Finite Group Databasebeta

← #13059617

Subgroups — #13059617

Order 1344.

496 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10621412C211yesmaximal, characteristic, complemented
2C2×C7×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
3C3×#6489C211yesmaximal, characteristic, complemented
4#10621137C211yesmaximal, characteristic, complemented
5#10621132C211yesmaximal, characteristic
6#10621118C211yesmaximal, characteristic, complemented
7D3×C22⋊Dic7C211yesmaximal, characteristic, complemented
8#10621000C211yesmaximal, characteristic, complemented
9#10620998C211yesmaximal, characteristic, complemented
10#10620989C211yesmaximal, characteristic, complemented
11#10620967C211yesmaximal, characteristic, complemented
12#10620960C211yesmaximal, characteristic, complemented
13#10620934C211yesmaximal, characteristic, complemented
14#10620912C211yesmaximal, characteristic, complemented
15#10620903C211yesmaximal, characteristic, complemented
16#90186—31nomaximal, Hall
17C23×D3×C7C2211yescharacteristic
18C22×C3×C4×C7C2211yescharacteristic
19C2×#4268C2211yescharacteristic
20C22×C7×Dic3C2211yescharacteristic
21C2×#4248C2211yescharacteristic, complemented
22C2×#4247C2211yescharacteristic
23C2×#4247C2211yescharacteristic
24C2×D21⋊C4C2211yescharacteristic, complemented
25C2×D3×Dic7C2211yescharacteristic
26C2×D3×Dic7C2211yescharacteristic
27#66636C2211yescharacteristic
28#66631C2211yescharacteristic, complemented
29#66631C2211yescharacteristic, complemented
30#66629C2211yescharacteristic, complemented
31#66629C2211yescharacteristic, complemented
32C7×(C2×D3)⋊C4C2211yescharacteristic
33C7×(C2×D3)⋊C4C2211yescharacteristic
34C7×(C2×D3)⋊C4C2211yescharacteristic
35C7×(C2×D3)⋊C4C2211yescharacteristic
36C3×C22⋊Dic7C2211yescharacteristic
37C3×C22⋊Dic7C2211yescharacteristic
38C3×C4⋊Dic7C2211yescharacteristic, complemented
39C3×C4⋊Dic7C2211yescharacteristic, complemented
40C3×C4×Dic7C2211yescharacteristic, complemented
41C3×C4×Dic7C2211yescharacteristic, complemented
42Dic3⋊Dic7C2211yescharacteristic, complemented
43#66577C2211yescharacteristic, complemented
44#66577C2211yescharacteristic, complemented
45Dic7⋊Dic3C2211yescharacteristic, complemented
46#66575C2211yescharacteristic, complemented
47(C2×D3)⋊Dic7C2211yescharacteristic
48(C2×D3)⋊Dic7C2211yescharacteristic
49(C2×D3)⋊Dic7C2211yescharacteristic
50(C2×D3)⋊Dic7C2211yescharacteristic
51Dic3×Dic7C2211yescharacteristic, complemented
52C2×C7×C22⋊C4—31no—
53#6516—31no—
54C2×C22⋊Dic7—31no—
55#6492—31no—
56C4×C22⋊D7—31no—
57#6489D311yescharacteristic, complemented
58#6487—31no—
59#6449—31no—
60#6448—31no—
61#6446—31no—
62(C22⋊D7)⋊C4—31no—
63#6442—31no—
64#6442—31no—
65#6441—31no—
66#6440—31no—
67#5527—71nomaximal, Hall
68C23×C3×C7C2311yescharacteristic
69C22×D21C2311yescharacteristic
70C22×D3×C7—22no—
71C22×D3×C7—22no—
72C22×D3×C7—41no—
73C22×D3×C7C2311yescharacteristic
74C22×D3×C7C2311yescharacteristic
75C2×C3×C4×C7—22no—
