Finite Group Databasebeta

← #13253963

Subgroups — #13253963

Order 1792.

684 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11731446C211yesmaximal, characteristic
2#11727662C211yesmaximal, characteristic
3Dic7×#95C211yesmaximal, characteristic
4C7×#1294C211yesmaximal, characteristic
5#11725481C211yesmaximal, characteristic
6#11725430C211yesmaximal, characteristic
7#11725418C211yesmaximal, characteristic
8C22×C4×Dic7—21no—
9C22×C4×Dic7C2211yescharacteristic
10C2×#6451C411yescharacteristic, complemented
11C2×#6441—21no—
12C2×C7×C22⋊C8C2211yescharacteristic
13C7×#380C2211yescharacteristic
14C2×C7×#95C2211yescharacteristic
15#89984C2211yescharacteristic
16C2×C7⋊#95—21no—
17C2×C7⋊#95C2211yescharacteristic
18C2×C22⋊(C7⋊C8)C2211yescharacteristic
19C2×Dic7⋊C8—21no—
20#89757C411yescharacteristic, complemented
21#89748C411yescharacteristic, complemented
22#89745C411yescharacteristic, complemented
23#89714—21no—
24#89419—21no—
25#89418—21no—
26#89345—21no—
27#9908—71nomaximal, Sylow
28C23×C4×C7—21no—
29C23×C4×C7C2311yescharacteristic
30C23×Dic7—21no—
31C23×Dic7D411yescharacteristic
32C23×Dic7D411yescharacteristic
33C22×Dic14—21no—
34C22×C7×C8—21no—
35C2×C7×C4⋊C4C2×C411yescharacteristic
36C2×C7×C4⋊C4C2×C411yescharacteristic
37C2×C7×C22⋊C4—21no—
38C2×C22⋊Dic7—21no—
39C2×C4⋊Dic7—21no—
40C2×C4⋊Dic7C2×C411yescharacteristic
41C2×C4⋊Dic7C2×C411yescharacteristic
42C2×Dic7⋊C4—21no—
43C2×Dic7⋊C4—21no—
44C2×Dic7⋊C4—21no—
45C2×Dic7⋊C4—21no—
46C2×C4×Dic7—24no—
47C2×C4×Dic7—42no—
48C2×C4×Dic7—42no—
49C2×C4×Dic7—42no—
50C2×C4×Dic7C2×C411yescharacteristic
51C2×C4×Dic7C2×C411yescharacteristic
52C2×C4×Dic7D411yescharacteristic
53C2×C4×Dic7D411yescharacteristic
54C22×C7⋊C8—21no—
55#6451—42no—
56#6441—42no—
57#6441—42no—
58C7×C22⋊C8—21no—
59C7×C22⋊C8—21no—
60C7×#95—21no—
61C7×#95—21no—
62C7×#95Q812yescomplemented
63C7⋊#95—24no—
64C7⋊#95—21no—
65C7⋊#95—21no—
66C7⋊#95—21no—
67C7⋊#95—21no—
68C7⋊#95Q812yescomplemented
69C22⋊(C7⋊C8)—21no—
70C22⋊(C7⋊C8)—21no—
71Dic7⋊C8—42no—
72#2857—71no—
73#1797—71no—
74C4×#95—71no—
75#1294—71no—
76#1294—71no—
77#1294—71no—
78#1294D711yescharacteristic
79C24×C7C2×D411yescharacteristic
80C22×C4×C7—22no—
81C22×C4×C7—22no—
82C22×C4×C7—22no—
83C22×C4×C7—21no—
84C22×C4×C7—21no—
85C22×C4×C7—41no—
86C22×C4×C7—41no—
87C22×C4×C7—41no—
88C22×C4×C7—41no—
89C22×C4×C7—41no—
90C22×C4×C7—41no—
91C22×C4×C7C22×C411yescharacteristic
92C22×C4×C7C2×D411yescharacteristic
93C22×C4×C7C2×Q811yescharacteristic
94C22×C4×C7C2×Q811yescharacteristic
95C22×C4×C7#4111yescharacteristic
96C22×C4×C7#4111yescharacteristic
97C22×Dic7—22no—
98C22×Dic7—22no—
99C22×Dic7—22no—
100C22×Dic7—22no—
101C22×Dic7—22no—
102C22×Dic7—21no—
103C22×Dic7—21no—
