Finite Group Databasebeta

← #13058557

Subgroups — #13058557

Order 1344.

660 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×D7C211yesmaximal, characteristic, complemented
2C2×#66670C211yesmaximal, characteristic, complemented
3#10621376C211yesmaximal, characteristic, complemented
4C7×#896C211yesmaximal, characteristic, complemented
5C3×#6457C211yesmaximal, characteristic, complemented
6#10621038C211yesmaximal, characteristic, complemented
7#10621036C211yesmaximal, characteristic, complemented
8#10621021C211yesmaximal, characteristic, complemented
9#10621016C211yesmaximal, characteristic, complemented
10#10621004C211yesmaximal, characteristic, complemented
11#10620986C211yesmaximal, characteristic, complemented
12#10620968C211yesmaximal, characteristic, complemented
13#10620958C211yesmaximal, characteristic, complemented
14#10620956C211yesmaximal, characteristic, complemented
15#10620910C211yesmaximal, characteristic, complemented
16#90318—31nomaximal, Hall
17C22×D3×D7C2211yescharacteristic
18C2×D84C2211yescharacteristic
19C2×C4×D21C2211yescharacteristic
20C2×C4×D21C2211yescharacteristic, complemented
21C2×C4×D3×C7C2211yescharacteristic
22C2×C7×Dic6C2211yescharacteristic, complemented
23C2×C3×D28C2211yescharacteristic
24C2×C3×C4×D7C2211yescharacteristic
25C2×#4247C2211yescharacteristic
26C2×#4246C2211yescharacteristic
27C2×#4246C2211yescharacteristic
28C2×#4246C2211yescharacteristic, complemented
29C2×#4245C2211yescharacteristic
30C2×D21⋊C4C2211yescharacteristic
31C2×D3×Dic7C2211yescharacteristic
32C2×Dic3×D7C2211yescharacteristic
33C2×Dic3×D7C2211yescharacteristic, complemented
34C4×D3×D7—24no—
35#66670—24no—
36C3×C7×C4⋊C4C2211yescharacteristic, complemented
37#66631C2211yescharacteristic
38#66631C2211yescharacteristic, complemented
39C4×Dic21C2211yescharacteristic, complemented
40C7×(C2×D3)⋊C4C2211yescharacteristic
41C7×(C2×D3)⋊C4C2211yescharacteristic
42C7×Dic3⋊C4C2211yescharacteristic, complemented
43C7×Dic3⋊C4C2211yescharacteristic, complemented
44C3×(C2×D7)⋊C4C2211yescharacteristic
45C3×(C2×D7)⋊C4C2211yescharacteristic, complemented
46C3×(C2×D7)⋊C4C2211yescharacteristic, complemented
47C3×Dic7⋊C4C2211yescharacteristic, complemented
48Dic3⋊Dic7C2211yescharacteristic, complemented
49#66577C2211yescharacteristic, complemented
50#66575C2211yescharacteristic
51#66575C2211yescharacteristic, complemented
52(C2×D7)⋊Dic3C2211yescharacteristic
53Dic3×Dic7C2211yescharacteristic, complemented
54C2×#1161—31no—
55C22×C4×D7—31no—
56C7×C22⋊Q8—31no—
57#6509—31no—
