Finite Group Databasebeta

← #13060042

Subgroups — #13060042

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#10621420C211yesmaximal, characteristic
2C7×D4×Dic3C211yesmaximal, characteristic, complemented
3C3×#6498C211yesmaximal, characteristic, complemented
4#10621137C211yesmaximal, characteristic, complemented
5#10621124C211yesmaximal, characteristic, complemented
6#10621123C211yesmaximal, characteristic, complemented
7#10621118C211yesmaximal, characteristic, complemented
8#10621104C211yesmaximal, characteristic, complemented
9C2×#66575C211yesmaximal, characteristic, complemented
10#10621090C211yesmaximal, characteristic, complemented
11#10621088C211yesmaximal, characteristic, complemented
12#10620981C211yesmaximal, characteristic, complemented
13#10620965C211yesmaximal, characteristic, complemented
14#10620942C211yesmaximal, characteristic, complemented
15#10620899C211yesmaximal, characteristic, complemented
16#90247—31nomaximal, Hall
17C23×D21C2211yescharacteristic
18C2×C3×C7×D4C2211yescharacteristic
19C2×#4268C2211yescharacteristic
20C2×#4268C2211yescharacteristic
21C22×C7×Dic3C2211yescharacteristic
22C22×C7×Dic3C2211yescharacteristic, complemented
23C22×C3×Dic7C2211yescharacteristic
24C2×#4248C2211yescharacteristic, complemented
25C2×D21⋊C4C2211yescharacteristic
26C2×D21⋊C4C2211yescharacteristic
27#66636C2211yescharacteristic
28#66631C2211yescharacteristic
29#66631C2211yescharacteristic
30C7×#217C2211yescharacteristic
31C7×#217C2211yescharacteristic, complemented
32C7×C4⋊Dic3C2211yescharacteristic, complemented
33C4×C7×Dic3C2211yescharacteristic, complemented
34C3×C22⋊Dic7C2211yescharacteristic
35C3×C22⋊Dic7C2211yescharacteristic, complemented
36C3×C22⋊Dic7C2211yescharacteristic, complemented
37C3×Dic7⋊C4C2211yescharacteristic, complemented
38C3×Dic7⋊C4C2211yescharacteristic, complemented
39Dic3⋊Dic7C2211yescharacteristic, complemented
40#66577C2211yescharacteristic, complemented
41Dic7⋊Dic3C2211yescharacteristic, complemented
42Dic7⋊Dic3C2211yescharacteristic, complemented
43Dic7⋊Dic3C2211yescharacteristic, complemented
44#66575C2211yescharacteristic
45#66575C2211yescharacteristic
46#66575C2211yescharacteristic
47#66575C2211yescharacteristic
48#66575C2211yescharacteristic
49#66575C2211yescharacteristic
50Dic3×Dic7C2211yescharacteristic, complemented
51Dic3×Dic7C2211yescharacteristic, complemented
52C4×C7×D4—31no—
53#6500—31no—
54#6498D311yescharacteristic, complemented
55#6492—31no—
56C4×C22⋊D7—31no—
57C2×(C2×D7)⋊C4—31no—
58#6487—31no—
59#6461—31no—
60#6459—31no—
61#6448—31no—
62#6446—31no—
63D7×C22⋊C4—31no—
64#6440—31no—
65#6439—31no—
66#6435—31no—
67#5658—71nomaximal, Hall
68C23×C3×C7C2311yescharacteristic
69C23×C3×C7C2311yescharacteristic
70C22×D21—22no—
71C22×D21—22no—
72C22×D21—41no—
73C22×D21C2311yescharacteristic
74C22×D21C2311yescharacteristic
75C3×C7×D4—22no—