104C22×Dic7—22no—
105C22×Dic7—21no—
106C22×Dic7—21no—
107C22×Dic7—41no—
108C22×Dic7—41no—
109C22×Dic7—41no—
110C22×Dic7—41no—
111C22×Dic7—41no—
112C22×Dic7C22⋊C411yescharacteristic
113C22×Dic7C22⋊C411yescharacteristic
114C22×Dic7C22⋊C411yescharacteristic
115C22×Dic7C22⋊C411yescharacteristic
116C22×Dic7SD1612yes—
117C22×Dic7Q1612yes—
118C2×Dic14—42no—
119C2×Dic14—42no—
120C2×Dic14—42no—
121C2×C7×C8—41no—
122C2×C7×C8—41no—
123C2×C7×C8—41no—
124C7×C4⋊C4—41no—
125C7×C4⋊C4—41no—
126C7×C22⋊C4—41no—
127C7×C22⋊C4—41no—
128C22⋊Dic7—41no—
129C22⋊Dic7—41no—
130C4⋊Dic7—42no—
131C4⋊Dic7—41no—
132C4⋊Dic7—41no—
133Dic7⋊C4—42no—
134Dic7⋊C4—42no—
135Dic7⋊C4—42no—
136Dic7⋊C4—42no—
137C4×Dic7—22no—
138C4×Dic7—22no—
139C4×Dic7—41no—
140C4×Dic7—41no—
141C4×Dic7—48no—
142C2×C7⋊C8—41no—
143C2×C7⋊C8—41no—
144C2×C7⋊C8—41no—
145C2×C4⋊Q8—71no—
146C2×C22⋊Q8—141no—
147C22×C42—71no—
148C22×C42—141no—
149C2×C4⋊C8—141no—
150C2×C22⋊C8—71no—
151C2×C22⋊C8C2×D711yescharacteristic
152#391—141no—
153#389—71no—
154#389—71no—
155#389—141no—
156#384—71no—
157#380—71no—
158#380—141no—
159#380C2×D711yescharacteristic
160C2×#95—71no—
161C2×#95—141no—
162C2×#95C2×D711yescharacteristic
163#336—141no—
164C23×C7—21no—
165C23×C7—21no—
166C23×C7—21no—
167C23×C7—21no—
168C23×C7C2×C22⋊C411yescharacteristic
169C23×C7C22⋊Q811yescharacteristic
170C23×C7C22⋊Q811yescharacteristic
171C23×C7C2×SD1611yescharacteristic
172C23×C7C2×Q1611yescharacteristic
173C23×C7AGL(1,ℤ/8)11yescharacteristic
174C23×C7AGL(1,ℤ/8)11yescharacteristic
175C2×C4×C7—21no—
176C2×C4×C7—21no—
177C2×C4×C7—21no—
178C2×C4×C7—21no—
179C2×C4×C7—24no—
180C2×C4×C7—41no—
181C2×C4×C7—41no—
182C2×C4×C7—41no—
183C2×C4×C7—41no—
184C2×C4×C7—42no—
185C2×C4×C7—42no—
186C2×C4×C7—42no—
187C2×C4×C7—42no—
188C2×C4×C7—42no—
189C2×C4×C7—42no—
190C2×C4×C7—41no—
191C2×C4×C7—41no—
192C2×C4×C7—41no—
193C2×C4×C7—41no—
194C2×C4×C7—41no—
195C2×C4×C7—41no—
196C2×C4×C7C4×Q811yescharacteristic
197C2×C4×C7C4×Q811yescharacteristic
198C2×C4×C7#12411yescharacteristic
199C2×C4×C7C4⋊Q811yescharacteristic
200C2×Dic7—21no—
201C2×Dic7—21no—
202C2×Dic7—21no—
203C2×Dic7—21no—
204C2×Dic7—24no—
205C2×Dic7—24no—
206C2×Dic7—24no—
207C2×Dic7—21no—
208C2×Dic7—21no—
209C2×Dic7—21no—
210C2×Dic7—42no—
211C2×Dic7—42no—
212C2×Dic7—42no—
213C2×Dic7—42no—
214C2×Dic7—42no—
215C2×Dic7—42no—
216C2×Dic7—42no—
217C2×Dic7—42no—
218C2×Dic7—41no—
219C2×Dic7—41no—
220C2×Dic7—41no—
221C2×Dic7—41no—
222C2×Dic7—41no—
223C2×Dic7—41no—
224C2×Dic7#9912yes—
225C2×Dic7#10312yes—
226C2×Dic7#10312yes—
227C2×Dic7#10412yes—
228C2×Dic7#10412yes—
229Dic14—84no—
230C7×C8—81no—
231C7⋊C8—81no—
232C22×Q8—141no—
233C23×C4—21no—
234C23×C4—71no—
235C23×C4—71no—
236C23×C4—141no—