58#6493—31no—
59#6458—31no—
60#6457—31no—
61#6457D311yescharacteristic, complemented
62#6456—31no—
63#6456—31no—
64#6455—31no—
65#6445—31no—
66#6445—31no—
67(C22⋊D7)⋊C4—31no—
68(C22⋊D7)⋊C4—31no—
69#5656—71nomaximal, Hall
70C22×D21C2311yescharacteristic
71C22×D21C2311yescharacteristic
72C22×D3×C7C2311yescharacteristic
73C22×C3×D7C2311yescharacteristic
74C22×C3×D7C2311yescharacteristic
75C2×D3×D7—22no—
76C2×D3×D7—22no—
77C2×D3×D7—22no—
78C2×C3×C4×C7C2311yescharacteristic
79C2×C3×C4×C7C2311yescharacteristic
80C2×C3×C4×C7C2311yescharacteristic
81C2×Dic21C2311yescharacteristic
82C2×Dic21C2311yescharacteristic
83D84—22no—
84C4×D21—22no—
85C4×D21—22no—
86C2×C7×Dic3C2311yescharacteristic
87C2×C7×Dic3C2311yescharacteristic
88C2×C7×Dic3C2311yescharacteristic
89C4×D3×C7—22no—
90C7×Dic6—22no—
91C2×C3×Dic7C2311yescharacteristic
92C2×C3×Dic7C2311yescharacteristic
93C3×D28—22no—
94C3×C4×D7—22no—
95#4247—22no—
96#4246—22no—
97#4246—22no—
98#4246—22no—
99#4245—22no—
100D21⋊C4—22no—
101D3×Dic7—22no—
102Dic3×D7—22no—
103Dic3×D7D414yescomplemented
104C23×D7—31no—
105C2×C7×Q8—31no—
106C22×C4×C7—31no—
107C2×C22⋊D7—31no—
108C2×C22⋊D7—31no—
109C22×Dic7—31no—
110#1161—64no—
111C2×D28—31no—
112C2×D28—31no—
113C2×D28—31no—
114C2×D28—31no—
115C2×D28C2×D311yescharacteristic
116C2×C4×D7—31no—
117C2×C4×D7—31no—
118C2×C4×D7—31no—
119C2×C4×D7—31no—
120C2×C4×D7—31no—
121C2×C4×D7—64no—
122C2×C4×D7C2×D311yescharacteristic
123C7×C4⋊C4—31no—
124C7×C4⋊C4—31no—
125C7×C4⋊C4C2×D311yescharacteristic, complemented
126C7×C22⋊C4—31no—
127C7×C22⋊C4—31no—
128(C2×D7)⋊C4—31no—
129(C2×D7)⋊C4—31no—
130(C2×D7)⋊C4—31no—
131(C2×D7)⋊C4—31no—
132(C2×D7)⋊C4—31no—
133(C2×D7)⋊C4C2×D311yescharacteristic
134(C2×D7)⋊C4C2×D311yescharacteristic, complemented
135(C2×D7)⋊C4C2×D311yescharacteristic, complemented
136C4⋊Dic7—31no—
137Dic7⋊C4—31no—
138Dic7⋊C4C2×D311yescharacteristic, complemented
139C4×Dic7—31no—
140C4×Dic7—31no—
141C2×#237—71no—
142C22×C4×D3—71no—
143C3×#123—71no—
144#937—71no—
145#929—71no—
146#896—71no—
147#896D711yescharacteristic, complemented
148#893—71no—
149#893—71no—
150#884—71no—
151#884—71no—
152#882—71no—
153#67⋊C4—71no—
154#67⋊C4—71no—
155#877—71no—
156C22×C3×C7C2411yescharacteristic
157C2×D21—21no—
158C2×D21—21no—
159C2×D21—21no—
160C2×D21—21no—
161C2×D21—21no—
162C2×D21#4112yescomplemented
163C2×D3×C7—21no—
164C2×D3×C7—21no—
165C2×D3×C7#4112yescomplemented
166C2×C3×D7—21no—
167C2×C3×D7—21no—
168C2×C3×D7—21no—
169C2×C3×D7—21no—
170C2×C3×D7—21no—
171C2×C3×D7C2×D412yes—
172D3×D7—28no—
173C3×C4×C7—21no—
