Finite Group Databasebeta

← #13319721

Subgroups — #13319721

Order 1792.

1206 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90237C211yesmaximal, characteristic
2#11736079C212yesmaximal, complemented
3C7×#1465C211yesmaximal, characteristic, complemented
4#11729356C211yesmaximal, characteristic, complemented
5#11727725C212yesmaximal, complemented
6#11725898C212yesmaximal, complemented
7#11725879C212yesmaximal, complemented
8#11725875C212yesmaximal, complemented
9#11725854C212yesmaximal, complemented
10C22×#1159C411yescharacteristic
11C2×C4×C7×D4C2211yescharacteristic
12C2×D4×Dic7C411yescharacteristic
13C2×C4×C22⋊D7C411yescharacteristic
14C2×C4×C22⋊D7C2211yescharacteristic
15C22×Dic7⋊C4C411yescharacteristic
16C22×Dic7⋊C4C2211yescharacteristic
17#90237—24no—
18#90237—24no—
19C2×D7×C4⋊C4C2211yescharacteristic
20C2×#6450C2211yescharacteristic
21C2×(C22⋊D7)⋊C4C411yescharacteristic
22C2×(C22⋊D7)⋊C4C2211yescharacteristic
23C2×#6440C411yescharacteristic
24C2×#6440C2211yescharacteristic
25C2×#6435C411yescharacteristic
26C2×C4×Dic14C411yescharacteristic
27C7×#407C2212yes—
28#89979C2212yes—
29#89900—24no—
30#89501—24no—
31#89498C2214yes—
32#89490C2214yes—
33C7×#324C2212yes—
34C7×#323C2212yes—
35#89323C2212yes—
36#89320C2212yes—
37#89264C2214yes—
38#89264C2214yes—
39#17370—71nomaximal, Sylow
40C22×C7×D4C2×C411yescharacteristic
41C23×C4×C7C2×C411yescharacteristic
42C23×C4×C7C2311yescharacteristic
43C22×C22⋊D7C2×C411yescharacteristic
44C22×C22⋊D7C2×C411yescharacteristic
45C23×Dic7C2×C411yescharacteristic
46C23×Dic7C2×C411yescharacteristic
47C23×Dic7C2×C411yescharacteristic
48C23×Dic7C2×C411yescharacteristic
49C2×#1159—24no—
50C2×#1159—24no—
51C2×#1159—24no—
52C22×C4×D7C2×C411yescharacteristic
53C22×C4×D7C2×C411yescharacteristic
54C22×C4×D7C2311yescharacteristic
55C22×Dic14C2×C411yescharacteristic
56C2×C7×M16—22no—
57C4×C7×D4—22no—
58C4×C7×D4—22no—
59C2×C7×C4⋊C4C2311yescharacteristic
60C2×C7×C22⋊C4C2×C411yescharacteristic
61C2×C7×C22⋊C4C2311yescharacteristic
62C2×C42×C7C2×C411yescharacteristic
63C2×C22⋊Dic7C2×C411yescharacteristic
64C2×C22⋊Dic7C2×C411yescharacteristic
65D4×Dic7—24no—
66C4×C22⋊D7—22no—
67C4×C22⋊D7—22no—
68C4×C22⋊D7D414yes—
69C4×C22⋊D7D414yes—
70C2×(C2×D7)⋊C4C2×C411yescharacteristic
71C2×(C2×D7)⋊C4C2×C411yescharacteristic
72C2×C4⋊Dic7C2×C411yescharacteristic
73C2×Dic7⋊C4—22no—
74C2×Dic7⋊C4—22no—
75C2×Dic7⋊C4—22no—
76C2×Dic7⋊C4—22no—
77C2×Dic7⋊C4C2×C411yescharacteristic
78C2×Dic7⋊C4C2×C411yescharacteristic
79C2×Dic7⋊C4C2×C411yescharacteristic
80C2×Dic7⋊C4C2×C411yescharacteristic
