Finite Group Databasebeta

← #13059891

Subgroups — #13059891

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
2C2×C4×D3×D7C211yesmaximal, characteristic, complemented
3C4×C7×#67C211yesmaximal, characteristic, complemented
4C3×C4×C22⋊D7C211yesmaximal, characteristic, complemented
5#10621139C211yesmaximal, characteristic, complemented
6#10621124C211yesmaximal, characteristic, complemented
7#10621120C211yesmaximal, characteristic, complemented
8#10621112C211yesmaximal, characteristic, complemented
9#10621038C211yesmaximal, characteristic, complemented
10C4×#4247C211yesmaximal, characteristic, complemented
11C4×#4246C211yesmaximal, characteristic, complemented
12#10620995C211yesmaximal, characteristic, complemented
13#10620994C211yesmaximal, characteristic, complemented
14#10620993C211yesmaximal, characteristic, complemented
15#10620948C211yesmaximal, characteristic, complemented
16#90238—31nomaximal, Hall
17C22×D3×D7C2211yescharacteristic
18C22×C3×C4×C7C2211yescharacteristic, complemented
19C2×#4268C2211yescharacteristic
20C2×#4268C2211yescharacteristic, complemented
21#66728—24no—
22C2×D84C2211yescharacteristic
23C2×C4×D21C2211yescharacteristic
24C2×C4×D21C2211yescharacteristic, complemented
25C2×Dic42C2211yescharacteristic, complemented
26C2×C7×#67C2211yescharacteristic
27C2×C4×D3×C7C2211yescharacteristic
28C2×C3×C22⋊D7C2211yescharacteristic
29C2×C3×C4×D7C2211yescharacteristic
30C2×#4247C2211yescharacteristic
31C2×#4246C2211yescharacteristic
32C2×D21⋊C4C2211yescharacteristic
33C2×D3×Dic7C2211yescharacteristic
34C2×Dic3×D7C2211yescharacteristic
35C4×D3×D7—24no—
36C7×#217C2211yescharacteristic, complemented
37C7×(C2×D3)⋊C4C2211yescharacteristic
38C7×Dic3⋊C4C2211yescharacteristic, complemented
39C4×C7×Dic3C2211yescharacteristic, complemented
40C3×C22⋊Dic7C2211yescharacteristic, complemented
41C3×(C2×D7)⋊C4C2211yescharacteristic
42C3×Dic7⋊C4C2211yescharacteristic, complemented
43C3×C4×Dic7C2211yescharacteristic, complemented
44Dic3⋊Dic7C2211yescharacteristic, complemented
45#66577C2211yescharacteristic, complemented
46#66577C2211yescharacteristic, complemented
47Dic7⋊Dic3C2211yescharacteristic, complemented
48#66575C2211yescharacteristic
49#66575C2211yescharacteristic
50#66575C2211yescharacteristic, complemented
51#66575C2211yescharacteristic, complemented
52(C2×D3)⋊Dic7C2211yescharacteristic
53(C2×D7)⋊Dic3C2211yescharacteristic
54C2×#1157—31no—
55C22×C4×D7—31no—
56C4×C7×D4—31no—
57#6502—31no—
58#6500—31no—
59C4×C22⋊D7—31no—
60C4×C22⋊D7D311yescharacteristic, complemented
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
71C22×D21C2311yescharacteristic
72C22×D21C2311yescharacteristic
73C22×D3×C7C2311yescharacteristic
74C22×C3×D7C2311yescharacteristic
75C2×D3×D7—22no—
76C2×D3×D7—22no—
77C2×D3×D7—22no—
78C2×C3×C4×C7—22no—
79C2×C3×C4×C7C2311yescharacteristic
80C2×C3×C4×C7C2311yescharacteristic
