Finite Group Databasebeta

← #13061795

Subgroups — #13061795

Order 1344.

500 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C7×#126C211yesmaximal, characteristic, complemented
2#10621381C211yesmaximal, characteristic, complemented
3#10621379C211yesmaximal, characteristic, complemented
4#10621378C211yesmaximal, characteristic, complemented
5#10621378C211yesmaximal, characteristic, complemented
6#10621377C211yesmaximal, characteristic, complemented
7#10621376C211yesmaximal, characteristic, complemented
8#10621368C211yesmaximal, characteristic, complemented
9#10621367C211yesmaximal, characteristic, complemented
10#10621366C211yesmaximal, characteristic, complemented
11#10621365C211yesmaximal, characteristic, complemented
12#10621365C211yesmaximal, characteristic, complemented
13C22⋊C4×D21C211yesmaximal, characteristic, complemented
14#10621358C211yesmaximal, characteristic, complemented
15C4×D84C211yesmaximal, characteristic, complemented
16#90395—31nomaximal, Hall
17C23×D21C2211yescharacteristic
18C2×#4268C2211yescharacteristic
19C2×#4268C2211yescharacteristic
20C2×D84C2211yescharacteristic
21C2×D84C2211yescharacteristic
22C2×D84C2211yescharacteristic
23C2×D84C2211yescharacteristic
24C2×D84C2211yescharacteristic, complemented
25C2×C4×D21C2211yescharacteristic
26C2×C4×D21C2211yescharacteristic
27C2×C4×D21C2211yescharacteristic, complemented
28C2×C4×D21C2211yescharacteristic, complemented
29C2×Dic42C2211yescharacteristic, complemented
30C3×C7×C4⋊C4C2211yescharacteristic, complemented
31C3×C7×C4⋊C4C2211yescharacteristic, complemented
32C3×C7×C4⋊C4C2211yescharacteristic, complemented
33C3×C7×C22⋊C4C2211yescharacteristic
34C3×C7×C22⋊C4C2211yescharacteristic
35C3×C7×C22⋊C4C2211yescharacteristic
36C3×C42×C7C2211yescharacteristic, complemented
37#66636C2211yescharacteristic
38#66631C2211yescharacteristic
39#66631C2211yescharacteristic
40#66631C2211yescharacteristic
41#66631C2211yescharacteristic
42#66631C2211yescharacteristic
43#66631C2211yescharacteristic
44#66631C2211yescharacteristic, complemented
45#66631C2211yescharacteristic, complemented
46#66631C2211yescharacteristic, complemented
47#66631C2211yescharacteristic, complemented
48C4⋊Dic21C2211yescharacteristic, complemented
49#66629C2211yescharacteristic, complemented
50#66629C2211yescharacteristic, complemented
51C4×Dic21C2211yescharacteristic, complemented
52C7×#126D311yescharacteristic, complemented
53#6461—31no—
54#6459—31no—
55#6458—31no—
56#6458—31no—
57#6457—31no—
58#6456—31no—
59#6448—31no—
60#6447—31no—
61#6446—31no—
62#6445—31no—
63#6445—31no—
64D7×C22⋊C4—31no—
65#6438—31no—
66C4×D28—31no—
67#5704—71nomaximal, Hall
68C23×C3×C7C2311yescharacteristic
69C22×D21—22no—
70C22×D21—41no—
71C22×D21—41no—
72C22×D21C2311yescharacteristic
73C22×D21C2311yescharacteristic
74C22×D21C2311yescharacteristic
75C22×D21C2311yescharacteristic
76C2×C3×C4×C7C2311yescharacteristic
77C2×C3×C4×C7C2311yescharacteristic
78C2×C3×C4×C7C2311yescharacteristic
79C2×C3×C4×C7C2311yescharacteristic
80C2×C3×C4×C7C2311yescharacteristic
81C2×C3×C4×C7C2311yescharacteristic
82#4268—41no—