76C2×C3×C4×C7C2311yescharacteristic
77#4268—22no—
78#4268—41no—
79C2×Dic21C2311yescharacteristic
80C2×Dic21C2311yescharacteristic
81C2×C7×Dic3—41no—
82C2×C7×Dic3—41no—
83C2×C7×Dic3C2311yescharacteristic
84C2×C7×Dic3C2311yescharacteristic
85C2×C7×Dic3C2311yescharacteristic
86C2×C7×Dic3C2311yescharacteristic
87C2×C3×Dic7—22no—
88C2×C3×Dic7C2311yescharacteristic
89C2×C3×Dic7C2311yescharacteristic
90C2×C3×Dic7C2311yescharacteristic
91C2×C3×Dic7C2311yescharacteristic
92#4248—41no—
93D21⋊C4—22no—
94D21⋊C4—41no—
95C23×D7—31no—
96C2×C7×D4C2×D311yescharacteristic
97C22×C4×C7—31no—
98C22×C4×C7—31no—
99C2×C22⋊D7—31no—
100C2×C22⋊D7—31no—
101C22×Dic7C2×D311yescharacteristic
102C2×C4×D7—31no—
103C2×C4×D7—31no—
104C2×Dic14—31no—
105C7×C4⋊C4—31no—
106C7×C22⋊C4—31no—
107C7×C22⋊C4—31no—
108C42×C7—31no—
109C22⋊Dic7—31no—
110C22⋊Dic7C2×D311yescharacteristic
111C22⋊Dic7C2×D311yescharacteristic, complemented
112C22⋊Dic7C2×D311yescharacteristic, complemented
113(C2×D7)⋊C4—31no—
114(C2×D7)⋊C4—31no—
115(C2×D7)⋊C4—31no—
116(C2×D7)⋊C4—31no—
117(C2×D7)⋊C4—31no—
118(C2×D7)⋊C4—31no—
119(C2×D7)⋊C4—31no—
120(C2×D7)⋊C4—31no—
121C4⋊Dic7—31no—
122Dic7⋊C4—31no—
123Dic7⋊C4—31no—
124Dic7⋊C4—31no—
125Dic7⋊C4—31no—
126Dic7⋊C4C2×D311yescharacteristic, complemented
127Dic7⋊C4C2×D311yescharacteristic, complemented
128C4×Dic7—31no—
129C4×Dic7—31no—
130C3×#123—71no—
131#937—71no—
132D4×Dic3D711yescharacteristic, complemented
133C2×(C2×D3)⋊C4—71no—
134#926—71no—
135#898—71no—
136#898—71no—
137#897—71no—
138#892—71no—
139#886—71no—
140#885—71no—
141#883—71no—
142#67⋊C4—71no—
143D3×C22⋊C4—71no—
144#878—71no—
145C22×C3×C7—21no—
146C22×C3×C7—21no—
147C22×C3×C7—21no—
148C22×C3×C7—21no—
149C22×C3×C7—21no—
150C22×C3×C7#4112yes—
151C22×C3×C7C2411yescharacteristic
152C2×D21—21no—
153C2×D21—21no—
154C2×D21—21no—
155C2×D21—21no—
156C2×D21—21no—
157C2×D21—44no—
158C2×D21#4112yes—
159C3×C4×C7—21no—
160Dic21—21no—
161Dic21—21no—
162C3×Dic7—21no—
163C3×Dic7—21no—
164C3×Dic7—21no—
165C3×Dic7—21no—
166C7×Dic3—21no—
167C7×Dic3—21no—
168C7×Dic3—21no—
169C7×Dic3—21no—
170#551—211noSylow
171C23×C7C22×D311yescharacteristic
172C23×C7C22×D311yescharacteristic
173C22×D7—31no—
174C22×D7—31no—
175C22×D7—62no—
176C22×D7—62no—
177C22×D7—121no—
178C7×D4—22no—
179C2×C4×C7—31no—
180C2×C4×C7—31no—
181C2×C4×C7—31no—
182C2×C4×C7—31no—
183C2×C4×C7—121no—
184C2×C4×C7—121no—
185C2×C4×C7C22×D311yescharacteristic
186C22⋊D7—62no—
187C22⋊D7—121no—
188C2×Dic7—22no—
189C2×Dic7—31no—
190C2×Dic7—31no—
191C2×Dic7C22×D311yescharacteristic
192C2×Dic7C22×D311yescharacteristic
193C2×Dic7C22×D311yescharacteristic
194C2×Dic7C22×D311yescharacteristic
195C4×D7—62no—
196C4×D7—121no—
197Dic14—121no—
198C23×D3—71no—
199C2×C3×D4C2×D711yescharacteristic
200C22×C3×C4—71no—
201C2×#67—71no—
202C2×#67—71no—
203C22×Dic3C2×D711yescharacteristic
204C22×Dic3C2×D711yescharacteristic, complemented