81#4268—22no—
82#4268—22no—
83C2×Dic21C2311yescharacteristic
84C2×Dic21C2311yescharacteristic
85D84—22no—
86C4×D21—22no—
87C4×D21D414yescomplemented
88Dic42—22no—
89C7×#67—22no—
90C2×C7×Dic3C2311yescharacteristic
91C2×C7×Dic3C2311yescharacteristic
92C2×C7×Dic3C2311yescharacteristic
93C4×D3×C7—22no—
94C3×C22⋊D7—22no—
95C2×C3×Dic7C2311yescharacteristic
96C2×C3×Dic7C2311yescharacteristic
97C2×C3×Dic7C2311yescharacteristic
98C3×C4×D7—22no—
99#4247—22no—
100#4246—22no—
101D21⋊C4—22no—
102D3×Dic7—22no—
103Dic3×D7—22no—
104C23×D7—31no—
105C2×C7×D4—31no—
106C22×C4×C7—31no—
107C22×C4×C7C2×D311yescharacteristic, complemented
108C2×C22⋊D7—31no—
109C2×C22⋊D7—31no—
110C2×C22⋊D7—31no—
111C2×C22⋊D7C2×D311yescharacteristic
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—64no—
121C2×C4×D7C2×D311yescharacteristic
122C2×Dic14—31no—
123C7×C4⋊C4—31no—
124C7×C22⋊C4—31no—
125C7×C22⋊C4—31no—
126C42×C7—31no—
127C22⋊Dic7—31no—
128C22⋊Dic7C2×D311yescharacteristic, complemented
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)⋊C4C2×D311yescharacteristic
135C4⋊Dic7—31no—
136Dic7⋊C4—31no—
137Dic7⋊C4—31no—
138Dic7⋊C4—31no—
139Dic7⋊C4C2×D311yescharacteristic, complemented
140C4×Dic7C2×D311yescharacteristic, complemented
141C2×#235—71no—
142C22×C4×D3—71no—
143C3×C4×D4—71no—
144#939—71no—
145#937—71no—
146C4×#67—71no—
147C4×#67D711yescharacteristic, complemented
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×C7C2411yescharacteristic
160C2×D21—21no—
161C2×D21—21no—
162C2×D21—21no—
163C2×D21—21no—
164C2×D21—21no—
165C2×D21C2×D412yes—
166C2×D3×C7—21no—
167C2×D3×C7—21no—
168C2×D3×C7#4112yescomplemented
169C2×C3×D7—21no—
170C2×C3×D7—21no—
171C2×C3×D7#4112yescomplemented
172D3×D7—28no—
173C3×C4×C7—21no—
174C3×C4×C7C2×D412yes—
175Dic21—21no—
176Dic21C2×D412yes—
177C3×Dic7—21no—
178C3×Dic7—21no—
179C3×Dic7—21no—
180C7×Dic3—21no—
181C7×Dic3—21no—
182C7×Dic3—21no—
183#525—211noSylow
184C23×C7—31no—
185C23×C7C22×D311yescharacteristic
186C22×D7—31no—
187C22×D7—31no—
188C22×D7—62no—
189C22×D7—62no—
190C22×D7—62no—
191C22×D7C22×D311yescharacteristic
192C7×D4—62no—
193C2×C4×C7—22no—
194C2×C4×C7—31no—
195C2×C4×C7—31no—
196C2×C4×C7—31no—
197C2×C4×C7—62no—
198C2×C4×C7C22×D311yescharacteristic
199C2×C4×C7C22×D311yescharacteristic
200C22⋊D7—22no—
201C22⋊D7—62no—
202C22⋊D7—62no—
203C22⋊D7—62no—
204C2×Dic7—31no—
205C2×Dic7—31no—
206C2×Dic7—62no—
207C2×Dic7C22×D311yescharacteristic
208C2×Dic7C22×D311yescharacteristic
209C2×Dic7C22×D311yescharacteristic
210D28—62no—
211D28—62no—
212C4×D7—22no—
213C4×D7—34no—
214C4×D7—62no—
215C4×D7—62no—
216C4×D7—62no—
217Dic14—62no—
218C23×D3—71no—
219C2×C3×D4—71no—
220C22×C3×C4—71no—
221C22×C3×C4C2×D711yescharacteristic, complemented
222C2×#67—71no—
223C2×#67—71no—
224C2×#67—71no—
225C2×#67C2×D711yescharacteristic
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—144no—
235C2×C4×D3C2×D711yescharacteristic