81C2×Dic7⋊C4C2×C411yescharacteristic
82C2×Dic7⋊C4C2×C411yescharacteristic
83C2×Dic7⋊C4C2311yescharacteristic
84C2×Dic7⋊C4C2311yescharacteristic
85C2×C4×Dic7C2×C411yescharacteristic
86C2×C4×Dic7C2×C411yescharacteristic
87C2×C4×Dic7C2×C411yescharacteristic
88C2×C4×Dic7C2×C411yescharacteristic
89C2×C4×Dic7C2311yescharacteristic
90C2×#1136—22no—
91C2×#1131—24no—
92D7×C4⋊C4—24no—
93#6450—24no—
94(C22⋊D7)⋊C4—24no—
95(C22⋊D7)⋊C4—24no—
96#6440—24no—
97#6440—24no—
98#6435—22no—
99#6435—22no—
100C4×Dic14—22no—
101C4×Dic14—22no—
102C7×C22⋊C8—22no—
103C7×C22⋊C8C2314yes—
104C22⋊(C7⋊C8)—22no—
105C22⋊(C7⋊C8)C2314yes—
106(C2×D7)⋊C8—24no—
107Dic7⋊C8—24no—
108C8×Dic7—24no—
109C2×#520—71no—
110#2975—72no—
111#1465—72no—
112#1465—71no—
113#1465D711yescharacteristic, complemented
114#1463—72no—
115#1463—72no—
116#1461—72no—
117#1458—72no—
118C24×C7C22×C411yescharacteristic
119C24×C7C22×C411yescharacteristic
120C23×D7C22×C411yescharacteristic
121C2×C7×D4—22no—
122C2×C7×D4—22no—
123C2×C7×D4—22no—
124C22×C4×C7—21no—
125C22×C4×C7—21no—
126C22×C4×C7—81no—
127C22×C4×C7—81no—
128C22×C4×C7C22×C411yescharacteristic
129C22×C4×C7C22×C411yescharacteristic
130C22×C4×C7C22×C411yescharacteristic
131C22×C4×C7C22×C411yescharacteristic
132C22×C4×C7C2×D412yes—
133C22×C4×C7C2×D412yes—
134C22×C4×C7C2411yescharacteristic
135C2×C22⋊D7—22no—
136C2×C22⋊D7—22no—
137C2×C22⋊D7—22no—
138C2×C22⋊D7—22no—
139C2×C22⋊D7—22no—
140C2×C22⋊D7C22⋊C414yes—
141C22×Dic7—22no—
142C22×Dic7—22no—
143C22×Dic7—22no—
144C22×Dic7—22no—
145C22×Dic7—22no—
146C22×Dic7—22no—
147C22×Dic7—22no—
148C22×Dic7—81no—
149C22×Dic7—81no—
150C22×Dic7M1614yescomplemented
151C22×Dic7C22×C411yescharacteristic
152C22×Dic7C22×C411yescharacteristic
153C22×Dic7C22×C411yescharacteristic
154C22×Dic7C22×C411yescharacteristic
155C22×Dic7C22×C411yescharacteristic
156C22×Dic7C22×C411yescharacteristic
157C22×Dic7C22×C411yescharacteristic
158#1159—232no—
159C2×C4×D7—22no—
160C2×C4×D7—22no—
161C2×C4×D7—22no—
162C2×C4×D7—22no—
163C2×C4×D7—81no—
164C2×C4×D7—81no—
165C2×C4×D7C2×D414yes—
166C2×Dic14—22no—
167C2×Dic14—22no—
168C2×Dic14M1614yescomplemented
169C7×M16—82no—
170C2×C7×C8—24no—
171C7×C4⋊C4—22no—
172C7×C22⋊C4—22no—
173C7×C22⋊C4—22no—
174C42×C7—21no—
175C42×C7—21no—
176C22⋊Dic7—22no—
177C22⋊Dic7C22⋊C414yes—
178(C2×D7)⋊C4—22no—
179(C2×D7)⋊C4C22⋊C412yes—
180(C2×D7)⋊C4C22⋊C412yes—
181C4⋊Dic7—22no—
182Dic7⋊C4—21no—
183Dic7⋊C4—21no—
184Dic7⋊C4—21no—
185Dic7⋊C4—21no—
186Dic7⋊C4—22no—
187Dic7⋊C4—22no—
188Dic7⋊C4—22no—
189Dic7⋊C4—22no—
190Dic7⋊C4—22no—
191Dic7⋊C4C22⋊C412yes—
192Dic7⋊C4C22⋊C412yes—
193C4×Dic7—22no—