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×C22⋊C4—71no—
213#217—71no—
214#217C2×D711yescharacteristic
215#217C2×D711yescharacteristic, complemented
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)⋊C4—71no—
223(C2×D3)⋊C4—71no—
224C4⋊Dic3—71no—
225C4⋊Dic3—71no—
226C4⋊Dic3—71no—
227C4⋊Dic3C2×D711yescharacteristic, complemented
228Dic3⋊C4—71no—
229Dic3⋊C4—71no—
230C4×Dic3—71no—
231C4×Dic3—71no—
232C4×Dic3C2×D711yescharacteristic, complemented
233C2×C3×C7—22no—
234C2×C3×C7—41no—
235C2×C3×C7C2×#4111yescharacteristic
236C2×C3×C7C2×#4111yescharacteristic
237C2×C3×C7H(5,𝔽2)11yescharacteristic
238D21—22no—
239D21—41no—
240#126—211no—
241#126—211no—
242#124—211no—
243#123—71no—
244#123—211no—
245#123—211no—
246C22⋊Q8—211no—
247C22⋊Q8—211no—
248#120—211no—
249C4×D4—31no—
250C4×D4—211no—
251#117—211no—
252#117—211no—
253C2×C22⋊C4—211no—
254C2×C22⋊C4—211no—
255C22×C7—21no—
256C22×C7—21no—
257C22×C7—21no—
258C22×C7—21no—
259C22×C7—21no—
260C22×C7#23712yes—
261C22×C7C23×D311yescharacteristic
262C2×D7—32no—
263C2×D7—61no—
264C2×D7—61no—
265C2×D7—61no—
266C2×D7—61no—
267C2×D7—61no—
268C2×D7—124no—
269C4×C7—21no—
270C4×C7—61no—
271C4×C7—61no—
272C4×C7—61no—
273C4×C7—61no—
274Dic7—21no—
275Dic7—21no—
276Dic7—21no—
277Dic7—21no—
278Dic7—61no—
279Dic7—61no—
280C23×C3C22×D711yescharacteristic
281C23×C3C22×D711yescharacteristic
282C22×D3—71no—
283C22×D3—71no—
284C22×D3—142no—
285C22×D3—142no—
286C22×D3—281no—
287C3×D4—22no—
288C2×C3×C4—71no—
289C2×C3×C4—71no—
290C2×C3×C4—71no—
291C2×C3×C4—71no—
292C2×C3×C4—142no—
293C2×C3×C4C22×D711yescharacteristic
294#67—142no—
295#67—281no—
296C2×Dic3—41no—
297C2×Dic3—41no—
298C2×Dic3—71no—
299C2×Dic3—71no—
300C2×Dic3C22×D711yescharacteristic
301C2×Dic3C22×D711yescharacteristic
302C2×Dic3C22×D711yescharacteristic
303C2×Dic3C22×D711yescharacteristic
304C4×D3—142no—
305C4×D3—281no—
306Dic6—281no—
307C3×C7#55111yescharacteristic, complemented, Hall
308C24—211no—
309C2×Q8—211no—
310C2×D4—211no—
311C2×D4—211no—
312C2×D4D3×D711yescharacteristic
313C22×C4—31no—
314C22×C4—31no—
315C22×C4—71no—
316C22×C4—211no—
317C22×C4—211no—
318C4⋊C4—31no—
319C4⋊C4—71no—
320C4⋊C4—71no—
321C4⋊C4—211no—
322C4⋊C4—211no—
323C4⋊C4—211no—
324C4⋊C4—211no—
325C4⋊C4—211no—
326C22⋊C4—31no—
327C22⋊C4—31no—
328C22⋊C4—71no—
329C22⋊C4—71no—
330C22⋊C4—71no—
331C22⋊C4—211no—
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—31no—
341C42—211no—
342C42—211no—
343C2×C7—22no—
344C2×C7—41no—
345C2×C7C2×#23711yescharacteristic
346C2×C7D3×#4111yescharacteristic
347C2×C7#100911yescharacteristic
348D7—62no—
349D7—121no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3#115712yes—
356C22×C3C23×D711yescharacteristic
357C2×D3—72no—
358C2×D3—141no—
359C2×D3—141no—
360C2×D3—141no—
361C2×D3—141no—
362C2×D3—141no—
363C2×D3—284no—
364C3×C4—21no—
365C3×C4—141no—
366C3×C4—141no—
367C3×C4—141no—
368C3×C4—141no—
369Dic3—21no—
