Finite Group Databasebeta

← #13387842

Subgroups — #13387842

Order 1792.

1204 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×#555C211yesmaximal, characteristic, complemented
2C2×#89859C211yesmaximal, characteristic, complemented
3#11739860C211yesmaximal, characteristic, complemented
4C2×#89786C211yesmaximal, characteristic, complemented
5#11729542C211yesmaximal, characteristic, complemented
6#11729438C212yesmaximal, complemented
7#11729433C212yesmaximal, complemented
8#11729369C211yesmaximal, characteristic, complemented
9#11729359C211yesmaximal, characteristic, complemented
10#11729340C212yesmaximal, complemented
11#11729330C212yesmaximal, complemented
12C7×#555—24no—
13C7×#555—24no—
14C2×C7×C4⋊Q8C2211yescharacteristic
15C2×C7×#124—22no—
16C2×C7×#121—21no—
17C2×C7×#121C2212yes—
18C2×C4×C7×D4C2211yescharacteristic
19C2×C4×C7×D4C2211yescharacteristic
20C2×C7×#117—21no—
21C2×C7×#117C2212yes—
22C22×#1141C2211yescharacteristic
23C2×#6493C2212yes—
24C2×C4×D28C2211yescharacteristic
25#89995—21no—
26C2×#6406C2211yescharacteristic
27C2×#6406C2212yes—
28#89984C2212yes—
29C2×C22⋊(C7⋊C8)C2212yes—
30C2×C22⋊(C7⋊C8)C2212yes—
31#89859—24no—
32#89786—24no—
33#89765—21no—
34C2×#6383C2212yes—
35C2×#6383C2211yescharacteristic
36C2×#6382C2211yescharacteristic
37C2×#6381C2212yes—
38#89728—22no—
39#89708C2211yescharacteristic
40C2×C4⋊(C7⋊C8)C2211yescharacteristic
41C2×#6377C2211yescharacteristic
42#89324C2212yes—
43#89324C2212yes—
44#89324C2212yes—
45#24129—71nomaximal, Sylow
46C22×C7×Q8—21no—
47C22×C7×D4—22no—
48C22×C7×D4D411yescharacteristic
49C22×C7×D4C2311yescharacteristic
50C23×C4×C7—21no—
51C23×C4×C7C2312yes—
52C22×C22⋊D7—22no—
53C22×D28C2311yescharacteristic
54C22×C4×D7—21no—
55C7×C4⋊Q8—22no—
56C7×C4⋊Q8D414yescomplemented
57C7×#124—216no—
58C7×#121—28no—
59C7×#121—24no—
60C7×#121—24no—
61C4×C7×D4—22no—
62C4×C7×D4—22no—
63C4×C7×D4—22no—
64C4×C7×D4D414yescomplemented
65C7×#117—28no—
66C7×#117—24no—
67C7×#117—24no—
68C2×C7×C4⋊C4—21no—
69C2×C7×C4⋊C4D411yescharacteristic
70C2×C7×C4⋊C4C2312yes—
71C2×C7×C4⋊C4C2311yescharacteristic
72C2×C7×C22⋊C4—22no—
73C2×C7×C22⋊C4—22no—
74C2×C7×C22⋊C4—21no—
75C2×C7×C22⋊C4D412yes—
76C2×C42×C7—22no—
77C2×C42×C7C2311yescharacteristic
78C2×C22⋊Dic7—22no—
79C2×#1141—22no—
80C2×#1141—22no—
81C2×#1141—22no—
82#6493—24no—
83#6493—42no—
84C2×(C2×D7)⋊C4—21no—
85C2×(C2×D7)⋊C4—22no—
86C2×C4⋊Dic7C2311yescharacteristic
87C2×C4⋊Dic7C2312yes—
88C22×C7⋊C8C2311yescharacteristic
89C22×C7⋊C8C2312yes—
90C22×C7⋊C8C2311yescharacteristic
91C4×D28—22no—
92C4×D28—22no—
93#6406—22no—
94#6406—42no—
95C7⋊#95—21no—
96C7⋊#95—21no—
97C7⋊#95—22no—
98C22⋊(C7⋊C8)—24no—
99C22⋊(C7⋊C8)—42no—
100#6383—24no—
101#6383—22no—
102#6382—22no—
103#6381—24no—
104C4⋊(C7⋊C8)—22no—
105#6377—22no—
106C2×#555D711yescharacteristic, complemented
107C2×#474—71no—
108C2×#442—71no—
109#2535—71no—
110#2033—72no—
111#1999—72no—
112#1993—71no—
113#1955—71no—
114#1875—72no—