174C3×C4×C7—21no—
175C3×C4×C7—21no—
176Dic21—21no—
177Dic21C2×D412yes—
178C3×Dic7—21no—
179C3×Dic7—21no—
180C7×Dic3—21no—
181C7×Dic3—21no—
182C7×Dic3C2×D412yes—
183#525—211noSylow
184C23×C7—31no—
185C22×D7—31no—
186C22×D7—31no—
187C22×D7—62no—
188C22×D7—62no—
189C22×D7—62no—
190C22×D7C22×D311yescharacteristic
191C22×D7C22×D311yescharacteristic
192C7×Q8—62no—
193C2×C4×C7—31no—
194C2×C4×C7—31no—
195C2×C4×C7—31no—
196C2×C4×C7—62no—
197C2×C4×C7C22×D311yescharacteristic
198C2×C4×C7C22×D311yescharacteristic
199C2×C4×C7C22×D311yescharacteristic
200C22⋊D7—62no—
201C22⋊D7—62no—
202C2×Dic7—31no—
203C2×Dic7—31no—
204C2×Dic7—62no—
205C2×Dic7C22×D311yescharacteristic
206C2×Dic7C22×D311yescharacteristic
207D28—22no—
208D28—62no—
209D28—62no—
210D28—62no—
211D28—62no—
212C4×D7—22no—
213C4×D7—34no—
214C4×D7—62no—
215C4×D7—62no—
216C4×D7—62no—
217C4×D7—62no—
218C23×D3—71no—
219C2×C3×D4—71no—
220C22×C3×C4—71no—
221C2×#67—71no—
222C2×#67—71no—
223C2×#67—71no—
224C2×#67—71no—
225C22×Dic3—71no—
226C22×Dic3—71no—
227#237—144no—
228C2×D12—71no—
229C2×D12—71no—
230C2×C4×D3—71no—
231C2×C4×D3—71no—
232C2×C4×D3—71no—
233C2×C4×D3—71no—
234C2×C4×D3—144no—
235C2×C4×D3C2×D711yescharacteristic
236C2×Dic6C2×D711yescharacteristic, complemented
237C3×C4⋊C4—71no—
238C3×C4⋊C4C2×D711yescharacteristic, complemented
239C3×C22⋊C4—71no—
240C3×C22⋊C4—71no—
241C3×C22⋊C4—71no—
242#217—71no—
243(C2×D3)⋊C4—71no—
244(C2×D3)⋊C4—71no—
245(C2×D3)⋊C4—71no—
246(C2×D3)⋊C4—71no—
247(C2×D3)⋊C4C2×D711yescharacteristic
248(C2×D3)⋊C4C2×D711yescharacteristic
249Dic3⋊C4—71no—
250Dic3⋊C4—71no—
251Dic3⋊C4C2×D711yescharacteristic, complemented
252Dic3⋊C4C2×D711yescharacteristic, complemented
253C4×Dic3—71no—
254C4×Dic3—71no—
255C2×C3×C7C22×D411yescharacteristic
256C2×C3×C7C2×#4111yescharacteristic
257C2×C3×C7C2×#4111yescharacteristic
258D21—22no—
259D21—41no—
260C3×D7—22no—
261C3×D7—41no—
262D3×C7—22no—
263C2×#41—211no—
264C23×C4—211no—
265#123—71no—
266#123—211no—
267C22⋊Q8—31no—
268C22⋊Q8—211no—
269#121—211no—
270#121—211no—
271#120—211no—
272#120—211no—
273C4×D4—211no—
274C4×D4—211no—
275C4×D4—211no—
276C4×D4—211no—
277#117—211no—
278C22×C7—32no—
279C22×C7—61no—
280C22×C7—61no—
281C22×C7C23×D311yescharacteristic
282C2×D7—21no—
283C2×D7—21no—
284C2×D7—21no—
285C2×D7—21no—
286C2×D7—21no—
287C2×D7—32no—
288C2×D7—68no—
289C2×D7—61no—
290C2×D7—61no—
291C2×D7—61no—
292C2×D7—61no—
293C2×D7—61no—
294C2×D7D3×D412yes—
295C4×C7—21no—
296C4×C7—21no—
297C4×C7—21no—
298C4×C7—32no—
299C4×C7—61no—
300C4×C7—61no—
301Dic7—21no—
302Dic7—21no—
303Dic7—32no—