370Dic3—21no—
371Dic3—21no—
372Dic3—21no—
373Dic3—141no—
374Dic3—141no—
375C23—211no—
376C23—211no—
377C23—422no—
378C23—422no—
379C23—841no—
380C23C2×D3×D711yescharacteristic
381C23C2×D3×D711yescharacteristic
382Q8—841no—
383D4—22no—
384D4—422no—
385D4—841no—
386C2×C4—31no—
387C2×C4—31no—
388C2×C4—31no—
389C2×C4—31no—
390C2×C4—71no—
391C2×C4—71no—
392C2×C4—71no—
393C2×C4—71no—
394C2×C4—121no—
395C2×C4—121no—
396C2×C4—142no—
397C2×C4—211no—
398C2×C4—211no—
399C2×C4—422no—
400C2×C4—841no—
401C2×C4C2×D3×D711yescharacteristic
402C7#565811yescharacteristic, complemented, Sylow
403C2×C3—22no—
404C2×C3—41no—
405C2×C3C2×#115711yescharacteristic
406C2×C3#654811yescharacteristic
407C2×C3D7×#4111yescharacteristic
408D3—142no—
409D3—281no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—212no—
416C22—421no—
417C22—421no—
418C22—421no—
419C22—421no—
420C22—421no—
421C22—844no—
422C22#6668312yes—
423C22C22×D3×D711yescharacteristic
424C4—21no—
425C4—61no—
426C4—61no—
427C4—61no—
428C4—61no—
429C4—141no—
430C4—141no—
431C4—141no—
432C4—141no—
433C4—421no—
434C4—421no—
435C3#9024711yescharacteristic, complemented, Sylow
436C2—22no—
437C2—41no—
438C2—422no—
439C2—841no—
440C2#1062157111yescharacteristic
441C2#1062157411yescharacteristic
442C2C2×#6668311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC2×C3×C7×D4C22
prime radical#10621420C2
hypercenterC2×D4D3×D7
hypocenterC3×C7#551
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C7×D4×Dic3C2semidirect
3. C3×#6498C2semidirect
4. #10621137C2semidirect
5. #10621124C2semidirect
6. #10621123C2semidirect
7. #10621118C2semidirect
8. #10621104C2semidirect
9. C2×#66575C2semidirect
10. #10621090C2semidirect
11. #10621088C2semidirect
12. #10620981C2semidirect
13. #10620965C2semidirect
14. #10620942C2semidirect
15. #10620899C2semidirect
22. C22×C7×Dic3C22semidirect
24. C2×#4248C22semidirect
31. C7×#217C22semidirect
32. C7×C4⋊Dic3C22semidirect
33. C4×C7×Dic3C22semidirect
35. C3×C22⋊Dic7C22semidirect
36. C3×C22⋊Dic7C22semidirect
37. C3×Dic7⋊C4C22semidirect
38. C3×Dic7⋊C4C22semidirect
39. Dic3⋊Dic7C22semidirect
40. #66577C22semidirect
41. Dic7⋊Dic3C22semidirect
42. Dic7⋊Dic3C22semidirect
43. Dic7⋊Dic3C22semidirect
50. Dic3×Dic7C22semidirect
51. Dic3×Dic7C22semidirect
54. #6498D3semidirect
111. C22⋊Dic7C2×D3semidirect
112. C22⋊Dic7C2×D3semidirect
126. Dic7⋊C4C2×D3semidirect
127. Dic7⋊C4C2×D3semidirect
132. D4×Dic3D7semidirect
204. C22×Dic3C2×D7semidirect
215. #217C2×D7semidirect
227. C4⋊Dic3C2×D7semidirect
232. C4×Dic3C2×D7semidirect
307. C3×C7#551semidirect
402. C7#5658semidirect
435. C3#90247semidirect

Maximal subgroups

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

subgroupindex
#106214202
C7×D4×Dic32
C3×#64982
#106211372
#106211242
#106211232
#106211182
#106211042
C2×#665752
#106210902
#106210882
#106209812
#106209652
#106209422
#106208992
#902473
#56587