83#4268—41no—
84C2×Dic21C2311yescharacteristic
85C2×Dic21C2311yescharacteristic
86C2×Dic21C2311yescharacteristic
87C2×Dic21C2311yescharacteristic
88D84—22no—
89D84—22no—
90D84—41no—
91D84—41no—
92D84—41no—
93C4×D21—41no—
94C4×D21—41no—
95C4×D21—41no—
96C4×D21—41no—
97Dic42—41no—
98C23×D7—31no—
99C2×C22⋊D7—31no—
100C2×C22⋊D7—31no—
101C2×D28—31no—
102C2×D28—31no—
103C2×D28—31no—
104C2×D28—31no—
105C2×D28—31no—
106C2×C4×D7—31no—
107C2×C4×D7—31no—
108C2×C4×D7—31no—
109C2×C4×D7—31no—
110C2×Dic14—31no—
111C7×C4⋊C4C2×D311yescharacteristic, complemented
112C7×C4⋊C4C2×D311yescharacteristic, complemented
113C7×C4⋊C4C2×D311yescharacteristic, complemented
114C7×C22⋊C4C2×D311yescharacteristic
115C7×C22⋊C4C2×D311yescharacteristic
116C7×C22⋊C4C2×D311yescharacteristic
117C42×C7C2×D311yescharacteristic, complemented
118C22⋊Dic7—31no—
119(C2×D7)⋊C4—31no—
120(C2×D7)⋊C4—31no—
121(C2×D7)⋊C4—31no—
122(C2×D7)⋊C4—31no—
123(C2×D7)⋊C4—31no—
124(C2×D7)⋊C4—31no—
125(C2×D7)⋊C4—31no—
126(C2×D7)⋊C4—31no—
127(C2×D7)⋊C4—31no—
128(C2×D7)⋊C4—31no—
129C4⋊Dic7—31no—
130Dic7⋊C4—31no—
131Dic7⋊C4—31no—
132C4×Dic7—31no—
133C3×#126D711yescharacteristic, complemented
134#898—71no—
135#896—71no—
136#895—71no—
137#895—71no—
138#894—71no—
139#893—71no—
140#885—71no—
141#884—71no—
142#883—71no—
143#882—71no—
144#882—71no—
145D3×C22⋊C4—71no—
146#875—71no—
147C4×D12—71no—
148C22×C3×C7—21no—
149C22×C3×C7—21no—
150C22×C3×C7—21no—
151C22×C3×C7C2411yescharacteristic
152C2×D21—21no—
153C2×D21—21no—
154C2×D21—21no—
155C2×D21—21no—
156C2×D21—21no—
157C2×D21—21no—
158C2×D21—21no—
159C2×D21—21no—
160C2×D21—21no—
161C2×D21—21no—
162C2×D21—21no—
163C2×D21—44no—
164C2×D21#4112yes—
165C3×C4×C7—21no—
166C3×C4×C7—21no—
167C3×C4×C7—21no—
168C3×C4×C7—21no—
169C3×C4×C7—21no—
170C3×C4×C7—21no—
171Dic21—21no—
172Dic21—21no—
173Dic21—21no—
174Dic21—21no—
175#538—211noSylow
176C23×C7C22×D311yescharacteristic
177C22×D7—31no—
178C22×D7—31no—
179C22×D7—31no—
180C22×D7—31no—
181C22×D7—62no—
182C22×D7—121no—
183C22×D7—121no—
184C2×C4×C7C22×D311yescharacteristic
185C2×C4×C7C22×D311yescharacteristic
186C2×C4×C7C22×D311yescharacteristic
187C2×C4×C7C22×D311yescharacteristic
188C2×C4×C7C22×D311yescharacteristic
189C2×C4×C7C22×D311yescharacteristic
190C22⋊D7—121no—
191C22⋊D7—121no—
192C2×Dic7—31no—
193C2×Dic7—31no—
194C2×Dic7—31no—
195C2×Dic7—31no—
196D28—62no—
197D28—62no—
198D28—121no—
199D28—121no—
200D28—121no—
201C4×D7—121no—
202C4×D7—121no—
203C4×D7—121no—
204C4×D7—121no—
205Dic14—121no—
206C23×D3—71no—
207C2×#67—71no—
208C2×#67—71no—
209C2×D12—71no—
210C2×D12—71no—
211C2×D12—71no—
212C2×D12—71no—
213C2×D12—71no—
214C2×C4×D3—71no—
215C2×C4×D3—71no—
216C2×C4×D3—71no—
217C2×C4×D3—71no—
218C2×Dic6—71no—
219C3×C4⋊C4C2×D711yescharacteristic, complemented
220C3×C4⋊C4C2×D711yescharacteristic, complemented
221C3×C4⋊C4C2×D711yescharacteristic, complemented
222C3×C22⋊C4C2×D711yescharacteristic
223C3×C22⋊C4C2×D711yescharacteristic
224C3×C22⋊C4C2×D711yescharacteristic
225C3×C42C2×D711yescharacteristic, complemented
226#217—71no—
227(C2×D3)⋊C4—71no—
228(C2×D3)⋊C4—71no—
229(C2×D3)⋊C4—71no—
230(C2×D3)⋊C4—71no—