115#1854—72no—
116#1804—71no—
117C24×C7—21no—
118C24×C7C2×D412yes—
119C23×D7—21no—
120C2×C7×Q8—24no—
121C2×C7×Q8—82no—
122C2×C7×D4—28no—
123C2×C7×D4—22no—
124C2×C7×D4—21no—
125C2×C7×D4—21no—
126C2×C7×D4—21no—
127C2×C7×D4—21no—
128C2×C7×D4—21no—
129C2×C7×D4—42no—
130C2×C7×D4—82no—
131C2×C7×D4—82no—
132C2×C7×D4C2×D412yes—
133C22×C4×C7—21no—
134C22×C4×C7—22no—
135C22×C4×C7—24no—
136C22×C4×C7—22no—
137C22×C4×C7—22no—
138C22×C4×C7—22no—
139C22×C4×C7—22no—
140C22×C4×C7—22no—
141C22×C4×C7—22no—
142C22×C4×C7—44no—
143C22×C4×C7C2×D412yes—
144C22×C4×C7C2×D411yescharacteristic
145C22×C4×C7C2×D411yescharacteristic
146C22×C4×C7C2411yescharacteristic
147C2×C22⋊D7—44no—
148C2×C22⋊D7—44no—
149C2×C22⋊D7—82no—
150C22×Dic7—22no—
151C22×Dic7—21no—
152C2×D28—21no—
153C2×D28—21no—
154C2×D28—21no—
155C2×D28—21no—
156C2×D28—21no—
157C2×D28#4112yes—
158C2×C4×D7—42no—
159C2×C4×D7—82no—
160C7×C4⋊C4—24no—
161C7×C4⋊C4—22no—
162C7×C4⋊C4—21no—
163C7×C4⋊C4—22no—
164C7×C4⋊C4C2×D412yes—
165C7×C4⋊C4C2×D414yes—
166C7×C22⋊C4—28no—
167C7×C22⋊C4—28no—
168C7×C22⋊C4—24no—
169C7×C22⋊C4—24no—
170C42×C7—28no—
171C42×C7C2×D412yes—
172C42×C7C2×D412yes—
173C22⋊Dic7—82no—
174#1141—28no—
175(C2×D7)⋊C4—44no—
176(C2×D7)⋊C4—42no—
177C4⋊Dic7—21no—
178C4⋊Dic7—21no—
179C4⋊Dic7—22no—
180C4⋊Dic7—22no—
181C2×C7⋊C8—21no—
182C2×C7⋊C8—21no—
183C2×C7⋊C8—21no—
184C2×C7⋊C8—22no—
185C2×C7⋊C8—22no—
186C2×C7⋊C8—21no—
187C2×C7⋊C8—22no—
188C2×C7⋊C8—21no—
189C2×C7⋊C8#4112yes—
190C22×D8—71no—
191#555—24no—
192#555—24no—
193C2×C4⋊Q8C2×D711yescharacteristic
194C2×#124—22no—
195C2×#121—21no—
196C2×#121—72no—
197C2×#121C2×D712yes—
198C2×C4×D4—71no—
199C2×C4×D4C2×D711yescharacteristic
200C2×C4×D4C2×D711yescharacteristic
201C2×#117—21no—
202C2×#117C2×D712yes—
203#474—144no—
204#442—144no—
205C2×#107—72no—
206C2×#106—71no—
207C2×C4⋊C8—71no—
208C2×#102—71no—
209C2×#102—71no—
210C2×#102—72no—
211C2×#102—72no—
212C2×C22⋊C8—72no—
213C2×C22⋊C8—72no—
214C2×#97—71no—
215#397—141no—
216#392—141no—
217#386—142no—
218#382—71no—
219#380—72no—
220#340—72no—
221#340—72no—
222#340—72no—
223C23×C7—22no—
224C23×C7—22no—
225C23×C7—22no—
226C23×C7—22no—
227C23×C7—22no—
228C23×C7—22no—
229C23×C7—22no—
230C23×C7—22no—
231C23×C7—41no—
232C23×C7—41no—
233C23×C7—42no—
234C23×C7—42no—
235C23×C7C22×D411yescharacteristic
236C22×D7—22no—
237C22×D7—41no—
238C22×D7—41no—
239C22×D7—42no—
240C22×D7—42no—
241C7×Q8—84no—
242C7×D4—22no—
243C7×D4—22no—
244C7×D4—44no—
245C7×D4—41no—
246C7×D4—41no—
247C7×D4—88no—
248C2×C4×C7—22no—
249C2×C4×C7—22no—
250C2×C4×C7—22no—
251C2×C4×C7—22no—
252C2×C4×C7—24no—
253C2×C4×C7—22no—
254C2×C4×C7—22no—
255C2×C4×C7—48no—
256C2×C4×C7—42no—
257C2×C4×C7—42no—
258C2×C4×C7—42no—
259C2×C4×C7—42no—
260C2×C4×C7—42no—
261C2×C4×C7—42no—
262C2×C4×C7—42no—
263C2×C4×C7#12012yes—
264C2×C4×C7#12012yes—
265C2×C4×C7C22×D411yescharacteristic
266C2×C4×C7C22×D411yescharacteristic
267C2×C4×C7C2×#4111yescharacteristic
268C2×C4×C7C2×#4111yescharacteristic