237C23×C4C22×D711yescharacteristic
238C22×C8—21no—
239C22×C8—141no—
240C4⋊Q8—282no—
241C22⋊Q8—282no—
242C22⋊Q8—282no—
243C2×C4⋊C4—71no—
244C2×C4⋊C4—71no—
245C2×C4⋊C4—141no—
246C2×C4⋊C4—141no—
247C2×C4⋊C4—141no—
248C2×C4⋊C4—141no—
249C2×C4⋊C4—141no—
250C2×C4⋊C4C4×D711yescharacteristic
251C2×C4⋊C4C4×D711yescharacteristic
252C2×C22⋊C4—21no—
253C2×C22⋊C4—141no—
254C2×C42—71no—
255C2×C42—71no—
256C2×C42—71no—
257C2×C42—71no—
258C2×C42—144no—
259C2×C42—282no—
260C2×C42—282no—
261C2×C42—282no—
262C4⋊C8—282no—
263C22⋊C8—21no—
264C22⋊C8—21no—
265C22⋊C8—141no—
266C22⋊C8—141no—
267#95—21no—
268#95—21no—
269#95—72no—
270#95—141no—
271#95—141no—
272#95—144no—
273#95—141no—
274#95—141no—
275#95Dic1412yescomplemented
276C22×C7—21no—
277C22×C7—21no—
278C22×C7—21no—
279C22×C7—21no—
280C22×C7—21no—
281C22×C7—21no—
282C22×C7—21no—
283C22×C7—21no—
284C22×C7—21no—
285C22×C7—21no—
286C22×C7—21no—
287C22×C7—21no—
288C22×C7#39111yescharacteristic
289C22×C7C2×#9911yescharacteristic
290C22×C7#41011yescharacteristic
291C22×C7C2×#10311yescharacteristic
292C22×C7#41811yescharacteristic
293C22×C7C2×#10411yescharacteristic
294C22×C7C2×#10411yescharacteristic
295C22×C7#47611yescharacteristic
296C22×C7#47611yescharacteristic
297C22×C7#47711yescharacteristic
298C22×C7#47711yescharacteristic
299C4×C7—21no—
300C4×C7—21no—
301C4×C7—21no—
302C4×C7—21no—
303C4×C7—44no—
304C4×C7—81no—
305C4×C7—81no—
306Dic7—22no—
307Dic7—22no—
308Dic7—44no—
309Dic7—41no—
310Dic7—81no—
311Dic7—81no—
312Dic7#32814yes—
313C24D4×D711yescharacteristic
314C2×Q8—282no—
315C2×Q8—282no—
316C2×Q8—282no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—71no—
329C22×C4—71no—
330C22×C4—71no—
331C22×C4—72no—
332C22×C4—72no—
333C22×C4—71no—
334C22×C4—142no—
335C22×C4—142no—
336C22×C4—142no—
337C22×C4—142no—
338C22×C4—142no—
339C22×C4—142no—
340C22×C4—141no—
341C22×C4—141no—
342C22×C4—141no—
343C22×C4—141no—
344C22×C4—281no—
345C22×C4—281no—
346C22×C4—281no—
347C22×C4—281no—
348C22×C4—281no—
349C22×C4C2×Dic1411yescharacteristic
350C22×C4C2×C4×D711yescharacteristic
351C22×C4#115711yescharacteristic
352C22×C4D4×D711yescharacteristic
353C22×C4#115911yescharacteristic
354C22×C4Q8×D711yescharacteristic
355C2×C8—41no—
356C2×C8—41no—
357C2×C8—41no—
358C2×C8—281no—
359C2×C8—281no—
360C2×C8—281no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—281no—
364C4⋊C4—281no—
365C4⋊C4—282no—
366C4⋊C4—282no—
367C4⋊C4—282no—
368C4⋊C4—282no—
369C4⋊C4—282no—
370C22⋊C4—41no—
371C22⋊C4—41no—
372C22⋊C4—281no—
373C22⋊C4—281no—
374C42—142no—
375C42—142no—
376C42—281no—
377C42—281no—
378C42—288no—
379C2×C7—21no—
380C2×C7—21no—
381C2×C7—21no—
382C2×C7—21no—
383C2×C7C2×#32811yescharacteristic
384C2×C7#150311yescharacteristic