231(C2×D3)⋊C4—71no—
232(C2×D3)⋊C4—71no—
233(C2×D3)⋊C4—71no—
234(C2×D3)⋊C4—71no—
235(C2×D3)⋊C4—71no—
236(C2×D3)⋊C4—71no—
237C4⋊Dic3—71no—
238Dic3⋊C4—71no—
239Dic3⋊C4—71no—
240C4×Dic3—71no—
241C2×C3×C7—41no—
242C2×C3×C7C2×#4111yescharacteristic
243C2×C3×C7H(5,𝔽2)11yescharacteristic
244C2×C3×C7H(5,𝔽2)11yescharacteristic
245D21—22no—
246D21—41no—
247D21—41no—
248D21—41no—
249#126—211no—
250#126D2111yescharacteristic, complemented
251#124—211no—
252#124—211no—
253#123—211no—
254#123—211no—
255C22⋊Q8—211no—
256#121—211no—
257#121—211no—
258#121—211no—
259#120—211no—
260#120—211no—
261C4×D4—211no—
262C4×D4—211no—
263C2×C22⋊C4—211no—
264C22×C7—21no—
265C22×C7—21no—
266C22×C7—21no—
267C22×C7C23×D311yescharacteristic
268C2×D7—32no—
269C2×D7—61no—
270C2×D7—61no—
271C2×D7—61no—
272C2×D7—61no—
273C2×D7—61no—
274C2×D7—61no—
275C2×D7—61no—
276C2×D7—61no—
277C2×D7—61no—
278C2×D7—61no—
279C2×D7—61no—
280C2×D7—124no—
281C4×C7—21no—
282C4×C7—21no—
283C4×C7—21no—
284C4×C7—21no—
285C4×C7—21no—
286C4×C7—21no—
287Dic7—61no—
288Dic7—61no—
289Dic7—61no—
290Dic7—61no—
291C23×C3C22×D711yescharacteristic
292C22×D3—71no—
293C22×D3—71no—
294C22×D3—71no—
295C22×D3—71no—
296C22×D3—142no—
297C22×D3—281no—
298C22×D3—281no—
299C2×C3×C4C22×D711yescharacteristic
300C2×C3×C4C22×D711yescharacteristic
301C2×C3×C4C22×D711yescharacteristic
302C2×C3×C4C22×D711yescharacteristic
303C2×C3×C4C22×D711yescharacteristic
304C2×C3×C4C22×D711yescharacteristic
305#67—281no—
306#67—281no—
307C2×Dic3—71no—
308C2×Dic3—71no—
309C2×Dic3—71no—
310C2×Dic3—71no—
311D12—142no—
312D12—142no—
313D12—281no—
314D12—281no—
315D12—281no—
316C4×D3—281no—
317C4×D3—281no—
318C4×D3—281no—
319C4×D3—281no—
320Dic6—281no—
321C3×C7#53811yescharacteristic, complemented, Hall
322C24—211no—
323C2×Q8—211no—
324C2×D4—211no—
325C2×D4—211no—
326C2×D4—211no—
327C2×D4—211no—
328C2×D4—211no—
329C2×D4—211no—
330C2×D4—211no—
331C22×C4—211no—
332C22×C4—211no—
333C22×C4—211no—
334C22×C4—211no—
335C4⋊C4—211no—
336C4⋊C4—211no—
337C4⋊C4—211no—
338C4⋊C4C2×D2111yescharacteristic, complemented
339C4⋊C4C2×D2111yescharacteristic, complemented
340C4⋊C4C2×D2111yescharacteristic, complemented
341C22⋊C4—211no—
342C22⋊C4—211no—
343C22⋊C4—211no—
344C22⋊C4—211no—
345C22⋊C4—211no—
346C22⋊C4—211no—
347C22⋊C4—211no—
348C22⋊C4—211no—
349C22⋊C4—211no—
350C22⋊C4—211no—
351C22⋊C4—211no—
352C22⋊C4C2×D2111yescharacteristic
353C22⋊C4C2×D2111yescharacteristic
354C22⋊C4C2×D2111yescharacteristic
355C42—211no—
356C42C2×D2111yescharacteristic, complemented
357C2×C7—41no—
358C2×C7D3×#4111yescharacteristic
359C2×C7#100911yescharacteristic
360C2×C7#100911yescharacteristic
361D7—62no—
362D7—121no—
363D7—121no—
364D7—121no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3C23×D711yescharacteristic
369C2×D3—72no—
370C2×D3—141no—
371C2×D3—141no—
372C2×D3—141no—
373C2×D3—141no—
374C2×D3—141no—
375C2×D3—141no—
376C2×D3—141no—
377C2×D3—141no—
378C2×D3—141no—
379C2×D3—141no—
380C2×D3—141no—
381C2×D3—284no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—21no—
388Dic3—141no—
389Dic3—141no—
390Dic3—141no—
391Dic3—141no—
392C23—211no—
