Finite Group Databasebeta

← #13061640

Subgroups — #13061640

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×#66728C211yesmaximal, characteristic, complemented
2C22×C4×D21C211yesmaximal, characteristic, complemented
3C3×C4×C7×D4C211yesmaximal, characteristic, complemented
4#10621422C211yesmaximal, characteristic, complemented
5#10621420C211yesmaximal, characteristic, complemented
6C4×#4268C211yesmaximal, characteristic, complemented
7C4×#4268C211yesmaximal, characteristic, complemented
8#10621379C211yesmaximal, characteristic, complemented
9#10621377C211yesmaximal, characteristic, complemented
10#10621367C211yesmaximal, characteristic, complemented
11#10621366C211yesmaximal, characteristic, complemented
12#10621365C211yesmaximal, characteristic, complemented
13#10621361C211yesmaximal, characteristic, complemented
14C4×D84C211yesmaximal, characteristic, complemented
15#10621355C211yesmaximal, characteristic, complemented
16#90238—31nomaximal, Hall
17C23×D21C2211yescharacteristic
18C2×C3×C7×D4C2211yescharacteristic
19C22×C3×C4×C7C2211yescharacteristic
20C22×C3×C4×C7C2211yescharacteristic, complemented
21C2×#4268C2211yescharacteristic
22C2×#4268C2211yescharacteristic
23C2×#4268C2211yescharacteristic
24C2×#4268C2211yescharacteristic, complemented
25C22×Dic21C2211yescharacteristic
26#66728—24no—
27C2×D84C2211yescharacteristic
28C2×D84C2211yescharacteristic
29C2×C4×D21—24no—
30C2×C4×D21C2211yescharacteristic
31C2×C4×D21C2211yescharacteristic
32C2×C4×D21C2211yescharacteristic
33C2×C4×D21C2211yescharacteristic
34C2×C4×D21C2211yescharacteristic, complemented
35C2×Dic42C2211yescharacteristic, complemented
36C3×C7×C4⋊C4C2211yescharacteristic, complemented
37C3×C7×C22⋊C4C2211yescharacteristic
38C3×C7×C22⋊C4C2211yescharacteristic, complemented
39C3×C42×C7C2211yescharacteristic, complemented
40#66636C2211yescharacteristic
41#66636C2211yescharacteristic, complemented
42#66631C2211yescharacteristic
43#66631C2211yescharacteristic
44#66631C2211yescharacteristic
45#66631C2211yescharacteristic
46#66631C2211yescharacteristic, complemented
47#66631C2211yescharacteristic, complemented
48C4⋊Dic21C2211yescharacteristic, complemented
49#66629C2211yescharacteristic, complemented
50#66629C2211yescharacteristic, complemented
51#66629C2211yescharacteristic, complemented
52#66629C2211yescharacteristic, complemented
53C4×Dic21C2211yescharacteristic, complemented
54C2×#1157—31no—
55C22×C4×D7—31no—
56C4×C7×D4D311yescharacteristic, complemented
57#6502—31no—
58#6500—31no—
59C4×C22⋊D7—31no—
60C4×C22⋊D7—31no—
61#6459—31no—
62#6457—31no—
63#6447—31no—
64#6446—31no—
65#6445—31no—
66#6441—31no—
67C4×D28—31no—
68#6435—31no—
69#5547—71nomaximal, Hall
70C23×C3×C7C2311yescharacteristic
71C23×C3×C7C2311yescharacteristic
72C22×D21—22no—
73C22×D21—22no—
74C22×D21—22no—
75C22×D21C2311yescharacteristic
76C22×D21C2311yescharacteristic
77C22×D21C2311yescharacteristic
78C3×C7×D4—22no—
79C2×C3×C4×C7—22no—
80C2×C3×C4×C7—22no—
81C2×C3×C4×C7C2311yescharacteristic
82C2×C3×C4×C7C2311yescharacteristic
83C2×C3×C4×C7C2311yescharacteristic
84C2×C3×C4×C7C2311yescharacteristic
85C2×C3×C4×C7C2311yescharacteristic
86#4268—22no—
87#4268—22no—
88#4268—22no—
89#4268—22no—
90C2×Dic21—22no—