76C2×C3×C4×C7C2311yescharacteristic
77C2×C3×C4×C7C2311yescharacteristic
78#4268—22no—
79C2×Dic21C2311yescharacteristic
80C2×Dic21C2311yescharacteristic
81C2×Dic21C2311yescharacteristic
82C2×C7×Dic3—41no—
83C2×C7×Dic3C2311yescharacteristic
84C2×C7×Dic3C2311yescharacteristic
85C2×C3×Dic7C2311yescharacteristic
86C2×C3×Dic7C2311yescharacteristic
87C2×C3×Dic7C2311yescharacteristic
88C2×C3×Dic7C2311yescharacteristic
89#4248—41no—
90#4247—22no—
91#4247—41no—
92D21⋊C4—41no—
93D3×Dic7—22no—
94D3×Dic7—41no—
95C24×C7—31no—
96C22×C4×C7—31no—
97C22×C4×C7C2×D311yescharacteristic
98C2×C22⋊D7—31no—
99C2×C22⋊D7—31no—
100C2×C22⋊D7—31no—
101C22×Dic7—31no—
102C22×Dic7—31no—
103C2×C4×D7—31no—
104C2×Dic14—31no—
105C7×C22⋊C4—31no—
106C7×C22⋊C4—31no—
107C7×C22⋊C4—31no—
108C7×C22⋊C4—31no—
109C22⋊Dic7—31no—
110C22⋊Dic7—31no—
111C22⋊Dic7—31no—
112C22⋊Dic7—31no—
113C22⋊Dic7—31no—
114C22⋊Dic7C2×D311yescharacteristic
115C22⋊Dic7C2×D311yescharacteristic
116(C2×D7)⋊C4—31no—
117(C2×D7)⋊C4—31no—
118(C2×D7)⋊C4—31no—
119C4⋊Dic7—31no—
120C4⋊Dic7C2×D311yescharacteristic, complemented
121C4⋊Dic7C2×D311yescharacteristic, complemented
122Dic7⋊C4—31no—
123Dic7⋊C4—31no—
124Dic7⋊C4—31no—
125Dic7⋊C4—31no—
126Dic7⋊C4—31no—
127C4×Dic7—31no—
128C4×Dic7C2×D311yescharacteristic, complemented
129C4×Dic7C2×D311yescharacteristic, complemented
130C3×#117—71no—
131#929—71no—
132C2×(C2×D3)⋊C4D711yescharacteristic, complemented
133#898—71no—
134#896—71no—
135#894—71no—
136#894—71no—
137#882—71no—
138#67⋊C4—71no—
139D3×C22⋊C4—71no—
140#878—71no—
141#876—71no—
142#875—71no—
143C4×D12—71no—
144#872—71no—
145C22×C3×C7—21no—
146C22×C3×C7—21no—
147C22×C3×C7#4112yes—
148C22×C3×C7C2411yescharacteristic
149C2×D21—21no—
150C2×D21—21no—
151C2×D21—21no—
152C2×D3×C7—21no—
153C2×D3×C7—21no—
154C2×D3×C7—21no—
155C2×D3×C7—21no—
156C2×D3×C7—21no—
157C2×D3×C7—44no—
158C2×D3×C7#4112yes—
159C3×C4×C7—21no—
160C3×C4×C7—21no—
161Dic21—21no—
162Dic21—21no—
163Dic21—21no—
164C3×Dic7—21no—
165C3×Dic7—21no—
166C3×Dic7—21no—
167C3×Dic7—21no—
168C7×Dic3—21no—
169C7×Dic3—21no—
170#551—211noSylow
171C23×C7—31no—
172C23×C7—31no—
173C23×C7—62no—
174C23×C7—62no—
175C23×C7—121no—
176C23×C7C22×D311yescharacteristic
177C22×D7—31no—
178C2×C4×C7—22no—
179C2×C4×C7—31no—
180C2×C4×C7—31no—
181C2×C4×C7—121no—
182C2×C4×C7C22×D311yescharacteristic
183C2×C4×C7C22×D311yescharacteristic
184C22⋊D7—62no—
185C22⋊D7—62no—
186C22⋊D7—121no—
187C2×Dic7—31no—
188C2×Dic7—31no—
189C2×Dic7—31no—
190C2×Dic7—62no—
191C2×Dic7—121no—
192C2×Dic7C22×D311yescharacteristic
193C2×Dic7C22×D311yescharacteristic
194C2×Dic7C22×D311yescharacteristic
195C2×Dic7C22×D311yescharacteristic
196C4×D7—121no—
197Dic14—121no—
198C23×D3C2×D711yescharacteristic
199C22×C3×C4C2×D711yescharacteristic
200C2×#67—71no—
201C22×Dic3C2×D711yescharacteristic
202C2×D12—71no—
203C2×D12—71no—
204C2×C4×D3—71no—
205C2×C4×D3—71no—
206C2×C4×D3—71no—
207C2×Dic6—71no—
208C3×C4⋊C4—71no—
209C3×C4⋊C4—71no—