393C23—211no—
394C23—211no—
395C23—211no—
396C23—422no—
397C23—841no—
398C23—841no—
399C23C22×D2111yescharacteristic
400Q8—841no—
401D4—422no—
402D4—422no—
403D4—841no—
404D4—841no—
405D4—841no—
406D4—841no—
407D4—841no—
408C2×C4—211no—
409C2×C4—211no—
410C2×C4—211no—
411C2×C4—211no—
412C2×C4—841no—
413C2×C4—841no—
414C2×C4—841no—
415C2×C4—841no—
416C2×C4C22×D2111yescharacteristic
417C2×C4C22×D2111yescharacteristic
418C2×C4C22×D2111yescharacteristic
419C2×C4C22×D2111yescharacteristic
420C2×C4C22×D2111yescharacteristic
421C2×C4C22×D2111yescharacteristic
422C7#570411yescharacteristic, complemented, Sylow
423C2×C3—41no—
424C2×C3D7×#4111yescharacteristic
425C2×C3#655311yescharacteristic
426C2×C3#655311yescharacteristic
427D3—142no—
428D3—281no—
429D3—281no—
430D3—281no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—212no—
435C22—421no—
436C22—421no—
437C22—421no—
438C22—421no—
439C22—421no—
440C22—421no—
441C22—421no—
442C22—421no—
443C22—421no—
444C22—421no—
445C22—421no—
446C22—844no—
447C22C23×D2111yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—21no—
453C4—21no—
454C4—421no—
455C4—421no—
456C4—421no—
457C4—421no—
458C3#9039511yescharacteristic, complemented, Sylow
459C2—41no—
460C2—422no—
461C2—841no—
462C2—841no—
463C2—841no—
464C2#41×D2111yescharacteristic
465C2#1062166211yescharacteristic
466C2#1062166211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D21
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C7×#126C2
hypercenter#126D21
hypocenterC3×C7#538
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. C3×C7×#126C2semidirect
2. #10621381C2semidirect
3. #10621379C2semidirect
4. #10621378C2semidirect
5. #10621378C2semidirect
6. #10621377C2semidirect
7. #10621376C2semidirect
8. #10621368C2semidirect
9. #10621367C2semidirect
10. #10621366C2semidirect
11. #10621365C2semidirect
12. #10621365C2semidirect
13. C22⋊C4×D21C2semidirect
14. #10621358C2semidirect
15. C4×D84C2semidirect
24. C2×D84C22semidirect
27. C2×C4×D21C22semidirect
28. C2×C4×D21C22semidirect
29. C2×Dic42C22semidirect
30. C3×C7×C4⋊C4C22semidirect
31. C3×C7×C4⋊C4C22semidirect
32. C3×C7×C4⋊C4C22semidirect
36. C3×C42×C7C22semidirect
44. #66631C22semidirect
45. #66631C22semidirect
46. #66631C22semidirect
47. #66631C22semidirect
48. C4⋊Dic21C22semidirect
49. #66629C22semidirect
50. #66629C22semidirect
51. C4×Dic21C22semidirect
52. C7×#126D3semidirect
111. C7×C4⋊C4C2×D3semidirect
112. C7×C4⋊C4C2×D3semidirect
113. C7×C4⋊C4C2×D3semidirect
117. C42×C7C2×D3semidirect
133. C3×#126D7semidirect
219. C3×C4⋊C4C2×D7semidirect
220. C3×C4⋊C4C2×D7semidirect
221. C3×C4⋊C4C2×D7semidirect
225. C3×C42C2×D7semidirect
250. #126D21semidirect
321. C3×C7#538semidirect
338. C4⋊C4C2×D21semidirect
339. C4⋊C4C2×D21semidirect
340. C4⋊C4C2×D21semidirect
356. C42C2×D21semidirect
422. C7#5704semidirect
458. C3#90395semidirect

Maximal subgroups

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

subgroupindex
C3×C7×#1262
#106213812
#106213792
#106213782
#106213772
#106213762
#106213682
#106213672
#106213662
#106213652
C22⋊C4×D212
#106213582
C4×D842
#903953
#57047