194C4×Dic7—22no—
195C4×Dic7—22no—
196C4×Dic7—22no—
197C4×Dic7C2×D414yes—
198#1136—82no—
199C2×C7⋊C8—24no—
200#1131—84no—
201C22×#41—71no—
202#520—144no—
203#520—144no—
204C2×C4×Q8—71no—
205C2×C4×Q8—71no—
206C2×C4×D4—71no—
207C2×C4×D4—71no—
208C2×C4×D4—71no—
209C2×C4×D4—71no—
210C2×C4×D4—71no—
211C2×C4×D4C2×D711yescharacteristic
212C2×#117—71no—
213C2×#117—71no—
214C2×#117—71no—
215C22×C4⋊C4—71no—
216C22×C4⋊C4—71no—
217C22×C4⋊C4—71no—
218#436—144no—
219#436—144no—
220#431—74no—
221#407—72no—
222#407—74no—
223#407C2×D712yes—
224#324—72no—
225#324—74no—
226#324—74no—
227#324C2×D712yes—
228#323—72no—
229#323C2×D712yes—
230C23×C7—21no—
231C23×C7—21no—
232C23×C7—21no—
233C23×C7—21no—
234C23×C7—41no—
235C23×C7—41no—
236C23×C7—41no—
237C23×C7—41no—
238C23×C7C2×C22⋊C412yes—
239C23×C7C2×M1612yes—
240C23×C7C23×C411yescharacteristic
241C22×D7—21no—
242C22×D7—21no—
243C22×D7—41no—
244C22×D7—41no—
245C22×D7C2×C22⋊C412yes—
246C7×D4—28no—
247C2×C4×C7—21no—
248C2×C4×C7—21no—
249C2×C4×C7—21no—
250C2×C4×C7—21no—
251C2×C4×C7—42no—
252C2×C4×C7—42no—
253C2×C4×C7—41no—
254C2×C4×C7—41no—
255C2×C4×C7—41no—
256C2×C4×C7—41no—
257C2×C4×C7—81no—
258C2×C4×C7—81no—
259C2×C4×C7C2×C22⋊C411yescharacteristic
260C2×C4×C7C2×C22⋊C411yescharacteristic
261C2×C4×C7C2×M1612yes—
262C2×C4×C7C22×D412yes—
263C22⋊D7—28no—
264C22⋊D7—28no—
265C2×Dic7—28no—
266C2×Dic7—21no—
267C2×Dic7—21no—
268C2×Dic7—21no—
269C2×Dic7—21no—
270C2×Dic7—28no—
271C2×Dic7—21no—
272C2×Dic7—21no—
273C2×Dic7—41no—
274C2×Dic7—41no—
275C2×Dic7—41no—
276C2×Dic7—41no—
277C2×Dic7—82no—
278C2×Dic7—82no—
279C2×Dic7C2×C22⋊C412yes—
280C2×Dic7C2×C22⋊C412yes—
281C2×Dic7C2×C22⋊C412yes—
282C2×Dic7C2×M1612yes—
283C2×Dic7C2×M1612yes—
284C2×Dic7C2×M1612yes—
285C2×Dic7C2×M1612yes—
286C4×D7—28no—
287C4×D7—44no—
288C4×D7—82no—
289Dic14—28no—
290C7×C8—44no—
291C7⋊C8—44no—
292C2×#41—144no—
293C2×#41—144no—
294C2×#41—144no—
295C22×Q8—71no—
296C22×D4—71no—
297C22×D4—71no—
298C22×D4C4×D711yescharacteristic
299C23×C4—71no—
300C23×C4—71no—
301C23×C4—71no—
302C23×C4—71no—
303C23×C4—71no—
304C23×C4—71no—
305C23×C4—71no—
306C23×C4C4×D711yescharacteristic
307C23×C4C22×D711yescharacteristic
308C2×M16—22no—
309C2×M16—144no—
310C2×M16—142no—
311C4×Q8—142no—
312C4×Q8—142no—
313C4×Q8—144no—
314C4×D4—22no—
315C4×D4—22no—
316C4×D4—74no—
317C4×D4—74no—
318C4×D4—144no—
319C4×D4—144no—
320C4×D4—142no—
321C4×D4—142no—
322C4×D4—144no—
323#117—142no—
324#117—142no—
325#117—144no—
326#117—144no—
327C2×C4⋊C4—71no—
328C2×C4⋊C4—71no—
329C2×C4⋊C4—71no—
330C2×C4⋊C4—71no—
331C2×C4⋊C4—71no—
332C2×C4⋊C4—71no—
333C2×C4⋊C4—71no—
