54811yescharacteristic
350C22×C7#55011yescharacteristic
351C22×C7#57512yes—
352C22×C7#57612yes—
353C2×D7—44no—
354C2×D7—42no—
355C2×D7—82no—
356C2×D7—81no—
357C2×D7—81no—
358C4×C7—22no—
359C4×C7—22no—
360C4×C7—42no—
361C4×C7—42no—
362C4×C7—42no—
363C4×C7—42no—
364C4×C7#52511yescharacteristic
365C4×C7#53711yescharacteristic
366C4×C7#54611yescharacteristic
367C4×C7#54711yescharacteristic
368Dic7—82no—
369Dic7—81no—
370C24—22no—
371C24—141no—
372C2×Q8—22no—
373C2×Q8—21no—
374C2×Q8—21no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—42no—
379C2×Q8C2×C22⋊D712yes—
380C2×D4—24no—
381C2×D4—24no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—44no—
388C2×D4—72no—
389C2×D4—82no—
390C2×D4—141no—
391C2×D4—141no—
392C2×D4—141no—
393C2×D4—141no—
394C2×D4—141no—
395C2×D4C2×C22⋊D714yes—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—28no—
399C22×C4—82no—
400C22×C4—82no—
401C22×C4—142no—
402C22×C4—141no—
403C22×C4—282no—
404C22×C4—562no—
405C22×C4C2×C22⋊D712yes—
406C22×C4C2×C22⋊D712yes—
407C22×C4C2×C22⋊D711yescharacteristic
408C22×C4C2×C22⋊D711yescharacteristic
409C22×C4C23×D711yescharacteristic
410SD16—148no—
411D8—288no—
412C2×C8—72no—
413C2×C8—141no—
414C2×C8—141no—
415C2×C8—142no—
416C2×C8—141no—
417C2×C8—142no—
418C2×C8—141no—
419C2×C8—141no—
420C2×C8—142no—
421C4⋊C4—24no—
422C4⋊C4—22no—
423C4⋊C4—24no—
424C4⋊C4—21no—
425C4⋊C4—142no—
426C4⋊C4—142no—
427C4⋊C4—141no—
428C4⋊C4—141no—
429C4⋊C4—562no—
430C4⋊C4C2×C22⋊D712yes—
431C22⋊C4—28no—
432C22⋊C4—28no—
433C22⋊C4—28no—
434C22⋊C4—284no—
435C22⋊C4—282no—
436C22⋊C4—562no—
437C42—24no—
438C42—22no—
439C42—22no—
440C42C2×C22⋊D712yes—
441C42C2×C22⋊D712yes—
442C2×C7—84no—
443C2×C7#240711yescharacteristic
444C2×C7#300511yescharacteristic
445C2×C7#300811yescharacteristic
446C2×C7#337012yes—
447C2×C7#340312yes—
448D7—82no—
449C23—24no—
450C23—42no—
451C23—42no—
452C23—42no—
453C23—42no—
454C23—42no—
455C23—42no—
456C23—142no—
457C23—282no—
458C23—281no—
459C23—282no—
460C23—281no—
461C23C22×C22⋊D711yescharacteristic
462Q8—22no—
463Q8—22no—
464Q8—44no—
465Q8—41no—
466Q8—41no—
467D4—24no—
468D4—24no—
469D4—48no—
470D4—42no—
471D4—42no—
472D4—84no—
473D4—142no—
474D4—142no—
475D4—281no—
476D4—281no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—88no—
491C2×C4—282no—
492C2×C4—282no—
493C2×C4—282no—
494C2×C4—282no—
495C2×C4—281no—
496C2×C4—564no—
497C2×C4#651612yes—
498C2×C4#651612yes—
499C2×C4D7×#4111yescharacteristic
500C2×C4D7×#4111yescharacteristic
501C2×C4#655311yescharacteristic
502C2×C4#655411yescharacteristic
503C2×C4C22×C22⋊D711yescharacteristic
504C2×C4C22×C22⋊D711yescharacteristic
505C8—142no—
506C8—282no—
507C8—281no—
508C7#2419811yescharacteristic, complemented, Sylow
509C22—44no—
510C22—44no—
511C22—44no—
512C22—82no—
513C22—82no—
514C22—82no—
515C22—82no—
516C22—282no—
517C22—284no—
518C22—561no—
519C22—561no—
520C22—562no—
521C22#9051312yes—
522C22#9052211yescharacteristic
523C22#9052511yescharacteristic
524C22#9052612yes—
525C22C2×#651611yescharacteristic
526C4—22no—
527C4—22no—
528C4—42no—
529C4—42no—
530C4—42no—
531C4—42no—
532C4—561no—
533C4—562no—
534C4#9051511yescharacteristic
535C4#9051911yescharacteristic
536C4#9052011yescharacteristic
537C4#9052411yescharacteristic
538C2—84no—
539C2—562no—
540C2#1174115912yes—
541C2#1174116112yes—
542C2#1174152611yescharacteristic
543C2#1174154211yescharacteristic
544C2#1174154611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC2×C7×#559C2
socleC23×C7C22×D4
prime radicalC2×#89844C2
hypercenterC2×#559D7
hypocenterC7#24198
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×C7×#559C2semidirect
3. #11739946C2semidirect
4. C2×#89798C2semidirect
5. #11729519C2semidirect
6. #11729482C2semidirect
7. #11729476C2semidirect
8. #11729389C2semidirect
9. #11729381C2semidirect
10. #11729367C2semidirect
11. #11729360C2semidirect
106. C2×#559D7semidirect
508. C7#24198semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5592
C2×#898442
#117399462
C2×#897982
#117295192
#117294822
#117294762
#117293892
#117293812
#117293672
#117293602
#241987