236C2×Dic6—71no—
237C3×C4⋊C4—71no—
238C3×C22⋊C4—71no—
239C3×C22⋊C4—71no—
240C3×C42—71no—
241#217—71no—
242#217C2×D711yescharacteristic, complemented
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)⋊C4C2×D711yescharacteristic
249C4⋊Dic3—71no—
250Dic3⋊C4—71no—
251Dic3⋊C4—71no—
252Dic3⋊C4—71no—
253Dic3⋊C4C2×D711yescharacteristic, complemented
254C4×Dic3C2×D711yescharacteristic, complemented
255C2×C3×C7—41no—
256C2×C3×C7C22×D411yescharacteristic
257C2×C3×C7C2×#4111yescharacteristic
258C2×C3×C7C2×#4111yescharacteristic
259D21—22no—
260D21—41no—
261C3×D7—22no—
262D3×C7—22no—
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—31no—
274C4×D4—71no—
275C4×D4—211no—
276C4×D4—211no—
277#117—211no—
278C22×C7—21no—
279C22×C7—21no—
280C22×C7—21no—
281C22×C7—32no—
282C22×C7—61no—
283C22×C7—61no—
284C22×C7C23×D311yescharacteristic
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×D7#23512yescomplemented
295C4×C7—21no—
296C4×C7—61no—
297C4×C7—61no—
298C4×C7—61no—
299C4×C7D3×D412yes—
300Dic7—21no—
301Dic7—21no—
302Dic7—21no—
303Dic7—32no—
304Dic7—61no—
305C23×C3—71no—
306C23×C3C22×D711yescharacteristic
307C22×D3—71no—
308C22×D3—71no—
309C22×D3—142no—
310C22×D3—142no—
311C22×D3—142no—
312C22×D3C22×D711yescharacteristic
313C3×D4—142no—
314C2×C3×C4—22no—
315C2×C3×C4—71no—
316C2×C3×C4—71no—
317C2×C3×C4—71no—
318C2×C3×C4—142no—
319C2×C3×C4C22×D711yescharacteristic
320C2×C3×C4C22×D711yescharacteristic
321#67—22no—
322#67—142no—
323#67—142no—
324#67—142no—
325C2×Dic3—71no—
326C2×Dic3—71no—
327C2×Dic3—142no—
328C2×Dic3C22×D711yescharacteristic
329C2×Dic3C22×D711yescharacteristic
330C2×Dic3C22×D711yescharacteristic
331D12—142no—
332D12—142no—
333C4×D3—22no—
334C4×D3—74no—
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—31no—
344C2×D4—71no—
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—424no—
358C22×C4D3×D711yescharacteristic, complemented
359C4⋊C4—31no—
360C4⋊C4—71no—
361C4⋊C4—211no—
362C4⋊C4—211no—
363C4⋊C4—211no—
364C4⋊C4—211no—
365C22⋊C4—31no—
366C22⋊C4—31no—
367C22⋊C4—71no—
368C22⋊C4—71no—
369C22⋊C4—211no—
370C22⋊C4—211no—
371C22⋊C4—211no—
372C22⋊C4—211no—
373C22⋊C4—211no—
374C22⋊C4—211no—
375C42—31no—
376C42—71no—
377C2×C7—41no—
378C2×C7—62no—
379C2×C7C2×#23511yescharacteristic
380C2×C7C2×D3×D411yescharacteristic
381C2×C7D3×#4111yescharacteristic
382D7—22no—
383D7—62no—
384D7—121no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—72no—
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#115712yescomplemented
402C3×C4—21no—
403C3×C4—141no—
404C3×C4—141no—
405C3×C4—141no—
406C3×C4D4×D712yes—
407Dic3—21no—
408Dic3—21no—
409Dic3—21no—
410Dic3—72no—
411Dic3—141no—
412C23—31no—
413C23—71no—
414C23—211no—
415C23—211no—
416C23—422no—
417C23—422no—
418C23—422no—
419C23C2×D3×D711yescharacteristic
420Q8—422no—
421D4—62no—
422D4—142no—
423D4—422no—
424D4—422no—
425D4—422no—
426D4—422no—