304Dic7—61no—
305C23×C3—71no—
306C23×C3—71no—
307C22×D3—71no—
308C22×D3—71no—
309C22×D3—142no—
310C22×D3—142no—
311C22×D3—142no—
312C22×D3C22×D711yescharacteristic
313C3×D4—142no—
314C2×C3×C4—71no—
315C2×C3×C4—71no—
316C2×C3×C4—142no—
317C2×C3×C4C22×D711yescharacteristic
318C2×C3×C4C22×D711yescharacteristic
319C2×C3×C4C22×D711yescharacteristic
320#67—142no—
321#67—142no—
322#67—142no—
323#67—142no—
324C2×Dic3—71no—
325C2×Dic3—74no—
326C2×Dic3—71no—
327C2×Dic3—142no—
328C2×Dic3C22×D711yescharacteristic
329C2×Dic3C22×D711yescharacteristic
330C2×Dic3C22×D711yescharacteristic
331D12—142no—
332D12—142no—
333C4×D3—22no—
334C4×D3—142no—
335C4×D3—142no—
336C4×D3—142no—
337C4×D3—142no—
338Dic6—22no—
339C3×C7#52511yescharacteristic, complemented, Hall
340C24—211no—
341#41—424no—
342C2×Q8—31no—
343C2×D4—71no—
344C2×D4—211no—
345C2×D4—211no—
346C2×D4—211no—
347C2×D4—211no—
348C2×D4—211no—
349C2×D4—211no—
350C22×C4—31no—
351C22×C4—71no—
352C22×C4—211no—
353C22×C4—211no—
354C22×C4—211no—
355C22×C4—211no—
356C22×C4—211no—
357C22×C4—211no—
358C22×C4—424no—
359C4⋊C4—31no—
360C4⋊C4—31no—
361C4⋊C4—71no—
362C4⋊C4—211no—
363C4⋊C4—211no—
364C4⋊C4D3×D711yescharacteristic, complemented
365C22⋊C4—31no—
366C22⋊C4—31no—
367C22⋊C4—71no—
368C22⋊C4—71no—
369C22⋊C4—71no—
370C22⋊C4—211no—
371C22⋊C4—211no—
372C22⋊C4—211no—
373C22⋊C4—211no—
374C22⋊C4—211no—
375C42—211no—
376C42—211no—
377C2×C7—62no—
378C2×C7C2×D3×D411yescharacteristic
379C2×C7D3×#4111yescharacteristic
380C2×C7D3×#4111yescharacteristic
381D7—22no—
382D7—41no—
383D7—62no—
384D7—121no—
385C22×C3—72no—
386C22×C3—141no—
387C22×C3—141no—
388C22×C3—141no—
389C22×C3—141no—
390C22×C3—141no—
391C22×C3C23×D711yescharacteristic
392C2×D3—21no—
393C2×D3—21no—
394C2×D3—72no—
395C2×D3—148no—
396C2×D3—141no—
397C2×D3—141no—
398C2×D3—141no—
399C2×D3—141no—
400C2×D3—141no—
401C2×D3#116112yescomplemented
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—141no—
406C3×C4—141no—
407Dic3—21no—
408Dic3—21no—
409Dic3—72no—
410Dic3—141no—
411Dic3D4×D712yes—
412C23—31no—
413C23—71no—
414C23—71no—
415C23—211no—
416C23—211no—
417C23—422no—
418C23—422no—
419C23—422no—
420Q8—62no—
421D4—142no—
422D4—422no—
423D4—422no—
424D4—422no—
425D4—422no—
426D4—422no—
427D4—422no—
428C2×C4—31no—
429C2×C4—31no—
430C2×C4—31no—
431C2×C4—62no—
432C2×C4—71no—
433C2×C4—71no—
434C2×C4—142no—
435C2×C4—214no—
436C2×C4—211no—
437C2×C4—211no—
438C2×C4—422no—
439C2×C4—422no—
440C2×C4—422no—
441C2×C4—422no—
442C2×C4—422no—
443C2×C4C2×D3×D711yescharacteristic
444C2×C4C2×D3×D711yescharacteristic