385C2×C7#150511yescharacteristic
386C2×C7#150711yescharacteristic
387C2×C7#198711yescharacteristic
388C2×C7#199411yescharacteristic
389C2×C7#199611yescharacteristic
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23#644111yescharacteristic
395C23D7×C22⋊C411yescharacteristic
396C23#645911yescharacteristic
397C23#647411yescharacteristic
398C23D7×SD1611yescharacteristic
399C23#647711yescharacteristic
400C23D7×Q1611yescharacteristic
401Q8—564no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—24no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—72no—
424C2×C4—72no—
425C2×C4—72no—
426C2×C4—72no—
427C2×C4—72no—
428C2×C4—144no—
429C2×C4—144no—
430C2×C4—141no—
431C2×C4—141no—
432C2×C4—141no—
433C2×C4—141no—
434C2×C4—144no—
435C2×C4—141no—
436C2×C4—141no—
437C2×C4—141no—
438C2×C4—282no—
439C2×C4—282no—
440C2×C4—282no—
441C2×C4—282no—
442C2×C4—282no—
443C2×C4—282no—
444C2×C4—282no—
445C2×C4—282no—
446C2×C4—281no—
447C2×C4—281no—
448C2×C4—281no—
449C2×C4—281no—
450C2×C4—281no—
451C2×C4—281no—
452C2×C4C4×Dic1411yescharacteristic
453C2×C4#644811yescharacteristic
454C2×C4#645011yescharacteristic
455C2×C4#645111yescharacteristic
456C8—81no—
457C8—561no—
458C7#990811yescharacteristic, complemented, Sylow
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22#8941811yescharacteristic
472C22#8951211yescharacteristic
473C22D7×#9911yescharacteristic
474C22#8953311yescharacteristic
475C22#8954211yescharacteristic
476C22#8956611yescharacteristic
477C22D7×#10311yescharacteristic
478C22D7×#10411yescharacteristic
479C22D7×#10411yescharacteristic
480C22#8964211yescharacteristic
481C22#8964711yescharacteristic
482C4—21no—
483C4—21no—
484C4—21no—
485C4—21no—
486C4—44no—
487C4—74no—
488C4—81no—
489C4—81no—
490C4—142no—
491C4—142no—
492C4—284no—
493C4—281no—
494C4—561no—
495C4—561no—
496C2—21no—
497C2—21no—
498C2—21no—
499C2—21no—
500C2#1172603211yescharacteristic
501C2#1172605711yescharacteristic
502C2#1172606311yescharacteristic
503C2D7×#32811yescharacteristic
504C2#1172648511yescharacteristic
505C2#1172655311yescharacteristic
506C2#1172670911yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC7×#1294C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C2×D4
cosocleC23×C4×C7C23
hypercenter#1294D7
hypocenterC7#9908
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
10. C2×#6451C4semidirect
20. #89757C4semidirect
21. #89748C4semidirect
22. #89745C4semidirect
62. C7×#95Q8semidirect
68. C7⋊#95Q8semidirect
275. #95Dic14semidirect
458. C7#9908semidirect

Maximal subgroups

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

subgroupindex
#117314462
#117276622
Dic7×#952
C7×#12942
#117254812
#117254302
#117254182
#99087