91C2×Dic21C2311yescharacteristic
92C2×Dic21C2311yescharacteristic
93C2×Dic21C2311yescharacteristic
94C2×Dic21C2311yescharacteristic
95C2×Dic21C2311yescharacteristic
96D84—22no—
97D84—22no—
98C4×D21—22no—
99C4×D21—22no—
100C4×D21—22no—
101C4×D21—22no—
102C4×D21D414yescomplemented
103Dic42—22no—
104C23×D7—31no—
105C2×C7×D4C2×D311yescharacteristic
106C22×C4×C7C2×D311yescharacteristic
107C22×C4×C7C2×D311yescharacteristic, complemented
108C2×C22⋊D7—31no—
109C2×C22⋊D7—31no—
110C2×C22⋊D7—31no—
111C2×C22⋊D7—31no—
112C22×Dic7—31no—
113#1157—64no—
114C2×D28—31no—
115C2×D28—31no—
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×Dic14—31no—
123C7×C4⋊C4C2×D311yescharacteristic, complemented
124C7×C22⋊C4C2×D311yescharacteristic
125C7×C22⋊C4C2×D311yescharacteristic, complemented
126C42×C7C2×D311yescharacteristic, complemented
127C22⋊Dic7—31no—
128C22⋊Dic7—31no—
129(C2×D7)⋊C4—31no—
130(C2×D7)⋊C4—31no—
131(C2×D7)⋊C4—31no—
132(C2×D7)⋊C4—31no—
133(C2×D7)⋊C4—31no—
134(C2×D7)⋊C4—31no—
135C4⋊Dic7—31no—
136Dic7⋊C4—31no—
137Dic7⋊C4—31no—
138Dic7⋊C4—31no—
139Dic7⋊C4—31no—
140C4×Dic7—31no—
141C2×#235—71no—
142C22×C4×D3—71no—
143C3×C4×D4D711yescharacteristic, complemented
144#939—71no—
145#937—71no—
146C4×#67—71no—
147C4×#67—71no—
148#896—71no—
149#894—71no—
150#884—71no—
151#883—71no—
152#882—71no—
153#878—71no—
154C4×D12—71no—
155#872—71no—
156C22×C3×C7—21no—
157C22×C3×C7—21no—
158C22×C3×C7—21no—
159C22×C3×C7—21no—
160C22×C3×C7—21no—
161C22×C3×C7#4112yescomplemented
162C22×C3×C7C2411yescharacteristic
163C2×D21—28no—
164C2×D21—21no—
165C2×D21—21no—
166C2×D21—21no—
167C2×D21—21no—
168C2×D21—21no—
169C2×D21—21no—
170C2×D21—21no—
171C2×D21C2×D412yes—
172C2×D21#4112yescomplemented
173C3×C4×C7—21no—
174C3×C4×C7—21no—
175C3×C4×C7—21no—
176C3×C4×C7—21no—
177C3×C4×C7C2×D412yes—
178Dic21—21no—
179Dic21—21no—
180Dic21—21no—
181Dic21—21no—
182Dic21C2×D412yes—
183#525—211noSylow
184C23×C7C22×D311yescharacteristic
185C23×C7C22×D311yescharacteristic
186C22×D7—31no—
187C22×D7—31no—
188C22×D7—31no—
189C22×D7—62no—
190C22×D7—62no—
191C22×D7—62no—
192C7×D4—22no—
193C2×C4×C7—22no—
194C2×C4×C7—22no—
195C2×C4×C7C22×D311yescharacteristic
196C2×C4×C7C22×D311yescharacteristic
197C2×C4×C7C22×D311yescharacteristic
198C2×C4×C7C22×D311yescharacteristic
199C2×C4×C7C22×D311yescharacteristic
200C22⋊D7—62no—
201C22⋊D7—62no—
202C22⋊D7—62no—
203C22⋊D7—62no—
204C2×Dic7—31no—
205C2×Dic7—31no—
206C2×Dic7—31no—
207C2×Dic7—31no—
208C2×Dic7—31no—
209C2×Dic7—62no—
210D28—62no—
211D28—62no—
212C4×D7—34no—
213C4×D7—62no—
214C4×D7—62no—
215C4×D7—62no—
216C4×D7—62no—
217Dic14—62no—
218C23×D3—71no—
219C2×C3×D4C2×D711yescharacteristic
220C22×C3×C4C2×D711yescharacteristic
221C22×C3×C4C2×D711yescharacteristic, complemented
222C2×#67—71no—
223C2×#67—71no—
224C2×#67—71no—
225C2×#67—71no—
226C22×Dic3—71no—
227#235—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—71no—
235C2×C4×D3—144no—
236C2×Dic6—71no—
237C3×C4⋊C4C2×D711yescharacteristic, complemented
238C3×C22⋊C4C2×D711yescharacteristic
239C3×C22⋊C4C2×D711yescharacteristic, complemented
240C3×C42C2×D711yescharacteristic, complemented
241#217—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)⋊C4—71no—
248(C2×D3)⋊C4—71no—
249C4⋊Dic3—71no—
250Dic3⋊C4—71no—