445C2×C4C2×D3×D711yescharacteristic
446C7#565611yescharacteristic, complemented, Sylow
447C2×C3—142no—
448C2×C3—281no—
449C2×C3C2×D4×D711yescharacteristic
450C2×C3C2×#116111yescharacteristic
451C2×C3D7×#4111yescharacteristic
452D3—22no—
453D3—142no—
454D3—281no—
455C22—32no—
456C22—61no—
457C22—61no—
458C22—72no—
459C22—141no—
460C22—141no—
461C22—141no—
462C22—141no—
463C22—141no—
464C22—212no—
465C22—428no—
466C22—421no—
467C22—421no—
468C22—421no—
469C22—421no—
470C22—421no—
471C22C22×D3×D711yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—32no—
476C4—61no—
477C4—61no—
478C4—141no—
479C4—141no—
480C4—212no—
481C4—421no—
482C3#9031811yescharacteristic, complemented, Sylow
483C2—62no—
484C2—142no—
485C2—281no—
486C2—422no—
487C2—841no—
488C2#1062156311yescharacteristic
489C2D3×D4×D711yescharacteristic
490C2D3×#116111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C7×C4⋊C4C22
hypercenterC4⋊C4D3×D7
hypocenterC3×C7#525
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×D3×D7C2semidirect
2. C2×#66670C2semidirect
3. #10621376C2semidirect
4. C7×#896C2semidirect
5. C3×#6457C2semidirect
6. #10621038C2semidirect
7. #10621036C2semidirect
8. #10621021C2semidirect
9. #10621016C2semidirect
10. #10621004C2semidirect
11. #10620986C2semidirect
12. #10620968C2semidirect
13. #10620958C2semidirect
14. #10620956C2semidirect
15. #10620910C2semidirect
20. C2×C4×D21C22semidirect
22. C2×C7×Dic6C22semidirect
28. C2×#4246C22semidirect
33. C2×Dic3×D7C22semidirect
36. C3×C7×C4⋊C4C22semidirect
38. #66631C22semidirect
39. C4×Dic21C22semidirect
42. C7×Dic3⋊C4C22semidirect
43. C7×Dic3⋊C4C22semidirect
45. C3×(C2×D7)⋊C4C22semidirect
46. C3×(C2×D7)⋊C4C22semidirect
47. C3×Dic7⋊C4C22semidirect
48. Dic3⋊Dic7C22semidirect
49. #66577C22semidirect
51. #66575C22semidirect
53. Dic3×Dic7C22semidirect
61. #6457D3semidirect
103. Dic3×D7D4semidirect
125. C7×C4⋊C4C2×D3semidirect
134. (C2×D7)⋊C4C2×D3semidirect
135. (C2×D7)⋊C4C2×D3semidirect
138. Dic7⋊C4C2×D3semidirect
147. #896D7semidirect
162. C2×D21#41semidirect
165. C2×D3×C7#41semidirect
236. C2×Dic6C2×D7semidirect
238. C3×C4⋊C4C2×D7semidirect
251. Dic3⋊C4C2×D7semidirect
252. Dic3⋊C4C2×D7semidirect
339. C3×C7#525semidirect
364. C4⋊C4D3×D7semidirect
401. C2×D3#1161semidirect
446. C7#5656semidirect
482. C3#90318semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×D72
C2×#666702
#106213762
C7×#8962
C3×#64572
#106210382
#106210362
#106210212
#106210162
#106210042
#106209862
#106209682
#106209582
#106209562
#106209102
#903183
#56567