269C2×C4×C7H(5,𝔽2)11yescharacteristic
270C2×C4×C72−1+411yescharacteristic
271C22⋊D7—88no—
272C2×Dic7—41no—
273C2×Dic7—42no—
274C2×Dic7—42no—
275C2×Dic7—42no—
276C2×Dic7—42no—
277D28—22no—
278D28—22no—
279D28—41no—
280D28—41no—
281C4×D7—84no—
282C7⋊C8—22no—
283C7⋊C8—41no—
284C7⋊C8—42no—
285C22×Q8—21no—
286C22×D4—22no—
287C22×D4—71no—
288C22×D4—142no—
289C22×D4C22⋊D711yescharacteristic
290C22×D4C22×D711yescharacteristic
291C23×C4—21no—
292C23×C4—141no—
293C23×C4C22×D712yes—
294C2×D8—142no—
295C2×D8—142no—
296C2×D8—142no—
297C22×C8—71no—
298C22×C8—71no—
299C22×C8—72no—
300C4⋊Q8—22no—
301C4⋊Q8C22⋊D714yescomplemented
302#124—216no—
303#121—28no—
304#121—24no—
305#121—24no—
306#121—144no—
307#121—282no—
308C4×D4—22no—
309C4×D4—22no—
310C4×D4—22no—
311C4×D4—142no—
312C4×D4—142no—
313C4×D4C22⋊D714yescomplemented
314#117—28no—
315#117—24no—
316#117—24no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—71no—
319C2×C4⋊C4—72no—
320C2×C4⋊C4C22⋊D711yescharacteristic
321C2×C4⋊C4C22×D711yescharacteristic
322C2×C4⋊C4C22×D712yes—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—141no—
327C2×C22⋊C4—142no—
328C2×C22⋊C4—142no—
329C2×C22⋊C4C22⋊D712yes—
330C2×C42—22no—
331C2×C42C22×D711yescharacteristic
332#107—144no—
333#106—142no—
334C4⋊C8—142no—
335#102—142no—
336#102—142no—
337#102—144no—
338#102—282no—
339C22⋊C8—144no—
340C22⋊C8—282no—
341#97—142no—
342#95—142no—
343#95—141no—
344#95—141no—
345C22×C7—42no—
346C22×C7—42no—
347C22×C7—42no—
348C22×C7—42no—
349C22×C7—42no—
350C22×C7—42no—
351C22×C7—42no—
352C22×C7—42no—
353C22×C7—42no—
354C22×C7—42no—
355C22×C7—82no—
356C22×C7—82no—
357C22×C7C2×#12011yescharacteristic
358C22×C7#54611yescharacteristic
359C22×C7#54711yescharacteristic
360C22×C7#57512yes—
361C22×C7#57612yes—
362C2×D7—42no—
363C2×D7—44no—
364C2×D7—82no—
365C2×D7—81no—
366C2×D7—81no—
367C4×C7—22no—
368C4×C7—22no—
369C4×C7—42no—
370C4×C7—42no—
371C4×C7—44no—
372C4×C7#52511yescharacteristic
373C4×C7#53711yescharacteristic
374C4×C7#54811yescharacteristic
375C4×C7#55011yescharacteristic
376Dic7—81no—
377Dic7—82no—
378C24—21no—
379C24—141no—
380C24C2×C22⋊D712yes—
381C2×Q8—24no—
382C2×Q8—82no—
383C2×D4—28no—
384C2×D4—22no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—42no—
391C2×D4—72no—
392C2×D4—82no—
393C2×D4—82no—
394C2×D4—141no—
395C2×D4—141no—
396C2×D4—141no—
397C2×D4—141no—
398C2×D4—141no—
399C2×D4—284no—
400C2×D4—284no—
401C2×D4—562no—
402C2×D4C2×C22⋊D712yes—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—24no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—44no—
413C22×C4—142no—
414C22×C4—141no—
415C22×C4—282no—
416C22×C4—562no—
417C22×C4C2×C22⋊D712yes—
418C22×C4C2×C22⋊D711yescharacteristic
419C22×C4C2×C22⋊D711yescharacteristic
420C22×C4C23×D711yescharacteristic
421D8—148no—
422C2×C8—72no—
423C2×C8—141no—
424C2×C8—141no—
425C2×C8—142no—
426C2×C8—141no—
427C2×C8—142no—
428C2×C8—141no—
429C2×C8—141no—