251Dic3⋊C4—71no—
252Dic3⋊C4—71no—
253Dic3⋊C4—71no—
254C4×Dic3—71no—
255C2×C3×C7—22no—
256C2×C3×C7—41no—
257C2×C3×C7C22×D411yescharacteristic
258C2×C3×C7C2×#4111yescharacteristic
259C2×C3×C7C2×#4111yescharacteristic
260D21—22no—
261D21—22no—
262D21—41no—
263C2×#41—211no—
264C23×C4—211no—
265#123—211no—
266#123—211no—
267C22⋊Q8—211no—
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×D4D2111yescharacteristic, complemented
277#117—211no—
278C22×C7—21no—
279C22×C7—21no—
280C22×C7—21no—
281C22×C7—21no—
282C22×C7—21no—
283C22×C7#23512yescomplemented
284C22×C7C23×D311yescharacteristic
285C2×D7—32no—
286C2×D7—32no—
287C2×D7—68no—
288C2×D7—61no—
289C2×D7—61no—
290C2×D7—61no—
291C2×D7—61no—
292C2×D7—61no—
293C2×D7—61no—
294C2×D7—61no—
295C4×C7—21no—
296C4×C7—21no—
297C4×C7—21no—
298C4×C7—21no—
299C4×C7D3×D412yes—
300Dic7—32no—
301Dic7—61no—
302Dic7—61no—
303Dic7—61no—
304Dic7—61no—
305C23×C3C22×D711yescharacteristic
306C23×C3C22×D711yescharacteristic
307C22×D3—71no—
308C22×D3—71no—
309C22×D3—71no—
310C22×D3—142no—
311C22×D3—142no—
312C22×D3—142no—
313C3×D4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4C22×D711yescharacteristic
317C2×C3×C4C22×D711yescharacteristic
318C2×C3×C4C22×D711yescharacteristic
319C2×C3×C4C22×D711yescharacteristic
320C2×C3×C4C22×D711yescharacteristic
321#67—142no—
322#67—142no—
323#67—142no—
324#67—142no—
325C2×Dic3—71no—
326C2×Dic3—71no—
327C2×Dic3—71no—
328C2×Dic3—71no—
329C2×Dic3—71no—
330C2×Dic3—142no—
331D12—142no—
332D12—142no—
333C4×D3—74no—
334C4×D3—142no—
335C4×D3—142no—
336C4×D3—142no—
337C4×D3—142no—
338Dic6—142no—
339C3×C7#52511yescharacteristic, complemented, Hall
340C24—211no—
341#41—424no—
342C2×Q8—211no—
343C2×D4—211no—
344C2×D4—211no—
345C2×D4—211no—
346C2×D4—211no—
347C2×D4—211no—
348C2×D4—211no—
349C2×D4C2×D2111yescharacteristic
350C22×C4—211no—
351C22×C4—211no—
352C22×C4—211no—
353C22×C4—211no—
354C22×C4—211no—
355C22×C4—211no—
356C22×C4—424no—
357C22×C4C2×D2111yescharacteristic
358C22×C4C2×D2111yescharacteristic, complemented
359C4⋊C4—211no—
360C4⋊C4—211no—
361C4⋊C4—211no—
362C4⋊C4—211no—
363C4⋊C4—211no—
364C4⋊C4C2×D2111yescharacteristic, complemented
365C22⋊C4—211no—
366C22⋊C4—211no—
367C22⋊C4—211no—
368C22⋊C4—211no—
369C22⋊C4—211no—
370C22⋊C4—211no—
371C22⋊C4—211no—
372C22⋊C4—211no—
373C22⋊C4C2×D2111yescharacteristic
374C22⋊C4C2×D2111yescharacteristic, complemented
375C42—211no—
376C42C2×D2111yescharacteristic, complemented
377C2×C7—22no—
378C2×C7—41no—
379C2×C7C2×#23511yescharacteristic
380C2×C7C2×D3×D411yescharacteristic
381C2×C7D3×#4111yescharacteristic
382D7—62no—
383D7—62no—
384D7—121no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3#115712yescomplemented
391C22×C3C23×D711yescharacteristic
392C2×D3—72no—
393C2×D3—72no—
394C2×D3—148no—
395C2×D3—141no—
396C2×D3—141no—
397C2×D3—141no—
398C2×D3—141no—
399C2×D3—141no—
400C2×D3—141no—
401C2×D3—141no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4D4×D712yes—
407Dic3—72no—
408Dic3—141no—
409Dic3—141no—
410Dic3—141no—
411Dic3—141no—
412C23—211no—
413C23—211no—
414C23—211no—
415C23—422no—
416C23—422no—
417C23—422no—
418C23C22×D2111yescharacteristic
419C23C22×D2111yescharacteristic
420Q8—422no—
421D4—22no—
422D4—422no—
423D4—422no—