427D4—422no—
428C2×C4—22no—
429C2×C4—31no—
430C2×C4—31no—
431C2×C4—31no—
432C2×C4—62no—
433C2×C4—71no—
434C2×C4—71no—
435C2×C4—71no—
436C2×C4—142no—
437C2×C4—211no—
438C2×C4—214no—
439C2×C4—211no—
440C2×C4—422no—
441C2×C4—422no—
442C2×C4—422no—
443C2×C4—422no—
444C2×C4C2×D3×D711yescharacteristic
445C2×C4C2×D3×D711yescharacteristic
446C7#554711yescharacteristic, complemented, Sylow
447C2×C3—41no—
448C2×C3—142no—
449C2×C3C2×#115711yescharacteristic
450C2×C3C2×D4×D711yescharacteristic
451C2×C3D7×#4111yescharacteristic
452D3—22no—
453D3—142no—
454D3—281no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—32no—
459C22—61no—
460C22—61no—
461C22—72no—
462C22—141no—
463C22—141no—
464C22—212no—
465C22—428no—
466C22—421no—
467C22—421no—
468C22—421no—
469C22—421no—
470C22—421no—
471C22C22×D3×D711yescharacteristic
472C4—21no—
473C4—61no—
474C4—61no—
475C4—61no—
476C4—141no—
477C4—141no—
478C4—141no—
479C4—212no—
480C4—421no—
481C4#6669412yes—
482C3#9023811yescharacteristic, complemented, Sylow
483C2—41no—
484C2—62no—
485C2—142no—
486C2—422no—
487C2—841no—
488C2D7×#23511yescharacteristic
489C2D3×#115711yescharacteristic
490C2C2×#6669411yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FrattiniC22C22×D3×D7
FittingC22×C3×C4×C7C22
hypercenterC22×C4D3×D7
hypocenterC3×C7#525
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#66728C2semidirect
2. C2×C4×D3×D7C2semidirect
3. C4×C7×#67C2semidirect
4. C3×C4×C22⋊D7C2semidirect
5. #10621139C2semidirect
6. #10621124C2semidirect
7. #10621120C2semidirect
8. #10621112C2semidirect
9. #10621038C2semidirect
10. C4×#4247C2semidirect
11. C4×#4246C2semidirect
12. #10620995C2semidirect
13. #10620994C2semidirect
14. #10620993C2semidirect
15. #10620948C2semidirect
18. C22×C3×C4×C7C22semidirect
20. C2×#4268C22semidirect
24. C2×C4×D21C22semidirect
25. C2×Dic42C22semidirect
36. C7×#217C22semidirect
38. C7×Dic3⋊C4C22semidirect
39. C4×C7×Dic3C22semidirect
40. C3×C22⋊Dic7C22semidirect
42. C3×Dic7⋊C4C22semidirect
43. C3×C4×Dic7C22semidirect
44. Dic3⋊Dic7C22semidirect
45. #66577C22semidirect
46. #66577C22semidirect
47. Dic7⋊Dic3C22semidirect
50. #66575C22semidirect
51. #66575C22semidirect
60. C4×C22⋊D7D3semidirect
87. C4×D21D4semidirect
107. C22×C4×C7C2×D3semidirect
128. C22⋊Dic7C2×D3semidirect
139. Dic7⋊C4C2×D3semidirect
140. C4×Dic7C2×D3semidirect
147. C4×#67D7semidirect
168. C2×D3×C7#41semidirect
171. C2×C3×D7#41semidirect
221. C22×C3×C4C2×D7semidirect
242. #217C2×D7semidirect
253. Dic3⋊C4C2×D7semidirect
254. C4×Dic3C2×D7semidirect
294. C2×D7#235semidirect
339. C3×C7#525semidirect
358. C22×C4D3×D7semidirect
401. C2×D3#1157semidirect
446. C7#5547semidirect
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
C2×C4×D3×D72
C4×C7×#672
C3×C4×C22⋊D72
#106211392
#106211242
#106211202
#106211122
#106210382
C4×#42472
C4×#42462
#106209952
#106209942
#106209932
#106209482
#902383
#55477