334C2×C4⋊C4—71no—
335C2×C4⋊C4—71no—
336C2×C4⋊C4—144no—
337C2×C4⋊C4—142no—
338C2×C4⋊C4—142no—
339C2×C4⋊C4—142no—
340C2×C4⋊C4—142no—
341C2×C4⋊C4C22×D711yescharacteristic
342C2×C22⋊C4—71no—
343C2×C22⋊C4—71no—
344C2×C22⋊C4—71no—
345C2×C22⋊C4—71no—
346C2×C22⋊C4C4×D711yescharacteristic
347C2×C22⋊C4C22×D711yescharacteristic
348C2×C42—71no—
349C2×C42—71no—
350C2×C42—71no—
351C2×C42—71no—
352C2×C42—71no—
353C2×C42C4×D711yescharacteristic
354C4⋊C8—144no—
355C22⋊C8—22no—
356C22⋊C8—74no—
357C22⋊C8—144no—
358C22⋊C8—142no—
359C22⋊C8C22×D714yes—
360C4×C8—144no—
361C22×C7—21no—
362C22×C7—21no—
363C22×C7—22no—
364C22×C7—22no—
365C22×C7—22no—
366C22×C7—22no—
367C22×C7—42no—
368C22×C7—42no—
369C22×C7—42no—
370C22×C7—42no—
371C22×C7—41no—
372C22×C7—41no—
373C22×C7C22×C22⋊C411yescharacteristic
374C22×C7C22×M1611yescharacteristic
375C22×C7C22×M1611yescharacteristic
376C2×D7—22no—
377C2×D7—22no—
378C2×D7—22no—
379C2×D7—42no—
380C2×D7—42no—
381C4×C7—22no—
382C4×C7—22no—
383C4×C7—21no—
384C4×C7—21no—
385C4×C7—41no—
386C4×C7—41no—
387Dic7—22no—
388Dic7—22no—
389Dic7—22no—
390Dic7—22no—
391Dic7—41no—
392Dic7—41no—
393Dic7#40714yes—
394C24—71no—
395C24C2×C4×D711yescharacteristic
396C24C2×C4×D711yescharacteristic
397#41—1432no—
398C2×Q8—74no—
399C2×Q8—142no—
400C2×Q8—142no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—74no—
405C2×D4—142no—
406C2×D4—142no—
407C2×D4—142no—
408C2×D4—142no—
409C2×D4—142no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—71no—
413C22×C4—74no—
414C22×C4—71no—
415C22×C4—71no—
416C22×C4—71no—
417C22×C4—71no—
418C22×C4—74no—
419C22×C4—71no—
420C22×C4—71no—
421C22×C4—81no—
422C22×C4—81no—
423C22×C4—142no—
424C22×C4—142no—
425C22×C4—142no—
426C22×C4—142no—
427C22×C4—142no—
428C22×C4—142no—
429C22×C4—142no—
430C22×C4—142no—
431C22×C4—142no—
432C22×C4—142no—
433C22×C4—142no—
434C22×C4—561no—
435C22×C4—561no—
436C22×C4—561no—
437C22×C4—561no—
438C22×C4C2×C4×D711yescharacteristic
439C22×C4C2×C4×D711yescharacteristic
440C22×C4C2×C4×D711yescharacteristic
441C22×C4C2×C4×D711yescharacteristic
442C22×C4D4×D712yes—
443C22×C4D4×D712yes—
444C22×C4C23×D711yescharacteristic
445M16—82no—
446M16—564no—
447M16—562no—
448C2×C8—24no—
449C2×C8—144no—
450C4⋊C4—22no—
451C4⋊C4—72no—
452C4⋊C4—72no—
453C4⋊C4—142no—
454C4⋊C4—142no—
455C4⋊C4—142no—
456C4⋊C4—142no—
457C4⋊C4—141no—
458C4⋊C4—141no—
459C4⋊C4—141no—
460C4⋊C4—141no—
461C4⋊C4—142no—
462C4⋊C4—142no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—74no—
466C22⋊C4—72no—
467C22⋊C4—72no—
468C22⋊C4—142no—
469C22⋊C4—142no—
470C42—21no—
471C42—21no—
472C42—74no—
473C42—142no—