210C3×C22⋊C4—71no—
211C3×C22⋊C4—71no—
212C3×C42—71no—
213C3×C42—71no—
214#217—71no—
215(C2×D3)⋊C4—71no—
216(C2×D3)⋊C4—71no—
217(C2×D3)⋊C4—71no—
218(C2×D3)⋊C4—71no—
219(C2×D3)⋊C4—71no—
220(C2×D3)⋊C4—71no—
221(C2×D3)⋊C4—71no—
222(C2×D3)⋊C4C2×D711yescharacteristic
223(C2×D3)⋊C4C2×D711yescharacteristic
224(C2×D3)⋊C4C2×D711yescharacteristic
225(C2×D3)⋊C4C2×D711yescharacteristic
226C4⋊Dic3—71no—
227Dic3⋊C4—71no—
228Dic3⋊C4—71no—
229Dic3⋊C4—71no—
230Dic3⋊C4—71no—
231Dic3⋊C4—71no—
232C4×Dic3—71no—
233C2×C3×C7—22no—
234C2×C3×C7C2×#4111yescharacteristic
235C2×C3×C7C2×#4111yescharacteristic
236C2×C3×C7H(5,𝔽2)11yescharacteristic
237D21—41no—
238D3×C7—22no—
239D3×C7—41no—
240#126—211no—
241#126—211no—
242#124—211no—
243#123—211no—
244#123—211no—
245#123—211no—
246C22⋊Q8—211no—
247C22⋊Q8—211no—
248#120—211no—
249C4×D4—211no—
250C4×D4—211no—
251#117—71no—
252#117—211no—
253C2×C22⋊C4—31no—
254C2×C22⋊C4—211no—
255C22×C7—21no—
256C22×C7—21no—
257C22×C7—32no—
258C22×C7—61no—
259C22×C7—61no—
260C22×C7—61no—
261C22×C7—61no—
262C22×C7—61no—
263C22×C7—124no—
264C22×C7#23512yes—
265C22×C7C23×D311yescharacteristic
266C2×D7—61no—
267C2×D7—61no—
268C2×D7—61no—
269C4×C7—21no—
270C4×C7—21no—
271C4×C7—61no—
272C4×C7—61no—
273Dic7—21no—
274Dic7—21no—
275Dic7—21no—
276Dic7—21no—
277Dic7—61no—
278Dic7—61no—
279Dic7—61no—
280C23×C3C22×D711yescharacteristic
281C22×D3—22no—
282C22×D3—22no—
283C22×D3—41no—
284C22×D3—71no—
285C22×D3C22×D711yescharacteristic
286C22×D3C22×D711yescharacteristic
287C2×C3×C4—22no—
288C2×C3×C4—71no—
289C2×C3×C4—71no—
290C2×C3×C4—71no—
291C2×C3×C4—71no—
292C2×C3×C4C22×D711yescharacteristic
293C2×C3×C4C22×D711yescharacteristic
294#67—142no—
295C2×Dic3—41no—
296C2×Dic3—71no—
297C2×Dic3—71no—
298C2×Dic3—71no—
299C2×Dic3C22×D711yescharacteristic
300C2×Dic3C22×D711yescharacteristic
301D12—142no—
302D12—281no—
303C4×D3—142no—
304C4×D3—281no—
305C4×D3—281no—
306Dic6—281no—
307C3×C7#55111yescharacteristic, complemented, Hall
308C24—31no—
309C2×Q8—211no—
310C2×D4—211no—
311C2×D4—211no—
312C2×D4—211no—
313C22×C4—31no—
314C22×C4—211no—
315C22×C4—211no—
316C22×C4—211no—
317C22×C4D3×D711yescharacteristic
318C4⋊C4—71no—
319C4⋊C4—71no—
320C4⋊C4—211no—
321C4⋊C4—211no—
322C4⋊C4—211no—
323C4⋊C4—211no—
324C4⋊C4—211no—
325C4⋊C4—211no—
326C22⋊C4—31no—
327C22⋊C4—31no—
328C22⋊C4—31no—
329C22⋊C4—31no—
330C22⋊C4—71no—
331C22⋊C4—71no—
332C22⋊C4—211no—
333C22⋊C4—211no—
334C22⋊C4—211no—
335C22⋊C4—211no—
336C22⋊C4—211no—
337C22⋊C4—211no—
338C22⋊C4—211no—
339C22⋊C4—211no—
340C42—71no—
341C42—71no—
342C42—211no—
343C2×C7—22no—
344C2×C7—62no—
345C2×C7—121no—
346C2×C7C2×#23511yescharacteristic
347C2×C7D3×#4111yescharacteristic
348C2×C7#100911yescharacteristic
349D7—121no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3#115912yes—
353C22×C3C23×D711yescharacteristic
354C2×D3—21no—
355C2×D3—21no—
356C2×D3—21no—
357C2×D3—21no—
358C2×D3—21no—
359C2×D3—44no—
360C2×D3—141no—
361C2×D3—141no—