424D4—422no—
425D4—422no—
426D4—422no—
427D4—422no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—211no—
431C2×C4—214no—
432C2×C4—211no—
433C2×C4—211no—
434C2×C4—211no—
435C2×C4—211no—
436C2×C4—422no—
437C2×C4—422no—
438C2×C4—422no—
439C2×C4—422no—
440C2×C4—422no—
441C2×C4C22×D2111yescharacteristic
442C2×C4C22×D2111yescharacteristic
443C2×C4C22×D2111yescharacteristic
444C2×C4C22×D2111yescharacteristic
445C2×C4C22×D2111yescharacteristic
446C7#554711yescharacteristic, complemented, Sylow
447C2×C3—22no—
448C2×C3—41no—
449C2×C3C2×#115711yescharacteristic
450C2×C3C2×D4×D711yescharacteristic
451C2×C3D7×#4111yescharacteristic
452D3—142no—
453D3—142no—
454D3—281no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—212no—
461C22—212no—
462C22—428no—
463C22—421no—
464C22—421no—
465C22—421no—
466C22—421no—
467C22—421no—
468C22—421no—
469C22—421no—
470C22#6672812yescomplemented
471C22C23×D2111yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—212no—
477C4—421no—
478C4—421no—
479C4—421no—
480C4—421no—
481C4D4×D2112yes—
482C3#9023811yescharacteristic, complemented, Sylow
483C2—22no—
484C2—41no—
485C2—422no—
486C2—422no—
487C2—841no—
488C2C2×#6672811yescharacteristic
489C2C2×D4×D2111yescharacteristic
490C2#41×D2111yescharacteristic
subgroupG/H
centerC2×C4C22×D21
commutator, socle, cosocleC22×C3×C7C24
FrattiniC22C23×D21
FittingC3×C4×C7×D4C2
hypercenterC4×D4D21
hypocenterC3×C7#525
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C2×C4 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#66728C2semidirect
2. C22×C4×D21C2semidirect
3. C3×C4×C7×D4C2semidirect
4. #10621422C2semidirect
5. #10621420C2semidirect
6. C4×#4268C2semidirect
7. C4×#4268C2semidirect
8. #10621379C2semidirect
9. #10621377C2semidirect
10. #10621367C2semidirect
11. #10621366C2semidirect
12. #10621365C2semidirect
13. #10621361C2semidirect
14. C4×D84C2semidirect
15. #10621355C2semidirect
20. C22×C3×C4×C7C22semidirect
24. C2×#4268C22semidirect
34. C2×C4×D21C22semidirect
35. C2×Dic42C22semidirect
36. C3×C7×C4⋊C4C22semidirect
38. C3×C7×C22⋊C4C22semidirect
39. C3×C42×C7C22semidirect
41. #66636C22semidirect
46. #66631C22semidirect
47. #66631C22semidirect
48. C4⋊Dic21C22semidirect
49. #66629C22semidirect
50. #66629C22semidirect
51. #66629C22semidirect
52. #66629C22semidirect
53. C4×Dic21C22semidirect
56. C4×C7×D4D3semidirect
102. C4×D21D4semidirect
107. C22×C4×C7C2×D3semidirect
123. C7×C4⋊C4C2×D3semidirect
125. C7×C22⋊C4C2×D3semidirect
126. C42×C7C2×D3semidirect
143. C3×C4×D4D7semidirect
161. C22×C3×C7#41semidirect
172. C2×D21#41semidirect
221. C22×C3×C4C2×D7semidirect
237. C3×C4⋊C4C2×D7semidirect
239. C3×C22⋊C4C2×D7semidirect
240. C3×C42C2×D7semidirect
276. C4×D4D21semidirect
283. C22×C7#235semidirect
339. C3×C7#525semidirect
358. C22×C4C2×D21semidirect
364. C4⋊C4C2×D21semidirect
374. C22⋊C4C2×D21semidirect
376. C42C2×D21semidirect
390. C22×C3#1157semidirect
446. C7#5547semidirect
470. C22#66728semidirect
482. C3#90238semidirect

Maximal subgroups

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

subgroupindex
C2×#667282
C22×C4×D212
C3×C4×C7×D42
#106214222
#106214202
C4×#42682
#106213792
#106213772
#106213672
#106213662
#106213652
#106213612
C4×D842
#106213552
#902383
#55477