430C2×C8—142no—
431C4⋊C4—24no—
432C4⋊C4—22no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—142no—
436C4⋊C4—142no—
437C4⋊C4—141no—
438C4⋊C4—141no—
439C4⋊C4C2×C22⋊D712yes—
440C4⋊C4C2×C22⋊D714yes—
441C22⋊C4—28no—
442C22⋊C4—28no—
443C22⋊C4—24no—
444C22⋊C4—24no—
445C22⋊C4—284no—
446C22⋊C4—282no—
447C22⋊C4—562no—
448C42—28no—
449C42C2×C22⋊D712yes—
450C42C2×C22⋊D712yes—
451C2×C7—82no—
452C2×C7—82no—
453C2×C7#240711yescharacteristic
454C2×C7#300511yescharacteristic
455C2×C7#300811yescharacteristic
456C2×C7#331912yes—
457C2×C7#334712yes—
458D7—82no—
459C23—22no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—42no—
468C23—41no—
469C23—41no—
470C23—42no—
471C23—142no—
472C23—282no—
473C23—281no—
474C23—282no—
475C23—281no—
476C23C22×C22⋊D711yescharacteristic
477Q8—84no—
478D4—22no—
479D4—22no—
480D4—44no—
481D4—41no—
482D4—41no—
483D4—88no—
484D4—142no—
485D4—142no—
486D4—281no—
487D4—281no—
488D4—568no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—48no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—282no—
505C2×C4—282no—
506C2×C4—282no—
507C2×C4—282no—
508C2×C4—281no—
509C2×C4—564no—
510C2×C4#651612yes—
511C2×C4#651612yes—
512C2×C4D7×#4111yescharacteristic
513C2×C4D7×#4111yescharacteristic
514C2×C4#655311yescharacteristic
515C2×C4#655411yescharacteristic
516C2×C4C22×C22⋊D711yescharacteristic
517C2×C4C22×C22⋊D711yescharacteristic
518C8—142no—
519C8—281no—
520C8—282no—
521C7#2412911yescharacteristic, complemented, Sylow
522C22—42no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—82no—
533C22—82no—
534C22—282no—
535C22—284no—
536C22—561no—
537C22—561no—
538C22—562no—
539C22#9051312yes—
540C22#9051511yescharacteristic
541C22#9052011yescharacteristic
542C22#9052612yes—
543C22C2×#651611yescharacteristic
544C4—22no—
545C4—22no—
546C4—42no—
547C4—42no—
548C4—44no—
549C4—561no—
550C4—562no—
551C4#9051911yescharacteristic
552C4#9052211yescharacteristic
553C4#9052411yescharacteristic
554C4#9052511yescharacteristic
555C2—82no—
556C2—82no—
557C2—562no—
558C2#1174109312yes—
559C2#1174109812yes—
560C2#1174152611yescharacteristic
561C2#1174154211yescharacteristic
562C2#1174154611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC2×C7×#555C2
socleC23×C7C22×D4
hypercenterC2×#555D7
hypocenterC7#24129
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. C2×C7×#555C2semidirect
2. C2×#89859C2semidirect
3. #11739860C2semidirect
4. C2×#89786C2semidirect
5. #11729542C2semidirect
6. #11729438C2semidirect
7. #11729433C2semidirect
8. #11729369C2semidirect
9. #11729359C2semidirect
10. #11729340C2semidirect
11. #11729330C2semidirect
56. C7×C4⋊Q8D4semidirect
64. C4×C7×D4D4semidirect
106. C2×#555D7semidirect
301. C4⋊Q8C22⋊D7semidirect
313. C4×D4C22⋊D7semidirect
521. C7#24129semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5552
C2×#898592
#117398602
C2×#897862
#117295422
#117294382
#117294332
#117293692
#117293592
#117293402
#117293302
#241297