362C2×D3—141no—
363C2×D3#115712yes—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—141no—
367C3×C4—141no—
368C3×C4—141no—
369C3×C4—141no—
370Dic3—21no—
371Dic3—21no—
372Dic3—141no—
373Dic3—141no—
374Dic3—141no—
375C23—31no—
376C23—31no—
377C23—62no—
378C23—62no—
379C23—121no—
380C23—211no—
381C23C2×D3×D711yescharacteristic
382Q8—841no—
383D4—422no—
384D4—422no—
385D4—841no—
386C2×C4—22no—
387C2×C4—31no—
388C2×C4—31no—
389C2×C4—71no—
390C2×C4—71no—
391C2×C4—71no—
392C2×C4—71no—
393C2×C4—121no—
394C2×C4—211no—
395C2×C4—211no—
396C2×C4—211no—
397C2×C4—422no—
398C2×C4—841no—
399C2×C4—841no—
400C2×C4C2×D3×D711yescharacteristic
401C2×C4C2×D3×D711yescharacteristic
402C7#552711yescharacteristic, complemented, Sylow
403C2×C3—22no—
404C2×C3C2×#115711yescharacteristic
405C2×C3C2×#115911yescharacteristic
406C2×C3#654811yescharacteristic
407D3—22no—
408D3—41no—
409D3—281no—
410C22—21no—
411C22—21no—
412C22—32no—
413C22—61no—
414C22—61no—
415C22—61no—
416C22—61no—
417C22—61no—
418C22—124no—
419C22—421no—
420C22—421no—
421C22—421no—
422C22#6668612yes—
423C22C22×D3×D711yescharacteristic
424C4—21no—
425C4—21no—
426C4—61no—
427C4—61no—
428C4—141no—
429C4—141no—
430C4—141no—
431C4—141no—
432C4—421no—
433C4—421no—
434C4—421no—
435C3#9018611yescharacteristic, complemented, Sylow
436C2—22no—
437C2—62no—
438C2—121no—
439C2—841no—
440C2D3×#115711yescharacteristic
441C2#1062156511yescharacteristic
442C2C2×#6668611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC22×C3×C4×C7C22
prime radical#10621132C2
hypercenterC22×C4D3×D7
hypocenterC3×C7#551
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. #10621412C2semidirect
2. C2×C7×(C2×D3)⋊C4C2semidirect
3. C3×#6489C2semidirect
4. #10621137C2semidirect
6. #10621118C2semidirect
7. D3×C22⋊Dic7C2semidirect
8. #10621000C2semidirect
9. #10620998C2semidirect
10. #10620989C2semidirect
11. #10620967C2semidirect
12. #10620960C2semidirect
13. #10620934C2semidirect
14. #10620912C2semidirect
15. #10620903C2semidirect
21. C2×#4248C22semidirect
24. C2×D21⋊C4C22semidirect
28. #66631C22semidirect
29. #66631C22semidirect
30. #66629C22semidirect
31. #66629C22semidirect
38. C3×C4⋊Dic7C22semidirect
39. C3×C4⋊Dic7C22semidirect
40. C3×C4×Dic7C22semidirect
41. C3×C4×Dic7C22semidirect
42. Dic3⋊Dic7C22semidirect
43. #66577C22semidirect
44. #66577C22semidirect
45. Dic7⋊Dic3C22semidirect
46. #66575C22semidirect
51. Dic3×Dic7C22semidirect
57. #6489D3semidirect
120. C4⋊Dic7C2×D3semidirect
121. C4⋊Dic7C2×D3semidirect
128. C4×Dic7C2×D3semidirect
129. C4×Dic7C2×D3semidirect
132. C2×(C2×D3)⋊C4D7semidirect
307. C3×C7#551semidirect
402. C7#5527semidirect
435. C3#90186semidirect

Maximal subgroups

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

subgroupindex
#106214122
C2×C7×(C2×D3)⋊C42
C3×#64892
#106211372
#106211322
#106211182
D3×C22⋊Dic72
#106210002
#106209982
#106209892
#106209672
#106209602
#106209342
#106209122
#106209032
#901863
#55277