474C42—142no—
475C42—142no—
476C42—142no—
477C2×C7—21no—
478C2×C7—21no—
479C2×C7—42no—
480C2×C7—42no—
481C2×C7C2×#40711yescharacteristic
482C2×C7#288311yescharacteristic
483C2×C7#288911yescharacteristic
484D7—42no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—72no—
494C23—141no—
495C23—141no—
496C23—281no—
497C23—281no—
498C23D7×C22⋊C412yes—
499C23D7×M1612yes—
500C23C22×C4×D711yescharacteristic
501Q8—148no—
502D4—28no—
503D4—148no—
504D4—148no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—72no—
516C2×C4—72no—
517C2×C4—72no—
518C2×C4—72no—
519C2×C4—72no—
520C2×C4—72no—
521C2×C4—72no—
522C2×C4—81no—
523C2×C4—81no—
524C2×C4—148no—
525C2×C4—148no—
526C2×C4—148no—
527C2×C4—141no—
528C2×C4—141no—
529C2×C4—141no—
530C2×C4—141no—
531C2×C4—141no—
532C2×C4—141no—
533C2×C4—284no—
534C2×C4—281no—
535C2×C4—281no—
536C2×C4—281no—
537C2×C4—281no—
538C2×C4—562no—
539C2×C4—562no—
540C2×C4—562no—
541C2×C4D7×C22⋊C411yescharacteristic
542C2×C4D7×C22⋊C411yescharacteristic
543C2×C4D7×M1612yes—
544C2×C4C2×D4×D712yes—
545C8—44no—
546C8—284no—
547C7#1737011yescharacteristic, complemented, Sylow
548C22—21no—
549C22—21no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22—41no—
559C22—41no—
560C22—142no—
561C22—142no—
562C22—142no—
563C22—282no—
564C22—282no—
565C22C2×D7×C22⋊C411yescharacteristic
566C22C2×D7×M1611yescharacteristic
567C22C2×D7×M1611yescharacteristic
568C4—22no—
569C4—22no—
570C4—21no—
571C4—21no—
572C4—41no—
573C4—41no—
574C4—74no—
575C4—142no—
576C4—142no—
577C4—142no—
578C4—142no—
579C4—281no—
580C4—281no—
581C2—21no—
582C2—21no—
583C2—42no—
584C2—42no—
585C2—282no—
586C2D7×#40711yescharacteristic
587C2#1173613311yescharacteristic
588C2#1173616011yescharacteristic
subgroupG/H
centerC22C2×D7×C22⋊C4
commutatorC23×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1465C2
socleC22×C7C22×C22⋊C4
prime radicalC22×#1159C4
cosocleC22×C4×C7C24
hypercenter#1465D7
hypocenterC7#17370
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1465

Complements

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

NH ≅ G/Ntype
2. #11736079C2semidirect
3. C7×#1465C2semidirect
4. #11729356C2semidirect
5. #11727725C2semidirect
6. #11725898C2semidirect
7. #11725879C2semidirect
8. #11725875C2semidirect
9. #11725854C2semidirect
113. #1465D7semidirect
150. C22×Dic7M16semidirect
168. C2×Dic14M16semidirect
547. C7#17370semidirect

Maximal subgroups

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

subgroupindex
C2×#902372
#117360792
C7×#14652
#117293562
#117277252
#117258982
#117258792
#117258752
#117258542
#173707